diff options
| author | Picca Frédéric-Emmanuel <picca@debian.org> | 2016-03-31 18:44:17 +0200 |
|---|---|---|
| committer | Picca Frédéric-Emmanuel <picca@debian.org> | 2016-03-31 18:44:17 +0200 |
| commit | 7be530f22592e2d2193230d863b85d2f5c91c116 (patch) | |
| tree | 3307f22f007d0cdd10e4837f0f6321180efb04cd | |
| parent | 2e1aa7f33e9b92c89174dc34881a280122f1b1b0 (diff) | |
Imported Upstream version 0.9.3+dfsg
105 files changed, 21898 insertions, 20545 deletions
@@ -1,12 +1,12 @@ -Installation instructions for LMFIT-py
-========================================
-
-To install the lmfit python module, use::
-
- python setup.py build
- python setup.py install
-
-Python 2.6 or higher is required, as are numpy and scipy.
-
-Matt Newville <newville@cars.uchicago.edu>
-Last Update: 2013-Dec-15
+Installation instructions for LMFIT-py +======================================== + +To install the lmfit python module, use:: + + python setup.py build + python setup.py install + +Python 2.6 or higher is required, as are numpy and scipy. + +Matt Newville <newville@cars.uchicago.edu> +Last Update: 2013-Dec-15 @@ -1,27 +1,27 @@ -Copyright, Licensing, and Re-distribution
------------------------------------------
-
-The LMFIT-py code is distribution under the following license:
-
- Copyright (c) 2014 Matthew Newville, The University of Chicago
- Till Stensitzki, Freie Universitat Berlin
- Daniel B. Allen, Johns Hopkins University
- Michal Rawlik, Eidgenossische Technische Hochschule, Zurich
- Antonino Ingargiola, University of California, Los Angeles
- A. R. J. Nelson, Australian Nuclear Science and Technology Organisation
-
- Permission to use and redistribute the source code or binary forms of this
- software and its documentation, with or without modification is hereby
- granted provided that the above notice of copyright, these terms of use,
- and the disclaimer of warranty below appear in the source code and
- documentation, and that none of the names of above institutions or
- authors appear in advertising or endorsement of works derived from this
- software without specific prior written permission from all parties.
-
- THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
- IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
- FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
- THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
- LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
- FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
- DEALINGS IN THIS SOFTWARE.
+Copyright, Licensing, and Re-distribution +----------------------------------------- + +The LMFIT-py code is distribution under the following license: + + Copyright (c) 2014 Matthew Newville, The University of Chicago + Till Stensitzki, Freie Universitat Berlin + Daniel B. Allen, Johns Hopkins University + Michal Rawlik, Eidgenossische Technische Hochschule, Zurich + Antonino Ingargiola, University of California, Los Angeles + A. R. J. Nelson, Australian Nuclear Science and Technology Organisation + + Permission to use and redistribute the source code or binary forms of this + software and its documentation, with or without modification is hereby + granted provided that the above notice of copyright, these terms of use, + and the disclaimer of warranty below appear in the source code and + documentation, and that none of the names of above institutions or + authors appear in advertising or endorsement of works derived from this + software without specific prior written permission from all parties. + + THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL + THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING + FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER + DEALINGS IN THIS SOFTWARE. diff --git a/MANIFEST.in b/MANIFEST.in index d83b8ba..1f48260 100644 --- a/MANIFEST.in +++ b/MANIFEST.in @@ -1,12 +1,12 @@ -include README.txt INSTALL LICENSE MANIFEST.in PKG-INFO THANKS.txt
-include setup.py publish_docs.sh
-include requirements.txt
-exclude *.pyc core.* *~ *.pdf
-recursive-include lmfit *.py
-recursive-include tests *.py *.dat
-recursive-include NIST_STRD *.dat
-recursive-include doc *
-recursive-exclude doc/_build *
-recursive-exclude doc *.pdf
-include versioneer.py
-include lmfit/_version.py
+include README.txt INSTALL LICENSE MANIFEST.in PKG-INFO THANKS.txt +include setup.py publish_docs.sh +include requirements.txt +exclude *.pyc core.* *~ *.pdf +recursive-include lmfit *.py +recursive-include tests *.py *.dat +recursive-include NIST_STRD *.dat +recursive-include doc * +recursive-exclude doc/_build * +recursive-exclude doc *.pdf +include versioneer.py +include lmfit/_version.py diff --git a/NIST_STRD/Bennett5.dat b/NIST_STRD/Bennett5.dat index eba218a..51335f4 100644 --- a/NIST_STRD/Bennett5.dat +++ b/NIST_STRD/Bennett5.dat @@ -1,214 +1,214 @@ -NIST/ITL StRD
-Dataset Name: Bennett5 (Bennett5.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 43)
- Certified Values (lines 41 to 48)
- Data (lines 61 to 214)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study involving
- superconductivity magnetization modeling. The
- response variable is magnetism, and the predictor
- variable is the log of time in minutes.
-
-Reference: Bennett, L., L. Swartzendruber, and H. Brown,
- NIST (1994).
- Superconductivity Magnetization Modeling.
-
-
-
-
-
-
-Data: 1 Response Variable (y = magnetism)
- 1 Predictor Variable (x = log[time])
- 154 Observations
- Higher Level of Difficulty
- Observed Data
-
-Model: Miscellaneous Class
- 3 Parameters (b1 to b3)
-
- y = b1 * (b2+x)**(-1/b3) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = -2000 -1500 -2.5235058043E+03 2.9715175411E+02
- b2 = 50 45 4.6736564644E+01 1.2448871856E+00
- b3 = 0.8 0.85 9.3218483193E-01 2.0272299378E-02
-
-Residual Sum of Squares: 5.2404744073E-04
-Residual Standard Deviation: 1.8629312528E-03
-Degrees of Freedom: 151
-Number of Observations: 154
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- -34.834702E0 7.447168E0
- -34.393200E0 8.102586E0
- -34.152901E0 8.452547E0
- -33.979099E0 8.711278E0
- -33.845901E0 8.916774E0
- -33.732899E0 9.087155E0
- -33.640301E0 9.232590E0
- -33.559200E0 9.359535E0
- -33.486801E0 9.472166E0
- -33.423100E0 9.573384E0
- -33.365101E0 9.665293E0
- -33.313000E0 9.749461E0
- -33.260899E0 9.827092E0
- -33.217400E0 9.899128E0
- -33.176899E0 9.966321E0
- -33.139198E0 10.029280E0
- -33.101601E0 10.088510E0
- -33.066799E0 10.144430E0
- -33.035000E0 10.197380E0
- -33.003101E0 10.247670E0
- -32.971298E0 10.295560E0
- -32.942299E0 10.341250E0
- -32.916302E0 10.384950E0
- -32.890202E0 10.426820E0
- -32.864101E0 10.467000E0
- -32.841000E0 10.505640E0
- -32.817799E0 10.542830E0
- -32.797501E0 10.578690E0
- -32.774300E0 10.613310E0
- -32.757000E0 10.646780E0
- -32.733799E0 10.679150E0
- -32.716400E0 10.710520E0
- -32.699100E0 10.740920E0
- -32.678799E0 10.770440E0
- -32.661400E0 10.799100E0
- -32.644001E0 10.826970E0
- -32.626701E0 10.854080E0
- -32.612202E0 10.880470E0
- -32.597698E0 10.906190E0
- -32.583199E0 10.931260E0
- -32.568699E0 10.955720E0
- -32.554298E0 10.979590E0
- -32.539799E0 11.002910E0
- -32.525299E0 11.025700E0
- -32.510799E0 11.047980E0
- -32.499199E0 11.069770E0
- -32.487598E0 11.091100E0
- -32.473202E0 11.111980E0
- -32.461601E0 11.132440E0
- -32.435501E0 11.152480E0
- -32.435501E0 11.172130E0
- -32.426800E0 11.191410E0
- -32.412300E0 11.210310E0
- -32.400799E0 11.228870E0
- -32.392101E0 11.247090E0
- -32.380501E0 11.264980E0
- -32.366001E0 11.282560E0
- -32.357300E0 11.299840E0
- -32.348598E0 11.316820E0
- -32.339901E0 11.333520E0
- -32.328400E0 11.349940E0
- -32.319698E0 11.366100E0
- -32.311001E0 11.382000E0
- -32.299400E0 11.397660E0
- -32.290699E0 11.413070E0
- -32.282001E0 11.428240E0
- -32.273300E0 11.443200E0
- -32.264599E0 11.457930E0
- -32.256001E0 11.472440E0
- -32.247299E0 11.486750E0
- -32.238602E0 11.500860E0
- -32.229900E0 11.514770E0
- -32.224098E0 11.528490E0
- -32.215401E0 11.542020E0
- -32.203800E0 11.555380E0
- -32.198002E0 11.568550E0
- -32.189400E0 11.581560E0
- -32.183601E0 11.594420E0
- -32.174900E0 11.607121E0
- -32.169102E0 11.619640E0
- -32.163300E0 11.632000E0
- -32.154598E0 11.644210E0
- -32.145901E0 11.656280E0
- -32.140099E0 11.668200E0
- -32.131401E0 11.679980E0
- -32.125599E0 11.691620E0
- -32.119801E0 11.703130E0
- -32.111198E0 11.714510E0
- -32.105400E0 11.725760E0
- -32.096699E0 11.736880E0
- -32.090900E0 11.747890E0
- -32.088001E0 11.758780E0
- -32.079300E0 11.769550E0
- -32.073502E0 11.780200E0
- -32.067699E0 11.790730E0
- -32.061901E0 11.801160E0
- -32.056099E0 11.811480E0
- -32.050301E0 11.821700E0
- -32.044498E0 11.831810E0
- -32.038799E0 11.841820E0
- -32.033001E0 11.851730E0
- -32.027199E0 11.861550E0
- -32.024300E0 11.871270E0
- -32.018501E0 11.880890E0
- -32.012699E0 11.890420E0
- -32.004002E0 11.899870E0
- -32.001099E0 11.909220E0
- -31.995300E0 11.918490E0
- -31.989500E0 11.927680E0
- -31.983700E0 11.936780E0
- -31.977900E0 11.945790E0
- -31.972099E0 11.954730E0
- -31.969299E0 11.963590E0
- -31.963501E0 11.972370E0
- -31.957701E0 11.981070E0
- -31.951900E0 11.989700E0
- -31.946100E0 11.998260E0
- -31.940300E0 12.006740E0
- -31.937401E0 12.015150E0
- -31.931601E0 12.023490E0
- -31.925800E0 12.031760E0
- -31.922899E0 12.039970E0
- -31.917101E0 12.048100E0
- -31.911301E0 12.056170E0
- -31.908400E0 12.064180E0
- -31.902599E0 12.072120E0
- -31.896900E0 12.080010E0
- -31.893999E0 12.087820E0
- -31.888201E0 12.095580E0
- -31.885300E0 12.103280E0
- -31.882401E0 12.110920E0
- -31.876600E0 12.118500E0
- -31.873699E0 12.126030E0
- -31.867901E0 12.133500E0
- -31.862101E0 12.140910E0
- -31.859200E0 12.148270E0
- -31.856300E0 12.155570E0
- -31.850500E0 12.162830E0
- -31.844700E0 12.170030E0
- -31.841801E0 12.177170E0
- -31.838900E0 12.184270E0
- -31.833099E0 12.191320E0
- -31.830200E0 12.198320E0
- -31.827299E0 12.205270E0
- -31.821600E0 12.212170E0
- -31.818701E0 12.219030E0
- -31.812901E0 12.225840E0
- -31.809999E0 12.232600E0
- -31.807100E0 12.239320E0
- -31.801300E0 12.245990E0
- -31.798401E0 12.252620E0
- -31.795500E0 12.259200E0
- -31.789700E0 12.265750E0
- -31.786800E0 12.272240E0
+NIST/ITL StRD +Dataset Name: Bennett5 (Bennett5.dat) + +File Format: ASCII + Starting Values (lines 41 to 43) + Certified Values (lines 41 to 48) + Data (lines 61 to 214) + +Procedure: Nonlinear Least Squares Regression + +Description: These data are the result of a NIST study involving + superconductivity magnetization modeling. The + response variable is magnetism, and the predictor + variable is the log of time in minutes. + +Reference: Bennett, L., L. Swartzendruber, and H. Brown, + NIST (1994). + Superconductivity Magnetization Modeling. + + + + + + +Data: 1 Response Variable (y = magnetism) + 1 Predictor Variable (x = log[time]) + 154 Observations + Higher Level of Difficulty + Observed Data + +Model: Miscellaneous Class + 3 Parameters (b1 to b3) + + y = b1 * (b2+x)**(-1/b3) + e + + + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = -2000 -1500 -2.5235058043E+03 2.9715175411E+02 + b2 = 50 45 4.6736564644E+01 1.2448871856E+00 + b3 = 0.8 0.85 9.3218483193E-01 2.0272299378E-02 + +Residual Sum of Squares: 5.2404744073E-04 +Residual Standard Deviation: 1.8629312528E-03 +Degrees of Freedom: 151 +Number of Observations: 154 + + + + + + + + + + + +Data: y x + -34.834702E0 7.447168E0 + -34.393200E0 8.102586E0 + -34.152901E0 8.452547E0 + -33.979099E0 8.711278E0 + -33.845901E0 8.916774E0 + -33.732899E0 9.087155E0 + -33.640301E0 9.232590E0 + -33.559200E0 9.359535E0 + -33.486801E0 9.472166E0 + -33.423100E0 9.573384E0 + -33.365101E0 9.665293E0 + -33.313000E0 9.749461E0 + -33.260899E0 9.827092E0 + -33.217400E0 9.899128E0 + -33.176899E0 9.966321E0 + -33.139198E0 10.029280E0 + -33.101601E0 10.088510E0 + -33.066799E0 10.144430E0 + -33.035000E0 10.197380E0 + -33.003101E0 10.247670E0 + -32.971298E0 10.295560E0 + -32.942299E0 10.341250E0 + -32.916302E0 10.384950E0 + -32.890202E0 10.426820E0 + -32.864101E0 10.467000E0 + -32.841000E0 10.505640E0 + -32.817799E0 10.542830E0 + -32.797501E0 10.578690E0 + -32.774300E0 10.613310E0 + -32.757000E0 10.646780E0 + -32.733799E0 10.679150E0 + -32.716400E0 10.710520E0 + -32.699100E0 10.740920E0 + -32.678799E0 10.770440E0 + -32.661400E0 10.799100E0 + -32.644001E0 10.826970E0 + -32.626701E0 10.854080E0 + -32.612202E0 10.880470E0 + -32.597698E0 10.906190E0 + -32.583199E0 10.931260E0 + -32.568699E0 10.955720E0 + -32.554298E0 10.979590E0 + -32.539799E0 11.002910E0 + -32.525299E0 11.025700E0 + -32.510799E0 11.047980E0 + -32.499199E0 11.069770E0 + -32.487598E0 11.091100E0 + -32.473202E0 11.111980E0 + -32.461601E0 11.132440E0 + -32.435501E0 11.152480E0 + -32.435501E0 11.172130E0 + -32.426800E0 11.191410E0 + -32.412300E0 11.210310E0 + -32.400799E0 11.228870E0 + -32.392101E0 11.247090E0 + -32.380501E0 11.264980E0 + -32.366001E0 11.282560E0 + -32.357300E0 11.299840E0 + -32.348598E0 11.316820E0 + -32.339901E0 11.333520E0 + -32.328400E0 11.349940E0 + -32.319698E0 11.366100E0 + -32.311001E0 11.382000E0 + -32.299400E0 11.397660E0 + -32.290699E0 11.413070E0 + -32.282001E0 11.428240E0 + -32.273300E0 11.443200E0 + -32.264599E0 11.457930E0 + -32.256001E0 11.472440E0 + -32.247299E0 11.486750E0 + -32.238602E0 11.500860E0 + -32.229900E0 11.514770E0 + -32.224098E0 11.528490E0 + -32.215401E0 11.542020E0 + -32.203800E0 11.555380E0 + -32.198002E0 11.568550E0 + -32.189400E0 11.581560E0 + -32.183601E0 11.594420E0 + -32.174900E0 11.607121E0 + -32.169102E0 11.619640E0 + -32.163300E0 11.632000E0 + -32.154598E0 11.644210E0 + -32.145901E0 11.656280E0 + -32.140099E0 11.668200E0 + -32.131401E0 11.679980E0 + -32.125599E0 11.691620E0 + -32.119801E0 11.703130E0 + -32.111198E0 11.714510E0 + -32.105400E0 11.725760E0 + -32.096699E0 11.736880E0 + -32.090900E0 11.747890E0 + -32.088001E0 11.758780E0 + -32.079300E0 11.769550E0 + -32.073502E0 11.780200E0 + -32.067699E0 11.790730E0 + -32.061901E0 11.801160E0 + -32.056099E0 11.811480E0 + -32.050301E0 11.821700E0 + -32.044498E0 11.831810E0 + -32.038799E0 11.841820E0 + -32.033001E0 11.851730E0 + -32.027199E0 11.861550E0 + -32.024300E0 11.871270E0 + -32.018501E0 11.880890E0 + -32.012699E0 11.890420E0 + -32.004002E0 11.899870E0 + -32.001099E0 11.909220E0 + -31.995300E0 11.918490E0 + -31.989500E0 11.927680E0 + -31.983700E0 11.936780E0 + -31.977900E0 11.945790E0 + -31.972099E0 11.954730E0 + -31.969299E0 11.963590E0 + -31.963501E0 11.972370E0 + -31.957701E0 11.981070E0 + -31.951900E0 11.989700E0 + -31.946100E0 11.998260E0 + -31.940300E0 12.006740E0 + -31.937401E0 12.015150E0 + -31.931601E0 12.023490E0 + -31.925800E0 12.031760E0 + -31.922899E0 12.039970E0 + -31.917101E0 12.048100E0 + -31.911301E0 12.056170E0 + -31.908400E0 12.064180E0 + -31.902599E0 12.072120E0 + -31.896900E0 12.080010E0 + -31.893999E0 12.087820E0 + -31.888201E0 12.095580E0 + -31.885300E0 12.103280E0 + -31.882401E0 12.110920E0 + -31.876600E0 12.118500E0 + -31.873699E0 12.126030E0 + -31.867901E0 12.133500E0 + -31.862101E0 12.140910E0 + -31.859200E0 12.148270E0 + -31.856300E0 12.155570E0 + -31.850500E0 12.162830E0 + -31.844700E0 12.170030E0 + -31.841801E0 12.177170E0 + -31.838900E0 12.184270E0 + -31.833099E0 12.191320E0 + -31.830200E0 12.198320E0 + -31.827299E0 12.205270E0 + -31.821600E0 12.212170E0 + -31.818701E0 12.219030E0 + -31.812901E0 12.225840E0 + -31.809999E0 12.232600E0 + -31.807100E0 12.239320E0 + -31.801300E0 12.245990E0 + -31.798401E0 12.252620E0 + -31.795500E0 12.259200E0 + -31.789700E0 12.265750E0 + -31.786800E0 12.272240E0 diff --git a/NIST_STRD/BoxBOD.dat b/NIST_STRD/BoxBOD.dat index 6a742fd..49163c7 100644 --- a/NIST_STRD/BoxBOD.dat +++ b/NIST_STRD/BoxBOD.dat @@ -1,66 +1,66 @@ -NIST/ITL StRD
-Dataset Name: BoxBOD (BoxBOD.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 42)
- Certified Values (lines 41 to 47)
- Data (lines 61 to 66)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are described in detail in Box, Hunter and
- Hunter (1978). The response variable is biochemical
- oxygen demand (BOD) in mg/l, and the predictor
- variable is incubation time in days.
-
-
-Reference: Box, G. P., W. G. Hunter, and J. S. Hunter (1978).
- Statistics for Experimenters.
- New York, NY: Wiley, pp. 483-487.
-
-
-
-
-
-Data: 1 Response (y = biochemical oxygen demand)
- 1 Predictor (x = incubation time)
- 6 Observations
- Higher Level of Difficulty
- Observed Data
-
-Model: Exponential Class
- 2 Parameters (b1 and b2)
-
- y = b1*(1-exp[-b2*x]) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 1 100 2.1380940889E+02 1.2354515176E+01
- b2 = 1 0.75 5.4723748542E-01 1.0455993237E-01
-
-Residual Sum of Squares: 1.1680088766E+03
-Residual Standard Deviation: 1.7088072423E+01
-Degrees of Freedom: 4
-Number of Observations: 6
-
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 109 1
- 149 2
- 149 3
- 191 5
- 213 7
- 224 10
+NIST/ITL StRD +Dataset Name: BoxBOD (BoxBOD.dat) + +File Format: ASCII + Starting Values (lines 41 to 42) + Certified Values (lines 41 to 47) + Data (lines 61 to 66) + +Procedure: Nonlinear Least Squares Regression + +Description: These data are described in detail in Box, Hunter and + Hunter (1978). The response variable is biochemical + oxygen demand (BOD) in mg/l, and the predictor + variable is incubation time in days. + + +Reference: Box, G. P., W. G. Hunter, and J. S. Hunter (1978). + Statistics for Experimenters. + New York, NY: Wiley, pp. 483-487. + + + + + +Data: 1 Response (y = biochemical oxygen demand) + 1 Predictor (x = incubation time) + 6 Observations + Higher Level of Difficulty + Observed Data + +Model: Exponential Class + 2 Parameters (b1 and b2) + + y = b1*(1-exp[-b2*x]) + e + + + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 1 100 2.1380940889E+02 1.2354515176E+01 + b2 = 1 0.75 5.4723748542E-01 1.0455993237E-01 + +Residual Sum of Squares: 1.1680088766E+03 +Residual Standard Deviation: 1.7088072423E+01 +Degrees of Freedom: 4 +Number of Observations: 6 + + + + + + + + + + + + +Data: y x + 109 1 + 149 2 + 149 3 + 191 5 + 213 7 + 224 10 diff --git a/NIST_STRD/Chwirut1.dat b/NIST_STRD/Chwirut1.dat index 4ad8aa5..5e72e4e 100644 --- a/NIST_STRD/Chwirut1.dat +++ b/NIST_STRD/Chwirut1.dat @@ -1,274 +1,274 @@ -NIST/ITL StRD
-Dataset Name: Chwirut1 (Chwirut1.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 43)
- Certified Values (lines 41 to 48)
- Data (lines 61 to 274)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study involving
- ultrasonic calibration. The response variable is
- ultrasonic response, and the predictor variable is
- metal distance.
-
-Reference: Chwirut, D., NIST (197?).
- Ultrasonic Reference Block Study.
-
-
-
-
-
-
-
-Data: 1 Response Variable (y = ultrasonic response)
- 1 Predictor Variable (x = metal distance)
- 214 Observations
- Lower Level of Difficulty
- Observed Data
-
-Model: Exponential Class
- 3 Parameters (b1 to b3)
-
- y = exp[-b1*x]/(b2+b3*x) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 0.1 0.15 1.9027818370E-01 2.1938557035E-02
- b2 = 0.01 0.008 6.1314004477E-03 3.4500025051E-04
- b3 = 0.02 0.010 1.0530908399E-02 7.9281847748E-04
-
-Residual Sum of Squares: 2.3844771393E+03
-Residual Standard Deviation: 3.3616721320E+00
-Degrees of Freedom: 211
-Number of Observations: 214
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 92.9000E0 0.5000E0
- 78.7000E0 0.6250E0
- 64.2000E0 0.7500E0
- 64.9000E0 0.8750E0
- 57.1000E0 1.0000E0
- 43.3000E0 1.2500E0
- 31.1000E0 1.7500E0
- 23.6000E0 2.2500E0
- 31.0500E0 1.7500E0
- 23.7750E0 2.2500E0
- 17.7375E0 2.7500E0
- 13.8000E0 3.2500E0
- 11.5875E0 3.7500E0
- 9.4125E0 4.2500E0
- 7.7250E0 4.7500E0
- 7.3500E0 5.2500E0
- 8.0250E0 5.7500E0
- 90.6000E0 0.5000E0
- 76.9000E0 0.6250E0
- 71.6000E0 0.7500E0
- 63.6000E0 0.8750E0
- 54.0000E0 1.0000E0
- 39.2000E0 1.2500E0
- 29.3000E0 1.7500E0
- 21.4000E0 2.2500E0
- 29.1750E0 1.7500E0
- 22.1250E0 2.2500E0
- 17.5125E0 2.7500E0
- 14.2500E0 3.2500E0
- 9.4500E0 3.7500E0
- 9.1500E0 4.2500E0
- 7.9125E0 4.7500E0
- 8.4750E0 5.2500E0
- 6.1125E0 5.7500E0
- 80.0000E0 0.5000E0
- 79.0000E0 0.6250E0
- 63.8000E0 0.7500E0
- 57.2000E0 0.8750E0
- 53.2000E0 1.0000E0
- 42.5000E0 1.2500E0
- 26.8000E0 1.7500E0
- 20.4000E0 2.2500E0
- 26.8500E0 1.7500E0
- 21.0000E0 2.2500E0
- 16.4625E0 2.7500E0
- 12.5250E0 3.2500E0
- 10.5375E0 3.7500E0
- 8.5875E0 4.2500E0
- 7.1250E0 4.7500E0
- 6.1125E0 5.2500E0
- 5.9625E0 5.7500E0
- 74.1000E0 0.5000E0
- 67.3000E0 0.6250E0
- 60.8000E0 0.7500E0
- 55.5000E0 0.8750E0
- 50.3000E0 1.0000E0
- 41.0000E0 1.2500E0
- 29.4000E0 1.7500E0
- 20.4000E0 2.2500E0
- 29.3625E0 1.7500E0
- 21.1500E0 2.2500E0
- 16.7625E0 2.7500E0
- 13.2000E0 3.2500E0
- 10.8750E0 3.7500E0
- 8.1750E0 4.2500E0
- 7.3500E0 4.7500E0
- 5.9625E0 5.2500E0
- 5.6250E0 5.7500E0
- 81.5000E0 .5000E0
- 62.4000E0 .7500E0
- 32.5000E0 1.5000E0
- 12.4100E0 3.0000E0
- 13.1200E0 3.0000E0
- 15.5600E0 3.0000E0
- 5.6300E0 6.0000E0
- 78.0000E0 .5000E0
- 59.9000E0 .7500E0
- 33.2000E0 1.5000E0
- 13.8400E0 3.0000E0
- 12.7500E0 3.0000E0
- 14.6200E0 3.0000E0
- 3.9400E0 6.0000E0
- 76.8000E0 .5000E0
- 61.0000E0 .7500E0
- 32.9000E0 1.5000E0
- 13.8700E0 3.0000E0
- 11.8100E0 3.0000E0
- 13.3100E0 3.0000E0
- 5.4400E0 6.0000E0
- 78.0000E0 .5000E0
- 63.5000E0 .7500E0
- 33.8000E0 1.5000E0
- 12.5600E0 3.0000E0
- 5.6300E0 6.0000E0
- 12.7500E0 3.0000E0
- 13.1200E0 3.0000E0
- 5.4400E0 6.0000E0
- 76.8000E0 .5000E0
- 60.0000E0 .7500E0
- 47.8000E0 1.0000E0
- 32.0000E0 1.5000E0
- 22.2000E0 2.0000E0
- 22.5700E0 2.0000E0
- 18.8200E0 2.5000E0
- 13.9500E0 3.0000E0
- 11.2500E0 4.0000E0
- 9.0000E0 5.0000E0
- 6.6700E0 6.0000E0
- 75.8000E0 .5000E0
- 62.0000E0 .7500E0
- 48.8000E0 1.0000E0
- 35.2000E0 1.5000E0
- 20.0000E0 2.0000E0
- 20.3200E0 2.0000E0
- 19.3100E0 2.5000E0
- 12.7500E0 3.0000E0
- 10.4200E0 4.0000E0
- 7.3100E0 5.0000E0
- 7.4200E0 6.0000E0
- 70.5000E0 .5000E0
- 59.5000E0 .7500E0
- 48.5000E0 1.0000E0
- 35.8000E0 1.5000E0
- 21.0000E0 2.0000E0
- 21.6700E0 2.0000E0
- 21.0000E0 2.5000E0
- 15.6400E0 3.0000E0
- 8.1700E0 4.0000E0
- 8.5500E0 5.0000E0
- 10.1200E0 6.0000E0
- 78.0000E0 .5000E0
- 66.0000E0 .6250E0
- 62.0000E0 .7500E0
- 58.0000E0 .8750E0
- 47.7000E0 1.0000E0
- 37.8000E0 1.2500E0
- 20.2000E0 2.2500E0
- 21.0700E0 2.2500E0
- 13.8700E0 2.7500E0
- 9.6700E0 3.2500E0
- 7.7600E0 3.7500E0
- 5.4400E0 4.2500E0
- 4.8700E0 4.7500E0
- 4.0100E0 5.2500E0
- 3.7500E0 5.7500E0
- 24.1900E0 3.0000E0
- 25.7600E0 3.0000E0
- 18.0700E0 3.0000E0
- 11.8100E0 3.0000E0
- 12.0700E0 3.0000E0
- 16.1200E0 3.0000E0
- 70.8000E0 .5000E0
- 54.7000E0 .7500E0
- 48.0000E0 1.0000E0
- 39.8000E0 1.5000E0
- 29.8000E0 2.0000E0
- 23.7000E0 2.5000E0
- 29.6200E0 2.0000E0
- 23.8100E0 2.5000E0
- 17.7000E0 3.0000E0
- 11.5500E0 4.0000E0
- 12.0700E0 5.0000E0
- 8.7400E0 6.0000E0
- 80.7000E0 .5000E0
- 61.3000E0 .7500E0
- 47.5000E0 1.0000E0
- 29.0000E0 1.5000E0
- 24.0000E0 2.0000E0
- 17.7000E0 2.5000E0
- 24.5600E0 2.0000E0
- 18.6700E0 2.5000E0
- 16.2400E0 3.0000E0
- 8.7400E0 4.0000E0
- 7.8700E0 5.0000E0
- 8.5100E0 6.0000E0
- 66.7000E0 .5000E0
- 59.2000E0 .7500E0
- 40.8000E0 1.0000E0
- 30.7000E0 1.5000E0
- 25.7000E0 2.0000E0
- 16.3000E0 2.5000E0
- 25.9900E0 2.0000E0
- 16.9500E0 2.5000E0
- 13.3500E0 3.0000E0
- 8.6200E0 4.0000E0
- 7.2000E0 5.0000E0
- 6.6400E0 6.0000E0
- 13.6900E0 3.0000E0
- 81.0000E0 .5000E0
- 64.5000E0 .7500E0
- 35.5000E0 1.5000E0
- 13.3100E0 3.0000E0
- 4.8700E0 6.0000E0
- 12.9400E0 3.0000E0
- 5.0600E0 6.0000E0
- 15.1900E0 3.0000E0
- 14.6200E0 3.0000E0
- 15.6400E0 3.0000E0
- 25.5000E0 1.7500E0
- 25.9500E0 1.7500E0
- 81.7000E0 .5000E0
- 61.6000E0 .7500E0
- 29.8000E0 1.7500E0
- 29.8100E0 1.7500E0
- 17.1700E0 2.7500E0
- 10.3900E0 3.7500E0
- 28.4000E0 1.7500E0
- 28.6900E0 1.7500E0
- 81.3000E0 .5000E0
- 60.9000E0 .7500E0
- 16.6500E0 2.7500E0
- 10.0500E0 3.7500E0
- 28.9000E0 1.7500E0
- 28.9500E0 1.7500E0
+NIST/ITL StRD +Dataset Name: Chwirut1 (Chwirut1.dat) + +File Format: ASCII + Starting Values (lines 41 to 43) + Certified Values (lines 41 to 48) + Data (lines 61 to 274) + +Procedure: Nonlinear Least Squares Regression + +Description: These data are the result of a NIST study involving + ultrasonic calibration. The response variable is + ultrasonic response, and the predictor variable is + metal distance. + +Reference: Chwirut, D., NIST (197?). + Ultrasonic Reference Block Study. + + + + + + + +Data: 1 Response Variable (y = ultrasonic response) + 1 Predictor Variable (x = metal distance) + 214 Observations + Lower Level of Difficulty + Observed Data + +Model: Exponential Class + 3 Parameters (b1 to b3) + + y = exp[-b1*x]/(b2+b3*x) + e + + + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 0.1 0.15 1.9027818370E-01 2.1938557035E-02 + b2 = 0.01 0.008 6.1314004477E-03 3.4500025051E-04 + b3 = 0.02 0.010 1.0530908399E-02 7.9281847748E-04 + +Residual Sum of Squares: 2.3844771393E+03 +Residual Standard Deviation: 3.3616721320E+00 +Degrees of Freedom: 211 +Number of Observations: 214 + + + + + + + + + + + +Data: y x + 92.9000E0 0.5000E0 + 78.7000E0 0.6250E0 + 64.2000E0 0.7500E0 + 64.9000E0 0.8750E0 + 57.1000E0 1.0000E0 + 43.3000E0 1.2500E0 + 31.1000E0 1.7500E0 + 23.6000E0 2.2500E0 + 31.0500E0 1.7500E0 + 23.7750E0 2.2500E0 + 17.7375E0 2.7500E0 + 13.8000E0 3.2500E0 + 11.5875E0 3.7500E0 + 9.4125E0 4.2500E0 + 7.7250E0 4.7500E0 + 7.3500E0 5.2500E0 + 8.0250E0 5.7500E0 + 90.6000E0 0.5000E0 + 76.9000E0 0.6250E0 + 71.6000E0 0.7500E0 + 63.6000E0 0.8750E0 + 54.0000E0 1.0000E0 + 39.2000E0 1.2500E0 + 29.3000E0 1.7500E0 + 21.4000E0 2.2500E0 + 29.1750E0 1.7500E0 + 22.1250E0 2.2500E0 + 17.5125E0 2.7500E0 + 14.2500E0 3.2500E0 + 9.4500E0 3.7500E0 + 9.1500E0 4.2500E0 + 7.9125E0 4.7500E0 + 8.4750E0 5.2500E0 + 6.1125E0 5.7500E0 + 80.0000E0 0.5000E0 + 79.0000E0 0.6250E0 + 63.8000E0 0.7500E0 + 57.2000E0 0.8750E0 + 53.2000E0 1.0000E0 + 42.5000E0 1.2500E0 + 26.8000E0 1.7500E0 + 20.4000E0 2.2500E0 + 26.8500E0 1.7500E0 + 21.0000E0 2.2500E0 + 16.4625E0 2.7500E0 + 12.5250E0 3.2500E0 + 10.5375E0 3.7500E0 + 8.5875E0 4.2500E0 + 7.1250E0 4.7500E0 + 6.1125E0 5.2500E0 + 5.9625E0 5.7500E0 + 74.1000E0 0.5000E0 + 67.3000E0 0.6250E0 + 60.8000E0 0.7500E0 + 55.5000E0 0.8750E0 + 50.3000E0 1.0000E0 + 41.0000E0 1.2500E0 + 29.4000E0 1.7500E0 + 20.4000E0 2.2500E0 + 29.3625E0 1.7500E0 + 21.1500E0 2.2500E0 + 16.7625E0 2.7500E0 + 13.2000E0 3.2500E0 + 10.8750E0 3.7500E0 + 8.1750E0 4.2500E0 + 7.3500E0 4.7500E0 + 5.9625E0 5.2500E0 + 5.6250E0 5.7500E0 + 81.5000E0 .5000E0 + 62.4000E0 .7500E0 + 32.5000E0 1.5000E0 + 12.4100E0 3.0000E0 + 13.1200E0 3.0000E0 + 15.5600E0 3.0000E0 + 5.6300E0 6.0000E0 + 78.0000E0 .5000E0 + 59.9000E0 .7500E0 + 33.2000E0 1.5000E0 + 13.8400E0 3.0000E0 + 12.7500E0 3.0000E0 + 14.6200E0 3.0000E0 + 3.9400E0 6.0000E0 + 76.8000E0 .5000E0 + 61.0000E0 .7500E0 + 32.9000E0 1.5000E0 + 13.8700E0 3.0000E0 + 11.8100E0 3.0000E0 + 13.3100E0 3.0000E0 + 5.4400E0 6.0000E0 + 78.0000E0 .5000E0 + 63.5000E0 .7500E0 + 33.8000E0 1.5000E0 + 12.5600E0 3.0000E0 + 5.6300E0 6.0000E0 + 12.7500E0 3.0000E0 + 13.1200E0 3.0000E0 + 5.4400E0 6.0000E0 + 76.8000E0 .5000E0 + 60.0000E0 .7500E0 + 47.8000E0 1.0000E0 + 32.0000E0 1.5000E0 + 22.2000E0 2.0000E0 + 22.5700E0 2.0000E0 + 18.8200E0 2.5000E0 + 13.9500E0 3.0000E0 + 11.2500E0 4.0000E0 + 9.0000E0 5.0000E0 + 6.6700E0 6.0000E0 + 75.8000E0 .5000E0 + 62.0000E0 .7500E0 + 48.8000E0 1.0000E0 + 35.2000E0 1.5000E0 + 20.0000E0 2.0000E0 + 20.3200E0 2.0000E0 + 19.3100E0 2.5000E0 + 12.7500E0 3.0000E0 + 10.4200E0 4.0000E0 + 7.3100E0 5.0000E0 + 7.4200E0 6.0000E0 + 70.5000E0 .5000E0 + 59.5000E0 .7500E0 + 48.5000E0 1.0000E0 + 35.8000E0 1.5000E0 + 21.0000E0 2.0000E0 + 21.6700E0 2.0000E0 + 21.0000E0 2.5000E0 + 15.6400E0 3.0000E0 + 8.1700E0 4.0000E0 + 8.5500E0 5.0000E0 + 10.1200E0 6.0000E0 + 78.0000E0 .5000E0 + 66.0000E0 .6250E0 + 62.0000E0 .7500E0 + 58.0000E0 .8750E0 + 47.7000E0 1.0000E0 + 37.8000E0 1.2500E0 + 20.2000E0 2.2500E0 + 21.0700E0 2.2500E0 + 13.8700E0 2.7500E0 + 9.6700E0 3.2500E0 + 7.7600E0 3.7500E0 + 5.4400E0 4.2500E0 + 4.8700E0 4.7500E0 + 4.0100E0 5.2500E0 + 3.7500E0 5.7500E0 + 24.1900E0 3.0000E0 + 25.7600E0 3.0000E0 + 18.0700E0 3.0000E0 + 11.8100E0 3.0000E0 + 12.0700E0 3.0000E0 + 16.1200E0 3.0000E0 + 70.8000E0 .5000E0 + 54.7000E0 .7500E0 + 48.0000E0 1.0000E0 + 39.8000E0 1.5000E0 + 29.8000E0 2.0000E0 + 23.7000E0 2.5000E0 + 29.6200E0 2.0000E0 + 23.8100E0 2.5000E0 + 17.7000E0 3.0000E0 + 11.5500E0 4.0000E0 + 12.0700E0 5.0000E0 + 8.7400E0 6.0000E0 + 80.7000E0 .5000E0 + 61.3000E0 .7500E0 + 47.5000E0 1.0000E0 + 29.0000E0 1.5000E0 + 24.0000E0 2.0000E0 + 17.7000E0 2.5000E0 + 24.5600E0 2.0000E0 + 18.6700E0 2.5000E0 + 16.2400E0 3.0000E0 + 8.7400E0 4.0000E0 + 7.8700E0 5.0000E0 + 8.5100E0 6.0000E0 + 66.7000E0 .5000E0 + 59.2000E0 .7500E0 + 40.8000E0 1.0000E0 + 30.7000E0 1.5000E0 + 25.7000E0 2.0000E0 + 16.3000E0 2.5000E0 + 25.9900E0 2.0000E0 + 16.9500E0 2.5000E0 + 13.3500E0 3.0000E0 + 8.6200E0 4.0000E0 + 7.2000E0 5.0000E0 + 6.6400E0 6.0000E0 + 13.6900E0 3.0000E0 + 81.0000E0 .5000E0 + 64.5000E0 .7500E0 + 35.5000E0 1.5000E0 + 13.3100E0 3.0000E0 + 4.8700E0 6.0000E0 + 12.9400E0 3.0000E0 + 5.0600E0 6.0000E0 + 15.1900E0 3.0000E0 + 14.6200E0 3.0000E0 + 15.6400E0 3.0000E0 + 25.5000E0 1.7500E0 + 25.9500E0 1.7500E0 + 81.7000E0 .5000E0 + 61.6000E0 .7500E0 + 29.8000E0 1.7500E0 + 29.8100E0 1.7500E0 + 17.1700E0 2.7500E0 + 10.3900E0 3.7500E0 + 28.4000E0 1.7500E0 + 28.6900E0 1.7500E0 + 81.3000E0 .5000E0 + 60.9000E0 .7500E0 + 16.6500E0 2.7500E0 + 10.0500E0 3.7500E0 + 28.9000E0 1.7500E0 + 28.9500E0 1.7500E0 diff --git a/NIST_STRD/Chwirut2.dat b/NIST_STRD/Chwirut2.dat index 03703de..0651faa 100644 --- a/NIST_STRD/Chwirut2.dat +++ b/NIST_STRD/Chwirut2.dat @@ -1,114 +1,114 @@ -NIST/ITL StRD
-Dataset Name: Chwirut2 (Chwirut2.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 43)
- Certified Values (lines 41 to 48)
- Data (lines 61 to 114)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study involving
- ultrasonic calibration. The response variable is
- ultrasonic response, and the predictor variable is
- metal distance.
-
-
-
-Reference: Chwirut, D., NIST (197?).
- Ultrasonic Reference Block Study.
-
-
-
-
-
-Data: 1 Response (y = ultrasonic response)
- 1 Predictor (x = metal distance)
- 54 Observations
- Lower Level of Difficulty
- Observed Data
-
-Model: Exponential Class
- 3 Parameters (b1 to b3)
-
- y = exp(-b1*x)/(b2+b3*x) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 0.1 0.15 1.6657666537E-01 3.8303286810E-02
- b2 = 0.01 0.008 5.1653291286E-03 6.6621605126E-04
- b3 = 0.02 0.010 1.2150007096E-02 1.5304234767E-03
-
-Residual Sum of Squares: 5.1304802941E+02
-Residual Standard Deviation: 3.1717133040E+00
-Degrees of Freedom: 51
-Number of Observations: 54
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 92.9000E0 0.500E0
- 57.1000E0 1.000E0
- 31.0500E0 1.750E0
- 11.5875E0 3.750E0
- 8.0250E0 5.750E0
- 63.6000E0 0.875E0
- 21.4000E0 2.250E0
- 14.2500E0 3.250E0
- 8.4750E0 5.250E0
- 63.8000E0 0.750E0
- 26.8000E0 1.750E0
- 16.4625E0 2.750E0
- 7.1250E0 4.750E0
- 67.3000E0 0.625E0
- 41.0000E0 1.250E0
- 21.1500E0 2.250E0
- 8.1750E0 4.250E0
- 81.5000E0 .500E0
- 13.1200E0 3.000E0
- 59.9000E0 .750E0
- 14.6200E0 3.000E0
- 32.9000E0 1.500E0
- 5.4400E0 6.000E0
- 12.5600E0 3.000E0
- 5.4400E0 6.000E0
- 32.0000E0 1.500E0
- 13.9500E0 3.000E0
- 75.8000E0 .500E0
- 20.0000E0 2.000E0
- 10.4200E0 4.000E0
- 59.5000E0 .750E0
- 21.6700E0 2.000E0
- 8.5500E0 5.000E0
- 62.0000E0 .750E0
- 20.2000E0 2.250E0
- 7.7600E0 3.750E0
- 3.7500E0 5.750E0
- 11.8100E0 3.000E0
- 54.7000E0 .750E0
- 23.7000E0 2.500E0
- 11.5500E0 4.000E0
- 61.3000E0 .750E0
- 17.7000E0 2.500E0
- 8.7400E0 4.000E0
- 59.2000E0 .750E0
- 16.3000E0 2.500E0
- 8.6200E0 4.000E0
- 81.0000E0 .500E0
- 4.8700E0 6.000E0
- 14.6200E0 3.000E0
- 81.7000E0 .500E0
- 17.1700E0 2.750E0
- 81.3000E0 .500E0
- 28.9000E0 1.750E0
+NIST/ITL StRD +Dataset Name: Chwirut2 (Chwirut2.dat) + +File Format: ASCII + Starting Values (lines 41 to 43) + Certified Values (lines 41 to 48) + Data (lines 61 to 114) + +Procedure: Nonlinear Least Squares Regression + +Description: These data are the result of a NIST study involving + ultrasonic calibration. The response variable is + ultrasonic response, and the predictor variable is + metal distance. + + + +Reference: Chwirut, D., NIST (197?). + Ultrasonic Reference Block Study. + + + + + +Data: 1 Response (y = ultrasonic response) + 1 Predictor (x = metal distance) + 54 Observations + Lower Level of Difficulty + Observed Data + +Model: Exponential Class + 3 Parameters (b1 to b3) + + y = exp(-b1*x)/(b2+b3*x) + e + + + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 0.1 0.15 1.6657666537E-01 3.8303286810E-02 + b2 = 0.01 0.008 5.1653291286E-03 6.6621605126E-04 + b3 = 0.02 0.010 1.2150007096E-02 1.5304234767E-03 + +Residual Sum of Squares: 5.1304802941E+02 +Residual Standard Deviation: 3.1717133040E+00 +Degrees of Freedom: 51 +Number of Observations: 54 + + + + + + + + + + + +Data: y x + 92.9000E0 0.500E0 + 57.1000E0 1.000E0 + 31.0500E0 1.750E0 + 11.5875E0 3.750E0 + 8.0250E0 5.750E0 + 63.6000E0 0.875E0 + 21.4000E0 2.250E0 + 14.2500E0 3.250E0 + 8.4750E0 5.250E0 + 63.8000E0 0.750E0 + 26.8000E0 1.750E0 + 16.4625E0 2.750E0 + 7.1250E0 4.750E0 + 67.3000E0 0.625E0 + 41.0000E0 1.250E0 + 21.1500E0 2.250E0 + 8.1750E0 4.250E0 + 81.5000E0 .500E0 + 13.1200E0 3.000E0 + 59.9000E0 .750E0 + 14.6200E0 3.000E0 + 32.9000E0 1.500E0 + 5.4400E0 6.000E0 + 12.5600E0 3.000E0 + 5.4400E0 6.000E0 + 32.0000E0 1.500E0 + 13.9500E0 3.000E0 + 75.8000E0 .500E0 + 20.0000E0 2.000E0 + 10.4200E0 4.000E0 + 59.5000E0 .750E0 + 21.6700E0 2.000E0 + 8.5500E0 5.000E0 + 62.0000E0 .750E0 + 20.2000E0 2.250E0 + 7.7600E0 3.750E0 + 3.7500E0 5.750E0 + 11.8100E0 3.000E0 + 54.7000E0 .750E0 + 23.7000E0 2.500E0 + 11.5500E0 4.000E0 + 61.3000E0 .750E0 + 17.7000E0 2.500E0 + 8.7400E0 4.000E0 + 59.2000E0 .750E0 + 16.3000E0 2.500E0 + 8.6200E0 4.000E0 + 81.0000E0 .500E0 + 4.8700E0 6.000E0 + 14.6200E0 3.000E0 + 81.7000E0 .500E0 + 17.1700E0 2.750E0 + 81.3000E0 .500E0 + 28.9000E0 1.750E0 diff --git a/NIST_STRD/DanWood.dat b/NIST_STRD/DanWood.dat index 479a9bd..317f6a7 100644 --- a/NIST_STRD/DanWood.dat +++ b/NIST_STRD/DanWood.dat @@ -1,66 +1,66 @@ -NIST/ITL StRD
-Dataset Name: DanWood (DanWood.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 42)
- Certified Values (lines 41 to 47)
- Data (lines 61 to 66)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data and model are described in Daniel and Wood
- (1980), and originally published in E.S.Keeping,
- "Introduction to Statistical Inference," Van Nostrand
- Company, Princeton, NJ, 1962, p. 354. The response
- variable is energy radieted from a carbon filament
- lamp per cm**2 per second, and the predictor variable
- is the absolute temperature of the filament in 1000
- degrees Kelvin.
-
-Reference: Daniel, C. and F. S. Wood (1980).
- Fitting Equations to Data, Second Edition.
- New York, NY: John Wiley and Sons, pp. 428-431.
-
-
-Data: 1 Response Variable (y = energy)
- 1 Predictor Variable (x = temperature)
- 6 Observations
- Lower Level of Difficulty
- Observed Data
-
-Model: Miscellaneous Class
- 2 Parameters (b1 and b2)
-
- y = b1*x**b2 + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 1 0.7 7.6886226176E-01 1.8281973860E-02
- b2 = 5 4 3.8604055871E+00 5.1726610913E-02
-
-Residual Sum of Squares: 4.3173084083E-03
-Residual Standard Deviation: 3.2853114039E-02
-Degrees of Freedom: 4
-Number of Observations: 6
-
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 2.138E0 1.309E0
- 3.421E0 1.471E0
- 3.597E0 1.490E0
- 4.340E0 1.565E0
- 4.882E0 1.611E0
- 5.660E0 1.680E0
+NIST/ITL StRD +Dataset Name: DanWood (DanWood.dat) + +File Format: ASCII + Starting Values (lines 41 to 42) + Certified Values (lines 41 to 47) + Data (lines 61 to 66) + +Procedure: Nonlinear Least Squares Regression + +Description: These data and model are described in Daniel and Wood + (1980), and originally published in E.S.Keeping, + "Introduction to Statistical Inference," Van Nostrand + Company, Princeton, NJ, 1962, p. 354. The response + variable is energy radieted from a carbon filament + lamp per cm**2 per second, and the predictor variable + is the absolute temperature of the filament in 1000 + degrees Kelvin. + +Reference: Daniel, C. and F. S. Wood (1980). + Fitting Equations to Data, Second Edition. + New York, NY: John Wiley and Sons, pp. 428-431. + + +Data: 1 Response Variable (y = energy) + 1 Predictor Variable (x = temperature) + 6 Observations + Lower Level of Difficulty + Observed Data + +Model: Miscellaneous Class + 2 Parameters (b1 and b2) + + y = b1*x**b2 + e + + + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 1 0.7 7.6886226176E-01 1.8281973860E-02 + b2 = 5 4 3.8604055871E+00 5.1726610913E-02 + +Residual Sum of Squares: 4.3173084083E-03 +Residual Standard Deviation: 3.2853114039E-02 +Degrees of Freedom: 4 +Number of Observations: 6 + + + + + + + + + + + + +Data: y x + 2.138E0 1.309E0 + 3.421E0 1.471E0 + 3.597E0 1.490E0 + 4.340E0 1.565E0 + 4.882E0 1.611E0 + 5.660E0 1.680E0 diff --git a/NIST_STRD/ENSO.dat b/NIST_STRD/ENSO.dat index f374db2..efe5cd8 100644 --- a/NIST_STRD/ENSO.dat +++ b/NIST_STRD/ENSO.dat @@ -1,228 +1,228 @@ -NIST/ITL StRD
-Dataset Name: ENSO (ENSO.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 49)
- Certified Values (lines 41 to 54)
- Data (lines 61 to 228)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: The data are monthly averaged atmospheric pressure
- differences between Easter Island and Darwin,
- Australia. This difference drives the trade winds in
- the southern hemisphere. Fourier analysis of the data
- reveals 3 significant cycles. The annual cycle is the
- strongest, but cycles with periods of approximately 44
- and 26 months are also present. These cycles
- correspond to the El Nino and the Southern Oscillation.
- Arguments to the SIN and COS functions are in radians.
-
-Reference: Kahaner, D., C. Moler, and S. Nash, (1989).
- Numerical Methods and Software.
- Englewood Cliffs, NJ: Prentice Hall, pp. 441-445.
-
-Data: 1 Response (y = atmospheric pressure)
- 1 Predictor (x = time)
- 168 Observations
- Average Level of Difficulty
- Observed Data
-
-Model: Miscellaneous Class
- 9 Parameters (b1 to b9)
-
- y = b1 + b2*cos( 2*pi*x/12 ) + b3*sin( 2*pi*x/12 )
- + b5*cos( 2*pi*x/b4 ) + b6*sin( 2*pi*x/b4 )
- + b8*cos( 2*pi*x/b7 ) + b9*sin( 2*pi*x/b7 ) + e
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 11.0 10.0 1.0510749193E+01 1.7488832467E-01
- b2 = 3.0 3.0 3.0762128085E+00 2.4310052139E-01
- b3 = 0.5 0.5 5.3280138227E-01 2.4354686618E-01
- b4 = 40.0 44.0 4.4311088700E+01 9.4408025976E-01
- b5 = -0.7 -1.5 -1.6231428586E+00 2.8078369611E-01
- b6 = -1.3 0.5 5.2554493756E-01 4.8073701119E-01
- b7 = 25.0 26.0 2.6887614440E+01 4.1612939130E-01
- b8 = -0.3 -0.1 2.1232288488E-01 5.1460022911E-01
- b9 = 1.4 1.5 1.4966870418E+00 2.5434468893E-01
-
-Residual Sum of Squares: 7.8853978668E+02
-Residual Standard Deviation: 2.2269642403E+00
-Degrees of Freedom: 159
-Number of Observations: 168
-
-
-
-
-
-Data: y x
- 12.90000 1.000000
- 11.30000 2.000000
- 10.60000 3.000000
- 11.20000 4.000000
- 10.90000 5.000000
- 7.500000 6.000000
- 7.700000 7.000000
- 11.70000 8.000000
- 12.90000 9.000000
- 14.30000 10.000000
- 10.90000 11.00000
- 13.70000 12.00000
- 17.10000 13.00000
- 14.00000 14.00000
- 15.30000 15.00000
- 8.500000 16.00000
- 5.700000 17.00000
- 5.500000 18.00000
- 7.600000 19.00000
- 8.600000 20.00000
- 7.300000 21.00000
- 7.600000 22.00000
- 12.70000 23.00000
- 11.00000 24.00000
- 12.70000 25.00000
- 12.90000 26.00000
- 13.00000 27.00000
- 10.90000 28.00000
- 10.400000 29.00000
- 10.200000 30.00000
- 8.000000 31.00000
- 10.90000 32.00000
- 13.60000 33.00000
- 10.500000 34.00000
- 9.200000 35.00000
- 12.40000 36.00000
- 12.70000 37.00000
- 13.30000 38.00000
- 10.100000 39.00000
- 7.800000 40.00000
- 4.800000 41.00000
- 3.000000 42.00000
- 2.500000 43.00000
- 6.300000 44.00000
- 9.700000 45.00000
- 11.60000 46.00000
- 8.600000 47.00000
- 12.40000 48.00000
- 10.500000 49.00000
- 13.30000 50.00000
- 10.400000 51.00000
- 8.100000 52.00000
- 3.700000 53.00000
- 10.70000 54.00000
- 5.100000 55.00000
- 10.400000 56.00000
- 10.90000 57.00000
- 11.70000 58.00000
- 11.40000 59.00000
- 13.70000 60.00000
- 14.10000 61.00000
- 14.00000 62.00000
- 12.50000 63.00000
- 6.300000 64.00000
- 9.600000 65.00000
- 11.70000 66.00000
- 5.000000 67.00000
- 10.80000 68.00000
- 12.70000 69.00000
- 10.80000 70.00000
- 11.80000 71.00000
- 12.60000 72.00000
- 15.70000 73.00000
- 12.60000 74.00000
- 14.80000 75.00000
- 7.800000 76.00000
- 7.100000 77.00000
- 11.20000 78.00000
- 8.100000 79.00000
- 6.400000 80.00000
- 5.200000 81.00000
- 12.00000 82.00000
- 10.200000 83.00000
- 12.70000 84.00000
- 10.200000 85.00000
- 14.70000 86.00000
- 12.20000 87.00000
- 7.100000 88.00000
- 5.700000 89.00000
- 6.700000 90.00000
- 3.900000 91.00000
- 8.500000 92.00000
- 8.300000 93.00000
- 10.80000 94.00000
- 16.70000 95.00000
- 12.60000 96.00000
- 12.50000 97.00000
- 12.50000 98.00000
- 9.800000 99.00000
- 7.200000 100.00000
- 4.100000 101.00000
- 10.60000 102.00000
- 10.100000 103.00000
- 10.100000 104.00000
- 11.90000 105.00000
- 13.60000 106.0000
- 16.30000 107.0000
- 17.60000 108.0000
- 15.50000 109.0000
- 16.00000 110.0000
- 15.20000 111.0000
- 11.20000 112.0000
- 14.30000 113.0000
- 14.50000 114.0000
- 8.500000 115.0000
- 12.00000 116.0000
- 12.70000 117.0000
- 11.30000 118.0000
- 14.50000 119.0000
- 15.10000 120.0000
- 10.400000 121.0000
- 11.50000 122.0000
- 13.40000 123.0000
- 7.500000 124.0000
- 0.6000000 125.0000
- 0.3000000 126.0000
- 5.500000 127.0000
- 5.000000 128.0000
- 4.600000 129.0000
- 8.200000 130.0000
- 9.900000 131.0000
- 9.200000 132.0000
- 12.50000 133.0000
- 10.90000 134.0000
- 9.900000 135.0000
- 8.900000 136.0000
- 7.600000 137.0000
- 9.500000 138.0000
- 8.400000 139.0000
- 10.70000 140.0000
- 13.60000 141.0000
- 13.70000 142.0000
- 13.70000 143.0000
- 16.50000 144.0000
- 16.80000 145.0000
- 17.10000 146.0000
- 15.40000 147.0000
- 9.500000 148.0000
- 6.100000 149.0000
- 10.100000 150.0000
- 9.300000 151.0000
- 5.300000 152.0000
- 11.20000 153.0000
- 16.60000 154.0000
- 15.60000 155.0000
- 12.00000 156.0000
- 11.50000 157.0000
- 8.600000 158.0000
- 13.80000 159.0000
- 8.700000 160.0000
- 8.600000 161.0000
- 8.600000 162.0000
- 8.700000 163.0000
- 12.80000 164.0000
- 13.20000 165.0000
- 14.00000 166.0000
- 13.40000 167.0000
- 14.80000 168.0000
+NIST/ITL StRD +Dataset Name: ENSO (ENSO.dat) + +File Format: ASCII + Starting Values (lines 41 to 49) + Certified Values (lines 41 to 54) + Data (lines 61 to 228) + +Procedure: Nonlinear Least Squares Regression + +Description: The data are monthly averaged atmospheric pressure + differences between Easter Island and Darwin, + Australia. This difference drives the trade winds in + the southern hemisphere. Fourier analysis of the data + reveals 3 significant cycles. The annual cycle is the + strongest, but cycles with periods of approximately 44 + and 26 months are also present. These cycles + correspond to the El Nino and the Southern Oscillation. + Arguments to the SIN and COS functions are in radians. + +Reference: Kahaner, D., C. Moler, and S. Nash, (1989). + Numerical Methods and Software. + Englewood Cliffs, NJ: Prentice Hall, pp. 441-445. + +Data: 1 Response (y = atmospheric pressure) + 1 Predictor (x = time) + 168 Observations + Average Level of Difficulty + Observed Data + +Model: Miscellaneous Class + 9 Parameters (b1 to b9) + + y = b1 + b2*cos( 2*pi*x/12 ) + b3*sin( 2*pi*x/12 ) + + b5*cos( 2*pi*x/b4 ) + b6*sin( 2*pi*x/b4 ) + + b8*cos( 2*pi*x/b7 ) + b9*sin( 2*pi*x/b7 ) + e + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 11.0 10.0 1.0510749193E+01 1.7488832467E-01 + b2 = 3.0 3.0 3.0762128085E+00 2.4310052139E-01 + b3 = 0.5 0.5 5.3280138227E-01 2.4354686618E-01 + b4 = 40.0 44.0 4.4311088700E+01 9.4408025976E-01 + b5 = -0.7 -1.5 -1.6231428586E+00 2.8078369611E-01 + b6 = -1.3 0.5 5.2554493756E-01 4.8073701119E-01 + b7 = 25.0 26.0 2.6887614440E+01 4.1612939130E-01 + b8 = -0.3 -0.1 2.1232288488E-01 5.1460022911E-01 + b9 = 1.4 1.5 1.4966870418E+00 2.5434468893E-01 + +Residual Sum of Squares: 7.8853978668E+02 +Residual Standard Deviation: 2.2269642403E+00 +Degrees of Freedom: 159 +Number of Observations: 168 + + + + + +Data: y x + 12.90000 1.000000 + 11.30000 2.000000 + 10.60000 3.000000 + 11.20000 4.000000 + 10.90000 5.000000 + 7.500000 6.000000 + 7.700000 7.000000 + 11.70000 8.000000 + 12.90000 9.000000 + 14.30000 10.000000 + 10.90000 11.00000 + 13.70000 12.00000 + 17.10000 13.00000 + 14.00000 14.00000 + 15.30000 15.00000 + 8.500000 16.00000 + 5.700000 17.00000 + 5.500000 18.00000 + 7.600000 19.00000 + 8.600000 20.00000 + 7.300000 21.00000 + 7.600000 22.00000 + 12.70000 23.00000 + 11.00000 24.00000 + 12.70000 25.00000 + 12.90000 26.00000 + 13.00000 27.00000 + 10.90000 28.00000 + 10.400000 29.00000 + 10.200000 30.00000 + 8.000000 31.00000 + 10.90000 32.00000 + 13.60000 33.00000 + 10.500000 34.00000 + 9.200000 35.00000 + 12.40000 36.00000 + 12.70000 37.00000 + 13.30000 38.00000 + 10.100000 39.00000 + 7.800000 40.00000 + 4.800000 41.00000 + 3.000000 42.00000 + 2.500000 43.00000 + 6.300000 44.00000 + 9.700000 45.00000 + 11.60000 46.00000 + 8.600000 47.00000 + 12.40000 48.00000 + 10.500000 49.00000 + 13.30000 50.00000 + 10.400000 51.00000 + 8.100000 52.00000 + 3.700000 53.00000 + 10.70000 54.00000 + 5.100000 55.00000 + 10.400000 56.00000 + 10.90000 57.00000 + 11.70000 58.00000 + 11.40000 59.00000 + 13.70000 60.00000 + 14.10000 61.00000 + 14.00000 62.00000 + 12.50000 63.00000 + 6.300000 64.00000 + 9.600000 65.00000 + 11.70000 66.00000 + 5.000000 67.00000 + 10.80000 68.00000 + 12.70000 69.00000 + 10.80000 70.00000 + 11.80000 71.00000 + 12.60000 72.00000 + 15.70000 73.00000 + 12.60000 74.00000 + 14.80000 75.00000 + 7.800000 76.00000 + 7.100000 77.00000 + 11.20000 78.00000 + 8.100000 79.00000 + 6.400000 80.00000 + 5.200000 81.00000 + 12.00000 82.00000 + 10.200000 83.00000 + 12.70000 84.00000 + 10.200000 85.00000 + 14.70000 86.00000 + 12.20000 87.00000 + 7.100000 88.00000 + 5.700000 89.00000 + 6.700000 90.00000 + 3.900000 91.00000 + 8.500000 92.00000 + 8.300000 93.00000 + 10.80000 94.00000 + 16.70000 95.00000 + 12.60000 96.00000 + 12.50000 97.00000 + 12.50000 98.00000 + 9.800000 99.00000 + 7.200000 100.00000 + 4.100000 101.00000 + 10.60000 102.00000 + 10.100000 103.00000 + 10.100000 104.00000 + 11.90000 105.00000 + 13.60000 106.0000 + 16.30000 107.0000 + 17.60000 108.0000 + 15.50000 109.0000 + 16.00000 110.0000 + 15.20000 111.0000 + 11.20000 112.0000 + 14.30000 113.0000 + 14.50000 114.0000 + 8.500000 115.0000 + 12.00000 116.0000 + 12.70000 117.0000 + 11.30000 118.0000 + 14.50000 119.0000 + 15.10000 120.0000 + 10.400000 121.0000 + 11.50000 122.0000 + 13.40000 123.0000 + 7.500000 124.0000 + 0.6000000 125.0000 + 0.3000000 126.0000 + 5.500000 127.0000 + 5.000000 128.0000 + 4.600000 129.0000 + 8.200000 130.0000 + 9.900000 131.0000 + 9.200000 132.0000 + 12.50000 133.0000 + 10.90000 134.0000 + 9.900000 135.0000 + 8.900000 136.0000 + 7.600000 137.0000 + 9.500000 138.0000 + 8.400000 139.0000 + 10.70000 140.0000 + 13.60000 141.0000 + 13.70000 142.0000 + 13.70000 143.0000 + 16.50000 144.0000 + 16.80000 145.0000 + 17.10000 146.0000 + 15.40000 147.0000 + 9.500000 148.0000 + 6.100000 149.0000 + 10.100000 150.0000 + 9.300000 151.0000 + 5.300000 152.0000 + 11.20000 153.0000 + 16.60000 154.0000 + 15.60000 155.0000 + 12.00000 156.0000 + 11.50000 157.0000 + 8.600000 158.0000 + 13.80000 159.0000 + 8.700000 160.0000 + 8.600000 161.0000 + 8.600000 162.0000 + 8.700000 163.0000 + 12.80000 164.0000 + 13.20000 165.0000 + 14.00000 166.0000 + 13.40000 167.0000 + 14.80000 168.0000 diff --git a/NIST_STRD/Eckerle4.dat b/NIST_STRD/Eckerle4.dat index 2d0d8bf..dd54f5a 100644 --- a/NIST_STRD/Eckerle4.dat +++ b/NIST_STRD/Eckerle4.dat @@ -1,95 +1,95 @@ -NIST/ITL StRD
-Dataset Name: Eckerle4 (Eckerle4.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 43)
- Certified Values (lines 41 to 48)
- Data (lines 61 to 95)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study involving
- circular interference transmittance. The response
- variable is transmittance, and the predictor variable
- is wavelength.
-
-
-Reference: Eckerle, K., NIST (197?).
- Circular Interference Transmittance Study.
-
-
-
-
-
-
-Data: 1 Response Variable (y = transmittance)
- 1 Predictor Variable (x = wavelength)
- 35 Observations
- Higher Level of Difficulty
- Observed Data
-
-Model: Exponential Class
- 3 Parameters (b1 to b3)
-
- y = (b1/b2) * exp[-0.5*((x-b3)/b2)**2] + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 1 1.5 1.5543827178E+00 1.5408051163E-02
- b2 = 10 5 4.0888321754E+00 4.6803020753E-02
- b3 = 500 450 4.5154121844E+02 4.6800518816E-02
-
-Residual Sum of Squares: 1.4635887487E-03
-Residual Standard Deviation: 6.7629245447E-03
-Degrees of Freedom: 32
-Number of Observations: 35
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 0.0001575E0 400.000000E0
- 0.0001699E0 405.000000E0
- 0.0002350E0 410.000000E0
- 0.0003102E0 415.000000E0
- 0.0004917E0 420.000000E0
- 0.0008710E0 425.000000E0
- 0.0017418E0 430.000000E0
- 0.0046400E0 435.000000E0
- 0.0065895E0 436.500000E0
- 0.0097302E0 438.000000E0
- 0.0149002E0 439.500000E0
- 0.0237310E0 441.000000E0
- 0.0401683E0 442.500000E0
- 0.0712559E0 444.000000E0
- 0.1264458E0 445.500000E0
- 0.2073413E0 447.000000E0
- 0.2902366E0 448.500000E0
- 0.3445623E0 450.000000E0
- 0.3698049E0 451.500000E0
- 0.3668534E0 453.000000E0
- 0.3106727E0 454.500000E0
- 0.2078154E0 456.000000E0
- 0.1164354E0 457.500000E0
- 0.0616764E0 459.000000E0
- 0.0337200E0 460.500000E0
- 0.0194023E0 462.000000E0
- 0.0117831E0 463.500000E0
- 0.0074357E0 465.000000E0
- 0.0022732E0 470.000000E0
- 0.0008800E0 475.000000E0
- 0.0004579E0 480.000000E0
- 0.0002345E0 485.000000E0
- 0.0001586E0 490.000000E0
- 0.0001143E0 495.000000E0
- 0.0000710E0 500.000000E0
+NIST/ITL StRD +Dataset Name: Eckerle4 (Eckerle4.dat) + +File Format: ASCII + Starting Values (lines 41 to 43) + Certified Values (lines 41 to 48) + Data (lines 61 to 95) + +Procedure: Nonlinear Least Squares Regression + +Description: These data are the result of a NIST study involving + circular interference transmittance. The response + variable is transmittance, and the predictor variable + is wavelength. + + +Reference: Eckerle, K., NIST (197?). + Circular Interference Transmittance Study. + + + + + + +Data: 1 Response Variable (y = transmittance) + 1 Predictor Variable (x = wavelength) + 35 Observations + Higher Level of Difficulty + Observed Data + +Model: Exponential Class + 3 Parameters (b1 to b3) + + y = (b1/b2) * exp[-0.5*((x-b3)/b2)**2] + e + + + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 1 1.5 1.5543827178E+00 1.5408051163E-02 + b2 = 10 5 4.0888321754E+00 4.6803020753E-02 + b3 = 500 450 4.5154121844E+02 4.6800518816E-02 + +Residual Sum of Squares: 1.4635887487E-03 +Residual Standard Deviation: 6.7629245447E-03 +Degrees of Freedom: 32 +Number of Observations: 35 + + + + + + + + + + + +Data: y x + 0.0001575E0 400.000000E0 + 0.0001699E0 405.000000E0 + 0.0002350E0 410.000000E0 + 0.0003102E0 415.000000E0 + 0.0004917E0 420.000000E0 + 0.0008710E0 425.000000E0 + 0.0017418E0 430.000000E0 + 0.0046400E0 435.000000E0 + 0.0065895E0 436.500000E0 + 0.0097302E0 438.000000E0 + 0.0149002E0 439.500000E0 + 0.0237310E0 441.000000E0 + 0.0401683E0 442.500000E0 + 0.0712559E0 444.000000E0 + 0.1264458E0 445.500000E0 + 0.2073413E0 447.000000E0 + 0.2902366E0 448.500000E0 + 0.3445623E0 450.000000E0 + 0.3698049E0 451.500000E0 + 0.3668534E0 453.000000E0 + 0.3106727E0 454.500000E0 + 0.2078154E0 456.000000E0 + 0.1164354E0 457.500000E0 + 0.0616764E0 459.000000E0 + 0.0337200E0 460.500000E0 + 0.0194023E0 462.000000E0 + 0.0117831E0 463.500000E0 + 0.0074357E0 465.000000E0 + 0.0022732E0 470.000000E0 + 0.0008800E0 475.000000E0 + 0.0004579E0 480.000000E0 + 0.0002345E0 485.000000E0 + 0.0001586E0 490.000000E0 + 0.0001143E0 495.000000E0 + 0.0000710E0 500.000000E0 diff --git a/NIST_STRD/Gauss1.dat b/NIST_STRD/Gauss1.dat index df8dfac..89c389e 100644 --- a/NIST_STRD/Gauss1.dat +++ b/NIST_STRD/Gauss1.dat @@ -1,310 +1,310 @@ -NIST/ITL StRD
-Dataset Name: Gauss1 (Gauss1.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 48)
- Certified Values (lines 41 to 53)
- Data (lines 61 to 310)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: The data are two well-separated Gaussians on a
- decaying exponential baseline plus normally
- distributed zero-mean noise with variance = 6.25.
-
-Reference: Rust, B., NIST (1996).
-
-
-
-
-
-
-
-
-
-Data: 1 Response (y)
- 1 Predictor (x)
- 250 Observations
- Lower Level of Difficulty
- Generated Data
-
-Model: Exponential Class
- 8 Parameters (b1 to b8)
-
- y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 )
- + b6*exp( -(x-b7)**2 / b8**2 ) + e
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 97.0 94.0 9.8778210871E+01 5.7527312730E-01
- b2 = 0.009 0.0105 1.0497276517E-02 1.1406289017E-04
- b3 = 100.0 99.0 1.0048990633E+02 5.8831775752E-01
- b4 = 65.0 63.0 6.7481111276E+01 1.0460593412E-01
- b5 = 20.0 25.0 2.3129773360E+01 1.7439951146E-01
- b6 = 70.0 71.0 7.1994503004E+01 6.2622793913E-01
- b7 = 178.0 180.0 1.7899805021E+02 1.2436988217E-01
- b8 = 16.5 20.0 1.8389389025E+01 2.0134312832E-01
-
-Residual Sum of Squares: 1.3158222432E+03
-Residual Standard Deviation: 2.3317980180E+00
-Degrees of Freedom: 242
-Number of Observations: 250
-
-
-
-
-
-
-Data: y x
- 97.62227 1.000000
- 97.80724 2.000000
- 96.62247 3.000000
- 92.59022 4.000000
- 91.23869 5.000000
- 95.32704 6.000000
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- 3.362571 248.0000
- 1.182746 249.0000
- 4.875359 250.0000
+NIST/ITL StRD +Dataset Name: Gauss1 (Gauss1.dat) + +File Format: ASCII + Starting Values (lines 41 to 48) + Certified Values (lines 41 to 53) + Data (lines 61 to 310) + +Procedure: Nonlinear Least Squares Regression + +Description: The data are two well-separated Gaussians on a + decaying exponential baseline plus normally + distributed zero-mean noise with variance = 6.25. + +Reference: Rust, B., NIST (1996). + + + + + + + + + +Data: 1 Response (y) + 1 Predictor (x) + 250 Observations + Lower Level of Difficulty + Generated Data + +Model: Exponential Class + 8 Parameters (b1 to b8) + + y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 ) + + b6*exp( -(x-b7)**2 / b8**2 ) + e + + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 97.0 94.0 9.8778210871E+01 5.7527312730E-01 + b2 = 0.009 0.0105 1.0497276517E-02 1.1406289017E-04 + b3 = 100.0 99.0 1.0048990633E+02 5.8831775752E-01 + b4 = 65.0 63.0 6.7481111276E+01 1.0460593412E-01 + b5 = 20.0 25.0 2.3129773360E+01 1.7439951146E-01 + b6 = 70.0 71.0 7.1994503004E+01 6.2622793913E-01 + b7 = 178.0 180.0 1.7899805021E+02 1.2436988217E-01 + b8 = 16.5 20.0 1.8389389025E+01 2.0134312832E-01 + +Residual Sum of Squares: 1.3158222432E+03 +Residual Standard Deviation: 2.3317980180E+00 +Degrees of Freedom: 242 +Number of Observations: 250 + + + + + + +Data: y x + 97.62227 1.000000 + 97.80724 2.000000 + 96.62247 3.000000 + 92.59022 4.000000 + 91.23869 5.000000 + 95.32704 6.000000 + 90.35040 7.000000 + 89.46235 8.000000 + 91.72520 9.000000 + 89.86916 10.000000 + 86.88076 11.00000 + 85.94360 12.00000 + 87.60686 13.00000 + 86.25839 14.00000 + 80.74976 15.00000 + 83.03551 16.00000 + 88.25837 17.00000 + 82.01316 18.00000 + 82.74098 19.00000 + 83.30034 20.00000 + 81.27850 21.00000 + 81.85506 22.00000 + 80.75195 23.00000 + 80.09573 24.00000 + 81.07633 25.00000 + 78.81542 26.00000 + 78.38596 27.00000 + 79.93386 28.00000 + 79.48474 29.00000 + 79.95942 30.00000 + 76.10691 31.00000 + 78.39830 32.00000 + 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6.790655 232.0000 + 8.783535 233.0000 + 4.600288 234.0000 + 8.400915 235.0000 + 7.216561 236.0000 + 10.017410 237.0000 + 7.331278 238.0000 + 6.527863 239.0000 + 2.842001 240.0000 + 10.325070 241.0000 + 4.790995 242.0000 + 8.377101 243.0000 + 6.264445 244.0000 + 2.706213 245.0000 + 8.362329 246.0000 + 8.983658 247.0000 + 3.362571 248.0000 + 1.182746 249.0000 + 4.875359 250.0000 diff --git a/NIST_STRD/Gauss2.dat b/NIST_STRD/Gauss2.dat index 38222eb..ff185d1 100644 --- a/NIST_STRD/Gauss2.dat +++ b/NIST_STRD/Gauss2.dat @@ -1,310 +1,310 @@ -NIST/ITL StRD
-Dataset Name: Gauss2 (Gauss2.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 48)
- Certified Values (lines 41 to 53)
- Data (lines 61 to 310)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: The data are two slightly-blended Gaussians on a
- decaying exponential baseline plus normally
- distributed zero-mean noise with variance = 6.25.
-
-Reference: Rust, B., NIST (1996).
-
-
-
-
-
-
-
-
-
-Data: 1 Response (y)
- 1 Predictor (x)
- 250 Observations
- Lower Level of Difficulty
- Generated Data
-
-Model: Exponential Class
- 8 Parameters (b1 to b8)
-
- y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 )
- + b6*exp( -(x-b7)**2 / b8**2 ) + e
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 96.0 98.0 9.9018328406E+01 5.3748766879E-01
- b2 = 0.009 0.0105 1.0994945399E-02 1.3335306766E-04
- b3 = 103.0 103.0 1.0188022528E+02 5.9217315772E-01
- b4 = 106.0 105.0 1.0703095519E+02 1.5006798316E-01
- b5 = 18.0 20.0 2.3578584029E+01 2.2695595067E-01
- b6 = 72.0 73.0 7.2045589471E+01 6.1721965884E-01
- b7 = 151.0 150.0 1.5327010194E+02 1.9466674341E-01
- b8 = 18.0 20.0 1.9525972636E+01 2.6416549393E-01
-
-Residual Sum of Squares: 1.2475282092E+03
-Residual Standard Deviation: 2.2704790782E+00
-Degrees of Freedom: 242
-Number of Observations: 250
-
-
-
-
-
-
-Data: y x
- 97.58776 1.000000
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+NIST/ITL StRD +Dataset Name: Gauss2 (Gauss2.dat) + +File Format: ASCII + Starting Values (lines 41 to 48) + Certified Values (lines 41 to 53) + Data (lines 61 to 310) + +Procedure: Nonlinear Least Squares Regression + +Description: The data are two slightly-blended Gaussians on a + decaying exponential baseline plus normally + distributed zero-mean noise with variance = 6.25. + +Reference: Rust, B., NIST (1996). + + + + + + + + + +Data: 1 Response (y) + 1 Predictor (x) + 250 Observations + Lower Level of Difficulty + Generated Data + +Model: Exponential Class + 8 Parameters (b1 to b8) + + y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 ) + + b6*exp( -(x-b7)**2 / b8**2 ) + e + + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 96.0 98.0 9.9018328406E+01 5.3748766879E-01 + b2 = 0.009 0.0105 1.0994945399E-02 1.3335306766E-04 + b3 = 103.0 103.0 1.0188022528E+02 5.9217315772E-01 + b4 = 106.0 105.0 1.0703095519E+02 1.5006798316E-01 + b5 = 18.0 20.0 2.3578584029E+01 2.2695595067E-01 + b6 = 72.0 73.0 7.2045589471E+01 6.1721965884E-01 + b7 = 151.0 150.0 1.5327010194E+02 1.9466674341E-01 + b8 = 18.0 20.0 1.9525972636E+01 2.6416549393E-01 + +Residual Sum of Squares: 1.2475282092E+03 +Residual Standard Deviation: 2.2704790782E+00 +Degrees of Freedom: 242 +Number of Observations: 250 + + + + + + +Data: y x + 97.58776 1.000000 + 97.76344 2.000000 + 96.56705 3.000000 + 92.52037 4.000000 + 91.15097 5.000000 + 95.21728 6.000000 + 90.21355 7.000000 + 89.29235 8.000000 + 91.51479 9.000000 + 89.60966 10.000000 + 86.56187 11.00000 + 85.55316 12.00000 + 87.13054 13.00000 + 85.67940 14.00000 + 80.04851 15.00000 + 82.18925 16.00000 + 87.24081 17.00000 + 80.79407 18.00000 + 81.28570 19.00000 + 81.56940 20.00000 + 79.22715 21.00000 + 79.43275 22.00000 + 77.90195 23.00000 + 76.75468 24.00000 + 77.17377 25.00000 + 74.27348 26.00000 + 73.11900 27.00000 + 73.84826 28.00000 + 72.47870 29.00000 + 71.92292 30.00000 + 66.92176 31.00000 + 67.93835 32.00000 + 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-Dataset Name: Gauss3 (Gauss3.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 48)
- Certified Values (lines 41 to 53)
- Data (lines 61 to 310)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: The data are two strongly-blended Gaussians on a
- decaying exponential baseline plus normally
- distributed zero-mean noise with variance = 6.25.
-
-Reference: Rust, B., NIST (1996).
-
-
-
-
-
-
-
-
-
-Data: 1 Response (y)
- 1 Predictor (x)
- 250 Observations
- Average Level of Difficulty
- Generated Data
-
-Model: Exponential Class
- 8 Parameters (b1 to b8)
-
- y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 )
- + b6*exp( -(x-b7)**2 / b8**2 ) + e
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 94.9 96.0 9.8940368970E+01 5.3005192833E-01
- b2 = 0.009 0.0096 1.0945879335E-02 1.2554058911E-04
- b3 = 90.1 80.0 1.0069553078E+02 8.1256587317E-01
- b4 = 113.0 110.0 1.1163619459E+02 3.5317859757E-01
- b5 = 20.0 25.0 2.3300500029E+01 3.6584783023E-01
- b6 = 73.8 74.0 7.3705031418E+01 1.2091239082E+00
- b7 = 140.0 139.0 1.4776164251E+02 4.0488183351E-01
- b8 = 20.0 25.0 1.9668221230E+01 3.7806634336E-01
-
-Residual Sum of Squares: 1.2444846360E+03
-Residual Standard Deviation: 2.2677077625E+00
-Degrees of Freedom: 242
-Number of Observations: 250
-
-
-
-
-
-
-Data: y x
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- 4.875312 250.0000
+NIST/ITL StRD +Dataset Name: Gauss3 (Gauss3.dat) + +File Format: ASCII + Starting Values (lines 41 to 48) + Certified Values (lines 41 to 53) + Data (lines 61 to 310) + +Procedure: Nonlinear Least Squares Regression + +Description: The data are two strongly-blended Gaussians on a + decaying exponential baseline plus normally + distributed zero-mean noise with variance = 6.25. + +Reference: Rust, B., NIST (1996). + + + + + + + + + +Data: 1 Response (y) + 1 Predictor (x) + 250 Observations + Average Level of Difficulty + Generated Data + +Model: Exponential Class + 8 Parameters (b1 to b8) + + y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 ) + + b6*exp( -(x-b7)**2 / b8**2 ) + e + + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 94.9 96.0 9.8940368970E+01 5.3005192833E-01 + b2 = 0.009 0.0096 1.0945879335E-02 1.2554058911E-04 + b3 = 90.1 80.0 1.0069553078E+02 8.1256587317E-01 + b4 = 113.0 110.0 1.1163619459E+02 3.5317859757E-01 + b5 = 20.0 25.0 2.3300500029E+01 3.6584783023E-01 + b6 = 73.8 74.0 7.3705031418E+01 1.2091239082E+00 + b7 = 140.0 139.0 1.4776164251E+02 4.0488183351E-01 + b8 = 20.0 25.0 1.9668221230E+01 3.7806634336E-01 + +Residual Sum of Squares: 1.2444846360E+03 +Residual Standard Deviation: 2.2677077625E+00 +Degrees of Freedom: 242 +Number of Observations: 250 + + + + + + +Data: y x + 97.58776 1.000000 + 97.76344 2.000000 + 96.56705 3.000000 + 92.52037 4.000000 + 91.15097 5.000000 + 95.21728 6.000000 + 90.21355 7.000000 + 89.29235 8.000000 + 91.51479 9.000000 + 89.60965 10.000000 + 86.56187 11.00000 + 85.55315 12.00000 + 87.13053 13.00000 + 85.67938 14.00000 + 80.04849 15.00000 + 82.18922 16.00000 + 87.24078 17.00000 + 80.79401 18.00000 + 81.28564 19.00000 + 81.56932 20.00000 + 79.22703 21.00000 + 79.43259 22.00000 + 77.90174 23.00000 + 76.75438 24.00000 + 77.17338 25.00000 + 74.27296 26.00000 + 73.11830 27.00000 + 73.84732 28.00000 + 72.47746 29.00000 + 71.92128 30.00000 + 66.91962 31.00000 + 67.93554 32.00000 + 69.55841 33.00000 + 69.06592 34.00000 + 66.53371 35.00000 + 63.87094 36.00000 + 69.70526 37.00000 + 63.59295 38.00000 + 63.35509 39.00000 + 59.99747 40.00000 + 62.64843 41.00000 + 65.77345 42.00000 + 59.10141 43.00000 + 56.57750 44.00000 + 61.15313 45.00000 + 54.30767 46.00000 + 62.83535 47.00000 + 56.52957 48.00000 + 56.98427 49.00000 + 58.11459 50.00000 + 58.69576 51.00000 + 58.23322 52.00000 + 54.90490 53.00000 + 57.91442 54.00000 + 56.96629 55.00000 + 51.13831 56.00000 + 49.27123 57.00000 + 52.92668 58.00000 + 54.47693 59.00000 + 51.81710 60.00000 + 51.05401 61.00000 + 52.51731 62.00000 + 51.83710 63.00000 + 54.48196 64.00000 + 49.05859 65.00000 + 50.52315 66.00000 + 50.32755 67.00000 + 46.44419 68.00000 + 50.89281 69.00000 + 52.13203 70.00000 + 49.78741 71.00000 + 49.01637 72.00000 + 54.18198 73.00000 + 53.17456 74.00000 + 53.20827 75.00000 + 57.43459 76.00000 + 51.95282 77.00000 + 54.20282 78.00000 + 57.46687 79.00000 + 53.60268 80.00000 + 58.86728 81.00000 + 57.66652 82.00000 + 63.71034 83.00000 + 65.24244 84.00000 + 65.10878 85.00000 + 69.96313 86.00000 + 68.85475 87.00000 + 73.32574 88.00000 + 76.21241 89.00000 + 78.06311 90.00000 + 75.37701 91.00000 + 87.54449 92.00000 + 89.50588 93.00000 + 95.82098 94.00000 + 97.48390 95.00000 + 100.86070 96.00000 + 102.48510 97.00000 + 105.7311 98.00000 + 111.3489 99.00000 + 111.0305 100.00000 + 110.1920 101.00000 + 118.3581 102.00000 + 118.8086 103.00000 + 122.4249 104.00000 + 124.0953 105.00000 + 125.9337 106.0000 + 127.8533 107.0000 + 131.0361 108.0000 + 133.3343 109.0000 + 135.1278 110.0000 + 131.7113 111.0000 + 131.9151 112.0000 + 132.1107 113.0000 + 127.6898 114.0000 + 133.2148 115.0000 + 128.2296 116.0000 + 133.5902 117.0000 + 127.2539 118.0000 + 128.3482 119.0000 + 124.8694 120.0000 + 124.6031 121.0000 + 117.0648 122.0000 + 118.1966 123.0000 + 119.5408 124.0000 + 114.7946 125.0000 + 114.2780 126.0000 + 120.3484 127.0000 + 114.8647 128.0000 + 111.6514 129.0000 + 110.1826 130.0000 + 108.4461 131.0000 + 109.0571 132.0000 + 106.5308 133.0000 + 109.4691 134.0000 + 106.8709 135.0000 + 107.3192 136.0000 + 106.9000 137.0000 + 109.6526 138.0000 + 107.1602 139.0000 + 108.2509 140.0000 + 104.96310 141.0000 + 109.3601 142.0000 + 107.6696 143.0000 + 99.77286 144.0000 + 104.96440 145.0000 + 106.1376 146.0000 + 106.5816 147.0000 + 100.12860 148.0000 + 101.66910 149.0000 + 96.44254 150.0000 + 97.34169 151.0000 + 96.97412 152.0000 + 90.73460 153.0000 + 93.37949 154.0000 + 82.12331 155.0000 + 83.01657 156.0000 + 78.87360 157.0000 + 74.86971 158.0000 + 72.79341 159.0000 + 65.14744 160.0000 + 67.02127 161.0000 + 60.16136 162.0000 + 57.13996 163.0000 + 54.05769 164.0000 + 50.42265 165.0000 + 47.82430 166.0000 + 42.85748 167.0000 + 42.45495 168.0000 + 38.30808 169.0000 + 36.95794 170.0000 + 33.94543 171.0000 + 34.19017 172.0000 + 31.66097 173.0000 + 23.56172 174.0000 + 29.61143 175.0000 + 23.88765 176.0000 + 22.49812 177.0000 + 24.86901 178.0000 + 17.29481 179.0000 + 18.09291 180.0000 + 15.34813 181.0000 + 14.77997 182.0000 + 13.87832 183.0000 + 12.88891 184.0000 + 16.20763 185.0000 + 16.29024 186.0000 + 15.29712 187.0000 + 14.97839 188.0000 + 12.11330 189.0000 + 14.24168 190.0000 + 12.53824 191.0000 + 15.19818 192.0000 + 11.70478 193.0000 + 15.83745 194.0000 + 10.035850 195.0000 + 9.307574 196.0000 + 12.86800 197.0000 + 8.571671 198.0000 + 11.60415 199.0000 + 12.42772 200.0000 + 11.23627 201.0000 + 11.13198 202.0000 + 7.761117 203.0000 + 6.758250 204.0000 + 14.23375 205.0000 + 10.63876 206.0000 + 8.893581 207.0000 + 11.55398 208.0000 + 11.57221 209.0000 + 11.58347 210.0000 + 9.724857 211.0000 + 11.43854 212.0000 + 11.22636 213.0000 + 10.170150 214.0000 + 12.50765 215.0000 + 6.200494 216.0000 + 9.018902 217.0000 + 10.80557 218.0000 + 13.09591 219.0000 + 3.914033 220.0000 + 9.567723 221.0000 + 8.038338 222.0000 + 10.230960 223.0000 + 9.367358 224.0000 + 7.695937 225.0000 + 6.118552 226.0000 + 8.793192 227.0000 + 7.796682 228.0000 + 12.45064 229.0000 + 10.61601 230.0000 + 6.001000 231.0000 + 6.765096 232.0000 + 8.764652 233.0000 + 4.586417 234.0000 + 8.390782 235.0000 + 7.209201 236.0000 + 10.012090 237.0000 + 7.327461 238.0000 + 6.525136 239.0000 + 2.840065 240.0000 + 10.323710 241.0000 + 4.790035 242.0000 + 8.376431 243.0000 + 6.263980 244.0000 + 2.705892 245.0000 + 8.362109 246.0000 + 8.983507 247.0000 + 3.362469 248.0000 + 1.182678 249.0000 + 4.875312 250.0000 diff --git a/NIST_STRD/Hahn1.dat b/NIST_STRD/Hahn1.dat index f3069d7..0e493a4 100644 --- a/NIST_STRD/Hahn1.dat +++ b/NIST_STRD/Hahn1.dat @@ -1,296 +1,296 @@ -NIST/ITL StRD
-Dataset Name: Hahn1 (Hahn1.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 47)
- Certified Values (lines 41 to 52)
- Data (lines 61 to 296)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study involving
- the thermal expansion of copper. The response
- variable is the coefficient of thermal expansion, and
- the predictor variable is temperature in degrees
- kelvin.
-
-
-Reference: Hahn, T., NIST (197?).
- Copper Thermal Expansion Study.
-
-
-
-
-
-Data: 1 Response (y = coefficient of thermal expansion)
- 1 Predictor (x = temperature, degrees kelvin)
- 236 Observations
- Average Level of Difficulty
- Observed Data
-
-Model: Rational Class (cubic/cubic)
- 7 Parameters (b1 to b7)
-
- y = (b1+b2*x+b3*x**2+b4*x**3) /
- (1+b5*x+b6*x**2+b7*x**3) + e
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 10 1 1.0776351733E+00 1.7070154742E-01
- b2 = -1 -0.1 -1.2269296921E-01 1.2000289189E-02
- b3 = 0.05 0.005 4.0863750610E-03 2.2508314937E-04
- b4 = -0.00001 -0.000001 -1.4262662514E-06 2.7578037666E-07
- b5 = -0.05 -0.005 -5.7609940901E-03 2.4712888219E-04
- b6 = 0.001 0.0001 2.4053735503E-04 1.0449373768E-05
- b7 = -0.000001 -0.0000001 -1.2314450199E-07 1.3027335327E-08
-
-Residual Sum of Squares: 1.5324382854E+00
-Residual Standard Deviation: 8.1803852243E-02
-Degrees of Freedom: 229
-Number of Observations: 236
-
-
-
-
-
-
-
-Data: y x
- .591E0 24.41E0
- 1.547E0 34.82E0
- 2.902E0 44.09E0
- 2.894E0 45.07E0
- 4.703E0 54.98E0
- 6.307E0 65.51E0
- 7.03E0 70.53E0
- 7.898E0 75.70E0
- 9.470E0 89.57E0
- 9.484E0 91.14E0
- 10.072E0 96.40E0
- 10.163E0 97.19E0
- 11.615E0 114.26E0
- 12.005E0 120.25E0
- 12.478E0 127.08E0
- 12.982E0 133.55E0
- 12.970E0 133.61E0
- 13.926E0 158.67E0
- 14.452E0 172.74E0
- 14.404E0 171.31E0
- 15.190E0 202.14E0
- 15.550E0 220.55E0
- 15.528E0 221.05E0
- 15.499E0 221.39E0
- 16.131E0 250.99E0
- 16.438E0 268.99E0
- 16.387E0 271.80E0
- 16.549E0 271.97E0
- 16.872E0 321.31E0
- 16.830E0 321.69E0
- 16.926E0 330.14E0
- 16.907E0 333.03E0
- 16.966E0 333.47E0
- 17.060E0 340.77E0
- 17.122E0 345.65E0
- 17.311E0 373.11E0
- 17.355E0 373.79E0
- 17.668E0 411.82E0
- 17.767E0 419.51E0
- 17.803E0 421.59E0
- 17.765E0 422.02E0
- 17.768E0 422.47E0
- 17.736E0 422.61E0
- 17.858E0 441.75E0
- 17.877E0 447.41E0
- 17.912E0 448.7E0
- 18.046E0 472.89E0
- 18.085E0 476.69E0
- 18.291E0 522.47E0
- 18.357E0 522.62E0
- 18.426E0 524.43E0
- 18.584E0 546.75E0
- 18.610E0 549.53E0
- 18.870E0 575.29E0
- 18.795E0 576.00E0
- 19.111E0 625.55E0
- .367E0 20.15E0
- .796E0 28.78E0
- 0.892E0 29.57E0
- 1.903E0 37.41E0
- 2.150E0 39.12E0
- 3.697E0 50.24E0
- 5.870E0 61.38E0
- 6.421E0 66.25E0
- 7.422E0 73.42E0
- 9.944E0 95.52E0
- 11.023E0 107.32E0
- 11.87E0 122.04E0
- 12.786E0 134.03E0
- 14.067E0 163.19E0
- 13.974E0 163.48E0
- 14.462E0 175.70E0
- 14.464E0 179.86E0
- 15.381E0 211.27E0
- 15.483E0 217.78E0
- 15.59E0 219.14E0
- 16.075E0 262.52E0
- 16.347E0 268.01E0
- 16.181E0 268.62E0
- 16.915E0 336.25E0
- 17.003E0 337.23E0
- 16.978E0 339.33E0
- 17.756E0 427.38E0
- 17.808E0 428.58E0
- 17.868E0 432.68E0
- 18.481E0 528.99E0
- 18.486E0 531.08E0
- 19.090E0 628.34E0
- 16.062E0 253.24E0
- 16.337E0 273.13E0
- 16.345E0 273.66E0
- 16.388E0 282.10E0
- 17.159E0 346.62E0
- 17.116E0 347.19E0
- 17.164E0 348.78E0
- 17.123E0 351.18E0
- 17.979E0 450.10E0
- 17.974E0 450.35E0
- 18.007E0 451.92E0
- 17.993E0 455.56E0
- 18.523E0 552.22E0
- 18.669E0 553.56E0
- 18.617E0 555.74E0
- 19.371E0 652.59E0
- 19.330E0 656.20E0
- 0.080E0 14.13E0
- 0.248E0 20.41E0
- 1.089E0 31.30E0
- 1.418E0 33.84E0
- 2.278E0 39.70E0
- 3.624E0 48.83E0
- 4.574E0 54.50E0
- 5.556E0 60.41E0
- 7.267E0 72.77E0
- 7.695E0 75.25E0
- 9.136E0 86.84E0
- 9.959E0 94.88E0
- 9.957E0 96.40E0
- 11.600E0 117.37E0
- 13.138E0 139.08E0
- 13.564E0 147.73E0
- 13.871E0 158.63E0
- 13.994E0 161.84E0
- 14.947E0 192.11E0
- 15.473E0 206.76E0
- 15.379E0 209.07E0
- 15.455E0 213.32E0
- 15.908E0 226.44E0
- 16.114E0 237.12E0
- 17.071E0 330.90E0
- 17.135E0 358.72E0
- 17.282E0 370.77E0
- 17.368E0 372.72E0
- 17.483E0 396.24E0
- 17.764E0 416.59E0
- 18.185E0 484.02E0
- 18.271E0 495.47E0
- 18.236E0 514.78E0
- 18.237E0 515.65E0
- 18.523E0 519.47E0
- 18.627E0 544.47E0
- 18.665E0 560.11E0
- 19.086E0 620.77E0
- 0.214E0 18.97E0
- 0.943E0 28.93E0
- 1.429E0 33.91E0
- 2.241E0 40.03E0
- 2.951E0 44.66E0
- 3.782E0 49.87E0
- 4.757E0 55.16E0
- 5.602E0 60.90E0
- 7.169E0 72.08E0
- 8.920E0 85.15E0
- 10.055E0 97.06E0
- 12.035E0 119.63E0
- 12.861E0 133.27E0
- 13.436E0 143.84E0
- 14.167E0 161.91E0
- 14.755E0 180.67E0
- 15.168E0 198.44E0
- 15.651E0 226.86E0
- 15.746E0 229.65E0
- 16.216E0 258.27E0
- 16.445E0 273.77E0
- 16.965E0 339.15E0
- 17.121E0 350.13E0
- 17.206E0 362.75E0
- 17.250E0 371.03E0
- 17.339E0 393.32E0
- 17.793E0 448.53E0
- 18.123E0 473.78E0
- 18.49E0 511.12E0
- 18.566E0 524.70E0
- 18.645E0 548.75E0
- 18.706E0 551.64E0
- 18.924E0 574.02E0
- 19.1E0 623.86E0
- 0.375E0 21.46E0
- 0.471E0 24.33E0
- 1.504E0 33.43E0
- 2.204E0 39.22E0
- 2.813E0 44.18E0
- 4.765E0 55.02E0
- 9.835E0 94.33E0
- 10.040E0 96.44E0
- 11.946E0 118.82E0
- 12.596E0 128.48E0
- 13.303E0 141.94E0
- 13.922E0 156.92E0
- 14.440E0 171.65E0
- 14.951E0 190.00E0
- 15.627E0 223.26E0
- 15.639E0 223.88E0
- 15.814E0 231.50E0
- 16.315E0 265.05E0
- 16.334E0 269.44E0
- 16.430E0 271.78E0
- 16.423E0 273.46E0
- 17.024E0 334.61E0
- 17.009E0 339.79E0
- 17.165E0 349.52E0
- 17.134E0 358.18E0
- 17.349E0 377.98E0
- 17.576E0 394.77E0
- 17.848E0 429.66E0
- 18.090E0 468.22E0
- 18.276E0 487.27E0
- 18.404E0 519.54E0
- 18.519E0 523.03E0
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- 19.398E0 663.97E0
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- 20.007E0 749.21E0
- 19.929E0 750.14E0
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- 20.107E0 748.43E0
- 20.062E0 747.35E0
- 20.065E0 749.27E0
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- 19.972E0 747.78E0
- 20.088E0 750.51E0
- 20.743E0 851.37E0
- 20.83E0 845.97E0
- 20.935E0 847.54E0
- 21.035E0 849.93E0
- 20.93E0 851.61E0
- 21.074E0 849.75E0
- 21.085E0 850.98E0
- 20.935E0 848.23E0
+NIST/ITL StRD +Dataset Name: Hahn1 (Hahn1.dat) + +File Format: ASCII + Starting Values (lines 41 to 47) + Certified Values (lines 41 to 52) + Data (lines 61 to 296) + +Procedure: Nonlinear Least Squares Regression + +Description: These data are the result of a NIST study involving + the thermal expansion of copper. The response + variable is the coefficient of thermal expansion, and + the predictor variable is temperature in degrees + kelvin. + + +Reference: Hahn, T., NIST (197?). + Copper Thermal Expansion Study. + + + + + +Data: 1 Response (y = coefficient of thermal expansion) + 1 Predictor (x = temperature, degrees kelvin) + 236 Observations + Average Level of Difficulty + Observed Data + +Model: Rational Class (cubic/cubic) + 7 Parameters (b1 to b7) + + y = (b1+b2*x+b3*x**2+b4*x**3) / + (1+b5*x+b6*x**2+b7*x**3) + e + + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 10 1 1.0776351733E+00 1.7070154742E-01 + b2 = -1 -0.1 -1.2269296921E-01 1.2000289189E-02 + b3 = 0.05 0.005 4.0863750610E-03 2.2508314937E-04 + b4 = -0.00001 -0.000001 -1.4262662514E-06 2.7578037666E-07 + b5 = -0.05 -0.005 -5.7609940901E-03 2.4712888219E-04 + b6 = 0.001 0.0001 2.4053735503E-04 1.0449373768E-05 + b7 = -0.000001 -0.0000001 -1.2314450199E-07 1.3027335327E-08 + +Residual Sum of Squares: 1.5324382854E+00 +Residual Standard Deviation: 8.1803852243E-02 +Degrees of Freedom: 229 +Number of Observations: 236 + + + + + + + +Data: y x + .591E0 24.41E0 + 1.547E0 34.82E0 + 2.902E0 44.09E0 + 2.894E0 45.07E0 + 4.703E0 54.98E0 + 6.307E0 65.51E0 + 7.03E0 70.53E0 + 7.898E0 75.70E0 + 9.470E0 89.57E0 + 9.484E0 91.14E0 + 10.072E0 96.40E0 + 10.163E0 97.19E0 + 11.615E0 114.26E0 + 12.005E0 120.25E0 + 12.478E0 127.08E0 + 12.982E0 133.55E0 + 12.970E0 133.61E0 + 13.926E0 158.67E0 + 14.452E0 172.74E0 + 14.404E0 171.31E0 + 15.190E0 202.14E0 + 15.550E0 220.55E0 + 15.528E0 221.05E0 + 15.499E0 221.39E0 + 16.131E0 250.99E0 + 16.438E0 268.99E0 + 16.387E0 271.80E0 + 16.549E0 271.97E0 + 16.872E0 321.31E0 + 16.830E0 321.69E0 + 16.926E0 330.14E0 + 16.907E0 333.03E0 + 16.966E0 333.47E0 + 17.060E0 340.77E0 + 17.122E0 345.65E0 + 17.311E0 373.11E0 + 17.355E0 373.79E0 + 17.668E0 411.82E0 + 17.767E0 419.51E0 + 17.803E0 421.59E0 + 17.765E0 422.02E0 + 17.768E0 422.47E0 + 17.736E0 422.61E0 + 17.858E0 441.75E0 + 17.877E0 447.41E0 + 17.912E0 448.7E0 + 18.046E0 472.89E0 + 18.085E0 476.69E0 + 18.291E0 522.47E0 + 18.357E0 522.62E0 + 18.426E0 524.43E0 + 18.584E0 546.75E0 + 18.610E0 549.53E0 + 18.870E0 575.29E0 + 18.795E0 576.00E0 + 19.111E0 625.55E0 + .367E0 20.15E0 + .796E0 28.78E0 + 0.892E0 29.57E0 + 1.903E0 37.41E0 + 2.150E0 39.12E0 + 3.697E0 50.24E0 + 5.870E0 61.38E0 + 6.421E0 66.25E0 + 7.422E0 73.42E0 + 9.944E0 95.52E0 + 11.023E0 107.32E0 + 11.87E0 122.04E0 + 12.786E0 134.03E0 + 14.067E0 163.19E0 + 13.974E0 163.48E0 + 14.462E0 175.70E0 + 14.464E0 179.86E0 + 15.381E0 211.27E0 + 15.483E0 217.78E0 + 15.59E0 219.14E0 + 16.075E0 262.52E0 + 16.347E0 268.01E0 + 16.181E0 268.62E0 + 16.915E0 336.25E0 + 17.003E0 337.23E0 + 16.978E0 339.33E0 + 17.756E0 427.38E0 + 17.808E0 428.58E0 + 17.868E0 432.68E0 + 18.481E0 528.99E0 + 18.486E0 531.08E0 + 19.090E0 628.34E0 + 16.062E0 253.24E0 + 16.337E0 273.13E0 + 16.345E0 273.66E0 + 16.388E0 282.10E0 + 17.159E0 346.62E0 + 17.116E0 347.19E0 + 17.164E0 348.78E0 + 17.123E0 351.18E0 + 17.979E0 450.10E0 + 17.974E0 450.35E0 + 18.007E0 451.92E0 + 17.993E0 455.56E0 + 18.523E0 552.22E0 + 18.669E0 553.56E0 + 18.617E0 555.74E0 + 19.371E0 652.59E0 + 19.330E0 656.20E0 + 0.080E0 14.13E0 + 0.248E0 20.41E0 + 1.089E0 31.30E0 + 1.418E0 33.84E0 + 2.278E0 39.70E0 + 3.624E0 48.83E0 + 4.574E0 54.50E0 + 5.556E0 60.41E0 + 7.267E0 72.77E0 + 7.695E0 75.25E0 + 9.136E0 86.84E0 + 9.959E0 94.88E0 + 9.957E0 96.40E0 + 11.600E0 117.37E0 + 13.138E0 139.08E0 + 13.564E0 147.73E0 + 13.871E0 158.63E0 + 13.994E0 161.84E0 + 14.947E0 192.11E0 + 15.473E0 206.76E0 + 15.379E0 209.07E0 + 15.455E0 213.32E0 + 15.908E0 226.44E0 + 16.114E0 237.12E0 + 17.071E0 330.90E0 + 17.135E0 358.72E0 + 17.282E0 370.77E0 + 17.368E0 372.72E0 + 17.483E0 396.24E0 + 17.764E0 416.59E0 + 18.185E0 484.02E0 + 18.271E0 495.47E0 + 18.236E0 514.78E0 + 18.237E0 515.65E0 + 18.523E0 519.47E0 + 18.627E0 544.47E0 + 18.665E0 560.11E0 + 19.086E0 620.77E0 + 0.214E0 18.97E0 + 0.943E0 28.93E0 + 1.429E0 33.91E0 + 2.241E0 40.03E0 + 2.951E0 44.66E0 + 3.782E0 49.87E0 + 4.757E0 55.16E0 + 5.602E0 60.90E0 + 7.169E0 72.08E0 + 8.920E0 85.15E0 + 10.055E0 97.06E0 + 12.035E0 119.63E0 + 12.861E0 133.27E0 + 13.436E0 143.84E0 + 14.167E0 161.91E0 + 14.755E0 180.67E0 + 15.168E0 198.44E0 + 15.651E0 226.86E0 + 15.746E0 229.65E0 + 16.216E0 258.27E0 + 16.445E0 273.77E0 + 16.965E0 339.15E0 + 17.121E0 350.13E0 + 17.206E0 362.75E0 + 17.250E0 371.03E0 + 17.339E0 393.32E0 + 17.793E0 448.53E0 + 18.123E0 473.78E0 + 18.49E0 511.12E0 + 18.566E0 524.70E0 + 18.645E0 548.75E0 + 18.706E0 551.64E0 + 18.924E0 574.02E0 + 19.1E0 623.86E0 + 0.375E0 21.46E0 + 0.471E0 24.33E0 + 1.504E0 33.43E0 + 2.204E0 39.22E0 + 2.813E0 44.18E0 + 4.765E0 55.02E0 + 9.835E0 94.33E0 + 10.040E0 96.44E0 + 11.946E0 118.82E0 + 12.596E0 128.48E0 + 13.303E0 141.94E0 + 13.922E0 156.92E0 + 14.440E0 171.65E0 + 14.951E0 190.00E0 + 15.627E0 223.26E0 + 15.639E0 223.88E0 + 15.814E0 231.50E0 + 16.315E0 265.05E0 + 16.334E0 269.44E0 + 16.430E0 271.78E0 + 16.423E0 273.46E0 + 17.024E0 334.61E0 + 17.009E0 339.79E0 + 17.165E0 349.52E0 + 17.134E0 358.18E0 + 17.349E0 377.98E0 + 17.576E0 394.77E0 + 17.848E0 429.66E0 + 18.090E0 468.22E0 + 18.276E0 487.27E0 + 18.404E0 519.54E0 + 18.519E0 523.03E0 + 19.133E0 612.99E0 + 19.074E0 638.59E0 + 19.239E0 641.36E0 + 19.280E0 622.05E0 + 19.101E0 631.50E0 + 19.398E0 663.97E0 + 19.252E0 646.9E0 + 19.89E0 748.29E0 + 20.007E0 749.21E0 + 19.929E0 750.14E0 + 19.268E0 647.04E0 + 19.324E0 646.89E0 + 20.049E0 746.9E0 + 20.107E0 748.43E0 + 20.062E0 747.35E0 + 20.065E0 749.27E0 + 19.286E0 647.61E0 + 19.972E0 747.78E0 + 20.088E0 750.51E0 + 20.743E0 851.37E0 + 20.83E0 845.97E0 + 20.935E0 847.54E0 + 21.035E0 849.93E0 + 20.93E0 851.61E0 + 21.074E0 849.75E0 + 21.085E0 850.98E0 + 20.935E0 848.23E0 diff --git a/NIST_STRD/Kirby2.dat b/NIST_STRD/Kirby2.dat index 04df176..75cd80f 100644 --- a/NIST_STRD/Kirby2.dat +++ b/NIST_STRD/Kirby2.dat @@ -1,211 +1,211 @@ -NIST/ITL StRD
-Dataset Name: Kirby2 (Kirby2.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 45)
- Certified Values (lines 41 to 50)
- Data (lines 61 to 211)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study involving
- scanning electron microscope line with standards.
-
-
-Reference: Kirby, R., NIST (197?).
- Scanning electron microscope line width standards.
-
-
-
-
-
-
-
-
-Data: 1 Response (y)
- 1 Predictor (x)
- 151 Observations
- Average Level of Difficulty
- Observed Data
-
-Model: Rational Class (quadratic/quadratic)
- 5 Parameters (b1 to b5)
-
- y = (b1 + b2*x + b3*x**2) /
- (1 + b4*x + b5*x**2) + e
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 2 1.5 1.6745063063E+00 8.7989634338E-02
- b2 = -0.1 -0.15 -1.3927397867E-01 4.1182041386E-03
- b3 = 0.003 0.0025 2.5961181191E-03 4.1856520458E-05
- b4 = -0.001 -0.0015 -1.7241811870E-03 5.8931897355E-05
- b5 = 0.00001 0.00002 2.1664802578E-05 2.0129761919E-07
-
-Residual Sum of Squares: 3.9050739624E+00
-Residual Standard Deviation: 1.6354535131E-01
-Degrees of Freedom: 146
-Number of Observations: 151
-
-
-
-
-
-
-
-
-
-Data: y x
- 0.0082E0 9.65E0
- 0.0112E0 10.74E0
- 0.0149E0 11.81E0
- 0.0198E0 12.88E0
- 0.0248E0 14.06E0
- 0.0324E0 15.28E0
- 0.0420E0 16.63E0
- 0.0549E0 18.19E0
- 0.0719E0 19.88E0
- 0.0963E0 21.84E0
- 0.1291E0 24.00E0
- 0.1710E0 26.25E0
- 0.2314E0 28.86E0
- 0.3227E0 31.85E0
- 0.4809E0 35.79E0
- 0.7084E0 40.18E0
- 1.0220E0 44.74E0
- 1.4580E0 49.53E0
- 1.9520E0 53.94E0
- 2.5410E0 58.29E0
- 3.2230E0 62.63E0
- 3.9990E0 67.03E0
- 4.8520E0 71.25E0
- 5.7320E0 75.22E0
- 6.7270E0 79.33E0
- 7.8350E0 83.56E0
- 9.0250E0 87.75E0
- 10.2670E0 91.93E0
- 11.5780E0 96.10E0
- 12.9440E0 100.28E0
- 14.3770E0 104.46E0
- 15.8560E0 108.66E0
- 17.3310E0 112.71E0
- 18.8850E0 116.88E0
- 20.5750E0 121.33E0
- 22.3200E0 125.79E0
- 22.3030E0 125.79E0
- 23.4600E0 128.74E0
- 24.0600E0 130.27E0
- 25.2720E0 133.33E0
- 25.8530E0 134.79E0
- 27.1100E0 137.93E0
- 27.6580E0 139.33E0
- 28.9240E0 142.46E0
- 29.5110E0 143.90E0
- 30.7100E0 146.91E0
- 31.3500E0 148.51E0
- 32.5200E0 151.41E0
- 33.2300E0 153.17E0
- 34.3300E0 155.97E0
- 35.0600E0 157.76E0
- 36.1700E0 160.56E0
- 36.8400E0 162.30E0
- 38.0100E0 165.21E0
- 38.6700E0 166.90E0
- 39.8700E0 169.92E0
- 40.0300E0 170.32E0
- 40.5000E0 171.54E0
- 41.3700E0 173.79E0
- 41.6700E0 174.57E0
- 42.3100E0 176.25E0
- 42.7300E0 177.34E0
- 43.4600E0 179.19E0
- 44.1400E0 181.02E0
- 44.5500E0 182.08E0
- 45.2200E0 183.88E0
- 45.9200E0 185.75E0
- 46.3000E0 186.80E0
- 47.0000E0 188.63E0
- 47.6800E0 190.45E0
- 48.0600E0 191.48E0
- 48.7400E0 193.35E0
- 49.4100E0 195.22E0
- 49.7600E0 196.23E0
- 50.4300E0 198.05E0
- 51.1100E0 199.97E0
- 51.5000E0 201.06E0
- 52.1200E0 202.83E0
- 52.7600E0 204.69E0
- 53.1800E0 205.86E0
- 53.7800E0 207.58E0
- 54.4600E0 209.50E0
- 54.8300E0 210.65E0
- 55.4000E0 212.33E0
- 56.4300E0 215.43E0
- 57.0300E0 217.16E0
- 58.0000E0 220.21E0
- 58.6100E0 221.98E0
- 59.5800E0 225.06E0
- 60.1100E0 226.79E0
- 61.1000E0 229.92E0
- 61.6500E0 231.69E0
- 62.5900E0 234.77E0
- 63.1200E0 236.60E0
- 64.0300E0 239.63E0
- 64.6200E0 241.50E0
- 65.4900E0 244.48E0
- 66.0300E0 246.40E0
- 66.8900E0 249.35E0
- 67.4200E0 251.32E0
- 68.2300E0 254.22E0
- 68.7700E0 256.24E0
- 69.5900E0 259.11E0
- 70.1100E0 261.18E0
- 70.8600E0 264.02E0
- 71.4300E0 266.13E0
- 72.1600E0 268.94E0
- 72.7000E0 271.09E0
- 73.4000E0 273.87E0
- 73.9300E0 276.08E0
- 74.6000E0 278.83E0
- 75.1600E0 281.08E0
- 75.8200E0 283.81E0
- 76.3400E0 286.11E0
- 76.9800E0 288.81E0
- 77.4800E0 291.08E0
- 78.0800E0 293.75E0
- 78.6000E0 295.99E0
- 79.1700E0 298.64E0
- 79.6200E0 300.84E0
- 79.8800E0 302.02E0
- 80.1900E0 303.48E0
- 80.6600E0 305.65E0
- 81.2200E0 308.27E0
- 81.6600E0 310.41E0
- 82.1600E0 313.01E0
- 82.5900E0 315.12E0
- 83.1400E0 317.71E0
- 83.5000E0 319.79E0
- 84.0000E0 322.36E0
- 84.4000E0 324.42E0
- 84.8900E0 326.98E0
- 85.2600E0 329.01E0
- 85.7400E0 331.56E0
- 86.0700E0 333.56E0
- 86.5400E0 336.10E0
- 86.8900E0 338.08E0
- 87.3200E0 340.60E0
- 87.6500E0 342.57E0
- 88.1000E0 345.08E0
- 88.4300E0 347.02E0
- 88.8300E0 349.52E0
- 89.1200E0 351.44E0
- 89.5400E0 353.93E0
- 89.8500E0 355.83E0
- 90.2500E0 358.32E0
- 90.5500E0 360.20E0
- 90.9300E0 362.67E0
- 91.2000E0 364.53E0
- 91.5500E0 367.00E0
- 92.2000E0 371.30E0
+NIST/ITL StRD +Dataset Name: Kirby2 (Kirby2.dat) + +File Format: ASCII + Starting Values (lines 41 to 45) + Certified Values (lines 41 to 50) + Data (lines 61 to 211) + +Procedure: Nonlinear Least Squares Regression + +Description: These data are the result of a NIST study involving + scanning electron microscope line with standards. + + +Reference: Kirby, R., NIST (197?). + Scanning electron microscope line width standards. + + + + + + + + +Data: 1 Response (y) + 1 Predictor (x) + 151 Observations + Average Level of Difficulty + Observed Data + +Model: Rational Class (quadratic/quadratic) + 5 Parameters (b1 to b5) + + y = (b1 + b2*x + b3*x**2) / + (1 + b4*x + b5*x**2) + e + + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 2 1.5 1.6745063063E+00 8.7989634338E-02 + b2 = -0.1 -0.15 -1.3927397867E-01 4.1182041386E-03 + b3 = 0.003 0.0025 2.5961181191E-03 4.1856520458E-05 + b4 = -0.001 -0.0015 -1.7241811870E-03 5.8931897355E-05 + b5 = 0.00001 0.00002 2.1664802578E-05 2.0129761919E-07 + +Residual Sum of Squares: 3.9050739624E+00 +Residual Standard Deviation: 1.6354535131E-01 +Degrees of Freedom: 146 +Number of Observations: 151 + + + + + + + + + +Data: y x + 0.0082E0 9.65E0 + 0.0112E0 10.74E0 + 0.0149E0 11.81E0 + 0.0198E0 12.88E0 + 0.0248E0 14.06E0 + 0.0324E0 15.28E0 + 0.0420E0 16.63E0 + 0.0549E0 18.19E0 + 0.0719E0 19.88E0 + 0.0963E0 21.84E0 + 0.1291E0 24.00E0 + 0.1710E0 26.25E0 + 0.2314E0 28.86E0 + 0.3227E0 31.85E0 + 0.4809E0 35.79E0 + 0.7084E0 40.18E0 + 1.0220E0 44.74E0 + 1.4580E0 49.53E0 + 1.9520E0 53.94E0 + 2.5410E0 58.29E0 + 3.2230E0 62.63E0 + 3.9990E0 67.03E0 + 4.8520E0 71.25E0 + 5.7320E0 75.22E0 + 6.7270E0 79.33E0 + 7.8350E0 83.56E0 + 9.0250E0 87.75E0 + 10.2670E0 91.93E0 + 11.5780E0 96.10E0 + 12.9440E0 100.28E0 + 14.3770E0 104.46E0 + 15.8560E0 108.66E0 + 17.3310E0 112.71E0 + 18.8850E0 116.88E0 + 20.5750E0 121.33E0 + 22.3200E0 125.79E0 + 22.3030E0 125.79E0 + 23.4600E0 128.74E0 + 24.0600E0 130.27E0 + 25.2720E0 133.33E0 + 25.8530E0 134.79E0 + 27.1100E0 137.93E0 + 27.6580E0 139.33E0 + 28.9240E0 142.46E0 + 29.5110E0 143.90E0 + 30.7100E0 146.91E0 + 31.3500E0 148.51E0 + 32.5200E0 151.41E0 + 33.2300E0 153.17E0 + 34.3300E0 155.97E0 + 35.0600E0 157.76E0 + 36.1700E0 160.56E0 + 36.8400E0 162.30E0 + 38.0100E0 165.21E0 + 38.6700E0 166.90E0 + 39.8700E0 169.92E0 + 40.0300E0 170.32E0 + 40.5000E0 171.54E0 + 41.3700E0 173.79E0 + 41.6700E0 174.57E0 + 42.3100E0 176.25E0 + 42.7300E0 177.34E0 + 43.4600E0 179.19E0 + 44.1400E0 181.02E0 + 44.5500E0 182.08E0 + 45.2200E0 183.88E0 + 45.9200E0 185.75E0 + 46.3000E0 186.80E0 + 47.0000E0 188.63E0 + 47.6800E0 190.45E0 + 48.0600E0 191.48E0 + 48.7400E0 193.35E0 + 49.4100E0 195.22E0 + 49.7600E0 196.23E0 + 50.4300E0 198.05E0 + 51.1100E0 199.97E0 + 51.5000E0 201.06E0 + 52.1200E0 202.83E0 + 52.7600E0 204.69E0 + 53.1800E0 205.86E0 + 53.7800E0 207.58E0 + 54.4600E0 209.50E0 + 54.8300E0 210.65E0 + 55.4000E0 212.33E0 + 56.4300E0 215.43E0 + 57.0300E0 217.16E0 + 58.0000E0 220.21E0 + 58.6100E0 221.98E0 + 59.5800E0 225.06E0 + 60.1100E0 226.79E0 + 61.1000E0 229.92E0 + 61.6500E0 231.69E0 + 62.5900E0 234.77E0 + 63.1200E0 236.60E0 + 64.0300E0 239.63E0 + 64.6200E0 241.50E0 + 65.4900E0 244.48E0 + 66.0300E0 246.40E0 + 66.8900E0 249.35E0 + 67.4200E0 251.32E0 + 68.2300E0 254.22E0 + 68.7700E0 256.24E0 + 69.5900E0 259.11E0 + 70.1100E0 261.18E0 + 70.8600E0 264.02E0 + 71.4300E0 266.13E0 + 72.1600E0 268.94E0 + 72.7000E0 271.09E0 + 73.4000E0 273.87E0 + 73.9300E0 276.08E0 + 74.6000E0 278.83E0 + 75.1600E0 281.08E0 + 75.8200E0 283.81E0 + 76.3400E0 286.11E0 + 76.9800E0 288.81E0 + 77.4800E0 291.08E0 + 78.0800E0 293.75E0 + 78.6000E0 295.99E0 + 79.1700E0 298.64E0 + 79.6200E0 300.84E0 + 79.8800E0 302.02E0 + 80.1900E0 303.48E0 + 80.6600E0 305.65E0 + 81.2200E0 308.27E0 + 81.6600E0 310.41E0 + 82.1600E0 313.01E0 + 82.5900E0 315.12E0 + 83.1400E0 317.71E0 + 83.5000E0 319.79E0 + 84.0000E0 322.36E0 + 84.4000E0 324.42E0 + 84.8900E0 326.98E0 + 85.2600E0 329.01E0 + 85.7400E0 331.56E0 + 86.0700E0 333.56E0 + 86.5400E0 336.10E0 + 86.8900E0 338.08E0 + 87.3200E0 340.60E0 + 87.6500E0 342.57E0 + 88.1000E0 345.08E0 + 88.4300E0 347.02E0 + 88.8300E0 349.52E0 + 89.1200E0 351.44E0 + 89.5400E0 353.93E0 + 89.8500E0 355.83E0 + 90.2500E0 358.32E0 + 90.5500E0 360.20E0 + 90.9300E0 362.67E0 + 91.2000E0 364.53E0 + 91.5500E0 367.00E0 + 92.2000E0 371.30E0 diff --git a/NIST_STRD/Lanczos1.dat b/NIST_STRD/Lanczos1.dat index 8107320..d23d5e4 100644 --- a/NIST_STRD/Lanczos1.dat +++ b/NIST_STRD/Lanczos1.dat @@ -1,84 +1,84 @@ -NIST/ITL StRD
-Dataset Name: Lanczos1 (Lanczos1.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 46)
- Certified Values (lines 41 to 51)
- Data (lines 61 to 84)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are taken from an example discussed in
- Lanczos (1956). The data were generated to 14-digits
- of accuracy using
- f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x)
- + 1.5576*exp(-5*x).
-
-
-Reference: Lanczos, C. (1956).
- Applied Analysis.
- Englewood Cliffs, NJ: Prentice Hall, pp. 272-280.
-
-
-
-
-Data: 1 Response (y)
- 1 Predictor (x)
- 24 Observations
- Average Level of Difficulty
- Generated Data
-
-Model: Exponential Class
- 6 Parameters (b1 to b6)
-
- y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 1.2 0.5 9.5100000027E-02 5.3347304234E-11
- b2 = 0.3 0.7 1.0000000001E+00 2.7473038179E-10
- b3 = 5.6 3.6 8.6070000013E-01 1.3576062225E-10
- b4 = 5.5 4.2 3.0000000002E+00 3.3308253069E-10
- b5 = 6.5 4 1.5575999998E+00 1.8815731448E-10
- b6 = 7.6 6.3 5.0000000001E+00 1.1057500538E-10
-
-Residual Sum of Squares: 1.4307867721E-25
-Residual Standard Deviation: 8.9156129349E-14
-Degrees of Freedom: 18
-Number of Observations: 24
-
-
-
-
-
-
-
-
-Data: y x
- 2.513400000000E+00 0.000000000000E+00
- 2.044333373291E+00 5.000000000000E-02
- 1.668404436564E+00 1.000000000000E-01
- 1.366418021208E+00 1.500000000000E-01
- 1.123232487372E+00 2.000000000000E-01
- 9.268897180037E-01 2.500000000000E-01
- 7.679338563728E-01 3.000000000000E-01
- 6.388775523106E-01 3.500000000000E-01
- 5.337835317402E-01 4.000000000000E-01
- 4.479363617347E-01 4.500000000000E-01
- 3.775847884350E-01 5.000000000000E-01
- 3.197393199326E-01 5.500000000000E-01
- 2.720130773746E-01 6.000000000000E-01
- 2.324965529032E-01 6.500000000000E-01
- 1.996589546065E-01 7.000000000000E-01
- 1.722704126914E-01 7.500000000000E-01
- 1.493405660168E-01 8.000000000000E-01
- 1.300700206922E-01 8.500000000000E-01
- 1.138119324644E-01 9.000000000000E-01
- 1.000415587559E-01 9.500000000000E-01
- 8.833209084540E-02 1.000000000000E+00
- 7.833544019350E-02 1.050000000000E+00
- 6.976693743449E-02 1.100000000000E+00
- 6.239312536719E-02 1.150000000000E+00
+NIST/ITL StRD +Dataset Name: Lanczos1 (Lanczos1.dat) + +File Format: ASCII + Starting Values (lines 41 to 46) + Certified Values (lines 41 to 51) + Data (lines 61 to 84) + +Procedure: Nonlinear Least Squares Regression + +Description: These data are taken from an example discussed in + Lanczos (1956). The data were generated to 14-digits + of accuracy using + f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x) + + 1.5576*exp(-5*x). + + +Reference: Lanczos, C. (1956). + Applied Analysis. + Englewood Cliffs, NJ: Prentice Hall, pp. 272-280. + + + + +Data: 1 Response (y) + 1 Predictor (x) + 24 Observations + Average Level of Difficulty + Generated Data + +Model: Exponential Class + 6 Parameters (b1 to b6) + + y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) + e + + + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 1.2 0.5 9.5100000027E-02 5.3347304234E-11 + b2 = 0.3 0.7 1.0000000001E+00 2.7473038179E-10 + b3 = 5.6 3.6 8.6070000013E-01 1.3576062225E-10 + b4 = 5.5 4.2 3.0000000002E+00 3.3308253069E-10 + b5 = 6.5 4 1.5575999998E+00 1.8815731448E-10 + b6 = 7.6 6.3 5.0000000001E+00 1.1057500538E-10 + +Residual Sum of Squares: 1.4307867721E-25 +Residual Standard Deviation: 8.9156129349E-14 +Degrees of Freedom: 18 +Number of Observations: 24 + + + + + + + + +Data: y x + 2.513400000000E+00 0.000000000000E+00 + 2.044333373291E+00 5.000000000000E-02 + 1.668404436564E+00 1.000000000000E-01 + 1.366418021208E+00 1.500000000000E-01 + 1.123232487372E+00 2.000000000000E-01 + 9.268897180037E-01 2.500000000000E-01 + 7.679338563728E-01 3.000000000000E-01 + 6.388775523106E-01 3.500000000000E-01 + 5.337835317402E-01 4.000000000000E-01 + 4.479363617347E-01 4.500000000000E-01 + 3.775847884350E-01 5.000000000000E-01 + 3.197393199326E-01 5.500000000000E-01 + 2.720130773746E-01 6.000000000000E-01 + 2.324965529032E-01 6.500000000000E-01 + 1.996589546065E-01 7.000000000000E-01 + 1.722704126914E-01 7.500000000000E-01 + 1.493405660168E-01 8.000000000000E-01 + 1.300700206922E-01 8.500000000000E-01 + 1.138119324644E-01 9.000000000000E-01 + 1.000415587559E-01 9.500000000000E-01 + 8.833209084540E-02 1.000000000000E+00 + 7.833544019350E-02 1.050000000000E+00 + 6.976693743449E-02 1.100000000000E+00 + 6.239312536719E-02 1.150000000000E+00 diff --git a/NIST_STRD/Lanczos2.dat b/NIST_STRD/Lanczos2.dat index fc98e69..f9f2b4b 100644 --- a/NIST_STRD/Lanczos2.dat +++ b/NIST_STRD/Lanczos2.dat @@ -1,84 +1,84 @@ -NIST/ITL StRD
-Dataset Name: Lanczos2 (Lanczos2.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 46)
- Certified Values (lines 41 to 51)
- Data (lines 61 to 84)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are taken from an example discussed in
- Lanczos (1956). The data were generated to 6-digits
- of accuracy using
- f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x)
- + 1.5576*exp(-5*x).
-
-
-Reference: Lanczos, C. (1956).
- Applied Analysis.
- Englewood Cliffs, NJ: Prentice Hall, pp. 272-280.
-
-
-
-
-Data: 1 Response (y)
- 1 Predictor (x)
- 24 Observations
- Average Level of Difficulty
- Generated Data
-
-Model: Exponential Class
- 6 Parameters (b1 to b6)
-
- y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 1.2 0.5 9.6251029939E-02 6.6770575477E-04
- b2 = 0.3 0.7 1.0057332849E+00 3.3989646176E-03
- b3 = 5.6 3.6 8.6424689056E-01 1.7185846685E-03
- b4 = 5.5 4.2 3.0078283915E+00 4.1707005856E-03
- b5 = 6.5 4 1.5529016879E+00 2.3744381417E-03
- b6 = 7.6 6.3 5.0028798100E+00 1.3958787284E-03
-
-Residual Sum of Squares: 2.2299428125E-11
-Residual Standard Deviation: 1.1130395851E-06
-Degrees of Freedom: 18
-Number of Observations: 24
-
-
-
-
-
-
-
-
-Data: y x
- 2.51340E+00 0.00000E+00
- 2.04433E+00 5.00000E-02
- 1.66840E+00 1.00000E-01
- 1.36642E+00 1.50000E-01
- 1.12323E+00 2.00000E-01
- 9.26890E-01 2.50000E-01
- 7.67934E-01 3.00000E-01
- 6.38878E-01 3.50000E-01
- 5.33784E-01 4.00000E-01
- 4.47936E-01 4.50000E-01
- 3.77585E-01 5.00000E-01
- 3.19739E-01 5.50000E-01
- 2.72013E-01 6.00000E-01
- 2.32497E-01 6.50000E-01
- 1.99659E-01 7.00000E-01
- 1.72270E-01 7.50000E-01
- 1.49341E-01 8.00000E-01
- 1.30070E-01 8.50000E-01
- 1.13812E-01 9.00000E-01
- 1.00042E-01 9.50000E-01
- 8.83321E-02 1.00000E+00
- 7.83354E-02 1.05000E+00
- 6.97669E-02 1.10000E+00
- 6.23931E-02 1.15000E+00
+NIST/ITL StRD +Dataset Name: Lanczos2 (Lanczos2.dat) + +File Format: ASCII + Starting Values (lines 41 to 46) + Certified Values (lines 41 to 51) + Data (lines 61 to 84) + +Procedure: Nonlinear Least Squares Regression + +Description: These data are taken from an example discussed in + Lanczos (1956). The data were generated to 6-digits + of accuracy using + f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x) + + 1.5576*exp(-5*x). + + +Reference: Lanczos, C. (1956). + Applied Analysis. + Englewood Cliffs, NJ: Prentice Hall, pp. 272-280. + + + + +Data: 1 Response (y) + 1 Predictor (x) + 24 Observations + Average Level of Difficulty + Generated Data + +Model: Exponential Class + 6 Parameters (b1 to b6) + + y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) + e + + + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 1.2 0.5 9.6251029939E-02 6.6770575477E-04 + b2 = 0.3 0.7 1.0057332849E+00 3.3989646176E-03 + b3 = 5.6 3.6 8.6424689056E-01 1.7185846685E-03 + b4 = 5.5 4.2 3.0078283915E+00 4.1707005856E-03 + b5 = 6.5 4 1.5529016879E+00 2.3744381417E-03 + b6 = 7.6 6.3 5.0028798100E+00 1.3958787284E-03 + +Residual Sum of Squares: 2.2299428125E-11 +Residual Standard Deviation: 1.1130395851E-06 +Degrees of Freedom: 18 +Number of Observations: 24 + + + + + + + + +Data: y x + 2.51340E+00 0.00000E+00 + 2.04433E+00 5.00000E-02 + 1.66840E+00 1.00000E-01 + 1.36642E+00 1.50000E-01 + 1.12323E+00 2.00000E-01 + 9.26890E-01 2.50000E-01 + 7.67934E-01 3.00000E-01 + 6.38878E-01 3.50000E-01 + 5.33784E-01 4.00000E-01 + 4.47936E-01 4.50000E-01 + 3.77585E-01 5.00000E-01 + 3.19739E-01 5.50000E-01 + 2.72013E-01 6.00000E-01 + 2.32497E-01 6.50000E-01 + 1.99659E-01 7.00000E-01 + 1.72270E-01 7.50000E-01 + 1.49341E-01 8.00000E-01 + 1.30070E-01 8.50000E-01 + 1.13812E-01 9.00000E-01 + 1.00042E-01 9.50000E-01 + 8.83321E-02 1.00000E+00 + 7.83354E-02 1.05000E+00 + 6.97669E-02 1.10000E+00 + 6.23931E-02 1.15000E+00 diff --git a/NIST_STRD/Lanczos3.dat b/NIST_STRD/Lanczos3.dat index d930d65..67c1512 100644 --- a/NIST_STRD/Lanczos3.dat +++ b/NIST_STRD/Lanczos3.dat @@ -1,84 +1,84 @@ -NIST/ITL StRD
-Dataset Name: Lanczos3 (Lanczos3.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 46)
- Certified Values (lines 41 to 51)
- Data (lines 61 to 84)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are taken from an example discussed in
- Lanczos (1956). The data were generated to 5-digits
- of accuracy using
- f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x)
- + 1.5576*exp(-5*x).
-
-
-Reference: Lanczos, C. (1956).
- Applied Analysis.
- Englewood Cliffs, NJ: Prentice Hall, pp. 272-280.
-
-
-
-
-Data: 1 Response (y)
- 1 Predictor (x)
- 24 Observations
- Lower Level of Difficulty
- Generated Data
-
-Model: Exponential Class
- 6 Parameters (b1 to b6)
-
- y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 1.2 0.5 8.6816414977E-02 1.7197908859E-02
- b2 = 0.3 0.7 9.5498101505E-01 9.7041624475E-02
- b3 = 5.6 3.6 8.4400777463E-01 4.1488663282E-02
- b4 = 5.5 4.2 2.9515951832E+00 1.0766312506E-01
- b5 = 6.5 4 1.5825685901E+00 5.8371576281E-02
- b6 = 7.6 6.3 4.9863565084E+00 3.4436403035E-02
-
-Residual Sum of Squares: 1.6117193594E-08
-Residual Standard Deviation: 2.9923229172E-05
-Degrees of Freedom: 18
-Number of Observations: 24
-
-
-
-
-
-
-
-
-Data: y x
- 2.5134E+00 0.00000E+00
- 2.0443E+00 5.00000E-02
- 1.6684E+00 1.00000E-01
- 1.3664E+00 1.50000E-01
- 1.1232E+00 2.00000E-01
- 0.9269E+00 2.50000E-01
- 0.7679E+00 3.00000E-01
- 0.6389E+00 3.50000E-01
- 0.5338E+00 4.00000E-01
- 0.4479E+00 4.50000E-01
- 0.3776E+00 5.00000E-01
- 0.3197E+00 5.50000E-01
- 0.2720E+00 6.00000E-01
- 0.2325E+00 6.50000E-01
- 0.1997E+00 7.00000E-01
- 0.1723E+00 7.50000E-01
- 0.1493E+00 8.00000E-01
- 0.1301E+00 8.50000E-01
- 0.1138E+00 9.00000E-01
- 0.1000E+00 9.50000E-01
- 0.0883E+00 1.00000E+00
- 0.0783E+00 1.05000E+00
- 0.0698E+00 1.10000E+00
- 0.0624E+00 1.15000E+00
+NIST/ITL StRD +Dataset Name: Lanczos3 (Lanczos3.dat) + +File Format: ASCII + Starting Values (lines 41 to 46) + Certified Values (lines 41 to 51) + Data (lines 61 to 84) + +Procedure: Nonlinear Least Squares Regression + +Description: These data are taken from an example discussed in + Lanczos (1956). The data were generated to 5-digits + of accuracy using + f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x) + + 1.5576*exp(-5*x). + + +Reference: Lanczos, C. (1956). + Applied Analysis. + Englewood Cliffs, NJ: Prentice Hall, pp. 272-280. + + + + +Data: 1 Response (y) + 1 Predictor (x) + 24 Observations + Lower Level of Difficulty + Generated Data + +Model: Exponential Class + 6 Parameters (b1 to b6) + + y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) + e + + + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 1.2 0.5 8.6816414977E-02 1.7197908859E-02 + b2 = 0.3 0.7 9.5498101505E-01 9.7041624475E-02 + b3 = 5.6 3.6 8.4400777463E-01 4.1488663282E-02 + b4 = 5.5 4.2 2.9515951832E+00 1.0766312506E-01 + b5 = 6.5 4 1.5825685901E+00 5.8371576281E-02 + b6 = 7.6 6.3 4.9863565084E+00 3.4436403035E-02 + +Residual Sum of Squares: 1.6117193594E-08 +Residual Standard Deviation: 2.9923229172E-05 +Degrees of Freedom: 18 +Number of Observations: 24 + + + + + + + + +Data: y x + 2.5134E+00 0.00000E+00 + 2.0443E+00 5.00000E-02 + 1.6684E+00 1.00000E-01 + 1.3664E+00 1.50000E-01 + 1.1232E+00 2.00000E-01 + 0.9269E+00 2.50000E-01 + 0.7679E+00 3.00000E-01 + 0.6389E+00 3.50000E-01 + 0.5338E+00 4.00000E-01 + 0.4479E+00 4.50000E-01 + 0.3776E+00 5.00000E-01 + 0.3197E+00 5.50000E-01 + 0.2720E+00 6.00000E-01 + 0.2325E+00 6.50000E-01 + 0.1997E+00 7.00000E-01 + 0.1723E+00 7.50000E-01 + 0.1493E+00 8.00000E-01 + 0.1301E+00 8.50000E-01 + 0.1138E+00 9.00000E-01 + 0.1000E+00 9.50000E-01 + 0.0883E+00 1.00000E+00 + 0.0783E+00 1.05000E+00 + 0.0698E+00 1.10000E+00 + 0.0624E+00 1.15000E+00 diff --git a/NIST_STRD/MGH09.dat b/NIST_STRD/MGH09.dat index 1f19af8..55a2d42 100644 --- a/NIST_STRD/MGH09.dat +++ b/NIST_STRD/MGH09.dat @@ -1,71 +1,71 @@ -NIST/ITL StRD
-Dataset Name: MGH09 (MGH09.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 44)
- Certified Values (lines 41 to 49)
- Data (lines 61 to 71)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: This problem was found to be difficult for some very
- good algorithms. There is a local minimum at (+inf,
- -14.07..., -inf, -inf) with final sum of squares
- 0.00102734....
-
- See More, J. J., Garbow, B. S., and Hillstrom, K. E.
- (1981). Testing unconstrained optimization software.
- ACM Transactions on Mathematical Software. 7(1):
- pp. 17-41.
-
-Reference: Kowalik, J.S., and M. R. Osborne, (1978).
- Methods for Unconstrained Optimization Problems.
- New York, NY: Elsevier North-Holland.
-
-Data: 1 Response (y)
- 1 Predictor (x)
- 11 Observations
- Higher Level of Difficulty
- Generated Data
-
-Model: Rational Class (linear/quadratic)
- 4 Parameters (b1 to b4)
-
- y = b1*(x**2+x*b2) / (x**2+x*b3+b4) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 25 0.25 1.9280693458E-01 1.1435312227E-02
- b2 = 39 0.39 1.9128232873E-01 1.9633220911E-01
- b3 = 41.5 0.415 1.2305650693E-01 8.0842031232E-02
- b4 = 39 0.39 1.3606233068E-01 9.0025542308E-02
-
-Residual Sum of Squares: 3.0750560385E-04
-Residual Standard Deviation: 6.6279236551E-03
-Degrees of Freedom: 7
-Number of Observations: 11
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 1.957000E-01 4.000000E+00
- 1.947000E-01 2.000000E+00
- 1.735000E-01 1.000000E+00
- 1.600000E-01 5.000000E-01
- 8.440000E-02 2.500000E-01
- 6.270000E-02 1.670000E-01
- 4.560000E-02 1.250000E-01
- 3.420000E-02 1.000000E-01
- 3.230000E-02 8.330000E-02
- 2.350000E-02 7.140000E-02
- 2.460000E-02 6.250000E-02
+NIST/ITL StRD +Dataset Name: MGH09 (MGH09.dat) + +File Format: ASCII + Starting Values (lines 41 to 44) + Certified Values (lines 41 to 49) + Data (lines 61 to 71) + +Procedure: Nonlinear Least Squares Regression + +Description: This problem was found to be difficult for some very + good algorithms. There is a local minimum at (+inf, + -14.07..., -inf, -inf) with final sum of squares + 0.00102734.... + + See More, J. J., Garbow, B. S., and Hillstrom, K. E. + (1981). Testing unconstrained optimization software. + ACM Transactions on Mathematical Software. 7(1): + pp. 17-41. + +Reference: Kowalik, J.S., and M. R. Osborne, (1978). + Methods for Unconstrained Optimization Problems. + New York, NY: Elsevier North-Holland. + +Data: 1 Response (y) + 1 Predictor (x) + 11 Observations + Higher Level of Difficulty + Generated Data + +Model: Rational Class (linear/quadratic) + 4 Parameters (b1 to b4) + + y = b1*(x**2+x*b2) / (x**2+x*b3+b4) + e + + + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 25 0.25 1.9280693458E-01 1.1435312227E-02 + b2 = 39 0.39 1.9128232873E-01 1.9633220911E-01 + b3 = 41.5 0.415 1.2305650693E-01 8.0842031232E-02 + b4 = 39 0.39 1.3606233068E-01 9.0025542308E-02 + +Residual Sum of Squares: 3.0750560385E-04 +Residual Standard Deviation: 6.6279236551E-03 +Degrees of Freedom: 7 +Number of Observations: 11 + + + + + + + + + + +Data: y x + 1.957000E-01 4.000000E+00 + 1.947000E-01 2.000000E+00 + 1.735000E-01 1.000000E+00 + 1.600000E-01 5.000000E-01 + 8.440000E-02 2.500000E-01 + 6.270000E-02 1.670000E-01 + 4.560000E-02 1.250000E-01 + 3.420000E-02 1.000000E-01 + 3.230000E-02 8.330000E-02 + 2.350000E-02 7.140000E-02 + 2.460000E-02 6.250000E-02 diff --git a/NIST_STRD/MGH10.dat b/NIST_STRD/MGH10.dat index df88ea4..b2ffbec 100644 --- a/NIST_STRD/MGH10.dat +++ b/NIST_STRD/MGH10.dat @@ -1,76 +1,76 @@ -NIST/ITL StRD
-Dataset Name: MGH10 (MGH10.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 43)
- Certified Values (lines 41 to 48)
- Data (lines 61 to 76)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: This problem was found to be difficult for some very
- good algorithms.
-
- See More, J. J., Garbow, B. S., and Hillstrom, K. E.
- (1981). Testing unconstrained optimization software.
- ACM Transactions on Mathematical Software. 7(1):
- pp. 17-41.
-
-Reference: Meyer, R. R. (1970).
- Theoretical and computational aspects of nonlinear
- regression. In Nonlinear Programming, Rosen,
- Mangasarian and Ritter (Eds).
- New York, NY: Academic Press, pp. 465-486.
-
-Data: 1 Response (y)
- 1 Predictor (x)
- 16 Observations
- Higher Level of Difficulty
- Generated Data
-
-Model: Exponential Class
- 3 Parameters (b1 to b3)
-
- y = b1 * exp[b2/(x+b3)] + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 2 0.02 5.6096364710E-03 1.5687892471E-04
- b2 = 400000 4000 6.1813463463E+03 2.3309021107E+01
- b3 = 25000 250 3.4522363462E+02 7.8486103508E-01
-
-Residual Sum of Squares: 8.7945855171E+01
-Residual Standard Deviation: 2.6009740065E+00
-Degrees of Freedom: 13
-Number of Observations: 16
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 3.478000E+04 5.000000E+01
- 2.861000E+04 5.500000E+01
- 2.365000E+04 6.000000E+01
- 1.963000E+04 6.500000E+01
- 1.637000E+04 7.000000E+01
- 1.372000E+04 7.500000E+01
- 1.154000E+04 8.000000E+01
- 9.744000E+03 8.500000E+01
- 8.261000E+03 9.000000E+01
- 7.030000E+03 9.500000E+01
- 6.005000E+03 1.000000E+02
- 5.147000E+03 1.050000E+02
- 4.427000E+03 1.100000E+02
- 3.820000E+03 1.150000E+02
- 3.307000E+03 1.200000E+02
- 2.872000E+03 1.250000E+02
+NIST/ITL StRD +Dataset Name: MGH10 (MGH10.dat) + +File Format: ASCII + Starting Values (lines 41 to 43) + Certified Values (lines 41 to 48) + Data (lines 61 to 76) + +Procedure: Nonlinear Least Squares Regression + +Description: This problem was found to be difficult for some very + good algorithms. + + See More, J. J., Garbow, B. S., and Hillstrom, K. E. + (1981). Testing unconstrained optimization software. + ACM Transactions on Mathematical Software. 7(1): + pp. 17-41. + +Reference: Meyer, R. R. (1970). + Theoretical and computational aspects of nonlinear + regression. In Nonlinear Programming, Rosen, + Mangasarian and Ritter (Eds). + New York, NY: Academic Press, pp. 465-486. + +Data: 1 Response (y) + 1 Predictor (x) + 16 Observations + Higher Level of Difficulty + Generated Data + +Model: Exponential Class + 3 Parameters (b1 to b3) + + y = b1 * exp[b2/(x+b3)] + e + + + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 2 0.02 5.6096364710E-03 1.5687892471E-04 + b2 = 400000 4000 6.1813463463E+03 2.3309021107E+01 + b3 = 25000 250 3.4522363462E+02 7.8486103508E-01 + +Residual Sum of Squares: 8.7945855171E+01 +Residual Standard Deviation: 2.6009740065E+00 +Degrees of Freedom: 13 +Number of Observations: 16 + + + + + + + + + + + +Data: y x + 3.478000E+04 5.000000E+01 + 2.861000E+04 5.500000E+01 + 2.365000E+04 6.000000E+01 + 1.963000E+04 6.500000E+01 + 1.637000E+04 7.000000E+01 + 1.372000E+04 7.500000E+01 + 1.154000E+04 8.000000E+01 + 9.744000E+03 8.500000E+01 + 8.261000E+03 9.000000E+01 + 7.030000E+03 9.500000E+01 + 6.005000E+03 1.000000E+02 + 5.147000E+03 1.050000E+02 + 4.427000E+03 1.100000E+02 + 3.820000E+03 1.150000E+02 + 3.307000E+03 1.200000E+02 + 2.872000E+03 1.250000E+02 diff --git a/NIST_STRD/MGH17.dat b/NIST_STRD/MGH17.dat index 3b3b7e8..584f73c 100644 --- a/NIST_STRD/MGH17.dat +++ b/NIST_STRD/MGH17.dat @@ -1,93 +1,93 @@ -NIST/ITL StRD
-Dataset Name: MGH17 (MGH17.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 45)
- Certified Values (lines 41 to 50)
- Data (lines 61 to 93)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: This problem was found to be difficult for some very
- good algorithms.
-
- See More, J. J., Garbow, B. S., and Hillstrom, K. E.
- (1981). Testing unconstrained optimization software.
- ACM Transactions on Mathematical Software. 7(1):
- pp. 17-41.
-
-Reference: Osborne, M. R. (1972).
- Some aspects of nonlinear least squares
- calculations. In Numerical Methods for Nonlinear
- Optimization, Lootsma (Ed).
- New York, NY: Academic Press, pp. 171-189.
-
-Data: 1 Response (y)
- 1 Predictor (x)
- 33 Observations
- Average Level of Difficulty
- Generated Data
-
-Model: Exponential Class
- 5 Parameters (b1 to b5)
-
- y = b1 + b2*exp[-x*b4] + b3*exp[-x*b5] + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 50 0.5 3.7541005211E-01 2.0723153551E-03
- b2 = 150 1.5 1.9358469127E+00 2.2031669222E-01
- b3 = -100 -1 -1.4646871366E+00 2.2175707739E-01
- b4 = 1 0.01 1.2867534640E-02 4.4861358114E-04
- b5 = 2 0.02 2.2122699662E-02 8.9471996575E-04
-
-Residual Sum of Squares: 5.4648946975E-05
-Residual Standard Deviation: 1.3970497866E-03
-Degrees of Freedom: 28
-Number of Observations: 33
-
-
-
-
-
-
-
-
-
-Data: y x
- 8.440000E-01 0.000000E+00
- 9.080000E-01 1.000000E+01
- 9.320000E-01 2.000000E+01
- 9.360000E-01 3.000000E+01
- 9.250000E-01 4.000000E+01
- 9.080000E-01 5.000000E+01
- 8.810000E-01 6.000000E+01
- 8.500000E-01 7.000000E+01
- 8.180000E-01 8.000000E+01
- 7.840000E-01 9.000000E+01
- 7.510000E-01 1.000000E+02
- 7.180000E-01 1.100000E+02
- 6.850000E-01 1.200000E+02
- 6.580000E-01 1.300000E+02
- 6.280000E-01 1.400000E+02
- 6.030000E-01 1.500000E+02
- 5.800000E-01 1.600000E+02
- 5.580000E-01 1.700000E+02
- 5.380000E-01 1.800000E+02
- 5.220000E-01 1.900000E+02
- 5.060000E-01 2.000000E+02
- 4.900000E-01 2.100000E+02
- 4.780000E-01 2.200000E+02
- 4.670000E-01 2.300000E+02
- 4.570000E-01 2.400000E+02
- 4.480000E-01 2.500000E+02
- 4.380000E-01 2.600000E+02
- 4.310000E-01 2.700000E+02
- 4.240000E-01 2.800000E+02
- 4.200000E-01 2.900000E+02
- 4.140000E-01 3.000000E+02
- 4.110000E-01 3.100000E+02
- 4.060000E-01 3.200000E+02
+NIST/ITL StRD +Dataset Name: MGH17 (MGH17.dat) + +File Format: ASCII + Starting Values (lines 41 to 45) + Certified Values (lines 41 to 50) + Data (lines 61 to 93) + +Procedure: Nonlinear Least Squares Regression + +Description: This problem was found to be difficult for some very + good algorithms. + + See More, J. J., Garbow, B. S., and Hillstrom, K. E. + (1981). Testing unconstrained optimization software. + ACM Transactions on Mathematical Software. 7(1): + pp. 17-41. + +Reference: Osborne, M. R. (1972). + Some aspects of nonlinear least squares + calculations. In Numerical Methods for Nonlinear + Optimization, Lootsma (Ed). + New York, NY: Academic Press, pp. 171-189. + +Data: 1 Response (y) + 1 Predictor (x) + 33 Observations + Average Level of Difficulty + Generated Data + +Model: Exponential Class + 5 Parameters (b1 to b5) + + y = b1 + b2*exp[-x*b4] + b3*exp[-x*b5] + e + + + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 50 0.5 3.7541005211E-01 2.0723153551E-03 + b2 = 150 1.5 1.9358469127E+00 2.2031669222E-01 + b3 = -100 -1 -1.4646871366E+00 2.2175707739E-01 + b4 = 1 0.01 1.2867534640E-02 4.4861358114E-04 + b5 = 2 0.02 2.2122699662E-02 8.9471996575E-04 + +Residual Sum of Squares: 5.4648946975E-05 +Residual Standard Deviation: 1.3970497866E-03 +Degrees of Freedom: 28 +Number of Observations: 33 + + + + + + + + + +Data: y x + 8.440000E-01 0.000000E+00 + 9.080000E-01 1.000000E+01 + 9.320000E-01 2.000000E+01 + 9.360000E-01 3.000000E+01 + 9.250000E-01 4.000000E+01 + 9.080000E-01 5.000000E+01 + 8.810000E-01 6.000000E+01 + 8.500000E-01 7.000000E+01 + 8.180000E-01 8.000000E+01 + 7.840000E-01 9.000000E+01 + 7.510000E-01 1.000000E+02 + 7.180000E-01 1.100000E+02 + 6.850000E-01 1.200000E+02 + 6.580000E-01 1.300000E+02 + 6.280000E-01 1.400000E+02 + 6.030000E-01 1.500000E+02 + 5.800000E-01 1.600000E+02 + 5.580000E-01 1.700000E+02 + 5.380000E-01 1.800000E+02 + 5.220000E-01 1.900000E+02 + 5.060000E-01 2.000000E+02 + 4.900000E-01 2.100000E+02 + 4.780000E-01 2.200000E+02 + 4.670000E-01 2.300000E+02 + 4.570000E-01 2.400000E+02 + 4.480000E-01 2.500000E+02 + 4.380000E-01 2.600000E+02 + 4.310000E-01 2.700000E+02 + 4.240000E-01 2.800000E+02 + 4.200000E-01 2.900000E+02 + 4.140000E-01 3.000000E+02 + 4.110000E-01 3.100000E+02 + 4.060000E-01 3.200000E+02 diff --git a/NIST_STRD/Misra1a.dat b/NIST_STRD/Misra1a.dat index 332f37e..24f92a8 100644 --- a/NIST_STRD/Misra1a.dat +++ b/NIST_STRD/Misra1a.dat @@ -1,74 +1,74 @@ -NIST/ITL StRD
-Dataset Name: Misra1a (Misra1a.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 42)
- Certified Values (lines 41 to 47)
- Data (lines 61 to 74)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study regarding
- dental research in monomolecular adsorption. The
- response variable is volume, and the predictor
- variable is pressure.
-
-Reference: Misra, D., NIST (1978).
- Dental Research Monomolecular Adsorption Study.
-
-
-
-
-
-
-
-Data: 1 Response Variable (y = volume)
- 1 Predictor Variable (x = pressure)
- 14 Observations
- Lower Level of Difficulty
- Observed Data
-
-Model: Exponential Class
- 2 Parameters (b1 and b2)
-
- y = b1*(1-exp[-b2*x]) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 500 250 2.3894212918E+02 2.7070075241E+00
- b2 = 0.0001 0.0005 5.5015643181E-04 7.2668688436E-06
-
-Residual Sum of Squares: 1.2455138894E-01
-Residual Standard Deviation: 1.0187876330E-01
-Degrees of Freedom: 12
-Number of Observations: 14
-
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 10.07E0 77.6E0
- 14.73E0 114.9E0
- 17.94E0 141.1E0
- 23.93E0 190.8E0
- 29.61E0 239.9E0
- 35.18E0 289.0E0
- 40.02E0 332.8E0
- 44.82E0 378.4E0
- 50.76E0 434.8E0
- 55.05E0 477.3E0
- 61.01E0 536.8E0
- 66.40E0 593.1E0
- 75.47E0 689.1E0
- 81.78E0 760.0E0
+NIST/ITL StRD +Dataset Name: Misra1a (Misra1a.dat) + +File Format: ASCII + Starting Values (lines 41 to 42) + Certified Values (lines 41 to 47) + Data (lines 61 to 74) + +Procedure: Nonlinear Least Squares Regression + +Description: These data are the result of a NIST study regarding + dental research in monomolecular adsorption. The + response variable is volume, and the predictor + variable is pressure. + +Reference: Misra, D., NIST (1978). + Dental Research Monomolecular Adsorption Study. + + + + + + + +Data: 1 Response Variable (y = volume) + 1 Predictor Variable (x = pressure) + 14 Observations + Lower Level of Difficulty + Observed Data + +Model: Exponential Class + 2 Parameters (b1 and b2) + + y = b1*(1-exp[-b2*x]) + e + + + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 500 250 2.3894212918E+02 2.7070075241E+00 + b2 = 0.0001 0.0005 5.5015643181E-04 7.2668688436E-06 + +Residual Sum of Squares: 1.2455138894E-01 +Residual Standard Deviation: 1.0187876330E-01 +Degrees of Freedom: 12 +Number of Observations: 14 + + + + + + + + + + + + +Data: y x + 10.07E0 77.6E0 + 14.73E0 114.9E0 + 17.94E0 141.1E0 + 23.93E0 190.8E0 + 29.61E0 239.9E0 + 35.18E0 289.0E0 + 40.02E0 332.8E0 + 44.82E0 378.4E0 + 50.76E0 434.8E0 + 55.05E0 477.3E0 + 61.01E0 536.8E0 + 66.40E0 593.1E0 + 75.47E0 689.1E0 + 81.78E0 760.0E0 diff --git a/NIST_STRD/Misra1b.dat b/NIST_STRD/Misra1b.dat index 7923d40..a0da9d3 100644 --- a/NIST_STRD/Misra1b.dat +++ b/NIST_STRD/Misra1b.dat @@ -1,74 +1,74 @@ -NIST/ITL StRD
-Dataset Name: Misra1b (Misra1b.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 42)
- Certified Values (lines 41 to 47)
- Data (lines 61 to 74)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study regarding
- dental research in monomolecular adsorption. The
- response variable is volume, and the predictor
- variable is pressure.
-
-Reference: Misra, D., NIST (1978).
- Dental Research Monomolecular Adsorption Study.
-
-
-
-
-
-
-
-Data: 1 Response (y = volume)
- 1 Predictor (x = pressure)
- 14 Observations
- Lower Level of Difficulty
- Observed Data
-
-Model: Miscellaneous Class
- 2 Parameters (b1 and b2)
-
- y = b1 * (1-(1+b2*x/2)**(-2)) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 500 300 3.3799746163E+02 3.1643950207E+00
- b2 = 0.0001 0.0002 3.9039091287E-04 4.2547321834E-06
-
-Residual Sum of Squares: 7.5464681533E-02
-Residual Standard Deviation: 7.9301471998E-02
-Degrees of Freedom: 12
-Number of Observations: 14
-
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 10.07E0 77.6E0
- 14.73E0 114.9E0
- 17.94E0 141.1E0
- 23.93E0 190.8E0
- 29.61E0 239.9E0
- 35.18E0 289.0E0
- 40.02E0 332.8E0
- 44.82E0 378.4E0
- 50.76E0 434.8E0
- 55.05E0 477.3E0
- 61.01E0 536.8E0
- 66.40E0 593.1E0
- 75.47E0 689.1E0
- 81.78E0 760.0E0
+NIST/ITL StRD +Dataset Name: Misra1b (Misra1b.dat) + +File Format: ASCII + Starting Values (lines 41 to 42) + Certified Values (lines 41 to 47) + Data (lines 61 to 74) + +Procedure: Nonlinear Least Squares Regression + +Description: These data are the result of a NIST study regarding + dental research in monomolecular adsorption. The + response variable is volume, and the predictor + variable is pressure. + +Reference: Misra, D., NIST (1978). + Dental Research Monomolecular Adsorption Study. + + + + + + + +Data: 1 Response (y = volume) + 1 Predictor (x = pressure) + 14 Observations + Lower Level of Difficulty + Observed Data + +Model: Miscellaneous Class + 2 Parameters (b1 and b2) + + y = b1 * (1-(1+b2*x/2)**(-2)) + e + + + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 500 300 3.3799746163E+02 3.1643950207E+00 + b2 = 0.0001 0.0002 3.9039091287E-04 4.2547321834E-06 + +Residual Sum of Squares: 7.5464681533E-02 +Residual Standard Deviation: 7.9301471998E-02 +Degrees of Freedom: 12 +Number of Observations: 14 + + + + + + + + + + + + +Data: y x + 10.07E0 77.6E0 + 14.73E0 114.9E0 + 17.94E0 141.1E0 + 23.93E0 190.8E0 + 29.61E0 239.9E0 + 35.18E0 289.0E0 + 40.02E0 332.8E0 + 44.82E0 378.4E0 + 50.76E0 434.8E0 + 55.05E0 477.3E0 + 61.01E0 536.8E0 + 66.40E0 593.1E0 + 75.47E0 689.1E0 + 81.78E0 760.0E0 diff --git a/NIST_STRD/Misra1c.dat b/NIST_STRD/Misra1c.dat index d86bc82..64681d3 100644 --- a/NIST_STRD/Misra1c.dat +++ b/NIST_STRD/Misra1c.dat @@ -1,74 +1,74 @@ -NIST/ITL StRD
-Dataset Name: Misra1c (Misra1c.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 42)
- Certified Values (lines 41 to 47)
- Data (lines 61 to 74)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study regarding
- dental research in monomolecular adsorption. The
- response variable is volume, and the predictor
- variable is pressure.
-
-Reference: Misra, D., NIST (1978).
- Dental Research Monomolecular Adsorption.
-
-
-
-
-
-
-
-Data: 1 Response (y = volume)
- 1 Predictor (x = pressure)
- 14 Observations
- Average Level of Difficulty
- Observed Data
-
-Model: Miscellaneous Class
- 2 Parameters (b1 and b2)
-
- y = b1 * (1-(1+2*b2*x)**(-.5)) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 500 600 6.3642725809E+02 4.6638326572E+00
- b2 = 0.0001 0.0002 2.0813627256E-04 1.7728423155E-06
-
-Residual Sum of Squares: 4.0966836971E-02
-Residual Standard Deviation: 5.8428615257E-02
-Degrees of Freedom: 12
-Number of Observations: 14
-
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 10.07E0 77.6E0
- 14.73E0 114.9E0
- 17.94E0 141.1E0
- 23.93E0 190.8E0
- 29.61E0 239.9E0
- 35.18E0 289.0E0
- 40.02E0 332.8E0
- 44.82E0 378.4E0
- 50.76E0 434.8E0
- 55.05E0 477.3E0
- 61.01E0 536.8E0
- 66.40E0 593.1E0
- 75.47E0 689.1E0
- 81.78E0 760.0E0
+NIST/ITL StRD +Dataset Name: Misra1c (Misra1c.dat) + +File Format: ASCII + Starting Values (lines 41 to 42) + Certified Values (lines 41 to 47) + Data (lines 61 to 74) + +Procedure: Nonlinear Least Squares Regression + +Description: These data are the result of a NIST study regarding + dental research in monomolecular adsorption. The + response variable is volume, and the predictor + variable is pressure. + +Reference: Misra, D., NIST (1978). + Dental Research Monomolecular Adsorption. + + + + + + + +Data: 1 Response (y = volume) + 1 Predictor (x = pressure) + 14 Observations + Average Level of Difficulty + Observed Data + +Model: Miscellaneous Class + 2 Parameters (b1 and b2) + + y = b1 * (1-(1+2*b2*x)**(-.5)) + e + + + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 500 600 6.3642725809E+02 4.6638326572E+00 + b2 = 0.0001 0.0002 2.0813627256E-04 1.7728423155E-06 + +Residual Sum of Squares: 4.0966836971E-02 +Residual Standard Deviation: 5.8428615257E-02 +Degrees of Freedom: 12 +Number of Observations: 14 + + + + + + + + + + + + +Data: y x + 10.07E0 77.6E0 + 14.73E0 114.9E0 + 17.94E0 141.1E0 + 23.93E0 190.8E0 + 29.61E0 239.9E0 + 35.18E0 289.0E0 + 40.02E0 332.8E0 + 44.82E0 378.4E0 + 50.76E0 434.8E0 + 55.05E0 477.3E0 + 61.01E0 536.8E0 + 66.40E0 593.1E0 + 75.47E0 689.1E0 + 81.78E0 760.0E0 diff --git a/NIST_STRD/Misra1d.dat b/NIST_STRD/Misra1d.dat index 237de46..fcf12d3 100644 --- a/NIST_STRD/Misra1d.dat +++ b/NIST_STRD/Misra1d.dat @@ -1,74 +1,74 @@ -NIST/ITL StRD
-Dataset Name: Misra1d (Misra1d.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 42)
- Certified Values (lines 41 to 47)
- Data (lines 61 to 74)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study regarding
- dental research in monomolecular adsorption. The
- response variable is volume, and the predictor
- variable is pressure.
-
-Reference: Misra, D., NIST (1978).
- Dental Research Monomolecular Adsorption Study.
-
-
-
-
-
-
-
-Data: 1 Response (y = volume)
- 1 Predictor (x = pressure)
- 14 Observations
- Average Level of Difficulty
- Observed Data
-
-Model: Miscellaneous Class
- 2 Parameters (b1 and b2)
-
- y = b1*b2*x*((1+b2*x)**(-1)) + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 500 450 4.3736970754E+02 3.6489174345E+00
- b2 = 0.0001 0.0003 3.0227324449E-04 2.9334354479E-06
-
-Residual Sum of Squares: 5.6419295283E-02
-Residual Standard Deviation: 6.8568272111E-02
-Degrees of Freedom: 12
-Number of Observations: 14
-
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 10.07E0 77.6E0
- 14.73E0 114.9E0
- 17.94E0 141.1E0
- 23.93E0 190.8E0
- 29.61E0 239.9E0
- 35.18E0 289.0E0
- 40.02E0 332.8E0
- 44.82E0 378.4E0
- 50.76E0 434.8E0
- 55.05E0 477.3E0
- 61.01E0 536.8E0
- 66.40E0 593.1E0
- 75.47E0 689.1E0
- 81.78E0 760.0E0
+NIST/ITL StRD +Dataset Name: Misra1d (Misra1d.dat) + +File Format: ASCII + Starting Values (lines 41 to 42) + Certified Values (lines 41 to 47) + Data (lines 61 to 74) + +Procedure: Nonlinear Least Squares Regression + +Description: These data are the result of a NIST study regarding + dental research in monomolecular adsorption. The + response variable is volume, and the predictor + variable is pressure. + +Reference: Misra, D., NIST (1978). + Dental Research Monomolecular Adsorption Study. + + + + + + + +Data: 1 Response (y = volume) + 1 Predictor (x = pressure) + 14 Observations + Average Level of Difficulty + Observed Data + +Model: Miscellaneous Class + 2 Parameters (b1 and b2) + + y = b1*b2*x*((1+b2*x)**(-1)) + e + + + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 500 450 4.3736970754E+02 3.6489174345E+00 + b2 = 0.0001 0.0003 3.0227324449E-04 2.9334354479E-06 + +Residual Sum of Squares: 5.6419295283E-02 +Residual Standard Deviation: 6.8568272111E-02 +Degrees of Freedom: 12 +Number of Observations: 14 + + + + + + + + + + + + +Data: y x + 10.07E0 77.6E0 + 14.73E0 114.9E0 + 17.94E0 141.1E0 + 23.93E0 190.8E0 + 29.61E0 239.9E0 + 35.18E0 289.0E0 + 40.02E0 332.8E0 + 44.82E0 378.4E0 + 50.76E0 434.8E0 + 55.05E0 477.3E0 + 61.01E0 536.8E0 + 66.40E0 593.1E0 + 75.47E0 689.1E0 + 81.78E0 760.0E0 diff --git a/NIST_STRD/Nelson.dat b/NIST_STRD/Nelson.dat index 5ce1003..a6dc9e2 100644 --- a/NIST_STRD/Nelson.dat +++ b/NIST_STRD/Nelson.dat @@ -1,188 +1,188 @@ -NIST/ITL StRD
-Dataset Name: Nelson (Nelson.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 43)
- Certified Values (lines 41 to 48)
- Data (lines 61 to 188)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a study involving
- the analysis of performance degradation data from
- accelerated tests, published in IEEE Transactions
- on Reliability. The response variable is dialectric
- breakdown strength in kilo-volts, and the predictor
- variables are time in weeks and temperature in degrees
- Celcius.
-
-
-Reference: Nelson, W. (1981).
- Analysis of Performance-Degradation Data.
- IEEE Transactions on Reliability.
- Vol. 2, R-30, No. 2, pp. 149-155.
-
-Data: 1 Response ( y = dialectric breakdown strength)
- 2 Predictors (x1 = time; x2 = temperature)
- 128 Observations
- Average Level of Difficulty
- Observed Data
-
-Model: Exponential Class
- 3 Parameters (b1 to b3)
-
- log[y] = b1 - b2*x1 * exp[-b3*x2] + e
-
-
-
- Starting values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 2 2.5 2.5906836021E+00 1.9149996413E-02
- b2 = 0.0001 0.000000005 5.6177717026E-09 6.1124096540E-09
- b3 = -0.01 -0.05 -5.7701013174E-02 3.9572366543E-03
-
-Residual Sum of Squares: 3.7976833176E+00
-Residual Standard Deviation: 1.7430280130E-01
-Degrees of Freedom: 125
-Number of Observations: 128
-
-
-
-
-
-
-
-
-
-
-
-Data: y x1 x2
- 15.00E0 1E0 180E0
- 17.00E0 1E0 180E0
- 15.50E0 1E0 180E0
- 16.50E0 1E0 180E0
- 15.50E0 1E0 225E0
- 15.00E0 1E0 225E0
- 16.00E0 1E0 225E0
- 14.50E0 1E0 225E0
- 15.00E0 1E0 250E0
- 14.50E0 1E0 250E0
- 12.50E0 1E0 250E0
- 11.00E0 1E0 250E0
- 14.00E0 1E0 275E0
- 13.00E0 1E0 275E0
- 14.00E0 1E0 275E0
- 11.50E0 1E0 275E0
- 14.00E0 2E0 180E0
- 16.00E0 2E0 180E0
- 13.00E0 2E0 180E0
- 13.50E0 2E0 180E0
- 13.00E0 2E0 225E0
- 13.50E0 2E0 225E0
- 12.50E0 2E0 225E0
- 12.50E0 2E0 225E0
- 12.50E0 2E0 250E0
- 12.00E0 2E0 250E0
- 11.50E0 2E0 250E0
- 12.00E0 2E0 250E0
- 13.00E0 2E0 275E0
- 11.50E0 2E0 275E0
- 13.00E0 2E0 275E0
- 12.50E0 2E0 275E0
- 13.50E0 4E0 180E0
- 17.50E0 4E0 180E0
- 17.50E0 4E0 180E0
- 13.50E0 4E0 180E0
- 12.50E0 4E0 225E0
- 12.50E0 4E0 225E0
- 15.00E0 4E0 225E0
- 13.00E0 4E0 225E0
- 12.00E0 4E0 250E0
- 13.00E0 4E0 250E0
- 12.00E0 4E0 250E0
- 13.50E0 4E0 250E0
- 10.00E0 4E0 275E0
- 11.50E0 4E0 275E0
- 11.00E0 4E0 275E0
- 9.50E0 4E0 275E0
- 15.00E0 8E0 180E0
- 15.00E0 8E0 180E0
- 15.50E0 8E0 180E0
- 16.00E0 8E0 180E0
- 13.00E0 8E0 225E0
- 10.50E0 8E0 225E0
- 13.50E0 8E0 225E0
- 14.00E0 8E0 225E0
- 12.50E0 8E0 250E0
- 12.00E0 8E0 250E0
- 11.50E0 8E0 250E0
- 11.50E0 8E0 250E0
- 6.50E0 8E0 275E0
- 5.50E0 8E0 275E0
- 6.00E0 8E0 275E0
- 6.00E0 8E0 275E0
- 18.50E0 16E0 180E0
- 17.00E0 16E0 180E0
- 15.30E0 16E0 180E0
- 16.00E0 16E0 180E0
- 13.00E0 16E0 225E0
- 14.00E0 16E0 225E0
- 12.50E0 16E0 225E0
- 11.00E0 16E0 225E0
- 12.00E0 16E0 250E0
- 12.00E0 16E0 250E0
- 11.50E0 16E0 250E0
- 12.00E0 16E0 250E0
- 6.00E0 16E0 275E0
- 6.00E0 16E0 275E0
- 5.00E0 16E0 275E0
- 5.50E0 16E0 275E0
- 12.50E0 32E0 180E0
- 13.00E0 32E0 180E0
- 16.00E0 32E0 180E0
- 12.00E0 32E0 180E0
- 11.00E0 32E0 225E0
- 9.50E0 32E0 225E0
- 11.00E0 32E0 225E0
- 11.00E0 32E0 225E0
- 11.00E0 32E0 250E0
- 10.00E0 32E0 250E0
- 10.50E0 32E0 250E0
- 10.50E0 32E0 250E0
- 2.70E0 32E0 275E0
- 2.70E0 32E0 275E0
- 2.50E0 32E0 275E0
- 2.40E0 32E0 275E0
- 13.00E0 48E0 180E0
- 13.50E0 48E0 180E0
- 16.50E0 48E0 180E0
- 13.60E0 48E0 180E0
- 11.50E0 48E0 225E0
- 10.50E0 48E0 225E0
- 13.50E0 48E0 225E0
- 12.00E0 48E0 225E0
- 7.00E0 48E0 250E0
- 6.90E0 48E0 250E0
- 8.80E0 48E0 250E0
- 7.90E0 48E0 250E0
- 1.20E0 48E0 275E0
- 1.50E0 48E0 275E0
- 1.00E0 48E0 275E0
- 1.50E0 48E0 275E0
- 13.00E0 64E0 180E0
- 12.50E0 64E0 180E0
- 16.50E0 64E0 180E0
- 16.00E0 64E0 180E0
- 11.00E0 64E0 225E0
- 11.50E0 64E0 225E0
- 10.50E0 64E0 225E0
- 10.00E0 64E0 225E0
- 7.27E0 64E0 250E0
- 7.50E0 64E0 250E0
- 6.70E0 64E0 250E0
- 7.60E0 64E0 250E0
- 1.50E0 64E0 275E0
- 1.00E0 64E0 275E0
- 1.20E0 64E0 275E0
- 1.20E0 64E0 275E0
+NIST/ITL StRD +Dataset Name: Nelson (Nelson.dat) + +File Format: ASCII + Starting Values (lines 41 to 43) + Certified Values (lines 41 to 48) + Data (lines 61 to 188) + +Procedure: Nonlinear Least Squares Regression + +Description: These data are the result of a study involving + the analysis of performance degradation data from + accelerated tests, published in IEEE Transactions + on Reliability. The response variable is dialectric + breakdown strength in kilo-volts, and the predictor + variables are time in weeks and temperature in degrees + Celcius. + + +Reference: Nelson, W. (1981). + Analysis of Performance-Degradation Data. + IEEE Transactions on Reliability. + Vol. 2, R-30, No. 2, pp. 149-155. + +Data: 1 Response ( y = dialectric breakdown strength) + 2 Predictors (x1 = time; x2 = temperature) + 128 Observations + Average Level of Difficulty + Observed Data + +Model: Exponential Class + 3 Parameters (b1 to b3) + + log[y] = b1 - b2*x1 * exp[-b3*x2] + e + + + + Starting values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 2 2.5 2.5906836021E+00 1.9149996413E-02 + b2 = 0.0001 0.000000005 5.6177717026E-09 6.1124096540E-09 + b3 = -0.01 -0.05 -5.7701013174E-02 3.9572366543E-03 + +Residual Sum of Squares: 3.7976833176E+00 +Residual Standard Deviation: 1.7430280130E-01 +Degrees of Freedom: 125 +Number of Observations: 128 + + + + + + + + + + + +Data: y x1 x2 + 15.00E0 1E0 180E0 + 17.00E0 1E0 180E0 + 15.50E0 1E0 180E0 + 16.50E0 1E0 180E0 + 15.50E0 1E0 225E0 + 15.00E0 1E0 225E0 + 16.00E0 1E0 225E0 + 14.50E0 1E0 225E0 + 15.00E0 1E0 250E0 + 14.50E0 1E0 250E0 + 12.50E0 1E0 250E0 + 11.00E0 1E0 250E0 + 14.00E0 1E0 275E0 + 13.00E0 1E0 275E0 + 14.00E0 1E0 275E0 + 11.50E0 1E0 275E0 + 14.00E0 2E0 180E0 + 16.00E0 2E0 180E0 + 13.00E0 2E0 180E0 + 13.50E0 2E0 180E0 + 13.00E0 2E0 225E0 + 13.50E0 2E0 225E0 + 12.50E0 2E0 225E0 + 12.50E0 2E0 225E0 + 12.50E0 2E0 250E0 + 12.00E0 2E0 250E0 + 11.50E0 2E0 250E0 + 12.00E0 2E0 250E0 + 13.00E0 2E0 275E0 + 11.50E0 2E0 275E0 + 13.00E0 2E0 275E0 + 12.50E0 2E0 275E0 + 13.50E0 4E0 180E0 + 17.50E0 4E0 180E0 + 17.50E0 4E0 180E0 + 13.50E0 4E0 180E0 + 12.50E0 4E0 225E0 + 12.50E0 4E0 225E0 + 15.00E0 4E0 225E0 + 13.00E0 4E0 225E0 + 12.00E0 4E0 250E0 + 13.00E0 4E0 250E0 + 12.00E0 4E0 250E0 + 13.50E0 4E0 250E0 + 10.00E0 4E0 275E0 + 11.50E0 4E0 275E0 + 11.00E0 4E0 275E0 + 9.50E0 4E0 275E0 + 15.00E0 8E0 180E0 + 15.00E0 8E0 180E0 + 15.50E0 8E0 180E0 + 16.00E0 8E0 180E0 + 13.00E0 8E0 225E0 + 10.50E0 8E0 225E0 + 13.50E0 8E0 225E0 + 14.00E0 8E0 225E0 + 12.50E0 8E0 250E0 + 12.00E0 8E0 250E0 + 11.50E0 8E0 250E0 + 11.50E0 8E0 250E0 + 6.50E0 8E0 275E0 + 5.50E0 8E0 275E0 + 6.00E0 8E0 275E0 + 6.00E0 8E0 275E0 + 18.50E0 16E0 180E0 + 17.00E0 16E0 180E0 + 15.30E0 16E0 180E0 + 16.00E0 16E0 180E0 + 13.00E0 16E0 225E0 + 14.00E0 16E0 225E0 + 12.50E0 16E0 225E0 + 11.00E0 16E0 225E0 + 12.00E0 16E0 250E0 + 12.00E0 16E0 250E0 + 11.50E0 16E0 250E0 + 12.00E0 16E0 250E0 + 6.00E0 16E0 275E0 + 6.00E0 16E0 275E0 + 5.00E0 16E0 275E0 + 5.50E0 16E0 275E0 + 12.50E0 32E0 180E0 + 13.00E0 32E0 180E0 + 16.00E0 32E0 180E0 + 12.00E0 32E0 180E0 + 11.00E0 32E0 225E0 + 9.50E0 32E0 225E0 + 11.00E0 32E0 225E0 + 11.00E0 32E0 225E0 + 11.00E0 32E0 250E0 + 10.00E0 32E0 250E0 + 10.50E0 32E0 250E0 + 10.50E0 32E0 250E0 + 2.70E0 32E0 275E0 + 2.70E0 32E0 275E0 + 2.50E0 32E0 275E0 + 2.40E0 32E0 275E0 + 13.00E0 48E0 180E0 + 13.50E0 48E0 180E0 + 16.50E0 48E0 180E0 + 13.60E0 48E0 180E0 + 11.50E0 48E0 225E0 + 10.50E0 48E0 225E0 + 13.50E0 48E0 225E0 + 12.00E0 48E0 225E0 + 7.00E0 48E0 250E0 + 6.90E0 48E0 250E0 + 8.80E0 48E0 250E0 + 7.90E0 48E0 250E0 + 1.20E0 48E0 275E0 + 1.50E0 48E0 275E0 + 1.00E0 48E0 275E0 + 1.50E0 48E0 275E0 + 13.00E0 64E0 180E0 + 12.50E0 64E0 180E0 + 16.50E0 64E0 180E0 + 16.00E0 64E0 180E0 + 11.00E0 64E0 225E0 + 11.50E0 64E0 225E0 + 10.50E0 64E0 225E0 + 10.00E0 64E0 225E0 + 7.27E0 64E0 250E0 + 7.50E0 64E0 250E0 + 6.70E0 64E0 250E0 + 7.60E0 64E0 250E0 + 1.50E0 64E0 275E0 + 1.00E0 64E0 275E0 + 1.20E0 64E0 275E0 + 1.20E0 64E0 275E0 diff --git a/NIST_STRD/Rat42.dat b/NIST_STRD/Rat42.dat index e112fbb..5468df8 100644 --- a/NIST_STRD/Rat42.dat +++ b/NIST_STRD/Rat42.dat @@ -1,69 +1,69 @@ -NIST/ITL StRD
-Dataset Name: Rat42 (Rat42.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 43)
- Certified Values (lines 41 to 48)
- Data (lines 61 to 69)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: This model and data are an example of fitting
- sigmoidal growth curves taken from Ratkowsky (1983).
- The response variable is pasture yield, and the
- predictor variable is growing time.
-
-
-Reference: Ratkowsky, D.A. (1983).
- Nonlinear Regression Modeling.
- New York, NY: Marcel Dekker, pp. 61 and 88.
-
-
-
-
-
-Data: 1 Response (y = pasture yield)
- 1 Predictor (x = growing time)
- 9 Observations
- Higher Level of Difficulty
- Observed Data
-
-Model: Exponential Class
- 3 Parameters (b1 to b3)
-
- y = b1 / (1+exp[b2-b3*x]) + e
-
-
-
- Starting Values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 100 75 7.2462237576E+01 1.7340283401E+00
- b2 = 1 2.5 2.6180768402E+00 8.8295217536E-02
- b3 = 0.1 0.07 6.7359200066E-02 3.4465663377E-03
-
-Residual Sum of Squares: 8.0565229338E+00
-Residual Standard Deviation: 1.1587725499E+00
-Degrees of Freedom: 6
-Number of Observations: 9
-
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 8.930E0 9.000E0
- 10.800E0 14.000E0
- 18.590E0 21.000E0
- 22.330E0 28.000E0
- 39.350E0 42.000E0
- 56.110E0 57.000E0
- 61.730E0 63.000E0
- 64.620E0 70.000E0
- 67.080E0 79.000E0
+NIST/ITL StRD +Dataset Name: Rat42 (Rat42.dat) + +File Format: ASCII + Starting Values (lines 41 to 43) + Certified Values (lines 41 to 48) + Data (lines 61 to 69) + +Procedure: Nonlinear Least Squares Regression + +Description: This model and data are an example of fitting + sigmoidal growth curves taken from Ratkowsky (1983). + The response variable is pasture yield, and the + predictor variable is growing time. + + +Reference: Ratkowsky, D.A. (1983). + Nonlinear Regression Modeling. + New York, NY: Marcel Dekker, pp. 61 and 88. + + + + + +Data: 1 Response (y = pasture yield) + 1 Predictor (x = growing time) + 9 Observations + Higher Level of Difficulty + Observed Data + +Model: Exponential Class + 3 Parameters (b1 to b3) + + y = b1 / (1+exp[b2-b3*x]) + e + + + + Starting Values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 100 75 7.2462237576E+01 1.7340283401E+00 + b2 = 1 2.5 2.6180768402E+00 8.8295217536E-02 + b3 = 0.1 0.07 6.7359200066E-02 3.4465663377E-03 + +Residual Sum of Squares: 8.0565229338E+00 +Residual Standard Deviation: 1.1587725499E+00 +Degrees of Freedom: 6 +Number of Observations: 9 + + + + + + + + + + + +Data: y x + 8.930E0 9.000E0 + 10.800E0 14.000E0 + 18.590E0 21.000E0 + 22.330E0 28.000E0 + 39.350E0 42.000E0 + 56.110E0 57.000E0 + 61.730E0 63.000E0 + 64.620E0 70.000E0 + 67.080E0 79.000E0 diff --git a/NIST_STRD/Rat43.dat b/NIST_STRD/Rat43.dat index 347d846..ca6d1dc 100644 --- a/NIST_STRD/Rat43.dat +++ b/NIST_STRD/Rat43.dat @@ -1,75 +1,75 @@ -NIST/ITL StRD
-Dataset Name: Rat43 (Rat43.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 44)
- Certified Values (lines 41 to 49)
- Data (lines 61 to 75)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: This model and data are an example of fitting
- sigmoidal growth curves taken from Ratkowsky (1983).
- The response variable is the dry weight of onion bulbs
- and tops, and the predictor variable is growing time.
-
-
-Reference: Ratkowsky, D.A. (1983).
- Nonlinear Regression Modeling.
- New York, NY: Marcel Dekker, pp. 62 and 88.
-
-
-
-
-
-Data: 1 Response (y = onion bulb dry weight)
- 1 Predictor (x = growing time)
- 15 Observations
- Higher Level of Difficulty
- Observed Data
-
-Model: Exponential Class
- 4 Parameters (b1 to b4)
-
- y = b1 / ((1+exp[b2-b3*x])**(1/b4)) + e
-
-
-
- Starting Values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 100 700 6.9964151270E+02 1.6302297817E+01
- b2 = 10 5 5.2771253025E+00 2.0828735829E+00
- b3 = 1 0.75 7.5962938329E-01 1.9566123451E-01
- b4 = 1 1.3 1.2792483859E+00 6.8761936385E-01
-
-Residual Sum of Squares: 8.7864049080E+03
-Residual Standard Deviation: 2.8262414662E+01
-Degrees of Freedom: 9
-Number of Observations: 15
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 16.08E0 1.0E0
- 33.83E0 2.0E0
- 65.80E0 3.0E0
- 97.20E0 4.0E0
- 191.55E0 5.0E0
- 326.20E0 6.0E0
- 386.87E0 7.0E0
- 520.53E0 8.0E0
- 590.03E0 9.0E0
- 651.92E0 10.0E0
- 724.93E0 11.0E0
- 699.56E0 12.0E0
- 689.96E0 13.0E0
- 637.56E0 14.0E0
- 717.41E0 15.0E0
+NIST/ITL StRD +Dataset Name: Rat43 (Rat43.dat) + +File Format: ASCII + Starting Values (lines 41 to 44) + Certified Values (lines 41 to 49) + Data (lines 61 to 75) + +Procedure: Nonlinear Least Squares Regression + +Description: This model and data are an example of fitting + sigmoidal growth curves taken from Ratkowsky (1983). + The response variable is the dry weight of onion bulbs + and tops, and the predictor variable is growing time. + + +Reference: Ratkowsky, D.A. (1983). + Nonlinear Regression Modeling. + New York, NY: Marcel Dekker, pp. 62 and 88. + + + + + +Data: 1 Response (y = onion bulb dry weight) + 1 Predictor (x = growing time) + 15 Observations + Higher Level of Difficulty + Observed Data + +Model: Exponential Class + 4 Parameters (b1 to b4) + + y = b1 / ((1+exp[b2-b3*x])**(1/b4)) + e + + + + Starting Values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 100 700 6.9964151270E+02 1.6302297817E+01 + b2 = 10 5 5.2771253025E+00 2.0828735829E+00 + b3 = 1 0.75 7.5962938329E-01 1.9566123451E-01 + b4 = 1 1.3 1.2792483859E+00 6.8761936385E-01 + +Residual Sum of Squares: 8.7864049080E+03 +Residual Standard Deviation: 2.8262414662E+01 +Degrees of Freedom: 9 +Number of Observations: 15 + + + + + + + + + + +Data: y x + 16.08E0 1.0E0 + 33.83E0 2.0E0 + 65.80E0 3.0E0 + 97.20E0 4.0E0 + 191.55E0 5.0E0 + 326.20E0 6.0E0 + 386.87E0 7.0E0 + 520.53E0 8.0E0 + 590.03E0 9.0E0 + 651.92E0 10.0E0 + 724.93E0 11.0E0 + 699.56E0 12.0E0 + 689.96E0 13.0E0 + 637.56E0 14.0E0 + 717.41E0 15.0E0 diff --git a/NIST_STRD/Roszman1.dat b/NIST_STRD/Roszman1.dat index 0296837..ddab210 100644 --- a/NIST_STRD/Roszman1.dat +++ b/NIST_STRD/Roszman1.dat @@ -1,85 +1,85 @@ -NIST/ITL StRD
-Dataset Name: Roszman1 (Roszman1.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 44)
- Certified Values (lines 41 to 49)
- Data (lines 61 to 85)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study involving
- quantum defects in iodine atoms. The response
- variable is the number of quantum defects, and the
- predictor variable is the excited energy state.
- The argument to the ARCTAN function is in radians.
-
-Reference: Roszman, L., NIST (19??).
- Quantum Defects for Sulfur I Atom.
-
-
-
-
-
-
-Data: 1 Response (y = quantum defect)
- 1 Predictor (x = excited state energy)
- 25 Observations
- Average Level of Difficulty
- Observed Data
-
-Model: Miscellaneous Class
- 4 Parameters (b1 to b4)
-
- pi = 3.141592653589793238462643383279E0
- y = b1 - b2*x - arctan[b3/(x-b4)]/pi + e
-
-
- Starting Values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 0.1 0.2 2.0196866396E-01 1.9172666023E-02
- b2 = -0.00001 -0.000005 -6.1953516256E-06 3.2058931691E-06
- b3 = 1000 1200 1.2044556708E+03 7.4050983057E+01
- b4 = -100 -150 -1.8134269537E+02 4.9573513849E+01
-
-Residual Sum of Squares: 4.9484847331E-04
-Residual Standard Deviation: 4.8542984060E-03
-Degrees of Freedom: 21
-Number of Observations: 25
-
-
-
-
-
-
-
-
-
-
-Data: y x
- 0.252429 -4868.68
- 0.252141 -4868.09
- 0.251809 -4867.41
- 0.297989 -3375.19
- 0.296257 -3373.14
- 0.295319 -3372.03
- 0.339603 -2473.74
- 0.337731 -2472.35
- 0.333820 -2469.45
- 0.389510 -1894.65
- 0.386998 -1893.40
- 0.438864 -1497.24
- 0.434887 -1495.85
- 0.427893 -1493.41
- 0.471568 -1208.68
- 0.461699 -1206.18
- 0.461144 -1206.04
- 0.513532 -997.92
- 0.506641 -996.61
- 0.505062 -996.31
- 0.535648 -834.94
- 0.533726 -834.66
- 0.568064 -710.03
- 0.612886 -530.16
- 0.624169 -464.17
+NIST/ITL StRD +Dataset Name: Roszman1 (Roszman1.dat) + +File Format: ASCII + Starting Values (lines 41 to 44) + Certified Values (lines 41 to 49) + Data (lines 61 to 85) + +Procedure: Nonlinear Least Squares Regression + +Description: These data are the result of a NIST study involving + quantum defects in iodine atoms. The response + variable is the number of quantum defects, and the + predictor variable is the excited energy state. + The argument to the ARCTAN function is in radians. + +Reference: Roszman, L., NIST (19??). + Quantum Defects for Sulfur I Atom. + + + + + + +Data: 1 Response (y = quantum defect) + 1 Predictor (x = excited state energy) + 25 Observations + Average Level of Difficulty + Observed Data + +Model: Miscellaneous Class + 4 Parameters (b1 to b4) + + pi = 3.141592653589793238462643383279E0 + y = b1 - b2*x - arctan[b3/(x-b4)]/pi + e + + + Starting Values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 0.1 0.2 2.0196866396E-01 1.9172666023E-02 + b2 = -0.00001 -0.000005 -6.1953516256E-06 3.2058931691E-06 + b3 = 1000 1200 1.2044556708E+03 7.4050983057E+01 + b4 = -100 -150 -1.8134269537E+02 4.9573513849E+01 + +Residual Sum of Squares: 4.9484847331E-04 +Residual Standard Deviation: 4.8542984060E-03 +Degrees of Freedom: 21 +Number of Observations: 25 + + + + + + + + + + +Data: y x + 0.252429 -4868.68 + 0.252141 -4868.09 + 0.251809 -4867.41 + 0.297989 -3375.19 + 0.296257 -3373.14 + 0.295319 -3372.03 + 0.339603 -2473.74 + 0.337731 -2472.35 + 0.333820 -2469.45 + 0.389510 -1894.65 + 0.386998 -1893.40 + 0.438864 -1497.24 + 0.434887 -1495.85 + 0.427893 -1493.41 + 0.471568 -1208.68 + 0.461699 -1206.18 + 0.461144 -1206.04 + 0.513532 -997.92 + 0.506641 -996.61 + 0.505062 -996.31 + 0.535648 -834.94 + 0.533726 -834.66 + 0.568064 -710.03 + 0.612886 -530.16 + 0.624169 -464.17 diff --git a/NIST_STRD/Thurber.dat b/NIST_STRD/Thurber.dat index 6d72fd9..6ecdc77 100644 --- a/NIST_STRD/Thurber.dat +++ b/NIST_STRD/Thurber.dat @@ -1,97 +1,97 @@ -NIST/ITL StRD
-Dataset Name: Thurber (Thurber.dat)
-
-File Format: ASCII
- Starting Values (lines 41 to 47)
- Certified Values (lines 41 to 52)
- Data (lines 61 to 97)
-
-Procedure: Nonlinear Least Squares Regression
-
-Description: These data are the result of a NIST study involving
- semiconductor electron mobility. The response
- variable is a measure of electron mobility, and the
- predictor variable is the natural log of the density.
-
-
-Reference: Thurber, R., NIST (197?).
- Semiconductor electron mobility modeling.
-
-
-
-
-
-
-Data: 1 Response Variable (y = electron mobility)
- 1 Predictor Variable (x = log[density])
- 37 Observations
- Higher Level of Difficulty
- Observed Data
-
-Model: Rational Class (cubic/cubic)
- 7 Parameters (b1 to b7)
-
- y = (b1 + b2*x + b3*x**2 + b4*x**3) /
- (1 + b5*x + b6*x**2 + b7*x**3) + e
-
-
- Starting Values Certified Values
-
- Start 1 Start 2 Parameter Standard Deviation
- b1 = 1000 1300 1.2881396800E+03 4.6647963344E+00
- b2 = 1000 1500 1.4910792535E+03 3.9571156086E+01
- b3 = 400 500 5.8323836877E+02 2.8698696102E+01
- b4 = 40 75 7.5416644291E+01 5.5675370270E+00
- b5 = 0.7 1 9.6629502864E-01 3.1333340687E-02
- b6 = 0.3 0.4 3.9797285797E-01 1.4984928198E-02
- b7 = 0.03 0.05 4.9727297349E-02 6.5842344623E-03
-
-Residual Sum of Squares: 5.6427082397E+03
-Residual Standard Deviation: 1.3714600784E+01
-Degrees of Freedom: 30
-Number of Observations: 37
-
-
-
-
-
-
-
-Data: y x
- 80.574E0 -3.067E0
- 84.248E0 -2.981E0
- 87.264E0 -2.921E0
- 87.195E0 -2.912E0
- 89.076E0 -2.840E0
- 89.608E0 -2.797E0
- 89.868E0 -2.702E0
- 90.101E0 -2.699E0
- 92.405E0 -2.633E0
- 95.854E0 -2.481E0
- 100.696E0 -2.363E0
- 101.060E0 -2.322E0
- 401.672E0 -1.501E0
- 390.724E0 -1.460E0
- 567.534E0 -1.274E0
- 635.316E0 -1.212E0
- 733.054E0 -1.100E0
- 759.087E0 -1.046E0
- 894.206E0 -0.915E0
- 990.785E0 -0.714E0
- 1090.109E0 -0.566E0
- 1080.914E0 -0.545E0
- 1122.643E0 -0.400E0
- 1178.351E0 -0.309E0
- 1260.531E0 -0.109E0
- 1273.514E0 -0.103E0
- 1288.339E0 0.010E0
- 1327.543E0 0.119E0
- 1353.863E0 0.377E0
- 1414.509E0 0.790E0
- 1425.208E0 0.963E0
- 1421.384E0 1.006E0
- 1442.962E0 1.115E0
- 1464.350E0 1.572E0
- 1468.705E0 1.841E0
- 1447.894E0 2.047E0
- 1457.628E0 2.200E0
+NIST/ITL StRD +Dataset Name: Thurber (Thurber.dat) + +File Format: ASCII + Starting Values (lines 41 to 47) + Certified Values (lines 41 to 52) + Data (lines 61 to 97) + +Procedure: Nonlinear Least Squares Regression + +Description: These data are the result of a NIST study involving + semiconductor electron mobility. The response + variable is a measure of electron mobility, and the + predictor variable is the natural log of the density. + + +Reference: Thurber, R., NIST (197?). + Semiconductor electron mobility modeling. + + + + + + +Data: 1 Response Variable (y = electron mobility) + 1 Predictor Variable (x = log[density]) + 37 Observations + Higher Level of Difficulty + Observed Data + +Model: Rational Class (cubic/cubic) + 7 Parameters (b1 to b7) + + y = (b1 + b2*x + b3*x**2 + b4*x**3) / + (1 + b5*x + b6*x**2 + b7*x**3) + e + + + Starting Values Certified Values + + Start 1 Start 2 Parameter Standard Deviation + b1 = 1000 1300 1.2881396800E+03 4.6647963344E+00 + b2 = 1000 1500 1.4910792535E+03 3.9571156086E+01 + b3 = 400 500 5.8323836877E+02 2.8698696102E+01 + b4 = 40 75 7.5416644291E+01 5.5675370270E+00 + b5 = 0.7 1 9.6629502864E-01 3.1333340687E-02 + b6 = 0.3 0.4 3.9797285797E-01 1.4984928198E-02 + b7 = 0.03 0.05 4.9727297349E-02 6.5842344623E-03 + +Residual Sum of Squares: 5.6427082397E+03 +Residual Standard Deviation: 1.3714600784E+01 +Degrees of Freedom: 30 +Number of Observations: 37 + + + + + + + +Data: y x + 80.574E0 -3.067E0 + 84.248E0 -2.981E0 + 87.264E0 -2.921E0 + 87.195E0 -2.912E0 + 89.076E0 -2.840E0 + 89.608E0 -2.797E0 + 89.868E0 -2.702E0 + 90.101E0 -2.699E0 + 92.405E0 -2.633E0 + 95.854E0 -2.481E0 + 100.696E0 -2.363E0 + 101.060E0 -2.322E0 + 401.672E0 -1.501E0 + 390.724E0 -1.460E0 + 567.534E0 -1.274E0 + 635.316E0 -1.212E0 + 733.054E0 -1.100E0 + 759.087E0 -1.046E0 + 894.206E0 -0.915E0 + 990.785E0 -0.714E0 + 1090.109E0 -0.566E0 + 1080.914E0 -0.545E0 + 1122.643E0 -0.400E0 + 1178.351E0 -0.309E0 + 1260.531E0 -0.109E0 + 1273.514E0 -0.103E0 + 1288.339E0 0.010E0 + 1327.543E0 0.119E0 + 1353.863E0 0.377E0 + 1414.509E0 0.790E0 + 1425.208E0 0.963E0 + 1421.384E0 1.006E0 + 1442.962E0 1.115E0 + 1464.350E0 1.572E0 + 1468.705E0 1.841E0 + 1447.894E0 2.047E0 + 1457.628E0 2.200E0 @@ -1,6 +1,6 @@ Metadata-Version: 1.1 Name: lmfit -Version: 0.9.2 +Version: 0.9.3 Summary: Least-Squares Minimization with Bounds and Constraints Home-page: http://lmfit.github.io/lmfit-py/ Author: LMFit Development Team @@ -1,65 +0,0 @@ -LMfit-py -======== - -[](https://travis-ci.org/lmfit/lmfit-py) - -LMfit-py provides a Least-Squares Minimization routine and class -with a simple, flexible approach to parameterizing a model for -fitting to data. Named Parameters can be held fixed or freely -adjusted in the fit, or held between lower and upper bounds. In -addition, parameters can be constrained as a simple mathematical -expression of other Parameters. - -To do this, the programmer defines a Parameters object, an enhanced -dictionary, containing named parameters: - - fit_params = Parameters() - fit_params['amp'] = Parameter(value=1.2, min=0.1, max=1000) - fit_params['cen'] = Parameter(value=40.0, vary=False), - fit_params['wid'] = Parameter(value=4, min=0)} - -or using the equivalent - - fit_params = Parameters() - fit_params.add('amp', value=1.2, min=0.1, max=1000) - fit_params.add('cen', value=40.0, vary=False), - fit_params.add('wid', value=4, min=0) - -The programmer will also write a function to be minimized (in the -least-squares sense) with its first argument being this Parameters object, -and additional positional and keyword arguments as desired: - - def myfunc(params, x, data, someflag=True): - amp = params['amp'].value - cen = params['cen'].value - wid = params['wid'].value - ... - return residual_array - -For each call of this function, the values for the params may have changed, -subject to the bounds and constraint settings for each Parameter. The function -should return the residual (ie, data-model) array to be minimized. - -The advantage here is that the function to be minimized does not have to be -changed if different bounds or constraints are placed on the fitting -Parameters. The fitting model (as described in myfunc) is instead written -in terms of physical parameters of the system, and remains remains -independent of what is actually varied in the fit. In addition, which -parameters are adjuested and which are fixed happens at run-time, so that -changing what is varied and what constraints are placed on the parameters -can easily be modified by the consumer in real-time data analysis. - -To perform the fit, the user calls - - result = minimize(myfunc, fit_params, args=(x, data), kws={'someflag':True}, ....) - -After the fit, each real variable in the ``fit_params`` dictionary is updated -to have best-fit values, estimated standard deviations, and correlations -with other variables in the fit, while the results dictionary holds fit -statistics and information. - -By default, the underlying fit algorithm is the Levenberg-Marquart -algorithm with numerically-calculated derivatives from MINPACK's lmdif -function, as used by scipy.optimize.leastsq. Other solvers (currently -Simulated Annealing and L-BFGS-B) are also available, though slightly less -well-tested and supported. @@ -1,24 +1,24 @@ -Many people have contributed to lmfit.
-
-Matthew Newville wrote the original version and maintains the project.
-Till Stensitzki wrote the improved estimates of confidence intervals, and
- contributed many tests, bug fixes, and documentation.
-Daniel B. Allan wrote much of the high level Model code, and many
- improvements to the testing and documentation.
-Antonino Ingargiola wrote much of the high level Model code and provided
- many bug fixes.
-J. J. Helmus wrote the MINUT bounds for leastsq, originally in
- leastsqbounds.py, and ported to lmfit.
-E. O. Le Bigot wrote the uncertainties package, a version of which is used
- by lmfit.
-Michal Rawlik added plotting capabilities for Models.
-A. R. J. Nelson added differential_evolution, and greatly improved the code
- in the docstrings.
-
-Additional patches, bug fixes, and suggestions have come from Christoph
- Deil, Francois Boulogne, Thomas Caswell, Colin Brosseau, nmearl,
- Gustavo Pasquevich, Clemens Prescher, LiCode, and Ben Gamari.
-
-The lmfit code obviously depends on, and owes a very large debt to the code
-in scipy.optimize. Several discussions on the scipy-user and lmfit mailing
-lists have also led to improvements in this code.
+Many people have contributed to lmfit. + +Matthew Newville wrote the original version and maintains the project. +Till Stensitzki wrote the improved estimates of confidence intervals, and + contributed many tests, bug fixes, and documentation. +Daniel B. Allan wrote much of the high level Model code, and many + improvements to the testing and documentation. +Antonino Ingargiola wrote much of the high level Model code and provided + many bug fixes. +J. J. Helmus wrote the MINUT bounds for leastsq, originally in + leastsqbounds.py, and ported to lmfit. +E. O. Le Bigot wrote the uncertainties package, a version of which is used + by lmfit. +Michal Rawlik added plotting capabilities for Models. +A. R. J. Nelson added differential_evolution, emcee, and greatly improved the + code in the docstrings. + +Additional patches, bug fixes, and suggestions have come from Christoph + Deil, Francois Boulogne, Thomas Caswell, Colin Brosseau, nmearl, + Gustavo Pasquevich, Clemens Prescher, LiCode, and Ben Gamari. + +The lmfit code obviously depends on, and owes a very large debt to the code +in scipy.optimize. Several discussions on the scipy-user and lmfit mailing +lists have also led to improvements in this code. diff --git a/doc/Makefile b/doc/Makefile index 5add84d..1c72ec9 100644 --- a/doc/Makefile +++ b/doc/Makefile @@ -1,112 +1,112 @@ -# Makefile for Sphinx documentation
-#
-
-# You can set these variables from the command line.
-SPHINXOPTS =
-SPHINXBUILD = sphinx-build
-PAPER =
-BUILDDIR = _build
-INSTALLDIR = /home/newville/public_html/lmfit/
-
-
-# Internal variables.
-PAPEROPT_a4 = -D latex_paper_size=a4
-PAPEROPT_letter = -D latex_paper_size=letter
-ALLSPHINXOPTS = -d $(BUILDDIR)/doctrees $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) .
-
-.PHONY: help clean html dirhtml pickle json htmlhelp qthelp latex changes linkcheck doctest latexpdf htmlzip
-.PHONY: all install pdf
-
-html:
- cp sphinx/ext_mathjax.py extensions.py
- $(SPHINXBUILD) -b html $(ALLSPHINXOPTS) $(BUILDDIR)/html
- @echo
- @echo "html build finished: $(BUILDDIR)/html."
-
-htmlzip: html
- cp sphinx/ext_pngmath.py extensions.py
- $(SPHINXBUILD) -b html $(ALLSPHINXOPTS) $(BUILDDIR)/lmfit_doc
- cd $(BUILDDIR) && zip -pur html/lmfit_doc.zip lmfit_doc
-
-epub:
- cp sphinx/ext_pngmath.py extensions.py
- $(SPHINXBUILD) -b epub $(ALLSPHINXOPTS) $(BUILDDIR)/epub
- cp -pr $(BUILDDIR)/epub/*.epub $(BUILDDIR)/html/.
-
-pdf: latex
- cd $(BUILDDIR)/latex && make all-pdf
- cp -pr $(BUILDDIR)/latex/lmfit.pdf $(BUILDDIR)/html/.
-
-all: html htmlzip epub pdf
-
-install: all
- cd $(BUILDDIR)/latex && pdflatex lmfit.tex
- cd $(BUILDDIR)/latex && makeindex -s python.ist lmfit.idx
- cd $(BUILDDIR)/latex && pdflatex lmfit.tex
- cp -pr $(BUILDDIR)/html/* $(INSTALLDIR)/.
-
-help:
- @echo "Please use \`make <target>' where <target> is one of"
- @echo " html to make standalone HTML files"
- @echo " dirhtml to make HTML files named index.html in directories"
- @echo " pickle to make pickle files"
- @echo " json to make JSON files"
- @echo " htmlhelp to make HTML files and a HTML help project"
- @echo " qthelp to make HTML files and a qthelp project"
- @echo " latex to make LaTeX files, you can set PAPER=a4 or PAPER=letter"
- @echo " changes to make an overview of all changed/added/deprecated items"
- @echo " linkcheck to check all external links for integrity"
- @echo " doctest to run all doctests embedded in the documentation (if enabled)"
-
-clean:
- -rm -rf $(BUILDDIR)/*
-
-dirhtml:
- $(SPHINXBUILD) -b dirhtml $(ALLSPHINXOPTS) $(BUILDDIR)/dirhtml
- @echo
- @echo "Build finished. The HTML pages are in $(BUILDDIR)/dirhtml."
-
-pickle:
- $(SPHINXBUILD) -b pickle $(ALLSPHINXOPTS) $(BUILDDIR)/pickle
- @echo
- @echo "Build finished; now you can process the pickle files."
-
-json:
- $(SPHINXBUILD) -b json $(ALLSPHINXOPTS) $(BUILDDIR)/json
- @echo
- @echo "Build finished; now you can process the JSON files."
-
-htmlhelp:
- $(SPHINXBUILD) -b htmlhelp $(ALLSPHINXOPTS) $(BUILDDIR)/htmlhelp
- @echo
- @echo "Build finished; now you can run HTML Help Workshop with the" \
- ".hhp project file in $(BUILDDIR)/htmlhelp."
-
-latex:
- $(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) _build/latex
- @echo
- @echo "Build finished; the LaTeX files are in _build/latex."
- @echo "Run \`make all-pdf' or \`make all-ps' in that directory to" \
- "run these through (pdf)latex."
-
-latexpdf:
- $(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) _build/latex
- @echo "Running LaTeX files through pdflatex..."
- make -C _build/latex all-pdf
- @echo "pdflatex finished; the PDF files are in _build/latex."
-
-changes:
- $(SPHINXBUILD) -b changes $(ALLSPHINXOPTS) $(BUILDDIR)/changes
- @echo
- @echo "The overview file is in $(BUILDDIR)/changes."
-
-linkcheck:
- $(SPHINXBUILD) -b linkcheck $(ALLSPHINXOPTS) $(BUILDDIR)/linkcheck
- @echo
- @echo "Link check complete; look for any errors in the above output " \
- "or in $(BUILDDIR)/linkcheck/output.txt."
-
-doctest:
- $(SPHINXBUILD) -b doctest $(ALLSPHINXOPTS) $(BUILDDIR)/doctest
- @echo "Testing of doctests in the sources finished, look at the " \
- "results in $(BUILDDIR)/doctest/output.txt."
+# Makefile for Sphinx documentation +# + +# You can set these variables from the command line. +SPHINXOPTS = +SPHINXBUILD = sphinx-build +PAPER = +BUILDDIR = _build +INSTALLDIR = /home/newville/public_html/lmfit/ + + +# Internal variables. +PAPEROPT_a4 = -D latex_paper_size=a4 +PAPEROPT_letter = -D latex_paper_size=letter +ALLSPHINXOPTS = -d $(BUILDDIR)/doctrees $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) . + +.PHONY: help clean html dirhtml pickle json htmlhelp qthelp latex changes linkcheck doctest latexpdf htmlzip +.PHONY: all install pdf + +html: + cp sphinx/ext_mathjax.py extensions.py + $(SPHINXBUILD) -b html $(ALLSPHINXOPTS) $(BUILDDIR)/html + @echo + @echo "html build finished: $(BUILDDIR)/html." + +htmlzip: html + cp sphinx/ext_pngmath.py extensions.py + $(SPHINXBUILD) -b html $(ALLSPHINXOPTS) $(BUILDDIR)/lmfit_doc + cd $(BUILDDIR) && zip -pur html/lmfit_doc.zip lmfit_doc + +epub: + cp sphinx/ext_pngmath.py extensions.py + $(SPHINXBUILD) -b epub $(ALLSPHINXOPTS) $(BUILDDIR)/epub + cp -pr $(BUILDDIR)/epub/*.epub $(BUILDDIR)/html/. + +pdf: latex + cd $(BUILDDIR)/latex && make all-pdf + cp -pr $(BUILDDIR)/latex/lmfit.pdf $(BUILDDIR)/html/. + +all: html htmlzip epub pdf + +install: all + cd $(BUILDDIR)/latex && pdflatex lmfit.tex + cd $(BUILDDIR)/latex && makeindex -s python.ist lmfit.idx + cd $(BUILDDIR)/latex && pdflatex lmfit.tex + cp -pr $(BUILDDIR)/html/* $(INSTALLDIR)/. + +help: + @echo "Please use \`make <target>' where <target> is one of" + @echo " html to make standalone HTML files" + @echo " dirhtml to make HTML files named index.html in directories" + @echo " pickle to make pickle files" + @echo " json to make JSON files" + @echo " htmlhelp to make HTML files and a HTML help project" + @echo " qthelp to make HTML files and a qthelp project" + @echo " latex to make LaTeX files, you can set PAPER=a4 or PAPER=letter" + @echo " changes to make an overview of all changed/added/deprecated items" + @echo " linkcheck to check all external links for integrity" + @echo " doctest to run all doctests embedded in the documentation (if enabled)" + +clean: + -rm -rf $(BUILDDIR)/* + +dirhtml: + $(SPHINXBUILD) -b dirhtml $(ALLSPHINXOPTS) $(BUILDDIR)/dirhtml + @echo + @echo "Build finished. The HTML pages are in $(BUILDDIR)/dirhtml." + +pickle: + $(SPHINXBUILD) -b pickle $(ALLSPHINXOPTS) $(BUILDDIR)/pickle + @echo + @echo "Build finished; now you can process the pickle files." + +json: + $(SPHINXBUILD) -b json $(ALLSPHINXOPTS) $(BUILDDIR)/json + @echo + @echo "Build finished; now you can process the JSON files." + +htmlhelp: + $(SPHINXBUILD) -b htmlhelp $(ALLSPHINXOPTS) $(BUILDDIR)/htmlhelp + @echo + @echo "Build finished; now you can run HTML Help Workshop with the" \ + ".hhp project file in $(BUILDDIR)/htmlhelp." + +latex: + $(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) _build/latex + @echo + @echo "Build finished; the LaTeX files are in _build/latex." + @echo "Run \`make all-pdf' or \`make all-ps' in that directory to" \ + "run these through (pdf)latex." + +latexpdf: + $(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) _build/latex + @echo "Running LaTeX files through pdflatex..." + make -C _build/latex all-pdf + @echo "pdflatex finished; the PDF files are in _build/latex." + +changes: + $(SPHINXBUILD) -b changes $(ALLSPHINXOPTS) $(BUILDDIR)/changes + @echo + @echo "The overview file is in $(BUILDDIR)/changes." + +linkcheck: + $(SPHINXBUILD) -b linkcheck $(ALLSPHINXOPTS) $(BUILDDIR)/linkcheck + @echo + @echo "Link check complete; look for any errors in the above output " \ + "or in $(BUILDDIR)/linkcheck/output.txt." + +doctest: + $(SPHINXBUILD) -b doctest $(ALLSPHINXOPTS) $(BUILDDIR)/doctest + @echo "Testing of doctests in the sources finished, look at the " \ + "results in $(BUILDDIR)/doctest/output.txt." diff --git a/doc/__pycache__/extensions.cpython-35.pyc b/doc/__pycache__/extensions.cpython-35.pyc Binary files differnew file mode 100644 index 0000000..a9f415c --- /dev/null +++ b/doc/__pycache__/extensions.cpython-35.pyc diff --git a/doc/_images/emcee_dbl_exp.png b/doc/_images/emcee_dbl_exp.png Binary files differnew file mode 100644 index 0000000..11bc045 --- /dev/null +++ b/doc/_images/emcee_dbl_exp.png diff --git a/doc/_images/emcee_dbl_exp2.png b/doc/_images/emcee_dbl_exp2.png Binary files differnew file mode 100644 index 0000000..b2dab72 --- /dev/null +++ b/doc/_images/emcee_dbl_exp2.png diff --git a/doc/_images/emcee_triangle.png b/doc/_images/emcee_triangle.png Binary files differnew file mode 100644 index 0000000..3e76a52 --- /dev/null +++ b/doc/_images/emcee_triangle.png diff --git a/doc/_templates/indexsidebar.html b/doc/_templates/indexsidebar.html index 4098133..ceb1a92 100644 --- a/doc/_templates/indexsidebar.html +++ b/doc/_templates/indexsidebar.html @@ -1,24 +1,24 @@ -<h3>Getting LMFIT</h3>
-<p>Current version: <b>{{ release }}</b></p>
-<p>Download: <a href="http://pypi.python.org/pypi/lmfit/">PyPI (Python.org)</a>
-<p>Install: <tt>pip install lmfit</tt>
-<p>
-<p>Development version: <br>
- <a href="https://github.com/lmfit/lmfit-py/">github.com</a> <br>
-
-<h3>Questions?</h3>
-
- <a href="faq.html">Frequently Asked Questions</a><br>
- <a href="https://groups.google.com/group/lmfit-py">Mailing List</a><br>
- <a href="support.html">Getting Help</a><br>
-
-<h3>Off-line Documentation</h3>
-
-[<a href="http://cars9.uchicago.edu/software/python/lmfit/lmfit.pdf">PDF</a>
-|<a href="http://cars9.uchicago.edu/software/python/lmfit/lmfit.epub">EPUB</a>
-|<a href="http://cars9.uchicago.edu/software/python/lmfit/lmfit_doc.zip">HTML(zip)</a>
-]
-
-
-<hr>
-<p>
+<h3>Getting LMFIT</h3> +<p>Current version: <b>{{ release }}</b></p> +<p>Download: <a href="http://pypi.python.org/pypi/lmfit/">PyPI (Python.org)</a> +<p>Install: <tt>pip install lmfit</tt> +<p> +<p>Development version: <br> + <a href="https://github.com/lmfit/lmfit-py/">github.com</a> <br> + +<h3>Questions?</h3> + + <a href="faq.html">Frequently Asked Questions</a><br> + <a href="https://groups.google.com/group/lmfit-py">Mailing List</a><br> + <a href="support.html">Getting Help</a><br> + +<h3>Off-line Documentation</h3> + +[<a href="http://cars9.uchicago.edu/software/python/lmfit/lmfit.pdf">PDF</a> +|<a href="http://cars9.uchicago.edu/software/python/lmfit/lmfit.epub">EPUB</a> +|<a href="http://cars9.uchicago.edu/software/python/lmfit/lmfit_doc.zip">HTML(zip)</a> +] + + +<hr> +<p> diff --git a/doc/bounds.rst b/doc/bounds.rst index f64ec6a..40f8390 100644 --- a/doc/bounds.rst +++ b/doc/bounds.rst @@ -1,79 +1,78 @@ -.. _bounds_chapter:
-
-=================================
-Bounds Implementation
-=================================
-
-.. _MINPACK-1: http://en.wikipedia.org/wiki/MINPACK
-.. _MINUIT: http://en.wikipedia.org/wiki/MINUIT
-.. _leastsqbound: https://github.com/jjhelmus/leastsqbound-scipy
-
-This section describes the implementation of :class:`Parameter` bounds.
-The `MINPACK-1`_ implementation used in :func:`scipy.optimize.leastsq` for
-the Levenberg-Marquardt algorithm does not explicitly support bounds on
-parameters, and expects to be able to fully explore the available range of
-values for any Parameter. Simply placing hard constraints (that is,
-resetting the value when it exceeds the desired bounds) prevents the
-algorithm from determining the partial derivatives, and leads to unstable
-results.
-
-Instead of placing such hard constraints, bounded parameters are
-mathematically transformed using the formulation devised (and documented)
-for `MINUIT`_. This is implemented following (and borrowing heavily from)
-the `leastsqbound`_ from J. J. Helmus. Parameter values are mapped from
-internally used, freely variable values :math:`P_{\rm internal}` to bounded
-parameters :math:`P_{\rm bounded}`. When both ``min`` and ``max`` bounds
-are specified, the mapping is
-
-.. math::
- :nowrap:
-
- \begin{eqnarray*}
- P_{\rm internal} &=& \arcsin\big(\frac{2 (P_{\rm bounded} - {\rm min})}{({\rm max} - {\rm min})} - 1\big) \\
- P_{\rm bounded} &=& {\rm min} + \big(\sin(P_{\rm internal}) + 1\big) \frac{({\rm max} - {\rm min})}{2}
- \end{eqnarray*}
-
-With only an upper limit ``max`` supplied, but ``min`` left unbounded, the
-mapping is:
-
-.. math::
- :nowrap:
-
- \begin{eqnarray*}
- P_{\rm internal} &=& \sqrt{({\rm max} - P_{\rm bounded} + 1)^2 - 1} \\
- P_{\rm bounded} &=& {\rm max} + 1 - \sqrt{P_{\rm internal}^2 + 1}
- \end{eqnarray*}
-
-With only a lower limit ``min`` supplied, but ``max`` left unbounded, the
-mapping is:
-
-.. math::
- :nowrap:
-
- \begin{eqnarray*}
- P_{\rm internal} &=& \sqrt{(P_{\rm bounded} - {\rm min} + 1)^2 - 1} \\
- P_{\rm bounded} &=& {\rm min} - 1 + \sqrt{P_{\rm internal}^2 + 1}
- \end{eqnarray*}
-
-With these mappings, the value for the bounded Parameter cannot exceed the
-specified bounds, though the internally varied value can be freely varied.
-
-It bears repeating that code from `leastsqbound`_ was adopted to implement
-the transformation described above. The challenging part (Thanks again to
-Jonathan J. Helmus!) here is to re-transform the covariance matrix so that
-the uncertainties can be estimated for bounded Parameters. This is
-included by using the derivate :math:`dP_{\rm internal}/dP_{\rm bounded}`
-from the equations above to re-scale the Jacobin matrix before
-constructing the covariance matrix from it. Tests show that this
-re-scaling of the covariance matrix works quite well, and that
-uncertainties estimated for bounded are quite reasonable. Of course, if
-the best fit value is very close to a boundary, the derivative estimated
-uncertainty and correlations for that parameter may not be reliable.
-
-The `MINUIT`_ documentation recommends caution in using bounds. Setting
-bounds can certainly increase the number of function evaluations (and so
-computation time), and in some cases may cause some instabilities, as the
-range of acceptable parameter values is not fully explored. On the other
-hand, preliminary tests suggest that using ``max`` and ``min`` to set
-clearly outlandish bounds does not greatly affect performance or results.
-
+.. _bounds_chapter: + +================================= +Bounds Implementation +================================= + +.. _MINPACK-1: http://en.wikipedia.org/wiki/MINPACK +.. _MINUIT: http://en.wikipedia.org/wiki/MINUIT +.. _leastsqbound: https://github.com/jjhelmus/leastsqbound-scipy + +This section describes the implementation of :class:`Parameter` bounds. +The `MINPACK-1`_ implementation used in :scipydoc:`optimize.leastsq` for +the Levenberg-Marquardt algorithm does not explicitly support bounds on +parameters, and expects to be able to fully explore the available range of +values for any Parameter. Simply placing hard constraints (that is, +resetting the value when it exceeds the desired bounds) prevents the +algorithm from determining the partial derivatives, and leads to unstable +results. + +Instead of placing such hard constraints, bounded parameters are +mathematically transformed using the formulation devised (and documented) +for `MINUIT`_. This is implemented following (and borrowing heavily from) +the `leastsqbound`_ from J. J. Helmus. Parameter values are mapped from +internally used, freely variable values :math:`P_{\rm internal}` to bounded +parameters :math:`P_{\rm bounded}`. When both ``min`` and ``max`` bounds +are specified, the mapping is + +.. math:: + :nowrap: + + \begin{eqnarray*} + P_{\rm internal} &=& \arcsin\big(\frac{2 (P_{\rm bounded} - {\rm min})}{({\rm max} - {\rm min})} - 1\big) \\ + P_{\rm bounded} &=& {\rm min} + \big(\sin(P_{\rm internal}) + 1\big) \frac{({\rm max} - {\rm min})}{2} + \end{eqnarray*} + +With only an upper limit ``max`` supplied, but ``min`` left unbounded, the +mapping is: + +.. math:: + :nowrap: + + \begin{eqnarray*} + P_{\rm internal} &=& \sqrt{({\rm max} - P_{\rm bounded} + 1)^2 - 1} \\ + P_{\rm bounded} &=& {\rm max} + 1 - \sqrt{P_{\rm internal}^2 + 1} + \end{eqnarray*} + +With only a lower limit ``min`` supplied, but ``max`` left unbounded, the +mapping is: + +.. math:: + :nowrap: + + \begin{eqnarray*} + P_{\rm internal} &=& \sqrt{(P_{\rm bounded} - {\rm min} + 1)^2 - 1} \\ + P_{\rm bounded} &=& {\rm min} - 1 + \sqrt{P_{\rm internal}^2 + 1} + \end{eqnarray*} + +With these mappings, the value for the bounded Parameter cannot exceed the +specified bounds, though the internally varied value can be freely varied. + +It bears repeating that code from `leastsqbound`_ was adopted to implement +the transformation described above. The challenging part (Thanks again to +Jonathan J. Helmus!) here is to re-transform the covariance matrix so that +the uncertainties can be estimated for bounded Parameters. This is +included by using the derivate :math:`dP_{\rm internal}/dP_{\rm bounded}` +from the equations above to re-scale the Jacobin matrix before +constructing the covariance matrix from it. Tests show that this +re-scaling of the covariance matrix works quite well, and that +uncertainties estimated for bounded are quite reasonable. Of course, if +the best fit value is very close to a boundary, the derivative estimated +uncertainty and correlations for that parameter may not be reliable. + +The `MINUIT`_ documentation recommends caution in using bounds. Setting +bounds can certainly increase the number of function evaluations (and so +computation time), and in some cases may cause some instabilities, as the +range of acceptable parameter values is not fully explored. On the other +hand, preliminary tests suggest that using ``max`` and ``min`` to set +clearly outlandish bounds does not greatly affect performance or results. diff --git a/doc/builtin_models.rst b/doc/builtin_models.rst index 9d2671e..d1e68b6 100644 --- a/doc/builtin_models.rst +++ b/doc/builtin_models.rst @@ -1,943 +1,980 @@ -.. _builtin_models_chapter:
-
-=====================================================
-Built-in Fitting Models in the :mod:`models` module
-=====================================================
-
-.. module:: models
-
-Lmfit provides several builtin fitting models in the :mod:`models` module.
-These pre-defined models each subclass from the :class:`model.Model` class of the
-previous chapter and wrap relatively well-known functional forms, such as
-Gaussians, Lorentzian, and Exponentials that are used in a wide range of
-scientific domains. In fact, all the models are all based on simple, plain
-python functions defined in the :mod:`lineshapes` module. In addition to
-wrapping a function into a :class:`model.Model`, these models also provide a
-:meth:`guess` method that is intended to give a reasonable
-set of starting values from a data array that closely approximates the
-data to be fit.
-
-As shown in the previous chapter, a key feature of the :class:`mode.Model` class
-is that models can easily be combined to give a composite
-:class:`model.Model`. Thus while some of the models listed here may seem pretty
-trivial (notably, :class:`ConstantModel` and :class:`LinearModel`), the
-main point of having these is to be able to used in composite models. For
-example, a Lorentzian plus a linear background might be represented as::
-
- >>> from lmfit.models import LinearModel, LorentzianModel
- >>> peak = LorentzianModel()
- >>> background = LinearModel()
- >>> model = peak + background
-
-All the models listed below are one dimensional, with an independent
-variable named ``x``. Many of these models represent a function with a
-distinct peak, and so share common features. To maintain uniformity,
-common parameter names are used whenever possible. Thus, most models have
-a parameter called ``amplitude`` that represents the overall height (or
-area of) a peak or function, a ``center`` parameter that represents a peak
-centroid position, and a ``sigma`` parameter that gives a characteristic
-width. Some peak shapes also have a parameter ``fwhm``, typically
-constrained by ``sigma`` to give the full width at half maximum.
-
-After a list of builtin models, a few examples of their use is given.
-
-Peak-like models
--------------------
-
-There are many peak-like models available. These include
-:class:`GaussianModel`, :class:`LorentzianModel`, :class:`VoigtModel` and
-some less commonly used variations. The :meth:`guess`
-methods for all of these make a fairly crude guess for the value of
-``amplitude``, but also set a lower bound of 0 on the value of ``sigma``.
-
-:class:`GaussianModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: GaussianModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model based on a `Gaussian or normal distribution lineshape
-<http://en.wikipedia.org/wiki/Normal_distribution>`_. Parameter names:
-``amplitude``, ``center``, and ``sigma``. In addition, a constrained
-parameter ``fwhm`` is included.
-
-.. math::
-
- f(x; A, \mu, \sigma) = \frac{A}{\sigma\sqrt{2\pi}} e^{[{-{(x-\mu)^2}/{{2\sigma}^2}}]}
-
-where the parameter ``amplitude`` corresponds to :math:`A`, ``center`` to
-:math:`\mu`, and ``sigma`` to :math:`\sigma`. The full width at
-half maximum is :math:`2\sigma\sqrt{2\ln{2}}`, approximately
-:math:`2.3548\sigma`
-
-
-:class:`LorentzianModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: LorentzianModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model based on a `Lorentzian or Cauchy-Lorentz distribution function
-<http://en.wikipedia.org/wiki/Cauchy_distribution>`_. Parameter names:
-``amplitude``, ``center``, and ``sigma``. In addition, a constrained
-parameter ``fwhm`` is included.
-
-.. math::
-
- f(x; A, \mu, \sigma) = \frac{A}{\pi} \big[\frac{\sigma}{(x - \mu)^2 + \sigma^2}\big]
-
-where the parameter ``amplitude`` corresponds to :math:`A`, ``center`` to
-:math:`\mu`, and ``sigma`` to :math:`\sigma`. The full width at
-half maximum is :math:`2\sigma`.
-
-
-:class:`VoigtModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: VoigtModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model based on a `Voigt distribution function
-<http://en.wikipedia.org/wiki/Voigt_profile>`_. Parameter names:
-``amplitude``, ``center``, and ``sigma``. A ``gamma`` parameter is also
-available. By default, it is constrained to have value equal to ``sigma``,
-though this can be varied independently. In addition, a constrained
-parameter ``fwhm`` is included. The definition for the Voigt function used
-here is
-
-.. math::
-
- f(x; A, \mu, \sigma, \gamma) = \frac{A \textrm{Re}[w(z)]}{\sigma\sqrt{2 \pi}}
-
-where
-
-.. math::
- :nowrap:
-
- \begin{eqnarray*}
- z &=& \frac{x-\mu +i\gamma}{\sigma\sqrt{2}} \\
- w(z) &=& e^{-z^2}{\operatorname{erfc}}(-iz)
- \end{eqnarray*}
-
-and :func:`erfc` is the complimentary error function. As above,
-``amplitude`` corresponds to :math:`A`, ``center`` to
-:math:`\mu`, and ``sigma`` to :math:`\sigma`. The parameter ``gamma``
-corresponds to :math:`\gamma`.
-If ``gamma`` is kept at the default value (constrained to ``sigma``),
-the full width at half maximum is approximately :math:`3.6013\sigma`.
-
-
-:class:`PseudoVoigtModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: PseudoVoigtModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-a model based on a `pseudo-Voigt distribution function
-<http://en.wikipedia.org/wiki/Voigt_profile#Pseudo-Voigt_Approximation>`_,
-which is a weighted sum of a Gaussian and Lorentzian distribution functions
-with that share values for ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`)
-and full width at half maximum (and so have constrained values of
-``sigma`` (:math:`\sigma`). A parameter ``fraction`` (:math:`\alpha`)
-controls the relative weight of the Gaussian and Lorentzian components,
-giving the full definition of
-
-.. math::
-
- f(x; A, \mu, \sigma, \alpha) = \frac{(1-\alpha)A}{\sigma_g\sqrt{2\pi}} e^{[{-{(x-\mu)^2}/{{2\sigma_g}^2}}]}
- + \frac{\alpha A}{\pi} \big[\frac{\sigma}{(x - \mu)^2 + \sigma^2}\big]
-
-where :math:`\sigma_g = {\sigma}/{\sqrt{2\ln{2}}}` so that the full width
-at half maximum of each component and of the sum is :math:`2\sigma`. The
-:meth:`guess` function always sets the starting value for ``fraction`` at 0.5.
-
-
-:class:`MoffatModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: MoffatModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-a model based on a `Moffat distribution function
-<https://en.wikipedia.org/wiki/Moffat_distribution>`_, the parameters are
-``amplitude`` (:math:`A`), ``center`` (:math:`\mu`),
-a width parameter ``sigma`` (:math:`\sigma`) and an exponent ``beta`` (:math:`\beta`).
-For (:math:`\beta=1`) the Moffat has a Lorentzian shape.
-
-.. math::
-
- f(x; A, \mu, \sigma, \beta) = A \big[(\frac{x-\mu}{\sigma})^2+1\big]^{-\beta}
-
-the full width have maximum is :math:`2\sigma\sqrt{2^{1/\beta}-1}`.
-:meth:`guess` function always sets the starting value for ``beta`` to 1.
-
-
-:class:`Pearson7Model`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: Pearson7Model(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model based on a `Pearson VII distribution
-<http://en.wikipedia.org/wiki/Pearson_distribution#The_Pearson_type_VII_distribution>`_.
-This is a Lorenztian-like distribution function. It has the usual
-parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and
-``sigma`` (:math:`\sigma`), and also an ``exponent`` (:math:`m`) in
-
-.. math::
-
- f(x; A, \mu, \sigma, m) = \frac{A}{\sigma{\beta(m-\frac{1}{2}, \frac{1}{2})}} \bigl[1 + \frac{(x-\mu)^2}{\sigma^2} \bigr]^{-m}
-
-where :math:`\beta` is the beta function (see :func:`scipy.special.beta` in
-:mod:`scipy.special`). The :meth:`guess` function always
-gives a starting value for ``exponent`` of 1.5.
-
-:class:`StudentsTModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: StudentsTModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model based on a `Student's t distribution function
-<http://en.wikipedia.org/wiki/Student%27s_t-distribution>`_, with the usual
-parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and
-``sigma`` (:math:`\sigma`) in
-
-.. math::
-
- f(x; A, \mu, \sigma) = \frac{A \Gamma(\frac{\sigma+1}{2})} {\sqrt{\sigma\pi}\,\Gamma(\frac{\sigma}{2})} \Bigl[1+\frac{(x-\mu)^2}{\sigma}\Bigr]^{-\frac{\sigma+1}{2}}
-
-
-where :math:`\Gamma(x)` is the gamma function.
-
-
-:class:`BreitWignerModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: BreitWignerModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model based on a `Breit-Wigner-Fano function
-<http://en.wikipedia.org/wiki/Fano_resonance>`_. It has the usual
-parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and
-``sigma`` (:math:`\sigma`), plus ``q`` (:math:`q`) in
-
-.. math::
-
- f(x; A, \mu, \sigma, q) = \frac{A (q\sigma/2 + x - \mu)^2}{(\sigma/2)^2 + (x - \mu)^2}
-
-
-:class:`LognormalModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: LognormalModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model based on the `Log-normal distribution function
-<http://en.wikipedia.org/wiki/Lognormal>`_.
-It has the usual parameters
-``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and ``sigma``
-(:math:`\sigma`) in
-
-.. math::
-
- f(x; A, \mu, \sigma) = \frac{A e^{-(\ln(x) - \mu)/ 2\sigma^2}}{x}
-
-
-:class:`DampedOcsillatorModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: DampedOcsillatorModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model based on the `Damped Harmonic Oscillator Amplitude
-<http://en.wikipedia.org/wiki/Harmonic_oscillator#Amplitude_part>`_.
-It has the usual parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and
-``sigma`` (:math:`\sigma`) in
-
-.. math::
-
- f(x; A, \mu, \sigma) = \frac{A}{\sqrt{ [1 - (x/\mu)^2]^2 + (2\sigma x/\mu)^2}}
-
-
-:class:`ExponentialGaussianModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: ExponentialGaussianModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model of an `Exponentially modified Gaussian distribution
-<http://en.wikipedia.org/wiki/Exponentially_modified_Gaussian_distribution>`_.
-It has the usual parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and
-``sigma`` (:math:`\sigma`), and also ``gamma`` (:math:`\gamma`) in
-
-.. math::
-
- f(x; A, \mu, \sigma, \gamma) = \frac{A\gamma}{2}
- \exp\bigl[\gamma({\mu - x + \gamma\sigma^2/2})\bigr]
- {\operatorname{erfc}}\Bigl(\frac{\mu + \gamma\sigma^2 - x}{\sqrt{2}\sigma}\Bigr)
-
-
-where :func:`erfc` is the complimentary error function.
-
-:class:`SkewedGaussianModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: SkewedGaussianModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A variation of the above model, this is a `Skewed normal distribution
-<http://en.wikipedia.org/wiki/Skew_normal_distribution>`_.
-It has the usual parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and
-``sigma`` (:math:`\sigma`), and also ``gamma`` (:math:`\gamma`) in
-
-.. math::
-
- f(x; A, \mu, \sigma, \gamma) = \frac{A}{\sigma\sqrt{2\pi}}
- e^{[{-{(x-\mu)^2}/{{2\sigma}^2}}]} \Bigl\{ 1 +
- {\operatorname{erf}}\bigl[
- \frac{\gamma(x-\mu)}{\sigma\sqrt{2}}
- \bigr] \Bigr\}
-
-
-where :func:`erf` is the error function.
-
-
-:class:`DonaichModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: DonaichModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model of an `Doniach Sunjic asymmetric lineshape
-<http://www.casaxps.com/help_manual/line_shapes.htm>`_, used in
-photo-emission. With the usual parameters ``amplitude`` (:math:`A`),
-``center`` (:math:`\mu`) and ``sigma`` (:math:`\sigma`), and also ``gamma``
-(:math:`\gamma`) in
-
-.. math::
-
- f(x; A, \mu, \sigma, \gamma) = A\frac{\cos\bigl[\pi\gamma/2 + (1-\gamma)
- \arctan{(x - \mu)}/\sigma\bigr]} {\bigr[1 + (x-\mu)/\sigma\bigl]^{(1-\gamma)/2}}
-
-
-Linear and Polynomial Models
-------------------------------------
-
-These models correspond to polynomials of some degree. Of course, lmfit is
-a very inefficient way to do linear regression (see :func:`numpy.polyfit`
-or :func:`scipy.stats.linregress`), but these models may be useful as one
-of many components of composite model.
-
-:class:`ConstantModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: ConstantModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
- a class that consists of a single value, ``c``. This is constant in the
- sense of having no dependence on the independent variable ``x``, not in
- the sense of being non-varying. To be clear, ``c`` will be a variable
- Parameter.
-
-:class:`LinearModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: LinearModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
- a class that gives a linear model:
-
-.. math::
-
- f(x; m, b) = m x + b
-
-with parameters ``slope`` for :math:`m` and ``intercept`` for :math:`b`.
-
-
-:class:`QuadraticModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: QuadraticModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-
- a class that gives a quadratic model:
-
-.. math::
-
- f(x; a, b, c) = a x^2 + b x + c
-
-with parameters ``a``, ``b``, and ``c``.
-
-
-:class:`ParabolicModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: ParabolicModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
- same as :class:`QuadraticModel`.
-
-
-:class:`PolynomialModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-
-.. class:: PolynomialModel(degree, missing=None[, prefix=''[, name=None[, **kws]]])
-
- a class that gives a polynomial model up to ``degree`` (with maximum
- value of 7).
-
-.. math::
-
- f(x; c_0, c_1, \ldots, c_7) = \sum_{i=0, 7} c_i x^i
-
-with parameters ``c0``, ``c1``, ..., ``c7``. The supplied ``degree``
-will specify how many of these are actual variable parameters. This uses
-:func:`numpy.polyval` for its calculation of the polynomial.
-
-
-
-Step-like models
------------------------------------------------
-
-Two models represent step-like functions, and share many characteristics.
-
-:class:`StepModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: StepModel(form='linear'[, missing=None[, prefix=''[, name=None[, **kws]]]])
-
-A model based on a Step function, with four choices for functional form.
-The step function starts with a value 0, and ends with a value of :math:`A`
-(``amplitude``), rising to :math:`A/2` at :math:`\mu` (``center``),
-with :math:`\sigma` (``sigma``) setting the characteristic width. The
-supported functional forms are ``linear`` (the default), ``atan`` or
-``arctan`` for an arc-tangent function, ``erf`` for an error function, or
-``logistic`` for a `logistic function <http://en.wikipedia.org/wiki/Logistic_function>`_.
-The forms are
-
-.. math::
- :nowrap:
-
- \begin{eqnarray*}
- & f(x; A, \mu, \sigma, {\mathrm{form={}'linear{}'}}) & = A \min{[1, \max{(0, \alpha)}]} \\
- & f(x; A, \mu, \sigma, {\mathrm{form={}'arctan{}'}}) & = A [1/2 + \arctan{(\alpha)}/{\pi}] \\
- & f(x; A, \mu, \sigma, {\mathrm{form={}'erf{}'}}) & = A [1 + {\operatorname{erf}}(\alpha)]/2 \\
- & f(x; A, \mu, \sigma, {\mathrm{form={}'logistic{}'}})& = A [1 - \frac{1}{1 + e^{\alpha}} ]
- \end{eqnarray*}
-
-where :math:`\alpha = (x - \mu)/{\sigma}`.
-
-:class:`RectangleModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-
-.. class:: RectangleModel(form='linear'[, missing=None[, prefix=''[, name=None[, **kws]]]])
-
-A model based on a Step-up and Step-down function of the same form. The
-same choices for functional form as for :class:`StepModel` are supported,
-with ``linear`` as the default. The function starts with a value 0, and
-ends with a value of :math:`A` (``amplitude``), rising to :math:`A/2` at
-:math:`\mu_1` (``center1``), with :math:`\sigma_1` (``sigma1``) setting the
-characteristic width. It drops to rising to :math:`A/2` at :math:`\mu_2`
-(``center2``), with characteristic width :math:`\sigma_2` (``sigma2``).
-
-.. math::
- :nowrap:
-
- \begin{eqnarray*}
- &f(x; A, \mu, \sigma, {\mathrm{form={}'linear{}'}}) &= A \{ \min{[1, \max{(0, \alpha_1)}]} + \min{[-1, \max{(0, \alpha_2)}]} \} \\
- &f(x; A, \mu, \sigma, {\mathrm{form={}'arctan{}'}}) &= A [\arctan{(\alpha_1)} + \arctan{(\alpha_2)}]/{\pi} \\
- &f(x; A, \mu, \sigma, {\mathrm{form={}'erf{}'}}) &= A [{\operatorname{erf}}(\alpha_1) + {\operatorname{erf}}(\alpha_2)]/2 \\
- &f(x; A, \mu, \sigma, {\mathrm{form={}'logistic{}'}}) &= A [1 - \frac{1}{1 + e^{\alpha_1}} - \frac{1}{1 + e^{\alpha_2}} ]
- \end{eqnarray*}
-
-
-where :math:`\alpha_1 = (x - \mu_1)/{\sigma_1}` and :math:`\alpha_2 = -(x - \mu_2)/{\sigma_2}`.
-
-
-Exponential and Power law models
------------------------------------------------
-
-:class:`ExponentialModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: ExponentialModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model based on an `exponential decay function
-<http://en.wikipedia.org/wiki/Exponential_decay>`_. With parameters named
-``amplitude`` (:math:`A`), and ``decay`` (:math:`\tau`), this has the form:
-
-.. math::
-
- f(x; A, \tau) = A e^{-x/\tau}
-
-
-:class:`PowerLawModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: PowerLawModel(missing=None[, prefix=''[, name=None[, **kws]]])
-
-A model based on a `Power Law <http://en.wikipedia.org/wiki/Power_law>`_.
-With parameters
-named ``amplitude`` (:math:`A`), and ``exponent`` (:math:`k`), this has the
-form:
-
-.. math::
-
- f(x; A, k) = A x^k
-
-
-User-defined Models
-----------------------------
-
-.. _asteval: http://newville.github.io/asteval/
-
-As shown in the previous chapter (:ref:`model_chapter`), it is fairly
-straightforward to build fitting models from parametrized python functions.
-The number of model classes listed so far in the present chapter should
-make it clear that this process is not too difficult. Still, it is
-sometimes desirable to build models from a user-supplied function. This
-may be especially true if model-building is built-in to some larger library
-or application for fitting in which the user may not be able to easily
-build and use a new model from python code.
-
-
-The :class:`ExpressionModel` allows a model to be built from a
-user-supplied expression. This uses the `asteval`_ module also used for
-mathematical constraints as discussed in :ref:`constraints_chapter`.
-
-
-:class:`ExpressionModel`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. class:: ExpressionModel(expr, independent_vars=None, init_script=None, **kws)
-
- A model using the user-supplied mathematical expression, which can be nearly any valid Python expresion.
-
- :param expr: expression use to build model
- :type expr: string
- :param independent_vars: list of argument names in expression that are independent variables.
- :type independent_vars: ``None`` (default) or list of strings for independent variables.
- :param init_script: python script to run before parsing and evaluating expression.
- :type init_script: ``None`` (default) or string
-
-with other parameters passed to :class:`model.Model`, with the notable
-exception that :class:`ExpressionModel` does **not** support the `prefix` argument.
-
-Since the point of this model is that an arbitrary expression will be
-supplied, the determination of what are the parameter names for the model
-happens when the model is created. To do this, the expression is parsed,
-and all symbol names are found. Names that are already known (there are
-over 500 function and value names in the asteval namespace, including most
-python builtins, more than 200 functions inherited from numpy, and more
-than 20 common lineshapes defined in the :mod:`lineshapes` module) are not
-converted to parameters. Unrecognized name are expected to be names either
-of parameters or independent variables. If `independent_vars` is the
-default value of ``None``, and if the expression contains a variable named
-`x`, that will be used as the independent variable. Otherwise,
-`independent_vars` must be given.
-
-For example, if one creates an :class:`ExpressionModel` as::
-
- >>> mod = ExpressionModel('off + amp * exp(-x/x0) * sin(x*phase)')
-
-The name `exp` will be recognized as the exponent function, so the model
-will be interpreted to have parameters named `off`, `amp`, `x0` and
-`phase`. In addition, `x` will be assumed to be the sole independent variable.
-In general, there is no obvious way to set default parameter values or
-parameter hints for bounds, so this will have to be handled explicitly.
-
-To evaluate this model, you might do the following::
-
- >>> x = numpy.linspace(0, 10, 501)
- >>> params = mod.make_params(off=0.25, amp=1.0, x0=2.0, phase=0.04)
- >>> y = mod.eval(params, x=x)
-
-
-While many custom models can be built with a single line expression
-(especially since the names of the lineshapes like `gaussian`, `lorentzian`
-and so on, as well as many numpy functions, are available), more complex
-models will inevitably require multiple line functions. You can include
-such Python code with the `init_script` argument. The text of this script
-is evaluated when the model is initialized (and before the actual
-expression is parsed), so that you can define functions to be used
-in your expression.
-
-As a probably unphysical example, to make a model that is the derivative of
-a Gaussian function times the logarithm of a Lorentzian function you may
-could to define this in a script::
-
- >>> script = """
- def mycurve(x, amp, cen, sig):
- loren = lorentzian(x, amplitude=amp, center=cen, sigma=sig)
- gauss = gaussian(x, amplitude=amp, center=cen, sigma=sig)
- return log(loren)*gradient(gauss)/gradient(x)
- """
-
-and then use this with :class:`ExpressionModel` as::
-
- >>> mod = ExpressionModel('mycurve(x, height, mid, wid)',
- init_script=script,
- independent_vars=['x'])
-
-As above, this will interpret the parameter names to be `height`, `mid`,
-and `wid`, and build a model that can be used to fit data.
-
-
-
-Example 1: Fit Peaked data to Gaussian, Lorentzian, and Voigt profiles
-------------------------------------------------------------------------
-
-Here, we will fit data to three similar line shapes, in order to decide which
-might be the better model. We will start with a Gaussian profile, as in
-the previous chapter, but use the built-in :class:`GaussianModel` instead
-of one we write ourselves. This is a slightly different version from the
-one in previous example in that the parameter names are different, and have
-built-in default values. So, we'll simply use::
-
- from numpy import loadtxt
- from lmfit.models import GaussianModel
-
- data = loadtxt('test_peak.dat')
- x = data[:, 0]
- y = data[:, 1]
-
- mod = GaussianModel()
- pars = mod.guess(y, x=x)
- out = mod.fit(y, pars, x=x)
- print(out.fit_report(min_correl=0.25))
-
-which prints out the results::
-
- [[Model]]
- gaussian
- [[Fit Statistics]]
- # function evals = 21
- # data points = 401
- # variables = 3
- chi-square = 29.994
- reduced chi-square = 0.075
- [[Variables]]
- amplitude: 30.3135571 +/- 0.157126 (0.52%) (init= 29.08159)
- center: 9.24277049 +/- 0.007374 (0.08%) (init= 9.25)
- fwhm: 2.90156963 +/- 0.017366 (0.60%) == '2.3548200*sigma'
- sigma: 1.23218319 +/- 0.007374 (0.60%) (init= 1.35)
- [[Correlations]] (unreported correlations are < 0.250)
- C(amplitude, sigma) = 0.577
-
-
-[We see a few interesting differences from the results of the previous
- chapter. First, the parameter names are longer. Second, there is a
- ``fwhm`` parameter, defined as :math:`\sim 2.355\sigma`. And third, the
- automated initial guesses are pretty good. A plot of the fit shows not
- such a great fit:
-
-.. _figA1:
-
- .. image:: _images/models_peak1.png
- :target: _images/models_peak1.png
- :width: 48 %
- .. image:: _images/models_peak2.png
- :target: _images/models_peak2.png
- :width: 48 %
-
- Fit to peak with Gaussian (left) and Lorentzian (right) models.
-
-suggesting that a different peak shape, with longer tails, should be used.
-Perhaps a Lorentzian would be better? To do this, we simply replace
-``GaussianModel`` with ``LorentzianModel`` to get a
-:class:`LorentzianModel`::
-
- from lmfit.models import LorentzianModel
- mod = LorentzianModel()
- pars = mod.guess(y, x=x)
- out = mod.fit(y, pars, x=x)
- print(out.fit_report(min_correl=0.25))
-
-Predictably, the first thing we try gives results that are worse::
-
- [[Model]]
- lorentzian
- [[Fit Statistics]]
- # function evals = 25
- # data points = 401
- # variables = 3
- chi-square = 53.754
- reduced chi-square = 0.135
- [[Variables]]
- amplitude: 38.9728645 +/- 0.313857 (0.81%) (init= 36.35199)
- center: 9.24438944 +/- 0.009275 (0.10%) (init= 9.25)
- fwhm: 2.30969034 +/- 0.026312 (1.14%) == '2.0000000*sigma'
- sigma: 1.15484517 +/- 0.013156 (1.14%) (init= 1.35)
- [[Correlations]] (unreported correlations are < 0.250)
- C(amplitude, sigma) = 0.709
-
-
-with the plot shown on the right in the figure above.
-
-A Voigt model does a better job. Using :class:`VoigtModel`, this is
-as simple as::
-
- from lmfit.models import VoigtModel
- mod = VoigtModel()
- pars = mod.guess(y, x=x)
- out = mod.fit(y, pars, x=x)
- print(out.fit_report(min_correl=0.25))
-
-which gives::
-
- [[Model]]
- voigt
- [[Fit Statistics]]
- # function evals = 17
- # data points = 401
- # variables = 3
- chi-square = 14.545
- reduced chi-square = 0.037
- [[Variables]]
- amplitude: 35.7554017 +/- 0.138614 (0.39%) (init= 43.62238)
- center: 9.24411142 +/- 0.005054 (0.05%) (init= 9.25)
- fwhm: 2.62951718 +/- 0.013269 (0.50%) == '3.6013100*sigma'
- gamma: 0.73015574 +/- 0.003684 (0.50%) == 'sigma'
- sigma: 0.73015574 +/- 0.003684 (0.50%) (init= 0.8775)
- [[Correlations]] (unreported correlations are < 0.250)
- C(amplitude, sigma) = 0.651
-
-
-with the much better value for :math:`\chi^2` and the obviously better
-match to the data as seen in the figure below (left).
-
-.. _figA2:
-
- .. image:: _images/models_peak3.png
- :target: _images/models_peak3.png
- :width: 48 %
- .. image:: _images/models_peak4.png
- :target: _images/models_peak4.png
- :width: 48 %
-
- Fit to peak with Voigt model (left) and Voigt model with ``gamma``
- varying independently of ``sigma`` (right).
-
-The Voigt function has a :math:`\gamma` parameter (``gamma``) that can be
-distinct from ``sigma``. The default behavior used above constrains
-``gamma`` to have exactly the same value as ``sigma``. If we allow these
-to vary separately, does the fit improve? To do this, we have to change
-the ``gamma`` parameter from a constrained expression and give it a
-starting value::
-
- mod = VoigtModel()
- pars = mod.guess(y, x=x)
- pars['gamma'].set(value=0.7, vary=True, expr='')
-
- out = mod.fit(y, pars, x=x)
- print(out.fit_report(min_correl=0.25))
-
-which gives::
-
- [[Model]]
- voigt
- [[Fit Statistics]]
- # function evals = 21
- # data points = 401
- # variables = 4
- chi-square = 10.930
- reduced chi-square = 0.028
- [[Variables]]
- amplitude: 34.1914716 +/- 0.179468 (0.52%) (init= 43.62238)
- center: 9.24374845 +/- 0.004419 (0.05%) (init= 9.25)
- fwhm: 3.22385491 +/- 0.050974 (1.58%) == '3.6013100*sigma'
- gamma: 0.52540157 +/- 0.018579 (3.54%) (init= 0.7)
- sigma: 0.89518950 +/- 0.014154 (1.58%) (init= 0.8775)
- [[Correlations]] (unreported correlations are < 0.250)
- C(amplitude, gamma) = 0.821
-
-
-and the fit shown on the right above.
-
-Comparing the two fits with the Voigt function, we see that :math:`\chi^2`
-is definitely improved with a separately varying ``gamma`` parameter. In
-addition, the two values for ``gamma`` and ``sigma`` differ significantly
--- well outside the estimated uncertainties. Even more compelling, reduced
-:math:`\chi^2` is improved even though a fourth variable has been added to
-the fit. In the simplest statistical sense, this suggests that ``gamma``
-is a significant variable in the model.
-
-
-This example shows how easy it can be to alter and compare fitting models
-for simple problems. The example is included in the ``doc_peakmodels.py``
-file in the examples directory.
-
-
-Example 2: Fit data to a Composite Model with pre-defined models
-------------------------------------------------------------------
-
-Here, we repeat the point made at the end of the last chapter that
-instances of :class:`model.Model` class can be added together to make a
-*composite model*. By using the large number of built-in models available,
-it is therefore very simple to build models that contain multiple peaks and
-various backgrounds. An example of a simple fit to a noisy step function
-plus a constant:
-
-.. literalinclude:: ../examples/doc_stepmodel.py
-
-After constructing step-like data, we first create a :class:`StepModel`
-telling it to use the ``erf`` form (see details above), and a
-:class:`ConstantModel`. We set initial values, in one case using the data
-and :meth:`guess` method for the initial step function paramaters, and
-:meth:`make_params` arguments for the linear component.
-After making a composite model, we run :meth:`fit` and report the
-results, which give::
-
-
- [[Model]]
- Composite Model:
- step(prefix='step_',form='erf')
- linear(prefix='line_')
- [[Fit Statistics]]
- # function evals = 49
- # data points = 201
- # variables = 5
- chi-square = 633.465
- reduced chi-square = 3.232
- [[Variables]]
- line_intercept: 11.5685248 +/- 0.285611 (2.47%) (init= 10.72406)
- line_slope: 2.03270159 +/- 0.096041 (4.72%) (init= 0)
- step_amplitude: 112.270535 +/- 0.674790 (0.60%) (init= 136.3006)
- step_center: 3.12343845 +/- 0.005370 (0.17%) (init= 2.5)
- step_sigma: 0.67468813 +/- 0.011336 (1.68%) (init= 1.428571)
- [[Correlations]] (unreported correlations are < 0.100)
- C(step_amplitude, step_sigma) = 0.564
- C(line_intercept, step_center) = 0.428
- C(step_amplitude, step_center) = 0.109
-
-with a plot of
-
-.. image:: _images/models_stepfit.png
- :target: _images/models_stepfit.png
- :width: 50 %
-
-
-Example 3: Fitting Multiple Peaks -- and using Prefixes
-------------------------------------------------------------------
-
-.. _NIST StRD: http://itl.nist.gov/div898/strd/nls/nls_main.shtml
-
-As shown above, many of the models have similar parameter names. For
-composite models, this could lead to a problem of having parameters for
-different parts of the model having the same name. To overcome this, each
-:class:`model.Model` can have a ``prefix`` attribute (normally set to a blank
-string) that will be put at the beginning of each parameter name. To
-illustrate, we fit one of the classic datasets from the `NIST StRD`_ suite
-involving a decaying exponential and two gaussians.
-
-.. literalinclude:: ../examples/doc_nistgauss.py
-
-
-where we give a separate prefix to each model (they all have an
-``amplitude`` parameter). The ``prefix`` values are attached transparently
-to the models.
-
-MN----: Note that the calls to :meth:`make_param` used the bare
-name, without the prefix. We could have used them, but because we used the
-individual model ``gauss1`` and ``gauss2``, there was no need.
-
-
-Note also in the example here that we explicitly set bounds on many of the
-parameter values.
-
-The fit results printed out are::
-
- [[Model]]
- Composite Model:
- gaussian(prefix='g1_')
- gaussian(prefix='g2_')
- exponential(prefix='exp_')
- [[Fit Statistics]]
- # function evals = 55
- # data points = 250
- # variables = 8
- chi-square = 1247.528
- reduced chi-square = 5.155
- [[Variables]]
- exp_amplitude: 99.0183291 +/- 0.537487 (0.54%) (init= 162.2102)
- exp_decay: 90.9508788 +/- 1.103104 (1.21%) (init= 93.24905)
- g1_amplitude: 4257.77384 +/- 42.38354 (1.00%) (init= 2000)
- g1_center: 107.030955 +/- 0.150068 (0.14%) (init= 105)
- g1_fwhm: 39.2609205 +/- 0.377907 (0.96%) == '2.3548200*g1_sigma'
- g1_sigma: 16.6725781 +/- 0.160482 (0.96%) (init= 15)
- g2_amplitude: 2493.41747 +/- 36.16907 (1.45%) (init= 2000)
- g2_center: 153.270103 +/- 0.194665 (0.13%) (init= 155)
- g2_fwhm: 32.5128760 +/- 0.439860 (1.35%) == '2.3548200*g2_sigma'
- g2_sigma: 13.8069474 +/- 0.186791 (1.35%) (init= 15)
- [[Correlations]] (unreported correlations are < 0.500)
- C(g1_amplitude, g1_sigma) = 0.824
- C(g2_amplitude, g2_sigma) = 0.815
- C(g1_sigma, g2_center) = 0.684
- C(g1_amplitude, g2_center) = 0.648
- C(g1_center, g2_center) = 0.621
- C(g1_center, g1_sigma) = 0.507
-
-
-
-We get a very good fit to this challenging problem (described at the NIST
-site as of average difficulty, but the tests there are generally hard) by
-applying reasonable initial guesses and putting modest but explicit bounds
-on the parameter values. This fit is shown on the left:
-
-.. _figA3:
-
- .. image:: _images/models_nistgauss.png
- :target: _images/models_nistgauss.png
- :width: 48 %
- .. image:: _images/models_nistgauss2.png
- :target: _images/models_nistgauss2.png
- :width: 48 %
-
-
-One final point on setting initial values. From looking at the data
-itself, we can see the two Gaussian peaks are reasonably well separated but
-do overlap. Furthermore, we can tell that the initial guess for the
-decaying exponential component was poorly estimated because we used the
-full data range. We can simplify the initial parameter values by using
-this, and by defining an :func:`index_of` function to limit the data range.
-That is, with::
-
- def index_of(arrval, value):
- "return index of array *at or below* value "
- if value < min(arrval): return 0
- return max(np.where(arrval<=value)[0])
-
- ix1 = index_of(x, 75)
- ix2 = index_of(x, 135)
- ix3 = index_of(x, 175)
-
- exp_mod.guess(y[:ix1], x=x[:ix1])
- gauss1.guess(y[ix1:ix2], x=x[ix1:ix2])
- gauss2.guess(y[ix2:ix3], x=x[ix2:ix3])
-
-we can get a better initial estimate, and the fit converges in fewer steps,
-getting to identical values (to the precision printed out in the report),
-and without any bounds on parameters at all::
-
- [[Model]]
- Composite Model:
- gaussian(prefix='g1_')
- gaussian(prefix='g2_')
- exponential(prefix='exp_')
- [[Fit Statistics]]
- # function evals = 46
- # data points = 250
- # variables = 8
- chi-square = 1247.528
- reduced chi-square = 5.155
- [[Variables]]
- exp_amplitude: 99.0183281 +/- 0.537487 (0.54%) (init= 94.53724)
- exp_decay: 90.9508863 +/- 1.103105 (1.21%) (init= 111.1985)
- g1_amplitude: 4257.77321 +/- 42.38338 (1.00%) (init= 2126.432)
- g1_center: 107.030954 +/- 0.150067 (0.14%) (init= 106.5)
- g1_fwhm: 39.2609141 +/- 0.377905 (0.96%) == '2.3548200*g1_sigma'
- g1_sigma: 16.6725754 +/- 0.160481 (0.96%) (init= 14.5)
- g2_amplitude: 2493.41766 +/- 36.16948 (1.45%) (init= 1878.892)
- g2_center: 153.270100 +/- 0.194667 (0.13%) (init= 150)
- g2_fwhm: 32.5128777 +/- 0.439866 (1.35%) == '2.3548200*g2_sigma'
- g2_sigma: 13.8069481 +/- 0.186794 (1.35%) (init= 15)
- [[Correlations]] (unreported correlations are < 0.500)
- C(g1_amplitude, g1_sigma) = 0.824
- C(g2_amplitude, g2_sigma) = 0.815
- C(g1_sigma, g2_center) = 0.684
- C(g1_amplitude, g2_center) = 0.648
- C(g1_center, g2_center) = 0.621
- C(g1_center, g1_sigma) = 0.507
-
-
-
-This example is in the file ``doc_nistgauss2.py`` in the examples folder,
-and the fit result shown on the right above shows an improved initial
-estimate of the data.
+.. _builtin_models_chapter: + +===================================================== +Built-in Fitting Models in the :mod:`models` module +===================================================== + +.. module:: models + +Lmfit provides several builtin fitting models in the :mod:`models` module. +These pre-defined models each subclass from the :class:`model.Model` class of the +previous chapter and wrap relatively well-known functional forms, such as +Gaussians, Lorentzian, and Exponentials that are used in a wide range of +scientific domains. In fact, all the models are all based on simple, plain +python functions defined in the :mod:`lineshapes` module. In addition to +wrapping a function into a :class:`model.Model`, these models also provide a +:meth:`guess` method that is intended to give a reasonable +set of starting values from a data array that closely approximates the +data to be fit. + +As shown in the previous chapter, a key feature of the :class:`mode.Model` class +is that models can easily be combined to give a composite +:class:`model.Model`. Thus while some of the models listed here may seem pretty +trivial (notably, :class:`ConstantModel` and :class:`LinearModel`), the +main point of having these is to be able to used in composite models. For +example, a Lorentzian plus a linear background might be represented as:: + + >>> from lmfit.models import LinearModel, LorentzianModel + >>> peak = LorentzianModel() + >>> background = LinearModel() + >>> model = peak + background + +All the models listed below are one dimensional, with an independent +variable named ``x``. Many of these models represent a function with a +distinct peak, and so share common features. To maintain uniformity, +common parameter names are used whenever possible. Thus, most models have +a parameter called ``amplitude`` that represents the overall height (or +area of) a peak or function, a ``center`` parameter that represents a peak +centroid position, and a ``sigma`` parameter that gives a characteristic +width. Many peak shapes also have a parameter ``fwhm`` (constrained by +``sigma``) giving the full width at half maximum and a parameter ``height`` +(constrained by ``sigma`` and ``amplitude``) to give the maximum peak +height. + +After a list of builtin models, a few examples of their use is given. + +Peak-like models +------------------- + +There are many peak-like models available. These include +:class:`GaussianModel`, :class:`LorentzianModel`, :class:`VoigtModel` and +some less commonly used variations. The :meth:`guess` +methods for all of these make a fairly crude guess for the value of +``amplitude``, but also set a lower bound of 0 on the value of ``sigma``. + +:class:`GaussianModel` +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. class:: GaussianModel(missing=None[, prefix=''[, name=None[, **kws]]]) + +A model based on a `Gaussian or normal distribution lineshape +<http://en.wikipedia.org/wiki/Normal_distribution>`_. Parameter names: +``amplitude``, ``center``, and ``sigma``. +In addition, parameters ``fwhm`` and ``height`` are included as constraints +to report full width at half maximum and maximum peak height, respectively. + +.. math:: + + f(x; A, \mu, \sigma) = \frac{A}{\sigma\sqrt{2\pi}} e^{[{-{(x-\mu)^2}/{{2\sigma}^2}}]} + +where the parameter ``amplitude`` corresponds to :math:`A`, ``center`` to +:math:`\mu`, and ``sigma`` to :math:`\sigma`. The full width at +half maximum is :math:`2\sigma\sqrt{2\ln{2}}`, approximately +:math:`2.3548\sigma` + + +:class:`LorentzianModel` +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. class:: LorentzianModel(missing=None[, prefix=''[, name=None[, **kws]]]) + +A model based on a `Lorentzian or Cauchy-Lorentz distribution function +<http://en.wikipedia.org/wiki/Cauchy_distribution>`_. Parameter names: +``amplitude``, ``center``, and ``sigma``. +In addition, parameters ``fwhm`` and ``height`` are included as constraints +to report full width at half maximum and maximum peak height, respectively. + +.. math:: + + f(x; A, \mu, \sigma) = \frac{A}{\pi} \big[\frac{\sigma}{(x - \mu)^2 + \sigma^2}\big] + +where the parameter ``amplitude`` corresponds to :math:`A`, ``center`` to +:math:`\mu`, and ``sigma`` to :math:`\sigma`. The full width at +half maximum is :math:`2\sigma`. + + +:class:`VoigtModel` +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. class:: VoigtModel(missing=None[, prefix=''[, name=None[, **kws]]]) + +A model based on a `Voigt distribution function +<http://en.wikipedia.org/wiki/Voigt_profile>`_. Parameter names: +``amplitude``, ``center``, and ``sigma``. A ``gamma`` parameter is also +available. By default, it is constrained to have value equal to ``sigma``, +though this can be varied independently. In addition, parameters ``fwhm`` +and ``height`` are included as constraints to report full width at half +maximum and maximum peak height, respectively. The definition for the +Voigt function used here is + +.. math:: + + f(x; A, \mu, \sigma, \gamma) = \frac{A \textrm{Re}[w(z)]}{\sigma\sqrt{2 \pi}} + +where + +.. math:: + :nowrap: + + \begin{eqnarray*} + z &=& \frac{x-\mu +i\gamma}{\sigma\sqrt{2}} \\ + w(z) &=& e^{-z^2}{\operatorname{erfc}}(-iz) + \end{eqnarray*} + +and :func:`erfc` is the complimentary error function. As above, +``amplitude`` corresponds to :math:`A`, ``center`` to +:math:`\mu`, and ``sigma`` to :math:`\sigma`. The parameter ``gamma`` +corresponds to :math:`\gamma`. +If ``gamma`` is kept at the default value (constrained to ``sigma``), +the full width at half maximum is approximately :math:`3.6013\sigma`. + + +:class:`PseudoVoigtModel` +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. class:: PseudoVoigtModel(missing=None[, prefix=''[, name=None[, **kws]]]) + +a model based on a `pseudo-Voigt distribution function +<http://en.wikipedia.org/wiki/Voigt_profile#Pseudo-Voigt_Approximation>`_, +which is a weighted sum of a Gaussian and Lorentzian distribution functions +with that share values for ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) +and full width at half maximum (and so have constrained values of +``sigma`` (:math:`\sigma`). A parameter ``fraction`` (:math:`\alpha`) +controls the relative weight of the Gaussian and Lorentzian components, +giving the full definition of + +.. math:: + + f(x; A, \mu, \sigma, \alpha) = \frac{(1-\alpha)A}{\sigma_g\sqrt{2\pi}} e^{[{-{(x-\mu)^2}/{{2\sigma_g}^2}}]} + + \frac{\alpha A}{\pi} \big[\frac{\sigma}{(x - \mu)^2 + \sigma^2}\big] + +where :math:`\sigma_g = {\sigma}/{\sqrt{2\ln{2}}}` so that the full width +at half maximum of each component and of the sum is :math:`2\sigma`. The +:meth:`guess` function always sets the starting value for ``fraction`` at 0.5. + + +:class:`MoffatModel` +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. class:: MoffatModel(missing=None[, prefix=''[, name=None[, **kws]]]) + +a model based on a `Moffat distribution function +<https://en.wikipedia.org/wiki/Moffat_distribution>`_, the parameters are +``amplitude`` (:math:`A`), ``center`` (:math:`\mu`), +a width parameter ``sigma`` (:math:`\sigma`) and an exponent ``beta`` (:math:`\beta`). +For (:math:`\beta=1`) the Moffat has a Lorentzian shape. + +.. math:: + + f(x; A, \mu, \sigma, \beta) = A \big[(\frac{x-\mu}{\sigma})^2+1\big]^{-\beta} + +the full width have maximum is :math:`2\sigma\sqrt{2^{1/\beta}-1}`. +:meth:`guess` function always sets the starting value for ``beta`` to 1. + + +:class:`Pearson7Model` +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. class:: Pearson7Model(missing=None[, prefix=''[, name=None[, **kws]]]) + +A model based on a `Pearson VII distribution +<http://en.wikipedia.org/wiki/Pearson_distribution#The_Pearson_type_VII_distribution>`_. +This is a Lorenztian-like distribution function. It has the usual +parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and +``sigma`` (:math:`\sigma`), and also an ``exponent`` (:math:`m`) in + +.. math:: + + f(x; A, \mu, \sigma, m) = \frac{A}{\sigma{\beta(m-\frac{1}{2}, \frac{1}{2})}} \bigl[1 + \frac{(x-\mu)^2}{\sigma^2} \bigr]^{-m} + +where :math:`\beta` is the beta function (see :scipydoc:`special.beta` in +:mod:`scipy.special`). The :meth:`guess` function always +gives a starting value for ``exponent`` of 1.5. + +:class:`StudentsTModel` +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. class:: StudentsTModel(missing=None[, prefix=''[, name=None[, **kws]]]) + +A model based on a `Student's t distribution function +<http://en.wikipedia.org/wiki/Student%27s_t-distribution>`_, with the usual +parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and +``sigma`` (:math:`\sigma`) in + +.. math:: + + f(x; A, \mu, \sigma) = \frac{A \Gamma(\frac{\sigma+1}{2})} {\sqrt{\sigma\pi}\,\Gamma(\frac{\sigma}{2})} \Bigl[1+\frac{(x-\mu)^2}{\sigma}\Bigr]^{-\frac{\sigma+1}{2}} + + +where :math:`\Gamma(x)` is the gamma function. + + +:class:`BreitWignerModel` +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. class:: BreitWignerModel(missing=None[, prefix=''[, name=None[, **kws]]]) + +A model based on a `Breit-Wigner-Fano function +<http://en.wikipedia.org/wiki/Fano_resonance>`_. It has the usual +parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and +``sigma`` (:math:`\sigma`), plus ``q`` (:math:`q`) in + +.. math:: + + f(x; A, \mu, \sigma, q) = \frac{A (q\sigma/2 + x - \mu)^2}{(\sigma/2)^2 + (x - \mu)^2} + + +:class:`LognormalModel` +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. class:: LognormalModel(missing=None[, prefix=''[, name=None[, **kws]]]) + +A model based on the `Log-normal distribution function +<http://en.wikipedia.org/wiki/Lognormal>`_. +It has the usual parameters +``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and ``sigma`` +(:math:`\sigma`) in + +.. math:: + + f(x; A, \mu, \sigma) = \frac{A e^{-(\ln(x) - \mu)/ 2\sigma^2}}{x} + + +:class:`DampedOcsillatorModel` +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. class:: DampedOcsillatorModel(missing=None[, prefix=''[, name=None[, **kws]]]) + +A model based on the `Damped Harmonic Oscillator Amplitude +<http://en.wikipedia.org/wiki/Harmonic_oscillator#Amplitude_part>`_. +It has the usual parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and +``sigma`` (:math:`\sigma`) in + +.. math:: + + f(x; A, \mu, \sigma) = \frac{A}{\sqrt{ [1 - (x/\mu)^2]^2 + (2\sigma x/\mu)^2}} + + +:class:`ExponentialGaussianModel` +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. class:: ExponentialGaussianModel(missing=None[, prefix=''[, name=None[, **kws]]]) + +A model of an `Exponentially modified Gaussian distribution +<http://en.wikipedia.org/wiki/Exponentially_modified_Gaussian_distribution>`_. +It has the usual parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and +``sigma`` (:math:`\sigma`), and also ``gamma`` (:math:`\gamma`) in + +.. math:: + + f(x; A, \mu, \sigma, \gamma) = \frac{A\gamma}{2} + \exp\bigl[\gamma({\mu - x + \gamma\sigma^2/2})\bigr] + {\operatorname{erfc}}\Bigl(\frac{\mu + \gamma\sigma^2 - x}{\sqrt{2}\sigma}\Bigr) + + +where :func:`erfc` is the complimentary error function. + +:class:`SkewedGaussianModel` +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. class:: SkewedGaussianModel(missing=None[, prefix=''[, name=None[, **kws]]]) + +A variation of the above model, this is a `Skewed normal distribution +<http://en.wikipedia.org/wiki/Skew_normal_distribution>`_. +It has the usual parameters ``amplitude`` (:math:`A`), ``center`` (:math:`\mu`) and +``sigma`` (:math:`\sigma`), and also ``gamma`` (:math:`\gamma`) in + +.. math:: + + f(x; A, \mu, \sigma, \gamma) = \frac{A}{\sigma\sqrt{2\pi}} + e^{[{-{(x-\mu)^2}/{{2\sigma}^2}}]} \Bigl\{ 1 + + {\operatorname{erf}}\bigl[ + \frac{\gamma(x-\mu)}{\sigma\sqrt{2}} + \bigr] \Bigr\} + + +where :func:`erf` is the error function. + + +:class:`DonaichModel` +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. class:: DonaichModel(missing=None[, prefix=''[, name=None[, **kws]]]) + +A model of an `Doniach Sunjic asymmetric lineshape +<http://www.casaxps.com/help_manual/line_shapes.htm>`_, used in +photo-emission. With the usual parameters ``amplitude`` (:math:`A`), +``center`` (:math:`\mu`) and ``sigma`` (:math:`\sigma`), and also ``gamma`` +(:math:`\gamma`) in + +.. math:: + + f(x; A, \mu, \sigma, \gamma) = A\frac{\cos\bigl[\pi\gamma/2 + (1-\gamma) + \arctan{(x - \mu)}/\sigma\bigr]} {\bigr[1 + (x-\mu)/\sigma\bigl]^{(1-\gamma)/2}} + + +Linear and Polynomial Models +------------------------------------ + +These models correspond to polynomials of some degree. Of course, lmfit is +a very inefficient way to do linear regression (see :numpydoc:`polyfit` +or :scipydoc:`stats.linregress`), but these models may be useful as one +of many components of composite model. + +:class:`ConstantModel` +~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. class:: ConstantModel(missing=None[, prefix=''[, name=None[, **kws]]]) + + a class that consists of a single value, ``c``. This is constant in the + sense of having no dependence on the independent variable ``x``, not in + the sense of being non-varying. To be clear, ``c`` will be a variable + Parameter. + +:class:`LinearModel` +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. class:: LinearModel(missing=None[, prefix=''[, name=None[, **kws]]]) + + a class that gives a linear model: + +.. math:: + + f(x; m, b) = m x + b + +with parameters ``slope`` for :math:`m` and ``intercept`` for :math:`b`. + + +:class:`QuadraticModel` +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. class:: QuadraticModel(missing=None[, prefix=''[, name=None[, **kws]]]) + + + a class that gives a quadratic model: + +.. math:: + + f(x; a, b, c) = a x^2 + b x + c + +with parameters ``a``, ``b``, and ``c``. + + +:class:`ParabolicModel` +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. class:: ParabolicModel(missing=None[, prefix=''[, name=None[, **kws]]]) + + same as :class:`QuadraticModel`. + + +:class:`PolynomialModel` +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + + +.. class:: PolynomialModel(degree, missing=None[, prefix=''[, name=None[, **kws]]]) + + a class that gives a polynomial model up to ``degree`` (with maximum + value of 7). + +.. math:: + + f(x; c_0, c_1, \ldots, c_7) = \sum_{i=0, 7} c_i x^i + +with parameters ``c0``, ``c1``, ..., ``c7``. The supplied ``degree`` +will specify how many of these are actual variable parameters. This uses +:numpydoc:`polyval` for its calculation of the polynomial. + + + +Step-like models +----------------------------------------------- + +Two models represent step-like functions, and share many characteristics. + +:class:`StepModel` +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. class:: StepModel(form='linear'[, missing=None[, prefix=''[, name=None[, **kws]]]]) + +A model based on a Step function, with four choices for functional form. +The step function starts with a value 0, and ends with a value of :math:`A` +(``amplitude``), rising to :math:`A/2` at :math:`\mu` (``center``), +with :math:`\sigma` (``sigma``) setting the characteristic width. The +supported functional forms are ``linear`` (the default), ``atan`` or +``arctan`` for an arc-tangent function, ``erf`` for an error function, or +``logistic`` for a `logistic function <http://en.wikipedia.org/wiki/Logistic_function>`_. +The forms are + +.. math:: + :nowrap: + + \begin{eqnarray*} + & f(x; A, \mu, \sigma, {\mathrm{form={}'linear{}'}}) & = A \min{[1, \max{(0, \alpha)}]} \\ + & f(x; A, \mu, \sigma, {\mathrm{form={}'arctan{}'}}) & = A [1/2 + \arctan{(\alpha)}/{\pi}] \\ + & f(x; A, \mu, \sigma, {\mathrm{form={}'erf{}'}}) & = A [1 + {\operatorname{erf}}(\alpha)]/2 \\ + & f(x; A, \mu, \sigma, {\mathrm{form={}'logistic{}'}})& = A [1 - \frac{1}{1 + e^{\alpha}} ] + \end{eqnarray*} + +where :math:`\alpha = (x - \mu)/{\sigma}`. + +:class:`RectangleModel` +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + + +.. class:: RectangleModel(form='linear'[, missing=None[, prefix=''[, name=None[, **kws]]]]) + +A model based on a Step-up and Step-down function of the same form. The +same choices for functional form as for :class:`StepModel` are supported, +with ``linear`` as the default. The function starts with a value 0, and +ends with a value of :math:`A` (``amplitude``), rising to :math:`A/2` at +:math:`\mu_1` (``center1``), with :math:`\sigma_1` (``sigma1``) setting the +characteristic width. It drops to rising to :math:`A/2` at :math:`\mu_2` +(``center2``), with characteristic width :math:`\sigma_2` (``sigma2``). + +.. math:: + :nowrap: + + \begin{eqnarray*} + &f(x; A, \mu, \sigma, {\mathrm{form={}'linear{}'}}) &= A \{ \min{[1, \max{(0, \alpha_1)}]} + \min{[-1, \max{(0, \alpha_2)}]} \} \\ + &f(x; A, \mu, \sigma, {\mathrm{form={}'arctan{}'}}) &= A [\arctan{(\alpha_1)} + \arctan{(\alpha_2)}]/{\pi} \\ + &f(x; A, \mu, \sigma, {\mathrm{form={}'erf{}'}}) &= A [{\operatorname{erf}}(\alpha_1) + {\operatorname{erf}}(\alpha_2)]/2 \\ + &f(x; A, \mu, \sigma, {\mathrm{form={}'logistic{}'}}) &= A [1 - \frac{1}{1 + e^{\alpha_1}} - \frac{1}{1 + e^{\alpha_2}} ] + \end{eqnarray*} + + +where :math:`\alpha_1 = (x - \mu_1)/{\sigma_1}` and :math:`\alpha_2 = -(x - \mu_2)/{\sigma_2}`. + + +Exponential and Power law models +----------------------------------------------- + +:class:`ExponentialModel` +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. class:: ExponentialModel(missing=None[, prefix=''[, name=None[, **kws]]]) + +A model based on an `exponential decay function +<http://en.wikipedia.org/wiki/Exponential_decay>`_. With parameters named +``amplitude`` (:math:`A`), and ``decay`` (:math:`\tau`), this has the form: + +.. math:: + + f(x; A, \tau) = A e^{-x/\tau} + + +:class:`PowerLawModel` +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. class:: PowerLawModel(missing=None[, prefix=''[, name=None[, **kws]]]) + +A model based on a `Power Law <http://en.wikipedia.org/wiki/Power_law>`_. +With parameters +named ``amplitude`` (:math:`A`), and ``exponent`` (:math:`k`), this has the +form: + +.. math:: + + f(x; A, k) = A x^k + + +User-defined Models +---------------------------- + +.. _asteval: http://newville.github.io/asteval/ + +As shown in the previous chapter (:ref:`model_chapter`), it is fairly +straightforward to build fitting models from parametrized python functions. +The number of model classes listed so far in the present chapter should +make it clear that this process is not too difficult. Still, it is +sometimes desirable to build models from a user-supplied function. This +may be especially true if model-building is built-in to some larger library +or application for fitting in which the user may not be able to easily +build and use a new model from python code. + + +The :class:`ExpressionModel` allows a model to be built from a +user-supplied expression. This uses the `asteval`_ module also used for +mathematical constraints as discussed in :ref:`constraints_chapter`. + + +:class:`ExpressionModel` +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. class:: ExpressionModel(expr, independent_vars=None, init_script=None, **kws) + + A model using the user-supplied mathematical expression, which can be nearly any valid Python expresion. + + :param expr: expression use to build model + :type expr: string + :param independent_vars: list of argument names in expression that are independent variables. + :type independent_vars: ``None`` (default) or list of strings for independent variables. + :param init_script: python script to run before parsing and evaluating expression. + :type init_script: ``None`` (default) or string + +with other parameters passed to :class:`model.Model`, with the notable +exception that :class:`ExpressionModel` does **not** support the `prefix` argument. + +Since the point of this model is that an arbitrary expression will be +supplied, the determination of what are the parameter names for the model +happens when the model is created. To do this, the expression is parsed, +and all symbol names are found. Names that are already known (there are +over 500 function and value names in the asteval namespace, including most +python builtins, more than 200 functions inherited from numpy, and more +than 20 common lineshapes defined in the :mod:`lineshapes` module) are not +converted to parameters. Unrecognized name are expected to be names either +of parameters or independent variables. If `independent_vars` is the +default value of ``None``, and if the expression contains a variable named +`x`, that will be used as the independent variable. Otherwise, +`independent_vars` must be given. + +For example, if one creates an :class:`ExpressionModel` as:: + + >>> mod = ExpressionModel('off + amp * exp(-x/x0) * sin(x*phase)') + +The name `exp` will be recognized as the exponent function, so the model +will be interpreted to have parameters named `off`, `amp`, `x0` and +`phase`. In addition, `x` will be assumed to be the sole independent variable. +In general, there is no obvious way to set default parameter values or +parameter hints for bounds, so this will have to be handled explicitly. + +To evaluate this model, you might do the following:: + + >>> x = numpy.linspace(0, 10, 501) + >>> params = mod.make_params(off=0.25, amp=1.0, x0=2.0, phase=0.04) + >>> y = mod.eval(params, x=x) + + +While many custom models can be built with a single line expression +(especially since the names of the lineshapes like `gaussian`, `lorentzian` +and so on, as well as many numpy functions, are available), more complex +models will inevitably require multiple line functions. You can include +such Python code with the `init_script` argument. The text of this script +is evaluated when the model is initialized (and before the actual +expression is parsed), so that you can define functions to be used +in your expression. + +As a probably unphysical example, to make a model that is the derivative of +a Gaussian function times the logarithm of a Lorentzian function you may +could to define this in a script:: + + >>> script = """ + def mycurve(x, amp, cen, sig): + loren = lorentzian(x, amplitude=amp, center=cen, sigma=sig) + gauss = gaussian(x, amplitude=amp, center=cen, sigma=sig) + return log(loren)*gradient(gauss)/gradient(x) + """ + +and then use this with :class:`ExpressionModel` as:: + + >>> mod = ExpressionModel('mycurve(x, height, mid, wid)', + init_script=script, + independent_vars=['x']) + +As above, this will interpret the parameter names to be `height`, `mid`, +and `wid`, and build a model that can be used to fit data. + + + +Example 1: Fit Peaked data to Gaussian, Lorentzian, and Voigt profiles +------------------------------------------------------------------------ + +Here, we will fit data to three similar line shapes, in order to decide which +might be the better model. We will start with a Gaussian profile, as in +the previous chapter, but use the built-in :class:`GaussianModel` instead +of writing one ourselves. This is a slightly different version rom the +one in previous example in that the parameter names are different, and have +built-in default values. We'll simply use:: + + from numpy import loadtxt + from lmfit.models import GaussianModel + + data = loadtxt('test_peak.dat') + x = data[:, 0] + y = data[:, 1] + + mod = GaussianModel() + + pars = mod.guess(y, x=x) + out = mod.fit(y, pars, x=x) + print(out.fit_report(min_correl=0.25)) + + +which prints out the results:: + + [[Model]] + gaussian + [[Fit Statistics]] + # function evals = 23 + # data points = 401 + # variables = 3 + chi-square = 29.994 + reduced chi-square = 0.075 + Akaike info crit = -1030.763 + Bayesian info crit = -1018.781 + [[Variables]] + sigma: 1.23218319 +/- 0.007374 (0.60%) (init= 1.35) + fwhm: 2.90156963 +/- 0.017366 (0.60%) == '2.3548200*sigma' + height: 9.81457973 +/- 0.050872 (0.52%) == '0.3989423*amplitude/sigma' + center: 9.24277049 +/- 0.007374 (0.08%) (init= 9.25) + amplitude: 30.3135571 +/- 0.157126 (0.52%) (init= 29.08159) + [[Correlations]] (unreported correlations are < 0.250) + C(sigma, amplitude) = 0.577 + +We see a few interesting differences from the results of the previous +chapter. First, the parameter names are longer. Second, there are ``fwhm`` +and ``height`` parameters, to give the full width at half maximum and +maximum peak height. And third, the automated initial guesses are pretty +good. A plot of the fit: + +.. _figA1: + + .. image:: _images/models_peak1.png + :target: _images/models_peak1.png + :width: 48 % + .. image:: _images/models_peak2.png + :target: _images/models_peak2.png + :width: 48 % + + Fit to peak with Gaussian (left) and Lorentzian (right) models. + +shows a decent match to the data -- the fit worked with no explicit setting +of initial parameter values. Looking more closing, the fit is not perfect, +especially in the tails of the peak, suggesting that a different peak +shape, with longer tails, should be used. Perhaps a Lorentzian would be +better? To do this, we simply replace ``GaussianModel`` with +``LorentzianModel`` to get a :class:`LorentzianModel`:: + + from lmfit.models import LorentzianModel + mod = LorentzianModel() + +with the rest of the script as above. Perhaps predictably, the first thing +we try gives results that are worse:: + + [[Model]] + Model(lorentzian) + [[Fit Statistics]] + # function evals = 27 + # data points = 401 + # variables = 3 + chi-square = 53.754 + reduced chi-square = 0.135 + Akaike info crit = -796.819 + Bayesian info crit = -784.837 + [[Variables]] + sigma: 1.15484517 +/- 0.013156 (1.14%) (init= 1.35) + fwhm: 2.30969034 +/- 0.026312 (1.14%) == '2.0000000*sigma' + height: 10.7420881 +/- 0.086336 (0.80%) == + '0.3183099*amplitude/sigm a' + center: 9.24438944 +/- 0.009275 (0.10%) (init= 9.25) + amplitude: 38.9728645 +/- 0.313857 (0.81%) (init= 36.35199) + [[Correlations]] (unreported correlations are < 0.250) + C(sigma, amplitude) = 0.709 + + +with the plot shown on the right in the figure above. The tails are now +too big, and the value for :math:`\chi^2` almost doubled. A Voigt model +does a better job. Using :class:`VoigtModel`, this is as simple as using:: + + from lmfit.models import VoigtModel + mod = VoigtModel() + +with all the rest of the script as above. This gives:: + + [[Model]] + Model(voigt) + [[Fit Statistics]] + # function evals = 19 + # data points = 401 + # variables = 3 + chi-square = 14.545 + reduced chi-square = 0.037 + Akaike info crit = -1320.995 + Bayesian info crit = -1309.013 + [[Variables]] + sigma: 0.73015574 +/- 0.003684 (0.50%) (init= 0.8775) + gamma: 0.73015574 +/- 0.003684 (0.50%) == 'sigma' + fwhm: 2.62951718 +/- 0.013269 (0.50%) == '3.6013100*sigma' + height: 19.5360268 +/- 0.075691 (0.39%) == '0.3989423*amplitude/sigm a' + center: 9.24411142 +/- 0.005054 (0.05%) (init= 9.25) + amplitude: 35.7554017 +/- 0.138614 (0.39%) (init= 43.62238) + [[Correlations]] (unreported correlations are < 0.250) + C(sigma, amplitude) = 0.651 + + +which has a much better value for :math:`\chi^2` and an obviously better +match to the data as seen in the figure below (left). + +.. _figA2: + + .. image:: _images/models_peak3.png + :target: _images/models_peak3.png + :width: 48 % + .. image:: _images/models_peak4.png + :target: _images/models_peak4.png + :width: 48 % + + Fit to peak with Voigt model (left) and Voigt model with ``gamma`` + varying independently of ``sigma`` (right). + +Can we do better? The Voigt function has a :math:`\gamma` parameter +(``gamma``) that can be distinct from ``sigma``. The default behavior used +above constrains ``gamma`` to have exactly the same value as ``sigma``. If +we allow these to vary separately, does the fit improve? To do this, we +have to change the ``gamma`` parameter from a constrained expression and +give it a starting value using something like:: + + mod = VoigtModel() + pars = mod.guess(y, x=x) + pars['gamma'].set(value=0.7, vary=True, expr='') + + +which gives:: + + [[Model]] + Model(voigt) + [[Fit Statistics]] + # function evals = 23 + # data points = 401 + # variables = 4 + chi-square = 10.930 + reduced chi-square = 0.028 + Akaike info crit = -1432.556 + Bayesian info crit = -1416.580 + [[Variables]] + sigma: 0.89518950 +/- 0.014154 (1.58%) (init= 0.8775) + gamma: 0.52540156 +/- 0.018579 (3.54%) (init= 0.7) + fwhm: 3.22385492 +/- 0.050974 (1.58%) == '3.6013100*sigma' + height: 15.2374711 +/- 0.299235 (1.96%) == + '0.3989423*amplitude/sigm a' + center: 9.24374845 +/- 0.004419 (0.05%) (init= 9.25) + amplitude: 34.1914716 +/- 0.179468 (0.52%) (init= 43.62238) + [[Correlations]] (unreported correlations are < 0.250) + C(sigma, gamma) = -0.928 + C(gamma, amplitude) = 0.821 + C(sigma, amplitude) = -0.651 + +and the fit shown on the right above. + +Comparing the two fits with the Voigt function, we see that :math:`\chi^2` +is definitely improved with a separately varying ``gamma`` parameter. In +addition, the two values for ``gamma`` and ``sigma`` differ significantly +-- well outside the estimated uncertainties. More compelling, reduced +:math:`\chi^2` is improved even though a fourth variable has been added to +the fit. In the simplest statistical sense, this suggests that ``gamma`` +is a significant variable in the model. In addition, we can use both the +Akaike or Bayesian Information Criteria (see +:ref:`information_criteria_label`) to assess how likely the model with +variable ``gamma`` is to explain the data than the model with ``gamma`` +fixed to the value of ``sigma``. According to theory, +:math:`\exp(-(\rm{AIC1}-\rm{AIC0})/2)` gives the probably that a model with +AIC` is more likely than a model with AIC0. For the two models here, with +AIC values of -1432 and -1321 (Note: if we had more carefully set the value +for ``weights`` based on the noise in the data, these values might be +positive, but there difference would be roughly the same), this says that +the model with ``gamma`` fixed to ``sigma`` has a probably less than 1.e-25 +of being the better model. + + +Example 2: Fit data to a Composite Model with pre-defined models +------------------------------------------------------------------ + +Here, we repeat the point made at the end of the last chapter that +instances of :class:`model.Model` class can be added together to make a +*composite model*. By using the large number of built-in models available, +it is therefore very simple to build models that contain multiple peaks and +various backgrounds. An example of a simple fit to a noisy step function +plus a constant: + +.. literalinclude:: ../examples/doc_stepmodel.py + +After constructing step-like data, we first create a :class:`StepModel` +telling it to use the ``erf`` form (see details above), and a +:class:`ConstantModel`. We set initial values, in one case using the data +and :meth:`guess` method for the initial step function paramaters, and +:meth:`make_params` arguments for the linear component. +After making a composite model, we run :meth:`fit` and report the +results, which gives:: + + [[Model]] + [[Model]] + (Model(step, prefix='step_', form='erf') + Model(linear, prefix='line_')) + [[Fit Statistics]] + # function evals = 51 + # data points = 201 + # variables = 5 + chi-square = 648.584 + reduced chi-square = 3.309 + Akaike info crit = 250.532 + Bayesian info crit = 267.048 + [[Variables]] + line_slope: 2.06986083 +/- 0.097005 (4.69%) (init= 0) + line_intercept: 11.7526825 +/- 0.288725 (2.46%) (init= 10.7017) + step_center: 3.12329688 +/- 0.005441 (0.17%) (init= 2.5) + step_sigma: 0.67050317 +/- 0.011480 (1.71%) (init= 1.428571) + step_amplitude: 111.673928 +/- 0.681024 (0.61%) (init= 134.6809) + [[Correlations]] (unreported correlations are < 0.100) + C(line_slope, step_amplitude) = -0.878 + C(step_sigma, step_amplitude) = 0.563 + C(line_slope, step_sigma) = -0.455 + C(line_intercept, step_center) = 0.426 + C(line_slope, line_intercept) = -0.307 + C(line_slope, step_center) = -0.234 + C(line_intercept, step_sigma) = -0.139 + C(line_intercept, step_amplitude) = -0.122 + C(step_center, step_amplitude) = 0.108 + +with a plot of + +.. image:: _images/models_stepfit.png + :target: _images/models_stepfit.png + :width: 50 % + + +Example 3: Fitting Multiple Peaks -- and using Prefixes +------------------------------------------------------------------ + +.. _NIST StRD: http://itl.nist.gov/div898/strd/nls/nls_main.shtml + +As shown above, many of the models have similar parameter names. For +composite models, this could lead to a problem of having parameters for +different parts of the model having the same name. To overcome this, each +:class:`model.Model` can have a ``prefix`` attribute (normally set to a blank +string) that will be put at the beginning of each parameter name. To +illustrate, we fit one of the classic datasets from the `NIST StRD`_ suite +involving a decaying exponential and two gaussians. + +.. literalinclude:: ../examples/doc_nistgauss.py + +where we give a separate prefix to each model (they all have an +``amplitude`` parameter). The ``prefix`` values are attached transparently +to the models. + +Note that the calls to :meth:`make_param` used the bare name, without the +prefix. We could have used the prefixes, but because we used the +individual model ``gauss1`` and ``gauss2``, there was no need. + +Note also in the example here that we explicitly set bounds on many of the +parameter values. + +The fit results printed out are:: + + [[Model]] + ((Model(gaussian, prefix='g1_') + Model(gaussian, prefix='g2_')) + Model(exponential, prefix='exp_')) + [[Fit Statistics]] + # function evals = 66 + # data points = 250 + # variables = 8 + chi-square = 1247.528 + reduced chi-square = 5.155 + Akaike info crit = 425.995 + Bayesian info crit = 454.167 + [[Variables]] + exp_amplitude: 99.0183282 +/- 0.537487 (0.54%) (init= 162.2102) + exp_decay: 90.9508861 +/- 1.103105 (1.21%) (init= 93.24905) + g1_amplitude: 4257.77318 +/- 42.38336 (1.00%) (init= 2000) + g1_sigma: 16.6725753 +/- 0.160481 (0.96%) (init= 15) + g1_center: 107.030954 +/- 0.150067 (0.14%) (init= 105) + g1_fwhm: 39.2609137 +/- 0.377905 (0.96%) == '2.3548200*g1_sigma' + g1_height: 101.880231 +/- 0.592170 (0.58%) == + '0.3989423*g1_amplitude/g1_ sigma' + g2_amplitude: 2493.41770 +/- 36.16947 (1.45%) (init= 2000) + g2_sigma: 13.8069484 +/- 0.186794 (1.35%) (init= 15) + g2_center: 153.270100 +/- 0.194667 (0.13%) (init= 155) + g2_fwhm: 32.5128783 +/- 0.439866 (1.35%) == '2.3548200*g2_sigma' + g2_height: 72.0455934 +/- 0.617220 (0.86%) == + '0.3989423*g2_amplitude/g2_ sigma' + [[Correlations]] (unreported correlations are < 0.500) + C(g1_amplitude, g1_sigma) = 0.824 + C(g2_amplitude, g2_sigma) = 0.815 + C(exp_amplitude, exp_decay) = -0.695 + C(g1_sigma, g2_center) = 0.684 + C(g1_center, g2_amplitude) = -0.669 + C(g1_center, g2_sigma) = -0.652 + C(g1_amplitude, g2_center) = 0.648 + C(g1_center, g2_center) = 0.621 + C(g1_sigma, g1_center) = 0.507 + C(exp_decay, g1_amplitude) = -0.507 + + +We get a very good fit to this problem (described at the NIST site as of +average difficulty, but the tests there are generally deliberately challenging) by +applying reasonable initial guesses and putting modest but explicit bounds +on the parameter values. This fit is shown on the left: + +.. _figA3: + + .. image:: _images/models_nistgauss.png + :target: _images/models_nistgauss.png + :width: 48 % + .. image:: _images/models_nistgauss2.png + :target: _images/models_nistgauss2.png + :width: 48 % + + +One final point on setting initial values. From looking at the data +itself, we can see the two Gaussian peaks are reasonably well separated but +do overlap. Furthermore, we can tell that the initial guess for the +decaying exponential component was poorly estimated because we used the +full data range. We can simplify the initial parameter values by using +this, and by defining an :func:`index_of` function to limit the data range. +That is, with:: + + def index_of(arrval, value): + "return index of array *at or below* value " + if value < min(arrval): return 0 + return max(np.where(arrval<=value)[0]) + + ix1 = index_of(x, 75) + ix2 = index_of(x, 135) + ix3 = index_of(x, 175) + + exp_mod.guess(y[:ix1], x=x[:ix1]) + gauss1.guess(y[ix1:ix2], x=x[ix1:ix2]) + gauss2.guess(y[ix2:ix3], x=x[ix2:ix3]) + +we can get a better initial estimate. The fit converges to the same answer, +giving to identical values (to the precision printed out in the report), +but in few steps, and without any bounds on parameters at all:: + + [[Model]] + ((Model(gaussian, prefix='g1_') + Model(gaussian, prefix='g2_')) + Model(exponential, prefix='exp_')) + [[Fit Statistics]] + # function evals = 48 + # data points = 250 + # variables = 8 + chi-square = 1247.528 + reduced chi-square = 5.155 + Akaike info crit = 425.995 + Bayesian info crit = 454.167 + [[Variables]] + exp_amplitude: 99.0183281 +/- 0.537487 (0.54%) (init= 94.53724) + exp_decay: 90.9508862 +/- 1.103105 (1.21%) (init= 111.1985) + g1_amplitude: 4257.77322 +/- 42.38338 (1.00%) (init= 2126.432) + g1_sigma: 16.6725754 +/- 0.160481 (0.96%) (init= 14.5) + g1_center: 107.030954 +/- 0.150067 (0.14%) (init= 106.5) + g1_fwhm: 39.2609141 +/- 0.377905 (0.96%) == '2.3548200*g1_sigma' + g1_height: 101.880231 +/- 0.592171 (0.58%) == + '0.3989423*g1_amplitude/g1_ sigma' + g2_amplitude: 2493.41766 +/- 36.16947 (1.45%) (init= 1878.892) + g2_sigma: 13.8069481 +/- 0.186794 (1.35%) (init= 15) + g2_center: 153.270100 +/- 0.194667 (0.13%) (init= 150) + g2_fwhm: 32.5128777 +/- 0.439866 (1.35%) == '2.3548200*g2_sigma' + g2_height: 72.0455935 +/- 0.617221 (0.86%) == + '0.3989423*g2_amplitude/g2_ sigma' + [[Correlations]] (unreported correlations are < 0.500) + C(g1_amplitude, g1_sigma) = 0.824 + C(g2_amplitude, g2_sigma) = 0.815 + C(exp_amplitude, exp_decay) = -0.695 + C(g1_sigma, g2_center) = 0.684 + C(g1_center, g2_amplitude) = -0.669 + C(g1_center, g2_sigma) = -0.652 + C(g1_amplitude, g2_center) = 0.648 + C(g1_center, g2_center) = 0.621 + C(g1_sigma, g1_center) = 0.507 + C(exp_decay, g1_amplitude) = -0.507 + + +This script is in the file ``doc_nistgauss2.py`` in the examples folder, +and the fit result shown on the right above shows an improved initial +estimate of the data. diff --git a/doc/conf.py b/doc/conf.py index e452697..490a01d 100644 --- a/doc/conf.py +++ b/doc/conf.py @@ -1,176 +1,187 @@ -# -*- coding: utf-8 -*-
-#
-# lmfit documentation build configuration file
-#
-# This file is execfile()d with the current directory set to its containing dir.
-#
-# Note that not all possible configuration values are present in this
-# autogenerated file.
-#
-# All configuration values have a default; values that are commented out
-# serve to show the default.
-
-import sys, os
-
-# If extensions (or modules to document with autodoc) are in another directory,
-# add these directories to sys.path here. If the directory is relative to the
-# documentation root, use os.path.abspath to make it absolute, like shown here.
-sys.path.append(os.path.abspath(os.path.join('..', 'lmfit')))
-sys.path.append(os.path.abspath(os.path.join('.', 'sphinx')))
-sys.path.append(os.path.abspath(os.path.join('.')))
-# -- General configuration -----------------------------------------------------
-
-# Add any Sphinx extension module names here, as strings. They can be extensions
-# coming with Sphinx (named 'sphinx.ext.*') or your custom ones.
-from extensions import extensions
-
-try:
- import IPython.sphinxext.ipython_directive
- extensions.extend(['IPython.sphinxext.ipython_directive',
- 'IPython.sphinxext.ipython_console_highlighting'])
-except ImportError:
- pass
-
-
-intersphinx_mapping = {'py': ('http://docs.python.org/2', None),
- 'numpy': ('http://docs.scipy.org/doc/numpy/', None),
- 'scipy': ('http://docs.scipy.org/doc/scipy/reference/', None),
- }
-
-intersphinx_cache_limit = 10
-
-# Add any paths that contain templates here, relative to this directory.
-templates_path = ['_templates']
-
-# The suffix of source filenames.
-source_suffix = '.rst'
-
-# The encoding of source files.
-#source_encoding = 'utf-8'
-
-# The master toctree document.
-master_doc = 'index'
-
-# General information about the project.
-project = u'lmfit'
-copyright = u'2014, Matthew Newville, The University of Chicago, Till Stensitzki, Freie Universitat Berlin'
-
-# The version info for the project you're documenting, acts as replacement for
-# |version| and |release|, also used in various other places throughout the
-# built documents.
-#
-# The short X.Y version.
-try:
- import lmfit
- release = lmfit.__version__
-# The full version, including alpha/beta/rc tags.
-except ImportError:
- release = 'latest'
-
-# The language for content autogenerated by Sphinx. Refer to documentation
-# for a list of supported languages.
-#language = None
-
-# There are two options for replacing |today|: either, you set today to some
-# non-false value, then it is used:
-#today = ''
-# Else, today_fmt is used as the format for a strftime call.
-#today_fmt = '%B %d, %Y'
-
-# List of documents that shouldn't be included in the build.
-#unused_docs = []
-
-# List of directories, relative to source directory, that shouldn't be searched
-# for source files.
-exclude_trees = ['_build']
-
-# The reST default role (used for this markup: `text`) to use for all documents.
-#default_role = None
-
-# If true, '()' will be appended to :func: etc. cross-reference text.
-add_function_parentheses = True
-
-# If true, the current module name will be prepended to all description
-# unit titles (such as .. function::).
-add_module_names = False
-
-# If true, sectionauthor and moduleauthor directives will be shown in the
-# output. They are ignored by default.
-#show_authors = False
-
-# The name of the Pygments (syntax highlighting) style to use.
-pygments_style = 'sphinx'
-
-# A list of ignored prefixes for module index sorting.
-#modindex_common_prefix = []
-
-
-# -- Options for HTML output ---------------------------------------------------
-
-html_theme_path = ['sphinx/theme']
-html_theme = 'lmfitdoc'
-
-# Add any paths that contain custom themes here, relative to this directory.
-#html_theme_path = []
-
-# The name for this set of Sphinx documents. If None, it defaults to
-# "<project> v<release> documentation".
-#html_title = None
-html_title = 'Non-Linear Least-Squares Minimization and Curve-Fitting for Python'
-
-# A shorter title for the navigation bar. Default is the same as html_title.
-html_short_title = 'Minimization and Curve-Fitting for Python'
-
-# The name of an image file (relative to this directory) to place at the top
-# of the sidebar.
-#html_logo = None
-
-# The name of an image file (within the static path) to use as favicon of the
-# docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32
-# pixels large.
-#html_favicon = None
-
-# Add any paths that contain custom static files (such as style sheets) here,
-# relative to this directory. They are copied after the builtin static files,
-# so a file named "default.css" will overwrite the builtin "default.css".
-html_static_path = ['_static']
-
-# If not '', a 'Last updated on:' timestamp is inserted at every page bottom,
-# using the given strftime format.
-#html_last_updated_fmt = '%b %d, %Y'
-
-# If true, SmartyPants will be used to convert quotes and dashes to
-# typographically correct entities.
-html_use_smartypants = True
-
-# Custom sidebar templates, maps document names to template names.
-html_sidebars = {'index': ['indexsidebar.html','searchbox.html']}
-
-html_domain_indices = False
-html_use_index = True
-#html_split_index = False
-
-# If true, links to the reST sources are added to the pages.
-html_show_sourcelink = True
-
-# If true, an OpenSearch description file will be output, and all pages will
-# contain a <link> tag referring to it. The value of this option must be the
-# base URL from which the finished HTML is served.
-#html_use_opensearch = ''
-
-# If nonempty, this is the file name suffix for HTML files (e.g. ".xhtml").
-#html_file_suffix = ''
-
-# Output file base name for HTML help builder.
-htmlhelp_basename = 'lmfitdoc'
-
-# -- Options for LaTeX output --------------------------------------------------
-
-# Grouping the document tree into LaTeX files. List of tuples
-# (source start file, target name, title, author, documentclass [howto/manual]).
-latex_documents = [
- ('index', 'lmfit.tex',
- 'Non-Linear Least-Squares Minimization and Curve-Fitting for Python',
- 'Matthew Newville, Till Stensitzki, and others', 'manual'),
-]
-
+# -*- coding: utf-8 -*- +# +# lmfit documentation build configuration file +# +# This file is execfile()d with the current directory set to its containing dir. +# +# Note that not all possible configuration values are present in this +# autogenerated file. +# +# All configuration values have a default; values that are commented out +# serve to show the default. + +import sys, os + +# If extensions (or modules to document with autodoc) are in another directory, +# add these directories to sys.path here. If the directory is relative to the +# documentation root, use os.path.abspath to make it absolute, like shown here. +sys.path.append(os.path.abspath(os.path.join('..', 'lmfit'))) +sys.path.append(os.path.abspath(os.path.join('.', 'sphinx'))) +sys.path.append(os.path.abspath(os.path.join('.'))) +# -- General configuration ----------------------------------------------------- + +# Add any Sphinx extension module names here, as strings. They can be extensions +# coming with Sphinx (named 'sphinx.ext.*') or your custom ones. +from extensions import extensions + +extensions = [ + 'sphinx.ext.extlinks', + 'sphinx.ext.autodoc', + 'sphinx.ext.napoleon', + 'sphinx.ext.mathjax', + ] + +try: + import IPython.sphinxext.ipython_directive + extensions.extend(['IPython.sphinxext.ipython_directive', + 'IPython.sphinxext.ipython_console_highlighting']) +except ImportError: + pass + +intersphinx_mapping = {'py': ('http://docs.python.org/2', None), + 'numpy': ('http://docs.scipy.org/doc/numpy/', None), + 'scipy': ('http://docs.scipy.org/doc/scipy/reference/', None), + } + +## intersphinx_cache_limit = 10 + +extlinks = { + 'scipydoc' : ('http://docs.scipy.org/doc/scipy/reference/generated/%s.html', ''), + 'numpydoc' : ('http://docs.scipy.org/doc/numpy/reference/generated/numpy.%s.html', ''), + } + +# Add any paths that contain templates here, relative to this directory. +templates_path = ['_templates'] + +# The suffix of source filenames. +source_suffix = '.rst' + +# The encoding of source files. +#source_encoding = 'utf-8' + +# The master toctree document. +master_doc = 'index' + +# General information about the project. +project = u'lmfit' +copyright = u'2014, Matthew Newville, The University of Chicago, Till Stensitzki, Freie Universitat Berlin' + +# The version info for the project you're documenting, acts as replacement for +# |version| and |release|, also used in various other places throughout the +# built documents. +# +# The short X.Y version. +sys.path.insert(0, os.path.abspath('../')) +try: + import lmfit + release = lmfit.__version__ +# The full version, including alpha/beta/rc tags. +except ImportError: + release = 'latest' + +# The language for content autogenerated by Sphinx. Refer to documentation +# for a list of supported languages. +#language = None + +# There are two options for replacing |today|: either, you set today to some +# non-false value, then it is used: +#today = '' +# Else, today_fmt is used as the format for a strftime call. +#today_fmt = '%B %d, %Y' + +# List of documents that shouldn't be included in the build. +#unused_docs = [] + +# List of directories, relative to source directory, that shouldn't be searched +# for source files. +exclude_trees = ['_build'] + +# The reST default role (used for this markup: `text`) to use for all documents. +#default_role = None + +# If true, '()' will be appended to :func: etc. cross-reference text. +add_function_parentheses = True + +# If true, the current module name will be prepended to all description +# unit titles (such as .. function::). +add_module_names = False + +# If true, sectionauthor and moduleauthor directives will be shown in the +# output. They are ignored by default. +#show_authors = False + +# The name of the Pygments (syntax highlighting) style to use. +pygments_style = 'sphinx' + +# A list of ignored prefixes for module index sorting. +#modindex_common_prefix = [] + + +# -- Options for HTML output --------------------------------------------------- + +html_theme_path = ['sphinx/theme'] +html_theme = 'lmfitdoc' + +# Add any paths that contain custom themes here, relative to this directory. +#html_theme_path = [] + +# The name for this set of Sphinx documents. If None, it defaults to +# "<project> v<release> documentation". +#html_title = None +html_title = 'Non-Linear Least-Squares Minimization and Curve-Fitting for Python' + +# A shorter title for the navigation bar. Default is the same as html_title. +html_short_title = 'Minimization and Curve-Fitting for Python' + +# The name of an image file (relative to this directory) to place at the top +# of the sidebar. +#html_logo = None + +# The name of an image file (within the static path) to use as favicon of the +# docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32 +# pixels large. +#html_favicon = None + +# Add any paths that contain custom static files (such as style sheets) here, +# relative to this directory. They are copied after the builtin static files, +# so a file named "default.css" will overwrite the builtin "default.css". +html_static_path = ['_static'] + +# If not '', a 'Last updated on:' timestamp is inserted at every page bottom, +# using the given strftime format. +#html_last_updated_fmt = '%b %d, %Y' + +# If true, SmartyPants will be used to convert quotes and dashes to +# typographically correct entities. +html_use_smartypants = True + +# Custom sidebar templates, maps document names to template names. +html_sidebars = {'index': ['indexsidebar.html','searchbox.html']} + +html_domain_indices = False +html_use_index = True +#html_split_index = False + +# If true, links to the reST sources are added to the pages. +html_show_sourcelink = True + +# If true, an OpenSearch description file will be output, and all pages will +# contain a <link> tag referring to it. The value of this option must be the +# base URL from which the finished HTML is served. +#html_use_opensearch = '' + +# If nonempty, this is the file name suffix for HTML files (e.g. ".xhtml"). +#html_file_suffix = '' + +# Output file base name for HTML help builder. +htmlhelp_basename = 'lmfitdoc' + +# -- Options for LaTeX output -------------------------------------------------- + +# Grouping the document tree into LaTeX files. List of tuples +# (source start file, target name, title, author, documentclass [howto/manual]). +latex_documents = [ + ('index', 'lmfit.tex', + 'Non-Linear Least-Squares Minimization and Curve-Fitting for Python', + 'Matthew Newville, Till Stensitzki, and others', 'manual'), +] diff --git a/doc/confidence.rst b/doc/confidence.rst index c678dfb..67c4f97 100644 --- a/doc/confidence.rst +++ b/doc/confidence.rst @@ -1,177 +1,193 @@ -.. _confidence_chapter:
-
-Calculation of confidence intervals
-====================================
-
-.. module:: confidence
-
-The lmfit :mod:`confidence` module allows you to explicitly calculate
-confidence intervals for variable parameters. For most models, it is not
-necessary: the estimation of the standard error from the estimated
-covariance matrix is normally quite good.
-
-But for some models, e.g. a sum of two exponentials, the approximation
-begins to fail. For this case, lmfit has the function :func:`conf_interval`
-to calculate confidence intervals directly. This is substantially slower
-than using the errors estimated from the covariance matrix, but the results
-are more robust.
-
-
-Method used for calculating confidence intervals
--------------------------------------------------
-
-The F-test is used to compare our null model, which is the best fit we have
-found, with an alternate model, where one of the parameters is fixed to a
-specific value. The value is changed until the difference between :math:`\chi^2_0`
-and :math:`\chi^2_{f}` can't be explained by the loss of a degree of freedom
-within a certain confidence.
-
-.. math::
-
- F(P_{fix},N-P) = \left(\frac{\chi^2_f}{\chi^2_{0}}-1\right)\frac{N-P}{P_{fix}}
-
-N is the number of data-points, P the number of parameter of the null model.
-:math:`P_{fix}` is the number of fixed parameters (or to be more clear, the
-difference of number of parameters between our null model and the alternate
-model).
-
-Adding a log-likelihood method is under consideration.
-
-A basic example
----------------
-
-First we create an example problem::
-
- >>> import lmfit
- >>> import numpy as np
- >>> x = np.linspace(0.3,10,100)
- >>> y = 1/(0.1*x)+2+0.1*np.random.randn(x.size)
- >>> pars = lmfit.Parameters()
- >>> pars.add_many(('a', 0.1), ('b', 1))
- >>> def residual(p):
- ... a = p['a'].value
- ... b = p['b'].value
- ... return 1/(a*x)+b-y
-
-
-before we can generate the confidence intervals, we have to run a fit, so
-that the automated estimate of the standard errors can be used as a
-starting point::
-
-
- >>> mini = lmfit.Minimizer(residual, pars)
- >>> result = mini.minimize()
- >>> print(lmfit.fit_report(result.params))
- [Variables]]
- a: 0.09943895 +/- 0.000193 (0.19%) (init= 0.1)
- b: 1.98476945 +/- 0.012226 (0.62%) (init= 1)
- [[Correlations]] (unreported correlations are < 0.100)
- C(a, b) = 0.601
-
-Now it is just a simple function call to calculate the confidence
-intervals::
-
- >>> ci = lmfit.conf_interval(mini, result)
- >>> lmfit.printfuncs.report_ci(ci)
- 99.70% 95.00% 67.40% 0.00% 67.40% 95.00% 99.70%
- a 0.09886 0.09905 0.09925 0.09944 0.09963 0.09982 0.10003
- b 1.94751 1.96049 1.97274 1.97741 1.99680 2.00905 2.02203
-
-This shows the best-fit values for the parameters in the `0.00%` column,
-and parameter values that are at the varying confidence levels given by
-steps in :math:`\sigma`. As we can see, the estimated error is almost the
-same, and the uncertainties are well behaved: Going from 1 :math:`\sigma`
-(68% confidence) to 3 :math:`\sigma` (99.7% confidence) uncertainties is
-fairly linear. It can also be seen that the errors are fairy symmetric
-around the best fit value. For this problem, it is not necessary to
-calculate confidence intervals, and the estimates of the uncertainties from
-the covariance matrix are sufficient.
-
-An advanced example
--------------------
-
-Now we look at a problem where calculating the error from approximated
-covariance can lead to misleading result -- two decaying exponentials. In
-fact such a problem is particularly hard for the Levenberg-Marquardt
-method, so we fitst estimate the results using the slower but robust
-Nelder-Mead method, and *then* use Levenberg-Marquardt to estimate the
-uncertainties and correlations
-
-
-.. literalinclude:: ../examples/doc_confidence2.py
-
-which will report::
-
- [[Variables]]
- a1: 2.98622120 +/- 0.148671 (4.98%) (init= 2.986237)
- a2: -4.33526327 +/- 0.115275 (2.66%) (init=-4.335256)
- t1: 1.30994233 +/- 0.131211 (10.02%) (init= 1.309932)
- t2: 11.8240350 +/- 0.463164 (3.92%) (init= 11.82408)
- [[Correlations]] (unreported correlations are < 0.500)
- C(a2, t2) = 0.987
- C(a2, t1) = -0.925
- C(t1, t2) = -0.881
- C(a1, t1) = -0.599
- 95.00% 68.00% 0.00% 68.00% 95.00%
- a1 2.71850 2.84525 2.98622 3.14874 3.34076
- a2 -4.63180 -4.46663 -4.33526 -4.22883 -4.14178
- t2 10.82699 11.33865 11.82404 12.28195 12.71094
- t1 1.08014 1.18566 1.30994 1.45566 1.62579
-
-
-Again we called :func:`conf_interval`, this time with tracing and only for
-1- and 2 :math:`\sigma`. Comparing these two different estimates, we see
-that the estimate for `a1` is reasonably well approximated from the
-covariance matrix, but the estimates for `a2` and especially for `t1`, and
-`t2` are very asymmetric and that going from 1 :math:`\sigma` (68%
-confidence) to 2 :math:`\sigma` (95% confidence) is not very predictable.
-
-Let plots mad of the confidence region are shown the figure on the left
-below for ``a1`` and ``t2``, and for ``a2`` and ``t2`` on the right:
-
-.. _figC1:
-
- .. image:: _images/conf_interval1.png
- :target: _images/conf_interval1.png
- :width: 48%
- .. image:: _images/conf_interval1a.png
- :target: _images/conf_interval1a.png
- :width: 48%
-
-Neither of these plots is very much like an ellipse, which is implicitly
-assumed by the approach using the covariance matrix.
-
-The trace returned as the optional second argument from
-:func:`conf_interval` contains a dictionary for each variable parameter.
-The values are dictionaries with arrays of values for each variable, and an
-array of corresponding probabilities for the corresponding cumulative
-variables. This can be used to show the dependence between two
-parameters::
-
- >>> x, y, prob = trace['a1']['a1'], trace['a1']['t2'],trace['a1']['prob']
- >>> x2, y2, prob2 = trace['t2']['t2'], trace['t2']['a1'],trace['t2']['prob']
- >>> plt.scatter(x, y, c=prob ,s=30)
- >>> plt.scatter(x2, y2, c=prob2, s=30)
- >>> plt.gca().set_xlim((1, 5))
- >>> plt.gca().set_ylim((5, 15))
- >>> plt.xlabel('a1')
- >>> plt.ylabel('t2')
- >>> plt.show()
-
-
-which shows the trace of values:
-
-.. image:: _images/conf_interval2.png
- :target: _images/conf_interval2.png
- :width: 50%
-
-
-
-Confidence Interval Functions
-----------------------------------
-
-.. autofunction:: lmfit.conf_interval
-
-.. autofunction:: lmfit.conf_interval2d
-
-.. autofunction:: lmfit.ci_report
+.. _confidence_chapter: + +Calculation of confidence intervals +==================================== + +.. module:: confidence + +The lmfit :mod:`confidence` module allows you to explicitly calculate +confidence intervals for variable parameters. For most models, it is not +necessary: the estimation of the standard error from the estimated +covariance matrix is normally quite good. + +But for some models, e.g. a sum of two exponentials, the approximation +begins to fail. For this case, lmfit has the function :func:`conf_interval` +to calculate confidence intervals directly. This is substantially slower +than using the errors estimated from the covariance matrix, but the results +are more robust. + + +Method used for calculating confidence intervals +------------------------------------------------- + +The F-test is used to compare our null model, which is the best fit we have +found, with an alternate model, where one of the parameters is fixed to a +specific value. The value is changed until the difference between :math:`\chi^2_0` +and :math:`\chi^2_{f}` can't be explained by the loss of a degree of freedom +within a certain confidence. + +.. math:: + + F(P_{fix},N-P) = \left(\frac{\chi^2_f}{\chi^2_{0}}-1\right)\frac{N-P}{P_{fix}} + +N is the number of data-points, P the number of parameter of the null model. +:math:`P_{fix}` is the number of fixed parameters (or to be more clear, the +difference of number of parameters between our null model and the alternate +model). + +Adding a log-likelihood method is under consideration. + +A basic example +--------------- + +First we create an example problem:: + + >>> import lmfit + >>> import numpy as np + >>> x = np.linspace(0.3,10,100) + >>> y = 1/(0.1*x)+2+0.1*np.random.randn(x.size) + >>> pars = lmfit.Parameters() + >>> pars.add_many(('a', 0.1), ('b', 1)) + >>> def residual(p): + ... a = p['a'].value + ... b = p['b'].value + ... return 1/(a*x)+b-y + + +before we can generate the confidence intervals, we have to run a fit, so +that the automated estimate of the standard errors can be used as a +starting point:: + + + >>> mini = lmfit.Minimizer(residual, pars) + >>> result = mini.minimize() + >>> print(lmfit.fit_report(result.params)) + [Variables]] + a: 0.09943895 +/- 0.000193 (0.19%) (init= 0.1) + b: 1.98476945 +/- 0.012226 (0.62%) (init= 1) + [[Correlations]] (unreported correlations are < 0.100) + C(a, b) = 0.601 + +Now it is just a simple function call to calculate the confidence +intervals:: + + >>> ci = lmfit.conf_interval(mini, result) + >>> lmfit.printfuncs.report_ci(ci) + 99.70% 95.00% 67.40% 0.00% 67.40% 95.00% 99.70% + a 0.09886 0.09905 0.09925 0.09944 0.09963 0.09982 0.10003 + b 1.94751 1.96049 1.97274 1.97741 1.99680 2.00905 2.02203 + +This shows the best-fit values for the parameters in the `0.00%` column, +and parameter values that are at the varying confidence levels given by +steps in :math:`\sigma`. As we can see, the estimated error is almost the +same, and the uncertainties are well behaved: Going from 1 :math:`\sigma` +(68% confidence) to 3 :math:`\sigma` (99.7% confidence) uncertainties is +fairly linear. It can also be seen that the errors are fairy symmetric +around the best fit value. For this problem, it is not necessary to +calculate confidence intervals, and the estimates of the uncertainties from +the covariance matrix are sufficient. + +An advanced example +------------------- + +Now we look at a problem where calculating the error from approximated +covariance can lead to misleading result -- two decaying exponentials. In +fact such a problem is particularly hard for the Levenberg-Marquardt +method, so we first estimate the results using the slower but robust +Nelder-Mead method, and *then* use Levenberg-Marquardt to estimate the +uncertainties and correlations + + +.. literalinclude:: ../examples/doc_confidence2.py + +which will report:: + + [[Variables]] + a1: 2.98622120 +/- 0.148671 (4.98%) (init= 2.986237) + a2: -4.33526327 +/- 0.115275 (2.66%) (init=-4.335256) + t1: 1.30994233 +/- 0.131211 (10.02%) (init= 1.309932) + t2: 11.8240350 +/- 0.463164 (3.92%) (init= 11.82408) + [[Correlations]] (unreported correlations are < 0.500) + C(a2, t2) = 0.987 + C(a2, t1) = -0.925 + C(t1, t2) = -0.881 + C(a1, t1) = -0.599 + 95.00% 68.00% 0.00% 68.00% 95.00% + a1 2.71850 2.84525 2.98622 3.14874 3.34076 + a2 -4.63180 -4.46663 -4.33526 -4.22883 -4.14178 + t2 10.82699 11.33865 11.82404 12.28195 12.71094 + t1 1.08014 1.18566 1.30994 1.45566 1.62579 + + +Again we called :func:`conf_interval`, this time with tracing and only for +1- and 2 :math:`\sigma`. Comparing these two different estimates, we see +that the estimate for `a1` is reasonably well approximated from the +covariance matrix, but the estimates for `a2` and especially for `t1`, and +`t2` are very asymmetric and that going from 1 :math:`\sigma` (68% +confidence) to 2 :math:`\sigma` (95% confidence) is not very predictable. + +Let plots mad of the confidence region are shown the figure on the left +below for ``a1`` and ``t2``, and for ``a2`` and ``t2`` on the right: + +.. _figC1: + + .. image:: _images/conf_interval1.png + :target: _images/conf_interval1.png + :width: 48% + .. image:: _images/conf_interval1a.png + :target: _images/conf_interval1a.png + :width: 48% + +Neither of these plots is very much like an ellipse, which is implicitly +assumed by the approach using the covariance matrix. + +The trace returned as the optional second argument from +:func:`conf_interval` contains a dictionary for each variable parameter. +The values are dictionaries with arrays of values for each variable, and an +array of corresponding probabilities for the corresponding cumulative +variables. This can be used to show the dependence between two +parameters:: + + >>> x, y, prob = trace['a1']['a1'], trace['a1']['t2'],trace['a1']['prob'] + >>> x2, y2, prob2 = trace['t2']['t2'], trace['t2']['a1'],trace['t2']['prob'] + >>> plt.scatter(x, y, c=prob ,s=30) + >>> plt.scatter(x2, y2, c=prob2, s=30) + >>> plt.gca().set_xlim((1, 5)) + >>> plt.gca().set_ylim((5, 15)) + >>> plt.xlabel('a1') + >>> plt.ylabel('t2') + >>> plt.show() + + +which shows the trace of values: + +.. image:: _images/conf_interval2.png + :target: _images/conf_interval2.png + :width: 50% + +The :meth:`Minimizer.emcee` method uses Markov Chain Monte Carlo to sample +the posterior probability distribution. These distributions demonstrate the +range of solutions that the data supports. The following image was obtained +by using :meth:`Minimizer.emcee` on the same problem. + +.. image:: _images/emcee_triangle.png + +Credible intervals (the Bayesian equivalent of the frequentist confidence +interval) can be obtained with this method. MCMC can be used for model +selection, to determine outliers, to marginalise over nuisance parameters, etc. +For example, you may have fractionally underestimated the uncertainties on a +dataset. MCMC can be used to estimate the true level of uncertainty on each +datapoint. A tutorial on the possibilities offered by MCMC can be found at [1]_. + +.. [1] http://jakevdp.github.io/blog/2014/03/11/frequentism-and-bayesianism-a-practical-intro/ + + + +Confidence Interval Functions +---------------------------------- + +.. autofunction:: lmfit.conf_interval + +.. autofunction:: lmfit.conf_interval2d + +.. autofunction:: lmfit.ci_report diff --git a/doc/constraints.rst b/doc/constraints.rst index 8d7fc6e..7d06b8d 100644 --- a/doc/constraints.rst +++ b/doc/constraints.rst @@ -1,166 +1,166 @@ -.. _constraints_chapter:
-
-=================================
-Using Mathematical Constraints
-=================================
-
-.. _asteval: http://newville.github.io/asteval/
-
-Being able to fix variables to a constant value or place upper and lower
-bounds on their values can greatly simplify modeling real data. These
-capabilities are key to lmfit's Parameters. In addition, it is sometimes
-highly desirable to place mathematical constraints on parameter values.
-For example, one might want to require that two Gaussian peaks have the
-same width, or have amplitudes that are constrained to add to some value.
-Of course, one could rewrite the objective or model function to place such
-requirements, but this is somewhat error prone, and limits the flexibility
-so that exploring constraints becomes laborious.
-
-To simplify the setting of constraints, Parameters can be assigned a
-mathematical expression of other Parameters, builtin constants, and builtin
-mathematical functions that will be used to determine its value. The
-expressions used for constraints are evaluated using the `asteval`_ module,
-which uses Python syntax, and evaluates the constraint expressions in a safe
-and isolated namespace.
-
-This approach to mathematical constraints allows one to not have to write a
-separate model function for two Gaussians where the two ``sigma`` values are
-forced to be equal, or where amplitudes are related. Instead, one can write a
-more general two Gaussian model (perhaps using :class:`GaussianModel`) and
-impose such constraints on the Parameters for a particular fit.
-
-
-Overview
-===============
-
-Just as one can place bounds on a Parameter, or keep it fixed during the
-fit, so too can one place mathematical constraints on parameters. The way
-this is done with lmfit is to write a Parameter as a mathematical
-expression of the other parameters and a set of pre-defined operators and
-functions. The constraint expressions are simple Python statements,
-allowing one to place constraints like::
-
- pars = Parameters()
- pars.add('frac_curve1', value=0.5, min=0, max=1)
- pars.add('frac_curve2', expr='1-frac_curve1')
-
-as the value of the `frac_curve1` parameter is updated at each step in the
-fit, the value of `frac_curve2` will be updated so that the two values are
-constrained to add to 1.0. Of course, such a constraint could be placed in
-the fitting function, but the use of such constraints allows the end-user
-to modify the model of a more general-purpose fitting function.
-
-Nearly any valid mathematical expression can be used, and a variety of
-built-in functions are available for flexible modeling.
-
-Supported Operators, Functions, and Constants
-=================================================
-
-The mathematical expressions used to define constrained Parameters need to
-be valid python expressions. As you'd expect, the operators '+', '-', '*',
-'/', '**', are supported. In fact, a much more complete set can be used,
-including Python's bit- and logical operators::
-
- +, -, *, /, **, &, |, ^, <<, >>, %, and, or,
- ==, >, >=, <, <=, !=, ~, not, is, is not, in, not in
-
-
-The values for `e` (2.7182818...) and `pi` (3.1415926...) are available, as
-are several supported mathematical and trigonometric function::
-
- abs, acos, acosh, asin, asinh, atan, atan2, atanh, ceil,
- copysign, cos, cosh, degrees, exp, fabs, factorial,
- floor, fmod, frexp, fsum, hypot, isinf, isnan, ldexp,
- log, log10, log1p, max, min, modf, pow, radians, sin,
- sinh, sqrt, tan, tanh, trunc
-
-
-In addition, all Parameter names will be available in the mathematical
-expressions. Thus, with parameters for a few peak-like functions::
-
- pars = Parameters()
- pars.add('amp_1', value=0.5, min=0, max=1)
- pars.add('cen_1', value=2.2)
- pars.add('wid_1', value=0.2)
-
-The following expression are all valid::
-
- pars.add('amp_2', expr='(2.0 - amp_1**2)')
- pars.add('cen_2', expr='cen_1 * wid_2 / max(wid_1, 0.001)')
- pars.add('wid_2', expr='sqrt(pi)*wid_1')
-
-In fact, almost any valid Python expression is allowed. A notable example
-is that Python's 1-line *if expression* is supported::
-
- pars.add('bounded', expr='param_a if test_val/2. > 100 else param_b')
-
-which is equivalent to the more familiar::
-
- if test_val/2. > 100:
- bounded = param_a
- else:
- bounded = param_b
-
-Using Inequality Constraints
-==============================
-
-A rather common question about how to set up constraints
-that use an inequality, say, :math:`x + y \le 10`. This
-can be done with algebraic constraints by recasting the
-problem, as :math:`x + y = \delta` and :math:`\delta \le
-10`. That is, first, allow :math:`x` to be held by the
-freely varying parameter `x`. Next, define a parameter
-`delta` to be variable with a maximum value of 10, and
-define parameter `y` as `delta - x`::
-
- pars = Parameters()
- pars.add('x', value = 5, vary=True)
- pars.add('delta', value = 5, max=10, vary=True)
- pars.add('y', expr='delta-x')
-
-The essential point is that an inequality still implies
-that a variable (here, `delta`) is needed to describe the
-constraint. The secondary point is that upper and lower
-bounds can be used as part of the inequality to make the
-definitions more convenient.
-
-
-Advanced usage of Expressions in lmfit
-=============================================
-
-The expression used in a constraint is converted to a
-Python `Abstract Syntax Tree
-<http://docs.python.org/library/ast.html>`_, which is an
-intermediate version of the expression -- a syntax-checked,
-partially compiled expression. Among other things, this
-means that Python's own parser is used to parse and convert
-the expression into something that can easily be evaluated
-within Python. It also means that the symbols in the
-expressions can point to any Python object.
-
-In fact, the use of Python's AST allows a nearly full version of Python to
-be supported, without using Python's built-in :meth:`eval` function. The
-`asteval`_ module actually supports most Python syntax, including for- and
-while-loops, conditional expressions, and user-defined functions. There
-are several unsupported Python constructs, most notably the class
-statement, so that new classes cannot be created, and the import statement,
-which helps make the `asteval`_ module safe from malicious use.
-
-One important feature of the `asteval`_ module is that you can add
-domain-specific functions into the it, for later use in constraint
-expressions. To do this, you would use the :attr:`asteval` attribute of
-the :class:`Minimizer` class, which contains a complete AST interpreter.
-The `asteval`_ interpreter uses a flat namespace, implemented as a single
-dictionary. That means you can preload any Python symbol into the namespace
-for the constraints::
-
- def mylorentzian(x, amp, cen, wid):
- "lorentzian function: wid = half-width at half-max"
- return (amp / (1 + ((x-cen)/wid)**2))
-
- fitter = Minimizer()
- fitter.asteval.symtable['lorentzian'] = mylorentzian
-
-and this :meth:`lorentzian` function can now be used in constraint
-expressions.
-
+.. _constraints_chapter: + +================================= +Using Mathematical Constraints +================================= + +.. _asteval: http://newville.github.io/asteval/ + +Being able to fix variables to a constant value or place upper and lower +bounds on their values can greatly simplify modeling real data. These +capabilities are key to lmfit's Parameters. In addition, it is sometimes +highly desirable to place mathematical constraints on parameter values. +For example, one might want to require that two Gaussian peaks have the +same width, or have amplitudes that are constrained to add to some value. +Of course, one could rewrite the objective or model function to place such +requirements, but this is somewhat error prone, and limits the flexibility +so that exploring constraints becomes laborious. + +To simplify the setting of constraints, Parameters can be assigned a +mathematical expression of other Parameters, builtin constants, and builtin +mathematical functions that will be used to determine its value. The +expressions used for constraints are evaluated using the `asteval`_ module, +which uses Python syntax, and evaluates the constraint expressions in a safe +and isolated namespace. + +This approach to mathematical constraints allows one to not have to write a +separate model function for two Gaussians where the two ``sigma`` values are +forced to be equal, or where amplitudes are related. Instead, one can write a +more general two Gaussian model (perhaps using :class:`GaussianModel`) and +impose such constraints on the Parameters for a particular fit. + + +Overview +=============== + +Just as one can place bounds on a Parameter, or keep it fixed during the +fit, so too can one place mathematical constraints on parameters. The way +this is done with lmfit is to write a Parameter as a mathematical +expression of the other parameters and a set of pre-defined operators and +functions. The constraint expressions are simple Python statements, +allowing one to place constraints like:: + + pars = Parameters() + pars.add('frac_curve1', value=0.5, min=0, max=1) + pars.add('frac_curve2', expr='1-frac_curve1') + +as the value of the `frac_curve1` parameter is updated at each step in the +fit, the value of `frac_curve2` will be updated so that the two values are +constrained to add to 1.0. Of course, such a constraint could be placed in +the fitting function, but the use of such constraints allows the end-user +to modify the model of a more general-purpose fitting function. + +Nearly any valid mathematical expression can be used, and a variety of +built-in functions are available for flexible modeling. + +Supported Operators, Functions, and Constants +================================================= + +The mathematical expressions used to define constrained Parameters need to +be valid python expressions. As you'd expect, the operators '+', '-', '*', +'/', '**', are supported. In fact, a much more complete set can be used, +including Python's bit- and logical operators:: + + +, -, *, /, **, &, |, ^, <<, >>, %, and, or, + ==, >, >=, <, <=, !=, ~, not, is, is not, in, not in + + +The values for `e` (2.7182818...) and `pi` (3.1415926...) are available, as +are several supported mathematical and trigonometric function:: + + abs, acos, acosh, asin, asinh, atan, atan2, atanh, ceil, + copysign, cos, cosh, degrees, exp, fabs, factorial, + floor, fmod, frexp, fsum, hypot, isinf, isnan, ldexp, + log, log10, log1p, max, min, modf, pow, radians, sin, + sinh, sqrt, tan, tanh, trunc + + +In addition, all Parameter names will be available in the mathematical +expressions. Thus, with parameters for a few peak-like functions:: + + pars = Parameters() + pars.add('amp_1', value=0.5, min=0, max=1) + pars.add('cen_1', value=2.2) + pars.add('wid_1', value=0.2) + +The following expression are all valid:: + + pars.add('amp_2', expr='(2.0 - amp_1**2)') + pars.add('cen_2', expr='cen_1 * wid_2 / max(wid_1, 0.001)') + pars.add('wid_2', expr='sqrt(pi)*wid_1') + +In fact, almost any valid Python expression is allowed. A notable example +is that Python's 1-line *if expression* is supported:: + + pars.add('bounded', expr='param_a if test_val/2. > 100 else param_b') + +which is equivalent to the more familiar:: + + if test_val/2. > 100: + bounded = param_a + else: + bounded = param_b + +Using Inequality Constraints +============================== + +A rather common question about how to set up constraints +that use an inequality, say, :math:`x + y \le 10`. This +can be done with algebraic constraints by recasting the +problem, as :math:`x + y = \delta` and :math:`\delta \le +10`. That is, first, allow :math:`x` to be held by the +freely varying parameter `x`. Next, define a parameter +`delta` to be variable with a maximum value of 10, and +define parameter `y` as `delta - x`:: + + pars = Parameters() + pars.add('x', value = 5, vary=True) + pars.add('delta', value = 5, max=10, vary=True) + pars.add('y', expr='delta-x') + +The essential point is that an inequality still implies +that a variable (here, `delta`) is needed to describe the +constraint. The secondary point is that upper and lower +bounds can be used as part of the inequality to make the +definitions more convenient. + + +Advanced usage of Expressions in lmfit +============================================= + +The expression used in a constraint is converted to a +Python `Abstract Syntax Tree +<http://docs.python.org/library/ast.html>`_, which is an +intermediate version of the expression -- a syntax-checked, +partially compiled expression. Among other things, this +means that Python's own parser is used to parse and convert +the expression into something that can easily be evaluated +within Python. It also means that the symbols in the +expressions can point to any Python object. + +In fact, the use of Python's AST allows a nearly full version of Python to +be supported, without using Python's built-in :meth:`eval` function. The +`asteval`_ module actually supports most Python syntax, including for- and +while-loops, conditional expressions, and user-defined functions. There +are several unsupported Python constructs, most notably the class +statement, so that new classes cannot be created, and the import statement, +which helps make the `asteval`_ module safe from malicious use. + +One important feature of the `asteval`_ module is that you can add +domain-specific functions into the it, for later use in constraint +expressions. To do this, you would use the :attr:`asteval` attribute of +the :class:`Minimizer` class, which contains a complete AST interpreter. +The `asteval`_ interpreter uses a flat namespace, implemented as a single +dictionary. That means you can preload any Python symbol into the namespace +for the constraints:: + + def mylorentzian(x, amp, cen, wid): + "lorentzian function: wid = half-width at half-max" + return (amp / (1 + ((x-cen)/wid)**2)) + + fitter = Minimizer() + fitter.asteval.symtable['lorentzian'] = mylorentzian + +and this :meth:`lorentzian` function can now be used in constraint +expressions. + diff --git a/doc/contents.rst b/doc/contents.rst index 8a1e5c2..46c61b2 100644 --- a/doc/contents.rst +++ b/doc/contents.rst @@ -1,18 +1,18 @@ -Contents
-=================
-
-.. toctree::
- :maxdepth: 3
-
- intro
- installation
- whatsnew
- support
- faq
- parameters
- fitting
- model
- builtin_models
- confidence
- bounds
- constraints
+Contents +================= + +.. toctree:: + :maxdepth: 3 + + intro + installation + whatsnew + support + faq + parameters + fitting + model + builtin_models + confidence + bounds + constraints diff --git a/doc/extensions.py b/doc/extensions.py index 3e54c82..40de659 100644 --- a/doc/extensions.py +++ b/doc/extensions.py @@ -1,10 +1,10 @@ -# sphinx extensions for mathjax
-extensions = ['sphinx.ext.autodoc',
- 'sphinx.ext.todo',
- 'sphinx.ext.coverage',
- 'sphinx.ext.intersphinx',
- 'numpydoc']
-mathjax = 'sphinx.ext.mathjax'
-pngmath = 'sphinx.ext.pngmath'
-
-extensions.append(mathjax)
+# sphinx extensions for mathjax +extensions = ['sphinx.ext.autodoc', + 'sphinx.ext.todo', + 'sphinx.ext.coverage', + 'sphinx.ext.intersphinx', + 'numpydoc'] +mathjax = 'sphinx.ext.mathjax' +pngmath = 'sphinx.ext.pngmath' + +extensions.append(mathjax) diff --git a/doc/extensions.pyc b/doc/extensions.pyc Binary files differindex 4dfb438..2ea9e41 100644 --- a/doc/extensions.pyc +++ b/doc/extensions.pyc diff --git a/doc/faq.rst b/doc/faq.rst index f54dc88..1bf26f9 100644 --- a/doc/faq.rst +++ b/doc/faq.rst @@ -1,100 +1,95 @@ -.. _faq_chapter:
-
-====================================
-Frequently Asked Questions
-====================================
-
-A list of common questions.
-
-What's the best way to ask for help or submit a bug report?
-================================================================
-
-See :ref:`support_chapter`.
-
-
-Why did my script break when upgrading from lmfit 0.8.3 to 0.9.0?
-====================================================================
-
-See :ref:`whatsnew_090_label`
-
-
-I get import errors from IPython
-==============================================================
-
-If you see something like::
-
- from IPython.html.widgets import Dropdown
-
- ImportError: No module named 'widgets'
-
-then you need to install the ipywidgets package. Try 'pip install ipywidgets'.
-
-
-
-
-How can I fit multi-dimensional data?
-========================================
-
-The fitting routines accept data arrays that are 1 dimensional and double
-precision. So you need to convert the data and model (or the value
-returned by the objective function) to be one dimensional. A simple way to
-do this is to use numpy's :meth:`numpy.ndarray.flatten`, for example::
-
- def residual(params, x, data=None):
- ....
- resid = calculate_multidim_residual()
- return resid.flatten()
-
-How can I fit multiple data sets?
-========================================
-
-As above, the fitting routines accept data arrays that are 1 dimensional and double
-precision. So you need to convert the sets of data and models (or the value
-returned by the objective function) to be one dimensional. A simple way to
-do this is to use numpy's :meth:`numpy.concatenate`. As an example, here
-is a residual function to simultaneously fit two lines to two different
-arrays. As a bonus, the two lines share the 'offset' parameter:
-
- def fit_function(params, x=None, dat1=None, dat2=None):
- model1 = params['offset'].value + x * params['slope1'].value
- model2 = params['offset'].value + x * params['slope2'].value
-
- resid1 = dat1 - model1
- resid2 = dat2 - model2
- return numpy.concatenate((resid1, resid2))
-
-
-
-How can I fit complex data?
-===================================
-
-As with working with multidimensional data, you need to convert your data
-and model (or the value returned by the objective function) to be double precision
-floating point numbers. One way to do this would be to use a function like this::
-
- def realimag(array):
- return np.array([(x.real, x.imag) for x in array]).flatten()
-
-to convert the complex array into an array of alternating real and
-imaginary values. You can then use this function on the result returned by
-your objective function::
-
- def residual(params, x, data=None):
- ....
- resid = calculate_complex_residual()
- return realimag(resid)
-
-
-Can I constrain values to have integer values?
-===============================================
-
-Basically, no. None of the minimizers in lmfit support integer
-programming. They all (I think) assume that they can make a very small
-change to a floating point value for a parameters value and see a change in
-the value to be minimized.
-
-
-How should I cite LMFIT?
-==================================
-
-See http://dx.doi.org/10.5281/zenodo.11813
+.. _faq_chapter: + +==================================== +Frequently Asked Questions +==================================== + +A list of common questions. + +What's the best way to ask for help or submit a bug report? +================================================================ + +See :ref:`support_chapter`. + + +Why did my script break when upgrading from lmfit 0.8.3 to 0.9.0? +==================================================================== + +See :ref:`whatsnew_090_label` + + +I get import errors from IPython +============================================================== + +If you see something like:: + + from IPython.html.widgets import Dropdown + + ImportError: No module named 'widgets' + +then you need to install the ipywidgets package. Try 'pip install ipywidgets'. + + + + +How can I fit multi-dimensional data? +======================================== + +The fitting routines accept data arrays that are 1 dimensional and double +precision. So you need to convert the data and model (or the value +returned by the objective function) to be one dimensional. A simple way to +do this is to use numpy's :numpydoc:`ndarray.flatten`, for example:: + + def residual(params, x, data=None): + .... + resid = calculate_multidim_residual() + return resid.flatten() + +How can I fit multiple data sets? +======================================== + +As above, the fitting routines accept data arrays that are 1 dimensional +and double precision. So you need to convert the sets of data and models +(or the value returned by the objective function) to be one dimensional. A +simple way to do this is to use numpy's :numpydoc:`concatenate`. As an +example, here is a residual function to simultaneously fit two lines to two +different arrays. As a bonus, the two lines share the 'offset' parameter:: + + def fit_function(params, x=None, dat1=None, dat2=None): + model1 = params['offset'].value + x * params['slope1'].value + model2 = params['offset'].value + x * params['slope2'].value + + resid1 = dat1 - model1 + resid2 = dat2 - model2 + return numpy.concatenate((resid1, resid2)) + + + +How can I fit complex data? +=================================== + +As with working with multidimensional data, you need to convert your data +and model (or the value returned by the objective function) to be double +precision floating point numbers. The simplest approach is to use numpy's +:numpydoc:`ndarray.view` method, perhaps like:: + + import numpy as np + def residual(params, x, data=None): + .... + resid = calculate_complex_residual() + return resid.view(np.float) + + +Can I constrain values to have integer values? +=============================================== + +Basically, no. None of the minimizers in lmfit support integer +programming. They all (I think) assume that they can make a very small +change to a floating point value for a parameters value and see a change in +the value to be minimized. + + +How should I cite LMFIT? +================================== + +See http://dx.doi.org/10.5281/zenodo.11813 diff --git a/doc/fitting.rst b/doc/fitting.rst index f07ce77..cde5d89 100644 --- a/doc/fitting.rst +++ b/doc/fitting.rst @@ -1,619 +1,900 @@ -.. _minimize_chapter:
-
-=======================================
-Performing Fits, Analyzing Outputs
-=======================================
-
-As shown in the previous chapter, a simple fit can be performed with the
-:func:`minimize` function. For more sophisticated modeling, the
-:class:`Minimizer` class can be used to gain a bit more control, especially
-when using complicated constraints or comparing results from related fits.
-
-
-.. warning::
-
- Upgrading scripts from version 0.8.3 to 0.9.0? See :ref:`whatsnew_090_label`
-
-
-The :func:`minimize` function
-===============================
-
-The :func:`minimize` function is a wrapper around :class:`Minimizer` for
-running an optimization problem. It takes an objective function (the
-function that calculates the array to be minimized), a :class:`Parameters`
-object, and several optional arguments. See :ref:`fit-func-label` for
-details on writing the objective.
-
-.. function:: minimize(function, params[, args=None[, kws=None[, method='leastsq'[, scale_covar=True[, iter_cb=None[, **fit_kws]]]]]])
-
- find values for the ``params`` so that the sum-of-squares of the array returned
- from ``function`` is minimized.
-
- :param function: function to return fit residual. See :ref:`fit-func-label` for details.
- :type function: callable.
- :param params: a :class:`Parameters` dictionary. Keywords must be strings
- that match ``[a-z_][a-z0-9_]*`` and cannot be a python
- reserved word. Each value must be :class:`Parameter`.
- :type params: :class:`Parameters`.
- :param args: arguments tuple to pass to the residual function as positional arguments.
- :type args: tuple
- :param kws: dictionary to pass to the residual function as keyword arguments.
- :type kws: dict
- :param method: name of fitting method to use. See :ref:`fit-methods-label` for details
- :type method: string (default ``leastsq``)
- :param scale_covar: whether to automatically scale covariance matrix (``leastsq`` only)
- :type scale_covar: bool (default ``True``)
- :param iter_cb: function to be called at each fit iteration. See :ref:`fit-itercb-label` for details.
- :type iter_cb: callable or ``None``
- :param fit_kws: dictionary to pass to :func:`scipy.optimize.leastsq` or :func:`scipy.optimize.minimize`.
- :type fit_kws: dict
-
- :return: :class:`MinimizerResult` instance, which will contain the
- optimized parameter, and several goodness-of-fit statistics.
-
-.. versionchanged:: 0.9.0
- return value changed to :class:`MinimizerResult`
-
-
- On output, the params will be unchanged. The best-fit values, and where
- appropriate, estimated uncertainties and correlations, will all be
- contained in the returned :class:`MinimizerResult`. See
- :ref:`fit-results-label` for further details.
-
- For clarity, it should be emphasized that this function is simply a
- wrapper around :class:`Minimizer` that runs a single fit, implemented as::
-
- fitter = Minimizer(fcn, params, fcn_args=args, fcn_kws=kws,
- iter_cb=iter_cb, scale_covar=scale_covar, **fit_kws)
- return fitter.minimize(method=method)
-
-
-.. _fit-func-label:
-
-
-Writing a Fitting Function
-===============================
-
-An important component of a fit is writing a function to be minimized --
-the *objective function*. Since this function will be called by other
-routines, there are fairly stringent requirements for its call signature
-and return value. In principle, your function can be any python callable,
-but it must look like this:
-
-.. function:: func(params, *args, **kws):
-
- calculate objective residual to be minimized from parameters.
-
- :param params: parameters.
- :type params: :class:`Parameters`.
- :param args: positional arguments. Must match ``args`` argument to :func:`minimize`
- :param kws: keyword arguments. Must match ``kws`` argument to :func:`minimize`
- :return: residual array (generally data-model) to be minimized in the least-squares sense.
- :rtype: numpy array. The length of this array cannot change between calls.
-
-
-A common use for the positional and keyword arguments would be to pass in other
-data needed to calculate the residual, including such things as the data array,
-dependent variable, uncertainties in the data, and other data structures for the
-model calculation.
-
-The objective function should return the value to be minimized. For the
-Levenberg-Marquardt algorithm from :meth:`leastsq`, this returned value **must** be an
-array, with a length greater than or equal to the number of fitting variables in the
-model. For the other methods, the return value can either be a scalar or an array. If an
-array is returned, the sum of squares of the array will be sent to the underlying fitting
-method, effectively doing a least-squares optimization of the return values.
-
-
-Since the function will be passed in a dictionary of :class:`Parameters`, it is advisable
-to unpack these to get numerical values at the top of the function. A
-simple way to do this is with :meth:`Parameters.valuesdict`, as with::
-
-
- def residual(pars, x, data=None, eps=None):
- # unpack parameters:
- # extract .value attribute for each parameter
- parvals = pars.valuesdict()
- period = parvals['period']
- shift = parvals['shift']
- decay = parvals['decay']
-
- if abs(shift) > pi/2:
- shift = shift - sign(shift)*pi
-
- if abs(period) < 1.e-10:
- period = sign(period)*1.e-10
-
- model = parvals['amp'] * sin(shift + x/period) * exp(-x*x*decay*decay)
-
- if data is None:
- return model
- if eps is None:
- return (model - data)
- return (model - data)/eps
-
-In this example, ``x`` is a positional (required) argument, while the
-``data`` array is actually optional (so that the function returns the model
-calculation if the data is neglected). Also note that the model
-calculation will divide ``x`` by the value of the 'period' Parameter. It
-might be wise to ensure this parameter cannot be 0. It would be possible
-to use the bounds on the :class:`Parameter` to do this::
-
- params['period'] = Parameter(value=2, min=1.e-10)
-
-but putting this directly in the function with::
-
- if abs(period) < 1.e-10:
- period = sign(period)*1.e-10
-
-is also a reasonable approach. Similarly, one could place bounds on the
-``decay`` parameter to take values only between ``-pi/2`` and ``pi/2``.
-
-.. _fit-methods-label:
-
-Choosing Different Fitting Methods
-===========================================
-
-By default, the `Levenberg-Marquardt
-<http://en.wikipedia.org/wiki/Levenberg-Marquardt_algorithm>`_ algorithm is
-used for fitting. While often criticized, including the fact it finds a
-*local* minima, this approach has some distinct advantages. These include
-being fast, and well-behaved for most curve-fitting needs, and making it
-easy to estimate uncertainties for and correlations between pairs of fit
-variables, as discussed in :ref:`fit-results-label`.
-
-Alternative algorithms can also be used by providing the ``method``
-keyword to the :func:`minimize` function or :meth:`Minimizer.minimize`
-class as listed in the :ref:`Table of Supported Fitting Methods
-<fit-methods-table>`.
-
-.. _fit-methods-table:
-
- Table of Supported Fitting Method, eithers:
-
- +-----------------------+------------------------------------------------------------------+
- | Fitting Method | ``method`` arg to :func:`minimize` or :meth:`Minimizer.minimize` |
- +=======================+==================================================================+
- | Levenberg-Marquardt | ``leastsq`` |
- +-----------------------+------------------------------------------------------------------+
- | Nelder-Mead | ``nelder`` |
- +-----------------------+------------------------------------------------------------------+
- | L-BFGS-B | ``lbfgsb`` |
- +-----------------------+------------------------------------------------------------------+
- | Powell | ``powell`` |
- +-----------------------+------------------------------------------------------------------+
- | Conjugate Gradient | ``cg`` |
- +-----------------------+------------------------------------------------------------------+
- | Newton-CG | ``newton`` |
- +-----------------------+------------------------------------------------------------------+
- | COBYLA | ``cobyla`` |
- +-----------------------+------------------------------------------------------------------+
- | Truncated Newton | ``tnc`` |
- +-----------------------+------------------------------------------------------------------+
- | Dogleg | ``dogleg`` |
- +-----------------------+------------------------------------------------------------------+
- | Sequential Linear | ``slsqp`` |
- | Squares Programming | |
- +-----------------------+------------------------------------------------------------------+
- | Differential | ``differential_evolution`` |
- | Evolution | |
- +-----------------------+------------------------------------------------------------------+
-
-
-.. note::
-
- The objective function for the Levenberg-Marquardt method **must**
- return an array, with more elements than variables. All other methods
- can return either a scalar value or an array.
-
-
-.. warning::
-
- Much of this documentation assumes that the Levenberg-Marquardt method is
- the method used. Many of the fit statistics and estimates for
- uncertainties in parameters discussed in :ref:`fit-results-label` are
- done only for this method.
-
-
-.. _fit-results-label:
-
-:class:`MinimizerResult` -- the optimization result
-========================================================
-
-
-
-.. class:: MinimizerResult(**kws)
-
-.. versionadded:: 0.9.0
-
-An optimization with :func:`minimize` or :meth:`Minimizer.minimize`
-will return a :class:`MinimizerResult` object. This is an otherwise
-plain container object (that is, with no methods of its own) that
-simply holds the results of the minimization. These results will
-include several pieces of informational data such as status and error
-messages, fit statistics, and the updated parameters themselves.
-
-Importantly, the parameters passed in to :meth:`Minimizer.minimize`
-will be not be changed. To to find the best-fit values, uncertainties
-and so on for each parameter, one must use the
-:attr:`MinimizerResult.params` attribute.
-
-.. attribute:: params
-
- the :class:`Parameters` actually used in the fit, with updated
- values, :attr:`stderr` and :attr:`correl`.
-
-.. attribute:: var_names
-
- ordered list of variable parameter names used in optimization, and
- useful for understanding the the values in :attr:`init_vals` and
- :attr:`covar`.
-
-.. attribute:: covar
-
- covariance matrix from minimization (`leastsq` only), with
- rows/columns using :attr:`var_names`.
-
-.. attribute:: init_vals
-
- list of initial values for variable parameters using :attr:`var_names`.
-
-.. attribute:: nfev
-
- number of function evaluations
-
-.. attribute:: success
-
- boolean (``True``/``False``) for whether fit succeeded.
-
-.. attribute:: errorbars
-
- boolean (``True``/``False``) for whether uncertainties were
- estimated.
-
-.. attribute:: message
-
- message about fit success.
-
-.. attribute:: ier
-
- integer error value from :func:`scipy.optimize.leastsq` (`leastsq`
- only).
-
-.. attribute:: lmdif_message
-
- message from :func:`scipy.optimize.leastsq` (`leastsq` only).
-
-
-.. attribute:: nvarys
-
- number of variables in fit :math:`N_{\rm varys}`
-
-.. attribute:: ndata
-
- number of data points: :math:`N`
-
-.. attribute:: nfree `
-
- degrees of freedom in fit: :math:`N - N_{\rm varys}`
-
-.. attribute:: residual
-
- residual array, return value of :func:`func`: :math:`{\rm Resid}`
-
-.. attribute:: chisqr
-
- chi-square: :math:`\chi^2 = \sum_i^N [{\rm Resid}_i]^2`
-
-.. attribute:: redchi
-
- reduced chi-square: :math:`\chi^2_{\nu}= {\chi^2} / {(N - N_{\rm
- varys})}`
-
-.. attribute:: aic
-
- Akaike Information Criterion statistic (see below)
-
-.. attribute:: bic
-
- Bayesian Information Criterion statistic (see below).
-
-
-
-
-
-Goodness-of-Fit Statistics
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. _goodfit-table:
-
- Table of Fit Results: These values, including the standard Goodness-of-Fit statistics,
- are all attributes of the :class:`MinimizerResult` object returned by
- :func:`minimize` or :meth:`Minimizer.minimize`.
-
-+----------------------+----------------------------------------------------------------------------+
-| Attribute Name | Description / Formula |
-+======================+============================================================================+
-| nfev | number of function evaluations |
-+----------------------+----------------------------------------------------------------------------+
-| nvarys | number of variables in fit :math:`N_{\rm varys}` |
-+----------------------+----------------------------------------------------------------------------+
-| ndata | number of data points: :math:`N` |
-+----------------------+----------------------------------------------------------------------------+
-| nfree ` | degrees of freedom in fit: :math:`N - N_{\rm varys}` |
-+----------------------+----------------------------------------------------------------------------+
-| residual | residual array, return value of :func:`func`: :math:`{\rm Resid}` |
-+----------------------+----------------------------------------------------------------------------+
-| chisqr | chi-square: :math:`\chi^2 = \sum_i^N [{\rm Resid}_i]^2` |
-+----------------------+----------------------------------------------------------------------------+
-| redchi | reduced chi-square: :math:`\chi^2_{\nu}= {\chi^2} / {(N - N_{\rm varys})}` |
-+----------------------+----------------------------------------------------------------------------+
-| aic | Akaike Information Criterion statistic (see below) |
-+----------------------+----------------------------------------------------------------------------+
-| bic | Bayesian Information Criterion statistic (see below) |
-+----------------------+----------------------------------------------------------------------------+
-| var_names | ordered list of variable parameter names used for init_vals and covar |
-+----------------------+----------------------------------------------------------------------------+
-| covar | covariance matrix (with rows/columns using var_names |
-+----------------------+----------------------------------------------------------------------------+
-| init_vals | list of initial values for variable parameters |
-+----------------------+----------------------------------------------------------------------------+
-
-Note that the calculation of chi-square and reduced chi-square assume
-that the returned residual function is scaled properly to the
-uncertainties in the data. For these statistics to be meaningful, the
-person writing the function to be minimized must scale them properly.
-
-After a fit using using the :meth:`leastsq` method has completed
-successfully, standard errors for the fitted variables and correlations
-between pairs of fitted variables are automatically calculated from the
-covariance matrix. The standard error (estimated :math:`1\sigma`
-error-bar) go into the :attr:`stderr` attribute of the Parameter. The
-correlations with all other variables will be put into the
-:attr:`correl` attribute of the Parameter -- a dictionary with keys for
-all other Parameters and values of the corresponding correlation.
-
-In some cases, it may not be possible to estimate the errors and
-correlations. For example, if a variable actually has no practical effect
-on the fit, it will likely cause the covariance matrix to be singular,
-making standard errors impossible to estimate. Placing bounds on varied
-Parameters makes it more likely that errors cannot be estimated, as being
-near the maximum or minimum value makes the covariance matrix singular. In
-these cases, the :attr:`errorbars` attribute of the fit result
-(:class:`Minimizer` object) will be ``False``.
-
-Akaike and Bayesian Information Criteria
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-The :class:`MinimizerResult` includes the tradtional chi-square and reduced chi-square statistics:
-
-.. math::
- :nowrap:
-
- \begin{eqnarray*}
- \chi^2 &=& \sum_i^N r_i^2 \\
- \chi^2_\nu &=& = \chi^2 / (N-N_{\rm varys})
- \end{eqnarray*}
-
-where :math:`r` is the residual array returned by the objective function
-(likely to be ``(data-model)/uncertainty`` for data modeling usages),
-:math:`N` is the number of data points (``ndata``), and :math:`N_{\rm
-varys}` is number of variable parameters.
-
-Also included are the `Akaike Information Criterion
-<http://en.wikipedia.org/wiki/Akaike_information_criterion>`_, and
-`Bayesian Information Criterion
-<http://en.wikipedia.org/wiki/Bayesian_information_criterion>`_ statistics,
-held in the ``aic`` and ``bic`` attributes, respectively. These give slightly
-different measures of the relative quality for a fit, trying to balance
-quality of fit with the number of variable parameters used in the fit.
-These are calculated as
-
-.. math::
- :nowrap:
-
- \begin{eqnarray*}
- {\rm aic} &=& N \ln(\chi^2/N) + 2 N_{\rm varys} \\
- {\rm bic} &=& N \ln(\chi^2/N) + \ln(N) *N_{\rm varys} \\
- \end{eqnarray*}
-
-
-When comparing fits with different numbers of varying parameters, one
-typically selects the model with lowest reduced chi-square, Akaike
-information criterion, and/or Bayesian information criterion. Generally,
-the Bayesian information criterion is considered the most conservative of
-these statistics.
-
-.. _fit-itercb-label:
-
-
-Using a Iteration Callback Function
-====================================
-
-An iteration callback function is a function to be called at each
-iteration, just after the objective function is called. The iteration
-callback allows user-supplied code to be run at each iteration, and can be
-used to abort a fit.
-
-.. function:: iter_cb(params, iter, resid, *args, **kws):
-
- user-supplied function to be run at each iteration
-
- :param params: parameters.
- :type params: :class:`Parameters`.
- :param iter: iteration number
- :type iter: integer
- :param resid: residual array.
- :type resid: ndarray
- :param args: positional arguments. Must match ``args`` argument to :func:`minimize`
- :param kws: keyword arguments. Must match ``kws`` argument to :func:`minimize`
- :return: residual array (generally data-model) to be minimized in the least-squares sense.
- :rtype: ``None`` for normal behavior, any value like ``True`` to abort fit.
-
-
-Normally, the iteration callback would have no return value or return
-``None``. To abort a fit, have this function return a value that is
-``True`` (including any non-zero integer). The fit will also abort if any
-exception is raised in the iteration callback. When a fit is aborted this
-way, the parameters will have the values from the last iteration. The fit
-statistics are not likely to be meaningful, and uncertainties will not be computed.
-
-
-.. module:: Minimizer
-
-.. _fit-minimizer-label:
-
-Using the :class:`Minimizer` class
-=======================================
-
-For full control of the fitting process, you'll want to create a
-:class:`Minimizer` object.
-
-.. class:: Minimizer(function, params, fcn_args=None, fcn_kws=None, iter_cb=None, scale_covar=True, **kws)
-
- creates a Minimizer, for more detailed access to fitting methods and attributes.
-
- :param function: objective function to return fit residual. See :ref:`fit-func-label` for details.
- :type function: callable.
- :param params: a dictionary of Parameters. Keywords must be strings
- that match ``[a-z_][a-z0-9_]*`` and is not a python
- reserved word. Each value must be :class:`Parameter`.
- :type params: dict
- :param fcn_args: arguments tuple to pass to the residual function as positional arguments.
- :type fcn_args: tuple
- :param fcn_kws: dictionary to pass to the residual function as keyword arguments.
- :type fcn_kws: dict
- :param iter_cb: function to be called at each fit iteration. See :ref:`fit-itercb-label` for details.
- :type iter_cb: callable or ``None``
- :param scale_covar: flag for automatically scaling covariance matrix and uncertainties to reduced chi-square (``leastsq`` only)
- :type scale_cover: bool (default ``True``).
- :param kws: dictionary to pass as keywords to the underlying :mod:`scipy.optimize` method.
- :type kws: dict
-
-The Minimizer object has a few public methods:
-
-.. method:: minimize(method='leastsq', params=None, **kws)
-
- perform fit using either :meth:`leastsq` or :meth:`scalar_minimize`.
-
- :param method: name of fitting method. Must be one of the naemes in
- :ref:`Table of Supported Fitting Methods <fit-methods-table>`
- :type method: str.
- :param params: a :class:`Parameters` dictionary for starting values
- :type params: :class:`Parameters` or `None`
-
- :return: :class:`MinimizerResult` object, containing updated
- parameters, fitting statistics, and information.
-
-.. versionchanged:: 0.9.0
- return value changed to :class:`MinimizerResult`
-
- Additonal keywords are passed on to the correspond :meth:`leastsq`
- or :meth:`scalar_minimize` method.
-
-
-.. method:: leastsq(params=None, scale_covar=True, **kws)
-
- perform fit with Levenberg-Marquardt algorithm. Keywords will be
- passed directly to :func:`scipy.optimize.leastsq`. By default,
- numerical derivatives are used, and the following arguments are set:
-
-
- +------------------+----------------+------------------------------------------------------------+
- | :meth:`leastsq` | Default Value | Description |
- | arg | | |
- +==================+================+============================================================+
- | xtol | 1.e-7 | Relative error in the approximate solution |
- +------------------+----------------+------------------------------------------------------------+
- | ftol | 1.e-7 | Relative error in the desired sum of squares |
- +------------------+----------------+------------------------------------------------------------+
- | maxfev | 2000*(nvar+1) | maximum number of function calls (nvar= # of variables) |
- +------------------+----------------+------------------------------------------------------------+
- | Dfun | ``None`` | function to call for Jacobian calculation |
- +------------------+----------------+------------------------------------------------------------+
-
-
-.. versionchanged:: 0.9.0
- return value changed to :class:`MinimizerResult`
-
-.. method:: scalar_minimize(method='Nelder-Mead', params=None, hess=None, tol=None, **kws)
-
- perform fit with any of the scalar minimization algorithms supported by
- :func:`scipy.optimize.minimize`.
-
- +-------------------------+-----------------+-----------------------------------------------------+
- | :meth:`scalar_minimize` | Default Value | Description |
- | arg | | |
- +=========================+=================+=====================================================+
- | method | ``Nelder-Mead`` | fitting method |
- +-------------------------+-----------------+-----------------------------------------------------+
- | tol | 1.e-7 | fitting and parameter tolerance |
- +-------------------------+-----------------+-----------------------------------------------------+
- | hess | None | Hessian of objective function |
- +-------------------------+-----------------+-----------------------------------------------------+
-
-.. versionchanged:: 0.9.0
- return value changed to :class:`MinimizerResult`
-
-.. method:: prepare_fit(**kws)
-
- prepares and initializes model and Parameters for subsequent
- fitting. This routine prepares the conversion of :class:`Parameters`
- into fit variables, organizes parameter bounds, and parses, "compiles"
- and checks constrain expressions. The method also creates and returns
- a new instance of a :class:`MinimizerResult` object that contains the
- copy of the Parameters that will actually be varied in the fit.
-
- This method is called directly by the fitting methods, and it is
- generally not necessary to call this function explicitly.
-
-.. versionchanged:: 0.9.0
- return value changed to :class:`MinimizerResult`
-
-
-
-Getting and Printing Fit Reports
-===========================================
-
-.. function:: fit_report(result, modelpars=None, show_correl=True, min_correl=0.1)
-
- generate and return text of report of best-fit values, uncertainties,
- and correlations from fit.
-
- :param result: :class:`MinimizerResult` object as returned by :func:`minimize`.
- :param modelpars: Parameters with "Known Values" (optional, default None)
- :param show_correl: whether to show list of sorted correlations [``True``]
- :param min_correl: smallest correlation absolute value to show [0.1]
-
- If the first argument is a :class:`Parameters` object,
- goodness-of-fit statistics will not be included.
-
-.. function:: report_fit(result, modelpars=None, show_correl=True, min_correl=0.1)
-
- print text of report from :func:`fit_report`.
-
-
-An example fit with report would be
-
-.. literalinclude:: ../examples/doc_withreport.py
-
-which would write out::
-
- [[Fit Statistics]]
- # function evals = 85
- # data points = 1001
- # variables = 4
- chi-square = 498.812
- reduced chi-square = 0.500
- [[Variables]]
- amp: 13.9121944 +/- 0.141202 (1.01%) (init= 13)
- period: 5.48507044 +/- 0.026664 (0.49%) (init= 2)
- shift: 0.16203677 +/- 0.014056 (8.67%) (init= 0)
- decay: 0.03264538 +/- 0.000380 (1.16%) (init= 0.02)
- [[Correlations]] (unreported correlations are < 0.100)
- C(period, shift) = 0.797
- C(amp, decay) = 0.582
- C(amp, shift) = -0.297
- C(amp, period) = -0.243
- C(shift, decay) = -0.182
- C(period, decay) = -0.150
+.. _minimize_chapter: + +======================================= +Performing Fits, Analyzing Outputs +======================================= + +As shown in the previous chapter, a simple fit can be performed with the +:func:`minimize` function. For more sophisticated modeling, the +:class:`Minimizer` class can be used to gain a bit more control, especially +when using complicated constraints or comparing results from related fits. + +.. warning:: + + Upgrading scripts from version 0.8.3 to 0.9.0? See :ref:`whatsnew_090_label` + + +The :func:`minimize` function +=============================== + +The :func:`minimize` function is a wrapper around :class:`Minimizer` for +running an optimization problem. It takes an objective function (the +function that calculates the array to be minimized), a :class:`Parameters` +object, and several optional arguments. See :ref:`fit-func-label` for +details on writing the objective. + +.. function:: minimize(function, params[, args=None[, kws=None[, method='leastsq'[, scale_covar=True[, iter_cb=None[, **fit_kws]]]]]]) + + find values for the ``params`` so that the sum-of-squares of the array returned + from ``function`` is minimized. + + :param function: function to return fit residual. See :ref:`fit-func-label` for details. + :type function: callable. + :param params: a :class:`Parameters` dictionary. Keywords must be strings + that match ``[a-z_][a-z0-9_]*`` and cannot be a python + reserved word. Each value must be :class:`Parameter`. + :type params: :class:`Parameters`. + :param args: arguments tuple to pass to the residual function as positional arguments. + :type args: tuple + :param kws: dictionary to pass to the residual function as keyword arguments. + :type kws: dict + :param method: name of fitting method to use. See :ref:`fit-methods-label` for details + :type method: string (default ``leastsq``) + :param scale_covar: whether to automatically scale covariance matrix (``leastsq`` only) + :type scale_covar: bool (default ``True``) + :param iter_cb: function to be called at each fit iteration. See :ref:`fit-itercb-label` for details. + :type iter_cb: callable or ``None`` + :param fit_kws: dictionary to pass to :scipydoc:`optimize.leastsq` or :scipydoc:`optimize.minimize`. + :type fit_kws: dict + + :return: :class:`MinimizerResult` instance, which will contain the + optimized parameter, and several goodness-of-fit statistics. + +.. versionchanged:: 0.9.0 + return value changed to :class:`MinimizerResult` + + + On output, the params will be unchanged. The best-fit values, and where + appropriate, estimated uncertainties and correlations, will all be + contained in the returned :class:`MinimizerResult`. See + :ref:`fit-results-label` for further details. + + For clarity, it should be emphasized that this function is simply a + wrapper around :class:`Minimizer` that runs a single fit, implemented as:: + + fitter = Minimizer(fcn, params, fcn_args=args, fcn_kws=kws, + iter_cb=iter_cb, scale_covar=scale_covar, **fit_kws) + return fitter.minimize(method=method) + + +.. _fit-func-label: + + +Writing a Fitting Function +=============================== + +An important component of a fit is writing a function to be minimized -- +the *objective function*. Since this function will be called by other +routines, there are fairly stringent requirements for its call signature +and return value. In principle, your function can be any python callable, +but it must look like this: + +.. function:: func(params, *args, **kws): + + calculate objective residual to be minimized from parameters. + + :param params: parameters. + :type params: :class:`Parameters`. + :param args: positional arguments. Must match ``args`` argument to :func:`minimize` + :param kws: keyword arguments. Must match ``kws`` argument to :func:`minimize` + :return: residual array (generally data-model) to be minimized in the least-squares sense. + :rtype: numpy array. The length of this array cannot change between calls. + + +A common use for the positional and keyword arguments would be to pass in other +data needed to calculate the residual, including such things as the data array, +dependent variable, uncertainties in the data, and other data structures for the +model calculation. + +The objective function should return the value to be minimized. For the +Levenberg-Marquardt algorithm from :meth:`leastsq`, this returned value **must** be an +array, with a length greater than or equal to the number of fitting variables in the +model. For the other methods, the return value can either be a scalar or an array. If an +array is returned, the sum of squares of the array will be sent to the underlying fitting +method, effectively doing a least-squares optimization of the return values. + + +Since the function will be passed in a dictionary of :class:`Parameters`, it is advisable +to unpack these to get numerical values at the top of the function. A +simple way to do this is with :meth:`Parameters.valuesdict`, as with:: + + + def residual(pars, x, data=None, eps=None): + # unpack parameters: + # extract .value attribute for each parameter + parvals = pars.valuesdict() + period = parvals['period'] + shift = parvals['shift'] + decay = parvals['decay'] + + if abs(shift) > pi/2: + shift = shift - sign(shift)*pi + + if abs(period) < 1.e-10: + period = sign(period)*1.e-10 + + model = parvals['amp'] * sin(shift + x/period) * exp(-x*x*decay*decay) + + if data is None: + return model + if eps is None: + return (model - data) + return (model - data)/eps + +In this example, ``x`` is a positional (required) argument, while the +``data`` array is actually optional (so that the function returns the model +calculation if the data is neglected). Also note that the model +calculation will divide ``x`` by the value of the 'period' Parameter. It +might be wise to ensure this parameter cannot be 0. It would be possible +to use the bounds on the :class:`Parameter` to do this:: + + params['period'] = Parameter(value=2, min=1.e-10) + +but putting this directly in the function with:: + + if abs(period) < 1.e-10: + period = sign(period)*1.e-10 + +is also a reasonable approach. Similarly, one could place bounds on the +``decay`` parameter to take values only between ``-pi/2`` and ``pi/2``. + +.. _fit-methods-label: + +Choosing Different Fitting Methods +=========================================== + +By default, the `Levenberg-Marquardt +<http://en.wikipedia.org/wiki/Levenberg-Marquardt_algorithm>`_ algorithm is +used for fitting. While often criticized, including the fact it finds a +*local* minima, this approach has some distinct advantages. These include +being fast, and well-behaved for most curve-fitting needs, and making it +easy to estimate uncertainties for and correlations between pairs of fit +variables, as discussed in :ref:`fit-results-label`. + +Alternative algorithms can also be used by providing the ``method`` +keyword to the :func:`minimize` function or :meth:`Minimizer.minimize` +class as listed in the :ref:`Table of Supported Fitting Methods +<fit-methods-table>`. + +.. _fit-methods-table: + + Table of Supported Fitting Methods: + + +-----------------------+------------------------------------------------------------------+ + | Fitting Method | ``method`` arg to :func:`minimize` or :meth:`Minimizer.minimize` | + +=======================+==================================================================+ + | Levenberg-Marquardt | ``leastsq`` | + +-----------------------+------------------------------------------------------------------+ + | Nelder-Mead | ``nelder`` | + +-----------------------+------------------------------------------------------------------+ + | L-BFGS-B | ``lbfgsb`` | + +-----------------------+------------------------------------------------------------------+ + | Powell | ``powell`` | + +-----------------------+------------------------------------------------------------------+ + | Conjugate Gradient | ``cg`` | + +-----------------------+------------------------------------------------------------------+ + | Newton-CG | ``newton`` | + +-----------------------+------------------------------------------------------------------+ + | COBYLA | ``cobyla`` | + +-----------------------+------------------------------------------------------------------+ + | Truncated Newton | ``tnc`` | + +-----------------------+------------------------------------------------------------------+ + | Dogleg | ``dogleg`` | + +-----------------------+------------------------------------------------------------------+ + | Sequential Linear | ``slsqp`` | + | Squares Programming | | + +-----------------------+------------------------------------------------------------------+ + | Differential | ``differential_evolution`` | + | Evolution | | + +-----------------------+------------------------------------------------------------------+ + + +.. note:: + + The objective function for the Levenberg-Marquardt method **must** + return an array, with more elements than variables. All other methods + can return either a scalar value or an array. + + +.. warning:: + + Much of this documentation assumes that the Levenberg-Marquardt method is + the method used. Many of the fit statistics and estimates for + uncertainties in parameters discussed in :ref:`fit-results-label` are + done only for this method. + +.. _fit-results-label: + +:class:`MinimizerResult` -- the optimization result +======================================================== + + + +.. class:: MinimizerResult(**kws) + +.. versionadded:: 0.9.0 + +An optimization with :func:`minimize` or :meth:`Minimizer.minimize` +will return a :class:`MinimizerResult` object. This is an otherwise +plain container object (that is, with no methods of its own) that +simply holds the results of the minimization. These results will +include several pieces of informational data such as status and error +messages, fit statistics, and the updated parameters themselves. + +Importantly, the parameters passed in to :meth:`Minimizer.minimize` +will be not be changed. To to find the best-fit values, uncertainties +and so on for each parameter, one must use the +:attr:`MinimizerResult.params` attribute. + +.. attribute:: params + + the :class:`Parameters` actually used in the fit, with updated + values, :attr:`stderr` and :attr:`correl`. + +.. attribute:: var_names + + ordered list of variable parameter names used in optimization, and + useful for understanding the the values in :attr:`init_vals` and + :attr:`covar`. + +.. attribute:: covar + + covariance matrix from minimization (`leastsq` only), with + rows/columns using :attr:`var_names`. + +.. attribute:: init_vals + + list of initial values for variable parameters using :attr:`var_names`. + +.. attribute:: nfev + + number of function evaluations + +.. attribute:: success + + boolean (``True``/``False``) for whether fit succeeded. + +.. attribute:: errorbars + + boolean (``True``/``False``) for whether uncertainties were + estimated. + +.. attribute:: message + + message about fit success. + +.. attribute:: ier + + integer error value from :scipydoc:`optimize.leastsq` (`leastsq` only). + +.. attribute:: lmdif_message + + message from :scipydoc:`optimize.leastsq` (`leastsq` only). + +.. attribute:: nvarys + + number of variables in fit :math:`N_{\rm varys}` + +.. attribute:: ndata + + number of data points: :math:`N` + +.. attribute:: nfree ` + + degrees of freedom in fit: :math:`N - N_{\rm varys}` + +.. attribute:: residual + + residual array, return value of :func:`func`: :math:`{\rm Resid}` + +.. attribute:: chisqr + + chi-square: :math:`\chi^2 = \sum_i^N [{\rm Resid}_i]^2` + +.. attribute:: redchi + + reduced chi-square: :math:`\chi^2_{\nu}= {\chi^2} / {(N - N_{\rm + varys})}` + +.. attribute:: aic + + Akaike Information Criterion statistic (see below) + +.. attribute:: bic + + Bayesian Information Criterion statistic (see below). + + + +Goodness-of-Fit Statistics +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. _goodfit-table: + + Table of Fit Results: These values, including the standard Goodness-of-Fit statistics, + are all attributes of the :class:`MinimizerResult` object returned by + :func:`minimize` or :meth:`Minimizer.minimize`. + ++----------------------+----------------------------------------------------------------------------+ +| Attribute Name | Description / Formula | ++======================+============================================================================+ +| nfev | number of function evaluations | ++----------------------+----------------------------------------------------------------------------+ +| nvarys | number of variables in fit :math:`N_{\rm varys}` | ++----------------------+----------------------------------------------------------------------------+ +| ndata | number of data points: :math:`N` | ++----------------------+----------------------------------------------------------------------------+ +| nfree ` | degrees of freedom in fit: :math:`N - N_{\rm varys}` | ++----------------------+----------------------------------------------------------------------------+ +| residual | residual array, return value of :func:`func`: :math:`{\rm Resid}` | ++----------------------+----------------------------------------------------------------------------+ +| chisqr | chi-square: :math:`\chi^2 = \sum_i^N [{\rm Resid}_i]^2` | ++----------------------+----------------------------------------------------------------------------+ +| redchi | reduced chi-square: :math:`\chi^2_{\nu}= {\chi^2} / {(N - N_{\rm varys})}` | ++----------------------+----------------------------------------------------------------------------+ +| aic | Akaike Information Criterion statistic (see below) | ++----------------------+----------------------------------------------------------------------------+ +| bic | Bayesian Information Criterion statistic (see below) | ++----------------------+----------------------------------------------------------------------------+ +| var_names | ordered list of variable parameter names used for init_vals and covar | ++----------------------+----------------------------------------------------------------------------+ +| covar | covariance matrix (with rows/columns using var_names | ++----------------------+----------------------------------------------------------------------------+ +| init_vals | list of initial values for variable parameters | ++----------------------+----------------------------------------------------------------------------+ + +Note that the calculation of chi-square and reduced chi-square assume +that the returned residual function is scaled properly to the +uncertainties in the data. For these statistics to be meaningful, the +person writing the function to be minimized must scale them properly. + +After a fit using using the :meth:`leastsq` method has completed +successfully, standard errors for the fitted variables and correlations +between pairs of fitted variables are automatically calculated from the +covariance matrix. The standard error (estimated :math:`1\sigma` +error-bar) go into the :attr:`stderr` attribute of the Parameter. The +correlations with all other variables will be put into the +:attr:`correl` attribute of the Parameter -- a dictionary with keys for +all other Parameters and values of the corresponding correlation. + +In some cases, it may not be possible to estimate the errors and +correlations. For example, if a variable actually has no practical effect +on the fit, it will likely cause the covariance matrix to be singular, +making standard errors impossible to estimate. Placing bounds on varied +Parameters makes it more likely that errors cannot be estimated, as being +near the maximum or minimum value makes the covariance matrix singular. In +these cases, the :attr:`errorbars` attribute of the fit result +(:class:`Minimizer` object) will be ``False``. + + +.. _information_criteria_label: + +Akaike and Bayesian Information Criteria +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The :class:`MinimizerResult` includes the traditional chi-square and reduced chi-square statistics: + +.. math:: + :nowrap: + + \begin{eqnarray*} + \chi^2 &=& \sum_i^N r_i^2 \\ + \chi^2_\nu &=& = \chi^2 / (N-N_{\rm varys}) + \end{eqnarray*} + +where :math:`r` is the residual array returned by the objective function +(likely to be ``(data-model)/uncertainty`` for data modeling usages), +:math:`N` is the number of data points (``ndata``), and :math:`N_{\rm +varys}` is number of variable parameters. + +Also included are the `Akaike Information Criterion +<http://en.wikipedia.org/wiki/Akaike_information_criterion>`_, and +`Bayesian Information Criterion +<http://en.wikipedia.org/wiki/Bayesian_information_criterion>`_ statistics, +held in the ``aic`` and ``bic`` attributes, respectively. These give slightly +different measures of the relative quality for a fit, trying to balance +quality of fit with the number of variable parameters used in the fit. +These are calculated as + +.. math:: + :nowrap: + + \begin{eqnarray*} + {\rm aic} &=& N \ln(\chi^2/N) + 2 N_{\rm varys} \\ + {\rm bic} &=& N \ln(\chi^2/N) + \ln(N) *N_{\rm varys} \\ + \end{eqnarray*} + + +When comparing fits with different numbers of varying parameters, one +typically selects the model with lowest reduced chi-square, Akaike +information criterion, and/or Bayesian information criterion. Generally, +the Bayesian information criterion is considered the most conservative of +these statistics. + +.. _fit-itercb-label: + + +Using a Iteration Callback Function +==================================== + +An iteration callback function is a function to be called at each +iteration, just after the objective function is called. The iteration +callback allows user-supplied code to be run at each iteration, and can be +used to abort a fit. + +.. function:: iter_cb(params, iter, resid, *args, **kws): + + user-supplied function to be run at each iteration + + :param params: parameters. + :type params: :class:`Parameters`. + :param iter: iteration number + :type iter: integer + :param resid: residual array. + :type resid: ndarray + :param args: positional arguments. Must match ``args`` argument to :func:`minimize` + :param kws: keyword arguments. Must match ``kws`` argument to :func:`minimize` + :return: residual array (generally data-model) to be minimized in the least-squares sense. + :rtype: ``None`` for normal behavior, any value like ``True`` to abort fit. + + +Normally, the iteration callback would have no return value or return +``None``. To abort a fit, have this function return a value that is +``True`` (including any non-zero integer). The fit will also abort if any +exception is raised in the iteration callback. When a fit is aborted this +way, the parameters will have the values from the last iteration. The fit +statistics are not likely to be meaningful, and uncertainties will not be computed. + + +.. module:: Minimizer + +.. _fit-minimizer-label: + +Using the :class:`Minimizer` class +======================================= + +For full control of the fitting process, you'll want to create a +:class:`Minimizer` object. + +.. class:: Minimizer(function, params, fcn_args=None, fcn_kws=None, iter_cb=None, scale_covar=True, **kws) + + creates a Minimizer, for more detailed access to fitting methods and attributes. + + :param function: objective function to return fit residual. See :ref:`fit-func-label` for details. + :type function: callable. + :param params: a dictionary of Parameters. Keywords must be strings + that match ``[a-z_][a-z0-9_]*`` and is not a python + reserved word. Each value must be :class:`Parameter`. + :type params: dict + :param fcn_args: arguments tuple to pass to the residual function as positional arguments. + :type fcn_args: tuple + :param fcn_kws: dictionary to pass to the residual function as keyword arguments. + :type fcn_kws: dict + :param iter_cb: function to be called at each fit iteration. See :ref:`fit-itercb-label` for details. + :type iter_cb: callable or ``None`` + :param scale_covar: flag for automatically scaling covariance matrix and uncertainties to reduced chi-square (``leastsq`` only) + :type scale_covar: bool (default ``True``). + :param kws: dictionary to pass as keywords to the underlying :mod:`scipy.optimize` method. + :type kws: dict + +The Minimizer object has a few public methods: + +.. method:: minimize(method='leastsq', params=None, **kws) + + perform fit using either :meth:`leastsq` or :meth:`scalar_minimize`. + + :param method: name of fitting method. Must be one of the names in + :ref:`Table of Supported Fitting Methods <fit-methods-table>` + :type method: str. + :param params: a :class:`Parameters` dictionary for starting values + :type params: :class:`Parameters` or `None` + + :return: :class:`MinimizerResult` object, containing updated + parameters, fitting statistics, and information. + +.. versionchanged:: 0.9.0 + return value changed to :class:`MinimizerResult` + + Additional keywords are passed on to the correspond :meth:`leastsq` + or :meth:`scalar_minimize` method. + + +.. method:: leastsq(params=None, scale_covar=True, **kws) + + perform fit with Levenberg-Marquardt algorithm. Keywords will be + passed directly to :scipydoc:`optimize.leastsq`. By default, + numerical derivatives are used, and the following arguments are set: + + + +------------------+----------------+------------------------------------------------------------+ + | :meth:`leastsq` | Default Value | Description | + | arg | | | + +==================+================+============================================================+ + | xtol | 1.e-7 | Relative error in the approximate solution | + +------------------+----------------+------------------------------------------------------------+ + | ftol | 1.e-7 | Relative error in the desired sum of squares | + +------------------+----------------+------------------------------------------------------------+ + | maxfev | 2000*(nvar+1) | maximum number of function calls (nvar= # of variables) | + +------------------+----------------+------------------------------------------------------------+ + | Dfun | ``None`` | function to call for Jacobian calculation | + +------------------+----------------+------------------------------------------------------------+ + + +.. versionchanged:: 0.9.0 + return value changed to :class:`MinimizerResult` + +.. method:: scalar_minimize(method='Nelder-Mead', params=None, hess=None, tol=None, **kws) + + perform fit with any of the scalar minimization algorithms supported by + :scipydoc:`optimize.minimize`. + + +-------------------------+-----------------+-----------------------------------------------------+ + | :meth:`scalar_minimize` | Default Value | Description | + | arg | | | + +=========================+=================+=====================================================+ + | method | ``Nelder-Mead`` | fitting method | + +-------------------------+-----------------+-----------------------------------------------------+ + | tol | 1.e-7 | fitting and parameter tolerance | + +-------------------------+-----------------+-----------------------------------------------------+ + | hess | None | Hessian of objective function | + +-------------------------+-----------------+-----------------------------------------------------+ + +.. versionchanged:: 0.9.0 + return value changed to :class:`MinimizerResult` + +.. method:: prepare_fit(**kws) + + prepares and initializes model and Parameters for subsequent + fitting. This routine prepares the conversion of :class:`Parameters` + into fit variables, organizes parameter bounds, and parses, "compiles" + and checks constrain expressions. The method also creates and returns + a new instance of a :class:`MinimizerResult` object that contains the + copy of the Parameters that will actually be varied in the fit. + + This method is called directly by the fitting methods, and it is + generally not necessary to call this function explicitly. + +.. versionchanged:: 0.9.0 + return value changed to :class:`MinimizerResult` + + + +.. method:: emcee(params=None, steps=1000, nwalkers=100, burn=0, thin=1, ntemps=1, pos=None, reuse_sampler=False, workers=1, float_behavior='posterior', is_weighted=True, seed=None) + + Bayesian sampling of the posterior distribution for the parameters using the `emcee` + Markov Chain Monte Carlo package. The method assumes that the prior is Uniform. You need + to have `emcee` installed to use this method. + + :param params: a :class:`Parameters` dictionary for starting values + :type params: :class:`Parameters` or `None` + :param steps: How many samples you would like to draw from the posterior + distribution for each of the walkers? + :type steps: int + :param nwalkers: Should be set so :math:`nwalkers >> nvarys`, where `nvarys` + are the number of parameters being varied during the fit. + "Walkers are the members of the ensemble. They are almost + like separate Metropolis-Hastings chains but, of course, + the proposal distribution for a given walker depends on the + positions of all the other walkers in the ensemble." - from + [1]_. + :type nwalkers: int + :param burn: Discard this many samples from the start of the sampling regime. + :type burn: int + :param thin: Only accept 1 in every `thin` samples. + :type thin: int + :param ntemps: If `ntemps > 1` perform a Parallel Tempering. + :type ntemps: int + :param pos: Specify the initial positions for the sampler. If `ntemps == 1` + then `pos.shape` should be `(nwalkers, nvarys)`. Otherwise, + `(ntemps, nwalkers, nvarys)`. You can also initialise using a + previous chain that had the same `ntemps`, `nwalkers` and `nvarys`. + :type pos: np.ndarray + :param reuse_sampler: If you have already run :meth:`emcee` on a given + :class:`Minimizer` object then it possesses an internal sampler + attribute. You can continue to draw from the same sampler (retaining + the chain history) if you set this option to `True`. Otherwise a new + sampler is created. The `nwalkers`, `ntemps` and `params` keywords + are ignored with this option. + **Important**: the :class:`Parameters` used to create the sampler + must not change in-between calls to :meth:`emcee`. Alteration of + :class:`Parameters` would include changed ``min``, ``max``, + ``vary`` and ``expr`` attributes. This may happen, for example, if + you use an altered :class:`Parameters` object and call the + :meth:`minimize` method in-between calls to :meth:`emcee` . + :type reuse_sampler: bool + :param workers: For parallelization of sampling. It can be any Pool-like object + with a map method that follows the same calling sequence as the + built-in map function. If int is given as the argument, then a + multiprocessing-based pool is spawned internally with the + corresponding number of parallel processes. 'mpi4py'-based + parallelization and 'joblib'-based parallelization pools can also + be used here. **Note**: because of multiprocessing overhead it may + only be worth parallelising if the objective function is expensive + to calculate, or if there are a large number of objective + evaluations per step (`ntemps * nwalkers * nvarys`). + :type workers: int or Pool-like + :type float_behavior: str + :param float_behavior: Specifies the meaning of the objective function if it + returns a float. One of: + + 'posterior' - the objective function returns a log-posterior probability + + 'chi2' - the objective function is returning :math:`\chi^2`. + + See Notes for further details. + :param is_weighted: Has your objective function been weighted by measurement + uncertainties? If `is_weighted is True` then your objective + function is assumed to return residuals that have been divided by + the true measurement uncertainty `(data - model) / sigma`. If + `is_weighted is False` then the objective function is assumed to + return unweighted residuals, `data - model`. In this case `emcee` + will employ a positive measurement uncertainty during the sampling. + This measurement uncertainty will be present in the output params + and output chain with the name `__lnsigma`. A side effect of this + is that you cannot use this parameter name yourself. + **Important** this parameter only has any effect if your objective + function returns an array. If your objective function returns a + float, then this parameter is ignored. See Notes for more details. + :type is_weighted: bool + :param seed: If `seed` is an int, a new `np.random.RandomState` instance is used, + seeded with `seed`. + If `seed` is already a `np.random.RandomState` instance, then that + `np.random.RandomState` instance is used. + Specify `seed` for repeatable sampling. + :type seed: int or np.random.RandomState + + :return: :class:`MinimizerResult` object containing updated params, statistics, + etc. The :class:`MinimizerResult` also contains the ``chain``, + ``flatchain`` and ``lnprob`` attributes. The ``chain`` + and ``flatchain`` attributes contain the samples and have the shape + `(nwalkers, (steps - burn) // thin, nvarys)` or + `(ntemps, nwalkers, (steps - burn) // thin, nvarys)`, + depending on whether Parallel tempering was used or not. + `nvarys` is the number of parameters that are allowed to vary. + The ``flatchain`` attribute is a :class:`pandas.DataFrame` of the + flattened chain, `chain.reshape(-1, nvarys)`. To access flattened + chain values for a particular parameter use + `result.flatchain[parname]`. The ``lnprob`` attribute contains the + log probability for each sample in ``chain``. The sample with the + highest probability corresponds to the maximum likelihood estimate. + + This method samples the posterior distribution of the parameters using + Markov Chain Monte Carlo. To do so it needs to calculate the + log-posterior probability of the model parameters, `F`, given the data, + `D`, :math:`\ln p(F_{true} | D)`. This 'posterior probability' is + calculated as: + + .. math:: + + \ln p(F_{true} | D) \propto \ln p(D | F_{true}) + \ln p(F_{true}) + + where :math:`\ln p(D | F_{true})` is the 'log-likelihood' and + :math:`\ln p(F_{true})` is the 'log-prior'. The default log-prior + encodes prior information already known about the model. This method + assumes that the log-prior probability is `-np.inf` (impossible) if the + one of the parameters is outside its limits. The log-prior probability + term is zero if all the parameters are inside their bounds (known as a + uniform prior). The log-likelihood function is given by [1]_: + + .. math:: + + \ln p(D|F_{true}) = -\frac{1}{2}\sum_n \left[\frac{\left(g_n(F_{true}) - D_n \right)^2}{s_n^2}+\ln (2\pi s_n^2)\right] + + The first summand in the square brackets represents the residual for a + given datapoint (:math:`g` being the generative model) . This term + represents :math:`\chi^2` when summed over all datapoints. + Ideally the objective function used to create :class:`lmfit.Minimizer` should + return the log-posterior probability, :math:`\ln p(F_{true} | D)`. + However, since the in-built log-prior term is zero, the objective + function can also just return the log-likelihood, unless you wish to + create a non-uniform prior. + + If a float value is returned by the objective function then this value + is assumed by default to be the log-posterior probability, i.e. + `float_behavior is 'posterior'`. If your objective function returns + :math:`\chi^2`, then you should use a value of `'chi2'` for + `float_behavior`. `emcee` will then multiply your :math:`\chi^2` value + by -0.5 to obtain the posterior probability. + + However, the default behaviour of many objective functions is to return + a vector of (possibly weighted) residuals. Therefore, if your objective + function returns a vector, `res`, then the vector is assumed to contain + the residuals. If `is_weighted is True` then your residuals are assumed + to be correctly weighted by the standard deviation of the data points + (`res = (data - model) / sigma`) and the log-likelihood (and + log-posterior probability) is calculated as: `-0.5 * np.sum(res **2)`. + This ignores the second summand in the square brackets. Consequently, in + order to calculate a fully correct log-posterior probability value your + objective function should return a single value. If `is_weighted is False` + then the data uncertainty, :math:`s_n`, will be treated as a nuisance + parameter and will be marginalised out. This is achieved by employing a + strictly positive uncertainty (homoscedasticity) for each data point, + :math:`s_n=exp(\_\_lnsigma)`. `__lnsigma` will be present in + `MinimizerResult.params`, as well as `Minimizer.chain`, `nvarys` will also be + increased by one. + + .. [1] http://dan.iel.fm/emcee/current/user/line/ + + +.. _label-emcee: + +:meth:`emcee` - calculating the posterior probability distribution of parameters +============================================================================================== + +:meth:`emcee` can be used to obtain the posterior probability distribution of +parameters, given a set of experimental data. An example problem is a double +exponential decay. A small amount of Gaussian noise is also added in:: + + >>> import numpy as np + >>> import lmfit + >>> import matplotlib.pyplot as plt + >>> x = np.linspace(1, 10, 250) + >>> np.random.seed(0) + >>> y = 3.0 * np.exp(-x / 2) - 5.0 * np.exp(-(x - 0.1) / 10.) + 0.1 * np.random.randn(len(x)) + >>> plt.plot(x, y) + >>> plt.show() + +.. image:: _images/emcee_dbl_exp.png + +Create a Parameter set for the initial guesses:: + + >>> p = lmfit.Parameters() + >>> p.add_many(('a1', 4.), ('a2', 4.), ('t1', 3.), ('t2', 3., True)) + + >>> def residual(p): + ... v = p.valuesdict() + ... return v['a1'] * np.exp(-x / v['t1']) + v['a2'] * np.exp(-(x - 0.1) / v['t2']) - y + +Solving with :func:`minimize` gives the Maximum Likelihood solution.:: + + >>> mi = lmfit.minimize(residual, p, method='Nelder') + >>> lmfit.printfuncs.report_fit(mi.params, min_correl=0.5) + [[Variables]] + a1: 2.98623688 (init= 4) + a2: -4.33525596 (init= 4) + t1: 1.30993185 (init= 3) + t2: 11.8240752 (init= 3) + [[Correlations]] (unreported correlations are < 0.500) + >>> plt.plot(x, y) + >>> plt.plot(x, residual(mi.params) + y, 'r') + >>> plt.show() + +.. image:: _images/emcee_dbl_exp2.png + +However, this doesn't give a probability distribution for the parameters. +Furthermore, we wish to deal with the data uncertainty. This is called +marginalisation of a nuisance parameter. emcee requires a function that returns +the log-posterior probability. The log-posterior probability is a sum of the +log-prior probability and log-likelihood functions. The log-prior probability is +assumed to be zero if all the parameters are within their bounds and `-np.inf` +if any of the parameters are outside their bounds.:: + + >>> # add a noise parameter + >>> mi.params.add('f', value=1, min=0.001, max=2) + + >>> # This is the log-likelihood probability for the sampling. We're going to estimate the + >>> # size of the uncertainties on the data as well. + >>> def lnprob(p): + ... resid = residual(p) + ... s = p['f'] + ... resid *= 1 / s + ... resid *= resid + ... resid += np.log(2 * np.pi * s**2) + ... return -0.5 * np.sum(resid) + +Now we have to set up the minimizer and do the sampling.:: + + >>> mini = lmfit.Minimizer(lnprob, mi.params) + >>> res = mini.emcee(burn=300, steps=600, thin=10, params=mi.params) + +Lets have a look at those posterior distributions for the parameters. This requires +installation of the `corner` package.:: + + >>> import corner + >>> corner.corner(res.flatchain, labels=res.var_names, truths=list(res.params.valuesdict().values())) + +.. image:: _images/emcee_triangle.png + +The values reported in the :class:`MinimizerResult` are the medians of the +probability distributions and a 1 sigma quantile, estimated as half the +difference between the 15.8 and 84.2 percentiles. The median value is not +necessarily the same as the Maximum Likelihood Estimate. We'll get that as well. +You can see that we recovered the right uncertainty level on the data.:: + + >>> print("median of posterior probability distribution") + >>> print('------------------------------------------') + >>> lmfit.report_fit(res.params) + median of posterior probability distribution + ------------------------------------------ + [[Variables]] + a1: 3.00975345 +/- 0.151034 (5.02%) (init= 2.986237) + a2: -4.35419204 +/- 0.127505 (2.93%) (init=-4.335256) + t1: 1.32726415 +/- 0.142995 (10.77%) (init= 1.309932) + t2: 11.7911935 +/- 0.495583 (4.20%) (init= 11.82408) + f: 0.09805494 +/- 0.004256 (4.34%) (init= 1) + [[Correlations]] (unreported correlations are < 0.100) + C(a2, t2) = 0.981 + C(a2, t1) = -0.927 + C(t1, t2) = -0.880 + C(a1, t1) = -0.519 + C(a1, a2) = 0.195 + C(a1, t2) = 0.146 + + >>> # find the maximum likelihood solution + >>> highest_prob = np.argmax(res.lnprob) + >>> hp_loc = np.unravel_index(highest_prob, res.lnprob.shape) + >>> mle_soln = res.chain[hp_loc] + >>> for i, par in enumerate(p): + ... p[par].value = mle_soln[i] + + >>> print("\nMaximum likelihood Estimation") + >>> print('-----------------------------') + >>> print(p) + Maximum likelihood Estimation + ----------------------------- + Parameters([('a1', <Parameter 'a1', 2.9943337359308981, bounds=[-inf:inf]>), + ('a2', <Parameter 'a2', -4.3364489105166593, bounds=[-inf:inf]>), + ('t1', <Parameter 't1', 1.3124544105342462, bounds=[-inf:inf]>), + ('t2', <Parameter 't2', 11.80612160586597, bounds=[-inf:inf]>)]) + + >>> # Finally lets work out a 1 and 2-sigma error estimate for 't1' + >>> quantiles = np.percentile(res.flatchain['t1'], [2.28, 15.9, 50, 84.2, 97.7]) + >>> print("2 sigma spread", 0.5 * (quantiles[-1] - quantiles[0])) + 2 sigma spread 0.298878202908 + +Getting and Printing Fit Reports +=========================================== + +.. function:: fit_report(result, modelpars=None, show_correl=True, min_correl=0.1) + + generate and return text of report of best-fit values, uncertainties, + and correlations from fit. + + :param result: :class:`MinimizerResult` object as returned by :func:`minimize`. + :param modelpars: Parameters with "Known Values" (optional, default None) + :param show_correl: whether to show list of sorted correlations [``True``] + :param min_correl: smallest correlation absolute value to show [0.1] + + If the first argument is a :class:`Parameters` object, + goodness-of-fit statistics will not be included. + +.. function:: report_fit(result, modelpars=None, show_correl=True, min_correl=0.1) + + print text of report from :func:`fit_report`. + +An example fit with report would be + +.. literalinclude:: ../examples/doc_withreport.py + +which would write out:: + + [[Fit Statistics]] + # function evals = 85 + # data points = 1001 + # variables = 4 + chi-square = 498.812 + reduced chi-square = 0.500 + Akaike info crit = -685.215 + Bayesian info crit = -665.579 + [[Variables]] + amp: 13.9121944 +/- 0.141202 (1.01%) (init= 13) + period: 5.48507044 +/- 0.026664 (0.49%) (init= 2) + shift: 0.16203676 +/- 0.014056 (8.67%) (init= 0) + decay: 0.03264538 +/- 0.000380 (1.16%) (init= 0.02) + [[Correlations]] (unreported correlations are < 0.100) + C(period, shift) = 0.797 + C(amp, decay) = 0.582 + C(amp, shift) = -0.297 + C(amp, period) = -0.243 + C(shift, decay) = -0.182 + C(period, decay) = -0.150 diff --git a/doc/index.rst b/doc/index.rst index 8430f2b..5a2205a 100644 --- a/doc/index.rst +++ b/doc/index.rst @@ -1,68 +1,68 @@ -.. lmfit documentation master file,
-
-Non-Linear Least-Square Minimization and Curve-Fitting for Python
-===========================================================================
-
-.. _Levenberg-Marquardt: http://en.wikipedia.org/wiki/Levenberg-Marquardt_algorithm
-.. _MINPACK-1: http://en.wikipedia.org/wiki/MINPACK
-
-
-.. warning::
-
- Upgrading scripts from version 0.8.3 to 0.9.0? See :ref:`whatsnew_090_label`
-
-
-Lmfit provides a high-level interface to non-linear optimization and curve
-fitting problems for Python. Lmfit builds on and extends many of the
-optimizatin algorithm of :mod:`scipy.optimize`, especially the
-`Levenberg-Marquardt`_ method from :func:`scipy.optimize.leastsq`.
-
-Lmfit provides a number of useful enhancements to optimization and data
-fitting problems, including:
-
- * Using :class:`Parameter` objects instead of plain floats as variables.
- A :class:`Parameter` has a value that can be varied in the fit, have a
- fixed value, or have upper and/or lower bounds. A Parameter can even
- have a value that is constrained by an algebraic expression of other
- Parameter values.
-
- * Ease of changing fitting algorithms. Once a fitting model is set up,
- one can change the fitting algorithm used to find the optimal solution
- without changing the objective function.
-
- * Improved estimation of confidence intervals. While
- :func:`scipy.optimize.leastsq` will automatically calculate
- uncertainties and correlations from the covariance matrix, the accuracy
- of these estimates are often questionable. To help address this, lmfit
- has functions to explicitly explore parameter space to determine
- confidence levels even for the most difficult cases.
-
- * Improved curve-fitting with the :class:`Model` class. This
- extends the capabilities of :func:`scipy.optimize.curve_fit`, allowing
- you to turn a function that models for your data into a python class
- that helps you parametrize and fit data with that model.
-
- * Many :ref:`pre-built models <builtin_models_chapter>` for common
- lineshapes are included and ready to use.
-
-.. _lmfit github repository: http://github.com/lmfit/lmfit-py
-
-The lmfit package is Free software, using an MIT license. The software and
-this document are works in progress. If you are interested in
-participating in this effort please use the `lmfit github repository`_.
-
-
-.. toctree::
- :maxdepth: 2
-
- intro
- installation
- support
- faq
- parameters
- fitting
- model
- builtin_models
- confidence
- bounds
- constraints
+.. lmfit documentation master file, + +Non-Linear Least-Square Minimization and Curve-Fitting for Python +=========================================================================== + +.. _Levenberg-Marquardt: http://en.wikipedia.org/wiki/Levenberg-Marquardt_algorithm +.. _MINPACK-1: http://en.wikipedia.org/wiki/MINPACK + + +.. warning:: + + Upgrading scripts from version 0.8.3 to 0.9.0? See :ref:`whatsnew_090_label` + + +Lmfit provides a high-level interface to non-linear optimization and curve +fitting problems for Python. Lmfit builds on and extends many of the +optimization algorithm of :mod:`scipy.optimize`, especially the +`Levenberg-Marquardt`_ method from :scipydoc:`optimize.leastsq`. + +Lmfit provides a number of useful enhancements to optimization and data +fitting problems, including: + + * Using :class:`Parameter` objects instead of plain floats as variables. + A :class:`Parameter` has a value that can be varied in the fit, have a + fixed value, or have upper and/or lower bounds. A Parameter can even + have a value that is constrained by an algebraic expression of other + Parameter values. + + * Ease of changing fitting algorithms. Once a fitting model is set up, + one can change the fitting algorithm used to find the optimal solution + without changing the objective function. + + * Improved estimation of confidence intervals. While + :scipydoc:`optimize.leastsq` will automatically calculate + uncertainties and correlations from the covariance matrix, the accuracy + of these estimates are often questionable. To help address this, lmfit + has functions to explicitly explore parameter space to determine + confidence levels even for the most difficult cases. + + * Improved curve-fitting with the :class:`Model` class. This + extends the capabilities of :scipydoc:`optimize.curve_fit`, allowing + you to turn a function that models for your data into a python class + that helps you parametrize and fit data with that model. + + * Many :ref:`pre-built models <builtin_models_chapter>` for common + lineshapes are included and ready to use. + +.. _lmfit github repository: http://github.com/lmfit/lmfit-py + +The lmfit package is Free software, using an MIT license. The software and +this document are works in progress. If you are interested in +participating in this effort please use the `lmfit github repository`_. + + +.. toctree:: + :maxdepth: 2 + + intro + installation + support + faq + parameters + fitting + model + builtin_models + confidence + bounds + constraints diff --git a/doc/installation.rst b/doc/installation.rst index 9112fc6..f9adadd 100644 --- a/doc/installation.rst +++ b/doc/installation.rst @@ -1,82 +1,82 @@ -====================================
-Downloading and Installation
-====================================
-
-.. _lmfit github repository: http://github.com/lmfit/lmfit-py
-.. _Python Setup Tools: http://pypi.python.org/pypi/setuptools
-.. _pip: https://pip.pypa.io/
-.. _nose: http://nose.readthedocs.org/
-
-Prerequisites
-~~~~~~~~~~~~~~~
-
-The lmfit package requires Python, Numpy, and Scipy. Scipy version 0.13 or
-higher is recommended, but extensive testing on compatibility with various
-versions of scipy has not been done. Lmfit works with Python 2.7, 3.3 and
-3.4. No testing has been done with Python 3.5, but as the package is pure
-Python, relying only on scipy and numpy, no significant troubles are
-expected. The `nose`_ framework is required for running the test suite,
-and IPython and matplotib are recommended. If Pandas is available, it will
-be used in portions of lmfit.
-
-
-Downloads
-~~~~~~~~~~~~~
-
-
-The latest stable version of lmfit is available from `PyPi <http://pypi.python.org/pypi/lmfit/>`_.
-
-Installation
-~~~~~~~~~~~~~~~~~
-
-If you have `pip`_ installed, you can install lmfit with::
-
- pip install lmfit
-
-or, if you have `Python Setup Tools`_ installed, you install lmfit with::
-
- easy_install -U lmfit
-
-
-or, you can download the source kit, unpack it and install with::
-
- python setup.py install
-
-
-Development Version
-~~~~~~~~~~~~~~~~~~~~~~~~
-
-To get the latest development version, use::
-
- git clone http://github.com/lmfit/lmfit-py.git
-
-
-and install using::
-
- python setup.py install
-
-
-Testing
-~~~~~~~~~~
-
-A battery of tests scripts that can be run with the `nose`_ testing
-framework is distributed with lmfit in the ``tests`` folder. These are
-routinely run on the development version. Running ``nosetests`` should run
-all of these tests to completion without errors or failures.
-
-Many of the examples in this documentation are distributed with lmfit in
-the ``examples`` folder, and should also run for you. Many of these require
-
-
-Acknowledgements
-~~~~~~~~~~~~~~~~~~
-
-.. literalinclude:: ../THANKS.txt
-
-
-License
-~~~~~~~~~~~~~
-
-The LMFIT-py code is distribution under the following license:
-
-.. literalinclude:: ../LICENSE
+==================================== +Downloading and Installation +==================================== + +.. _lmfit github repository: http://github.com/lmfit/lmfit-py +.. _Python Setup Tools: http://pypi.python.org/pypi/setuptools +.. _pip: https://pip.pypa.io/ +.. _nose: http://nose.readthedocs.org/ + +Prerequisites +~~~~~~~~~~~~~~~ + +The lmfit package requires Python, Numpy, and Scipy. Scipy version 0.13 or +higher is recommended, but extensive testing on compatibility with various +versions of scipy has not been done. Lmfit works with Python 2.7, 3.3 and +3.4. No testing has been done with Python 3.5, but as the package is pure +Python, relying only on scipy and numpy, no significant troubles are +expected. The `nose`_ framework is required for running the test suite, +and IPython and matplotib are recommended. If Pandas is available, it will +be used in portions of lmfit. + + +Downloads +~~~~~~~~~~~~~ + + +The latest stable version of lmfit is available from `PyPi <http://pypi.python.org/pypi/lmfit/>`_. + +Installation +~~~~~~~~~~~~~~~~~ + +If you have `pip`_ installed, you can install lmfit with:: + + pip install lmfit + +or, if you have `Python Setup Tools`_ installed, you install lmfit with:: + + easy_install -U lmfit + + +or, you can download the source kit, unpack it and install with:: + + python setup.py install + + +Development Version +~~~~~~~~~~~~~~~~~~~~~~~~ + +To get the latest development version, use:: + + git clone http://github.com/lmfit/lmfit-py.git + + +and install using:: + + python setup.py install + + +Testing +~~~~~~~~~~ + +A battery of tests scripts that can be run with the `nose`_ testing +framework is distributed with lmfit in the ``tests`` folder. These are +routinely run on the development version. Running ``nosetests`` should run +all of these tests to completion without errors or failures. + +Many of the examples in this documentation are distributed with lmfit in +the ``examples`` folder, and should also run for you. Many of these require + + +Acknowledgements +~~~~~~~~~~~~~~~~~~ + +.. literalinclude:: ../THANKS.txt + + +License +~~~~~~~~~~~~~ + +The LMFIT-py code is distribution under the following license: + +.. literalinclude:: ../LICENSE diff --git a/doc/intro.rst b/doc/intro.rst index c480ae6..bc854f4 100644 --- a/doc/intro.rst +++ b/doc/intro.rst @@ -1,150 +1,150 @@ -.. _intro_chapter:
-
-===========================================================
-Getting started with Non-Linear Least-Squares Fitting
-===========================================================
-
-The lmfit package is designed to provide simple tools to help you build
-complex fitting models for non-linear least-squares problems and apply
-these models to real data. This section gives an overview of the concepts
-and describes how to set up and perform simple fits. Some basic knowledge
-of Python, numpy, and modeling data are assumed.
-
-To do a non-linear least-squares fit of a model to data or for a variety of other
-optimization problems, the main task is to write an *objective function*
-that takes the values of the fitting variables and calculates either a
-scalar value to be minimized or an array of values that is to be minimized
-in the least-squares sense. For many data fitting processes, the
-least-squares approach is used, and the objective function should
-return an array of (data-model), perhaps scaled by some weighting factor
-such as the inverse of the uncertainty in the data. For such a problem,
-the chi-square (:math:`\chi^2`) statistic is often defined as:
-
-.. math::
-
- \chi^2 = \sum_i^{N} \frac{[y^{\rm meas}_i - y_i^{\rm model}({\bf{v}})]^2}{\epsilon_i^2}
-
-where :math:`y_i^{\rm meas}` is the set of measured data, :math:`y_i^{\rm
-model}({\bf{v}})` is the model calculation, :math:`{\bf{v}}` is the set of
-variables in the model to be optimized in the fit, and :math:`\epsilon_i`
-is the estimated uncertainty in the data.
-
-In a traditional non-linear fit, one writes an objective function that takes the
-variable values and calculates the residual :math:`y^{\rm meas}_i -
-y_i^{\rm model}({\bf{v}})`, or the residual scaled by the data
-uncertainties, :math:`[y^{\rm meas}_i - y_i^{\rm
-model}({\bf{v}})]/{\epsilon_i}`, or some other weighting factor. As a
-simple example, one might write an objective function like this::
-
- def residual(vars, x, data, eps_data):
- amp = vars[0]
- phaseshift = vars[1]
- freq = vars[2]
- decay = vars[3]
-
- model = amp * sin(x * freq + phaseshift) * exp(-x*x*decay)
-
- return (data-model)/eps_data
-
-To perform the minimization with :mod:`scipy.optimize`, one would do::
-
- from scipy.optimize import leastsq
- vars = [10.0, 0.2, 3.0, 0.007]
- out = leastsq(residual, vars, args=(x, data, eps_data))
-
-Though it is wonderful to be able to use python for such optimization
-problems, and the scipy library is robust and easy to use, the approach
-here is not terribly different from how one would do the same fit in C or
-Fortran. There are several practical challenges to using this approach,
-including:
-
- a) The user has to keep track of the order of the variables, and their
- meaning -- vars[0] is the amplitude, vars[2] is the frequency, and so
- on, although there is no intrinsic meaning to this order.
-
- b) If the user wants to fix a particular variable (*not* vary it in the
- fit), the residual function has to be altered to have fewer variables,
- and have the corresponding constant value passed in some other way.
- While reasonable for simple cases, this quickly becomes a significant
- work for more complex models, and greatly complicates modeling for
- people not intimately familiar with the details of the fitting code.
-
- c) There is no simple, robust way to put bounds on values for the
- variables, or enforce mathematical relationships between the
- variables. In fact, those optimization methods that do provide
- bounds, require bounds to be set for all variables with separate
- arrays that are in the same arbitrary order as variable values.
- Again, this is acceptable for small or one-off cases, but becomes
- painful if the fitting model needs to change.
-
-These shortcomings are really do solely to the use of traditional arrays of
-variables, as matches closely the implementation of the Fortran code. The
-lmfit module overcomes these shortcomings by using objects -- a core reason for wokring with
-Python. The key concept for lmfit is to use :class:`Parameter`
-objects instead of plain floating point numbers as the variables for the
-fit. By using :class:`Parameter` objects (or the closely related
-:class:`Parameters` -- a dictionary of :class:`Parameter` objects), one can
-
- a) forget about the order of variables and refer to Parameters
- by meaningful names.
- b) place bounds on Parameters as attributes, without worrying about order.
- c) fix Parameters, without having to rewrite the objective function.
- d) place algebraic constraints on Parameters.
-
-To illustrate the value of this approach, we can rewrite the above example
-as::
-
- from lmfit import minimize, Parameters
-
- def residual(params, x, data, eps_data):
- amp = params['amp'].value
- pshift = params['phase'].value
- freq = params['frequency'].value
- decay = params['decay'].value
-
- model = amp * sin(x * freq + pshift) * exp(-x*x*decay)
-
- return (data-model)/eps_data
-
- params = Parameters()
- params.add('amp', value=10)
- params.add('decay', value=0.007)
- params.add('phase', value=0.2)
- params.add('frequency', value=3.0)
-
- out = minimize(residual, params, args=(x, data, eps_data))
-
-
-At first look, we simply replaced a list of values with a dictionary,
-accessed by name -- not a huge improvement. But each of the named
-:class:`Parameter` in the :class:`Parameters` object holds additional
-attributes to modify the value during the fit. For example, Parameters can
-be fixed or bounded. This can be done during definition::
-
- params = Parameters()
- params.add('amp', value=10, vary=False)
- params.add('decay', value=0.007, min=0.0)
- params.add('phase', value=0.2)
- params.add('frequency', value=3.0, max=10)
-
-where ``vary=False`` will prevent the value from changing in the fit, and
-``min=0.0`` will set a lower bound on that parameters value). It can also be done
-later by setting the corresponding attributes after they have been
-created::
-
- params['amp'].vary = False
- params['decay'].min = 0.10
-
-Importantly, our objective function remains unchanged.
-
-The `params` object can be copied and modified to make many user-level
-changes to the model and fitting process. Of course, most of the
-information about how your data is modeled goes into the objective
-function, but the approach here allows some external control; that is, control by
-the **user** performing the fit, instead of by the author of the
-objective function.
-
-Finally, in addition to the :class:`Parameters` approach to fitting data,
-lmfit allows switching optimization methods without changing
-the objective function, provides tools for writing fitting reports, and
-provides better determination of Parameters confidence levels.
+.. _intro_chapter: + +=========================================================== +Getting started with Non-Linear Least-Squares Fitting +=========================================================== + +The lmfit package is designed to provide simple tools to help you build +complex fitting models for non-linear least-squares problems and apply +these models to real data. This section gives an overview of the concepts +and describes how to set up and perform simple fits. Some basic knowledge +of Python, numpy, and modeling data are assumed. + +To do a non-linear least-squares fit of a model to data or for a variety of other +optimization problems, the main task is to write an *objective function* +that takes the values of the fitting variables and calculates either a +scalar value to be minimized or an array of values that is to be minimized +in the least-squares sense. For many data fitting processes, the +least-squares approach is used, and the objective function should +return an array of (data-model), perhaps scaled by some weighting factor +such as the inverse of the uncertainty in the data. For such a problem, +the chi-square (:math:`\chi^2`) statistic is often defined as: + +.. math:: + + \chi^2 = \sum_i^{N} \frac{[y^{\rm meas}_i - y_i^{\rm model}({\bf{v}})]^2}{\epsilon_i^2} + +where :math:`y_i^{\rm meas}` is the set of measured data, :math:`y_i^{\rm +model}({\bf{v}})` is the model calculation, :math:`{\bf{v}}` is the set of +variables in the model to be optimized in the fit, and :math:`\epsilon_i` +is the estimated uncertainty in the data. + +In a traditional non-linear fit, one writes an objective function that takes the +variable values and calculates the residual :math:`y^{\rm meas}_i - +y_i^{\rm model}({\bf{v}})`, or the residual scaled by the data +uncertainties, :math:`[y^{\rm meas}_i - y_i^{\rm +model}({\bf{v}})]/{\epsilon_i}`, or some other weighting factor. As a +simple example, one might write an objective function like this:: + + def residual(vars, x, data, eps_data): + amp = vars[0] + phaseshift = vars[1] + freq = vars[2] + decay = vars[3] + + model = amp * sin(x * freq + phaseshift) * exp(-x*x*decay) + + return (data-model)/eps_data + +To perform the minimization with :mod:`scipy.optimize`, one would do:: + + from scipy.optimize import leastsq + vars = [10.0, 0.2, 3.0, 0.007] + out = leastsq(residual, vars, args=(x, data, eps_data)) + +Though it is wonderful to be able to use python for such optimization +problems, and the scipy library is robust and easy to use, the approach +here is not terribly different from how one would do the same fit in C or +Fortran. There are several practical challenges to using this approach, +including: + + a) The user has to keep track of the order of the variables, and their + meaning -- vars[0] is the amplitude, vars[2] is the frequency, and so + on, although there is no intrinsic meaning to this order. + + b) If the user wants to fix a particular variable (*not* vary it in the + fit), the residual function has to be altered to have fewer variables, + and have the corresponding constant value passed in some other way. + While reasonable for simple cases, this quickly becomes a significant + work for more complex models, and greatly complicates modeling for + people not intimately familiar with the details of the fitting code. + + c) There is no simple, robust way to put bounds on values for the + variables, or enforce mathematical relationships between the + variables. In fact, those optimization methods that do provide + bounds, require bounds to be set for all variables with separate + arrays that are in the same arbitrary order as variable values. + Again, this is acceptable for small or one-off cases, but becomes + painful if the fitting model needs to change. + +These shortcomings are really do solely to the use of traditional arrays of +variables, as matches closely the implementation of the Fortran code. The +lmfit module overcomes these shortcomings by using objects -- a core reason for working with +Python. The key concept for lmfit is to use :class:`Parameter` +objects instead of plain floating point numbers as the variables for the +fit. By using :class:`Parameter` objects (or the closely related +:class:`Parameters` -- a dictionary of :class:`Parameter` objects), one can + + a) forget about the order of variables and refer to Parameters + by meaningful names. + b) place bounds on Parameters as attributes, without worrying about order. + c) fix Parameters, without having to rewrite the objective function. + d) place algebraic constraints on Parameters. + +To illustrate the value of this approach, we can rewrite the above example +as:: + + from lmfit import minimize, Parameters + + def residual(params, x, data, eps_data): + amp = params['amp'].value + pshift = params['phase'].value + freq = params['frequency'].value + decay = params['decay'].value + + model = amp * sin(x * freq + pshift) * exp(-x*x*decay) + + return (data-model)/eps_data + + params = Parameters() + params.add('amp', value=10) + params.add('decay', value=0.007) + params.add('phase', value=0.2) + params.add('frequency', value=3.0) + + out = minimize(residual, params, args=(x, data, eps_data)) + + +At first look, we simply replaced a list of values with a dictionary, +accessed by name -- not a huge improvement. But each of the named +:class:`Parameter` in the :class:`Parameters` object holds additional +attributes to modify the value during the fit. For example, Parameters can +be fixed or bounded. This can be done during definition:: + + params = Parameters() + params.add('amp', value=10, vary=False) + params.add('decay', value=0.007, min=0.0) + params.add('phase', value=0.2) + params.add('frequency', value=3.0, max=10) + +where ``vary=False`` will prevent the value from changing in the fit, and +``min=0.0`` will set a lower bound on that parameters value). It can also be done +later by setting the corresponding attributes after they have been +created:: + + params['amp'].vary = False + params['decay'].min = 0.10 + +Importantly, our objective function remains unchanged. + +The `params` object can be copied and modified to make many user-level +changes to the model and fitting process. Of course, most of the +information about how your data is modeled goes into the objective +function, but the approach here allows some external control; that is, control by +the **user** performing the fit, instead of by the author of the +objective function. + +Finally, in addition to the :class:`Parameters` approach to fitting data, +lmfit allows switching optimization methods without changing +the objective function, provides tools for writing fitting reports, and +provides better determination of Parameters confidence levels. diff --git a/doc/model.rst b/doc/model.rst index 1e1054b..9b0b595 100644 --- a/doc/model.rst +++ b/doc/model.rst @@ -1,1140 +1,1150 @@ -.. _model_chapter:
-
-=================================================
-Modeling Data and Curve Fitting
-=================================================
-
-.. module:: model
-
-A common use of least-squares minimization is *curve fitting*, where one
-has a parametrized model function meant to explain some phenomena and wants
-to adjust the numerical values for the model to most closely match some
-data. With :mod:`scipy`, such problems are commonly solved with
-:func:`scipy.optimize.curve_fit`, which is a wrapper around
-:func:`scipy.optimize.leastsq`. Since Lmfit's :func:`minimize` is also a
-high-level wrapper around :func:`scipy.optimize.leastsq` it can be used for
-curve-fitting problems, but requires more effort than using
-:func:`scipy.optimize.curve_fit`.
-
-Here we discuss lmfit's :class:`Model` class. This takes a model function
--- a function that calculates a model for some data -- and provides methods
-to create parameters for that model and to fit data using that model
-function. This is closer in spirit to :func:`scipy.optimize.curve_fit`,
-but with the advantages of using :class:`Parameters` and lmfit.
-
-In addition to allowing you turn any model function into a curve-fitting
-method, Lmfit also provides canonical definitions for many known line shapes
-such as Gaussian or Lorentzian peaks and Exponential decays that are widely
-used in many scientific domains. These are available in the :mod:`models`
-module that will be discussed in more detail in the next chapter
-(:ref:`builtin_models_chapter`). We mention it here as you may want to
-consult that list before writing your own model. For now, we focus on
-turning python function into high-level fitting models with the
-:class:`Model` class, and using these to fit data.
-
-
-Example: Fit data to Gaussian profile
-================================================
-
-Let's start with a simple and common example of fitting data to a Gaussian
-peak. As we will see, there is a buit-in :class:`GaussianModel` class that
-provides a model function for a Gaussian profile, but here we'll build our
-own. We start with a simple definition of the model function:
-
- >>> from numpy import sqrt, pi, exp, linspace
- >>>
- >>> def gaussian(x, amp, cen, wid):
- ... return amp * exp(-(x-cen)**2 /wid)
- ...
-
-We want to fit this objective function to data :math:`y(x)` represented by the
-arrays ``y`` and ``x``. This can be done easily wit :func:`scipy.optimize.curve_fit`::
-
- >>> from scipy.optimize import curve_fit
- >>>
- >>> x = linspace(-10,10)
- >>> y = y = gaussian(x, 2.33, 0.21, 1.51) + np.random.normal(0, 0.2, len(x))
- >>>
- >>> init_vals = [1, 0, 1] # for [amp, cen, wid]
- >>> best_vals, covar = curve_fit(gaussian, x, y, p0=init_vals)
- >>> print best_vals
-
-
-We sample random data point, make an initial guess of the model
-values, and run :func:`scipy.optimize.curve_fit` with the model function,
-data arrays, and initial guesses. The results returned are the optimal
-values for the parameters and the covariance matrix. It's simple and very
-useful. But it misses the benefits of lmfit.
-
-
-To solve this with lmfit we would have to write an objective function. But
-such a function would be fairly simple (essentially, ``data - model``,
-possibly with some weighting), and we would need to define and use
-appropriately named parameters. Though convenient, it is somewhat of a
-burden to keep the named parameter straight (on the other hand, with
-:func:`scipy.optimize.curve_fit` you are required to remember the parameter
-order). After doing this a few times it appears as a recurring pattern,
-and we can imagine automating this process. That's where the
-:class:`Model` class comes in.
-
-:class:`Model` allows us to easily wrap a model function such as the
-``gaussian`` function. This automatically generate the appropriate
-residual function, and determines the corresponding parameter names from
-the function signature itself::
-
- >>> from lmfit import Model
- >>> gmod = Model(gaussian)
- >>> gmod.param_names
- set(['amp', 'wid', 'cen'])
- >>> gmod.independent_vars)
- ['x']
-
-The Model ``gmod`` knows the names of the parameters and the independent
-variables. By default, the first argument of the function is taken as the
-independent variable, held in :attr:`independent_vars`, and the rest of the
-functions positional arguments (and, in certain cases, keyword arguments --
-see below) are used for Parameter names. Thus, for the ``gaussian``
-function above, the parameters are named ``amp``, ``cen``, and ``wid``, and
-``x`` is the independent variable -- all taken directly from the signature
-of the model function. As we will see below, you can specify what the
-independent variable is, and you can add or alter parameters, too.
-
-The parameters are *not* created when the model is created. The model knows
-what the parameters should be named, but not anything about the scale and
-range of your data. You will normally have to make these parameters and
-assign initial values and other attributes. To help you do this, each
-model has a :meth:`make_params` method that will generate parameters with
-the expected names:
-
- >>> params = gmod.make_params()
-
-This creates the :class:`Parameters` but doesn't necessarily give them
-initial values -- again, the model has no idea what the scale should be.
-You can set initial values for parameters with keyword arguments to
-:meth:`make_params`:
-
-
- >>> params = gmod.make_params(cen=5, amp=200, wid=1)
-
-or assign them (and other parameter properties) after the
-:class:`Parameters` has been created.
-
-A :class:`Model` has several methods associated with it. For example, one
-can use the :meth:`eval` method to evaluate the model or the :meth:`fit`
-method to fit data to this model with a :class:`Parameter` object. Both of
-these methods can take explicit keyword arguments for the parameter values.
-For example, one could use :meth:`eval` to calculate the predicted
-function::
-
- >>> x = linspace(0, 10, 201)
- >>> y = gmod.eval(x=x, amp=10, cen=6.2, wid=0.75)
-
-Admittedly, this a slightly long-winded way to calculate a Gaussian
-function. But now that the model is set up, we can also use its
-:meth:`fit` method to fit this model to data, as with::
-
- >>> result = gmod.fit(y, x=x, amp=5, cen=5, wid=1)
-
-Putting everything together, the script to do such a fit (included in the
-``examples`` folder with the source code) is:
-
-.. literalinclude:: ../examples/doc_model1.py
-
-which is pretty compact and to the point. The returned ``result`` will be
-a :class:`ModelResult` object. As we will see below, this has many
-components, including a :meth:`fit_report` method, which will show::
-
- [[Model]]
- gaussian
- [[Fit Statistics]]
- # function evals = 33
- # data points = 101
- # variables = 3
- chi-square = 3.409
- reduced chi-square = 0.035
- [[Variables]]
- amp: 8.88021829 +/- 0.113594 (1.28%) (init= 5)
- cen: 5.65866102 +/- 0.010304 (0.18%) (init= 5)
- wid: 0.69765468 +/- 0.010304 (1.48%) (init= 1)
- [[Correlations]] (unreported correlations are < 0.100)
- C(amp, wid) = 0.577
-
-The result will also have :attr:`init_fit` for the fit with the initial
-parameter values and a :attr:`best_fit` for the fit with the best fit
-parameter values. These can be used to generate the following plot:
-
-
-.. image:: _images/model_fit1.png
- :target: _images/model_fit1.png
- :width: 50%
-
-which shows the data in blue dots, the best fit as a solid red line, and
-the initial fit as a dashed black line.
-
-Note that the model fitting was really performed with 2 lines of code::
-
- gmod = Model(gaussian)
- result = gmod.fit(y, x=x, amp=5, cen=5, wid=1)
-
-These lines clearly express that we want to turn the ``gaussian`` function
-into a fitting model, and then fit the :math:`y(x)` data to this model,
-starting with values of 5 for ``amp``, 5 for ``cen`` and 1 for ``wid``.
-This is much more expressive than :func:`scipy.optimize.curve_fit`::
-
- best_vals, covar = curve_fit(gaussian, x, y, p0=[5, 5, 1])
-
-In addition, all the other features of lmfit are included:
-:class:`Parameters` can have bounds and constraints and the result is a
-rich object that can be reused to explore the model fit in detail.
-
-
-The :class:`Model` class
-=======================================
-
-The :class:`Model` class provides a general way to wrap a pre-defined
-function as a fitting model.
-
-.. class:: Model(func[, independent_vars=None[, param_names=None[, missing=None[, prefix=''[, name=None[, **kws]]]]]])
-
- Create a model based on the user-supplied function. This uses
- introspection to automatically converting argument names of the
- function to Parameter names.
-
- :param func: model function to be wrapped
- :type func: callable
- :param independent_vars: list of argument names to ``func`` that are independent variables.
- :type independent_vars: ``None`` (default) or list of strings.
- :param param_names: list of argument names to ``func`` that should be made into Parameters.
- :type param_names: ``None`` (default) or list of strings
- :param missing: how to handle missing values.
- :type missing: one of ``None`` (default), 'none', 'drop', or 'raise'.
- :param prefix: prefix to add to all parameter names to distinguish components in a :class:`CompositeModel`.
- :type prefix: string
- :param name: name for the model. When ``None`` (default) the name is the same as the model function (``func``).
- :type name: ``None`` or string.
- :param kws: additional keyword arguments to pass to model function.
-
-
-Of course, the model function will have to return an array that will be the
-same size as the data being modeled. Generally this is handled by also
-specifying one or more independent variables.
-
-
-:class:`Model` class Methods
----------------------------------
-
-.. method:: Model.eval(params=None[, **kws])
-
- evaluate the model function for a set of parameters and inputs.
-
- :param params: parameters to use for fit.
- :type params: ``None`` (default) or Parameters
- :param kws: additional keyword arguments to pass to model function.
- :return: ndarray for model given the parameters and other arguments.
-
- If ``params`` is ``None``, the values for all parameters are expected to
- be provided as keyword arguments. If ``params`` is given, and a keyword
- argument for a parameter value is also given, the keyword argument will
- be used.
-
- Note that all non-parameter arguments for the model function --
- **including all the independent variables!** -- will need to be passed
- in using keyword arguments.
-
-
-.. method:: Model.fit(data[, params=None[, weights=None[, method='leastsq'[, scale_covar=True[, iter_cb=None[, **kws]]]]]])
-
- perform a fit of the model to the ``data`` array with a set of
- parameters.
-
- :param data: array of data to be fitted.
- :type data: ndarray-like
- :param params: parameters to use for fit.
- :type params: ``None`` (default) or Parameters
- :param weights: weights to use for residual calculation in fit.
- :type weights: ``None`` (default) or ndarray-like.
- :param method: name of fitting method to use. See :ref:`fit-methods-label` for details
- :type method: string (default ``leastsq``)
- :param scale_covar: whether to automatically scale covariance matrix (``leastsq`` only)
- :type scale_covar: bool (default ``True``)
- :param iter_cb: function to be called at each fit iteration. See :ref:`fit-itercb-label` for details.
- :type iter_cb: callable or ``None``
- :param verbose: print a message when a new parameter is created due to a *hint*
- :type verbose: bool (default ``True``)
- :param kws: additional keyword arguments to pass to model function.
- :return: :class:`ModelResult` object.
-
- If ``params`` is ``None``, the internal ``params`` will be used. If it
- is supplied, these will replace the internal ones. If supplied,
- ``weights`` will be used to weight the calculated residual so that the
- quantitiy minimized in the least-squares sense is ``weights*(data -
- fit)``. ``weights`` must be an ndarray-like object of same size and
- shape as ``data``.
-
- Note that other arguments for the model function (including all the
- independent variables!) will need to be passed in using keyword
- arguments.
-
-
-.. method:: Model.guess(data, **kws)
-
- Guess starting values for model parameters.
-
- :param data: data array used to guess parameter values
- :type func: ndarray
- :param kws: additional options to pass to model function.
- :return: :class:`Parameters` with guessed initial values for each parameter.
-
- by default this is left to raise a ``NotImplementedError``, but may be
- overwritten by subclasses. Generally, this method should take some
- values for ``data`` and use it to construct reasonable starting values for
- the parameters.
-
-
-.. method:: Model.make_params(**kws)
-
- Create a set of parameters for model.
-
- :param kws: optional keyword/value pairs to set initial values for parameters.
- :return: :class:`Parameters`.
-
- The parameters may or may not have decent initial values for each
- parameter.
-
-
-.. method:: Model.set_param_hint(name, value=None[, min=None[, max=None[, vary=True[, expr=None]]]])
-
- set *hints* to use when creating parameters with :meth:`Model.make_param` for
- the named parameter. This is especially convenient for setting initial
- values. The ``name`` can include the models ``prefix`` or not.
-
- :param name: parameter name.
- :type name: string
- :param value: value for parameter
- :type value: float
- :param min: lower bound for parameter value
- :type min: ``None`` or float
- :param max: upper bound for parameter value
- :type max: ``None`` or float
- :param vary: whether to vary parameter in fit.
- :type vary: boolean
- :param expr: mathematical expression for constraint
- :type expr: string
-
- See :ref:`model_param_hints_section`.
-
-
-:class:`Model` class Attributes
----------------------------------
-
-.. attribute:: func
-
- The model function used to calculate the model.
-
-.. attribute:: independent_vars
-
- list of strings for names of the independent variables.
-
-.. attribute:: missing
-
- describes what to do for missing values. The choices are
-
- * ``None``: Do not check for null or missing values (default)
- * ``'none'``: Do not check for null or missing values.
- * ``'drop'``: Drop null or missing observations in data. If pandas is
- installed, ``pandas.isnull`` is used, otherwise :attr:`numpy.isnan` is used.
- * ``'raise'``: Raise a (more helpful) exception when data contains null
- or missing values.
-
-.. attribute:: name
-
- name of the model, used only in the string representation of the
- model. By default this will be taken from the model function.
-
-.. attribute:: opts
-
- extra keyword arguments to pass to model function. Normally this will
- be determined internally and should not be changed.
-
-.. attribute:: param_hints
-
- Dictionary of parameter hints. See :ref:`model_param_hints_section`.
-
-.. attribute:: param_names
-
- list of strings of parameter names.
-
-.. attribute:: prefix
-
- prefix used for name-mangling of parameter names. The default is ''.
- If a particular :class:`Model` has arguments ``amplitude``,
- ``center``, and ``sigma``, these would become the parameter names.
- Using a prefix of ``g1_`` would convert these parameter names to
- ``g1_amplitude``, ``g1_center``, and ``g1_sigma``. This can be
- essential to avoid name collision in composite models.
-
-
-Determining parameter names and independent variables for a function
------------------------------------------------------------------------
-
-The :class:`Model` created from the supplied function ``func`` will create
-a :class:`Parameters` object, and names are inferred from the function
-arguments, and a residual function is automatically constructed.
-
-
-By default, the independent variable is take as the first argument to the
-function. You can explicitly set this, of course, and will need to if the
-independent variable is not first in the list, or if there are actually more
-than one independent variables.
-
-If not specified, Parameters are constructed from all positional arguments
-and all keyword arguments that have a default value that is numerical, except
-the independent variable, of course. Importantly, the Parameters can be
-modified after creation. In fact, you'll have to do this because none of the
-parameters have valid initial values. You can place bounds and constraints
-on Parameters, or fix their values.
-
-
-
-Explicitly specifying ``independent_vars``
--------------------------------------------------
-
-As we saw for the Gaussian example above, creating a :class:`Model` from a
-function is fairly easy. Let's try another::
-
- >>> def decay(t, tau, N):
- ... return N*np.exp(-t/tau)
- ...
- >>> decay_model = Model(decay)
- >>> print decay_model.independent_vars
- ['t']
- >>> for pname, par in decay_model.params.items():
- ... print pname, par
- ...
- tau <Parameter 'tau', None, bounds=[None:None]>
- N <Parameter 'N', None, bounds=[None:None]>
-
-Here, ``t`` is assumed to be the independent variable because it is the
-first argument to the function. The other function arguments are used to
-create parameters for the model.
-
-If you want ``tau`` to be the independent variable in the above example,
-you can say so::
-
- >>> decay_model = Model(decay, independent_vars=['tau'])
- >>> print decay_model.independent_vars
- ['tau']
- >>> for pname, par in decay_model.params.items():
- ... print pname, par
- ...
- t <Parameter 't', None, bounds=[None:None]>
- N <Parameter 'N', None, bounds=[None:None]>
-
-
-You can also supply multiple values for multi-dimensional functions with
-multiple independent variables. In fact, the meaning of *independent
-variable* here is simple, and based on how it treats arguments of the
-function you are modeling:
-
-independent variable
- a function argument that is not a parameter or otherwise part of the
- model, and that will be required to be explicitly provided as a
- keyword argument for each fit with :meth:`Model.fit` or evaluation
- with :meth:`Model.eval`.
-
-Note that independent variables are not required to be arrays, or even
-floating point numbers.
-
-
-Functions with keyword arguments
------------------------------------------
-
-If the model function had keyword parameters, these would be turned into
-Parameters if the supplied default value was a valid number (but not
-``None``, ``True``, or ``False``).
-
- >>> def decay2(t, tau, N=10, check_positive=False):
- ... if check_small:
- ... arg = abs(t)/max(1.e-9, abs(tau))
- ... else:
- ... arg = t/tau
- ... return N*np.exp(arg)
- ...
- >>> mod = Model(decay2)
- >>> for pname, par in mod.params.items():
- ... print pname, par
- ...
- t <Parameter 't', None, bounds=[None:None]>
- N <Parameter 'N', 10, bounds=[None:None]>
-
-Here, even though ``N`` is a keyword argument to the function, it is turned
-into a parameter, with the default numerical value as its initial value.
-By default, it is permitted to be varied in the fit -- the 10 is taken as
-an initial value, not a fixed value. On the other hand, the
-``check_positive`` keyword argument, was not converted to a parameter
-because it has a boolean default value. In some sense,
-``check_positive`` becomes like an independent variable to the model.
-However, because it has a default value it is not required to be given for
-each model evaluation or fit, as independent variables are.
-
-Defining a ``prefix`` for the Parameters
---------------------------------------------
-
-As we will see in the next chapter when combining models, it is sometimes
-necessary to decorate the parameter names in the model, but still have them
-be correctly used in the underlying model function. This would be
-necessary, for example, if two parameters in a composite model (see
-:ref:`composite_models_section` or examples in the next chapter) would have
-the same name. To avoid this, we can add a ``prefix`` to the
-:class:`Model` which will automatically do this mapping for us.
-
- >>> def myfunc(x, amplitude=1, center=0, sigma=1):
- ...
-
- >>> mod = Model(myfunc, prefix='f1_')
- >>> for pname, par in mod.params.items():
- ... print pname, par
- ...
- f1_amplitude <Parameter 'f1_amplitude', None, bounds=[None:None]>
- f1_center <Parameter 'f1_center', None, bounds=[None:None]>
- f1_sigma <Parameter 'f1_sigma', None, bounds=[None:None]>
-
-You would refer to these parameters as ``f1_amplitude`` and so forth, and
-the model will know to map these to the ``amplitude`` argument of ``myfunc``.
-
-
-Initializing model parameters
------------------------------------------
-
-As mentioned above, the parameters created by :meth:`Model.make_params` are
-generally created with invalid initial values of ``None``. These values
-**must** be initialized in order for the model to be evaluated or used in a
-fit. There are four different ways to do this initialization that can be
-used in any combination:
-
- 1. You can supply initial values in the definition of the model function.
- 2. You can initialize the parameters when creating parameters with :meth:`Model.make_params`.
- 3. You can give parameter hints with :meth:`Model.set_param_hint`.
- 4. You can supply initial values for the parameters when you use the
- :meth:`Model.eval` or :meth:`Model.fit` methods.
-
-Of course these methods can be mixed, allowing you to overwrite initial
-values at any point in the process of defining and using the model.
-
-Initializing values in the function definition
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-To supply initial values for parameters in the definition of the model
-function, you can simply supply a default value::
-
- >>> def myfunc(x, a=1, b=0):
- >>> ...
-
-instead of using::
-
- >>> def myfunc(x, a, b):
- >>> ...
-
-This has the advantage of working at the function level -- all parameters
-with keywords can be treated as options. It also means that some default
-initial value will always be available for the parameter.
-
-
-Initializing values with :meth:`Model.make_params`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-When creating parameters with :meth:`Model.make_params` you can specify initial
-values. To do this, use keyword arguments for the parameter names and
-initial values::
-
- >>> mod = Model(myfunc)
- >>> pars = mod.make_params(a=3, b=0.5)
-
-
-Initializing values by setting parameter hints
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-After a model has been created, but prior to creating parameters with
-:meth:`Model.make_params`, you can set parameter hints. These allows you to set
-not only a default initial value but also to set other parameter attributes
-controlling bounds, whether it is varied in the fit, or a constraint
-expression. To set a parameter hint, you can use :meth:`Model.set_param_hint`,
-as with::
-
- >>> mod = Model(myfunc)
- >>> mod.set_param_hint('a', value = 1.0)
- >>> mod.set_param_hint('b', value = 0.3, min=0, max=1.0)
- >>> pars = mod.make_params()
-
-Parameter hints are discussed in more detail in section
-:ref:`model_param_hints_section`.
-
-
-Initializing values when using a model
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-Finally, you can explicitly supply initial values when using a model. That
-is, as with :meth:`Model.make_params`, you can include values
-as keyword arguments to either the :meth:`Model.eval` or :meth:`Model.fit` methods::
-
- >>> y1 = mod.eval(x=x, a=7.0, b=-2.0)
-
- >>> out = mod.fit(x=x, pars, a=3.0, b=-0.0)
-
-These approaches to initialization provide many opportunities for setting
-initial values for parameters. The methods can be combined, so that you
-can set parameter hints but then change the initial value explicitly with
-:meth:`Model.fit`.
-
-.. _model_param_hints_section:
-
-Using parameter hints
---------------------------------
-
-
-After a model has been created, you can give it hints for how to create
-parameters with :meth:`Model.make_params`. This allows you to set not only a
-default initial value but also to set other parameter attributes
-controlling bounds, whether it is varied in the fit, or a constraint
-expression. To set a parameter hint, you can use :meth:`Model.set_param_hint`,
-as with::
-
- >>> mod = Model(myfunc)
- >>> mod.set_param_hint('a', value = 1.0)
- >>> mod.set_param_hint('b', value = 0.3, min=0, max=1.0)
-
-Parameter hints are stored in a model's :attr:`param_hints` attribute,
-which is simply a nested dictionary::
-
- >>> print mod.param_hints
- {'a': {'value': 1}, 'b': {'max': 1.0, 'value': 0.3, 'min': 0}}
-
-
-You can change this dictionary directly, or with the :meth:`Model.set_param_hint`
-method. Either way, these parameter hints are used by :meth:`Model.make_params`
-when making parameters.
-
-An important feature of parameter hints is that you can force the creation
-of new parameters with parameter hints. This can be useful to make derived
-parameters with constraint expressions. For example to get the full-width
-at half maximum of a Gaussian model, one could use a parameter hint of::
-
- >>> mod = Model(gaussian)
- >>> mod.set_param_hint('fwhm', expr='2.3548*sigma')
-
-
-
-The :class:`ModelResult` class
-=======================================
-
-A :class:`ModelResult` (which had been called `ModelFit` prior to version
-0.9) is the object returned by :meth:`Model.fit`. It is a subclass of
-:class:`Minimizer`, and so contains many of the fit results. Of course, it
-knows the :class:`Model` and the set of :class:`Parameters` used in the
-fit, and it has methods to evaluate the model, to fit the data (or re-fit
-the data with changes to the parameters, or fit with different or modified
-data) and to print out a report for that fit.
-
-While a :class:`Model` encapsulates your model function, it is fairly
-abstract and does not contain the parameters or data used in a particular
-fit. A :class:`ModelResult` *does* contain parameters and data as well as
-methods to alter and re-do fits. Thus the :class:`Model` is the idealized
-model while the :class:`ModelResult` is the messier, more complex (but perhaps
-more useful) object that represents a fit with a set of parameters to data
-with a model.
-
-
-A :class:`ModelResult` has several attributes holding values for fit results,
-and several methods for working with fits. These include statistics
-inherited from :class:`Minimizer` useful for comparing different models,
-includind `chisqr`, `redchi`, `aic`, and `bic`.
-
-.. class:: ModelResult()
-
- Model fit is intended to be created and returned by :meth:`Model.fit`.
-
-
-
-:class:`ModelResult` methods
----------------------------------
-
-These methods are all inherited from :class:`Minimize` or from
-:class:`Model`.
-
-.. method:: ModelResult.eval(**kwargs)
-
- evaluate the model using the best-fit parameters and supplied
- independent variables. The ``**kwargs`` arguments can be used to update
- parameter values and/or independent variables.
-
-
-.. method:: ModelResult.eval_components(**kwargs)
-
- evaluate each component of a :class:`CompositeModel`, returning an
- ordered dictionary of with the values for each component model. The
- returned dictionary will have keys of the model prefix or (if no prefix
- is given), the model name. The ``**kwargs`` arguments can be used to
- update parameter values and/or independent variables.
-
-.. method:: ModelResult.fit(data=None[, params=None[, weights=None[, method=None[, **kwargs]]]])
-
- fit (or re-fit), optionally changing ``data``, ``params``, ``weights``,
- or ``method``, or changing the independent variable(s) with the
- ``**kwargs`` argument. See :meth:`Model.fit` for argument
- descriptions, and note that any value of ``None`` defaults to the last
- used value.
-
-.. method:: ModelResult.fit_report(modelpars=None[, show_correl=True[,`< min_correl=0.1]])
-
- return a printable fit report for the fit with fit statistics, best-fit
- values with uncertainties and correlations. As with :func:`fit_report`.
-
- :param modelpars: Parameters with "Known Values" (optional, default None)
- :param show_correl: whether to show list of sorted correlations [``True``]
- :param min_correl: smallest correlation absolute value to show [0.1]
-
-
-.. method:: ModelResult.conf_interval(**kwargs)
-
- calculate the confidence intervals for the variable parameters using
- :func:`confidence.conf_interval() <lmfit.conf_interval>`. All keyword
- arguments are passed to that function. The result is stored in
- :attr:`ci_out`, and so can be accessed without recalculating them.
-
-.. method:: ModelResult.ci_report(with_offset=True)
-
- return a nicely formatted text report of the confidence intervals, as
- from :func:`ci_report() <lmfit.ci_report>`.
-
-
-.. method:: ModelResult.plot(datafmt='o', fitfmt='-', initfmt='--', yerr=None, numpoints=None, fig=None, data_kws=None, fit_kws=None, init_kws=None, ax_res_kws=None, ax_fit_kws=None, fig_kws=None)
-
- Plot the fit results and residuals using matplotlib, if available. The
- plot will include two panels, one showing the fit residual, and the
- other with the data points, the initial fit curve, and the best-fit
- curve. If the fit model included weights or if ``yerr`` is specified,
- errorbars will also be plotted.
-
- :param datafmt: matplotlib format string for data curve.
- :type datafmt: ``None`` or string.
- :param fitfmt: matplotlib format string for best-fit curve.
- :type fitfmt: ``None`` or string.
- :param initfmt: matplotlib format string for initial curve.
- :type intfmt: ``None`` or string.
- :param yerr: array of uncertainties for data array.
- :type yerr: ``None`` or ndarray.
- :param numpoints: number of points to display
- :type numpoints: ``None`` or integer
- :param fig: matplotlib Figure to plot on.
- :type fig: ``None`` or matplotlib.figure.Figure
- :param data_kws: keyword arguments passed to plot for data curve.
- :type data_kws: ``None`` or dictionary
- :param fit_kws: keyword arguments passed to plot for best-fit curve.
- :type fit_kws: ``None`` or dictionary
- :param init_kws: keyword arguments passed to plot for initial curve.
- :type init_kws: ``None`` or dictionary
- :param ax_res_kws: keyword arguments passed to creation of matplotlib axes for the residual plot.
- :type ax_res_kws: ``None`` or dictionary
- :param ax_fit_kws: keyword arguments passed to creation of matplotlib axes for the fit plot.
- :type ax_fit_kws: ``None`` or dictionary
- :param fig_kws: keyword arguments passed to creation of matplotlib figure.
- :type fig_kws: ``None`` or dictionary
- :returns: matplotlib.figure.Figure
-
- This combines :meth:`ModelResult.plot_fit` and :meth:`ModelResult.plot_residual`.
-
- If ``yerr`` is specified or if the fit model included weights, then
- matplotlib.axes.Axes.errorbar is used to plot the data. If ``yerr`` is
- not specified and the fit includes weights, ``yerr`` set to ``1/self.weights``
-
- If ``fig`` is None then ``matplotlib.pyplot.figure(**fig_kws)`` is called.
-
-.. method:: ModelResult.plot_fit(ax=None, datafmt='o', fitfmt='-', initfmt='--', yerr=None, numpoints=None, data_kws=None, fit_kws=None, init_kws=None, ax_kws=None)
-
- Plot the fit results using matplotlib, if available. The plot will include
- the data points, the initial fit curve, and the best-fit curve. If the fit
- model included weights or if ``yerr`` is specified, errorbars will also
- be plotted.
-
- :param ax: matplotlib axes to plot on.
- :type ax: ``None`` or matplotlib.axes.Axes.
- :param datafmt: matplotlib format string for data curve.
- :type datafmt: ``None`` or string.
- :param fitfmt: matplotlib format string for best-fit curve.
- :type fitfmt: ``None`` or string.
- :param initfmt: matplotlib format string for initial curve.
- :type intfmt: ``None`` or string.
- :param yerr: array of uncertainties for data array.
- :type yerr: ``None`` or ndarray.
- :param numpoints: number of points to display
- :type numpoints: ``None`` or integer
- :param data_kws: keyword arguments passed to plot for data curve.
- :type data_kws: ``None`` or dictionary
- :param fit_kws: keyword arguments passed to plot for best-fit curve.
- :type fit_kws: ``None`` or dictionary
- :param init_kws: keyword arguments passed to plot for initial curve.
- :type init_kws: ``None`` or dictionary
- :param ax_kws: keyword arguments passed to creation of matplotlib axes.
- :type ax_kws: ``None`` or dictionary
- :returns: matplotlib.axes.Axes
-
- For details about plot format strings and keyword arguments see
- documentation of :func:`matplotlib.axes.Axes.plot`.
-
- If ``yerr`` is specified or if the fit model included weights, then
- matplotlib.axes.Axes.errorbar is used to plot the data. If ``yerr`` is
- not specified and the fit includes weights, ``yerr`` set to ``1/self.weights``
-
- If ``ax`` is None then ``matplotlib.pyplot.gca(**ax_kws)`` is called.
-
-.. method:: ModelResult.plot_residuals(ax=None, datafmt='o', yerr=None, data_kws=None, fit_kws=None, ax_kws=None)
-
- Plot the fit residuals (data - fit) using matplotlib. If ``yerr`` is
- supplied or if the model included weights, errorbars will also be plotted.
-
- :param ax: matplotlib axes to plot on.
- :type ax: ``None`` or matplotlib.axes.Axes.
- :param datafmt: matplotlib format string for data curve.
- :type datafmt: ``None`` or string.
- :param yerr: array of uncertainties for data array.
- :type yerr: ``None`` or ndarray.
- :param numpoints: number of points to display
- :type numpoints: ``None`` or integer
- :param data_kws: keyword arguments passed to plot for data curve.
- :type data_kws: ``None`` or dictionary
- :param fit_kws: keyword arguments passed to plot for best-fit curve.
- :type fit_kws: ``None`` or dictionary
- :param ax_kws: keyword arguments passed to creation of matplotlib axes.
- :type ax_kws: ``None`` or dictionary
- :returns: matplotlib.axes.Axes
-
- For details about plot format strings and keyword arguments see
- documentation of :func:`matplotlib.axes.Axes.plot`.
-
- If ``yerr`` is specified or if the fit model included weights, then
- matplotlib.axes.Axes.errorbar is used to plot the data. If ``yerr`` is
- not specified and the fit includes weights, ``yerr`` set to ``1/self.weights``
-
- If ``ax`` is None then ``matplotlib.pyplot.gca(**ax_kws)`` is called.
-
-
-
-
-:class:`ModelResult` attributes
----------------------------------
-
-.. attribute:: aic
-
- floating point best-fit Akaike Information Criterion statistic (see :ref:`fit-results-label`).
-
-.. attribute:: best_fit
-
- ndarray result of model function, evaluated at provided
- independent variables and with best-fit parameters.
-
-.. attribute:: best_values
-
- dictionary with parameter names as keys, and best-fit values as values.
-
-.. attribute:: bic
-
- floating point best-fit Bayesian Information Criterion statistic (see :ref:`fit-results-label`).
-
-.. attribute:: chisqr
-
- floating point best-fit chi-square statistic (see :ref:`fit-results-label`).
-
-.. attribute:: ci_out
-
- confidence interval data (see :ref:`confidence_chapter`) or `None` if
- the confidence intervals have not been calculated.
-
-.. attribute:: covar
-
- ndarray (square) covariance matrix returned from fit.
-
-.. attribute:: data
-
- ndarray of data to compare to model.
-
-.. attribute:: errorbars
-
- boolean for whether error bars were estimated by fit.
-
-.. attribute:: ier
-
- integer returned code from :func:`scipy.optimize.leastsq`.
-
-.. attribute:: init_fit
-
- ndarray result of model function, evaluated at provided
- independent variables and with initial parameters.
-
-.. attribute:: init_params
-
- initial parameters.
-
-.. attribute:: init_values
-
- dictionary with parameter names as keys, and initial values as values.
-
-.. attribute:: iter_cb
-
- optional callable function, to be called at each fit iteration. This
- must take take arguments of ``params, iter, resid, *args, **kws``, where
- ``params`` will have the current parameter values, ``iter`` the
- iteration, ``resid`` the current residual array, and ``*args`` and
- ``**kws`` as passed to the objective function. See :ref:`fit-itercb-label`.
-
-.. attribute:: jacfcn
-
- optional callable function, to be called to calculate jacobian array.
-
-.. attribute:: lmdif_message
-
- string message returned from :func:`scipy.optimize.leastsq`.
-
-.. attribute:: message
-
- string message returned from :func:`minimize`.
-
-.. attribute:: method
-
- string naming fitting method for :func:`minimize`.
-
-.. attribute:: model
-
- instance of :class:`Model` used for model.
-
-.. attribute:: ndata
-
- integer number of data points.
-
-.. attribute:: nfev
-
- integer number of function evaluations used for fit.
-
-.. attribute:: nfree
-
- integer number of free parameters in fit.
-
-.. attribute:: nvarys
-
- integer number of independent, freely varying variables in fit.
-
-.. attribute:: params
-
- Parameters used in fit. Will have best-fit values.
-
-.. attribute:: redchi
-
- floating point reduced chi-square statistic (see :ref:`fit-results-label`).
-
-.. attribute:: residual
-
- ndarray for residual.
-
-.. attribute:: scale_covar
-
- boolean flag for whether to automatically scale covariance matrix.
-
-.. attribute:: success
-
- boolean value of whether fit succeeded.
-
-.. attribute:: weights
-
- ndarray (or ``None``) of weighting values to be used in fit. If not
- ``None``, it will be used as a multiplicative factor of the residual
- array, so that ``weights*(data - fit)`` is minimized in the
- least-squares sense.
-
-.. index:: Composite models
-
-.. _composite_models_section:
-
-
-Composite Models : adding (or multiplying) Models
-==============================================================
-
-One of the more interesting features of the :class:`Model` class is that
-Models can be added together or combined with basic algebraic operations
-(add, subtract, multiply, and divide) to give a composite model. The
-composite model will have parameters from each of the component models,
-with all parameters being available to influence the whole model. This
-ability to combine models will become even more useful in the next chapter,
-when pre-built subclasses of :class:`Model` are discussed. For now, we'll
-consider a simple example, and build a model of a Gaussian plus a line, as
-to model a peak with a background. For such a simple problem, we could just
-build a model that included both components::
-
- def gaussian_plus_line(x, amp, cen, wid, slope, intercept):
- "line + 1-d gaussian"
-
- gauss = (amp/(sqrt(2*pi)*wid)) * exp(-(x-cen)**2 /(2*wid**2))
- line = slope * x + intercept
- return gauss + line
-
-and use that with::
-
- mod = Model(gaussian_plus_line)
-
-But we already had a function for a gaussian function, and maybe we'll
-discover that a linear background isn't sufficient which would mean the
-model function would have to be changed. As an alternative we could define
-a linear function::
-
- def line(x, slope, intercept):
- "a line"
- return slope * x + intercept
-
-and build a composite model with just::
-
- mod = Model(gaussian) + Model(line)
-
-This model has parameters for both component models, and can be used as:
-
-.. literalinclude:: ../examples/doc_model2.py
-
-which prints out the results::
-
- [[Model]]
- (Model(gaussian) + Model(line))
- [[Fit Statistics]]
- # function evals = 44
- # data points = 101
- # variables = 5
- chi-square = 2.579
- reduced chi-square = 0.027
- [[Variables]]
- amp: 8.45931061 +/- 0.124145 (1.47%) (init= 5)
- cen: 5.65547872 +/- 0.009176 (0.16%) (init= 5)
- intercept: -0.96860201 +/- 0.033522 (3.46%) (init= 1)
- slope: 0.26484403 +/- 0.005748 (2.17%) (init= 0)
- wid: 0.67545523 +/- 0.009916 (1.47%) (init= 1)
- [[Correlations]] (unreported correlations are < 0.100)
- C(amp, wid) = 0.666
- C(cen, intercept) = 0.129
-
-
-and shows the plot on the left.
-
-.. _figModel2:
-
- .. image:: _images/model_fit2.png
- :target: _images/model_fit2.png
- :width: 48%
- .. image:: _images/model_fit2a.png
- :target: _images/model_fit2a.png
- :width: 48%
-
-
-On the left, data is shown in blue dots, the total fit is shown in solid
-red line, and the initial fit is shown as a black dashed line. In the
-figure on the right, the data is again shown in blue dots, and the Gaussian
-component shown as a black dashed line, and the linear component shown as a
-red dashed line. These components were generated after the fit using the
-Models :meth:`ModelResult.eval_components` method of the `result`::
-
- comps = result.eval_components()
-
-which returns a dictionary of the components, using keys of the model name
-(or `prefix` if that is set). This will use the parameter values in
-``result.params`` and the independent variables (``x``) used during the
-fit. Note that while the :class:`ModelResult` held in `result` does store the
-best parameters and the best estimate of the model in ``result.best_fit``,
-the original model and parameters in ``pars`` are left unaltered.
-
-You can apply this composite model to other data sets, or evaluate the
-model at other values of ``x``. You may want to do this to give a finer or
-coarser spacing of data point, or to extrapolate the model outside the
-fitting range. This can be done with::
-
- xwide = np.linspace(-5, 25, 3001)
- predicted = mod.eval(x=xwide)
-
-In this example, the argument names for the model functions do not overlap.
-If they had, the ``prefix`` argument to :class:`Model` would have allowed
-us to identify which parameter went with which component model. As we will
-see in the next chapter, using composite models with the built-in models
-provides a simple way to build up complex models.
-
-.. class:: CompositeModel(left, right, op[, **kws])
-
- Create a composite model from two models (`left` and `right` and an
- binary operator (`op`). Additional keywords are passed to
- :class:`Model`.
-
- :param left: left-hand side Model
- :type left: :class:`Model`
- :param right: right-hand side Model
- :type right: :class:`Model`
- :param op: binary operator
- :type op: callable, and taking 2 arguments (`left` and `right`).
-
-Normally, one does not have to explicitly create a :class:`CompositeModel`,
-as doing::
-
- mod = Model(fcn1) + Model(fcn2) * Model(fcn3)
-
-will automatically create a :class:`CompositeModel`. In this example,
-`mod.left` will be `Model(fcn1)`, `mod.op` will be :meth:`operator.add`,
-and `mod.right` will be another CompositeModel that has a `left` attribute
-of `Model(fcn2)`, an `op` of :meth:`operator.mul`, and a `right` of
-`Model(fcn3)`.
-
-If you want to use a binary operator other than add, subtract, multiply, or
-divide that are supported through normal Python syntax, you'll need to
-explicitly create a :class:`CompositeModel` with the appropriate binary
-operator. For example, to convolve two models, you could define a simple
-convolution function, perhaps as::
-
- import numpy as np
- def convolve(dat, kernel):
- # simple convolution
- npts = min(len(dat), len(kernel))
- pad = np.ones(npts)
- tmp = np.concatenate((pad*dat[0], dat, pad*dat[-1]))
- out = np.convolve(tmp, kernel, mode='valid')
- noff = int((len(out) - npts)/2)
- return (out[noff:])[:npts]
-
-which extends the data in both directions so that the convolving kernel
-function gives a valid result over the data range. Because this function
-takes two array arguments and returns an array, it can be used as the
-binary operator. A full script using this technique is here:
-
-.. literalinclude:: ../examples/doc_model3.py
-
-which prints out the results::
-
- [[Model]]
- (Model(jump) <function convolve at 0x109ee4488> Model(gaussian))
- [[Fit Statistics]]
- # function evals = 25
- # data points = 201
- # variables = 3
- chi-square = 21.692
- reduced chi-square = 0.110
- [[Variables]]
- amplitude: 0.62106099 +/- 0.001783 (0.29%) (init= 1)
- center: 4.49913218 +/- 0.009373 (0.21%) (init= 3.5)
- mid: 5 (fixed)
- sigma: 0.61936067 +/- 0.012977 (2.10%) (init= 1)
- [[Correlations]] (unreported correlations are < 0.100)
- C(amplitude, center) = 0.336
- C(amplitude, sigma) = 0.274
-
-and shows the plots:
-
-.. _figModel3:
-
- .. image:: _images/model_fit3a.png
- :target: _images/model_fit3a.png
- :width: 48%
- .. image:: _images/model_fit3b.png
- :target: _images/model_fit3b.png
- :width: 48%
-
-Using composite models with built-in or custom operators allows you to
-build complex models from testable sub-components.
+.. _model_chapter: + +================================================= +Modeling Data and Curve Fitting +================================================= + +.. module:: model + +A common use of least-squares minimization is *curve fitting*, where one +has a parametrized model function meant to explain some phenomena and wants +to adjust the numerical values for the model to most closely match some +data. With :mod:`scipy`, such problems are commonly solved with +:scipydoc:`scipy.optimize.curve_fit`, which is a wrapper around +:scipydoc:`scipy.optimize.leastsq`. Since Lmfit's :func:`minimize` is also +a high-level wrapper around :scipydoc:`scipy.optimize.leastsq` it can be used +for curve-fitting problems, but requires more effort than using +:scipydoc:`scipy.optimize.curve_fit`. + + +Here we discuss lmfit's :class:`Model` class. This takes a model function +-- a function that calculates a model for some data -- and provides methods +to create parameters for that model and to fit data using that model +function. This is closer in spirit to :scipydoc:`scipy.optimize.curve_fit`, +but with the advantages of using :class:`Parameters` and lmfit. + +In addition to allowing you turn any model function into a curve-fitting +method, Lmfit also provides canonical definitions for many known line shapes +such as Gaussian or Lorentzian peaks and Exponential decays that are widely +used in many scientific domains. These are available in the :mod:`models` +module that will be discussed in more detail in the next chapter +(:ref:`builtin_models_chapter`). We mention it here as you may want to +consult that list before writing your own model. For now, we focus on +turning python function into high-level fitting models with the +:class:`Model` class, and using these to fit data. + + +Example: Fit data to Gaussian profile +================================================ + +Let's start with a simple and common example of fitting data to a Gaussian +peak. As we will see, there is a buit-in :class:`GaussianModel` class that +provides a model function for a Gaussian profile, but here we'll build our +own. We start with a simple definition of the model function: + + >>> from numpy import sqrt, pi, exp, linspace + >>> + >>> def gaussian(x, amp, cen, wid): + ... return amp * exp(-(x-cen)**2 /wid) + ... + +We want to fit this objective function to data :math:`y(x)` represented by the +arrays ``y`` and ``x``. This can be done easily with :scipydoc:`optimize.curve_fit`:: + + >>> from scipy.optimize import curve_fit + >>> + >>> x = linspace(-10,10) + >>> y = y = gaussian(x, 2.33, 0.21, 1.51) + np.random.normal(0, 0.2, len(x)) + >>> + >>> init_vals = [1, 0, 1] # for [amp, cen, wid] + >>> best_vals, covar = curve_fit(gaussian, x, y, p0=init_vals) + >>> print best_vals + + +We sample random data point, make an initial guess of the model +values, and run :scipydoc:`optimize.curve_fit` with the model function, +data arrays, and initial guesses. The results returned are the optimal +values for the parameters and the covariance matrix. It's simple and very +useful. But it misses the benefits of lmfit. + + +To solve this with lmfit we would have to write an objective function. But +such a function would be fairly simple (essentially, ``data - model``, +possibly with some weighting), and we would need to define and use +appropriately named parameters. Though convenient, it is somewhat of a +burden to keep the named parameter straight (on the other hand, with +:scipydoc:`optimize.curve_fit` you are required to remember the parameter +order). After doing this a few times it appears as a recurring pattern, +and we can imagine automating this process. That's where the +:class:`Model` class comes in. + +:class:`Model` allows us to easily wrap a model function such as the +``gaussian`` function. This automatically generate the appropriate +residual function, and determines the corresponding parameter names from +the function signature itself:: + + >>> from lmfit import Model + >>> gmod = Model(gaussian) + >>> gmod.param_names + set(['amp', 'wid', 'cen']) + >>> gmod.independent_vars) + ['x'] + +The Model ``gmod`` knows the names of the parameters and the independent +variables. By default, the first argument of the function is taken as the +independent variable, held in :attr:`independent_vars`, and the rest of the +functions positional arguments (and, in certain cases, keyword arguments -- +see below) are used for Parameter names. Thus, for the ``gaussian`` +function above, the parameters are named ``amp``, ``cen``, and ``wid``, and +``x`` is the independent variable -- all taken directly from the signature +of the model function. As we will see below, you can specify what the +independent variable is, and you can add or alter parameters, too. + +The parameters are *not* created when the model is created. The model knows +what the parameters should be named, but not anything about the scale and +range of your data. You will normally have to make these parameters and +assign initial values and other attributes. To help you do this, each +model has a :meth:`make_params` method that will generate parameters with +the expected names: + + >>> params = gmod.make_params() + +This creates the :class:`Parameters` but doesn't necessarily give them +initial values -- again, the model has no idea what the scale should be. +You can set initial values for parameters with keyword arguments to +:meth:`make_params`: + + + >>> params = gmod.make_params(cen=5, amp=200, wid=1) + +or assign them (and other parameter properties) after the +:class:`Parameters` has been created. + +A :class:`Model` has several methods associated with it. For example, one +can use the :meth:`eval` method to evaluate the model or the :meth:`fit` +method to fit data to this model with a :class:`Parameter` object. Both of +these methods can take explicit keyword arguments for the parameter values. +For example, one could use :meth:`eval` to calculate the predicted +function:: + + >>> x = linspace(0, 10, 201) + >>> y = gmod.eval(x=x, amp=10, cen=6.2, wid=0.75) + +Admittedly, this a slightly long-winded way to calculate a Gaussian +function. But now that the model is set up, we can also use its +:meth:`fit` method to fit this model to data, as with:: + + >>> result = gmod.fit(y, x=x, amp=5, cen=5, wid=1) + +Putting everything together, the script to do such a fit (included in the +``examples`` folder with the source code) is: + +.. literalinclude:: ../examples/doc_model1.py + +which is pretty compact and to the point. The returned ``result`` will be +a :class:`ModelResult` object. As we will see below, this has many +components, including a :meth:`fit_report` method, which will show:: + + [[Model]] + gaussian + [[Fit Statistics]] + # function evals = 33 + # data points = 101 + # variables = 3 + chi-square = 3.409 + reduced chi-square = 0.035 + Akaike info crit = -333.218 + Bayesian info crit = -325.373 + [[Variables]] + amp: 8.88021829 +/- 0.113594 (1.28%) (init= 5) + cen: 5.65866102 +/- 0.010304 (0.18%) (init= 5) + wid: 0.69765468 +/- 0.010304 (1.48%) (init= 1) + [[Correlations]] (unreported correlations are < 0.100) + C(amp, wid) = 0.577 + +The result will also have :attr:`init_fit` for the fit with the initial +parameter values and a :attr:`best_fit` for the fit with the best fit +parameter values. These can be used to generate the following plot: + + +.. image:: _images/model_fit1.png + :target: _images/model_fit1.png + :width: 50% + +which shows the data in blue dots, the best fit as a solid red line, and +the initial fit as a dashed black line. + +Note that the model fitting was really performed with 2 lines of code:: + + gmod = Model(gaussian) + result = gmod.fit(y, x=x, amp=5, cen=5, wid=1) + +These lines clearly express that we want to turn the ``gaussian`` function +into a fitting model, and then fit the :math:`y(x)` data to this model, +starting with values of 5 for ``amp``, 5 for ``cen`` and 1 for ``wid``. +This is much more expressive than :scipydoc:`optimize.curve_fit`:: + + best_vals, covar = curve_fit(gaussian, x, y, p0=[5, 5, 1]) + +In addition, all the other features of lmfit are included: +:class:`Parameters` can have bounds and constraints and the result is a +rich object that can be reused to explore the model fit in detail. + + +The :class:`Model` class +======================================= + +The :class:`Model` class provides a general way to wrap a pre-defined +function as a fitting model. + +.. class:: Model(func[, independent_vars=None[, param_names=None[, missing=None[, prefix=''[, name=None[, **kws]]]]]]) + + Create a model based on the user-supplied function. This uses + introspection to automatically converting argument names of the + function to Parameter names. + + :param func: model function to be wrapped + :type func: callable + :param independent_vars: list of argument names to ``func`` that are independent variables. + :type independent_vars: ``None`` (default) or list of strings. + :param param_names: list of argument names to ``func`` that should be made into Parameters. + :type param_names: ``None`` (default) or list of strings + :param missing: how to handle missing values. + :type missing: one of ``None`` (default), 'none', 'drop', or 'raise'. + :param prefix: prefix to add to all parameter names to distinguish components in a :class:`CompositeModel`. + :type prefix: string + :param name: name for the model. When ``None`` (default) the name is the same as the model function (``func``). + :type name: ``None`` or string. + :param kws: additional keyword arguments to pass to model function. + + +Of course, the model function will have to return an array that will be the +same size as the data being modeled. Generally this is handled by also +specifying one or more independent variables. + + +:class:`Model` class Methods +--------------------------------- + +.. method:: Model.eval(params=None[, **kws]) + + evaluate the model function for a set of parameters and inputs. + + :param params: parameters to use for fit. + :type params: ``None`` (default) or Parameters + :param kws: additional keyword arguments to pass to model function. + :return: ndarray for model given the parameters and other arguments. + + If ``params`` is ``None``, the values for all parameters are expected to + be provided as keyword arguments. If ``params`` is given, and a keyword + argument for a parameter value is also given, the keyword argument will + be used. + + Note that all non-parameter arguments for the model function -- + **including all the independent variables!** -- will need to be passed + in using keyword arguments. + + +.. method:: Model.fit(data[, params=None[, weights=None[, method='leastsq'[, scale_covar=True[, iter_cb=None[, **kws]]]]]]) + + perform a fit of the model to the ``data`` array with a set of + parameters. + + :param data: array of data to be fitted. + :type data: ndarray-like + :param params: parameters to use for fit. + :type params: ``None`` (default) or Parameters + :param weights: weights to use for residual calculation in fit. + :type weights: ``None`` (default) or ndarray-like. + :param method: name of fitting method to use. See :ref:`fit-methods-label` for details + :type method: string (default ``leastsq``) + :param scale_covar: whether to automatically scale covariance matrix (``leastsq`` only) + :type scale_covar: bool (default ``True``) + :param iter_cb: function to be called at each fit iteration. See :ref:`fit-itercb-label` for details. + :type iter_cb: callable or ``None`` + :param verbose: print a message when a new parameter is created due to a *hint* + :type verbose: bool (default ``True``) + :param kws: additional keyword arguments to pass to model function. + :return: :class:`ModelResult` object. + + If ``params`` is ``None``, the internal ``params`` will be used. If it + is supplied, these will replace the internal ones. If supplied, + ``weights`` will be used to weight the calculated residual so that the + quantity minimized in the least-squares sense is ``weights*(data - + fit)``. ``weights`` must be an ndarray-like object of same size and + shape as ``data``. + + Note that other arguments for the model function (including all the + independent variables!) will need to be passed in using keyword + arguments. + + +.. method:: Model.guess(data, **kws) + + Guess starting values for model parameters. + + :param data: data array used to guess parameter values + :type func: ndarray + :param kws: additional options to pass to model function. + :return: :class:`Parameters` with guessed initial values for each parameter. + + by default this is left to raise a ``NotImplementedError``, but may be + overwritten by subclasses. Generally, this method should take some + values for ``data`` and use it to construct reasonable starting values for + the parameters. + + +.. method:: Model.make_params(**kws) + + Create a set of parameters for model. + + :param kws: optional keyword/value pairs to set initial values for parameters. + :return: :class:`Parameters`. + + The parameters may or may not have decent initial values for each + parameter. + + +.. method:: Model.set_param_hint(name, value=None[, min=None[, max=None[, vary=True[, expr=None]]]]) + + set *hints* to use when creating parameters with :meth:`Model.make_param` for + the named parameter. This is especially convenient for setting initial + values. The ``name`` can include the models ``prefix`` or not. + + :param name: parameter name. + :type name: string + :param value: value for parameter + :type value: float + :param min: lower bound for parameter value + :type min: ``None`` or float + :param max: upper bound for parameter value + :type max: ``None`` or float + :param vary: whether to vary parameter in fit. + :type vary: boolean + :param expr: mathematical expression for constraint + :type expr: string + + See :ref:`model_param_hints_section`. + + +.. automethod:: lmfit.model.Model.print_param_hints + + +:class:`Model` class Attributes +--------------------------------- + +.. attribute:: func + + The model function used to calculate the model. + +.. attribute:: independent_vars + + list of strings for names of the independent variables. + +.. attribute:: missing + + describes what to do for missing values. The choices are + + * ``None``: Do not check for null or missing values (default) + * ``'none'``: Do not check for null or missing values. + * ``'drop'``: Drop null or missing observations in data. If pandas is + installed, ``pandas.isnull`` is used, otherwise :attr:`numpy.isnan` is used. + * ``'raise'``: Raise a (more helpful) exception when data contains null + or missing values. + +.. attribute:: name + + name of the model, used only in the string representation of the + model. By default this will be taken from the model function. + +.. attribute:: opts + + extra keyword arguments to pass to model function. Normally this will + be determined internally and should not be changed. + +.. attribute:: param_hints + + Dictionary of parameter hints. See :ref:`model_param_hints_section`. + +.. attribute:: param_names + + list of strings of parameter names. + +.. attribute:: prefix + + prefix used for name-mangling of parameter names. The default is ''. + If a particular :class:`Model` has arguments ``amplitude``, + ``center``, and ``sigma``, these would become the parameter names. + Using a prefix of ``g1_`` would convert these parameter names to + ``g1_amplitude``, ``g1_center``, and ``g1_sigma``. This can be + essential to avoid name collision in composite models. + + +Determining parameter names and independent variables for a function +----------------------------------------------------------------------- + +The :class:`Model` created from the supplied function ``func`` will create +a :class:`Parameters` object, and names are inferred from the function +arguments, and a residual function is automatically constructed. + + +By default, the independent variable is take as the first argument to the +function. You can explicitly set this, of course, and will need to if the +independent variable is not first in the list, or if there are actually more +than one independent variables. + +If not specified, Parameters are constructed from all positional arguments +and all keyword arguments that have a default value that is numerical, except +the independent variable, of course. Importantly, the Parameters can be +modified after creation. In fact, you'll have to do this because none of the +parameters have valid initial values. You can place bounds and constraints +on Parameters, or fix their values. + + + +Explicitly specifying ``independent_vars`` +------------------------------------------------- + +As we saw for the Gaussian example above, creating a :class:`Model` from a +function is fairly easy. Let's try another:: + + >>> def decay(t, tau, N): + ... return N*np.exp(-t/tau) + ... + >>> decay_model = Model(decay) + >>> print decay_model.independent_vars + ['t'] + >>> for pname, par in decay_model.params.items(): + ... print pname, par + ... + tau <Parameter 'tau', None, bounds=[None:None]> + N <Parameter 'N', None, bounds=[None:None]> + +Here, ``t`` is assumed to be the independent variable because it is the +first argument to the function. The other function arguments are used to +create parameters for the model. + +If you want ``tau`` to be the independent variable in the above example, +you can say so:: + + >>> decay_model = Model(decay, independent_vars=['tau']) + >>> print decay_model.independent_vars + ['tau'] + >>> for pname, par in decay_model.params.items(): + ... print pname, par + ... + t <Parameter 't', None, bounds=[None:None]> + N <Parameter 'N', None, bounds=[None:None]> + + +You can also supply multiple values for multi-dimensional functions with +multiple independent variables. In fact, the meaning of *independent +variable* here is simple, and based on how it treats arguments of the +function you are modeling: + +independent variable + a function argument that is not a parameter or otherwise part of the + model, and that will be required to be explicitly provided as a + keyword argument for each fit with :meth:`Model.fit` or evaluation + with :meth:`Model.eval`. + +Note that independent variables are not required to be arrays, or even +floating point numbers. + + +Functions with keyword arguments +----------------------------------------- + +If the model function had keyword parameters, these would be turned into +Parameters if the supplied default value was a valid number (but not +``None``, ``True``, or ``False``). + + >>> def decay2(t, tau, N=10, check_positive=False): + ... if check_small: + ... arg = abs(t)/max(1.e-9, abs(tau)) + ... else: + ... arg = t/tau + ... return N*np.exp(arg) + ... + >>> mod = Model(decay2) + >>> for pname, par in mod.params.items(): + ... print pname, par + ... + t <Parameter 't', None, bounds=[None:None]> + N <Parameter 'N', 10, bounds=[None:None]> + +Here, even though ``N`` is a keyword argument to the function, it is turned +into a parameter, with the default numerical value as its initial value. +By default, it is permitted to be varied in the fit -- the 10 is taken as +an initial value, not a fixed value. On the other hand, the +``check_positive`` keyword argument, was not converted to a parameter +because it has a boolean default value. In some sense, +``check_positive`` becomes like an independent variable to the model. +However, because it has a default value it is not required to be given for +each model evaluation or fit, as independent variables are. + +Defining a ``prefix`` for the Parameters +-------------------------------------------- + +As we will see in the next chapter when combining models, it is sometimes +necessary to decorate the parameter names in the model, but still have them +be correctly used in the underlying model function. This would be +necessary, for example, if two parameters in a composite model (see +:ref:`composite_models_section` or examples in the next chapter) would have +the same name. To avoid this, we can add a ``prefix`` to the +:class:`Model` which will automatically do this mapping for us. + + >>> def myfunc(x, amplitude=1, center=0, sigma=1): + ... + + >>> mod = Model(myfunc, prefix='f1_') + >>> for pname, par in mod.params.items(): + ... print pname, par + ... + f1_amplitude <Parameter 'f1_amplitude', None, bounds=[None:None]> + f1_center <Parameter 'f1_center', None, bounds=[None:None]> + f1_sigma <Parameter 'f1_sigma', None, bounds=[None:None]> + +You would refer to these parameters as ``f1_amplitude`` and so forth, and +the model will know to map these to the ``amplitude`` argument of ``myfunc``. + + +Initializing model parameters +----------------------------------------- + +As mentioned above, the parameters created by :meth:`Model.make_params` are +generally created with invalid initial values of ``None``. These values +**must** be initialized in order for the model to be evaluated or used in a +fit. There are four different ways to do this initialization that can be +used in any combination: + + 1. You can supply initial values in the definition of the model function. + 2. You can initialize the parameters when creating parameters with :meth:`Model.make_params`. + 3. You can give parameter hints with :meth:`Model.set_param_hint`. + 4. You can supply initial values for the parameters when you use the + :meth:`Model.eval` or :meth:`Model.fit` methods. + +Of course these methods can be mixed, allowing you to overwrite initial +values at any point in the process of defining and using the model. + +Initializing values in the function definition +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +To supply initial values for parameters in the definition of the model +function, you can simply supply a default value:: + + >>> def myfunc(x, a=1, b=0): + >>> ... + +instead of using:: + + >>> def myfunc(x, a, b): + >>> ... + +This has the advantage of working at the function level -- all parameters +with keywords can be treated as options. It also means that some default +initial value will always be available for the parameter. + + +Initializing values with :meth:`Model.make_params` +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +When creating parameters with :meth:`Model.make_params` you can specify initial +values. To do this, use keyword arguments for the parameter names and +initial values:: + + >>> mod = Model(myfunc) + >>> pars = mod.make_params(a=3, b=0.5) + + +Initializing values by setting parameter hints +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +After a model has been created, but prior to creating parameters with +:meth:`Model.make_params`, you can set parameter hints. These allows you to set +not only a default initial value but also to set other parameter attributes +controlling bounds, whether it is varied in the fit, or a constraint +expression. To set a parameter hint, you can use :meth:`Model.set_param_hint`, +as with:: + + >>> mod = Model(myfunc) + >>> mod.set_param_hint('a', value = 1.0) + >>> mod.set_param_hint('b', value = 0.3, min=0, max=1.0) + >>> pars = mod.make_params() + +Parameter hints are discussed in more detail in section +:ref:`model_param_hints_section`. + + +Initializing values when using a model +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Finally, you can explicitly supply initial values when using a model. That +is, as with :meth:`Model.make_params`, you can include values +as keyword arguments to either the :meth:`Model.eval` or :meth:`Model.fit` methods:: + + >>> y1 = mod.eval(x=x, a=7.0, b=-2.0) + + >>> out = mod.fit(x=x, pars, a=3.0, b=-0.0) + +These approaches to initialization provide many opportunities for setting +initial values for parameters. The methods can be combined, so that you +can set parameter hints but then change the initial value explicitly with +:meth:`Model.fit`. + +.. _model_param_hints_section: + +Using parameter hints +-------------------------------- + + +After a model has been created, you can give it hints for how to create +parameters with :meth:`Model.make_params`. This allows you to set not only a +default initial value but also to set other parameter attributes +controlling bounds, whether it is varied in the fit, or a constraint +expression. To set a parameter hint, you can use :meth:`Model.set_param_hint`, +as with:: + + >>> mod = Model(myfunc) + >>> mod.set_param_hint('a', value = 1.0) + >>> mod.set_param_hint('b', value = 0.3, min=0, max=1.0) + +Parameter hints are stored in a model's :attr:`param_hints` attribute, +which is simply a nested dictionary:: + + >>> print mod.param_hints + {'a': {'value': 1}, 'b': {'max': 1.0, 'value': 0.3, 'min': 0}} + + +You can change this dictionary directly, or with the :meth:`Model.set_param_hint` +method. Either way, these parameter hints are used by :meth:`Model.make_params` +when making parameters. + +An important feature of parameter hints is that you can force the creation +of new parameters with parameter hints. This can be useful to make derived +parameters with constraint expressions. For example to get the full-width +at half maximum of a Gaussian model, one could use a parameter hint of:: + + >>> mod = Model(gaussian) + >>> mod.set_param_hint('fwhm', expr='2.3548*sigma') + + + +The :class:`ModelResult` class +======================================= + +A :class:`ModelResult` (which had been called `ModelFit` prior to version +0.9) is the object returned by :meth:`Model.fit`. It is a subclass of +:class:`Minimizer`, and so contains many of the fit results. Of course, it +knows the :class:`Model` and the set of :class:`Parameters` used in the +fit, and it has methods to evaluate the model, to fit the data (or re-fit +the data with changes to the parameters, or fit with different or modified +data) and to print out a report for that fit. + +While a :class:`Model` encapsulates your model function, it is fairly +abstract and does not contain the parameters or data used in a particular +fit. A :class:`ModelResult` *does* contain parameters and data as well as +methods to alter and re-do fits. Thus the :class:`Model` is the idealized +model while the :class:`ModelResult` is the messier, more complex (but perhaps +more useful) object that represents a fit with a set of parameters to data +with a model. + + +A :class:`ModelResult` has several attributes holding values for fit results, +and several methods for working with fits. These include statistics +inherited from :class:`Minimizer` useful for comparing different models, +including `chisqr`, `redchi`, `aic`, and `bic`. + +.. class:: ModelResult() + + Model fit is intended to be created and returned by :meth:`Model.fit`. + + + +:class:`ModelResult` methods +--------------------------------- + +These methods are all inherited from :class:`Minimize` or from +:class:`Model`. + +.. method:: ModelResult.eval(**kwargs) + + evaluate the model using the best-fit parameters and supplied + independent variables. The ``**kwargs`` arguments can be used to update + parameter values and/or independent variables. + + +.. method:: ModelResult.eval_components(**kwargs) + + evaluate each component of a :class:`CompositeModel`, returning an + ordered dictionary of with the values for each component model. The + returned dictionary will have keys of the model prefix or (if no prefix + is given), the model name. The ``**kwargs`` arguments can be used to + update parameter values and/or independent variables. + +.. method:: ModelResult.fit(data=None[, params=None[, weights=None[, method=None[, **kwargs]]]]) + + fit (or re-fit), optionally changing ``data``, ``params``, ``weights``, + or ``method``, or changing the independent variable(s) with the + ``**kwargs`` argument. See :meth:`Model.fit` for argument + descriptions, and note that any value of ``None`` defaults to the last + used value. + +.. method:: ModelResult.fit_report(modelpars=None[, show_correl=True[,`< min_correl=0.1]]) + + return a printable fit report for the fit with fit statistics, best-fit + values with uncertainties and correlations. As with :func:`fit_report`. + + :param modelpars: Parameters with "Known Values" (optional, default None) + :param show_correl: whether to show list of sorted correlations [``True``] + :param min_correl: smallest correlation absolute value to show [0.1] + + +.. method:: ModelResult.conf_interval(**kwargs) + + calculate the confidence intervals for the variable parameters using + :func:`confidence.conf_interval() <lmfit.conf_interval>`. All keyword + arguments are passed to that function. The result is stored in + :attr:`ci_out`, and so can be accessed without recalculating them. + +.. method:: ModelResult.ci_report(with_offset=True) + + return a nicely formatted text report of the confidence intervals, as + from :func:`ci_report() <lmfit.ci_report>`. + + +.. method:: ModelResult.plot(datafmt='o', fitfmt='-', initfmt='--', yerr=None, numpoints=None, fig=None, data_kws=None, fit_kws=None, init_kws=None, ax_res_kws=None, ax_fit_kws=None, fig_kws=None) + + Plot the fit results and residuals using matplotlib, if available. The + plot will include two panels, one showing the fit residual, and the + other with the data points, the initial fit curve, and the best-fit + curve. If the fit model included weights or if ``yerr`` is specified, + errorbars will also be plotted. + + :param datafmt: matplotlib format string for data curve. + :type datafmt: ``None`` or string. + :param fitfmt: matplotlib format string for best-fit curve. + :type fitfmt: ``None`` or string. + :param initfmt: matplotlib format string for initial curve. + :type intfmt: ``None`` or string. + :param yerr: array of uncertainties for data array. + :type yerr: ``None`` or ndarray. + :param numpoints: number of points to display + :type numpoints: ``None`` or integer + :param fig: matplotlib Figure to plot on. + :type fig: ``None`` or matplotlib.figure.Figure + :param data_kws: keyword arguments passed to plot for data curve. + :type data_kws: ``None`` or dictionary + :param fit_kws: keyword arguments passed to plot for best-fit curve. + :type fit_kws: ``None`` or dictionary + :param init_kws: keyword arguments passed to plot for initial curve. + :type init_kws: ``None`` or dictionary + :param ax_res_kws: keyword arguments passed to creation of matplotlib axes for the residual plot. + :type ax_res_kws: ``None`` or dictionary + :param ax_fit_kws: keyword arguments passed to creation of matplotlib axes for the fit plot. + :type ax_fit_kws: ``None`` or dictionary + :param fig_kws: keyword arguments passed to creation of matplotlib figure. + :type fig_kws: ``None`` or dictionary + :returns: matplotlib.figure.Figure + + This combines :meth:`ModelResult.plot_fit` and :meth:`ModelResult.plot_residual`. + + If ``yerr`` is specified or if the fit model included weights, then + matplotlib.axes.Axes.errorbar is used to plot the data. If ``yerr`` is + not specified and the fit includes weights, ``yerr`` set to ``1/self.weights`` + + If ``fig`` is None then ``matplotlib.pyplot.figure(**fig_kws)`` is called. + +.. method:: ModelResult.plot_fit(ax=None, datafmt='o', fitfmt='-', initfmt='--', yerr=None, numpoints=None, data_kws=None, fit_kws=None, init_kws=None, ax_kws=None) + + Plot the fit results using matplotlib, if available. The plot will include + the data points, the initial fit curve, and the best-fit curve. If the fit + model included weights or if ``yerr`` is specified, errorbars will also + be plotted. + + :param ax: matplotlib axes to plot on. + :type ax: ``None`` or matplotlib.axes.Axes. + :param datafmt: matplotlib format string for data curve. + :type datafmt: ``None`` or string. + :param fitfmt: matplotlib format string for best-fit curve. + :type fitfmt: ``None`` or string. + :param initfmt: matplotlib format string for initial curve. + :type intfmt: ``None`` or string. + :param yerr: array of uncertainties for data array. + :type yerr: ``None`` or ndarray. + :param numpoints: number of points to display + :type numpoints: ``None`` or integer + :param data_kws: keyword arguments passed to plot for data curve. + :type data_kws: ``None`` or dictionary + :param fit_kws: keyword arguments passed to plot for best-fit curve. + :type fit_kws: ``None`` or dictionary + :param init_kws: keyword arguments passed to plot for initial curve. + :type init_kws: ``None`` or dictionary + :param ax_kws: keyword arguments passed to creation of matplotlib axes. + :type ax_kws: ``None`` or dictionary + :returns: matplotlib.axes.Axes + + For details about plot format strings and keyword arguments see + documentation of :func:`matplotlib.axes.Axes.plot`. + + If ``yerr`` is specified or if the fit model included weights, then + matplotlib.axes.Axes.errorbar is used to plot the data. If ``yerr`` is + not specified and the fit includes weights, ``yerr`` set to ``1/self.weights`` + + If ``ax`` is None then ``matplotlib.pyplot.gca(**ax_kws)`` is called. + +.. method:: ModelResult.plot_residuals(ax=None, datafmt='o', yerr=None, data_kws=None, fit_kws=None, ax_kws=None) + + Plot the fit residuals (data - fit) using matplotlib. If ``yerr`` is + supplied or if the model included weights, errorbars will also be plotted. + + :param ax: matplotlib axes to plot on. + :type ax: ``None`` or matplotlib.axes.Axes. + :param datafmt: matplotlib format string for data curve. + :type datafmt: ``None`` or string. + :param yerr: array of uncertainties for data array. + :type yerr: ``None`` or ndarray. + :param numpoints: number of points to display + :type numpoints: ``None`` or integer + :param data_kws: keyword arguments passed to plot for data curve. + :type data_kws: ``None`` or dictionary + :param fit_kws: keyword arguments passed to plot for best-fit curve. + :type fit_kws: ``None`` or dictionary + :param ax_kws: keyword arguments passed to creation of matplotlib axes. + :type ax_kws: ``None`` or dictionary + :returns: matplotlib.axes.Axes + + For details about plot format strings and keyword arguments see + documentation of :func:`matplotlib.axes.Axes.plot`. + + If ``yerr`` is specified or if the fit model included weights, then + matplotlib.axes.Axes.errorbar is used to plot the data. If ``yerr`` is + not specified and the fit includes weights, ``yerr`` set to ``1/self.weights`` + + If ``ax`` is None then ``matplotlib.pyplot.gca(**ax_kws)`` is called. + + + + +:class:`ModelResult` attributes +--------------------------------- + +.. attribute:: aic + + floating point best-fit Akaike Information Criterion statistic (see :ref:`fit-results-label`). + +.. attribute:: best_fit + + ndarray result of model function, evaluated at provided + independent variables and with best-fit parameters. + +.. attribute:: best_values + + dictionary with parameter names as keys, and best-fit values as values. + +.. attribute:: bic + + floating point best-fit Bayesian Information Criterion statistic (see :ref:`fit-results-label`). + +.. attribute:: chisqr + + floating point best-fit chi-square statistic (see :ref:`fit-results-label`). + +.. attribute:: ci_out + + confidence interval data (see :ref:`confidence_chapter`) or `None` if + the confidence intervals have not been calculated. + +.. attribute:: covar + + ndarray (square) covariance matrix returned from fit. + +.. attribute:: data + + ndarray of data to compare to model. + +.. attribute:: errorbars + + boolean for whether error bars were estimated by fit. + +.. attribute:: ier + + integer returned code from :scipydoc:`optimize.leastsq`. + +.. attribute:: init_fit + + ndarray result of model function, evaluated at provided + independent variables and with initial parameters. + +.. attribute:: init_params + + initial parameters. + +.. attribute:: init_values + + dictionary with parameter names as keys, and initial values as values. + +.. attribute:: iter_cb + + optional callable function, to be called at each fit iteration. This + must take take arguments of ``params, iter, resid, *args, **kws``, where + ``params`` will have the current parameter values, ``iter`` the + iteration, ``resid`` the current residual array, and ``*args`` and + ``**kws`` as passed to the objective function. See :ref:`fit-itercb-label`. + +.. attribute:: jacfcn + + optional callable function, to be called to calculate jacobian array. + +.. attribute:: lmdif_message + + string message returned from :scipydoc:`optimize.leastsq`. + +.. attribute:: message + + string message returned from :func:`minimize`. + +.. attribute:: method + + string naming fitting method for :func:`minimize`. + +.. attribute:: model + + instance of :class:`Model` used for model. + +.. attribute:: ndata + + integer number of data points. + +.. attribute:: nfev + + integer number of function evaluations used for fit. + +.. attribute:: nfree + + integer number of free parameters in fit. + +.. attribute:: nvarys + + integer number of independent, freely varying variables in fit. + +.. attribute:: params + + Parameters used in fit. Will have best-fit values. + +.. attribute:: redchi + + floating point reduced chi-square statistic (see :ref:`fit-results-label`). + +.. attribute:: residual + + ndarray for residual. + +.. attribute:: scale_covar + + boolean flag for whether to automatically scale covariance matrix. + +.. attribute:: success + + boolean value of whether fit succeeded. + +.. attribute:: weights + + ndarray (or ``None``) of weighting values to be used in fit. If not + ``None``, it will be used as a multiplicative factor of the residual + array, so that ``weights*(data - fit)`` is minimized in the + least-squares sense. + +.. index:: Composite models + +.. _composite_models_section: + + +Composite Models : adding (or multiplying) Models +============================================================== + +One of the more interesting features of the :class:`Model` class is that +Models can be added together or combined with basic algebraic operations +(add, subtract, multiply, and divide) to give a composite model. The +composite model will have parameters from each of the component models, +with all parameters being available to influence the whole model. This +ability to combine models will become even more useful in the next chapter, +when pre-built subclasses of :class:`Model` are discussed. For now, we'll +consider a simple example, and build a model of a Gaussian plus a line, as +to model a peak with a background. For such a simple problem, we could just +build a model that included both components:: + + def gaussian_plus_line(x, amp, cen, wid, slope, intercept): + "line + 1-d gaussian" + + gauss = (amp/(sqrt(2*pi)*wid)) * exp(-(x-cen)**2 /(2*wid**2)) + line = slope * x + intercept + return gauss + line + +and use that with:: + + mod = Model(gaussian_plus_line) + +But we already had a function for a gaussian function, and maybe we'll +discover that a linear background isn't sufficient which would mean the +model function would have to be changed. As an alternative we could define +a linear function:: + + def line(x, slope, intercept): + "a line" + return slope * x + intercept + +and build a composite model with just:: + + mod = Model(gaussian) + Model(line) + +This model has parameters for both component models, and can be used as: + +.. literalinclude:: ../examples/doc_model2.py + +which prints out the results:: + + [[Model]] + (Model(gaussian) + Model(line)) + [[Fit Statistics]] + # function evals = 44 + # data points = 101 + # variables = 5 + chi-square = 2.579 + reduced chi-square = 0.027 + Akaike info crit = -355.329 + Bayesian info crit = -342.253 + [[Variables]] + amp: 8.45931061 +/- 0.124145 (1.47%) (init= 5) + cen: 5.65547872 +/- 0.009176 (0.16%) (init= 5) + intercept: -0.96860201 +/- 0.033522 (3.46%) (init= 1) + slope: 0.26484403 +/- 0.005748 (2.17%) (init= 0) + wid: 0.67545523 +/- 0.009916 (1.47%) (init= 1) + [[Correlations]] (unreported correlations are < 0.100) + C(amp, wid) = 0.666 + C(cen, intercept) = 0.129 + + +and shows the plot on the left. + +.. _figModel2: + + .. image:: _images/model_fit2.png + :target: _images/model_fit2.png + :width: 48% + .. image:: _images/model_fit2a.png + :target: _images/model_fit2a.png + :width: 48% + + +On the left, data is shown in blue dots, the total fit is shown in solid +red line, and the initial fit is shown as a black dashed line. In the +figure on the right, the data is again shown in blue dots, and the Gaussian +component shown as a black dashed line, and the linear component shown as a +red dashed line. These components were generated after the fit using the +Models :meth:`ModelResult.eval_components` method of the `result`:: + + comps = result.eval_components() + +which returns a dictionary of the components, using keys of the model name +(or `prefix` if that is set). This will use the parameter values in +``result.params`` and the independent variables (``x``) used during the +fit. Note that while the :class:`ModelResult` held in `result` does store the +best parameters and the best estimate of the model in ``result.best_fit``, +the original model and parameters in ``pars`` are left unaltered. + +You can apply this composite model to other data sets, or evaluate the +model at other values of ``x``. You may want to do this to give a finer or +coarser spacing of data point, or to extrapolate the model outside the +fitting range. This can be done with:: + + xwide = np.linspace(-5, 25, 3001) + predicted = mod.eval(x=xwide) + +In this example, the argument names for the model functions do not overlap. +If they had, the ``prefix`` argument to :class:`Model` would have allowed +us to identify which parameter went with which component model. As we will +see in the next chapter, using composite models with the built-in models +provides a simple way to build up complex models. + +.. class:: CompositeModel(left, right, op[, **kws]) + + Create a composite model from two models (`left` and `right` and an + binary operator (`op`). Additional keywords are passed to + :class:`Model`. + + :param left: left-hand side Model + :type left: :class:`Model` + :param right: right-hand side Model + :type right: :class:`Model` + :param op: binary operator + :type op: callable, and taking 2 arguments (`left` and `right`). + +Normally, one does not have to explicitly create a :class:`CompositeModel`, +as doing:: + + mod = Model(fcn1) + Model(fcn2) * Model(fcn3) + +will automatically create a :class:`CompositeModel`. In this example, +`mod.left` will be `Model(fcn1)`, `mod.op` will be :meth:`operator.add`, +and `mod.right` will be another CompositeModel that has a `left` attribute +of `Model(fcn2)`, an `op` of :meth:`operator.mul`, and a `right` of +`Model(fcn3)`. + +If you want to use a binary operator other than add, subtract, multiply, or +divide that are supported through normal Python syntax, you'll need to +explicitly create a :class:`CompositeModel` with the appropriate binary +operator. For example, to convolve two models, you could define a simple +convolution function, perhaps as:: + + import numpy as np + def convolve(dat, kernel): + # simple convolution + npts = min(len(dat), len(kernel)) + pad = np.ones(npts) + tmp = np.concatenate((pad*dat[0], dat, pad*dat[-1])) + out = np.convolve(tmp, kernel, mode='valid') + noff = int((len(out) - npts)/2) + return (out[noff:])[:npts] + +which extends the data in both directions so that the convolving kernel +function gives a valid result over the data range. Because this function +takes two array arguments and returns an array, it can be used as the +binary operator. A full script using this technique is here: + +.. literalinclude:: ../examples/doc_model3.py + +which prints out the results:: + + [[Model]] + (Model(jump) <function convolve at 0x109ee4488> Model(gaussian)) + [[Fit Statistics]] + # function evals = 23 + # data points = 201 + # variables = 3 + chi-square = 25.789 + reduced chi-square = 0.130 + Akaike info crit = -403.702 + Bayesian info crit = -393.793 + [[Variables]] + mid: 5 (fixed) + amplitude: 0.62249894 +/- 0.001946 (0.31%) (init= 1) + sigma: 0.61438887 +/- 0.014057 (2.29%) (init= 1.5) + center: 4.51710256 +/- 0.010152 (0.22%) (init= 3.5) + [[Correlations]] (unreported correlations are < 0.100) + C(amplitude, center) = 0.335 + C(amplitude, sigma) = 0.273 + +and shows the plots: + +.. _figModel3: + + .. image:: _images/model_fit3a.png + :target: _images/model_fit3a.png + :width: 48% + .. image:: _images/model_fit3b.png + :target: _images/model_fit3b.png + :width: 48% + +Using composite models with built-in or custom operators allows you to +build complex models from testable sub-components. diff --git a/doc/parameters.rst b/doc/parameters.rst index 980d809..e9b53d7 100644 --- a/doc/parameters.rst +++ b/doc/parameters.rst @@ -1,240 +1,237 @@ -.. _parameters_chapter:
-
-================================================
-:class:`Parameter` and :class:`Parameters`
-================================================
-
-This chapter describes :class:`Parameter` objects which is the key concept
-of lmfit.
-
-A :class:`Parameter` is the quantity to be optimized in all minimization
-problems, replacing the plain floating point number used in the
-optimization routines from :mod:`scipy.optimize`. A :class:`Parameter` has
-a value that can be varied in the fit or have a fixed value, have upper
-and/or lower bounds. It can even have a value that is constrained by an
-algebraic expression of other Parameter values. Since :class:`Parameters`
-live outside the core optimization routines, they can be used in **all**
-optimization routines from :mod:`scipy.optimize`. By using
-:class:`Parameter` objects instead of plain variables, the objective
-function does not have to be modified to reflect every change of what is
-varied in the fit. This simplifies the writing of models, allowing general
-models that describe the phenomenon to be written, and gives the user more
-flexibility in using and testing variations of that model.
-
-Whereas a :class:`Parameter` expands on an individual floating point
-variable, the optimization methods need an ordered group of floating point
-variables. In the :mod:`scipy.optimize` routines this is required to be a
-1-dimensional numpy ndarray. For lmfit, where each :class:`Parameter` has
-a name, this is replaced by a :class:`Parameters` class, which works as an
-ordered dictionary of :class:`Parameter` objects, with a few additional
-features and methods. That is, while the concept of a :class:`Parameter`
-is central to lmfit, one normally creates and interacts with a
-:class:`Parameters` instance that contains many :class:`Parameter` objects.
-The objective functions you write for lmfit will take an instance of
-:class:`Parameters` as its first argument.
-
-
-The :class:`Parameter` class
-========================================
-
-.. class:: Parameter(name=None[, value=None[, vary=True[, min=None[, max=None[, expr=None]]]]])
-
- create a Parameter object.
-
- :param name: parameter name
- :type name: ``None`` or string -- will be overwritten during fit if ``None``.
- :param value: the numerical value for the parameter
- :param vary: whether to vary the parameter or not.
- :type vary: boolean (``True``/``False``) [default ``True``]
- :param min: lower bound for value (``None`` = no lower bound).
- :param max: upper bound for value (``None`` = no upper bound).
- :param expr: mathematical expression to use to evaluate value during fit.
- :type expr: ``None`` or string
-
-
-Each of these inputs is turned into an attribute of the same name.
-
-After a fit, a Parameter for a fitted variable (that is with ``vary =
-True``) may have its :attr:`value` attribute to hold the best-fit value.
-Depending on the success of the fit and fitting algorithm used, it may also
-have attributes :attr:`stderr` and :attr:`correl`.
-
-.. attribute:: stderr
-
- the estimated standard error for the best-fit value.
-
-.. attribute:: correl
-
- a dictionary of the correlation with the other fitted variables in the
- fit, of the form::
-
- {'decay': 0.404, 'phase': -0.020, 'frequency': 0.102}
-
-See :ref:`bounds_chapter` for details on the math used to implement the
-bounds with :attr:`min` and :attr:`max`.
-
-The :attr:`expr` attribute can contain a mathematical expression that will
-be used to compute the value for the Parameter at each step in the fit.
-See :ref:`constraints_chapter` for more details and examples of this
-feature.
-
-.. index:: Removing a Constraint Expression
-
-.. method:: set(value=None[, vary=None[, min=None[, max=None[, expr=None]]]])
-
- set or update a Parameters value or other attributes.
-
- :param name: parameter name
- :param value: the numerical value for the parameter
- :param vary: whether to vary the parameter or not.
- :param min: lower bound for value
- :param max: upper bound for value
- :param expr: mathematical expression to use to evaluate value during fit.
-
-Each argument of :meth:`set` has a default value of ``None``, and will
-be set only if the provided value is not ``None``. You can use this to
-update some Parameter attribute without affecting others, for example::
-
- p1 = Parameter('a', value=2.0)
- p2 = Parameter('b', value=0.0)
- p1.set(min=0)
- p2.set(vary=False)
-
- to set a lower bound, or to set a Parameter as have a fixed value.
-
- Note that to use this approach to lift a lower or upper bound, doing::
-
- p1.set(min=0)
- .....
- # now lift the lower bound
- p1.set(min=None) # won't work! lower bound NOT changed
-
- won't work -- this will not change the current lower bound. Instead
- you'll have to use ``np.inf`` to remove a lower or upper bound::
-
- # now lift the lower bound
- p1.set(min=-np.inf) # will work!
-
- Similarly, to clear an expression of a parameter, you need to pass an
- empty string, not ``None``. You also need to give a value and
- explicitly tell it to vary::
-
- p3 = Parameter('c', expr='(a+b)/2')
- p3.set(expr=None) # won't work! expression NOT changed
-
- # remove constraint expression
- p3.set(value=1.0, vary=True, expr='') # will work! parameter now unconstrained
-
-
-The :class:`Parameters` class
-========================================
-
-.. class:: Parameters()
-
- create a Parameters object. This is little more than a fancy ordered
- dictionary, with the restrictions that:
-
- 1. keys must be valid Python symbol names, so that they can be used in
- expressions of mathematical constraints. This means the names must
- match ``[a-z_][a-z0-9_]*`` and cannot be a Python reserved word.
-
- 2. values must be valid :class:`Parameter` objects.
-
-
- Two methods are for provided for convenient initialization of a :class:`Parameters`,
- and one for extracting :class:`Parameter` values into a plain dictionary.
-
-.. method:: add(name[, value=None[, vary=True[, min=None[, max=None[, expr=None]]]]])
-
- add a named parameter. This creates a :class:`Parameter`
- object associated with the key `name`, with optional arguments
- passed to :class:`Parameter`::
-
- p = Parameters()
- p.add('myvar', value=1, vary=True)
-
-.. method:: add_many(self, paramlist)
-
- add a list of named parameters. Each entry must be a tuple
- with the following entries::
-
- name, value, vary, min, max, expr
-
- This method is somewhat rigid and verbose (no default values), but can
- be useful when initially defining a parameter list so that it looks
- table-like::
-
- p = Parameters()
- # (Name, Value, Vary, Min, Max, Expr)
- p.add_many(('amp1', 10, True, None, None, None),
- ('cen1', 1.2, True, 0.5, 2.0, None),
- ('wid1', 0.8, True, 0.1, None, None),
- ('amp2', 7.5, True, None, None, None),
- ('cen2', 1.9, True, 1.0, 3.0, None),
- ('wid2', None, False, None, None, '2*wid1/3'))
-
-
-.. method:: pretty_print(oneline=False)
-
- prints a clean representation on the Parameters. If `oneline` is
- `True`, the result will be printed to a single (long) line.
-
-.. method:: valuesdict()
-
- return an ordered dictionary of name:value pairs with the
- Paramater name as the key and Parameter value as value.
-
- This is distinct from the :class:`Parameters` itself, as the dictionary
- values are not :class:`Parameter` objects, just the :attr:`value`.
- Using :method:`valuesdict` can be a very convenient way to get updated
- values in a objective function.
-
-.. method:: dumps(**kws):
-
- return a JSON string representation of the :class:`Parameter` object.
- This can be saved or used to re-create or re-set parameters, using the
- :meth:`loads` method.
-
- Optional keywords are sent :py:func:`json.dumps`.
-
-.. method:: dump(file, **kws):
-
- write a JSON representation of the :class:`Parameter` object to a file
- or file-like object in `file` -- really any object with a :meth:`write`
- method. Optional keywords are sent :py:func:`json.dumps`.
-
-.. method:: loads(sval, **kws):
-
- use a JSON string representation of the :class:`Parameter` object in
- `sval` to set all parameter settins. Optional keywords are sent
- :py:func:`json.loads`.
-
-.. method:: load(file, **kws):
-
- read and use a JSON string representation of the :class:`Parameter`
- object from a file or file-like object in `file` -- really any object
- with a :meth:`read` method. Optional keywords are sent
- :py:func:`json.loads`.
-
-
-Simple Example
-==================
-
-Using :class:`Parameters`` and :func:`minimize` function (discussed in the
-next chapter) might look like this:
-
-.. literalinclude:: ../examples/doc_basic.py
-
-
-Here, the objective function explicitly unpacks each Parameter value. This
-can be simplified using the :class:`Parameters` :meth:`valuesdict` method,
-which would make the objective function ``fcn2min`` above look like::
-
- def fcn2min(params, x, data):
- """ model decaying sine wave, subtract data"""
- v = params.valuesdict()
-
- model = v['amp'] * np.sin(x * v['omega'] + v['shift']) * np.exp(-x*x*v['decay'])
- return model - data
-
-The results are identical, and the difference is a stylistic choice.
+.. _parameters_chapter: + +================================================ +:class:`Parameter` and :class:`Parameters` +================================================ + +This chapter describes :class:`Parameter` objects which is the key concept +of lmfit. + +A :class:`Parameter` is the quantity to be optimized in all minimization +problems, replacing the plain floating point number used in the +optimization routines from :mod:`scipy.optimize`. A :class:`Parameter` has +a value that can be varied in the fit or have a fixed value, have upper +and/or lower bounds. It can even have a value that is constrained by an +algebraic expression of other Parameter values. Since :class:`Parameters` +live outside the core optimization routines, they can be used in **all** +optimization routines from :mod:`scipy.optimize`. By using +:class:`Parameter` objects instead of plain variables, the objective +function does not have to be modified to reflect every change of what is +varied in the fit. This simplifies the writing of models, allowing general +models that describe the phenomenon to be written, and gives the user more +flexibility in using and testing variations of that model. + +Whereas a :class:`Parameter` expands on an individual floating point +variable, the optimization methods need an ordered group of floating point +variables. In the :mod:`scipy.optimize` routines this is required to be a +1-dimensional numpy ndarray. For lmfit, where each :class:`Parameter` has +a name, this is replaced by a :class:`Parameters` class, which works as an +ordered dictionary of :class:`Parameter` objects, with a few additional +features and methods. That is, while the concept of a :class:`Parameter` +is central to lmfit, one normally creates and interacts with a +:class:`Parameters` instance that contains many :class:`Parameter` objects. +The objective functions you write for lmfit will take an instance of +:class:`Parameters` as its first argument. + + +The :class:`Parameter` class +======================================== + +.. class:: Parameter(name=None[, value=None[, vary=True[, min=None[, max=None[, expr=None]]]]]) + + create a Parameter object. + + :param name: parameter name + :type name: ``None`` or string -- will be overwritten during fit if ``None``. + :param value: the numerical value for the parameter + :param vary: whether to vary the parameter or not. + :type vary: boolean (``True``/``False``) [default ``True``] + :param min: lower bound for value (``None`` = no lower bound). + :param max: upper bound for value (``None`` = no upper bound). + :param expr: mathematical expression to use to evaluate value during fit. + :type expr: ``None`` or string + + Each of these inputs is turned into an attribute of the same name. + + After a fit, a Parameter for a fitted variable (that is with ``vary = + True``) may have its :attr:`value` attribute to hold the best-fit value. + Depending on the success of the fit and fitting algorithm used, it may also + have attributes :attr:`stderr` and :attr:`correl`. + + .. attribute:: stderr + + the estimated standard error for the best-fit value. + + .. attribute:: correl + + a dictionary of the correlation with the other fitted variables in the + fit, of the form:: + + {'decay': 0.404, 'phase': -0.020, 'frequency': 0.102} + + See :ref:`bounds_chapter` for details on the math used to implement the + bounds with :attr:`min` and :attr:`max`. + + The :attr:`expr` attribute can contain a mathematical expression that will + be used to compute the value for the Parameter at each step in the fit. + See :ref:`constraints_chapter` for more details and examples of this + feature. + + .. index:: Removing a Constraint Expression + + .. method:: set(value=None[, vary=None[, min=None[, max=None[, expr=None]]]]) + + set or update a Parameters value or other attributes. + + :param name: parameter name + :param value: the numerical value for the parameter + :param vary: whether to vary the parameter or not. + :param min: lower bound for value + :param max: upper bound for value + :param expr: mathematical expression to use to evaluate value during fit. + + Each argument of :meth:`set` has a default value of ``None``, and will + be set only if the provided value is not ``None``. You can use this to + update some Parameter attribute without affecting others, for example:: + + p1 = Parameter('a', value=2.0) + p2 = Parameter('b', value=0.0) + p1.set(min=0) + p2.set(vary=False) + + to set a lower bound, or to set a Parameter as have a fixed value. + + Note that to use this approach to lift a lower or upper bound, doing:: + + p1.set(min=0) + ..... + # now lift the lower bound + p1.set(min=None) # won't work! lower bound NOT changed + + won't work -- this will not change the current lower bound. Instead + you'll have to use ``np.inf`` to remove a lower or upper bound:: + + # now lift the lower bound + p1.set(min=-np.inf) # will work! + + Similarly, to clear an expression of a parameter, you need to pass an + empty string, not ``None``. You also need to give a value and + explicitly tell it to vary:: + + p3 = Parameter('c', expr='(a+b)/2') + p3.set(expr=None) # won't work! expression NOT changed + + # remove constraint expression + p3.set(value=1.0, vary=True, expr='') # will work! parameter now unconstrained + + +The :class:`Parameters` class +======================================== + +.. currentmodule:: lmfit.parameter + +.. class:: Parameters() + + create a Parameters object. This is little more than a fancy ordered + dictionary, with the restrictions that: + + 1. keys must be valid Python symbol names, so that they can be used in + expressions of mathematical constraints. This means the names must + match ``[a-z_][a-z0-9_]*`` and cannot be a Python reserved word. + + 2. values must be valid :class:`Parameter` objects. + + Two methods are provided for convenient initialization of a :class:`Parameters`, + and one for extracting :class:`Parameter` values into a plain dictionary. + + .. method:: add(name[, value=None[, vary=True[, min=None[, max=None[, expr=None]]]]]) + + add a named parameter. This creates a :class:`Parameter` + object associated with the key `name`, with optional arguments + passed to :class:`Parameter`:: + + p = Parameters() + p.add('myvar', value=1, vary=True) + + .. method:: add_many(self, paramlist) + + add a list of named parameters. Each entry must be a tuple + with the following entries:: + + name, value, vary, min, max, expr + + This method is somewhat rigid and verbose (no default values), but can + be useful when initially defining a parameter list so that it looks + table-like:: + + p = Parameters() + # (Name, Value, Vary, Min, Max, Expr) + p.add_many(('amp1', 10, True, None, None, None), + ('cen1', 1.2, True, 0.5, 2.0, None), + ('wid1', 0.8, True, 0.1, None, None), + ('amp2', 7.5, True, None, None, None), + ('cen2', 1.9, True, 1.0, 3.0, None), + ('wid2', None, False, None, None, '2*wid1/3')) + + + .. automethod:: Parameters.pretty_print + + .. method:: valuesdict() + + return an ordered dictionary of name:value pairs with the + Paramater name as the key and Parameter value as value. + + This is distinct from the :class:`Parameters` itself, as the dictionary + values are not :class:`Parameter` objects, just the :attr:`value`. + Using :meth:`valuesdict` can be a very convenient way to get updated + values in a objective function. + + .. method:: dumps(**kws) + + return a JSON string representation of the :class:`Parameter` object. + This can be saved or used to re-create or re-set parameters, using the + :meth:`loads` method. + + Optional keywords are sent :py:func:`json.dumps`. + + .. method:: dump(file, **kws) + + write a JSON representation of the :class:`Parameter` object to a file + or file-like object in `file` -- really any object with a :meth:`write` + method. Optional keywords are sent :py:func:`json.dumps`. + + .. method:: loads(sval, **kws) + + use a JSON string representation of the :class:`Parameter` object in + `sval` to set all parameter settings. Optional keywords are sent + :py:func:`json.loads`. + + .. method:: load(file, **kws) + + read and use a JSON string representation of the :class:`Parameter` + object from a file or file-like object in `file` -- really any object + with a :meth:`read` method. Optional keywords are sent + :py:func:`json.loads`. + + +Simple Example +================== + +Using :class:`Parameters`` and :func:`minimize` function (discussed in the +next chapter) might look like this: + +.. literalinclude:: ../examples/doc_basic.py + + +Here, the objective function explicitly unpacks each Parameter value. This +can be simplified using the :class:`Parameters` :meth:`valuesdict` method, +which would make the objective function ``fcn2min`` above look like:: + + def fcn2min(params, x, data): + """ model decaying sine wave, subtract data""" + v = params.valuesdict() + + model = v['amp'] * np.sin(x * v['omega'] + v['shift']) * np.exp(-x*x*v['decay']) + return model - data + +The results are identical, and the difference is a stylistic choice. diff --git a/doc/sphinx/ext_mathjax.py b/doc/sphinx/ext_mathjax.py index 3e54c82..40de659 100644 --- a/doc/sphinx/ext_mathjax.py +++ b/doc/sphinx/ext_mathjax.py @@ -1,10 +1,10 @@ -# sphinx extensions for mathjax
-extensions = ['sphinx.ext.autodoc',
- 'sphinx.ext.todo',
- 'sphinx.ext.coverage',
- 'sphinx.ext.intersphinx',
- 'numpydoc']
-mathjax = 'sphinx.ext.mathjax'
-pngmath = 'sphinx.ext.pngmath'
-
-extensions.append(mathjax)
+# sphinx extensions for mathjax +extensions = ['sphinx.ext.autodoc', + 'sphinx.ext.todo', + 'sphinx.ext.coverage', + 'sphinx.ext.intersphinx', + 'numpydoc'] +mathjax = 'sphinx.ext.mathjax' +pngmath = 'sphinx.ext.pngmath' + +extensions.append(mathjax) diff --git a/doc/sphinx/ext_pngmath.py b/doc/sphinx/ext_pngmath.py index 10997b0..cf153fe 100644 --- a/doc/sphinx/ext_pngmath.py +++ b/doc/sphinx/ext_pngmath.py @@ -1,10 +1,10 @@ -# sphinx extensions for pngmath
-extensions = ['sphinx.ext.autodoc',
- 'sphinx.ext.todo',
- 'sphinx.ext.coverage',
- 'sphinx.ext.intersphinx',
- 'numpydoc']
-mathjax = 'sphinx.ext.mathjax'
-pngmath = 'sphinx.ext.pngmath'
-
-extensions.append(pngmath)
+# sphinx extensions for pngmath +extensions = ['sphinx.ext.autodoc', + 'sphinx.ext.todo', + 'sphinx.ext.coverage', + 'sphinx.ext.intersphinx', + 'numpydoc'] +mathjax = 'sphinx.ext.mathjax' +pngmath = 'sphinx.ext.pngmath' + +extensions.append(pngmath) diff --git a/doc/sphinx/theme/lmfitdoc/layout.html b/doc/sphinx/theme/lmfitdoc/layout.html index 42409a1..6a31b9d 100644 --- a/doc/sphinx/theme/lmfitdoc/layout.html +++ b/doc/sphinx/theme/lmfitdoc/layout.html @@ -1,66 +1,66 @@ -{#
- sphinxdoc/layout.html
- ~~~~~~~~~~~~~~~~~~~~~
-
- Sphinx layout template for the sphinxdoc theme.
-
- :copyright: Copyright 2007-2014 by the Sphinx team, see AUTHORS.
- :license: BSD, see LICENSE for details.
-#}
-{%- extends "basic/layout.html" %}
-
-{%- block extrahead %}
- <script type="text/x-mathjax-config">
- MathJax.Hub.Config({
- "TeX": {Macros: {AA : "{\\unicode{x212B}}"}},
- "HTML-CSS": {scale: 90}
- });</script>
-{% endblock %}
-
-
-
-{% block rootrellink %}
- <li>[<a href="{{ pathto('intro') }}">intro</a>|</li>
- <li><a href="{{ pathto('parameters') }}">parameters</a>|</li>
- <li><a href="{{ pathto('fitting') }}"> minimize</a>|</li>
- <li><a href="{{ pathto('model') }}"> model</a>|</li>
- <li><a href="{{ pathto('builtin_models') }}"> builtin models</a>|</li>
- <li><a href="{{ pathto('confidence') }}">confidence intervals</a>|</li>
- <li><a href="{{ pathto('bounds') }}">bounds</a>|</li>
- <li><a href="{{ pathto('constraints') }}">constraints</a>]</li>
-{% endblock %}
-
-{% block relbar1 %}
-<div>
-<table border=0>
- <tr><td></td><td width=85% padding=5 align=left>
- <a href="index.html" style="color: #157"> <font size=+3>LMFIT</font></a>
- </td>
- <td width=7% align=left>
- <a href="contents.html" style="color: #882222">
- <font size+=1>Contents</font></a> </td>
- <td width=7% align=left>
- <a href="installation.html" style="color: #882222">
- <font size+=1>Download</font></a></td>
- <td></td>
- </tr>
- <tr><td></td><td width=75% padding=5 align=left>
- <a href="index.html" style="color: #157"> <font size=+2>
- Non-Linear Least-Squares Minimization and Curve-Fitting for Python</font></a>
- </td>
- <td width=7% align=left>
- <a href="faq.html" style="color: #882222">
- <font size+=1>FAQ</font></a> </td>
- <td width=7% align=left>
- <a href="https://github.com/lmfit/lmfit-py/" style="color: #882222">
- <font size+=1>Develop</font></a></td>
- <td></td>
- </tr>
-</table>
-</div>
-{{ super() }}
-{% endblock %}
-
-{# put the sidebar before the body #}
-{% block sidebar1 %}{{ sidebar() }}{% endblock %}
-{% block sidebar2 %}{% endblock %}
+{# + sphinxdoc/layout.html + ~~~~~~~~~~~~~~~~~~~~~ + + Sphinx layout template for the sphinxdoc theme. + + :copyright: Copyright 2007-2014 by the Sphinx team, see AUTHORS. + :license: BSD, see LICENSE for details. +#} +{%- extends "basic/layout.html" %} + +{%- block extrahead %} + <script type="text/x-mathjax-config"> + MathJax.Hub.Config({ + "TeX": {Macros: {AA : "{\\unicode{x212B}}"}}, + "HTML-CSS": {scale: 90} + });</script> +{% endblock %} + + + +{% block rootrellink %} + <li>[<a href="{{ pathto('intro') }}">intro</a>|</li> + <li><a href="{{ pathto('parameters') }}">parameters</a>|</li> + <li><a href="{{ pathto('fitting') }}"> minimize</a>|</li> + <li><a href="{{ pathto('model') }}"> model</a>|</li> + <li><a href="{{ pathto('builtin_models') }}"> builtin models</a>|</li> + <li><a href="{{ pathto('confidence') }}">confidence intervals</a>|</li> + <li><a href="{{ pathto('bounds') }}">bounds</a>|</li> + <li><a href="{{ pathto('constraints') }}">constraints</a>]</li> +{% endblock %} + +{% block relbar1 %} +<div> +<table border=0> + <tr><td></td><td width=85% padding=5 align=left> + <a href="index.html" style="color: #157"> <font size=+3>LMFIT</font></a> + </td> + <td width=7% align=left> + <a href="contents.html" style="color: #882222"> + <font size+=1>Contents</font></a> </td> + <td width=7% align=left> + <a href="installation.html" style="color: #882222"> + <font size+=1>Download</font></a></td> + <td></td> + </tr> + <tr><td></td><td width=75% padding=5 align=left> + <a href="index.html" style="color: #157"> <font size=+2> + Non-Linear Least-Squares Minimization and Curve-Fitting for Python</font></a> + </td> + <td width=7% align=left> + <a href="faq.html" style="color: #882222"> + <font size+=1>FAQ</font></a> </td> + <td width=7% align=left> + <a href="https://github.com/lmfit/lmfit-py/" style="color: #882222"> + <font size+=1>Develop</font></a></td> + <td></td> + </tr> +</table> +</div> +{{ super() }} +{% endblock %} + +{# put the sidebar before the body #} +{% block sidebar1 %}{{ sidebar() }}{% endblock %} +{% block sidebar2 %}{% endblock %} diff --git a/doc/sphinx/theme/lmfitdoc/static/lmfitdoc.css_t b/doc/sphinx/theme/lmfitdoc/static/lmfitdoc.css_t index 89bd30c..92b6913 100644 --- a/doc/sphinx/theme/lmfitdoc/static/lmfitdoc.css_t +++ b/doc/sphinx/theme/lmfitdoc/static/lmfitdoc.css_t @@ -1,348 +1,348 @@ -/*
- * lmfitdoc.css_t
- * minor riff on sphinxdoc.css_t
- * ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
- *
- * Sphinx stylesheet -- sphinxdoc theme. Originally created by
- * Armin Ronacher for Werkzeug.
- *
- * :copyright: Copyright 2007-2014 by the Sphinx team, see AUTHORS.
- * :license: BSD, see LICENSE for details.
- *
- */
-
-@import url("basic.css");
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-}
+/* + * lmfitdoc.css_t + * minor riff on sphinxdoc.css_t + * ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + * + * Sphinx stylesheet -- sphinxdoc theme. Originally created by + * Armin Ronacher for Werkzeug. + * + * :copyright: Copyright 2007-2014 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ + +@import url("basic.css"); + +/* -- page layout ----------------------------------------------------------- */ + +body { + font-family: 'Lucida Grande', 'Lucida Sans Unicode', 'Geneva', 'Verdana', sans-serif; + font-size: 14px; + letter-spacing: -0.01em; + line-height: 150%; + text-align: center; + background-color: #D6DAC4; + color: black; + padding: 0; + border: 0px solid #D0D0C0; + margin: 15px 15px 15px 15px; + min-width: 740px; +} + +div.document { + background-color: white; + text-align: left; + background-image: url(contents.png); + background-repeat: repeat-x; +} + +div.bodywrapper { + margin: 0 {{ theme_sidebarwidth|toint + 10 }}px 0 0; + border-right: 1px solid #ccc; +} + +div.body { + margin: 0; + padding: 0.5em 20px 20px 20px; +} + +div.related { + font-size: 1em; + background-color: #0D0; +} + +div.related ul { + height: 2em; + border-top: 1px solid #ddd; + border-bottom: 1px solid #ddd; + background-color: #F0EFE4; + color: #157; +} + +div.related ul li { + margin: 0; + padding: 0; + height: 2em; + float: left; + background-color: #D0000; +} + +div.related ul li.right { + float: right; + margin-right: 5px; +} + +div.related ul li a { + margin: 0; + padding: 0 5px 0 5px; + line-height: 1.75em; + color: #EE9816; + color: #157; +} + +div.related ul li a:hover { + color: #822; +} + +div.sphinxsidebarwrapper { + padding: 0; +} + +div.sphinxsidebar { + margin: 0; + padding: 0.5em 15px 15px 0; + width: {{ theme_sidebarwidth|toint - 20 }}px; + float: right; + font-size: 1em; + text-align: left; +} + +div.sphinxsidebar h3, div.sphinxsidebar h4 { + margin: 1em 0 0.5em 0; + font-size: 1em; + padding: 0.1em 0 0.1em 0.5em; + color: #157; + border: 1px solid #A0A090; + background-color: #D0D0C4; +} + +div.sphinxsidebar h3 a { + color: #157; + background-color: #D0D0C4; +} + +div.sphinxsidebar ul { + padding-left: 1.5em; + margin-top: 7px; + padding: 0; + line-height: 130%; +} + +div.sphinxsidebar ul ul { + margin-left: 20px; +} + +div.footer { + background-color: #E0E8D4; + color: #86989B; + padding: 3px 8px 3px 0; + clear: both; + font-size: 0.8em; + text-align: right; +} + +div.footer a { + color: #86989B; + text-decoration: underline; +} + +/* -- body styles ----------------------------------------------------------- */ + +p { + margin: 0.8em 0 0.5em 0; +} + +a { + color: #CA7900; + text-decoration: none; +} + +a:hover { + color: #2491CF; +} + +div.body a { + text-decoration: underline; +} + +h1 { + padding: 0.2em 0 0.2em 0; + margin: 0.7em 0 0.3em 0; + font-size: 1.5em; + color: #157; + background-color: #F0EFE4; +} + +h2 { + padding: 0.2em 0 0.2em 0; + margin: 1.3em 0 0.2em 0; + font-size: 1.35em; + padding: 0; + background-color: #FAFAF0; +} + +h3 { + padding: 0.2em 0 0.2em 0; + margin: 1em 0 -0.3em 0; + font-size: 1.2em; + background-color: #FBFBF3; +} + +div.body h1 a, div.body h2 a, div.body h3 a, div.body h4 a, div.body h5 a, div.body h6 a { + color: black!important; +} + +h1 a.anchor, h2 a.anchor, h3 a.anchor, h4 a.anchor, h5 a.anchor, h6 a.anchor { + display: none; + margin: 0 0 0 0.3em; + padding: 0 0.2em 0 0.2em; + color: #aaa!important; +} + +h1:hover a.anchor, h2:hover a.anchor, h3:hover a.anchor, h4:hover a.anchor, +h5:hover a.anchor, h6:hover a.anchor { + display: inline; +} + +h1 a.anchor:hover, h2 a.anchor:hover, h3 a.anchor:hover, h4 a.anchor:hover, +h5 a.anchor:hover, h6 a.anchor:hover { + color: #777; + background-color: #eee; +} + +a.headerlink { + color: #c60f0f!important; + font-size: 1em; + margin-left: 6px; + padding: 0 4px 0 4px; + text-decoration: none!important; +} + +a.headerlink:hover { + background-color: #ccc; + color: white!important; +} + +cite, code, tt { + font-family: 'Consolas', 'Deja Vu Sans Mono', + 'Bitstream Vera Sans Mono', monospace; + font-size: 0.95em; + letter-spacing: 0.01em; +} + +tt { + background-color: #f2f2f2; + border-bottom: 1px solid #ddd; + color: #333; +} + +tt.descname, tt.descclassname, tt.xref { + border: 0; +} + +hr { + border: 1px solid #abc; + margin: 2em; +} + +a tt { + border: 0; + color: #CA7900; +} + +a tt:hover { + color: #2491CF; +} + +pre { + font-family: 'Consolas', 'Deja Vu Sans Mono', + 'Bitstream Vera Sans Mono', monospace; + font-size: 0.95em; + letter-spacing: 0.015em; + line-height: 120%; + padding: 0.5em; + border: 1px solid #ccc; + background-color: #f8f8f8; +} + +pre a { + color: inherit; + text-decoration: underline; +} + +td.linenos pre { + padding: 0.5em 0; +} + +div.quotebar { + background-color: #f8f8f8; + max-width: 250px; + float: right; + padding: 2px 7px; + border: 1px solid #ccc; +} + +div.topic { + background-color: #f8f8f8; +} + +table { + border-collapse: collapse; + margin: 0 -0.5em 0 -0.5em; +} + +table td, table th { + padding: 0.2em 0.5em 0.2em 0.5em; +} + +div.admonition, div.warning { + font-size: 0.9em; + margin: 1em 0 1em 0; + border: 1px solid #86989B; + background-color: #f7f7f7; + padding: 0; +} + +div.admonition p, div.warning p { + margin: 0.5em 1em 0.5em 1em; + padding: 0; +} + +div.admonition pre, div.warning pre { + margin: 0.4em 1em 0.4em 1em; +} + +div.admonition p.admonition-title, +div.warning p.admonition-title { + margin: 0; + padding: 0.1em 0 0.1em 0.5em; + color: white; + border-bottom: 1px solid #86989B; + font-weight: bold; + background-color: #AFC1C4; +} + +div.warning { + border: 1px solid #940000; +} + +div.warning p.admonition-title { + background-color: #CF0000; + border-bottom-color: #940000; +} + +div.admonition ul, div.admonition ol, +div.warning ul, div.warning ol { + margin: 0.1em 0.5em 0.5em 3em; + padding: 0; +} + +div.versioninfo { + margin: 1em 0 0 0; + border: 1px solid #ccc; + background-color: #DDEAF0; + padding: 8px; + line-height: 1.3em; + font-size: 0.9em; +} + +.viewcode-back { + font-family: 'Lucida Grande', 'Lucida Sans Unicode', 'Geneva', + 'Verdana', sans-serif; +} + +div.viewcode-block:target { + background-color: #f4debf; + border-top: 1px solid #ac9; + border-bottom: 1px solid #ac9; +} diff --git a/doc/sphinx/theme/lmfitdoc/theme.conf b/doc/sphinx/theme/lmfitdoc/theme.conf index 82db5fb..d3bfaad 100644 --- a/doc/sphinx/theme/lmfitdoc/theme.conf +++ b/doc/sphinx/theme/lmfitdoc/theme.conf @@ -1,4 +1,4 @@ -[theme]
-inherit = basic
-stylesheet = lmfitdoc.css
-pygments_style = friendly
+[theme] +inherit = basic +stylesheet = lmfitdoc.css +pygments_style = friendly diff --git a/doc/support.rst b/doc/support.rst index 9a08328..4fe2c3e 100644 --- a/doc/support.rst +++ b/doc/support.rst @@ -1,30 +1,30 @@ -.. _support_chapter:
-
-===========================
-Getting Help
-===========================
-
-.. _mailing list: https://groups.google.com/group/lmfit-py
-.. _github issues: https://github.com/lmfit/lmfit-py/issues
-
-If you have questions, comments, or suggestions for LMFIT, please use the
-`mailing list`_. This provides an on-line conversation that is and
-archived well and can be searched well with standard web searches. If you
-find a bug with the code or documentation, use the `github issues`_ Issue
-tracker to submit a report. If you have an idea for how to solve the
-problem and are familiar with python and github, submitting a github Pull
-Request would be greatly appreciated.
-
-If you are unsure whether to use the mailing list or the Issue tracker,
-please start a conversation on the `mailing list`_. That is, the problem
-you're having may or may not be due to a bug. If it is due to a bug,
-creating an Issue from the conversation is easy. If it is not a bug, the
-problem will be discussed and then the Issue will be closed. While one
-*can* search through closed Issues on github, these are not so easily
-searched, and the conversation is not easily useful to others later.
-Starting the conversation on the mailing list with "How do I do this?" or
-"Why didn't this work?" instead of "This should work and doesn't" is
-generally preferred, and will better help others with similar questions.
-Of course, there is not always an obvious way to decide if something is a
-Question or an Issue, and we will try our best to engage in all
-discussions.
+.. _support_chapter: + +=========================== +Getting Help +=========================== + +.. _mailing list: https://groups.google.com/group/lmfit-py +.. _github issues: https://github.com/lmfit/lmfit-py/issues + +If you have questions, comments, or suggestions for LMFIT, please use the +`mailing list`_. This provides an on-line conversation that is and +archived well and can be searched well with standard web searches. If you +find a bug with the code or documentation, use the `github issues`_ Issue +tracker to submit a report. If you have an idea for how to solve the +problem and are familiar with python and github, submitting a github Pull +Request would be greatly appreciated. + +If you are unsure whether to use the mailing list or the Issue tracker, +please start a conversation on the `mailing list`_. That is, the problem +you're having may or may not be due to a bug. If it is due to a bug, +creating an Issue from the conversation is easy. If it is not a bug, the +problem will be discussed and then the Issue will be closed. While one +*can* search through closed Issues on github, these are not so easily +searched, and the conversation is not easily useful to others later. +Starting the conversation on the mailing list with "How do I do this?" or +"Why didn't this work?" instead of "This should work and doesn't" is +generally preferred, and will better help others with similar questions. +Of course, there is not always an obvious way to decide if something is a +Question or an Issue, and we will try our best to engage in all +discussions. diff --git a/doc/whatsnew.rst b/doc/whatsnew.rst index 2d94a51..125f2c7 100644 --- a/doc/whatsnew.rst +++ b/doc/whatsnew.rst @@ -1,97 +1,97 @@ -.. _whatsnew_chapter:
-
-=====================
-Release Notes
-=====================
-
-.. _lmfit github repository: http://github.com/lmfit/lmfit-py
-
-This section discusses changes between versions, especially significant
-changes to the use and behavior of the library. This is not meant to be a
-comprehensive list of changes. For such a complete record, consult the
-`lmfit github repository`_.
-
-.. _whatsnew_090_label:
-
-Version 0.9.0 Release Notes
-==========================================
-
-This upgrade makes an important, non-backward-compatible change to the way
-many fitting scripts and programs will work. Scripts that work with
-version 0.8.3 will not work with version 0.9.0 and vice versa. The change
-was not made lightly or without ample discussion, and is really an
-improvement. Modifying scripts that did work with 0.8.3 to work with 0.9.0
-is easy, but needs to be done.
-
-
-
-Summary
-~~~~~~~~~~~~
-
-The upgrade from 0.8.3 to 0.9.0 introduced the :class:`MinimizerResult`
-class (see :ref:`fit-results-label`) which is now used to hold the return
-value from :func:`minimize` and :meth:`Minimizer.minimize`. This returned
-object contains many goodness of fit statistics, and holds the optimized
-parameters from the fit. Importantly, the parameters passed into
-:func:`minimize` and :meth:`Minimizer.minimize` are no longer modified by
-the fit. Instead, a copy of the passed-in parameters is made which is
-changed and returns as the :attr:`params` attribute of the returned
-:class:`MinimizerResult`.
-
-
-Impact
-~~~~~~~~~~~~~
-
-This upgrade means that a script that does::
-
- my_pars = Parameters()
- my_pars.add('amp', value=300.0, min=0)
- my_pars.add('center', value= 5.0, min=0, max=10)
- my_pars.add('decay', value= 1.0, vary=False)
-
- result = minimize(objfunc, my_pars)
-
-will still work, but that ``my_pars`` will **NOT** be changed by the fit.
-Instead, ``my_pars`` is copied to an internal set of parameters that is
-changed in the fit, and this copy is then put in ``result.params``. To
-look at fit results, use ``result.params``, not ``my_pars``.
-
-This has the effect that ``my_pars`` will still hold the starting parameter
-values, while all of the results from the fit are held in the ``result``
-object returned by :func:`minimize`.
-
-If you want to do an initial fit, then refine that fit to, for example, do
-a pre-fit, then refine that result different fitting method, such as::
-
- result1 = minimize(objfunc, my_pars, method='nelder')
- result1.params['decay'].vary = True
- result2 = minimize(objfunc, result1.params, method='leastsq')
-
-and have access to all of the starting parameters ``my_pars``, the result of the
-first fit ``result1``, and the result of the final fit ``result2``.
-
-
-
-Discussion
-~~~~~~~~~~~~~~
-
-The main goal for making this change were to
-
- 1. give a better return value to :func:`minimize` and
- :meth:`Minimizer.minimize` that can hold all of the information
- about a fit. By having the return value be an instance of the
- :class:`MinimizerResult` class, it can hold an arbitrary amount of
- information that is easily accessed by attribute name, and even
- be given methods. Using objects is good!
-
- 2. To limit or even elimate the amount of "state information" a
- :class:`Minimizer` holds. By state information, we mean how much of
- the previous fit is remembered after a fit is done. Keeping (and
- especially using) such information about a previous fit means that
- a :class:`Minimizer` might give different results even for the same
- problem if run a second time. While it's desirable to be able to
- adjust a set of :class:`Parameters` re-run a fit to get an improved
- result, doing this by changing an *internal attribute
- (:attr:`Minimizer.params`) has the undesirable side-effect of not
- being able to "go back", and makes it somewhat cumbersome to keep
- track of changes made while adjusting parameters and re-running fits.
+.. _whatsnew_chapter: + +===================== +Release Notes +===================== + +.. _lmfit github repository: http://github.com/lmfit/lmfit-py + +This section discusses changes between versions, especially significant +changes to the use and behavior of the library. This is not meant to be a +comprehensive list of changes. For such a complete record, consult the +`lmfit github repository`_. + +.. _whatsnew_090_label: + +Version 0.9.0 Release Notes +========================================== + +This upgrade makes an important, non-backward-compatible change to the way +many fitting scripts and programs will work. Scripts that work with +version 0.8.3 will not work with version 0.9.0 and vice versa. The change +was not made lightly or without ample discussion, and is really an +improvement. Modifying scripts that did work with 0.8.3 to work with 0.9.0 +is easy, but needs to be done. + + + +Summary +~~~~~~~~~~~~ + +The upgrade from 0.8.3 to 0.9.0 introduced the :class:`MinimizerResult` +class (see :ref:`fit-results-label`) which is now used to hold the return +value from :func:`minimize` and :meth:`Minimizer.minimize`. This returned +object contains many goodness of fit statistics, and holds the optimized +parameters from the fit. Importantly, the parameters passed into +:func:`minimize` and :meth:`Minimizer.minimize` are no longer modified by +the fit. Instead, a copy of the passed-in parameters is made which is +changed and returns as the :attr:`params` attribute of the returned +:class:`MinimizerResult`. + + +Impact +~~~~~~~~~~~~~ + +This upgrade means that a script that does:: + + my_pars = Parameters() + my_pars.add('amp', value=300.0, min=0) + my_pars.add('center', value= 5.0, min=0, max=10) + my_pars.add('decay', value= 1.0, vary=False) + + result = minimize(objfunc, my_pars) + +will still work, but that ``my_pars`` will **NOT** be changed by the fit. +Instead, ``my_pars`` is copied to an internal set of parameters that is +changed in the fit, and this copy is then put in ``result.params``. To +look at fit results, use ``result.params``, not ``my_pars``. + +This has the effect that ``my_pars`` will still hold the starting parameter +values, while all of the results from the fit are held in the ``result`` +object returned by :func:`minimize`. + +If you want to do an initial fit, then refine that fit to, for example, do +a pre-fit, then refine that result different fitting method, such as:: + + result1 = minimize(objfunc, my_pars, method='nelder') + result1.params['decay'].vary = True + result2 = minimize(objfunc, result1.params, method='leastsq') + +and have access to all of the starting parameters ``my_pars``, the result of the +first fit ``result1``, and the result of the final fit ``result2``. + + + +Discussion +~~~~~~~~~~~~~~ + +The main goal for making this change were to + +1. give a better return value to :func:`minimize` and + :meth:`Minimizer.minimize` that can hold all of the information + about a fit. By having the return value be an instance of the + :class:`MinimizerResult` class, it can hold an arbitrary amount of + information that is easily accessed by attribute name, and even + be given methods. Using objects is good! + +2. To limit or even eliminate the amount of "state information" a + :class:`Minimizer` holds. By state information, we mean how much of + the previous fit is remembered after a fit is done. Keeping (and + especially using) such information about a previous fit means that + a :class:`Minimizer` might give different results even for the same + problem if run a second time. While it's desirable to be able to + adjust a set of :class:`Parameters` re-run a fit to get an improved + result, doing this by changing an internal attribute + (:attr:`Minimizer.params`) has the undesirable side-effect of not + being able to "go back", and makes it somewhat cumbersome to keep + track of changes made while adjusting parameters and re-running fits. diff --git a/lmfit/__init__.py b/lmfit/__init__.py index df6a441..30d0d6b 100644 --- a/lmfit/__init__.py +++ b/lmfit/__init__.py @@ -1,53 +1,53 @@ -"""
-Lmfit provides a high-level interface to non-linear optimization and curve
-fitting problems for Python. Lmfit builds on Levenberg-Marquardt algorithm of
-scipy.optimize.leastsq(), but also supports most of the optimization methods
-from scipy.optimize. It has a number of useful enhancements, including:
-
- * Using Parameter objects instead of plain floats as variables. A Parameter
- has a value that can be varied in the fit, fixed, have upper and/or lower
- bounds. It can even have a value that is constrained by an algebraic
- expression of other Parameter values.
-
- * Ease of changing fitting algorithms. Once a fitting model is set up, one
- can change the fitting algorithm without changing the objective function.
-
- * Improved estimation of confidence intervals. While
- scipy.optimize.leastsq() will automatically calculate uncertainties and
- correlations from the covariance matrix, lmfit also has functions to
- explicitly explore parameter space to determine confidence levels even for
- the most difficult cases.
-
- * Improved curve-fitting with the Model class. This which extends the
- capabilities of scipy.optimize.curve_fit(), allowing you to turn a function
- that models for your data into a python class that helps you parametrize
- and fit data with that model.
-
- * Many pre-built models for common lineshapes are included and ready to use.
-
- version: 0.8.0
- last update: 2014-Sep-21
- License: MIT
- Authors: Matthew Newville, The University of Chicago
- Till Stensitzki, Freie Universitat Berlin
- Daniel B. Allen, Johns Hopkins University
- Antonino Ingargiola, University of California, Los Angeles
-"""
-
-from .minimizer import minimize, Minimizer, MinimizerException
-from .parameter import Parameter, Parameters
-from .confidence import conf_interval, conf_interval2d
-from .printfuncs import (fit_report, ci_report,
- report_fit, report_ci, report_errors)
-
-from .model import Model, CompositeModel
-from . import models
-
-from . import uncertainties
-from .uncertainties import ufloat, correlated_values
-
-
-## versioneer code
-from ._version import get_versions
-__version__ = get_versions()['version']
-del get_versions
+""" +Lmfit provides a high-level interface to non-linear optimization and curve +fitting problems for Python. Lmfit builds on Levenberg-Marquardt algorithm of +scipy.optimize.leastsq(), but also supports most of the optimization methods +from scipy.optimize. It has a number of useful enhancements, including: + + * Using Parameter objects instead of plain floats as variables. A Parameter + has a value that can be varied in the fit, fixed, have upper and/or lower + bounds. It can even have a value that is constrained by an algebraic + expression of other Parameter values. + + * Ease of changing fitting algorithms. Once a fitting model is set up, one + can change the fitting algorithm without changing the objective function. + + * Improved estimation of confidence intervals. While + scipy.optimize.leastsq() will automatically calculate uncertainties and + correlations from the covariance matrix, lmfit also has functions to + explicitly explore parameter space to determine confidence levels even for + the most difficult cases. + + * Improved curve-fitting with the Model class. This which extends the + capabilities of scipy.optimize.curve_fit(), allowing you to turn a function + that models for your data into a python class that helps you parametrize + and fit data with that model. + + * Many pre-built models for common lineshapes are included and ready to use. + + version: 0.8.0 + last update: 2014-Sep-21 + License: MIT + Authors: Matthew Newville, The University of Chicago + Till Stensitzki, Freie Universitat Berlin + Daniel B. Allen, Johns Hopkins University + Antonino Ingargiola, University of California, Los Angeles +""" + +from .minimizer import minimize, Minimizer, MinimizerException +from .parameter import Parameter, Parameters +from .confidence import conf_interval, conf_interval2d +from .printfuncs import (fit_report, ci_report, + report_fit, report_ci, report_errors) + +from .model import Model, CompositeModel +from . import models + +from . import uncertainties +from .uncertainties import ufloat, correlated_values + + +## versioneer code +from ._version import get_versions +__version__ = get_versions()['version'] +del get_versions diff --git a/lmfit/_differentialevolution.py b/lmfit/_differentialevolution.py index 48f6336..1e1fb66 100644 --- a/lmfit/_differentialevolution.py +++ b/lmfit/_differentialevolution.py @@ -1,750 +1,750 @@ -"""
-differential_evolution: The differential evolution global optimization algorithm
-Added by Andrew Nelson 2014
-"""
-from __future__ import division, print_function, absolute_import
-import numpy as np
-from scipy.optimize import minimize
-from scipy.optimize.optimize import _status_message
-import numbers
-
-__all__ = ['differential_evolution']
-
-_MACHEPS = np.finfo(np.float64).eps
-
-
-#------------------------------------------------------------------------------
-# scipy.optimize does not contain OptimizeResult until 0.14. Include here as a
-# fix for scipy < 0.14.
-
-class OptimizeResult(dict):
- """ Represents the optimization result.
- Attributes
- ----------
- x : ndarray
- The solution of the optimization.
- success : bool
- Whether or not the optimizer exited successfully.
- status : int
- Termination status of the optimizer. Its value depends on the
- underlying solver. Refer to `message` for details.
- message : str
- Description of the cause of the termination.
- fun, jac, hess, hess_inv : ndarray
- Values of objective function, Jacobian, Hessian or its inverse (if
- available). The Hessians may be approximations, see the documentation
- of the function in question.
- nfev, njev, nhev : int
- Number of evaluations of the objective functions and of its
- Jacobian and Hessian.
- nit : int
- Number of iterations performed by the optimizer.
- maxcv : float
- The maximum constraint violation.
- Notes
- -----
- There may be additional attributes not listed above depending of the
- specific solver. Since this class is essentially a subclass of dict
- with attribute accessors, one can see which attributes are available
- using the `keys()` method.
- """
- def __getattr__(self, name):
- try:
- return self[name]
- except KeyError:
- raise AttributeError(name)
-
- __setattr__ = dict.__setitem__
- __delattr__ = dict.__delitem__
-
- def __repr__(self):
- if self.keys():
- m = max(map(len, list(self.keys()))) + 1
- return '\n'.join([k.rjust(m) + ': ' + repr(v)
- for k, v in self.items()])
- else:
- return self.__class__.__name__ + "()"
-#------------------------------------------------------------------------------
-
-
-def differential_evolution(func, bounds, args=(), strategy='best1bin',
- maxiter=None, popsize=15, tol=0.01,
- mutation=(0.5, 1), recombination=0.7, seed=None,
- callback=None, disp=False, polish=True,
- init='latinhypercube'):
- """Finds the global minimum of a multivariate function.
- Differential Evolution is stochastic in nature (does not use gradient
- methods) to find the minimium, and can search large areas of candidate
- space, but often requires larger numbers of function evaluations than
- conventional gradient based techniques.
-
- The algorithm is due to Storn and Price [1]_.
-
- Parameters
- ----------
- func : callable
- The objective function to be minimized. Must be in the form
- ``f(x, *args)``, where ``x`` is the argument in the form of a 1-D array
- and ``args`` is a tuple of any additional fixed parameters needed to
- completely specify the function.
- bounds : sequence
- Bounds for variables. ``(min, max)`` pairs for each element in ``x``,
- defining the lower and upper bounds for the optimizing argument of
- `func`. It is required to have ``len(bounds) == len(x)``.
- ``len(bounds)`` is used to determine the number of parameters in ``x``.
- args : tuple, optional
- Any additional fixed parameters needed to
- completely specify the objective function.
- strategy : str, optional
- The differential evolution strategy to use. Should be one of:
-
- - 'best1bin'
- - 'best1exp'
- - 'rand1exp'
- - 'randtobest1exp'
- - 'best2exp'
- - 'rand2exp'
- - 'randtobest1bin'
- - 'best2bin'
- - 'rand2bin'
- - 'rand1bin'
-
- The default is 'best1bin'.
- maxiter : int, optional
- The maximum number of times the entire population is evolved.
- The maximum number of function evaluations is:
- ``maxiter * popsize * len(x)``
- popsize : int, optional
- A multiplier for setting the total population size. The population has
- ``popsize * len(x)`` individuals.
- tol : float, optional
- When the mean of the population energies, multiplied by tol,
- divided by the standard deviation of the population energies
- is greater than 1 the solving process terminates:
- ``convergence = mean(pop) * tol / stdev(pop) > 1``
- mutation : float or tuple(float, float), optional
- The mutation constant.
- If specified as a float it should be in the range [0, 2].
- If specified as a tuple ``(min, max)`` dithering is employed. Dithering
- randomly changes the mutation constant on a generation by generation
- basis. The mutation constant for that generation is taken from
- ``U[min, max)``. Dithering can help speed convergence significantly.
- Increasing the mutation constant increases the search radius, but will
- slow down convergence.
- recombination : float, optional
- The recombination constant, should be in the range [0, 1]. Increasing
- this value allows a larger number of mutants to progress into the next
- generation, but at the risk of population stability.
- seed : int or `np.random.RandomState`, optional
- If `seed` is not specified the `np.RandomState` singleton is used.
- If `seed` is an int, a new `np.random.RandomState` instance is used,
- seeded with seed.
- If `seed` is already a `np.random.RandomState instance`, then that
- `np.random.RandomState` instance is used.
- Specify `seed` for repeatable minimizations.
- disp : bool, optional
- Display status messages
- callback : callable, `callback(xk, convergence=val)`, optional:
- A function to follow the progress of the minimization. ``xk`` is
- the current value of ``x0``. ``val`` represents the fractional
- value of the population convergence. When ``val`` is greater than one
- the function halts. If callback returns `True`, then the minimization
- is halted (any polishing is still carried out).
- polish : bool, optional
- If True (default), then `scipy.optimize.minimize` with the `L-BFGS-B`
- method is used to polish the best population member at the end, which
- can improve the minimization slightly.
- init : string, optional
- Specify how the population initialization is performed. Should be
- one of:
-
- - 'latinhypercube'
- - 'random'
-
- The default is 'latinhypercube'. Latin Hypercube sampling tries to
- maximize coverage of the available parameter space. 'random' initializes
- the population randomly - this has the drawback that clustering can
- occur, preventing the whole of parameter space being covered.
-
- Returns
- -------
- res : OptimizeResult
- The optimization result represented as a `OptimizeResult` object.
- Important attributes are: ``x`` the solution array, ``success`` a
- Boolean flag indicating if the optimizer exited successfully and
- ``message`` which describes the cause of the termination. See
- `OptimizeResult` for a description of other attributes. If `polish`
- was employed, then OptimizeResult also contains the `jac` attribute.
-
- Notes
- -----
- Differential evolution is a stochastic population based method that is
- useful for global optimization problems. At each pass through the population
- the algorithm mutates each candidate solution by mixing with other candidate
- solutions to create a trial candidate. There are several strategies [2]_ for
- creating trial candidates, which suit some problems more than others. The
- 'best1bin' strategy is a good starting point for many systems. In this
- strategy two members of the population are randomly chosen. Their difference
- is used to mutate the best member (the `best` in `best1bin`), :math:`b_0`,
- so far:
-
- .. math::
-
- b' = b_0 + mutation * (population[rand0] - population[rand1])
-
- A trial vector is then constructed. Starting with a randomly chosen 'i'th
- parameter the trial is sequentially filled (in modulo) with parameters from
- `b'` or the original candidate. The choice of whether to use `b'` or the
- original candidate is made with a binomial distribution (the 'bin' in
- 'best1bin') - a random number in [0, 1) is generated. If this number is
- less than the `recombination` constant then the parameter is loaded from
- `b'`, otherwise it is loaded from the original candidate. The final
- parameter is always loaded from `b'`. Once the trial candidate is built
- its fitness is assessed. If the trial is better than the original candidate
- then it takes its place. If it is also better than the best overall
- candidate it also replaces that.
- To improve your chances of finding a global minimum use higher `popsize`
- values, with higher `mutation` and (dithering), but lower `recombination`
- values. This has the effect of widening the search radius, but slowing
- convergence.
-
- .. versionadded:: 0.15.0
-
- Examples
- --------
- Let us consider the problem of minimizing the Rosenbrock function. This
- function is implemented in `rosen` in `scipy.optimize`.
-
- >>> from scipy.optimize import rosen, differential_evolution
- >>> bounds = [(0,2), (0, 2), (0, 2), (0, 2), (0, 2)]
- >>> result = differential_evolution(rosen, bounds)
- >>> result.x, result.fun
- (array([1., 1., 1., 1., 1.]), 1.9216496320061384e-19)
-
- Next find the minimum of the Ackley function
- (http://en.wikipedia.org/wiki/Test_functions_for_optimization).
-
- >>> from scipy.optimize import differential_evolution
- >>> import numpy as np
- >>> def ackley(x):
- ... arg1 = -0.2 * np.sqrt(0.5 * (x[0] ** 2 + x[1] ** 2))
- ... arg2 = 0.5 * (np.cos(2. * np.pi * x[0]) + np.cos(2. * np.pi * x[1]))
- ... return -20. * np.exp(arg1) - np.exp(arg2) + 20. + np.e
- >>> bounds = [(-5, 5), (-5, 5)]
- >>> result = differential_evolution(ackley, bounds)
- >>> result.x, result.fun
- (array([ 0., 0.]), 4.4408920985006262e-16)
-
- References
- ----------
- .. [1] Storn, R and Price, K, Differential Evolution - a Simple and
- Efficient Heuristic for Global Optimization over Continuous Spaces,
- Journal of Global Optimization, 1997, 11, 341 - 359.
- .. [2] http://www1.icsi.berkeley.edu/~storn/code.html
- .. [3] http://en.wikipedia.org/wiki/Differential_evolution
- """
-
- solver = DifferentialEvolutionSolver(func, bounds, args=args,
- strategy=strategy, maxiter=maxiter,
- popsize=popsize, tol=tol,
- mutation=mutation,
- recombination=recombination,
- seed=seed, polish=polish,
- callback=callback,
- disp=disp,
- init=init)
- return solver.solve()
-
-
-class DifferentialEvolutionSolver(object):
-
- """This class implements the differential evolution solver
-
- Parameters
- ----------
- func : callable
- The objective function to be minimized. Must be in the form
- ``f(x, *args)``, where ``x`` is the argument in the form of a 1-D array
- and ``args`` is a tuple of any additional fixed parameters needed to
- completely specify the function.
- bounds : sequence
- Bounds for variables. ``(min, max)`` pairs for each element in ``x``,
- defining the lower and upper bounds for the optimizing argument of
- `func`. It is required to have ``len(bounds) == len(x)``.
- ``len(bounds)`` is used to determine the number of parameters in ``x``.
- args : tuple, optional
- Any additional fixed parameters needed to
- completely specify the objective function.
- strategy : str, optional
- The differential evolution strategy to use. Should be one of:
-
- - 'best1bin'
- - 'best1exp'
- - 'rand1exp'
- - 'randtobest1exp'
- - 'best2exp'
- - 'rand2exp'
- - 'randtobest1bin'
- - 'best2bin'
- - 'rand2bin'
- - 'rand1bin'
-
- The default is 'best1bin'
-
- maxiter : int, optional
- The maximum number of times the entire population is evolved. The
- maximum number of function evaluations is:
- ``maxiter * popsize * len(x)``
- popsize : int, optional
- A multiplier for setting the total population size. The population has
- ``popsize * len(x)`` individuals.
- tol : float, optional
- When the mean of the population energies, multiplied by tol,
- divided by the standard deviation of the population energies
- is greater than 1 the solving process terminates:
- ``convergence = mean(pop) * tol / stdev(pop) > 1``
- mutation : float or tuple(float, float), optional
- The mutation constant.
- If specified as a float it should be in the range [0, 2].
- If specified as a tuple ``(min, max)`` dithering is employed. Dithering
- randomly changes the mutation constant on a generation by generation
- basis. The mutation constant for that generation is taken from
- U[min, max). Dithering can help speed convergence significantly.
- Increasing the mutation constant increases the search radius, but will
- slow down convergence.
- recombination : float, optional
- The recombination constant, should be in the range [0, 1]. Increasing
- this value allows a larger number of mutants to progress into the next
- generation, but at the risk of population stability.
- seed : int or `np.random.RandomState`, optional
- If `seed` is not specified the `np.random.RandomState` singleton is
- used.
- If `seed` is an int, a new `np.random.RandomState` instance is used,
- seeded with `seed`.
- If `seed` is already a `np.random.RandomState` instance, then that
- `np.random.RandomState` instance is used.
- Specify `seed` for repeatable minimizations.
- disp : bool, optional
- Display status messages
- callback : callable, `callback(xk, convergence=val)`, optional
- A function to follow the progress of the minimization. ``xk`` is
- the current value of ``x0``. ``val`` represents the fractional
- value of the population convergence. When ``val`` is greater than one
- the function halts. If callback returns `True`, then the minimization
- is halted (any polishing is still carried out).
- polish : bool, optional
- If True, then `scipy.optimize.minimize` with the `L-BFGS-B` method
- is used to polish the best population member at the end. This requires
- a few more function evaluations.
- maxfun : int, optional
- Set the maximum number of function evaluations. However, it probably
- makes more sense to set `maxiter` instead.
- init : string, optional
- Specify which type of population initialization is performed. Should be
- one of:
-
- - 'latinhypercube'
- - 'random'
- """
-
- # Dispatch of mutation strategy method (binomial or exponential).
- _binomial = {'best1bin': '_best1',
- 'randtobest1bin': '_randtobest1',
- 'best2bin': '_best2',
- 'rand2bin': '_rand2',
- 'rand1bin': '_rand1'}
- _exponential = {'best1exp': '_best1',
- 'rand1exp': '_rand1',
- 'randtobest1exp': '_randtobest1',
- 'best2exp': '_best2',
- 'rand2exp': '_rand2'}
-
- def __init__(self, func, bounds, args=(),
- strategy='best1bin', maxiter=None, popsize=15,
- tol=0.01, mutation=(0.5, 1), recombination=0.7, seed=None,
- maxfun=None, callback=None, disp=False, polish=True,
- init='latinhypercube'):
-
- if strategy in self._binomial:
- self.mutation_func = getattr(self, self._binomial[strategy])
- elif strategy in self._exponential:
- self.mutation_func = getattr(self, self._exponential[strategy])
- else:
- raise ValueError("Please select a valid mutation strategy")
- self.strategy = strategy
-
- self.callback = callback
- self.polish = polish
- self.tol = tol
-
- #Mutation constant should be in [0, 2). If specified as a sequence
- #then dithering is performed.
- self.scale = mutation
- if (not np.all(np.isfinite(mutation)) or
- np.any(np.array(mutation) >= 2) or
- np.any(np.array(mutation) < 0)):
- raise ValueError('The mutation constant must be a float in '
- 'U[0, 2), or specified as a tuple(min, max)'
- ' where min < max and min, max are in U[0, 2).')
-
- self.dither = None
- if hasattr(mutation, '__iter__') and len(mutation) > 1:
- self.dither = [mutation[0], mutation[1]]
- self.dither.sort()
-
- self.cross_over_probability = recombination
-
- self.func = func
- self.args = args
-
- # convert tuple of lower and upper bounds to limits
- # [(low_0, high_0), ..., (low_n, high_n]
- # -> [[low_0, ..., low_n], [high_0, ..., high_n]]
- self.limits = np.array(bounds, dtype='float').T
- if (np.size(self.limits, 0) != 2
- or not np.all(np.isfinite(self.limits))):
- raise ValueError('bounds should be a sequence containing '
- 'real valued (min, max) pairs for each value'
- ' in x')
-
- self.maxiter = maxiter or 1000
- self.maxfun = (maxfun or ((self.maxiter + 1) * popsize *
- np.size(self.limits, 1)))
-
- # population is scaled to between [0, 1].
- # We have to scale between parameter <-> population
- # save these arguments for _scale_parameter and
- # _unscale_parameter. This is an optimization
- self.__scale_arg1 = 0.5 * (self.limits[0] + self.limits[1])
- self.__scale_arg2 = np.fabs(self.limits[0] - self.limits[1])
-
- parameter_count = np.size(self.limits, 1)
- self.random_number_generator = _make_random_gen(seed)
-
- #default initialization is a latin hypercube design, but there
- #are other population initializations possible.
- self.population = np.zeros((popsize * parameter_count,
- parameter_count))
- if init == 'latinhypercube':
- self.init_population_lhs()
- elif init == 'random':
- self.init_population_random()
- else:
- raise ValueError("The population initialization method must be one"
- "of 'latinhypercube' or 'random'")
-
- self.population_energies = np.ones(
- popsize * parameter_count) * np.inf
-
- self.disp = disp
-
- def init_population_lhs(self):
- """
- Initializes the population with Latin Hypercube Sampling
- Latin Hypercube Sampling ensures that the sampling of parameter space
- is maximised.
- """
- samples = np.size(self.population, 0)
- N = np.size(self.population, 1)
- rng = self.random_number_generator
-
- # Generate the intervals
- segsize = 1.0 / samples
-
- # Fill points uniformly in each interval
- rdrange = rng.rand(samples, N) * segsize
- rdrange += np.atleast_2d(np.arange(0., 1., segsize)).T
-
- # Make the random pairings
- self.population = np.zeros_like(rdrange)
-
- for j in range(N):
- order = rng.permutation(range(samples))
- self.population[:, j] = rdrange[order, j]
-
- def init_population_random(self):
- """
- Initialises the population at random. This type of initialization
- can possess clustering, Latin Hypercube sampling is generally better.
- """
- rng = self.random_number_generator
- self.population = rng.random_sample(self.population.shape)
-
- @property
- def x(self):
- """
- The best solution from the solver
-
- Returns
- -------
- x - ndarray
- The best solution from the solver.
- """
- return self._scale_parameters(self.population[0])
-
- def solve(self):
- """
- Runs the DifferentialEvolutionSolver.
-
- Returns
- -------
- res : OptimizeResult
- The optimization result represented as a ``OptimizeResult`` object.
- Important attributes are: ``x`` the solution array, ``success`` a
- Boolean flag indicating if the optimizer exited successfully and
- ``message`` which describes the cause of the termination. See
- `OptimizeResult` for a description of other attributes. If polish
- was employed, then OptimizeResult also contains the ``hess_inv`` and
- ``jac`` attributes.
- """
-
- nfev, nit, warning_flag = 0, 0, False
- status_message = _status_message['success']
-
- # calculate energies to start with
- for index, candidate in enumerate(self.population):
- parameters = self._scale_parameters(candidate)
- self.population_energies[index] = self.func(parameters,
- *self.args)
- nfev += 1
-
- if nfev > self.maxfun:
- warning_flag = True
- status_message = _status_message['maxfev']
- break
-
- minval = np.argmin(self.population_energies)
-
- # put the lowest energy into the best solution position.
- lowest_energy = self.population_energies[minval]
- self.population_energies[minval] = self.population_energies[0]
- self.population_energies[0] = lowest_energy
-
- self.population[[0, minval], :] = self.population[[minval, 0], :]
-
- if warning_flag:
- return OptimizeResult(
- x=self.x,
- fun=self.population_energies[0],
- nfev=nfev,
- nit=nit,
- message=status_message,
- success=(warning_flag != True))
-
- # do the optimisation.
- for nit in range(1, self.maxiter + 1):
- if self.dither is not None:
- self.scale = self.random_number_generator.rand(
- ) * (self.dither[1] - self.dither[0]) + self.dither[0]
- for candidate in range(np.size(self.population, 0)):
- if nfev > self.maxfun:
- warning_flag = True
- status_message = _status_message['maxfev']
- break
-
- trial = self._mutate(candidate)
- self._ensure_constraint(trial)
- parameters = self._scale_parameters(trial)
-
- energy = self.func(parameters, *self.args)
- nfev += 1
-
- if energy < self.population_energies[candidate]:
- self.population[candidate] = trial
- self.population_energies[candidate] = energy
-
- if energy < self.population_energies[0]:
- self.population_energies[0] = energy
- self.population[0] = trial
-
- # stop when the fractional s.d. of the population is less than tol
- # of the mean energy
- convergence = (np.std(self.population_energies) /
- np.abs(np.mean(self.population_energies) +
- _MACHEPS))
-
- if self.disp:
- print("differential_evolution step %d: f(x)= %g"
- % (nit,
- self.population_energies[0]))
-
- if (self.callback and
- self.callback(self._scale_parameters(self.population[0]),
- convergence=self.tol / convergence) is True):
-
- warning_flag = True
- status_message = ('callback function requested stop early '
- 'by returning True')
- break
-
- if convergence < self.tol or warning_flag:
- break
-
- else:
- status_message = _status_message['maxiter']
- warning_flag = True
-
- DE_result = OptimizeResult(
- x=self.x,
- fun=self.population_energies[0],
- nfev=nfev,
- nit=nit,
- message=status_message,
- success=(warning_flag != True))
-
- if self.polish:
- result = minimize(self.func,
- np.copy(DE_result.x),
- method='L-BFGS-B',
- bounds=self.limits.T,
- args=self.args)
-
- nfev += result.nfev
- DE_result.nfev = nfev
-
- if result.fun < DE_result.fun:
- DE_result.fun = result.fun
- DE_result.x = result.x
- DE_result.jac = result.jac
- # to keep internal state consistent
- self.population_energies[0] = result.fun
- self.population[0] = self._unscale_parameters(result.x)
-
- return DE_result
-
- def _scale_parameters(self, trial):
- """
- scale from a number between 0 and 1 to parameters
- """
- return self.__scale_arg1 + (trial - 0.5) * self.__scale_arg2
-
- def _unscale_parameters(self, parameters):
- """
- scale from parameters to a number between 0 and 1.
- """
- return (parameters - self.__scale_arg1) / self.__scale_arg2 + 0.5
-
- def _ensure_constraint(self, trial):
- """
- make sure the parameters lie between the limits
- """
- for index, param in enumerate(trial):
- if param > 1 or param < 0:
- trial[index] = self.random_number_generator.rand()
-
- def _mutate(self, candidate):
- """
- create a trial vector based on a mutation strategy
- """
- trial = np.copy(self.population[candidate])
- parameter_count = np.size(trial, 0)
-
- fill_point = self.random_number_generator.randint(0, parameter_count)
-
- if (self.strategy == 'randtobest1exp'
- or self.strategy == 'randtobest1bin'):
- bprime = self.mutation_func(candidate,
- self._select_samples(candidate, 5))
- else:
- bprime = self.mutation_func(self._select_samples(candidate, 5))
-
- if self.strategy in self._binomial:
- crossovers = self.random_number_generator.rand(parameter_count)
- crossovers = crossovers < self.cross_over_probability
- # the last one is always from the bprime vector for binomial
- # If you fill in modulo with a loop you have to set the last one to
- # true. If you don't use a loop then you can have any random entry
- # be True.
- crossovers[fill_point] = True
- trial = np.where(crossovers, bprime, trial)
- return trial
-
- elif self.strategy in self._exponential:
- i = 0
- while (i < parameter_count and
- self.random_number_generator.rand() <
- self.cross_over_probability):
-
- trial[fill_point] = bprime[fill_point]
- fill_point = (fill_point + 1) % parameter_count
- i += 1
-
- return trial
-
- def _best1(self, samples):
- """
- best1bin, best1exp
- """
- r0, r1 = samples[:2]
- return (self.population[0] + self.scale *
- (self.population[r0] - self.population[r1]))
-
- def _rand1(self, samples):
- """
- rand1bin, rand1exp
- """
- r0, r1, r2 = samples[:3]
- return (self.population[r0] + self.scale *
- (self.population[r1] - self.population[r2]))
-
- def _randtobest1(self, candidate, samples):
- """
- randtobest1bin, randtobest1exp
- """
- r0, r1 = samples[:2]
- bprime = np.copy(self.population[candidate])
- bprime += self.scale * (self.population[0] - bprime)
- bprime += self.scale * (self.population[r0] -
- self.population[r1])
- return bprime
-
- def _best2(self, samples):
- """
- best2bin, best2exp
- """
- r0, r1, r2, r3 = samples[:4]
- bprime = (self.population[0] + self.scale *
- (self.population[r0] + self.population[r1]
- - self.population[r2] - self.population[r3]))
-
- return bprime
-
- def _rand2(self, samples):
- """
- rand2bin, rand2exp
- """
- r0, r1, r2, r3, r4 = samples
- bprime = (self.population[r0] + self.scale *
- (self.population[r1] + self.population[r2] -
- self.population[r3] - self.population[r4]))
-
- return bprime
-
- def _select_samples(self, candidate, number_samples):
- """
- obtain random integers from range(np.size(self.population, 0)),
- without replacement. You can't have the original candidate either.
- """
- idxs = list(range(np.size(self.population, 0)))
- idxs.remove(candidate)
- self.random_number_generator.shuffle(idxs)
- idxs = idxs[:number_samples]
- return idxs
-
-
-def _make_random_gen(seed):
- """Turn seed into a np.random.RandomState instance
-
- If seed is None, return the RandomState singleton used by np.random.
- If seed is an int, return a new RandomState instance seeded with seed.
- If seed is already a RandomState instance, return it.
- Otherwise raise ValueError.
- """
- if seed is None or seed is np.random:
- return np.random.mtrand._rand
- if isinstance(seed, (numbers.Integral, np.integer)):
- return np.random.RandomState(seed)
- if isinstance(seed, np.random.RandomState):
- return seed
- raise ValueError('%r cannot be used to seed a numpy.random.RandomState'
- ' instance' % seed)
+""" +differential_evolution: The differential evolution global optimization algorithm +Added by Andrew Nelson 2014 +""" +from __future__ import division, print_function, absolute_import +import numpy as np +from scipy.optimize import minimize +from scipy.optimize.optimize import _status_message +import numbers + +__all__ = ['differential_evolution'] + +_MACHEPS = np.finfo(np.float64).eps + + +#------------------------------------------------------------------------------ +# scipy.optimize does not contain OptimizeResult until 0.14. Include here as a +# fix for scipy < 0.14. + +class OptimizeResult(dict): + """ Represents the optimization result. + Attributes + ---------- + x : ndarray + The solution of the optimization. + success : bool + Whether or not the optimizer exited successfully. + status : int + Termination status of the optimizer. Its value depends on the + underlying solver. Refer to `message` for details. + message : str + Description of the cause of the termination. + fun, jac, hess, hess_inv : ndarray + Values of objective function, Jacobian, Hessian or its inverse (if + available). The Hessians may be approximations, see the documentation + of the function in question. + nfev, njev, nhev : int + Number of evaluations of the objective functions and of its + Jacobian and Hessian. + nit : int + Number of iterations performed by the optimizer. + maxcv : float + The maximum constraint violation. + Notes + ----- + There may be additional attributes not listed above depending of the + specific solver. Since this class is essentially a subclass of dict + with attribute accessors, one can see which attributes are available + using the `keys()` method. + """ + def __getattr__(self, name): + try: + return self[name] + except KeyError: + raise AttributeError(name) + + __setattr__ = dict.__setitem__ + __delattr__ = dict.__delitem__ + + def __repr__(self): + if self.keys(): + m = max(map(len, list(self.keys()))) + 1 + return '\n'.join([k.rjust(m) + ': ' + repr(v) + for k, v in self.items()]) + else: + return self.__class__.__name__ + "()" +#------------------------------------------------------------------------------ + + +def differential_evolution(func, bounds, args=(), strategy='best1bin', + maxiter=None, popsize=15, tol=0.01, + mutation=(0.5, 1), recombination=0.7, seed=None, + callback=None, disp=False, polish=True, + init='latinhypercube'): + """Finds the global minimum of a multivariate function. + Differential Evolution is stochastic in nature (does not use gradient + methods) to find the minimium, and can search large areas of candidate + space, but often requires larger numbers of function evaluations than + conventional gradient based techniques. + + The algorithm is due to Storn and Price [1]_. + + Parameters + ---------- + func : callable + The objective function to be minimized. Must be in the form + ``f(x, *args)``, where ``x`` is the argument in the form of a 1-D array + and ``args`` is a tuple of any additional fixed parameters needed to + completely specify the function. + bounds : sequence + Bounds for variables. ``(min, max)`` pairs for each element in ``x``, + defining the lower and upper bounds for the optimizing argument of + `func`. It is required to have ``len(bounds) == len(x)``. + ``len(bounds)`` is used to determine the number of parameters in ``x``. + args : tuple, optional + Any additional fixed parameters needed to + completely specify the objective function. + strategy : str, optional + The differential evolution strategy to use. Should be one of: + + - 'best1bin' + - 'best1exp' + - 'rand1exp' + - 'randtobest1exp' + - 'best2exp' + - 'rand2exp' + - 'randtobest1bin' + - 'best2bin' + - 'rand2bin' + - 'rand1bin' + + The default is 'best1bin'. + maxiter : int, optional + The maximum number of times the entire population is evolved. + The maximum number of function evaluations is: + ``maxiter * popsize * len(x)`` + popsize : int, optional + A multiplier for setting the total population size. The population has + ``popsize * len(x)`` individuals. + tol : float, optional + When the mean of the population energies, multiplied by tol, + divided by the standard deviation of the population energies + is greater than 1 the solving process terminates: + ``convergence = mean(pop) * tol / stdev(pop) > 1`` + mutation : float or tuple(float, float), optional + The mutation constant. + If specified as a float it should be in the range [0, 2]. + If specified as a tuple ``(min, max)`` dithering is employed. Dithering + randomly changes the mutation constant on a generation by generation + basis. The mutation constant for that generation is taken from + ``U[min, max)``. Dithering can help speed convergence significantly. + Increasing the mutation constant increases the search radius, but will + slow down convergence. + recombination : float, optional + The recombination constant, should be in the range [0, 1]. Increasing + this value allows a larger number of mutants to progress into the next + generation, but at the risk of population stability. + seed : int or `np.random.RandomState`, optional + If `seed` is not specified the `np.RandomState` singleton is used. + If `seed` is an int, a new `np.random.RandomState` instance is used, + seeded with seed. + If `seed` is already a `np.random.RandomState instance`, then that + `np.random.RandomState` instance is used. + Specify `seed` for repeatable minimizations. + disp : bool, optional + Display status messages + callback : callable, `callback(xk, convergence=val)`, optional: + A function to follow the progress of the minimization. ``xk`` is + the current value of ``x0``. ``val`` represents the fractional + value of the population convergence. When ``val`` is greater than one + the function halts. If callback returns `True`, then the minimization + is halted (any polishing is still carried out). + polish : bool, optional + If True (default), then `scipy.optimize.minimize` with the `L-BFGS-B` + method is used to polish the best population member at the end, which + can improve the minimization slightly. + init : string, optional + Specify how the population initialization is performed. Should be + one of: + + - 'latinhypercube' + - 'random' + + The default is 'latinhypercube'. Latin Hypercube sampling tries to + maximize coverage of the available parameter space. 'random' initializes + the population randomly - this has the drawback that clustering can + occur, preventing the whole of parameter space being covered. + + Returns + ------- + res : OptimizeResult + The optimization result represented as a `OptimizeResult` object. + Important attributes are: ``x`` the solution array, ``success`` a + Boolean flag indicating if the optimizer exited successfully and + ``message`` which describes the cause of the termination. See + `OptimizeResult` for a description of other attributes. If `polish` + was employed, then OptimizeResult also contains the `jac` attribute. + + Notes + ----- + Differential evolution is a stochastic population based method that is + useful for global optimization problems. At each pass through the population + the algorithm mutates each candidate solution by mixing with other candidate + solutions to create a trial candidate. There are several strategies [2]_ for + creating trial candidates, which suit some problems more than others. The + 'best1bin' strategy is a good starting point for many systems. In this + strategy two members of the population are randomly chosen. Their difference + is used to mutate the best member (the `best` in `best1bin`), :math:`b_0`, + so far: + + .. math:: + + b' = b_0 + mutation * (population[rand0] - population[rand1]) + + A trial vector is then constructed. Starting with a randomly chosen 'i'th + parameter the trial is sequentially filled (in modulo) with parameters from + `b'` or the original candidate. The choice of whether to use `b'` or the + original candidate is made with a binomial distribution (the 'bin' in + 'best1bin') - a random number in [0, 1) is generated. If this number is + less than the `recombination` constant then the parameter is loaded from + `b'`, otherwise it is loaded from the original candidate. The final + parameter is always loaded from `b'`. Once the trial candidate is built + its fitness is assessed. If the trial is better than the original candidate + then it takes its place. If it is also better than the best overall + candidate it also replaces that. + To improve your chances of finding a global minimum use higher `popsize` + values, with higher `mutation` and (dithering), but lower `recombination` + values. This has the effect of widening the search radius, but slowing + convergence. + + .. versionadded:: 0.15.0 + + Examples + -------- + Let us consider the problem of minimizing the Rosenbrock function. This + function is implemented in `rosen` in `scipy.optimize`. + + >>> from scipy.optimize import rosen, differential_evolution + >>> bounds = [(0,2), (0, 2), (0, 2), (0, 2), (0, 2)] + >>> result = differential_evolution(rosen, bounds) + >>> result.x, result.fun + (array([1., 1., 1., 1., 1.]), 1.9216496320061384e-19) + + Next find the minimum of the Ackley function + (http://en.wikipedia.org/wiki/Test_functions_for_optimization). + + >>> from scipy.optimize import differential_evolution + >>> import numpy as np + >>> def ackley(x): + ... arg1 = -0.2 * np.sqrt(0.5 * (x[0] ** 2 + x[1] ** 2)) + ... arg2 = 0.5 * (np.cos(2. * np.pi * x[0]) + np.cos(2. * np.pi * x[1])) + ... return -20. * np.exp(arg1) - np.exp(arg2) + 20. + np.e + >>> bounds = [(-5, 5), (-5, 5)] + >>> result = differential_evolution(ackley, bounds) + >>> result.x, result.fun + (array([ 0., 0.]), 4.4408920985006262e-16) + + References + ---------- + .. [1] Storn, R and Price, K, Differential Evolution - a Simple and + Efficient Heuristic for Global Optimization over Continuous Spaces, + Journal of Global Optimization, 1997, 11, 341 - 359. + .. [2] http://www1.icsi.berkeley.edu/~storn/code.html + .. [3] http://en.wikipedia.org/wiki/Differential_evolution + """ + + solver = DifferentialEvolutionSolver(func, bounds, args=args, + strategy=strategy, maxiter=maxiter, + popsize=popsize, tol=tol, + mutation=mutation, + recombination=recombination, + seed=seed, polish=polish, + callback=callback, + disp=disp, + init=init) + return solver.solve() + + +class DifferentialEvolutionSolver(object): + + """This class implements the differential evolution solver + + Parameters + ---------- + func : callable + The objective function to be minimized. Must be in the form + ``f(x, *args)``, where ``x`` is the argument in the form of a 1-D array + and ``args`` is a tuple of any additional fixed parameters needed to + completely specify the function. + bounds : sequence + Bounds for variables. ``(min, max)`` pairs for each element in ``x``, + defining the lower and upper bounds for the optimizing argument of + `func`. It is required to have ``len(bounds) == len(x)``. + ``len(bounds)`` is used to determine the number of parameters in ``x``. + args : tuple, optional + Any additional fixed parameters needed to + completely specify the objective function. + strategy : str, optional + The differential evolution strategy to use. Should be one of: + + - 'best1bin' + - 'best1exp' + - 'rand1exp' + - 'randtobest1exp' + - 'best2exp' + - 'rand2exp' + - 'randtobest1bin' + - 'best2bin' + - 'rand2bin' + - 'rand1bin' + + The default is 'best1bin' + + maxiter : int, optional + The maximum number of times the entire population is evolved. The + maximum number of function evaluations is: + ``maxiter * popsize * len(x)`` + popsize : int, optional + A multiplier for setting the total population size. The population has + ``popsize * len(x)`` individuals. + tol : float, optional + When the mean of the population energies, multiplied by tol, + divided by the standard deviation of the population energies + is greater than 1 the solving process terminates: + ``convergence = mean(pop) * tol / stdev(pop) > 1`` + mutation : float or tuple(float, float), optional + The mutation constant. + If specified as a float it should be in the range [0, 2]. + If specified as a tuple ``(min, max)`` dithering is employed. Dithering + randomly changes the mutation constant on a generation by generation + basis. The mutation constant for that generation is taken from + U[min, max). Dithering can help speed convergence significantly. + Increasing the mutation constant increases the search radius, but will + slow down convergence. + recombination : float, optional + The recombination constant, should be in the range [0, 1]. Increasing + this value allows a larger number of mutants to progress into the next + generation, but at the risk of population stability. + seed : int or `np.random.RandomState`, optional + If `seed` is not specified the `np.random.RandomState` singleton is + used. + If `seed` is an int, a new `np.random.RandomState` instance is used, + seeded with `seed`. + If `seed` is already a `np.random.RandomState` instance, then that + `np.random.RandomState` instance is used. + Specify `seed` for repeatable minimizations. + disp : bool, optional + Display status messages + callback : callable, `callback(xk, convergence=val)`, optional + A function to follow the progress of the minimization. ``xk`` is + the current value of ``x0``. ``val`` represents the fractional + value of the population convergence. When ``val`` is greater than one + the function halts. If callback returns `True`, then the minimization + is halted (any polishing is still carried out). + polish : bool, optional + If True, then `scipy.optimize.minimize` with the `L-BFGS-B` method + is used to polish the best population member at the end. This requires + a few more function evaluations. + maxfun : int, optional + Set the maximum number of function evaluations. However, it probably + makes more sense to set `maxiter` instead. + init : string, optional + Specify which type of population initialization is performed. Should be + one of: + + - 'latinhypercube' + - 'random' + """ + + # Dispatch of mutation strategy method (binomial or exponential). + _binomial = {'best1bin': '_best1', + 'randtobest1bin': '_randtobest1', + 'best2bin': '_best2', + 'rand2bin': '_rand2', + 'rand1bin': '_rand1'} + _exponential = {'best1exp': '_best1', + 'rand1exp': '_rand1', + 'randtobest1exp': '_randtobest1', + 'best2exp': '_best2', + 'rand2exp': '_rand2'} + + def __init__(self, func, bounds, args=(), + strategy='best1bin', maxiter=None, popsize=15, + tol=0.01, mutation=(0.5, 1), recombination=0.7, seed=None, + maxfun=None, callback=None, disp=False, polish=True, + init='latinhypercube'): + + if strategy in self._binomial: + self.mutation_func = getattr(self, self._binomial[strategy]) + elif strategy in self._exponential: + self.mutation_func = getattr(self, self._exponential[strategy]) + else: + raise ValueError("Please select a valid mutation strategy") + self.strategy = strategy + + self.callback = callback + self.polish = polish + self.tol = tol + + #Mutation constant should be in [0, 2). If specified as a sequence + #then dithering is performed. + self.scale = mutation + if (not np.all(np.isfinite(mutation)) or + np.any(np.array(mutation) >= 2) or + np.any(np.array(mutation) < 0)): + raise ValueError('The mutation constant must be a float in ' + 'U[0, 2), or specified as a tuple(min, max)' + ' where min < max and min, max are in U[0, 2).') + + self.dither = None + if hasattr(mutation, '__iter__') and len(mutation) > 1: + self.dither = [mutation[0], mutation[1]] + self.dither.sort() + + self.cross_over_probability = recombination + + self.func = func + self.args = args + + # convert tuple of lower and upper bounds to limits + # [(low_0, high_0), ..., (low_n, high_n] + # -> [[low_0, ..., low_n], [high_0, ..., high_n]] + self.limits = np.array(bounds, dtype='float').T + if (np.size(self.limits, 0) != 2 + or not np.all(np.isfinite(self.limits))): + raise ValueError('bounds should be a sequence containing ' + 'real valued (min, max) pairs for each value' + ' in x') + + self.maxiter = maxiter or 1000 + self.maxfun = (maxfun or ((self.maxiter + 1) * popsize * + np.size(self.limits, 1))) + + # population is scaled to between [0, 1]. + # We have to scale between parameter <-> population + # save these arguments for _scale_parameter and + # _unscale_parameter. This is an optimization + self.__scale_arg1 = 0.5 * (self.limits[0] + self.limits[1]) + self.__scale_arg2 = np.fabs(self.limits[0] - self.limits[1]) + + parameter_count = np.size(self.limits, 1) + self.random_number_generator = _make_random_gen(seed) + + #default initialization is a latin hypercube design, but there + #are other population initializations possible. + self.population = np.zeros((popsize * parameter_count, + parameter_count)) + if init == 'latinhypercube': + self.init_population_lhs() + elif init == 'random': + self.init_population_random() + else: + raise ValueError("The population initialization method must be one" + "of 'latinhypercube' or 'random'") + + self.population_energies = np.ones( + popsize * parameter_count) * np.inf + + self.disp = disp + + def init_population_lhs(self): + """ + Initializes the population with Latin Hypercube Sampling + Latin Hypercube Sampling ensures that the sampling of parameter space + is maximised. + """ + samples = np.size(self.population, 0) + N = np.size(self.population, 1) + rng = self.random_number_generator + + # Generate the intervals + segsize = 1.0 / samples + + # Fill points uniformly in each interval + rdrange = rng.rand(samples, N) * segsize + rdrange += np.atleast_2d(np.arange(0., 1., segsize)).T + + # Make the random pairings + self.population = np.zeros_like(rdrange) + + for j in range(N): + order = rng.permutation(range(samples)) + self.population[:, j] = rdrange[order, j] + + def init_population_random(self): + """ + Initialises the population at random. This type of initialization + can possess clustering, Latin Hypercube sampling is generally better. + """ + rng = self.random_number_generator + self.population = rng.random_sample(self.population.shape) + + @property + def x(self): + """ + The best solution from the solver + + Returns + ------- + x - ndarray + The best solution from the solver. + """ + return self._scale_parameters(self.population[0]) + + def solve(self): + """ + Runs the DifferentialEvolutionSolver. + + Returns + ------- + res : OptimizeResult + The optimization result represented as a ``OptimizeResult`` object. + Important attributes are: ``x`` the solution array, ``success`` a + Boolean flag indicating if the optimizer exited successfully and + ``message`` which describes the cause of the termination. See + `OptimizeResult` for a description of other attributes. If polish + was employed, then OptimizeResult also contains the ``hess_inv`` and + ``jac`` attributes. + """ + + nfev, nit, warning_flag = 0, 0, False + status_message = _status_message['success'] + + # calculate energies to start with + for index, candidate in enumerate(self.population): + parameters = self._scale_parameters(candidate) + self.population_energies[index] = self.func(parameters, + *self.args) + nfev += 1 + + if nfev > self.maxfun: + warning_flag = True + status_message = _status_message['maxfev'] + break + + minval = np.argmin(self.population_energies) + + # put the lowest energy into the best solution position. + lowest_energy = self.population_energies[minval] + self.population_energies[minval] = self.population_energies[0] + self.population_energies[0] = lowest_energy + + self.population[[0, minval], :] = self.population[[minval, 0], :] + + if warning_flag: + return OptimizeResult( + x=self.x, + fun=self.population_energies[0], + nfev=nfev, + nit=nit, + message=status_message, + success=(warning_flag != True)) + + # do the optimisation. + for nit in range(1, self.maxiter + 1): + if self.dither is not None: + self.scale = self.random_number_generator.rand( + ) * (self.dither[1] - self.dither[0]) + self.dither[0] + for candidate in range(np.size(self.population, 0)): + if nfev > self.maxfun: + warning_flag = True + status_message = _status_message['maxfev'] + break + + trial = self._mutate(candidate) + self._ensure_constraint(trial) + parameters = self._scale_parameters(trial) + + energy = self.func(parameters, *self.args) + nfev += 1 + + if energy < self.population_energies[candidate]: + self.population[candidate] = trial + self.population_energies[candidate] = energy + + if energy < self.population_energies[0]: + self.population_energies[0] = energy + self.population[0] = trial + + # stop when the fractional s.d. of the population is less than tol + # of the mean energy + convergence = (np.std(self.population_energies) / + np.abs(np.mean(self.population_energies) + + _MACHEPS)) + + if self.disp: + print("differential_evolution step %d: f(x)= %g" + % (nit, + self.population_energies[0])) + + if (self.callback and + self.callback(self._scale_parameters(self.population[0]), + convergence=self.tol / convergence) is True): + + warning_flag = True + status_message = ('callback function requested stop early ' + 'by returning True') + break + + if convergence < self.tol or warning_flag: + break + + else: + status_message = _status_message['maxiter'] + warning_flag = True + + DE_result = OptimizeResult( + x=self.x, + fun=self.population_energies[0], + nfev=nfev, + nit=nit, + message=status_message, + success=(warning_flag != True)) + + if self.polish: + result = minimize(self.func, + np.copy(DE_result.x), + method='L-BFGS-B', + bounds=self.limits.T, + args=self.args) + + nfev += result.nfev + DE_result.nfev = nfev + + if result.fun < DE_result.fun: + DE_result.fun = result.fun + DE_result.x = result.x + DE_result.jac = result.jac + # to keep internal state consistent + self.population_energies[0] = result.fun + self.population[0] = self._unscale_parameters(result.x) + + return DE_result + + def _scale_parameters(self, trial): + """ + scale from a number between 0 and 1 to parameters + """ + return self.__scale_arg1 + (trial - 0.5) * self.__scale_arg2 + + def _unscale_parameters(self, parameters): + """ + scale from parameters to a number between 0 and 1. + """ + return (parameters - self.__scale_arg1) / self.__scale_arg2 + 0.5 + + def _ensure_constraint(self, trial): + """ + make sure the parameters lie between the limits + """ + for index, param in enumerate(trial): + if param > 1 or param < 0: + trial[index] = self.random_number_generator.rand() + + def _mutate(self, candidate): + """ + create a trial vector based on a mutation strategy + """ + trial = np.copy(self.population[candidate]) + parameter_count = np.size(trial, 0) + + fill_point = self.random_number_generator.randint(0, parameter_count) + + if (self.strategy == 'randtobest1exp' + or self.strategy == 'randtobest1bin'): + bprime = self.mutation_func(candidate, + self._select_samples(candidate, 5)) + else: + bprime = self.mutation_func(self._select_samples(candidate, 5)) + + if self.strategy in self._binomial: + crossovers = self.random_number_generator.rand(parameter_count) + crossovers = crossovers < self.cross_over_probability + # the last one is always from the bprime vector for binomial + # If you fill in modulo with a loop you have to set the last one to + # true. If you don't use a loop then you can have any random entry + # be True. + crossovers[fill_point] = True + trial = np.where(crossovers, bprime, trial) + return trial + + elif self.strategy in self._exponential: + i = 0 + while (i < parameter_count and + self.random_number_generator.rand() < + self.cross_over_probability): + + trial[fill_point] = bprime[fill_point] + fill_point = (fill_point + 1) % parameter_count + i += 1 + + return trial + + def _best1(self, samples): + """ + best1bin, best1exp + """ + r0, r1 = samples[:2] + return (self.population[0] + self.scale * + (self.population[r0] - self.population[r1])) + + def _rand1(self, samples): + """ + rand1bin, rand1exp + """ + r0, r1, r2 = samples[:3] + return (self.population[r0] + self.scale * + (self.population[r1] - self.population[r2])) + + def _randtobest1(self, candidate, samples): + """ + randtobest1bin, randtobest1exp + """ + r0, r1 = samples[:2] + bprime = np.copy(self.population[candidate]) + bprime += self.scale * (self.population[0] - bprime) + bprime += self.scale * (self.population[r0] - + self.population[r1]) + return bprime + + def _best2(self, samples): + """ + best2bin, best2exp + """ + r0, r1, r2, r3 = samples[:4] + bprime = (self.population[0] + self.scale * + (self.population[r0] + self.population[r1] + - self.population[r2] - self.population[r3])) + + return bprime + + def _rand2(self, samples): + """ + rand2bin, rand2exp + """ + r0, r1, r2, r3, r4 = samples + bprime = (self.population[r0] + self.scale * + (self.population[r1] + self.population[r2] - + self.population[r3] - self.population[r4])) + + return bprime + + def _select_samples(self, candidate, number_samples): + """ + obtain random integers from range(np.size(self.population, 0)), + without replacement. You can't have the original candidate either. + """ + idxs = list(range(np.size(self.population, 0))) + idxs.remove(candidate) + self.random_number_generator.shuffle(idxs) + idxs = idxs[:number_samples] + return idxs + + +def _make_random_gen(seed): + """Turn seed into a np.random.RandomState instance + + If seed is None, return the RandomState singleton used by np.random. + If seed is an int, return a new RandomState instance seeded with seed. + If seed is already a RandomState instance, return it. + Otherwise raise ValueError. + """ + if seed is None or seed is np.random: + return np.random.mtrand._rand + if isinstance(seed, (numbers.Integral, np.integer)): + return np.random.RandomState(seed) + if isinstance(seed, np.random.RandomState): + return seed + raise ValueError('%r cannot be used to seed a numpy.random.RandomState' + ' instance' % seed) diff --git a/lmfit/_version.py b/lmfit/_version.py index b0cc39e..fa233a4 100644 --- a/lmfit/_version.py +++ b/lmfit/_version.py @@ -4,8 +4,8 @@ # unpacked source archive. Distribution tarballs contain a pre-generated copy # of this file. -version_version = '0.9.2' -version_full = '208871db96689c911e00b9d59dace2de68df3220' +version_version = '0.9.3' +version_full = '8a4eb4f5675628bc8ee2d0da70b9e9397f80c280' def get_versions(default={}, verbose=False): return {'version': version_version, 'full': version_full} diff --git a/lmfit/asteval.py b/lmfit/asteval.py index 87daadc..e8409aa 100644 --- a/lmfit/asteval.py +++ b/lmfit/asteval.py @@ -1,802 +1,804 @@ -"""
-Safe(ish) evaluator of python expressions, using ast module.
-The emphasis here is on mathematical expressions, and so
-numpy functions are imported if available and used.
-
-Symbols are held in the Interpreter symtable -- a simple
-dictionary supporting a simple, flat namespace.
-
-Expressions can be compiled into ast node and then evaluated
-later, using the current values in the
-"""
-
-from __future__ import division, print_function
-from sys import exc_info, stdout, version_info
-import ast
-import math
-
-from .astutils import (FROM_PY, FROM_MATH, FROM_NUMPY, UNSAFE_ATTRS,
- LOCALFUNCS, NUMPY_RENAMES, op2func,
- ExceptionHolder, ReturnedNone, valid_symbol_name)
-
-HAS_NUMPY = False
-try:
- import numpy
- HAS_NUMPY = True
-except ImportError:
- print("Warning: numpy not available... functionality will be limited.")
-
-
-class Interpreter:
- """mathematical expression compiler and interpreter.
-
- This module compiles expressions and statements to AST representation,
- using python's ast module, and then executes the AST representation
- using a dictionary of named object (variable, functions).
-
- The result is a restricted, simplified version of Python meant for
- numerical caclulations that is somewhat safer than 'eval' because some
- operations (such as 'import' and 'eval') are simply not allowed. The
- resulting language uses a flat namespace that works on Python objects,
- but does not allow new classes to be defined.
-
- Many parts of Python syntax are supported, including:
- for loops, while loops, if-then-elif-else conditionals
- try-except (including 'finally')
- function definitions with def
- advanced slicing: a[::-1], array[-3:, :, ::2]
- if-expressions: out = one_thing if TEST else other
- list comprehension out = [sqrt(i) for i in values]
-
- The following Python syntax elements are not supported:
- Import, Exec, Lambda, Class, Global, Generators,
- Yield, Decorators
-
- In addition, while many builtin functions are supported, several
- builtin functions are missing ('eval', 'exec', and 'getattr' for
- example) that can be considered unsafe.
-
- If numpy is installed, many numpy functions are also imported.
-
- """
-
- supported_nodes = ('arg', 'assert', 'assign', 'attribute', 'augassign',
- 'binop', 'boolop', 'break', 'call', 'compare',
- 'continue', 'delete', 'dict', 'ellipsis',
- 'excepthandler', 'expr', 'extslice', 'for',
- 'functiondef', 'if', 'ifexp', 'index', 'interrupt',
- 'list', 'listcomp', 'module', 'name', 'num', 'pass',
- 'print', 'raise', 'repr', 'return', 'slice', 'str',
- 'subscript', 'try', 'tuple', 'unaryop', 'while')
-
- def __init__(self, symtable=None, writer=None, use_numpy=True):
- self.writer = writer or stdout
-
- if symtable is None:
- symtable = {}
- self.symtable = symtable
- self._interrupt = None
- self.error = []
- self.error_msg = None
- self.expr = None
- self.retval = None
- self.lineno = 0
- self.use_numpy = HAS_NUMPY and use_numpy
-
- symtable['print'] = self._printer
-
- # add python symbols
- py_symtable = {sym: __builtins__[sym] for sym in FROM_PY
- if sym in __builtins__}
- symtable.update(py_symtable)
-
- # add local symbols
- local_symtable = {sym: obj for (sym, obj) in LOCALFUNCS.items()}
- symtable.update(local_symtable)
-
- # add math symbols
- math_symtable = {sym: getattr(math, sym) for sym in FROM_MATH
- if hasattr(math, sym)}
- symtable.update(math_symtable)
-
- # add numpy symbols
- if self.use_numpy:
- numpy_symtable = {sym: getattr(numpy, sym) for sym in FROM_NUMPY
- if hasattr(numpy, sym)}
- symtable.update(numpy_symtable)
-
- npy_rename_symtable = {name: getattr(numpy, sym) for name, sym
- in NUMPY_RENAMES.items()
- if hasattr(numpy, sym)}
- symtable.update(npy_rename_symtable)
-
- self.node_handlers = dict(((node, getattr(self, "on_%s" % node))
- for node in self.supported_nodes))
-
- # to rationalize try/except try/finally for Python2.6 through Python3.3
- self.node_handlers['tryexcept'] = self.node_handlers['try']
- self.node_handlers['tryfinally'] = self.node_handlers['try']
-
- self.no_deepcopy = [key for key, val in symtable.items()
- if (callable(val)
- or 'numpy.lib.index_tricks' in repr(val))]
-
- def user_defined_symbols(self):
- """
- Return a set of symbols that have been added to symtable after
- construction. I.e. the symbols from self.symtable that are not in
- self.no_deepcopy.
-
- Returns
- -------
- unique_symbols : set
- symbols in symtable that are not in self.no_deepcopy
- """
- sym_in_current = set(self.symtable.keys())
- sym_from_construction = set(self.no_deepcopy)
- unique_symbols = sym_in_current.difference(sym_from_construction)
- return unique_symbols
-
- def unimplemented(self, node):
- "unimplemented nodes"
- self.raise_exception(node, exc=NotImplementedError,
- msg="'%s' not supported" %
- (node.__class__.__name__))
-
- def raise_exception(self, node, exc=None, msg='', expr=None,
- lineno=None):
- "add an exception"
- if self.error is None:
- self.error = []
- if expr is None:
- expr = self.expr
- if len(self.error) > 0 and not isinstance(node, ast.Module):
- msg = '%s' % msg
- err = ExceptionHolder(node, exc=exc, msg=msg, expr=expr, lineno=lineno)
- self._interrupt = ast.Break()
- self.error.append(err)
- if self.error_msg is None:
- self.error_msg = "%s in expr='%s'" % (msg, self.expr)
- elif len(msg) > 0:
- self.error_msg = "%s\n %s" % (self.error_msg, msg)
- if exc is None:
- try:
- exc = self.error[0].exc
- except:
- exc = RuntimeError
- raise exc(self.error_msg)
-
-
- # main entry point for Ast node evaluation
- # parse: text of statements -> ast
- # run: ast -> result
- # eval: string statement -> result = run(parse(statement))
- def parse(self, text):
- """parse statement/expression to Ast representation"""
- self.expr = text
- try:
- return ast.parse(text)
- except SyntaxError:
- self.raise_exception(None, msg='Syntax Error', expr=text)
- except:
- self.raise_exception(None, msg='Runtime Error', expr=text)
-
- def run(self, node, expr=None, lineno=None, with_raise=True):
- """executes parsed Ast representation for an expression"""
- # Note: keep the 'node is None' test: internal code here may run
- # run(None) and expect a None in return.
- if len(self.error) > 0:
- return
- if node is None:
- return None
- if isinstance(node, str):
- node = self.parse(node)
- if lineno is not None:
- self.lineno = lineno
- if expr is not None:
- self.expr = expr
-
- # get handler for this node:
- # on_xxx with handle nodes of type 'xxx', etc
- try:
- handler = self.node_handlers[node.__class__.__name__.lower()]
- except KeyError:
- return self.unimplemented(node)
-
- # run the handler: this will likely generate
- # recursive calls into this run method.
- try:
- ret = handler(node)
- if isinstance(ret, enumerate):
- ret = list(ret)
- return ret
- except:
- if with_raise:
- self.raise_exception(node, expr=expr)
-
- def __call__(self, expr, **kw):
- return self.eval(expr, **kw)
-
- def eval(self, expr, lineno=0, show_errors=True):
- """evaluates a single statement"""
- self.lineno = lineno
- self.error = []
- try:
- node = self.parse(expr)
- except:
- errmsg = exc_info()[1]
- if len(self.error) > 0:
- errmsg = "\n".join(self.error[0].get_error())
- if not show_errors:
- try:
- exc = self.error[0].exc
- except:
- exc = RuntimeError
- raise exc(errmsg)
- print(errmsg, file=self.writer)
- return
- try:
- return self.run(node, expr=expr, lineno=lineno)
- except:
- errmsg = exc_info()[1]
- if len(self.error) > 0:
- errmsg = "\n".join(self.error[0].get_error())
- if not show_errors:
- try:
- exc = self.error[0].exc
- except:
- exc = RuntimeError
- raise exc(errmsg)
- print(errmsg, file=self.writer)
- return
-
- def dump(self, node, **kw):
- "simple ast dumper"
- return ast.dump(node, **kw)
-
- # handlers for ast components
- def on_expr(self, node):
- "expression"
- return self.run(node.value) # ('value',)
-
- def on_index(self, node):
- "index"
- return self.run(node.value) # ('value',)
-
- def on_return(self, node): # ('value',)
- "return statement: look for None, return special sentinal"
- self.retval = self.run(node.value)
- if self.retval is None:
- self.retval = ReturnedNone
- return
-
- def on_repr(self, node):
- "repr "
- return repr(self.run(node.value)) # ('value',)
-
- def on_module(self, node): # ():('body',)
- "module def"
- out = None
- for tnode in node.body:
- out = self.run(tnode)
- return out
-
- def on_pass(self, node):
- "pass statement"
- return None # ()
-
- def on_ellipsis(self, node):
- "ellipses"
- return Ellipsis
-
- # for break and continue: set the instance variable _interrupt
- def on_interrupt(self, node): # ()
- "interrupt handler"
- self._interrupt = node
- return node
-
- def on_break(self, node):
- "break"
- return self.on_interrupt(node)
-
- def on_continue(self, node):
- "continue"
- return self.on_interrupt(node)
-
- def on_assert(self, node): # ('test', 'msg')
- "assert statement"
- if not self.run(node.test):
- self.raise_exception(node, exc=AssertionError, msg=node.msg)
- return True
-
- def on_list(self, node): # ('elt', 'ctx')
- "list"
- return [self.run(e) for e in node.elts]
-
- def on_tuple(self, node): # ('elts', 'ctx')
- "tuple"
- return tuple(self.on_list(node))
-
- def on_dict(self, node): # ('keys', 'values')
- "dictionary"
- return dict([(self.run(k), self.run(v)) for k, v in
- zip(node.keys, node.values)])
-
- def on_num(self, node): # ('n',)
- 'return number'
- return node.n
-
- def on_str(self, node): # ('s',)
- 'return string'
- return node.s
-
- def on_name(self, node): # ('id', 'ctx')
- """ Name node """
- ctx = node.ctx.__class__
- if ctx in (ast.Param, ast.Del):
- return str(node.id)
- else:
- if node.id in self.symtable:
- return self.symtable[node.id]
- else:
- msg = "name '%s' is not defined" % node.id
- self.raise_exception(node, exc=NameError, msg=msg)
-
- def node_assign(self, node, val):
- """here we assign a value (not the node.value object) to a node
- this is used by on_assign, but also by for, list comprehension, etc.
- """
- if node.__class__ == ast.Name:
- if not valid_symbol_name(node.id):
- errmsg = "invalid symbol name (reserved word?) %s" % node.id
- self.raise_exception(node, exc=NameError, msg=errmsg)
- sym = self.symtable[node.id] = val
- if node.id in self.no_deepcopy:
- self.no_deepcopy.pop(node.id)
-
- elif node.__class__ == ast.Attribute:
- if node.ctx.__class__ == ast.Load:
- msg = "cannot assign to attribute %s" % node.attr
- self.raise_exception(node, exc=AttributeError, msg=msg)
-
- setattr(self.run(node.value), node.attr, val)
-
- elif node.__class__ == ast.Subscript:
- sym = self.run(node.value)
- xslice = self.run(node.slice)
- if isinstance(node.slice, ast.Index):
- sym[xslice] = val
- elif isinstance(node.slice, ast.Slice):
- sym[slice(xslice.start, xslice.stop)] = val
- elif isinstance(node.slice, ast.ExtSlice):
- sym[(xslice)] = val
- elif node.__class__ in (ast.Tuple, ast.List):
- if len(val) == len(node.elts):
- for telem, tval in zip(node.elts, val):
- self.node_assign(telem, tval)
- else:
- raise ValueError('too many values to unpack')
-
- def on_attribute(self, node): # ('value', 'attr', 'ctx')
- "extract attribute"
- ctx = node.ctx.__class__
- if ctx == ast.Store:
- msg = "attribute for storage: shouldn't be here!"
- self.raise_exception(node, exc=RuntimeError, msg=msg)
-
- sym = self.run(node.value)
- if ctx == ast.Del:
- return delattr(sym, node.attr)
-
- # ctx is ast.Load
- fmt = "cannnot access attribute '%s' for %s"
- if node.attr not in UNSAFE_ATTRS:
- fmt = "no attribute '%s' for %s"
- try:
- return getattr(sym, node.attr)
- except AttributeError:
- pass
-
- # AttributeError or accessed unsafe attribute
- obj = self.run(node.value)
- msg = fmt % (node.attr, obj)
- self.raise_exception(node, exc=AttributeError, msg=msg)
-
- def on_assign(self, node): # ('targets', 'value')
- "simple assignment"
- val = self.run(node.value)
- for tnode in node.targets:
- self.node_assign(tnode, val)
- return
-
- def on_augassign(self, node): # ('target', 'op', 'value')
- "augmented assign"
- return self.on_assign(ast.Assign(targets=[node.target],
- value=ast.BinOp(left=node.target,
- op=node.op,
- right=node.value)))
-
- def on_slice(self, node): # ():('lower', 'upper', 'step')
- "simple slice"
- return slice(self.run(node.lower),
- self.run(node.upper),
- self.run(node.step))
-
- def on_extslice(self, node): # ():('dims',)
- "extended slice"
- return tuple([self.run(tnode) for tnode in node.dims])
-
- def on_subscript(self, node): # ('value', 'slice', 'ctx')
- "subscript handling -- one of the tricky parts"
- val = self.run(node.value)
- nslice = self.run(node.slice)
- ctx = node.ctx.__class__
- if ctx in (ast.Load, ast.Store):
- if isinstance(node.slice, (ast.Index, ast.Slice, ast.Ellipsis)):
- return val.__getitem__(nslice)
- elif isinstance(node.slice, ast.ExtSlice):
- return val[(nslice)]
- else:
- msg = "subscript with unknown context"
- self.raise_exception(node, msg=msg)
-
- def on_delete(self, node): # ('targets',)
- "delete statement"
- for tnode in node.targets:
- if tnode.ctx.__class__ != ast.Del:
- break
- children = []
- while tnode.__class__ == ast.Attribute:
- children.append(tnode.attr)
- tnode = tnode.value
-
- if tnode.__class__ == ast.Name:
- children.append(tnode.id)
- children.reverse()
- self.symtable.pop('.'.join(children))
- else:
- msg = "could not delete symbol"
- self.raise_exception(node, msg=msg)
-
- def on_unaryop(self, node): # ('op', 'operand')
- "unary operator"
- return op2func(node.op)(self.run(node.operand))
-
- def on_binop(self, node): # ('left', 'op', 'right')
- "binary operator"
- return op2func(node.op)(self.run(node.left),
- self.run(node.right))
-
- def on_boolop(self, node): # ('op', 'values')
- "boolean operator"
- val = self.run(node.values[0])
- is_and = ast.And == node.op.__class__
- if (is_and and val) or (not is_and and not val):
- for n in node.values:
- val = op2func(node.op)(val, self.run(n))
- if (is_and and not val) or (not is_and and val):
- break
- return val
-
- def on_compare(self, node): # ('left', 'ops', 'comparators')
- "comparison operators"
- lval = self.run(node.left)
- out = True
- for op, rnode in zip(node.ops, node.comparators):
- rval = self.run(rnode)
- out = op2func(op)(lval, rval)
- lval = rval
- if self.use_numpy and isinstance(out, numpy.ndarray) and out.any():
- break
- elif not out:
- break
- return out
-
- def on_print(self, node): # ('dest', 'values', 'nl')
- """ note: implements Python2 style print statement, not
- print() function. May need improvement...."""
- dest = self.run(node.dest) or self.writer
- end = ''
- if node.nl:
- end = '\n'
- out = [self.run(tnode) for tnode in node.values]
- if out and len(self.error) == 0:
- self._printer(*out, file=dest, end=end)
-
- def _printer(self, *out, **kws):
- "generic print function"
- flush = kws.pop('flush', True)
- fileh = kws.pop('file', self.writer)
- sep = kws.pop('sep', ' ')
- end = kws.pop('sep', '\n')
-
- print(*out, file=fileh, sep=sep, end=end)
- if flush:
- fileh.flush()
-
- def on_if(self, node): # ('test', 'body', 'orelse')
- "regular if-then-else statement"
- block = node.body
- if not self.run(node.test):
- block = node.orelse
- for tnode in block:
- self.run(tnode)
-
- def on_ifexp(self, node): # ('test', 'body', 'orelse')
- "if expressions"
- expr = node.orelse
- if self.run(node.test):
- expr = node.body
- return self.run(expr)
-
- def on_while(self, node): # ('test', 'body', 'orelse')
- "while blocks"
- while self.run(node.test):
- self._interrupt = None
- for tnode in node.body:
- self.run(tnode)
- if self._interrupt is not None:
- break
- if isinstance(self._interrupt, ast.Break):
- break
- else:
- for tnode in node.orelse:
- self.run(tnode)
- self._interrupt = None
-
- def on_for(self, node): # ('target', 'iter', 'body', 'orelse')
- "for blocks"
- for val in self.run(node.iter):
- self.node_assign(node.target, val)
- self._interrupt = None
- for tnode in node.body:
- self.run(tnode)
- if self._interrupt is not None:
- break
- if isinstance(self._interrupt, ast.Break):
- break
- else:
- for tnode in node.orelse:
- self.run(tnode)
- self._interrupt = None
-
- def on_listcomp(self, node): # ('elt', 'generators')
- "list comprehension"
- out = []
- for tnode in node.generators:
- if tnode.__class__ == ast.comprehension:
- for val in self.run(tnode.iter):
- self.node_assign(tnode.target, val)
- add = True
- for cond in tnode.ifs:
- add = add and self.run(cond)
- if add:
- out.append(self.run(node.elt))
- return out
-
- def on_excepthandler(self, node): # ('type', 'name', 'body')
- "exception handler..."
- return (self.run(node.type), node.name, node.body)
-
- def on_try(self, node): # ('body', 'handlers', 'orelse', 'finalbody')
- "try/except/else/finally blocks"
- no_errors = True
- for tnode in node.body:
- self.run(tnode, with_raise=False)
- no_errors = no_errors and len(self.error) == 0
- if len(self.error) > 0:
- e_type, e_value, e_tback = self.error[-1].exc_info
- for hnd in node.handlers:
- htype = None
- if hnd.type is not None:
- htype = __builtins__.get(hnd.type.id, None)
- if htype is None or isinstance(e_type(), htype):
- self.error = []
- if hnd.name is not None:
- self.node_assign(hnd.name, e_value)
- for tline in hnd.body:
- self.run(tline)
- break
- if no_errors and hasattr(node, 'orelse'):
- for tnode in node.orelse:
- self.run(tnode)
-
- if hasattr(node, 'finalbody'):
- for tnode in node.finalbody:
- self.run(tnode)
-
- def on_raise(self, node): # ('type', 'inst', 'tback')
- "raise statement: note difference for python 2 and 3"
- if version_info[0] == 3:
- excnode = node.exc
- msgnode = node.cause
- else:
- excnode = node.type
- msgnode = node.inst
- out = self.run(excnode)
- msg = ' '.join(out.args)
- msg2 = self.run(msgnode)
- if msg2 not in (None, 'None'):
- msg = "%s: %s" % (msg, msg2)
- self.raise_exception(None, exc=out.__class__, msg=msg, expr='')
-
- def on_call(self, node):
- "function execution"
- # ('func', 'args', 'keywords', 'starargs', 'kwargs')
- func = self.run(node.func)
- if not hasattr(func, '__call__') and not isinstance(func, type):
- msg = "'%s' is not callable!!" % (func)
- self.raise_exception(node, exc=TypeError, msg=msg)
-
- args = [self.run(targ) for targ in node.args]
- if node.starargs is not None:
- args = args + self.run(node.starargs)
-
- keywords = {}
- for key in node.keywords:
- if not isinstance(key, ast.keyword):
- msg = "keyword error in function call '%s'" % (func)
- self.raise_exception(node, msg=msg)
-
- keywords[key.arg] = self.run(key.value)
- if node.kwargs is not None:
- keywords.update(self.run(node.kwargs))
-
- try:
- return func(*args, **keywords)
- except:
- self.raise_exception(node, msg="Error running %s" % (func))
-
- def on_arg(self, node): # ('test', 'msg')
- "arg for function definitions"
- # print(" ON ARG ! ", node, node.arg)
- return node.arg
-
- def on_functiondef(self, node):
- "define procedures"
- # ('name', 'args', 'body', 'decorator_list')
- if node.decorator_list != []:
- raise Warning("decorated procedures not supported!")
- kwargs = []
-
- offset = len(node.args.args) - len(node.args.defaults)
- for idef, defnode in enumerate(node.args.defaults):
- defval = self.run(defnode)
- keyval = self.run(node.args.args[idef+offset])
- kwargs.append((keyval, defval))
-
- if version_info[0] == 3:
- args = [tnode.arg for tnode in node.args.args[:offset]]
- else:
- args = [tnode.id for tnode in node.args.args[:offset]]
-
- doc = None
- nb0 = node.body[0]
- if isinstance(nb0, ast.Expr) and isinstance(nb0.value, ast.Str):
- doc = nb0.value.s
-
- self.symtable[node.name] = Procedure(node.name, self, doc=doc,
- lineno=self.lineno,
- body=node.body,
- args=args, kwargs=kwargs,
- vararg=node.args.vararg,
- varkws=node.args.kwarg)
- if node.name in self.no_deepcopy:
- self.no_deepcopy.pop(node.name)
-
-
-class Procedure(object):
- """Procedure: user-defined function for asteval
-
- This stores the parsed ast nodes as from the
- 'functiondef' ast node for later evaluation.
- """
- def __init__(self, name, interp, doc=None, lineno=0,
- body=None, args=None, kwargs=None,
- vararg=None, varkws=None):
- self.name = name
- self.__asteval__ = interp
- self.raise_exc = self.__asteval__.raise_exception
- self.__doc__ = doc
- self.body = body
- self.argnames = args
- self.kwargs = kwargs
- self.vararg = vararg
- self.varkws = varkws
- self.lineno = lineno
-
- def __repr__(self):
- sig = ""
- if len(self.argnames) > 0:
- sig = "%s%s" % (sig, ', '.join(self.argnames))
- if self.vararg is not None:
- sig = "%s, *%s" % (sig, self.vararg)
- if len(self.kwargs) > 0:
- if len(sig) > 0:
- sig = "%s, " % sig
- _kw = ["%s=%s" % (k, v) for k, v in self.kwargs]
- sig = "%s%s" % (sig, ', '.join(_kw))
-
- if self.varkws is not None:
- sig = "%s, **%s" % (sig, self.varkws)
- sig = "<Procedure %s(%s)>" % (self.name, sig)
- if self.__doc__ is not None:
- sig = "%s\n %s" % (sig, self.__doc__)
- return sig
-
- def __call__(self, *args, **kwargs):
- symlocals = {}
- args = list(args)
- n_args = len(args)
- n_names = len(self.argnames)
- n_kws = len(kwargs)
-
- # may need to move kwargs to args if names align!
- if (n_args < n_names) and n_kws > 0:
- for name in self.argnames[n_args:]:
- if name in kwargs:
- args.append(kwargs.pop(name))
- n_args = len(args)
- n_names = len(self.argnames)
- n_kws = len(kwargs)
-
- if len(self.argnames) > 0 and kwargs is not None:
- msg = "multiple values for keyword argument '%s' in Procedure %s"
- for targ in self.argnames:
- if targ in kwargs:
- self.raise_exc(None, exc=TypeError,
- msg=msg % (targ, self.name),
- lineno=self.lineno)
-
- if n_args != n_names:
- msg = None
- if n_args < n_names:
- msg = 'not enough arguments for Procedure %s()' % self.name
- msg = '%s (expected %i, got %i)' % (msg, n_names, n_args)
- self.raise_exc(None, exc=TypeError, msg=msg)
-
- for argname in self.argnames:
- symlocals[argname] = args.pop(0)
-
- try:
- if self.vararg is not None:
- symlocals[self.vararg] = tuple(args)
-
- for key, val in self.kwargs:
- if key in kwargs:
- val = kwargs.pop(key)
- symlocals[key] = val
-
- if self.varkws is not None:
- symlocals[self.varkws] = kwargs
-
- elif len(kwargs) > 0:
- msg = 'extra keyword arguments for Procedure %s (%s)'
- msg = msg % (self.name, ','.join(list(kwargs.keys())))
- self.raise_exc(None, msg=msg, exc=TypeError,
- lineno=self.lineno)
-
- except (ValueError, LookupError, TypeError,
- NameError, AttributeError):
- msg = 'incorrect arguments for Procedure %s' % self.name
- self.raise_exc(None, msg=msg, lineno=self.lineno)
-
- save_symtable = self.__asteval__.symtable.copy()
- self.__asteval__.symtable.update(symlocals)
- self.__asteval__.retval = None
- retval = None
-
- # evaluate script of function
- for node in self.body:
- self.__asteval__.run(node, expr='<>', lineno=self.lineno)
- if len(self.__asteval__.error) > 0:
- break
- if self.__asteval__.retval is not None:
- retval = self.__asteval__.retval
- if retval is ReturnedNone:
- retval = None
- break
-
- self.__asteval__.symtable = save_symtable
- symlocals = None
- return retval
+""" +Safe(ish) evaluator of python expressions, using ast module. +The emphasis here is on mathematical expressions, and so +numpy functions are imported if available and used. + +Symbols are held in the Interpreter symtable -- a simple +dictionary supporting a simple, flat namespace. + +Expressions can be compiled into ast node and then evaluated +later, using the current values in the +""" + +from __future__ import division, print_function +from sys import exc_info, stdout, version_info +import ast +import math + +from .astutils import (FROM_PY, FROM_MATH, FROM_NUMPY, UNSAFE_ATTRS, + LOCALFUNCS, NUMPY_RENAMES, op2func, + ExceptionHolder, ReturnedNone, valid_symbol_name) + +HAS_NUMPY = False +try: + import numpy + HAS_NUMPY = True +except ImportError: + print("Warning: numpy not available... functionality will be limited.") + + +class Interpreter: + """mathematical expression compiler and interpreter. + + This module compiles expressions and statements to AST representation, + using python's ast module, and then executes the AST representation + using a dictionary of named object (variable, functions). + + The result is a restricted, simplified version of Python meant for + numerical caclulations that is somewhat safer than 'eval' because some + operations (such as 'import' and 'eval') are simply not allowed. The + resulting language uses a flat namespace that works on Python objects, + but does not allow new classes to be defined. + + Many parts of Python syntax are supported, including: + for loops, while loops, if-then-elif-else conditionals + try-except (including 'finally') + function definitions with def + advanced slicing: a[::-1], array[-3:, :, ::2] + if-expressions: out = one_thing if TEST else other + list comprehension out = [sqrt(i) for i in values] + + The following Python syntax elements are not supported: + Import, Exec, Lambda, Class, Global, Generators, + Yield, Decorators + + In addition, while many builtin functions are supported, several + builtin functions are missing ('eval', 'exec', and 'getattr' for + example) that can be considered unsafe. + + If numpy is installed, many numpy functions are also imported. + + """ + + supported_nodes = ('arg', 'assert', 'assign', 'attribute', 'augassign', + 'binop', 'boolop', 'break', 'call', 'compare', + 'continue', 'delete', 'dict', 'ellipsis', + 'excepthandler', 'expr', 'extslice', 'for', + 'functiondef', 'if', 'ifexp', 'index', 'interrupt', + 'list', 'listcomp', 'module', 'name', 'num', 'pass', + 'print', 'raise', 'repr', 'return', 'slice', 'str', + 'subscript', 'try', 'tuple', 'unaryop', 'while') + + def __init__(self, symtable=None, writer=None, use_numpy=True): + self.writer = writer or stdout + + if symtable is None: + symtable = {} + self.symtable = symtable + self._interrupt = None + self.error = [] + self.error_msg = None + self.expr = None + self.retval = None + self.lineno = 0 + self.use_numpy = HAS_NUMPY and use_numpy + + symtable['print'] = self._printer + + # add python symbols + py_symtable = {sym: __builtins__[sym] for sym in FROM_PY + if sym in __builtins__} + symtable.update(py_symtable) + + # add local symbols + local_symtable = {sym: obj for (sym, obj) in LOCALFUNCS.items()} + symtable.update(local_symtable) + + # add math symbols + math_symtable = {sym: getattr(math, sym) for sym in FROM_MATH + if hasattr(math, sym)} + symtable.update(math_symtable) + + # add numpy symbols + if self.use_numpy: + numpy_symtable = {sym: getattr(numpy, sym) for sym in FROM_NUMPY + if hasattr(numpy, sym)} + symtable.update(numpy_symtable) + + npy_rename_symtable = {name: getattr(numpy, sym) for name, sym + in NUMPY_RENAMES.items() + if hasattr(numpy, sym)} + symtable.update(npy_rename_symtable) + + self.node_handlers = dict(((node, getattr(self, "on_%s" % node)) + for node in self.supported_nodes)) + + # to rationalize try/except try/finally for Python2.6 through Python3.3 + self.node_handlers['tryexcept'] = self.node_handlers['try'] + self.node_handlers['tryfinally'] = self.node_handlers['try'] + + self.no_deepcopy = [key for key, val in symtable.items() + if (callable(val) + or 'numpy.lib.index_tricks' in repr(val))] + + def user_defined_symbols(self): + """ + Return a set of symbols that have been added to symtable after + construction. I.e. the symbols from self.symtable that are not in + self.no_deepcopy. + + Returns + ------- + unique_symbols : set + symbols in symtable that are not in self.no_deepcopy + """ + sym_in_current = set(self.symtable.keys()) + sym_from_construction = set(self.no_deepcopy) + unique_symbols = sym_in_current.difference(sym_from_construction) + return unique_symbols + + def unimplemented(self, node): + "unimplemented nodes" + self.raise_exception(node, exc=NotImplementedError, + msg="'%s' not supported" % + (node.__class__.__name__)) + + def raise_exception(self, node, exc=None, msg='', expr=None, + lineno=None): + "add an exception" + if self.error is None: + self.error = [] + if expr is None: + expr = self.expr + if len(self.error) > 0 and not isinstance(node, ast.Module): + msg = '%s' % msg + err = ExceptionHolder(node, exc=exc, msg=msg, expr=expr, lineno=lineno) + self._interrupt = ast.Break() + self.error.append(err) + if self.error_msg is None: + self.error_msg = "%s in expr='%s'" % (msg, self.expr) + elif len(msg) > 0: + self.error_msg = "%s\n %s" % (self.error_msg, msg) + if exc is None: + try: + exc = self.error[0].exc + except: + exc = RuntimeError + raise exc(self.error_msg) + + + # main entry point for Ast node evaluation + # parse: text of statements -> ast + # run: ast -> result + # eval: string statement -> result = run(parse(statement)) + def parse(self, text): + """parse statement/expression to Ast representation""" + self.expr = text + try: + return ast.parse(text) + except SyntaxError: + self.raise_exception(None, msg='Syntax Error', expr=text) + except: + self.raise_exception(None, msg='Runtime Error', expr=text) + + def run(self, node, expr=None, lineno=None, with_raise=True): + """executes parsed Ast representation for an expression""" + # Note: keep the 'node is None' test: internal code here may run + # run(None) and expect a None in return. + if len(self.error) > 0: + return + if node is None: + return None + if isinstance(node, str): + node = self.parse(node) + if lineno is not None: + self.lineno = lineno + if expr is not None: + self.expr = expr + + # get handler for this node: + # on_xxx with handle nodes of type 'xxx', etc + try: + handler = self.node_handlers[node.__class__.__name__.lower()] + except KeyError: + return self.unimplemented(node) + + # run the handler: this will likely generate + # recursive calls into this run method. + try: + ret = handler(node) + if isinstance(ret, enumerate): + ret = list(ret) + return ret + except: + if with_raise: + self.raise_exception(node, expr=expr) + + def __call__(self, expr, **kw): + return self.eval(expr, **kw) + + def eval(self, expr, lineno=0, show_errors=True): + """evaluates a single statement""" + self.lineno = lineno + self.error = [] + try: + node = self.parse(expr) + except: + errmsg = exc_info()[1] + if len(self.error) > 0: + errmsg = "\n".join(self.error[0].get_error()) + if not show_errors: + try: + exc = self.error[0].exc + except: + exc = RuntimeError + raise exc(errmsg) + print(errmsg, file=self.writer) + return + try: + return self.run(node, expr=expr, lineno=lineno) + except: + errmsg = exc_info()[1] + if len(self.error) > 0: + errmsg = "\n".join(self.error[0].get_error()) + if not show_errors: + try: + exc = self.error[0].exc + except: + exc = RuntimeError + raise exc(errmsg) + print(errmsg, file=self.writer) + return + + def dump(self, node, **kw): + "simple ast dumper" + return ast.dump(node, **kw) + + # handlers for ast components + def on_expr(self, node): + "expression" + return self.run(node.value) # ('value',) + + def on_index(self, node): + "index" + return self.run(node.value) # ('value',) + + def on_return(self, node): # ('value',) + "return statement: look for None, return special sentinal" + self.retval = self.run(node.value) + if self.retval is None: + self.retval = ReturnedNone + return + + def on_repr(self, node): + "repr " + return repr(self.run(node.value)) # ('value',) + + def on_module(self, node): # ():('body',) + "module def" + out = None + for tnode in node.body: + out = self.run(tnode) + return out + + def on_pass(self, node): + "pass statement" + return None # () + + def on_ellipsis(self, node): + "ellipses" + return Ellipsis + + # for break and continue: set the instance variable _interrupt + def on_interrupt(self, node): # () + "interrupt handler" + self._interrupt = node + return node + + def on_break(self, node): + "break" + return self.on_interrupt(node) + + def on_continue(self, node): + "continue" + return self.on_interrupt(node) + + def on_assert(self, node): # ('test', 'msg') + "assert statement" + if not self.run(node.test): + self.raise_exception(node, exc=AssertionError, msg=node.msg) + return True + + def on_list(self, node): # ('elt', 'ctx') + "list" + return [self.run(e) for e in node.elts] + + def on_tuple(self, node): # ('elts', 'ctx') + "tuple" + return tuple(self.on_list(node)) + + def on_dict(self, node): # ('keys', 'values') + "dictionary" + return dict([(self.run(k), self.run(v)) for k, v in + zip(node.keys, node.values)]) + + def on_num(self, node): # ('n',) + 'return number' + return node.n + + def on_str(self, node): # ('s',) + 'return string' + return node.s + + def on_name(self, node): # ('id', 'ctx') + """ Name node """ + ctx = node.ctx.__class__ + if ctx in (ast.Param, ast.Del): + return str(node.id) + else: + if node.id in self.symtable: + return self.symtable[node.id] + else: + msg = "name '%s' is not defined" % node.id + self.raise_exception(node, exc=NameError, msg=msg) + + def node_assign(self, node, val): + """here we assign a value (not the node.value object) to a node + this is used by on_assign, but also by for, list comprehension, etc. + """ + if node.__class__ == ast.Name: + if not valid_symbol_name(node.id): + errmsg = "invalid symbol name (reserved word?) %s" % node.id + self.raise_exception(node, exc=NameError, msg=errmsg) + sym = self.symtable[node.id] = val + if node.id in self.no_deepcopy: + self.no_deepcopy.pop(node.id) + + elif node.__class__ == ast.Attribute: + if node.ctx.__class__ == ast.Load: + msg = "cannot assign to attribute %s" % node.attr + self.raise_exception(node, exc=AttributeError, msg=msg) + + setattr(self.run(node.value), node.attr, val) + + elif node.__class__ == ast.Subscript: + sym = self.run(node.value) + xslice = self.run(node.slice) + if isinstance(node.slice, ast.Index): + sym[xslice] = val + elif isinstance(node.slice, ast.Slice): + sym[slice(xslice.start, xslice.stop)] = val + elif isinstance(node.slice, ast.ExtSlice): + sym[(xslice)] = val + elif node.__class__ in (ast.Tuple, ast.List): + if len(val) == len(node.elts): + for telem, tval in zip(node.elts, val): + self.node_assign(telem, tval) + else: + raise ValueError('too many values to unpack') + + def on_attribute(self, node): # ('value', 'attr', 'ctx') + "extract attribute" + ctx = node.ctx.__class__ + if ctx == ast.Store: + msg = "attribute for storage: shouldn't be here!" + self.raise_exception(node, exc=RuntimeError, msg=msg) + + sym = self.run(node.value) + if ctx == ast.Del: + return delattr(sym, node.attr) + + # ctx is ast.Load + fmt = "cannnot access attribute '%s' for %s" + if node.attr not in UNSAFE_ATTRS: + fmt = "no attribute '%s' for %s" + try: + return getattr(sym, node.attr) + except AttributeError: + pass + + # AttributeError or accessed unsafe attribute + obj = self.run(node.value) + msg = fmt % (node.attr, obj) + self.raise_exception(node, exc=AttributeError, msg=msg) + + def on_assign(self, node): # ('targets', 'value') + "simple assignment" + val = self.run(node.value) + for tnode in node.targets: + self.node_assign(tnode, val) + return + + def on_augassign(self, node): # ('target', 'op', 'value') + "augmented assign" + return self.on_assign(ast.Assign(targets=[node.target], + value=ast.BinOp(left=node.target, + op=node.op, + right=node.value))) + + def on_slice(self, node): # ():('lower', 'upper', 'step') + "simple slice" + return slice(self.run(node.lower), + self.run(node.upper), + self.run(node.step)) + + def on_extslice(self, node): # ():('dims',) + "extended slice" + return tuple([self.run(tnode) for tnode in node.dims]) + + def on_subscript(self, node): # ('value', 'slice', 'ctx') + "subscript handling -- one of the tricky parts" + val = self.run(node.value) + nslice = self.run(node.slice) + ctx = node.ctx.__class__ + if ctx in (ast.Load, ast.Store): + if isinstance(node.slice, (ast.Index, ast.Slice, ast.Ellipsis)): + return val.__getitem__(nslice) + elif isinstance(node.slice, ast.ExtSlice): + return val[(nslice)] + else: + msg = "subscript with unknown context" + self.raise_exception(node, msg=msg) + + def on_delete(self, node): # ('targets',) + "delete statement" + for tnode in node.targets: + if tnode.ctx.__class__ != ast.Del: + break + children = [] + while tnode.__class__ == ast.Attribute: + children.append(tnode.attr) + tnode = tnode.value + + if tnode.__class__ == ast.Name: + children.append(tnode.id) + children.reverse() + self.symtable.pop('.'.join(children)) + else: + msg = "could not delete symbol" + self.raise_exception(node, msg=msg) + + def on_unaryop(self, node): # ('op', 'operand') + "unary operator" + return op2func(node.op)(self.run(node.operand)) + + def on_binop(self, node): # ('left', 'op', 'right') + "binary operator" + return op2func(node.op)(self.run(node.left), + self.run(node.right)) + + def on_boolop(self, node): # ('op', 'values') + "boolean operator" + val = self.run(node.values[0]) + is_and = ast.And == node.op.__class__ + if (is_and and val) or (not is_and and not val): + for n in node.values: + val = op2func(node.op)(val, self.run(n)) + if (is_and and not val) or (not is_and and val): + break + return val + + def on_compare(self, node): # ('left', 'ops', 'comparators') + "comparison operators" + lval = self.run(node.left) + out = True + for op, rnode in zip(node.ops, node.comparators): + rval = self.run(rnode) + out = op2func(op)(lval, rval) + lval = rval + if self.use_numpy and isinstance(out, numpy.ndarray) and out.any(): + break + elif not out: + break + return out + + def on_print(self, node): # ('dest', 'values', 'nl') + """ note: implements Python2 style print statement, not + print() function. May need improvement....""" + dest = self.run(node.dest) or self.writer + end = '' + if node.nl: + end = '\n' + out = [self.run(tnode) for tnode in node.values] + if out and len(self.error) == 0: + self._printer(*out, file=dest, end=end) + + def _printer(self, *out, **kws): + "generic print function" + flush = kws.pop('flush', True) + fileh = kws.pop('file', self.writer) + sep = kws.pop('sep', ' ') + end = kws.pop('sep', '\n') + + print(*out, file=fileh, sep=sep, end=end) + if flush: + fileh.flush() + + def on_if(self, node): # ('test', 'body', 'orelse') + "regular if-then-else statement" + block = node.body + if not self.run(node.test): + block = node.orelse + for tnode in block: + self.run(tnode) + + def on_ifexp(self, node): # ('test', 'body', 'orelse') + "if expressions" + expr = node.orelse + if self.run(node.test): + expr = node.body + return self.run(expr) + + def on_while(self, node): # ('test', 'body', 'orelse') + "while blocks" + while self.run(node.test): + self._interrupt = None + for tnode in node.body: + self.run(tnode) + if self._interrupt is not None: + break + if isinstance(self._interrupt, ast.Break): + break + else: + for tnode in node.orelse: + self.run(tnode) + self._interrupt = None + + def on_for(self, node): # ('target', 'iter', 'body', 'orelse') + "for blocks" + for val in self.run(node.iter): + self.node_assign(node.target, val) + self._interrupt = None + for tnode in node.body: + self.run(tnode) + if self._interrupt is not None: + break + if isinstance(self._interrupt, ast.Break): + break + else: + for tnode in node.orelse: + self.run(tnode) + self._interrupt = None + + def on_listcomp(self, node): # ('elt', 'generators') + "list comprehension" + out = [] + for tnode in node.generators: + if tnode.__class__ == ast.comprehension: + for val in self.run(tnode.iter): + self.node_assign(tnode.target, val) + add = True + for cond in tnode.ifs: + add = add and self.run(cond) + if add: + out.append(self.run(node.elt)) + return out + + def on_excepthandler(self, node): # ('type', 'name', 'body') + "exception handler..." + return (self.run(node.type), node.name, node.body) + + def on_try(self, node): # ('body', 'handlers', 'orelse', 'finalbody') + "try/except/else/finally blocks" + no_errors = True + for tnode in node.body: + self.run(tnode, with_raise=False) + no_errors = no_errors and len(self.error) == 0 + if len(self.error) > 0: + e_type, e_value, e_tback = self.error[-1].exc_info + for hnd in node.handlers: + htype = None + if hnd.type is not None: + htype = __builtins__.get(hnd.type.id, None) + if htype is None or isinstance(e_type(), htype): + self.error = [] + if hnd.name is not None: + self.node_assign(hnd.name, e_value) + for tline in hnd.body: + self.run(tline) + break + if no_errors and hasattr(node, 'orelse'): + for tnode in node.orelse: + self.run(tnode) + + if hasattr(node, 'finalbody'): + for tnode in node.finalbody: + self.run(tnode) + + def on_raise(self, node): # ('type', 'inst', 'tback') + "raise statement: note difference for python 2 and 3" + if version_info[0] == 3: + excnode = node.exc + msgnode = node.cause + else: + excnode = node.type + msgnode = node.inst + out = self.run(excnode) + msg = ' '.join(out.args) + msg2 = self.run(msgnode) + if msg2 not in (None, 'None'): + msg = "%s: %s" % (msg, msg2) + self.raise_exception(None, exc=out.__class__, msg=msg, expr='') + + def on_call(self, node): + "function execution" + # ('func', 'args', 'keywords'. Py<3.5 has 'starargs' and 'kwargs' too) + func = self.run(node.func) + if not hasattr(func, '__call__') and not isinstance(func, type): + msg = "'%s' is not callable!!" % (func) + self.raise_exception(node, exc=TypeError, msg=msg) + + args = [self.run(targ) for targ in node.args] + starargs = getattr(node, 'starargs', None) + if starargs is not None: + args = args + self.run(starargs) + + keywords = {} + for key in node.keywords: + if not isinstance(key, ast.keyword): + msg = "keyword error in function call '%s'" % (func) + self.raise_exception(node, msg=msg) + keywords[key.arg] = self.run(key.value) + + kwargs = getattr(node, 'kwargs', None) + if kwargs is not None: + keywords.update(self.run(kwargs)) + + try: + return func(*args, **keywords) + except: + self.raise_exception(node, msg="Error running %s" % (func)) + + def on_arg(self, node): # ('test', 'msg') + "arg for function definitions" + # print(" ON ARG ! ", node, node.arg) + return node.arg + + def on_functiondef(self, node): + "define procedures" + # ('name', 'args', 'body', 'decorator_list') + if node.decorator_list != []: + raise Warning("decorated procedures not supported!") + kwargs = [] + + offset = len(node.args.args) - len(node.args.defaults) + for idef, defnode in enumerate(node.args.defaults): + defval = self.run(defnode) + keyval = self.run(node.args.args[idef+offset]) + kwargs.append((keyval, defval)) + + if version_info[0] == 3: + args = [tnode.arg for tnode in node.args.args[:offset]] + else: + args = [tnode.id for tnode in node.args.args[:offset]] + + doc = None + nb0 = node.body[0] + if isinstance(nb0, ast.Expr) and isinstance(nb0.value, ast.Str): + doc = nb0.value.s + + self.symtable[node.name] = Procedure(node.name, self, doc=doc, + lineno=self.lineno, + body=node.body, + args=args, kwargs=kwargs, + vararg=node.args.vararg, + varkws=node.args.kwarg) + if node.name in self.no_deepcopy: + self.no_deepcopy.pop(node.name) + + +class Procedure(object): + """Procedure: user-defined function for asteval + + This stores the parsed ast nodes as from the + 'functiondef' ast node for later evaluation. + """ + def __init__(self, name, interp, doc=None, lineno=0, + body=None, args=None, kwargs=None, + vararg=None, varkws=None): + self.name = name + self.__asteval__ = interp + self.raise_exc = self.__asteval__.raise_exception + self.__doc__ = doc + self.body = body + self.argnames = args + self.kwargs = kwargs + self.vararg = vararg + self.varkws = varkws + self.lineno = lineno + + def __repr__(self): + sig = "" + if len(self.argnames) > 0: + sig = "%s%s" % (sig, ', '.join(self.argnames)) + if self.vararg is not None: + sig = "%s, *%s" % (sig, self.vararg) + if len(self.kwargs) > 0: + if len(sig) > 0: + sig = "%s, " % sig + _kw = ["%s=%s" % (k, v) for k, v in self.kwargs] + sig = "%s%s" % (sig, ', '.join(_kw)) + + if self.varkws is not None: + sig = "%s, **%s" % (sig, self.varkws) + sig = "<Procedure %s(%s)>" % (self.name, sig) + if self.__doc__ is not None: + sig = "%s\n %s" % (sig, self.__doc__) + return sig + + def __call__(self, *args, **kwargs): + symlocals = {} + args = list(args) + n_args = len(args) + n_names = len(self.argnames) + n_kws = len(kwargs) + + # may need to move kwargs to args if names align! + if (n_args < n_names) and n_kws > 0: + for name in self.argnames[n_args:]: + if name in kwargs: + args.append(kwargs.pop(name)) + n_args = len(args) + n_names = len(self.argnames) + n_kws = len(kwargs) + + if len(self.argnames) > 0 and kwargs is not None: + msg = "multiple values for keyword argument '%s' in Procedure %s" + for targ in self.argnames: + if targ in kwargs: + self.raise_exc(None, exc=TypeError, + msg=msg % (targ, self.name), + lineno=self.lineno) + + if n_args != n_names: + msg = None + if n_args < n_names: + msg = 'not enough arguments for Procedure %s()' % self.name + msg = '%s (expected %i, got %i)' % (msg, n_names, n_args) + self.raise_exc(None, exc=TypeError, msg=msg) + + for argname in self.argnames: + symlocals[argname] = args.pop(0) + + try: + if self.vararg is not None: + symlocals[self.vararg] = tuple(args) + + for key, val in self.kwargs: + if key in kwargs: + val = kwargs.pop(key) + symlocals[key] = val + + if self.varkws is not None: + symlocals[self.varkws] = kwargs + + elif len(kwargs) > 0: + msg = 'extra keyword arguments for Procedure %s (%s)' + msg = msg % (self.name, ','.join(list(kwargs.keys()))) + self.raise_exc(None, msg=msg, exc=TypeError, + lineno=self.lineno) + + except (ValueError, LookupError, TypeError, + NameError, AttributeError): + msg = 'incorrect arguments for Procedure %s' % self.name + self.raise_exc(None, msg=msg, lineno=self.lineno) + + save_symtable = self.__asteval__.symtable.copy() + self.__asteval__.symtable.update(symlocals) + self.__asteval__.retval = None + retval = None + + # evaluate script of function + for node in self.body: + self.__asteval__.run(node, expr='<>', lineno=self.lineno) + if len(self.__asteval__.error) > 0: + break + if self.__asteval__.retval is not None: + retval = self.__asteval__.retval + if retval is ReturnedNone: + retval = None + break + + self.__asteval__.symtable = save_symtable + symlocals = None + return retval diff --git a/lmfit/astutils.py b/lmfit/astutils.py index 0a8c25a..9df7146 100644 --- a/lmfit/astutils.py +++ b/lmfit/astutils.py @@ -1,258 +1,258 @@ -"""
-utility functions for asteval
-
- Matthew Newville <newville@cars.uchicago.edu>,
- The University of Chicago
-"""
-from __future__ import division, print_function
-import re
-import ast
-from sys import exc_info
-
-RESERVED_WORDS = ('and', 'as', 'assert', 'break', 'class', 'continue',
- 'def', 'del', 'elif', 'else', 'except', 'exec',
- 'finally', 'for', 'from', 'global', 'if', 'import',
- 'in', 'is', 'lambda', 'not', 'or', 'pass', 'print',
- 'raise', 'return', 'try', 'while', 'with', 'True',
- 'False', 'None', 'eval', 'execfile', '__import__',
- '__package__')
-
-NAME_MATCH = re.compile(r"[a-zA-Z_][a-zA-Z0-9_]*$").match
-
-UNSAFE_ATTRS = ('__subclasses__', '__bases__', '__globals__', '__code__',
- '__closure__', '__func__', '__self__', '__module__',
- '__dict__', '__class__', '__call__', '__get__',
- '__getattribute__', '__subclasshook__', '__new__',
- '__init__', 'func_globals', 'func_code', 'func_closure',
- 'im_class', 'im_func', 'im_self', 'gi_code', 'gi_frame',
- '__asteval__')
-
-# inherit these from python's __builtins__
-FROM_PY = ('ArithmeticError', 'AssertionError', 'AttributeError',
- 'BaseException', 'BufferError', 'BytesWarning',
- 'DeprecationWarning', 'EOFError', 'EnvironmentError',
- 'Exception', 'False', 'FloatingPointError', 'GeneratorExit',
- 'IOError', 'ImportError', 'ImportWarning', 'IndentationError',
- 'IndexError', 'KeyError', 'KeyboardInterrupt', 'LookupError',
- 'MemoryError', 'NameError', 'None',
- 'NotImplementedError', 'OSError', 'OverflowError',
- 'ReferenceError', 'RuntimeError', 'RuntimeWarning',
- 'StopIteration', 'SyntaxError', 'SyntaxWarning', 'SystemError',
- 'SystemExit', 'True', 'TypeError', 'UnboundLocalError',
- 'UnicodeDecodeError', 'UnicodeEncodeError', 'UnicodeError',
- 'UnicodeTranslateError', 'UnicodeWarning', 'ValueError',
- 'Warning', 'ZeroDivisionError', 'abs', 'all', 'any', 'bin',
- 'bool', 'bytearray', 'bytes', 'chr', 'complex', 'dict', 'dir',
- 'divmod', 'enumerate', 'filter', 'float', 'format', 'frozenset',
- 'hash', 'hex', 'id', 'int', 'isinstance', 'len', 'list', 'map',
- 'max', 'min', 'oct', 'ord', 'pow', 'range', 'repr',
- 'reversed', 'round', 'set', 'slice', 'sorted', 'str', 'sum',
- 'tuple', 'type', 'zip')
-
-# inherit these from python's math
-FROM_MATH = ('acos', 'acosh', 'asin', 'asinh', 'atan', 'atan2', 'atanh',
- 'ceil', 'copysign', 'cos', 'cosh', 'degrees', 'e', 'exp',
- 'fabs', 'factorial', 'floor', 'fmod', 'frexp', 'fsum',
- 'hypot', 'isinf', 'isnan', 'ldexp', 'log', 'log10', 'log1p',
- 'modf', 'pi', 'pow', 'radians', 'sin', 'sinh', 'sqrt', 'tan',
- 'tanh', 'trunc')
-
-FROM_NUMPY = ('Inf', 'NAN', 'abs', 'add', 'alen', 'all', 'amax', 'amin',
- 'angle', 'any', 'append', 'arange', 'arccos', 'arccosh',
- 'arcsin', 'arcsinh', 'arctan', 'arctan2', 'arctanh',
- 'argmax', 'argmin', 'argsort', 'argwhere', 'around', 'array',
- 'array2string', 'asanyarray', 'asarray', 'asarray_chkfinite',
- 'ascontiguousarray', 'asfarray', 'asfortranarray',
- 'asmatrix', 'asscalar', 'atleast_1d', 'atleast_2d',
- 'atleast_3d', 'average', 'bartlett', 'base_repr',
- 'bitwise_and', 'bitwise_not', 'bitwise_or', 'bitwise_xor',
- 'blackman', 'bool', 'broadcast', 'broadcast_arrays', 'byte',
- 'c_', 'cdouble', 'ceil', 'cfloat', 'chararray', 'choose',
- 'clip', 'clongdouble', 'clongfloat', 'column_stack',
- 'common_type', 'complex', 'complex128', 'complex64',
- 'complex_', 'complexfloating', 'compress', 'concatenate',
- 'conjugate', 'convolve', 'copy', 'copysign', 'corrcoef',
- 'correlate', 'cos', 'cosh', 'cov', 'cross', 'csingle',
- 'cumprod', 'cumsum', 'datetime_data', 'deg2rad', 'degrees',
- 'delete', 'diag', 'diag_indices', 'diag_indices_from',
- 'diagflat', 'diagonal', 'diff', 'digitize', 'divide', 'dot',
- 'double', 'dsplit', 'dstack', 'dtype', 'e', 'ediff1d',
- 'empty', 'empty_like', 'equal', 'exp', 'exp2', 'expand_dims',
- 'expm1', 'extract', 'eye', 'fabs', 'fill_diagonal', 'finfo',
- 'fix', 'flatiter', 'flatnonzero', 'fliplr', 'flipud',
- 'float', 'float32', 'float64', 'float_', 'floating', 'floor',
- 'floor_divide', 'fmax', 'fmin', 'fmod', 'format_parser',
- 'frexp', 'frombuffer', 'fromfile', 'fromfunction',
- 'fromiter', 'frompyfunc', 'fromregex', 'fromstring', 'fv',
- 'genfromtxt', 'getbufsize', 'geterr', 'gradient', 'greater',
- 'greater_equal', 'hamming', 'hanning', 'histogram',
- 'histogram2d', 'histogramdd', 'hsplit', 'hstack', 'hypot',
- 'i0', 'identity', 'iinfo', 'imag', 'in1d', 'index_exp',
- 'indices', 'inexact', 'inf', 'info', 'infty', 'inner',
- 'insert', 'int', 'int0', 'int16', 'int32', 'int64', 'int8',
- 'int_', 'int_asbuffer', 'intc', 'integer', 'interp',
- 'intersect1d', 'intp', 'invert', 'ipmt', 'irr', 'iscomplex',
- 'iscomplexobj', 'isfinite', 'isfortran', 'isinf', 'isnan',
- 'isneginf', 'isposinf', 'isreal', 'isrealobj', 'isscalar',
- 'issctype', 'iterable', 'ix_', 'kaiser', 'kron', 'ldexp',
- 'left_shift', 'less', 'less_equal', 'linspace',
- 'little_endian', 'load', 'loads', 'loadtxt', 'log', 'log10',
- 'log1p', 'log2', 'logaddexp', 'logaddexp2', 'logical_and',
- 'logical_not', 'logical_or', 'logical_xor', 'logspace',
- 'long', 'longcomplex', 'longdouble', 'longfloat', 'longlong',
- 'mafromtxt', 'mask_indices', 'mat', 'matrix', 'max',
- 'maximum', 'maximum_sctype', 'may_share_memory', 'mean',
- 'median', 'memmap', 'meshgrid', 'mgrid', 'min', 'minimum',
- 'mintypecode', 'mirr', 'mod', 'modf', 'msort', 'multiply',
- 'nan', 'nan_to_num', 'nanargmax', 'nanargmin', 'nanmax',
- 'nanmin', 'nansum', 'ndarray', 'ndenumerate', 'ndfromtxt',
- 'ndim', 'ndindex', 'negative', 'newaxis', 'nextafter',
- 'nonzero', 'not_equal', 'nper', 'npv', 'number',
- 'obj2sctype', 'ogrid', 'ones', 'ones_like', 'outer',
- 'packbits', 'percentile', 'pi', 'piecewise', 'place', 'pmt',
- 'poly', 'poly1d', 'polyadd', 'polyder', 'polydiv', 'polyfit',
- 'polyint', 'polymul', 'polysub', 'polyval', 'power', 'ppmt',
- 'prod', 'product', 'ptp', 'put', 'putmask', 'pv', 'r_',
- 'rad2deg', 'radians', 'rank', 'rate', 'ravel', 'real',
- 'real_if_close', 'reciprocal', 'record', 'remainder',
- 'repeat', 'reshape', 'resize', 'restoredot', 'right_shift',
- 'rint', 'roll', 'rollaxis', 'roots', 'rot90', 'round',
- 'round_', 'row_stack', 's_', 'sctype2char', 'searchsorted',
- 'select', 'setbufsize', 'setdiff1d', 'seterr', 'setxor1d',
- 'shape', 'short', 'sign', 'signbit', 'signedinteger', 'sin',
- 'sinc', 'single', 'singlecomplex', 'sinh', 'size',
- 'sometrue', 'sort', 'sort_complex', 'spacing', 'split',
- 'sqrt', 'square', 'squeeze', 'std', 'str', 'str_',
- 'subtract', 'sum', 'swapaxes', 'take', 'tan', 'tanh',
- 'tensordot', 'tile', 'trace', 'transpose', 'trapz', 'tri',
- 'tril', 'tril_indices', 'tril_indices_from', 'trim_zeros',
- 'triu', 'triu_indices', 'triu_indices_from', 'true_divide',
- 'trunc', 'ubyte', 'uint', 'uint0', 'uint16', 'uint32',
- 'uint64', 'uint8', 'uintc', 'uintp', 'ulonglong', 'union1d',
- 'unique', 'unravel_index', 'unsignedinteger', 'unwrap',
- 'ushort', 'vander', 'var', 'vdot', 'vectorize', 'vsplit',
- 'vstack', 'where', 'who', 'zeros', 'zeros_like')
-
-NUMPY_RENAMES = {'ln': 'log', 'asin': 'arcsin', 'acos': 'arccos',
- 'atan': 'arctan', 'atan2': 'arctan2', 'atanh':
- 'arctanh', 'acosh': 'arccosh', 'asinh': 'arcsinh'}
-
-def _open(filename, mode='r', buffering=0):
- """read only version of open()"""
- umode = 'r'
- if mode == 'rb':
- umode = 'rb'
- return open(filename, umode, buffering)
-
-LOCALFUNCS = {'open': _open}
-
-OPERATORS = {ast.Is: lambda a, b: a is b,
- ast.IsNot: lambda a, b: a is not b,
- ast.In: lambda a, b: a in b,
- ast.NotIn: lambda a, b: a not in b,
- ast.Add: lambda a, b: a + b,
- ast.BitAnd: lambda a, b: a & b,
- ast.BitOr: lambda a, b: a | b,
- ast.BitXor: lambda a, b: a ^ b,
- ast.Div: lambda a, b: a / b,
- ast.FloorDiv: lambda a, b: a // b,
- ast.LShift: lambda a, b: a << b,
- ast.RShift: lambda a, b: a >> b,
- ast.Mult: lambda a, b: a * b,
- ast.Pow: lambda a, b: a ** b,
- ast.Sub: lambda a, b: a - b,
- ast.Mod: lambda a, b: a % b,
- ast.And: lambda a, b: a and b,
- ast.Or: lambda a, b: a or b,
- ast.Eq: lambda a, b: a == b,
- ast.Gt: lambda a, b: a > b,
- ast.GtE: lambda a, b: a >= b,
- ast.Lt: lambda a, b: a < b,
- ast.LtE: lambda a, b: a <= b,
- ast.NotEq: lambda a, b: a != b,
- ast.Invert: lambda a: ~a,
- ast.Not: lambda a: not a,
- ast.UAdd: lambda a: +a,
- ast.USub: lambda a: -a}
-
-
-def valid_symbol_name(name):
- """determines whether the input symbol name is a valid name
-
- This checks for reserved words, and that the name matches the
- regular expression ``[a-zA-Z_][a-zA-Z0-9_]``
- """
- if name in RESERVED_WORDS:
- return False
- return NAME_MATCH(name) is not None
-
-
-def op2func(op):
- "return function for operator nodes"
- return OPERATORS[op.__class__]
-
-
-class Empty:
- """empty class"""
- def __init__(self):
- pass
-
- def __nonzero__(self):
- return False
-
-ReturnedNone = Empty()
-
-
-class ExceptionHolder(object):
- "basic exception handler"
- def __init__(self, node, exc=None, msg='', expr=None, lineno=None):
- self.node = node
- self.expr = expr
- self.msg = msg
- self.exc = exc
- self.lineno = lineno
- self.exc_info = exc_info()
- if self.exc is None and self.exc_info[0] is not None:
- self.exc = self.exc_info[0]
- if self.msg is '' and self.exc_info[1] is not None:
- self.msg = self.exc_info[1]
-
- def get_error(self):
- "retrieve error data"
- col_offset = -1
- if self.node is not None:
- try:
- col_offset = self.node.col_offset
- except AttributeError:
- pass
- try:
- exc_name = self.exc.__name__
- except AttributeError:
- exc_name = str(self.exc)
- if exc_name in (None, 'None'):
- exc_name = 'UnknownError'
-
- out = [" %s" % self.expr]
- if col_offset > 0:
- out.append(" %s^^^" % ((col_offset)*' '))
- out.append(str(self.msg))
- return (exc_name, '\n'.join(out))
-
-
-class NameFinder(ast.NodeVisitor):
- """find all symbol names used by a parsed node"""
- def __init__(self):
- self.names = []
- ast.NodeVisitor.__init__(self)
-
- def generic_visit(self, node):
- if node.__class__.__name__ == 'Name':
- if node.ctx.__class__ == ast.Load and node.id not in self.names:
- self.names.append(node.id)
- ast.NodeVisitor.generic_visit(self, node)
-
-def get_ast_names(astnode):
- "returns symbol Names from an AST node"
- finder = NameFinder()
- finder.generic_visit(astnode)
- return finder.names
+""" +utility functions for asteval + + Matthew Newville <newville@cars.uchicago.edu>, + The University of Chicago +""" +from __future__ import division, print_function +import re +import ast +from sys import exc_info + +RESERVED_WORDS = ('and', 'as', 'assert', 'break', 'class', 'continue', + 'def', 'del', 'elif', 'else', 'except', 'exec', + 'finally', 'for', 'from', 'global', 'if', 'import', + 'in', 'is', 'lambda', 'not', 'or', 'pass', 'print', + 'raise', 'return', 'try', 'while', 'with', 'True', + 'False', 'None', 'eval', 'execfile', '__import__', + '__package__') + +NAME_MATCH = re.compile(r"[a-zA-Z_][a-zA-Z0-9_]*$").match + +UNSAFE_ATTRS = ('__subclasses__', '__bases__', '__globals__', '__code__', + '__closure__', '__func__', '__self__', '__module__', + '__dict__', '__class__', '__call__', '__get__', + '__getattribute__', '__subclasshook__', '__new__', + '__init__', 'func_globals', 'func_code', 'func_closure', + 'im_class', 'im_func', 'im_self', 'gi_code', 'gi_frame', + '__asteval__') + +# inherit these from python's __builtins__ +FROM_PY = ('ArithmeticError', 'AssertionError', 'AttributeError', + 'BaseException', 'BufferError', 'BytesWarning', + 'DeprecationWarning', 'EOFError', 'EnvironmentError', + 'Exception', 'False', 'FloatingPointError', 'GeneratorExit', + 'IOError', 'ImportError', 'ImportWarning', 'IndentationError', + 'IndexError', 'KeyError', 'KeyboardInterrupt', 'LookupError', + 'MemoryError', 'NameError', 'None', + 'NotImplementedError', 'OSError', 'OverflowError', + 'ReferenceError', 'RuntimeError', 'RuntimeWarning', + 'StopIteration', 'SyntaxError', 'SyntaxWarning', 'SystemError', + 'SystemExit', 'True', 'TypeError', 'UnboundLocalError', + 'UnicodeDecodeError', 'UnicodeEncodeError', 'UnicodeError', + 'UnicodeTranslateError', 'UnicodeWarning', 'ValueError', + 'Warning', 'ZeroDivisionError', 'abs', 'all', 'any', 'bin', + 'bool', 'bytearray', 'bytes', 'chr', 'complex', 'dict', 'dir', + 'divmod', 'enumerate', 'filter', 'float', 'format', 'frozenset', + 'hash', 'hex', 'id', 'int', 'isinstance', 'len', 'list', 'map', + 'max', 'min', 'oct', 'ord', 'pow', 'range', 'repr', + 'reversed', 'round', 'set', 'slice', 'sorted', 'str', 'sum', + 'tuple', 'type', 'zip') + +# inherit these from python's math +FROM_MATH = ('acos', 'acosh', 'asin', 'asinh', 'atan', 'atan2', 'atanh', + 'ceil', 'copysign', 'cos', 'cosh', 'degrees', 'e', 'exp', + 'fabs', 'factorial', 'floor', 'fmod', 'frexp', 'fsum', + 'hypot', 'isinf', 'isnan', 'ldexp', 'log', 'log10', 'log1p', + 'modf', 'pi', 'pow', 'radians', 'sin', 'sinh', 'sqrt', 'tan', + 'tanh', 'trunc') + +FROM_NUMPY = ('Inf', 'NAN', 'abs', 'add', 'alen', 'all', 'amax', 'amin', + 'angle', 'any', 'append', 'arange', 'arccos', 'arccosh', + 'arcsin', 'arcsinh', 'arctan', 'arctan2', 'arctanh', + 'argmax', 'argmin', 'argsort', 'argwhere', 'around', 'array', + 'array2string', 'asanyarray', 'asarray', 'asarray_chkfinite', + 'ascontiguousarray', 'asfarray', 'asfortranarray', + 'asmatrix', 'asscalar', 'atleast_1d', 'atleast_2d', + 'atleast_3d', 'average', 'bartlett', 'base_repr', + 'bitwise_and', 'bitwise_not', 'bitwise_or', 'bitwise_xor', + 'blackman', 'bool', 'broadcast', 'broadcast_arrays', 'byte', + 'c_', 'cdouble', 'ceil', 'cfloat', 'chararray', 'choose', + 'clip', 'clongdouble', 'clongfloat', 'column_stack', + 'common_type', 'complex', 'complex128', 'complex64', + 'complex_', 'complexfloating', 'compress', 'concatenate', + 'conjugate', 'convolve', 'copy', 'copysign', 'corrcoef', + 'correlate', 'cos', 'cosh', 'cov', 'cross', 'csingle', + 'cumprod', 'cumsum', 'datetime_data', 'deg2rad', 'degrees', + 'delete', 'diag', 'diag_indices', 'diag_indices_from', + 'diagflat', 'diagonal', 'diff', 'digitize', 'divide', 'dot', + 'double', 'dsplit', 'dstack', 'dtype', 'e', 'ediff1d', + 'empty', 'empty_like', 'equal', 'exp', 'exp2', 'expand_dims', + 'expm1', 'extract', 'eye', 'fabs', 'fill_diagonal', 'finfo', + 'fix', 'flatiter', 'flatnonzero', 'fliplr', 'flipud', + 'float', 'float32', 'float64', 'float_', 'floating', 'floor', + 'floor_divide', 'fmax', 'fmin', 'fmod', 'format_parser', + 'frexp', 'frombuffer', 'fromfile', 'fromfunction', + 'fromiter', 'frompyfunc', 'fromregex', 'fromstring', 'fv', + 'genfromtxt', 'getbufsize', 'geterr', 'gradient', 'greater', + 'greater_equal', 'hamming', 'hanning', 'histogram', + 'histogram2d', 'histogramdd', 'hsplit', 'hstack', 'hypot', + 'i0', 'identity', 'iinfo', 'imag', 'in1d', 'index_exp', + 'indices', 'inexact', 'inf', 'info', 'infty', 'inner', + 'insert', 'int', 'int0', 'int16', 'int32', 'int64', 'int8', + 'int_', 'int_asbuffer', 'intc', 'integer', 'interp', + 'intersect1d', 'intp', 'invert', 'ipmt', 'irr', 'iscomplex', + 'iscomplexobj', 'isfinite', 'isfortran', 'isinf', 'isnan', + 'isneginf', 'isposinf', 'isreal', 'isrealobj', 'isscalar', + 'issctype', 'iterable', 'ix_', 'kaiser', 'kron', 'ldexp', + 'left_shift', 'less', 'less_equal', 'linspace', + 'little_endian', 'load', 'loads', 'loadtxt', 'log', 'log10', + 'log1p', 'log2', 'logaddexp', 'logaddexp2', 'logical_and', + 'logical_not', 'logical_or', 'logical_xor', 'logspace', + 'long', 'longcomplex', 'longdouble', 'longfloat', 'longlong', + 'mafromtxt', 'mask_indices', 'mat', 'matrix', 'max', + 'maximum', 'maximum_sctype', 'may_share_memory', 'mean', + 'median', 'memmap', 'meshgrid', 'mgrid', 'min', 'minimum', + 'mintypecode', 'mirr', 'mod', 'modf', 'msort', 'multiply', + 'nan', 'nan_to_num', 'nanargmax', 'nanargmin', 'nanmax', + 'nanmin', 'nansum', 'ndarray', 'ndenumerate', 'ndfromtxt', + 'ndim', 'ndindex', 'negative', 'newaxis', 'nextafter', + 'nonzero', 'not_equal', 'nper', 'npv', 'number', + 'obj2sctype', 'ogrid', 'ones', 'ones_like', 'outer', + 'packbits', 'percentile', 'pi', 'piecewise', 'place', 'pmt', + 'poly', 'poly1d', 'polyadd', 'polyder', 'polydiv', 'polyfit', + 'polyint', 'polymul', 'polysub', 'polyval', 'power', 'ppmt', + 'prod', 'product', 'ptp', 'put', 'putmask', 'pv', 'r_', + 'rad2deg', 'radians', 'rank', 'rate', 'ravel', 'real', + 'real_if_close', 'reciprocal', 'record', 'remainder', + 'repeat', 'reshape', 'resize', 'restoredot', 'right_shift', + 'rint', 'roll', 'rollaxis', 'roots', 'rot90', 'round', + 'round_', 'row_stack', 's_', 'sctype2char', 'searchsorted', + 'select', 'setbufsize', 'setdiff1d', 'seterr', 'setxor1d', + 'shape', 'short', 'sign', 'signbit', 'signedinteger', 'sin', + 'sinc', 'single', 'singlecomplex', 'sinh', 'size', + 'sometrue', 'sort', 'sort_complex', 'spacing', 'split', + 'sqrt', 'square', 'squeeze', 'std', 'str', 'str_', + 'subtract', 'sum', 'swapaxes', 'take', 'tan', 'tanh', + 'tensordot', 'tile', 'trace', 'transpose', 'trapz', 'tri', + 'tril', 'tril_indices', 'tril_indices_from', 'trim_zeros', + 'triu', 'triu_indices', 'triu_indices_from', 'true_divide', + 'trunc', 'ubyte', 'uint', 'uint0', 'uint16', 'uint32', + 'uint64', 'uint8', 'uintc', 'uintp', 'ulonglong', 'union1d', + 'unique', 'unravel_index', 'unsignedinteger', 'unwrap', + 'ushort', 'vander', 'var', 'vdot', 'vectorize', 'vsplit', + 'vstack', 'where', 'who', 'zeros', 'zeros_like') + +NUMPY_RENAMES = {'ln': 'log', 'asin': 'arcsin', 'acos': 'arccos', + 'atan': 'arctan', 'atan2': 'arctan2', 'atanh': + 'arctanh', 'acosh': 'arccosh', 'asinh': 'arcsinh'} + +def _open(filename, mode='r', buffering=0): + """read only version of open()""" + umode = 'r' + if mode == 'rb': + umode = 'rb' + return open(filename, umode, buffering) + +LOCALFUNCS = {'open': _open} + +OPERATORS = {ast.Is: lambda a, b: a is b, + ast.IsNot: lambda a, b: a is not b, + ast.In: lambda a, b: a in b, + ast.NotIn: lambda a, b: a not in b, + ast.Add: lambda a, b: a + b, + ast.BitAnd: lambda a, b: a & b, + ast.BitOr: lambda a, b: a | b, + ast.BitXor: lambda a, b: a ^ b, + ast.Div: lambda a, b: a / b, + ast.FloorDiv: lambda a, b: a // b, + ast.LShift: lambda a, b: a << b, + ast.RShift: lambda a, b: a >> b, + ast.Mult: lambda a, b: a * b, + ast.Pow: lambda a, b: a ** b, + ast.Sub: lambda a, b: a - b, + ast.Mod: lambda a, b: a % b, + ast.And: lambda a, b: a and b, + ast.Or: lambda a, b: a or b, + ast.Eq: lambda a, b: a == b, + ast.Gt: lambda a, b: a > b, + ast.GtE: lambda a, b: a >= b, + ast.Lt: lambda a, b: a < b, + ast.LtE: lambda a, b: a <= b, + ast.NotEq: lambda a, b: a != b, + ast.Invert: lambda a: ~a, + ast.Not: lambda a: not a, + ast.UAdd: lambda a: +a, + ast.USub: lambda a: -a} + + +def valid_symbol_name(name): + """determines whether the input symbol name is a valid name + + This checks for reserved words, and that the name matches the + regular expression ``[a-zA-Z_][a-zA-Z0-9_]`` + """ + if name in RESERVED_WORDS: + return False + return NAME_MATCH(name) is not None + + +def op2func(op): + "return function for operator nodes" + return OPERATORS[op.__class__] + + +class Empty: + """empty class""" + def __init__(self): + pass + + def __nonzero__(self): + return False + +ReturnedNone = Empty() + + +class ExceptionHolder(object): + "basic exception handler" + def __init__(self, node, exc=None, msg='', expr=None, lineno=None): + self.node = node + self.expr = expr + self.msg = msg + self.exc = exc + self.lineno = lineno + self.exc_info = exc_info() + if self.exc is None and self.exc_info[0] is not None: + self.exc = self.exc_info[0] + if self.msg is '' and self.exc_info[1] is not None: + self.msg = self.exc_info[1] + + def get_error(self): + "retrieve error data" + col_offset = -1 + if self.node is not None: + try: + col_offset = self.node.col_offset + except AttributeError: + pass + try: + exc_name = self.exc.__name__ + except AttributeError: + exc_name = str(self.exc) + if exc_name in (None, 'None'): + exc_name = 'UnknownError' + + out = [" %s" % self.expr] + if col_offset > 0: + out.append(" %s^^^" % ((col_offset)*' ')) + out.append(str(self.msg)) + return (exc_name, '\n'.join(out)) + + +class NameFinder(ast.NodeVisitor): + """find all symbol names used by a parsed node""" + def __init__(self): + self.names = [] + ast.NodeVisitor.__init__(self) + + def generic_visit(self, node): + if node.__class__.__name__ == 'Name': + if node.ctx.__class__ == ast.Load and node.id not in self.names: + self.names.append(node.id) + ast.NodeVisitor.generic_visit(self, node) + +def get_ast_names(astnode): + "returns symbol Names from an AST node" + finder = NameFinder() + finder.generic_visit(astnode) + return finder.names diff --git a/lmfit/confidence.py b/lmfit/confidence.py index d8a2934..b1bce11 100644 --- a/lmfit/confidence.py +++ b/lmfit/confidence.py @@ -1,419 +1,416 @@ -#!/usr/bin/python
-# -*- coding: utf-8 -*-
-"""
-Contains functions to calculate confidence intervals.
-"""
-from __future__ import print_function
-from warnings import warn
-import numpy as np
-from scipy.stats import f
-from scipy.optimize import brentq
-from .minimizer import MinimizerException
-
-try:
- from collections import OrderedDict
-except ImportError:
- from ordereddict import OrderedDict
-
-CONF_ERR_GEN = 'Cannot determine Confidence Intervals'
-CONF_ERR_STDERR = '%s without sensible uncertainty estimates' % CONF_ERR_GEN
-CONF_ERR_NVARS = '%s with < 2 variables' % CONF_ERR_GEN
-
-def f_compare(ndata, nparas, new_chi, best_chi, nfix=1.):
- """
- Returns the probalitiy for two given parameter sets.
- nfix is the number of fixed parameters.
- """
- nparas = nparas + nfix
- nfree = ndata - nparas
- nfix = 1.0*nfix
- dchi = new_chi / best_chi - 1.0
- return f.cdf(dchi * nfree / nfix, nfix, nfree)
-
-
-def copy_vals(params):
- """Saves the values and stderrs of params in temporay dict"""
- tmp_params = {}
- for para_key in params:
- tmp_params[para_key] = (params[para_key].value,
- params[para_key].stderr)
- return tmp_params
-
-
-def restore_vals(tmp_params, params):
- """Restores values and stderrs of params in temporay dict"""
- for para_key in params:
- params[para_key].value, params[para_key].stderr = tmp_params[para_key]
-
-
-def conf_interval(minimizer, result, p_names=None, sigmas=(0.674, 0.95, 0.997),
- trace=False, maxiter=200, verbose=False, prob_func=None):
- r"""Calculates the confidence interval for parameters
- from the given a MinimizerResult, output from minimize.
-
- The parameter for which the ci is calculated will be varied, while
- the remaining parameters are re-optimized for minimizing chi-square.
- The resulting chi-square is used to calculate the probability with
- a given statistic e.g. F-statistic. This function uses a 1d-rootfinder
- from scipy to find the values resulting in the searched confidence
- region.
-
- Parameters
- ----------
- minimizer : Minimizer
- The minimizer to use, holding objective function.
- result : MinimizerResult
- The result of running minimize().
- p_names : list, optional
- Names of the parameters for which the ci is calculated. If None,
- the ci is calculated for every parameter.
- sigmas : list, optional
- The probabilities (1-alpha) to find. Default is 1,2 and 3-sigma.
- trace : bool, optional
- Defaults to False, if true, each result of a probability calculation
- is saved along with the parameter. This can be used to plot so
- called "profile traces".
-
- Returns
- -------
- output : dict
- A dict, which contains a list of (sigma, vals)-tuples for each name.
- trace_dict : dict
- Only if trace is set true. Is a dict, the key is the parameter which
- was fixed.The values are again a dict with the names as keys, but with
- an additional key 'prob'. Each contains an array of the corresponding
- values.
-
- See also
- --------
- conf_interval2d
-
- Other Parameters
- ----------------
- maxiter : int
- Maximum of iteration to find an upper limit.
- prob_func : ``None`` or callable
- Function to calculate the probability from the optimized chi-square.
- Default (``None``) uses built-in f_compare (F test).
- verbose: bool
- print extra debuggin information. Default is ``False``.
-
-
- Examples
- --------
-
- >>> from lmfit.printfuncs import *
- >>> mini = minimize(some_func, params)
- >>> mini.leastsq()
- True
- >>> report_errors(params)
- ... #report
- >>> ci = conf_interval(mini)
- >>> report_ci(ci)
- ... #report
-
- Now with quantiles for the sigmas and using the trace.
-
- >>> ci, trace = conf_interval(mini, sigmas=(0.25, 0.5, 0.75, 0.999), trace=True)
- >>> fixed = trace['para1']['para1']
- >>> free = trace['para1']['not_para1']
- >>> prob = trace['para1']['prob']
-
- This makes it possible to plot the dependence between free and fixed.
- """
- ci = ConfidenceInterval(minimizer, result, p_names, prob_func, sigmas,
- trace, verbose, maxiter)
- output = ci.calc_all_ci()
- if trace:
- return output, ci.trace_dict
- return output
-
-
-def map_trace_to_names(trace, params):
- "maps trace to param names"
- out = {}
- allnames = list(params.keys()) + ['prob']
- for name in trace.keys():
- tmp_dict = {}
- tmp = np.array(trace[name])
- for para_name, values in zip(allnames, tmp.T):
- tmp_dict[para_name] = values
- out[name] = tmp_dict
- return out
-
-
-class ConfidenceInterval(object):
- """
- Class used to calculate the confidence interval.
- """
- def __init__(self, minimizer, result, p_names=None, prob_func=None,
- sigmas=(0.674, 0.95, 0.997), trace=False, verbose=False,
- maxiter=50):
- """
-
- """
- self.verbose = verbose
- self.minimizer = minimizer
- self.result = result
- self.params = result.params
- self.org = copy_vals(self.params)
- self.best_chi = result.chisqr
-
- if p_names is None:
- p_names = [i for i in self.params if self.params[i].vary]
-
- self.p_names = p_names
- self.fit_params = [self.params[p] for p in self.p_names]
-
- # check that there are at least 2 true variables!
- # check that all stderrs are sensible (including not None or NaN)
- nvars = 0
- for par in self.fit_params:
- if par.vary:
- nvars += 1
- try:
- if not (par.vary and par.stderr > 0.0):
- raise MinimizerException(CONF_ERR_STDERR)
- except TypeError:
- raise MinimizerException(CONF_ERR_STDERR)
- if nvars < 2:
- raise MinimizerException(CONF_ERR_NVARS)
-
- if prob_func is None or not hasattr(prob_func, '__call__'):
- self.prob_func = f_compare
- if trace:
- self.trace_dict = dict([(i, []) for i in self.p_names])
-
- self.trace = trace
- self.maxiter = maxiter
- self.min_rel_change = 1e-5
-
- self.sigmas = list(sigmas)
- self.sigmas.sort()
-
- def calc_all_ci(self):
- """
- Calculates all cis.
- """
- out = OrderedDict()
-
- for p in self.p_names:
- out[p] = (self.calc_ci(p, -1)[::-1] +
- [(0., self.params[p].value)] +
- self.calc_ci(p, 1))
- if self.trace:
- self.trace_dict = map_trace_to_names(self.trace_dict,
- self.params)
-
- return out
-
- def calc_ci(self, para, direction):
- """
- Calculate the ci for a single parameter for a single direction.
- Direction is either positive or negative 1.
- """
-
- if isinstance(para, str):
- para = self.params[para]
-
- #function used to calculate the pro
- calc_prob = lambda val, prob: self.calc_prob(para, val, prob)
- if self.trace:
- x = [i.value for i in self.params.values()]
- self.trace_dict[para.name].append(x + [0])
-
- para.vary = False
- limit, max_prob = self.find_limit(para, direction)
- start_val = para.value.copy()
- a_limit = start_val.copy()
- ret = []
- orig_warn_settings = np.geterr()
- np.seterr(all='ignore')
- for prob in self.sigmas:
- if prob > max_prob:
- ret.append((prob, direction*np.inf))
- continue
-
- try:
- val = brentq(calc_prob, a_limit,
- limit, rtol=.5e-4, args=prob)
-
- except ValueError:
- self.reset_vals()
- try:
- val = brentq(calc_prob, start_val,
- limit, rtol=.5e-4, args=prob)
- except ValueError:
- val = np.nan
-
- a_limit = val
- ret.append((prob, val))
-
- para.vary = True
- self.reset_vals()
- np.seterr(**orig_warn_settings)
- return ret
-
- def reset_vals(self):
- restore_vals(self.org, self.params)
-
- def find_limit(self, para, direction):
- """
- For given para, search a value so that prob(val) > sigmas.
- """
- if self.verbose:
- print('Calculating CI for ' + para.name)
- self.reset_vals()
-
- #starting steps:
- if para.stderr > 0 and para.stderr < abs(para.value):
- step = para.stderr
- else:
- step = max(abs(para.value) * 0.2, 0.001)
- para.vary = False
- start_val = para.value
-
- old_prob = 0
- limit = start_val
- i = 0
-
- while old_prob < max(self.sigmas):
- i = i + 1
- limit += step * direction
-
- new_prob = self.calc_prob(para, limit)
- rel_change = (new_prob - old_prob) / max(new_prob, old_prob, 1.e-12)
- old_prob = new_prob
-
- # Check convergence.
- if i > self.maxiter:
- errmsg = "Warning, maxiter={0} reached".format(self.maxiter)
- errmsg += "and prob({0}={1}) = {2} < max(sigmas).".format(para.name, limit, new_prob)
- warn(errmsg)
- break
-
- if rel_change < self.min_rel_change:
- errmsg = "Warning, rel_change={0} < 0.01 ".format(rel_change)
- errmsg += " at iteration {3} and prob({0}={1}) = {2} < max(sigmas).".format(para.name, limit, new_prob, i)
- warn(errmsg)
- break
-
- self.reset_vals()
-
- return limit, new_prob
-
- def calc_prob(self, para, val, offset=0., restore=False):
- """Returns the probability for given Value."""
- if restore:
- restore_vals(self.org, self.params)
- para.value = val
- save_para = self.params[para.name]
- self.params[para.name] = para
- self.minimizer.prepare_fit(self.params)
- out = self.minimizer.leastsq()
- prob = self.prob_func(out.ndata, out.ndata - out.nfree,
- out.chisqr, self.best_chi)
-
- if self.trace:
- x = [i.value for i in out.params.values()]
- self.trace_dict[para.name].append(x + [prob])
- self.params[para.name] = save_para
- return prob - offset
-
-def conf_interval2d(minimizer, result, x_name, y_name, nx=10, ny=10,
- limits=None, prob_func=None):
- r"""Calculates confidence regions for two fixed parameters.
-
- The method is explained in *conf_interval*: here we are fixing
- two parameters.
-
- Parameters
- ----------
- minimizer : Minimizer
- The minimizer to use, holding objective function.
- result : MinimizerResult
- The result of running minimize().
- x_name : string
- The name of the parameter which will be the x direction.
- y_name : string
- The name of the parameter which will be the y direction.
- nx, ny : ints, optional
- Number of points.
- limits : tuple: optional
- Should have the form ((x_upper, x_lower),(y_upper, y_lower)). If not
- given, the default is 5 std-errs in each direction.
-
- Returns
- -------
- x : (nx)-array
- x-coordinates
- y : (ny)-array
- y-coordinates
- grid : (nx,ny)-array
- grid contains the calculated probabilities.
-
- Examples
- --------
-
- >>> mini = Minimizer(some_func, params)
- >>> result = mini.leastsq()
- >>> x, y, gr = conf_interval2d(mini, result, 'para1','para2')
- >>> plt.contour(x,y,gr)
-
- Other Parameters
- ----------------
- prob_func : ``None`` or callable
- Function to calculate the probability from the optimized chi-square.
- Default (``None``) uses built-in f_compare (F test).
- """
- # used to detect that .leastsq() has run!
- params = result.params
-
- best_chi = result.chisqr
- org = copy_vals(result.params)
-
- if prob_func is None or not hasattr(prob_func, '__call__'):
- prob_func = f_compare
-
- x = params[x_name]
- y = params[y_name]
-
- if limits is None:
- (x_upper, x_lower) = (x.value + 5 * x.stderr, x.value - 5
- * x.stderr)
- (y_upper, y_lower) = (y.value + 5 * y.stderr, y.value - 5
- * y.stderr)
- elif len(limits) == 2:
- (x_upper, x_lower) = limits[0]
- (y_upper, y_lower) = limits[1]
-
- x_points = np.linspace(x_lower, x_upper, nx)
- y_points = np.linspace(y_lower, y_upper, ny)
- grid = np.dstack(np.meshgrid(x_points, y_points))
-
- x.vary = False
- y.vary = False
-
- def calc_prob(vals, restore=False):
- if restore:
- restore_vals(org, result.params)
- x.value = vals[0]
- y.value = vals[1]
- save_x = result.params[x.name]
- save_y = result.params[y.name]
- result.params[x.name] = x
- result.params[y.name] = y
- minimizer.prepare_fit(params=result.params)
- out = minimizer.leastsq()
- prob = prob_func(out.ndata, out.ndata - out.nfree, out.chisqr,
- best_chi, nfix=2.)
- result.params[x.name] = save_x
- result.params[y.name] = save_y
- return prob
-
- out = x_points, y_points, np.apply_along_axis(calc_prob, -1, grid)
-
- x.vary, y.vary = True, True
- restore_vals(org, result.params)
- result.chisqr = best_chi
- return out
+#!/usr/bin/python +# -*- coding: utf-8 -*- +""" +Contains functions to calculate confidence intervals. +""" +from __future__ import print_function +from warnings import warn +import numpy as np +from scipy.stats import f +from scipy.optimize import brentq +from .minimizer import MinimizerException + +try: + from collections import OrderedDict +except ImportError: + from ordereddict import OrderedDict + +CONF_ERR_GEN = 'Cannot determine Confidence Intervals' +CONF_ERR_STDERR = '%s without sensible uncertainty estimates' % CONF_ERR_GEN +CONF_ERR_NVARS = '%s with < 2 variables' % CONF_ERR_GEN + +def f_compare(ndata, nparas, new_chi, best_chi, nfix=1.): + """ + Returns the probalitiy for two given parameter sets. + nfix is the number of fixed parameters. + """ + nparas = nparas + nfix + nfree = ndata - nparas + nfix = 1.0*nfix + dchi = new_chi / best_chi - 1.0 + return f.cdf(dchi * nfree / nfix, nfix, nfree) + + +def copy_vals(params): + """Saves the values and stderrs of params in temporay dict""" + tmp_params = {} + for para_key in params: + tmp_params[para_key] = (params[para_key].value, + params[para_key].stderr) + return tmp_params + + +def restore_vals(tmp_params, params): + """Restores values and stderrs of params in temporay dict""" + for para_key in params: + params[para_key].value, params[para_key].stderr = tmp_params[para_key] + + +def conf_interval(minimizer, result, p_names=None, sigmas=(0.674, 0.95, 0.997), + trace=False, maxiter=200, verbose=False, prob_func=None): + """Calculates the confidence interval for parameters + from the given a MinimizerResult, output from minimize. + + The parameter for which the ci is calculated will be varied, while + the remaining parameters are re-optimized for minimizing chi-square. + The resulting chi-square is used to calculate the probability with + a given statistic e.g. F-statistic. This function uses a 1d-rootfinder + from scipy to find the values resulting in the searched confidence + region. + + Parameters + ---------- + minimizer : Minimizer + The minimizer to use, holding objective function. + result : MinimizerResult + The result of running minimize(). + p_names : list, optional + Names of the parameters for which the ci is calculated. If None, + the ci is calculated for every parameter. + sigmas : list, optional + The probabilities (1-alpha) to find. Default is 1,2 and 3-sigma. + trace : bool, optional + Defaults to False, if true, each result of a probability calculation + is saved along with the parameter. This can be used to plot so + called "profile traces". + maxiter : int + Maximum of iteration to find an upper limit. Default is 200. + prob_func : ``None`` or callable + Function to calculate the probability from the optimized chi-square. + Default (``None``) uses built-in f_compare (F test). + verbose: bool + print extra debuging information. Default is ``False``. + + + Returns + ------- + output : dict + A dict, which contains a list of (sigma, vals)-tuples for each name. + trace_dict : dict + Only if trace is set true. Is a dict, the key is the parameter which + was fixed. The values are again a dict with the names as keys, but with + an additional key 'prob'. Each contains an array of the corresponding + values. + + See also + -------- + conf_interval2d + + Examples + -------- + + >>> from lmfit.printfuncs import * + >>> mini = minimize(some_func, params) + >>> mini.leastsq() + True + >>> report_errors(params) + ... #report + >>> ci = conf_interval(mini) + >>> report_ci(ci) + ... #report + + Now with quantiles for the sigmas and using the trace. + + >>> ci, trace = conf_interval(mini, sigmas=(0.25, 0.5, 0.75, 0.999), trace=True) + >>> fixed = trace['para1']['para1'] + >>> free = trace['para1']['not_para1'] + >>> prob = trace['para1']['prob'] + + This makes it possible to plot the dependence between free and fixed. + + """ + ci = ConfidenceInterval(minimizer, result, p_names, prob_func, sigmas, + trace, verbose, maxiter) + output = ci.calc_all_ci() + if trace: + return output, ci.trace_dict + return output + + +def map_trace_to_names(trace, params): + "maps trace to param names" + out = {} + allnames = list(params.keys()) + ['prob'] + for name in trace.keys(): + tmp_dict = {} + tmp = np.array(trace[name]) + for para_name, values in zip(allnames, tmp.T): + tmp_dict[para_name] = values + out[name] = tmp_dict + return out + + +class ConfidenceInterval(object): + """ + Class used to calculate the confidence interval. + """ + def __init__(self, minimizer, result, p_names=None, prob_func=None, + sigmas=(0.674, 0.95, 0.997), trace=False, verbose=False, + maxiter=50): + """ + + """ + self.verbose = verbose + self.minimizer = minimizer + self.result = result + self.params = result.params + self.org = copy_vals(self.params) + self.best_chi = result.chisqr + + if p_names is None: + p_names = [i for i in self.params if self.params[i].vary] + + self.p_names = p_names + self.fit_params = [self.params[p] for p in self.p_names] + + # check that there are at least 2 true variables! + # check that all stderrs are sensible (including not None or NaN) + nvars = 0 + for par in self.fit_params: + if par.vary: + nvars += 1 + try: + if not (par.vary and par.stderr > 0.0): + raise MinimizerException(CONF_ERR_STDERR) + except TypeError: + raise MinimizerException(CONF_ERR_STDERR) + if nvars < 2: + raise MinimizerException(CONF_ERR_NVARS) + + if prob_func is None or not hasattr(prob_func, '__call__'): + self.prob_func = f_compare + if trace: + self.trace_dict = dict([(i, []) for i in self.p_names]) + + self.trace = trace + self.maxiter = maxiter + self.min_rel_change = 1e-5 + + self.sigmas = list(sigmas) + self.sigmas.sort() + + def calc_all_ci(self): + """ + Calculates all cis. + """ + out = OrderedDict() + + for p in self.p_names: + out[p] = (self.calc_ci(p, -1)[::-1] + + [(0., self.params[p].value)] + + self.calc_ci(p, 1)) + if self.trace: + self.trace_dict = map_trace_to_names(self.trace_dict, + self.params) + + return out + + def calc_ci(self, para, direction): + """ + Calculate the ci for a single parameter for a single direction. + Direction is either positive or negative 1. + """ + + if isinstance(para, str): + para = self.params[para] + + #function used to calculate the pro + calc_prob = lambda val, prob: self.calc_prob(para, val, prob) + if self.trace: + x = [i.value for i in self.params.values()] + self.trace_dict[para.name].append(x + [0]) + + para.vary = False + limit, max_prob = self.find_limit(para, direction) + start_val = a_limit = float(para.value) + ret = [] + orig_warn_settings = np.geterr() + np.seterr(all='ignore') + for prob in self.sigmas: + if prob > max_prob: + ret.append((prob, direction*np.inf)) + continue + + try: + val = brentq(calc_prob, a_limit, + limit, rtol=.5e-4, args=prob) + + except ValueError: + self.reset_vals() + try: + val = brentq(calc_prob, start_val, + limit, rtol=.5e-4, args=prob) + except ValueError: + val = np.nan + + a_limit = val + ret.append((prob, val)) + + para.vary = True + self.reset_vals() + np.seterr(**orig_warn_settings) + return ret + + def reset_vals(self): + restore_vals(self.org, self.params) + + def find_limit(self, para, direction): + """ + For given para, search a value so that prob(val) > sigmas. + """ + if self.verbose: + print('Calculating CI for ' + para.name) + self.reset_vals() + + #starting steps: + if para.stderr > 0 and para.stderr < abs(para.value): + step = para.stderr + else: + step = max(abs(para.value) * 0.2, 0.001) + para.vary = False + start_val = para.value + + old_prob = 0 + limit = start_val + i = 0 + + while old_prob < max(self.sigmas): + i = i + 1 + limit += step * direction + + new_prob = self.calc_prob(para, limit) + rel_change = (new_prob - old_prob) / max(new_prob, old_prob, 1.e-12) + old_prob = new_prob + + # Check convergence. + if i > self.maxiter: + errmsg = "Warning, maxiter={0} reached".format(self.maxiter) + errmsg += "and prob({0}={1}) = {2} < max(sigmas).".format(para.name, limit, new_prob) + warn(errmsg) + break + + if rel_change < self.min_rel_change: + errmsg = "Warning, rel_change={0} < 0.01 ".format(rel_change) + errmsg += " at iteration {3} and prob({0}={1}) = {2} < max(sigmas).".format(para.name, limit, new_prob, i) + warn(errmsg) + break + + self.reset_vals() + + return limit, new_prob + + def calc_prob(self, para, val, offset=0., restore=False): + """Returns the probability for given Value.""" + if restore: + restore_vals(self.org, self.params) + para.value = val + save_para = self.params[para.name] + self.params[para.name] = para + self.minimizer.prepare_fit(self.params) + out = self.minimizer.leastsq() + prob = self.prob_func(out.ndata, out.ndata - out.nfree, + out.chisqr, self.best_chi) + + if self.trace: + x = [i.value for i in out.params.values()] + self.trace_dict[para.name].append(x + [prob]) + self.params[para.name] = save_para + return prob - offset + +def conf_interval2d(minimizer, result, x_name, y_name, nx=10, ny=10, + limits=None, prob_func=None): + r"""Calculates confidence regions for two fixed parameters. + + The method is explained in *conf_interval*: here we are fixing + two parameters. + + Parameters + ---------- + minimizer : Minimizer + The minimizer to use, holding objective function. + result : MinimizerResult + The result of running minimize(). + x_name : string + The name of the parameter which will be the x direction. + y_name : string + The name of the parameter which will be the y direction. + nx, ny : ints, optional + Number of points. + limits : tuple: optional + Should have the form ((x_upper, x_lower),(y_upper, y_lower)). If not + given, the default is 5 std-errs in each direction. + + Returns + ------- + x : (nx)-array + x-coordinates + y : (ny)-array + y-coordinates + grid : (nx,ny)-array + grid contains the calculated probabilities. + + Examples + -------- + + >>> mini = Minimizer(some_func, params) + >>> result = mini.leastsq() + >>> x, y, gr = conf_interval2d(mini, result, 'para1','para2') + >>> plt.contour(x,y,gr) + + Other Parameters + ---------------- + prob_func : ``None`` or callable + Function to calculate the probability from the optimized chi-square. + Default (``None``) uses built-in f_compare (F test). + """ + # used to detect that .leastsq() has run! + params = result.params + + best_chi = result.chisqr + org = copy_vals(result.params) + + if prob_func is None or not hasattr(prob_func, '__call__'): + prob_func = f_compare + + x = params[x_name] + y = params[y_name] + + if limits is None: + (x_upper, x_lower) = (x.value + 5 * x.stderr, x.value - 5 + * x.stderr) + (y_upper, y_lower) = (y.value + 5 * y.stderr, y.value - 5 + * y.stderr) + elif len(limits) == 2: + (x_upper, x_lower) = limits[0] + (y_upper, y_lower) = limits[1] + + x_points = np.linspace(x_lower, x_upper, nx) + y_points = np.linspace(y_lower, y_upper, ny) + grid = np.dstack(np.meshgrid(x_points, y_points)) + + x.vary = False + y.vary = False + + def calc_prob(vals, restore=False): + if restore: + restore_vals(org, result.params) + x.value = vals[0] + y.value = vals[1] + save_x = result.params[x.name] + save_y = result.params[y.name] + result.params[x.name] = x + result.params[y.name] = y + minimizer.prepare_fit(params=result.params) + out = minimizer.leastsq() + prob = prob_func(out.ndata, out.ndata - out.nfree, out.chisqr, + best_chi, nfix=2.) + result.params[x.name] = save_x + result.params[y.name] = save_y + return prob + + out = x_points, y_points, np.apply_along_axis(calc_prob, -1, grid) + + x.vary, y.vary = True, True + restore_vals(org, result.params) + result.chisqr = best_chi + return out diff --git a/lmfit/lineshapes.py b/lmfit/lineshapes.py index a71bb3f..6c55279 100644 --- a/lmfit/lineshapes.py +++ b/lmfit/lineshapes.py @@ -1,286 +1,286 @@ -#!/usr/bin/env python
-"""
-basic model line shapes and distribution functions
-"""
-from __future__ import division
-from numpy import (pi, log, exp, sqrt, arctan, cos, where)
-from numpy.testing import assert_allclose
-
-from scipy.special import gamma as gamfcn
-from scipy.special import gammaln, erf, erfc, wofz
-
-log2 = log(2)
-s2pi = sqrt(2*pi)
-spi = sqrt(pi)
-s2 = sqrt(2.0)
-
-functions = ('gaussian', 'lorentzian', 'voigt', 'pvoigt', 'moffat', 'pearson7',
- 'breit_wigner', 'damped_oscillator', 'logistic', 'lognormal',
- 'students_t', 'expgaussian', 'donaich', 'skewed_gaussian',
- 'skewed_voigt', 'step', 'rectangle', 'erf', 'erfc', 'wofz',
- 'gamma', 'gammaln', 'exponential', 'powerlaw', 'linear',
- 'parabolic')
-
-def gaussian(x, amplitude=1.0, center=0.0, sigma=1.0):
- """1 dimensional gaussian:
- gaussian(x, amplitude, center, sigma)
- """
- return (amplitude/(s2pi*sigma)) * exp(-(1.0*x-center)**2 /(2*sigma**2))
-
-def lorentzian(x, amplitude=1.0, center=0.0, sigma=1.0):
- """1 dimensional lorentzian
- lorentzian(x, amplitude, center, sigma)
- """
- return (amplitude/(1 + ((1.0*x-center)/sigma)**2) ) / (pi*sigma)
-
-def voigt(x, amplitude=1.0, center=0.0, sigma=1.0, gamma=None):
- """1 dimensional voigt function.
- see http://en.wikipedia.org/wiki/Voigt_profile
- """
- if gamma is None:
- gamma = sigma
- z = (x-center + 1j*gamma)/ (sigma*s2)
- return amplitude*wofz(z).real / (sigma*s2pi)
-
-def pvoigt(x, amplitude=1.0, center=0.0, sigma=1.0, fraction=0.5):
- """1 dimensional pseudo-voigt:
- pvoigt(x, amplitude, center, sigma, fraction)
- = amplitude*(1-fraction)*gaussion(x, center, sigma_g) +
- amplitude*fraction*lorentzian(x, center, sigma)
-
- where sigma_g (the sigma for the Gaussian component) is
-
- sigma_g = sigma / sqrt(2*log(2)) ~= sigma / 1.17741
-
- so that the Gaussian and Lorentzian components have the
- same FWHM of 2*sigma.
- """
- sigma_g = sigma / sqrt(2*log2)
- return ((1-fraction)*gaussian(x, amplitude, center, sigma_g) +
- fraction*lorentzian(x, amplitude, center, sigma))
-
-def moffat(x, amplitude=1, center=0., sigma=1, beta=1.):
- """ 1 dimensional moffat function:
-
- moffat(amplitude, center, sigma, beta) = amplitude / (((x - center)/sigma)**2 + 1)**beta
- """
- return amplitude / (((x - center)/sigma)**2 + 1)**beta
-
-def pearson7(x, amplitude=1.0, center=0.0, sigma=1.0, expon=1.0):
- """pearson7 lineshape, using the wikipedia definition:
-
- pearson7(x, center, sigma, expon) =
- amplitude*(1+arg**2)**(-expon)/(sigma*beta(expon-0.5, 0.5))
-
- where arg = (x-center)/sigma
- and beta() is the beta function.
- """
- arg = (x-center)/sigma
- scale = amplitude * gamfcn(expon)/(gamfcn(0.5)*gamfcn(expon-0.5))
- return scale*(1+arg**2)**(-expon)/sigma
-
-def breit_wigner(x, amplitude=1.0, center=0.0, sigma=1.0, q=1.0):
- """Breit-Wigner-Fano lineshape:
- = amplitude*(q*sigma/2 + x - center)**2 / ( (sigma/2)**2 + (x - center)**2 )
- """
- gam = sigma/2.0
- return amplitude*(q*gam + x - center)**2 / (gam*gam + (x-center)**2)
-
-def damped_oscillator(x, amplitude=1.0, center=1., sigma=0.1):
- """amplitude for a damped harmonic oscillator
- amplitude/sqrt( (1.0 - (x/center)**2)**2 + (2*sigma*x/center)**2))
- """
- center = max(1.e-9, abs(center))
- return (amplitude/sqrt( (1.0 - (x/center)**2)**2 + (2*sigma*x/center)**2))
-
-def logistic(x, amplitude=1., center=0., sigma=1.):
- """Logistic lineshape (yet another sigmoidal curve)
- = amplitude*(1. - 1. / (1 + exp((x-center)/sigma)))
- """
- return amplitude*(1. - 1./(1. + exp((x-center)/sigma)))
-
-def lognormal(x, amplitude=1.0, center=0., sigma=1):
- """log-normal function
- lognormal(x, center, sigma)
- = (amplitude/x) * exp(-(ln(x) - center)/ (2* sigma**2))
- """
- x[where(x<=1.e-19)] = 1.e-19
- return (amplitude/(x*sigma*s2pi)) * exp(-(log(x)-center)**2/ (2* sigma**2))
-
-def students_t(x, amplitude=1.0, center=0.0, sigma=1.0):
- """Student's t distribution:
- gamma((sigma+1)/2) (1 + (x-center)**2/sigma)^(-(sigma+1)/2)
- = -------------------------
- sqrt(sigma*pi)gamma(sigma/2)
-
- """
- s1 = (sigma+1)/2.0
- denom = (sqrt(sigma*pi)*gamfcn(sigma/2))
- return amplitude*(1 + (x-center)**2/sigma)**(-s1) * gamfcn(s1) / denom
-
-
-def expgaussian(x, amplitude=1, center=0, sigma=1.0, gamma=1.0):
- """exponentially modified Gaussian
-
- = (gamma/2) exp[center*gamma + (gamma*sigma)**2/2 - gamma*x] *
- erfc[(center + gamma*sigma**2 - x)/(sqrt(2)*sigma)]
-
- http://en.wikipedia.org/wiki/Exponentially_modified_Gaussian_distribution
- """
- gss = gamma*sigma*sigma
- arg1 = gamma*(center +gss/2.0 - x)
- arg2 = (center + gss - x)/(s2*sigma)
- return amplitude*(gamma/2) * exp(arg1) * erfc(arg2)
-
-def donaich(x, amplitude=1.0, center=0, sigma=1.0, gamma=0.0):
- """Doniach Sunjic asymmetric lineshape, used for photo-emission
-
- = amplitude* cos(pi*gamma/2 + (1-gamma) arctan((x-center)/sigma) /
- (sigma**2 + (x-center)**2)**[(1-gamma)/2]
-
- see http://www.casaxps.com/help_manual/line_shapes.htm
- """
- arg = (x-center)/sigma
- gm1 = (1.0 - gamma)
- scale = amplitude/(sigma**gm1)
- return scale*cos(pi*gamma/2 + gm1*arctan(arg))/(1 + arg**2)**(gm1/2)
-
-def skewed_gaussian(x, amplitude=1.0, center=0.0, sigma=1.0, gamma=0.0):
- """Gaussian, skewed with error function, equal to
-
- gaussian(x, center, sigma)*(1+erf(beta*(x-center)))
-
- with beta = gamma/(sigma*sqrt(2))
-
- with gamma < 0: tail to low value of centroid
- gamma > 0: tail to high value of centroid
-
- see http://en.wikipedia.org/wiki/Skew_normal_distribution
- """
- asym = 1 + erf(gamma*(x-center)/(s2*sigma))
- return asym * gaussian(x, amplitude, center, sigma)
-
-def skewed_voigt(x, amplitude=1.0, center=0.0, sigma=1.0, gamma=None, skew=0.0):
- """Skewed Voigt lineshape, skewed with error function
- useful for ad-hoc Compton scatter profile
-
- with beta = skew/(sigma*sqrt(2))
- = voigt(x, center, sigma, gamma)*(1+erf(beta*(x-center)))
-
- skew < 0: tail to low value of centroid
- skew > 0: tail to high value of centroid
-
- see http://en.wikipedia.org/wiki/Skew_normal_distribution
- """
- beta = skew/(s2*sigma)
- asym = 1 + erf(beta*(x-center))
- return asym * voigt(x, amplitude, center, sigma, gamma=gamma)
-
-def step(x, amplitude=1.0, center=0.0, sigma=1.0, form='linear'):
- """step function:
- starts at 0.0, ends at amplitude, with half-max at center, and
- rising with form:
- 'linear' (default) = amplitude * min(1, max(0, arg))
- 'atan', 'arctan' = amplitude * (0.5 + atan(arg)/pi)
- 'erf' = amplitude * (1 + erf(arg))/2.0
- 'logistic' = amplitude * [1 - 1/(1 + exp(arg))]
-
- where arg = (x - center)/sigma
- """
- if abs(sigma) < 1.e-13:
- sigma = 1.e-13
-
- out = (x - center)/sigma
- if form == 'erf':
- out = 0.5*(1 + erf(out))
- elif form.startswith('logi'):
- out = (1. - 1./(1. + exp(out)))
- elif form in ('atan', 'arctan'):
- out = 0.5 + arctan(out)/pi
- else:
- out[where(out < 0)] = 0.0
- out[where(out > 1)] = 1.0
- return amplitude*out
-
-def rectangle(x, amplitude=1.0, center1=0.0, sigma1=1.0,
- center2=1.0, sigma2=1.0, form='linear'):
- """rectangle function: step up, step down (see step function)
- starts at 0.0, rises to amplitude (at center1 with width sigma1)
- then drops to 0.0 (at center2 with width sigma2) with form:
- 'linear' (default) = ramp_up + ramp_down
- 'atan', 'arctan' = amplitude*(atan(arg1) + atan(arg2))/pi
- 'erf' = amplitude*(erf(arg1) + erf(arg2))/2.
- 'logisitic' = amplitude*[1 - 1/(1 + exp(arg1)) - 1/(1+exp(arg2))]
-
- where arg1 = (x - center1)/sigma1
- and arg2 = -(x - center2)/sigma2
- """
- if abs(sigma1) < 1.e-13:
- sigma1 = 1.e-13
- if abs(sigma2) < 1.e-13:
- sigma2 = 1.e-13
-
- arg1 = (x - center1)/sigma1
- arg2 = (center2 - x)/sigma2
- if form == 'erf':
- out = 0.5*(erf(arg1) + erf(arg2))
- elif form.startswith('logi'):
- out = (1. - 1./(1. + exp(arg1)) - 1./(1. + exp(arg2)))
- elif form in ('atan', 'arctan'):
- out = (arctan(arg1) + arctan(arg2))/pi
- else:
- arg1[where(arg1 < 0)] = 0.0
- arg1[where(arg1 > 1)] = 1.0
- arg2[where(arg2 > 0)] = 0.0
- arg2[where(arg2 < -1)] = -1.0
- out = arg1 + arg2
- return amplitude*out
-
-def _erf(x):
- """error function. = 2/sqrt(pi)*integral(exp(-t**2), t=[0, z])"""
- return erf(x)
-
-def _erfc(x):
- """complented error function. = 1 - erf(x)"""
- return erfc(x)
-
-def _wofz(x):
- """fadeeva function for complex argument. = exp(-x**2)*erfc(-i*x)"""
- return wofz(x)
-
-def _gamma(x):
- """gamma function"""
- return gamfcn(x)
-
-def _gammaln(x):
- """log of absolute value of gamma function"""
- return gammaln(x)
-
-
-def exponential(x, amplitude=1, decay=1):
- "x -> amplitude * exp(-x/decay)"
- return amplitude * exp(-x/decay)
-
-
-def powerlaw(x, amplitude=1, exponent=1.0):
- "x -> amplitude * x**exponent"
- return amplitude * x**exponent
-
-
-def linear(x, slope, intercept):
- "x -> slope * x + intercept"
- return slope * x + intercept
-
-
-def parabolic(x, a, b, c):
- "x -> a * x**2 + b * x + c"
- return a * x**2 + b * x + c
-
-
-def assert_results_close(actual, desired, rtol=1e-03, atol=1e-03,
- err_msg='', verbose=True):
- """returns whether all parameter values in actual are close to
- those in desired"""
- for param_name, value in desired.items():
- assert_allclose(actual[param_name], value, rtol,
- atol, err_msg, verbose)
+#!/usr/bin/env python +""" +basic model line shapes and distribution functions +""" +from __future__ import division +from numpy import (pi, log, exp, sqrt, arctan, cos, where) +from numpy.testing import assert_allclose + +from scipy.special import gamma as gamfcn +from scipy.special import gammaln, erf, erfc, wofz + +log2 = log(2) +s2pi = sqrt(2*pi) +spi = sqrt(pi) +s2 = sqrt(2.0) + +functions = ('gaussian', 'lorentzian', 'voigt', 'pvoigt', 'moffat', 'pearson7', + 'breit_wigner', 'damped_oscillator', 'logistic', 'lognormal', + 'students_t', 'expgaussian', 'donaich', 'skewed_gaussian', + 'skewed_voigt', 'step', 'rectangle', 'erf', 'erfc', 'wofz', + 'gamma', 'gammaln', 'exponential', 'powerlaw', 'linear', + 'parabolic') + +def gaussian(x, amplitude=1.0, center=0.0, sigma=1.0): + """1 dimensional gaussian: + gaussian(x, amplitude, center, sigma) + """ + return (amplitude/(s2pi*sigma)) * exp(-(1.0*x-center)**2 /(2*sigma**2)) + +def lorentzian(x, amplitude=1.0, center=0.0, sigma=1.0): + """1 dimensional lorentzian + lorentzian(x, amplitude, center, sigma) + """ + return (amplitude/(1 + ((1.0*x-center)/sigma)**2) ) / (pi*sigma) + +def voigt(x, amplitude=1.0, center=0.0, sigma=1.0, gamma=None): + """1 dimensional voigt function. + see http://en.wikipedia.org/wiki/Voigt_profile + """ + if gamma is None: + gamma = sigma + z = (x-center + 1j*gamma)/ (sigma*s2) + return amplitude*wofz(z).real / (sigma*s2pi) + +def pvoigt(x, amplitude=1.0, center=0.0, sigma=1.0, fraction=0.5): + """1 dimensional pseudo-voigt: + pvoigt(x, amplitude, center, sigma, fraction) + = amplitude*(1-fraction)*gaussion(x, center, sigma_g) + + amplitude*fraction*lorentzian(x, center, sigma) + + where sigma_g (the sigma for the Gaussian component) is + + sigma_g = sigma / sqrt(2*log(2)) ~= sigma / 1.17741 + + so that the Gaussian and Lorentzian components have the + same FWHM of 2*sigma. + """ + sigma_g = sigma / sqrt(2*log2) + return ((1-fraction)*gaussian(x, amplitude, center, sigma_g) + + fraction*lorentzian(x, amplitude, center, sigma)) + +def moffat(x, amplitude=1, center=0., sigma=1, beta=1.): + """ 1 dimensional moffat function: + + moffat(amplitude, center, sigma, beta) = amplitude / (((x - center)/sigma)**2 + 1)**beta + """ + return amplitude / (((x - center)/sigma)**2 + 1)**beta + +def pearson7(x, amplitude=1.0, center=0.0, sigma=1.0, expon=1.0): + """pearson7 lineshape, using the wikipedia definition: + + pearson7(x, center, sigma, expon) = + amplitude*(1+arg**2)**(-expon)/(sigma*beta(expon-0.5, 0.5)) + + where arg = (x-center)/sigma + and beta() is the beta function. + """ + arg = (x-center)/sigma + scale = amplitude * gamfcn(expon)/(gamfcn(0.5)*gamfcn(expon-0.5)) + return scale*(1+arg**2)**(-expon)/sigma + +def breit_wigner(x, amplitude=1.0, center=0.0, sigma=1.0, q=1.0): + """Breit-Wigner-Fano lineshape: + = amplitude*(q*sigma/2 + x - center)**2 / ( (sigma/2)**2 + (x - center)**2 ) + """ + gam = sigma/2.0 + return amplitude*(q*gam + x - center)**2 / (gam*gam + (x-center)**2) + +def damped_oscillator(x, amplitude=1.0, center=1., sigma=0.1): + """amplitude for a damped harmonic oscillator + amplitude/sqrt( (1.0 - (x/center)**2)**2 + (2*sigma*x/center)**2)) + """ + center = max(1.e-9, abs(center)) + return (amplitude/sqrt( (1.0 - (x/center)**2)**2 + (2*sigma*x/center)**2)) + +def logistic(x, amplitude=1., center=0., sigma=1.): + """Logistic lineshape (yet another sigmoidal curve) + = amplitude*(1. - 1. / (1 + exp((x-center)/sigma))) + """ + return amplitude*(1. - 1./(1. + exp((x-center)/sigma))) + +def lognormal(x, amplitude=1.0, center=0., sigma=1): + """log-normal function + lognormal(x, center, sigma) + = (amplitude/x) * exp(-(ln(x) - center)/ (2* sigma**2)) + """ + x[where(x<=1.e-19)] = 1.e-19 + return (amplitude/(x*sigma*s2pi)) * exp(-(log(x)-center)**2/ (2* sigma**2)) + +def students_t(x, amplitude=1.0, center=0.0, sigma=1.0): + """Student's t distribution: + gamma((sigma+1)/2) (1 + (x-center)**2/sigma)^(-(sigma+1)/2) + = ------------------------- + sqrt(sigma*pi)gamma(sigma/2) + + """ + s1 = (sigma+1)/2.0 + denom = (sqrt(sigma*pi)*gamfcn(sigma/2)) + return amplitude*(1 + (x-center)**2/sigma)**(-s1) * gamfcn(s1) / denom + + +def expgaussian(x, amplitude=1, center=0, sigma=1.0, gamma=1.0): + """exponentially modified Gaussian + + = (gamma/2) exp[center*gamma + (gamma*sigma)**2/2 - gamma*x] * + erfc[(center + gamma*sigma**2 - x)/(sqrt(2)*sigma)] + + http://en.wikipedia.org/wiki/Exponentially_modified_Gaussian_distribution + """ + gss = gamma*sigma*sigma + arg1 = gamma*(center +gss/2.0 - x) + arg2 = (center + gss - x)/(s2*sigma) + return amplitude*(gamma/2) * exp(arg1) * erfc(arg2) + +def donaich(x, amplitude=1.0, center=0, sigma=1.0, gamma=0.0): + """Doniach Sunjic asymmetric lineshape, used for photo-emission + + = amplitude* cos(pi*gamma/2 + (1-gamma) arctan((x-center)/sigma) / + (sigma**2 + (x-center)**2)**[(1-gamma)/2] + + see http://www.casaxps.com/help_manual/line_shapes.htm + """ + arg = (x-center)/sigma + gm1 = (1.0 - gamma) + scale = amplitude/(sigma**gm1) + return scale*cos(pi*gamma/2 + gm1*arctan(arg))/(1 + arg**2)**(gm1/2) + +def skewed_gaussian(x, amplitude=1.0, center=0.0, sigma=1.0, gamma=0.0): + """Gaussian, skewed with error function, equal to + + gaussian(x, center, sigma)*(1+erf(beta*(x-center))) + + with beta = gamma/(sigma*sqrt(2)) + + with gamma < 0: tail to low value of centroid + gamma > 0: tail to high value of centroid + + see http://en.wikipedia.org/wiki/Skew_normal_distribution + """ + asym = 1 + erf(gamma*(x-center)/(s2*sigma)) + return asym * gaussian(x, amplitude, center, sigma) + +def skewed_voigt(x, amplitude=1.0, center=0.0, sigma=1.0, gamma=None, skew=0.0): + """Skewed Voigt lineshape, skewed with error function + useful for ad-hoc Compton scatter profile + + with beta = skew/(sigma*sqrt(2)) + = voigt(x, center, sigma, gamma)*(1+erf(beta*(x-center))) + + skew < 0: tail to low value of centroid + skew > 0: tail to high value of centroid + + see http://en.wikipedia.org/wiki/Skew_normal_distribution + """ + beta = skew/(s2*sigma) + asym = 1 + erf(beta*(x-center)) + return asym * voigt(x, amplitude, center, sigma, gamma=gamma) + +def step(x, amplitude=1.0, center=0.0, sigma=1.0, form='linear'): + """step function: + starts at 0.0, ends at amplitude, with half-max at center, and + rising with form: + 'linear' (default) = amplitude * min(1, max(0, arg)) + 'atan', 'arctan' = amplitude * (0.5 + atan(arg)/pi) + 'erf' = amplitude * (1 + erf(arg))/2.0 + 'logistic' = amplitude * [1 - 1/(1 + exp(arg))] + + where arg = (x - center)/sigma + """ + if abs(sigma) < 1.e-13: + sigma = 1.e-13 + + out = (x - center)/sigma + if form == 'erf': + out = 0.5*(1 + erf(out)) + elif form.startswith('logi'): + out = (1. - 1./(1. + exp(out))) + elif form in ('atan', 'arctan'): + out = 0.5 + arctan(out)/pi + else: + out[where(out < 0)] = 0.0 + out[where(out > 1)] = 1.0 + return amplitude*out + +def rectangle(x, amplitude=1.0, center1=0.0, sigma1=1.0, + center2=1.0, sigma2=1.0, form='linear'): + """rectangle function: step up, step down (see step function) + starts at 0.0, rises to amplitude (at center1 with width sigma1) + then drops to 0.0 (at center2 with width sigma2) with form: + 'linear' (default) = ramp_up + ramp_down + 'atan', 'arctan' = amplitude*(atan(arg1) + atan(arg2))/pi + 'erf' = amplitude*(erf(arg1) + erf(arg2))/2. + 'logisitic' = amplitude*[1 - 1/(1 + exp(arg1)) - 1/(1+exp(arg2))] + + where arg1 = (x - center1)/sigma1 + and arg2 = -(x - center2)/sigma2 + """ + if abs(sigma1) < 1.e-13: + sigma1 = 1.e-13 + if abs(sigma2) < 1.e-13: + sigma2 = 1.e-13 + + arg1 = (x - center1)/sigma1 + arg2 = (center2 - x)/sigma2 + if form == 'erf': + out = 0.5*(erf(arg1) + erf(arg2)) + elif form.startswith('logi'): + out = (1. - 1./(1. + exp(arg1)) - 1./(1. + exp(arg2))) + elif form in ('atan', 'arctan'): + out = (arctan(arg1) + arctan(arg2))/pi + else: + arg1[where(arg1 < 0)] = 0.0 + arg1[where(arg1 > 1)] = 1.0 + arg2[where(arg2 > 0)] = 0.0 + arg2[where(arg2 < -1)] = -1.0 + out = arg1 + arg2 + return amplitude*out + +def _erf(x): + """error function. = 2/sqrt(pi)*integral(exp(-t**2), t=[0, z])""" + return erf(x) + +def _erfc(x): + """complented error function. = 1 - erf(x)""" + return erfc(x) + +def _wofz(x): + """fadeeva function for complex argument. = exp(-x**2)*erfc(-i*x)""" + return wofz(x) + +def _gamma(x): + """gamma function""" + return gamfcn(x) + +def _gammaln(x): + """log of absolute value of gamma function""" + return gammaln(x) + + +def exponential(x, amplitude=1, decay=1): + "x -> amplitude * exp(-x/decay)" + return amplitude * exp(-x/decay) + + +def powerlaw(x, amplitude=1, exponent=1.0): + "x -> amplitude * x**exponent" + return amplitude * x**exponent + + +def linear(x, slope, intercept): + "x -> slope * x + intercept" + return slope * x + intercept + + +def parabolic(x, a, b, c): + "x -> a * x**2 + b * x + c" + return a * x**2 + b * x + c + + +def assert_results_close(actual, desired, rtol=1e-03, atol=1e-03, + err_msg='', verbose=True): + """returns whether all parameter values in actual are close to + those in desired""" + for param_name, value in desired.items(): + assert_allclose(actual[param_name], value, rtol, + atol, err_msg, verbose) diff --git a/lmfit/minimizer.py b/lmfit/minimizer.py index 7fca545..c67a396 100644 --- a/lmfit/minimizer.py +++ b/lmfit/minimizer.py @@ -1,774 +1,1282 @@ -"""
-Simple minimizer is a wrapper around scipy.leastsq, allowing a
-user to build a fitting model as a function of general purpose
-Fit Parameters that can be fixed or floated, bounded, and written
-as a simple expression of other Fit Parameters.
-
-The user sets up a model in terms of instance of Parameters, writes a
-function-to-be-minimized (residual function) in terms of these Parameters.
-
- Copyright (c) 2011 Matthew Newville, The University of Chicago
- <newville@cars.uchicago.edu>
-"""
-
-from copy import deepcopy
-import numpy as np
-from numpy import (dot, eye, ndarray, ones_like,
- sqrt, take, transpose, triu, deprecate)
-from numpy.dual import inv
-from numpy.linalg import LinAlgError
-
-from scipy.optimize import leastsq as scipy_leastsq
-from scipy.optimize import fmin as scipy_fmin
-from scipy.optimize.lbfgsb import fmin_l_bfgs_b as scipy_lbfgsb
-
-# differential_evolution is only present in scipy >= 0.15
-try:
- from scipy.optimize import differential_evolution as scipy_diffev
-except ImportError:
- from ._differentialevolution import differential_evolution as scipy_diffev
-
-# check for scipy.optimize.minimize
-HAS_SCALAR_MIN = False
-try:
- from scipy.optimize import minimize as scipy_minimize
- HAS_SCALAR_MIN = True
-except ImportError:
- pass
-
-from .asteval import Interpreter
-from .parameter import Parameter, Parameters
-
-# use locally modified version of uncertainties package
-from . import uncertainties
-
-
-def asteval_with_uncertainties(*vals, **kwargs):
- """
- given values for variables, calculate object value.
- This is used by the uncertainties package to calculate
- the uncertainty in an object even with a complicated
- expression.
- """
- _obj = kwargs.get('_obj', None)
- _pars = kwargs.get('_pars', None)
- _names = kwargs.get('_names', None)
- _asteval = _pars._asteval
- if (_obj is None or _pars is None or _names is None or
- _asteval is None or _obj._expr_ast is None):
- return 0
- for val, name in zip(vals, _names):
- _asteval.symtable[name] = val
- return _asteval.eval(_obj._expr_ast)
-
-wrap_ueval = uncertainties.wrap(asteval_with_uncertainties)
-
-def eval_stderr(obj, uvars, _names, _pars):
- """evaluate uncertainty and set .stderr for a parameter `obj`
- given the uncertain values `uvars` (a list of uncertainties.ufloats),
- a list of parameter names that matches uvars, and a dict of param
- objects, keyed by name.
-
- This uses the uncertainties package wrapped function to evaluate the
- uncertainty for an arbitrary expression (in obj._expr_ast) of parameters.
- """
- if not isinstance(obj, Parameter) or getattr(obj, '_expr_ast', None) is None:
- return
- uval = wrap_ueval(*uvars, _obj=obj, _names=_names, _pars=_pars)
- try:
- obj.stderr = uval.std_dev()
- except:
- obj.stderr = 0
-
-
-class MinimizerException(Exception):
- """General Purpose Exception"""
- def __init__(self, msg):
- Exception.__init__(self)
- self.msg = msg
-
- def __str__(self):
- return "\n%s" % (self.msg)
-
-
-def _differential_evolution(func, x0, **kwds):
- """
- A wrapper for differential_evolution that can be used with scipy.minimize
- """
- kwargs = dict(args=(), strategy='best1bin', maxiter=None, popsize=15,
- tol=0.01, mutation=(0.5, 1), recombination=0.7, seed=None,
- callback=None, disp=False, polish=True,
- init='latinhypercube')
-
- for k, v in kwds.items():
- if k in kwargs:
- kwargs[k] = v
-
- return scipy_diffev(func, kwds['bounds'], **kwargs)
-
-SCALAR_METHODS = {'nelder': 'Nelder-Mead',
- 'powell': 'Powell',
- 'cg': 'CG',
- 'bfgs': 'BFGS',
- 'newton': 'Newton-CG',
- 'lbfgsb': 'L-BFGS-B',
- 'l-bfgsb':'L-BFGS-B',
- 'tnc': 'TNC',
- 'cobyla': 'COBYLA',
- 'slsqp': 'SLSQP',
- 'dogleg': 'dogleg',
- 'trust-ncg': 'trust-ncg',
- 'differential_evolution': 'differential_evolution'}
-
-
-class MinimizerResult(object):
- """ The result of a minimization.
-
- Attributes
- ----------
- params : Parameters
- The best-fit parameters
- success : bool
- Whether the minimization was successful
- status : int
- Termination status of the optimizer. Its value depends on the
- underlying solver. Refer to `message` for details.
-
- Notes
- -----
- additional attributes not listed above depending of the
- specific solver. Since this class is essentially a subclass of dict
- with attribute accessors, one can see which attributes are available
- using the `keys()` method.
- """
- def __init__(self, **kws):
- for key, val in kws.items():
- setattr(self, key, val)
-
-class Minimizer(object):
- """A general minimizer for curve fitting"""
- err_nonparam = ("params must be a minimizer.Parameters() instance or list "
- "of Parameters()")
- err_maxfev = ("Too many function calls (max set to %i)! Use:"
- " minimize(func, params, ..., maxfev=NNN)"
- "or set leastsq_kws['maxfev'] to increase this maximum.")
-
- def __init__(self, userfcn, params, fcn_args=None, fcn_kws=None,
- iter_cb=None, scale_covar=True, **kws):
- """
- Initialization of the Minimzer class
-
- Parameters
- ----------
- userfcn : callable
- objective function that returns the residual (difference between
- model and data) to be minimized in a least squares sense. The
- function must have the signature:
- `userfcn(params, *fcn_args, **fcn_kws)`
- params : lmfit.parameter.Parameters object.
- contains the Parameters for the model.
- fcn_args : tuple, optional
- positional arguments to pass to userfcn.
- fcn_kws : dict, optional
- keyword arguments to pass to userfcn.
- iter_cb : callable, optional
- Function to be called at each fit iteration. This function should
- have the signature:
- `iter_cb(params, iter, resid, *fcn_args, **fcn_kws)`,
- where where `params` will have the current parameter values, `iter`
- the iteration, `resid` the current residual array, and `*fcn_args`
- and `**fcn_kws` as passed to the objective function.
- scale_covar : bool, optional
- Whether to automatically scale the covariance matrix (leastsq
- only).
- kws : dict, optional
- Options to pass to the minimizer being used.
-
- Notes
- -----
- The objective function should return the value to be minimized. For the
- Levenberg-Marquardt algorithm from leastsq(), this returned value must
- be an array, with a length greater than or equal to the number of
- fitting variables in the model. For the other methods, the return value
- can either be a scalar or an array. If an array is returned, the sum of
- squares of the array will be sent to the underlying fitting method,
- effectively doing a least-squares optimization of the return values.
-
- A common use for the fcn_args and fcn_kwds would be to pass in other
- data needed to calculate the residual, including such things as the
- data array, dependent variable, uncertainties in the data, and other
- data structures for the model calculation.
- """
- self.userfcn = userfcn
- self.userargs = fcn_args
- if self.userargs is None:
- self.userargs = []
-
- self.userkws = fcn_kws
- if self.userkws is None:
- self.userkws = {}
- self.kws = kws
- self.iter_cb = iter_cb
- self.scale_covar = scale_covar
- self.nfev = 0
- self.nfree = 0
- self.ndata = 0
- self.ier = 0
- self._abort = False
- self.success = True
- self.errorbars = False
- self.message = None
- self.lmdif_message = None
- self.chisqr = None
- self.redchi = None
- self.covar = None
- self.residual = None
-
- self.params = params
- self.jacfcn = None
-
- @property
- def values(self):
- """
- Returns
- -------
- param_values : dict
- Parameter values in a simple dictionary.
- """
-
- return dict([(name, p.value) for name, p in self.result.params.items()])
-
- def __residual(self, fvars):
- """
- Residual function used for least-squares fit.
- With the new, candidate values of fvars (the fitting variables), this
- evaluates all parameters, including setting bounds and evaluating
- constraints, and then passes those to the user-supplied function to
- calculate the residual.
- """
- # set parameter values
- if self._abort:
- return None
- params = self.result.params
- for name, val in zip(self.result.var_names, fvars):
- params[name].value = params[name].from_internal(val)
- self.result.nfev = self.result.nfev + 1
-
- params.update_constraints()
- out = self.userfcn(params, *self.userargs, **self.userkws)
- if callable(self.iter_cb):
- abort = self.iter_cb(params, self.result.nfev, out,
- *self.userargs, **self.userkws)
- self._abort = self._abort or abort
- if not self._abort:
- return np.asarray(out).ravel()
-
- def __jacobian(self, fvars):
- """
- analytical jacobian to be used with the Levenberg-Marquardt
-
- modified 02-01-2012 by Glenn Jones, Aberystwyth University
- modified 06-29-2015 M Newville to apply gradient scaling
- for bounded variables (thanks to JJ Helmus, N Mayorov)
- """
- pars = self.result.params
- grad_scale = ones_like(fvars)
- for ivar, name in enumerate(self.result.var_names):
- val = fvars[ivar]
- pars[name].value = pars[name].from_internal(val)
- grad_scale[ivar] = pars[name].scale_gradient(val)
-
- self.result.nfev = self.result.nfev + 1
- pars.update_constraints()
- # compute the jacobian for "internal" unbounded variables,
- # the rescale for bounded "external" variables.
- jac = self.jacfcn(pars, *self.userargs, **self.userkws)
- if self.col_deriv:
- jac = (jac.transpose()*grad_scale).transpose()
- else:
- jac = jac*grad_scale
- return jac
-
- def penalty(self, fvars):
- """
- Penalty function for scalar minimizers:
-
- Parameters
- ----------
- fvars : array of values for the variable parameters
-
- Returns
- -------
- r - float
- The user evaluated user-supplied objective function. If the
- objective function is an array, return the array sum-of-squares
- """
- r = self.__residual(fvars)
- if isinstance(r, ndarray):
- r = (r*r).sum()
- return r
-
- def prepare_fit(self, params=None):
- """
- Prepares parameters for fitting,
- return array of initial values
- """
- # determine which parameters are actually variables
- # and which are defined expressions.
- result = self.result = MinimizerResult()
- if params is not None:
- self.params = params
- if isinstance(self.params, Parameters):
- result.params = deepcopy(self.params)
- elif isinstance(self.params, (list, tuple)):
- result.params = Parameters()
- for par in self.params:
- if not isinstance(par, Parameter):
- raise MinimizerException(self.err_nonparam)
- else:
- result.params[par.name] = par
- elif self.params is None:
- raise MinimizerException(self.err_nonparam)
-
- # determine which parameters are actually variables
- # and which are defined expressions.
-
- result.var_names = [] # note that this *does* belong to self...
- result.init_vals = []
- result.params.update_constraints()
- result.nfev = 0
- result.errorbars = False
- result.aborted = False
- for name, par in self.result.params.items():
- par.stderr = None
- par.correl = None
- if par.expr is not None:
- par.vary = False
- if par.vary:
- result.var_names.append(name)
- result.init_vals.append(par.setup_bounds())
-
- par.init_value = par.value
- if par.name is None:
- par.name = name
- result.nvarys = len(result.var_names)
- return result
-
- def unprepare_fit(self):
- """
- Unprepares the fit, so that subsequent fits will be
- forced to run prepare_fit.
-
- removes ast compilations of constraint expressions
- """
- pass
-
- @deprecate(message=' Deprecated in lmfit 0.8.2, use scalar_minimize '
- 'and method=\'L-BFGS-B\' instead')
- def lbfgsb(self, **kws):
- """
- Use l-bfgs-b minimization
-
- Parameters
- ----------
- kws : dict
- Minimizer options to pass to the
- scipy.optimize.lbfgsb.fmin_l_bfgs_b function.
-
- """
- raise NotImplementedError("use scalar_minimize(method='L-BFGS-B')")
-
-
- @deprecate(message=' Deprecated in lmfit 0.8.2, use scalar_minimize '
- 'and method=\'Nelder-Mead\' instead')
- def fmin(self, **kws):
- """
- Use Nelder-Mead (simplex) minimization
-
- Parameters
- ----------
- kws : dict
- Minimizer options to pass to the scipy.optimize.fmin minimizer.
- """
- raise NotImplementedError("use scalar_minimize(method='Nelder-Mead')")
-
- def scalar_minimize(self, method='Nelder-Mead', params=None, **kws):
- """
- Use one of the scalar minimization methods from
- scipy.optimize.minimize.
-
- Parameters
- ----------
- method : str, optional
- Name of the fitting method to use.
- One of:
- 'Nelder-Mead' (default)
- 'L-BFGS-B'
- 'Powell'
- 'CG'
- 'Newton-CG'
- 'COBYLA'
- 'TNC'
- 'trust-ncg'
- 'dogleg'
- 'SLSQP'
- 'differential_evolution'
-
- params : Parameters, optional
- Parameters to use as starting points.
- kws : dict, optional
- Minimizer options pass to scipy.optimize.minimize.
-
- If the objective function returns a numpy array instead
- of the expected scalar, the sum of squares of the array
- will be used.
-
- Note that bounds and constraints can be set on Parameters
- for any of these methods, so are not supported separately
- for those designed to use bounds. However, if you use the
- differential_evolution option you must specify finite
- (min, max) for each Parameter.
-
- Returns
- -------
- success : bool
- Whether the fit was successful.
-
- """
- if not HAS_SCALAR_MIN:
- raise NotImplementedError
-
- result = self.prepare_fit(params=params)
- vars = result.init_vals
- params = result.params
-
- fmin_kws = dict(method=method,
- options={'maxiter': 1000 * (len(vars) + 1)})
- fmin_kws.update(self.kws)
- fmin_kws.update(kws)
-
- # hess supported only in some methods
- if 'hess' in fmin_kws and method not in ('Newton-CG',
- 'dogleg', 'trust-ncg'):
- fmin_kws.pop('hess')
-
- # jac supported only in some methods (and Dfun could be used...)
- if 'jac' not in fmin_kws and fmin_kws.get('Dfun', None) is not None:
- self.jacfcn = fmin_kws.pop('jac')
- fmin_kws['jac'] = self.__jacobian
-
- if 'jac' in fmin_kws and method not in ('CG', 'BFGS', 'Newton-CG',
- 'dogleg', 'trust-ncg'):
- self.jacfcn = None
- fmin_kws.pop('jac')
-
- if method == 'differential_evolution':
- fmin_kws['method'] = _differential_evolution
- bounds = [(par.min, par.max) for par in params.values()]
- if not np.all(np.isfinite(bounds)):
- raise ValueError('With differential evolution finite bounds '
- 'are required for each parameter')
- bounds = [(-np.pi / 2., np.pi / 2.)] * len(vars)
- fmin_kws['bounds'] = bounds
-
- # in scipy 0.14 this can be called directly from scipy_minimize
- # When minimum scipy is 0.14 the following line and the else
- # can be removed.
- ret = _differential_evolution(self.penalty, vars, **fmin_kws)
- else:
- ret = scipy_minimize(self.penalty, vars, **fmin_kws)
-
- result.aborted = self._abort
- self._abort = False
-
- for attr in dir(ret):
- if not attr.startswith('_'):
- setattr(result, attr, getattr(ret, attr))
-
- result.chisqr = result.residual = self.__residual(ret.x)
- result.nvarys = len(vars)
- result.ndata = 1
- result.nfree = 1
- if isinstance(result.residual, ndarray):
- result.chisqr = (result.chisqr**2).sum()
- result.ndata = len(result.residual)
- result.nfree = result.ndata - result.nvarys
- result.redchi = result.chisqr / result.nfree
- _log_likelihood = result.ndata * np.log(result.redchi)
- result.aic = _log_likelihood + 2 * result.nvarys
- result.bic = _log_likelihood + np.log(result.ndata) * result.nvarys
-
- return result
-
- def leastsq(self, params=None, **kws):
- """
- Use Levenberg-Marquardt minimization to perform a fit.
- This assumes that ModelParameters have been stored, and a function to
- minimize has been properly set up.
-
- This wraps scipy.optimize.leastsq.
-
- When possible, this calculates the estimated uncertainties and
- variable correlations from the covariance matrix.
-
- Writes outputs to many internal attributes.
-
- Parameters
- ----------
- params : Parameters, optional
- Parameters to use as starting points.
- kws : dict, optional
- Minimizer options to pass to scipy.optimize.leastsq.
-
- Returns
- -------
- success : bool
- True if fit was successful, False if not.
- """
- result = self.prepare_fit(params=params)
- vars = result.init_vals
- nvars = len(vars)
- lskws = dict(full_output=1, xtol=1.e-7, ftol=1.e-7, col_deriv=False,
- gtol=1.e-7, maxfev=2000*(nvars+1), Dfun=None)
-
- lskws.update(self.kws)
- lskws.update(kws)
-
- self.col_deriv = False
- if lskws['Dfun'] is not None:
- self.jacfcn = lskws['Dfun']
- self.col_deriv = lskws['col_deriv']
- lskws['Dfun'] = self.__jacobian
-
- # suppress runtime warnings during fit and error analysis
- orig_warn_settings = np.geterr()
- np.seterr(all='ignore')
-
- lsout = scipy_leastsq(self.__residual, vars, **lskws)
- _best, _cov, infodict, errmsg, ier = lsout
- result.aborted = self._abort
- self._abort = False
-
- result.residual = resid = infodict['fvec']
- result.ier = ier
- result.lmdif_message = errmsg
- result.message = 'Fit succeeded.'
- result.success = ier in [1, 2, 3, 4]
- if result.aborted:
- result.message = 'Fit aborted by user callback.'
- result.success = False
- elif ier == 0:
- result.message = 'Invalid Input Parameters.'
- elif ier == 5:
- result.message = self.err_maxfev % lskws['maxfev']
- else:
- result.message = 'Tolerance seems to be too small.'
-
- result.ndata = len(resid)
-
- result.chisqr = (resid**2).sum()
- result.nfree = (result.ndata - nvars)
- result.redchi = result.chisqr / result.nfree
- _log_likelihood = result.ndata * np.log(result.redchi)
- result.aic = _log_likelihood + 2 * nvars
- result.bic = _log_likelihood + np.log(result.ndata) * nvars
-
- params = result.params
-
- # need to map _best values to params, then calculate the
- # grad for the variable parameters
- grad = ones_like(_best)
- vbest = ones_like(_best)
-
- # ensure that _best, vbest, and grad are not
- # broken 1-element ndarrays.
- if len(np.shape(_best)) == 0:
- _best = np.array([_best])
- if len(np.shape(vbest)) == 0:
- vbest = np.array([vbest])
- if len(np.shape(grad)) == 0:
- grad = np.array([grad])
-
- for ivar, name in enumerate(result.var_names):
- grad[ivar] = params[name].scale_gradient(_best[ivar])
- vbest[ivar] = params[name].value
-
- # modified from JJ Helmus' leastsqbound.py
- infodict['fjac'] = transpose(transpose(infodict['fjac']) /
- take(grad, infodict['ipvt'] - 1))
- rvec = dot(triu(transpose(infodict['fjac'])[:nvars, :]),
- take(eye(nvars), infodict['ipvt'] - 1, 0))
- try:
- result.covar = inv(dot(transpose(rvec), rvec))
- except (LinAlgError, ValueError):
- result.covar = None
-
- has_expr = False
- for par in params.values():
- par.stderr, par.correl = 0, None
- has_expr = has_expr or par.expr is not None
-
- # self.errorbars = error bars were successfully estimated
- result.errorbars = (result.covar is not None)
- if result.aborted:
- result.errorbars = False
- if result.errorbars:
- if self.scale_covar:
- result.covar *= result.redchi
- for ivar, name in enumerate(result.var_names):
- par = params[name]
- par.stderr = sqrt(result.covar[ivar, ivar])
- par.correl = {}
- try:
- result.errorbars = result.errorbars and (par.stderr > 0.0)
- for jvar, varn2 in enumerate(result.var_names):
- if jvar != ivar:
- par.correl[varn2] = (result.covar[ivar, jvar] /
- (par.stderr * sqrt(result.covar[jvar, jvar])))
- except:
- result.errorbars = False
-
- uvars = None
- if has_expr:
- # uncertainties on constrained parameters:
- # get values with uncertainties (including correlations),
- # temporarily set Parameter values to these,
- # re-evaluate contrained parameters to extract stderr
- # and then set Parameters back to best-fit value
- try:
- uvars = uncertainties.correlated_values(vbest, result.covar)
- except (LinAlgError, ValueError):
- uvars = None
- if uvars is not None:
- for par in params.values():
- eval_stderr(par, uvars, result.var_names, params)
- # restore nominal values
- for v, nam in zip(uvars, result.var_names):
- params[nam].value = v.nominal_value
-
- if not result.errorbars:
- result.message = '%s. Could not estimate error-bars'% result.message
-
- np.seterr(**orig_warn_settings)
- return result
-
- def minimize(self, method='leastsq', params=None, **kws):
- """
- Perform the minimization.
-
- Parameters
- ----------
- method : str, optional
- Name of the fitting method to use.
- One of:
- 'leastsq' - Levenberg-Marquardt (default)
- 'nelder' - Nelder-Mead
- 'lbfgsb' - L-BFGS-B
- 'powell' - Powell
- 'cg' - Conjugate-Gradient
- 'newton' - Newton-CG
- 'cobyla' - Cobyla
- 'tnc' - Truncate Newton
- 'trust-ncg' - Trust Newton-CGn
- 'dogleg' - Dogleg
- 'slsqp' - Sequential Linear Squares Programming
- 'differential_evolution' - differential evolution
-
- params : Parameters, optional
- parameters to use as starting values
-
- Returns
- -------
- result : MinimizerResult
-
- MinimizerResult object contains updated params, fit statistics, etc.
-
- """
-
- function = self.leastsq
- kwargs = {'params': params}
- kwargs.update(kws)
-
- user_method = method.lower()
- if user_method.startswith('least'):
- function = self.leastsq
- elif HAS_SCALAR_MIN:
- function = self.scalar_minimize
- for key, val in SCALAR_METHODS.items():
- if (key.lower().startswith(user_method) or
- val.lower().startswith(user_method)):
- kwargs['method'] = val
- elif (user_method.startswith('nelder') or
- user_method.startswith('fmin')):
- function = self.fmin
- elif user_method.startswith('lbfgsb'):
- function = self.lbfgsb
- return function(**kwargs)
-
-def minimize(fcn, params, method='leastsq', args=None, kws=None,
- scale_covar=True, iter_cb=None, **fit_kws):
- """
- A general purpose curvefitting function
- The minimize function takes a objective function to be minimized, a
- dictionary (lmfit.parameter.Parameters) containing the model parameters,
- and several optional arguments.
-
- Parameters
- ----------
- fcn : callable
- objective function that returns the residual (difference between
- model and data) to be minimized in a least squares sense. The
- function must have the signature:
- `fcn(params, *args, **kws)`
- params : lmfit.parameter.Parameters object.
- contains the Parameters for the model.
- method : str, optional
- Name of the fitting method to use.
- One of:
- 'leastsq' - Levenberg-Marquardt (default)
- 'nelder' - Nelder-Mead
- 'lbfgsb' - L-BFGS-B
- 'powell' - Powell
- 'cg' - Conjugate-Gradient
- 'newton' - Newton-CG
- 'cobyla' - Cobyla
- 'tnc' - Truncate Newton
- 'trust-ncg' - Trust Newton-CGn
- 'dogleg' - Dogleg
- 'slsqp' - Sequential Linear Squares Programming
- 'differential_evolution' - differential evolution
-
- args : tuple, optional
- Positional arguments to pass to fcn.
- kws : dict, optional
- keyword arguments to pass to fcn.
- iter_cb : callable, optional
- Function to be called at each fit iteration. This function should
- have the signature `iter_cb(params, iter, resid, *args, **kws)`,
- where where `params` will have the current parameter values, `iter`
- the iteration, `resid` the current residual array, and `*args`
- and `**kws` as passed to the objective function.
- scale_covar : bool, optional
- Whether to automatically scale the covariance matrix (leastsq
- only).
- fit_kws : dict, optional
- Options to pass to the minimizer being used.
-
- Notes
- -----
- The objective function should return the value to be minimized. For the
- Levenberg-Marquardt algorithm from leastsq(), this returned value must
- be an array, with a length greater than or equal to the number of
- fitting variables in the model. For the other methods, the return value
- can either be a scalar or an array. If an array is returned, the sum of
- squares of the array will be sent to the underlying fitting method,
- effectively doing a least-squares optimization of the return values.
-
- A common use for `args` and `kwds` would be to pass in other
- data needed to calculate the residual, including such things as the
- data array, dependent variable, uncertainties in the data, and other
- data structures for the model calculation.
- """
- fitter = Minimizer(fcn, params, fcn_args=args, fcn_kws=kws,
- iter_cb=iter_cb, scale_covar=scale_covar, **fit_kws)
- return fitter.minimize(method=method)
+""" +Simple minimizer is a wrapper around scipy.leastsq, allowing a +user to build a fitting model as a function of general purpose +Fit Parameters that can be fixed or floated, bounded, and written +as a simple expression of other Fit Parameters. + +The user sets up a model in terms of instance of Parameters, writes a +function-to-be-minimized (residual function) in terms of these Parameters. + + Copyright (c) 2011 Matthew Newville, The University of Chicago + <newville@cars.uchicago.edu> +""" + +from copy import deepcopy +import numpy as np +from numpy import (dot, eye, ndarray, ones_like, + sqrt, take, transpose, triu, deprecate) +from numpy.dual import inv +from numpy.linalg import LinAlgError +import multiprocessing +import numbers + +from scipy.optimize import leastsq as scipy_leastsq + +# differential_evolution is only present in scipy >= 0.15 +try: + from scipy.optimize import differential_evolution as scipy_diffev +except ImportError: + from ._differentialevolution import differential_evolution as scipy_diffev + +# check for EMCEE +HAS_EMCEE = False +try: + import emcee as emcee + HAS_EMCEE = True +except ImportError: + pass + +# check for pandas +HAS_PANDAS = False +try: + import pandas as pd + HAS_PANDAS = True +except ImportError: + pass + +# check for scipy.optimize.minimize +HAS_SCALAR_MIN = False +try: + from scipy.optimize import minimize as scipy_minimize + HAS_SCALAR_MIN = True +except ImportError: + pass + +from .parameter import Parameter, Parameters + +# use locally modified version of uncertainties package +from . import uncertainties + + +def asteval_with_uncertainties(*vals, **kwargs): + """ + given values for variables, calculate object value. + This is used by the uncertainties package to calculate + the uncertainty in an object even with a complicated + expression. + """ + _obj = kwargs.get('_obj', None) + _pars = kwargs.get('_pars', None) + _names = kwargs.get('_names', None) + _asteval = _pars._asteval + if (_obj is None or _pars is None or _names is None or + _asteval is None or _obj._expr_ast is None): + return 0 + for val, name in zip(vals, _names): + _asteval.symtable[name] = val + return _asteval.eval(_obj._expr_ast) + +wrap_ueval = uncertainties.wrap(asteval_with_uncertainties) + + +def eval_stderr(obj, uvars, _names, _pars): + """evaluate uncertainty and set .stderr for a parameter `obj` + given the uncertain values `uvars` (a list of uncertainties.ufloats), + a list of parameter names that matches uvars, and a dict of param + objects, keyed by name. + + This uses the uncertainties package wrapped function to evaluate the + uncertainty for an arbitrary expression (in obj._expr_ast) of parameters. + """ + if not isinstance(obj, Parameter) or getattr(obj, '_expr_ast', None) is None: + return + uval = wrap_ueval(*uvars, _obj=obj, _names=_names, _pars=_pars) + try: + obj.stderr = uval.std_dev() + except: + obj.stderr = 0 + + +class MinimizerException(Exception): + """General Purpose Exception""" + def __init__(self, msg): + Exception.__init__(self) + self.msg = msg + + def __str__(self): + return "\n%s" % self.msg + + +def _differential_evolution(func, x0, **kwds): + """ + A wrapper for differential_evolution that can be used with scipy.minimize + """ + kwargs = dict(args=(), strategy='best1bin', maxiter=None, popsize=15, + tol=0.01, mutation=(0.5, 1), recombination=0.7, seed=None, + callback=None, disp=False, polish=True, + init='latinhypercube') + + for k, v in kwds.items(): + if k in kwargs: + kwargs[k] = v + + return scipy_diffev(func, kwds['bounds'], **kwargs) + +SCALAR_METHODS = {'nelder': 'Nelder-Mead', + 'powell': 'Powell', + 'cg': 'CG', + 'bfgs': 'BFGS', + 'newton': 'Newton-CG', + 'lbfgsb': 'L-BFGS-B', + 'l-bfgsb': 'L-BFGS-B', + 'tnc': 'TNC', + 'cobyla': 'COBYLA', + 'slsqp': 'SLSQP', + 'dogleg': 'dogleg', + 'trust-ncg': 'trust-ncg', + 'differential_evolution': 'differential_evolution'} + + +class MinimizerResult(object): + """ The result of a minimization. + + Attributes + ---------- + params : Parameters + The best-fit parameters + success : bool + Whether the minimization was successful + status : int + Termination status of the optimizer. Its value depends on the + underlying solver. Refer to `message` for details. + + Notes + ----- + Additional attributes not listed above may be present, depending on the + specific solver. Since this class is essentially a subclass of dict + with attribute accessors, one can see which attributes are available + using the `keys()` method. + """ + def __init__(self, **kws): + for key, val in kws.items(): + setattr(self, key, val) + + @property + def flatchain(self): + """ + A flatchain view of the sampling chain from the `emcee` method. + """ + if hasattr(self, 'chain'): + if HAS_PANDAS: + return pd.DataFrame(self.chain.reshape((-1, self.nvarys)), + columns=self.var_names) + else: + raise NotImplementedError('Please install Pandas to see the ' + 'flattened chain') + else: + return None + + +class Minimizer(object): + """A general minimizer for curve fitting""" + err_nonparam = ("params must be a minimizer.Parameters() instance or list " + "of Parameters()") + err_maxfev = ("Too many function calls (max set to %i)! Use:" + " minimize(func, params, ..., maxfev=NNN)" + "or set leastsq_kws['maxfev'] to increase this maximum.") + + def __init__(self, userfcn, params, fcn_args=None, fcn_kws=None, + iter_cb=None, scale_covar=True, **kws): + """ + Initialization of the Minimzer class + + Parameters + ---------- + userfcn : callable + objective function that returns the residual (difference between + model and data) to be minimized in a least squares sense. The + function must have the signature: + `userfcn(params, *fcn_args, **fcn_kws)` + params : lmfit.parameter.Parameters object. + contains the Parameters for the model. + fcn_args : tuple, optional + positional arguments to pass to userfcn. + fcn_kws : dict, optional + keyword arguments to pass to userfcn. + iter_cb : callable, optional + Function to be called at each fit iteration. This function should + have the signature: + `iter_cb(params, iter, resid, *fcn_args, **fcn_kws)`, + where where `params` will have the current parameter values, `iter` + the iteration, `resid` the current residual array, and `*fcn_args` + and `**fcn_kws` as passed to the objective function. + scale_covar : bool, optional + Whether to automatically scale the covariance matrix (leastsq + only). + kws : dict, optional + Options to pass to the minimizer being used. + + Notes + ----- + The objective function should return the value to be minimized. For the + Levenberg-Marquardt algorithm from leastsq(), this returned value must + be an array, with a length greater than or equal to the number of + fitting variables in the model. For the other methods, the return value + can either be a scalar or an array. If an array is returned, the sum of + squares of the array will be sent to the underlying fitting method, + effectively doing a least-squares optimization of the return values. + + A common use for the fcn_args and fcn_kwds would be to pass in other + data needed to calculate the residual, including such things as the + data array, dependent variable, uncertainties in the data, and other + data structures for the model calculation. + """ + self.userfcn = userfcn + self.userargs = fcn_args + if self.userargs is None: + self.userargs = [] + + self.userkws = fcn_kws + if self.userkws is None: + self.userkws = {} + self.kws = kws + self.iter_cb = iter_cb + self.scale_covar = scale_covar + self.nfev = 0 + self.nfree = 0 + self.ndata = 0 + self.ier = 0 + self._abort = False + self.success = True + self.errorbars = False + self.message = None + self.lmdif_message = None + self.chisqr = None + self.redchi = None + self.covar = None + self.residual = None + + self.params = params + self.jacfcn = None + + @property + def values(self): + """ + Returns + ------- + param_values : dict + Parameter values in a simple dictionary. + """ + + return dict([(name, p.value) for name, p in self.result.params.items()]) + + def __residual(self, fvars): + """ + Residual function used for least-squares fit. + With the new, candidate values of fvars (the fitting variables), this + evaluates all parameters, including setting bounds and evaluating + constraints, and then passes those to the user-supplied function to + calculate the residual. + """ + # set parameter values + if self._abort: + return None + params = self.result.params + for name, val in zip(self.result.var_names, fvars): + params[name].value = params[name].from_internal(val) + self.result.nfev += 1 + + params.update_constraints() + out = self.userfcn(params, *self.userargs, **self.userkws) + if callable(self.iter_cb): + abort = self.iter_cb(params, self.result.nfev, out, + *self.userargs, **self.userkws) + self._abort = self._abort or abort + self._abort = self._abort and self.result.nfev > len(fvars) + if not self._abort: + return np.asarray(out).ravel() + + def __jacobian(self, fvars): + """ + analytical jacobian to be used with the Levenberg-Marquardt + + modified 02-01-2012 by Glenn Jones, Aberystwyth University + modified 06-29-2015 M Newville to apply gradient scaling + for bounded variables (thanks to JJ Helmus, N Mayorov) + """ + pars = self.result.params + grad_scale = ones_like(fvars) + for ivar, name in enumerate(self.result.var_names): + val = fvars[ivar] + pars[name].value = pars[name].from_internal(val) + grad_scale[ivar] = pars[name].scale_gradient(val) + + self.result.nfev += 1 + pars.update_constraints() + # compute the jacobian for "internal" unbounded variables, + # the rescale for bounded "external" variables. + jac = self.jacfcn(pars, *self.userargs, **self.userkws) + if self.col_deriv: + jac = (jac.transpose()*grad_scale).transpose() + else: + jac *= grad_scale + return jac + + def penalty(self, fvars): + """ + Penalty function for scalar minimizers: + + Parameters + ---------- + fvars : array of values for the variable parameters + + Returns + ------- + r - float + The user evaluated user-supplied objective function. If the + objective function is an array, return the array sum-of-squares + """ + r = self.__residual(fvars) + if isinstance(r, ndarray): + r = (r*r).sum() + return r + + def prepare_fit(self, params=None): + """ + Prepares parameters for fitting, + return array of initial values + """ + # determine which parameters are actually variables + # and which are defined expressions. + result = self.result = MinimizerResult() + if params is not None: + self.params = params + if isinstance(self.params, Parameters): + result.params = deepcopy(self.params) + elif isinstance(self.params, (list, tuple)): + result.params = Parameters() + for par in self.params: + if not isinstance(par, Parameter): + raise MinimizerException(self.err_nonparam) + else: + result.params[par.name] = par + elif self.params is None: + raise MinimizerException(self.err_nonparam) + + # determine which parameters are actually variables + # and which are defined expressions. + + result.var_names = [] # note that this *does* belong to self... + result.init_vals = [] + result.params.update_constraints() + result.nfev = 0 + result.errorbars = False + result.aborted = False + for name, par in self.result.params.items(): + par.stderr = None + par.correl = None + if par.expr is not None: + par.vary = False + if par.vary: + result.var_names.append(name) + result.init_vals.append(par.setup_bounds()) + + par.init_value = par.value + if par.name is None: + par.name = name + result.nvarys = len(result.var_names) + return result + + def unprepare_fit(self): + """ + Unprepares the fit, so that subsequent fits will be + forced to run prepare_fit. + + removes ast compilations of constraint expressions + """ + pass + + @deprecate(message=' Deprecated in lmfit 0.8.2, use scalar_minimize ' + 'and method=\'L-BFGS-B\' instead') + def lbfgsb(self, **kws): + """ + Use l-bfgs-b minimization + + Parameters + ---------- + kws : dict + Minimizer options to pass to the + scipy.optimize.lbfgsb.fmin_l_bfgs_b function. + + """ + raise NotImplementedError("use scalar_minimize(method='L-BFGS-B')") + + @deprecate(message=' Deprecated in lmfit 0.8.2, use scalar_minimize ' + 'and method=\'Nelder-Mead\' instead') + def fmin(self, **kws): + """ + Use Nelder-Mead (simplex) minimization + + Parameters + ---------- + kws : dict + Minimizer options to pass to the scipy.optimize.fmin minimizer. + """ + raise NotImplementedError("use scalar_minimize(method='Nelder-Mead')") + + def scalar_minimize(self, method='Nelder-Mead', params=None, **kws): + """ + Use one of the scalar minimization methods from + scipy.optimize.minimize. + + Parameters + ---------- + method : str, optional + Name of the fitting method to use. + One of: + 'Nelder-Mead' (default) + 'L-BFGS-B' + 'Powell' + 'CG' + 'Newton-CG' + 'COBYLA' + 'TNC' + 'trust-ncg' + 'dogleg' + 'SLSQP' + 'differential_evolution' + + params : Parameters, optional + Parameters to use as starting points. + kws : dict, optional + Minimizer options pass to scipy.optimize.minimize. + + If the objective function returns a numpy array instead + of the expected scalar, the sum of squares of the array + will be used. + + Note that bounds and constraints can be set on Parameters + for any of these methods, so are not supported separately + for those designed to use bounds. However, if you use the + differential_evolution option you must specify finite + (min, max) for each Parameter. + + Returns + ------- + success : bool + Whether the fit was successful. + + """ + if not HAS_SCALAR_MIN: + raise NotImplementedError + + result = self.prepare_fit(params=params) + vars = result.init_vals + params = result.params + + fmin_kws = dict(method=method, + options={'maxiter': 1000 * (len(vars) + 1)}) + fmin_kws.update(self.kws) + fmin_kws.update(kws) + + # hess supported only in some methods + if 'hess' in fmin_kws and method not in ('Newton-CG', + 'dogleg', 'trust-ncg'): + fmin_kws.pop('hess') + + # jac supported only in some methods (and Dfun could be used...) + if 'jac' not in fmin_kws and fmin_kws.get('Dfun', None) is not None: + self.jacfcn = fmin_kws.pop('jac') + fmin_kws['jac'] = self.__jacobian + + if 'jac' in fmin_kws and method not in ('CG', 'BFGS', 'Newton-CG', + 'dogleg', 'trust-ncg'): + self.jacfcn = None + fmin_kws.pop('jac') + + if method == 'differential_evolution': + fmin_kws['method'] = _differential_evolution + bounds = [(par.min, par.max) for par in params.values()] + if not np.all(np.isfinite(bounds)): + raise ValueError('With differential evolution finite bounds ' + 'are required for each parameter') + bounds = [(-np.pi / 2., np.pi / 2.)] * len(vars) + fmin_kws['bounds'] = bounds + + # in scipy 0.14 this can be called directly from scipy_minimize + # When minimum scipy is 0.14 the following line and the else + # can be removed. + ret = _differential_evolution(self.penalty, vars, **fmin_kws) + else: + ret = scipy_minimize(self.penalty, vars, **fmin_kws) + + result.aborted = self._abort + self._abort = False + if isinstance(ret, dict): + for attr, value in ret.items(): + setattr(result, attr, value) + else: + for attr in dir(ret): + if not attr.startswith('_'): + setattr(result, attr, getattr(ret, attr)) + + result.x = np.atleast_1d(result.x) + result.chisqr = result.residual = self.__residual(result.x) + result.nvarys = len(vars) + result.ndata = 1 + result.nfree = 1 + if isinstance(result.residual, ndarray): + result.chisqr = (result.chisqr**2).sum() + result.ndata = len(result.residual) + result.nfree = result.ndata - result.nvarys + result.redchi = result.chisqr / result.nfree + _log_likelihood = result.ndata * np.log(result.redchi) + result.aic = _log_likelihood + 2 * result.nvarys + result.bic = _log_likelihood + np.log(result.ndata) * result.nvarys + + return result + + def emcee(self, params=None, steps=1000, nwalkers=100, burn=0, thin=1, + ntemps=1, pos=None, reuse_sampler=False, workers=1, + float_behavior='posterior', is_weighted=True, seed=None): + """ + Bayesian sampling of the posterior distribution for the parameters + using the `emcee` Markov Chain Monte Carlo package. The method assumes + that the prior is Uniform. You need to have `emcee` installed to use + this method. + + Parameters + ---------- + params : lmfit.Parameters, optional + Parameters to use as starting point. If this is not specified + then the Parameters used to initialise the Minimizer object are + used. + steps : int, optional + How many samples you would like to draw from the posterior + distribution for each of the walkers? + nwalkers : int, optional + Should be set so :math:`nwalkers >> nvarys`, where `nvarys` are + the number of parameters being varied during the fit. + "Walkers are the members of the ensemble. They are almost like + separate Metropolis-Hastings chains but, of course, the proposal + distribution for a given walker depends on the positions of all + the other walkers in the ensemble." - from the `emcee` webpage. + burn : int, optional + Discard this many samples from the start of the sampling regime. + thin : int, optional + Only accept 1 in every `thin` samples. + ntemps : int, optional + If `ntemps > 1` perform a Parallel Tempering. + pos : np.ndarray, optional + Specify the initial positions for the sampler. If `ntemps == 1` + then `pos.shape` should be `(nwalkers, nvarys)`. Otherwise, + `(ntemps, nwalkers, nvarys)`. You can also initialise using a + previous chain that had the same `ntemps`, `nwalkers` and + `nvarys`. Note that `nvarys` may be one larger than you expect it + to be if your `userfcn` returns an array and `is_weighted is + False`. + reuse_sampler : bool, optional + If you have already run `emcee` on a given `Minimizer` object then + it possesses an internal ``sampler`` attribute. You can continue to + draw from the same sampler (retaining the chain history) if you set + this option to `True`. Otherwise a new sampler is created. The + `nwalkers`, `ntemps`, `pos`, and `params` keywords are ignored with + this option. + **Important**: the Parameters used to create the sampler must not + change in-between calls to `emcee`. Alteration of Parameters + would include changed ``min``, ``max``, ``vary`` and ``expr`` + attributes. This may happen, for example, if you use an altered + Parameters object and call the `minimize` method in-between calls + to `emcee`. + workers : Pool-like or int, optional + For parallelization of sampling. It can be any Pool-like object + with a map method that follows the same calling sequence as the + built-in `map` function. If int is given as the argument, then a + multiprocessing-based pool is spawned internally with the + corresponding number of parallel processes. 'mpi4py'-based + parallelization and 'joblib'-based parallelization pools can also + be used here. **Note**: because of multiprocessing overhead it may + only be worth parallelising if the objective function is expensive + to calculate, or if there are a large number of objective + evaluations per step (`ntemps * nwalkers * nvarys`). + float_behavior : str, optional + Specifies meaning of the objective function output if it returns a + float. One of: + + 'posterior' - objective function returns a log-posterior + probability + 'chi2' - objective function returns :math:`\chi^2`. + + See Notes for further details. + is_weighted : bool, optional + Has your objective function been weighted by measurement + uncertainties? If `is_weighted is True` then your objective + function is assumed to return residuals that have been divided by + the true measurement uncertainty `(data - model) / sigma`. If + `is_weighted is False` then the objective function is assumed to + return unweighted residuals, `data - model`. In this case `emcee` + will employ a positive measurement uncertainty during the sampling. + This measurement uncertainty will be present in the output params + and output chain with the name `__lnsigma`. A side effect of this + is that you cannot use this parameter name yourself. + **Important** this parameter only has any effect if your objective + function returns an array. If your objective function returns a + float, then this parameter is ignored. See Notes for more details. + seed : int or `np.random.RandomState`, optional + If `seed` is an int, a new `np.random.RandomState` instance is used, + seeded with `seed`. + If `seed` is already a `np.random.RandomState` instance, then that + `np.random.RandomState` instance is used. + Specify `seed` for repeatable minimizations. + + Returns + ------- + result : MinimizerResult + MinimizerResult object containing updated params, statistics, + etc. The `MinimizerResult` also contains the ``chain``, + ``flatchain`` and ``lnprob`` attributes. The ``chain`` + and ``flatchain`` attributes contain the samples and have the shape + `(nwalkers, (steps - burn) // thin, nvarys)` or + `(ntemps, nwalkers, (steps - burn) // thin, nvarys)`, + depending on whether Parallel tempering was used or not. + `nvarys` is the number of parameters that are allowed to vary. + The ``flatchain`` attribute is a `pandas.DataFrame` of the + flattened chain, `chain.reshape(-1, nvarys)`. To access flattened + chain values for a particular parameter use + `result.flatchain[parname]`. The ``lnprob`` attribute contains the + log probability for each sample in ``chain``. The sample with the + highest probability corresponds to the maximum likelihood estimate. + + Notes + ----- + This method samples the posterior distribution of the parameters using + Markov Chain Monte Carlo. To do so it needs to calculate the + log-posterior probability of the model parameters, `F`, given the data, + `D`, :math:`\ln p(F_{true} | D)`. This 'posterior probability' is + calculated as: + + ..math:: + + \ln p(F_{true} | D) \propto \ln p(D | F_{true}) + \ln p(F_{true}) + + where :math:`\ln p(D | F_{true})` is the 'log-likelihood' and + :math:`\ln p(F_{true})` is the 'log-prior'. The default log-prior + encodes prior information already known about the model. This method + assumes that the log-prior probability is `-np.inf` (impossible) if the + one of the parameters is outside its limits. The log-prior probability + term is zero if all the parameters are inside their bounds (known as a + uniform prior). The log-likelihood function is given by [1]_: + + ..math:: + + \ln p(D|F_{true}) = -\frac{1}{2}\sum_n \left[\frac{\left(g_n(F_{true}) - D_n \right)^2}{s_n^2}+\ln (2\pi s_n^2)\right] + + The first summand in the square brackets represents the residual for a + given datapoint (:math:`g` being the generative model) . This term + represents :math:`\chi^2` when summed over all datapoints. + Ideally the objective function used to create `lmfit.Minimizer` should + return the log-posterior probability, :math:`\ln p(F_{true} | D)`. + However, since the in-built log-prior term is zero, the objective + function can also just return the log-likelihood, unless you wish to + create a non-uniform prior. + + If a float value is returned by the objective function then this value + is assumed by default to be the log-posterior probability, i.e. + `float_behavior is 'posterior'`. If your objective function returns + :math:`\chi^2`, then you should use a value of `'chi2'` for + `float_behavior`. `emcee` will then multiply your :math:`\chi^2` value + by -0.5 to obtain the posterior probability. + + However, the default behaviour of many objective functions is to return + a vector of (possibly weighted) residuals. Therefore, if your objective + function returns a vector, `res`, then the vector is assumed to contain + the residuals. If `is_weighted is True` then your residuals are assumed + to be correctly weighted by the standard deviation of the data points + (`res = (data - model) / sigma`) and the log-likelihood (and + log-posterior probability) is calculated as: `-0.5 * np.sum(res **2)`. + This ignores the second summand in the square brackets. Consequently, + in order to calculate a fully correct log-posterior probability value + your objective function should return a single value. If + `is_weighted is False` then the data uncertainty, `s_n`, will be + treated as a nuisance parameter and will be marginalised out. This is + achieved by employing a strictly positive uncertainty + (homoscedasticity) for each data point, :math:`s_n = exp(__lnsigma)`. + `__lnsigma` will be present in `MinimizerResult.params`, as well as + `Minimizer.chain`, `nvarys` will also be increased by one. + + References + ---------- + .. [1] http://dan.iel.fm/emcee/current/user/line/ + """ + if not HAS_EMCEE: + raise NotImplementedError('You must have emcee to use' + ' the emcee method') + tparams = params + # if you're reusing the sampler then ntemps, nwalkers have to be + # determined from the previous sampling + if reuse_sampler: + if not hasattr(self, 'sampler') or not hasattr(self, '_lastpos'): + raise ValueError("You wanted to use an existing sampler, but" + "it hasn't been created yet") + if len(self._lastpos.shape) == 2: + ntemps = 1 + nwalkers = self._lastpos.shape[0] + elif len(self._lastpos.shape) == 3: + ntemps = self._lastpos.shape[0] + nwalkers = self._lastpos.shape[1] + tparams = None + + result = self.prepare_fit(params=tparams) + params = result.params + + # check if the userfcn returns a vector of residuals + out = self.userfcn(params, *self.userargs, **self.userkws) + out = np.asarray(out).ravel() + if out.size > 1 and is_weighted is False: + # we need to marginalise over a constant data uncertainty + if '__lnsigma' not in params: + # __lnsigma should already be in params if is_weighted was + # previously set to True. + params.add('__lnsigma', value=0.01, min=-np.inf, max=np.inf, vary=True) + # have to re-prepare the fit + result = self.prepare_fit(params) + params = result.params + + # Removing internal parameter scaling. We could possibly keep it, + # but I don't know how this affects the emcee sampling. + bounds = [] + var_arr = np.zeros(len(result.var_names)) + i = 0 + for par in params: + param = params[par] + if param.expr is not None: + param.vary = False + if param.vary: + var_arr[i] = param.value + i += 1 + else: + # don't want to append bounds if they're not being varied. + continue + + param.from_internal = lambda val: val + lb, ub = param.min, param.max + if lb is None or lb is np.nan: + lb = -np.inf + if ub is None or ub is np.nan: + ub = np.inf + bounds.append((lb, ub)) + bounds = np.array(bounds) + + self.nvarys = len(result.var_names) + + # set up multiprocessing options for the samplers + auto_pool = None + sampler_kwargs = {} + if type(workers) is int and workers > 1: + auto_pool = multiprocessing.Pool(workers) + sampler_kwargs['pool'] = auto_pool + elif hasattr(workers, 'map'): + sampler_kwargs['pool'] = workers + + # function arguments for the log-probability functions + # these values are sent to the log-probability functions by the sampler. + lnprob_args = (self.userfcn, params, result.var_names, bounds) + lnprob_kwargs = {'is_weighted': is_weighted, + 'float_behavior': float_behavior, + 'userargs': self.userargs, + 'userkws': self.userkws} + + if ntemps > 1: + # the prior and likelihood function args and kwargs are the same + sampler_kwargs['loglargs'] = lnprob_args + sampler_kwargs['loglkwargs'] = lnprob_kwargs + sampler_kwargs['logpargs'] = (bounds,) + else: + sampler_kwargs['args'] = lnprob_args + sampler_kwargs['kwargs'] = lnprob_kwargs + + # set up the random number generator + rng = _make_random_gen(seed) + + # now initialise the samplers + if reuse_sampler: + if auto_pool is not None: + self.sampler.pool = auto_pool + + p0 = self._lastpos + if p0.shape[-1] != self.nvarys: + raise ValueError("You cannot reuse the sampler if the number" + "of varying parameters has changed") + elif ntemps > 1: + # Parallel Tempering + # jitter the starting position by scaled Gaussian noise + p0 = 1 + rng.randn(ntemps, nwalkers, self.nvarys) * 1.e-4 + p0 *= var_arr + self.sampler = emcee.PTSampler(ntemps, nwalkers, self.nvarys, + _lnpost, _lnprior, **sampler_kwargs) + else: + p0 = 1 + rng.randn(nwalkers, self.nvarys) * 1.e-4 + p0 *= var_arr + self.sampler = emcee.EnsembleSampler(nwalkers, self.nvarys, + _lnpost, **sampler_kwargs) + + # user supplies an initialisation position for the chain + # If you try to run the sampler with p0 of a wrong size then you'll get + # a ValueError. Note, you can't initialise with a position if you are + # reusing the sampler. + if pos is not None and not reuse_sampler: + tpos = np.asfarray(pos) + if p0.shape == tpos.shape: + pass + # trying to initialise with a previous chain + elif (tpos.shape[0::2] == (nwalkers, self.nvarys)): + tpos = tpos[:, -1, :] + # initialising with a PTsampler chain. + elif ntemps > 1 and tpos.ndim == 4: + tpos_shape = list(tpos.shape) + tpos_shape.pop(2) + if tpos_shape == (ntemps, nwalkers, self.nvarys): + tpos = tpos[..., -1, :] + else: + raise ValueError('pos should have shape (nwalkers, nvarys)' + 'or (ntemps, nwalkers, nvarys) if ntemps > 1') + p0 = tpos + + # if you specified a seed then you also need to seed the sampler + if seed is not None: + self.sampler.random_state = rng.get_state() + + # now do a production run, sampling all the time + output = self.sampler.run_mcmc(p0, steps) + self._lastpos = output[0] + + # discard the burn samples and thin + chain = self.sampler.chain[..., burn::thin, :] + lnprobability = self.sampler.lnprobability[:, burn::thin] + + flatchain = chain.reshape((-1, self.nvarys)) + + quantiles = np.percentile(flatchain, [15.87, 50, 84.13], axis=0) + + for i, var_name in enumerate(result.var_names): + std_l, median, std_u = quantiles[:, i] + params[var_name].value = median + params[var_name].stderr = 0.5 * (std_u - std_l) + params[var_name].correl = {} + + params.update_constraints() + + # work out correlation coefficients + corrcoefs = np.corrcoef(flatchain.T) + + for i, var_name in enumerate(result.var_names): + for j, var_name2 in enumerate(result.var_names): + if i != j: + result.params[var_name].correl[var_name2] = corrcoefs[i, j] + + result.chain = np.copy(chain) + result.lnprob = np.copy(lnprobability) + result.errorbars = True + result.nvarys = len(result.var_names) + + if auto_pool is not None: + auto_pool.terminate() + + return result + + def leastsq(self, params=None, **kws): + """ + Use Levenberg-Marquardt minimization to perform a fit. + This assumes that ModelParameters have been stored, and a function to + minimize has been properly set up. + + This wraps scipy.optimize.leastsq. + + When possible, this calculates the estimated uncertainties and + variable correlations from the covariance matrix. + + Writes outputs to many internal attributes. + + Parameters + ---------- + params : Parameters, optional + Parameters to use as starting points. + kws : dict, optional + Minimizer options to pass to scipy.optimize.leastsq. + + Returns + ------- + success : bool + True if fit was successful, False if not. + """ + result = self.prepare_fit(params=params) + vars = result.init_vals + nvars = len(vars) + lskws = dict(full_output=1, xtol=1.e-7, ftol=1.e-7, col_deriv=False, + gtol=1.e-7, maxfev=2000*(nvars+1), Dfun=None) + + lskws.update(self.kws) + lskws.update(kws) + + self.col_deriv = False + if lskws['Dfun'] is not None: + self.jacfcn = lskws['Dfun'] + self.col_deriv = lskws['col_deriv'] + lskws['Dfun'] = self.__jacobian + + # suppress runtime warnings during fit and error analysis + orig_warn_settings = np.geterr() + np.seterr(all='ignore') + + lsout = scipy_leastsq(self.__residual, vars, **lskws) + _best, _cov, infodict, errmsg, ier = lsout + result.aborted = self._abort + self._abort = False + + result.residual = resid = infodict['fvec'] + result.ier = ier + result.lmdif_message = errmsg + result.message = 'Fit succeeded.' + result.success = ier in [1, 2, 3, 4] + if result.aborted: + result.message = 'Fit aborted by user callback.' + result.success = False + elif ier == 0: + result.message = 'Invalid Input Parameters.' + elif ier == 5: + result.message = self.err_maxfev % lskws['maxfev'] + else: + result.message = 'Tolerance seems to be too small.' + + result.ndata = len(resid) + + result.chisqr = (resid**2).sum() + result.nfree = (result.ndata - nvars) + result.redchi = result.chisqr / result.nfree + _log_likelihood = result.ndata * np.log(result.redchi) + result.aic = _log_likelihood + 2 * nvars + result.bic = _log_likelihood + np.log(result.ndata) * nvars + + params = result.params + + # need to map _best values to params, then calculate the + # grad for the variable parameters + grad = ones_like(_best) + vbest = ones_like(_best) + + # ensure that _best, vbest, and grad are not + # broken 1-element ndarrays. + if len(np.shape(_best)) == 0: + _best = np.array([_best]) + if len(np.shape(vbest)) == 0: + vbest = np.array([vbest]) + if len(np.shape(grad)) == 0: + grad = np.array([grad]) + + for ivar, name in enumerate(result.var_names): + grad[ivar] = params[name].scale_gradient(_best[ivar]) + vbest[ivar] = params[name].value + + # modified from JJ Helmus' leastsqbound.py + infodict['fjac'] = transpose(transpose(infodict['fjac']) / + take(grad, infodict['ipvt'] - 1)) + rvec = dot(triu(transpose(infodict['fjac'])[:nvars, :]), + take(eye(nvars), infodict['ipvt'] - 1, 0)) + try: + result.covar = inv(dot(transpose(rvec), rvec)) + except (LinAlgError, ValueError): + result.covar = None + + has_expr = False + for par in params.values(): + par.stderr, par.correl = 0, None + has_expr = has_expr or par.expr is not None + + # self.errorbars = error bars were successfully estimated + result.errorbars = (result.covar is not None) + if result.aborted: + result.errorbars = False + if result.errorbars: + if self.scale_covar: + result.covar *= result.redchi + for ivar, name in enumerate(result.var_names): + par = params[name] + par.stderr = sqrt(result.covar[ivar, ivar]) + par.correl = {} + try: + result.errorbars = result.errorbars and (par.stderr > 0.0) + for jvar, varn2 in enumerate(result.var_names): + if jvar != ivar: + par.correl[varn2] = (result.covar[ivar, jvar] / + (par.stderr * sqrt(result.covar[jvar, jvar]))) + except: + result.errorbars = False + + if has_expr: + # uncertainties on constrained parameters: + # get values with uncertainties (including correlations), + # temporarily set Parameter values to these, + # re-evaluate contrained parameters to extract stderr + # and then set Parameters back to best-fit value + try: + uvars = uncertainties.correlated_values(vbest, result.covar) + except (LinAlgError, ValueError): + uvars = None + if uvars is not None: + for par in params.values(): + eval_stderr(par, uvars, result.var_names, params) + # restore nominal values + for v, nam in zip(uvars, result.var_names): + params[nam].value = v.nominal_value + + if not result.errorbars: + result.message = '%s. Could not estimate error-bars' % result.message + + np.seterr(**orig_warn_settings) + return result + + def minimize(self, method='leastsq', params=None, **kws): + """ + Perform the minimization. + + Parameters + ---------- + method : str, optional + Name of the fitting method to use. + One of: + 'leastsq' - Levenberg-Marquardt (default) + 'nelder' - Nelder-Mead + 'lbfgsb' - L-BFGS-B + 'powell' - Powell + 'cg' - Conjugate-Gradient + 'newton' - Newton-CG + 'cobyla' - Cobyla + 'tnc' - Truncate Newton + 'trust-ncg' - Trust Newton-CGn + 'dogleg' - Dogleg + 'slsqp' - Sequential Linear Squares Programming + 'differential_evolution' - differential evolution + + params : Parameters, optional + parameters to use as starting values + + Returns + ------- + result : MinimizerResult + + MinimizerResult object contains updated params, fit statistics, etc. + + """ + + function = self.leastsq + kwargs = {'params': params} + kwargs.update(kws) + + user_method = method.lower() + if user_method.startswith('least'): + function = self.leastsq + elif HAS_SCALAR_MIN: + function = self.scalar_minimize + for key, val in SCALAR_METHODS.items(): + if (key.lower().startswith(user_method) or + val.lower().startswith(user_method)): + kwargs['method'] = val + elif (user_method.startswith('nelder') or + user_method.startswith('fmin')): + function = self.fmin + elif user_method.startswith('lbfgsb'): + function = self.lbfgsb + return function(**kwargs) + + +def _lnprior(theta, bounds): + """ + Calculates an improper uniform log-prior probability + + Parameters + ---------- + theta : sequence + float parameter values (only those being varied) + bounds : np.ndarray + Lower and upper bounds of parameters that are varying. + Has shape (nvarys, 2). + + Returns + ------- + lnprob : float + Log prior probability + """ + if (np.any(theta > bounds[:, 1]) + or np.any(theta < bounds[:, 0])): + return -np.inf + else: + return 0 + + +def _lnpost(theta, userfcn, params, var_names, bounds, userargs=(), + userkws=None, float_behavior='posterior', is_weighted=True): + """ + Calculates the log-posterior probability. See the `Minimizer.emcee` method + for more details + + Parameters + ---------- + theta : sequence + float parameter values (only those being varied) + userfcn : callable + User objective function + params : lmfit.Parameters + The entire set of Parameters + var_names : list + The names of the parameters that are varying + bounds : np.ndarray + Lower and upper bounds of parameters. Has shape (nvarys, 2). + userargs : tuple, optional + Extra positional arguments required for user objective function + userkws : dict, optional + Extra keyword arguments required for user objective function + float_behavior : str, optional + Specifies meaning of objective when it returns a float. One of: + + 'posterior' - objective function returnins a log-posterior + probability. + 'chi2' - objective function returns a chi2 value. + + is_weighted : bool + If `userfcn` returns a vector of residuals then `is_weighted` + specifies if the residuals have been weighted by data uncertainties. + + Returns + ------- + lnprob : float + Log posterior probability + """ + # the comparison has to be done on theta and bounds. DO NOT inject theta + # values into Parameters, then compare Parameters values to the bounds. + # Parameters values are clipped to stay within bounds. + if (np.any(theta > bounds[:, 1]) + or np.any(theta < bounds[:, 0])): + return -np.inf + + for name, val in zip(var_names, theta): + params[name].value = val + + userkwargs = {} + if userkws is not None: + userkwargs = userkws + + # update the constraints + params.update_constraints() + + # now calculate the log-likelihood + out = userfcn(params, *userargs, **userkwargs) + lnprob = np.asarray(out).ravel() + + if lnprob.size > 1: + # objective function returns a vector of residuals + if '__lnsigma' in params and not is_weighted: + # marginalise over a constant data uncertainty + __lnsigma = params['__lnsigma'].value + c = np.log(2 * np.pi) + 2 * __lnsigma + lnprob = -0.5 * np.sum((lnprob / np.exp(__lnsigma)) ** 2 + c) + else: + lnprob = -0.5 * (lnprob * lnprob).sum() + else: + # objective function returns a single value. + # use float_behaviour to figure out if the value is posterior or chi2 + if float_behavior == 'posterior': + pass + elif float_behavior == 'chi2': + lnprob *= -0.5 + else: + raise ValueError("float_behaviour must be either 'posterior' or" + " 'chi2' " + float_behavior) + + return lnprob + + +def _make_random_gen(seed): + """Turn seed into a np.random.RandomState instance + + If seed is None, return the RandomState singleton used by np.random. + If seed is an int, return a new RandomState instance seeded with seed. + If seed is already a RandomState instance, return it. + Otherwise raise ValueError. + """ + if seed is None or seed is np.random: + return np.random.mtrand._rand + if isinstance(seed, (numbers.Integral, np.integer)): + return np.random.RandomState(seed) + if isinstance(seed, np.random.RandomState): + return seed + raise ValueError('%r cannot be used to seed a numpy.random.RandomState' + ' instance' % seed) + + +def minimize(fcn, params, method='leastsq', args=None, kws=None, + scale_covar=True, iter_cb=None, **fit_kws): + """ + A general purpose curvefitting function + The minimize function takes a objective function to be minimized, a + dictionary (lmfit.parameter.Parameters) containing the model parameters, + and several optional arguments. + + Parameters + ---------- + fcn : callable + objective function that returns the residual (difference between + model and data) to be minimized in a least squares sense. The + function must have the signature: + `fcn(params, *args, **kws)` + params : lmfit.parameter.Parameters object. + contains the Parameters for the model. + method : str, optional + Name of the fitting method to use. + One of: + 'leastsq' - Levenberg-Marquardt (default) + 'nelder' - Nelder-Mead + 'lbfgsb' - L-BFGS-B + 'powell' - Powell + 'cg' - Conjugate-Gradient + 'newton' - Newton-CG + 'cobyla' - Cobyla + 'tnc' - Truncate Newton + 'trust-ncg' - Trust Newton-CGn + 'dogleg' - Dogleg + 'slsqp' - Sequential Linear Squares Programming + 'differential_evolution' - differential evolution + + args : tuple, optional + Positional arguments to pass to fcn. + kws : dict, optional + keyword arguments to pass to fcn. + iter_cb : callable, optional + Function to be called at each fit iteration. This function should + have the signature `iter_cb(params, iter, resid, *args, **kws)`, + where where `params` will have the current parameter values, `iter` + the iteration, `resid` the current residual array, and `*args` + and `**kws` as passed to the objective function. + scale_covar : bool, optional + Whether to automatically scale the covariance matrix (leastsq + only). + fit_kws : dict, optional + Options to pass to the minimizer being used. + + Notes + ----- + The objective function should return the value to be minimized. For the + Levenberg-Marquardt algorithm from leastsq(), this returned value must + be an array, with a length greater than or equal to the number of + fitting variables in the model. For the other methods, the return value + can either be a scalar or an array. If an array is returned, the sum of + squares of the array will be sent to the underlying fitting method, + effectively doing a least-squares optimization of the return values. + + A common use for `args` and `kwds` would be to pass in other + data needed to calculate the residual, including such things as the + data array, dependent variable, uncertainties in the data, and other + data structures for the model calculation. + """ + fitter = Minimizer(fcn, params, fcn_args=args, fcn_kws=kws, + iter_cb=iter_cb, scale_covar=scale_covar, **fit_kws) + return fitter.minimize(method=method) diff --git a/lmfit/model.py b/lmfit/model.py index d627c72..5dd1643 100644 --- a/lmfit/model.py +++ b/lmfit/model.py @@ -1,1031 +1,1067 @@ -"""
-Concise nonlinear curve fitting.
-"""
-from __future__ import print_function
-import warnings
-import inspect
-import operator
-from copy import deepcopy
-import numpy as np
-from . import Parameters, Parameter, Minimizer
-from .printfuncs import fit_report, ci_report
-from .confidence import conf_interval
-
-from collections import MutableSet
-
-try:
- from collections import OrderedDict
-except ImportError:
- from ordereddict import OrderedDict
-
-# Use pandas.isnull for aligning missing data is pandas is available.
-# otherwise use numpy.isnan
-try:
- from pandas import isnull, Series
-except ImportError:
- isnull = np.isnan
- Series = type(NotImplemented)
-
-def _align(var, mask, data):
- "align missing data, with pandas is available"
- if isinstance(data, Series) and isinstance(var, Series):
- return var.reindex_like(data).dropna()
- elif mask is not None:
- return var[mask]
- return var
-
-
-try:
- from matplotlib import pyplot as plt
- _HAS_MATPLOTLIB = True
-except ImportError:
- _HAS_MATPLOTLIB = False
-
-
-def _ensureMatplotlib(function):
- if _HAS_MATPLOTLIB:
- return function
- else:
- def no_op(*args, **kwargs):
- print('matplotlib module is required for plotting the results')
-
- return no_op
-
-
-class Model(object):
- """Create a model from a user-defined function.
-
- Parameters
- ----------
- func: function to be wrapped
- independent_vars: list of strings or None (default)
- arguments to func that are independent variables
- param_names: list of strings or None (default)
- names of arguments to func that are to be made into parameters
- missing: None, 'none', 'drop', or 'raise'
- 'none' or None: Do not check for null or missing values (default)
- 'drop': Drop null or missing observations in data.
- if pandas is installed, pandas.isnull is used, otherwise
- numpy.isnan is used.
- 'raise': Raise a (more helpful) exception when data contains null
- or missing values.
- name: None or string
- name for the model. When `None` (default) the name is the same as
- the model function (`func`).
-
- Note
- ----
- Parameter names are inferred from the function arguments,
- and a residual function is automatically constructed.
-
- Example
- -------
- >>> def decay(t, tau, N):
- ... return N*np.exp(-t/tau)
- ...
- >>> my_model = Model(decay, independent_vars=['t'])
- """
-
- _forbidden_args = ('data', 'weights', 'params')
- _invalid_ivar = "Invalid independent variable name ('%s') for function %s"
- _invalid_par = "Invalid parameter name ('%s') for function %s"
- _invalid_missing = "missing must be None, 'none', 'drop', or 'raise'."
- _valid_missing = (None, 'none', 'drop', 'raise')
-
- _invalid_hint = "unknown parameter hint '%s' for param '%s'"
- _hint_names = ('value', 'vary', 'min', 'max', 'expr')
-
- def __init__(self, func, independent_vars=None, param_names=None,
- missing='none', prefix='', name=None, **kws):
- self.func = func
- self._prefix = prefix
- self._param_root_names = param_names # will not include prefixes
- self.independent_vars = independent_vars
- self._func_allargs = []
- self._func_haskeywords = False
- if not missing in self._valid_missing:
- raise ValueError(self._invalid_missing)
- self.missing = missing
- self.opts = kws
- self.param_hints = OrderedDict()
- # the following has been changed from OrderedSet for the time being
- self._param_names = []
- self._parse_params()
- if self.independent_vars is None:
- self.independent_vars = []
- if name is None and hasattr(self.func, '__name__'):
- name = self.func.__name__
- self._name = name
-
- def _reprstring(self, long=False):
- out = self._name
- opts = []
- if len(self._prefix) > 0:
- opts.append("prefix='%s'" % (self._prefix))
- if long:
- for k, v in self.opts.items():
- opts.append("%s='%s'" % (k, v))
- if len(opts) > 0:
- out = "%s, %s" % (out, ', '.join(opts))
- return "Model(%s)" % out
-
- @property
- def name(self):
- return self._reprstring(long=False)
-
- @name.setter
- def name(self, value):
- self._name = value
-
- @property
- def prefix(self):
- return self._prefix
-
- @property
- def param_names(self):
- return self._param_names
-
- def __repr__(self):
- return "<lmfit.Model: %s>" % (self.name)
-
- def copy(self, **kwargs):
- """DOES NOT WORK"""
- raise NotImplementedError("Model.copy does not work. Make a new Model")
-
- def _parse_params(self):
- "build params from function arguments"
- if self.func is None:
- return
- argspec = inspect.getargspec(self.func)
- pos_args = argspec.args[:]
- keywords = argspec.keywords
- kw_args = {}
- if argspec.defaults is not None:
- for val in reversed(argspec.defaults):
- kw_args[pos_args.pop()] = val
-
- self._func_haskeywords = keywords is not None
- self._func_allargs = pos_args + list(kw_args.keys())
- allargs = self._func_allargs
-
- if len(allargs) == 0 and keywords is not None:
- return
-
- # default independent_var = 1st argument
- if self.independent_vars is None:
- self.independent_vars = [pos_args[0]]
-
- # default param names: all positional args
- # except independent variables
- self.def_vals = {}
- might_be_param = []
- if self._param_root_names is None:
- self._param_root_names = pos_args[:]
- for key, val in kw_args.items():
- if (not isinstance(val, bool) and
- isinstance(val, (float, int))):
- self._param_root_names.append(key)
- self.def_vals[key] = val
- elif val is None:
- might_be_param.append(key)
- for p in self.independent_vars:
- if p in self._param_root_names:
- self._param_root_names.remove(p)
-
- new_opts = {}
- for opt, val in self.opts.items():
- if (opt in self._param_root_names or opt in might_be_param and
- isinstance(val, Parameter)):
- self.set_param_hint(opt, value=val.value,
- min=val.min, max=val.max, expr=val.expr)
- elif opt in self._func_allargs:
- new_opts[opt] = val
- self.opts = new_opts
-
- names = []
- if self._prefix is None:
- self._prefix = ''
- for pname in self._param_root_names:
- names.append("%s%s" % (self._prefix, pname))
-
- # check variables names for validity
- # The implicit magic in fit() requires us to disallow some
- fname = self.func.__name__
- for arg in self.independent_vars:
- if arg not in allargs or arg in self._forbidden_args:
- raise ValueError(self._invalid_ivar % (arg, fname))
- for arg in names:
- if (self._strip_prefix(arg) not in allargs or
- arg in self._forbidden_args):
- raise ValueError(self._invalid_par % (arg, fname))
- # the following as been changed from OrderedSet for the time being.
- self._param_names = names[:]
-
- def set_param_hint(self, name, **kwargs):
- """set hints for parameter, including optional bounds
- and constraints (value, vary, min, max, expr)
- these will be used by make_params() when building
- default parameters
-
- example:
- model = GaussianModel()
- model.set_param_hint('amplitude', min=-100.0, max=0.)
- """
- npref = len(self._prefix)
- if npref > 0 and name.startswith(self._prefix):
- name = name[npref:]
-
- thishint = {}
- if name in self.param_hints:
- thishint = self.param_hints.pop(name)
- thishint.update(kwargs)
-
- self.param_hints[name] = OrderedDict()
- for key, val in thishint.items():
- if key in self._hint_names:
- self.param_hints[name][key] = val
- else:
- warnings.warn(self._invalid_hint % (key, name))
-
- def make_params(self, verbose=False, **kwargs):
- """create and return a Parameters object for a Model.
- This applies any default values
- """
- params = Parameters()
- # first build parameters defined in param_hints
- # note that composites may define their own additional
- # convenience parameters here
- for basename, hint in self.param_hints.items():
- name = "%s%s" % (self._prefix, basename)
- if name in params:
- par = params[name]
- else:
- par = Parameter(name=name)
- par._delay_asteval = True
- for item in self._hint_names:
- if item in hint:
- setattr(par, item, hint[item])
- # Add the new parameter to self._param_names
- if name not in self._param_names:
- self._param_names.append(name)
- params.add(par)
- if verbose:
- print( ' - Adding parameter for hint "%s"' % name)
-
- # next, make sure that all named parameters are included
- for name in self.param_names:
- if name in params:
- par = params[name]
- else:
- par = Parameter(name=name)
- par._delay_asteval = True
- basename = name[len(self._prefix):]
- # apply defaults from model function definition
- if basename in self.def_vals:
- par.value = self.def_vals[basename]
- # apply defaults from parameter hints
- if basename in self.param_hints:
- hint = self.param_hints[basename]
- for item in self._hint_names:
- if item in hint:
- setattr(par, item, hint[item])
- # apply values passed in through kw args
- if basename in kwargs:
- # kw parameter names with no prefix
- par.value = kwargs[basename]
- if name in kwargs:
- # kw parameter names with prefix
- par.value = kwargs[name]
- params.add(par)
- if verbose:
- print( ' - Adding parameter "%s"' % name)
-
- for p in params.values():
- p._delay_asteval = False
- return params
-
- def guess(self, data=None, **kws):
- """stub for guess starting values --
- should be implemented for each model subclass to
- run self.make_params(), update starting values
- and return a Parameters object"""
- cname = self.__class__.__name__
- msg = 'guess() not implemented for %s' % cname
- raise NotImplementedError(msg)
-
- def _residual(self, params, data, weights, **kwargs):
- "default residual: (data-model)*weights"
- diff = self.eval(params, **kwargs) - data
- if weights is not None:
- diff *= weights
- return np.asarray(diff).ravel() # for compatibility with pandas.Series
-
- def _handle_missing(self, data):
- "handle missing data"
- if self.missing == 'raise':
- if np.any(isnull(data)):
- raise ValueError("Data contains a null value.")
- elif self.missing == 'drop':
- mask = ~isnull(data)
- if np.all(mask):
- return None # short-circuit this -- no missing values
- mask = np.asarray(mask) # for compatibility with pandas.Series
- return mask
-
- def _strip_prefix(self, name):
- npref = len(self._prefix)
- if npref > 0 and name.startswith(self._prefix):
- name = name[npref:]
- return name
-
- def make_funcargs(self, params=None, kwargs=None, strip=True):
- """convert parameter values and keywords to function arguments"""
- if params is None: params = {}
- if kwargs is None: kwargs = {}
- out = {}
- out.update(self.opts)
- for name, par in params.items():
- if strip:
- name = self._strip_prefix(name)
- if name in self._func_allargs or self._func_haskeywords:
- out[name] = par.value
-
- # kwargs handled slightly differently -- may set param value too!
- for name, val in kwargs.items():
- if strip:
- name = self._strip_prefix(name)
- if name in self._func_allargs or self._func_haskeywords:
- out[name] = val
- if name in params:
- params[name].value = val
- return out
-
- def _make_all_args(self, params=None, **kwargs):
- """generate **all** function args for all functions"""
- args = {}
- for key, val in self.make_funcargs(params, kwargs).items():
- args["%s%s" % (self._prefix, key)] = val
- return args
-
- def eval(self, params=None, **kwargs):
- """evaluate the model with the supplied parameters"""
- result = self.func(**self.make_funcargs(params, kwargs))
- # Handle special case of constant result and one
- # independent variable (of any dimension).
- if np.ndim(result) == 0 and len(self.independent_vars) == 1:
- result = np.tile(result, kwargs[self.independent_vars[0]].shape)
- return result
-
- @property
- def components(self):
- """return components for composite model"""
- return [self]
-
- def eval_components(self, params=None, **kwargs):
- """
- evaluate the model with the supplied parameters and returns a ordered
- dict containting name, result pairs.
- """
- key = self._prefix
- if len(key) < 1:
- key = self._name
- return {key: self.eval(params=params, **kwargs)}
-
- def fit(self, data, params=None, weights=None, method='leastsq',
- iter_cb=None, scale_covar=True, verbose=True, fit_kws=None, **kwargs):
- """Fit the model to the data.
-
- Parameters
- ----------
- data: array-like
- params: Parameters object
- weights: array-like of same size as data
- used for weighted fit
- method: fitting method to use (default = 'leastsq')
- iter_cb: None or callable callback function to call at each iteration.
- scale_covar: bool (default True) whether to auto-scale covariance matrix
- verbose: bool (default True) print a message when a new parameter is
- added because of a hint.
- fit_kws: dict
- default fitting options, such as xtol and maxfev, for scipy optimizer
- keyword arguments: optional, named like the arguments of the
- model function, will override params. See examples below.
-
- Returns
- -------
- lmfit.ModelResult
-
- Examples
- --------
- # Take t to be the independent variable and data to be the
- # curve we will fit.
-
- # Using keyword arguments to set initial guesses
- >>> result = my_model.fit(data, tau=5, N=3, t=t)
-
- # Or, for more control, pass a Parameters object.
- >>> result = my_model.fit(data, params, t=t)
-
- # Keyword arguments override Parameters.
- >>> result = my_model.fit(data, params, tau=5, t=t)
-
- Note
- ----
- All parameters, however passed, are copied on input, so the original
- Parameter objects are unchanged.
-
- """
- if params is None:
- params = self.make_params(verbose=verbose)
- else:
- params = deepcopy(params)
-
- # If any kwargs match parameter names, override params.
- param_kwargs = set(kwargs.keys()) & set(self.param_names)
- for name in param_kwargs:
- p = kwargs[name]
- if isinstance(p, Parameter):
- p.name = name # allows N=Parameter(value=5) with implicit name
- params[name] = deepcopy(p)
- else:
- params[name].set(value=p)
- del kwargs[name]
-
- # All remaining kwargs should correspond to independent variables.
- for name in kwargs.keys():
- if name not in self.independent_vars:
- warnings.warn("The keyword argument %s does not" % name +
- "match any arguments of the model function." +
- "It will be ignored.", UserWarning)
-
- # If any parameter is not initialized raise a more helpful error.
- missing_param = any([p not in params.keys()
- for p in self.param_names])
- blank_param = any([(p.value is None and p.expr is None)
- for p in params.values()])
- if missing_param or blank_param:
- msg = ('Assign each parameter an initial value by passing '
- 'Parameters or keyword arguments to fit.\n')
- missing = [p for p in self.param_names if p not in params.keys()]
- blank = [name for name, p in params.items()
- if (p.value is None and p.expr is None)]
- msg += 'Missing parameters: %s\n' % str(missing)
- msg += 'Non initialized parameters: %s' % str(blank)
- raise ValueError(msg)
-
- # Do not alter anything that implements the array interface (np.array, pd.Series)
- # but convert other iterables (e.g., Python lists) to numpy arrays.
- if not hasattr(data, '__array__'):
- data = np.asfarray(data)
- for var in self.independent_vars:
- var_data = kwargs[var]
- if (not hasattr(var_data, '__array__')) and (not np.isscalar(var_data)):
- kwargs[var] = np.asfarray(var_data)
-
- # Handle null/missing values.
- mask = None
- if self.missing not in (None, 'none'):
- mask = self._handle_missing(data) # This can raise.
- if mask is not None:
- data = data[mask]
- if weights is not None:
- weights = _align(weights, mask, data)
-
- # If independent_vars and data are alignable (pandas), align them,
- # and apply the mask from above if there is one.
- for var in self.independent_vars:
- if not np.isscalar(kwargs[var]):
- kwargs[var] = _align(kwargs[var], mask, data)
-
- if fit_kws is None:
- fit_kws = {}
-
- output = ModelResult(self, params, method=method, iter_cb=iter_cb,
- scale_covar=scale_covar, fcn_kws=kwargs,
- **fit_kws)
- output.fit(data=data, weights=weights)
- output.components = self.components
- return output
-
- def __add__(self, other):
- return CompositeModel(self, other, operator.add)
-
- def __sub__(self, other):
- return CompositeModel(self, other, operator.sub)
-
- def __mul__(self, other):
- return CompositeModel(self, other, operator.mul)
-
- def __div__(self, other):
- return CompositeModel(self, other, operator.truediv)
-
- def __truediv__(self, other):
- return CompositeModel(self, other, operator.truediv)
-
-
-class CompositeModel(Model):
- """Create a composite model -- a binary operator of two Models
-
- Parameters
- ----------
- left_model: left-hand side model-- must be a Model()
- right_model: right-hand side model -- must be a Model()
- oper: callable binary operator (typically, operator.add, operator.mul, etc)
-
- independent_vars: list of strings or None (default)
- arguments to func that are independent variables
- param_names: list of strings or None (default)
- names of arguments to func that are to be made into parameters
- missing: None, 'none', 'drop', or 'raise'
- 'none' or None: Do not check for null or missing values (default)
- 'drop': Drop null or missing observations in data.
- if pandas is installed, pandas.isnull is used, otherwise
- numpy.isnan is used.
- 'raise': Raise a (more helpful) exception when data contains null
- or missing values.
- name: None or string
- name for the model. When `None` (default) the name is the same as
- the model function (`func`).
-
- """
- _names_collide = ("\nTwo models have parameters named '{clash}'. "
- "Use distinct names.")
- _bad_arg = "CompositeModel: argument {arg} is not a Model"
- _bad_op = "CompositeModel: operator {op} is not callable"
- _known_ops = {operator.add: '+', operator.sub: '-',
- operator.mul: '*', operator.truediv: '/'}
-
- def __init__(self, left, right, op, **kws):
- if not isinstance(left, Model):
- raise ValueError(self._bad_arg.format(arg=left))
- if not isinstance(right, Model):
- raise ValueError(self._bad_arg.format(arg=right))
- if not callable(op):
- raise ValueError(self._bad_op.format(op=op))
-
- self.left = left
- self.right = right
- self.op = op
-
- name_collisions = set(left.param_names) & set(right.param_names)
- if len(name_collisions) > 0:
- msg = ''
- for collision in name_collisions:
- msg += self._names_collide.format(clash=collision)
- raise NameError(msg)
-
- # we assume that all the sub-models have the same independent vars
- if 'independent_vars' not in kws:
- kws['independent_vars'] = self.left.independent_vars
- if 'missing' not in kws:
- kws['missing'] = self.left.missing
-
- def _tmp(self, *args, **kws): pass
- Model.__init__(self, _tmp, **kws)
-
- for side in (left, right):
- prefix = side.prefix
- for basename, hint in side.param_hints.items():
- self.param_hints["%s%s" % (prefix, basename)] = hint
-
- def _parse_params(self):
- self._func_haskeywords = (self.left._func_haskeywords or
- self.right._func_haskeywords)
- self._func_allargs = (self.left._func_allargs +
- self.right._func_allargs)
- self.def_vals = deepcopy(self.right.def_vals)
- self.def_vals.update(self.left.def_vals)
- self.opts = deepcopy(self.right.opts)
- self.opts.update(self.left.opts)
-
- def _reprstring(self, long=False):
- return "(%s %s %s)" % (self.left._reprstring(long=long),
- self._known_ops.get(self.op, self.op),
- self.right._reprstring(long=long))
-
- def eval(self, params=None, **kwargs):
- return self.op(self.left.eval(params=params, **kwargs),
- self.right.eval(params=params, **kwargs))
-
- def eval_components(self, **kwargs):
- """return ordered dict of name, results for each component"""
- out = OrderedDict(self.left.eval_components(**kwargs))
- out.update(self.right.eval_components(**kwargs))
- return out
-
- @property
- def param_names(self):
- return self.left.param_names + self.right.param_names
-
- @property
- def components(self):
- """return components for composite model"""
- return self.left.components + self.right.components
-
- def _make_all_args(self, params=None, **kwargs):
- """generate **all** function args for all functions"""
- out = self.right._make_all_args(params=params, **kwargs)
- out.update(self.left._make_all_args(params=params, **kwargs))
- return out
-
-
-class ModelResult(Minimizer):
- """Result from Model fit
-
- Attributes
- -----------
- model instance of Model -- the model function
- params instance of Parameters -- the fit parameters
- data array of data values to compare to model
- weights array of weights used in fitting
- init_params copy of params, before being updated by fit()
- init_values array of parameter values, before being updated by fit()
- init_fit model evaluated with init_params.
- best_fit model evaluated with params after being updated by fit()
-
- Methods:
- --------
- fit(data=None, params=None, weights=None, method=None, **kwargs)
- fit (or re-fit) model with params to data (with weights)
- using supplied method. The keyword arguments are sent to
- as keyword arguments to the model function.
-
- all inputs are optional, defaulting to the value used in
- the previous fit. This allows easily changing data or
- parameter settings, or both.
-
- eval(**kwargs)
- evaluate the current model, with the current parameter values,
- with values in kwargs sent to the model function.
-
- eval_components(**kwargs)
- evaluate the current model, with the current parameter values,
- with values in kwargs sent to the model function and returns
- a ordered dict with the model names as the key and the component
- results as the values.
-
- fit_report(modelpars=None, show_correl=True, min_correl=0.1)
- return a fit report.
-
- plot_fit(self, ax=None, datafmt='o', fitfmt='-', initfmt='--',
- numpoints=None, data_kws=None, fit_kws=None, init_kws=None,
- ax_kws=None)
- Plot the fit results using matplotlib.
-
- plot_residuals(self, ax=None, datafmt='o', data_kws=None, fit_kws=None,
- ax_kws=None)
- Plot the fit residuals using matplotlib.
-
- plot(self, datafmt='o', fitfmt='-', initfmt='--', numpoints=None,
- data_kws=None, fit_kws=None, init_kws=None, ax_res_kws=None,
- ax_fit_kws=None, fig_kws=None)
- Plot the fit results and residuals using matplotlib.
- """
- def __init__(self, model, params, data=None, weights=None,
- method='leastsq', fcn_args=None, fcn_kws=None,
- iter_cb=None, scale_covar=True, **fit_kws):
- self.model = model
- self.data = data
- self.weights = weights
- self.method = method
- self.ci_out = None
- self.init_params = deepcopy(params)
- Minimizer.__init__(self, model._residual, params, fcn_args=fcn_args,
- fcn_kws=fcn_kws, iter_cb=iter_cb,
- scale_covar=scale_covar, **fit_kws)
-
- def fit(self, data=None, params=None, weights=None, method=None, **kwargs):
- """perform fit for a Model, given data and params"""
- if data is not None:
- self.data = data
- if params is not None:
- self.init_params = params
- if weights is not None:
- self.weights = weights
- if method is not None:
- self.method = method
- self.ci_out = None
- self.userargs = (self.data, self.weights)
- self.userkws.update(kwargs)
- self.init_fit = self.model.eval(params=self.params, **self.userkws)
-
- _ret = self.minimize(method=self.method)
-
- for attr in dir(_ret):
- if not attr.startswith('_') :
- try:
- setattr(self, attr, getattr(_ret, attr))
- except AttributeError:
- pass
-
- self.init_values = self.model._make_all_args(self.init_params)
- self.best_values = self.model._make_all_args(_ret.params)
- self.best_fit = self.model.eval(params=_ret.params, **self.userkws)
-
- def eval(self, **kwargs):
- self.userkws.update(kwargs)
- return self.model.eval(params=self.params, **self.userkws)
-
- def eval_components(self, **kwargs):
- self.userkws.update(kwargs)
- return self.model.eval_components(params=self.params, **self.userkws)
-
- def conf_interval(self, **kwargs):
- """return explicitly calculated confidence intervals"""
- if self.ci_out is None:
- self.ci_out = conf_interval(self, self, **kwargs)
- return self.ci_out
-
- def ci_report(self, with_offset=True, ndigits=5, **kwargs):
- """return nicely formatted report about confidence intervals"""
- return ci_report(self.conf_interval(**kwargs),
- with_offset=with_offset, ndigits=ndigits)
-
- def fit_report(self, **kwargs):
- "return fit report"
- return '[[Model]]\n %s\n%s\n' % (self.model._reprstring(long=True),
- fit_report(self, **kwargs))
-
- @_ensureMatplotlib
- def plot_fit(self, ax=None, datafmt='o', fitfmt='-', initfmt='--', yerr=None,
- numpoints=None, data_kws=None, fit_kws=None, init_kws=None,
- ax_kws=None):
- """Plot the fit results using matplotlib.
-
- The method will plot results of the fit using matplotlib, including:
- the data points, the initial fit curve and the fitted curve. If the fit
- model included weights, errorbars will also be plotted.
-
- Parameters
- ----------
- ax : matplotlib.axes.Axes, optional
- The axes to plot on. The default in None, which means use the
- current pyplot axis or create one if there is none.
- datafmt : string, optional
- matplotlib format string for data points
- fitfmt : string, optional
- matplotlib format string for fitted curve
- initfmt : string, optional
- matplotlib format string for initial conditions for the fit
- yerr : ndarray, optional
- array of uncertainties for data array
- numpoints : int, optional
- If provided, the final and initial fit curves are evaluated not
- only at data points, but refined to contain `numpoints` points in
- total.
- data_kws : dictionary, optional
- keyword arguments passed on to the plot function for data points
- fit_kws : dictionary, optional
- keyword arguments passed on to the plot function for fitted curve
- init_kws : dictionary, optional
- keyword arguments passed on to the plot function for the initial
- conditions of the fit
- ax_kws : dictionary, optional
- keyword arguments for a new axis, if there is one being created
-
- Returns
- -------
- matplotlib.axes.Axes
-
- Notes
- ----
- For details about plot format strings and keyword arguments see
- documentation of matplotlib.axes.Axes.plot.
-
- If yerr is specified or if the fit model included weights, then
- matplotlib.axes.Axes.errorbar is used to plot the data. If yerr is
- not specified and the fit includes weights, yerr set to 1/self.weights
-
- If `ax` is None then matplotlib.pyplot.gca(**ax_kws) is called.
-
- See Also
- --------
- ModelResult.plot_residuals : Plot the fit residuals using matplotlib.
- ModelResult.plot : Plot the fit results and residuals using matplotlib.
- """
- if data_kws is None:
- data_kws = {}
- if fit_kws is None:
- fit_kws = {}
- if init_kws is None:
- init_kws = {}
- if ax_kws is None:
- ax_kws = {}
-
- if len(self.model.independent_vars) == 1:
- independent_var = self.model.independent_vars[0]
- else:
- print('Fit can only be plotted if the model function has one '
- 'independent variable.')
- return False
-
- if not isinstance(ax, plt.Axes):
- ax = plt.gca(**ax_kws)
-
- x_array = self.userkws[independent_var]
-
- # make a dense array for x-axis if data is not dense
- if numpoints is not None and len(self.data) < numpoints:
- x_array_dense = np.linspace(min(x_array), max(x_array), numpoints)
- else:
- x_array_dense = x_array
-
- ax.plot(x_array_dense, self.model.eval(self.init_params,
- **{independent_var: x_array_dense}), initfmt,
- label='init', **init_kws)
- ax.plot(x_array_dense, self.model.eval(self.params,
- **{independent_var: x_array_dense}), fitfmt,
- label='best-fit', **fit_kws)
-
- if yerr is None and self.weights is not None:
- yerr = 1.0/self.weights
- if yerr is not None:
- ax.errorbar(x_array, self.data, yerr=yerr,
- fmt=datafmt, label='data', **data_kws)
- else:
- ax.plot(x_array, self.data, datafmt, label='data', **data_kws)
-
- ax.set_title(self.model.name)
- ax.set_xlabel(independent_var)
- ax.set_ylabel('y')
- ax.legend()
-
- return ax
-
- @_ensureMatplotlib
- def plot_residuals(self, ax=None, datafmt='o', yerr=None, data_kws=None,
- fit_kws=None, ax_kws=None):
- """Plot the fit residuals using matplotlib.
-
- The method will plot residuals of the fit using matplotlib, including:
- the data points and the fitted curve (as horizontal line). If the fit
- model included weights, errorbars will also be plotted.
-
- Parameters
- ----------
- ax : matplotlib.axes.Axes, optional
- The axes to plot on. The default in None, which means use the
- current pyplot axis or create one if there is none.
- datafmt : string, optional
- matplotlib format string for data points
- yerr : ndarray, optional
- array of uncertainties for data array
- data_kws : dictionary, optional
- keyword arguments passed on to the plot function for data points
- fit_kws : dictionary, optional
- keyword arguments passed on to the plot function for fitted curve
- ax_kws : dictionary, optional
- keyword arguments for a new axis, if there is one being created
-
- Returns
- -------
- matplotlib.axes.Axes
-
- Notes
- ----
- For details about plot format strings and keyword arguments see
- documentation of matplotlib.axes.Axes.plot.
-
- If yerr is specified or if the fit model included weights, then
- matplotlib.axes.Axes.errorbar is used to plot the data. If yerr is
- not specified and the fit includes weights, yerr set to 1/self.weights
-
- If `ax` is None then matplotlib.pyplot.gca(**ax_kws) is called.
-
- See Also
- --------
- ModelResult.plot_fit : Plot the fit results using matplotlib.
- ModelResult.plot : Plot the fit results and residuals using matplotlib.
- """
- if data_kws is None:
- data_kws = {}
- if fit_kws is None:
- fit_kws = {}
- if fit_kws is None:
- fit_kws = {}
- if ax_kws is None:
- ax_kws = {}
-
- if len(self.model.independent_vars) == 1:
- independent_var = self.model.independent_vars[0]
- else:
- print('Fit can only be plotted if the model function has one '
- 'independent variable.')
- return False
-
- if not isinstance(ax, plt.Axes):
- ax = plt.gca(**ax_kws)
-
- x_array = self.userkws[independent_var]
-
- ax.axhline(0, **fit_kws)
-
- if yerr is None and self.weights is not None:
- yerr = 1.0/self.weights
- if yerr is not None:
- ax.errorbar(x_array, self.eval() - self.data, yerr=yerr,
- fmt=datafmt, label='residuals', **data_kws)
- else:
- ax.plot(x_array, self.eval() - self.data, datafmt,
- label='residuals', **data_kws)
-
- ax.set_title(self.model.name)
- ax.set_ylabel('residuals')
- ax.legend()
-
- return ax
-
- @_ensureMatplotlib
- def plot(self, datafmt='o', fitfmt='-', initfmt='--', yerr=None,
- numpoints=None, fig=None, data_kws=None, fit_kws=None,
- init_kws=None, ax_res_kws=None, ax_fit_kws=None,
- fig_kws=None):
- """Plot the fit results and residuals using matplotlib.
-
- The method will produce a matplotlib figure with both results of the
- fit and the residuals plotted. If the fit model included weights,
- errorbars will also be plotted.
-
- Parameters
- ----------
- datafmt : string, optional
- matplotlib format string for data points
- fitfmt : string, optional
- matplotlib format string for fitted curve
- initfmt : string, optional
- matplotlib format string for initial conditions for the fit
- yerr : ndarray, optional
- array of uncertainties for data array
- numpoints : int, optional
- If provided, the final and initial fit curves are evaluated not
- only at data points, but refined to contain `numpoints` points in
- total.
- fig : matplotlib.figure.Figure, optional
- The figure to plot on. The default in None, which means use the
- current pyplot figure or create one if there is none.
- data_kws : dictionary, optional
- keyword arguments passed on to the plot function for data points
- fit_kws : dictionary, optional
- keyword arguments passed on to the plot function for fitted curve
- init_kws : dictionary, optional
- keyword arguments passed on to the plot function for the initial
- conditions of the fit
- ax_res_kws : dictionary, optional
- keyword arguments for the axes for the residuals plot
- ax_fit_kws : dictionary, optional
- keyword arguments for the axes for the fit plot
- fig_kws : dictionary, optional
- keyword arguments for a new figure, if there is one being created
-
- Returns
- -------
- matplotlib.figure.Figure
-
- Notes
- ----
- The method combines ModelResult.plot_fit and ModelResult.plot_residuals.
-
- If yerr is specified or if the fit model included weights, then
- matplotlib.axes.Axes.errorbar is used to plot the data. If yerr is
- not specified and the fit includes weights, yerr set to 1/self.weights
-
- If `fig` is None then matplotlib.pyplot.figure(**fig_kws) is called.
-
- See Also
- --------
- ModelResult.plot_fit : Plot the fit results using matplotlib.
- ModelResult.plot_residuals : Plot the fit residuals using matplotlib.
- """
- if data_kws is None:
- data_kws = {}
- if fit_kws is None:
- fit_kws = {}
- if init_kws is None:
- init_kws = {}
- if ax_res_kws is None:
- ax_res_kws = {}
- if ax_fit_kws is None:
- ax_fit_kws = {}
- if fig_kws is None:
- fig_kws = {}
-
- if len(self.model.independent_vars) != 1:
- print('Fit can only be plotted if the model function has one '
- 'independent variable.')
- return False
-
- if not isinstance(fig, plt.Figure):
- fig = plt.figure(**fig_kws)
-
- gs = plt.GridSpec(nrows=2, ncols=1, height_ratios=[1, 4])
- ax_res = fig.add_subplot(gs[0], **ax_res_kws)
- ax_fit = fig.add_subplot(gs[1], sharex=ax_res, **ax_fit_kws)
-
- self.plot_fit(ax=ax_fit, datafmt=datafmt, fitfmt=fitfmt, yerr=yerr,
- initfmt=initfmt, numpoints=numpoints, data_kws=data_kws,
- fit_kws=fit_kws, init_kws=init_kws, ax_kws=ax_fit_kws)
- self.plot_residuals(ax=ax_res, datafmt=datafmt, yerr=yerr,
- data_kws=data_kws, fit_kws=fit_kws,
- ax_kws=ax_res_kws)
-
- return fig
+""" +Concise nonlinear curve fitting. +""" +from __future__ import print_function +import warnings +import inspect +import operator +from copy import deepcopy +import numpy as np +from . import Parameters, Parameter, Minimizer +from .printfuncs import fit_report, ci_report +from .confidence import conf_interval + +try: + from collections import OrderedDict +except ImportError: + from ordereddict import OrderedDict + +# Use pandas.isnull for aligning missing data is pandas is available. +# otherwise use numpy.isnan +try: + from pandas import isnull, Series +except ImportError: + isnull = np.isnan + Series = type(NotImplemented) + +def _align(var, mask, data): + "align missing data, with pandas is available" + if isinstance(data, Series) and isinstance(var, Series): + return var.reindex_like(data).dropna() + elif mask is not None: + return var[mask] + return var + + +try: + from matplotlib import pyplot as plt + _HAS_MATPLOTLIB = True +except ImportError: + _HAS_MATPLOTLIB = False + + +def _ensureMatplotlib(function): + if _HAS_MATPLOTLIB: + return function + else: + def no_op(*args, **kwargs): + print('matplotlib module is required for plotting the results') + + return no_op + + +class Model(object): + """Create a model from a user-defined function. + + Parameters + ---------- + func: function to be wrapped + independent_vars: list of strings or None (default) + arguments to func that are independent variables + param_names: list of strings or None (default) + names of arguments to func that are to be made into parameters + missing: None, 'none', 'drop', or 'raise' + 'none' or None: Do not check for null or missing values (default) + 'drop': Drop null or missing observations in data. + if pandas is installed, pandas.isnull is used, otherwise + numpy.isnan is used. + 'raise': Raise a (more helpful) exception when data contains null + or missing values. + name: None or string + name for the model. When `None` (default) the name is the same as + the model function (`func`). + + Note + ---- + Parameter names are inferred from the function arguments, + and a residual function is automatically constructed. + + Example + ------- + >>> def decay(t, tau, N): + ... return N*np.exp(-t/tau) + ... + >>> my_model = Model(decay, independent_vars=['t']) + """ + + _forbidden_args = ('data', 'weights', 'params') + _invalid_ivar = "Invalid independent variable name ('%s') for function %s" + _invalid_par = "Invalid parameter name ('%s') for function %s" + _invalid_missing = "missing must be None, 'none', 'drop', or 'raise'." + _valid_missing = (None, 'none', 'drop', 'raise') + + _invalid_hint = "unknown parameter hint '%s' for param '%s'" + _hint_names = ('value', 'vary', 'min', 'max', 'expr') + + def __init__(self, func, independent_vars=None, param_names=None, + missing='none', prefix='', name=None, **kws): + self.func = func + self._prefix = prefix + self._param_root_names = param_names # will not include prefixes + self.independent_vars = independent_vars + self._func_allargs = [] + self._func_haskeywords = False + if not missing in self._valid_missing: + raise ValueError(self._invalid_missing) + self.missing = missing + self.opts = kws + self.param_hints = OrderedDict() + # the following has been changed from OrderedSet for the time being + self._param_names = [] + self._parse_params() + if self.independent_vars is None: + self.independent_vars = [] + if name is None and hasattr(self.func, '__name__'): + name = self.func.__name__ + self._name = name + + def _reprstring(self, long=False): + out = self._name + opts = [] + if len(self._prefix) > 0: + opts.append("prefix='%s'" % (self._prefix)) + if long: + for k, v in self.opts.items(): + opts.append("%s='%s'" % (k, v)) + if len(opts) > 0: + out = "%s, %s" % (out, ', '.join(opts)) + return "Model(%s)" % out + + @property + def name(self): + return self._reprstring(long=False) + + @name.setter + def name(self, value): + self._name = value + + @property + def prefix(self): + return self._prefix + + @property + def param_names(self): + return self._param_names + + def __repr__(self): + return "<lmfit.Model: %s>" % (self.name) + + def copy(self, **kwargs): + """DOES NOT WORK""" + raise NotImplementedError("Model.copy does not work. Make a new Model") + + def _parse_params(self): + "build params from function arguments" + if self.func is None: + return + argspec = inspect.getargspec(self.func) + pos_args = argspec.args[:] + keywords = argspec.keywords + kw_args = {} + if argspec.defaults is not None: + for val in reversed(argspec.defaults): + kw_args[pos_args.pop()] = val + + self._func_haskeywords = keywords is not None + self._func_allargs = pos_args + list(kw_args.keys()) + allargs = self._func_allargs + + if len(allargs) == 0 and keywords is not None: + return + + # default independent_var = 1st argument + if self.independent_vars is None: + self.independent_vars = [pos_args[0]] + + # default param names: all positional args + # except independent variables + self.def_vals = {} + might_be_param = [] + if self._param_root_names is None: + self._param_root_names = pos_args[:] + for key, val in kw_args.items(): + if (not isinstance(val, bool) and + isinstance(val, (float, int))): + self._param_root_names.append(key) + self.def_vals[key] = val + elif val is None: + might_be_param.append(key) + for p in self.independent_vars: + if p in self._param_root_names: + self._param_root_names.remove(p) + + new_opts = {} + for opt, val in self.opts.items(): + if (opt in self._param_root_names or opt in might_be_param and + isinstance(val, Parameter)): + self.set_param_hint(opt, value=val.value, + min=val.min, max=val.max, expr=val.expr) + elif opt in self._func_allargs: + new_opts[opt] = val + self.opts = new_opts + + names = [] + if self._prefix is None: + self._prefix = '' + for pname in self._param_root_names: + names.append("%s%s" % (self._prefix, pname)) + + # check variables names for validity + # The implicit magic in fit() requires us to disallow some + fname = self.func.__name__ + for arg in self.independent_vars: + if arg not in allargs or arg in self._forbidden_args: + raise ValueError(self._invalid_ivar % (arg, fname)) + for arg in names: + if (self._strip_prefix(arg) not in allargs or + arg in self._forbidden_args): + raise ValueError(self._invalid_par % (arg, fname)) + # the following as been changed from OrderedSet for the time being. + self._param_names = names[:] + + def set_param_hint(self, name, **kwargs): + """set hints for parameter, including optional bounds + and constraints (value, vary, min, max, expr) + these will be used by make_params() when building + default parameters + + example: + model = GaussianModel() + model.set_param_hint('amplitude', min=-100.0, max=0.) + """ + npref = len(self._prefix) + if npref > 0 and name.startswith(self._prefix): + name = name[npref:] + + if name not in self.param_hints: + self.param_hints[name] = OrderedDict() + + for key, val in kwargs.items(): + if key in self._hint_names: + self.param_hints[name][key] = val + else: + warnings.warn(self._invalid_hint % (key, name)) + + def print_param_hints(self, colwidth=8): + """Prints a nicely aligned text-table of parameters hints. + + The argument `colwidth` is the width of each column, + except for first and last columns. + """ + name_len = max(len(s) for s in self.param_hints) + print('{:{name_len}} {:>{n}} {:>{n}} {:>{n}} {:>{n}} {:{n}}' + .format('Name', 'Value', 'Min', 'Max', 'Vary', 'Expr', + name_len=name_len, n=colwidth)) + line = ('{name:<{name_len}} {value:{n}g} {min:{n}g} {max:{n}g} ' + '{vary!s:>{n}} {expr}') + for name, values in sorted(self.param_hints.items()): + pvalues = dict(name=name, value=np.nan, min=-np.inf, max=np.inf, + vary=True, expr='') + pvalues.update(**values) + print(line.format(name_len=name_len, n=colwidth, **pvalues)) + + def make_params(self, verbose=False, **kwargs): + """create and return a Parameters object for a Model. + This applies any default values + """ + params = Parameters() + + # make sure that all named parameters are in params + for name in self.param_names: + if name in params: + par = params[name] + else: + par = Parameter(name=name) + par._delay_asteval = True + basename = name[len(self._prefix):] + # apply defaults from model function definition + if basename in self.def_vals: + par.value = self.def_vals[basename] + # apply defaults from parameter hints + if basename in self.param_hints: + hint = self.param_hints[basename] + for item in self._hint_names: + if item in hint: + setattr(par, item, hint[item]) + # apply values passed in through kw args + if basename in kwargs: + # kw parameter names with no prefix + par.value = kwargs[basename] + if name in kwargs: + # kw parameter names with prefix + par.value = kwargs[name] + params.add(par) + if verbose: + print( ' - Adding parameter "%s"' % name) + + # next build parameters defined in param_hints + # note that composites may define their own additional + # convenience parameters here + for basename, hint in self.param_hints.items(): + name = "%s%s" % (self._prefix, basename) + if name in params: + par = params[name] + else: + par = Parameter(name=name) + params.add(par) + if verbose: + print( ' - Adding parameter for hint "%s"' % name) + par._delay_asteval = True + for item in self._hint_names: + if item in hint: + setattr(par, item, hint[item]) + # Add the new parameter to self._param_names + if name not in self._param_names: + self._param_names.append(name) + + for p in params.values(): + p._delay_asteval = False + return params + + def guess(self, data=None, **kws): + """stub for guess starting values -- + should be implemented for each model subclass to + run self.make_params(), update starting values + and return a Parameters object""" + cname = self.__class__.__name__ + msg = 'guess() not implemented for %s' % cname + raise NotImplementedError(msg) + + def _residual(self, params, data, weights, **kwargs): + """default residual: (data-model)*weights + + If the model returns complex values, the residual is computed by treating the real and imaginary + parts separately. In this case, if the weights provided are real, they are assumed to apply equally to the + real and imaginary parts. If the weights are complex, the real part of the weights are applied to the real + part of the residual and the imaginary part is treated correspondingly. + + Since the underlying scipy.optimize routines expect np.float arrays, the only complex type supported is + np.complex. + + The "ravels" throughout are necessary to support pandas.Series. + """ + diff = self.eval(params, **kwargs) - data + + if diff.dtype == np.complex: + # data/model are complex + diff = diff.ravel().view(np.float) + if weights is not None: + if weights.dtype == np.complex: + # weights are complex + weights = weights.ravel().view(np.float) + else: + # real weights but complex data + weights = (weights + 1j * weights).ravel().view(np.float) + if weights is not None: + diff *= weights + return np.asarray(diff).ravel() # for compatibility with pandas.Series + + def _handle_missing(self, data): + "handle missing data" + if self.missing == 'raise': + if np.any(isnull(data)): + raise ValueError("Data contains a null value.") + elif self.missing == 'drop': + mask = ~isnull(data) + if np.all(mask): + return None # short-circuit this -- no missing values + mask = np.asarray(mask) # for compatibility with pandas.Series + return mask + + def _strip_prefix(self, name): + npref = len(self._prefix) + if npref > 0 and name.startswith(self._prefix): + name = name[npref:] + return name + + def make_funcargs(self, params=None, kwargs=None, strip=True): + """convert parameter values and keywords to function arguments""" + if params is None: params = {} + if kwargs is None: kwargs = {} + out = {} + out.update(self.opts) + for name, par in params.items(): + if strip: + name = self._strip_prefix(name) + if name in self._func_allargs or self._func_haskeywords: + out[name] = par.value + + # kwargs handled slightly differently -- may set param value too! + for name, val in kwargs.items(): + if strip: + name = self._strip_prefix(name) + if name in self._func_allargs or self._func_haskeywords: + out[name] = val + if name in params: + params[name].value = val + return out + + def _make_all_args(self, params=None, **kwargs): + """generate **all** function args for all functions""" + args = {} + for key, val in self.make_funcargs(params, kwargs).items(): + args["%s%s" % (self._prefix, key)] = val + return args + + def eval(self, params=None, **kwargs): + """evaluate the model with the supplied parameters""" + result = self.func(**self.make_funcargs(params, kwargs)) + # Handle special case of constant result and one + # independent variable (of any dimension). + if np.ndim(result) == 0 and len(self.independent_vars) == 1: + result = np.tile(result, kwargs[self.independent_vars[0]].shape) + return result + + @property + def components(self): + """return components for composite model""" + return [self] + + def eval_components(self, params=None, **kwargs): + """ + evaluate the model with the supplied parameters and returns a ordered + dict containting name, result pairs. + """ + key = self._prefix + if len(key) < 1: + key = self._name + return {key: self.eval(params=params, **kwargs)} + + def fit(self, data, params=None, weights=None, method='leastsq', + iter_cb=None, scale_covar=True, verbose=False, fit_kws=None, **kwargs): + """Fit the model to the data. + + Parameters + ---------- + data: array-like + params: Parameters object + weights: array-like of same size as data + used for weighted fit + method: fitting method to use (default = 'leastsq') + iter_cb: None or callable callback function to call at each iteration. + scale_covar: bool (default True) whether to auto-scale covariance matrix + verbose: bool (default True) print a message when a new parameter is + added because of a hint. + fit_kws: dict + default fitting options, such as xtol and maxfev, for scipy optimizer + keyword arguments: optional, named like the arguments of the + model function, will override params. See examples below. + + Returns + ------- + lmfit.ModelResult + + Examples + -------- + # Take t to be the independent variable and data to be the + # curve we will fit. + + # Using keyword arguments to set initial guesses + >>> result = my_model.fit(data, tau=5, N=3, t=t) + + # Or, for more control, pass a Parameters object. + >>> result = my_model.fit(data, params, t=t) + + # Keyword arguments override Parameters. + >>> result = my_model.fit(data, params, tau=5, t=t) + + Note + ---- + All parameters, however passed, are copied on input, so the original + Parameter objects are unchanged. + + """ + if params is None: + params = self.make_params(verbose=verbose) + else: + params = deepcopy(params) + + # If any kwargs match parameter names, override params. + param_kwargs = set(kwargs.keys()) & set(self.param_names) + for name in param_kwargs: + p = kwargs[name] + if isinstance(p, Parameter): + p.name = name # allows N=Parameter(value=5) with implicit name + params[name] = deepcopy(p) + else: + params[name].set(value=p) + del kwargs[name] + + # All remaining kwargs should correspond to independent variables. + for name in kwargs.keys(): + if name not in self.independent_vars: + warnings.warn("The keyword argument %s does not" % name + + "match any arguments of the model function." + + "It will be ignored.", UserWarning) + + # If any parameter is not initialized raise a more helpful error. + missing_param = any([p not in params.keys() + for p in self.param_names]) + blank_param = any([(p.value is None and p.expr is None) + for p in params.values()]) + if missing_param or blank_param: + msg = ('Assign each parameter an initial value by passing ' + 'Parameters or keyword arguments to fit.\n') + missing = [p for p in self.param_names if p not in params.keys()] + blank = [name for name, p in params.items() + if (p.value is None and p.expr is None)] + msg += 'Missing parameters: %s\n' % str(missing) + msg += 'Non initialized parameters: %s' % str(blank) + raise ValueError(msg) + + # Do not alter anything that implements the array interface (np.array, pd.Series) + # but convert other iterables (e.g., Python lists) to numpy arrays. + if not hasattr(data, '__array__'): + data = np.asfarray(data) + for var in self.independent_vars: + var_data = kwargs[var] + if (not hasattr(var_data, '__array__')) and (not np.isscalar(var_data)): + kwargs[var] = np.asfarray(var_data) + + # Handle null/missing values. + mask = None + if self.missing not in (None, 'none'): + mask = self._handle_missing(data) # This can raise. + if mask is not None: + data = data[mask] + if weights is not None: + weights = _align(weights, mask, data) + + # If independent_vars and data are alignable (pandas), align them, + # and apply the mask from above if there is one. + for var in self.independent_vars: + if not np.isscalar(kwargs[var]): + kwargs[var] = _align(kwargs[var], mask, data) + + if fit_kws is None: + fit_kws = {} + + output = ModelResult(self, params, method=method, iter_cb=iter_cb, + scale_covar=scale_covar, fcn_kws=kwargs, + **fit_kws) + output.fit(data=data, weights=weights) + output.components = self.components + return output + + def __add__(self, other): + return CompositeModel(self, other, operator.add) + + def __sub__(self, other): + return CompositeModel(self, other, operator.sub) + + def __mul__(self, other): + return CompositeModel(self, other, operator.mul) + + def __div__(self, other): + return CompositeModel(self, other, operator.truediv) + + def __truediv__(self, other): + return CompositeModel(self, other, operator.truediv) + + +class CompositeModel(Model): + """Create a composite model -- a binary operator of two Models + + Parameters + ---------- + left_model: left-hand side model-- must be a Model() + right_model: right-hand side model -- must be a Model() + oper: callable binary operator (typically, operator.add, operator.mul, etc) + + independent_vars: list of strings or None (default) + arguments to func that are independent variables + param_names: list of strings or None (default) + names of arguments to func that are to be made into parameters + missing: None, 'none', 'drop', or 'raise' + 'none' or None: Do not check for null or missing values (default) + 'drop': Drop null or missing observations in data. + if pandas is installed, pandas.isnull is used, otherwise + numpy.isnan is used. + 'raise': Raise a (more helpful) exception when data contains null + or missing values. + name: None or string + name for the model. When `None` (default) the name is the same as + the model function (`func`). + + """ + _names_collide = ("\nTwo models have parameters named '{clash}'. " + "Use distinct names.") + _bad_arg = "CompositeModel: argument {arg} is not a Model" + _bad_op = "CompositeModel: operator {op} is not callable" + _known_ops = {operator.add: '+', operator.sub: '-', + operator.mul: '*', operator.truediv: '/'} + + def __init__(self, left, right, op, **kws): + if not isinstance(left, Model): + raise ValueError(self._bad_arg.format(arg=left)) + if not isinstance(right, Model): + raise ValueError(self._bad_arg.format(arg=right)) + if not callable(op): + raise ValueError(self._bad_op.format(op=op)) + + self.left = left + self.right = right + self.op = op + + name_collisions = set(left.param_names) & set(right.param_names) + if len(name_collisions) > 0: + msg = '' + for collision in name_collisions: + msg += self._names_collide.format(clash=collision) + raise NameError(msg) + + # we assume that all the sub-models have the same independent vars + if 'independent_vars' not in kws: + kws['independent_vars'] = self.left.independent_vars + if 'missing' not in kws: + kws['missing'] = self.left.missing + + def _tmp(self, *args, **kws): pass + Model.__init__(self, _tmp, **kws) + + for side in (left, right): + prefix = side.prefix + for basename, hint in side.param_hints.items(): + self.param_hints["%s%s" % (prefix, basename)] = hint + + def _parse_params(self): + self._func_haskeywords = (self.left._func_haskeywords or + self.right._func_haskeywords) + self._func_allargs = (self.left._func_allargs + + self.right._func_allargs) + self.def_vals = deepcopy(self.right.def_vals) + self.def_vals.update(self.left.def_vals) + self.opts = deepcopy(self.right.opts) + self.opts.update(self.left.opts) + + def _reprstring(self, long=False): + return "(%s %s %s)" % (self.left._reprstring(long=long), + self._known_ops.get(self.op, self.op), + self.right._reprstring(long=long)) + + def eval(self, params=None, **kwargs): + return self.op(self.left.eval(params=params, **kwargs), + self.right.eval(params=params, **kwargs)) + + def eval_components(self, **kwargs): + """return ordered dict of name, results for each component""" + out = OrderedDict(self.left.eval_components(**kwargs)) + out.update(self.right.eval_components(**kwargs)) + return out + + @property + def param_names(self): + return self.left.param_names + self.right.param_names + + @property + def components(self): + """return components for composite model""" + return self.left.components + self.right.components + + def _make_all_args(self, params=None, **kwargs): + """generate **all** function args for all functions""" + out = self.right._make_all_args(params=params, **kwargs) + out.update(self.left._make_all_args(params=params, **kwargs)) + return out + + +class ModelResult(Minimizer): + """Result from Model fit + + Attributes + ----------- + model instance of Model -- the model function + params instance of Parameters -- the fit parameters + data array of data values to compare to model + weights array of weights used in fitting + init_params copy of params, before being updated by fit() + init_values array of parameter values, before being updated by fit() + init_fit model evaluated with init_params. + best_fit model evaluated with params after being updated by fit() + + Methods: + -------- + fit(data=None, params=None, weights=None, method=None, **kwargs) + fit (or re-fit) model with params to data (with weights) + using supplied method. The keyword arguments are sent to + as keyword arguments to the model function. + + all inputs are optional, defaulting to the value used in + the previous fit. This allows easily changing data or + parameter settings, or both. + + eval(**kwargs) + evaluate the current model, with the current parameter values, + with values in kwargs sent to the model function. + + eval_components(**kwargs) + evaluate the current model, with the current parameter values, + with values in kwargs sent to the model function and returns + a ordered dict with the model names as the key and the component + results as the values. + + fit_report(modelpars=None, show_correl=True, min_correl=0.1) + return a fit report. + + plot_fit(self, ax=None, datafmt='o', fitfmt='-', initfmt='--', + numpoints=None, data_kws=None, fit_kws=None, init_kws=None, + ax_kws=None) + Plot the fit results using matplotlib. + + plot_residuals(self, ax=None, datafmt='o', data_kws=None, fit_kws=None, + ax_kws=None) + Plot the fit residuals using matplotlib. + + plot(self, datafmt='o', fitfmt='-', initfmt='--', numpoints=None, + data_kws=None, fit_kws=None, init_kws=None, ax_res_kws=None, + ax_fit_kws=None, fig_kws=None) + Plot the fit results and residuals using matplotlib. + """ + def __init__(self, model, params, data=None, weights=None, + method='leastsq', fcn_args=None, fcn_kws=None, + iter_cb=None, scale_covar=True, **fit_kws): + self.model = model + self.data = data + self.weights = weights + self.method = method + self.ci_out = None + self.init_params = deepcopy(params) + Minimizer.__init__(self, model._residual, params, fcn_args=fcn_args, + fcn_kws=fcn_kws, iter_cb=iter_cb, + scale_covar=scale_covar, **fit_kws) + + def fit(self, data=None, params=None, weights=None, method=None, **kwargs): + """perform fit for a Model, given data and params""" + if data is not None: + self.data = data + if params is not None: + self.init_params = params + if weights is not None: + self.weights = weights + if method is not None: + self.method = method + self.ci_out = None + self.userargs = (self.data, self.weights) + self.userkws.update(kwargs) + self.init_fit = self.model.eval(params=self.params, **self.userkws) + + _ret = self.minimize(method=self.method) + + for attr in dir(_ret): + if not attr.startswith('_') : + try: + setattr(self, attr, getattr(_ret, attr)) + except AttributeError: + pass + + self.init_values = self.model._make_all_args(self.init_params) + self.best_values = self.model._make_all_args(_ret.params) + self.best_fit = self.model.eval(params=_ret.params, **self.userkws) + + def eval(self, **kwargs): + self.userkws.update(kwargs) + return self.model.eval(params=self.params, **self.userkws) + + def eval_components(self, **kwargs): + self.userkws.update(kwargs) + return self.model.eval_components(params=self.params, **self.userkws) + + def conf_interval(self, **kwargs): + """return explicitly calculated confidence intervals""" + if self.ci_out is None: + self.ci_out = conf_interval(self, self, **kwargs) + return self.ci_out + + def ci_report(self, with_offset=True, ndigits=5, **kwargs): + """return nicely formatted report about confidence intervals""" + return ci_report(self.conf_interval(**kwargs), + with_offset=with_offset, ndigits=ndigits) + + def fit_report(self, **kwargs): + "return fit report" + return '[[Model]]\n %s\n%s\n' % (self.model._reprstring(long=True), + fit_report(self, **kwargs)) + + @_ensureMatplotlib + def plot_fit(self, ax=None, datafmt='o', fitfmt='-', initfmt='--', yerr=None, + numpoints=None, data_kws=None, fit_kws=None, init_kws=None, + ax_kws=None): + """Plot the fit results using matplotlib. + + The method will plot results of the fit using matplotlib, including: + the data points, the initial fit curve and the fitted curve. If the fit + model included weights, errorbars will also be plotted. + + Parameters + ---------- + ax : matplotlib.axes.Axes, optional + The axes to plot on. The default in None, which means use the + current pyplot axis or create one if there is none. + datafmt : string, optional + matplotlib format string for data points + fitfmt : string, optional + matplotlib format string for fitted curve + initfmt : string, optional + matplotlib format string for initial conditions for the fit + yerr : ndarray, optional + array of uncertainties for data array + numpoints : int, optional + If provided, the final and initial fit curves are evaluated not + only at data points, but refined to contain `numpoints` points in + total. + data_kws : dictionary, optional + keyword arguments passed on to the plot function for data points + fit_kws : dictionary, optional + keyword arguments passed on to the plot function for fitted curve + init_kws : dictionary, optional + keyword arguments passed on to the plot function for the initial + conditions of the fit + ax_kws : dictionary, optional + keyword arguments for a new axis, if there is one being created + + Returns + ------- + matplotlib.axes.Axes + + Notes + ---- + For details about plot format strings and keyword arguments see + documentation of matplotlib.axes.Axes.plot. + + If yerr is specified or if the fit model included weights, then + matplotlib.axes.Axes.errorbar is used to plot the data. If yerr is + not specified and the fit includes weights, yerr set to 1/self.weights + + If `ax` is None then matplotlib.pyplot.gca(**ax_kws) is called. + + See Also + -------- + ModelResult.plot_residuals : Plot the fit residuals using matplotlib. + ModelResult.plot : Plot the fit results and residuals using matplotlib. + """ + if data_kws is None: + data_kws = {} + if fit_kws is None: + fit_kws = {} + if init_kws is None: + init_kws = {} + if ax_kws is None: + ax_kws = {} + + if len(self.model.independent_vars) == 1: + independent_var = self.model.independent_vars[0] + else: + print('Fit can only be plotted if the model function has one ' + 'independent variable.') + return False + + if not isinstance(ax, plt.Axes): + ax = plt.gca(**ax_kws) + + x_array = self.userkws[independent_var] + + # make a dense array for x-axis if data is not dense + if numpoints is not None and len(self.data) < numpoints: + x_array_dense = np.linspace(min(x_array), max(x_array), numpoints) + else: + x_array_dense = x_array + + ax.plot(x_array_dense, self.model.eval(self.init_params, + **{independent_var: x_array_dense}), initfmt, + label='init', **init_kws) + ax.plot(x_array_dense, self.model.eval(self.params, + **{independent_var: x_array_dense}), fitfmt, + label='best-fit', **fit_kws) + + if yerr is None and self.weights is not None: + yerr = 1.0/self.weights + if yerr is not None: + ax.errorbar(x_array, self.data, yerr=yerr, + fmt=datafmt, label='data', **data_kws) + else: + ax.plot(x_array, self.data, datafmt, label='data', **data_kws) + + ax.set_title(self.model.name) + ax.set_xlabel(independent_var) + ax.set_ylabel('y') + ax.legend() + + return ax + + @_ensureMatplotlib + def plot_residuals(self, ax=None, datafmt='o', yerr=None, data_kws=None, + fit_kws=None, ax_kws=None): + """Plot the fit residuals using matplotlib. + + The method will plot residuals of the fit using matplotlib, including: + the data points and the fitted curve (as horizontal line). If the fit + model included weights, errorbars will also be plotted. + + Parameters + ---------- + ax : matplotlib.axes.Axes, optional + The axes to plot on. The default in None, which means use the + current pyplot axis or create one if there is none. + datafmt : string, optional + matplotlib format string for data points + yerr : ndarray, optional + array of uncertainties for data array + data_kws : dictionary, optional + keyword arguments passed on to the plot function for data points + fit_kws : dictionary, optional + keyword arguments passed on to the plot function for fitted curve + ax_kws : dictionary, optional + keyword arguments for a new axis, if there is one being created + + Returns + ------- + matplotlib.axes.Axes + + Notes + ---- + For details about plot format strings and keyword arguments see + documentation of matplotlib.axes.Axes.plot. + + If yerr is specified or if the fit model included weights, then + matplotlib.axes.Axes.errorbar is used to plot the data. If yerr is + not specified and the fit includes weights, yerr set to 1/self.weights + + If `ax` is None then matplotlib.pyplot.gca(**ax_kws) is called. + + See Also + -------- + ModelResult.plot_fit : Plot the fit results using matplotlib. + ModelResult.plot : Plot the fit results and residuals using matplotlib. + """ + if data_kws is None: + data_kws = {} + if fit_kws is None: + fit_kws = {} + if fit_kws is None: + fit_kws = {} + if ax_kws is None: + ax_kws = {} + + if len(self.model.independent_vars) == 1: + independent_var = self.model.independent_vars[0] + else: + print('Fit can only be plotted if the model function has one ' + 'independent variable.') + return False + + if not isinstance(ax, plt.Axes): + ax = plt.gca(**ax_kws) + + x_array = self.userkws[independent_var] + + ax.axhline(0, **fit_kws) + + if yerr is None and self.weights is not None: + yerr = 1.0/self.weights + if yerr is not None: + ax.errorbar(x_array, self.eval() - self.data, yerr=yerr, + fmt=datafmt, label='residuals', **data_kws) + else: + ax.plot(x_array, self.eval() - self.data, datafmt, + label='residuals', **data_kws) + + ax.set_title(self.model.name) + ax.set_ylabel('residuals') + ax.legend() + + return ax + + @_ensureMatplotlib + def plot(self, datafmt='o', fitfmt='-', initfmt='--', yerr=None, + numpoints=None, fig=None, data_kws=None, fit_kws=None, + init_kws=None, ax_res_kws=None, ax_fit_kws=None, + fig_kws=None): + """Plot the fit results and residuals using matplotlib. + + The method will produce a matplotlib figure with both results of the + fit and the residuals plotted. If the fit model included weights, + errorbars will also be plotted. + + Parameters + ---------- + datafmt : string, optional + matplotlib format string for data points + fitfmt : string, optional + matplotlib format string for fitted curve + initfmt : string, optional + matplotlib format string for initial conditions for the fit + yerr : ndarray, optional + array of uncertainties for data array + numpoints : int, optional + If provided, the final and initial fit curves are evaluated not + only at data points, but refined to contain `numpoints` points in + total. + fig : matplotlib.figure.Figure, optional + The figure to plot on. The default in None, which means use the + current pyplot figure or create one if there is none. + data_kws : dictionary, optional + keyword arguments passed on to the plot function for data points + fit_kws : dictionary, optional + keyword arguments passed on to the plot function for fitted curve + init_kws : dictionary, optional + keyword arguments passed on to the plot function for the initial + conditions of the fit + ax_res_kws : dictionary, optional + keyword arguments for the axes for the residuals plot + ax_fit_kws : dictionary, optional + keyword arguments for the axes for the fit plot + fig_kws : dictionary, optional + keyword arguments for a new figure, if there is one being created + + Returns + ------- + matplotlib.figure.Figure + + Notes + ---- + The method combines ModelResult.plot_fit and ModelResult.plot_residuals. + + If yerr is specified or if the fit model included weights, then + matplotlib.axes.Axes.errorbar is used to plot the data. If yerr is + not specified and the fit includes weights, yerr set to 1/self.weights + + If `fig` is None then matplotlib.pyplot.figure(**fig_kws) is called. + + See Also + -------- + ModelResult.plot_fit : Plot the fit results using matplotlib. + ModelResult.plot_residuals : Plot the fit residuals using matplotlib. + """ + if data_kws is None: + data_kws = {} + if fit_kws is None: + fit_kws = {} + if init_kws is None: + init_kws = {} + if ax_res_kws is None: + ax_res_kws = {} + if ax_fit_kws is None: + ax_fit_kws = {} + if fig_kws is None: + fig_kws = {} + + if len(self.model.independent_vars) != 1: + print('Fit can only be plotted if the model function has one ' + 'independent variable.') + return False + + if not isinstance(fig, plt.Figure): + fig = plt.figure(**fig_kws) + + gs = plt.GridSpec(nrows=2, ncols=1, height_ratios=[1, 4]) + ax_res = fig.add_subplot(gs[0], **ax_res_kws) + ax_fit = fig.add_subplot(gs[1], sharex=ax_res, **ax_fit_kws) + + self.plot_fit(ax=ax_fit, datafmt=datafmt, fitfmt=fitfmt, yerr=yerr, + initfmt=initfmt, numpoints=numpoints, data_kws=data_kws, + fit_kws=fit_kws, init_kws=init_kws, ax_kws=ax_fit_kws) + self.plot_residuals(ax=ax_res, datafmt=datafmt, yerr=yerr, + data_kws=data_kws, fit_kws=fit_kws, + ax_kws=ax_res_kws) + + return fig diff --git a/lmfit/models.py b/lmfit/models.py index 87139b0..78d024d 100644 --- a/lmfit/models.py +++ b/lmfit/models.py @@ -1,454 +1,484 @@ -import numpy as np
-from .model import Model
-
-from .lineshapes import (gaussian, lorentzian, voigt, pvoigt, moffat, pearson7,
- step, rectangle, breit_wigner, logistic,
- students_t, lognormal, damped_oscillator,
- expgaussian, skewed_gaussian, donaich,
- skewed_voigt, exponential, powerlaw, linear,
- parabolic)
-
-from . import lineshapes
-
-from .asteval import Interpreter
-from .astutils import get_ast_names
-
-class DimensionalError(Exception):
- pass
-
-def _validate_1d(independent_vars):
- if len(independent_vars) != 1:
- raise DimensionalError(
- "This model requires exactly one independent variable.")
-
-def index_of(arr, val):
- """return index of array nearest to a value
- """
- if val < min(arr):
- return 0
- return np.abs(arr-val).argmin()
-
-def fwhm_expr(model):
- "return constraint expression for fwhm"
- return "%.7f*%ssigma" % (model.fwhm_factor, model.prefix)
-
-def guess_from_peak(model, y, x, negative, ampscale=1.0, sigscale=1.0):
- "estimate amp, cen, sigma for a peak, create params"
- if x is None:
- return 1.0, 0.0, 1.0
- maxy, miny = max(y), min(y)
- maxx, minx = max(x), min(x)
- imaxy = index_of(y, maxy)
- cen = x[imaxy]
- amp = (maxy - miny)*2.0
- sig = (maxx-minx)/6.0
-
- halfmax_vals = np.where(y > (maxy+miny)/2.0)[0]
- if negative:
- imaxy = index_of(y, miny)
- amp = -(maxy - miny)*2.0
- halfmax_vals = np.where(y < (maxy+miny)/2.0)[0]
- if len(halfmax_vals) > 2:
- sig = (x[halfmax_vals[-1]] - x[halfmax_vals[0]])/2.0
- cen = x[halfmax_vals].mean()
- amp = amp*sig*ampscale
- sig = sig*sigscale
-
- pars = model.make_params(amplitude=amp, center=cen, sigma=sig)
- pars['%ssigma' % model.prefix].set(min=0.0)
- return pars
-
-def update_param_vals(pars, prefix, **kwargs):
- """convenience function to update parameter values
- with keyword arguments"""
- for key, val in kwargs.items():
- pname = "%s%s" % (prefix, key)
- if pname in pars:
- pars[pname].value = val
- return pars
-
-COMMON_DOC = """
-
-Parameters
-----------
-independent_vars: list of strings to be set as variable names
-missing: None, 'drop', or 'raise'
- None: Do not check for null or missing values.
- 'drop': Drop null or missing observations in data.
- Use pandas.isnull if pandas is available; otherwise,
- silently fall back to numpy.isnan.
- 'raise': Raise a (more helpful) exception when data contains null
- or missing values.
-prefix: string to prepend to paramter names, needed to add two Models that
- have parameter names in common. None by default.
-"""
-
-class ConstantModel(Model):
- __doc__ = "x -> c" + COMMON_DOC
- def __init__(self, *args, **kwargs):
- def constant(x, c):
- return c
- super(ConstantModel, self).__init__(constant, *args, **kwargs)
-
- def guess(self, data, **kwargs):
- pars = self.make_params()
- pars['%sc' % self.prefix].set(value=data.mean())
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class LinearModel(Model):
- __doc__ = linear.__doc__ + COMMON_DOC if linear.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(LinearModel, self).__init__(linear, *args, **kwargs)
-
- def guess(self, data, x=None, **kwargs):
- sval, oval = 0., 0.
- if x is not None:
- sval, oval = np.polyfit(x, data, 1)
- pars = self.make_params(intercept=oval, slope=sval)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class QuadraticModel(Model):
- __doc__ = parabolic.__doc__ + COMMON_DOC if parabolic.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(QuadraticModel, self).__init__(parabolic, *args, **kwargs)
-
- def guess(self, data, x=None, **kwargs):
- a, b, c = 0., 0., 0.
- if x is not None:
- a, b, c = np.polyfit(x, data, 2)
- pars = self.make_params(a=a, b=b, c=c)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-ParabolicModel = QuadraticModel
-
-class PolynomialModel(Model):
- __doc__ = "x -> c0 + c1 * x + c2 * x**2 + ... c7 * x**7" + COMMON_DOC
- MAX_DEGREE=7
- DEGREE_ERR = "degree must be an integer less than %d."
- def __init__(self, degree, *args, **kwargs):
- if not isinstance(degree, int) or degree > self.MAX_DEGREE:
- raise TypeError(self.DEGREE_ERR % self.MAX_DEGREE)
-
- self.poly_degree = degree
- pnames = ['c%i' % (i) for i in range(degree + 1)]
- kwargs['param_names'] = pnames
-
- def polynomial(x, c0=0, c1=0, c2=0, c3=0, c4=0, c5=0, c6=0, c7=0):
- return np.polyval([c7, c6, c5, c4, c3, c2, c1, c0], x)
-
- super(PolynomialModel, self).__init__(polynomial, *args, **kwargs)
-
- def guess(self, data, x=None, **kwargs):
- pars = self.make_params()
- if x is not None:
- out = np.polyfit(x, data, self.poly_degree)
- for i, coef in enumerate(out[::-1]):
- pars['%sc%i'% (self.prefix, i)].set(value=coef)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class GaussianModel(Model):
- __doc__ = gaussian.__doc__ + COMMON_DOC if gaussian.__doc__ else ""
- fwhm_factor = 2.354820
- def __init__(self, *args, **kwargs):
- super(GaussianModel, self).__init__(gaussian, *args, **kwargs)
- self.set_param_hint('sigma', min=0)
- self.set_param_hint('fwhm', expr=fwhm_expr(self))
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = guess_from_peak(self, data, x, negative)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class LorentzianModel(Model):
- __doc__ = lorentzian.__doc__ + COMMON_DOC if lorentzian.__doc__ else ""
- fwhm_factor = 2.0
- def __init__(self, *args, **kwargs):
- super(LorentzianModel, self).__init__(lorentzian, *args, **kwargs)
- self.set_param_hint('sigma', min=0)
- self.set_param_hint('fwhm', expr=fwhm_expr(self))
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = guess_from_peak(self, data, x, negative, ampscale=1.25)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class VoigtModel(Model):
- __doc__ = voigt.__doc__ + COMMON_DOC if voigt.__doc__ else ""
- fwhm_factor = 3.60131
- def __init__(self, *args, **kwargs):
- super(VoigtModel, self).__init__(voigt, *args, **kwargs)
- self.set_param_hint('sigma', min=0)
- self.set_param_hint('gamma', expr='%ssigma' % self.prefix)
- self.set_param_hint('fwhm', expr=fwhm_expr(self))
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = guess_from_peak(self, data, x, negative,
- ampscale=1.5, sigscale=0.65)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class PseudoVoigtModel(Model):
- __doc__ = pvoigt.__doc__ + COMMON_DOC if pvoigt.__doc__ else ""
- fwhm_factor = 2.0
- def __init__(self, *args, **kwargs):
- super(PseudoVoigtModel, self).__init__(pvoigt, *args, **kwargs)
- self.set_param_hint('fraction', value=0.5)
- self.set_param_hint('fwhm', expr=fwhm_expr(self))
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = guess_from_peak(self, data, x, negative, ampscale=1.25)
- pars['%sfraction' % self.prefix].set(value=0.5)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class MoffatModel(Model):
- __doc__ = moffat.__doc__ + COMMON_DOC if moffat.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(MoffatModel, self).__init__(moffat, *args, **kwargs)
- self.set_param_hint('fwhm', expr="2*%ssigma*sqrt(2**(1.0/%sbeta)-1)" % (self.prefix, self.prefix))
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = guess_from_peak(self, data, x, negative, ampscale=0.5, sigscale=1.)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class Pearson7Model(Model):
- __doc__ = pearson7.__doc__ + COMMON_DOC if pearson7.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(Pearson7Model, self).__init__(pearson7, *args, **kwargs)
- self.set_param_hint('expon', value=1.5)
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = guess_from_peak(self, data, x, negative)
- pars['%sexpon' % self.prefix].set(value=1.5)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class StudentsTModel(Model):
- __doc__ = students_t.__doc__ + COMMON_DOC if students_t.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(StudentsTModel, self).__init__(students_t, *args, **kwargs)
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = guess_from_peak(self, data, x, negative)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class BreitWignerModel(Model):
- __doc__ = breit_wigner.__doc__ + COMMON_DOC if breit_wigner.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(BreitWignerModel, self).__init__(breit_wigner, *args, **kwargs)
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = guess_from_peak(self, data, x, negative)
- pars['%sq' % self.prefix].set(value=1.0)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class LognormalModel(Model):
- __doc__ = lognormal.__doc__ + COMMON_DOC if lognormal.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(LognormalModel, self).__init__(lognormal, *args, **kwargs)
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = self.make_params(amplitude=1.0, center=0.0, sigma=0.25)
- pars['%ssigma' % self.prefix].set(min=0.0)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class DampedOscillatorModel(Model):
- __doc__ = damped_oscillator.__doc__ + COMMON_DOC if damped_oscillator.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(DampedOscillatorModel, self).__init__(damped_oscillator, *args, **kwargs)
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars =guess_from_peak(self, data, x, negative,
- ampscale=0.1, sigscale=0.1)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-class ExponentialGaussianModel(Model):
- __doc__ = expgaussian.__doc__ + COMMON_DOC if expgaussian.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(ExponentialGaussianModel, self).__init__(expgaussian, *args, **kwargs)
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = guess_from_peak(self, data, x, negative)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-class SkewedGaussianModel(Model):
- __doc__ = skewed_gaussian.__doc__ + COMMON_DOC if skewed_gaussian.__doc__ else ""
- fwhm_factor = 2.354820
- def __init__(self, *args, **kwargs):
- super(SkewedGaussianModel, self).__init__(skewed_gaussian, *args, **kwargs)
- self.set_param_hint('sigma', min=0)
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = guess_from_peak(self, data, x, negative)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-class DonaichModel(Model):
- __doc__ = donaich.__doc__ + COMMON_DOC if donaich.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(DonaichModel, self).__init__(donaich, *args, **kwargs)
-
- def guess(self, data, x=None, negative=False, **kwargs):
- pars = guess_from_peak(self, data, x, negative, ampscale=0.5)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class PowerLawModel(Model):
- __doc__ = powerlaw.__doc__ + COMMON_DOC if powerlaw.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(PowerLawModel, self).__init__(powerlaw, *args, **kwargs)
-
- def guess(self, data, x=None, **kwargs):
- try:
- expon, amp = np.polyfit(np.log(x+1.e-14), np.log(data+1.e-14), 1)
- except:
- expon, amp = 1, np.log(abs(max(data)+1.e-9))
-
- pars = self.make_params(amplitude=np.exp(amp), exponent=expon)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class ExponentialModel(Model):
- __doc__ = exponential.__doc__ + COMMON_DOC if exponential.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(ExponentialModel, self).__init__(exponential, *args, **kwargs)
-
- def guess(self, data, x=None, **kwargs):
- try:
- sval, oval = np.polyfit(x, np.log(abs(data)+1.e-15), 1)
- except:
- sval, oval = 1., np.log(abs(max(data)+1.e-9))
- pars = self.make_params(amplitude=np.exp(oval), decay=-1.0/sval)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class StepModel(Model):
- __doc__ = step.__doc__ + COMMON_DOC if step.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(StepModel, self).__init__(step, *args, **kwargs)
-
- def guess(self, data, x=None, **kwargs):
- if x is None:
- return
- ymin, ymax = min(data), max(data)
- xmin, xmax = min(x), max(x)
- pars = self.make_params(amplitude=(ymax-ymin),
- center=(xmax+xmin)/2.0)
- pars['%ssigma' % self.prefix].set(value=(xmax-xmin)/7.0, min=0.0)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class RectangleModel(Model):
- __doc__ = rectangle.__doc__ + COMMON_DOC if rectangle.__doc__ else ""
- def __init__(self, *args, **kwargs):
- super(RectangleModel, self).__init__(rectangle, *args, **kwargs)
- self.set_param_hint('midpoint',
- expr='(%scenter1+%scenter2)/2.0' % (self.prefix,
- self.prefix))
- def guess(self, data, x=None, **kwargs):
- if x is None:
- return
- ymin, ymax = min(data), max(data)
- xmin, xmax = min(x), max(x)
- pars = self.make_params(amplitude=(ymax-ymin),
- center1=(xmax+xmin)/4.0,
- center2=3*(xmax+xmin)/4.0)
- pars['%ssigma1' % self.prefix].set(value=(xmax-xmin)/7.0, min=0.0)
- pars['%ssigma2' % self.prefix].set(value=(xmax-xmin)/7.0, min=0.0)
- return update_param_vals(pars, self.prefix, **kwargs)
-
-
-class ExpressionModel(Model):
- """Model from User-supplied expression
-
-Parameters
-----------
-expr: string of mathematical expression for model.
-independent_vars: list of strings to be set as variable names
-missing: None, 'drop', or 'raise'
- None: Do not check for null or missing values.
- 'drop': Drop null or missing observations in data.
- Use pandas.isnull if pandas is available; otherwise,
- silently fall back to numpy.isnan.
- 'raise': Raise a (more helpful) exception when data contains null
- or missing values.
-prefix: NOT supported for ExpressionModel
-"""
-
- idvar_missing = "No independent variable found in\n %s"
- idvar_notfound = "Cannot find independent variables '%s' in\n %s"
- no_prefix = "ExpressionModel does not support `prefix` argument"
- def __init__(self, expr, independent_vars=None, init_script=None,
- *args, **kwargs):
-
- # create ast evaluator, load custom functions
- self.asteval = Interpreter()
- for name in lineshapes.functions:
- self.asteval.symtable[name] = getattr(lineshapes, name, None)
- if init_script is not None:
- self.asteval.eval(init_script)
-
- # save expr as text, parse to ast, save for later use
- self.expr = expr.strip()
- self.astcode = self.asteval.parse(self.expr)
-
- # find all symbol names found in expression
- sym_names = get_ast_names(self.astcode)
-
- if independent_vars is None and 'x' in sym_names:
- independent_vars = ['x']
- if independent_vars is None:
- raise ValueError(self.idvar_missing % (self.expr))
-
- # determine which named symbols are parameter names,
- # try to find all independent variables
- idvar_found = [False]*len(independent_vars)
- param_names = []
- for name in sym_names:
- if name in independent_vars:
- idvar_found[independent_vars.index(name)] = True
- elif name not in self.asteval.symtable:
- param_names.append(name)
-
- # make sure we have all independent parameters
- if not all(idvar_found):
- lost = []
- for ix, found in enumerate(idvar_found):
- if not found:
- lost.append(independent_vars[ix])
- lost = ', '.join(lost)
- raise ValueError(self.idvar_notfound % (lost, self.expr))
-
- kwargs['independent_vars'] = independent_vars
- if 'prefix' in kwargs:
- raise Warning(self.no_prefix)
-
- def _eval(**kwargs):
- for name, val in kwargs.items():
- self.asteval.symtable[name] = val
- return self.asteval.run(self.astcode)
-
- super(ExpressionModel, self).__init__(_eval, *args, **kwargs)
-
- # set param names here, and other things normally
- # set in _parse_params(), which will be short-circuited.
- self.independent_vars = independent_vars
- self._func_allargs = independent_vars + param_names
- self._param_names = set(param_names)
- self._func_haskeywords = True
- self.def_vals = {}
-
- def __repr__(self):
- return "<lmfit.ExpressionModel('%s')>" % (self.expr)
-
- def _parse_params(self):
- """ExpressionModel._parse_params is over-written (as `pass`)
- to prevent normal parsing of function for parameter names
- """
- pass
+import numpy as np +from .model import Model + +from .lineshapes import (gaussian, lorentzian, voigt, pvoigt, moffat, pearson7, + step, rectangle, breit_wigner, logistic, + students_t, lognormal, damped_oscillator, + expgaussian, skewed_gaussian, donaich, + skewed_voigt, exponential, powerlaw, linear, + parabolic) + +from . import lineshapes + +from .asteval import Interpreter +from .astutils import get_ast_names + +class DimensionalError(Exception): + pass + +def _validate_1d(independent_vars): + if len(independent_vars) != 1: + raise DimensionalError( + "This model requires exactly one independent variable.") + +def index_of(arr, val): + """return index of array nearest to a value + """ + if val < min(arr): + return 0 + return np.abs(arr-val).argmin() + +def fwhm_expr(model): + "return constraint expression for fwhm" + fmt = "{factor:.7f}*{prefix:s}sigma" + return fmt.format(factor=model.fwhm_factor, prefix=model.prefix) + +def height_expr(model): + "return constraint expression for maximum peak height" + fmt = "{factor:.7f}*{prefix:s}amplitude/{prefix:s}sigma" + return fmt.format(factor=model.height_factor, prefix=model.prefix) + +def guess_from_peak(model, y, x, negative, ampscale=1.0, sigscale=1.0): + "estimate amp, cen, sigma for a peak, create params" + if x is None: + return 1.0, 0.0, 1.0 + maxy, miny = max(y), min(y) + maxx, minx = max(x), min(x) + imaxy = index_of(y, maxy) + cen = x[imaxy] + amp = (maxy - miny)*2.0 + sig = (maxx-minx)/6.0 + + halfmax_vals = np.where(y > (maxy+miny)/2.0)[0] + if negative: + imaxy = index_of(y, miny) + amp = -(maxy - miny)*2.0 + halfmax_vals = np.where(y < (maxy+miny)/2.0)[0] + if len(halfmax_vals) > 2: + sig = (x[halfmax_vals[-1]] - x[halfmax_vals[0]])/2.0 + cen = x[halfmax_vals].mean() + amp = amp*sig*ampscale + sig = sig*sigscale + + pars = model.make_params(amplitude=amp, center=cen, sigma=sig) + pars['%ssigma' % model.prefix].set(min=0.0) + return pars + +def update_param_vals(pars, prefix, **kwargs): + """convenience function to update parameter values + with keyword arguments""" + for key, val in kwargs.items(): + pname = "%s%s" % (prefix, key) + if pname in pars: + pars[pname].value = val + return pars + +COMMON_DOC = """ + +Parameters +---------- +independent_vars: list of strings to be set as variable names +missing: None, 'drop', or 'raise' + None: Do not check for null or missing values. + 'drop': Drop null or missing observations in data. + Use pandas.isnull if pandas is available; otherwise, + silently fall back to numpy.isnan. + 'raise': Raise a (more helpful) exception when data contains null + or missing values. +prefix: string to prepend to paramter names, needed to add two Models that + have parameter names in common. None by default. +""" + +class ConstantModel(Model): + __doc__ = "x -> c" + COMMON_DOC + def __init__(self, *args, **kwargs): + def constant(x, c): + return c + super(ConstantModel, self).__init__(constant, *args, **kwargs) + + def guess(self, data, **kwargs): + pars = self.make_params() + pars['%sc' % self.prefix].set(value=data.mean()) + return update_param_vals(pars, self.prefix, **kwargs) + +class ComplexConstantModel(Model): + __doc__ = "x -> re+1j*im" + COMMON_DOC + def __init__(self, *args, **kwargs): + def constant(x, re, im): + return re + 1j*im + super(ComplexConstantModel, self).__init__(constant, *args, **kwargs) + + def guess(self, data, **kwargs): + pars = self.make_params() + pars['%sre' % self.prefix].set(value=data.real.mean()) + pars['%sim' % self.prefix].set(value=data.imag.mean()) + return update_param_vals(pars, self.prefix, **kwargs) + +class LinearModel(Model): + __doc__ = linear.__doc__ + COMMON_DOC if linear.__doc__ else "" + def __init__(self, *args, **kwargs): + super(LinearModel, self).__init__(linear, *args, **kwargs) + + def guess(self, data, x=None, **kwargs): + sval, oval = 0., 0. + if x is not None: + sval, oval = np.polyfit(x, data, 1) + pars = self.make_params(intercept=oval, slope=sval) + return update_param_vals(pars, self.prefix, **kwargs) + + +class QuadraticModel(Model): + __doc__ = parabolic.__doc__ + COMMON_DOC if parabolic.__doc__ else "" + def __init__(self, *args, **kwargs): + super(QuadraticModel, self).__init__(parabolic, *args, **kwargs) + + def guess(self, data, x=None, **kwargs): + a, b, c = 0., 0., 0. + if x is not None: + a, b, c = np.polyfit(x, data, 2) + pars = self.make_params(a=a, b=b, c=c) + return update_param_vals(pars, self.prefix, **kwargs) + +ParabolicModel = QuadraticModel + +class PolynomialModel(Model): + __doc__ = "x -> c0 + c1 * x + c2 * x**2 + ... c7 * x**7" + COMMON_DOC + MAX_DEGREE=7 + DEGREE_ERR = "degree must be an integer less than %d." + def __init__(self, degree, *args, **kwargs): + if not isinstance(degree, int) or degree > self.MAX_DEGREE: + raise TypeError(self.DEGREE_ERR % self.MAX_DEGREE) + + self.poly_degree = degree + pnames = ['c%i' % (i) for i in range(degree + 1)] + kwargs['param_names'] = pnames + + def polynomial(x, c0=0, c1=0, c2=0, c3=0, c4=0, c5=0, c6=0, c7=0): + return np.polyval([c7, c6, c5, c4, c3, c2, c1, c0], x) + + super(PolynomialModel, self).__init__(polynomial, *args, **kwargs) + + def guess(self, data, x=None, **kwargs): + pars = self.make_params() + if x is not None: + out = np.polyfit(x, data, self.poly_degree) + for i, coef in enumerate(out[::-1]): + pars['%sc%i'% (self.prefix, i)].set(value=coef) + return update_param_vals(pars, self.prefix, **kwargs) + + +class GaussianModel(Model): + __doc__ = gaussian.__doc__ + COMMON_DOC if gaussian.__doc__ else "" + fwhm_factor = 2.354820 + height_factor = 1./np.sqrt(2*np.pi) + def __init__(self, *args, **kwargs): + super(GaussianModel, self).__init__(gaussian, *args, **kwargs) + self.set_param_hint('sigma', min=0) + self.set_param_hint('fwhm', expr=fwhm_expr(self)) + self.set_param_hint('height', expr=height_expr(self)) + + def guess(self, data, x=None, negative=False, **kwargs): + pars = guess_from_peak(self, data, x, negative) + return update_param_vals(pars, self.prefix, **kwargs) + + +class LorentzianModel(Model): + __doc__ = lorentzian.__doc__ + COMMON_DOC if lorentzian.__doc__ else "" + fwhm_factor = 2.0 + height_factor = 1./np.pi + def __init__(self, *args, **kwargs): + super(LorentzianModel, self).__init__(lorentzian, *args, **kwargs) + self.set_param_hint('sigma', min=0) + self.set_param_hint('fwhm', expr=fwhm_expr(self)) + self.set_param_hint('height', expr=height_expr(self)) + + def guess(self, data, x=None, negative=False, **kwargs): + pars = guess_from_peak(self, data, x, negative, ampscale=1.25) + return update_param_vals(pars, self.prefix, **kwargs) + + +class VoigtModel(Model): + __doc__ = voigt.__doc__ + COMMON_DOC if voigt.__doc__ else "" + fwhm_factor = 3.60131 + height_factor = 1./np.sqrt(2*np.pi) + def __init__(self, *args, **kwargs): + super(VoigtModel, self).__init__(voigt, *args, **kwargs) + self.set_param_hint('sigma', min=0) + self.set_param_hint('gamma', expr='%ssigma' % self.prefix) + self.set_param_hint('fwhm', expr=fwhm_expr(self)) + self.set_param_hint('height', expr=height_expr(self)) + + def guess(self, data, x=None, negative=False, **kwargs): + pars = guess_from_peak(self, data, x, negative, + ampscale=1.5, sigscale=0.65) + return update_param_vals(pars, self.prefix, **kwargs) + + +class PseudoVoigtModel(Model): + __doc__ = pvoigt.__doc__ + COMMON_DOC if pvoigt.__doc__ else "" + fwhm_factor = 2.0 + def __init__(self, *args, **kwargs): + super(PseudoVoigtModel, self).__init__(pvoigt, *args, **kwargs) + self.set_param_hint('sigma', min=0) + self.set_param_hint('fraction', value=0.5) + self.set_param_hint('fwhm', expr=fwhm_expr(self)) + + def guess(self, data, x=None, negative=False, **kwargs): + pars = guess_from_peak(self, data, x, negative, ampscale=1.25) + pars['%sfraction' % self.prefix].set(value=0.5) + return update_param_vals(pars, self.prefix, **kwargs) + + +class MoffatModel(Model): + __doc__ = moffat.__doc__ + COMMON_DOC if moffat.__doc__ else "" + def __init__(self, *args, **kwargs): + super(MoffatModel, self).__init__(moffat, *args, **kwargs) + self.set_param_hint('sigma', min=0) + self.set_param_hint('beta') + self.set_param_hint('fwhm', expr="2*%ssigma*sqrt(2**(1.0/%sbeta)-1)" % (self.prefix, self.prefix)) + + def guess(self, data, x=None, negative=False, **kwargs): + pars = guess_from_peak(self, data, x, negative, ampscale=0.5, sigscale=1.) + return update_param_vals(pars, self.prefix, **kwargs) + + +class Pearson7Model(Model): + __doc__ = pearson7.__doc__ + COMMON_DOC if pearson7.__doc__ else "" + def __init__(self, *args, **kwargs): + super(Pearson7Model, self).__init__(pearson7, *args, **kwargs) + self.set_param_hint('expon', value=1.5) + + def guess(self, data, x=None, negative=False, **kwargs): + pars = guess_from_peak(self, data, x, negative) + pars['%sexpon' % self.prefix].set(value=1.5) + return update_param_vals(pars, self.prefix, **kwargs) + + +class StudentsTModel(Model): + __doc__ = students_t.__doc__ + COMMON_DOC if students_t.__doc__ else "" + def __init__(self, *args, **kwargs): + super(StudentsTModel, self).__init__(students_t, *args, **kwargs) + + def guess(self, data, x=None, negative=False, **kwargs): + pars = guess_from_peak(self, data, x, negative) + return update_param_vals(pars, self.prefix, **kwargs) + + +class BreitWignerModel(Model): + __doc__ = breit_wigner.__doc__ + COMMON_DOC if breit_wigner.__doc__ else "" + def __init__(self, *args, **kwargs): + super(BreitWignerModel, self).__init__(breit_wigner, *args, **kwargs) + + def guess(self, data, x=None, negative=False, **kwargs): + pars = guess_from_peak(self, data, x, negative) + pars['%sq' % self.prefix].set(value=1.0) + return update_param_vals(pars, self.prefix, **kwargs) + + +class LognormalModel(Model): + __doc__ = lognormal.__doc__ + COMMON_DOC if lognormal.__doc__ else "" + def __init__(self, *args, **kwargs): + super(LognormalModel, self).__init__(lognormal, *args, **kwargs) + + def guess(self, data, x=None, negative=False, **kwargs): + pars = self.make_params(amplitude=1.0, center=0.0, sigma=0.25) + pars['%ssigma' % self.prefix].set(min=0.0) + return update_param_vals(pars, self.prefix, **kwargs) + + +class DampedOscillatorModel(Model): + __doc__ = damped_oscillator.__doc__ + COMMON_DOC if damped_oscillator.__doc__ else "" + def __init__(self, *args, **kwargs): + super(DampedOscillatorModel, self).__init__(damped_oscillator, *args, **kwargs) + + def guess(self, data, x=None, negative=False, **kwargs): + pars =guess_from_peak(self, data, x, negative, + ampscale=0.1, sigscale=0.1) + return update_param_vals(pars, self.prefix, **kwargs) + +class ExponentialGaussianModel(Model): + __doc__ = expgaussian.__doc__ + COMMON_DOC if expgaussian.__doc__ else "" + def __init__(self, *args, **kwargs): + super(ExponentialGaussianModel, self).__init__(expgaussian, *args, **kwargs) + + def guess(self, data, x=None, negative=False, **kwargs): + pars = guess_from_peak(self, data, x, negative) + return update_param_vals(pars, self.prefix, **kwargs) + +class SkewedGaussianModel(Model): + __doc__ = skewed_gaussian.__doc__ + COMMON_DOC if skewed_gaussian.__doc__ else "" + fwhm_factor = 2.354820 + def __init__(self, *args, **kwargs): + super(SkewedGaussianModel, self).__init__(skewed_gaussian, *args, **kwargs) + self.set_param_hint('sigma', min=0) + + def guess(self, data, x=None, negative=False, **kwargs): + pars = guess_from_peak(self, data, x, negative) + return update_param_vals(pars, self.prefix, **kwargs) + +class DonaichModel(Model): + __doc__ = donaich.__doc__ + COMMON_DOC if donaich.__doc__ else "" + def __init__(self, *args, **kwargs): + super(DonaichModel, self).__init__(donaich, *args, **kwargs) + + def guess(self, data, x=None, negative=False, **kwargs): + pars = guess_from_peak(self, data, x, negative, ampscale=0.5) + return update_param_vals(pars, self.prefix, **kwargs) + + +class PowerLawModel(Model): + __doc__ = powerlaw.__doc__ + COMMON_DOC if powerlaw.__doc__ else "" + def __init__(self, *args, **kwargs): + super(PowerLawModel, self).__init__(powerlaw, *args, **kwargs) + + def guess(self, data, x=None, **kwargs): + try: + expon, amp = np.polyfit(np.log(x+1.e-14), np.log(data+1.e-14), 1) + except: + expon, amp = 1, np.log(abs(max(data)+1.e-9)) + + pars = self.make_params(amplitude=np.exp(amp), exponent=expon) + return update_param_vals(pars, self.prefix, **kwargs) + + +class ExponentialModel(Model): + __doc__ = exponential.__doc__ + COMMON_DOC if exponential.__doc__ else "" + def __init__(self, *args, **kwargs): + super(ExponentialModel, self).__init__(exponential, *args, **kwargs) + + def guess(self, data, x=None, **kwargs): + try: + sval, oval = np.polyfit(x, np.log(abs(data)+1.e-15), 1) + except: + sval, oval = 1., np.log(abs(max(data)+1.e-9)) + pars = self.make_params(amplitude=np.exp(oval), decay=-1.0/sval) + return update_param_vals(pars, self.prefix, **kwargs) + + +class StepModel(Model): + __doc__ = step.__doc__ + COMMON_DOC if step.__doc__ else "" + def __init__(self, *args, **kwargs): + super(StepModel, self).__init__(step, *args, **kwargs) + + def guess(self, data, x=None, **kwargs): + if x is None: + return + ymin, ymax = min(data), max(data) + xmin, xmax = min(x), max(x) + pars = self.make_params(amplitude=(ymax-ymin), + center=(xmax+xmin)/2.0) + pars['%ssigma' % self.prefix].set(value=(xmax-xmin)/7.0, min=0.0) + return update_param_vals(pars, self.prefix, **kwargs) + + +class RectangleModel(Model): + __doc__ = rectangle.__doc__ + COMMON_DOC if rectangle.__doc__ else "" + def __init__(self, *args, **kwargs): + super(RectangleModel, self).__init__(rectangle, *args, **kwargs) + + self.set_param_hint('center1') + self.set_param_hint('center2') + self.set_param_hint('midpoint', + expr='(%scenter1+%scenter2)/2.0' % (self.prefix, + self.prefix)) + def guess(self, data, x=None, **kwargs): + if x is None: + return + ymin, ymax = min(data), max(data) + xmin, xmax = min(x), max(x) + pars = self.make_params(amplitude=(ymax-ymin), + center1=(xmax+xmin)/4.0, + center2=3*(xmax+xmin)/4.0) + pars['%ssigma1' % self.prefix].set(value=(xmax-xmin)/7.0, min=0.0) + pars['%ssigma2' % self.prefix].set(value=(xmax-xmin)/7.0, min=0.0) + return update_param_vals(pars, self.prefix, **kwargs) + + +class ExpressionModel(Model): + """Model from User-supplied expression + +Parameters +---------- +expr: string of mathematical expression for model. +independent_vars: list of strings to be set as variable names +missing: None, 'drop', or 'raise' + None: Do not check for null or missing values. + 'drop': Drop null or missing observations in data. + Use pandas.isnull if pandas is available; otherwise, + silently fall back to numpy.isnan. + 'raise': Raise a (more helpful) exception when data contains null + or missing values. +prefix: NOT supported for ExpressionModel +""" + + idvar_missing = "No independent variable found in\n %s" + idvar_notfound = "Cannot find independent variables '%s' in\n %s" + no_prefix = "ExpressionModel does not support `prefix` argument" + def __init__(self, expr, independent_vars=None, init_script=None, + *args, **kwargs): + + # create ast evaluator, load custom functions + self.asteval = Interpreter() + for name in lineshapes.functions: + self.asteval.symtable[name] = getattr(lineshapes, name, None) + if init_script is not None: + self.asteval.eval(init_script) + + # save expr as text, parse to ast, save for later use + self.expr = expr.strip() + self.astcode = self.asteval.parse(self.expr) + + # find all symbol names found in expression + sym_names = get_ast_names(self.astcode) + + if independent_vars is None and 'x' in sym_names: + independent_vars = ['x'] + if independent_vars is None: + raise ValueError(self.idvar_missing % (self.expr)) + + # determine which named symbols are parameter names, + # try to find all independent variables + idvar_found = [False]*len(independent_vars) + param_names = [] + for name in sym_names: + if name in independent_vars: + idvar_found[independent_vars.index(name)] = True + elif name not in self.asteval.symtable: + param_names.append(name) + + # make sure we have all independent parameters + if not all(idvar_found): + lost = [] + for ix, found in enumerate(idvar_found): + if not found: + lost.append(independent_vars[ix]) + lost = ', '.join(lost) + raise ValueError(self.idvar_notfound % (lost, self.expr)) + + kwargs['independent_vars'] = independent_vars + if 'prefix' in kwargs: + raise Warning(self.no_prefix) + + def _eval(**kwargs): + for name, val in kwargs.items(): + self.asteval.symtable[name] = val + return self.asteval.run(self.astcode) + + super(ExpressionModel, self).__init__(_eval, *args, **kwargs) + + # set param names here, and other things normally + # set in _parse_params(), which will be short-circuited. + self.independent_vars = independent_vars + self._func_allargs = independent_vars + param_names + self._param_names = set(param_names) + self._func_haskeywords = True + self.def_vals = {} + + def __repr__(self): + return "<lmfit.ExpressionModel('%s')>" % (self.expr) + + def _parse_params(self): + """ExpressionModel._parse_params is over-written (as `pass`) + to prevent normal parsing of function for parameter names + """ + pass diff --git a/lmfit/ordereddict.py b/lmfit/ordereddict.py index 524a5c9..2d1d813 100644 --- a/lmfit/ordereddict.py +++ b/lmfit/ordereddict.py @@ -1,128 +1,128 @@ -# Copyright (c) 2009 Raymond Hettinger
-#
-# Permission is hereby granted, free of charge, to any person
-# obtaining a copy of this software and associated documentation files
-# (the "Software"), to deal in the Software without restriction,
-# including without limitation the rights to use, copy, modify, merge,
-# publish, distribute, sublicense, and/or sell copies of the Software,
-# and to permit persons to whom the Software is furnished to do so,
-# subject to the following conditions:
-#
-# The above copyright notice and this permission notice shall be
-# included in all copies or substantial portions of the Software.
-#
-# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
-# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
-# OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
-# NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
-# HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
-# WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
-# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
-# OTHER DEALINGS IN THE SOFTWARE.
-
-from UserDict import DictMixin
-
-
-class OrderedDict(dict, DictMixin):
-
- def __init__(self, *args, **kwds):
- if len(args) > 1:
- raise TypeError('expected at most 1 arguments, got %d' % len(args))
- try:
- self.__end
- except AttributeError:
- self.clear()
- self.update(*args, **kwds)
-
- def clear(self):
- self.__end = end = []
- end += [None, end, end] # sentinel node for doubly linked list
- self.__map = {} # key --> [key, prev, next]
- dict.clear(self)
-
- def __setitem__(self, key, value):
- if key not in self:
- end = self.__end
- curr = end[1]
- curr[2] = end[1] = self.__map[key] = [key, curr, end]
- dict.__setitem__(self, key, value)
-
- def __delitem__(self, key):
- dict.__delitem__(self, key)
- key, prev, next = self.__map.pop(key)
- prev[2] = next
- next[1] = prev
-
- def __iter__(self):
- end = self.__end
- curr = end[2]
- while curr is not end:
- yield curr[0]
- curr = curr[2]
-
- def __reversed__(self):
- end = self.__end
- curr = end[1]
- while curr is not end:
- yield curr[0]
- curr = curr[1]
-
- def popitem(self, last=True):
- if not self:
- raise KeyError('dictionary is empty')
- if last:
- key = reversed(self).next()
- else:
- key = iter(self).next()
- value = self.pop(key)
- return key, value
-
- def __reduce__(self):
- items = [[k, self[k]] for k in self]
- tmp = self.__map, self.__end
- del self.__map, self.__end
- inst_dict = vars(self).copy()
- self.__map, self.__end = tmp
- if inst_dict:
- return (self.__class__, (items,), inst_dict)
- return self.__class__, (items,)
-
- def keys(self):
- return list(self)
-
- setdefault = DictMixin.setdefault
- update = DictMixin.update
- pop = DictMixin.pop
- values = DictMixin.values
- items = DictMixin.items
- iterkeys = DictMixin.iterkeys
- itervalues = DictMixin.itervalues
- iteritems = DictMixin.iteritems
-
- def __repr__(self):
- if not self:
- return '%s()' % (self.__class__.__name__,)
- return '%s(%r)' % (self.__class__.__name__, self.items())
-
- def copy(self):
- return self.__class__(self)
-
- @classmethod
- def fromkeys(cls, iterable, value=None):
- d = cls()
- for key in iterable:
- d[key] = value
- return d
-
- def __eq__(self, other):
- if isinstance(other, OrderedDict):
- if len(self) != len(other):
- return False
- for p, q in zip(self.items(), other.items()):
- if p != q:
- return False
- return True
- return dict.__eq__(self, other)
-
- def __ne__(self, other):
- return not self == other
+# Copyright (c) 2009 Raymond Hettinger +# +# Permission is hereby granted, free of charge, to any person +# obtaining a copy of this software and associated documentation files +# (the "Software"), to deal in the Software without restriction, +# including without limitation the rights to use, copy, modify, merge, +# publish, distribute, sublicense, and/or sell copies of the Software, +# and to permit persons to whom the Software is furnished to do so, +# subject to the following conditions: +# +# The above copyright notice and this permission notice shall be +# included in all copies or substantial portions of the Software. +# +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, +# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES +# OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND +# NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT +# HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, +# WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR +# OTHER DEALINGS IN THE SOFTWARE. + +from UserDict import DictMixin + + +class OrderedDict(dict, DictMixin): + + def __init__(self, *args, **kwds): + if len(args) > 1: + raise TypeError('expected at most 1 arguments, got %d' % len(args)) + try: + self.__end + except AttributeError: + self.clear() + self.update(*args, **kwds) + + def clear(self): + self.__end = end = [] + end += [None, end, end] # sentinel node for doubly linked list + self.__map = {} # key --> [key, prev, next] + dict.clear(self) + + def __setitem__(self, key, value): + if key not in self: + end = self.__end + curr = end[1] + curr[2] = end[1] = self.__map[key] = [key, curr, end] + dict.__setitem__(self, key, value) + + def __delitem__(self, key): + dict.__delitem__(self, key) + key, prev, next = self.__map.pop(key) + prev[2] = next + next[1] = prev + + def __iter__(self): + end = self.__end + curr = end[2] + while curr is not end: + yield curr[0] + curr = curr[2] + + def __reversed__(self): + end = self.__end + curr = end[1] + while curr is not end: + yield curr[0] + curr = curr[1] + + def popitem(self, last=True): + if not self: + raise KeyError('dictionary is empty') + if last: + key = reversed(self).next() + else: + key = iter(self).next() + value = self.pop(key) + return key, value + + def __reduce__(self): + items = [[k, self[k]] for k in self] + tmp = self.__map, self.__end + del self.__map, self.__end + inst_dict = vars(self).copy() + self.__map, self.__end = tmp + if inst_dict: + return (self.__class__, (items,), inst_dict) + return self.__class__, (items,) + + def keys(self): + return list(self) + + setdefault = DictMixin.setdefault + update = DictMixin.update + pop = DictMixin.pop + values = DictMixin.values + items = DictMixin.items + iterkeys = DictMixin.iterkeys + itervalues = DictMixin.itervalues + iteritems = DictMixin.iteritems + + def __repr__(self): + if not self: + return '%s()' % (self.__class__.__name__,) + return '%s(%r)' % (self.__class__.__name__, self.items()) + + def copy(self): + return self.__class__(self) + + @classmethod + def fromkeys(cls, iterable, value=None): + d = cls() + for key in iterable: + d[key] = value + return d + + def __eq__(self, other): + if isinstance(other, OrderedDict): + if len(self) != len(other): + return False + for p, q in zip(self.items(), other.items()): + if p != q: + return False + return True + return dict.__eq__(self, other) + + def __ne__(self, other): + return not self == other diff --git a/lmfit/parameter.py b/lmfit/parameter.py index b90d009..0581148 100644 --- a/lmfit/parameter.py +++ b/lmfit/parameter.py @@ -1,725 +1,818 @@ -"""
-Parameter class
-"""
-from __future__ import division
-from numpy import arcsin, cos, sin, sqrt, inf, nan
-import json
-from copy import deepcopy
-try:
- from collections import OrderedDict
-except ImportError:
- from ordereddict import OrderedDict
-
-from . import uncertainties
-
-from .asteval import Interpreter
-from .astutils import get_ast_names, valid_symbol_name
-
-
-def check_ast_errors(expr_eval):
- """check for errors derived from asteval"""
- if len(expr_eval.error) > 0:
- expr_eval.raise_exception(None)
-
-
-class Parameters(OrderedDict):
- """
- A dictionary of all the Parameters required to specify a fit model.
-
- All keys must be strings, and valid Python symbol names, and all values
- must be Parameters.
-
- Custom methods:
- ---------------
-
- add()
- add_many()
- dumps() / dump()
- loads() / load()
- """
- def __init__(self, asteval=None, *args, **kwds):
- super(Parameters, self).__init__(self)
- self._asteval = asteval
-
- if asteval is None:
- self._asteval = Interpreter()
- self.update(*args, **kwds)
-
- def __deepcopy__(self, memo):
- _pars = Parameters()
-
- # find the symbols that were added by users, not during construction
- sym_unique = self._asteval.user_defined_symbols()
- unique_symbols = {key: deepcopy(self._asteval.symtable[key], memo)
- for key in sym_unique}
- _pars._asteval.symtable.update(unique_symbols)
-
- # we're just about to add a lot of Parameter objects to the newly
- parameter_list = []
- for key, par in self.items():
- if isinstance(par, Parameter):
- param = Parameter(name=par.name,
- value=par.value,
- min=par.min,
- max=par.max)
- param.vary = par.vary
- param.stderr = par.stderr
- param.correl = par.correl
- param.init_value = par.init_value
- param.expr = par.expr
- parameter_list.append(param)
-
- _pars.add_many(*parameter_list)
-
- return _pars
-
- def __setitem__(self, key, par):
- if key not in self:
- if not valid_symbol_name(key):
- raise KeyError("'%s' is not a valid Parameters name" % key)
- if par is not None and not isinstance(par, Parameter):
- raise ValueError("'%s' is not a Parameter" % par)
- OrderedDict.__setitem__(self, key, par)
- par.name = key
- par._expr_eval = self._asteval
- self._asteval.symtable[key] = par.value
-
- def __add__(self, other):
- "add Parameters objects"
- if not isinstance(other, Parameters):
- raise ValueError("'%s' is not a Parameters object" % other)
- out = deepcopy(self)
- params = other.values()
- out.add_many(*params)
- return out
-
- def __iadd__(self, other):
- """
- add/assign Parameters objects
- """
- if not isinstance(other, Parameters):
- raise ValueError("'%s' is not a Parameters object" % other)
- params = other.values()
- self.add_many(*params)
- return self
-
- def __reduce__(self):
- """
- Required to pickle a Parameters instance.
- """
- # make a list of all the parameters
- params = [self[k] for k in self]
-
- # find the symbols from _asteval.symtable, that need to be remembered.
- sym_unique = self._asteval.user_defined_symbols()
- unique_symbols = {key: deepcopy(self._asteval.symtable[key])
- for key in sym_unique}
-
- return self.__class__, (), {'unique_symbols': unique_symbols,
- 'params': params}
-
- def __setstate__(self, state):
- """
- Unpickle a Parameters instance.
-
- Parameters
- ----------
- state : list
- state[0] is a dictionary containing symbols that need to be
- injected into _asteval.symtable
- state[1:] are the Parameter instances to be added
- is list of parameters
- """
- # first add all the parameters
- self.add_many(*state['params'])
-
- # now update the Interpreter symbol table
- self._asteval.symtable.update(state['unique_symbols'])
-
- def update_constraints(self):
- """
- Update all constrained parameters, checking that dependencies are
- evaluated as needed.
- """
- _updated = [name for name,par in self.items() if par._expr is None]
-
- def _update_param(name):
- """
- Update a parameter value, including setting bounds.
- For a constrained parameter (one with an expr defined),
- this first updates (recursively) all parameters on which
- the parameter depends (using the 'deps' field).
- """
- # Has this param already been updated?
- if name in _updated:
- return
- par = self.__getitem__(name)
- if par._expr_eval is None:
- par._expr_eval = self._asteval
- if par._expr is not None:
- par.expr = par._expr
- if par._expr_ast is not None:
- for dep in par._expr_deps:
- if dep in self.keys():
- _update_param(dep)
- self._asteval.symtable[name] = par.value
- _updated.append(name)
-
- for name in self.keys():
- if name not in _updated:
- _update_param(name)
-
- def pretty_repr(self, oneline=False):
- if oneline:
- return super(Parameters, self).__repr__()
- s = "Parameters({\n"
- for key in self.keys():
- s += " '%s': %s, \n" % (key, self[key])
- s += " })\n"
- return s
-
- def pretty_print(self, oneline=False):
- print(self.pretty_repr(oneline=oneline))
-
- def add(self, name, value=None, vary=True, min=None, max=None, expr=None):
- """
- Convenience function for adding a Parameter:
-
- Example
- -------
- p = Parameters()
- p.add(name, value=XX, ...)
-
- is equivalent to:
- p[name] = Parameter(name=name, value=XX, ....
- """
- if isinstance(name, Parameter):
- self.__setitem__(name.name, name)
- else:
- self.__setitem__(name, Parameter(value=value, name=name, vary=vary,
- min=min, max=max, expr=expr))
-
- def add_many(self, *parlist):
- """
- Convenience function for adding a list of Parameters.
-
- Parameters
- ----------
- parlist : sequence
- A sequence of tuples, or a sequence of `Parameter` instances. If it
- is a sequence of tuples, then each tuple must contain at least the
- name. The order in each tuple is the following:
-
- name, value, vary, min, max, expr
-
- Example
- -------
- p = Parameters()
- # add a sequence of tuples
- p.add_many( (name1, val1, True, None, None, None),
- (name2, val2, True, 0.0, None, None),
- (name3, val3, False, None, None, None),
- (name4, val4))
-
- # add a sequence of Parameter
- f = Parameter('name5', val5)
- g = Parameter('name6', val6)
- p.add_many(f, g)
- """
- for para in parlist:
- if isinstance(para, Parameter):
- self.__setitem__(para.name, para)
- else:
- param = Parameter(*para)
- self.__setitem__(param.name, param)
-
- def valuesdict(self):
- """
- Returns
- -------
- An ordered dictionary of name:value pairs for each Parameter.
- This is distinct from the Parameters itself, as it has values of
- the Parameter values, not the full Parameter object.
- """
-
- return OrderedDict(((p.name, p.value) for p in self.values()))
-
- def dumps(self, **kws):
- """represent Parameters as a JSON string.
-
- all keyword arguments are passed to `json.dumps()`
-
- Returns
- -------
- json string representation of Parameters
-
- See Also
- --------
- dump(), loads(), load(), json.dumps()
- """
- out = [p.__getstate__() for p in self.values()]
- return json.dumps(out, **kws)
-
- def loads(self, s, **kws):
- """load Parameters from a JSON string.
-
- current Parameters will be cleared before loading.
-
- all keyword arguments are passed to `json.loads()`
-
- Returns
- -------
- None. Parameters are updated as a side-effect
-
- See Also
- --------
- dump(), dumps(), load(), json.loads()
-
- """
- self.clear()
- for parstate in json.loads(s, **kws):
- _par = Parameter()
- _par.__setstate__(parstate)
- self.__setitem__(parstate[0], _par)
-
- def dump(self, fp, **kws):
- """write JSON representation of Parameters to a file
- or file-like object (must have a `write()` method).
-
- Arguments
- ---------
- fp open file-like object with `write()` method.
-
- all keyword arguments are passed to `dumps()`
-
- Returns
- -------
- return value from `fp.write()`
-
- See Also
- --------
- dump(), load(), json.dump()
- """
- return fp.write(self.dumps(**kws))
-
- def load(self, fp, **kws):
- """load JSON representation of Parameters from a file
- or file-like object (must have a `read()` method).
-
- Arguments
- ---------
- fp open file-like object with `read()` method.
-
- all keyword arguments are passed to `loads()`
-
- Returns
- -------
- None. Parameters are updated as a side-effect
-
- See Also
- --------
- dump(), loads(), json.load()
- """
- return self.loads(fp.read(), **kws)
-
-
-class Parameter(object):
- """
- A Parameter is an object used to define a Fit Model.
- Attributes
- ----------
- name : str
- Parameter name.
- value : float
- The numerical value of the Parameter.
- vary : bool
- Whether the Parameter is fixed during a fit.
- min : float
- Lower bound for value (None = no lower bound).
- max : float
- Upper bound for value (None = no upper bound).
- expr : str
- An expression specifying constraints for the parameter.
- stderr : float
- The estimated standard error for the best-fit value.
- correl : dict
- Specifies correlation with the other fitted Parameter after a fit.
- Of the form `{'decay': 0.404, 'phase': -0.020, 'frequency': 0.102}`
- """
- def __init__(self, name=None, value=None, vary=True,
- min=None, max=None, expr=None):
- """
- Parameters
- ----------
- name : str, optional
- Name of the parameter.
- value : float, optional
- Numerical Parameter value.
- vary : bool, optional
- Whether the Parameter is fixed during a fit.
- min : float, optional
- Lower bound for value (None = no lower bound).
- max : float, optional
- Upper bound for value (None = no upper bound).
- expr : str, optional
- Mathematical expression used to constrain the value during the fit.
- """
- self.name = name
- self._val = value
- self.user_value = value
- self.init_value = value
- self.min = min
- self.max = max
- self.vary = vary
- self._expr = expr
- self._expr_ast = None
- self._expr_eval = None
- self._expr_deps = []
- self._delay_asteval = False
- self.stderr = None
- self.correl = None
- self.from_internal = lambda val: val
- self._init_bounds()
-
- def set(self, value=None, vary=None, min=None, max=None, expr=None):
- """
- Set or update Parameter attributes.
-
- Parameters
- ----------
- value : float, optional
- Numerical Parameter value.
- vary : bool, optional
- Whether the Parameter is fixed during a fit.
- min : float, optional
- Lower bound for value. To remove a lower bound you must use -np.inf
- max : float, optional
- Upper bound for value. To remove an upper bound you must use np.inf
- expr : str, optional
- Mathematical expression used to constrain the value during the fit.
- To remove a constraint you must supply an empty string.
- """
-
- self.__set_expression(expr)
- if value is not None:
- self._val = value
- if vary is not None:
- self.vary = vary
- if min is not None:
- self.min = min
- if max is not None:
- self.max = max
-
- def _init_bounds(self):
- """make sure initial bounds are self-consistent"""
- #_val is None means - infinity.
- if self._val is not None:
- if self.max is not None and self._val > self.max:
- self._val = self.max
- if self.min is not None and self._val < self.min:
- self._val = self.min
- elif self.min is not None and self._expr is None:
- self._val = self.min
- elif self.max is not None and self._expr is None:
- self._val = self.max
- self.setup_bounds()
-
- def __getstate__(self):
- """get state for pickle"""
- return (self.name, self.value, self.vary, self.expr, self.min,
- self.max, self.stderr, self.correl, self.init_value)
-
- def __setstate__(self, state):
- """set state for pickle"""
- (self.name, self.value, self.vary, self.expr, self.min,
- self.max, self.stderr, self.correl, self.init_value) = state
- self._expr_ast = None
- self._expr_eval = None
- self._expr_deps = []
- self._delay_asteval = False
- self._init_bounds()
-
- def __repr__(self):
- s = []
- if self.name is not None:
- s.append("'%s'" % self.name)
- sval = repr(self._getval())
- if not self.vary and self._expr is None:
- sval = "value=%s (fixed)" % (sval)
- elif self.stderr is not None:
- sval = "value=%s +/- %.3g" % (sval, self.stderr)
- s.append(sval)
- s.append("bounds=[%s:%s]" % (repr(self.min), repr(self.max)))
- if self._expr is not None:
- s.append("expr='%s'" % (self.expr))
- return "<Parameter %s>" % ', '.join(s)
-
- def setup_bounds(self):
- """
- Set up Minuit-style internal/external parameter transformation
- of min/max bounds.
-
- As a side-effect, this also defines the self.from_internal method
- used to re-calculate self.value from the internal value, applying
- the inverse Minuit-style transformation. This method should be
- called prior to passing a Parameter to the user-defined objective
- function.
-
- This code borrows heavily from JJ Helmus' leastsqbound.py
-
- Returns
- -------
- The internal value for parameter from self.value (which holds
- the external, user-expected value). This internal value should
- actually be used in a fit.
- """
- if self.min in (None, -inf) and self.max in (None, inf):
- self.from_internal = lambda val: val
- _val = self._val
- elif self.max in (None, inf):
- self.from_internal = lambda val: self.min - 1.0 + sqrt(val*val + 1)
- _val = sqrt((self._val - self.min + 1.0)**2 - 1)
- elif self.min in (None, -inf):
- self.from_internal = lambda val: self.max + 1 - sqrt(val*val + 1)
- _val = sqrt((self.max - self._val + 1.0)**2 - 1)
- else:
- self.from_internal = lambda val: self.min + (sin(val) + 1) * \
- (self.max - self.min) / 2.0
- _val = arcsin(2*(self._val - self.min)/(self.max - self.min) - 1)
- return _val
-
- def scale_gradient(self, val):
- """
- Returns
- -------
- scaling factor for gradient the according to Minuit-style
- transformation.
- """
- if self.min in (None, -inf) and self.max in (None, inf):
- return 1.0
- elif self.max in (None, inf):
- return val / sqrt(val*val + 1)
- elif self.min in (None, -inf):
- return -val / sqrt(val*val + 1)
- else:
- return cos(val) * (self.max - self.min) / 2.0
-
-
- def _getval(self):
- """get value, with bounds applied"""
-
- # Note assignment to self._val has been changed to self.value
- # The self.value property setter makes sure that the
- # _expr_eval.symtable is kept updated.
- # If you just assign to self._val then
- # _expr_eval.symtable[self.name]
- # becomes stale if parameter.expr is not None.
- if (isinstance(self._val, uncertainties.Variable)
- and self._val is not nan):
- try:
- self.value = self._val.nominal_value
- except AttributeError:
- pass
- if not self.vary and self._expr is None:
- return self._val
- if not hasattr(self, '_expr_eval'):
- self._expr_eval = None
- if not hasattr(self, '_expr_ast'):
- self._expr_ast = None
- if self._expr_ast is None and self._expr is not None:
- self.__set_expression(self._expr)
-
- if self._expr_ast is not None and self._expr_eval is not None:
- if not self._delay_asteval:
- self.value = self._expr_eval(self._expr_ast)
- check_ast_errors(self._expr_eval)
-
- if self.min is None:
- self.min = -inf
- if self.max is None:
- self.max = inf
- if self.max < self.min:
- self.max, self.min = self.min, self.max
- if (abs((1.0 * self.max - self.min)/
- max(abs(self.max), abs(self.min), 1.e-13)) < 1.e-13):
- raise ValueError("Parameter '%s' has min == max" % self.name)
- try:
- self.value = max(self.min, min(self._val, self.max))
- except(TypeError, ValueError):
- self.value = nan
- return self._val
-
- def set_expr_eval(self, evaluator):
- "set expression evaluator instance"
- self._expr_eval = evaluator
-
- @property
- def value(self):
- "The numerical value of the Parameter, with bounds applied"
- return self._getval()
-
- @value.setter
- def value(self, val):
- "Set the numerical Parameter value."
- self._val = val
- if not hasattr(self, '_expr_eval'): self._expr_eval = None
- if self._expr_eval is not None:
- self._expr_eval.symtable[self.name] = val
-
- @property
- def expr(self):
- """
- The mathematical expression used to constrain the value during the fit.
- """
- return self._expr
-
- @expr.setter
- def expr(self, val):
- """
- The mathematical expression used to constrain the value during the fit.
- To remove a constraint you must supply an empty string.
- """
- self.__set_expression(val)
-
- def __set_expression(self, val):
- if val == '':
- val = None
- self._expr = val
- if val is not None:
- self.vary = False
- if not hasattr(self, '_expr_eval'): self._expr_eval = None
- if val is None: self._expr_ast = None
- if val is not None and self._expr_eval is not None:
- self._expr_ast = self._expr_eval.parse(val)
- check_ast_errors(self._expr_eval)
- self._expr_deps = get_ast_names(self._expr_ast)
-
- def __str__(self):
- "string"
- return self.__repr__()
-
- def __abs__(self):
- "abs"
- return abs(self._getval())
-
- def __neg__(self):
- "neg"
- return -self._getval()
-
- def __pos__(self):
- "positive"
- return +self._getval()
-
- def __nonzero__(self):
- "not zero"
- return self._getval() != 0
-
- def __int__(self):
- "int"
- return int(self._getval())
-
- def __long__(self):
- "long"
- return long(self._getval())
-
- def __float__(self):
- "float"
- return float(self._getval())
-
- def __trunc__(self):
- "trunc"
- return self._getval().__trunc__()
-
- def __add__(self, other):
- "+"
- return self._getval() + other
-
- def __sub__(self, other):
- "-"
- return self._getval() - other
-
- def __div__(self, other):
- "/"
- return self._getval() / other
- __truediv__ = __div__
-
- def __floordiv__(self, other):
- "//"
- return self._getval() // other
-
- def __divmod__(self, other):
- "divmod"
- return divmod(self._getval(), other)
-
- def __mod__(self, other):
- "%"
- return self._getval() % other
-
- def __mul__(self, other):
- "*"
- return self._getval() * other
-
- def __pow__(self, other):
- "**"
- return self._getval() ** other
-
- def __gt__(self, other):
- ">"
- return self._getval() > other
-
- def __ge__(self, other):
- ">="
- return self._getval() >= other
-
- def __le__(self, other):
- "<="
- return self._getval() <= other
-
- def __lt__(self, other):
- "<"
- return self._getval() < other
-
- def __eq__(self, other):
- "=="
- return self._getval() == other
- def __ne__(self, other):
- "!="
- return self._getval() != other
-
- def __radd__(self, other):
- "+ (right)"
- return other + self._getval()
-
- def __rdiv__(self, other):
- "/ (right)"
- return other / self._getval()
- __rtruediv__ = __rdiv__
-
- def __rdivmod__(self, other):
- "divmod (right)"
- return divmod(other, self._getval())
-
- def __rfloordiv__(self, other):
- "// (right)"
- return other // self._getval()
-
- def __rmod__(self, other):
- "% (right)"
- return other % self._getval()
-
- def __rmul__(self, other):
- "* (right)"
- return other * self._getval()
-
- def __rpow__(self, other):
- "** (right)"
- return other ** self._getval()
-
- def __rsub__(self, other):
- "- (right)"
- return other - self._getval()
-
-def isParameter(x):
- "test for Parameter-ness"
- return (isinstance(x, Parameter) or
- x.__class__.__name__ == 'Parameter')
+""" +Parameter class +""" +from __future__ import division +from numpy import arcsin, cos, sin, sqrt, inf, nan, isfinite +import json +from copy import deepcopy +try: + from collections import OrderedDict +except ImportError: + from ordereddict import OrderedDict + +from . import uncertainties + +from .asteval import Interpreter +from .astutils import get_ast_names, valid_symbol_name + + +def check_ast_errors(expr_eval): + """check for errors derived from asteval""" + if len(expr_eval.error) > 0: + expr_eval.raise_exception(None) + + +def isclose(x, y, rtol=1e-5, atol=1e-8): + """ + The truth whether two numbers are the same, within an absolute and + relative tolerance. + + i.e. abs(`x` - `y`) <= (`atol` + `rtol` * absolute(`y`)) + + Parameters + ---------- + x, y : float + Input values + rtol : float + The relative tolerance parameter (see Notes). + atol : float + The absolute tolerance parameter (see Notes). + + Returns + ------- + y : bool + Are `x` and `x` are equal within tolerance? + """ + def within_tol(x, y, atol, rtol): + return abs(x - y) <= atol + rtol * abs(y) + + xfin = isfinite(x) + yfin = isfinite(y) + + # both are finite + if xfin and yfin: + return within_tol(x, y, atol, rtol) + elif x == y: + return True + else: + return False + + +class Parameters(OrderedDict): + """ + A dictionary of all the Parameters required to specify a fit model. + + All keys must be strings, and valid Python symbol names, and all values + must be Parameters. + + Custom methods: + --------------- + + add() + add_many() + dumps() / dump() + loads() / load() + """ + def __init__(self, asteval=None, *args, **kwds): + super(Parameters, self).__init__(self) + self._asteval = asteval + + if asteval is None: + self._asteval = Interpreter() + self.update(*args, **kwds) + + def copy(self): + """Parameters.copy() should always be a deepcopy""" + return self.__deepcopy__(None) + + def __copy__(self, memo): + """Parameters.copy() should always be a deepcopy""" + self.__deepcopy__(memo) + + def __deepcopy__(self, memo): + """Parameters deepcopy needs to make sure that + asteval is available and that all individula + parameter objects are copied""" + _pars = Parameters(asteval=None) + + # find the symbols that were added by users, not during construction + sym_unique = self._asteval.user_defined_symbols() + unique_symbols = {key: deepcopy(self._asteval.symtable[key], memo) + for key in sym_unique} + _pars._asteval.symtable.update(unique_symbols) + + # we're just about to add a lot of Parameter objects to the newly + parameter_list = [] + for key, par in self.items(): + if isinstance(par, Parameter): + param = Parameter(name=par.name, + value=par.value, + min=par.min, + max=par.max) + param.vary = par.vary + param.stderr = par.stderr + param.correl = par.correl + param.init_value = par.init_value + param.expr = par.expr + parameter_list.append(param) + + _pars.add_many(*parameter_list) + + return _pars + + def __setitem__(self, key, par): + if key not in self: + if not valid_symbol_name(key): + raise KeyError("'%s' is not a valid Parameters name" % key) + if par is not None and not isinstance(par, Parameter): + raise ValueError("'%s' is not a Parameter" % par) + OrderedDict.__setitem__(self, key, par) + par.name = key + par._expr_eval = self._asteval + self._asteval.symtable[key] = par.value + + def __add__(self, other): + """ + Add Parameters objects + """ + if not isinstance(other, Parameters): + raise ValueError("'%s' is not a Parameters object" % other) + out = deepcopy(self) + params = other.values() + out.add_many(*params) + return out + + def __iadd__(self, other): + """ + Add/assign Parameters objects + """ + if not isinstance(other, Parameters): + raise ValueError("'%s' is not a Parameters object" % other) + params = other.values() + self.add_many(*params) + return self + + def __reduce__(self): + """ + Required to pickle a Parameters instance. + """ + # make a list of all the parameters + params = [self[k] for k in self] + + # find the symbols from _asteval.symtable, that need to be remembered. + sym_unique = self._asteval.user_defined_symbols() + unique_symbols = {key: deepcopy(self._asteval.symtable[key]) + for key in sym_unique} + + return self.__class__, (), {'unique_symbols': unique_symbols, + 'params': params} + + def __setstate__(self, state): + """ + Unpickle a Parameters instance. + + Parameters + ---------- + state : dict + state['unique_symbols'] is a dictionary containing symbols that + need to be injected into _asteval.symtable + state['params'] is a list of Parameter instances to be added + """ + # first update the Interpreter symbol table. This needs to be done + # first because Parameter's early in the list may depend on later + # Parameter's. This leads to problems because add_many eventually leads + # to a Parameter value being retrieved with _getval, which, if the + # dependent value hasn't already been added to the symtable, leads to + # an Error. Another way of doing this would be to remove all the expr + # from the Parameter instances before they get added, then to restore + # them. + self._asteval.symtable.update(state['unique_symbols']) + + # then add all the parameters + self.add_many(*state['params']) + + + def update_constraints(self): + """ + Update all constrained parameters, checking that dependencies are + evaluated as needed. + """ + requires_update = {name for name, par in self.items() + if par._expr is not None} + updated_tracker = set(requires_update) + + def _update_param(name): + """ + Update a parameter value, including setting bounds. + For a constrained parameter (one with an expr defined), + this first updates (recursively) all parameters on which + the parameter depends (using the 'deps' field). + """ + par = self.__getitem__(name) + if par._expr_eval is None: + par._expr_eval = self._asteval + for dep in par._expr_deps: + if dep in updated_tracker: + _update_param(dep) + self._asteval.symtable[name] = par.value + updated_tracker.discard(name) + + for name in requires_update: + _update_param(name) + + def pretty_repr(self, oneline=False): + if oneline: + return super(Parameters, self).__repr__() + s = "Parameters({\n" + for key in self.keys(): + s += " '%s': %s, \n" % (key, self[key]) + s += " })\n" + return s + + def pretty_print(self, oneline=False, colwidth=8, precision=4, fmt='g', + columns=['value', 'min', 'max', 'stderr', 'vary', 'expr']): + """Pretty-print parameters data. + + Parameters + ---------- + oneline : boolean + If True prints a one-line parameters representation. Default False. + colwidth : int + column width for all except the first (i.e. name) column. + columns : list of strings + list of columns names to print. All values must be valid + :class:`Parameter` attributes. + precision : int + number of digits to be printed after floating point. + format : string + single-char numeric formatter. Valid values: 'f' floating point, + 'g' floating point and exponential, 'e' exponential. + """ + if oneline: + print(self.pretty_repr(oneline=oneline)) + return + + name_len = max(len(s) for s in self) + allcols = ['name'] + columns + title = '{:{name_len}} ' + len(columns) * ' {:>{n}}' + print(title.format(*allcols, name_len=name_len, n=colwidth).title()) + numstyle = '{%s:>{n}.{p}{f}}' # format for numeric columns + otherstyles = dict(name='{name:<{name_len}} ', stderr='{stderr!s:>{n}}', + vary='{vary!s:>{n}}', expr='{expr!s:>{n}}') + line = ' '.join([otherstyles.get(k, numstyle % k) for k in allcols]) + for name, values in sorted(self.items()): + pvalues = {k: getattr(values, k) for k in columns} + pvalues['name'] = name + # stderr is a special case: it is either numeric or None (i.e. str) + if 'stderr' in columns and pvalues['stderr'] is not None: + pvalues['stderr'] = (numstyle % '').format( + pvalues['stderr'], n=colwidth, p=precision, f=fmt) + print(line.format(name_len=name_len, n=colwidth, p=precision, f=fmt, + **pvalues)) + + def add(self, name, value=None, vary=True, min=-inf, max=inf, expr=None): + """ + Convenience function for adding a Parameter: + + Example + ------- + p = Parameters() + p.add(name, value=XX, ...) + + is equivalent to: + p[name] = Parameter(name=name, value=XX, .... + """ + if isinstance(name, Parameter): + self.__setitem__(name.name, name) + else: + self.__setitem__(name, Parameter(value=value, name=name, vary=vary, + min=min, max=max, expr=expr)) + + def add_many(self, *parlist): + """ + Convenience function for adding a list of Parameters. + + Parameters + ---------- + parlist : sequence + A sequence of tuples, or a sequence of `Parameter` instances. If it + is a sequence of tuples, then each tuple must contain at least the + name. The order in each tuple is the following: + + name, value, vary, min, max, expr + + Example + ------- + p = Parameters() + # add a sequence of tuples + p.add_many( (name1, val1, True, None, None, None), + (name2, val2, True, 0.0, None, None), + (name3, val3, False, None, None, None), + (name4, val4)) + + # add a sequence of Parameter + f = Parameter('name5', val5) + g = Parameter('name6', val6) + p.add_many(f, g) + """ + for para in parlist: + if isinstance(para, Parameter): + self.__setitem__(para.name, para) + else: + param = Parameter(*para) + self.__setitem__(param.name, param) + + def valuesdict(self): + """ + Returns + ------- + An ordered dictionary of name:value pairs for each Parameter. + This is distinct from the Parameters itself, as it has values of + the Parameter values, not the full Parameter object. + """ + + return OrderedDict(((p.name, p.value) for p in self.values())) + + def dumps(self, **kws): + """represent Parameters as a JSON string. + + all keyword arguments are passed to `json.dumps()` + + Returns + ------- + json string representation of Parameters + + See Also + -------- + dump(), loads(), load(), json.dumps() + """ + out = [p.__getstate__() for p in self.values()] + return json.dumps(out, **kws) + + def loads(self, s, **kws): + """load Parameters from a JSON string. + + current Parameters will be cleared before loading. + + all keyword arguments are passed to `json.loads()` + + Returns + ------- + None. Parameters are updated as a side-effect + + See Also + -------- + dump(), dumps(), load(), json.loads() + + """ + self.clear() + for parstate in json.loads(s, **kws): + _par = Parameter() + _par.__setstate__(parstate) + self.__setitem__(parstate[0], _par) + + def dump(self, fp, **kws): + """write JSON representation of Parameters to a file + or file-like object (must have a `write()` method). + + Arguments + --------- + fp open file-like object with `write()` method. + + all keyword arguments are passed to `dumps()` + + Returns + ------- + return value from `fp.write()` + + See Also + -------- + dump(), load(), json.dump() + """ + return fp.write(self.dumps(**kws)) + + def load(self, fp, **kws): + """load JSON representation of Parameters from a file + or file-like object (must have a `read()` method). + + Arguments + --------- + fp open file-like object with `read()` method. + + all keyword arguments are passed to `loads()` + + Returns + ------- + None. Parameters are updated as a side-effect + + See Also + -------- + dump(), loads(), json.load() + """ + return self.loads(fp.read(), **kws) + + +class Parameter(object): + """ + A Parameter is an object used to define a Fit Model. + Attributes + ---------- + name : str + Parameter name. + value : float + The numerical value of the Parameter. + vary : bool + Whether the Parameter is fixed during a fit. + min : float + Lower bound for value (None or -inf means no lower bound). + max : float + Upper bound for value (None or inf means no upper bound). + expr : str + An expression specifying constraints for the parameter. + stderr : float + The estimated standard error for the best-fit value. + correl : dict + Specifies correlation with the other fitted Parameter after a fit. + Of the form `{'decay': 0.404, 'phase': -0.020, 'frequency': 0.102}` + """ + def __init__(self, name=None, value=None, vary=True, + min=-inf, max=inf, expr=None): + """ + Parameters + ---------- + name : str, optional + Name of the parameter. + value : float, optional + Numerical Parameter value. + vary : bool, optional + Whether the Parameter is fixed during a fit. + min : float, optional + Lower bound for value (None or -inf means no lower bound). + max : float, optional + Upper bound for value (None or inf means no upper bound). + expr : str, optional + Mathematical expression used to constrain the value during the fit. + """ + self.name = name + self._val = value + self.user_value = value + self.init_value = value + self.min = min + self.max = max + self.vary = vary + self._expr = expr + self._expr_ast = None + self._expr_eval = None + self._expr_deps = [] + self._delay_asteval = False + self.stderr = None + self.correl = None + self.from_internal = lambda val: val + self._init_bounds() + + def set(self, value=None, vary=None, min=-inf, max=inf, expr=None): + """ + Set or update Parameter attributes. + + Parameters + ---------- + value : float, optional + Numerical Parameter value. + vary : bool, optional + Whether the Parameter is fixed during a fit. + min : float, optional + Lower bound for value. To remove a lower bound you must use -np.inf + max : float, optional + Upper bound for value. To remove an upper bound you must use np.inf + expr : str, optional + Mathematical expression used to constrain the value during the fit. + To remove a constraint you must supply an empty string. + """ + + self.__set_expression(expr) + if value is not None: + self._val = value + if vary is not None: + self.vary = vary + if min is None: + min = -inf + if max is None: + max = inf + self.min = min + self.max = max + + def _init_bounds(self): + """make sure initial bounds are self-consistent""" + # _val is None means - infinity. + if self.max is None: + self.max = inf + if self.min is None: + self.min = -inf + if self._val is not None: + if self.min > self.max: + self.min, self.max = self.max, self.min + if isclose(self.min, self.max, atol=1e-13, rtol=1e-13): + raise ValueError("Parameter '%s' has min == max" % self.name) + + if self._val > self.max: + self._val = self.max + if self._val < self.min: + self._val = self.min + elif self._expr is None: + self._val = self.min + self.setup_bounds() + + def __getstate__(self): + """get state for pickle""" + return (self.name, self.value, self.vary, self.expr, self.min, + self.max, self.stderr, self.correl, self.init_value) + + def __setstate__(self, state): + """set state for pickle""" + (self.name, self.value, self.vary, self.expr, self.min, + self.max, self.stderr, self.correl, self.init_value) = state + self._expr_ast = None + self._expr_eval = None + self._expr_deps = [] + self._delay_asteval = False + self._init_bounds() + + def __repr__(self): + s = [] + if self.name is not None: + s.append("'%s'" % self.name) + sval = repr(self._getval()) + if not self.vary and self._expr is None: + sval = "value=%s (fixed)" % sval + elif self.stderr is not None: + sval = "value=%s +/- %.3g" % (sval, self.stderr) + s.append(sval) + s.append("bounds=[%s:%s]" % (repr(self.min), repr(self.max))) + if self._expr is not None: + s.append("expr='%s'" % self.expr) + return "<Parameter %s>" % ', '.join(s) + + def setup_bounds(self): + """ + Set up Minuit-style internal/external parameter transformation + of min/max bounds. + + As a side-effect, this also defines the self.from_internal method + used to re-calculate self.value from the internal value, applying + the inverse Minuit-style transformation. This method should be + called prior to passing a Parameter to the user-defined objective + function. + + This code borrows heavily from JJ Helmus' leastsqbound.py + + Returns + ------- + The internal value for parameter from self.value (which holds + the external, user-expected value). This internal value should + actually be used in a fit. + """ + if self.min is None: + self.min = -inf + if self.max is None: + self.max = inf + if self.min == -inf and self.max == inf: + self.from_internal = lambda val: val + _val = self._val + elif self.max == inf: + self.from_internal = lambda val: self.min - 1.0 + sqrt(val*val + 1) + _val = sqrt((self._val - self.min + 1.0)**2 - 1) + elif self.min == -inf: + self.from_internal = lambda val: self.max + 1 - sqrt(val*val + 1) + _val = sqrt((self.max - self._val + 1.0)**2 - 1) + else: + self.from_internal = lambda val: self.min + (sin(val) + 1) * \ + (self.max - self.min) / 2.0 + _val = arcsin(2*(self._val - self.min)/(self.max - self.min) - 1) + return _val + + def scale_gradient(self, val): + """ + Returns + ------- + scaling factor for gradient the according to Minuit-style + transformation. + """ + if self.min == -inf and self.max == inf: + return 1.0 + elif self.max == inf: + return val / sqrt(val*val + 1) + elif self.min == -inf: + return -val / sqrt(val*val + 1) + else: + return cos(val) * (self.max - self.min) / 2.0 + + def _getval(self): + """get value, with bounds applied""" + + # Note assignment to self._val has been changed to self.value + # The self.value property setter makes sure that the + # _expr_eval.symtable is kept updated. + # If you just assign to self._val then + # _expr_eval.symtable[self.name] + # becomes stale if parameter.expr is not None. + if (isinstance(self._val, uncertainties.Variable) + and self._val is not nan): + try: + self.value = self._val.nominal_value + except AttributeError: + pass + if not self.vary and self._expr is None: + return self._val + + if self._expr is not None: + if self._expr_ast is None: + self.__set_expression(self._expr) + + if self._expr_eval is not None: + if not self._delay_asteval: + self.value = self._expr_eval(self._expr_ast) + check_ast_errors(self._expr_eval) + + v = self._val + if v > self.max: v = self.max + if v < self.min: v = self.min + self.value = self._val = v + return self._val + + def set_expr_eval(self, evaluator): + """set expression evaluator instance""" + self._expr_eval = evaluator + + @property + def value(self): + """The numerical value of the Parameter, with bounds applied""" + return self._getval() + + @value.setter + def value(self, val): + """ + Set the numerical Parameter value. + """ + self._val = val + if not hasattr(self, '_expr_eval'): + self._expr_eval = None + if self._expr_eval is not None: + self._expr_eval.symtable[self.name] = val + + @property + def expr(self): + """ + The mathematical expression used to constrain the value during the fit. + """ + return self._expr + + @expr.setter + def expr(self, val): + """ + The mathematical expression used to constrain the value during the fit. + To remove a constraint you must supply an empty string. + """ + self.__set_expression(val) + + def __set_expression(self, val): + if val == '': + val = None + self._expr = val + if val is not None: + self.vary = False + if not hasattr(self, '_expr_eval'): + self._expr_eval = None + if val is None: + self._expr_ast = None + if val is not None and self._expr_eval is not None: + self._expr_ast = self._expr_eval.parse(val) + check_ast_errors(self._expr_eval) + self._expr_deps = get_ast_names(self._expr_ast) + + def __str__(self): + """string""" + return self.__repr__() + + def __abs__(self): + """abs""" + return abs(self._getval()) + + def __neg__(self): + """neg""" + return -self._getval() + + def __pos__(self): + """positive""" + return +self._getval() + + def __nonzero__(self): + """not zero""" + return self._getval() != 0 + + def __int__(self): + """int""" + return int(self._getval()) + + def __float__(self): + """float""" + return float(self._getval()) + + def __trunc__(self): + """trunc""" + return self._getval().__trunc__() + + def __add__(self, other): + """+""" + return self._getval() + other + + def __sub__(self, other): + """-""" + return self._getval() - other + + def __div__(self, other): + """/""" + return self._getval() / other + __truediv__ = __div__ + + def __floordiv__(self, other): + """//""" + return self._getval() // other + + def __divmod__(self, other): + """divmod""" + return divmod(self._getval(), other) + + def __mod__(self, other): + """%""" + return self._getval() % other + + def __mul__(self, other): + """*""" + return self._getval() * other + + def __pow__(self, other): + """**""" + return self._getval() ** other + + def __gt__(self, other): + """>""" + return self._getval() > other + + def __ge__(self, other): + """>=""" + return self._getval() >= other + + def __le__(self, other): + """<=""" + return self._getval() <= other + + def __lt__(self, other): + """<""" + return self._getval() < other + + def __eq__(self, other): + """==""" + return self._getval() == other + + def __ne__(self, other): + """!=""" + return self._getval() != other + + def __radd__(self, other): + """+ (right)""" + return other + self._getval() + + def __rdiv__(self, other): + """/ (right)""" + return other / self._getval() + __rtruediv__ = __rdiv__ + + def __rdivmod__(self, other): + """divmod (right)""" + return divmod(other, self._getval()) + + def __rfloordiv__(self, other): + """// (right)""" + return other // self._getval() + + def __rmod__(self, other): + """% (right)""" + return other % self._getval() + + def __rmul__(self, other): + """* (right)""" + return other * self._getval() + + def __rpow__(self, other): + """** (right)""" + return other ** self._getval() + + def __rsub__(self, other): + """- (right)""" + return other - self._getval() + + +def isParameter(x): + """Test for Parameter-ness""" + return (isinstance(x, Parameter) or + x.__class__.__name__ == 'Parameter') diff --git a/lmfit/printfuncs.py b/lmfit/printfuncs.py index 76537bc..4b279b0 100644 --- a/lmfit/printfuncs.py +++ b/lmfit/printfuncs.py @@ -1,227 +1,229 @@ -# -*- coding: utf-8 -*-
-"""
-Created on Fri Apr 20 19:24:21 2012
-
-@author: Tillsten
-
-Changes:
- - 13-Feb-2013 M Newville
- complemented "report_errors" and "report_ci" with
- "error_report" and "ci_report" (respectively) which
- return the text of the report. Thus report_errors()
- is simply:
- def report_errors(params, modelpars=None, show_correl=True):
- print error_report(params, modelpars=modelpars,
- show_correl=show_correl)
- and similar for report_ci() / ci_report()
-
-"""
-
-from __future__ import print_function
-from .parameter import Parameters
-import re
-
-def alphanumeric_sort(s, _nsre=re.compile('([0-9]+)')):
- return [int(text) if text.isdigit() else text.lower()
- for text in re.split(_nsre, s)]
-
-def getfloat_attr(obj, attr, fmt='%.3f'):
- "format an attribute of an object for printing"
- val = getattr(obj, attr, None)
- if val is None:
- return 'unknown'
- if isinstance(val, int):
- return '%d' % val
- if isinstance(val, float):
- return fmt % val
- else:
- return repr(val)
-
-def gformat(val, length=11):
- """format a number with '%g'-like format, except that
- the return will be length ``length`` (default=12)
- and have at least length-6 significant digits
- """
- length = max(length, 7)
- fmt = '{: .%ig}' % (length-6)
- if isinstance(val, int):
- out = ('{: .%ig}' % (length-2)).format(val)
- if len(out) > length:
- out = fmt.format(val)
- else:
- out = fmt.format(val)
- if len(out) < length:
- if 'e' in out:
- ie = out.find('e')
- if '.' not in out[:ie]:
- out = out[:ie] + '.' + out[ie:]
- out = out.replace('e', '0'*(length-len(out))+'e')
- else:
- fmt = '{: .%ig}' % (length-1)
- out = fmt.format(val)[:length]
- if len(out) < length:
- pad = '0' if '.' in out else ' '
- out += pad*(length-len(out))
- return out
-
-CORREL_HEAD = '[[Correlations]] (unreported correlations are < % .3f)'
-
-def fit_report(inpars, modelpars=None, show_correl=True, min_correl=0.1,
- sort_pars=False):
- """return text of a report for fitted params best-fit values,
- uncertainties and correlations
-
- arguments
- ----------
- inpars Parameters from fit or Minizer object returned from a fit.
- modelpars Optional Known Model Parameters [None]
- show_correl whether to show list of sorted correlations [True]
- min_correl smallest correlation absolute value to show [0.1]
- sort_pars If True, then fit_report will show parameter names
- sorted in alphanumerical order. If False, then the
- parameters will be listed in the order they were added to
- the Parameters dictionary. If sort_pars is callable, then
- this (one argument) function is used to extract a
- comparison key from each list element.
- """
- if isinstance(inpars, Parameters):
- result, params = None, inpars
- if hasattr(inpars, 'params'):
- result = inpars
- params = inpars.params
-
- if sort_pars:
- if callable(sort_pars):
- key = sort_pars
- else:
- key = alphanumeric_sort
- parnames = sorted(params, key=key)
- else:
- # dict.keys() returns a KeysView in py3, and they're indexed further
- # down
- parnames = list(params.keys())
-
- buff = []
- add = buff.append
- if result is not None:
- add("[[Fit Statistics]]")
- add(" # function evals = %s" % getfloat_attr(result, 'nfev'))
- add(" # data points = %s" % getfloat_attr(result, 'ndata'))
- add(" # variables = %s" % getfloat_attr(result, 'nvarys'))
- add(" chi-square = %s" % getfloat_attr(result, 'chisqr'))
- add(" reduced chi-square = %s" % getfloat_attr(result, 'redchi'))
-
- namelen = max([len(n) for n in parnames])
- add("[[Variables]]")
- for name in parnames:
- par = params[name]
- space = ' '*(namelen+1-len(name))
- nout = "%s:%s" % (name, space)
- inval = '(init= ?)'
- if par.init_value is not None:
- inval = '(init=% .7g)' % par.init_value
- if modelpars is not None and name in modelpars:
- inval = '%s, model_value =% .7g' % (inval, modelpars[name].value)
- try:
- sval = gformat(par.value)
- except (TypeError, ValueError):
- sval = 'Non Numeric Value?'
-
- if par.stderr is not None:
- serr = gformat(par.stderr, length=9)
-
- try:
- spercent = '({:.2%})'.format(abs(par.stderr/par.value))
- except ZeroDivisionError:
- spercent = ''
- sval = '%s +/-%s %s' % (sval, serr, spercent)
-
- if par.vary:
- add(" %s %s %s" % (nout, sval, inval))
- elif par.expr is not None:
- add(" %s %s == '%s'" % (nout, sval, par.expr))
- else:
- add(" %s % .7g (fixed)" % (nout, par.value))
-
- if show_correl:
- add(CORREL_HEAD % min_correl)
- correls = {}
- for i, name in enumerate(parnames):
- par = params[name]
- if not par.vary:
- continue
- if hasattr(par, 'correl') and par.correl is not None:
- for name2 in parnames[i+1:]:
- if (name != name2 and name2 in par.correl and
- abs(par.correl[name2]) > min_correl):
- correls["%s, %s" % (name, name2)] = par.correl[name2]
-
- sort_correl = sorted(correls.items(), key=lambda it: abs(it[1]))
- sort_correl.reverse()
- for name, val in sort_correl:
- lspace = max(1, 25 - len(name))
- add(' C(%s)%s = % .3f ' % (name, (' '*30)[:lspace], val))
- return '\n'.join(buff)
-
-
-def report_errors(params, **kws):
- """print a report for fitted params: see error_report()"""
- print(fit_report(params, **kws))
-
-
-def report_fit(params, **kws):
- """print a report for fitted params: see error_report()"""
- print(fit_report(params, **kws))
-
-
-def ci_report(ci, with_offset=True, ndigits=5):
- """return text of a report for confidence intervals
-
- Parameters
- ----------
- with_offset : bool (default `True`)
- whether to subtract best value from all other values.
- ndigits : int (default 5)
- number of significant digits to show
-
- Returns
- -------
- text of formatted report on confidence intervals.
- """
- maxlen = max([len(i) for i in ci])
- buff = []
- add = buff.append
- def convp(x):
- if abs(x[0]) < 1.e-2:
- return "_BEST_"
- return "%.2f%%" % (x[0]*100)
-
- title_shown = False
- fmt_best = fmt_diff = "{0:.%if}" % ndigits
- if with_offset:
- fmt_diff = "{0:+.%if}" % ndigits
- for name, row in ci.items():
- if not title_shown:
- add("".join([''.rjust(maxlen+1)]+[i.rjust(ndigits+5)
- for i in map(convp, row)]))
- title_shown = True
- thisrow = [" %s:" % name.ljust(maxlen)]
- offset = 0.0
- if with_offset:
- for cval, val in row:
- if abs(cval) < 1.e-2:
- offset = val
- for cval, val in row:
- if cval < 1.e-2:
- sval = fmt_best.format(val)
- else:
- sval = fmt_diff.format(val-offset)
- thisrow.append(sval.rjust(ndigits+5))
- add("".join(thisrow))
-
- return '\n'.join(buff)
-
-
-def report_ci(ci):
- """print a report for confidence intervals"""
- print(ci_report(ci))
+# -*- coding: utf-8 -*- +""" +Created on Fri Apr 20 19:24:21 2012 + +@author: Tillsten + +Changes: + - 13-Feb-2013 M Newville + complemented "report_errors" and "report_ci" with + "error_report" and "ci_report" (respectively) which + return the text of the report. Thus report_errors() + is simply: + def report_errors(params, modelpars=None, show_correl=True): + print error_report(params, modelpars=modelpars, + show_correl=show_correl) + and similar for report_ci() / ci_report() + +""" + +from __future__ import print_function +from .parameter import Parameters +import re + +def alphanumeric_sort(s, _nsre=re.compile('([0-9]+)')): + return [int(text) if text.isdigit() else text.lower() + for text in re.split(_nsre, s)] + +def getfloat_attr(obj, attr, fmt='%.3f'): + "format an attribute of an object for printing" + val = getattr(obj, attr, None) + if val is None: + return 'unknown' + if isinstance(val, int): + return '%d' % val + if isinstance(val, float): + return fmt % val + else: + return repr(val) + +def gformat(val, length=11): + """format a number with '%g'-like format, except that + the return will be length ``length`` (default=12) + and have at least length-6 significant digits + """ + length = max(length, 7) + fmt = '{: .%ig}' % (length-6) + if isinstance(val, int): + out = ('{: .%ig}' % (length-2)).format(val) + if len(out) > length: + out = fmt.format(val) + else: + out = fmt.format(val) + if len(out) < length: + if 'e' in out: + ie = out.find('e') + if '.' not in out[:ie]: + out = out[:ie] + '.' + out[ie:] + out = out.replace('e', '0'*(length-len(out))+'e') + else: + fmt = '{: .%ig}' % (length-1) + out = fmt.format(val)[:length] + if len(out) < length: + pad = '0' if '.' in out else ' ' + out += pad*(length-len(out)) + return out + +CORREL_HEAD = '[[Correlations]] (unreported correlations are < % .3f)' + +def fit_report(inpars, modelpars=None, show_correl=True, min_correl=0.1, + sort_pars=False): + """return text of a report for fitted params best-fit values, + uncertainties and correlations + + arguments + ---------- + inpars Parameters from fit or Minizer object returned from a fit. + modelpars Optional Known Model Parameters [None] + show_correl whether to show list of sorted correlations [True] + min_correl smallest correlation absolute value to show [0.1] + sort_pars If True, then fit_report will show parameter names + sorted in alphanumerical order. If False, then the + parameters will be listed in the order they were added to + the Parameters dictionary. If sort_pars is callable, then + this (one argument) function is used to extract a + comparison key from each list element. + """ + if isinstance(inpars, Parameters): + result, params = None, inpars + if hasattr(inpars, 'params'): + result = inpars + params = inpars.params + + if sort_pars: + if callable(sort_pars): + key = sort_pars + else: + key = alphanumeric_sort + parnames = sorted(params, key=key) + else: + # dict.keys() returns a KeysView in py3, and they're indexed further + # down + parnames = list(params.keys()) + + buff = [] + add = buff.append + if result is not None: + add("[[Fit Statistics]]") + add(" # function evals = %s" % getfloat_attr(result, 'nfev')) + add(" # data points = %s" % getfloat_attr(result, 'ndata')) + add(" # variables = %s" % getfloat_attr(result, 'nvarys')) + add(" chi-square = %s" % getfloat_attr(result, 'chisqr')) + add(" reduced chi-square = %s" % getfloat_attr(result, 'redchi')) + add(" Akaike info crit = %s" % getfloat_attr(result, 'aic')) + add(" Bayesian info crit = %s" % getfloat_attr(result, 'bic')) + + namelen = max([len(n) for n in parnames]) + add("[[Variables]]") + for name in parnames: + par = params[name] + space = ' '*(namelen+1-len(name)) + nout = "%s:%s" % (name, space) + inval = '(init= ?)' + if par.init_value is not None: + inval = '(init=% .7g)' % par.init_value + if modelpars is not None and name in modelpars: + inval = '%s, model_value =% .7g' % (inval, modelpars[name].value) + try: + sval = gformat(par.value) + except (TypeError, ValueError): + sval = 'Non Numeric Value?' + + if par.stderr is not None: + serr = gformat(par.stderr, length=9) + + try: + spercent = '({:.2%})'.format(abs(par.stderr/par.value)) + except ZeroDivisionError: + spercent = '' + sval = '%s +/-%s %s' % (sval, serr, spercent) + + if par.vary: + add(" %s %s %s" % (nout, sval, inval)) + elif par.expr is not None: + add(" %s %s == '%s'" % (nout, sval, par.expr)) + else: + add(" %s % .7g (fixed)" % (nout, par.value)) + + if show_correl: + add(CORREL_HEAD % min_correl) + correls = {} + for i, name in enumerate(parnames): + par = params[name] + if not par.vary: + continue + if hasattr(par, 'correl') and par.correl is not None: + for name2 in parnames[i+1:]: + if (name != name2 and name2 in par.correl and + abs(par.correl[name2]) > min_correl): + correls["%s, %s" % (name, name2)] = par.correl[name2] + + sort_correl = sorted(correls.items(), key=lambda it: abs(it[1])) + sort_correl.reverse() + for name, val in sort_correl: + lspace = max(1, 25 - len(name)) + add(' C(%s)%s = % .3f ' % (name, (' '*30)[:lspace], val)) + return '\n'.join(buff) + + +def report_errors(params, **kws): + """print a report for fitted params: see error_report()""" + print(fit_report(params, **kws)) + + +def report_fit(params, **kws): + """print a report for fitted params: see error_report()""" + print(fit_report(params, **kws)) + + +def ci_report(ci, with_offset=True, ndigits=5): + """return text of a report for confidence intervals + + Parameters + ---------- + with_offset : bool (default `True`) + whether to subtract best value from all other values. + ndigits : int (default 5) + number of significant digits to show + + Returns + ------- + text of formatted report on confidence intervals. + """ + maxlen = max([len(i) for i in ci]) + buff = [] + add = buff.append + def convp(x): + if abs(x[0]) < 1.e-2: + return "_BEST_" + return "%.2f%%" % (x[0]*100) + + title_shown = False + fmt_best = fmt_diff = "{0:.%if}" % ndigits + if with_offset: + fmt_diff = "{0:+.%if}" % ndigits + for name, row in ci.items(): + if not title_shown: + add("".join([''.rjust(maxlen+1)]+[i.rjust(ndigits+5) + for i in map(convp, row)])) + title_shown = True + thisrow = [" %s:" % name.ljust(maxlen)] + offset = 0.0 + if with_offset: + for cval, val in row: + if abs(cval) < 1.e-2: + offset = val + for cval, val in row: + if cval < 1.e-2: + sval = fmt_best.format(val) + else: + sval = fmt_diff.format(val-offset) + thisrow.append(sval.rjust(ndigits+5)) + add("".join(thisrow)) + + return '\n'.join(buff) + + +def report_ci(ci): + """print a report for confidence intervals""" + print(ci_report(ci)) diff --git a/lmfit/ui/__init__.py b/lmfit/ui/__init__.py index b6e3431..e835e21 100644 --- a/lmfit/ui/__init__.py +++ b/lmfit/ui/__init__.py @@ -1,48 +1,48 @@ -# These variables are used at the end of the module to decide
-# which BaseFitter subclass the Fitter will point to.
-import warnings
-
-has_ipython, has_matplotlib = False, False
-
-try:
- import matplotlib
-except ImportError:
- pass
-else:
- has_matplotlib = True
-
-try:
- import IPython
-except ImportError:
- warnings.warn("lmfit.Fitter will use basic mode, not IPython: need matplotlib")
-else:
- _ipy_msg1 = "lmfit.Fitter will use basic mode, not IPython: need IPython2."
- _ipy_msg2 = "lmfit.Fitter will use basic mode, not IPython: could not get IPython version"
- _ipy_msg3 = "lmfit.Fitter will use basic mode, not IPython: need ipywidgets."
- try:
- major_version = IPython.release.version_info[0]
- if major_version < 2:
- warnings.warn(_ipy_msg1)
- elif major_version > 3:
- # After IPython 3, widgets were moved to a separate package.
- # There is a shim to allow the old import, but the package has to be
- # installed for that to work.
- try:
- import ipywidgets
- except ImportError:
- warnings.warn(_ipy_msg3)
- else:
- # has_ipython = iPython installed and we are in an IPython session.
- has_ipython = IPython.get_ipython() is not None
- except Exception as e:
- warnings.warn(_ipy_msg2)
-
-from .basefitter import BaseFitter
-Fitter = BaseFitter
-if has_matplotlib:
- from .basefitter import MPLFitter
- Fitter = MPLFitter
-
-if has_ipython:
- from .ipy_fitter import NotebookFitter
- Fitter = NotebookFitter
+# These variables are used at the end of the module to decide +# which BaseFitter subclass the Fitter will point to. +import warnings + +has_ipython, has_matplotlib = False, False + +try: + import matplotlib +except ImportError: + pass +else: + has_matplotlib = True + +try: + import IPython +except ImportError: + warnings.warn("lmfit.Fitter will use basic mode, not IPython: need matplotlib") +else: + _ipy_msg1 = "lmfit.Fitter will use basic mode, not IPython: need IPython2." + _ipy_msg2 = "lmfit.Fitter will use basic mode, not IPython: could not get IPython version" + _ipy_msg3 = "lmfit.Fitter will use basic mode, not IPython: need ipywidgets." + try: + major_version = IPython.release.version_info[0] + if major_version < 2: + warnings.warn(_ipy_msg1) + elif major_version > 3: + # After IPython 3, widgets were moved to a separate package. + # There is a shim to allow the old import, but the package has to be + # installed for that to work. + try: + import ipywidgets + except ImportError: + warnings.warn(_ipy_msg3) + else: + # has_ipython = iPython installed and we are in an IPython session. + has_ipython = IPython.get_ipython() is not None + except Exception as e: + warnings.warn(_ipy_msg2) + +from .basefitter import BaseFitter +Fitter = BaseFitter +if has_matplotlib: + from .basefitter import MPLFitter + Fitter = MPLFitter + +if has_ipython: + from .ipy_fitter import NotebookFitter + Fitter = NotebookFitter diff --git a/lmfit/ui/basefitter.py b/lmfit/ui/basefitter.py index 8b4eace..1f8f815 100644 --- a/lmfit/ui/basefitter.py +++ b/lmfit/ui/basefitter.py @@ -1,320 +1,320 @@ -import warnings
-import numpy as np
-
-from ..model import Model
-from ..models import ExponentialModel # arbitrary default
-from ..asteval import Interpreter
-from ..astutils import NameFinder
-from ..parameter import check_ast_errors
-
-
-_COMMON_DOC = """
- This an interactive container for fitting models to particular data.
-
- It maintains the attributes `current_params` and `current_result`. When
- its fit() method is called, the best fit becomes the new `current_params`.
- The most basic usage is iteratively fitting data, taking advantage of
- this stateful memory that keep the parameters between each fit.
-"""
-
-_COMMON_EXAMPLES_DOC = """
-
- Examples
- --------
- >>> fitter = Fitter(data, model=SomeModel, x=x)
-
- >>> fitter.model
- # This property can be changed, to try different models on the same
- # data with the same independent vars.
- # (This is especially handy in the notebook.)
-
- >>> fitter.current_params
- # This copy of the model's Parameters is updated after each fit.
-
- >>> fitter.fit()
- # Perform a fit using fitter.current_params as a guess.
- # Optionally, pass a params argument or individual keyword arguments
- # to override current_params.
-
- >>> fitter.current_result
- # This is the result of the latest fit. It contain the usual
- # copies of the Parameters, in the attributes params and init_params.
-
- >>> fitter.data = new_data
- # If this property is updated, the `current_params` are retained an used
- # as an initial guess if fit() is called again.
- """
-
-
-class BaseFitter(object):
- __doc__ = _COMMON_DOC + """
-
- Parameters
- ----------
- data : array-like
- model : lmfit.Model
- optional initial Model to use, maybe be set or changed later
- """ + _COMMON_EXAMPLES_DOC
- def __init__(self, data, model=None, **kwargs):
- self._data = data
- self.kwargs = kwargs
-
- # GUI-based subclasses need a default value for the menu of models,
- # and so an arbitrary default is applied here, for uniformity
- # among the subclasses.
- if model is None:
- model = ExponentialModel
- self.model = model
-
- def _on_model_value_change(self, name, value):
- self.model = value
-
- def _on_fit_button_click(self, b):
- self.fit()
-
- def _on_guess_button_click(self, b):
- self.guess()
-
- @property
- def data(self):
- return self._data
-
- @data.setter
- def data(self, value):
- self._data = value
-
- @property
- def model(self):
- return self._model
-
- @model.setter
- def model(self, value):
- if callable(value):
- model = value()
- else:
- model = value
- self._model = model
- self.current_result = None
- self._current_params = model.make_params()
-
- # Use these to evaluate any Parameters that use expressions.
- self.asteval = Interpreter()
- self.namefinder = NameFinder()
-
- self._finalize_model(value)
-
- self.guess()
-
- def _finalize_model(self, value):
- # subclasses optionally override to update display here
- pass
-
- @property
- def current_params(self):
- """Each time fit() is called, these will be updated to reflect
- the latest best params. They will be used as the initial guess
- for the next fit, unless overridden by arguments to fit()."""
- return self._current_params
-
- @current_params.setter
- def current_params(self, new_params):
- # Copy contents, but retain original params objects.
- for name, par in new_params.items():
- self._current_params[name].value = par.value
- self._current_params[name].expr = par.expr
- self._current_params[name].vary = par.vary
- self._current_params[name].min = par.min
- self._current_params[name].max = par.max
-
- # Compute values for expression-based Parameters.
- self.__assign_deps(self._current_params)
- for _, par in self._current_params.items():
- if par.value is None:
- self.__update_paramval(self._current_params, par.name)
-
- self._finalize_params()
-
- def _finalize_params(self):
- # subclasses can override this to pass params to display
- pass
-
- def guess(self):
- count_indep_vars = len(self.model.independent_vars)
- guessing_successful = True
- try:
- if count_indep_vars == 0:
- guess = self.model.guess(self._data)
- elif count_indep_vars == 1:
- key = self.model.independent_vars[0]
- val = self.kwargs[key]
- d = {key: val}
- guess = self.model.guess(self._data, **d)
- except NotImplementedError:
- guessing_successful = False
- self.current_params = guess
- return guessing_successful
-
- def __assign_deps(self, params):
- # N.B. This does not use self.current_params but rather
- # new Parameters that are being built by self.guess().
- for name, par in params.items():
- if par.expr is not None:
- par.ast = self.asteval.parse(par.expr)
- check_ast_errors(self.asteval.error)
- par.deps = []
- self.namefinder.names = []
- self.namefinder.generic_visit(par.ast)
- for symname in self.namefinder.names:
- if (symname in self.current_params and
- symname not in par.deps):
- par.deps.append(symname)
- self.asteval.symtable[name] = par.value
- if par.name is None:
- par.name = name
-
- def __update_paramval(self, params, name):
- # N.B. This does not use self.current_params but rather
- # new Parameters that are being built by self.guess().
- par = params[name]
- if getattr(par, 'expr', None) is not None:
- if getattr(par, 'ast', None) is None:
- par.ast = self.asteval.parse(par.expr)
- if par.deps is not None:
- for dep in par.deps:
- self.__update_paramval(params, dep)
- par.value = self.asteval.run(par.ast)
- out = check_ast_errors(self.asteval.error)
- if out is not None:
- self.asteval.raise_exception(None)
- self.asteval.symtable[name] = par.value
-
- def fit(self, *args, **kwargs):
- "Use current_params unless overridden by arguments passed here."
- guess = dict(self.current_params)
- guess.update(self.kwargs) # from __init__, e.g. x=x
- guess.update(kwargs)
- self.current_result = self.model.fit(self._data, *args, **guess)
- self.current_params = self.current_result.params
-
-
-class MPLFitter(BaseFitter):
- # This is a small elaboration on BaseModel; it adds a plot()
- # method that depends on matplotlib. It adds several plot-
- # styling arguments to the signature.
- __doc__ = _COMMON_DOC + """
-
- Parameters
- ----------
- data : array-like
- model : lmfit.Model
- optional initial Model to use, maybe be set or changed later
-
- Additional Parameters
- ---------------------
- axes_style : dictionary representing style keyword arguments to be
- passed through to `Axes.set(...)`
- data_style : dictionary representing style keyword arguments to be passed
- through to the matplotlib `plot()` command the plots the data points
- init_style : dictionary representing style keyword arguments to be passed
- through to the matplotlib `plot()` command the plots the initial fit
- line
- best_style : dictionary representing style keyword arguments to be passed
- through to the matplotlib `plot()` command the plots the best fit
- line
- **kwargs : independent variables or extra arguments, passed like `x=x`
- """ + _COMMON_EXAMPLES_DOC
- def __init__(self, data, model=None, axes_style={},
- data_style={}, init_style={}, best_style={}, **kwargs):
- self.axes_style = axes_style
- self.data_style = data_style
- self.init_style = init_style
- self.best_style = best_style
- super(MPLFitter, self).__init__(data, model, **kwargs)
-
- def plot(self, axes_style={}, data_style={}, init_style={}, best_style={},
- ax=None):
- """Plot data, initial guess fit, and best fit.
-
- Optional style arguments pass keyword dictionaries through to their
- respective components of the matplotlib plot.
-
- Precedence is:
- 1. arguments passed to this function, plot()
- 2. arguments passed to the Fitter when it was first declared
- 3. hard-coded defaults
-
- Parameters
- ---------------------
- axes_style : dictionary representing style keyword arguments to be
- passed through to `Axes.set(...)`
- data_style : dictionary representing style keyword arguments to be passed
- through to the matplotlib `plot()` command the plots the data points
- init_style : dictionary representing style keyword arguments to be passed
- through to the matplotlib `plot()` command the plots the initial fit
- line
- best_style : dictionary representing style keyword arguments to be passed
- through to the matplotlib `plot()` command the plots the best fit
- line
- ax : matplotlib.Axes
- optional `Axes` object. Axes will be generated if not provided.
- """
- try:
- import matplotlib.pyplot as plt
- except ImportError:
- raise ImportError("Matplotlib is required to use this Fitter. "
- "Use BaseFitter or a subclass thereof "
- "that does not depend on matplotlib.")
-
- # Configure style
- _axes_style= dict() # none, but this is here for possible future use
- _axes_style.update(self.axes_style)
- _axes_style.update(axes_style)
- _data_style= dict(color='blue', marker='o', linestyle='none')
- _data_style.update(**_normalize_kwargs(self.data_style, 'line2d'))
- _data_style.update(**_normalize_kwargs(data_style, 'line2d'))
- _init_style = dict(color='gray')
- _init_style.update(**_normalize_kwargs(self.init_style, 'line2d'))
- _init_style.update(**_normalize_kwargs(init_style, 'line2d'))
- _best_style= dict(color='red')
- _best_style.update(**_normalize_kwargs(self.best_style, 'line2d'))
- _best_style.update(**_normalize_kwargs(best_style, 'line2d'))
-
- if ax is None:
- fig, ax = plt.subplots()
- count_indep_vars = len(self.model.independent_vars)
- if count_indep_vars == 0:
- ax.plot(self._data, **_data_style)
- elif count_indep_vars == 1:
- indep_var = self.kwargs[self.model.independent_vars[0]]
- ax.plot(indep_var, self._data, **_data_style)
- else:
- raise NotImplementedError("Cannot plot models with more than one "
- "indepedent variable.")
- result = self.current_result # alias for brevity
- if not result:
- ax.set(**_axes_style)
- return # short-circuit the rest of the plotting
- if count_indep_vars == 0:
- ax.plot(result.init_fit, **_init_style)
- ax.plot(result.best_fit, **_best_style)
- elif count_indep_vars == 1:
- ax.plot(indep_var, result.init_fit, **_init_style)
- ax.plot(indep_var, result.best_fit, **_best_style)
- ax.set(**_axes_style)
-
-
-def _normalize_kwargs(kwargs, kind='patch'):
- """Convert matplotlib keywords from short to long form."""
- # Source:
- # github.com/tritemio/FRETBursts/blob/fit_experim/fretbursts/burst_plot.py
- if kind == 'line2d':
- long_names = dict(c='color', ls='linestyle', lw='linewidth',
- mec='markeredgecolor', mew='markeredgewidth',
- mfc='markerfacecolor', ms='markersize',)
- elif kind == 'patch':
- long_names = dict(c='color', ls='linestyle', lw='linewidth',
- ec='edgecolor', fc='facecolor',)
- for short_name in long_names:
- if short_name in kwargs:
- kwargs[long_names[short_name]] = kwargs.pop(short_name)
- return kwargs
+import warnings +import numpy as np + +from ..model import Model +from ..models import ExponentialModel # arbitrary default +from ..asteval import Interpreter +from ..astutils import NameFinder +from ..parameter import check_ast_errors + + +_COMMON_DOC = """ + This an interactive container for fitting models to particular data. + + It maintains the attributes `current_params` and `current_result`. When + its fit() method is called, the best fit becomes the new `current_params`. + The most basic usage is iteratively fitting data, taking advantage of + this stateful memory that keep the parameters between each fit. +""" + +_COMMON_EXAMPLES_DOC = """ + + Examples + -------- + >>> fitter = Fitter(data, model=SomeModel, x=x) + + >>> fitter.model + # This property can be changed, to try different models on the same + # data with the same independent vars. + # (This is especially handy in the notebook.) + + >>> fitter.current_params + # This copy of the model's Parameters is updated after each fit. + + >>> fitter.fit() + # Perform a fit using fitter.current_params as a guess. + # Optionally, pass a params argument or individual keyword arguments + # to override current_params. + + >>> fitter.current_result + # This is the result of the latest fit. It contain the usual + # copies of the Parameters, in the attributes params and init_params. + + >>> fitter.data = new_data + # If this property is updated, the `current_params` are retained an used + # as an initial guess if fit() is called again. + """ + + +class BaseFitter(object): + __doc__ = _COMMON_DOC + """ + + Parameters + ---------- + data : array-like + model : lmfit.Model + optional initial Model to use, maybe be set or changed later + """ + _COMMON_EXAMPLES_DOC + def __init__(self, data, model=None, **kwargs): + self._data = data + self.kwargs = kwargs + + # GUI-based subclasses need a default value for the menu of models, + # and so an arbitrary default is applied here, for uniformity + # among the subclasses. + if model is None: + model = ExponentialModel + self.model = model + + def _on_model_value_change(self, name, value): + self.model = value + + def _on_fit_button_click(self, b): + self.fit() + + def _on_guess_button_click(self, b): + self.guess() + + @property + def data(self): + return self._data + + @data.setter + def data(self, value): + self._data = value + + @property + def model(self): + return self._model + + @model.setter + def model(self, value): + if callable(value): + model = value() + else: + model = value + self._model = model + self.current_result = None + self._current_params = model.make_params() + + # Use these to evaluate any Parameters that use expressions. + self.asteval = Interpreter() + self.namefinder = NameFinder() + + self._finalize_model(value) + + self.guess() + + def _finalize_model(self, value): + # subclasses optionally override to update display here + pass + + @property + def current_params(self): + """Each time fit() is called, these will be updated to reflect + the latest best params. They will be used as the initial guess + for the next fit, unless overridden by arguments to fit().""" + return self._current_params + + @current_params.setter + def current_params(self, new_params): + # Copy contents, but retain original params objects. + for name, par in new_params.items(): + self._current_params[name].value = par.value + self._current_params[name].expr = par.expr + self._current_params[name].vary = par.vary + self._current_params[name].min = par.min + self._current_params[name].max = par.max + + # Compute values for expression-based Parameters. + self.__assign_deps(self._current_params) + for _, par in self._current_params.items(): + if par.value is None: + self.__update_paramval(self._current_params, par.name) + + self._finalize_params() + + def _finalize_params(self): + # subclasses can override this to pass params to display + pass + + def guess(self): + count_indep_vars = len(self.model.independent_vars) + guessing_successful = True + try: + if count_indep_vars == 0: + guess = self.model.guess(self._data) + elif count_indep_vars == 1: + key = self.model.independent_vars[0] + val = self.kwargs[key] + d = {key: val} + guess = self.model.guess(self._data, **d) + except NotImplementedError: + guessing_successful = False + self.current_params = guess + return guessing_successful + + def __assign_deps(self, params): + # N.B. This does not use self.current_params but rather + # new Parameters that are being built by self.guess(). + for name, par in params.items(): + if par.expr is not None: + par.ast = self.asteval.parse(par.expr) + check_ast_errors(self.asteval.error) + par.deps = [] + self.namefinder.names = [] + self.namefinder.generic_visit(par.ast) + for symname in self.namefinder.names: + if (symname in self.current_params and + symname not in par.deps): + par.deps.append(symname) + self.asteval.symtable[name] = par.value + if par.name is None: + par.name = name + + def __update_paramval(self, params, name): + # N.B. This does not use self.current_params but rather + # new Parameters that are being built by self.guess(). + par = params[name] + if getattr(par, 'expr', None) is not None: + if getattr(par, 'ast', None) is None: + par.ast = self.asteval.parse(par.expr) + if par.deps is not None: + for dep in par.deps: + self.__update_paramval(params, dep) + par.value = self.asteval.run(par.ast) + out = check_ast_errors(self.asteval.error) + if out is not None: + self.asteval.raise_exception(None) + self.asteval.symtable[name] = par.value + + def fit(self, *args, **kwargs): + "Use current_params unless overridden by arguments passed here." + guess = dict(self.current_params) + guess.update(self.kwargs) # from __init__, e.g. x=x + guess.update(kwargs) + self.current_result = self.model.fit(self._data, *args, **guess) + self.current_params = self.current_result.params + + +class MPLFitter(BaseFitter): + # This is a small elaboration on BaseModel; it adds a plot() + # method that depends on matplotlib. It adds several plot- + # styling arguments to the signature. + __doc__ = _COMMON_DOC + """ + + Parameters + ---------- + data : array-like + model : lmfit.Model + optional initial Model to use, maybe be set or changed later + + Additional Parameters + --------------------- + axes_style : dictionary representing style keyword arguments to be + passed through to `Axes.set(...)` + data_style : dictionary representing style keyword arguments to be passed + through to the matplotlib `plot()` command the plots the data points + init_style : dictionary representing style keyword arguments to be passed + through to the matplotlib `plot()` command the plots the initial fit + line + best_style : dictionary representing style keyword arguments to be passed + through to the matplotlib `plot()` command the plots the best fit + line + **kwargs : independent variables or extra arguments, passed like `x=x` + """ + _COMMON_EXAMPLES_DOC + def __init__(self, data, model=None, axes_style={}, + data_style={}, init_style={}, best_style={}, **kwargs): + self.axes_style = axes_style + self.data_style = data_style + self.init_style = init_style + self.best_style = best_style + super(MPLFitter, self).__init__(data, model, **kwargs) + + def plot(self, axes_style={}, data_style={}, init_style={}, best_style={}, + ax=None): + """Plot data, initial guess fit, and best fit. + + Optional style arguments pass keyword dictionaries through to their + respective components of the matplotlib plot. + + Precedence is: + 1. arguments passed to this function, plot() + 2. arguments passed to the Fitter when it was first declared + 3. hard-coded defaults + + Parameters + --------------------- + axes_style : dictionary representing style keyword arguments to be + passed through to `Axes.set(...)` + data_style : dictionary representing style keyword arguments to be passed + through to the matplotlib `plot()` command the plots the data points + init_style : dictionary representing style keyword arguments to be passed + through to the matplotlib `plot()` command the plots the initial fit + line + best_style : dictionary representing style keyword arguments to be passed + through to the matplotlib `plot()` command the plots the best fit + line + ax : matplotlib.Axes + optional `Axes` object. Axes will be generated if not provided. + """ + try: + import matplotlib.pyplot as plt + except ImportError: + raise ImportError("Matplotlib is required to use this Fitter. " + "Use BaseFitter or a subclass thereof " + "that does not depend on matplotlib.") + + # Configure style + _axes_style= dict() # none, but this is here for possible future use + _axes_style.update(self.axes_style) + _axes_style.update(axes_style) + _data_style= dict(color='blue', marker='o', linestyle='none') + _data_style.update(**_normalize_kwargs(self.data_style, 'line2d')) + _data_style.update(**_normalize_kwargs(data_style, 'line2d')) + _init_style = dict(color='gray') + _init_style.update(**_normalize_kwargs(self.init_style, 'line2d')) + _init_style.update(**_normalize_kwargs(init_style, 'line2d')) + _best_style= dict(color='red') + _best_style.update(**_normalize_kwargs(self.best_style, 'line2d')) + _best_style.update(**_normalize_kwargs(best_style, 'line2d')) + + if ax is None: + fig, ax = plt.subplots() + count_indep_vars = len(self.model.independent_vars) + if count_indep_vars == 0: + ax.plot(self._data, **_data_style) + elif count_indep_vars == 1: + indep_var = self.kwargs[self.model.independent_vars[0]] + ax.plot(indep_var, self._data, **_data_style) + else: + raise NotImplementedError("Cannot plot models with more than one " + "indepedent variable.") + result = self.current_result # alias for brevity + if not result: + ax.set(**_axes_style) + return # short-circuit the rest of the plotting + if count_indep_vars == 0: + ax.plot(result.init_fit, **_init_style) + ax.plot(result.best_fit, **_best_style) + elif count_indep_vars == 1: + ax.plot(indep_var, result.init_fit, **_init_style) + ax.plot(indep_var, result.best_fit, **_best_style) + ax.set(**_axes_style) + + +def _normalize_kwargs(kwargs, kind='patch'): + """Convert matplotlib keywords from short to long form.""" + # Source: + # github.com/tritemio/FRETBursts/blob/fit_experim/fretbursts/burst_plot.py + if kind == 'line2d': + long_names = dict(c='color', ls='linestyle', lw='linewidth', + mec='markeredgecolor', mew='markeredgewidth', + mfc='markerfacecolor', ms='markersize',) + elif kind == 'patch': + long_names = dict(c='color', ls='linestyle', lw='linewidth', + ec='edgecolor', fc='facecolor',) + for short_name in long_names: + if short_name in kwargs: + kwargs[long_names[short_name]] = kwargs.pop(short_name) + return kwargs diff --git a/lmfit/ui/ipy_fitter.py b/lmfit/ui/ipy_fitter.py index 29c9446..80edda5 100644 --- a/lmfit/ui/ipy_fitter.py +++ b/lmfit/ui/ipy_fitter.py @@ -1,282 +1,282 @@ -import warnings
-import numpy as np
-
-from ..model import Model
-
-from .basefitter import MPLFitter, _COMMON_DOC, _COMMON_EXAMPLES_DOC
-
-# Note: If IPython is not available of the version is < 2,
-# this module will not be imported, and a different Fitter.
-
-import IPython
-from IPython.display import display, clear_output
-# Widgets were only experimental in IPython 2.x, but this does work there.
-# Handle the change in naming from 2.x to 3.x.
-IPY2 = IPython.release.version_info[0] == 2
-IPY3 = IPython.release.version_info[0] == 3
-if IPY2:
- from IPython.html.widgets import DropdownWidget as Dropdown
- from IPython.html.widgets import ButtonWidget as Button
- from IPython.html.widgets import ContainerWidget
- from IPython.html.widgets import FloatTextWidget as FloatText
- from IPython.html.widgets import CheckboxWidget as Checkbox
- class HBox(ContainerWidget):
- def __init__(self, *args, **kwargs):
- self.add_class('hbox')
- super(self, ContainerWidget).__init__(*args, **kwargs)
-elif IPY3:
- # as of IPython 3.x:
- from IPython.html.widgets import Dropdown
- from IPython.html.widgets import Button
- from IPython.html.widgets import HBox
- from IPython.html.widgets import FloatText
- from IPython.html.widgets import Checkbox
-else:
- # as of IPython 4.x+:
- from ipywidgets import Dropdown
- from ipywidgets import Button
- from ipywidgets import HBox
- from ipywidgets import FloatText
- from ipywidgets import Checkbox
-
-
-class ParameterWidgetGroup(object):
- """Construct several widgets that together represent a Parameter.
-
- This will only be used if IPython is available."""
- def __init__(self, par):
- self.par = par
-
- # Define widgets.
- self.value_text = FloatText(description=par.name,
- min=self.par.min, max=self.par.max)
- self.value_text.width = 100
- self.min_text = FloatText(description='min', max=self.par.max)
- self.min_text.width = 100
- self.max_text = FloatText(description='max', min=self.par.min)
- self.max_text.width = 100
- self.min_checkbox = Checkbox(description='min')
- self.max_checkbox = Checkbox(description='max')
- self.vary_checkbox = Checkbox(description='vary')
-
- # Set widget values and visibility.
- if par.value is not None:
- self.value_text.value = self.par.value
- min_unset = self.par.min is None or self.par.min == -np.inf
- max_unset = self.par.max is None or self.par.max == np.inf
- self.min_checkbox.value = not min_unset
- self.min_text.visible = not min_unset
- self.min_text.value = self.par.min
- self.max_checkbox.value = not max_unset
- self.max_text.visible = not max_unset
- self.max_text.value = self.par.max
- self.vary_checkbox.value = self.par.vary
-
- # Configure widgets to sync with par attributes.
- self.value_text.on_trait_change(self._on_value_change, 'value')
- self.min_text.on_trait_change(self._on_min_value_change, 'value')
- self.max_text.on_trait_change(self._on_max_value_change, 'value')
- self.min_checkbox.on_trait_change(self._on_min_checkbox_change,
- 'value')
- self.max_checkbox.on_trait_change(self._on_max_checkbox_change,
- 'value')
- self.vary_checkbox.on_trait_change(self._on_vary_change, 'value')
-
- def _on_value_change(self, name, value):
- self.par.value = value
-
- def _on_min_checkbox_change(self, name, value):
- self.min_text.visible = value
- if value:
- # -np.inf does not play well with a numerical text field,
- # so set min to -1 if activated (and back to -inf if deactivated).
- self.min_text.value = -1
- self.par.min = self.min_text.value
- self.value_text.min = self.min_text.value
- else:
- self.par.min = None
-
- def _on_max_checkbox_change(self, name, value):
- self.max_text.visible = value
- if value:
- # np.inf does not play well with a numerical text field,
- # so set max to 1 if activated (and back to inf if deactivated).
- self.max_text.value = 1
- self.par.max = self.max_text.value
- self.value_text.max = self.max_text.value
- else:
- self.par.max = None
-
- def _on_min_value_change(self, name, value):
- self.par.min = value
- self.value_text.min = value
- self.max_text.min = value
-
- def _on_max_value_change(self, name, value):
- self.par.max = value
- self.value_text.max = value
- self.min_text.max = value
-
- def _on_vary_change(self, name, value):
- self.par.vary = value
- # self.value_text.disabled = not value
-
- def close(self):
- # one convenience method to close (i.e., hide and disconnect) all
- # widgets in this group
- self.value_text.close()
- self.min_text.close()
- self.max_text.close()
- self.vary_checkbox.close()
- self.min_checkbox.close()
- self.max_checkbox.close()
-
- def _repr_html_(self):
- box = HBox()
- box.children = [self.value_text, self.vary_checkbox,
- self.min_checkbox, self.min_text,
- self.max_checkbox, self.max_text]
- display(box)
-
- # Make it easy to set the widget attributes directly.
- @property
- def value(self):
- return self.value_text.value
-
- @value.setter
- def value(self, value):
- self.value_text.value = value
-
- @property
- def vary(self):
- return self.vary_checkbox.value
-
- @vary.setter
- def vary(self, value):
- self.vary_checkbox.value = value
-
- @property
- def min(self):
- return self.min_text.value
-
- @min.setter
- def min(self, value):
- self.min_text.value = value
-
- @property
- def max(self):
- return self.max_text.value
-
- @max.setter
- def max(self, value):
- self.max_text.value = value
-
- @property
- def name(self):
- return self.par.name
-
-
-class NotebookFitter(MPLFitter):
- __doc__ = _COMMON_DOC + """
- If IPython is available, it uses the IPython notebook's rich display
- to fit data interactively in a web-based GUI. The Parameters are
- represented in a web-based form that is kept in sync with `current_params`.
- All subclasses to Model, including user-defined ones, are shown in a
- drop-down menu.
-
- Clicking the "Fit" button updates a plot, as above, and updates the
- Parameters in the form to reflect the best fit.
-
- Parameters
- ----------
- data : array-like
- model : lmfit.Model
- optional initial Model to use, maybe be set or changed later
- all_models : list
- optional list of Models to populate drop-down menu, by default
- all built-in and user-defined subclasses of Model are used
-
- Additional Parameters
- ---------------------
- axes_style : dictionary representing style keyword arguments to be
- passed through to `Axes.set(...)`
- data_style : dictionary representing style keyword arguments to be passed
- through to the matplotlib `plot()` command the plots the data points
- init_style : dictionary representing style keyword arguments to be passed
- through to the matplotlib `plot()` command the plots the initial fit
- line
- best_style : dictionary representing style keyword arguments to be passed
- through to the matplotlib `plot()` command the plots the best fit
- line
- **kwargs : independent variables or extra arguments, passed like `x=x`
- """ + _COMMON_EXAMPLES_DOC
- def __init__(self, data, model=None, all_models=None, axes_style={},
- data_style={}, init_style={}, best_style={}, **kwargs):
- # Dropdown menu of all subclasses of Model, incl. user-defined.
- self.models_menu = Dropdown()
- # Dropbox API is very different between IPy 2.x and 3.x.
- if IPY2:
- if all_models is None:
- all_models = dict([(m.__name__, m) for m in Model.__subclasses__()])
- self.models_menu.values = all_models
- else:
- if all_models is None:
- all_models = [(m.__name__, m) for m in Model.__subclasses__()]
- self.models_menu.options = all_models
- self.models_menu.on_trait_change(self._on_model_value_change,
- 'value')
- # Button to trigger fitting.
- self.fit_button = Button(description='Fit')
- self.fit_button.on_click(self._on_fit_button_click)
-
- # Button to trigger guessing.
- self.guess_button = Button(description='Auto-Guess')
- self.guess_button.on_click(self._on_guess_button_click)
-
- # Parameter widgets are not built here. They are (re-)built when
- # the model is (re-)set.
- super(NotebookFitter, self).__init__(data, model, axes_style,
- data_style, init_style,
- best_style, **kwargs)
-
- def _repr_html_(self):
- display(self.models_menu)
- button_box = HBox()
- button_box.children = [self.fit_button, self.guess_button]
- display(button_box)
- for pw in self.param_widgets:
- display(pw)
- self.plot()
-
- def guess(self):
- guessing_successful = super(NotebookFitter, self).guess()
- self.guess_button.disabled = not guessing_successful
-
- def _finalize_model(self, value):
- first_run = not hasattr(self, 'param_widgets')
- if not first_run:
- # Remove all Parameter widgets, and replace them with widgets
- # for the new model.
- for pw in self.param_widgets:
- pw.close()
- self.models_menu.value = value
- self.param_widgets = [ParameterWidgetGroup(p)
- for _, p in self._current_params.items()]
- if not first_run:
- for pw in self.param_widgets:
- display(pw)
-
- def _finalize_params(self):
- for pw in self.param_widgets:
- pw.value = self._current_params[pw.name].value
- pw.min = self._current_params[pw.name].min
- pw.max = self._current_params[pw.name].max
- pw.vary = self._current_params[pw.name].vary
-
- def plot(self):
- clear_output(wait=True)
- super(NotebookFitter, self).plot()
-
- def fit(self):
- super(NotebookFitter, self).fit()
- self.plot()
+import warnings +import numpy as np + +from ..model import Model + +from .basefitter import MPLFitter, _COMMON_DOC, _COMMON_EXAMPLES_DOC + +# Note: If IPython is not available of the version is < 2, +# this module will not be imported, and a different Fitter. + +import IPython +from IPython.display import display, clear_output +# Widgets were only experimental in IPython 2.x, but this does work there. +# Handle the change in naming from 2.x to 3.x. +IPY2 = IPython.release.version_info[0] == 2 +IPY3 = IPython.release.version_info[0] == 3 +if IPY2: + from IPython.html.widgets import DropdownWidget as Dropdown + from IPython.html.widgets import ButtonWidget as Button + from IPython.html.widgets import ContainerWidget + from IPython.html.widgets import FloatTextWidget as FloatText + from IPython.html.widgets import CheckboxWidget as Checkbox + class HBox(ContainerWidget): + def __init__(self, *args, **kwargs): + self.add_class('hbox') + super(self, ContainerWidget).__init__(*args, **kwargs) +elif IPY3: + # as of IPython 3.x: + from IPython.html.widgets import Dropdown + from IPython.html.widgets import Button + from IPython.html.widgets import HBox + from IPython.html.widgets import FloatText + from IPython.html.widgets import Checkbox +else: + # as of IPython 4.x+: + from ipywidgets import Dropdown + from ipywidgets import Button + from ipywidgets import HBox + from ipywidgets import FloatText + from ipywidgets import Checkbox + + +class ParameterWidgetGroup(object): + """Construct several widgets that together represent a Parameter. + + This will only be used if IPython is available.""" + def __init__(self, par): + self.par = par + + # Define widgets. + self.value_text = FloatText(description=par.name, + min=self.par.min, max=self.par.max) + self.value_text.width = 100 + self.min_text = FloatText(description='min', max=self.par.max) + self.min_text.width = 100 + self.max_text = FloatText(description='max', min=self.par.min) + self.max_text.width = 100 + self.min_checkbox = Checkbox(description='min') + self.max_checkbox = Checkbox(description='max') + self.vary_checkbox = Checkbox(description='vary') + + # Set widget values and visibility. + if par.value is not None: + self.value_text.value = self.par.value + min_unset = self.par.min is None or self.par.min == -np.inf + max_unset = self.par.max is None or self.par.max == np.inf + self.min_checkbox.value = not min_unset + self.min_text.visible = not min_unset + self.min_text.value = self.par.min + self.max_checkbox.value = not max_unset + self.max_text.visible = not max_unset + self.max_text.value = self.par.max + self.vary_checkbox.value = self.par.vary + + # Configure widgets to sync with par attributes. + self.value_text.on_trait_change(self._on_value_change, 'value') + self.min_text.on_trait_change(self._on_min_value_change, 'value') + self.max_text.on_trait_change(self._on_max_value_change, 'value') + self.min_checkbox.on_trait_change(self._on_min_checkbox_change, + 'value') + self.max_checkbox.on_trait_change(self._on_max_checkbox_change, + 'value') + self.vary_checkbox.on_trait_change(self._on_vary_change, 'value') + + def _on_value_change(self, name, value): + self.par.value = value + + def _on_min_checkbox_change(self, name, value): + self.min_text.visible = value + if value: + # -np.inf does not play well with a numerical text field, + # so set min to -1 if activated (and back to -inf if deactivated). + self.min_text.value = -1 + self.par.min = self.min_text.value + self.value_text.min = self.min_text.value + else: + self.par.min = None + + def _on_max_checkbox_change(self, name, value): + self.max_text.visible = value + if value: + # np.inf does not play well with a numerical text field, + # so set max to 1 if activated (and back to inf if deactivated). + self.max_text.value = 1 + self.par.max = self.max_text.value + self.value_text.max = self.max_text.value + else: + self.par.max = None + + def _on_min_value_change(self, name, value): + self.par.min = value + self.value_text.min = value + self.max_text.min = value + + def _on_max_value_change(self, name, value): + self.par.max = value + self.value_text.max = value + self.min_text.max = value + + def _on_vary_change(self, name, value): + self.par.vary = value + # self.value_text.disabled = not value + + def close(self): + # one convenience method to close (i.e., hide and disconnect) all + # widgets in this group + self.value_text.close() + self.min_text.close() + self.max_text.close() + self.vary_checkbox.close() + self.min_checkbox.close() + self.max_checkbox.close() + + def _repr_html_(self): + box = HBox() + box.children = [self.value_text, self.vary_checkbox, + self.min_checkbox, self.min_text, + self.max_checkbox, self.max_text] + display(box) + + # Make it easy to set the widget attributes directly. + @property + def value(self): + return self.value_text.value + + @value.setter + def value(self, value): + self.value_text.value = value + + @property + def vary(self): + return self.vary_checkbox.value + + @vary.setter + def vary(self, value): + self.vary_checkbox.value = value + + @property + def min(self): + return self.min_text.value + + @min.setter + def min(self, value): + self.min_text.value = value + + @property + def max(self): + return self.max_text.value + + @max.setter + def max(self, value): + self.max_text.value = value + + @property + def name(self): + return self.par.name + + +class NotebookFitter(MPLFitter): + __doc__ = _COMMON_DOC + """ + If IPython is available, it uses the IPython notebook's rich display + to fit data interactively in a web-based GUI. The Parameters are + represented in a web-based form that is kept in sync with `current_params`. + All subclasses to Model, including user-defined ones, are shown in a + drop-down menu. + + Clicking the "Fit" button updates a plot, as above, and updates the + Parameters in the form to reflect the best fit. + + Parameters + ---------- + data : array-like + model : lmfit.Model + optional initial Model to use, maybe be set or changed later + all_models : list + optional list of Models to populate drop-down menu, by default + all built-in and user-defined subclasses of Model are used + + Additional Parameters + --------------------- + axes_style : dictionary representing style keyword arguments to be + passed through to `Axes.set(...)` + data_style : dictionary representing style keyword arguments to be passed + through to the matplotlib `plot()` command the plots the data points + init_style : dictionary representing style keyword arguments to be passed + through to the matplotlib `plot()` command the plots the initial fit + line + best_style : dictionary representing style keyword arguments to be passed + through to the matplotlib `plot()` command the plots the best fit + line + **kwargs : independent variables or extra arguments, passed like `x=x` + """ + _COMMON_EXAMPLES_DOC + def __init__(self, data, model=None, all_models=None, axes_style={}, + data_style={}, init_style={}, best_style={}, **kwargs): + # Dropdown menu of all subclasses of Model, incl. user-defined. + self.models_menu = Dropdown() + # Dropbox API is very different between IPy 2.x and 3.x. + if IPY2: + if all_models is None: + all_models = dict([(m.__name__, m) for m in Model.__subclasses__()]) + self.models_menu.values = all_models + else: + if all_models is None: + all_models = [(m.__name__, m) for m in Model.__subclasses__()] + self.models_menu.options = all_models + self.models_menu.on_trait_change(self._on_model_value_change, + 'value') + # Button to trigger fitting. + self.fit_button = Button(description='Fit') + self.fit_button.on_click(self._on_fit_button_click) + + # Button to trigger guessing. + self.guess_button = Button(description='Auto-Guess') + self.guess_button.on_click(self._on_guess_button_click) + + # Parameter widgets are not built here. They are (re-)built when + # the model is (re-)set. + super(NotebookFitter, self).__init__(data, model, axes_style, + data_style, init_style, + best_style, **kwargs) + + def _repr_html_(self): + display(self.models_menu) + button_box = HBox() + button_box.children = [self.fit_button, self.guess_button] + display(button_box) + for pw in self.param_widgets: + display(pw) + self.plot() + + def guess(self): + guessing_successful = super(NotebookFitter, self).guess() + self.guess_button.disabled = not guessing_successful + + def _finalize_model(self, value): + first_run = not hasattr(self, 'param_widgets') + if not first_run: + # Remove all Parameter widgets, and replace them with widgets + # for the new model. + for pw in self.param_widgets: + pw.close() + self.models_menu.value = value + self.param_widgets = [ParameterWidgetGroup(p) + for _, p in self._current_params.items()] + if not first_run: + for pw in self.param_widgets: + display(pw) + + def _finalize_params(self): + for pw in self.param_widgets: + pw.value = self._current_params[pw.name].value + pw.min = self._current_params[pw.name].min + pw.max = self._current_params[pw.name].max + pw.vary = self._current_params[pw.name].vary + + def plot(self): + clear_output(wait=True) + super(NotebookFitter, self).plot() + + def fit(self): + super(NotebookFitter, self).fit() + self.plot() diff --git a/lmfit/uncertainties/__init__.py b/lmfit/uncertainties/__init__.py index 829a283..5c2ec34 100644 --- a/lmfit/uncertainties/__init__.py +++ b/lmfit/uncertainties/__init__.py @@ -1,1645 +1,1645 @@ -#!! Whenever the documentation below is updated, setup.py should be
-# checked for consistency.
-
-'''
-Calculations with full error propagation for quantities with uncertainties.
-Derivatives can also be calculated.
-
-Web user guide: http://packages.python.org/uncertainties/.
-
-Example of possible calculation: (0.2 +/- 0.01)**2 = 0.04 +/- 0.004.
-
-Correlations between expressions are correctly taken into account (for
-instance, with x = 0.2+/-0.01, 2*x-x-x is exactly zero, as is y-x-x
-with y = 2*x).
-
-Examples:
-
- import uncertainties
- from uncertainties import ufloat
- from uncertainties.umath import * # sin(), etc.
-
- # Mathematical operations:
- x = ufloat((0.20, 0.01)) # x = 0.20+/-0.01
- x = ufloat("0.20+/-0.01") # Other representation
- x = ufloat("0.20(1)") # Other representation
- x = ufloat("0.20") # Implicit uncertainty of +/-1 on the last digit
- print x**2 # Square: prints "0.04+/-0.004"
- print sin(x**2) # Prints "0.0399...+/-0.00399..."
-
- print x.std_score(0.17) # Prints "-3.0": deviation of -3 sigmas
-
- # Access to the nominal value, and to the uncertainty:
- square = x**2 # Square
- print square # Prints "0.04+/-0.004"
- print square.nominal_value # Prints "0.04"
- print square.std_dev() # Prints "0.004..."
-
- print square.derivatives[x] # Partial derivative: 0.4 (= 2*0.20)
-
- # Correlations:
- u = ufloat((1, 0.05), "u variable") # Tag
- v = ufloat((10, 0.1), "v variable")
- sum_value = u+v
-
- u.set_std_dev(0.1) # Standard deviations can be updated on the fly
- print sum_value - u - v # Prints "0.0" (exact result)
-
- # List of all sources of error:
- print sum_value # Prints "11+/-0.1414..."
- for (var, error) in sum_value.error_components().items():
- print "%s: %f" % (var.tag, error) # Individual error components
-
- # Covariance matrices:
- cov_matrix = uncertainties.covariance_matrix([u, v, sum_value])
- print cov_matrix # 3x3 matrix
-
- # Correlated variables can be constructed from a covariance matrix, if
- # NumPy is available:
- (u2, v2, sum2) = uncertainties.correlated_values([1, 10, 11],
- cov_matrix)
- print u2 # Value and uncertainty of u: correctly recovered (1+/-0.1)
- print uncertainties.covariance_matrix([u2, v2, sum2]) # == cov_matrix
-
-- The main function provided by this module is ufloat, which creates
-numbers with uncertainties (Variable objects). Variable objects can
-be used as if they were regular Python numbers. The main attributes
-and methods of Variable objects are defined in the documentation of
-the Variable class.
-
-- Valid operations on numbers with uncertainties include basic
-mathematical functions (addition, etc.).
-
-Most operations from the standard math module (sin, etc.) can be applied
-on numbers with uncertainties by using their generalization from the
-uncertainties.umath module:
-
- from uncertainties.umath import sin
- print sin(ufloat("1+/-0.01")) # 0.841...+/-0.005...
- print sin(1) # umath.sin() also works on floats, exactly like math.sin()
-
-Logical operations (>, ==, etc.) are also supported.
-
-Basic operations on NumPy arrays or matrices of numbers with
-uncertainties can be performed:
-
- 2*numpy.array([ufloat((1, 0.01)), ufloat((2, 0.1))])
-
-More complex operations on NumPy arrays can be performed through the
-dedicated uncertainties.unumpy sub-module (see its documentation).
-
-Calculations that are performed through non-Python code (Fortran, C,
-etc.) can handle numbers with uncertainties instead of floats through
-the provided wrap() wrapper:
-
- import uncertainties
-
- # wrapped_f is a version of f that can take arguments with
- # uncertainties, even if f only takes floats:
- wrapped_f = uncertainties.wrap(f)
-
-If some derivatives of the wrapped function f are known (analytically,
-or numerically), they can be given to wrap()--see the documentation
-for wrap().
-
-- Utility functions are also provided: the covariance matrix between
-random variables can be calculated with covariance_matrix(), or used
-as input for the definition of correlated quantities (correlated_values()
-function--defined only if the NumPy module is available).
-
-- Mathematical expressions involving numbers with uncertainties
-generally return AffineScalarFunc objects, which also print as a value
-with uncertainty. Their most useful attributes and methods are
-described in the documentation for AffineScalarFunc. Note that
-Variable objects are also AffineScalarFunc objects. UFloat is an
-alias for AffineScalarFunc, provided as a convenience: testing whether
-a value carries an uncertainty handled by this module should be done
-with insinstance(my_value, UFloat).
-
-- Mathematically, numbers with uncertainties are, in this package,
-probability distributions. These probabilities are reduced to two
-numbers: a nominal value and an uncertainty. Thus, both variables
-(Variable objects) and the result of mathematical operations
-(AffineScalarFunc objects) contain these two values (respectively in
-their nominal_value attribute and through their std_dev() method).
-
-The uncertainty of a number with uncertainty is simply defined in
-this package as the standard deviation of the underlying probability
-distribution.
-
-The numbers with uncertainties manipulated by this package are assumed
-to have a probability distribution mostly contained around their
-nominal value, in an interval of about the size of their standard
-deviation. This should cover most practical cases. A good choice of
-nominal value for a number with uncertainty is thus the median of its
-probability distribution, the location of highest probability, or the
-average value.
-
-- When manipulating ensembles of numbers, some of which contain
-uncertainties, it can be useful to access the nominal value and
-uncertainty of all numbers in a uniform manner:
-
- x = ufloat("3+/-0.1")
- print nominal_value(x) # Prints 3
- print std_dev(x) # Prints 0.1
- print nominal_value(3) # Prints 3: nominal_value works on floats
- print std_dev(3) # Prints 0: std_dev works on floats
-
-- Probability distributions (random variables and calculation results)
-are printed as:
-
- nominal value +/- standard deviation
-
-but this does not imply any property on the nominal value (beyond the
-fact that the nominal value is normally inside the region of high
-probability density), or that the probability distribution of the
-result is symmetrical (this is rarely strictly the case).
-
-- Linear approximations of functions (around the nominal values) are
-used for the calculation of the standard deviation of mathematical
-expressions with this package.
-
-The calculated standard deviations and nominal values are thus
-meaningful approximations as long as the functions involved have
-precise linear expansions in the region where the probability
-distribution of their variables is the largest. It is therefore
-important that uncertainties be small. Mathematically, this means
-that the linear term of functions around the nominal values of their
-variables should be much larger than the remaining higher-order terms
-over the region of significant probability.
-
-For instance, sin(0+/-0.01) yields a meaningful standard deviation
-since it is quite linear over 0+/-0.01. However, cos(0+/-0.01) yields
-an approximate standard deviation of 0 (because the cosine is not well
-approximated by a line around 0), which might not be precise enough
-for all applications.
-
-- Comparison operations (>, ==, etc.) on numbers with uncertainties
-have a pragmatic semantics, in this package: numbers with
-uncertainties can be used wherever Python numbers are used, most of
-the time with a result identical to the one that would be obtained
-with their nominal value only. However, since the objects defined in
-this module represent probability distributions and not pure numbers,
-comparison operator are interpreted in a specific way.
-
-The result of a comparison operation ("==", ">", etc.) is defined so as
-to be essentially consistent with the requirement that uncertainties
-be small: the value of a comparison operation is True only if the
-operation yields True for all infinitesimal variations of its random
-variables, except, possibly, for an infinitely small number of cases.
-
-Example:
-
- "x = 3.14; y = 3.14" is such that x == y
-
-but
-
- x = ufloat((3.14, 0.01))
- y = ufloat((3.14, 0.01))
-
-is not such that x == y, since x and y are independent random
-variables that almost never give the same value. However, x == x
-still holds.
-
-The boolean value (bool(x), "if x...") of a number with uncertainty x
-is the result of x != 0.
-
-- The uncertainties package is for Python 2.5 and above.
-
-- This package contains tests. They can be run either manually or
-automatically with the nose unit testing framework (nosetests).
-
-(c) 2009-2013 by Eric O. LEBIGOT (EOL) <eric.lebigot@normalesup.org>.
-Please send feature requests, bug reports, or feedback to this address.
-
-Please support future development by donating $5 or more through PayPal!
-
-This software is released under a dual license. (1) The BSD license.
-(2) Any other license, as long as it is obtained from the original
-author.'''
-
-# The idea behind this module is to replace the result of mathematical
-# operations by a local approximation of the defining function. For
-# example, sin(0.2+/-0.01) becomes the affine function
-# (AffineScalarFunc object) whose nominal value is sin(0.2) and
-# whose variations are given by sin(0.2+delta) = 0.98...*delta.
-# Uncertainties can then be calculated by using this local linear
-# approximation of the original function.
-
-from __future__ import division # Many analytical derivatives depend on this
-
-import re
-import math
-from math import sqrt, log # Optimization: no attribute look-up
-import copy
-import warnings
-
-# Numerical version:
-__version_info__ = (1, 9)
-__version__ = '.'.join(map(str, __version_info__))
-
-__author__ = 'Eric O. LEBIGOT (EOL) <eric.lebigot@normalesup.org>'
-
-# Attributes that are always exported (some other attributes are
-# exported only if the NumPy module is available...):
-__all__ = [
-
- # All sub-modules and packages are not imported by default,
- # in particular because NumPy might be unavailable.
- 'ufloat', # Main function: returns a number with uncertainty
-
- # Uniform access to nominal values and standard deviations:
- 'nominal_value',
- 'std_dev',
-
- # Utility functions (more are exported if NumPy is present):
- 'covariance_matrix',
-
- # Class for testing whether an object is a number with
- # uncertainty. Not usually created by users (except through the
- # Variable subclass), but possibly manipulated by external code
- # ['derivatives()' method, etc.].
- 'UFloat',
-
- # Wrapper for allowing non-pure-Python function to handle
- # quantities with uncertainties:
- 'wrap',
-
- # The documentation for wrap() indicates that numerical
- # derivatives are calculated through partial_derivative(). The
- # user might also want to change the size of the numerical
- # differentiation step.
- 'partial_derivative'
- ]
-
-###############################################################################
-
-def set_doc(doc_string):
- """
- Decorator function that sets the docstring to the given text.
-
- It is useful for functions whose docstring is calculated
- (including string substitutions).
- """
- def set_doc_string(func):
- func.__doc__ = doc_string
- return func
- return set_doc_string
-
-# Some types known to not depend on Variable objects are put in
-# CONSTANT_TYPES. The most common types can be put in front, as this
-# may slightly improve the execution speed.
-CONSTANT_TYPES = (float, int, complex) # , long)
-
-###############################################################################
-# Utility for issuing deprecation warnings
-
-def deprecation(message):
- '''
- Warns the user with the given message, by issuing a
- DeprecationWarning.
- '''
- warnings.warn(message, DeprecationWarning, stacklevel=2)
-
-
-###############################################################################
-
-## Definitions that depend on the availability of NumPy:
-
-
-try:
- import numpy
-except ImportError:
- pass
-else:
-
- # NumPy numbers do not depend on Variable objects:
- CONSTANT_TYPES += (numpy.number,)
-
- # Entering variables as a block of correlated values. Only available
- # if NumPy is installed.
-
- #! It would be possible to dispense with NumPy, but a routine should be
- # written for obtaining the eigenvectors of a symmetric matrix. See
- # for instance Numerical Recipes: (1) reduction to tri-diagonal
- # [Givens or Householder]; (2) QR / QL decomposition.
-
- def correlated_values(nom_values, covariance_mat, tags=None):
- """
- Returns numbers with uncertainties (AffineScalarFunc objects)
- that correctly reproduce the given covariance matrix, and have
- the given (float) values as their nominal value.
-
- The correlated_values_norm() function returns the same result,
- but takes a correlation matrix instead of a covariance matrix.
-
- The list of values and the covariance matrix must have the
- same length, and the matrix must be a square (symmetric) one.
-
- The numbers with uncertainties returned depend on newly
- created, independent variables (Variable objects).
-
- If 'tags' is not None, it must list the tag of each new
- independent variable.
-
- nom_values -- sequence with the nominal (real) values of the
- numbers with uncertainties to be returned.
-
- covariance_mat -- full covariance matrix of the returned
- numbers with uncertainties (not the statistical correlation
- matrix, i.e., not the normalized covariance matrix). For
- example, the first element of this matrix is the variance of
- the first returned number with uncertainty.
- """
-
- # If no tags were given, we prepare tags for the newly created
- # variables:
- if tags is None:
- tags = (None,) * len(nom_values)
-
- # The covariance matrix is diagonalized in order to define
- # the independent variables that model the given values:
-
- (variances, transform) = numpy.linalg.eigh(covariance_mat)
-
- # Numerical errors might make some variances negative: we set
- # them to zero:
- variances[variances < 0] = 0.
-
- # Creation of new, independent variables:
-
- # We use the fact that the eigenvectors in 'transform' are
- # special: 'transform' is unitary: its inverse is its transpose:
-
- variables = tuple(
- # The variables represent "pure" uncertainties:
- Variable(0, sqrt(variance), tag)
- for (variance, tag) in zip(variances, tags))
-
- # Representation of the initial correlated values:
- values_funcs = tuple(
- AffineScalarFunc(value, dict(zip(variables, coords)))
- for (coords, value) in zip(transform, nom_values))
-
- return values_funcs
-
- __all__.append('correlated_values')
-
- def correlated_values_norm(values_with_std_dev, correlation_mat,
- tags=None):
- '''
- Returns correlated values like correlated_values(), but takes
- instead as input:
-
- - nominal (float) values along with their standard deviation, and
-
- - a correlation matrix (i.e. a normalized covariance matrix
- normalized with individual standard deviations).
-
- values_with_std_dev -- sequence of (nominal value, standard
- deviation) pairs. The returned, correlated values have these
- nominal values and standard deviations.
-
- correlation_mat -- correlation matrix (i.e. the normalized
- covariance matrix, a matrix with ones on its diagonal).
- '''
-
- (nominal_values, std_devs) = numpy.transpose(values_with_std_dev)
-
- return correlated_values(
- nominal_values,
- correlation_mat*std_devs*std_devs[numpy.newaxis].T,
- tags)
-
- __all__.append('correlated_values_norm')
-
-###############################################################################
-
-# Mathematical operations with local approximations (affine scalar
-# functions)
-
-class NotUpcast(Exception):
- 'Raised when an object cannot be converted to a number with uncertainty'
-
-def to_affine_scalar(x):
- """
- Transforms x into a constant affine scalar function
- (AffineScalarFunc), unless it is already an AffineScalarFunc (in
- which case x is returned unchanged).
-
- Raises an exception unless 'x' belongs to some specific classes of
- objects that are known not to depend on AffineScalarFunc objects
- (which then cannot be considered as constants).
- """
-
- if isinstance(x, AffineScalarFunc):
- return x
-
- #! In Python 2.6+, numbers.Number could be used instead, here:
- if isinstance(x, CONSTANT_TYPES):
- # No variable => no derivative to define:
- return AffineScalarFunc(x, {})
-
- # Case of lists, etc.
- raise NotUpcast("%s cannot be converted to a number with"
- " uncertainty" % type(x))
-
-def partial_derivative(f, param_num):
- """
- Returns a function that numerically calculates the partial
- derivative of function f with respect to its argument number
- param_num.
-
- The step parameter represents the shift of the parameter used in
- the numerical approximation.
- """
-
- def partial_derivative_of_f(*args, **kws):
- """
- Partial derivative, calculated with the (-epsilon, +epsilon)
- method, which is more precise than the (0, +epsilon) method.
- """
- # f_nominal_value = f(*args)
- param_kw = None
- if '__param__kw__' in kws:
- param_kw = kws.pop('__param__kw__')
- shifted_args = list(args) # Copy, and conversion to a mutable
- shifted_kws = {}
- for k, v in kws.items():
- shifted_kws[k] = v
- step = 1.e-8
- if param_kw in shifted_kws:
- step = step*abs(shifted_kws[param_kw])
- elif param_num < len(shifted_args):
- # The step is relative to the parameter being varied, so that
- # shsifting it does not suffer from finite precision:
- step = step*abs(shifted_args[param_num])
-
- if param_kw in shifted_kws:
- shifted_kws[param_kw] += step
- elif param_num < len(shifted_args):
- shifted_args[param_num] += step
-
- shifted_f_plus = f(*shifted_args, **shifted_kws)
-
- if param_kw in shifted_kws:
- shifted_kws[param_kw] -= 2*step
- elif param_num < len(shifted_args):
- shifted_args[param_num] -= 2*step
- shifted_f_minus = f(*shifted_args, **shifted_kws)
-
- return (shifted_f_plus - shifted_f_minus)/2/step
-
- return partial_derivative_of_f
-
-class NumericalDerivatives(object):
- """
- Convenient access to the partial derivatives of a function,
- calculated numerically.
- """
- # This is not a list because the number of arguments of the
- # function is not known in advance, in general.
-
- def __init__(self, function):
- """
- 'function' is the function whose derivatives can be computed.
- """
- self._function = function
-
- def __getitem__(self, n):
- """
- Returns the n-th numerical derivative of the function.
- """
- return partial_derivative(self._function, n)
-
-def wrap(f, derivatives_iter=None):
- """
- Wraps a function f into a function that also accepts numbers with
- uncertainties (UFloat objects) and returns a number with
- uncertainties. Doing so may be necessary when function f cannot
- be expressed analytically (with uncertainties-compatible operators
- and functions like +, *, umath.sin(), etc.).
-
- f must return a scalar (not a list, etc.).
-
- In the wrapped function, the standard Python scalar arguments of f
- (float, int, etc.) can be replaced by numbers with
- uncertainties. The result will contain the appropriate
- uncertainty.
-
- If no argument to the wrapped function has an uncertainty, f
- simply returns its usual, scalar result.
-
- If supplied, derivatives_iter can be an iterable that generally
- contains functions; each successive function is the partial
- derivative of f with respect to the corresponding variable (one
- function for each argument of f, which takes as many arguments as
- f). If instead of a function, an element of derivatives_iter
- contains None, then it is automatically replaced by the relevant
- numerical derivative; this can be used for non-scalar arguments of
- f (like string arguments).
-
- If derivatives_iter is None, or if derivatives_iter contains a
- fixed (and finite) number of elements, then any missing derivative
- is calculated numerically.
-
- An infinite number of derivatives can be specified by having
- derivatives_iter be an infinite iterator; this can for instance
- be used for specifying the derivatives of functions with a
- undefined number of argument (like sum(), whose partial
- derivatives all return 1).
-
- Example (for illustration purposes only, as
- uncertainties.umath.sin() runs faster than the examples that
- follow): wrap(math.sin) is a sine function that can be applied to
- numbers with uncertainties. Its derivative will be calculated
- numerically. wrap(math.sin, [None]) would have produced the same
- result. wrap(math.sin, [math.cos]) is the same function, but with
- an analytically defined derivative.
- """
-
- if derivatives_iter is None:
- derivatives_iter = NumericalDerivatives(f)
- else:
- # Derivatives that are not defined are calculated numerically,
- # if there is a finite number of them (the function lambda
- # *args: fsum(args) has a non-defined number of arguments, as
- # it just performs a sum):
- try: # Is the number of derivatives fixed?
- len(derivatives_iter)
- except TypeError:
- pass
- else:
- derivatives_iter = [
- partial_derivative(f, k) if derivative is None
- else derivative
- for (k, derivative) in enumerate(derivatives_iter)]
-
- #! Setting the doc string after "def f_with...()" does not
- # seem to work. We define it explicitly:
- @set_doc("""\
- Version of %s(...) that returns an affine approximation
- (AffineScalarFunc object), if its result depends on variables
- (Variable objects). Otherwise, returns a simple constant (when
- applied to constant arguments).
-
- Warning: arguments of the function that are not AffineScalarFunc
- objects must not depend on uncertainties.Variable objects in any
- way. Otherwise, the dependence of the result in
- uncertainties.Variable objects will be incorrect.
-
- Original documentation:
- %s""" % (f.__name__, f.__doc__))
- def f_with_affine_output(*args, **kwargs):
- # Can this function perform the calculation of an
- # AffineScalarFunc (or maybe float) result?
- try:
- old_funcs = map(to_affine_scalar, args)
- aff_funcs = [to_affine_scalar(a) for a in args]
- aff_kws = kwargs
- aff_varkws = []
- for key, val in kwargs.items():
- if isinstance(val, Variable):
- aff_kws[key] = to_affine_scalar(val)
- aff_varkws.append(key)
-
- except NotUpcast:
-
- # This function does not know how to itself perform
- # calculations with non-float-like arguments (as they
- # might for instance be objects whose value really changes
- # if some Variable objects had different values):
-
- # Is it clear that we can't delegate the calculation?
-
- if any(isinstance(arg, AffineScalarFunc) for arg in args):
- # This situation arises for instance when calculating
- # AffineScalarFunc(...)*numpy.array(...). In this
- # case, we must let NumPy handle the multiplication
- # (which is then performed element by element):
- return NotImplemented
- else:
- # If none of the arguments is an AffineScalarFunc, we
- # can delegate the calculation to the original
- # function. This can be useful when it is called with
- # only one argument (as in
- # numpy.log10(numpy.ndarray(...)):
- return f(*args, **kwargs)
-
- ########################################
- # Nominal value of the constructed AffineScalarFunc:
- args_values = [e.nominal_value for e in aff_funcs]
- kw_values = {}
- for key, val in aff_kws.items():
- kw_values[key] = val
- if key in aff_varkws:
- kw_values[key] = val.nominal_value
- f_nominal_value = f(*args_values, **kw_values)
-
- ########################################
-
- # List of involved variables (Variable objects):
- variables = set()
- for expr in aff_funcs:
- variables |= set(expr.derivatives)
- for vname in aff_varkws:
- variables |= set(aff_kws[vname].derivatives)
- ## It is sometimes useful to only return a regular constant:
-
- # (1) Optimization / convenience behavior: when 'f' is called
- # on purely constant values (e.g., sin(2)), there is no need
- # for returning a more complex AffineScalarFunc object.
-
- # (2) Functions that do not return a "float-like" value might
- # not have a relevant representation as an AffineScalarFunc.
- # This includes boolean functions, since their derivatives are
- # either 0 or are undefined: they are better represented as
- # Python constants than as constant AffineScalarFunc functions.
-
- if not variables or isinstance(f_nominal_value, bool):
- return f_nominal_value
-
- # The result of 'f' does depend on 'variables'...
-
- ########################################
-
- # Calculation of the derivatives with respect to the arguments
- # of f (aff_funcs):
-
- # The chain rule is applied. This is because, in the case of
- # numerical derivatives, it allows for a better-controlled
- # numerical stability than numerically calculating the partial
- # derivatives through '[f(x + dx, y + dy, ...) -
- # f(x,y,...)]/da' where dx, dy,... are calculated by varying
- # 'a'. In fact, it is numerically better to control how big
- # (dx, dy,...) are: 'f' is a simple mathematical function and
- # it is possible to know how precise the df/dx are (which is
- # not possible with the numerical df/da calculation above).
-
- # We use numerical derivatives, if we don't already have a
- # list of derivatives:
-
- #! Note that this test could be avoided by requiring the
- # caller to always provide derivatives. When changing the
- # functions of the math module, this would force this module
- # to know about all the math functions. Another possibility
- # would be to force derivatives_iter to contain, say, the
- # first 3 derivatives of f. But any of these two ideas has a
- # chance to break, one day... (if new functions are added to
- # the math module, or if some function has more than 3
- # arguments).
-
- derivatives_wrt_args = []
- for (arg, derivative) in zip(aff_funcs, derivatives_iter):
- derivatives_wrt_args.append(derivative(*args_values, **aff_kws)
- if arg.derivatives
- else 0)
-
-
- kws_values = []
- for vname in aff_varkws:
- kws_values.append( aff_kws[vname].nominal_value)
- for (vname, derivative) in zip(aff_varkws, derivatives_iter):
- derivatives_wrt_args.append(derivative(__param__kw__=vname,
- **kw_values)
- if aff_kws[vname].derivatives
- else 0)
-
- ########################################
- # Calculation of the derivative of f with respect to all the
- # variables (Variable) involved.
-
- # Initial value (is updated below):
- derivatives_wrt_vars = dict((var, 0.) for var in variables)
-
- # The chain rule is used (we already have
- # derivatives_wrt_args):
-
- for (func, f_derivative) in zip(aff_funcs, derivatives_wrt_args):
- for (var, func_derivative) in func.derivatives.items():
- derivatives_wrt_vars[var] += f_derivative * func_derivative
-
- for (vname, f_derivative) in zip(aff_varkws, derivatives_wrt_args):
- func = aff_kws[vname]
- for (var, func_derivative) in func.derivatives.items():
- derivatives_wrt_vars[var] += f_derivative * func_derivative
-
- # The function now returns an AffineScalarFunc object:
- return AffineScalarFunc(f_nominal_value, derivatives_wrt_vars)
-
- # It is easier to work with f_with_affine_output, which represents
- # a wrapped version of 'f', when it bears the same name as 'f':
- f_with_affine_output.__name__ = f.__name__
-
- return f_with_affine_output
-
-def _force_aff_func_args(func):
- """
- Takes an operator op(x, y) and wraps it.
-
- The constructed operator returns func(x, to_affine_scalar(y)) if y
- can be upcast with to_affine_scalar(); otherwise, it returns
- NotImplemented.
-
- Thus, func() is only called on two AffineScalarFunc objects, if
- its first argument is an AffineScalarFunc.
- """
-
- def op_on_upcast_args(x, y):
- """
- Returns %s(self, to_affine_scalar(y)) if y can be upcast
- through to_affine_scalar. Otherwise returns NotImplemented.
- """ % func.__name__
-
- try:
- y_with_uncert = to_affine_scalar(y)
- except NotUpcast:
- # This module does not know how to handle the comparison:
- # (example: y is a NumPy array, in which case the NumPy
- # array will decide that func() should be applied
- # element-wise between x and all the elements of y):
- return NotImplemented
- else:
- return func(x, y_with_uncert)
-
- return op_on_upcast_args
-
-########################################
-
-# Definition of boolean operators, that assume that self and
-# y_with_uncert are AffineScalarFunc.
-
-# The fact that uncertainties must be smalled is used, here: the
-# comparison functions are supposed to be constant for most values of
-# the random variables.
-
-# Even though uncertainties are supposed to be small, comparisons
-# between 3+/-0.1 and 3.0 are handled (even though x == 3.0 is not a
-# constant function in the 3+/-0.1 interval). The comparison between
-# x and x is handled too, when x has an uncertainty. In fact, as
-# explained in the main documentation, it is possible to give a useful
-# meaning to the comparison operators, in these cases.
-
-def _eq_on_aff_funcs(self, y_with_uncert):
- """
- __eq__ operator, assuming that both self and y_with_uncert are
- AffineScalarFunc objects.
- """
- difference = self - y_with_uncert
- # Only an exact zero difference means that self and y are
- # equal numerically:
- return not(difference._nominal_value or difference.std_dev())
-
-def _ne_on_aff_funcs(self, y_with_uncert):
- """
- __ne__ operator, assuming that both self and y_with_uncert are
- AffineScalarFunc objects.
- """
-
- return not _eq_on_aff_funcs(self, y_with_uncert)
-
-def _gt_on_aff_funcs(self, y_with_uncert):
- """
- __gt__ operator, assuming that both self and y_with_uncert are
- AffineScalarFunc objects.
- """
- return self._nominal_value > y_with_uncert._nominal_value
-
-def _ge_on_aff_funcs(self, y_with_uncert):
- """
- __ge__ operator, assuming that both self and y_with_uncert are
- AffineScalarFunc objects.
- """
-
- return (_gt_on_aff_funcs(self, y_with_uncert)
- or _eq_on_aff_funcs(self, y_with_uncert))
-
-def _lt_on_aff_funcs(self, y_with_uncert):
- """
- __lt__ operator, assuming that both self and y_with_uncert are
- AffineScalarFunc objects.
- """
- return self._nominal_value < y_with_uncert._nominal_value
-
-def _le_on_aff_funcs(self, y_with_uncert):
- """
- __le__ operator, assuming that both self and y_with_uncert are
- AffineScalarFunc objects.
- """
-
- return (_lt_on_aff_funcs(self, y_with_uncert)
- or _eq_on_aff_funcs(self, y_with_uncert))
-
-########################################
-
-class AffineScalarFunc(object):
- """
- Affine functions that support basic mathematical operations
- (addition, etc.). Such functions can for instance be used for
- representing the local (linear) behavior of any function.
-
- This class is mostly meant to be used internally.
-
- This class can also be used to represent constants.
-
- The variables of affine scalar functions are Variable objects.
-
- AffineScalarFunc objects include facilities for calculating the
- 'error' on the function, from the uncertainties on its variables.
-
- Main attributes and methods:
-
- - nominal_value, std_dev(): value at the origin / nominal value,
- and standard deviation.
-
- - error_components(): error_components()[x] is the error due to
- Variable x.
-
- - derivatives: derivatives[x] is the (value of the) derivative
- with respect to Variable x. This attribute is a dictionary
- whose keys are the Variable objects on which the function
- depends.
-
- All the Variable objects on which the function depends are in
- 'derivatives'.
-
- - std_score(x): position of number x with respect to the
- nominal value, in units of the standard deviation.
- """
-
- # To save memory in large arrays:
- __slots__ = ('_nominal_value', 'derivatives')
-
- #! The code could be modify in order to accommodate for non-float
- # nominal values. This could for instance be done through
- # the operator module: instead of delegating operations to
- # float.__*__ operations, they could be delegated to
- # operator.__*__ functions (while taking care of properly handling
- # reverse operations: __radd__, etc.).
-
- def __init__(self, nominal_value, derivatives):
- """
- nominal_value -- value of the function at the origin.
- nominal_value must not depend in any way of the Variable
- objects in 'derivatives' (the value at the origin of the
- function being defined is a constant).
-
- derivatives -- maps each Variable object on which the function
- being defined depends to the value of the derivative with
- respect to that variable, taken at the nominal value of all
- variables.
-
- Warning: the above constraint is not checked, and the user is
- responsible for complying with it.
- """
-
- # Defines the value at the origin:
-
- # Only float-like values are handled. One reason is that it
- # does not make sense for a scalar function to be affine to
- # not yield float values. Another reason is that it would not
- # make sense to have a complex nominal value, here (it would
- # not be handled correctly at all): converting to float should
- # be possible.
- self._nominal_value = float(nominal_value)
- self.derivatives = derivatives
-
- # The following prevents the 'nominal_value' attribute from being
- # modified by the user:
- @property
- def nominal_value(self):
- "Nominal value of the random number."
- return self._nominal_value
-
- ############################################################
-
-
- ### Operators: operators applied to AffineScalarFunc and/or
- ### float-like objects only are supported. This is why methods
- ### from float are used for implementing these operators.
-
- # Operators with no reflection:
-
- ########################################
-
- # __nonzero__() is supposed to return a boolean value (it is used
- # by bool()). It is for instance used for converting the result
- # of comparison operators to a boolean, in sorted(). If we want
- # to be able to sort AffineScalarFunc objects, __nonzero__ cannot
- # return a AffineScalarFunc object. Since boolean results (such
- # as the result of bool()) don't have a very meaningful
- # uncertainty unless it is zero, this behavior is fine.
-
- def __nonzero__(self):
- """
- Equivalent to self != 0.
- """
- #! This might not be relevant for AffineScalarFunc objects
- # that contain values in a linear space which does not convert
- # the float 0 into the null vector (see the __eq__ function:
- # __nonzero__ works fine if subtracting the 0 float from a
- # vector of the linear space works as if 0 were the null
- # vector of that space):
- return self != 0. # Uses the AffineScalarFunc.__ne__ function
-
- ########################################
-
- ## Logical operators: warning: the resulting value cannot always
- ## be differentiated.
-
- # The boolean operations are not differentiable everywhere, but
- # almost...
-
- # (1) I can rely on the assumption that the user only has "small"
- # errors on variables, as this is used in the calculation of the
- # standard deviation (which performs linear approximations):
-
- # (2) However, this assumption is not relevant for some
- # operations, and does not have to hold, in some cases. This
- # comes from the fact that logical operations (e.g. __eq__(x,y))
- # are not differentiable for many usual cases. For instance, it
- # is desirable to have x == x for x = n+/-e, whatever the size of e.
- # Furthermore, n+/-e != n+/-e', if e != e', whatever the size of e or
- # e'.
-
- # (3) The result of logical operators does not have to be a
- # function with derivatives, as these derivatives are either 0 or
- # don't exist (i.e., the user should probably not rely on
- # derivatives for his code).
-
- # __eq__ is used in "if data in [None, ()]", for instance. It is
- # therefore important to be able to handle this case too, which is
- # taken care of when _force_aff_func_args(_eq_on_aff_funcs)
- # returns NotImplemented.
- __eq__ = _force_aff_func_args(_eq_on_aff_funcs)
-
- __ne__ = _force_aff_func_args(_ne_on_aff_funcs)
- __gt__ = _force_aff_func_args(_gt_on_aff_funcs)
-
- # __ge__ is not the opposite of __lt__ because these operators do
- # not always yield a boolean (for instance, 0 <= numpy.arange(10)
- # yields an array).
- __ge__ = _force_aff_func_args(_ge_on_aff_funcs)
-
- __lt__ = _force_aff_func_args(_lt_on_aff_funcs)
- __le__ = _force_aff_func_args(_le_on_aff_funcs)
-
- ########################################
-
- # Uncertainties handling:
-
- def error_components(self):
- """
- Individual components of the standard deviation of the affine
- function (in absolute value), returned as a dictionary with
- Variable objects as keys.
-
- This method assumes that the derivatives contained in the
- object take scalar values (and are not a tuple, like what
- math.frexp() returns, for instance).
- """
-
- # Calculation of the variance:
- error_components = {}
- for (variable, derivative) in self.derivatives.items():
- # Individual standard error due to variable:
- error_components[variable] = abs(derivative*variable._std_dev)
-
- return error_components
-
- def std_dev(self):
- """
- Standard deviation of the affine function.
-
- This method assumes that the function returns scalar results.
-
- This returned standard deviation depends on the current
- standard deviations [std_dev()] of the variables (Variable
- objects) involved.
- """
- #! It would be possible to not allow the user to update the
- #std dev of Variable objects, in which case AffineScalarFunc
- #objects could have a pre-calculated or, better, cached
- #std_dev value (in fact, many intermediate AffineScalarFunc do
- #not need to have their std_dev calculated: only the final
- #AffineScalarFunc returned to the user does).
- return sqrt(sum(
- delta**2 for delta in self.error_components().values()))
-
- def _general_representation(self, to_string):
- """
- Uses the to_string() conversion function on both the nominal
- value and the standard deviation, and returns a string that
- describes them.
-
- to_string() is typically repr() or str().
- """
-
- (nominal_value, std_dev) = (self._nominal_value, self.std_dev())
-
- # String representation:
-
- # Not putting spaces around "+/-" helps with arrays of
- # Variable, as each value with an uncertainty is a
- # block of signs (otherwise, the standard deviation can be
- # mistaken for another element of the array).
-
- return ("%s+/-%s" % (to_string(nominal_value), to_string(std_dev))
- if std_dev
- else to_string(nominal_value))
-
- def __repr__(self):
- return self._general_representation(repr)
-
- def __str__(self):
- return self._general_representation(str)
-
- def std_score(self, value):
- """
- Returns 'value' - nominal value, in units of the standard
- deviation.
-
- Raises a ValueError exception if the standard deviation is zero.
- """
- try:
- # The ._nominal_value is a float: there is no integer division,
- # here:
- return (value - self._nominal_value) / self.std_dev()
- except ZeroDivisionError:
- raise ValueError("The standard deviation is zero:"
- " undefined result.")
-
- def __deepcopy__(self, memo):
- """
- Hook for the standard copy module.
-
- The returned AffineScalarFunc is a completely fresh copy,
- which is fully independent of any variable defined so far.
- New variables are specially created for the returned
- AffineScalarFunc object.
- """
- return AffineScalarFunc(
- self._nominal_value,
- dict((copy.deepcopy(var), deriv)
- for (var, deriv) in self.derivatives.items()))
-
- def __getstate__(self):
- """
- Hook for the pickle module.
- """
- obj_slot_values = dict((k, getattr(self, k)) for k in
- # self.__slots__ would not work when
- # self is an instance of a subclass:
- AffineScalarFunc.__slots__)
- return obj_slot_values
-
- def __setstate__(self, data_dict):
- """
- Hook for the pickle module.
- """
- for (name, value) in data_dict.items():
- setattr(self, name, value)
-
-# Nicer name, for users: isinstance(ufloat(...), UFloat) is True:
-UFloat = AffineScalarFunc
-
-def get_ops_with_reflection():
-
- """
- Returns operators with a reflection, along with their derivatives
- (for float operands).
- """
-
- # Operators with a reflection:
-
- # We do not include divmod(). This operator could be included, by
- # allowing its result (a tuple) to be differentiated, in
- # derivative_value(). However, a similar result can be achieved
- # by the user by calculating separately the division and the
- # result.
-
- # {operator(x, y): (derivative wrt x, derivative wrt y)}:
-
- # Note that unknown partial derivatives can be numerically
- # calculated by expressing them as something like
- # "partial_derivative(float.__...__, 1)(x, y)":
-
- # String expressions are used, so that reversed operators are easy
- # to code, and execute relatively efficiently:
-
- derivatives_list = {
- 'add': ("1.", "1."),
- # 'div' is the '/' operator when __future__.division is not in
- # effect. Since '/' is applied to
- # AffineScalarFunc._nominal_value numbers, it is applied on
- # floats, and is therefore the "usual" mathematical division.
- 'div': ("1/y", "-x/y**2"),
- 'floordiv': ("0.", "0."), # Non exact: there is a discontinuities
- # The derivative wrt the 2nd arguments is something like (..., x//y),
- # but it is calculated numerically, for convenience:
- 'mod': ("1.", "partial_derivative(float.__mod__, 1)(x, y)"),
- 'mul': ("y", "x"),
- 'pow': ("y*x**(y-1)", "log(x)*x**y"),
- 'sub': ("1.", "-1."),
- 'truediv': ("1/y", "-x/y**2")
- }
-
- # Conversion to Python functions:
- ops_with_reflection = {}
- for (op, derivatives) in derivatives_list.items():
- ops_with_reflection[op] = [
- eval("lambda x, y: %s" % expr) for expr in derivatives ]
-
- ops_with_reflection["r"+op] = [
- eval("lambda y, x: %s" % expr) for expr in reversed(derivatives)]
-
- return ops_with_reflection
-
-# Operators that have a reflection, along with their derivatives:
-_ops_with_reflection = get_ops_with_reflection()
-
-# Some effectively modified operators (for the automated tests):
-_modified_operators = []
-_modified_ops_with_reflection = []
-
-def add_operators_to_AffineScalarFunc():
- """
- Adds many operators (__add__, etc.) to the AffineScalarFunc class.
- """
-
- ########################################
-
- #! Derivatives are set to return floats. For one thing,
- # uncertainties generally involve floats, as they are based on
- # small variations of the parameters. It is also better to
- # protect the user from unexpected integer result that behave
- # badly with the division.
-
- ## Operators that return a numerical value:
-
- # Single-argument operators that should be adapted from floats to
- # AffineScalarFunc objects, associated to their derivative:
- simple_numerical_operators_derivatives = {
- 'abs': lambda x: 1. if x>=0 else -1.,
- 'neg': lambda x: -1.,
- 'pos': lambda x: 1.,
- 'trunc': lambda x: 0.
- }
-
- for (op, derivative) in (
- simple_numerical_operators_derivatives.items()):
-
- attribute_name = "__%s__" % op
- # float objects don't exactly have the same attributes between
- # different versions of Python (for instance, __trunc__ was
- # introduced with Python 2.6):
- try:
- setattr(AffineScalarFunc, attribute_name,
- wrap(getattr(float, attribute_name),
- [derivative]))
- except AttributeError:
- pass
- else:
- _modified_operators.append(op)
-
- ########################################
-
- # Reversed versions (useful for float*AffineScalarFunc, for instance):
- for (op, derivatives) in _ops_with_reflection.items():
- attribute_name = '__%s__' % op
- # float objects don't exactly have the same attributes between
- # different versions of Python (for instance, __div__ and
- # __rdiv__ were removed, in Python 3):
- try:
- setattr(AffineScalarFunc, attribute_name,
- wrap(getattr(float, attribute_name), derivatives))
- except AttributeError:
- pass
- else:
- _modified_ops_with_reflection.append(op)
-
- ########################################
- # Conversions to pure numbers are meaningless. Note that the
- # behavior of float(1j) is similar.
- for coercion_type in ('complex', 'int', 'long', 'float'):
- def raise_error(self):
- raise TypeError("can't convert an affine function (%s)"
- ' to %s; use x.nominal_value'
- # In case AffineScalarFunc is sub-classed:
- % (self.__class__, coercion_type))
-
- setattr(AffineScalarFunc, '__%s__' % coercion_type, raise_error)
-
-add_operators_to_AffineScalarFunc() # Actual addition of class attributes
-
-class Variable(AffineScalarFunc):
- """
- Representation of a float-like scalar random variable, along with
- its uncertainty.
-
- Objects are meant to represent variables that are independent from
- each other (correlations are handled through the AffineScalarFunc
- class).
- """
-
- # To save memory in large arrays:
- __slots__ = ('_std_dev', 'tag')
-
- def __init__(self, value, std_dev, tag=None):
- """
- The nominal value and the standard deviation of the variable
- are set. These values must be scalars.
-
- 'tag' is a tag that the user can associate to the variable. This
- is useful for tracing variables.
-
- The meaning of the nominal value is described in the main
- module documentation.
- """
-
- #! The value, std_dev, and tag are assumed by __copy__() not to
- # be copied. Either this should be guaranteed here, or __copy__
- # should be updated.
-
- # Only float-like values are handled. One reason is that the
- # division operator on integers would not produce a
- # differentiable functions: for instance, Variable(3, 0.1)/2
- # has a nominal value of 3/2 = 1, but a "shifted" value
- # of 3.1/2 = 1.55.
- value = float(value)
-
- # If the variable changes by dx, then the value of the affine
- # function that gives its value changes by 1*dx:
-
- # ! Memory cycles are created. However, they are garbage
- # collected, if possible. Using a weakref.WeakKeyDictionary
- # takes much more memory. Thus, this implementation chooses
- # more cycles and a smaller memory footprint instead of no
- # cycles and a larger memory footprint.
-
- # ! Using AffineScalarFunc instead of super() results only in
- # a 3 % speed loss (Python 2.6, Mac OS X):
- super(Variable, self).__init__(value, {self: 1.})
-
- # We force the error to be float-like. Since it is considered
- # as a Gaussian standard deviation, it is semantically
- # positive (even though there would be no problem defining it
- # as a sigma, where sigma can be negative and still define a
- # Gaussian):
-
- assert std_dev >= 0, "the error must be a positive number"
- # Since AffineScalarFunc.std_dev is a property, we cannot do
- # "self.std_dev = ...":
- self._std_dev = std_dev
-
- self.tag = tag
-
- # Standard deviations can be modified (this is a feature).
- # AffineScalarFunc objects that depend on the Variable have their
- # std_dev() automatically modified (recalculated with the new
- # std_dev of their Variables):
- def set_std_dev(self, value):
- """
- Updates the standard deviation of the variable to a new value.
- """
-
- # A zero variance is accepted. Thus, it is possible to
- # conveniently use infinitely precise variables, for instance
- # to study special cases.
-
- self._std_dev = value
-
- # The following method is overridden so that we can represent the tag:
- def _general_representation(self, to_string):
- """
- Uses the to_string() conversion function on both the nominal
- value and standard deviation and returns a string that
- describes the number.
-
- to_string() is typically repr() or str().
- """
- num_repr = super(Variable, self)._general_representation(to_string)
-
- # Optional tag: only full representations (to_string == repr)
- # contain the tag, as the tag is required in order to recreate
- # the variable. Outputting the tag for regular string ("print
- # x") would be too heavy and produce an unusual representation
- # of a number with uncertainty.
- return (num_repr if ((self.tag is None) or (to_string != repr))
- else "< %s = %s >" % (self.tag, num_repr))
-
- def __hash__(self):
- # All Variable objects are by definition independent
- # variables, so they never compare equal; therefore, their
- # id() are therefore allowed to differ
- # (http://docs.python.org/reference/datamodel.html#object.__hash__):
- return id(self)
-
- def __copy__(self):
- """
- Hook for the standard copy module.
- """
-
- # This copy implicitly takes care of the reference of the
- # variable to itself (in self.derivatives): the new Variable
- # object points to itself, not to the original Variable.
-
- # Reference: http://www.doughellmann.com/PyMOTW/copy/index.html
-
- #! The following assumes that the arguments to Variable are
- # *not* copied upon construction, since __copy__ is not supposed
- # to copy "inside" information:
- return Variable(self.nominal_value, self.std_dev(), self.tag)
-
- def __deepcopy__(self, memo):
- """
- Hook for the standard copy module.
-
- A new variable is created.
- """
-
- # This deep copy implicitly takes care of the reference of the
- # variable to itself (in self.derivatives): the new Variable
- # object points to itself, not to the original Variable.
-
- # Reference: http://www.doughellmann.com/PyMOTW/copy/index.html
-
- return self.__copy__()
-
- def __getstate__(self):
- """
- Hook for the standard pickle module.
- """
- obj_slot_values = dict((k, getattr(self, k)) for k in self.__slots__)
- obj_slot_values.update(AffineScalarFunc.__getstate__(self))
- # Conversion to a usual dictionary:
- return obj_slot_values
-
- def __setstate__(self, data_dict):
- """
- Hook for the standard pickle module.
- """
- for (name, value) in data_dict.items():
- setattr(self, name, value)
-
-###############################################################################
-
-# Utilities
-
-def nominal_value(x):
- """
- Returns the nominal value of x if it is a quantity with
- uncertainty (i.e., an AffineScalarFunc object); otherwise, returns
- x unchanged.
-
- This utility function is useful for transforming a series of
- numbers, when only some of them generally carry an uncertainty.
- """
-
- return x.nominal_value if isinstance(x, AffineScalarFunc) else x
-
-def std_dev(x):
- """
- Returns the standard deviation of x if it is a quantity with
- uncertainty (i.e., an AffineScalarFunc object); otherwise, returns
- the float 0.
-
- This utility function is useful for transforming a series of
- numbers, when only some of them generally carry an uncertainty.
- """
-
- return x.std_dev() if isinstance(x, AffineScalarFunc) else 0.
-
-def covariance_matrix(nums_with_uncert):
- """
- Returns a matrix that contains the covariances between the given
- sequence of numbers with uncertainties (AffineScalarFunc objects).
- The resulting matrix implicitly depends on their ordering in
- 'nums_with_uncert'.
-
- The covariances are floats (never int objects).
-
- The returned covariance matrix is the exact linear approximation
- result, if the nominal values of the numbers with uncertainties
- and of their variables are their mean. Otherwise, the returned
- covariance matrix should be close to its linear approximation
- value.
-
- The returned matrix is a list of lists.
- """
- # See PSI.411 in EOL's notes.
-
- covariance_matrix = []
- for (i1, expr1) in enumerate(nums_with_uncert):
- derivatives1 = expr1.derivatives # Optimization
- vars1 = set(derivatives1)
- coefs_expr1 = []
- for (i2, expr2) in enumerate(nums_with_uncert[:i1+1]):
- derivatives2 = expr2.derivatives # Optimization
- coef = 0.
- for var in vars1.intersection(derivatives2):
- # var is a variable common to both numbers with
- # uncertainties:
- coef += (derivatives1[var]*derivatives2[var]*var._std_dev**2)
- coefs_expr1.append(coef)
- covariance_matrix.append(coefs_expr1)
-
- # We symmetrize the matrix:
- for (i, covariance_coefs) in enumerate(covariance_matrix):
- covariance_coefs.extend(covariance_matrix[j][i]
- for j in range(i+1, len(covariance_matrix)))
-
- return covariance_matrix
-
-try:
- import numpy
-except ImportError:
- pass
-else:
- def correlation_matrix(nums_with_uncert):
- '''
- Returns the correlation matrix of the given sequence of
- numbers with uncertainties, as a NumPy array of floats.
- '''
-
- cov_mat = numpy.array(covariance_matrix(nums_with_uncert))
-
- std_devs = numpy.sqrt(cov_mat.diagonal())
-
- return cov_mat/std_devs/std_devs[numpy.newaxis].T
-
- __all__.append('correlation_matrix')
-
-###############################################################################
-# Parsing of values with uncertainties:
-
-POSITIVE_DECIMAL_UNSIGNED = r'(\d+)(\.\d*)?'
-
-# Regexp for a number with uncertainty (e.g., "-1.234(2)e-6"), where the
-# uncertainty is optional (in which case the uncertainty is implicit):
-NUMBER_WITH_UNCERT_RE_STR = '''
- ([+-])? # Sign
- %s # Main number
- (?:\(%s\))? # Optional uncertainty
- ([eE][+-]?\d+)? # Optional exponent
- ''' % (POSITIVE_DECIMAL_UNSIGNED, POSITIVE_DECIMAL_UNSIGNED)
-
-NUMBER_WITH_UNCERT_RE = re.compile(
- "^%s$" % NUMBER_WITH_UNCERT_RE_STR, re.VERBOSE)
-
-def parse_error_in_parentheses(representation):
- """
- Returns (value, error) from a string representing a number with
- uncertainty like 12.34(5), 12.34(142), 12.5(3.4) or 12.3(4.2)e3.
- If no parenthesis is given, an uncertainty of one on the last
- digit is assumed.
-
- Raises ValueError if the string cannot be parsed.
- """
-
- match = NUMBER_WITH_UNCERT_RE.search(representation)
-
- if match:
- # The 'main' part is the nominal value, with 'int'eger part, and
- # 'dec'imal part. The 'uncert'ainty is similarly broken into its
- # integer and decimal parts.
- (sign, main_int, main_dec, uncert_int, uncert_dec,
- exponent) = match.groups()
- else:
- raise ValueError("Unparsable number representation: '%s'."
- " Was expecting a string of the form 1.23(4)"
- " or 1.234" % representation)
-
- # The value of the number is its nominal value:
- value = float(''.join((sign or '',
- main_int,
- main_dec or '.0',
- exponent or '')))
-
- if uncert_int is None:
- # No uncertainty was found: an uncertainty of 1 on the last
- # digit is assumed:
- uncert_int = '1'
-
- # Do we have a fully explicit uncertainty?
- if uncert_dec is not None:
- uncert = float("%s%s" % (uncert_int, uncert_dec or ''))
- else:
- # uncert_int represents an uncertainty on the last digits:
-
- # The number of digits after the period defines the power of
- # 10 than must be applied to the provided uncertainty:
- num_digits_after_period = (0 if main_dec is None
- else len(main_dec)-1)
- uncert = int(uncert_int)/10**num_digits_after_period
-
- # We apply the exponent to the uncertainty as well:
- uncert *= float("1%s" % (exponent or ''))
-
- return (value, uncert)
-
-
-# The following function is not exposed because it can in effect be
-# obtained by doing x = ufloat(representation) and
-# x.nominal_value and x.std_dev():
-def str_to_number_with_uncert(representation):
- """
- Given a string that represents a number with uncertainty, returns the
- nominal value and the uncertainty.
-
- The string can be of the form:
- - 124.5+/-0.15
- - 124.50(15)
- - 124.50(123)
- - 124.5
-
- When no numerical error is given, an uncertainty of 1 on the last
- digit is implied.
-
- Raises ValueError if the string cannot be parsed.
- """
-
- try:
- # Simple form 1234.45+/-1.2:
- (value, uncert) = representation.split('+/-')
- except ValueError:
- # Form with parentheses or no uncertainty:
- parsed_value = parse_error_in_parentheses(representation)
- else:
- try:
- parsed_value = (float(value), float(uncert))
- except ValueError:
- raise ValueError('Cannot parse %s: was expecting a number'
- ' like 1.23+/-0.1' % representation)
-
- return parsed_value
-
-def ufloat(representation, tag=None):
- """
- Returns a random variable (Variable object).
-
- Converts the representation of a number into a number with
- uncertainty (a random variable, defined by a nominal value and
- a standard deviation).
-
- The representation can be a (value, standard deviation) sequence,
- or a string.
-
- Strings of the form '12.345+/-0.015', '12.345(15)', or '12.3' are
- recognized (see full list below). In the last case, an
- uncertainty of +/-1 is assigned to the last digit.
-
- 'tag' is an optional string tag for the variable. Variables
- don't have to have distinct tags. Tags are useful for tracing
- what values (and errors) enter in a given result (through the
- error_components() method).
-
- Examples of valid string representations:
-
- -1.23(3.4)
- -1.34(5)
- 1(6)
- 3(4.2)
- -9(2)
- 1234567(1.2)
- 12.345(15)
- -12.3456(78)e-6
- 12.3(0.4)e-5
- 0.29
- 31.
- -31.
- 31
- -3.1e10
- 169.0(7)
- 169.1(15)
- """
-
- # This function is somewhat optimized so as to help with the
- # creation of lots of Variable objects (through unumpy.uarray, for
- # instance).
-
- # representations is "normalized" so as to be a valid sequence of
- # 2 arguments for Variable().
-
- #! Accepting strings and any kind of sequence slows down the code
- # by about 5 %. On the other hand, massive initializations of
- # numbers with uncertainties are likely to be performed with
- # unumpy.uarray, which does not support parsing from strings and
- # thus does not have any overhead.
-
- #! Different, in Python 3:
- if isinstance(representation, basestring):
- representation = str_to_number_with_uncert(representation)
-
- #! The tag is forced to be a string, so that the user does not
- # create a Variable(2.5, 0.5) in order to represent 2.5 +/- 0.5.
- # Forcing 'tag' to be a string prevents numerical uncertainties
- # from being considered as tags, here:
- if tag is not None:
- #! 'unicode' is removed in Python3:
- assert isinstance(tag, (str, unicode)), "The tag can only be a string."
-
- #! The special ** syntax is for Python 2.5 and before (Python 2.6+
- # understands tag=tag):
- return Variable(*representation, **{'tag': tag})
-
+#!! Whenever the documentation below is updated, setup.py should be +# checked for consistency. + +''' +Calculations with full error propagation for quantities with uncertainties. +Derivatives can also be calculated. + +Web user guide: http://packages.python.org/uncertainties/. + +Example of possible calculation: (0.2 +/- 0.01)**2 = 0.04 +/- 0.004. + +Correlations between expressions are correctly taken into account (for +instance, with x = 0.2+/-0.01, 2*x-x-x is exactly zero, as is y-x-x +with y = 2*x). + +Examples: + + import uncertainties + from uncertainties import ufloat + from uncertainties.umath import * # sin(), etc. + + # Mathematical operations: + x = ufloat((0.20, 0.01)) # x = 0.20+/-0.01 + x = ufloat("0.20+/-0.01") # Other representation + x = ufloat("0.20(1)") # Other representation + x = ufloat("0.20") # Implicit uncertainty of +/-1 on the last digit + print x**2 # Square: prints "0.04+/-0.004" + print sin(x**2) # Prints "0.0399...+/-0.00399..." + + print x.std_score(0.17) # Prints "-3.0": deviation of -3 sigmas + + # Access to the nominal value, and to the uncertainty: + square = x**2 # Square + print square # Prints "0.04+/-0.004" + print square.nominal_value # Prints "0.04" + print square.std_dev() # Prints "0.004..." + + print square.derivatives[x] # Partial derivative: 0.4 (= 2*0.20) + + # Correlations: + u = ufloat((1, 0.05), "u variable") # Tag + v = ufloat((10, 0.1), "v variable") + sum_value = u+v + + u.set_std_dev(0.1) # Standard deviations can be updated on the fly + print sum_value - u - v # Prints "0.0" (exact result) + + # List of all sources of error: + print sum_value # Prints "11+/-0.1414..." + for (var, error) in sum_value.error_components().items(): + print "%s: %f" % (var.tag, error) # Individual error components + + # Covariance matrices: + cov_matrix = uncertainties.covariance_matrix([u, v, sum_value]) + print cov_matrix # 3x3 matrix + + # Correlated variables can be constructed from a covariance matrix, if + # NumPy is available: + (u2, v2, sum2) = uncertainties.correlated_values([1, 10, 11], + cov_matrix) + print u2 # Value and uncertainty of u: correctly recovered (1+/-0.1) + print uncertainties.covariance_matrix([u2, v2, sum2]) # == cov_matrix + +- The main function provided by this module is ufloat, which creates +numbers with uncertainties (Variable objects). Variable objects can +be used as if they were regular Python numbers. The main attributes +and methods of Variable objects are defined in the documentation of +the Variable class. + +- Valid operations on numbers with uncertainties include basic +mathematical functions (addition, etc.). + +Most operations from the standard math module (sin, etc.) can be applied +on numbers with uncertainties by using their generalization from the +uncertainties.umath module: + + from uncertainties.umath import sin + print sin(ufloat("1+/-0.01")) # 0.841...+/-0.005... + print sin(1) # umath.sin() also works on floats, exactly like math.sin() + +Logical operations (>, ==, etc.) are also supported. + +Basic operations on NumPy arrays or matrices of numbers with +uncertainties can be performed: + + 2*numpy.array([ufloat((1, 0.01)), ufloat((2, 0.1))]) + +More complex operations on NumPy arrays can be performed through the +dedicated uncertainties.unumpy sub-module (see its documentation). + +Calculations that are performed through non-Python code (Fortran, C, +etc.) can handle numbers with uncertainties instead of floats through +the provided wrap() wrapper: + + import uncertainties + + # wrapped_f is a version of f that can take arguments with + # uncertainties, even if f only takes floats: + wrapped_f = uncertainties.wrap(f) + +If some derivatives of the wrapped function f are known (analytically, +or numerically), they can be given to wrap()--see the documentation +for wrap(). + +- Utility functions are also provided: the covariance matrix between +random variables can be calculated with covariance_matrix(), or used +as input for the definition of correlated quantities (correlated_values() +function--defined only if the NumPy module is available). + +- Mathematical expressions involving numbers with uncertainties +generally return AffineScalarFunc objects, which also print as a value +with uncertainty. Their most useful attributes and methods are +described in the documentation for AffineScalarFunc. Note that +Variable objects are also AffineScalarFunc objects. UFloat is an +alias for AffineScalarFunc, provided as a convenience: testing whether +a value carries an uncertainty handled by this module should be done +with insinstance(my_value, UFloat). + +- Mathematically, numbers with uncertainties are, in this package, +probability distributions. These probabilities are reduced to two +numbers: a nominal value and an uncertainty. Thus, both variables +(Variable objects) and the result of mathematical operations +(AffineScalarFunc objects) contain these two values (respectively in +their nominal_value attribute and through their std_dev() method). + +The uncertainty of a number with uncertainty is simply defined in +this package as the standard deviation of the underlying probability +distribution. + +The numbers with uncertainties manipulated by this package are assumed +to have a probability distribution mostly contained around their +nominal value, in an interval of about the size of their standard +deviation. This should cover most practical cases. A good choice of +nominal value for a number with uncertainty is thus the median of its +probability distribution, the location of highest probability, or the +average value. + +- When manipulating ensembles of numbers, some of which contain +uncertainties, it can be useful to access the nominal value and +uncertainty of all numbers in a uniform manner: + + x = ufloat("3+/-0.1") + print nominal_value(x) # Prints 3 + print std_dev(x) # Prints 0.1 + print nominal_value(3) # Prints 3: nominal_value works on floats + print std_dev(3) # Prints 0: std_dev works on floats + +- Probability distributions (random variables and calculation results) +are printed as: + + nominal value +/- standard deviation + +but this does not imply any property on the nominal value (beyond the +fact that the nominal value is normally inside the region of high +probability density), or that the probability distribution of the +result is symmetrical (this is rarely strictly the case). + +- Linear approximations of functions (around the nominal values) are +used for the calculation of the standard deviation of mathematical +expressions with this package. + +The calculated standard deviations and nominal values are thus +meaningful approximations as long as the functions involved have +precise linear expansions in the region where the probability +distribution of their variables is the largest. It is therefore +important that uncertainties be small. Mathematically, this means +that the linear term of functions around the nominal values of their +variables should be much larger than the remaining higher-order terms +over the region of significant probability. + +For instance, sin(0+/-0.01) yields a meaningful standard deviation +since it is quite linear over 0+/-0.01. However, cos(0+/-0.01) yields +an approximate standard deviation of 0 (because the cosine is not well +approximated by a line around 0), which might not be precise enough +for all applications. + +- Comparison operations (>, ==, etc.) on numbers with uncertainties +have a pragmatic semantics, in this package: numbers with +uncertainties can be used wherever Python numbers are used, most of +the time with a result identical to the one that would be obtained +with their nominal value only. However, since the objects defined in +this module represent probability distributions and not pure numbers, +comparison operator are interpreted in a specific way. + +The result of a comparison operation ("==", ">", etc.) is defined so as +to be essentially consistent with the requirement that uncertainties +be small: the value of a comparison operation is True only if the +operation yields True for all infinitesimal variations of its random +variables, except, possibly, for an infinitely small number of cases. + +Example: + + "x = 3.14; y = 3.14" is such that x == y + +but + + x = ufloat((3.14, 0.01)) + y = ufloat((3.14, 0.01)) + +is not such that x == y, since x and y are independent random +variables that almost never give the same value. However, x == x +still holds. + +The boolean value (bool(x), "if x...") of a number with uncertainty x +is the result of x != 0. + +- The uncertainties package is for Python 2.5 and above. + +- This package contains tests. They can be run either manually or +automatically with the nose unit testing framework (nosetests). + +(c) 2009-2013 by Eric O. LEBIGOT (EOL) <eric.lebigot@normalesup.org>. +Please send feature requests, bug reports, or feedback to this address. + +Please support future development by donating $5 or more through PayPal! + +This software is released under a dual license. (1) The BSD license. +(2) Any other license, as long as it is obtained from the original +author.''' + +# The idea behind this module is to replace the result of mathematical +# operations by a local approximation of the defining function. For +# example, sin(0.2+/-0.01) becomes the affine function +# (AffineScalarFunc object) whose nominal value is sin(0.2) and +# whose variations are given by sin(0.2+delta) = 0.98...*delta. +# Uncertainties can then be calculated by using this local linear +# approximation of the original function. + +from __future__ import division # Many analytical derivatives depend on this + +import re +import math +from math import sqrt, log # Optimization: no attribute look-up +import copy +import warnings + +# Numerical version: +__version_info__ = (1, 9) +__version__ = '.'.join(map(str, __version_info__)) + +__author__ = 'Eric O. LEBIGOT (EOL) <eric.lebigot@normalesup.org>' + +# Attributes that are always exported (some other attributes are +# exported only if the NumPy module is available...): +__all__ = [ + + # All sub-modules and packages are not imported by default, + # in particular because NumPy might be unavailable. + 'ufloat', # Main function: returns a number with uncertainty + + # Uniform access to nominal values and standard deviations: + 'nominal_value', + 'std_dev', + + # Utility functions (more are exported if NumPy is present): + 'covariance_matrix', + + # Class for testing whether an object is a number with + # uncertainty. Not usually created by users (except through the + # Variable subclass), but possibly manipulated by external code + # ['derivatives()' method, etc.]. + 'UFloat', + + # Wrapper for allowing non-pure-Python function to handle + # quantities with uncertainties: + 'wrap', + + # The documentation for wrap() indicates that numerical + # derivatives are calculated through partial_derivative(). The + # user might also want to change the size of the numerical + # differentiation step. + 'partial_derivative' + ] + +############################################################################### + +def set_doc(doc_string): + """ + Decorator function that sets the docstring to the given text. + + It is useful for functions whose docstring is calculated + (including string substitutions). + """ + def set_doc_string(func): + func.__doc__ = doc_string + return func + return set_doc_string + +# Some types known to not depend on Variable objects are put in +# CONSTANT_TYPES. The most common types can be put in front, as this +# may slightly improve the execution speed. +CONSTANT_TYPES = (float, int, complex) # , long) + +############################################################################### +# Utility for issuing deprecation warnings + +def deprecation(message): + ''' + Warns the user with the given message, by issuing a + DeprecationWarning. + ''' + warnings.warn(message, DeprecationWarning, stacklevel=2) + + +############################################################################### + +## Definitions that depend on the availability of NumPy: + + +try: + import numpy +except ImportError: + pass +else: + + # NumPy numbers do not depend on Variable objects: + CONSTANT_TYPES += (numpy.number,) + + # Entering variables as a block of correlated values. Only available + # if NumPy is installed. + + #! It would be possible to dispense with NumPy, but a routine should be + # written for obtaining the eigenvectors of a symmetric matrix. See + # for instance Numerical Recipes: (1) reduction to tri-diagonal + # [Givens or Householder]; (2) QR / QL decomposition. + + def correlated_values(nom_values, covariance_mat, tags=None): + """ + Returns numbers with uncertainties (AffineScalarFunc objects) + that correctly reproduce the given covariance matrix, and have + the given (float) values as their nominal value. + + The correlated_values_norm() function returns the same result, + but takes a correlation matrix instead of a covariance matrix. + + The list of values and the covariance matrix must have the + same length, and the matrix must be a square (symmetric) one. + + The numbers with uncertainties returned depend on newly + created, independent variables (Variable objects). + + If 'tags' is not None, it must list the tag of each new + independent variable. + + nom_values -- sequence with the nominal (real) values of the + numbers with uncertainties to be returned. + + covariance_mat -- full covariance matrix of the returned + numbers with uncertainties (not the statistical correlation + matrix, i.e., not the normalized covariance matrix). For + example, the first element of this matrix is the variance of + the first returned number with uncertainty. + """ + + # If no tags were given, we prepare tags for the newly created + # variables: + if tags is None: + tags = (None,) * len(nom_values) + + # The covariance matrix is diagonalized in order to define + # the independent variables that model the given values: + + (variances, transform) = numpy.linalg.eigh(covariance_mat) + + # Numerical errors might make some variances negative: we set + # them to zero: + variances[variances < 0] = 0. + + # Creation of new, independent variables: + + # We use the fact that the eigenvectors in 'transform' are + # special: 'transform' is unitary: its inverse is its transpose: + + variables = tuple( + # The variables represent "pure" uncertainties: + Variable(0, sqrt(variance), tag) + for (variance, tag) in zip(variances, tags)) + + # Representation of the initial correlated values: + values_funcs = tuple( + AffineScalarFunc(value, dict(zip(variables, coords))) + for (coords, value) in zip(transform, nom_values)) + + return values_funcs + + __all__.append('correlated_values') + + def correlated_values_norm(values_with_std_dev, correlation_mat, + tags=None): + ''' + Returns correlated values like correlated_values(), but takes + instead as input: + + - nominal (float) values along with their standard deviation, and + + - a correlation matrix (i.e. a normalized covariance matrix + normalized with individual standard deviations). + + values_with_std_dev -- sequence of (nominal value, standard + deviation) pairs. The returned, correlated values have these + nominal values and standard deviations. + + correlation_mat -- correlation matrix (i.e. the normalized + covariance matrix, a matrix with ones on its diagonal). + ''' + + (nominal_values, std_devs) = numpy.transpose(values_with_std_dev) + + return correlated_values( + nominal_values, + correlation_mat*std_devs*std_devs[numpy.newaxis].T, + tags) + + __all__.append('correlated_values_norm') + +############################################################################### + +# Mathematical operations with local approximations (affine scalar +# functions) + +class NotUpcast(Exception): + 'Raised when an object cannot be converted to a number with uncertainty' + +def to_affine_scalar(x): + """ + Transforms x into a constant affine scalar function + (AffineScalarFunc), unless it is already an AffineScalarFunc (in + which case x is returned unchanged). + + Raises an exception unless 'x' belongs to some specific classes of + objects that are known not to depend on AffineScalarFunc objects + (which then cannot be considered as constants). + """ + + if isinstance(x, AffineScalarFunc): + return x + + #! In Python 2.6+, numbers.Number could be used instead, here: + if isinstance(x, CONSTANT_TYPES): + # No variable => no derivative to define: + return AffineScalarFunc(x, {}) + + # Case of lists, etc. + raise NotUpcast("%s cannot be converted to a number with" + " uncertainty" % type(x)) + +def partial_derivative(f, param_num): + """ + Returns a function that numerically calculates the partial + derivative of function f with respect to its argument number + param_num. + + The step parameter represents the shift of the parameter used in + the numerical approximation. + """ + + def partial_derivative_of_f(*args, **kws): + """ + Partial derivative, calculated with the (-epsilon, +epsilon) + method, which is more precise than the (0, +epsilon) method. + """ + # f_nominal_value = f(*args) + param_kw = None + if '__param__kw__' in kws: + param_kw = kws.pop('__param__kw__') + shifted_args = list(args) # Copy, and conversion to a mutable + shifted_kws = {} + for k, v in kws.items(): + shifted_kws[k] = v + step = 1.e-8 + if param_kw in shifted_kws: + step = step*abs(shifted_kws[param_kw]) + elif param_num < len(shifted_args): + # The step is relative to the parameter being varied, so that + # shsifting it does not suffer from finite precision: + step = step*abs(shifted_args[param_num]) + + if param_kw in shifted_kws: + shifted_kws[param_kw] += step + elif param_num < len(shifted_args): + shifted_args[param_num] += step + + shifted_f_plus = f(*shifted_args, **shifted_kws) + + if param_kw in shifted_kws: + shifted_kws[param_kw] -= 2*step + elif param_num < len(shifted_args): + shifted_args[param_num] -= 2*step + shifted_f_minus = f(*shifted_args, **shifted_kws) + + return (shifted_f_plus - shifted_f_minus)/2/step + + return partial_derivative_of_f + +class NumericalDerivatives(object): + """ + Convenient access to the partial derivatives of a function, + calculated numerically. + """ + # This is not a list because the number of arguments of the + # function is not known in advance, in general. + + def __init__(self, function): + """ + 'function' is the function whose derivatives can be computed. + """ + self._function = function + + def __getitem__(self, n): + """ + Returns the n-th numerical derivative of the function. + """ + return partial_derivative(self._function, n) + +def wrap(f, derivatives_iter=None): + """ + Wraps a function f into a function that also accepts numbers with + uncertainties (UFloat objects) and returns a number with + uncertainties. Doing so may be necessary when function f cannot + be expressed analytically (with uncertainties-compatible operators + and functions like +, *, umath.sin(), etc.). + + f must return a scalar (not a list, etc.). + + In the wrapped function, the standard Python scalar arguments of f + (float, int, etc.) can be replaced by numbers with + uncertainties. The result will contain the appropriate + uncertainty. + + If no argument to the wrapped function has an uncertainty, f + simply returns its usual, scalar result. + + If supplied, derivatives_iter can be an iterable that generally + contains functions; each successive function is the partial + derivative of f with respect to the corresponding variable (one + function for each argument of f, which takes as many arguments as + f). If instead of a function, an element of derivatives_iter + contains None, then it is automatically replaced by the relevant + numerical derivative; this can be used for non-scalar arguments of + f (like string arguments). + + If derivatives_iter is None, or if derivatives_iter contains a + fixed (and finite) number of elements, then any missing derivative + is calculated numerically. + + An infinite number of derivatives can be specified by having + derivatives_iter be an infinite iterator; this can for instance + be used for specifying the derivatives of functions with a + undefined number of argument (like sum(), whose partial + derivatives all return 1). + + Example (for illustration purposes only, as + uncertainties.umath.sin() runs faster than the examples that + follow): wrap(math.sin) is a sine function that can be applied to + numbers with uncertainties. Its derivative will be calculated + numerically. wrap(math.sin, [None]) would have produced the same + result. wrap(math.sin, [math.cos]) is the same function, but with + an analytically defined derivative. + """ + + if derivatives_iter is None: + derivatives_iter = NumericalDerivatives(f) + else: + # Derivatives that are not defined are calculated numerically, + # if there is a finite number of them (the function lambda + # *args: fsum(args) has a non-defined number of arguments, as + # it just performs a sum): + try: # Is the number of derivatives fixed? + len(derivatives_iter) + except TypeError: + pass + else: + derivatives_iter = [ + partial_derivative(f, k) if derivative is None + else derivative + for (k, derivative) in enumerate(derivatives_iter)] + + #! Setting the doc string after "def f_with...()" does not + # seem to work. We define it explicitly: + @set_doc("""\ + Version of %s(...) that returns an affine approximation + (AffineScalarFunc object), if its result depends on variables + (Variable objects). Otherwise, returns a simple constant (when + applied to constant arguments). + + Warning: arguments of the function that are not AffineScalarFunc + objects must not depend on uncertainties.Variable objects in any + way. Otherwise, the dependence of the result in + uncertainties.Variable objects will be incorrect. + + Original documentation: + %s""" % (f.__name__, f.__doc__)) + def f_with_affine_output(*args, **kwargs): + # Can this function perform the calculation of an + # AffineScalarFunc (or maybe float) result? + try: + old_funcs = map(to_affine_scalar, args) + aff_funcs = [to_affine_scalar(a) for a in args] + aff_kws = kwargs + aff_varkws = [] + for key, val in kwargs.items(): + if isinstance(val, Variable): + aff_kws[key] = to_affine_scalar(val) + aff_varkws.append(key) + + except NotUpcast: + + # This function does not know how to itself perform + # calculations with non-float-like arguments (as they + # might for instance be objects whose value really changes + # if some Variable objects had different values): + + # Is it clear that we can't delegate the calculation? + + if any(isinstance(arg, AffineScalarFunc) for arg in args): + # This situation arises for instance when calculating + # AffineScalarFunc(...)*numpy.array(...). In this + # case, we must let NumPy handle the multiplication + # (which is then performed element by element): + return NotImplemented + else: + # If none of the arguments is an AffineScalarFunc, we + # can delegate the calculation to the original + # function. This can be useful when it is called with + # only one argument (as in + # numpy.log10(numpy.ndarray(...)): + return f(*args, **kwargs) + + ######################################## + # Nominal value of the constructed AffineScalarFunc: + args_values = [e.nominal_value for e in aff_funcs] + kw_values = {} + for key, val in aff_kws.items(): + kw_values[key] = val + if key in aff_varkws: + kw_values[key] = val.nominal_value + f_nominal_value = f(*args_values, **kw_values) + + ######################################## + + # List of involved variables (Variable objects): + variables = set() + for expr in aff_funcs: + variables |= set(expr.derivatives) + for vname in aff_varkws: + variables |= set(aff_kws[vname].derivatives) + ## It is sometimes useful to only return a regular constant: + + # (1) Optimization / convenience behavior: when 'f' is called + # on purely constant values (e.g., sin(2)), there is no need + # for returning a more complex AffineScalarFunc object. + + # (2) Functions that do not return a "float-like" value might + # not have a relevant representation as an AffineScalarFunc. + # This includes boolean functions, since their derivatives are + # either 0 or are undefined: they are better represented as + # Python constants than as constant AffineScalarFunc functions. + + if not variables or isinstance(f_nominal_value, bool): + return f_nominal_value + + # The result of 'f' does depend on 'variables'... + + ######################################## + + # Calculation of the derivatives with respect to the arguments + # of f (aff_funcs): + + # The chain rule is applied. This is because, in the case of + # numerical derivatives, it allows for a better-controlled + # numerical stability than numerically calculating the partial + # derivatives through '[f(x + dx, y + dy, ...) - + # f(x,y,...)]/da' where dx, dy,... are calculated by varying + # 'a'. In fact, it is numerically better to control how big + # (dx, dy,...) are: 'f' is a simple mathematical function and + # it is possible to know how precise the df/dx are (which is + # not possible with the numerical df/da calculation above). + + # We use numerical derivatives, if we don't already have a + # list of derivatives: + + #! Note that this test could be avoided by requiring the + # caller to always provide derivatives. When changing the + # functions of the math module, this would force this module + # to know about all the math functions. Another possibility + # would be to force derivatives_iter to contain, say, the + # first 3 derivatives of f. But any of these two ideas has a + # chance to break, one day... (if new functions are added to + # the math module, or if some function has more than 3 + # arguments). + + derivatives_wrt_args = [] + for (arg, derivative) in zip(aff_funcs, derivatives_iter): + derivatives_wrt_args.append(derivative(*args_values, **aff_kws) + if arg.derivatives + else 0) + + + kws_values = [] + for vname in aff_varkws: + kws_values.append( aff_kws[vname].nominal_value) + for (vname, derivative) in zip(aff_varkws, derivatives_iter): + derivatives_wrt_args.append(derivative(__param__kw__=vname, + **kw_values) + if aff_kws[vname].derivatives + else 0) + + ######################################## + # Calculation of the derivative of f with respect to all the + # variables (Variable) involved. + + # Initial value (is updated below): + derivatives_wrt_vars = dict((var, 0.) for var in variables) + + # The chain rule is used (we already have + # derivatives_wrt_args): + + for (func, f_derivative) in zip(aff_funcs, derivatives_wrt_args): + for (var, func_derivative) in func.derivatives.items(): + derivatives_wrt_vars[var] += f_derivative * func_derivative + + for (vname, f_derivative) in zip(aff_varkws, derivatives_wrt_args): + func = aff_kws[vname] + for (var, func_derivative) in func.derivatives.items(): + derivatives_wrt_vars[var] += f_derivative * func_derivative + + # The function now returns an AffineScalarFunc object: + return AffineScalarFunc(f_nominal_value, derivatives_wrt_vars) + + # It is easier to work with f_with_affine_output, which represents + # a wrapped version of 'f', when it bears the same name as 'f': + f_with_affine_output.__name__ = f.__name__ + + return f_with_affine_output + +def _force_aff_func_args(func): + """ + Takes an operator op(x, y) and wraps it. + + The constructed operator returns func(x, to_affine_scalar(y)) if y + can be upcast with to_affine_scalar(); otherwise, it returns + NotImplemented. + + Thus, func() is only called on two AffineScalarFunc objects, if + its first argument is an AffineScalarFunc. + """ + + def op_on_upcast_args(x, y): + """ + Returns %s(self, to_affine_scalar(y)) if y can be upcast + through to_affine_scalar. Otherwise returns NotImplemented. + """ % func.__name__ + + try: + y_with_uncert = to_affine_scalar(y) + except NotUpcast: + # This module does not know how to handle the comparison: + # (example: y is a NumPy array, in which case the NumPy + # array will decide that func() should be applied + # element-wise between x and all the elements of y): + return NotImplemented + else: + return func(x, y_with_uncert) + + return op_on_upcast_args + +######################################## + +# Definition of boolean operators, that assume that self and +# y_with_uncert are AffineScalarFunc. + +# The fact that uncertainties must be smalled is used, here: the +# comparison functions are supposed to be constant for most values of +# the random variables. + +# Even though uncertainties are supposed to be small, comparisons +# between 3+/-0.1 and 3.0 are handled (even though x == 3.0 is not a +# constant function in the 3+/-0.1 interval). The comparison between +# x and x is handled too, when x has an uncertainty. In fact, as +# explained in the main documentation, it is possible to give a useful +# meaning to the comparison operators, in these cases. + +def _eq_on_aff_funcs(self, y_with_uncert): + """ + __eq__ operator, assuming that both self and y_with_uncert are + AffineScalarFunc objects. + """ + difference = self - y_with_uncert + # Only an exact zero difference means that self and y are + # equal numerically: + return not(difference._nominal_value or difference.std_dev()) + +def _ne_on_aff_funcs(self, y_with_uncert): + """ + __ne__ operator, assuming that both self and y_with_uncert are + AffineScalarFunc objects. + """ + + return not _eq_on_aff_funcs(self, y_with_uncert) + +def _gt_on_aff_funcs(self, y_with_uncert): + """ + __gt__ operator, assuming that both self and y_with_uncert are + AffineScalarFunc objects. + """ + return self._nominal_value > y_with_uncert._nominal_value + +def _ge_on_aff_funcs(self, y_with_uncert): + """ + __ge__ operator, assuming that both self and y_with_uncert are + AffineScalarFunc objects. + """ + + return (_gt_on_aff_funcs(self, y_with_uncert) + or _eq_on_aff_funcs(self, y_with_uncert)) + +def _lt_on_aff_funcs(self, y_with_uncert): + """ + __lt__ operator, assuming that both self and y_with_uncert are + AffineScalarFunc objects. + """ + return self._nominal_value < y_with_uncert._nominal_value + +def _le_on_aff_funcs(self, y_with_uncert): + """ + __le__ operator, assuming that both self and y_with_uncert are + AffineScalarFunc objects. + """ + + return (_lt_on_aff_funcs(self, y_with_uncert) + or _eq_on_aff_funcs(self, y_with_uncert)) + +######################################## + +class AffineScalarFunc(object): + """ + Affine functions that support basic mathematical operations + (addition, etc.). Such functions can for instance be used for + representing the local (linear) behavior of any function. + + This class is mostly meant to be used internally. + + This class can also be used to represent constants. + + The variables of affine scalar functions are Variable objects. + + AffineScalarFunc objects include facilities for calculating the + 'error' on the function, from the uncertainties on its variables. + + Main attributes and methods: + + - nominal_value, std_dev(): value at the origin / nominal value, + and standard deviation. + + - error_components(): error_components()[x] is the error due to + Variable x. + + - derivatives: derivatives[x] is the (value of the) derivative + with respect to Variable x. This attribute is a dictionary + whose keys are the Variable objects on which the function + depends. + + All the Variable objects on which the function depends are in + 'derivatives'. + + - std_score(x): position of number x with respect to the + nominal value, in units of the standard deviation. + """ + + # To save memory in large arrays: + __slots__ = ('_nominal_value', 'derivatives') + + #! The code could be modify in order to accommodate for non-float + # nominal values. This could for instance be done through + # the operator module: instead of delegating operations to + # float.__*__ operations, they could be delegated to + # operator.__*__ functions (while taking care of properly handling + # reverse operations: __radd__, etc.). + + def __init__(self, nominal_value, derivatives): + """ + nominal_value -- value of the function at the origin. + nominal_value must not depend in any way of the Variable + objects in 'derivatives' (the value at the origin of the + function being defined is a constant). + + derivatives -- maps each Variable object on which the function + being defined depends to the value of the derivative with + respect to that variable, taken at the nominal value of all + variables. + + Warning: the above constraint is not checked, and the user is + responsible for complying with it. + """ + + # Defines the value at the origin: + + # Only float-like values are handled. One reason is that it + # does not make sense for a scalar function to be affine to + # not yield float values. Another reason is that it would not + # make sense to have a complex nominal value, here (it would + # not be handled correctly at all): converting to float should + # be possible. + self._nominal_value = float(nominal_value) + self.derivatives = derivatives + + # The following prevents the 'nominal_value' attribute from being + # modified by the user: + @property + def nominal_value(self): + "Nominal value of the random number." + return self._nominal_value + + ############################################################ + + + ### Operators: operators applied to AffineScalarFunc and/or + ### float-like objects only are supported. This is why methods + ### from float are used for implementing these operators. + + # Operators with no reflection: + + ######################################## + + # __nonzero__() is supposed to return a boolean value (it is used + # by bool()). It is for instance used for converting the result + # of comparison operators to a boolean, in sorted(). If we want + # to be able to sort AffineScalarFunc objects, __nonzero__ cannot + # return a AffineScalarFunc object. Since boolean results (such + # as the result of bool()) don't have a very meaningful + # uncertainty unless it is zero, this behavior is fine. + + def __nonzero__(self): + """ + Equivalent to self != 0. + """ + #! This might not be relevant for AffineScalarFunc objects + # that contain values in a linear space which does not convert + # the float 0 into the null vector (see the __eq__ function: + # __nonzero__ works fine if subtracting the 0 float from a + # vector of the linear space works as if 0 were the null + # vector of that space): + return self != 0. # Uses the AffineScalarFunc.__ne__ function + + ######################################## + + ## Logical operators: warning: the resulting value cannot always + ## be differentiated. + + # The boolean operations are not differentiable everywhere, but + # almost... + + # (1) I can rely on the assumption that the user only has "small" + # errors on variables, as this is used in the calculation of the + # standard deviation (which performs linear approximations): + + # (2) However, this assumption is not relevant for some + # operations, and does not have to hold, in some cases. This + # comes from the fact that logical operations (e.g. __eq__(x,y)) + # are not differentiable for many usual cases. For instance, it + # is desirable to have x == x for x = n+/-e, whatever the size of e. + # Furthermore, n+/-e != n+/-e', if e != e', whatever the size of e or + # e'. + + # (3) The result of logical operators does not have to be a + # function with derivatives, as these derivatives are either 0 or + # don't exist (i.e., the user should probably not rely on + # derivatives for his code). + + # __eq__ is used in "if data in [None, ()]", for instance. It is + # therefore important to be able to handle this case too, which is + # taken care of when _force_aff_func_args(_eq_on_aff_funcs) + # returns NotImplemented. + __eq__ = _force_aff_func_args(_eq_on_aff_funcs) + + __ne__ = _force_aff_func_args(_ne_on_aff_funcs) + __gt__ = _force_aff_func_args(_gt_on_aff_funcs) + + # __ge__ is not the opposite of __lt__ because these operators do + # not always yield a boolean (for instance, 0 <= numpy.arange(10) + # yields an array). + __ge__ = _force_aff_func_args(_ge_on_aff_funcs) + + __lt__ = _force_aff_func_args(_lt_on_aff_funcs) + __le__ = _force_aff_func_args(_le_on_aff_funcs) + + ######################################## + + # Uncertainties handling: + + def error_components(self): + """ + Individual components of the standard deviation of the affine + function (in absolute value), returned as a dictionary with + Variable objects as keys. + + This method assumes that the derivatives contained in the + object take scalar values (and are not a tuple, like what + math.frexp() returns, for instance). + """ + + # Calculation of the variance: + error_components = {} + for (variable, derivative) in self.derivatives.items(): + # Individual standard error due to variable: + error_components[variable] = abs(derivative*variable._std_dev) + + return error_components + + def std_dev(self): + """ + Standard deviation of the affine function. + + This method assumes that the function returns scalar results. + + This returned standard deviation depends on the current + standard deviations [std_dev()] of the variables (Variable + objects) involved. + """ + #! It would be possible to not allow the user to update the + #std dev of Variable objects, in which case AffineScalarFunc + #objects could have a pre-calculated or, better, cached + #std_dev value (in fact, many intermediate AffineScalarFunc do + #not need to have their std_dev calculated: only the final + #AffineScalarFunc returned to the user does). + return sqrt(sum( + delta**2 for delta in self.error_components().values())) + + def _general_representation(self, to_string): + """ + Uses the to_string() conversion function on both the nominal + value and the standard deviation, and returns a string that + describes them. + + to_string() is typically repr() or str(). + """ + + (nominal_value, std_dev) = (self._nominal_value, self.std_dev()) + + # String representation: + + # Not putting spaces around "+/-" helps with arrays of + # Variable, as each value with an uncertainty is a + # block of signs (otherwise, the standard deviation can be + # mistaken for another element of the array). + + return ("%s+/-%s" % (to_string(nominal_value), to_string(std_dev)) + if std_dev + else to_string(nominal_value)) + + def __repr__(self): + return self._general_representation(repr) + + def __str__(self): + return self._general_representation(str) + + def std_score(self, value): + """ + Returns 'value' - nominal value, in units of the standard + deviation. + + Raises a ValueError exception if the standard deviation is zero. + """ + try: + # The ._nominal_value is a float: there is no integer division, + # here: + return (value - self._nominal_value) / self.std_dev() + except ZeroDivisionError: + raise ValueError("The standard deviation is zero:" + " undefined result.") + + def __deepcopy__(self, memo): + """ + Hook for the standard copy module. + + The returned AffineScalarFunc is a completely fresh copy, + which is fully independent of any variable defined so far. + New variables are specially created for the returned + AffineScalarFunc object. + """ + return AffineScalarFunc( + self._nominal_value, + dict((copy.deepcopy(var), deriv) + for (var, deriv) in self.derivatives.items())) + + def __getstate__(self): + """ + Hook for the pickle module. + """ + obj_slot_values = dict((k, getattr(self, k)) for k in + # self.__slots__ would not work when + # self is an instance of a subclass: + AffineScalarFunc.__slots__) + return obj_slot_values + + def __setstate__(self, data_dict): + """ + Hook for the pickle module. + """ + for (name, value) in data_dict.items(): + setattr(self, name, value) + +# Nicer name, for users: isinstance(ufloat(...), UFloat) is True: +UFloat = AffineScalarFunc + +def get_ops_with_reflection(): + + """ + Returns operators with a reflection, along with their derivatives + (for float operands). + """ + + # Operators with a reflection: + + # We do not include divmod(). This operator could be included, by + # allowing its result (a tuple) to be differentiated, in + # derivative_value(). However, a similar result can be achieved + # by the user by calculating separately the division and the + # result. + + # {operator(x, y): (derivative wrt x, derivative wrt y)}: + + # Note that unknown partial derivatives can be numerically + # calculated by expressing them as something like + # "partial_derivative(float.__...__, 1)(x, y)": + + # String expressions are used, so that reversed operators are easy + # to code, and execute relatively efficiently: + + derivatives_list = { + 'add': ("1.", "1."), + # 'div' is the '/' operator when __future__.division is not in + # effect. Since '/' is applied to + # AffineScalarFunc._nominal_value numbers, it is applied on + # floats, and is therefore the "usual" mathematical division. + 'div': ("1/y", "-x/y**2"), + 'floordiv': ("0.", "0."), # Non exact: there is a discontinuities + # The derivative wrt the 2nd arguments is something like (..., x//y), + # but it is calculated numerically, for convenience: + 'mod': ("1.", "partial_derivative(float.__mod__, 1)(x, y)"), + 'mul': ("y", "x"), + 'pow': ("y*x**(y-1)", "log(x)*x**y"), + 'sub': ("1.", "-1."), + 'truediv': ("1/y", "-x/y**2") + } + + # Conversion to Python functions: + ops_with_reflection = {} + for (op, derivatives) in derivatives_list.items(): + ops_with_reflection[op] = [ + eval("lambda x, y: %s" % expr) for expr in derivatives ] + + ops_with_reflection["r"+op] = [ + eval("lambda y, x: %s" % expr) for expr in reversed(derivatives)] + + return ops_with_reflection + +# Operators that have a reflection, along with their derivatives: +_ops_with_reflection = get_ops_with_reflection() + +# Some effectively modified operators (for the automated tests): +_modified_operators = [] +_modified_ops_with_reflection = [] + +def add_operators_to_AffineScalarFunc(): + """ + Adds many operators (__add__, etc.) to the AffineScalarFunc class. + """ + + ######################################## + + #! Derivatives are set to return floats. For one thing, + # uncertainties generally involve floats, as they are based on + # small variations of the parameters. It is also better to + # protect the user from unexpected integer result that behave + # badly with the division. + + ## Operators that return a numerical value: + + # Single-argument operators that should be adapted from floats to + # AffineScalarFunc objects, associated to their derivative: + simple_numerical_operators_derivatives = { + 'abs': lambda x: 1. if x>=0 else -1., + 'neg': lambda x: -1., + 'pos': lambda x: 1., + 'trunc': lambda x: 0. + } + + for (op, derivative) in ( + simple_numerical_operators_derivatives.items()): + + attribute_name = "__%s__" % op + # float objects don't exactly have the same attributes between + # different versions of Python (for instance, __trunc__ was + # introduced with Python 2.6): + try: + setattr(AffineScalarFunc, attribute_name, + wrap(getattr(float, attribute_name), + [derivative])) + except AttributeError: + pass + else: + _modified_operators.append(op) + + ######################################## + + # Reversed versions (useful for float*AffineScalarFunc, for instance): + for (op, derivatives) in _ops_with_reflection.items(): + attribute_name = '__%s__' % op + # float objects don't exactly have the same attributes between + # different versions of Python (for instance, __div__ and + # __rdiv__ were removed, in Python 3): + try: + setattr(AffineScalarFunc, attribute_name, + wrap(getattr(float, attribute_name), derivatives)) + except AttributeError: + pass + else: + _modified_ops_with_reflection.append(op) + + ######################################## + # Conversions to pure numbers are meaningless. Note that the + # behavior of float(1j) is similar. + for coercion_type in ('complex', 'int', 'long', 'float'): + def raise_error(self): + raise TypeError("can't convert an affine function (%s)" + ' to %s; use x.nominal_value' + # In case AffineScalarFunc is sub-classed: + % (self.__class__, coercion_type)) + + setattr(AffineScalarFunc, '__%s__' % coercion_type, raise_error) + +add_operators_to_AffineScalarFunc() # Actual addition of class attributes + +class Variable(AffineScalarFunc): + """ + Representation of a float-like scalar random variable, along with + its uncertainty. + + Objects are meant to represent variables that are independent from + each other (correlations are handled through the AffineScalarFunc + class). + """ + + # To save memory in large arrays: + __slots__ = ('_std_dev', 'tag') + + def __init__(self, value, std_dev, tag=None): + """ + The nominal value and the standard deviation of the variable + are set. These values must be scalars. + + 'tag' is a tag that the user can associate to the variable. This + is useful for tracing variables. + + The meaning of the nominal value is described in the main + module documentation. + """ + + #! The value, std_dev, and tag are assumed by __copy__() not to + # be copied. Either this should be guaranteed here, or __copy__ + # should be updated. + + # Only float-like values are handled. One reason is that the + # division operator on integers would not produce a + # differentiable functions: for instance, Variable(3, 0.1)/2 + # has a nominal value of 3/2 = 1, but a "shifted" value + # of 3.1/2 = 1.55. + value = float(value) + + # If the variable changes by dx, then the value of the affine + # function that gives its value changes by 1*dx: + + # ! Memory cycles are created. However, they are garbage + # collected, if possible. Using a weakref.WeakKeyDictionary + # takes much more memory. Thus, this implementation chooses + # more cycles and a smaller memory footprint instead of no + # cycles and a larger memory footprint. + + # ! Using AffineScalarFunc instead of super() results only in + # a 3 % speed loss (Python 2.6, Mac OS X): + super(Variable, self).__init__(value, {self: 1.}) + + # We force the error to be float-like. Since it is considered + # as a Gaussian standard deviation, it is semantically + # positive (even though there would be no problem defining it + # as a sigma, where sigma can be negative and still define a + # Gaussian): + + assert std_dev >= 0, "the error must be a positive number" + # Since AffineScalarFunc.std_dev is a property, we cannot do + # "self.std_dev = ...": + self._std_dev = std_dev + + self.tag = tag + + # Standard deviations can be modified (this is a feature). + # AffineScalarFunc objects that depend on the Variable have their + # std_dev() automatically modified (recalculated with the new + # std_dev of their Variables): + def set_std_dev(self, value): + """ + Updates the standard deviation of the variable to a new value. + """ + + # A zero variance is accepted. Thus, it is possible to + # conveniently use infinitely precise variables, for instance + # to study special cases. + + self._std_dev = value + + # The following method is overridden so that we can represent the tag: + def _general_representation(self, to_string): + """ + Uses the to_string() conversion function on both the nominal + value and standard deviation and returns a string that + describes the number. + + to_string() is typically repr() or str(). + """ + num_repr = super(Variable, self)._general_representation(to_string) + + # Optional tag: only full representations (to_string == repr) + # contain the tag, as the tag is required in order to recreate + # the variable. Outputting the tag for regular string ("print + # x") would be too heavy and produce an unusual representation + # of a number with uncertainty. + return (num_repr if ((self.tag is None) or (to_string != repr)) + else "< %s = %s >" % (self.tag, num_repr)) + + def __hash__(self): + # All Variable objects are by definition independent + # variables, so they never compare equal; therefore, their + # id() are therefore allowed to differ + # (http://docs.python.org/reference/datamodel.html#object.__hash__): + return id(self) + + def __copy__(self): + """ + Hook for the standard copy module. + """ + + # This copy implicitly takes care of the reference of the + # variable to itself (in self.derivatives): the new Variable + # object points to itself, not to the original Variable. + + # Reference: http://www.doughellmann.com/PyMOTW/copy/index.html + + #! The following assumes that the arguments to Variable are + # *not* copied upon construction, since __copy__ is not supposed + # to copy "inside" information: + return Variable(self.nominal_value, self.std_dev(), self.tag) + + def __deepcopy__(self, memo): + """ + Hook for the standard copy module. + + A new variable is created. + """ + + # This deep copy implicitly takes care of the reference of the + # variable to itself (in self.derivatives): the new Variable + # object points to itself, not to the original Variable. + + # Reference: http://www.doughellmann.com/PyMOTW/copy/index.html + + return self.__copy__() + + def __getstate__(self): + """ + Hook for the standard pickle module. + """ + obj_slot_values = dict((k, getattr(self, k)) for k in self.__slots__) + obj_slot_values.update(AffineScalarFunc.__getstate__(self)) + # Conversion to a usual dictionary: + return obj_slot_values + + def __setstate__(self, data_dict): + """ + Hook for the standard pickle module. + """ + for (name, value) in data_dict.items(): + setattr(self, name, value) + +############################################################################### + +# Utilities + +def nominal_value(x): + """ + Returns the nominal value of x if it is a quantity with + uncertainty (i.e., an AffineScalarFunc object); otherwise, returns + x unchanged. + + This utility function is useful for transforming a series of + numbers, when only some of them generally carry an uncertainty. + """ + + return x.nominal_value if isinstance(x, AffineScalarFunc) else x + +def std_dev(x): + """ + Returns the standard deviation of x if it is a quantity with + uncertainty (i.e., an AffineScalarFunc object); otherwise, returns + the float 0. + + This utility function is useful for transforming a series of + numbers, when only some of them generally carry an uncertainty. + """ + + return x.std_dev() if isinstance(x, AffineScalarFunc) else 0. + +def covariance_matrix(nums_with_uncert): + """ + Returns a matrix that contains the covariances between the given + sequence of numbers with uncertainties (AffineScalarFunc objects). + The resulting matrix implicitly depends on their ordering in + 'nums_with_uncert'. + + The covariances are floats (never int objects). + + The returned covariance matrix is the exact linear approximation + result, if the nominal values of the numbers with uncertainties + and of their variables are their mean. Otherwise, the returned + covariance matrix should be close to its linear approximation + value. + + The returned matrix is a list of lists. + """ + # See PSI.411 in EOL's notes. + + covariance_matrix = [] + for (i1, expr1) in enumerate(nums_with_uncert): + derivatives1 = expr1.derivatives # Optimization + vars1 = set(derivatives1) + coefs_expr1 = [] + for (i2, expr2) in enumerate(nums_with_uncert[:i1+1]): + derivatives2 = expr2.derivatives # Optimization + coef = 0. + for var in vars1.intersection(derivatives2): + # var is a variable common to both numbers with + # uncertainties: + coef += (derivatives1[var]*derivatives2[var]*var._std_dev**2) + coefs_expr1.append(coef) + covariance_matrix.append(coefs_expr1) + + # We symmetrize the matrix: + for (i, covariance_coefs) in enumerate(covariance_matrix): + covariance_coefs.extend(covariance_matrix[j][i] + for j in range(i+1, len(covariance_matrix))) + + return covariance_matrix + +try: + import numpy +except ImportError: + pass +else: + def correlation_matrix(nums_with_uncert): + ''' + Returns the correlation matrix of the given sequence of + numbers with uncertainties, as a NumPy array of floats. + ''' + + cov_mat = numpy.array(covariance_matrix(nums_with_uncert)) + + std_devs = numpy.sqrt(cov_mat.diagonal()) + + return cov_mat/std_devs/std_devs[numpy.newaxis].T + + __all__.append('correlation_matrix') + +############################################################################### +# Parsing of values with uncertainties: + +POSITIVE_DECIMAL_UNSIGNED = r'(\d+)(\.\d*)?' + +# Regexp for a number with uncertainty (e.g., "-1.234(2)e-6"), where the +# uncertainty is optional (in which case the uncertainty is implicit): +NUMBER_WITH_UNCERT_RE_STR = ''' + ([+-])? # Sign + %s # Main number + (?:\(%s\))? # Optional uncertainty + ([eE][+-]?\d+)? # Optional exponent + ''' % (POSITIVE_DECIMAL_UNSIGNED, POSITIVE_DECIMAL_UNSIGNED) + +NUMBER_WITH_UNCERT_RE = re.compile( + "^%s$" % NUMBER_WITH_UNCERT_RE_STR, re.VERBOSE) + +def parse_error_in_parentheses(representation): + """ + Returns (value, error) from a string representing a number with + uncertainty like 12.34(5), 12.34(142), 12.5(3.4) or 12.3(4.2)e3. + If no parenthesis is given, an uncertainty of one on the last + digit is assumed. + + Raises ValueError if the string cannot be parsed. + """ + + match = NUMBER_WITH_UNCERT_RE.search(representation) + + if match: + # The 'main' part is the nominal value, with 'int'eger part, and + # 'dec'imal part. The 'uncert'ainty is similarly broken into its + # integer and decimal parts. + (sign, main_int, main_dec, uncert_int, uncert_dec, + exponent) = match.groups() + else: + raise ValueError("Unparsable number representation: '%s'." + " Was expecting a string of the form 1.23(4)" + " or 1.234" % representation) + + # The value of the number is its nominal value: + value = float(''.join((sign or '', + main_int, + main_dec or '.0', + exponent or ''))) + + if uncert_int is None: + # No uncertainty was found: an uncertainty of 1 on the last + # digit is assumed: + uncert_int = '1' + + # Do we have a fully explicit uncertainty? + if uncert_dec is not None: + uncert = float("%s%s" % (uncert_int, uncert_dec or '')) + else: + # uncert_int represents an uncertainty on the last digits: + + # The number of digits after the period defines the power of + # 10 than must be applied to the provided uncertainty: + num_digits_after_period = (0 if main_dec is None + else len(main_dec)-1) + uncert = int(uncert_int)/10**num_digits_after_period + + # We apply the exponent to the uncertainty as well: + uncert *= float("1%s" % (exponent or '')) + + return (value, uncert) + + +# The following function is not exposed because it can in effect be +# obtained by doing x = ufloat(representation) and +# x.nominal_value and x.std_dev(): +def str_to_number_with_uncert(representation): + """ + Given a string that represents a number with uncertainty, returns the + nominal value and the uncertainty. + + The string can be of the form: + - 124.5+/-0.15 + - 124.50(15) + - 124.50(123) + - 124.5 + + When no numerical error is given, an uncertainty of 1 on the last + digit is implied. + + Raises ValueError if the string cannot be parsed. + """ + + try: + # Simple form 1234.45+/-1.2: + (value, uncert) = representation.split('+/-') + except ValueError: + # Form with parentheses or no uncertainty: + parsed_value = parse_error_in_parentheses(representation) + else: + try: + parsed_value = (float(value), float(uncert)) + except ValueError: + raise ValueError('Cannot parse %s: was expecting a number' + ' like 1.23+/-0.1' % representation) + + return parsed_value + +def ufloat(representation, tag=None): + """ + Returns a random variable (Variable object). + + Converts the representation of a number into a number with + uncertainty (a random variable, defined by a nominal value and + a standard deviation). + + The representation can be a (value, standard deviation) sequence, + or a string. + + Strings of the form '12.345+/-0.015', '12.345(15)', or '12.3' are + recognized (see full list below). In the last case, an + uncertainty of +/-1 is assigned to the last digit. + + 'tag' is an optional string tag for the variable. Variables + don't have to have distinct tags. Tags are useful for tracing + what values (and errors) enter in a given result (through the + error_components() method). + + Examples of valid string representations: + + -1.23(3.4) + -1.34(5) + 1(6) + 3(4.2) + -9(2) + 1234567(1.2) + 12.345(15) + -12.3456(78)e-6 + 12.3(0.4)e-5 + 0.29 + 31. + -31. + 31 + -3.1e10 + 169.0(7) + 169.1(15) + """ + + # This function is somewhat optimized so as to help with the + # creation of lots of Variable objects (through unumpy.uarray, for + # instance). + + # representations is "normalized" so as to be a valid sequence of + # 2 arguments for Variable(). + + #! Accepting strings and any kind of sequence slows down the code + # by about 5 %. On the other hand, massive initializations of + # numbers with uncertainties are likely to be performed with + # unumpy.uarray, which does not support parsing from strings and + # thus does not have any overhead. + + #! Different, in Python 3: + if isinstance(representation, basestring): + representation = str_to_number_with_uncert(representation) + + #! The tag is forced to be a string, so that the user does not + # create a Variable(2.5, 0.5) in order to represent 2.5 +/- 0.5. + # Forcing 'tag' to be a string prevents numerical uncertainties + # from being considered as tags, here: + if tag is not None: + #! 'unicode' is removed in Python3: + assert isinstance(tag, (str, unicode)), "The tag can only be a string." + + #! The special ** syntax is for Python 2.5 and before (Python 2.6+ + # understands tag=tag): + return Variable(*representation, **{'tag': tag}) + diff --git a/lmfit/uncertainties/umath.py b/lmfit/uncertainties/umath.py index 5487b63..e0608c8 100644 --- a/lmfit/uncertainties/umath.py +++ b/lmfit/uncertainties/umath.py @@ -1,350 +1,350 @@ -'''
-Mathematical operations that generalize many operations from the
-standard math module so that they also work on numbers with
-uncertainties.
-
-Examples:
-
- from umath import sin
-
- # Manipulation of numbers with uncertainties:
- x = uncertainties.ufloat((3, 0.1))
- print sin(x) # prints 0.141120008...+/-0.098999...
-
- # The umath functions also work on regular Python floats:
- print sin(3) # prints 0.141120008... This is a Python float.
-
-Importing all the functions from this module into the global namespace
-is possible. This is encouraged when using a Python shell as a
-calculator. Example:
-
- import uncertainties
- from uncertainties.umath import * # Imports tan(), etc.
-
- x = uncertainties.ufloat((3, 0.1))
- print tan(x) # tan() is the uncertainties.umath.tan function
-
-The numbers with uncertainties handled by this module are objects from
-the uncertainties module, from either the Variable or the
-AffineScalarFunc class.
-
-(c) 2009-2013 by Eric O. LEBIGOT (EOL) <eric.lebigot@normalesup.org>.
-Please send feature requests, bug reports, or feedback to this address.
-
-This software is released under a dual license. (1) The BSD license.
-(2) Any other license, as long as it is obtained from the original
-author.'''
-
-from __future__ import division # Many analytical derivatives depend on this
-
-# Standard modules
-import math
-import sys
-import itertools
-import functools
-
-# Local modules
-from __init__ import wrap, set_doc, __author__, to_affine_scalar, AffineScalarFunc
-
-###############################################################################
-
-# We wrap the functions from the math module so that they keep track of
-# uncertainties by returning a AffineScalarFunc object.
-
-# Some functions from the math module cannot be adapted in a standard
-# way so to work with AffineScalarFunc objects (either as their result
-# or as their arguments):
-
-# (1) Some functions return a result of a type whose value and
-# variations (uncertainties) cannot be represented by AffineScalarFunc
-# (e.g., math.frexp, which returns a tuple). The exception raised
-# when not wrapping them with wrap() is more obvious than the
-# one obtained when wrapping them (in fact, the wrapped functions
-# attempts operations that are not supported, such as calculation a
-# subtraction on a result of type tuple).
-
-# (2) Some functions don't take continuous scalar arguments (which can
-# be varied during differentiation): math.fsum, math.factorial...
-# Such functions can either be:
-
-# - wrapped in a special way.
-
-# - excluded from standard wrapping by adding their name to
-# no_std_wrapping
-
-# Math functions that have a standard interface: they take
-# one or more float arguments, and return a scalar:
-many_scalars_to_scalar_funcs = []
-
-# Some functions require a specific treatment and must therefore be
-# excluded from standard wrapping. Functions
-# no_std_wrapping = ['modf', 'frexp', 'ldexp', 'fsum', 'factorial']
-
-# Functions with numerical derivatives:
-num_deriv_funcs = ['fmod', 'gamma', 'isinf', 'isnan',
- 'lgamma', 'trunc']
-
-# Functions that do not belong in many_scalars_to_scalar_funcs, but
-# that have a version that handles uncertainties:
-non_std_wrapped_funcs = []
-
-# Function that copies the relevant attributes from generalized
-# functions from the math module:
-wraps = functools.partial(functools.update_wrapper,
- assigned=('__doc__', '__name__'))
-
-########################################
-# Wrapping of math functions:
-
-# Fixed formulas for the derivatives of some functions from the math
-# module (some functions might not be present in all version of
-# Python). Singular points are not taken into account. The user
-# should never give "large" uncertainties: problems could only appear
-# if this assumption does not hold.
-
-# Functions not mentioned in _fixed_derivatives have their derivatives
-# calculated numerically.
-
-# Functions that have singularities (possibly at infinity) benefit
-# from analytical calculations (instead of the default numerical
-# calculation) because their derivatives generally change very fast.
-# Even slowly varying functions (e.g., abs()) yield more precise
-# results when differentiated analytically, because of the loss of
-# precision in numerical calculations.
-
-#def log_1arg_der(x):
-# """
-# Derivative of log(x) (1-argument form).
-# """
-# return 1/x
-
-
-def log_der0(*args):
- """
- Derivative of math.log() with respect to its first argument.
-
- Works whether 1 or 2 arguments are given.
- """
- if len(args) == 1:
- return 1/args[0]
- else:
- return 1/args[0]/math.log(args[1]) # 2-argument form
-
- # The following version goes about as fast:
-
- ## A 'try' is used for the most common case because it is fast when no
- ## exception is raised:
- #try:
- # return log_1arg_der(*args) # Argument number check
- #except TypeError:
- # return 1/args[0]/math.log(args[1]) # 2-argument form
-
-_erf_coef = 2/math.sqrt(math.pi) # Optimization for erf()
-
-fixed_derivatives = {
- # In alphabetical order, here:
- 'acos': [lambda x: -1/math.sqrt(1-x**2)],
- 'acosh': [lambda x: 1/math.sqrt(x**2-1)],
- 'asin': [lambda x: 1/math.sqrt(1-x**2)],
- 'asinh': [lambda x: 1/math.sqrt(1+x**2)],
- 'atan': [lambda x: 1/(1+x**2)],
- 'atan2': [lambda y, x: x/(x**2+y**2), # Correct for x == 0
- lambda y, x: -y/(x**2+y**2)], # Correct for x == 0
- 'atanh': [lambda x: 1/(1-x**2)],
- 'ceil': [lambda x: 0],
- 'copysign': [lambda x, y: (1 if x >= 0 else -1) * math.copysign(1, y),
- lambda x, y: 0],
- 'cos': [lambda x: -math.sin(x)],
- 'cosh': [math.sinh],
- 'degrees': [lambda x: math.degrees(1)],
- 'erf': [lambda x: math.exp(-x**2)*_erf_coef],
- 'erfc': [lambda x: -math.exp(-x**2)*_erf_coef],
- 'exp': [math.exp],
- 'expm1': [math.exp],
- 'fabs': [lambda x: 1 if x >= 0 else -1],
- 'floor': [lambda x: 0],
- 'hypot': [lambda x, y: x/math.hypot(x, y),
- lambda x, y: y/math.hypot(x, y)],
- 'log': [log_der0,
- lambda x, y: -math.log(x, y)/y/math.log(y)],
- 'log10': [lambda x: 1/x/math.log(10)],
- 'log1p': [lambda x: 1/(1+x)],
- 'pow': [lambda x, y: y*math.pow(x, y-1),
- lambda x, y: math.log(x) * math.pow(x, y)],
- 'radians': [lambda x: math.radians(1)],
- 'sin': [math.cos],
- 'sinh': [math.cosh],
- 'sqrt': [lambda x: 0.5/math.sqrt(x)],
- 'tan': [lambda x: 1+math.tan(x)**2],
- 'tanh': [lambda x: 1-math.tanh(x)**2]
- }
-
-# Many built-in functions in the math module are wrapped with a
-# version which is uncertainty aware:
-
-this_module = sys.modules[__name__]
-
-# for (name, attr) in vars(math).items():
-for name in dir(math):
-
- if name in fixed_derivatives: # Priority to functions in fixed_derivatives
- derivatives = fixed_derivatives[name]
- elif name in num_deriv_funcs:
- # Functions whose derivatives are calculated numerically by
- # this module fall here (isinf, fmod,...):
- derivatives = None # Means: numerical calculation required
- else:
- continue # 'name' not wrapped by this module (__doc__, e, etc.)
-
- func = getattr(math, name)
-
- setattr(this_module, name,
- wraps(wrap(func, derivatives), func))
-
- many_scalars_to_scalar_funcs.append(name)
-
-###############################################################################
-
-########################################
-# Special cases: some of the functions from no_std_wrapping:
-
-##########
-# The math.factorial function is not converted to an uncertainty-aware
-# function, because it does not handle non-integer arguments: it does
-# not make sense to give it an argument with a numerical error
-# (whereas this would be relevant for the gamma function).
-
-##########
-
-# fsum takes a single argument, which cannot be differentiated.
-# However, each of the arguments inside this single list can
-# be a variable. We handle this in a specific way:
-
-if sys.version_info[:2] >= (2, 6):
-
- # For drop-in compatibility with the math module:
- factorial = math.factorial
- non_std_wrapped_funcs.append('factorial')
-
-
- # We wrap math.fsum
- original_func = math.fsum # For optimization purposes
-
- # The function below exists so that temporary variables do not
- # pollute the module namespace:
- def wrapped_fsum():
- """
- Returns an uncertainty-aware version of math.fsum, which must
- be contained in _original_func.
- """
-
- # The fsum function is flattened, in order to use the
- # wrap() wrapper:
-
- flat_fsum = lambda *args: original_func(args)
-
- flat_fsum_wrap = wrap(
- flat_fsum, itertools.repeat(lambda *args: 1))
-
- return wraps(lambda arg_list: flat_fsum_wrap(*arg_list),
- original_func)
-
- fsum = wrapped_fsum()
- non_std_wrapped_funcs.append('fsum')
-
-
-@set_doc(math.modf.__doc__)
-def modf(x):
- """
- Version of modf that works for numbers with uncertainty, and also
- for regular numbers.
- """
-
- # The code below is inspired by wrap(). It is
- # simpler because only 1 argument is given, and there is no
- # delegation to other functions involved (as for __mul__, etc.).
-
- aff_func = to_affine_scalar(x)
-
- (frac_part, int_part) = math.modf(aff_func.nominal_value)
-
- if aff_func.derivatives:
- # The derivative of the fractional part is simply 1: the
- # derivatives of modf(x)[0] are the derivatives of x:
- return (AffineScalarFunc(frac_part, aff_func.derivatives), int_part)
- else:
- # This function was not called with an AffineScalarFunc
- # argument: there is no need to return numbers with uncertainties:
- return (frac_part, int_part)
-
-many_scalars_to_scalar_funcs.append('modf')
-
-
-@set_doc(math.ldexp.__doc__)
-def ldexp(x, y):
- # The code below is inspired by wrap(). It is
- # simpler because only 1 argument is given, and there is no
- # delegation to other functions involved (as for __mul__, etc.).
-
- # Another approach would be to add an additional argument to
- # wrap() so that some arguments are automatically
- # considered as constants.
-
- aff_func = to_affine_scalar(x) # y must be an integer, for math.ldexp
-
- if aff_func.derivatives:
- factor = 2**y
- return AffineScalarFunc(
- math.ldexp(aff_func.nominal_value, y),
- # Chain rule:
- dict((var, factor*deriv)
- for (var, deriv) in aff_func.derivatives.iteritems()))
- else:
- # This function was not called with an AffineScalarFunc
- # argument: there is no need to return numbers with uncertainties:
-
- # aff_func.nominal_value is not passed instead of x, because
- # we do not have to care about the type of the return value of
- # math.ldexp, this way (aff_func.nominal_value might be the
- # value of x coerced to a difference type [int->float, for
- # instance]):
- return math.ldexp(x, y)
-many_scalars_to_scalar_funcs.append('ldexp')
-
-
-@set_doc(math.frexp.__doc__)
-def frexp(x):
- """
- Version of frexp that works for numbers with uncertainty, and also
- for regular numbers.
- """
-
- # The code below is inspired by wrap(). It is
- # simpler because only 1 argument is given, and there is no
- # delegation to other functions involved (as for __mul__, etc.).
-
- aff_func = to_affine_scalar(x)
-
- if aff_func.derivatives:
- result = math.frexp(aff_func.nominal_value)
- # With frexp(x) = (m, e), dm/dx = 1/(2**e):
- factor = 1/(2**result[1])
- return (
- AffineScalarFunc(
- result[0],
- # Chain rule:
- dict((var, factor*deriv)
- for (var, deriv) in aff_func.derivatives.iteritems())),
- # The exponent is an integer and is supposed to be
- # continuous (small errors):
- result[1])
- else:
- # This function was not called with an AffineScalarFunc
- # argument: there is no need to return numbers with uncertainties:
- return math.frexp(x)
-non_std_wrapped_funcs.append('frexp')
-
-###############################################################################
-# Exported functions:
-
-__all__ = many_scalars_to_scalar_funcs + non_std_wrapped_funcs
+''' +Mathematical operations that generalize many operations from the +standard math module so that they also work on numbers with +uncertainties. + +Examples: + + from umath import sin + + # Manipulation of numbers with uncertainties: + x = uncertainties.ufloat((3, 0.1)) + print sin(x) # prints 0.141120008...+/-0.098999... + + # The umath functions also work on regular Python floats: + print sin(3) # prints 0.141120008... This is a Python float. + +Importing all the functions from this module into the global namespace +is possible. This is encouraged when using a Python shell as a +calculator. Example: + + import uncertainties + from uncertainties.umath import * # Imports tan(), etc. + + x = uncertainties.ufloat((3, 0.1)) + print tan(x) # tan() is the uncertainties.umath.tan function + +The numbers with uncertainties handled by this module are objects from +the uncertainties module, from either the Variable or the +AffineScalarFunc class. + +(c) 2009-2013 by Eric O. LEBIGOT (EOL) <eric.lebigot@normalesup.org>. +Please send feature requests, bug reports, or feedback to this address. + +This software is released under a dual license. (1) The BSD license. +(2) Any other license, as long as it is obtained from the original +author.''' + +from __future__ import division # Many analytical derivatives depend on this + +# Standard modules +import math +import sys +import itertools +import functools + +# Local modules +from __init__ import wrap, set_doc, __author__, to_affine_scalar, AffineScalarFunc + +############################################################################### + +# We wrap the functions from the math module so that they keep track of +# uncertainties by returning a AffineScalarFunc object. + +# Some functions from the math module cannot be adapted in a standard +# way so to work with AffineScalarFunc objects (either as their result +# or as their arguments): + +# (1) Some functions return a result of a type whose value and +# variations (uncertainties) cannot be represented by AffineScalarFunc +# (e.g., math.frexp, which returns a tuple). The exception raised +# when not wrapping them with wrap() is more obvious than the +# one obtained when wrapping them (in fact, the wrapped functions +# attempts operations that are not supported, such as calculation a +# subtraction on a result of type tuple). + +# (2) Some functions don't take continuous scalar arguments (which can +# be varied during differentiation): math.fsum, math.factorial... +# Such functions can either be: + +# - wrapped in a special way. + +# - excluded from standard wrapping by adding their name to +# no_std_wrapping + +# Math functions that have a standard interface: they take +# one or more float arguments, and return a scalar: +many_scalars_to_scalar_funcs = [] + +# Some functions require a specific treatment and must therefore be +# excluded from standard wrapping. Functions +# no_std_wrapping = ['modf', 'frexp', 'ldexp', 'fsum', 'factorial'] + +# Functions with numerical derivatives: +num_deriv_funcs = ['fmod', 'gamma', 'isinf', 'isnan', + 'lgamma', 'trunc'] + +# Functions that do not belong in many_scalars_to_scalar_funcs, but +# that have a version that handles uncertainties: +non_std_wrapped_funcs = [] + +# Function that copies the relevant attributes from generalized +# functions from the math module: +wraps = functools.partial(functools.update_wrapper, + assigned=('__doc__', '__name__')) + +######################################## +# Wrapping of math functions: + +# Fixed formulas for the derivatives of some functions from the math +# module (some functions might not be present in all version of +# Python). Singular points are not taken into account. The user +# should never give "large" uncertainties: problems could only appear +# if this assumption does not hold. + +# Functions not mentioned in _fixed_derivatives have their derivatives +# calculated numerically. + +# Functions that have singularities (possibly at infinity) benefit +# from analytical calculations (instead of the default numerical +# calculation) because their derivatives generally change very fast. +# Even slowly varying functions (e.g., abs()) yield more precise +# results when differentiated analytically, because of the loss of +# precision in numerical calculations. + +#def log_1arg_der(x): +# """ +# Derivative of log(x) (1-argument form). +# """ +# return 1/x + + +def log_der0(*args): + """ + Derivative of math.log() with respect to its first argument. + + Works whether 1 or 2 arguments are given. + """ + if len(args) == 1: + return 1/args[0] + else: + return 1/args[0]/math.log(args[1]) # 2-argument form + + # The following version goes about as fast: + + ## A 'try' is used for the most common case because it is fast when no + ## exception is raised: + #try: + # return log_1arg_der(*args) # Argument number check + #except TypeError: + # return 1/args[0]/math.log(args[1]) # 2-argument form + +_erf_coef = 2/math.sqrt(math.pi) # Optimization for erf() + +fixed_derivatives = { + # In alphabetical order, here: + 'acos': [lambda x: -1/math.sqrt(1-x**2)], + 'acosh': [lambda x: 1/math.sqrt(x**2-1)], + 'asin': [lambda x: 1/math.sqrt(1-x**2)], + 'asinh': [lambda x: 1/math.sqrt(1+x**2)], + 'atan': [lambda x: 1/(1+x**2)], + 'atan2': [lambda y, x: x/(x**2+y**2), # Correct for x == 0 + lambda y, x: -y/(x**2+y**2)], # Correct for x == 0 + 'atanh': [lambda x: 1/(1-x**2)], + 'ceil': [lambda x: 0], + 'copysign': [lambda x, y: (1 if x >= 0 else -1) * math.copysign(1, y), + lambda x, y: 0], + 'cos': [lambda x: -math.sin(x)], + 'cosh': [math.sinh], + 'degrees': [lambda x: math.degrees(1)], + 'erf': [lambda x: math.exp(-x**2)*_erf_coef], + 'erfc': [lambda x: -math.exp(-x**2)*_erf_coef], + 'exp': [math.exp], + 'expm1': [math.exp], + 'fabs': [lambda x: 1 if x >= 0 else -1], + 'floor': [lambda x: 0], + 'hypot': [lambda x, y: x/math.hypot(x, y), + lambda x, y: y/math.hypot(x, y)], + 'log': [log_der0, + lambda x, y: -math.log(x, y)/y/math.log(y)], + 'log10': [lambda x: 1/x/math.log(10)], + 'log1p': [lambda x: 1/(1+x)], + 'pow': [lambda x, y: y*math.pow(x, y-1), + lambda x, y: math.log(x) * math.pow(x, y)], + 'radians': [lambda x: math.radians(1)], + 'sin': [math.cos], + 'sinh': [math.cosh], + 'sqrt': [lambda x: 0.5/math.sqrt(x)], + 'tan': [lambda x: 1+math.tan(x)**2], + 'tanh': [lambda x: 1-math.tanh(x)**2] + } + +# Many built-in functions in the math module are wrapped with a +# version which is uncertainty aware: + +this_module = sys.modules[__name__] + +# for (name, attr) in vars(math).items(): +for name in dir(math): + + if name in fixed_derivatives: # Priority to functions in fixed_derivatives + derivatives = fixed_derivatives[name] + elif name in num_deriv_funcs: + # Functions whose derivatives are calculated numerically by + # this module fall here (isinf, fmod,...): + derivatives = None # Means: numerical calculation required + else: + continue # 'name' not wrapped by this module (__doc__, e, etc.) + + func = getattr(math, name) + + setattr(this_module, name, + wraps(wrap(func, derivatives), func)) + + many_scalars_to_scalar_funcs.append(name) + +############################################################################### + +######################################## +# Special cases: some of the functions from no_std_wrapping: + +########## +# The math.factorial function is not converted to an uncertainty-aware +# function, because it does not handle non-integer arguments: it does +# not make sense to give it an argument with a numerical error +# (whereas this would be relevant for the gamma function). + +########## + +# fsum takes a single argument, which cannot be differentiated. +# However, each of the arguments inside this single list can +# be a variable. We handle this in a specific way: + +if sys.version_info[:2] >= (2, 6): + + # For drop-in compatibility with the math module: + factorial = math.factorial + non_std_wrapped_funcs.append('factorial') + + + # We wrap math.fsum + original_func = math.fsum # For optimization purposes + + # The function below exists so that temporary variables do not + # pollute the module namespace: + def wrapped_fsum(): + """ + Returns an uncertainty-aware version of math.fsum, which must + be contained in _original_func. + """ + + # The fsum function is flattened, in order to use the + # wrap() wrapper: + + flat_fsum = lambda *args: original_func(args) + + flat_fsum_wrap = wrap( + flat_fsum, itertools.repeat(lambda *args: 1)) + + return wraps(lambda arg_list: flat_fsum_wrap(*arg_list), + original_func) + + fsum = wrapped_fsum() + non_std_wrapped_funcs.append('fsum') + + +@set_doc(math.modf.__doc__) +def modf(x): + """ + Version of modf that works for numbers with uncertainty, and also + for regular numbers. + """ + + # The code below is inspired by wrap(). It is + # simpler because only 1 argument is given, and there is no + # delegation to other functions involved (as for __mul__, etc.). + + aff_func = to_affine_scalar(x) + + (frac_part, int_part) = math.modf(aff_func.nominal_value) + + if aff_func.derivatives: + # The derivative of the fractional part is simply 1: the + # derivatives of modf(x)[0] are the derivatives of x: + return (AffineScalarFunc(frac_part, aff_func.derivatives), int_part) + else: + # This function was not called with an AffineScalarFunc + # argument: there is no need to return numbers with uncertainties: + return (frac_part, int_part) + +many_scalars_to_scalar_funcs.append('modf') + + +@set_doc(math.ldexp.__doc__) +def ldexp(x, y): + # The code below is inspired by wrap(). It is + # simpler because only 1 argument is given, and there is no + # delegation to other functions involved (as for __mul__, etc.). + + # Another approach would be to add an additional argument to + # wrap() so that some arguments are automatically + # considered as constants. + + aff_func = to_affine_scalar(x) # y must be an integer, for math.ldexp + + if aff_func.derivatives: + factor = 2**y + return AffineScalarFunc( + math.ldexp(aff_func.nominal_value, y), + # Chain rule: + dict((var, factor*deriv) + for (var, deriv) in aff_func.derivatives.iteritems())) + else: + # This function was not called with an AffineScalarFunc + # argument: there is no need to return numbers with uncertainties: + + # aff_func.nominal_value is not passed instead of x, because + # we do not have to care about the type of the return value of + # math.ldexp, this way (aff_func.nominal_value might be the + # value of x coerced to a difference type [int->float, for + # instance]): + return math.ldexp(x, y) +many_scalars_to_scalar_funcs.append('ldexp') + + +@set_doc(math.frexp.__doc__) +def frexp(x): + """ + Version of frexp that works for numbers with uncertainty, and also + for regular numbers. + """ + + # The code below is inspired by wrap(). It is + # simpler because only 1 argument is given, and there is no + # delegation to other functions involved (as for __mul__, etc.). + + aff_func = to_affine_scalar(x) + + if aff_func.derivatives: + result = math.frexp(aff_func.nominal_value) + # With frexp(x) = (m, e), dm/dx = 1/(2**e): + factor = 1/(2**result[1]) + return ( + AffineScalarFunc( + result[0], + # Chain rule: + dict((var, factor*deriv) + for (var, deriv) in aff_func.derivatives.iteritems())), + # The exponent is an integer and is supposed to be + # continuous (small errors): + result[1]) + else: + # This function was not called with an AffineScalarFunc + # argument: there is no need to return numbers with uncertainties: + return math.frexp(x) +non_std_wrapped_funcs.append('frexp') + +############################################################################### +# Exported functions: + +__all__ = many_scalars_to_scalar_funcs + non_std_wrapped_funcs diff --git a/publish_docs.sh b/publish_docs.sh index e3badfe..5ffd2ba 100644 --- a/publish_docs.sh +++ b/publish_docs.sh @@ -1,59 +1,59 @@ -installdir='/www/apache/htdocs/software/python/lmfit'
-docbuild='doc/_build'
-
-cd doc
-echo '# Making docs'
-make all
-cd ../
-
-echo '# Building tarball of docs'
-mkdir _tmpdoc
-cp -pr doc/lmfit.pdf _tmpdoc/lmfit.pdf
-cp -pr doc/_build/html/* _tmpdoc/.
-cd _tmpdoc
-tar czf ../../lmfit_docs.tar.gz .
-cd ..
-rm -rf _tmpdoc
-
-#
-echo "# Switching to gh-pages branch"
-git checkout gh-pages
-
-if [ $? -ne 0 ] ; then
- echo ' failed.'
- exit
-fi
-
-tar xzf ../lmfit_docs.tar.gz .
-
-echo "# commit changes to gh-pages branch"
-git commit -am "changed docs"
-
-if [ $? -ne 0 ] ; then
- echo ' failed.'
- exit
-fi
-
-echo "# Pushing docs to github"
-git push
-
-
-echo "# switch back to master branch"
-git checkout master
-
-if [ $? -ne 0 ] ; then
- echo ' failed.'
- exit
-fi
-
-# install locally
-echo "# Installing docs to CARS web pages"
-cp ../lmfit_docs.tar.gz $installdir/..
-
-cd $installdir
-if [ $? -ne 0 ] ; then
- echo ' failed.'
- exit
-fi
-
-tar xvzf ../lmfit_docs.tar.gz
+installdir='/www/apache/htdocs/software/python/lmfit' +docbuild='doc/_build' + +cd doc +echo '# Making docs' +make all +cd ../ + +echo '# Building tarball of docs' +mkdir _tmpdoc +cp -pr doc/lmfit.pdf _tmpdoc/lmfit.pdf +cp -pr doc/_build/html/* _tmpdoc/. +cd _tmpdoc +tar czf ../../lmfit_docs.tar.gz . +cd .. +rm -rf _tmpdoc + +# +echo "# Switching to gh-pages branch" +git checkout gh-pages + +if [ $? -ne 0 ] ; then + echo ' failed.' + exit +fi + +tar xzf ../lmfit_docs.tar.gz . + +echo "# commit changes to gh-pages branch" +git commit -am "changed docs" + +if [ $? -ne 0 ] ; then + echo ' failed.' + exit +fi + +echo "# Pushing docs to github" +git push + + +echo "# switch back to master branch" +git checkout master + +if [ $? -ne 0 ] ; then + echo ' failed.' + exit +fi + +# install locally +echo "# Installing docs to CARS web pages" +cp ../lmfit_docs.tar.gz $installdir/.. + +cd $installdir +if [ $? -ne 0 ] ; then + echo ' failed.' + exit +fi + +tar xvzf ../lmfit_docs.tar.gz diff --git a/requirements.txt b/requirements.txt index fecf23c..fe73b4f 100644 --- a/requirements.txt +++ b/requirements.txt @@ -1,2 +1,2 @@ -numpy>=1.5
-scipy>=0.13
+numpy>=1.5 +scipy>=0.13 @@ -1,54 +1,54 @@ -#!/usr/bin/env python
-# from distutils.core import setup
-from setuptools import setup
-
-import versioneer
-versioneer.VCS = 'git'
-versioneer.versionfile_source = 'lmfit/_version.py'
-versioneer.versionfile_build = 'lmfit/_version.py'
-versioneer.tag_prefix = ''
-versioneer.parentdir_prefix = 'lmfit-'
-
-
-long_desc = """A library for least-squares minimization and data fitting in
-Python. Built on top of scipy.optimize, lmfit provides a Parameter object
-which can be set as fixed or free, can have upper and/or lower bounds, or
-can be written in terms of algebraic constraints of other Parameters. The
-user writes a function to be minimized as a function of these Parameters,
-and the scipy.optimize methods are used to find the optimal values for the
-Parameters. The Levenberg-Marquardt (leastsq) is the default minimization
-algorithm, and provides estimated standard errors and correlations between
-varied Parameters. Other minimization methods, including Nelder-Mead's
-downhill simplex, Powell's method, BFGS, Sequential Least Squares, and
-others are also supported. Bounds and contraints can be placed on
-Parameters for all of these methods.
-
-In addition, methods for explicitly calculating confidence intervals are
-provided for exploring minmization problems where the approximation of
-estimating Parameter uncertainties from the covariance matrix is
-questionable. """
-
-
-setup(name = 'lmfit',
- version = versioneer.get_version(),
- cmdclass = versioneer.get_cmdclass(),
- author = 'LMFit Development Team',
- author_email = 'matt.newville@gmail.com',
- url = 'http://lmfit.github.io/lmfit-py/',
- download_url = 'http://lmfit.github.io//lmfit-py/',
- install_requires = ['numpy', 'scipy'],
- license = 'BSD',
- description = "Least-Squares Minimization with Bounds and Constraints",
- long_description = long_desc,
- platforms = ['Windows', 'Linux', 'Mac OS X'],
- classifiers=['Intended Audience :: Science/Research',
- 'Operating System :: OS Independent',
- 'Programming Language :: Python',
- 'Topic :: Scientific/Engineering',
- ],
- # test_suite='nose.collector',
- # test_requires=['Nose'],
- package_dir = {'lmfit': 'lmfit'},
- packages = ['lmfit', 'lmfit.ui', 'lmfit.uncertainties'],
- )
-
+#!/usr/bin/env python +# from distutils.core import setup +from setuptools import setup + +import versioneer +versioneer.VCS = 'git' +versioneer.versionfile_source = 'lmfit/_version.py' +versioneer.versionfile_build = 'lmfit/_version.py' +versioneer.tag_prefix = '' +versioneer.parentdir_prefix = 'lmfit-' + + +long_desc = """A library for least-squares minimization and data fitting in +Python. Built on top of scipy.optimize, lmfit provides a Parameter object +which can be set as fixed or free, can have upper and/or lower bounds, or +can be written in terms of algebraic constraints of other Parameters. The +user writes a function to be minimized as a function of these Parameters, +and the scipy.optimize methods are used to find the optimal values for the +Parameters. The Levenberg-Marquardt (leastsq) is the default minimization +algorithm, and provides estimated standard errors and correlations between +varied Parameters. Other minimization methods, including Nelder-Mead's +downhill simplex, Powell's method, BFGS, Sequential Least Squares, and +others are also supported. Bounds and contraints can be placed on +Parameters for all of these methods. + +In addition, methods for explicitly calculating confidence intervals are +provided for exploring minmization problems where the approximation of +estimating Parameter uncertainties from the covariance matrix is +questionable. """ + + +setup(name = 'lmfit', + version = versioneer.get_version(), + cmdclass = versioneer.get_cmdclass(), + author = 'LMFit Development Team', + author_email = 'matt.newville@gmail.com', + url = 'http://lmfit.github.io/lmfit-py/', + download_url = 'http://lmfit.github.io//lmfit-py/', + install_requires = ['numpy', 'scipy'], + license = 'BSD', + description = "Least-Squares Minimization with Bounds and Constraints", + long_description = long_desc, + platforms = ['Windows', 'Linux', 'Mac OS X'], + classifiers=['Intended Audience :: Science/Research', + 'Operating System :: OS Independent', + 'Programming Language :: Python', + 'Topic :: Scientific/Engineering', + ], + # test_suite='nose.collector', + # test_requires=['Nose'], + package_dir = {'lmfit': 'lmfit'}, + packages = ['lmfit', 'lmfit.ui', 'lmfit.uncertainties'], + ) + diff --git a/tests/NISTModels.py b/tests/NISTModels.py index 1795653..197856f 100644 --- a/tests/NISTModels.py +++ b/tests/NISTModels.py @@ -1,198 +1,198 @@ -import os
-import sys
-from numpy import exp, log, log10, sin, cos, arctan, array
-from lmfit import Parameters
-thisdir, thisfile = os.path.split(__file__)
-NIST_DIR = os.path.join(thisdir, '..', 'NIST_STRD')
-
-def read_params(params):
- if isinstance(params, Parameters):
- return [par.value for par in params.values()]
- else:
- return params
-
-def Bennet5(b, x, y=0):
- b = read_params(b)
- return y - b[0] * (b[1]+x)**(-1/b[2])
-
-def BoxBOD(b, x, y=0):
- b = read_params(b)
- return y - b[0]*(1-exp(-b[1]*x))
-
-def Chwirut(b, x, y=0):
- b = read_params(b)
- return y - exp(-b[0]*x)/(b[1]+b[2]*x)
-
-def DanWood(b, x, y=0):
- b = read_params(b)
- return y - b[0]*x**b[1]
-
-def ENSO(b, x, y=0):
- b = read_params(b)
- pi = 3.141592653589793238462643383279
-
- return y - b[0] + (b[1]*cos( 2*pi*x/12 ) + b[2]*sin( 2*pi*x/12 ) +
- b[4]*cos( 2*pi*x/b[3] ) + b[5]*sin( 2*pi*x/b[3] ) +
- b[7]*cos( 2*pi*x/b[6] ) + b[8]*sin( 2*pi*x/b[6] ) )
-
-def Eckerle4(b, x, y=0):
- b = read_params(b)
- return y - (b[0]/b[1]) * exp(-0.5*((x-b[2])/b[1])**2)
-
-def Gauss(b, x, y=0):
- b = read_params(b)
- return y - b[0]*exp( -b[1]*x ) + (b[2]*exp( -(x-b[3])**2 / b[4]**2 ) +
- b[5]*exp( -(x-b[6])**2 / b[7]**2 ) )
-
-def Hahn1(b, x, y=0):
- b = read_params(b)
- return y - ((b[0]+b[1]*x+b[2]*x**2+b[3]*x**3) /
- (1+b[4]*x+b[5]*x**2+b[6]*x**3) )
-
-def Kirby(b, x, y=0):
- b = read_params(b)
- return y - (b[0] + b[1]*x + b[2]*x**2) / (1 + b[3]*x + b[4]*x**2)
-
-def Lanczos(b, x, y=0):
- b = read_params(b)
- return y - b[0]*exp(-b[1]*x) + b[2]*exp(-b[3]*x) + b[4]*exp(-b[5]*x)
-
-def MGH09(b, x, y=0):
- b = read_params(b)
- return y - b[0]*(x**2+x*b[1]) / (x**2+x*b[2]+b[3])
-
-def MGH10(b, x, y=0):
- b = read_params(b)
- return y - b[0] * exp( b[1]/(x+b[2]) )
-
-def MGH17(b, x, y=0):
- b = read_params(b)
- return y - b[0] + b[1]*exp(-x*b[3]) + b[2]*exp(-x*b[4])
-
-def Misra1a(b, x, y=0):
- b = read_params(b)
- return y - b[0]*(1-exp(-b[1]*x))
-
-def Misra1b(b, x, y=0):
- b = read_params(b)
- return y - b[0] * (1-(1+b[1]*x/2)**(-2))
-
-def Misra1c(b, x, y=0):
- b = read_params(b)
- return y - b[0] * (1-(1+2*b[1]*x)**(-.5))
-
-def Misra1d(b, x, y=0):
- b = read_params(b)
- return y - b[0]*b[1]*x*((1+b[1]*x)**(-1))
-
-def Nelson(b, x, y=None):
- b = read_params(b)
- x1 = x[:,0]
- x2 = x[:,1]
- if y is None:
- return - exp(b[0] - b[1]*x1 * exp(-b[2]*x2))
- return log(y) - (b[0] - b[1]*x1 * exp(-b[2]*x2) )
-
-def Rat42(b, x, y=0):
- b = read_params(b)
- return y - b[0] / (1+exp(b[1]-b[2]*x))
-
-def Rat43(b, x, y=0):
- b = read_params(b)
- return y - b[0] / ((1+exp(b[1]-b[2]*x))**(1/b[3]))
-
-def Roszman1(b, x, y=0):
- b = read_params(b)
- pi = 3.141592653589793238462643383279
- return y - b[0] - b[1]*x - arctan(b[2]/(x-b[3]))/pi
-
-def Thurber(b, x, y=0):
- b = read_params(b)
- return y - ( (b[0] + b[1]*x + b[2]*x**2 + b[3]*x**3) /
- (1 + b[4]*x + b[5]*x**2 + b[6]*x**3) )
-
-# Model name fcn, #fitting params, dim of x
-Models = {'Bennett5': (Bennet5, 3, 1),
- 'BoxBOD': (BoxBOD, 2, 1),
- 'Chwirut1': (Chwirut, 3, 1),
- 'Chwirut2': (Chwirut, 3, 1),
- 'DanWood': (DanWood, 2, 1),
- 'ENSO': (ENSO, 9, 1),
- 'Eckerle4': (Eckerle4, 3, 1),
- 'Gauss1': (Gauss, 8, 1),
- 'Gauss2': (Gauss, 8, 1),
- 'Gauss3': (Gauss, 8, 1),
- 'Hahn1': (Hahn1, 7, 1),
- 'Kirby2': (Kirby, 5, 1),
- 'Lanczos1': (Lanczos, 6, 1),
- 'Lanczos2': (Lanczos, 6, 1),
- 'Lanczos3': (Lanczos, 6, 1),
- 'MGH09': (MGH09, 4, 1),
- 'MGH10': (MGH10, 3, 1),
- 'MGH17': (MGH17, 5, 1),
- 'Misra1a': (Misra1a, 2, 1),
- 'Misra1b' : (Misra1b, 2, 1),
- 'Misra1c' : (Misra1c, 2, 1),
- 'Misra1d' : (Misra1d, 2, 1),
- 'Nelson': (Nelson, 3, 2),
- 'Rat42': (Rat42, 3, 1),
- 'Rat43': (Rat43, 4, 1),
- 'Roszman1': (Roszman1, 4, 1),
- 'Thurber': (Thurber, 7, 1) }
-
-def ReadNistData(dataset):
- """NIST STRD data is in a simple, fixed format with
- line numbers being significant!
- """
- finp = open(os.path.join(NIST_DIR, "%s.dat" % dataset), 'r')
- lines = [l[:-1] for l in finp.readlines()]
- finp.close()
- ModelLines = lines[30:39]
- ParamLines = lines[40:58]
- DataLines = lines[60:]
-
- words = ModelLines[1].strip().split()
- nparams = int(words[0])
-
- start1 = [0]*nparams
- start2 = [0]*nparams
- certval = [0]*nparams
- certerr = [0]*nparams
- for i, text in enumerate(ParamLines[:nparams]):
- [s1, s2, val, err] = [float(x) for x in text.split('=')[1].split()]
- start1[i] = s1
- start2[i] = s2
- certval[i] = val
- certerr[i] = err
-
- #
- for t in ParamLines[nparams:]:
- t = t.strip()
- if ':' not in t:
- continue
- val = float(t.split(':')[1])
- if t.startswith('Residual Sum of Squares'):
- sum_squares = val
- elif t.startswith('Residual Standard Deviation'):
- std_dev = val
- elif t.startswith('Degrees of Freedom'):
- nfree = int(val)
- elif t.startswith('Number of Observations'):
- ndata = int(val)
-
- y, x = [], []
- for d in DataLines:
- vals = [float(i) for i in d.strip().split()]
- y.append(vals[0])
- if len(vals) > 2:
- x.append(vals[1:])
- else:
- x.append(vals[1])
-
- y = array(y)
- x = array(x)
- out = {'y': y, 'x': x, 'nparams': nparams, 'ndata': ndata,
- 'nfree': nfree, 'start1': start1, 'start2': start2,
- 'sum_squares': sum_squares, 'std_dev': std_dev,
- 'cert': certval, 'cert_values': certval, 'cert_stderr': certerr }
- return out
+import os +import sys +from numpy import exp, log, log10, sin, cos, arctan, array +from lmfit import Parameters +thisdir, thisfile = os.path.split(__file__) +NIST_DIR = os.path.join(thisdir, '..', 'NIST_STRD') + +def read_params(params): + if isinstance(params, Parameters): + return [par.value for par in params.values()] + else: + return params + +def Bennet5(b, x, y=0): + b = read_params(b) + return y - b[0] * (b[1]+x)**(-1/b[2]) + +def BoxBOD(b, x, y=0): + b = read_params(b) + return y - b[0]*(1-exp(-b[1]*x)) + +def Chwirut(b, x, y=0): + b = read_params(b) + return y - exp(-b[0]*x)/(b[1]+b[2]*x) + +def DanWood(b, x, y=0): + b = read_params(b) + return y - b[0]*x**b[1] + +def ENSO(b, x, y=0): + b = read_params(b) + pi = 3.141592653589793238462643383279 + + return y - b[0] + (b[1]*cos( 2*pi*x/12 ) + b[2]*sin( 2*pi*x/12 ) + + b[4]*cos( 2*pi*x/b[3] ) + b[5]*sin( 2*pi*x/b[3] ) + + b[7]*cos( 2*pi*x/b[6] ) + b[8]*sin( 2*pi*x/b[6] ) ) + +def Eckerle4(b, x, y=0): + b = read_params(b) + return y - (b[0]/b[1]) * exp(-0.5*((x-b[2])/b[1])**2) + +def Gauss(b, x, y=0): + b = read_params(b) + return y - b[0]*exp( -b[1]*x ) + (b[2]*exp( -(x-b[3])**2 / b[4]**2 ) + + b[5]*exp( -(x-b[6])**2 / b[7]**2 ) ) + +def Hahn1(b, x, y=0): + b = read_params(b) + return y - ((b[0]+b[1]*x+b[2]*x**2+b[3]*x**3) / + (1+b[4]*x+b[5]*x**2+b[6]*x**3) ) + +def Kirby(b, x, y=0): + b = read_params(b) + return y - (b[0] + b[1]*x + b[2]*x**2) / (1 + b[3]*x + b[4]*x**2) + +def Lanczos(b, x, y=0): + b = read_params(b) + return y - b[0]*exp(-b[1]*x) + b[2]*exp(-b[3]*x) + b[4]*exp(-b[5]*x) + +def MGH09(b, x, y=0): + b = read_params(b) + return y - b[0]*(x**2+x*b[1]) / (x**2+x*b[2]+b[3]) + +def MGH10(b, x, y=0): + b = read_params(b) + return y - b[0] * exp( b[1]/(x+b[2]) ) + +def MGH17(b, x, y=0): + b = read_params(b) + return y - b[0] + b[1]*exp(-x*b[3]) + b[2]*exp(-x*b[4]) + +def Misra1a(b, x, y=0): + b = read_params(b) + return y - b[0]*(1-exp(-b[1]*x)) + +def Misra1b(b, x, y=0): + b = read_params(b) + return y - b[0] * (1-(1+b[1]*x/2)**(-2)) + +def Misra1c(b, x, y=0): + b = read_params(b) + return y - b[0] * (1-(1+2*b[1]*x)**(-.5)) + +def Misra1d(b, x, y=0): + b = read_params(b) + return y - b[0]*b[1]*x*((1+b[1]*x)**(-1)) + +def Nelson(b, x, y=None): + b = read_params(b) + x1 = x[:,0] + x2 = x[:,1] + if y is None: + return - exp(b[0] - b[1]*x1 * exp(-b[2]*x2)) + return log(y) - (b[0] - b[1]*x1 * exp(-b[2]*x2) ) + +def Rat42(b, x, y=0): + b = read_params(b) + return y - b[0] / (1+exp(b[1]-b[2]*x)) + +def Rat43(b, x, y=0): + b = read_params(b) + return y - b[0] / ((1+exp(b[1]-b[2]*x))**(1/b[3])) + +def Roszman1(b, x, y=0): + b = read_params(b) + pi = 3.141592653589793238462643383279 + return y - b[0] - b[1]*x - arctan(b[2]/(x-b[3]))/pi + +def Thurber(b, x, y=0): + b = read_params(b) + return y - ( (b[0] + b[1]*x + b[2]*x**2 + b[3]*x**3) / + (1 + b[4]*x + b[5]*x**2 + b[6]*x**3) ) + +# Model name fcn, #fitting params, dim of x +Models = {'Bennett5': (Bennet5, 3, 1), + 'BoxBOD': (BoxBOD, 2, 1), + 'Chwirut1': (Chwirut, 3, 1), + 'Chwirut2': (Chwirut, 3, 1), + 'DanWood': (DanWood, 2, 1), + 'ENSO': (ENSO, 9, 1), + 'Eckerle4': (Eckerle4, 3, 1), + 'Gauss1': (Gauss, 8, 1), + 'Gauss2': (Gauss, 8, 1), + 'Gauss3': (Gauss, 8, 1), + 'Hahn1': (Hahn1, 7, 1), + 'Kirby2': (Kirby, 5, 1), + 'Lanczos1': (Lanczos, 6, 1), + 'Lanczos2': (Lanczos, 6, 1), + 'Lanczos3': (Lanczos, 6, 1), + 'MGH09': (MGH09, 4, 1), + 'MGH10': (MGH10, 3, 1), + 'MGH17': (MGH17, 5, 1), + 'Misra1a': (Misra1a, 2, 1), + 'Misra1b' : (Misra1b, 2, 1), + 'Misra1c' : (Misra1c, 2, 1), + 'Misra1d' : (Misra1d, 2, 1), + 'Nelson': (Nelson, 3, 2), + 'Rat42': (Rat42, 3, 1), + 'Rat43': (Rat43, 4, 1), + 'Roszman1': (Roszman1, 4, 1), + 'Thurber': (Thurber, 7, 1) } + +def ReadNistData(dataset): + """NIST STRD data is in a simple, fixed format with + line numbers being significant! + """ + finp = open(os.path.join(NIST_DIR, "%s.dat" % dataset), 'r') + lines = [l[:-1] for l in finp.readlines()] + finp.close() + ModelLines = lines[30:39] + ParamLines = lines[40:58] + DataLines = lines[60:] + + words = ModelLines[1].strip().split() + nparams = int(words[0]) + + start1 = [0]*nparams + start2 = [0]*nparams + certval = [0]*nparams + certerr = [0]*nparams + for i, text in enumerate(ParamLines[:nparams]): + [s1, s2, val, err] = [float(x) for x in text.split('=')[1].split()] + start1[i] = s1 + start2[i] = s2 + certval[i] = val + certerr[i] = err + + # + for t in ParamLines[nparams:]: + t = t.strip() + if ':' not in t: + continue + val = float(t.split(':')[1]) + if t.startswith('Residual Sum of Squares'): + sum_squares = val + elif t.startswith('Residual Standard Deviation'): + std_dev = val + elif t.startswith('Degrees of Freedom'): + nfree = int(val) + elif t.startswith('Number of Observations'): + ndata = int(val) + + y, x = [], [] + for d in DataLines: + vals = [float(i) for i in d.strip().split()] + y.append(vals[0]) + if len(vals) > 2: + x.append(vals[1:]) + else: + x.append(vals[1]) + + y = array(y) + x = array(x) + out = {'y': y, 'x': x, 'nparams': nparams, 'ndata': ndata, + 'nfree': nfree, 'start1': start1, 'start2': start2, + 'sum_squares': sum_squares, 'std_dev': std_dev, + 'cert': certval, 'cert_values': certval, 'cert_stderr': certerr } + return out diff --git a/tests/_test_ci.py b/tests/_test_ci.py index bbb767e..86afcaf 100644 --- a/tests/_test_ci.py +++ b/tests/_test_ci.py @@ -1,58 +1,58 @@ -from __future__ import print_function
-from lmfit import minimize, Parameters, conf_interval, report_ci, report_errors
-import numpy as np
-pi = np.pi
-import nose
-
-def test_ci():
- np.random.seed(1)
- p_true = Parameters()
- p_true.add('amp', value=14.0)
- p_true.add('period', value=5.33)
- p_true.add('shift', value=0.123)
- p_true.add('decay', value=0.010)
-
- def residual(pars, x, data=None):
- amp = pars['amp'].value
- per = pars['period'].value
- shift = pars['shift'].value
- decay = pars['decay'].value
-
- if abs(shift) > pi / 2:
- shift = shift - np.sign(shift) * pi
- model = amp * np.sin(shift + x / per) * np.exp(-x * x * decay * decay)
- if data is None:
- return model
- return model - data
-
-
- n = 2500
- xmin = 0.
- xmax = 250.0
- noise = np.random.normal(scale=0.7215, size=n)
- x = np.linspace(xmin, xmax, n)
- data = residual(p_true, x) + noise
-
- fit_params = Parameters()
- fit_params.add('amp', value=13.0)
- fit_params.add('period', value=4)
- fit_params.add('shift', value=0.1)
- fit_params.add('decay', value=0.02)
-
- out = minimize(residual, fit_params, args=(x,), kws={'data': data})
-
- fit = residual(fit_params, x)
-
- print( ' N fev = ', out.nfev)
- print( out.chisqr, out.redchi, out.nfree)
-
- report_errors(fit_params)
- ci, tr = conf_interval(out, sigmas=[0.674], trace=True)
- report_ci(ci)
- for p in out.params:
- diff1 = ci[p][1][1] - ci[p][0][1]
- diff2 = ci[p][2][1] - ci[p][1][1]
- stderr = out.params[p].stderr
- assert(abs(diff1 - stderr) / stderr < 0.05)
- assert(abs(diff2 - stderr) / stderr < 0.05)
-
+from __future__ import print_function +from lmfit import minimize, Parameters, conf_interval, report_ci, report_errors +import numpy as np +pi = np.pi +import nose + +def test_ci(): + np.random.seed(1) + p_true = Parameters() + p_true.add('amp', value=14.0) + p_true.add('period', value=5.33) + p_true.add('shift', value=0.123) + p_true.add('decay', value=0.010) + + def residual(pars, x, data=None): + amp = pars['amp'].value + per = pars['period'].value + shift = pars['shift'].value + decay = pars['decay'].value + + if abs(shift) > pi / 2: + shift = shift - np.sign(shift) * pi + model = amp * np.sin(shift + x / per) * np.exp(-x * x * decay * decay) + if data is None: + return model + return model - data + + + n = 2500 + xmin = 0. + xmax = 250.0 + noise = np.random.normal(scale=0.7215, size=n) + x = np.linspace(xmin, xmax, n) + data = residual(p_true, x) + noise + + fit_params = Parameters() + fit_params.add('amp', value=13.0) + fit_params.add('period', value=4) + fit_params.add('shift', value=0.1) + fit_params.add('decay', value=0.02) + + out = minimize(residual, fit_params, args=(x,), kws={'data': data}) + + fit = residual(fit_params, x) + + print( ' N fev = ', out.nfev) + print( out.chisqr, out.redchi, out.nfree) + + report_errors(fit_params) + ci, tr = conf_interval(out, sigmas=[0.674], trace=True) + report_ci(ci) + for p in out.params: + diff1 = ci[p][1][1] - ci[p][0][1] + diff2 = ci[p][2][1] - ci[p][1][1] + stderr = out.params[p].stderr + assert(abs(diff1 - stderr) / stderr < 0.05) + assert(abs(diff2 - stderr) / stderr < 0.05) + diff --git a/tests/_test_make_paras_and_func.py b/tests/_test_make_paras_and_func.py index ee0a251..7a7b27f 100644 --- a/tests/_test_make_paras_and_func.py +++ b/tests/_test_make_paras_and_func.py @@ -1,31 +1,31 @@ -# -*- coding: utf-8 -*-
-
-import lmfit
-
-
-def test_wrap_function():
- get_names = lambda p: [p_key for p_key in p ]
-
- def func(A, b, c, d=5, e=10):
- return A + b + c + d
-
- x0 = [1, 2, 3]
- para, f = lmfit.make_paras_and_func(func, x0)
- assert(get_names(para) == ['A', 'b', 'c'])
- y1 = f(para)
- y2 = func(*x0)
- assert(y1==y2)
-
- x0 = [1, 2, 3, 4]
- para, f = lmfit.make_paras_and_func(func, x0)
- assert(get_names(para) == ['A', 'b', 'c', 'd'])
- y1 = f(para)
- y2 = func(*x0)
- assert(y1==y2)
-
- x0 = [1, 2, 3]
- para, f = lmfit.make_paras_and_func(func, x0, {'e': 3})
- assert(get_names(para) == ['A', 'b', 'c', 'e'])
- y1 = f(para)
- y2 = func(*x0)
- assert(y1==y2)
+# -*- coding: utf-8 -*- + +import lmfit + + +def test_wrap_function(): + get_names = lambda p: [p_key for p_key in p ] + + def func(A, b, c, d=5, e=10): + return A + b + c + d + + x0 = [1, 2, 3] + para, f = lmfit.make_paras_and_func(func, x0) + assert(get_names(para) == ['A', 'b', 'c']) + y1 = f(para) + y2 = func(*x0) + assert(y1==y2) + + x0 = [1, 2, 3, 4] + para, f = lmfit.make_paras_and_func(func, x0) + assert(get_names(para) == ['A', 'b', 'c', 'd']) + y1 = f(para) + y2 = func(*x0) + assert(y1==y2) + + x0 = [1, 2, 3] + para, f = lmfit.make_paras_and_func(func, x0, {'e': 3}) + assert(get_names(para) == ['A', 'b', 'c', 'e']) + y1 = f(para) + y2 = func(*x0) + assert(y1==y2) diff --git a/tests/lmfit_testutils.py b/tests/lmfit_testutils.py index f399f2c..79e89d4 100644 --- a/tests/lmfit_testutils.py +++ b/tests/lmfit_testutils.py @@ -1,18 +1,18 @@ -from lmfit import Parameter
-from numpy.testing import assert_allclose
-
-def assert_paramval(param, val, tol=1.e-3):
- """assert that a named parameter's value is close to expected value"""
-
- assert(isinstance(param, Parameter))
- pval = param.value
-
- assert_allclose([pval], [val], rtol=tol, atol=tol,
- err_msg='',verbose=True)
-
-def assert_paramattr(param, attr, val):
- """assert that a named parameter's value is a value"""
- assert(isinstance(param, Parameter))
- assert(hasattr(param, attr))
- assert(getattr(param, attr) == val)
-
+from lmfit import Parameter +from numpy.testing import assert_allclose + +def assert_paramval(param, val, tol=1.e-3): + """assert that a named parameter's value is close to expected value""" + + assert(isinstance(param, Parameter)) + pval = param.value + + assert_allclose([pval], [val], rtol=tol, atol=tol, + err_msg='',verbose=True) + +def assert_paramattr(param, attr, val): + """assert that a named parameter's value is a value""" + assert(isinstance(param, Parameter)) + assert(hasattr(param, attr)) + assert(getattr(param, attr) == val) + diff --git a/tests/test_1variable.py b/tests/test_1variable.py index a832f79..3e3d530 100644 --- a/tests/test_1variable.py +++ b/tests/test_1variable.py @@ -1,57 +1,57 @@ -# test of fitting one variable
-# From Nick Schurch
-
-import lmfit, numpy
-from numpy.testing import assert_allclose
-
-def linear_chisq(params, x, data, errs=None):
-
- ''' Calcs chi-squared residuals linear model (weighted by errors if given)
- '''
-
- if type(params) is not lmfit.parameter.Parameters:
- msg = "Params argument is not a lmfit parameter set"
- raise TypeError(msg)
-
- if "m" not in params.keys():
- msg = "No slope parameter (m) defined in the model"
- raise KeyError(msg)
-
- if "c" not in params.keys():
- msg = "No intercept parameter (c) defined in the model"
- raise KeyError(msg)
-
- m = params["m"].value
- c = params["c"].value
-
- model = m*x+c
-
- residuals = (data-model)
- if errs is not None:
- residuals = residuals/errs
-
- return(residuals)
-
-def test_1var():
- rands = [-0.21698284, 0.41900591, 0.02349374, -0.218552, -0.3513699,
- 0.33418304, 0.04226855, 0.213303, 0.45948731, 0.33587736]
-
- x = numpy.arange(10)+1
- y = numpy.arange(10)+1+rands
- y_errs = numpy.sqrt(y)/2
-
- params = lmfit.Parameters()
- params.add(name="m", value=1.0, vary=True)
- params.add(name="c", value=0.0, vary=False)
-
- out = lmfit.minimize(linear_chisq, params, args=(x, y))
-
- lmfit.report_fit(out)
- assert_allclose(params['m'].value, 1.025, rtol=0.02, atol=0.02)
- assert(len(params)==2)
- assert(out.nvarys == 1)
- assert(out.chisqr > 0.01)
- assert(out.chisqr < 5.00)
-
-if __name__ == '__main__':
- test_1var()
+# test of fitting one variable +# From Nick Schurch + +import lmfit, numpy +from numpy.testing import assert_allclose + +def linear_chisq(params, x, data, errs=None): + + ''' Calcs chi-squared residuals linear model (weighted by errors if given) + ''' + + if type(params) is not lmfit.parameter.Parameters: + msg = "Params argument is not a lmfit parameter set" + raise TypeError(msg) + + if "m" not in params.keys(): + msg = "No slope parameter (m) defined in the model" + raise KeyError(msg) + + if "c" not in params.keys(): + msg = "No intercept parameter (c) defined in the model" + raise KeyError(msg) + + m = params["m"].value + c = params["c"].value + + model = m*x+c + + residuals = (data-model) + if errs is not None: + residuals = residuals/errs + + return(residuals) + +def test_1var(): + rands = [-0.21698284, 0.41900591, 0.02349374, -0.218552, -0.3513699, + 0.33418304, 0.04226855, 0.213303, 0.45948731, 0.33587736] + + x = numpy.arange(10)+1 + y = numpy.arange(10)+1+rands + y_errs = numpy.sqrt(y)/2 + + params = lmfit.Parameters() + params.add(name="m", value=1.0, vary=True) + params.add(name="c", value=0.0, vary=False) + + out = lmfit.minimize(linear_chisq, params, args=(x, y)) + + lmfit.report_fit(out) + assert_allclose(params['m'].value, 1.025, rtol=0.02, atol=0.02) + assert(len(params)==2) + assert(out.nvarys == 1) + assert(out.chisqr > 0.01) + assert(out.chisqr < 5.00) + +if __name__ == '__main__': + test_1var() diff --git a/tests/test_NIST_Strd.py b/tests/test_NIST_Strd.py index 0ce77f6..aec9a8f 100644 --- a/tests/test_NIST_Strd.py +++ b/tests/test_NIST_Strd.py @@ -1,267 +1,267 @@ -from __future__ import print_function
-import sys
-import math
-from optparse import OptionParser
-
-from lmfit import Parameters, minimize
-
-from NISTModels import Models, ReadNistData
-
-HASPYLAB = False
-for arg in sys.argv:
- if 'nose' in arg:
- HASPYLAB = False
-
-if HASPYLAB:
- try:
- import matplotlib
- import pylab
- HASPYLAB = True
- except ImportError:
- HASPYLAB = False
-
-def ndig(a, b):
- "precision for NIST values"
- return round(-math.log10((abs(abs(a)-abs(b)) +1.e-15)/ abs(b)))
-
-ABAR = ' |----------------+----------------+------------------+-------------------|'
-def Compare_NIST_Results(DataSet, myfit, params, NISTdata):
- buff = [' ======================================',
- ' %s: ' % DataSet,
- ' | Parameter Name | Value Found | Certified Value | # Matching Digits |']
- buff.append(ABAR)
-
- val_dig_min = 200
- err_dig_min = 200
- fmt = ' | %s | % -.7e | % -.7e | %2i |'
- for i in range(NISTdata['nparams']):
- parname = 'b%i' % (i+1)
- par = params[parname]
- thisval = par.value
- certval = NISTdata['cert_values'][i]
- vdig = ndig(thisval, certval)
- pname = (parname + ' value ' + ' '*14)[:14]
- buff.append(fmt % (pname, thisval, certval, vdig))
- val_dig_min = min(val_dig_min, vdig)
-
- thiserr = par.stderr
- certerr = NISTdata['cert_stderr'][i]
- if thiserr is not None and myfit.errorbars:
- edig = ndig(thiserr, certerr)
- ename = (parname + ' stderr' + ' '*14)[:14]
- buff.append(fmt % (ename, thiserr, certerr, edig))
- err_dig_min = min(err_dig_min, edig)
-
- buff.append(ABAR)
- sumsq = NISTdata['sum_squares']
- try:
- chi2 = myfit.chisqr
- buff.append(' | Sum of Squares | %.7e | %.7e | %2i |'
- % (chi2, sumsq, ndig(chi2, sumsq)))
- except:
- pass
- buff.append(ABAR)
- if not myfit.errorbars:
- buff.append(' | * * * * COULD NOT ESTIMATE UNCERTAINTIES * * * * |')
- err_dig_min = 0
- if err_dig_min < 199:
- buff.append(' Worst agreement: %i digits for value, %i digits for error '
- % (val_dig_min, err_dig_min))
- else:
- buff.append(' Worst agreement: %i digits' % (val_dig_min))
- return val_dig_min, '\n'.join(buff)
-
-def NIST_Dataset(DataSet, method='leastsq', start='start2',
- plot=True, verbose=False):
-
- NISTdata = ReadNistData(DataSet)
- resid, npar, dimx = Models[DataSet]
- y = NISTdata['y']
- x = NISTdata['x']
-
- params = Parameters()
- for i in range(npar):
- pname = 'b%i' % (i+1)
- cval = NISTdata['cert_values'][i]
- cerr = NISTdata['cert_stderr'][i]
- pval1 = NISTdata[start][i]
- params.add(pname, value=pval1)
-
- myfit = minimize(resid, params, method=method, args=(x,), kws={'y':y})
- digs, buff = Compare_NIST_Results(DataSet, myfit, myfit.params, NISTdata)
- if verbose:
- print(buff)
- if plot and HASPYLAB:
- fit = -resid(myfit.params, x, )
- pylab.plot(x, y, 'ro')
- pylab.plot(x, fit, 'k+-')
- pylab.show()
-
- return digs > 1
-
-def build_usage():
- modelnames = []
- ms = ''
- for d in sorted(Models.keys()):
- ms = ms + ' %s ' % d
- if len(ms) > 55:
- modelnames.append(ms)
- ms = ' '
- modelnames.append(ms)
- modelnames = '\n'.join(modelnames)
-
- usage = """
- === Test Fit to NIST StRD Models ===
-
-usage:
-------
- python fit_NIST.py [options] Model Start
-
-where Start is one of 'start1','start2' or 'cert', for different
-starting values, and Model is one of
-
- %s
-
-if Model = 'all', all models and starting values will be run.
-
-options:
---------
- -m name of fitting method. One of:
- leastsq, nelder, powell, lbfgsb, bfgs,
- tnc, cobyla, slsqp, cg, newto-cg
- leastsq (Levenberg-Marquardt) is the default
-""" % modelnames
- return usage
-
-############################
-def run_interactive():
- usage = build_usage()
- parser = OptionParser(usage=usage, prog="fit-NIST.py")
-
- parser.add_option("-m", "--method", dest="method",
- metavar='METH',
- default='leastsq',
- help="set method name, default = 'leastsq'")
-
- (opts, args) = parser.parse_args()
- dset = ''
- start = 'start2'
- if len(args) > 0:
- dset = args[0]
- if len(args) > 1:
- start = args[1]
-
- if dset.lower() == 'all':
- tpass = 0
- tfail = 0
- failures = []
- dsets = sorted(Models.keys())
- for dset in dsets:
- for start in ('start1', 'start2', 'cert'):
- if NIST_Dataset(dset, method=opts.method, start=start,
- plot=False, verbose=True):
- tpass += 1
- else:
- tfail += 1
- failures.append(" %s (starting at '%s')" % (dset, start))
- print('--------------------------------------')
- print(' Fit Method: %s ' % opts.method)
- print(' Final Results: %i pass, %i fail.' % (tpass, tfail))
- print(' Tests Failed for:\n %s' % '\n '.join(failures))
- print('--------------------------------------')
- elif dset not in Models:
- print(usage)
- else:
- return NIST_Dataset(dset, method=opts.method,
- start=start, plot=True, verbose=True)
-
-def RunNIST_Model(model):
- out1 = NIST_Dataset(model, start='start1', plot=False, verbose=False)
- out2 = NIST_Dataset(model, start='start2', plot=False, verbose=False)
- print("NIST Test" , model, out1, out2)
- assert(out1 or out2)
- return out1 or out2
-
-def test_Bennett5():
- return RunNIST_Model('Bennett5')
-
-def test_BoxBOD():
- return RunNIST_Model('BoxBOD')
-
-def test_Chwirut1():
- return RunNIST_Model('Chwirut1')
-
-def test_Chwirut2():
- return RunNIST_Model('Chwirut2')
-
-def test_DanWood():
- return RunNIST_Model('DanWood')
-
-def test_ENSO():
- return RunNIST_Model('ENSO')
-
-def test_Eckerle4():
- return RunNIST_Model('Eckerle4')
-
-def test_Gauss1():
- return RunNIST_Model('Gauss1')
-
-def test_Gauss2():
- return RunNIST_Model('Gauss2')
-
-def test_Gauss3():
- return RunNIST_Model('Gauss3')
-
-def test_Hahn1():
- return RunNIST_Model('Hahn1')
-
-def test_Kirby2():
- return RunNIST_Model('Kirby2')
-
-def test_Lanczos1():
- return RunNIST_Model('Lanczos1')
-
-def test_Lanczos2():
- return RunNIST_Model('Lanczos2')
-
-def test_Lanczos3():
- return RunNIST_Model('Lanczos3')
-
-def test_MGH09():
- return RunNIST_Model('MGH09')
-
-def test_MGH10():
- return RunNIST_Model('MGH10')
-
-def test_MGH17():
- return RunNIST_Model('MGH17')
-
-def test_Misra1a():
- return RunNIST_Model('Misra1a')
-
-def test_Misra1b():
- return RunNIST_Model('Misra1b')
-
-def test_Misra1c():
- return RunNIST_Model('Misra1c')
-
-def test_Misra1d():
- return RunNIST_Model('Misra1d')
-
-def test_Nelson():
- return RunNIST_Model('Nelson')
-
-def test_Rat42():
- return RunNIST_Model('Rat42')
-
-def test_Rat43():
- return RunNIST_Model('Rat43')
-
-def test_Roszman1():
- return RunNIST_Model('Roszman1')
-
-def test_Thurber():
- return RunNIST_Model('Thurber')
-
-if __name__ == '__main__':
- run_interactive()
+from __future__ import print_function +import sys +import math +from optparse import OptionParser + +from lmfit import Parameters, minimize + +from NISTModels import Models, ReadNistData + +HASPYLAB = False +for arg in sys.argv: + if 'nose' in arg: + HASPYLAB = False + +if HASPYLAB: + try: + import matplotlib + import pylab + HASPYLAB = True + except ImportError: + HASPYLAB = False + +def ndig(a, b): + "precision for NIST values" + return round(-math.log10((abs(abs(a)-abs(b)) +1.e-15)/ abs(b))) + +ABAR = ' |----------------+----------------+------------------+-------------------|' +def Compare_NIST_Results(DataSet, myfit, params, NISTdata): + buff = [' ======================================', + ' %s: ' % DataSet, + ' | Parameter Name | Value Found | Certified Value | # Matching Digits |'] + buff.append(ABAR) + + val_dig_min = 200 + err_dig_min = 200 + fmt = ' | %s | % -.7e | % -.7e | %2i |' + for i in range(NISTdata['nparams']): + parname = 'b%i' % (i+1) + par = params[parname] + thisval = par.value + certval = NISTdata['cert_values'][i] + vdig = ndig(thisval, certval) + pname = (parname + ' value ' + ' '*14)[:14] + buff.append(fmt % (pname, thisval, certval, vdig)) + val_dig_min = min(val_dig_min, vdig) + + thiserr = par.stderr + certerr = NISTdata['cert_stderr'][i] + if thiserr is not None and myfit.errorbars: + edig = ndig(thiserr, certerr) + ename = (parname + ' stderr' + ' '*14)[:14] + buff.append(fmt % (ename, thiserr, certerr, edig)) + err_dig_min = min(err_dig_min, edig) + + buff.append(ABAR) + sumsq = NISTdata['sum_squares'] + try: + chi2 = myfit.chisqr + buff.append(' | Sum of Squares | %.7e | %.7e | %2i |' + % (chi2, sumsq, ndig(chi2, sumsq))) + except: + pass + buff.append(ABAR) + if not myfit.errorbars: + buff.append(' | * * * * COULD NOT ESTIMATE UNCERTAINTIES * * * * |') + err_dig_min = 0 + if err_dig_min < 199: + buff.append(' Worst agreement: %i digits for value, %i digits for error ' + % (val_dig_min, err_dig_min)) + else: + buff.append(' Worst agreement: %i digits' % (val_dig_min)) + return val_dig_min, '\n'.join(buff) + +def NIST_Dataset(DataSet, method='leastsq', start='start2', + plot=True, verbose=False): + + NISTdata = ReadNistData(DataSet) + resid, npar, dimx = Models[DataSet] + y = NISTdata['y'] + x = NISTdata['x'] + + params = Parameters() + for i in range(npar): + pname = 'b%i' % (i+1) + cval = NISTdata['cert_values'][i] + cerr = NISTdata['cert_stderr'][i] + pval1 = NISTdata[start][i] + params.add(pname, value=pval1) + + myfit = minimize(resid, params, method=method, args=(x,), kws={'y':y}) + digs, buff = Compare_NIST_Results(DataSet, myfit, myfit.params, NISTdata) + if verbose: + print(buff) + if plot and HASPYLAB: + fit = -resid(myfit.params, x, ) + pylab.plot(x, y, 'ro') + pylab.plot(x, fit, 'k+-') + pylab.show() + + return digs > 1 + +def build_usage(): + modelnames = [] + ms = '' + for d in sorted(Models.keys()): + ms = ms + ' %s ' % d + if len(ms) > 55: + modelnames.append(ms) + ms = ' ' + modelnames.append(ms) + modelnames = '\n'.join(modelnames) + + usage = """ + === Test Fit to NIST StRD Models === + +usage: +------ + python fit_NIST.py [options] Model Start + +where Start is one of 'start1','start2' or 'cert', for different +starting values, and Model is one of + + %s + +if Model = 'all', all models and starting values will be run. + +options: +-------- + -m name of fitting method. One of: + leastsq, nelder, powell, lbfgsb, bfgs, + tnc, cobyla, slsqp, cg, newto-cg + leastsq (Levenberg-Marquardt) is the default +""" % modelnames + return usage + +############################ +def run_interactive(): + usage = build_usage() + parser = OptionParser(usage=usage, prog="fit-NIST.py") + + parser.add_option("-m", "--method", dest="method", + metavar='METH', + default='leastsq', + help="set method name, default = 'leastsq'") + + (opts, args) = parser.parse_args() + dset = '' + start = 'start2' + if len(args) > 0: + dset = args[0] + if len(args) > 1: + start = args[1] + + if dset.lower() == 'all': + tpass = 0 + tfail = 0 + failures = [] + dsets = sorted(Models.keys()) + for dset in dsets: + for start in ('start1', 'start2', 'cert'): + if NIST_Dataset(dset, method=opts.method, start=start, + plot=False, verbose=True): + tpass += 1 + else: + tfail += 1 + failures.append(" %s (starting at '%s')" % (dset, start)) + print('--------------------------------------') + print(' Fit Method: %s ' % opts.method) + print(' Final Results: %i pass, %i fail.' % (tpass, tfail)) + print(' Tests Failed for:\n %s' % '\n '.join(failures)) + print('--------------------------------------') + elif dset not in Models: + print(usage) + else: + return NIST_Dataset(dset, method=opts.method, + start=start, plot=True, verbose=True) + +def RunNIST_Model(model): + out1 = NIST_Dataset(model, start='start1', plot=False, verbose=False) + out2 = NIST_Dataset(model, start='start2', plot=False, verbose=False) + print("NIST Test" , model, out1, out2) + assert(out1 or out2) + return out1 or out2 + +def test_Bennett5(): + return RunNIST_Model('Bennett5') + +def test_BoxBOD(): + return RunNIST_Model('BoxBOD') + +def test_Chwirut1(): + return RunNIST_Model('Chwirut1') + +def test_Chwirut2(): + return RunNIST_Model('Chwirut2') + +def test_DanWood(): + return RunNIST_Model('DanWood') + +def test_ENSO(): + return RunNIST_Model('ENSO') + +def test_Eckerle4(): + return RunNIST_Model('Eckerle4') + +def test_Gauss1(): + return RunNIST_Model('Gauss1') + +def test_Gauss2(): + return RunNIST_Model('Gauss2') + +def test_Gauss3(): + return RunNIST_Model('Gauss3') + +def test_Hahn1(): + return RunNIST_Model('Hahn1') + +def test_Kirby2(): + return RunNIST_Model('Kirby2') + +def test_Lanczos1(): + return RunNIST_Model('Lanczos1') + +def test_Lanczos2(): + return RunNIST_Model('Lanczos2') + +def test_Lanczos3(): + return RunNIST_Model('Lanczos3') + +def test_MGH09(): + return RunNIST_Model('MGH09') + +def test_MGH10(): + return RunNIST_Model('MGH10') + +def test_MGH17(): + return RunNIST_Model('MGH17') + +def test_Misra1a(): + return RunNIST_Model('Misra1a') + +def test_Misra1b(): + return RunNIST_Model('Misra1b') + +def test_Misra1c(): + return RunNIST_Model('Misra1c') + +def test_Misra1d(): + return RunNIST_Model('Misra1d') + +def test_Nelson(): + return RunNIST_Model('Nelson') + +def test_Rat42(): + return RunNIST_Model('Rat42') + +def test_Rat43(): + return RunNIST_Model('Rat43') + +def test_Roszman1(): + return RunNIST_Model('Roszman1') + +def test_Thurber(): + return RunNIST_Model('Thurber') + +if __name__ == '__main__': + run_interactive() diff --git a/tests/test_algebraic_constraint.py b/tests/test_algebraic_constraint.py index a256169..1764b7f 100644 --- a/tests/test_algebraic_constraint.py +++ b/tests/test_algebraic_constraint.py @@ -1,135 +1,159 @@ -from numpy import linspace, zeros, sin, exp, random, sqrt, pi, sign
-from lmfit import Parameters, Parameter, Minimizer
-from lmfit.lineshapes import gaussian, lorentzian, pvoigt
-from lmfit.printfuncs import report_fit
-
-def test_constraints1():
- def residual(pars, x, sigma=None, data=None):
- yg = gaussian(x, pars['amp_g'].value,
- pars['cen_g'].value, pars['wid_g'].value)
- yl = lorentzian(x, pars['amp_l'].value,
- pars['cen_l'].value, pars['wid_l'].value)
-
- slope = pars['line_slope'].value
- offset = pars['line_off'].value
- model = yg + yl + offset + x * slope
- if data is None:
- return model
- if sigma is None:
- return (model - data)
- return (model - data)/sigma
-
-
- n = 601
- xmin = 0.
- xmax = 20.0
- x = linspace(xmin, xmax, n)
-
- data = (gaussian(x, 21, 8.1, 1.2) +
- lorentzian(x, 10, 9.6, 2.4) +
- random.normal(scale=0.23, size=n) +
- x*0.5)
-
-
- pfit = Parameters()
- pfit.add(name='amp_g', value=10)
- pfit.add(name='cen_g', value=9)
- pfit.add(name='wid_g', value=1)
-
- pfit.add(name='amp_tot', value=20)
- pfit.add(name='amp_l', expr='amp_tot - amp_g')
- pfit.add(name='cen_l', expr='1.5+cen_g')
- pfit.add(name='wid_l', expr='2*wid_g')
-
- pfit.add(name='line_slope', value=0.0)
- pfit.add(name='line_off', value=0.0)
-
- sigma = 0.021 # estimate of data error (for all data points)
-
- myfit = Minimizer(residual, pfit,
- fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data},
- scale_covar=True)
-
- myfit.prepare_fit()
- init = residual(myfit.params, x)
-
- result = myfit.leastsq()
-
- print(' Nfev = ', result.nfev)
- print( result.chisqr, result.redchi, result.nfree)
-
- report_fit(result.params)
- pfit= result.params
- fit = residual(result.params, x)
- assert(pfit['cen_l'].value == 1.5 + pfit['cen_g'].value)
- assert(pfit['amp_l'].value == pfit['amp_tot'].value - pfit['amp_g'].value)
- assert(pfit['wid_l'].value == 2 * pfit['wid_g'].value)
-
-
-def test_constraints2():
- """add a user-defined function to symbol table"""
- def residual(pars, x, sigma=None, data=None):
- yg = gaussian(x, pars['amp_g'].value,
- pars['cen_g'].value, pars['wid_g'].value)
- yl = lorentzian(x, pars['amp_l'].value,
- pars['cen_l'].value, pars['wid_l'].value)
-
- slope = pars['line_slope'].value
- offset = pars['line_off'].value
- model = yg + yl + offset + x * slope
- if data is None:
- return model
- if sigma is None:
- return (model - data)
- return (model - data)/sigma
-
-
- n = 601
- xmin = 0.
- xmax = 20.0
- x = linspace(xmin, xmax, n)
-
- data = (gaussian(x, 21, 8.1, 1.2) +
- lorentzian(x, 10, 9.6, 2.4) +
- random.normal(scale=0.23, size=n) +
- x*0.5)
-
- pfit = Parameters()
- pfit.add(name='amp_g', value=10)
- pfit.add(name='cen_g', value=9)
- pfit.add(name='wid_g', value=1)
-
- pfit.add(name='amp_tot', value=20)
- pfit.add(name='amp_l', expr='amp_tot - amp_g')
- pfit.add(name='cen_l', expr='1.5+cen_g')
- pfit.add(name='line_slope', value=0.0)
- pfit.add(name='line_off', value=0.0)
-
- sigma = 0.021 # estimate of data error (for all data points)
-
- myfit = Minimizer(residual, pfit,
- fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data},
- scale_covar=True)
-
- def width_func(wpar):
- """ """
- return 2*wpar
-
- myfit.params._asteval.symtable['wfun'] = width_func
- myfit.params.add(name='wid_l', expr='wfun(wid_g)')
-
- result = myfit.leastsq()
-
- print(' Nfev = ', result.nfev)
- print( result.chisqr, result.redchi, result.nfree)
-
- report_fit(result.params)
- pfit= result.params
- fit = residual(result.params, x)
- assert(pfit['cen_l'].value == 1.5 + pfit['cen_g'].value)
- assert(pfit['amp_l'].value == pfit['amp_tot'].value - pfit['amp_g'].value)
- assert(pfit['wid_l'].value == 2 * pfit['wid_g'].value)
-
-if __name__ == '__main__':
- test_constraints1()
- test_constraints2()
+from numpy import linspace, zeros, sin, exp, random, sqrt, pi, sign +from lmfit import Parameters, Parameter, Minimizer, Model +from lmfit.lineshapes import gaussian, lorentzian, pvoigt +from lmfit.printfuncs import report_fit + +def test_constraints1(): + def residual(pars, x, sigma=None, data=None): + yg = gaussian(x, pars['amp_g'].value, + pars['cen_g'].value, pars['wid_g'].value) + yl = lorentzian(x, pars['amp_l'].value, + pars['cen_l'].value, pars['wid_l'].value) + + slope = pars['line_slope'].value + offset = pars['line_off'].value + model = yg + yl + offset + x * slope + if data is None: + return model + if sigma is None: + return (model - data) + return (model - data)/sigma + + + n = 601 + xmin = 0. + xmax = 20.0 + x = linspace(xmin, xmax, n) + + data = (gaussian(x, 21, 8.1, 1.2) + + lorentzian(x, 10, 9.6, 2.4) + + random.normal(scale=0.23, size=n) + + x*0.5) + + + pfit = Parameters() + pfit.add(name='amp_g', value=10) + pfit.add(name='cen_g', value=9) + pfit.add(name='wid_g', value=1) + + pfit.add(name='amp_tot', value=20) + pfit.add(name='amp_l', expr='amp_tot - amp_g') + pfit.add(name='cen_l', expr='1.5+cen_g') + pfit.add(name='wid_l', expr='2*wid_g') + + pfit.add(name='line_slope', value=0.0) + pfit.add(name='line_off', value=0.0) + + sigma = 0.021 # estimate of data error (for all data points) + + myfit = Minimizer(residual, pfit, + fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data}, + scale_covar=True) + + myfit.prepare_fit() + init = residual(myfit.params, x) + + result = myfit.leastsq() + + print(' Nfev = ', result.nfev) + print( result.chisqr, result.redchi, result.nfree) + + report_fit(result.params) + pfit= result.params + fit = residual(result.params, x) + assert(pfit['cen_l'].value == 1.5 + pfit['cen_g'].value) + assert(pfit['amp_l'].value == pfit['amp_tot'].value - pfit['amp_g'].value) + assert(pfit['wid_l'].value == 2 * pfit['wid_g'].value) + +def test_constraints2(): + """add a user-defined function to symbol table""" + def residual(pars, x, sigma=None, data=None): + yg = gaussian(x, pars['amp_g'].value, + pars['cen_g'].value, pars['wid_g'].value) + yl = lorentzian(x, pars['amp_l'].value, + pars['cen_l'].value, pars['wid_l'].value) + + slope = pars['line_slope'].value + offset = pars['line_off'].value + model = yg + yl + offset + x * slope + if data is None: + return model + if sigma is None: + return (model - data) + return (model - data)/sigma + + + n = 601 + xmin = 0. + xmax = 20.0 + x = linspace(xmin, xmax, n) + + data = (gaussian(x, 21, 8.1, 1.2) + + lorentzian(x, 10, 9.6, 2.4) + + random.normal(scale=0.23, size=n) + + x*0.5) + + pfit = Parameters() + pfit.add(name='amp_g', value=10) + pfit.add(name='cen_g', value=9) + pfit.add(name='wid_g', value=1) + + pfit.add(name='amp_tot', value=20) + pfit.add(name='amp_l', expr='amp_tot - amp_g') + pfit.add(name='cen_l', expr='1.5+cen_g') + pfit.add(name='line_slope', value=0.0) + pfit.add(name='line_off', value=0.0) + + sigma = 0.021 # estimate of data error (for all data points) + + myfit = Minimizer(residual, pfit, + fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data}, + scale_covar=True) + + def width_func(wpar): + """ """ + return 2*wpar + + myfit.params._asteval.symtable['wfun'] = width_func + + try: + myfit.params.add(name='wid_l', expr='wfun(wid_g)') + except: + assert(False) + + result = myfit.leastsq() + + print(' Nfev = ', result.nfev) + print( result.chisqr, result.redchi, result.nfree) + report_fit(result.params) + pfit= result.params + fit = residual(result.params, x) + assert(pfit['cen_l'].value == 1.5 + pfit['cen_g'].value) + assert(pfit['amp_l'].value == pfit['amp_tot'].value - pfit['amp_g'].value) + assert(pfit['wid_l'].value == 2 * pfit['wid_g'].value) + + +def test_constraints3(): + """test a constraint with simple function call""" + x = [1723, 1773, 1823, 1523, 1773, 1033.03078, + 1042.98077, 1047.90937, 1053.95899, 1057.94906, + 1063.13788, 1075.74218, 1086.03102] + y = [0.79934, -0.31876, -0.46852, 0.05, -0.21, + 11.1708, 10.31844, 9.73069, 9.21319, 9.12457, + 9.05243, 8.66407, 8.29664] + + def VFT(T, ninf=-3, A=5e3, T0=800): + return ninf + A/(T-T0) + + vftModel = Model(VFT) + vftModel.set_param_hint('D', vary=False, expr=r'A*log(10)/T0') + result = vftModel.fit(y, T=x) + assert(result.params['A'].value > 2600.0) + assert(result.params['A'].value < 2650.0) + assert(result.params['D'].value > 7.0) + assert(result.params['D'].value < 7.5) + +if __name__ == '__main__': + test_constraints1() + test_constraints2() + test_constraints3() diff --git a/tests/test_algebraic_constraint2.py b/tests/test_algebraic_constraint2.py index 9b4cd88..45a9b6a 100644 --- a/tests/test_algebraic_constraint2.py +++ b/tests/test_algebraic_constraint2.py @@ -1,103 +1,103 @@ -from numpy import linspace, zeros, sin, exp, random, sqrt, pi, sign
-from lmfit import Parameters, Parameter, Minimizer
-from lmfit.lineshapes import gaussian, lorentzian, pvoigt
-from lmfit.printfuncs import report_fit
-import sys
-
-
-# Turn off plotting if run by nosetests.
-WITHPLOT = True
-for arg in sys.argv:
- if 'nose' in arg:
- WITHPLOT = False
-
-if WITHPLOT:
- try:
- import matplotlib
- import pylab
- except ImportError:
- WITHPLOT = False
-
-
-def test_constraints(with_plot=True):
- with_plot = with_plot and WITHPLOT
-
- def residual(pars, x, sigma=None, data=None):
- yg = gaussian(x, pars['amp_g'].value,
- pars['cen_g'].value, pars['wid_g'].value)
- yl = lorentzian(x, pars['amp_l'].value,
- pars['cen_l'].value, pars['wid_l'].value)
-
- slope = pars['line_slope'].value
- offset = pars['line_off'].value
- model = yg + yl + offset + x * slope
- if data is None:
- return model
- if sigma is None:
- return (model - data)
- return (model - data) / sigma
-
-
- n = 201
- xmin = 0.
- xmax = 20.0
- x = linspace(xmin, xmax, n)
-
- data = (gaussian(x, 21, 8.1, 1.2) +
- lorentzian(x, 10, 9.6, 2.4) +
- random.normal(scale=0.23, size=n) +
- x*0.5)
-
- if with_plot:
- pylab.plot(x, data, 'r+')
-
- pfit = Parameters()
- pfit.add(name='amp_g', value=10)
- pfit.add(name='cen_g', value=9)
- pfit.add(name='wid_g', value=1)
-
- pfit.add(name='amp_tot', value=20)
- pfit.add(name='amp_l', expr='amp_tot - amp_g')
- pfit.add(name='cen_l', expr='1.5+cen_g')
- pfit.add(name='wid_l', expr='2*wid_g')
-
- pfit.add(name='line_slope', value=0.0)
- pfit.add(name='line_off', value=0.0)
-
- sigma = 0.021 # estimate of data error (for all data points)
-
- myfit = Minimizer(residual, pfit,
- fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data},
- scale_covar=True)
-
- myfit.prepare_fit()
- init = residual(myfit.params, x)
-
- result = myfit.leastsq()
-
- print(' Nfev = ', result.nfev)
- print( result.chisqr, result.redchi, result.nfree)
-
- report_fit(result.params, min_correl=0.3)
-
- fit = residual(result.params, x)
- if with_plot:
- pylab.plot(x, fit, 'b-')
- assert(result.params['cen_l'].value == 1.5 + result.params['cen_g'].value)
- assert(result.params['amp_l'].value == result.params['amp_tot'].value - result.params['amp_g'].value)
- assert(result.params['wid_l'].value == 2 * result.params['wid_g'].value)
-
- # now, change fit slightly and re-run
- myfit.params['wid_l'].expr = '1.25*wid_g'
- result = myfit.leastsq()
- report_fit(result.params, min_correl=0.4)
- fit2 = residual(result.params, x)
- if with_plot:
- pylab.plot(x, fit2, 'k')
- pylab.show()
-
- assert(result.params['cen_l'].value == 1.5 + result.params['cen_g'].value)
- assert(result.params['amp_l'].value == result.params['amp_tot'].value - result.params['amp_g'].value)
- assert(result.params['wid_l'].value == 1.25 * result.params['wid_g'].value)
-
-test_constraints()
+from numpy import linspace, zeros, sin, exp, random, sqrt, pi, sign +from lmfit import Parameters, Parameter, Minimizer +from lmfit.lineshapes import gaussian, lorentzian, pvoigt +from lmfit.printfuncs import report_fit +import sys + + +# Turn off plotting if run by nosetests. +WITHPLOT = True +for arg in sys.argv: + if 'nose' in arg: + WITHPLOT = False + +if WITHPLOT: + try: + import matplotlib + import pylab + except ImportError: + WITHPLOT = False + + +def test_constraints(with_plot=True): + with_plot = with_plot and WITHPLOT + + def residual(pars, x, sigma=None, data=None): + yg = gaussian(x, pars['amp_g'].value, + pars['cen_g'].value, pars['wid_g'].value) + yl = lorentzian(x, pars['amp_l'].value, + pars['cen_l'].value, pars['wid_l'].value) + + slope = pars['line_slope'].value + offset = pars['line_off'].value + model = yg + yl + offset + x * slope + if data is None: + return model + if sigma is None: + return (model - data) + return (model - data) / sigma + + + n = 201 + xmin = 0. + xmax = 20.0 + x = linspace(xmin, xmax, n) + + data = (gaussian(x, 21, 8.1, 1.2) + + lorentzian(x, 10, 9.6, 2.4) + + random.normal(scale=0.23, size=n) + + x*0.5) + + if with_plot: + pylab.plot(x, data, 'r+') + + pfit = Parameters() + pfit.add(name='amp_g', value=10) + pfit.add(name='cen_g', value=9) + pfit.add(name='wid_g', value=1) + + pfit.add(name='amp_tot', value=20) + pfit.add(name='amp_l', expr='amp_tot - amp_g') + pfit.add(name='cen_l', expr='1.5+cen_g') + pfit.add(name='wid_l', expr='2*wid_g') + + pfit.add(name='line_slope', value=0.0) + pfit.add(name='line_off', value=0.0) + + sigma = 0.021 # estimate of data error (for all data points) + + myfit = Minimizer(residual, pfit, + fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data}, + scale_covar=True) + + myfit.prepare_fit() + init = residual(myfit.params, x) + + result = myfit.leastsq() + + print(' Nfev = ', result.nfev) + print( result.chisqr, result.redchi, result.nfree) + + report_fit(result.params, min_correl=0.3) + + fit = residual(result.params, x) + if with_plot: + pylab.plot(x, fit, 'b-') + assert(result.params['cen_l'].value == 1.5 + result.params['cen_g'].value) + assert(result.params['amp_l'].value == result.params['amp_tot'].value - result.params['amp_g'].value) + assert(result.params['wid_l'].value == 2 * result.params['wid_g'].value) + + # now, change fit slightly and re-run + myfit.params['wid_l'].expr = '1.25*wid_g' + result = myfit.leastsq() + report_fit(result.params, min_correl=0.4) + fit2 = residual(result.params, x) + if with_plot: + pylab.plot(x, fit2, 'k') + pylab.show() + + assert(result.params['cen_l'].value == 1.5 + result.params['cen_g'].value) + assert(result.params['amp_l'].value == result.params['amp_tot'].value - result.params['amp_g'].value) + assert(result.params['wid_l'].value == 1.25 * result.params['wid_g'].value) + +test_constraints() diff --git a/tests/test_basicfit.py b/tests/test_basicfit.py index bcad50c..98b6338 100644 --- a/tests/test_basicfit.py +++ b/tests/test_basicfit.py @@ -1,47 +1,47 @@ -import numpy as np
-from lmfit import minimize, Parameters, Parameter, report_fit
-from lmfit_testutils import assert_paramval, assert_paramattr
-
-
-def test_basic():
- # create data to be fitted
- x = np.linspace(0, 15, 301)
- data = (5. * np.sin(2 * x - 0.1) * np.exp(-x*x*0.025) +
- np.random.normal(size=len(x), scale=0.2) )
-
- # define objective function: returns the array to be minimized
- def fcn2min(params, x, data):
- """ model decaying sine wave, subtract data"""
- amp = params['amp'].value
- shift = params['shift'].value
- omega = params['omega'].value
- decay = params['decay'].value
-
- model = amp * np.sin(x * omega + shift) * np.exp(-x*x*decay)
- return model - data
-
- # create a set of Parameters
- params = Parameters()
- params.add('amp', value= 10, min=0)
- params.add('decay', value= 0.1)
- params.add('shift', value= 0.0, min=-np.pi/2., max=np.pi/2)
- params.add('omega', value= 3.0)
-
- # do fit, here with leastsq model
- result = minimize(fcn2min, params, args=(x, data))
-
- # calculate final result
- final = data + result.residual
-
- # report_fit(result)
-
- assert(result.nfev > 5)
- assert(result.nfev < 500)
- assert(result.chisqr > 1)
- assert(result.nvarys == 4)
- assert_paramval(result.params['amp'], 5.03, tol=0.05)
- assert_paramval(result.params['omega'], 2.0, tol=0.05)
-
-
-if __name__ == '__main__':
- test_basic()
+import numpy as np +from lmfit import minimize, Parameters, Parameter, report_fit +from lmfit_testutils import assert_paramval, assert_paramattr + + +def test_basic(): + # create data to be fitted + x = np.linspace(0, 15, 301) + data = (5. * np.sin(2 * x - 0.1) * np.exp(-x*x*0.025) + + np.random.normal(size=len(x), scale=0.2) ) + + # define objective function: returns the array to be minimized + def fcn2min(params, x, data): + """ model decaying sine wave, subtract data""" + amp = params['amp'].value + shift = params['shift'].value + omega = params['omega'].value + decay = params['decay'].value + + model = amp * np.sin(x * omega + shift) * np.exp(-x*x*decay) + return model - data + + # create a set of Parameters + params = Parameters() + params.add('amp', value= 10, min=0) + params.add('decay', value= 0.1) + params.add('shift', value= 0.0, min=-np.pi/2., max=np.pi/2) + params.add('omega', value= 3.0) + + # do fit, here with leastsq model + result = minimize(fcn2min, params, args=(x, data)) + + # calculate final result + final = data + result.residual + + # report_fit(result) + + assert(result.nfev > 5) + assert(result.nfev < 500) + assert(result.chisqr > 1) + assert(result.nvarys == 4) + assert_paramval(result.params['amp'], 5.03, tol=0.05) + assert_paramval(result.params['omega'], 2.0, tol=0.05) + + +if __name__ == '__main__': + test_basic() diff --git a/tests/test_bounded_jacobian.py b/tests/test_bounded_jacobian.py index a8fc2f4..810a505 100644 --- a/tests/test_bounded_jacobian.py +++ b/tests/test_bounded_jacobian.py @@ -1,43 +1,43 @@ -from lmfit import Parameters, minimize, fit_report
-from lmfit_testutils import assert_paramval, assert_paramattr
-
-import numpy as np
-
-
-def test_bounded_jacobian():
- pars = Parameters()
- pars.add('x0', value=2.0)
- pars.add('x1', value=2.0, min=1.5)
-
- global jac_count
-
- jac_count = 0
-
- def resid(params):
- x0 = params['x0'].value
- x1 = params['x1'].value
- return np.array([10 * (x1 - x0*x0), 1-x0])
-
- def jac(params):
- global jac_count
- jac_count += 1
- x0 = params['x0'].value
- return np.array([[-20*x0, 10], [-1, 0]])
-
- out0 = minimize(resid, pars, Dfun=None)
-
- assert_paramval(out0.params['x0'], 1.2243, tol=0.02)
- assert_paramval(out0.params['x1'], 1.5000, tol=0.02)
- assert(jac_count == 0)
-
- out1 = minimize(resid, pars, Dfun=jac)
-
- assert_paramval(out1.params['x0'], 1.2243, tol=0.02)
- assert_paramval(out1.params['x1'], 1.5000, tol=0.02)
- assert(jac_count > 5)
-
- print(fit_report(out1, show_correl=True))
-
-
-if __name__ == '__main__':
- test_bounded_jacobian()
+from lmfit import Parameters, minimize, fit_report +from lmfit_testutils import assert_paramval, assert_paramattr + +import numpy as np + + +def test_bounded_jacobian(): + pars = Parameters() + pars.add('x0', value=2.0) + pars.add('x1', value=2.0, min=1.5) + + global jac_count + + jac_count = 0 + + def resid(params): + x0 = params['x0'].value + x1 = params['x1'].value + return np.array([10 * (x1 - x0*x0), 1-x0]) + + def jac(params): + global jac_count + jac_count += 1 + x0 = params['x0'].value + return np.array([[-20*x0, 10], [-1, 0]]) + + out0 = minimize(resid, pars, Dfun=None) + + assert_paramval(out0.params['x0'], 1.2243, tol=0.02) + assert_paramval(out0.params['x1'], 1.5000, tol=0.02) + assert(jac_count == 0) + + out1 = minimize(resid, pars, Dfun=jac) + + assert_paramval(out1.params['x0'], 1.2243, tol=0.02) + assert_paramval(out1.params['x1'], 1.5000, tol=0.02) + assert(jac_count > 5) + + print(fit_report(out1, show_correl=True)) + + +if __name__ == '__main__': + test_bounded_jacobian() diff --git a/tests/test_bounds.py b/tests/test_bounds.py index c23ee94..99c962d 100644 --- a/tests/test_bounds.py +++ b/tests/test_bounds.py @@ -1,54 +1,54 @@ -from lmfit import Parameters, minimize, fit_report
-from lmfit_testutils import assert_paramval, assert_paramattr
-
-from numpy import linspace, zeros, sin, exp, random, pi, sign
-
-def test_bounds():
- p_true = Parameters()
- p_true.add('amp', value=14.0)
- p_true.add('period', value=5.4321)
- p_true.add('shift', value=0.12345)
- p_true.add('decay', value=0.01000)
-
- def residual(pars, x, data=None):
- amp = pars['amp'].value
- per = pars['period'].value
- shift = pars['shift'].value
- decay = pars['decay'].value
-
- if abs(shift) > pi/2:
- shift = shift - sign(shift)*pi
-
- model = amp*sin(shift + x/per) * exp(-x*x*decay*decay)
- if data is None:
- return model
- return (model - data)
-
- n = 1500
- xmin = 0.
- xmax = 250.0
- random.seed(0)
- noise = random.normal(scale=2.80, size=n)
- x = linspace(xmin, xmax, n)
- data = residual(p_true, x) + noise
-
- fit_params = Parameters()
- fit_params.add('amp', value=13.0, max=20, min=0.0)
- fit_params.add('period', value=2, max=10)
- fit_params.add('shift', value=0.0, max=pi/2., min=-pi/2.)
- fit_params.add('decay', value=0.02, max=0.10, min=0.00)
-
- out = minimize(residual, fit_params, args=(x,), kws={'data':data})
-
- fit = residual(out.params, x)
-
- assert(out.nfev > 10)
- assert(out.nfree > 50)
- assert(out.chisqr > 1.0)
-
- print(fit_report(out, show_correl=True, modelpars=p_true))
- assert_paramval(out.params['decay'], 0.01, tol=1.e-2)
- assert_paramval(out.params['shift'], 0.123, tol=1.e-2)
-
-if __name__ == '__main__':
- test_bounds()
+from lmfit import Parameters, minimize, fit_report +from lmfit_testutils import assert_paramval, assert_paramattr + +from numpy import linspace, zeros, sin, exp, random, pi, sign + +def test_bounds(): + p_true = Parameters() + p_true.add('amp', value=14.0) + p_true.add('period', value=5.4321) + p_true.add('shift', value=0.12345) + p_true.add('decay', value=0.01000) + + def residual(pars, x, data=None): + amp = pars['amp'].value + per = pars['period'].value + shift = pars['shift'].value + decay = pars['decay'].value + + if abs(shift) > pi/2: + shift = shift - sign(shift)*pi + + model = amp*sin(shift + x/per) * exp(-x*x*decay*decay) + if data is None: + return model + return (model - data) + + n = 1500 + xmin = 0. + xmax = 250.0 + random.seed(0) + noise = random.normal(scale=2.80, size=n) + x = linspace(xmin, xmax, n) + data = residual(p_true, x) + noise + + fit_params = Parameters() + fit_params.add('amp', value=13.0, max=20, min=0.0) + fit_params.add('period', value=2, max=10) + fit_params.add('shift', value=0.0, max=pi/2., min=-pi/2.) + fit_params.add('decay', value=0.02, max=0.10, min=0.00) + + out = minimize(residual, fit_params, args=(x,), kws={'data':data}) + + fit = residual(out.params, x) + + assert(out.nfev > 10) + assert(out.nfree > 50) + assert(out.chisqr > 1.0) + + print(fit_report(out, show_correl=True, modelpars=p_true)) + assert_paramval(out.params['decay'], 0.01, tol=1.e-2) + assert_paramval(out.params['shift'], 0.123, tol=1.e-2) + +if __name__ == '__main__': + test_bounds() diff --git a/tests/test_confidence.py b/tests/test_confidence.py index 7d90d00..2b5d290 100644 --- a/tests/test_confidence.py +++ b/tests/test_confidence.py @@ -1,44 +1,88 @@ -import numpy as np
-from numpy.testing import assert_allclose
-
-import lmfit
-from lmfit_testutils import assert_paramval
-
-def residual(params, x, data):
- a = params['a'].value
- b = params['b'].value
- return data - 1.0/(a*x)+b
-
-def test_confidence1():
- x = np.linspace(0.3,10,100)
- np.random.seed(0)
-
- y = 1/(0.1*x)+2+0.1*np.random.randn(x.size)
-
- pars = lmfit.Parameters()
- pars.add_many(('a', 0.1), ('b', 1))
-
- minimizer = lmfit.Minimizer(residual, pars, fcn_args=(x, y) )
- out = minimizer.leastsq()
- # lmfit.report_fit(out)
-
- assert(out.nfev > 5)
- assert(out.nfev < 500)
- assert(out.chisqr < 3.0)
- assert(out.nvarys == 2)
-
- assert_paramval(out.params['a'], 0.1, tol=0.1)
- assert_paramval(out.params['b'], -2.0, tol=0.1)
-
- ci = lmfit.conf_interval(minimizer, out)
- assert_allclose(ci['b'][0][0], 0.997, rtol=0.01)
- assert_allclose(ci['b'][0][1], -2.022, rtol=0.01)
- assert_allclose(ci['b'][2][0], 0.674, rtol=0.01)
- assert_allclose(ci['b'][2][1], -1.997, rtol=0.01)
- assert_allclose(ci['b'][5][0], 0.95, rtol=0.01)
- assert_allclose(ci['b'][5][1], -1.96, rtol=0.01)
-
- # lmfit.printfuncs.report_ci(ci)
-
-if __name__ == '__main__':
- test_confidence1()
+import numpy as np +from numpy.testing import assert_allclose + +import lmfit +from lmfit_testutils import assert_paramval + +def residual(params, x, data): + a = params['a'].value + b = params['b'].value + return data - 1.0/(a*x)+b + +def residual2(params, x, data): + a = params['a'].value + b = params['b'].value + c = params['c'].value + return data - c/(a*x)+b + +def test_confidence1(): + x = np.linspace(0.3,10,100) + np.random.seed(0) + + y = 1/(0.1*x)+2+0.1*np.random.randn(x.size) + + pars = lmfit.Parameters() + pars.add_many(('a', 0.1), ('b', 1)) + + minimizer = lmfit.Minimizer(residual, pars, fcn_args=(x, y) ) + out = minimizer.leastsq() + # lmfit.report_fit(out) + + assert(out.nfev > 5) + assert(out.nfev < 500) + assert(out.chisqr < 3.0) + assert(out.nvarys == 2) + + assert_paramval(out.params['a'], 0.1, tol=0.1) + assert_paramval(out.params['b'], -2.0, tol=0.1) + + ci = lmfit.conf_interval(minimizer, out) + assert_allclose(ci['b'][0][0], 0.997, rtol=0.01) + assert_allclose(ci['b'][0][1], -2.022, rtol=0.01) + assert_allclose(ci['b'][2][0], 0.674, rtol=0.01) + assert_allclose(ci['b'][2][1], -1.997, rtol=0.01) + assert_allclose(ci['b'][5][0], 0.95, rtol=0.01) + assert_allclose(ci['b'][5][1], -1.96, rtol=0.01) + + # lmfit.printfuncs.report_ci(ci) + + +def test_confidence2(): + x = np.linspace(0.3,10,100) + np.random.seed(0) + + y = 1/(0.1*x)+2+0.1*np.random.randn(x.size) + + pars = lmfit.Parameters() + pars.add_many(('a', 0.1), ('b', 1), ('c', 1.0)) + pars['a'].max = 0.25 + pars['a'].min = 0.00 + pars['a'].value = 0.2 + pars['c'].vary = False + + minimizer = lmfit.Minimizer(residual2, pars, fcn_args=(x, y) ) + out = minimizer.minimize(method='nelder') + out = minimizer.minimize(method='leastsq', params=out.params) + # lmfit.report_fit(out) + + assert(out.nfev > 5) + assert(out.nfev < 500) + assert(out.chisqr < 3.0) + assert(out.nvarys == 2) + + assert_paramval(out.params['a'], 0.1, tol=0.1) + assert_paramval(out.params['b'], -2.0, tol=0.1) + + ci = lmfit.conf_interval(minimizer, out) + assert_allclose(ci['b'][0][0], 0.997, rtol=0.01) + assert_allclose(ci['b'][0][1], -2.022, rtol=0.01) + assert_allclose(ci['b'][2][0], 0.674, rtol=0.01) + assert_allclose(ci['b'][2][1], -1.997, rtol=0.01) + assert_allclose(ci['b'][5][0], 0.95, rtol=0.01) + assert_allclose(ci['b'][5][1], -1.96, rtol=0.01) + + lmfit.printfuncs.report_ci(ci) + +if __name__ == '__main__': + test_confidence1() + test_confidence2() diff --git a/tests/test_copy_params.py b/tests/test_copy_params.py index d68387b..e17aa18 100644 --- a/tests/test_copy_params.py +++ b/tests/test_copy_params.py @@ -1,36 +1,36 @@ -import numpy as np
-from lmfit import Parameters, minimize, report_fit
-
-def get_data():
- x = np.arange(0, 1, 0.01)
- y1 = 1.5*np.exp(0.9*x) + np.random.normal(scale=0.001, size=len(x))
- y2 = 2.0 + x + 1/2.*x**2 +1/3.*x**3
- y2 = y2 + np.random.normal(scale=0.001, size=len(x))
- return x, y1, y2
-
-def residual(params, x, data):
- a = params['a'].value
- b = params['b'].value
-
- model = a*np.exp(b*x)
- return (data-model)
-
-def test_copy_params():
- x, y1, y2 = get_data()
-
- params = Parameters()
- params.add('a', value = 2.0)
- params.add('b', value = 2.0)
-
- # fit to first data set
- out1 = minimize(residual, params, args=(x, y1))
-
- # fit to second data set
- out2 = minimize(residual, params, args=(x, y2))
-
- adiff = out1.params['a'].value - out2.params['a'].value
- bdiff = out1.params['b'].value - out2.params['b'].value
-
- assert(abs(adiff) > 1.e-2)
- assert(abs(bdiff) > 1.e-2)
-
+import numpy as np +from lmfit import Parameters, minimize, report_fit + +def get_data(): + x = np.arange(0, 1, 0.01) + y1 = 1.5*np.exp(0.9*x) + np.random.normal(scale=0.001, size=len(x)) + y2 = 2.0 + x + 1/2.*x**2 +1/3.*x**3 + y2 = y2 + np.random.normal(scale=0.001, size=len(x)) + return x, y1, y2 + +def residual(params, x, data): + a = params['a'].value + b = params['b'].value + + model = a*np.exp(b*x) + return (data-model) + +def test_copy_params(): + x, y1, y2 = get_data() + + params = Parameters() + params.add('a', value = 2.0) + params.add('b', value = 2.0) + + # fit to first data set + out1 = minimize(residual, params, args=(x, y1)) + + # fit to second data set + out2 = minimize(residual, params, args=(x, y2)) + + adiff = out1.params['a'].value - out2.params['a'].value + bdiff = out1.params['b'].value - out2.params['b'].value + + assert(abs(adiff) > 1.e-2) + assert(abs(bdiff) > 1.e-2) + diff --git a/tests/test_default_kws.py b/tests/test_default_kws.py index 93a1c8f..8ab835f 100644 --- a/tests/test_default_kws.py +++ b/tests/test_default_kws.py @@ -1,24 +1,24 @@ -import numpy as np
-from nose.tools import assert_true
-from lmfit.lineshapes import gaussian
-from lmfit.models import GaussianModel
-
-
-def test_default_inputs_gauss():
-
- area = 1
- cen = 0
- std = 0.2
- x = np.arange(-3, 3, 0.01)
- y = gaussian(x, area, cen, std)
-
- g = GaussianModel()
-
- fit_option1 = {'maxfev': 5000, 'xtol': 1e-2}
- result1 = g.fit(y, x=x, amplitude=1, center=0, sigma=0.5, fit_kws=fit_option1)
-
- fit_option2 = {'maxfev': 5000, 'xtol': 1e-6}
- result2 = g.fit(y, x=x, amplitude=1, center=0, sigma=0.5, fit_kws=fit_option2)
-
- assert_true(result1.values!=result2.values)
- return
+import numpy as np +from nose.tools import assert_true +from lmfit.lineshapes import gaussian +from lmfit.models import GaussianModel + + +def test_default_inputs_gauss(): + + area = 1 + cen = 0 + std = 0.2 + x = np.arange(-3, 3, 0.01) + y = gaussian(x, area, cen, std) + + g = GaussianModel() + + fit_option1 = {'maxfev': 5000, 'xtol': 1e-2} + result1 = g.fit(y, x=x, amplitude=1, center=0, sigma=0.5, fit_kws=fit_option1) + + fit_option2 = {'maxfev': 5000, 'xtol': 1e-6} + result2 = g.fit(y, x=x, amplitude=1, center=0, sigma=0.5, fit_kws=fit_option2) + + assert_true(result1.values!=result2.values) + return diff --git a/tests/test_itercb.py b/tests/test_itercb.py index cefcc5d..f77eb48 100644 --- a/tests/test_itercb.py +++ b/tests/test_itercb.py @@ -1,29 +1,29 @@ -import numpy as np
-from lmfit import Parameters, minimize, report_fit
-from lmfit.models import LinearModel, GaussianModel
-from lmfit.lineshapes import gaussian
-
-def per_iteration(pars, iter, resid, *args, **kws):
- """iteration callback, will abort at iteration 23
- """
- # print( iter, ', '.join(["%s=%.4f" % (p.name, p.value) for p in pars.values()]))
- return iter == 23
-
-def test_itercb():
- x = np.linspace(0, 20, 401)
- y = gaussian(x, amplitude=24.56, center=7.6543, sigma=1.23)
- y = y - .20*x + 3.333 + np.random.normal(scale=0.23, size=len(x))
- mod = GaussianModel(prefix='peak_') + LinearModel(prefix='bkg_')
-
- pars = mod.make_params(peak_amplitude=21.0,
- peak_center=7.0,
- peak_sigma=2.0,
- bkg_intercept=2,
- bkg_slope=0.0)
-
- out = mod.fit(y, pars, x=x, iter_cb=per_iteration)
-
- assert(out.nfev == 23)
- assert(out.aborted)
- assert(not out.errorbars)
- assert(not out.success)
+import numpy as np +from lmfit import Parameters, minimize, report_fit +from lmfit.models import LinearModel, GaussianModel +from lmfit.lineshapes import gaussian + +def per_iteration(pars, iter, resid, *args, **kws): + """iteration callback, will abort at iteration 23 + """ + # print( iter, ', '.join(["%s=%.4f" % (p.name, p.value) for p in pars.values()])) + return iter == 23 + +def test_itercb(): + x = np.linspace(0, 20, 401) + y = gaussian(x, amplitude=24.56, center=7.6543, sigma=1.23) + y = y - .20*x + 3.333 + np.random.normal(scale=0.23, size=len(x)) + mod = GaussianModel(prefix='peak_') + LinearModel(prefix='bkg_') + + pars = mod.make_params(peak_amplitude=21.0, + peak_center=7.0, + peak_sigma=2.0, + bkg_intercept=2, + bkg_slope=0.0) + + out = mod.fit(y, pars, x=x, iter_cb=per_iteration) + + assert(out.nfev == 23) + assert(out.aborted) + assert(not out.errorbars) + assert(not out.success) diff --git a/tests/test_manypeaks_speed.py b/tests/test_manypeaks_speed.py index 4f870ac..c756936 100644 --- a/tests/test_manypeaks_speed.py +++ b/tests/test_manypeaks_speed.py @@ -1,37 +1,37 @@ -#
-# test speed of building complex model
-#
-import time
-import sys
-import numpy as np
-from lmfit import Model
-from lmfit.lineshapes import gaussian
-from copy import deepcopy
-
-
-sys.setrecursionlimit(2000)
-
-def test_manypeaks_speed():
- x = np.linspace( -5, 5, 251)
- model = None
- t0 = time.time()
- for i in np.arange(500):
- g = Model(gaussian, prefix='g%i_' % i)
- if model is None:
- model = g
- else:
- model += g
- t1 = time.time()
- pars = model.make_params()
- t2 = time.time()
- cpars = deepcopy(pars)
- t3 = time.time()
-
- # these are very conservative tests that
- # should be satisfied on nearly any machine
- assert((t3-t2) < 0.5)
- assert((t2-t1) < 0.5)
- assert((t1-t0) < 5.0)
-
-if __name__ == '__main__':
- test_manypeaks_speed()
+# +# test speed of building complex model +# +import time +import sys +import numpy as np +from lmfit import Model +from lmfit.lineshapes import gaussian +from copy import deepcopy + + +sys.setrecursionlimit(2000) + +def test_manypeaks_speed(): + x = np.linspace( -5, 5, 251) + model = None + t0 = time.time() + for i in np.arange(500): + g = Model(gaussian, prefix='g%i_' % i) + if model is None: + model = g + else: + model += g + t1 = time.time() + pars = model.make_params() + t2 = time.time() + cpars = deepcopy(pars) + t3 = time.time() + + # these are very conservative tests that + # should be satisfied on nearly any machine + assert((t3-t2) < 0.5) + assert((t2-t1) < 0.5) + assert((t1-t0) < 5.0) + +if __name__ == '__main__': + test_manypeaks_speed() diff --git a/tests/test_model.py b/tests/test_model.py index bcc389d..9cede12 100644 --- a/tests/test_model.py +++ b/tests/test_model.py @@ -1,503 +1,585 @@ -import unittest
-import warnings
-import nose
-from numpy.testing import assert_allclose
-from numpy.testing.decorators import knownfailureif
-import numpy as np
-
-from lmfit import Model, Parameter, models
-from lmfit.lineshapes import gaussian
-
-def assert_results_close(actual, desired, rtol=1e-03, atol=1e-03,
- err_msg='', verbose=True):
- for param_name, value in desired.items():
- assert_allclose(actual[param_name], value, rtol, atol, err_msg, verbose)
-
-def _skip_if_no_pandas():
- try:
- import pandas
- except ImportError:
- raise nose.SkipTest("Skipping tests that require pandas.")
-
-
-class CommonTests(object):
- # to be subclassed for testing predefined models
-
- def setUp(self):
- np.random.seed(1)
- self.noise = 0.0001*np.random.randn(*self.x.shape)
- # Some Models need args (e.g., polynomial order), and others don't.
- try:
- args = self.args
- except AttributeError:
- self.model = self.model_constructor()
- self.model_drop = self.model_constructor(missing='drop')
- self.model_raise = self.model_constructor(missing='raise')
- self.model_explicit_var = self.model_constructor(['x'])
- func = self.model.func
- else:
- self.model = self.model_constructor(*args)
- self.model_drop = self.model_constructor(*args, missing='drop')
- self.model_raise = self.model_constructor(*args, missing='raise')
- self.model_explicit_var = self.model_constructor(
- *args, independent_vars=['x'])
- func = self.model.func
- self.data = func(x=self.x, **self.true_values()) + self.noise
-
- @property
- def x(self):
- return np.linspace(1, 10, num=1000)
-
- def test_fit(self):
- model = self.model
-
- # Pass Parameters object.
- params = model.make_params(**self.guess())
- result = model.fit(self.data, params, x=self.x)
- assert_results_close(result.values, self.true_values())
-
- # Pass inidividual Parameter objects as kwargs.
- kwargs = {name: p for name, p in params.items()}
- result = self.model.fit(self.data, x=self.x, **kwargs)
- assert_results_close(result.values, self.true_values())
-
- # Pass guess values (not Parameter objects) as kwargs.
- kwargs = {name: p.value for name, p in params.items()}
- result = self.model.fit(self.data, x=self.x, **kwargs)
- assert_results_close(result.values, self.true_values())
-
- def test_explicit_independent_vars(self):
- self.check_skip_independent_vars()
- model = self.model_explicit_var
- pars = model.make_params(**self.guess())
- result = model.fit(self.data, pars, x=self.x)
- assert_results_close(result.values, self.true_values())
-
- def test_fit_with_weights(self):
- model = self.model
-
- # fit without weights
- params = model.make_params(**self.guess())
- out1 = model.fit(self.data, params, x=self.x)
-
- # fit with weights
- weights = 1.0/(0.5 + self.x**2)
- out2 = model.fit(self.data, params, weights=weights, x=self.x)
-
- max_diff = 0.0
- for parname, val1 in out1.values.items():
- val2 = out2.values[parname]
- if max_diff < abs(val1-val2):
- max_diff = abs(val1-val2)
- assert(max_diff > 1.e-8)
-
- def test_result_attributes(self):
- pars = self.model.make_params(**self.guess())
- result = self.model.fit(self.data, pars, x=self.x)
-
- # result.init_values
- assert_results_close(result.values, self.true_values())
- self.assertEqual(result.init_values, self.guess())
-
- # result.init_params
- params = self.model.make_params()
- for param_name, value in self.guess().items():
- params[param_name].value = value
- self.assertEqual(result.init_params, params)
-
- # result.best_fit
- assert_allclose(result.best_fit, self.data, atol=self.noise.max())
-
- # result.init_fit
- init_fit = self.model.func(x=self.x, **self.guess())
- assert_allclose(result.init_fit, init_fit)
-
- # result.model
- self.assertTrue(result.model is self.model)
-
- def test_result_eval(self):
- # Check eval() output against init_fit and best_fit.
- pars = self.model.make_params(**self.guess())
- result = self.model.fit(self.data, pars, x=self.x)
-
- assert_allclose(result.eval(x=self.x, **result.values),
- result.best_fit)
- assert_allclose(result.eval(x=self.x, **result.init_values),
- result.init_fit)
-
- def test_result_eval_custom_x(self):
- self.check_skip_independent_vars()
- pars = self.model.make_params(**self.guess())
- result = self.model.fit(self.data, pars, x=self.x)
-
- # Check that the independent variable is respected.
- short_eval = result.eval(x=np.array([0, 1, 2]), **result.values)
- self.assertEqual(len(short_eval), 3)
-
- def test_data_alignment(self):
- _skip_if_no_pandas()
- from pandas import Series
-
- # Align data and indep var of different lengths using pandas index.
- data = Series(self.data.copy()).iloc[10:-10]
- x = Series(self.x.copy())
-
- model = self.model
- params = model.make_params(**self.guess())
- result = model.fit(data, params, x=x)
- result = model.fit(data, params, x=x)
- assert_results_close(result.values, self.true_values())
-
- # Skip over missing (NaN) values, aligning via pandas index.
- data.iloc[500:510] = np.nan
- result = self.model_drop.fit(data, params, x=x)
- assert_results_close(result.values, self.true_values())
-
- # Raise if any NaN values are present.
- raises = lambda: self.model_raise.fit(data, params, x=x)
- self.assertRaises(ValueError, raises)
-
- def check_skip_independent_vars(self):
- # to be overridden for models that do not accept indep vars
- pass
-
- def test_aic(self):
- model = self.model
-
- # Pass Parameters object.
- params = model.make_params(**self.guess())
- result = model.fit(self.data, params, x=self.x)
- aic = result.aic
- self.assertTrue(aic < 0) # aic must be negative
-
- # Pass extra unused Parameter.
- params.add("unused_param", value=1.0, vary=True)
- result = model.fit(self.data, params, x=self.x)
- aic_extra = result.aic
- self.assertTrue(aic_extra < 0) # aic must be negative
- self.assertTrue(aic < aic_extra) # the extra param should lower the aic
-
-
- def test_bic(self):
- model = self.model
-
- # Pass Parameters object.
- params = model.make_params(**self.guess())
- result = model.fit(self.data, params, x=self.x)
- bic = result.bic
- self.assertTrue(bic < 0) # aic must be negative
-
- # Compare to AIC
- aic = result.aic
- self.assertTrue(aic < bic) # aic should be lower than bic
-
- # Pass extra unused Parameter.
- params.add("unused_param", value=1.0, vary=True)
- result = model.fit(self.data, params, x=self.x)
- bic_extra = result.bic
- self.assertTrue(bic_extra < 0) # bic must be negative
- self.assertTrue(bic < bic_extra) # the extra param should lower the bic
-
-
-class TestUserDefiniedModel(CommonTests, unittest.TestCase):
- # mainly aimed at checking that the API does what it says it does
- # and raises the right exceptions or warnings when things are not right
-
- def setUp(self):
- self.true_values = lambda: dict(amplitude=7.1, center=1.1, sigma=2.40)
- self.guess = lambda: dict(amplitude=5, center=2, sigma=4)
- # return a fresh copy
- self.model_constructor = (
- lambda *args, **kwargs: Model(gaussian, *args, **kwargs))
- super(TestUserDefiniedModel, self).setUp()
-
- @property
- def x(self):
- return np.linspace(-10, 10, num=1000)
-
- def test_lists_become_arrays(self):
- # smoke test
- self.model.fit([1, 2, 3], x=[1, 2, 3], **self.guess())
- self.model.fit([1, 2, None, 3], x=[1, 2, 3, 4], **self.guess())
-
- def test_missing_param_raises_error(self):
-
- # using keyword argument parameters
- guess_missing_sigma = self.guess()
- del guess_missing_sigma['sigma']
- # f = lambda: self.model.fit(self.data, x=self.x, **guess_missing_sigma)
- # self.assertRaises(ValueError, f)
-
- # using Parameters
- params = self.model.make_params()
- for param_name, value in guess_missing_sigma.items():
- params[param_name].value = value
- f = lambda: self.model.fit(self.data, params, x=self.x)
-
- def test_extra_param_issues_warning(self):
- # The function accepts extra params, Model will warn but not raise.
- def flexible_func(x, amplitude, center, sigma, **kwargs):
- return gaussian(x, amplitude, center, sigma)
-
- flexible_model = Model(flexible_func)
- pars = flexible_model.make_params(**self.guess())
- with warnings.catch_warnings(record=True) as w:
- warnings.simplefilter("always")
- flexible_model.fit(self.data, pars, x=self.x, extra=5)
- self.assertTrue(len(w) == 1)
- self.assertTrue(issubclass(w[-1].category, UserWarning))
-
- def test_missing_independent_variable_raises_error(self):
- pars = self.model.make_params(**self.guess())
- f = lambda: self.model.fit(self.data, pars)
- self.assertRaises(KeyError, f)
-
- def test_bounding(self):
- true_values = self.true_values()
- true_values['center'] = 1.3 # as close as it's allowed to get
- pars = self.model.make_params(**self.guess())
- pars['center'].set(value=2, min=1.3)
- result = self.model.fit(self.data, pars, x=self.x)
- assert_results_close(result.values, true_values, rtol=0.05)
-
- def test_vary_false(self):
- true_values = self.true_values()
- true_values['center'] = 1.3
- pars = self.model.make_params(**self.guess())
- pars['center'].set(value=1.3, vary=False)
- result = self.model.fit(self.data, pars, x=self.x)
- assert_results_close(result.values, true_values, rtol=0.05)
-
- # testing model addition...
-
- def test_user_defined_gaussian_plus_constant(self):
- data = self.data + 5.0
- model = self.model + models.ConstantModel()
- guess = self.guess()
- pars = model.make_params(c= 10.1, **guess)
- true_values = self.true_values()
- true_values['c'] = 5.0
-
- result = model.fit(data, pars, x=self.x)
- assert_results_close(result.values, true_values, rtol=0.01, atol=0.01)
-
- def test_model_with_prefix(self):
- # model with prefix of 'a' and 'b'
- mod = models.GaussianModel(prefix='a')
- vals = {'center': 2.45, 'sigma':0.8, 'amplitude':3.15}
- data = gaussian(x=self.x, **vals) + self.noise/3.0
- pars = mod.guess(data, x=self.x)
- self.assertTrue('aamplitude' in pars)
- self.assertTrue('asigma' in pars)
- out = mod.fit(data, pars, x=self.x)
- self.assertTrue(out.params['aamplitude'].value > 2.0)
- self.assertTrue(out.params['acenter'].value > 2.0)
- self.assertTrue(out.params['acenter'].value < 3.0)
-
- mod = models.GaussianModel(prefix='b')
- data = gaussian(x=self.x, **vals) + self.noise/3.0
- pars = mod.guess(data, x=self.x)
- self.assertTrue('bamplitude' in pars)
- self.assertTrue('bsigma' in pars)
-
- def test_change_prefix(self):
- "should fail"
- mod = models.GaussianModel(prefix='b')
- set_prefix_failed = None
- try:
- mod.prefix = 'c'
- set_prefix_failed = False
- except AttributeError:
- set_prefix_failed = True
- except:
- set_prefix_failed = None
- self.assertTrue(set_prefix_failed)
-
-
- def test_sum_of_two_gaussians(self):
- # two user-defined gaussians
- model1 = self.model
- f2 = lambda x, amp, cen, sig: gaussian(x, amplitude=amp, center=cen, sigma=sig)
- model2 = Model(f2)
- values1 = self.true_values()
- values2 = {'cen': 2.45, 'sig':0.8, 'amp':3.15}
-
- data = gaussian(x=self.x, **values1) + f2(x=self.x, **values2) + self.noise/3.0
- model = self.model + model2
- pars = model.make_params()
- pars['sigma'].set(value=2, min=0)
- pars['center'].set(value=1, min=0.2, max=1.8)
- pars['amplitude'].set(value=3, min=0)
- pars['sig'].set(value=1, min=0)
- pars['cen'].set(value=2.4, min=2, max=3.5)
- pars['amp'].set(value=1, min=0)
-
- true_values = dict(list(values1.items()) + list(values2.items()))
- result = model.fit(data, pars, x=self.x)
- assert_results_close(result.values, true_values, rtol=0.01, atol=0.01)
-
- # user-defined models with common parameter names
- # cannot be added, and should raise
- f = lambda: model1 + model1
- self.assertRaises(NameError, f)
-
- # two predefined_gaussians, using suffix to differentiate
- model1 = models.GaussianModel(prefix='g1_')
- model2 = models.GaussianModel(prefix='g2_')
- model = model1 + model2
- true_values = {'g1_center': values1['center'],
- 'g1_amplitude': values1['amplitude'],
- 'g1_sigma': values1['sigma'],
- 'g2_center': values2['cen'],
- 'g2_amplitude': values2['amp'],
- 'g2_sigma': values2['sig']}
- pars = model.make_params()
- pars['g1_sigma'].set(2)
- pars['g1_center'].set(1)
- pars['g1_amplitude'].set(3)
- pars['g2_sigma'].set(1)
- pars['g2_center'].set(2.4)
- pars['g2_amplitude'].set(1)
-
- result = model.fit(data, pars, x=self.x)
- assert_results_close(result.values, true_values, rtol=0.01, atol=0.01)
-
- # without suffix, the names collide and Model should raise
- model1 = models.GaussianModel()
- model2 = models.GaussianModel()
- f = lambda: model1 + model2
- self.assertRaises(NameError, f)
-
- def test_sum_composite_models(self):
- # test components of composite model created adding composite model
- model1 = models.GaussianModel(prefix='g1_')
- model2 = models.GaussianModel(prefix='g2_')
- model3 = models.GaussianModel(prefix='g3_')
- model4 = models.GaussianModel(prefix='g4_')
-
- model_total1 = (model1 + model2) + model3
- for mod in [model1, model2, model3]:
- self.assertTrue(mod in model_total1.components)
-
- model_total2 = model1 + (model2 + model3)
- for mod in [model1, model2, model3]:
- self.assertTrue(mod in model_total2.components)
-
- model_total3 = (model1 + model2) + (model3 + model4)
- for mod in [model1, model2, model3, model4]:
- self.assertTrue(mod in model_total3.components)
-
- def test_composite_has_bestvalues(self):
- # test that a composite model has non-empty best_values
- model1 = models.GaussianModel(prefix='g1_')
- model2 = models.GaussianModel(prefix='g2_')
-
- mod = model1 + model2
- pars = mod.make_params()
-
- values1 = dict(amplitude=7.10, center=1.1, sigma=2.40)
- values2 = dict(amplitude=12.2, center=2.5, sigma=0.5)
- data = gaussian(x=self.x, **values1) + gaussian(x=self.x, **values2) + 0.1*self.noise
-
- pars['g1_sigma'].set(2)
- pars['g1_center'].set(1, max=1.5)
- pars['g1_amplitude'].set(3)
- pars['g2_sigma'].set(1)
- pars['g2_center'].set(2.6, min=2.0)
- pars['g2_amplitude'].set(1)
-
- result = mod.fit(data, params=pars, x=self.x)
-
- self.assertTrue(len(result.best_values) == 6)
-
- self.assertTrue(abs(result.params['g1_amplitude'].value - 7.1) < 0.5)
- self.assertTrue(abs(result.params['g2_amplitude'].value - 12.2) < 0.5)
- self.assertTrue(abs(result.params['g1_center'].value - 1.1) < 0.2)
- self.assertTrue(abs(result.params['g2_center'].value - 2.5) < 0.2)
-
-
- def test_hints_in_composite_models(self):
- # test propagation of hints from base models to composite model
- def func(x, amplitude):
- pass
-
- m1 = Model(func, prefix='p1_')
- m2 = Model(func, prefix='p2_')
-
- m1.set_param_hint('amplitude', value=1)
- m2.set_param_hint('amplitude', value=2)
-
- mx = (m1 + m2)
- params = mx.make_params()
- param_values = {name: p.value for name, p in params.items()}
- self.assertEqual(param_values['p1_amplitude'], 1)
- self.assertEqual(param_values['p2_amplitude'], 2)
-
-
-class TestLinear(CommonTests, unittest.TestCase):
-
- def setUp(self):
- self.true_values = lambda: dict(slope=5, intercept=2)
- self.guess = lambda: dict(slope=10, intercept=6)
- self.model_constructor = models.LinearModel
- super(TestLinear, self).setUp()
-
-
-class TestParabolic(CommonTests, unittest.TestCase):
-
- def setUp(self):
- self.true_values = lambda: dict(a=5, b=2, c=8)
- self.guess = lambda: dict(a=1, b=6, c=3)
- self.model_constructor = models.ParabolicModel
- super(TestParabolic, self).setUp()
-
-
-class TestPolynomialOrder2(CommonTests, unittest.TestCase):
- # class Polynomial constructed with order=2
-
- def setUp(self):
- self.true_values = lambda: dict(c2=5, c1=2, c0=8)
- self.guess = lambda: dict(c1=1, c2=6, c0=3)
- self.model_constructor = models.PolynomialModel
- self.args = (2,)
- super(TestPolynomialOrder2, self).setUp()
-
-
-class TestPolynomialOrder3(CommonTests, unittest.TestCase):
- # class Polynomial constructed with order=3
-
- def setUp(self):
- self.true_values = lambda: dict(c3=2, c2=5, c1=2, c0=8)
- self.guess = lambda: dict(c3=1, c1=1, c2=6, c0=3)
- self.model_constructor = models.PolynomialModel
- self.args = (3,)
- super(TestPolynomialOrder3, self).setUp()
-
-
-class TestConstant(CommonTests, unittest.TestCase):
-
- def setUp(self):
- self.true_values = lambda: dict(c=5)
- self.guess = lambda: dict(c=2)
- self.model_constructor = models.ConstantModel
- super(TestConstant, self).setUp()
-
- def check_skip_independent_vars(self):
- raise nose.SkipTest("ConstantModel has not independent_vars.")
-
-class TestPowerlaw(CommonTests, unittest.TestCase):
-
- def setUp(self):
- self.true_values = lambda: dict(amplitude=5, exponent=3)
- self.guess = lambda: dict(amplitude=2, exponent=8)
- self.model_constructor = models.PowerLawModel
- super(TestPowerlaw, self).setUp()
-
-
-class TestExponential(CommonTests, unittest.TestCase):
-
- def setUp(self):
- self.true_values = lambda: dict(amplitude=5, decay=3)
- self.guess = lambda: dict(amplitude=2, decay=8)
- self.model_constructor = models.ExponentialModel
- super(TestExponential, self).setUp()
+import unittest +import warnings +import nose +from numpy.testing import assert_allclose +from numpy.testing.decorators import knownfailureif +import numpy as np + +from lmfit import Model, Parameter, models +from lmfit.lineshapes import gaussian + +def assert_results_close(actual, desired, rtol=1e-03, atol=1e-03, + err_msg='', verbose=True): + for param_name, value in desired.items(): + assert_allclose(actual[param_name], value, rtol, atol, err_msg, verbose) + +def _skip_if_no_pandas(): + try: + import pandas + except ImportError: + raise nose.SkipTest("Skipping tests that require pandas.") + + +class CommonTests(object): + # to be subclassed for testing predefined models + + def setUp(self): + np.random.seed(1) + self.noise = 0.0001*np.random.randn(*self.x.shape) + # Some Models need args (e.g., polynomial order), and others don't. + try: + args = self.args + except AttributeError: + self.model = self.model_constructor() + self.model_drop = self.model_constructor(missing='drop') + self.model_raise = self.model_constructor(missing='raise') + self.model_explicit_var = self.model_constructor(['x']) + func = self.model.func + else: + self.model = self.model_constructor(*args) + self.model_drop = self.model_constructor(*args, missing='drop') + self.model_raise = self.model_constructor(*args, missing='raise') + self.model_explicit_var = self.model_constructor( + *args, independent_vars=['x']) + func = self.model.func + self.data = func(x=self.x, **self.true_values()) + self.noise + + @property + def x(self): + return np.linspace(1, 10, num=1000) + + def test_fit(self): + model = self.model + + # Pass Parameters object. + params = model.make_params(**self.guess()) + result = model.fit(self.data, params, x=self.x) + assert_results_close(result.values, self.true_values()) + + # Pass inidividual Parameter objects as kwargs. + kwargs = {name: p for name, p in params.items()} + result = self.model.fit(self.data, x=self.x, **kwargs) + assert_results_close(result.values, self.true_values()) + + # Pass guess values (not Parameter objects) as kwargs. + kwargs = {name: p.value for name, p in params.items()} + result = self.model.fit(self.data, x=self.x, **kwargs) + assert_results_close(result.values, self.true_values()) + + def test_explicit_independent_vars(self): + self.check_skip_independent_vars() + model = self.model_explicit_var + pars = model.make_params(**self.guess()) + result = model.fit(self.data, pars, x=self.x) + assert_results_close(result.values, self.true_values()) + + def test_fit_with_weights(self): + model = self.model + + # fit without weights + params = model.make_params(**self.guess()) + out1 = model.fit(self.data, params, x=self.x) + + # fit with weights + weights = 1.0/(0.5 + self.x**2) + out2 = model.fit(self.data, params, weights=weights, x=self.x) + + max_diff = 0.0 + for parname, val1 in out1.values.items(): + val2 = out2.values[parname] + if max_diff < abs(val1-val2): + max_diff = abs(val1-val2) + assert(max_diff > 1.e-8) + + def test_result_attributes(self): + pars = self.model.make_params(**self.guess()) + result = self.model.fit(self.data, pars, x=self.x) + + # result.init_values + assert_results_close(result.values, self.true_values()) + self.assertEqual(result.init_values, self.guess()) + + # result.init_params + params = self.model.make_params() + for param_name, value in self.guess().items(): + params[param_name].value = value + self.assertEqual(result.init_params, params) + + # result.best_fit + assert_allclose(result.best_fit, self.data, atol=self.noise.max()) + + # result.init_fit + init_fit = self.model.func(x=self.x, **self.guess()) + assert_allclose(result.init_fit, init_fit) + + # result.model + self.assertTrue(result.model is self.model) + + def test_result_eval(self): + # Check eval() output against init_fit and best_fit. + pars = self.model.make_params(**self.guess()) + result = self.model.fit(self.data, pars, x=self.x) + + assert_allclose(result.eval(x=self.x, **result.values), + result.best_fit) + assert_allclose(result.eval(x=self.x, **result.init_values), + result.init_fit) + + def test_result_eval_custom_x(self): + self.check_skip_independent_vars() + pars = self.model.make_params(**self.guess()) + result = self.model.fit(self.data, pars, x=self.x) + + # Check that the independent variable is respected. + short_eval = result.eval(x=np.array([0, 1, 2]), **result.values) + self.assertEqual(len(short_eval), 3) + + def test_data_alignment(self): + _skip_if_no_pandas() + from pandas import Series + + # Align data and indep var of different lengths using pandas index. + data = Series(self.data.copy()).iloc[10:-10] + x = Series(self.x.copy()) + + model = self.model + params = model.make_params(**self.guess()) + result = model.fit(data, params, x=x) + result = model.fit(data, params, x=x) + assert_results_close(result.values, self.true_values()) + + # Skip over missing (NaN) values, aligning via pandas index. + data.iloc[500:510] = np.nan + result = self.model_drop.fit(data, params, x=x) + assert_results_close(result.values, self.true_values()) + + # Raise if any NaN values are present. + raises = lambda: self.model_raise.fit(data, params, x=x) + self.assertRaises(ValueError, raises) + + def check_skip_independent_vars(self): + # to be overridden for models that do not accept indep vars + pass + + def test_aic(self): + model = self.model + + # Pass Parameters object. + params = model.make_params(**self.guess()) + result = model.fit(self.data, params, x=self.x) + aic = result.aic + self.assertTrue(aic < 0) # aic must be negative + + # Pass extra unused Parameter. + params.add("unused_param", value=1.0, vary=True) + result = model.fit(self.data, params, x=self.x) + aic_extra = result.aic + self.assertTrue(aic_extra < 0) # aic must be negative + self.assertTrue(aic < aic_extra) # the extra param should lower the aic + + + def test_bic(self): + model = self.model + + # Pass Parameters object. + params = model.make_params(**self.guess()) + result = model.fit(self.data, params, x=self.x) + bic = result.bic + self.assertTrue(bic < 0) # aic must be negative + + # Compare to AIC + aic = result.aic + self.assertTrue(aic < bic) # aic should be lower than bic + + # Pass extra unused Parameter. + params.add("unused_param", value=1.0, vary=True) + result = model.fit(self.data, params, x=self.x) + bic_extra = result.bic + self.assertTrue(bic_extra < 0) # bic must be negative + self.assertTrue(bic < bic_extra) # the extra param should lower the bic + + +class TestUserDefiniedModel(CommonTests, unittest.TestCase): + # mainly aimed at checking that the API does what it says it does + # and raises the right exceptions or warnings when things are not right + + def setUp(self): + self.true_values = lambda: dict(amplitude=7.1, center=1.1, sigma=2.40) + self.guess = lambda: dict(amplitude=5, center=2, sigma=4) + # return a fresh copy + self.model_constructor = ( + lambda *args, **kwargs: Model(gaussian, *args, **kwargs)) + super(TestUserDefiniedModel, self).setUp() + + @property + def x(self): + return np.linspace(-10, 10, num=1000) + + def test_lists_become_arrays(self): + # smoke test + self.model.fit([1, 2, 3], x=[1, 2, 3], **self.guess()) + self.model.fit([1, 2, None, 3], x=[1, 2, 3, 4], **self.guess()) + + def test_missing_param_raises_error(self): + + # using keyword argument parameters + guess_missing_sigma = self.guess() + del guess_missing_sigma['sigma'] + # f = lambda: self.model.fit(self.data, x=self.x, **guess_missing_sigma) + # self.assertRaises(ValueError, f) + + # using Parameters + params = self.model.make_params() + for param_name, value in guess_missing_sigma.items(): + params[param_name].value = value + f = lambda: self.model.fit(self.data, params, x=self.x) + + def test_extra_param_issues_warning(self): + # The function accepts extra params, Model will warn but not raise. + def flexible_func(x, amplitude, center, sigma, **kwargs): + return gaussian(x, amplitude, center, sigma) + + flexible_model = Model(flexible_func) + pars = flexible_model.make_params(**self.guess()) + with warnings.catch_warnings(record=True) as w: + warnings.simplefilter("always") + flexible_model.fit(self.data, pars, x=self.x, extra=5) + self.assertTrue(len(w) == 1) + self.assertTrue(issubclass(w[-1].category, UserWarning)) + + def test_missing_independent_variable_raises_error(self): + pars = self.model.make_params(**self.guess()) + f = lambda: self.model.fit(self.data, pars) + self.assertRaises(KeyError, f) + + def test_bounding(self): + true_values = self.true_values() + true_values['center'] = 1.3 # as close as it's allowed to get + pars = self.model.make_params(**self.guess()) + pars['center'].set(value=2, min=1.3) + result = self.model.fit(self.data, pars, x=self.x) + assert_results_close(result.values, true_values, rtol=0.05) + + def test_vary_false(self): + true_values = self.true_values() + true_values['center'] = 1.3 + pars = self.model.make_params(**self.guess()) + pars['center'].set(value=1.3, vary=False) + result = self.model.fit(self.data, pars, x=self.x) + assert_results_close(result.values, true_values, rtol=0.05) + + # testing model addition... + + def test_user_defined_gaussian_plus_constant(self): + data = self.data + 5.0 + model = self.model + models.ConstantModel() + guess = self.guess() + pars = model.make_params(c= 10.1, **guess) + true_values = self.true_values() + true_values['c'] = 5.0 + + result = model.fit(data, pars, x=self.x) + assert_results_close(result.values, true_values, rtol=0.01, atol=0.01) + + def test_model_with_prefix(self): + # model with prefix of 'a' and 'b' + mod = models.GaussianModel(prefix='a') + vals = {'center': 2.45, 'sigma':0.8, 'amplitude':3.15} + data = gaussian(x=self.x, **vals) + self.noise/3.0 + pars = mod.guess(data, x=self.x) + self.assertTrue('aamplitude' in pars) + self.assertTrue('asigma' in pars) + out = mod.fit(data, pars, x=self.x) + self.assertTrue(out.params['aamplitude'].value > 2.0) + self.assertTrue(out.params['acenter'].value > 2.0) + self.assertTrue(out.params['acenter'].value < 3.0) + + mod = models.GaussianModel(prefix='b') + data = gaussian(x=self.x, **vals) + self.noise/3.0 + pars = mod.guess(data, x=self.x) + self.assertTrue('bamplitude' in pars) + self.assertTrue('bsigma' in pars) + + def test_change_prefix(self): + "should fail" + mod = models.GaussianModel(prefix='b') + set_prefix_failed = None + try: + mod.prefix = 'c' + set_prefix_failed = False + except AttributeError: + set_prefix_failed = True + except: + set_prefix_failed = None + self.assertTrue(set_prefix_failed) + + + def test_sum_of_two_gaussians(self): + # two user-defined gaussians + model1 = self.model + f2 = lambda x, amp, cen, sig: gaussian(x, amplitude=amp, center=cen, sigma=sig) + model2 = Model(f2) + values1 = self.true_values() + values2 = {'cen': 2.45, 'sig':0.8, 'amp':3.15} + + data = gaussian(x=self.x, **values1) + f2(x=self.x, **values2) + self.noise/3.0 + model = self.model + model2 + pars = model.make_params() + pars['sigma'].set(value=2, min=0) + pars['center'].set(value=1, min=0.2, max=1.8) + pars['amplitude'].set(value=3, min=0) + pars['sig'].set(value=1, min=0) + pars['cen'].set(value=2.4, min=2, max=3.5) + pars['amp'].set(value=1, min=0) + + true_values = dict(list(values1.items()) + list(values2.items())) + result = model.fit(data, pars, x=self.x) + assert_results_close(result.values, true_values, rtol=0.01, atol=0.01) + + # user-defined models with common parameter names + # cannot be added, and should raise + f = lambda: model1 + model1 + self.assertRaises(NameError, f) + + # two predefined_gaussians, using suffix to differentiate + model1 = models.GaussianModel(prefix='g1_') + model2 = models.GaussianModel(prefix='g2_') + model = model1 + model2 + true_values = {'g1_center': values1['center'], + 'g1_amplitude': values1['amplitude'], + 'g1_sigma': values1['sigma'], + 'g2_center': values2['cen'], + 'g2_amplitude': values2['amp'], + 'g2_sigma': values2['sig']} + pars = model.make_params() + pars['g1_sigma'].set(2) + pars['g1_center'].set(1) + pars['g1_amplitude'].set(3) + pars['g2_sigma'].set(1) + pars['g2_center'].set(2.4) + pars['g2_amplitude'].set(1) + + result = model.fit(data, pars, x=self.x) + assert_results_close(result.values, true_values, rtol=0.01, atol=0.01) + + # without suffix, the names collide and Model should raise + model1 = models.GaussianModel() + model2 = models.GaussianModel() + f = lambda: model1 + model2 + self.assertRaises(NameError, f) + + def test_sum_composite_models(self): + # test components of composite model created adding composite model + model1 = models.GaussianModel(prefix='g1_') + model2 = models.GaussianModel(prefix='g2_') + model3 = models.GaussianModel(prefix='g3_') + model4 = models.GaussianModel(prefix='g4_') + + model_total1 = (model1 + model2) + model3 + for mod in [model1, model2, model3]: + self.assertTrue(mod in model_total1.components) + + model_total2 = model1 + (model2 + model3) + for mod in [model1, model2, model3]: + self.assertTrue(mod in model_total2.components) + + model_total3 = (model1 + model2) + (model3 + model4) + for mod in [model1, model2, model3, model4]: + self.assertTrue(mod in model_total3.components) + + def test_composite_has_bestvalues(self): + # test that a composite model has non-empty best_values + model1 = models.GaussianModel(prefix='g1_') + model2 = models.GaussianModel(prefix='g2_') + + mod = model1 + model2 + pars = mod.make_params() + + values1 = dict(amplitude=7.10, center=1.1, sigma=2.40) + values2 = dict(amplitude=12.2, center=2.5, sigma=0.5) + data = gaussian(x=self.x, **values1) + gaussian(x=self.x, **values2) + 0.1*self.noise + + pars['g1_sigma'].set(2) + pars['g1_center'].set(1, max=1.5) + pars['g1_amplitude'].set(3) + pars['g2_sigma'].set(1) + pars['g2_center'].set(2.6, min=2.0) + pars['g2_amplitude'].set(1) + + result = mod.fit(data, params=pars, x=self.x) + + self.assertTrue(len(result.best_values) == 6) + + self.assertTrue(abs(result.params['g1_amplitude'].value - 7.1) < 0.5) + self.assertTrue(abs(result.params['g2_amplitude'].value - 12.2) < 0.5) + self.assertTrue(abs(result.params['g1_center'].value - 1.1) < 0.2) + self.assertTrue(abs(result.params['g2_center'].value - 2.5) < 0.2) + + + def test_hints_in_composite_models(self): + # test propagation of hints from base models to composite model + def func(x, amplitude): + pass + + m1 = Model(func, prefix='p1_') + m2 = Model(func, prefix='p2_') + + m1.set_param_hint('amplitude', value=1) + m2.set_param_hint('amplitude', value=2) + + mx = (m1 + m2) + params = mx.make_params() + param_values = {name: p.value for name, p in params.items()} + self.assertEqual(param_values['p1_amplitude'], 1) + self.assertEqual(param_values['p2_amplitude'], 2) + + def test_hints_for_peakmodels(self): + # test that height/fwhm do not cause asteval errors. + + x = np.linspace(-10, 10, 101) + y = np.sin(x / 3) + x /100. + + m1 = models.LinearModel(prefix='m1_') + + params = m1.guess(y, x=x) + + m2 = models.GaussianModel(prefix='m2_') + params.update(m2.make_params()) + + m = m1 + m2 + + param_values = {name: p.value for name, p in params.items()} + self.assertTrue(param_values['m1_intercept'] < -0.0) + self.assertEqual(param_values['m2_amplitude'], 1) + + def test_weird_param_hints(self): + # tests Github Issue 312, a very weird way to access param_hints + def func(x, amp): + return amp*x + + m = Model(func) + models = {} + for i in range(2): + m.set_param_hint('amp', value=1) + m.set_param_hint('amp', value=25) + + models[i] = Model(func, prefix='mod%i_' % i) + models[i].param_hints['amp'] = m.param_hints['amp'] + + self.assertEqual(models[0].param_hints['amp'], + models[1].param_hints['amp']) + + + def test_composite_model_with_expr_constrains(self): + """Smoke test for composite model fitting with expr constraints. + """ + y = [ 0, 0, 4, 2, 1, 8, 21, 21, 23, 35, 50, 54, 46, + 70, 77, 87, 98, 113, 148, 136, 185, 195, 194, 168, 170, 139, + 155, 115, 132, 109, 102, 85, 69, 81, 82, 80, 71, 64, 79, + 88, 111, 97, 97, 73, 72, 62, 41, 30, 13, 3, 9, 7, + 0, 0, 0] + x = np.arange(-0.2, 1.2, 0.025)[:-1] + 0.5*0.025 + + def gauss(x, sigma, mu, A): + return A*np.exp(-(x-mu)**2/(2*sigma**2)) + + # Initial values + p1_mu = 0.2 + p1_sigma = 0.1 + #p2_mu = 0.8 + p2_sigma = 0.1 + + peak1 = Model(gauss, prefix='p1_') + peak2 = Model(gauss, prefix='p2_') + model = peak1 + peak2 + + model.set_param_hint('p1_mu', value=p1_mu, min=-1, max=2) + #model.set_param_hint('p2_mu', value=p2_mu, min=-1, max=2) + model.set_param_hint('p1_sigma', value=p1_sigma, min=0.01, max=0.2) + model.set_param_hint('p2_sigma', value=p2_sigma, min=0.01, max=0.2) + model.set_param_hint('p1_A', value=100, min=0.01) + model.set_param_hint('p2_A', value=50, min=0.01) + + # Constrains the distance between peaks to be > 0 + model.set_param_hint('pos_delta', value=0.3, min=0) + model.set_param_hint('p2_mu', min=-1, expr='p1_mu + pos_delta') + + # Test fitting + result = model.fit(y, x=x) + self.assertTrue(result.params['pos_delta'].value > 0) + + +class TestLinear(CommonTests, unittest.TestCase): + + def setUp(self): + self.true_values = lambda: dict(slope=5, intercept=2) + self.guess = lambda: dict(slope=10, intercept=6) + self.model_constructor = models.LinearModel + super(TestLinear, self).setUp() + + +class TestParabolic(CommonTests, unittest.TestCase): + + def setUp(self): + self.true_values = lambda: dict(a=5, b=2, c=8) + self.guess = lambda: dict(a=1, b=6, c=3) + self.model_constructor = models.ParabolicModel + super(TestParabolic, self).setUp() + + +class TestPolynomialOrder2(CommonTests, unittest.TestCase): + # class Polynomial constructed with order=2 + + def setUp(self): + self.true_values = lambda: dict(c2=5, c1=2, c0=8) + self.guess = lambda: dict(c1=1, c2=6, c0=3) + self.model_constructor = models.PolynomialModel + self.args = (2,) + super(TestPolynomialOrder2, self).setUp() + + +class TestPolynomialOrder3(CommonTests, unittest.TestCase): + # class Polynomial constructed with order=3 + + def setUp(self): + self.true_values = lambda: dict(c3=2, c2=5, c1=2, c0=8) + self.guess = lambda: dict(c3=1, c1=1, c2=6, c0=3) + self.model_constructor = models.PolynomialModel + self.args = (3,) + super(TestPolynomialOrder3, self).setUp() + + +class TestConstant(CommonTests, unittest.TestCase): + def setUp(self): + self.true_values = lambda: dict(c=5) + self.guess = lambda: dict(c=2) + self.model_constructor = models.ConstantModel + super(TestConstant, self).setUp() + + def check_skip_independent_vars(self): + raise nose.SkipTest("ConstantModel has not independent_vars.") + +class TestPowerlaw(CommonTests, unittest.TestCase): + def setUp(self): + self.true_values = lambda: dict(amplitude=5, exponent=3) + self.guess = lambda: dict(amplitude=2, exponent=8) + self.model_constructor = models.PowerLawModel + super(TestPowerlaw, self).setUp() + + +class TestExponential(CommonTests, unittest.TestCase): + def setUp(self): + self.true_values = lambda: dict(amplitude=5, decay=3) + self.guess = lambda: dict(amplitude=2, decay=8) + self.model_constructor = models.ExponentialModel + super(TestExponential, self).setUp() + + +class TestComplexConstant(CommonTests, unittest.TestCase): + def setUp(self): + self.true_values = lambda: dict(re=5,im=5) + self.guess = lambda: dict(re=2,im=2) + self.model_constructor = models.ComplexConstantModel + super(TestComplexConstant, self).setUp() + +# diff --git a/tests/test_multidatasets.py b/tests/test_multidatasets.py index 105a8cf..985a70c 100644 --- a/tests/test_multidatasets.py +++ b/tests/test_multidatasets.py @@ -1,74 +1,74 @@ -#
-# example fitting to multiple (simulated) data sets
-#
-import numpy as np
-from lmfit import minimize, Parameters, fit_report
-from lmfit.lineshapes import gaussian
-
-def gauss_dataset(params, i, x):
- """calc gaussian from params for data set i
- using simple, hardwired naming convention"""
- amp = params['amp_%i' % (i+1)].value
- cen = params['cen_%i' % (i+1)].value
- sig = params['sig_%i' % (i+1)].value
- return gaussian(x, amp, cen, sig)
-
-def objective(params, x, data):
- """ calculate total residual for fits to several data sets held
- in a 2-D array, and modeled by Gaussian functions"""
- ndata, nx = data.shape
- resid = 0.0*data[:]
- # make residual per data set
- for i in range(ndata):
- resid[i, :] = data[i, :] - gauss_dataset(params, i, x)
- # now flatten this to a 1D array, as minimize() needs
- return resid.flatten()
-
-def test_multidatasets():
- # create 5 datasets
- x = np.linspace( -1, 2, 151)
- data = []
- for i in np.arange(5):
- amp = 2.60 + 1.50*np.random.rand()
- cen = -0.20 + 1.50*np.random.rand()
- sig = 0.25 + 0.03*np.random.rand()
- dat = gaussian(x, amp, cen, sig) + \
- np.random.normal(size=len(x), scale=0.1)
- data.append(dat)
-
- # data has shape (5, 151)
- data = np.array(data)
- assert(data.shape) == (5, 151)
-
- # create 5 sets of parameters, one per data set
- pars = Parameters()
- for iy, y in enumerate(data):
- pars.add( 'amp_%i' % (iy+1), value=0.5, min=0.0, max=200)
- pars.add( 'cen_%i' % (iy+1), value=0.4, min=-2.0, max=2.0)
- pars.add( 'sig_%i' % (iy+1), value=0.3, min=0.01, max=3.0)
-
- # but now constrain all values of sigma to have the same value
- # by assigning sig_2, sig_3, .. sig_5 to be equal to sig_1
- for iy in (2, 3, 4, 5):
- pars['sig_%i' % iy].expr='sig_1'
-
- # run the global fit to all the data sets
- out = minimize(objective, pars, args=(x, data))
-
- assert(len(pars) == 15)
- assert(out.nvarys == 11)
- assert(out.nfev > 15)
- assert(out.chisqr > 1.0)
- assert(pars['amp_1'].value > 0.1)
- assert(pars['sig_1'].value > 0.1)
- assert(pars['sig_2'].value == pars['sig_1'].value)
-
- ## plot the data sets and fits
- # plt.figure()
- # for i in range(5):
- # y_fit = gauss_dataset(pars, i, x)
- # plt.plot(x, data[i, :], 'o', x, y_fit, '-')
- # plt.show()
-
-if __name__ == '__main__':
- test_multidatasets()
+# +# example fitting to multiple (simulated) data sets +# +import numpy as np +from lmfit import minimize, Parameters, fit_report +from lmfit.lineshapes import gaussian + +def gauss_dataset(params, i, x): + """calc gaussian from params for data set i + using simple, hardwired naming convention""" + amp = params['amp_%i' % (i+1)].value + cen = params['cen_%i' % (i+1)].value + sig = params['sig_%i' % (i+1)].value + return gaussian(x, amp, cen, sig) + +def objective(params, x, data): + """ calculate total residual for fits to several data sets held + in a 2-D array, and modeled by Gaussian functions""" + ndata, nx = data.shape + resid = 0.0*data[:] + # make residual per data set + for i in range(ndata): + resid[i, :] = data[i, :] - gauss_dataset(params, i, x) + # now flatten this to a 1D array, as minimize() needs + return resid.flatten() + +def test_multidatasets(): + # create 5 datasets + x = np.linspace( -1, 2, 151) + data = [] + for i in np.arange(5): + amp = 2.60 + 1.50*np.random.rand() + cen = -0.20 + 1.50*np.random.rand() + sig = 0.25 + 0.03*np.random.rand() + dat = gaussian(x, amp, cen, sig) + \ + np.random.normal(size=len(x), scale=0.1) + data.append(dat) + + # data has shape (5, 151) + data = np.array(data) + assert(data.shape) == (5, 151) + + # create 5 sets of parameters, one per data set + pars = Parameters() + for iy, y in enumerate(data): + pars.add( 'amp_%i' % (iy+1), value=0.5, min=0.0, max=200) + pars.add( 'cen_%i' % (iy+1), value=0.4, min=-2.0, max=2.0) + pars.add( 'sig_%i' % (iy+1), value=0.3, min=0.01, max=3.0) + + # but now constrain all values of sigma to have the same value + # by assigning sig_2, sig_3, .. sig_5 to be equal to sig_1 + for iy in (2, 3, 4, 5): + pars['sig_%i' % iy].expr='sig_1' + + # run the global fit to all the data sets + out = minimize(objective, pars, args=(x, data)) + + assert(len(pars) == 15) + assert(out.nvarys == 11) + assert(out.nfev > 15) + assert(out.chisqr > 1.0) + assert(pars['amp_1'].value > 0.1) + assert(pars['sig_1'].value > 0.1) + assert(pars['sig_2'].value == pars['sig_1'].value) + + ## plot the data sets and fits + # plt.figure() + # for i in range(5): + # y_fit = gauss_dataset(pars, i, x) + # plt.plot(x, data[i, :], 'o', x, y_fit, '-') + # plt.show() + +if __name__ == '__main__': + test_multidatasets() diff --git a/tests/test_nose.py b/tests/test_nose.py index 3d0095f..b5ad44a 100644 --- a/tests/test_nose.py +++ b/tests/test_nose.py @@ -1,399 +1,608 @@ -# -*- coding: utf-8 -*-
-from __future__ import print_function
-from lmfit import minimize, Parameters, Parameter, report_fit, Minimizer
-from lmfit.minimizer import SCALAR_METHODS
-from lmfit.lineshapes import gaussian
-import numpy as np
-from numpy import pi
-from numpy.testing import assert_
-import unittest
-import nose
-from nose import SkipTest
-
-def check(para, real_val, sig=3):
- err = abs(para.value - real_val)
- print( para.name, para.value, real_val, para.stderr)
- assert(err < sig * para.stderr)
-
-def check_wo_stderr(para, real_val, sig=0.1):
- err = abs(para.value - real_val)
- print (para.name, para.value, real_val)
- assert(err < sig)
-
-def check_paras(para_fit, para_real):
- for i in para_fit:
- check(para_fit[i], para_real[i].value)
-
-def test_simple():
- # create data to be fitted
- np.random.seed(1)
- x = np.linspace(0, 15, 301)
- data = (5. * np.sin(2 * x - 0.1) * np.exp(-x*x*0.025) +
- np.random.normal(size=len(x), scale=0.2) )
-
- # define objective function: returns the array to be minimized
- def fcn2min(params, x, data):
- """ model decaying sine wave, subtract data"""
- amp = params['amp'].value
- shift = params['shift'].value
- omega = params['omega'].value
- decay = params['decay'].value
-
- model = amp * np.sin(x * omega + shift) * np.exp(-x*x*decay)
- return model - data
-
- # create a set of Parameters
- params = Parameters()
- params.add('amp', value= 10, min=0)
- params.add('decay', value= 0.1)
- params.add('shift', value= 0.0, min=-pi / 2., max=pi / 2)
- params.add('omega', value= 3.0)
-
- # do fit, here with leastsq model
- result = minimize(fcn2min, params, args=(x, data))
-
- # calculate final result
- final = data + result.residual
-
- # write error report
- print(" --> SIMPLE --> ")
- print(result.params)
- report_fit(result.params)
-
- #assert that the real parameters are found
-
- for para, val in zip(result.params.values(), [5, 0.025, -.1, 2]):
-
- check(para, val)
-
-def test_lbfgsb():
- p_true = Parameters()
- p_true.add('amp', value=14.0)
- p_true.add('period', value=5.33)
- p_true.add('shift', value=0.123)
- p_true.add('decay', value=0.010)
-
- def residual(pars, x, data=None):
- amp = pars['amp'].value
- per = pars['period'].value
- shift = pars['shift'].value
- decay = pars['decay'].value
-
- if abs(shift) > pi/2:
- shift = shift - np.sign(shift) * pi
- model = amp * np.sin(shift + x / per) * np.exp(-x * x * decay * decay)
- if data is None:
- return model
- return (model - data)
-
- n = 2500
- xmin = 0.
- xmax = 250.0
- noise = np.random.normal(scale=0.7215, size=n)
- x = np.linspace(xmin, xmax, n)
- data = residual(p_true, x) + noise
-
- fit_params = Parameters()
- fit_params.add('amp', value=11.0, min=5, max=20)
- fit_params.add('period', value=5., min=1., max=7)
- fit_params.add('shift', value=.10, min=0.0, max=0.2)
- fit_params.add('decay', value=6.e-3, min=0, max=0.1)
-
- init = residual(fit_params, x)
-
- out = minimize(residual, fit_params, method='lbfgsb', args=(x,), kws={'data':data})
-
- fit = residual(fit_params, x)
-
- for name, par in out.params.items():
- nout = "%s:%s" % (name, ' '*(20-len(name)))
- print("%s: %s (%s) " % (nout, par.value, p_true[name].value))
-
- for para, true_para in zip(out.params.values(), p_true.values()):
- check_wo_stderr(para, true_para.value)
-
-def test_derive():
- def func(pars, x, data=None):
- a = pars['a'].value
- b = pars['b'].value
- c = pars['c'].value
-
- model=a * np.exp(-b * x)+c
- if data is None:
- return model
- return (model - data)
-
- def dfunc(pars, x, data=None):
- a = pars['a'].value
- b = pars['b'].value
- c = pars['c'].value
- v = np.exp(-b*x)
- return np.array([v, -a*x*v, np.ones(len(x))])
-
- def f(var, x):
- return var[0]* np.exp(-var[1] * x)+var[2]
-
- params1 = Parameters()
- params1.add('a', value=10)
- params1.add('b', value=10)
- params1.add('c', value=10)
-
- params2 = Parameters()
- params2.add('a', value=10)
- params2.add('b', value=10)
- params2.add('c', value=10)
-
- a, b, c = 2.5, 1.3, 0.8
- x = np.linspace(0,4,50)
- y = f([a, b, c], x)
- data = y + 0.15*np.random.normal(size=len(x))
-
- # fit without analytic derivative
- min1 = Minimizer(func, params1, fcn_args=(x,), fcn_kws={'data':data})
- out1 = min1.leastsq()
- fit1 = func(out1.params, x)
-
- # fit with analytic derivative
- min2 = Minimizer(func, params2, fcn_args=(x,), fcn_kws={'data':data})
- out2 = min2.leastsq(Dfun=dfunc, col_deriv=1)
- fit2 = func(out2.params, x)
-
-
- print ('''Comparison of fit to exponential decay
- with and without analytic derivatives, to
- model = a*exp(-b*x) + c
- for a = %.2f, b = %.2f, c = %.2f
- ==============================================
- Statistic/Parameter| Without | With |
- ----------------------------------------------
- N Function Calls | %3i | %3i |
- Chi-square | %.4f | %.4f |
- a | %.4f | %.4f |
- b | %.4f | %.4f |
- c | %.4f | %.4f |
- ----------------------------------------------
- ''' % (a, b, c,
- out1.nfev, out2.nfev,
- out1.chisqr, out2.chisqr,
- out1.params['a'].value, out2.params['a'].value,
- out1.params['b'].value, out2.params['b'].value,
- out1.params['c'].value, out2.params['c'].value ))
-
- check_wo_stderr(out1.params['a'], out2.params['a'].value, 0.00005)
- check_wo_stderr(out1.params['b'], out2.params['b'].value, 0.00005)
- check_wo_stderr(out1.params['c'], out2.params['c'].value, 0.00005)
-
-def test_peakfit():
- def residual(pars, x, data=None):
- g1 = gaussian(x, pars['a1'].value, pars['c1'].value, pars['w1'].value)
- g2 = gaussian(x, pars['a2'].value, pars['c2'].value, pars['w2'].value)
- model = g1 + g2
- if data is None:
- return model
- return (model - data)
-
- n = 601
- xmin = 0.
- xmax = 15.0
- noise = np.random.normal(scale=.65, size=n)
- x = np.linspace(xmin, xmax, n)
-
- org_params = Parameters()
- org_params.add_many(('a1', 12.0, True, None, None, None),
- ('c1', 5.3, True, None, None, None),
- ('w1', 1.0, True, None, None, None),
- ('a2', 9.1, True, None, None, None),
- ('c2', 8.1, True, None, None, None),
- ('w2', 2.5, True, None, None, None))
-
- data = residual(org_params, x) + noise
-
-
- fit_params = Parameters()
- fit_params.add_many(('a1', 8.0, True, None, 14., None),
- ('c1', 5.0, True, None, None, None),
- ('w1', 0.7, True, None, None, None),
- ('a2', 3.1, True, None, None, None),
- ('c2', 8.8, True, None, None, None))
-
- fit_params.add('w2', expr='2.5*w1')
-
- myfit = Minimizer(residual, fit_params,
- fcn_args=(x,), fcn_kws={'data':data})
-
- myfit.prepare_fit()
-
- init = residual(fit_params, x)
-
-
- out = myfit.leastsq()
-
- # print(' N fev = ', myfit.nfev)
- # print(myfit.chisqr, myfit.redchi, myfit.nfree)
-
- report_fit(out.params)
-
- fit = residual(out.params, x)
- check_paras(out.params, org_params)
-
-
-def test_scalar_minimize_has_no_uncertainties():
- # scalar_minimize doesn't calculate uncertainties.
- # when a scalar_minimize is run the stderr and correl for each parameter
- # should be None. (stderr and correl are set to None when a Parameter is
- # initialised).
- # This requires a reset after a leastsq fit has been done.
- # Only when scalar_minimize calculates stderr and correl can this test
- # be removed.
-
- np.random.seed(1)
- x = np.linspace(0, 15, 301)
- data = (5. * np.sin(2 * x - 0.1) * np.exp(-x*x*0.025) +
- np.random.normal(size=len(x), scale=0.2) )
-
- # define objective function: returns the array to be minimized
- def fcn2min(params, x, data):
- """ model decaying sine wave, subtract data"""
- amp = params['amp'].value
- shift = params['shift'].value
- omega = params['omega'].value
- decay = params['decay'].value
-
- model = amp * np.sin(x * omega + shift) * np.exp(-x*x*decay)
- return model - data
-
- # create a set of Parameters
- params = Parameters()
- params.add('amp', value= 10, min=0)
- params.add('decay', value= 0.1)
- params.add('shift', value= 0.0, min=-pi / 2., max=pi / 2)
- params.add('omega', value= 3.0)
-
- mini = Minimizer(fcn2min, params, fcn_args=(x, data))
- out = mini.minimize()
- assert_(np.isfinite(out.params['amp'].stderr))
- print(out.errorbars)
- assert_(out.errorbars == True)
- out2 = mini.minimize(method='nelder-mead')
- assert_(out2.params['amp'].stderr is None)
- assert_(out2.params['decay'].stderr is None)
- assert_(out2.params['shift'].stderr is None)
- assert_(out2.params['omega'].stderr is None)
- assert_(out2.params['amp'].correl is None)
- assert_(out2.params['decay'].correl is None)
- assert_(out2.params['shift'].correl is None)
- assert_(out2.params['omega'].correl is None)
- assert_(out2.errorbars == False)
-
-
-def test_multidimensional_fit_GH205():
- # test that you don't need to flatten the output from the objective
- # function. Tests regression for GH205.
- pos = np.linspace(0, 99, 100)
- xv, yv = np.meshgrid(pos, pos)
- f = lambda xv, yv, lambda1, lambda2: (np.sin(xv * lambda1)
- + np.cos(yv * lambda2))
-
- data = f(xv, yv, 0.3, 3)
- assert_(data.ndim, 2)
-
- def fcn2min(params, xv, yv, data):
- """ model decaying sine wave, subtract data"""
- lambda1 = params['lambda1'].value
- lambda2 = params['lambda2'].value
- model = f(xv, yv, lambda1, lambda2)
- return model - data
-
- # create a set of Parameters
- params = Parameters()
- params.add('lambda1', value=0.4)
- params.add('lambda2', value=3.2)
-
- mini = Minimizer(fcn2min, params, fcn_args=(xv, yv, data))
- res = mini.minimize()
-
-class CommonMinimizerTest(unittest.TestCase):
-
- def setUp(self):
- """
- test scale minimizers except newton-cg (needs jacobian) and
- anneal (doesn't work out of the box).
- """
- p_true = Parameters()
- p_true.add('amp', value=14.0)
- p_true.add('period', value=5.33)
- p_true.add('shift', value=0.123)
- p_true.add('decay', value=0.010)
- self.p_true = p_true
-
- n = 2500
- xmin = 0.
- xmax = 250.0
- noise = np.random.normal(scale=0.7215, size=n)
- self.x = np.linspace(xmin, xmax, n)
- data = self.residual(p_true, self.x) + noise
-
- fit_params = Parameters()
- fit_params.add('amp', value=11.0, min=5, max=20)
- fit_params.add('period', value=5., min=1., max=7)
- fit_params.add('shift', value=.10, min=0.0, max=0.2)
- fit_params.add('decay', value=6.e-3, min=0, max=0.1)
- self.fit_params = fit_params
-
- init = self.residual(fit_params, self.x)
- self.mini = Minimizer(self.residual, fit_params, [self.x, data])
-
- def residual(self, pars, x, data=None):
- amp = pars['amp'].value
- per = pars['period'].value
- shift = pars['shift'].value
- decay = pars['decay'].value
-
- if abs(shift) > pi/2:
- shift = shift - np.sign(shift) * pi
- model = amp*np.sin(shift + x/per) * np.exp(-x*x*decay*decay)
- if data is None:
- return model
- return (model - data)
-
- def test_diffev_bounds_check(self):
- # You need finite (min, max) for each parameter if you're using
- # differential_evolution.
- self.fit_params['decay'].min = None
- self.minimizer = 'differential_evolution'
- np.testing.assert_raises(ValueError, self.scalar_minimizer)
-
- def test_scalar_minimizers(self):
- # test all the scalar minimizers
- for method in SCALAR_METHODS:
- if method in ['newton', 'dogleg', 'trust-ncg']:
- continue
- self.minimizer = SCALAR_METHODS[method]
- if method == 'Nelder-Mead':
- sig = 0.2
- else:
- sig = 0.15
- self.scalar_minimizer(sig=sig)
-
- def scalar_minimizer(self, sig=0.15):
- try:
- from scipy.optimize import minimize as scipy_minimize
- except ImportError:
- raise SkipTest
-
- print(self.minimizer)
- out = self.mini.scalar_minimize(method=self.minimizer)
-
- fit = self.residual(out.params, self.x)
-
- for name, par in out.params.items():
- nout = "%s:%s" % (name, ' '*(20-len(name)))
- print("%s: %s (%s) " % (nout, par.value, self.p_true[name].value))
-
- for para, true_para in zip(out.params.values(),
- self.p_true.values()):
- check_wo_stderr(para, true_para.value, sig=sig)
-
-
-if __name__ == '__main__':
- nose.main()
+# -*- coding: utf-8 -*- +from __future__ import print_function +from lmfit import minimize, Parameters, Parameter, report_fit, Minimizer +from lmfit.minimizer import (SCALAR_METHODS, HAS_EMCEE, + MinimizerResult, _lnpost) +from lmfit.lineshapes import gaussian +import numpy as np +from numpy import pi +from numpy.testing import (assert_, decorators, assert_raises, + assert_almost_equal) +import unittest +import nose +from nose import SkipTest + + +def check(para, real_val, sig=3): + err = abs(para.value - real_val) + print('Check Param w/ stderr: ', para.name, para.value, real_val, para.stderr) + assert(err < sig * para.stderr) + +def check_wo_stderr(para, real_val, sig=0.1): + err = abs(para.value - real_val) + print('Check Param w/o stderr: ', para.name, para.value, real_val, sig) + assert(err < sig) + +def check_paras(para_fit, para_real, sig=3): + for i in para_fit: + check(para_fit[i], para_real[i].value, sig=sig) + +def test_simple(): + # create data to be fitted + np.random.seed(1) + x = np.linspace(0, 15, 301) + data = (5. * np.sin(2 * x - 0.1) * np.exp(-x*x*0.025) + + np.random.normal(size=len(x), scale=0.2)) + + # define objective function: returns the array to be minimized + def fcn2min(params, x, data): + """ model decaying sine wave, subtract data""" + amp = params['amp'].value + shift = params['shift'].value + omega = params['omega'].value + decay = params['decay'].value + + model = amp * np.sin(x * omega + shift) * np.exp(-x*x*decay) + return model - data + + # create a set of Parameters + params = Parameters() + params.add('amp', value= 10, min=0) + params.add('decay', value= 0.1) + params.add('shift', value= 0.0, min=-pi / 2., max=pi / 2) + params.add('omega', value= 3.0) + + # do fit, here with leastsq model + result = minimize(fcn2min, params, args=(x, data)) + + # calculate final result + final = data + result.residual + + # write error report + print(" --> SIMPLE --> ") + print(result.params) + report_fit(result.params) + + #assert that the real parameters are found + + for para, val in zip(result.params.values(), [5, 0.025, -.1, 2]): + + check(para, val) + +def test_lbfgsb(): + p_true = Parameters() + p_true.add('amp', value=14.0) + p_true.add('period', value=5.33) + p_true.add('shift', value=0.123) + p_true.add('decay', value=0.010) + + def residual(pars, x, data=None): + amp = pars['amp'].value + per = pars['period'].value + shift = pars['shift'].value + decay = pars['decay'].value + + if abs(shift) > pi/2: + shift = shift - np.sign(shift) * pi + model = amp * np.sin(shift + x / per) * np.exp(-x * x * decay * decay) + if data is None: + return model + return (model - data) + + n = 2500 + xmin = 0. + xmax = 250.0 + noise = np.random.normal(scale=0.7215, size=n) + x = np.linspace(xmin, xmax, n) + data = residual(p_true, x) + noise + + fit_params = Parameters() + fit_params.add('amp', value=11.0, min=5, max=20) + fit_params.add('period', value=5., min=1., max=7) + fit_params.add('shift', value=.10, min=0.0, max=0.2) + fit_params.add('decay', value=6.e-3, min=0, max=0.1) + + init = residual(fit_params, x) + + out = minimize(residual, fit_params, method='lbfgsb', args=(x,), kws={'data':data}) + + fit = residual(fit_params, x) + + for name, par in out.params.items(): + nout = "%s:%s" % (name, ' '*(20-len(name))) + print("%s: %s (%s) " % (nout, par.value, p_true[name].value)) + + for para, true_para in zip(out.params.values(), p_true.values()): + check_wo_stderr(para, true_para.value) + +def test_derive(): + def func(pars, x, data=None): + a = pars['a'].value + b = pars['b'].value + c = pars['c'].value + + model=a * np.exp(-b * x)+c + if data is None: + return model + return model - data + + def dfunc(pars, x, data=None): + a = pars['a'].value + b = pars['b'].value + c = pars['c'].value + v = np.exp(-b*x) + return np.array([v, -a*x*v, np.ones(len(x))]) + + def f(var, x): + return var[0]* np.exp(-var[1] * x)+var[2] + + params1 = Parameters() + params1.add('a', value=10) + params1.add('b', value=10) + params1.add('c', value=10) + + params2 = Parameters() + params2.add('a', value=10) + params2.add('b', value=10) + params2.add('c', value=10) + + a, b, c = 2.5, 1.3, 0.8 + x = np.linspace(0,4,50) + y = f([a, b, c], x) + data = y + 0.15*np.random.normal(size=len(x)) + + # fit without analytic derivative + min1 = Minimizer(func, params1, fcn_args=(x,), fcn_kws={'data':data}) + out1 = min1.leastsq() + fit1 = func(out1.params, x) + + # fit with analytic derivative + min2 = Minimizer(func, params2, fcn_args=(x,), fcn_kws={'data':data}) + out2 = min2.leastsq(Dfun=dfunc, col_deriv=1) + fit2 = func(out2.params, x) + + print ('''Comparison of fit to exponential decay + with and without analytic derivatives, to + model = a*exp(-b*x) + c + for a = %.2f, b = %.2f, c = %.2f + ============================================== + Statistic/Parameter| Without | With | + ---------------------------------------------- + N Function Calls | %3i | %3i | + Chi-square | %.4f | %.4f | + a | %.4f | %.4f | + b | %.4f | %.4f | + c | %.4f | %.4f | + ---------------------------------------------- + ''' % (a, b, c, + out1.nfev, out2.nfev, + out1.chisqr, out2.chisqr, + out1.params['a'].value, out2.params['a'].value, + out1.params['b'].value, out2.params['b'].value, + out1.params['c'].value, out2.params['c'].value )) + + check_wo_stderr(out1.params['a'], out2.params['a'].value, 0.00005) + check_wo_stderr(out1.params['b'], out2.params['b'].value, 0.00005) + check_wo_stderr(out1.params['c'], out2.params['c'].value, 0.00005) + +def test_peakfit(): + def residual(pars, x, data=None): + g1 = gaussian(x, pars['a1'].value, pars['c1'].value, pars['w1'].value) + g2 = gaussian(x, pars['a2'].value, pars['c2'].value, pars['w2'].value) + model = g1 + g2 + if data is None: + return model + return (model - data) + + n = 601 + xmin = 0. + xmax = 15.0 + noise = np.random.normal(scale=.65, size=n) + x = np.linspace(xmin, xmax, n) + + org_params = Parameters() + org_params.add_many(('a1', 12.0, True, None, None, None), + ('c1', 5.3, True, None, None, None), + ('w1', 1.0, True, None, None, None), + ('a2', 9.1, True, None, None, None), + ('c2', 8.1, True, None, None, None), + ('w2', 2.5, True, None, None, None)) + + data = residual(org_params, x) + noise + + + fit_params = Parameters() + fit_params.add_many(('a1', 8.0, True, None, 14., None), + ('c1', 5.0, True, None, None, None), + ('w1', 0.7, True, None, None, None), + ('a2', 3.1, True, None, None, None), + ('c2', 8.8, True, None, None, None)) + + fit_params.add('w2', expr='2.5*w1') + + myfit = Minimizer(residual, fit_params, + fcn_args=(x,), fcn_kws={'data': data}) + + myfit.prepare_fit() + + init = residual(fit_params, x) + + + out = myfit.leastsq() + + # print(' N fev = ', myfit.nfev) + # print(myfit.chisqr, myfit.redchi, myfit.nfree) + + report_fit(out.params) + + fit = residual(out.params, x) + check_paras(out.params, org_params) + + +def test_scalar_minimize_has_no_uncertainties(): + # scalar_minimize doesn't calculate uncertainties. + # when a scalar_minimize is run the stderr and correl for each parameter + # should be None. (stderr and correl are set to None when a Parameter is + # initialised). + # This requires a reset after a leastsq fit has been done. + # Only when scalar_minimize calculates stderr and correl can this test + # be removed. + + np.random.seed(1) + x = np.linspace(0, 15, 301) + data = (5. * np.sin(2 * x - 0.1) * np.exp(-x*x*0.025) + + np.random.normal(size=len(x), scale=0.2) ) + + # define objective function: returns the array to be minimized + def fcn2min(params, x, data): + """ model decaying sine wave, subtract data""" + amp = params['amp'].value + shift = params['shift'].value + omega = params['omega'].value + decay = params['decay'].value + + model = amp * np.sin(x * omega + shift) * np.exp(-x*x*decay) + return model - data + + # create a set of Parameters + params = Parameters() + params.add('amp', value= 10, min=0) + params.add('decay', value= 0.1) + params.add('shift', value= 0.0, min=-pi / 2., max=pi / 2) + params.add('omega', value= 3.0) + + mini = Minimizer(fcn2min, params, fcn_args=(x, data)) + out = mini.minimize() + assert_(np.isfinite(out.params['amp'].stderr)) + print(out.errorbars) + assert_(out.errorbars == True) + out2 = mini.minimize(method='nelder-mead') + assert_(out2.params['amp'].stderr is None) + assert_(out2.params['decay'].stderr is None) + assert_(out2.params['shift'].stderr is None) + assert_(out2.params['omega'].stderr is None) + assert_(out2.params['amp'].correl is None) + assert_(out2.params['decay'].correl is None) + assert_(out2.params['shift'].correl is None) + assert_(out2.params['omega'].correl is None) + assert_(out2.errorbars == False) + + +def test_multidimensional_fit_GH205(): + # test that you don't need to flatten the output from the objective + # function. Tests regression for GH205. + pos = np.linspace(0, 99, 100) + xv, yv = np.meshgrid(pos, pos) + f = lambda xv, yv, lambda1, lambda2: (np.sin(xv * lambda1) + + np.cos(yv * lambda2)) + + data = f(xv, yv, 0.3, 3) + assert_(data.ndim, 2) + + def fcn2min(params, xv, yv, data): + """ model decaying sine wave, subtract data""" + lambda1 = params['lambda1'].value + lambda2 = params['lambda2'].value + model = f(xv, yv, lambda1, lambda2) + return model - data + + # create a set of Parameters + params = Parameters() + params.add('lambda1', value=0.4) + params.add('lambda2', value=3.2) + + mini = Minimizer(fcn2min, params, fcn_args=(xv, yv, data)) + res = mini.minimize() + +class CommonMinimizerTest(unittest.TestCase): + + def setUp(self): + """ + test scale minimizers except newton-cg (needs jacobian) and + anneal (doesn't work out of the box). + """ + p_true = Parameters() + p_true.add('amp', value=14.0) + p_true.add('period', value=5.33) + p_true.add('shift', value=0.123) + p_true.add('decay', value=0.010) + self.p_true = p_true + + n = 2500 + xmin = 0. + xmax = 250.0 + noise = np.random.normal(scale=0.7215, size=n) + self.x = np.linspace(xmin, xmax, n) + self.data = self.residual(p_true, self.x) + noise + + fit_params = Parameters() + fit_params.add('amp', value=11.0, min=5, max=20) + fit_params.add('period', value=5., min=1., max=7) + fit_params.add('shift', value=.10, min=0.0, max=0.2) + fit_params.add('decay', value=6.e-3, min=0, max=0.1) + self.fit_params = fit_params + + self.mini = Minimizer(self.residual, fit_params, [self.x, self.data]) + + def residual(self, pars, x, data=None): + amp = pars['amp'].value + per = pars['period'].value + shift = pars['shift'].value + decay = pars['decay'].value + + if abs(shift) > pi/2: + shift = shift - np.sign(shift) * pi + model = amp*np.sin(shift + x/per) * np.exp(-x*x*decay*decay) + if data is None: + return model + return model - data + + def test_diffev_bounds_check(self): + # You need finite (min, max) for each parameter if you're using + # differential_evolution. + self.fit_params['decay'].min = -np.inf + self.minimizer = 'differential_evolution' + np.testing.assert_raises(ValueError, self.scalar_minimizer) + + def test_scalar_minimizers(self): + # test all the scalar minimizers + for method in SCALAR_METHODS: + if method in ['newton', 'dogleg', 'trust-ncg', 'cg']: + continue + self.minimizer = SCALAR_METHODS[method] + if method == 'Nelder-Mead': + sig = 0.2 + else: + sig = 0.15 + self.scalar_minimizer(sig=sig) + + def scalar_minimizer(self, sig=0.15): + try: + from scipy.optimize import minimize as scipy_minimize + except ImportError: + raise SkipTest + + print(self.minimizer) + out = self.mini.scalar_minimize(method=self.minimizer) + + self.residual(out.params, self.x) + + for name, par in out.params.items(): + nout = "%s:%s" % (name, ' '*(20-len(name))) + print("%s: %s (%s) " % (nout, par.value, self.p_true[name].value)) + + for para, true_para in zip(out.params.values(), + self.p_true.values()): + check_wo_stderr(para, true_para.value, sig=sig) + + @decorators.slow + def test_emcee(self): + # test emcee + if not HAS_EMCEE: + return True + + np.random.seed(123456) + out = self.mini.emcee(nwalkers=100, steps=200, + burn=50, thin=10) + + check_paras(out.params, self.p_true, sig=3) + + @decorators.slow + def test_emcee_PT(self): + # test emcee with parallel tempering + if not HAS_EMCEE: + return True + + np.random.seed(123456) + self.mini.userfcn = residual_for_multiprocessing + out = self.mini.emcee(ntemps=4, nwalkers=50, steps=200, + burn=100, thin=10, workers=2) + + check_paras(out.params, self.p_true, sig=3) + + @decorators.slow + def test_emcee_multiprocessing(self): + # test multiprocessing runs + if not HAS_EMCEE: + return True + + np.random.seed(123456) + self.mini.userfcn = residual_for_multiprocessing + out = self.mini.emcee(steps=10, workers=4) + + def test_emcee_bounds_length(self): + # the log-probability functions check if the parameters are + # inside the bounds. Check that the bounds and parameters + # are the right lengths for comparison. This can be done + # if nvarys != nparams + if not HAS_EMCEE: + return True + self.mini.params['amp'].vary=False + self.mini.params['period'].vary=False + self.mini.params['shift'].vary=False + + out = self.mini.emcee(steps=10) + + @decorators.slow + def test_emcee_partial_bounds(self): + # mcmc with partial bounds + if not HAS_EMCEE: + return True + + np.random.seed(123456) + # test mcmc output vs lm, some parameters not bounded + self.fit_params['amp'].max = np.inf + # self.fit_params['amp'].min = -np.inf + out = self.mini.emcee(nwalkers=100, steps=300, + burn=100, thin=10) + + check_paras(out.params, self.p_true, sig=3) + + def test_emcee_init_with_chain(self): + # can you initialise with a previous chain + if not HAS_EMCEE: + return True + + out = self.mini.emcee(nwalkers=100, steps=5) + # can initialise with a chain + out2 = self.mini.emcee(nwalkers=100, steps=1, pos=out.chain) + + # can initialise with a correct subset of a chain + out3 = self.mini.emcee(nwalkers=100, + steps=1, + pos=out.chain[..., -1, :]) + + # but you can't initialise if the shape is wrong. + assert_raises(ValueError, + self.mini.emcee, + nwalkers=100, + steps=1, + pos=out.chain[..., -1, :-1]) + + def test_emcee_reuse_sampler(self): + if not HAS_EMCEE: + return True + + self.mini.emcee(nwalkers=100, steps=5) + + # if you've run the sampler the Minimizer object should have a _lastpos + # attribute + assert_(hasattr(self.mini, '_lastpos')) + + # now try and re-use sampler + out2 = self.mini.emcee(steps=10, reuse_sampler=True) + assert_(out2.chain.shape[1] == 15) + + # you shouldn't be able to reuse the sampler if nvarys has changed. + self.mini.params['amp'].vary = False + assert_raises(ValueError, self.mini.emcee, reuse_sampler=True) + + def test_emcee_lnpost(self): + # check ln likelihood is calculated correctly. It should be + # -0.5 * chi**2. + result = self.mini.minimize() + + # obtain the numeric values + # note - in this example all the parameters are varied + fvars = np.array([par.value for par in result.params.values()]) + + # calculate the cost function with scaled values (parameters all have + # lower and upper bounds. + scaled_fvars = [] + for par, fvar in zip(result.params.values(), fvars): + par.value = fvar + scaled_fvars.append(par.setup_bounds()) + + val = self.mini.penalty(np.array(scaled_fvars)) + + # calculate the log-likelihood value + bounds = np.array([(par.min, par.max) + for par in result.params.values()]) + val2 = _lnpost(fvars, + self.residual, + result.params, + result.var_names, + bounds, + userargs=(self.x, self.data)) + + assert_almost_equal(-0.5 * val, val2) + + def test_emcee_output(self): + # test mcmc output + if not HAS_EMCEE: + return True + try: + from pandas import DataFrame + except ImportError: + return True + out = self.mini.emcee(nwalkers=10, steps=20, burn=5, thin=2) + assert_(isinstance(out, MinimizerResult)) + assert_(isinstance(out.flatchain, DataFrame)) + + # check that we can access the chains via parameter name + assert_(out.flatchain['amp'].shape[0] == 80) + assert_(out.errorbars is True) + assert_(np.isfinite(out.params['amp'].correl['period'])) + + # the lnprob array should be the same as the chain size + assert_(np.size(out.chain)//4 == np.size(out.lnprob)) + + @decorators.slow + def test_emcee_float(self): + # test that it works if the residuals returns a float, not a vector + if not HAS_EMCEE: + return True + + def resid(pars, x, data=None): + return -0.5 * np.sum(self.residual(pars, x, data=data)**2) + + # just return chi2 + def resid2(pars, x, data=None): + return np.sum(self.residual(pars, x, data=data)**2) + + self.mini.userfcn = resid + np.random.seed(123456) + out = self.mini.emcee(nwalkers=100, steps=200, + burn=50, thin=10) + check_paras(out.params, self.p_true, sig=3) + + self.mini.userfcn = resid2 + np.random.seed(123456) + out = self.mini.emcee(nwalkers=100, steps=200, + burn=50, thin=10, float_behavior='chi2') + check_paras(out.params, self.p_true, sig=3) + + @decorators.slow + def test_emcee_seed(self): + # test emcee seeding can reproduce a sampling run + if not HAS_EMCEE: + return True + + out = self.mini.emcee(params=self.fit_params, + nwalkers=100, + steps=1, seed=1) + out2 = self.mini.emcee(params=self.fit_params, + nwalkers=100, + steps=1, seed=1) + + assert_almost_equal(out.chain, out2.chain) + + +def residual_for_multiprocessing(pars, x, data=None): + # a residual function defined in the top level is needed for + # multiprocessing. bound methods don't work. + amp = pars['amp'].value + per = pars['period'].value + shift = pars['shift'].value + decay = pars['decay'].value + + if abs(shift) > pi/2: + shift = shift - np.sign(shift) * pi + model = amp*np.sin(shift + x/per) * np.exp(-x*x*decay*decay) + if data is None: + return model + return (model - data) + + +if __name__ == '__main__': + nose.main() diff --git a/tests/test_parameters.py b/tests/test_parameters.py index beed610..29f3c2d 100644 --- a/tests/test_parameters.py +++ b/tests/test_parameters.py @@ -1,107 +1,152 @@ -from __future__ import print_function
-from lmfit import Parameters, Parameter
-from numpy.testing import assert_, assert_almost_equal
-import unittest
-from copy import deepcopy
-import numpy as np
-import pickle
-
-
-class TestParameters(unittest.TestCase):
-
- def setUp(self):
- self.params = Parameters()
- self.params.add_many(('a', 1., True, None, None, None),
- ('b', 2., True, None, None, None),
- ('c', 3., True, None, None, '2. * a'))
-
- def test_expr_was_evaluated(self):
- self.params.update_constraints()
- assert_almost_equal(self.params['c'].value,
- 2 * self.params['a'].value)
-
- def test_deepcopy(self):
- # check that a simple copy works
- b = deepcopy(self.params)
- assert_(self.params == b)
-
- # check that we can add a symbol to the interpreter
- self.params['b'].expr = 'sin(1)'
- self.params['b'].value = 10
- assert_almost_equal(self.params['b'].value, np.sin(1))
- assert_almost_equal(self.params._asteval.symtable['b'], np.sin(1))
-
- # check that the symbols in the interpreter are still the same after
- # deepcopying
- b = deepcopy(self.params)
-
- unique_symbols_params = self.params._asteval.user_defined_symbols()
- unique_symbols_b = self.params._asteval.user_defined_symbols()
- assert_(unique_symbols_b == unique_symbols_params)
- for unique_symbol in unique_symbols_b:
- if self.params._asteval.symtable[unique_symbol] is np.nan:
- continue
-
- assert_(self.params._asteval.symtable[unique_symbol]
- ==
- b._asteval.symtable[unique_symbol])
-
- def test_add_many_params(self):
- # test that we can add many parameters, but only parameters are added.
- a = Parameter('a', 1)
- b = Parameter('b', 2)
-
- p = Parameters()
- p.add_many(a, b)
-
- assert_(list(p.keys()) == ['a', 'b'])
-
- def test_expr_and_constraints_GH265(self):
- # test that parameters are reevaluated if they have bounds and expr
- # see GH265
- p = Parameters()
-
- p['a'] = Parameter('a', 10, True)
- p['b'] = Parameter('b', 10, True, 0, 20)
-
- p['a'].expr = '2 * b'
- assert_almost_equal(p['a'].value, 20)
-
- p['b'].value = 15
- assert_almost_equal(p['b'].value, 15)
- assert_almost_equal(p['a'].value, 30)
-
- p['b'].value = 30
- assert_almost_equal(p['b'].value, 20)
- assert_almost_equal(p['a'].value, 40)
-
- def test_pickle_parameter(self):
- # test that we can pickle a Parameter
- p = Parameter('a', 10, True, 0, 1)
- pkl = pickle.dumps(p)
-
- q = pickle.loads(pkl)
-
- assert_(p == q)
-
- def test_pickle_parameters(self):
- # test that we can pickle a Parameters object
- p = Parameters()
- p.add('a', 10, True, 0, 100)
- p.add('b', 10, True, 0, 100, 'a * sin(1)')
- p.update_constraints()
- p._asteval.symtable['abc'] = '2 * 3.142'
-
- pkl = pickle.dumps(p, -1)
- q = pickle.loads(pkl)
-
- q.update_constraints()
- assert_(p == q)
- assert_(not p is q)
-
- # now test if the asteval machinery survived
- assert_(q._asteval.symtable['abc'] == '2 * 3.142')
-
-
-if __name__ == '__main__':
- unittest.main()
+from __future__ import print_function +from lmfit import Parameters, Parameter +from lmfit.parameter import isclose +from numpy.testing import assert_, assert_almost_equal, assert_equal +import unittest +from copy import deepcopy +import numpy as np +import pickle + + +class TestParameters(unittest.TestCase): + + def setUp(self): + self.params = Parameters() + self.params.add_many(('a', 1., True, None, None, None), + ('b', 2., True, None, None, None), + ('c', 3., True, None, None, '2. * a')) + + def test_expr_was_evaluated(self): + self.params.update_constraints() + assert_almost_equal(self.params['c'].value, + 2 * self.params['a'].value) + + def test_copy(self): + # check simple Parameters.copy() does not fail + # on non-trivial Parameters + p1 = Parameters() + p1.add('t', 2.0, min=0.0, max=5.0) + p1.add('x', 10.0) + p1.add('y', expr='x*t + sqrt(t)/3.0') + + p2 = p1.copy() + assert(isinstance(p2, Parameters)) + assert('t' in p2) + assert('y' in p2) + assert(p2['t'].max < 6.0) + assert(np.isinf(p2['x'].max) and p2['x'].max > 0) + assert(np.isinf(p2['x'].min) and p2['x'].min < 0) + assert('sqrt(t)' in p2['y'].expr ) + assert(p2._asteval is not None) + assert(p2._asteval.symtable is not None) + assert((p2['y'].value > 20) and (p2['y'].value < 21)) + + + def test_deepcopy(self): + # check that a simple copy works + b = deepcopy(self.params) + assert_(self.params == b) + + # check that we can add a symbol to the interpreter + self.params['b'].expr = 'sin(1)' + self.params['b'].value = 10 + assert_almost_equal(self.params['b'].value, np.sin(1)) + assert_almost_equal(self.params._asteval.symtable['b'], np.sin(1)) + + # check that the symbols in the interpreter are still the same after + # deepcopying + b = deepcopy(self.params) + + unique_symbols_params = self.params._asteval.user_defined_symbols() + unique_symbols_b = self.params._asteval.user_defined_symbols() + assert_(unique_symbols_b == unique_symbols_params) + for unique_symbol in unique_symbols_b: + if self.params._asteval.symtable[unique_symbol] is np.nan: + continue + + assert_(self.params._asteval.symtable[unique_symbol] + == + b._asteval.symtable[unique_symbol]) + + def test_add_many_params(self): + # test that we can add many parameters, but only parameters are added. + a = Parameter('a', 1) + b = Parameter('b', 2) + + p = Parameters() + p.add_many(a, b) + + assert_(list(p.keys()) == ['a', 'b']) + + def test_expr_and_constraints_GH265(self): + # test that parameters are reevaluated if they have bounds and expr + # see GH265 + p = Parameters() + + p['a'] = Parameter('a', 10, True) + p['b'] = Parameter('b', 10, True, 0, 20) + + assert_equal(p['b'].min, 0) + assert_equal(p['b'].max, 20) + + p['a'].expr = '2 * b' + assert_almost_equal(p['a'].value, 20) + + p['b'].value = 15 + assert_almost_equal(p['b'].value, 15) + assert_almost_equal(p['a'].value, 30) + + p['b'].value = 30 + assert_almost_equal(p['b'].value, 20) + assert_almost_equal(p['a'].value, 40) + + def test_pickle_parameter(self): + # test that we can pickle a Parameter + p = Parameter('a', 10, True, 0, 1) + pkl = pickle.dumps(p) + + q = pickle.loads(pkl) + + assert_(p == q) + + def test_pickle_parameters(self): + # test that we can pickle a Parameters object + p = Parameters() + p.add('a', 10, True, 0, 100) + p.add('b', 10, True, 0, 100, 'a * sin(1)') + p.update_constraints() + p._asteval.symtable['abc'] = '2 * 3.142' + + pkl = pickle.dumps(p, -1) + q = pickle.loads(pkl) + + q.update_constraints() + assert_(p == q) + assert_(not p is q) + + # now test if the asteval machinery survived + assert_(q._asteval.symtable['abc'] == '2 * 3.142') + + # check that unpickling of Parameters is not affected by expr that + # refer to Parameter that are added later on. In the following + # example var_0.expr refers to var_1, which is a Parameter later + # on in the Parameters OrderedDict. + p = Parameters() + p.add('var_0', value=1) + p.add('var_1', value=2) + p['var_0'].expr = 'var_1' + pkl = pickle.dumps(p) + q = pickle.loads(pkl) + + def test_isclose(self): + assert_(isclose(1., 1+1e-5, atol=1e-4, rtol=0)) + assert_(not isclose(1., 1+1e-5, atol=1e-6, rtol=0)) + assert_(isclose(1e10, 1.00001e10, rtol=1e-5, atol=1e-8)) + assert_(not isclose(0, np.inf)) + assert_(not isclose(-np.inf, np.inf)) + assert_(isclose(np.inf, np.inf)) + assert_(not isclose(np.nan, np.nan)) + + +if __name__ == '__main__': + unittest.main() diff --git a/tests/test_params_set.py b/tests/test_params_set.py index 26125ea..24b1089 100644 --- a/tests/test_params_set.py +++ b/tests/test_params_set.py @@ -1,48 +1,48 @@ -import numpy as np
-from numpy.testing import assert_allclose
-from lmfit import Parameters, minimize, report_fit
-from lmfit.lineshapes import gaussian
-from lmfit.models import VoigtModel
-
-def test_param_set():
- np.random.seed(2015)
- x = np.arange(0, 20, 0.05)
- y = gaussian(x, amplitude=15.43, center=4.5, sigma=2.13)
- y = y + 0.05 - 0.01*x + np.random.normal(scale=0.03, size=len(x))
-
- model = VoigtModel()
- params = model.guess(y, x=x)
-
- # test #1: gamma is constrained to equal sigma
- assert(params['gamma'].expr == 'sigma')
- params.update_constraints()
- sigval = params['gamma'].value
- assert_allclose(params['gamma'].value, sigval, 1e-4, 1e-4, '', True)
-
- # test #2: explicitly setting a param value should work, even when
- # it had been an expression. The value will be left as fixed
- gamval = 0.87543
- params['gamma'].set(value=gamval)
- assert(params['gamma'].expr is None)
- assert(not params['gamma'].vary)
- assert_allclose(params['gamma'].value, gamval, 1e-4, 1e-4, '', True)
-
- # test #3: explicitly setting an expression should work
- # Note, the only way to ensure that **ALL** constraints are up to date
- # is to call params.update_constraints(). This is because the constraint
- # may have multiple dependencies.
- params['gamma'].set(expr='sigma/2.0')
- assert(params['gamma'].expr is not None)
- assert(not params['gamma'].vary)
- params.update_constraints()
- assert_allclose(params['gamma'].value, sigval/2.0, 1e-4, 1e-4, '', True)
-
- # test #4: explicitly setting a param value WITH vary=True
- # will set it to be variable
- gamval = 0.7777
- params['gamma'].set(value=gamval, vary=True)
- assert(params['gamma'].expr is None)
- assert(params['gamma'].vary)
- assert_allclose(params['gamma'].value, gamval, 1e-4, 1e-4, '', True)
-
+import numpy as np +from numpy.testing import assert_allclose +from lmfit import Parameters, minimize, report_fit +from lmfit.lineshapes import gaussian +from lmfit.models import VoigtModel + +def test_param_set(): + np.random.seed(2015) + x = np.arange(0, 20, 0.05) + y = gaussian(x, amplitude=15.43, center=4.5, sigma=2.13) + y = y + 0.05 - 0.01*x + np.random.normal(scale=0.03, size=len(x)) + + model = VoigtModel() + params = model.guess(y, x=x) + + # test #1: gamma is constrained to equal sigma + assert(params['gamma'].expr == 'sigma') + params.update_constraints() + sigval = params['gamma'].value + assert_allclose(params['gamma'].value, sigval, 1e-4, 1e-4, '', True) + + # test #2: explicitly setting a param value should work, even when + # it had been an expression. The value will be left as fixed + gamval = 0.87543 + params['gamma'].set(value=gamval) + assert(params['gamma'].expr is None) + assert(not params['gamma'].vary) + assert_allclose(params['gamma'].value, gamval, 1e-4, 1e-4, '', True) + + # test #3: explicitly setting an expression should work + # Note, the only way to ensure that **ALL** constraints are up to date + # is to call params.update_constraints(). This is because the constraint + # may have multiple dependencies. + params['gamma'].set(expr='sigma/2.0') + assert(params['gamma'].expr is not None) + assert(not params['gamma'].vary) + params.update_constraints() + assert_allclose(params['gamma'].value, sigval/2.0, 1e-4, 1e-4, '', True) + + # test #4: explicitly setting a param value WITH vary=True + # will set it to be variable + gamval = 0.7777 + params['gamma'].set(value=gamval, vary=True) + assert(params['gamma'].expr is None) + assert(params['gamma'].vary) + assert_allclose(params['gamma'].value, gamval, 1e-4, 1e-4, '', True) + test_param_set()
\ No newline at end of file diff --git a/tests/test_stepmodel.py b/tests/test_stepmodel.py index d854467..cabf118 100644 --- a/tests/test_stepmodel.py +++ b/tests/test_stepmodel.py @@ -1,58 +1,58 @@ -import numpy as np
-from lmfit import fit_report
-from lmfit.models import StepModel, ConstantModel
-from lmfit_testutils import assert_paramval, assert_paramattr
-
-def get_data():
- x = np.linspace(0, 10, 201)
- dat = np.ones_like(x)
- dat[:48] = 0.0
- dat[48:77] = np.arange(77-48)/(77.0-48)
- dat = dat + 5e-2*np.random.randn(len(x))
- dat = 110.2 * dat + 12.0
- return x, dat
-
-def test_stepmodel_linear():
- x, y = get_data()
- stepmod = StepModel(form='linear')
- const = ConstantModel()
- pars = stepmod.guess(y, x)
- pars = pars + const.make_params(c=3*y.min())
- mod = stepmod + const
-
- out = mod.fit(y, pars, x=x)
-
- assert(out.nfev > 5)
- assert(out.nvarys == 4)
- assert(out.chisqr > 1)
- assert(out.params['c'].value > 3)
- assert(out.params['center'].value > 1)
- assert(out.params['center'].value < 4)
- assert(out.params['sigma'].value > 0.5)
- assert(out.params['sigma'].value < 3.5)
- assert(out.params['amplitude'].value > 50)
-
-
-def test_stepmodel_erf():
- x, y = get_data()
- stepmod = StepModel(form='linear')
- const = ConstantModel()
- pars = stepmod.guess(y, x)
- pars = pars + const.make_params(c=3*y.min())
- mod = stepmod + const
-
- out = mod.fit(y, pars, x=x)
-
- assert(out.nfev > 5)
- assert(out.nvarys == 4)
- assert(out.chisqr > 1)
- assert(out.params['c'].value > 3)
- assert(out.params['center'].value > 1)
- assert(out.params['center'].value < 4)
- assert(out.params['amplitude'].value > 50)
- assert(out.params['sigma'].value > 0.2)
- assert(out.params['sigma'].value < 1.5)
-
-if __name__ == '__main__':
- # test_stepmodel_linear()
- test_stepmodel_erf()
+import numpy as np +from lmfit import fit_report +from lmfit.models import StepModel, ConstantModel +from lmfit_testutils import assert_paramval, assert_paramattr + +def get_data(): + x = np.linspace(0, 10, 201) + dat = np.ones_like(x) + dat[:48] = 0.0 + dat[48:77] = np.arange(77-48)/(77.0-48) + dat = dat + 5e-2*np.random.randn(len(x)) + dat = 110.2 * dat + 12.0 + return x, dat + +def test_stepmodel_linear(): + x, y = get_data() + stepmod = StepModel(form='linear') + const = ConstantModel() + pars = stepmod.guess(y, x) + pars = pars + const.make_params(c=3*y.min()) + mod = stepmod + const + + out = mod.fit(y, pars, x=x) + + assert(out.nfev > 5) + assert(out.nvarys == 4) + assert(out.chisqr > 1) + assert(out.params['c'].value > 3) + assert(out.params['center'].value > 1) + assert(out.params['center'].value < 4) + assert(out.params['sigma'].value > 0.5) + assert(out.params['sigma'].value < 3.5) + assert(out.params['amplitude'].value > 50) + + +def test_stepmodel_erf(): + x, y = get_data() + stepmod = StepModel(form='linear') + const = ConstantModel() + pars = stepmod.guess(y, x) + pars = pars + const.make_params(c=3*y.min()) + mod = stepmod + const + + out = mod.fit(y, pars, x=x) + + assert(out.nfev > 5) + assert(out.nvarys == 4) + assert(out.chisqr > 1) + assert(out.params['c'].value > 3) + assert(out.params['center'].value > 1) + assert(out.params['center'].value < 4) + assert(out.params['amplitude'].value > 50) + assert(out.params['sigma'].value > 0.2) + assert(out.params['sigma'].value < 1.5) + +if __name__ == '__main__': + # test_stepmodel_linear() + test_stepmodel_erf() diff --git a/versioneer.py b/versioneer.py index 4162e8a..481180d 100644 --- a/versioneer.py +++ b/versioneer.py @@ -1,901 +1,901 @@ -
-# Version: 0.12
-
-"""
-The Versioneer
-==============
-
-* like a rocketeer, but for versions!
-* https://github.com/warner/python-versioneer
-* Brian Warner
-* License: Public Domain
-* Compatible With: python2.6, 2.7, 3.2, 3.3, 3.4, and pypy
-
-[](https://travis-ci.org/warner/python-versioneer)
-
-This is a tool for managing a recorded version number in distutils-based
-python projects. The goal is to remove the tedious and error-prone "update
-the embedded version string" step from your release process. Making a new
-release should be as easy as recording a new tag in your version-control
-system, and maybe making new tarballs.
-
-
-## Quick Install
-
-* `pip install versioneer` to somewhere to your $PATH
-* run `versioneer-installer` in your source tree: this installs `versioneer.py`
-* follow the instructions below (also in the `versioneer.py` docstring)
-
-## Version Identifiers
-
-Source trees come from a variety of places:
-
-* a version-control system checkout (mostly used by developers)
-* a nightly tarball, produced by build automation
-* a snapshot tarball, produced by a web-based VCS browser, like github's
- "tarball from tag" feature
-* a release tarball, produced by "setup.py sdist", distributed through PyPI
-
-Within each source tree, the version identifier (either a string or a number,
-this tool is format-agnostic) can come from a variety of places:
-
-* ask the VCS tool itself, e.g. "git describe" (for checkouts), which knows
- about recent "tags" and an absolute revision-id
-* the name of the directory into which the tarball was unpacked
-* an expanded VCS keyword ($Id$, etc)
-* a `_version.py` created by some earlier build step
-
-For released software, the version identifier is closely related to a VCS
-tag. Some projects use tag names that include more than just the version
-string (e.g. "myproject-1.2" instead of just "1.2"), in which case the tool
-needs to strip the tag prefix to extract the version identifier. For
-unreleased software (between tags), the version identifier should provide
-enough information to help developers recreate the same tree, while also
-giving them an idea of roughly how old the tree is (after version 1.2, before
-version 1.3). Many VCS systems can report a description that captures this,
-for example 'git describe --tags --dirty --always' reports things like
-"0.7-1-g574ab98-dirty" to indicate that the checkout is one revision past the
-0.7 tag, has a unique revision id of "574ab98", and is "dirty" (it has
-uncommitted changes.
-
-The version identifier is used for multiple purposes:
-
-* to allow the module to self-identify its version: `myproject.__version__`
-* to choose a name and prefix for a 'setup.py sdist' tarball
-
-## Theory of Operation
-
-Versioneer works by adding a special `_version.py` file into your source
-tree, where your `__init__.py` can import it. This `_version.py` knows how to
-dynamically ask the VCS tool for version information at import time. However,
-when you use "setup.py build" or "setup.py sdist", `_version.py` in the new
-copy is replaced by a small static file that contains just the generated
-version data.
-
-`_version.py` also contains `$Revision$` markers, and the installation
-process marks `_version.py` to have this marker rewritten with a tag name
-during the "git archive" command. As a result, generated tarballs will
-contain enough information to get the proper version.
-
-
-## Installation
-
-First, decide on values for the following configuration variables:
-
-* `VCS`: the version control system you use. Currently accepts "git".
-
-* `versionfile_source`:
-
- A project-relative pathname into which the generated version strings should
- be written. This is usually a `_version.py` next to your project's main
- `__init__.py` file, so it can be imported at runtime. If your project uses
- `src/myproject/__init__.py`, this should be `src/myproject/_version.py`.
- This file should be checked in to your VCS as usual: the copy created below
- by `setup.py versioneer` will include code that parses expanded VCS
- keywords in generated tarballs. The 'build' and 'sdist' commands will
- replace it with a copy that has just the calculated version string.
-
- This must be set even if your project does not have any modules (and will
- therefore never import `_version.py`), since "setup.py sdist" -based trees
- still need somewhere to record the pre-calculated version strings. Anywhere
- in the source tree should do. If there is a `__init__.py` next to your
- `_version.py`, the `setup.py versioneer` command (described below) will
- append some `__version__`-setting assignments, if they aren't already
- present.
-
-* `versionfile_build`:
-
- Like `versionfile_source`, but relative to the build directory instead of
- the source directory. These will differ when your setup.py uses
- 'package_dir='. If you have `package_dir={'myproject': 'src/myproject'}`,
- then you will probably have `versionfile_build='myproject/_version.py'` and
- `versionfile_source='src/myproject/_version.py'`.
-
- If this is set to None, then `setup.py build` will not attempt to rewrite
- any `_version.py` in the built tree. If your project does not have any
- libraries (e.g. if it only builds a script), then you should use
- `versionfile_build = None` and override `distutils.command.build_scripts`
- to explicitly insert a copy of `versioneer.get_version()` into your
- generated script.
-
-* `tag_prefix`:
-
- a string, like 'PROJECTNAME-', which appears at the start of all VCS tags.
- If your tags look like 'myproject-1.2.0', then you should use
- tag_prefix='myproject-'. If you use unprefixed tags like '1.2.0', this
- should be an empty string.
-
-* `parentdir_prefix`:
-
- a string, frequently the same as tag_prefix, which appears at the start of
- all unpacked tarball filenames. If your tarball unpacks into
- 'myproject-1.2.0', this should be 'myproject-'.
-
-This tool provides one script, named `versioneer-installer`. That script does
-one thing: write a copy of `versioneer.py` into the current directory.
-
-To versioneer-enable your project:
-
-* 1: Run `versioneer-installer` to copy `versioneer.py` into the top of your
- source tree.
-
-* 2: add the following lines to the top of your `setup.py`, with the
- configuration values you decided earlier:
-
- import versioneer
- versioneer.VCS = 'git'
- versioneer.versionfile_source = 'src/myproject/_version.py'
- versioneer.versionfile_build = 'myproject/_version.py'
- versioneer.tag_prefix = '' # tags are like 1.2.0
- versioneer.parentdir_prefix = 'myproject-' # dirname like 'myproject-1.2.0'
-
-* 3: add the following arguments to the setup() call in your setup.py:
-
- version=versioneer.get_version(),
- cmdclass=versioneer.get_cmdclass(),
-
-* 4: now run `setup.py versioneer`, which will create `_version.py`, and will
- modify your `__init__.py` (if one exists next to `_version.py`) to define
- `__version__` (by calling a function from `_version.py`). It will also
- modify your `MANIFEST.in` to include both `versioneer.py` and the generated
- `_version.py` in sdist tarballs.
-
-* 5: commit these changes to your VCS. To make sure you won't forget,
- `setup.py versioneer` will mark everything it touched for addition.
-
-## Post-Installation Usage
-
-Once established, all uses of your tree from a VCS checkout should get the
-current version string. All generated tarballs should include an embedded
-version string (so users who unpack them will not need a VCS tool installed).
-
-If you distribute your project through PyPI, then the release process should
-boil down to two steps:
-
-* 1: git tag 1.0
-* 2: python setup.py register sdist upload
-
-If you distribute it through github (i.e. users use github to generate
-tarballs with `git archive`), the process is:
-
-* 1: git tag 1.0
-* 2: git push; git push --tags
-
-Currently, all version strings must be based upon a tag. Versioneer will
-report "unknown" until your tree has at least one tag in its history. This
-restriction will be fixed eventually (see issue #12).
-
-## Version-String Flavors
-
-Code which uses Versioneer can learn about its version string at runtime by
-importing `_version` from your main `__init__.py` file and running the
-`get_versions()` function. From the "outside" (e.g. in `setup.py`), you can
-import the top-level `versioneer.py` and run `get_versions()`.
-
-Both functions return a dictionary with different keys for different flavors
-of the version string:
-
-* `['version']`: condensed tag+distance+shortid+dirty identifier. For git,
- this uses the output of `git describe --tags --dirty --always` but strips
- the tag_prefix. For example "0.11-2-g1076c97-dirty" indicates that the tree
- is like the "1076c97" commit but has uncommitted changes ("-dirty"), and
- that this commit is two revisions ("-2-") beyond the "0.11" tag. For
- released software (exactly equal to a known tag), the identifier will only
- contain the stripped tag, e.g. "0.11".
-
-* `['full']`: detailed revision identifier. For Git, this is the full SHA1
- commit id, followed by "-dirty" if the tree contains uncommitted changes,
- e.g. "1076c978a8d3cfc70f408fe5974aa6c092c949ac-dirty".
-
-Some variants are more useful than others. Including `full` in a bug report
-should allow developers to reconstruct the exact code being tested (or
-indicate the presence of local changes that should be shared with the
-developers). `version` is suitable for display in an "about" box or a CLI
-`--version` output: it can be easily compared against release notes and lists
-of bugs fixed in various releases.
-
-In the future, this will also include a
-[PEP-0440](http://legacy.python.org/dev/peps/pep-0440/) -compatible flavor
-(e.g. `1.2.post0.dev123`). This loses a lot of information (and has no room
-for a hash-based revision id), but is safe to use in a `setup.py`
-"`version=`" argument. It also enables tools like *pip* to compare version
-strings and evaluate compatibility constraint declarations.
-
-The `setup.py versioneer` command adds the following text to your
-`__init__.py` to place a basic version in `YOURPROJECT.__version__`:
-
- from ._version import get_versions
- __version__ = get_versions()['version']
- del get_versions
-
-## Updating Versioneer
-
-To upgrade your project to a new release of Versioneer, do the following:
-
-* install the new Versioneer (`pip install -U versioneer` or equivalent)
-* re-run `versioneer-installer` in your source tree to replace your copy of
- `versioneer.py`
-* edit `setup.py`, if necessary, to include any new configuration settings
- indicated by the release notes
-* re-run `setup.py versioneer` to replace `SRC/_version.py`
-* commit any changed files
-
-### Upgrading from 0.10 to 0.11
-
-You must add a `versioneer.VCS = "git"` to your `setup.py` before re-running
-`setup.py versioneer`. This will enable the use of additional version-control
-systems (SVN, etc) in the future.
-
-### Upgrading from 0.11 to 0.12
-
-Nothing special.
-
-## Future Directions
-
-This tool is designed to make it easily extended to other version-control
-systems: all VCS-specific components are in separate directories like
-src/git/ . The top-level `versioneer.py` script is assembled from these
-components by running make-versioneer.py . In the future, make-versioneer.py
-will take a VCS name as an argument, and will construct a version of
-`versioneer.py` that is specific to the given VCS. It might also take the
-configuration arguments that are currently provided manually during
-installation by editing setup.py . Alternatively, it might go the other
-direction and include code from all supported VCS systems, reducing the
-number of intermediate scripts.
-
-
-## License
-
-To make Versioneer easier to embed, all its code is hereby released into the
-public domain. The `_version.py` that it creates is also in the public
-domain.
-
-"""
-
-import os, sys, re, subprocess, errno
-from distutils.core import Command
-from distutils.command.sdist import sdist as _sdist
-from distutils.command.build import build as _build
-
-# these configuration settings will be overridden by setup.py after it
-# imports us
-versionfile_source = None
-versionfile_build = None
-tag_prefix = None
-parentdir_prefix = None
-VCS = None
-
-# these dictionaries contain VCS-specific tools
-LONG_VERSION_PY = {}
-
-def run_command(commands, args, cwd=None, verbose=False, hide_stderr=False):
- assert isinstance(commands, list)
- p = None
- for c in commands:
- try:
- # remember shell=False, so use git.cmd on windows, not just git
- p = subprocess.Popen([c] + args, cwd=cwd, stdout=subprocess.PIPE,
- stderr=(subprocess.PIPE if hide_stderr
- else None))
- break
- except EnvironmentError:
- e = sys.exc_info()[1]
- if e.errno == errno.ENOENT:
- continue
- if verbose:
- print("unable to run %s" % args[0])
- print(e)
- return None
- else:
- if verbose:
- print("unable to find command, tried %s" % (commands,))
- return None
- stdout = p.communicate()[0].strip()
- if sys.version >= '3':
- stdout = stdout.decode()
- if p.returncode != 0:
- if verbose:
- print("unable to run %s (error)" % args[0])
- return None
- return stdout
-
-LONG_VERSION_PY['git'] = '''
-# This file helps to compute a version number in source trees obtained from
-# git-archive tarball (such as those provided by githubs download-from-tag
-# feature). Distribution tarballs (built by setup.py sdist) and build
-# directories (produced by setup.py build) will contain a much shorter file
-# that just contains the computed version number.
-
-# This file is released into the public domain. Generated by
-# versioneer-0.12 (https://github.com/warner/python-versioneer)
-
-# these strings will be replaced by git during git-archive
-git_refnames = "%(DOLLAR)sFormat:%%d%(DOLLAR)s"
-git_full = "%(DOLLAR)sFormat:%%H%(DOLLAR)s"
-
-# these strings are filled in when 'setup.py versioneer' creates _version.py
-tag_prefix = "%(TAG_PREFIX)s"
-parentdir_prefix = "%(PARENTDIR_PREFIX)s"
-versionfile_source = "%(VERSIONFILE_SOURCE)s"
-
-import os, sys, re, subprocess, errno
-
-def run_command(commands, args, cwd=None, verbose=False, hide_stderr=False):
- assert isinstance(commands, list)
- p = None
- for c in commands:
- try:
- # remember shell=False, so use git.cmd on windows, not just git
- p = subprocess.Popen([c] + args, cwd=cwd, stdout=subprocess.PIPE,
- stderr=(subprocess.PIPE if hide_stderr
- else None))
- break
- except EnvironmentError:
- e = sys.exc_info()[1]
- if e.errno == errno.ENOENT:
- continue
- if verbose:
- print("unable to run %%s" %% args[0])
- print(e)
- return None
- else:
- if verbose:
- print("unable to find command, tried %%s" %% (commands,))
- return None
- stdout = p.communicate()[0].strip()
- if sys.version >= '3':
- stdout = stdout.decode()
- if p.returncode != 0:
- if verbose:
- print("unable to run %%s (error)" %% args[0])
- return None
- return stdout
-
-
-def versions_from_parentdir(parentdir_prefix, root, verbose=False):
- # Source tarballs conventionally unpack into a directory that includes
- # both the project name and a version string.
- dirname = os.path.basename(root)
- if not dirname.startswith(parentdir_prefix):
- if verbose:
- print("guessing rootdir is '%%s', but '%%s' doesn't start with prefix '%%s'" %%
- (root, dirname, parentdir_prefix))
- return None
- return {"version": dirname[len(parentdir_prefix):], "full": ""}
-
-def git_get_keywords(versionfile_abs):
- # the code embedded in _version.py can just fetch the value of these
- # keywords. When used from setup.py, we don't want to import _version.py,
- # so we do it with a regexp instead. This function is not used from
- # _version.py.
- keywords = {}
- try:
- f = open(versionfile_abs,"r")
- for line in f.readlines():
- if line.strip().startswith("git_refnames ="):
- mo = re.search(r'=\s*"(.*)"', line)
- if mo:
- keywords["refnames"] = mo.group(1)
- if line.strip().startswith("git_full ="):
- mo = re.search(r'=\s*"(.*)"', line)
- if mo:
- keywords["full"] = mo.group(1)
- f.close()
- except EnvironmentError:
- pass
- return keywords
-
-def git_versions_from_keywords(keywords, tag_prefix, verbose=False):
- if not keywords:
- return {} # keyword-finding function failed to find keywords
- refnames = keywords["refnames"].strip()
- if refnames.startswith("$Format"):
- if verbose:
- print("keywords are unexpanded, not using")
- return {} # unexpanded, so not in an unpacked git-archive tarball
- refs = set([r.strip() for r in refnames.strip("()").split(",")])
- # starting in git-1.8.3, tags are listed as "tag: foo-1.0" instead of
- # just "foo-1.0". If we see a "tag: " prefix, prefer those.
- TAG = "tag: "
- tags = set([r[len(TAG):] for r in refs if r.startswith(TAG)])
- if not tags:
- # Either we're using git < 1.8.3, or there really are no tags. We use
- # a heuristic: assume all version tags have a digit. The old git %%d
- # expansion behaves like git log --decorate=short and strips out the
- # refs/heads/ and refs/tags/ prefixes that would let us distinguish
- # between branches and tags. By ignoring refnames without digits, we
- # filter out many common branch names like "release" and
- # "stabilization", as well as "HEAD" and "master".
- tags = set([r for r in refs if re.search(r'\d', r)])
- if verbose:
- print("discarding '%%s', no digits" %% ",".join(refs-tags))
- if verbose:
- print("likely tags: %%s" %% ",".join(sorted(tags)))
- for ref in sorted(tags):
- # sorting will prefer e.g. "2.0" over "2.0rc1"
- if ref.startswith(tag_prefix):
- r = ref[len(tag_prefix):]
- if verbose:
- print("picking %%s" %% r)
- return { "version": r,
- "full": keywords["full"].strip() }
- # no suitable tags, so we use the full revision id
- if verbose:
- print("no suitable tags, using full revision id")
- return { "version": keywords["full"].strip(),
- "full": keywords["full"].strip() }
-
-
-def git_versions_from_vcs(tag_prefix, root, verbose=False):
- # this runs 'git' from the root of the source tree. This only gets called
- # if the git-archive 'subst' keywords were *not* expanded, and
- # _version.py hasn't already been rewritten with a short version string,
- # meaning we're inside a checked out source tree.
-
- if not os.path.exists(os.path.join(root, ".git")):
- if verbose:
- print("no .git in %%s" %% root)
- return {}
-
- GITS = ["git"]
- if sys.platform == "win32":
- GITS = ["git.cmd", "git.exe"]
- stdout = run_command(GITS, ["describe", "--tags", "--dirty", "--always"],
- cwd=root)
- if stdout is None:
- return {}
- if not stdout.startswith(tag_prefix):
- if verbose:
- print("tag '%%s' doesn't start with prefix '%%s'" %% (stdout, tag_prefix))
- return {}
- tag = stdout[len(tag_prefix):]
- stdout = run_command(GITS, ["rev-parse", "HEAD"], cwd=root)
- if stdout is None:
- return {}
- full = stdout.strip()
- if tag.endswith("-dirty"):
- full += "-dirty"
- return {"version": tag, "full": full}
-
-
-def get_versions(default={"version": "unknown", "full": ""}, verbose=False):
- # I am in _version.py, which lives at ROOT/VERSIONFILE_SOURCE. If we have
- # __file__, we can work backwards from there to the root. Some
- # py2exe/bbfreeze/non-CPython implementations don't do __file__, in which
- # case we can only use expanded keywords.
-
- keywords = { "refnames": git_refnames, "full": git_full }
- ver = git_versions_from_keywords(keywords, tag_prefix, verbose)
- if ver:
- return ver
-
- try:
- root = os.path.abspath(__file__)
- # versionfile_source is the relative path from the top of the source
- # tree (where the .git directory might live) to this file. Invert
- # this to find the root from __file__.
- for i in range(len(versionfile_source.split(os.sep))):
- root = os.path.dirname(root)
- except NameError:
- return default
-
- return (git_versions_from_vcs(tag_prefix, root, verbose)
- or versions_from_parentdir(parentdir_prefix, root, verbose)
- or default)
-'''
-
-def git_get_keywords(versionfile_abs):
- # the code embedded in _version.py can just fetch the value of these
- # keywords. When used from setup.py, we don't want to import _version.py,
- # so we do it with a regexp instead. This function is not used from
- # _version.py.
- keywords = {}
- try:
- f = open(versionfile_abs,"r")
- for line in f.readlines():
- if line.strip().startswith("git_refnames ="):
- mo = re.search(r'=\s*"(.*)"', line)
- if mo:
- keywords["refnames"] = mo.group(1)
- if line.strip().startswith("git_full ="):
- mo = re.search(r'=\s*"(.*)"', line)
- if mo:
- keywords["full"] = mo.group(1)
- f.close()
- except EnvironmentError:
- pass
- return keywords
-
-def git_versions_from_keywords(keywords, tag_prefix, verbose=False):
- if not keywords:
- return {} # keyword-finding function failed to find keywords
- refnames = keywords["refnames"].strip()
- if refnames.startswith("$Format"):
- if verbose:
- print("keywords are unexpanded, not using")
- return {} # unexpanded, so not in an unpacked git-archive tarball
- refs = set([r.strip() for r in refnames.strip("()").split(",")])
- # starting in git-1.8.3, tags are listed as "tag: foo-1.0" instead of
- # just "foo-1.0". If we see a "tag: " prefix, prefer those.
- TAG = "tag: "
- tags = set([r[len(TAG):] for r in refs if r.startswith(TAG)])
- if not tags:
- # Either we're using git < 1.8.3, or there really are no tags. We use
- # a heuristic: assume all version tags have a digit. The old git %d
- # expansion behaves like git log --decorate=short and strips out the
- # refs/heads/ and refs/tags/ prefixes that would let us distinguish
- # between branches and tags. By ignoring refnames without digits, we
- # filter out many common branch names like "release" and
- # "stabilization", as well as "HEAD" and "master".
- tags = set([r for r in refs if re.search(r'\d', r)])
- if verbose:
- print("discarding '%s', no digits" % ",".join(refs-tags))
- if verbose:
- print("likely tags: %s" % ",".join(sorted(tags)))
- for ref in sorted(tags):
- # sorting will prefer e.g. "2.0" over "2.0rc1"
- if ref.startswith(tag_prefix):
- r = ref[len(tag_prefix):]
- if verbose:
- print("picking %s" % r)
- return { "version": r,
- "full": keywords["full"].strip() }
- # no suitable tags, so we use the full revision id
- if verbose:
- print("no suitable tags, using full revision id")
- return { "version": keywords["full"].strip(),
- "full": keywords["full"].strip() }
-
-
-def git_versions_from_vcs(tag_prefix, root, verbose=False):
- # this runs 'git' from the root of the source tree. This only gets called
- # if the git-archive 'subst' keywords were *not* expanded, and
- # _version.py hasn't already been rewritten with a short version string,
- # meaning we're inside a checked out source tree.
-
- if not os.path.exists(os.path.join(root, ".git")):
- if verbose:
- print("no .git in %s" % root)
- return {}
-
- GITS = ["git"]
- if sys.platform == "win32":
- GITS = ["git.cmd", "git.exe"]
- stdout = run_command(GITS, ["describe", "--tags", "--dirty", "--always"],
- cwd=root)
- if stdout is None:
- return {}
- if not stdout.startswith(tag_prefix):
- if verbose:
- print("tag '%s' doesn't start with prefix '%s'" % (stdout, tag_prefix))
- return {}
- tag = stdout[len(tag_prefix):]
- stdout = run_command(GITS, ["rev-parse", "HEAD"], cwd=root)
- if stdout is None:
- return {}
- full = stdout.strip()
- if tag.endswith("-dirty"):
- full += "-dirty"
- return {"version": tag, "full": full}
-
-
-def do_vcs_install(manifest_in, versionfile_source, ipy):
- GITS = ["git"]
- if sys.platform == "win32":
- GITS = ["git.cmd", "git.exe"]
- files = [manifest_in, versionfile_source]
- if ipy:
- files.append(ipy)
- try:
- me = __file__
- if me.endswith(".pyc") or me.endswith(".pyo"):
- me = os.path.splitext(me)[0] + ".py"
- versioneer_file = os.path.relpath(me)
- except NameError:
- versioneer_file = "versioneer.py"
- files.append(versioneer_file)
- present = False
- try:
- f = open(".gitattributes", "r")
- for line in f.readlines():
- if line.strip().startswith(versionfile_source):
- if "export-subst" in line.strip().split()[1:]:
- present = True
- f.close()
- except EnvironmentError:
- pass
- if not present:
- f = open(".gitattributes", "a+")
- f.write("%s export-subst\n" % versionfile_source)
- f.close()
- files.append(".gitattributes")
- run_command(GITS, ["add", "--"] + files)
-
-def versions_from_parentdir(parentdir_prefix, root, verbose=False):
- # Source tarballs conventionally unpack into a directory that includes
- # both the project name and a version string.
- dirname = os.path.basename(root)
- if not dirname.startswith(parentdir_prefix):
- if verbose:
- print("guessing rootdir is '%s', but '%s' doesn't start with prefix '%s'" %
- (root, dirname, parentdir_prefix))
- return None
- return {"version": dirname[len(parentdir_prefix):], "full": ""}
-
-SHORT_VERSION_PY = """
-# This file was generated by 'versioneer.py' (0.12) from
-# revision-control system data, or from the parent directory name of an
-# unpacked source archive. Distribution tarballs contain a pre-generated copy
-# of this file.
-
-version_version = '%(version)s'
-version_full = '%(full)s'
-def get_versions(default={}, verbose=False):
- return {'version': version_version, 'full': version_full}
-
-"""
-
-DEFAULT = {"version": "unknown", "full": "unknown"}
-
-def versions_from_file(filename):
- versions = {}
- try:
- with open(filename) as f:
- for line in f.readlines():
- mo = re.match("version_version = '([^']+)'", line)
- if mo:
- versions["version"] = mo.group(1)
- mo = re.match("version_full = '([^']+)'", line)
- if mo:
- versions["full"] = mo.group(1)
- except EnvironmentError:
- return {}
-
- return versions
-
-def write_to_version_file(filename, versions):
- with open(filename, "w") as f:
- f.write(SHORT_VERSION_PY % versions)
-
- print("set %s to '%s'" % (filename, versions["version"]))
-
-
-def get_root():
- try:
- return os.path.dirname(os.path.abspath(__file__))
- except NameError:
- return os.path.dirname(os.path.abspath(sys.argv[0]))
-
-def vcs_function(vcs, suffix):
- return getattr(sys.modules[__name__], '%s_%s' % (vcs, suffix), None)
-
-def get_versions(default=DEFAULT, verbose=False):
- # returns dict with two keys: 'version' and 'full'
- assert versionfile_source is not None, "please set versioneer.versionfile_source"
- assert tag_prefix is not None, "please set versioneer.tag_prefix"
- assert parentdir_prefix is not None, "please set versioneer.parentdir_prefix"
- assert VCS is not None, "please set versioneer.VCS"
-
- # I am in versioneer.py, which must live at the top of the source tree,
- # which we use to compute the root directory. py2exe/bbfreeze/non-CPython
- # don't have __file__, in which case we fall back to sys.argv[0] (which
- # ought to be the setup.py script). We prefer __file__ since that's more
- # robust in cases where setup.py was invoked in some weird way (e.g. pip)
- root = get_root()
- versionfile_abs = os.path.join(root, versionfile_source)
-
- # extract version from first of _version.py, VCS command (e.g. 'git
- # describe'), parentdir. This is meant to work for developers using a
- # source checkout, for users of a tarball created by 'setup.py sdist',
- # and for users of a tarball/zipball created by 'git archive' or github's
- # download-from-tag feature or the equivalent in other VCSes.
-
- get_keywords_f = vcs_function(VCS, "get_keywords")
- versions_from_keywords_f = vcs_function(VCS, "versions_from_keywords")
- if get_keywords_f and versions_from_keywords_f:
- vcs_keywords = get_keywords_f(versionfile_abs)
- ver = versions_from_keywords_f(vcs_keywords, tag_prefix)
- if ver:
- if verbose: print("got version from expanded keyword %s" % ver)
- return ver
-
- ver = versions_from_file(versionfile_abs)
- if ver:
- if verbose: print("got version from file %s %s" % (versionfile_abs,ver))
- return ver
-
- versions_from_vcs_f = vcs_function(VCS, "versions_from_vcs")
- if versions_from_vcs_f:
- ver = versions_from_vcs_f(tag_prefix, root, verbose)
- if ver:
- if verbose: print("got version from VCS %s" % ver)
- return ver
-
- ver = versions_from_parentdir(parentdir_prefix, root, verbose)
- if ver:
- if verbose: print("got version from parentdir %s" % ver)
- return ver
-
- if verbose: print("got version from default %s" % default)
- return default
-
-def get_version(verbose=False):
- return get_versions(verbose=verbose)["version"]
-
-class cmd_version(Command):
- description = "report generated version string"
- user_options = []
- boolean_options = []
- def initialize_options(self):
- pass
- def finalize_options(self):
- pass
- def run(self):
- ver = get_version(verbose=True)
- print("Version is currently: %s" % ver)
-
-
-class cmd_build(_build):
- def run(self):
- versions = get_versions(verbose=True)
- _build.run(self)
- # now locate _version.py in the new build/ directory and replace it
- # with an updated value
- if versionfile_build:
- target_versionfile = os.path.join(self.build_lib, versionfile_build)
- print("UPDATING %s" % target_versionfile)
- os.unlink(target_versionfile)
- with open(target_versionfile, "w") as f:
- f.write(SHORT_VERSION_PY % versions)
-
-if 'cx_Freeze' in sys.modules: # cx_freeze enabled?
- from cx_Freeze.dist import build_exe as _build_exe
-
- class cmd_build_exe(_build_exe):
- def run(self):
- versions = get_versions(verbose=True)
- target_versionfile = versionfile_source
- print("UPDATING %s" % target_versionfile)
- os.unlink(target_versionfile)
- with open(target_versionfile, "w") as f:
- f.write(SHORT_VERSION_PY % versions)
-
- _build_exe.run(self)
- os.unlink(target_versionfile)
- with open(versionfile_source, "w") as f:
- assert VCS is not None, "please set versioneer.VCS"
- LONG = LONG_VERSION_PY[VCS]
- f.write(LONG % {"DOLLAR": "$",
- "TAG_PREFIX": tag_prefix,
- "PARENTDIR_PREFIX": parentdir_prefix,
- "VERSIONFILE_SOURCE": versionfile_source,
- })
-
-class cmd_sdist(_sdist):
- def run(self):
- versions = get_versions(verbose=True)
- self._versioneer_generated_versions = versions
- # unless we update this, the command will keep using the old version
- self.distribution.metadata.version = versions["version"]
- return _sdist.run(self)
-
- def make_release_tree(self, base_dir, files):
- _sdist.make_release_tree(self, base_dir, files)
- # now locate _version.py in the new base_dir directory (remembering
- # that it may be a hardlink) and replace it with an updated value
- target_versionfile = os.path.join(base_dir, versionfile_source)
- print("UPDATING %s" % target_versionfile)
- os.unlink(target_versionfile)
- with open(target_versionfile, "w") as f:
- f.write(SHORT_VERSION_PY % self._versioneer_generated_versions)
-
-INIT_PY_SNIPPET = """
-from ._version import get_versions
-__version__ = get_versions()['version']
-del get_versions
-"""
-
-class cmd_update_files(Command):
- description = "install/upgrade Versioneer files: __init__.py SRC/_version.py"
- user_options = []
- boolean_options = []
- def initialize_options(self):
- pass
- def finalize_options(self):
- pass
- def run(self):
- print(" creating %s" % versionfile_source)
- with open(versionfile_source, "w") as f:
- assert VCS is not None, "please set versioneer.VCS"
- LONG = LONG_VERSION_PY[VCS]
- f.write(LONG % {"DOLLAR": "$",
- "TAG_PREFIX": tag_prefix,
- "PARENTDIR_PREFIX": parentdir_prefix,
- "VERSIONFILE_SOURCE": versionfile_source,
- })
-
- ipy = os.path.join(os.path.dirname(versionfile_source), "__init__.py")
- if os.path.exists(ipy):
- try:
- with open(ipy, "r") as f:
- old = f.read()
- except EnvironmentError:
- old = ""
- if INIT_PY_SNIPPET not in old:
- print(" appending to %s" % ipy)
- with open(ipy, "a") as f:
- f.write(INIT_PY_SNIPPET)
- else:
- print(" %s unmodified" % ipy)
- else:
- print(" %s doesn't exist, ok" % ipy)
- ipy = None
-
- # Make sure both the top-level "versioneer.py" and versionfile_source
- # (PKG/_version.py, used by runtime code) are in MANIFEST.in, so
- # they'll be copied into source distributions. Pip won't be able to
- # install the package without this.
- manifest_in = os.path.join(get_root(), "MANIFEST.in")
- simple_includes = set()
- try:
- with open(manifest_in, "r") as f:
- for line in f:
- if line.startswith("include "):
- for include in line.split()[1:]:
- simple_includes.add(include)
- except EnvironmentError:
- pass
- # That doesn't cover everything MANIFEST.in can do
- # (http://docs.python.org/2/distutils/sourcedist.html#commands), so
- # it might give some false negatives. Appending redundant 'include'
- # lines is safe, though.
- if "versioneer.py" not in simple_includes:
- print(" appending 'versioneer.py' to MANIFEST.in")
- with open(manifest_in, "a") as f:
- f.write("include versioneer.py\n")
- else:
- print(" 'versioneer.py' already in MANIFEST.in")
- if versionfile_source not in simple_includes:
- print(" appending versionfile_source ('%s') to MANIFEST.in" %
- versionfile_source)
- with open(manifest_in, "a") as f:
- f.write("include %s\n" % versionfile_source)
- else:
- print(" versionfile_source already in MANIFEST.in")
-
- # Make VCS-specific changes. For git, this means creating/changing
- # .gitattributes to mark _version.py for export-time keyword
- # substitution.
- do_vcs_install(manifest_in, versionfile_source, ipy)
-
-def get_cmdclass():
- cmds = {'version': cmd_version,
- 'versioneer': cmd_update_files,
- 'build': cmd_build,
- 'sdist': cmd_sdist,
- }
- if 'cx_Freeze' in sys.modules: # cx_freeze enabled?
- cmds['build_exe'] = cmd_build_exe
- del cmds['build']
-
- return cmds
+ +# Version: 0.12 + +""" +The Versioneer +============== + +* like a rocketeer, but for versions! +* https://github.com/warner/python-versioneer +* Brian Warner +* License: Public Domain +* Compatible With: python2.6, 2.7, 3.2, 3.3, 3.4, and pypy + +[](https://travis-ci.org/warner/python-versioneer) + +This is a tool for managing a recorded version number in distutils-based +python projects. The goal is to remove the tedious and error-prone "update +the embedded version string" step from your release process. Making a new +release should be as easy as recording a new tag in your version-control +system, and maybe making new tarballs. + + +## Quick Install + +* `pip install versioneer` to somewhere to your $PATH +* run `versioneer-installer` in your source tree: this installs `versioneer.py` +* follow the instructions below (also in the `versioneer.py` docstring) + +## Version Identifiers + +Source trees come from a variety of places: + +* a version-control system checkout (mostly used by developers) +* a nightly tarball, produced by build automation +* a snapshot tarball, produced by a web-based VCS browser, like github's + "tarball from tag" feature +* a release tarball, produced by "setup.py sdist", distributed through PyPI + +Within each source tree, the version identifier (either a string or a number, +this tool is format-agnostic) can come from a variety of places: + +* ask the VCS tool itself, e.g. "git describe" (for checkouts), which knows + about recent "tags" and an absolute revision-id +* the name of the directory into which the tarball was unpacked +* an expanded VCS keyword ($Id$, etc) +* a `_version.py` created by some earlier build step + +For released software, the version identifier is closely related to a VCS +tag. Some projects use tag names that include more than just the version +string (e.g. "myproject-1.2" instead of just "1.2"), in which case the tool +needs to strip the tag prefix to extract the version identifier. For +unreleased software (between tags), the version identifier should provide +enough information to help developers recreate the same tree, while also +giving them an idea of roughly how old the tree is (after version 1.2, before +version 1.3). Many VCS systems can report a description that captures this, +for example 'git describe --tags --dirty --always' reports things like +"0.7-1-g574ab98-dirty" to indicate that the checkout is one revision past the +0.7 tag, has a unique revision id of "574ab98", and is "dirty" (it has +uncommitted changes. + +The version identifier is used for multiple purposes: + +* to allow the module to self-identify its version: `myproject.__version__` +* to choose a name and prefix for a 'setup.py sdist' tarball + +## Theory of Operation + +Versioneer works by adding a special `_version.py` file into your source +tree, where your `__init__.py` can import it. This `_version.py` knows how to +dynamically ask the VCS tool for version information at import time. However, +when you use "setup.py build" or "setup.py sdist", `_version.py` in the new +copy is replaced by a small static file that contains just the generated +version data. + +`_version.py` also contains `$Revision$` markers, and the installation +process marks `_version.py` to have this marker rewritten with a tag name +during the "git archive" command. As a result, generated tarballs will +contain enough information to get the proper version. + + +## Installation + +First, decide on values for the following configuration variables: + +* `VCS`: the version control system you use. Currently accepts "git". + +* `versionfile_source`: + + A project-relative pathname into which the generated version strings should + be written. This is usually a `_version.py` next to your project's main + `__init__.py` file, so it can be imported at runtime. If your project uses + `src/myproject/__init__.py`, this should be `src/myproject/_version.py`. + This file should be checked in to your VCS as usual: the copy created below + by `setup.py versioneer` will include code that parses expanded VCS + keywords in generated tarballs. The 'build' and 'sdist' commands will + replace it with a copy that has just the calculated version string. + + This must be set even if your project does not have any modules (and will + therefore never import `_version.py`), since "setup.py sdist" -based trees + still need somewhere to record the pre-calculated version strings. Anywhere + in the source tree should do. If there is a `__init__.py` next to your + `_version.py`, the `setup.py versioneer` command (described below) will + append some `__version__`-setting assignments, if they aren't already + present. + +* `versionfile_build`: + + Like `versionfile_source`, but relative to the build directory instead of + the source directory. These will differ when your setup.py uses + 'package_dir='. If you have `package_dir={'myproject': 'src/myproject'}`, + then you will probably have `versionfile_build='myproject/_version.py'` and + `versionfile_source='src/myproject/_version.py'`. + + If this is set to None, then `setup.py build` will not attempt to rewrite + any `_version.py` in the built tree. If your project does not have any + libraries (e.g. if it only builds a script), then you should use + `versionfile_build = None` and override `distutils.command.build_scripts` + to explicitly insert a copy of `versioneer.get_version()` into your + generated script. + +* `tag_prefix`: + + a string, like 'PROJECTNAME-', which appears at the start of all VCS tags. + If your tags look like 'myproject-1.2.0', then you should use + tag_prefix='myproject-'. If you use unprefixed tags like '1.2.0', this + should be an empty string. + +* `parentdir_prefix`: + + a string, frequently the same as tag_prefix, which appears at the start of + all unpacked tarball filenames. If your tarball unpacks into + 'myproject-1.2.0', this should be 'myproject-'. + +This tool provides one script, named `versioneer-installer`. That script does +one thing: write a copy of `versioneer.py` into the current directory. + +To versioneer-enable your project: + +* 1: Run `versioneer-installer` to copy `versioneer.py` into the top of your + source tree. + +* 2: add the following lines to the top of your `setup.py`, with the + configuration values you decided earlier: + + import versioneer + versioneer.VCS = 'git' + versioneer.versionfile_source = 'src/myproject/_version.py' + versioneer.versionfile_build = 'myproject/_version.py' + versioneer.tag_prefix = '' # tags are like 1.2.0 + versioneer.parentdir_prefix = 'myproject-' # dirname like 'myproject-1.2.0' + +* 3: add the following arguments to the setup() call in your setup.py: + + version=versioneer.get_version(), + cmdclass=versioneer.get_cmdclass(), + +* 4: now run `setup.py versioneer`, which will create `_version.py`, and will + modify your `__init__.py` (if one exists next to `_version.py`) to define + `__version__` (by calling a function from `_version.py`). It will also + modify your `MANIFEST.in` to include both `versioneer.py` and the generated + `_version.py` in sdist tarballs. + +* 5: commit these changes to your VCS. To make sure you won't forget, + `setup.py versioneer` will mark everything it touched for addition. + +## Post-Installation Usage + +Once established, all uses of your tree from a VCS checkout should get the +current version string. All generated tarballs should include an embedded +version string (so users who unpack them will not need a VCS tool installed). + +If you distribute your project through PyPI, then the release process should +boil down to two steps: + +* 1: git tag 1.0 +* 2: python setup.py register sdist upload + +If you distribute it through github (i.e. users use github to generate +tarballs with `git archive`), the process is: + +* 1: git tag 1.0 +* 2: git push; git push --tags + +Currently, all version strings must be based upon a tag. Versioneer will +report "unknown" until your tree has at least one tag in its history. This +restriction will be fixed eventually (see issue #12). + +## Version-String Flavors + +Code which uses Versioneer can learn about its version string at runtime by +importing `_version` from your main `__init__.py` file and running the +`get_versions()` function. From the "outside" (e.g. in `setup.py`), you can +import the top-level `versioneer.py` and run `get_versions()`. + +Both functions return a dictionary with different keys for different flavors +of the version string: + +* `['version']`: condensed tag+distance+shortid+dirty identifier. For git, + this uses the output of `git describe --tags --dirty --always` but strips + the tag_prefix. For example "0.11-2-g1076c97-dirty" indicates that the tree + is like the "1076c97" commit but has uncommitted changes ("-dirty"), and + that this commit is two revisions ("-2-") beyond the "0.11" tag. For + released software (exactly equal to a known tag), the identifier will only + contain the stripped tag, e.g. "0.11". + +* `['full']`: detailed revision identifier. For Git, this is the full SHA1 + commit id, followed by "-dirty" if the tree contains uncommitted changes, + e.g. "1076c978a8d3cfc70f408fe5974aa6c092c949ac-dirty". + +Some variants are more useful than others. Including `full` in a bug report +should allow developers to reconstruct the exact code being tested (or +indicate the presence of local changes that should be shared with the +developers). `version` is suitable for display in an "about" box or a CLI +`--version` output: it can be easily compared against release notes and lists +of bugs fixed in various releases. + +In the future, this will also include a +[PEP-0440](http://legacy.python.org/dev/peps/pep-0440/) -compatible flavor +(e.g. `1.2.post0.dev123`). This loses a lot of information (and has no room +for a hash-based revision id), but is safe to use in a `setup.py` +"`version=`" argument. It also enables tools like *pip* to compare version +strings and evaluate compatibility constraint declarations. + +The `setup.py versioneer` command adds the following text to your +`__init__.py` to place a basic version in `YOURPROJECT.__version__`: + + from ._version import get_versions + __version__ = get_versions()['version'] + del get_versions + +## Updating Versioneer + +To upgrade your project to a new release of Versioneer, do the following: + +* install the new Versioneer (`pip install -U versioneer` or equivalent) +* re-run `versioneer-installer` in your source tree to replace your copy of + `versioneer.py` +* edit `setup.py`, if necessary, to include any new configuration settings + indicated by the release notes +* re-run `setup.py versioneer` to replace `SRC/_version.py` +* commit any changed files + +### Upgrading from 0.10 to 0.11 + +You must add a `versioneer.VCS = "git"` to your `setup.py` before re-running +`setup.py versioneer`. This will enable the use of additional version-control +systems (SVN, etc) in the future. + +### Upgrading from 0.11 to 0.12 + +Nothing special. + +## Future Directions + +This tool is designed to make it easily extended to other version-control +systems: all VCS-specific components are in separate directories like +src/git/ . The top-level `versioneer.py` script is assembled from these +components by running make-versioneer.py . In the future, make-versioneer.py +will take a VCS name as an argument, and will construct a version of +`versioneer.py` that is specific to the given VCS. It might also take the +configuration arguments that are currently provided manually during +installation by editing setup.py . Alternatively, it might go the other +direction and include code from all supported VCS systems, reducing the +number of intermediate scripts. + + +## License + +To make Versioneer easier to embed, all its code is hereby released into the +public domain. The `_version.py` that it creates is also in the public +domain. + +""" + +import os, sys, re, subprocess, errno +from distutils.core import Command +from distutils.command.sdist import sdist as _sdist +from distutils.command.build import build as _build + +# these configuration settings will be overridden by setup.py after it +# imports us +versionfile_source = None +versionfile_build = None +tag_prefix = None +parentdir_prefix = None +VCS = None + +# these dictionaries contain VCS-specific tools +LONG_VERSION_PY = {} + +def run_command(commands, args, cwd=None, verbose=False, hide_stderr=False): + assert isinstance(commands, list) + p = None + for c in commands: + try: + # remember shell=False, so use git.cmd on windows, not just git + p = subprocess.Popen([c] + args, cwd=cwd, stdout=subprocess.PIPE, + stderr=(subprocess.PIPE if hide_stderr + else None)) + break + except EnvironmentError: + e = sys.exc_info()[1] + if e.errno == errno.ENOENT: + continue + if verbose: + print("unable to run %s" % args[0]) + print(e) + return None + else: + if verbose: + print("unable to find command, tried %s" % (commands,)) + return None + stdout = p.communicate()[0].strip() + if sys.version >= '3': + stdout = stdout.decode() + if p.returncode != 0: + if verbose: + print("unable to run %s (error)" % args[0]) + return None + return stdout + +LONG_VERSION_PY['git'] = ''' +# This file helps to compute a version number in source trees obtained from +# git-archive tarball (such as those provided by githubs download-from-tag +# feature). Distribution tarballs (built by setup.py sdist) and build +# directories (produced by setup.py build) will contain a much shorter file +# that just contains the computed version number. + +# This file is released into the public domain. Generated by +# versioneer-0.12 (https://github.com/warner/python-versioneer) + +# these strings will be replaced by git during git-archive +git_refnames = "%(DOLLAR)sFormat:%%d%(DOLLAR)s" +git_full = "%(DOLLAR)sFormat:%%H%(DOLLAR)s" + +# these strings are filled in when 'setup.py versioneer' creates _version.py +tag_prefix = "%(TAG_PREFIX)s" +parentdir_prefix = "%(PARENTDIR_PREFIX)s" +versionfile_source = "%(VERSIONFILE_SOURCE)s" + +import os, sys, re, subprocess, errno + +def run_command(commands, args, cwd=None, verbose=False, hide_stderr=False): + assert isinstance(commands, list) + p = None + for c in commands: + try: + # remember shell=False, so use git.cmd on windows, not just git + p = subprocess.Popen([c] + args, cwd=cwd, stdout=subprocess.PIPE, + stderr=(subprocess.PIPE if hide_stderr + else None)) + break + except EnvironmentError: + e = sys.exc_info()[1] + if e.errno == errno.ENOENT: + continue + if verbose: + print("unable to run %%s" %% args[0]) + print(e) + return None + else: + if verbose: + print("unable to find command, tried %%s" %% (commands,)) + return None + stdout = p.communicate()[0].strip() + if sys.version >= '3': + stdout = stdout.decode() + if p.returncode != 0: + if verbose: + print("unable to run %%s (error)" %% args[0]) + return None + return stdout + + +def versions_from_parentdir(parentdir_prefix, root, verbose=False): + # Source tarballs conventionally unpack into a directory that includes + # both the project name and a version string. + dirname = os.path.basename(root) + if not dirname.startswith(parentdir_prefix): + if verbose: + print("guessing rootdir is '%%s', but '%%s' doesn't start with prefix '%%s'" %% + (root, dirname, parentdir_prefix)) + return None + return {"version": dirname[len(parentdir_prefix):], "full": ""} + +def git_get_keywords(versionfile_abs): + # the code embedded in _version.py can just fetch the value of these + # keywords. When used from setup.py, we don't want to import _version.py, + # so we do it with a regexp instead. This function is not used from + # _version.py. + keywords = {} + try: + f = open(versionfile_abs,"r") + for line in f.readlines(): + if line.strip().startswith("git_refnames ="): + mo = re.search(r'=\s*"(.*)"', line) + if mo: + keywords["refnames"] = mo.group(1) + if line.strip().startswith("git_full ="): + mo = re.search(r'=\s*"(.*)"', line) + if mo: + keywords["full"] = mo.group(1) + f.close() + except EnvironmentError: + pass + return keywords + +def git_versions_from_keywords(keywords, tag_prefix, verbose=False): + if not keywords: + return {} # keyword-finding function failed to find keywords + refnames = keywords["refnames"].strip() + if refnames.startswith("$Format"): + if verbose: + print("keywords are unexpanded, not using") + return {} # unexpanded, so not in an unpacked git-archive tarball + refs = set([r.strip() for r in refnames.strip("()").split(",")]) + # starting in git-1.8.3, tags are listed as "tag: foo-1.0" instead of + # just "foo-1.0". If we see a "tag: " prefix, prefer those. + TAG = "tag: " + tags = set([r[len(TAG):] for r in refs if r.startswith(TAG)]) + if not tags: + # Either we're using git < 1.8.3, or there really are no tags. We use + # a heuristic: assume all version tags have a digit. The old git %%d + # expansion behaves like git log --decorate=short and strips out the + # refs/heads/ and refs/tags/ prefixes that would let us distinguish + # between branches and tags. By ignoring refnames without digits, we + # filter out many common branch names like "release" and + # "stabilization", as well as "HEAD" and "master". + tags = set([r for r in refs if re.search(r'\d', r)]) + if verbose: + print("discarding '%%s', no digits" %% ",".join(refs-tags)) + if verbose: + print("likely tags: %%s" %% ",".join(sorted(tags))) + for ref in sorted(tags): + # sorting will prefer e.g. "2.0" over "2.0rc1" + if ref.startswith(tag_prefix): + r = ref[len(tag_prefix):] + if verbose: + print("picking %%s" %% r) + return { "version": r, + "full": keywords["full"].strip() } + # no suitable tags, so we use the full revision id + if verbose: + print("no suitable tags, using full revision id") + return { "version": keywords["full"].strip(), + "full": keywords["full"].strip() } + + +def git_versions_from_vcs(tag_prefix, root, verbose=False): + # this runs 'git' from the root of the source tree. This only gets called + # if the git-archive 'subst' keywords were *not* expanded, and + # _version.py hasn't already been rewritten with a short version string, + # meaning we're inside a checked out source tree. + + if not os.path.exists(os.path.join(root, ".git")): + if verbose: + print("no .git in %%s" %% root) + return {} + + GITS = ["git"] + if sys.platform == "win32": + GITS = ["git.cmd", "git.exe"] + stdout = run_command(GITS, ["describe", "--tags", "--dirty", "--always"], + cwd=root) + if stdout is None: + return {} + if not stdout.startswith(tag_prefix): + if verbose: + print("tag '%%s' doesn't start with prefix '%%s'" %% (stdout, tag_prefix)) + return {} + tag = stdout[len(tag_prefix):] + stdout = run_command(GITS, ["rev-parse", "HEAD"], cwd=root) + if stdout is None: + return {} + full = stdout.strip() + if tag.endswith("-dirty"): + full += "-dirty" + return {"version": tag, "full": full} + + +def get_versions(default={"version": "unknown", "full": ""}, verbose=False): + # I am in _version.py, which lives at ROOT/VERSIONFILE_SOURCE. If we have + # __file__, we can work backwards from there to the root. Some + # py2exe/bbfreeze/non-CPython implementations don't do __file__, in which + # case we can only use expanded keywords. + + keywords = { "refnames": git_refnames, "full": git_full } + ver = git_versions_from_keywords(keywords, tag_prefix, verbose) + if ver: + return ver + + try: + root = os.path.abspath(__file__) + # versionfile_source is the relative path from the top of the source + # tree (where the .git directory might live) to this file. Invert + # this to find the root from __file__. + for i in range(len(versionfile_source.split(os.sep))): + root = os.path.dirname(root) + except NameError: + return default + + return (git_versions_from_vcs(tag_prefix, root, verbose) + or versions_from_parentdir(parentdir_prefix, root, verbose) + or default) +''' + +def git_get_keywords(versionfile_abs): + # the code embedded in _version.py can just fetch the value of these + # keywords. When used from setup.py, we don't want to import _version.py, + # so we do it with a regexp instead. This function is not used from + # _version.py. + keywords = {} + try: + f = open(versionfile_abs,"r") + for line in f.readlines(): + if line.strip().startswith("git_refnames ="): + mo = re.search(r'=\s*"(.*)"', line) + if mo: + keywords["refnames"] = mo.group(1) + if line.strip().startswith("git_full ="): + mo = re.search(r'=\s*"(.*)"', line) + if mo: + keywords["full"] = mo.group(1) + f.close() + except EnvironmentError: + pass + return keywords + +def git_versions_from_keywords(keywords, tag_prefix, verbose=False): + if not keywords: + return {} # keyword-finding function failed to find keywords + refnames = keywords["refnames"].strip() + if refnames.startswith("$Format"): + if verbose: + print("keywords are unexpanded, not using") + return {} # unexpanded, so not in an unpacked git-archive tarball + refs = set([r.strip() for r in refnames.strip("()").split(",")]) + # starting in git-1.8.3, tags are listed as "tag: foo-1.0" instead of + # just "foo-1.0". If we see a "tag: " prefix, prefer those. + TAG = "tag: " + tags = set([r[len(TAG):] for r in refs if r.startswith(TAG)]) + if not tags: + # Either we're using git < 1.8.3, or there really are no tags. We use + # a heuristic: assume all version tags have a digit. The old git %d + # expansion behaves like git log --decorate=short and strips out the + # refs/heads/ and refs/tags/ prefixes that would let us distinguish + # between branches and tags. By ignoring refnames without digits, we + # filter out many common branch names like "release" and + # "stabilization", as well as "HEAD" and "master". + tags = set([r for r in refs if re.search(r'\d', r)]) + if verbose: + print("discarding '%s', no digits" % ",".join(refs-tags)) + if verbose: + print("likely tags: %s" % ",".join(sorted(tags))) + for ref in sorted(tags): + # sorting will prefer e.g. "2.0" over "2.0rc1" + if ref.startswith(tag_prefix): + r = ref[len(tag_prefix):] + if verbose: + print("picking %s" % r) + return { "version": r, + "full": keywords["full"].strip() } + # no suitable tags, so we use the full revision id + if verbose: + print("no suitable tags, using full revision id") + return { "version": keywords["full"].strip(), + "full": keywords["full"].strip() } + + +def git_versions_from_vcs(tag_prefix, root, verbose=False): + # this runs 'git' from the root of the source tree. This only gets called + # if the git-archive 'subst' keywords were *not* expanded, and + # _version.py hasn't already been rewritten with a short version string, + # meaning we're inside a checked out source tree. + + if not os.path.exists(os.path.join(root, ".git")): + if verbose: + print("no .git in %s" % root) + return {} + + GITS = ["git"] + if sys.platform == "win32": + GITS = ["git.cmd", "git.exe"] + stdout = run_command(GITS, ["describe", "--tags", "--dirty", "--always"], + cwd=root) + if stdout is None: + return {} + if not stdout.startswith(tag_prefix): + if verbose: + print("tag '%s' doesn't start with prefix '%s'" % (stdout, tag_prefix)) + return {} + tag = stdout[len(tag_prefix):] + stdout = run_command(GITS, ["rev-parse", "HEAD"], cwd=root) + if stdout is None: + return {} + full = stdout.strip() + if tag.endswith("-dirty"): + full += "-dirty" + return {"version": tag, "full": full} + + +def do_vcs_install(manifest_in, versionfile_source, ipy): + GITS = ["git"] + if sys.platform == "win32": + GITS = ["git.cmd", "git.exe"] + files = [manifest_in, versionfile_source] + if ipy: + files.append(ipy) + try: + me = __file__ + if me.endswith(".pyc") or me.endswith(".pyo"): + me = os.path.splitext(me)[0] + ".py" + versioneer_file = os.path.relpath(me) + except NameError: + versioneer_file = "versioneer.py" + files.append(versioneer_file) + present = False + try: + f = open(".gitattributes", "r") + for line in f.readlines(): + if line.strip().startswith(versionfile_source): + if "export-subst" in line.strip().split()[1:]: + present = True + f.close() + except EnvironmentError: + pass + if not present: + f = open(".gitattributes", "a+") + f.write("%s export-subst\n" % versionfile_source) + f.close() + files.append(".gitattributes") + run_command(GITS, ["add", "--"] + files) + +def versions_from_parentdir(parentdir_prefix, root, verbose=False): + # Source tarballs conventionally unpack into a directory that includes + # both the project name and a version string. + dirname = os.path.basename(root) + if not dirname.startswith(parentdir_prefix): + if verbose: + print("guessing rootdir is '%s', but '%s' doesn't start with prefix '%s'" % + (root, dirname, parentdir_prefix)) + return None + return {"version": dirname[len(parentdir_prefix):], "full": ""} + +SHORT_VERSION_PY = """ +# This file was generated by 'versioneer.py' (0.12) from +# revision-control system data, or from the parent directory name of an +# unpacked source archive. Distribution tarballs contain a pre-generated copy +# of this file. + +version_version = '%(version)s' +version_full = '%(full)s' +def get_versions(default={}, verbose=False): + return {'version': version_version, 'full': version_full} + +""" + +DEFAULT = {"version": "unknown", "full": "unknown"} + +def versions_from_file(filename): + versions = {} + try: + with open(filename) as f: + for line in f.readlines(): + mo = re.match("version_version = '([^']+)'", line) + if mo: + versions["version"] = mo.group(1) + mo = re.match("version_full = '([^']+)'", line) + if mo: + versions["full"] = mo.group(1) + except EnvironmentError: + return {} + + return versions + +def write_to_version_file(filename, versions): + with open(filename, "w") as f: + f.write(SHORT_VERSION_PY % versions) + + print("set %s to '%s'" % (filename, versions["version"])) + + +def get_root(): + try: + return os.path.dirname(os.path.abspath(__file__)) + except NameError: + return os.path.dirname(os.path.abspath(sys.argv[0])) + +def vcs_function(vcs, suffix): + return getattr(sys.modules[__name__], '%s_%s' % (vcs, suffix), None) + +def get_versions(default=DEFAULT, verbose=False): + # returns dict with two keys: 'version' and 'full' + assert versionfile_source is not None, "please set versioneer.versionfile_source" + assert tag_prefix is not None, "please set versioneer.tag_prefix" + assert parentdir_prefix is not None, "please set versioneer.parentdir_prefix" + assert VCS is not None, "please set versioneer.VCS" + + # I am in versioneer.py, which must live at the top of the source tree, + # which we use to compute the root directory. py2exe/bbfreeze/non-CPython + # don't have __file__, in which case we fall back to sys.argv[0] (which + # ought to be the setup.py script). We prefer __file__ since that's more + # robust in cases where setup.py was invoked in some weird way (e.g. pip) + root = get_root() + versionfile_abs = os.path.join(root, versionfile_source) + + # extract version from first of _version.py, VCS command (e.g. 'git + # describe'), parentdir. This is meant to work for developers using a + # source checkout, for users of a tarball created by 'setup.py sdist', + # and for users of a tarball/zipball created by 'git archive' or github's + # download-from-tag feature or the equivalent in other VCSes. + + get_keywords_f = vcs_function(VCS, "get_keywords") + versions_from_keywords_f = vcs_function(VCS, "versions_from_keywords") + if get_keywords_f and versions_from_keywords_f: + vcs_keywords = get_keywords_f(versionfile_abs) + ver = versions_from_keywords_f(vcs_keywords, tag_prefix) + if ver: + if verbose: print("got version from expanded keyword %s" % ver) + return ver + + ver = versions_from_file(versionfile_abs) + if ver: + if verbose: print("got version from file %s %s" % (versionfile_abs,ver)) + return ver + + versions_from_vcs_f = vcs_function(VCS, "versions_from_vcs") + if versions_from_vcs_f: + ver = versions_from_vcs_f(tag_prefix, root, verbose) + if ver: + if verbose: print("got version from VCS %s" % ver) + return ver + + ver = versions_from_parentdir(parentdir_prefix, root, verbose) + if ver: + if verbose: print("got version from parentdir %s" % ver) + return ver + + if verbose: print("got version from default %s" % default) + return default + +def get_version(verbose=False): + return get_versions(verbose=verbose)["version"] + +class cmd_version(Command): + description = "report generated version string" + user_options = [] + boolean_options = [] + def initialize_options(self): + pass + def finalize_options(self): + pass + def run(self): + ver = get_version(verbose=True) + print("Version is currently: %s" % ver) + + +class cmd_build(_build): + def run(self): + versions = get_versions(verbose=True) + _build.run(self) + # now locate _version.py in the new build/ directory and replace it + # with an updated value + if versionfile_build: + target_versionfile = os.path.join(self.build_lib, versionfile_build) + print("UPDATING %s" % target_versionfile) + os.unlink(target_versionfile) + with open(target_versionfile, "w") as f: + f.write(SHORT_VERSION_PY % versions) + +if 'cx_Freeze' in sys.modules: # cx_freeze enabled? + from cx_Freeze.dist import build_exe as _build_exe + + class cmd_build_exe(_build_exe): + def run(self): + versions = get_versions(verbose=True) + target_versionfile = versionfile_source + print("UPDATING %s" % target_versionfile) + os.unlink(target_versionfile) + with open(target_versionfile, "w") as f: + f.write(SHORT_VERSION_PY % versions) + + _build_exe.run(self) + os.unlink(target_versionfile) + with open(versionfile_source, "w") as f: + assert VCS is not None, "please set versioneer.VCS" + LONG = LONG_VERSION_PY[VCS] + f.write(LONG % {"DOLLAR": "$", + "TAG_PREFIX": tag_prefix, + "PARENTDIR_PREFIX": parentdir_prefix, + "VERSIONFILE_SOURCE": versionfile_source, + }) + +class cmd_sdist(_sdist): + def run(self): + versions = get_versions(verbose=True) + self._versioneer_generated_versions = versions + # unless we update this, the command will keep using the old version + self.distribution.metadata.version = versions["version"] + return _sdist.run(self) + + def make_release_tree(self, base_dir, files): + _sdist.make_release_tree(self, base_dir, files) + # now locate _version.py in the new base_dir directory (remembering + # that it may be a hardlink) and replace it with an updated value + target_versionfile = os.path.join(base_dir, versionfile_source) + print("UPDATING %s" % target_versionfile) + os.unlink(target_versionfile) + with open(target_versionfile, "w") as f: + f.write(SHORT_VERSION_PY % self._versioneer_generated_versions) + +INIT_PY_SNIPPET = """ +from ._version import get_versions +__version__ = get_versions()['version'] +del get_versions +""" + +class cmd_update_files(Command): + description = "install/upgrade Versioneer files: __init__.py SRC/_version.py" + user_options = [] + boolean_options = [] + def initialize_options(self): + pass + def finalize_options(self): + pass + def run(self): + print(" creating %s" % versionfile_source) + with open(versionfile_source, "w") as f: + assert VCS is not None, "please set versioneer.VCS" + LONG = LONG_VERSION_PY[VCS] + f.write(LONG % {"DOLLAR": "$", + "TAG_PREFIX": tag_prefix, + "PARENTDIR_PREFIX": parentdir_prefix, + "VERSIONFILE_SOURCE": versionfile_source, + }) + + ipy = os.path.join(os.path.dirname(versionfile_source), "__init__.py") + if os.path.exists(ipy): + try: + with open(ipy, "r") as f: + old = f.read() + except EnvironmentError: + old = "" + if INIT_PY_SNIPPET not in old: + print(" appending to %s" % ipy) + with open(ipy, "a") as f: + f.write(INIT_PY_SNIPPET) + else: + print(" %s unmodified" % ipy) + else: + print(" %s doesn't exist, ok" % ipy) + ipy = None + + # Make sure both the top-level "versioneer.py" and versionfile_source + # (PKG/_version.py, used by runtime code) are in MANIFEST.in, so + # they'll be copied into source distributions. Pip won't be able to + # install the package without this. + manifest_in = os.path.join(get_root(), "MANIFEST.in") + simple_includes = set() + try: + with open(manifest_in, "r") as f: + for line in f: + if line.startswith("include "): + for include in line.split()[1:]: + simple_includes.add(include) + except EnvironmentError: + pass + # That doesn't cover everything MANIFEST.in can do + # (http://docs.python.org/2/distutils/sourcedist.html#commands), so + # it might give some false negatives. Appending redundant 'include' + # lines is safe, though. + if "versioneer.py" not in simple_includes: + print(" appending 'versioneer.py' to MANIFEST.in") + with open(manifest_in, "a") as f: + f.write("include versioneer.py\n") + else: + print(" 'versioneer.py' already in MANIFEST.in") + if versionfile_source not in simple_includes: + print(" appending versionfile_source ('%s') to MANIFEST.in" % + versionfile_source) + with open(manifest_in, "a") as f: + f.write("include %s\n" % versionfile_source) + else: + print(" versionfile_source already in MANIFEST.in") + + # Make VCS-specific changes. For git, this means creating/changing + # .gitattributes to mark _version.py for export-time keyword + # substitution. + do_vcs_install(manifest_in, versionfile_source, ipy) + +def get_cmdclass(): + cmds = {'version': cmd_version, + 'versioneer': cmd_update_files, + 'build': cmd_build, + 'sdist': cmd_sdist, + } + if 'cx_Freeze' in sys.modules: # cx_freeze enabled? + cmds['build_exe'] = cmd_build_exe + del cmds['build'] + + return cmds |
