New upstream version 0.9.11+dfsg

1 files changed, 173 insertions, 165 deletions

diff --git a/doc/builtin_models.rst b/doc/builtin_models.rst
index 06c79bb..ea15939 100644
--- a/doc/builtin_models.rst
+++ b/doc/builtin_models.rst
@@ -6,27 +6,27 @@ Built-in Fitting Models in the :mod:`models` module
 
 .. module:: lmfit.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
+Lmfit provides several built-in fitting models in the :mod:`models` module.
+These pre-defined models each subclass from the :class:`~lmfit.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
+scientific domains.  In fact, all the models are based on simple, plain
+Python functions defined in the :mod:`~lmfit.lineshapes` module.  In addition to
+wrapping a function into a :class:`~lmfit.model.Model`, these models also provide a
+:meth:`~lmfit.model.Model.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
+As shown in the previous chapter, a key feature of the :class:`~lmfit.model.Model` class
 is that models can easily be combined to give a composite
-:class:`model.CompositeModel`. Thus, while some of the models listed here may
+:class:`~lmfit.model.CompositeModel`. 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 use them 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()
+    >>> background = LinearModel()
     >>> model = peak + background
 
 All the models listed below are one dimensional, with an independent
@@ -41,7 +41,7 @@ width.  Many peak shapes also have a parameter ``fwhm`` (constrained by
 (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.
+After a list of built-in models, a few examples of their use are given.
 
 Peak-like models
 -------------------
@@ -138,7 +138,7 @@ 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.
+of many components of a composite model.
 
 :class:`ConstantModel`
 ~~~~~~~~~~~~~~~~~~~~~~~~~~
@@ -194,7 +194,7 @@ Exponential and Power law models
 User-defined Models
 ----------------------------
 
-.. _asteval: http://newville.github.io/asteval/
+.. _asteval: https://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.
@@ -221,10 +221,10 @@ 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
+Python built-ins, 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
+converted to parameters.  Unrecognized names are expected to be names of either
+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.
@@ -262,7 +262,7 @@ could to define this in a 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)
+        return log(loren) * gradient(gauss) / gradient(x)
     """
 
 and then use this with :class:`ExpressionModel` as::
@@ -276,7 +276,7 @@ and `wid`, and build a model that can be used to fit data.
 
 
 
-Example 1: Fit Peaked data to Gaussian, Lorentzian, and  Voigt profiles
+Example 1: Fit Peak data to Gaussian, Lorentzian, and  Voigt profiles
 ------------------------------------------------------------------------
 
 Here, we will fit data to three similar line shapes, in order to decide which
@@ -287,6 +287,7 @@ one in previous example in that the parameter names are different, and have
 built-in default values.  We will simply use::
 
      from numpy import loadtxt
+
      from lmfit.models import GaussianModel
 
      data = loadtxt('test_peak.dat')
@@ -296,7 +297,7 @@ built-in default values.  We will simply use::
      mod = GaussianModel()
 
      pars = mod.guess(y, x=x)
-     out  = mod.fit(y, pars, x=x)
+     out = mod.fit(y, pars, x=x)
      print(out.fit_report(min_correl=0.25))
 
 
@@ -305,21 +306,22 @@ which prints out the results::
     [[Model]]
         Model(gaussian)
     [[Fit Statistics]]
-        # function evals   = 23
+        # fitting method   = leastsq
+        # function evals   = 27
         # data points      = 401
         # variables        = 3
-        chi-square         = 29.994
-        reduced chi-square = 0.075
-        Akaike info crit   = -1033.774
-        Bayesian info crit = -1021.792
+        chi-square         = 29.9943157
+        reduced chi-square = 0.07536260
+        Akaike info crit   = -1033.77437
+        Bayesian info crit = -1021.79248
     [[Variables]]
-        sigma:       1.23218319 +/- 0.007374 (0.60%) (init= 1.35)
-        center:      9.24277049 +/- 0.007374 (0.08%) (init= 9.25)
-        amplitude:   30.3135571 +/- 0.157126 (0.52%) (init= 29.08159)
-        fwhm:        2.90156963 +/- 0.017366 (0.60%)  == '2.3548200*sigma'
-        height:      9.81457973 +/- 0.050872 (0.52%)  == '0.3989423*amplitude/max(1.e-15, sigma)'
-    [[Correlations]] (unreported correlations are <  0.250)
-        C(sigma, amplitude)          =  0.577
+        sigma:      1.23218359 +/- 0.00737496 (0.60%) (init = 1.35)
+        amplitude:  30.3135620 +/- 0.15712686 (0.52%) (init = 43.62238)
+        center:     9.24277047 +/- 0.00737496 (0.08%) (init = 9.25)
+        fwhm:       2.90157056 +/- 0.01736670 (0.60%) == '2.3548200*sigma'
+        height:     9.81457817 +/- 0.05087283 (0.52%) == '0.3989423*amplitude/max(1.e-15, sigma)'
+    [[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``
@@ -339,7 +341,7 @@ good. A plot of the fit:
   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,
+of initial parameter values.  Looking more closely, 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
@@ -354,22 +356,22 @@ we try gives results that are worse::
     [[Model]]
         Model(lorentzian)
     [[Fit Statistics]]
-        # function evals   = 27
+        # fitting method   = leastsq
+        # function evals   = 23
         # data points      = 401
         # variables        = 3
-        chi-square         = 53.754
-        reduced chi-square = 0.135
-        Akaike info crit   = -799.830
-        Bayesian info crit = -787.848
+        chi-square         = 53.7535387
+        reduced chi-square = 0.13505914
+        Akaike info crit   = -799.830322
+        Bayesian info crit = -787.848438
     [[Variables]]
-        sigma:       1.15484517 +/- 0.013156 (1.14%) (init= 1.35)
-        center:      9.24438944 +/- 0.009275 (0.10%) (init= 9.25)
-        amplitude:   38.9728645 +/- 0.313857 (0.81%) (init= 36.35199)
-        fwhm:        2.30969034 +/- 0.026312 (1.14%)  == '2.0000000*sigma'
-        height:      10.7420881 +/- 0.086336 (0.80%)  == '0.3183099*amplitude/max(1.e-15, sigma)'
-    [[Correlations]] (unreported correlations are <  0.250)
-        C(sigma, amplitude)          =  0.709
-
+        sigma:      1.15483925 +/- 0.01315659 (1.14%) (init = 1.35)
+        center:     9.24438944 +/- 0.00927619 (0.10%) (init = 9.25)
+        amplitude:  38.9727645 +/- 0.31386183 (0.81%) (init = 54.52798)
+        fwhm:       2.30967850 +/- 0.02631318 (1.14%) == '2.0000000*sigma'
+        height:     10.7421156 +/- 0.08633945 (0.80%) == '0.3183099*amplitude/max(1.e-15, sigma)'
+    [[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
@@ -383,26 +385,27 @@ with all the rest of the script as above.  This gives::
     [[Model]]
         Model(voigt)
     [[Fit Statistics]]
-        # function evals   = 19
+        # fitting method   = leastsq
+        # function evals   = 23
         # data points      = 401
         # variables        = 3
-        chi-square         = 14.545
-        reduced chi-square = 0.037
-        Akaike info crit   = -1324.006
-        Bayesian info crit = -1312.024
+        chi-square         = 14.5448627
+        reduced chi-square = 0.03654488
+        Akaike info crit   = -1324.00615
+        Bayesian info crit = -1312.02427
     [[Variables]]
-        amplitude:   35.7554017 +/- 0.138614 (0.39%) (init= 43.62238)
-        sigma:       0.73015574 +/- 0.003684 (0.50%) (init= 0.8775)
-        center:      9.24411142 +/- 0.005054 (0.05%) (init= 9.25)
-        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/max(1.e-15, sigma)'
-    [[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).
+        center:     9.24411150 +/- 0.00505482 (0.05%) (init = 9.25)
+        sigma:      0.73015627 +/- 0.00368460 (0.50%) (init = 0.8775)
+        amplitude:  35.7554146 +/- 0.13861321 (0.39%) (init = 65.43358)
+        gamma:      0.73015627 +/- 0.00368460 (0.50%) == 'sigma'
+        fwhm:       2.62951907 +/- 0.01326940 (0.50%) == '3.6013100*sigma'
+        height:     10.2203969 +/- 0.03009415 (0.29%) == 'amplitude*wofz((1j*gamma)/(sigma*sqrt(2))).real/(sigma*sqrt(2*pi))'
+    [[Correlations]] (unreported correlations are < 0.250)
+        C(sigma, amplitude) =  0.651
+
+which has a much better value for :math:`\chi^2` and the other
+goodness-of-fit measures, and an obviously better match to the data as seen
+in the figure below (left).
 
 .. _figA2:
 
@@ -433,24 +436,25 @@ which gives::
     [[Model]]
         Model(voigt)
     [[Fit Statistics]]
+        # fitting method   = leastsq
         # function evals   = 23
         # data points      = 401
         # variables        = 4
-        chi-square         = 10.930
-        reduced chi-square = 0.028
-        Akaike info crit   = -1436.576
-        Bayesian info crit = -1420.600
+        chi-square         = 10.9301767
+        reduced chi-square = 0.02753193
+        Akaike info crit   = -1436.57602
+        Bayesian info crit = -1420.60017
     [[Variables]]
-        amplitude:   34.1914716 +/- 0.179468 (0.52%) (init= 43.62238)
-        sigma:       0.89518950 +/- 0.014154 (1.58%) (init= 0.8775)
-        center:      9.24374845 +/- 0.004419 (0.05%) (init= 9.25)
-        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/max(1.e-15, sigma)'
-    [[Correlations]] (unreported correlations are <  0.250)
-        C(sigma, gamma)              = -0.928
-        C(gamma, amplitude)          =  0.821
-        C(sigma, amplitude)          = -0.651
+        sigma:      0.89518909 +/- 0.01415450 (1.58%) (init = 0.8775)
+        amplitude:  34.1914737 +/- 0.17946860 (0.52%) (init = 65.43358)
+        center:     9.24374847 +/- 0.00441903 (0.05%) (init = 9.25)
+        gamma:      0.52540199 +/- 0.01857955 (3.54%) (init = 0.7)
+        fwhm:       3.22385342 +/- 0.05097475 (1.58%) == '3.6013100*sigma'
+        height:     10.0872204 +/- 0.03482129 (0.35%) == 'amplitude*wofz((1j*gamma)/(sigma*sqrt(2))).real/(sigma*sqrt(2*pi))'
+    [[Correlations]] (unreported correlations are < 0.250)
+        C(sigma, gamma)     = -0.928
+        C(amplitude, gamma) =  0.821
+        C(sigma, amplitude) = -0.651
 
 and the fit shown on the right above.
 
@@ -467,10 +471,10 @@ 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 probability that a model with
 AIC1 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
+AIC values of -1436 and -1324 (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 probability less than 1.e-25
+the model with ``gamma`` fixed to ``sigma`` has a probability less than 5.e-25
 of being the better model.
 
 
@@ -478,13 +482,13 @@ 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
+instances of :class:`~lmfit.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
+.. literalinclude:: ../examples/doc_builtinmodels_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
@@ -497,29 +501,30 @@ results, which gives::
     [[Model]]
         (Model(step, prefix='step_', form='erf') + Model(linear, prefix='line_'))
     [[Fit Statistics]]
-        # function evals   = 51
+        # fitting method   = leastsq
+        # function evals   = 49
         # data points      = 201
         # variables        = 5
-        chi-square         = 584.829
-        reduced chi-square = 2.984
-        Akaike info crit   = 224.671
-        Bayesian info crit = 241.187
+        chi-square         = 593.709622
+        reduced chi-square = 3.02913072
+        Akaike info crit   = 227.700173
+        Bayesian info crit = 244.216698
     [[Variables]]
-        line_slope:       2.03039786 +/- 0.092221 (4.54%) (init= 0)
-        line_intercept:   11.7234542 +/- 0.274094 (2.34%) (init= 10.7816)
-        step_amplitude:   112.071629 +/- 0.647316 (0.58%) (init= 134.0885)
-        step_sigma:       0.67132341 +/- 0.010873 (1.62%) (init= 1.428571)
-        step_center:      3.12697699 +/- 0.005151 (0.16%) (init= 2.5)
-    [[Correlations]] (unreported correlations are <  0.100)
-        C(line_slope, step_amplitude)  = -0.878
-        C(step_amplitude, step_sigma)  =  0.563
-        C(line_slope, step_sigma)    = -0.455
-        C(line_intercept, step_center)  =  0.427
-        C(line_slope, line_intercept)  = -0.308
-        C(line_slope, step_center)   = -0.234
-        C(line_intercept, step_sigma)  = -0.139
-        C(line_intercept, step_amplitude)  = -0.121
-        C(step_amplitude, step_center)  =  0.109
+        line_intercept:  12.0964833 +/- 0.27606235 (2.28%) (init = 11.58574)
+        line_slope:      1.87164655 +/- 0.09318714 (4.98%) (init = 0)
+        step_sigma:      0.67392841 +/- 0.01091168 (1.62%) (init = 1.428571)
+        step_center:     3.13494792 +/- 0.00516615 (0.16%) (init = 2.5)
+        step_amplitude:  112.858376 +/- 0.65392949 (0.58%) (init = 134.7378)
+    [[Correlations]] (unreported correlations are < 0.100)
+        C(line_slope, step_amplitude)     = -0.879
+        C(step_sigma, step_amplitude)     =  0.564
+        C(line_slope, step_sigma)         = -0.457
+        C(line_intercept, step_center)    =  0.427
+        C(line_intercept, line_slope)     = -0.309
+        C(line_slope, step_center)        = -0.234
+        C(line_intercept, step_sigma)     = -0.137
+        C(line_intercept, step_amplitude) = -0.117
+        C(step_center, step_amplitude)    =  0.109
 
 with a plot of
 
@@ -531,17 +536,17 @@ with a plot of
 Example 3: Fitting Multiple Peaks -- and using Prefixes
 ------------------------------------------------------------------
 
-.. _NIST StRD: http://itl.nist.gov/div898/strd/nls/nls_main.shtml
+.. _NIST StRD: https://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
+:class:`~lmfit.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
+.. literalinclude:: ../examples/doc_builtinmodels_nistgauss.py
 
 where we give a separate prefix to each model (they all have an
 ``amplitude`` parameter).  The ``prefix`` values are attached transparently
@@ -559,37 +564,38 @@ The fit results printed out are::
     [[Model]]
         ((Model(gaussian, prefix='g1_') + Model(gaussian, prefix='g2_')) + Model(exponential, prefix='exp_'))
     [[Fit Statistics]]
-        # function evals   = 66
+        # fitting method   = leastsq
+        # function evals   = 48
         # data points      = 250
         # variables        = 8
-        chi-square         = 1247.528
-        reduced chi-square = 5.155
-        Akaike info crit   = 417.865
-        Bayesian info crit = 446.036
+        chi-square         = 1247.52821
+        reduced chi-square = 5.15507524
+        Akaike info crit   = 417.864631
+        Bayesian info crit = 446.036318
     [[Variables]]
-        exp_amplitude:   99.0183282 +/- 0.537487 (0.54%) (init= 162.2102)
-        exp_decay:       90.9508859 +/- 1.103105 (1.21%) (init= 93.24905)
-        g1_sigma:        16.6725753 +/- 0.160481 (0.96%) (init= 15)
-        g1_center:       107.030954 +/- 0.150067 (0.14%) (init= 105)
-        g1_amplitude:    4257.77319 +/- 42.38336 (1.00%) (init= 2000)
-        g1_fwhm:         39.2609139 +/- 0.377905 (0.96%)  == '2.3548200*g1_sigma'
-        g1_height:       101.880231 +/- 0.592170 (0.58%)  == '0.3989423*g1_amplitude/max(1.e-15, g1_sigma)'
-        g2_sigma:        13.8069484 +/- 0.186794 (1.35%) (init= 15)
-        g2_center:       153.270100 +/- 0.194667 (0.13%) (init= 155)
-        g2_amplitude:    2493.41770 +/- 36.16947 (1.45%) (init= 2000)
-        g2_fwhm:         32.5128782 +/- 0.439866 (1.35%)  == '2.3548200*g2_sigma'
-        g2_height:       72.0455934 +/- 0.617220 (0.86%)  == '0.3989423*g2_amplitude/max(1.e-15, g2_sigma)'
-    [[Correlations]] (unreported correlations are <  0.500)
-        C(g1_sigma, g1_amplitude)    =  0.824
-        C(g2_sigma, g2_amplitude)    =  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
+        exp_decay:      90.9508860 +/- 1.10310509 (1.21%) (init = 93.24905)
+        exp_amplitude:  99.0183283 +/- 0.53748735 (0.54%) (init = 162.2102)
+        g1_center:      107.030954 +/- 0.15006786 (0.14%) (init = 105)
+        g1_sigma:       16.6725753 +/- 0.16048161 (0.96%) (init = 15)
+        g1_amplitude:   4257.77319 +/- 42.3833645 (1.00%) (init = 2000)
+        g1_fwhm:        39.2609138 +/- 0.37790530 (0.96%) == '2.3548200*g1_sigma'
+        g1_height:      101.880231 +/- 0.59217100 (0.58%) == '0.3989423*g1_amplitude/max(1.e-15, g1_sigma)'
+        g2_center:      153.270101 +/- 0.19466743 (0.13%) (init = 155)
+        g2_sigma:       13.8069484 +/- 0.18679415 (1.35%) (init = 15)
+        g2_amplitude:   2493.41771 +/- 36.1694731 (1.45%) (init = 2000)
+        g2_fwhm:        32.5128783 +/- 0.43986659 (1.35%) == '2.3548200*g2_sigma'
+        g2_height:      72.0455934 +/- 0.61722094 (0.86%) == '0.3989423*g2_amplitude/max(1.e-15, g2_sigma)'
+    [[Correlations]] (unreported correlations are < 0.500)
+        C(g1_sigma, g1_amplitude)   =  0.824
+        C(g2_sigma, g2_amplitude)   =  0.815
+        C(exp_decay, exp_amplitude) = -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_center, g1_sigma)      =  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
@@ -615,11 +621,12 @@ 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])
+        """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)
+    ix1 = index_of(x, 75)
     ix2 = index_of(x, 135)
     ix3 = index_of(x, 175)
 
@@ -632,40 +639,41 @@ 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_'))
+        ((Model(gaussian, prefix='g1_') + Model(gaussian, prefix='g2_')) + Model(exponential, prefix='exp_'))
     [[Fit Statistics]]
-        # function evals   = 48
+        # fitting method   = leastsq
+        # function evals   = 39
         # data points      = 250
         # variables        = 8
-        chi-square         = 1247.528
-        reduced chi-square = 5.155
-        Akaike info crit   = 417.865
-        Bayesian info crit = 446.036
+        chi-square         = 1247.52821
+        reduced chi-square = 5.15507524
+        Akaike info crit   = 417.864631
+        Bayesian info crit = 446.036318
     [[Variables]]
-        exp_amplitude:   99.0183281 +/- 0.537487 (0.54%) (init= 94.53724)
-        exp_decay:       90.9508862 +/- 1.103105 (1.21%) (init= 111.1985)
-        g1_sigma:        16.6725754 +/- 0.160481 (0.96%) (init= 14.5)
-        g1_center:       107.030954 +/- 0.150067 (0.14%) (init= 106.5)
-        g1_amplitude:    4257.77322 +/- 42.38338 (1.00%) (init= 2126.432)
-        g1_fwhm:         39.2609141 +/- 0.377905 (0.96%)  == '2.3548200*g1_sigma'
-        g1_height:       101.880231 +/- 0.592171 (0.58%)  == '0.3989423*g1_amplitude/max(1.e-15, g1_sigma)'
-        g2_sigma:        13.8069481 +/- 0.186794 (1.35%) (init= 15)
-        g2_center:       153.270100 +/- 0.194667 (0.13%) (init= 150)
-        g2_amplitude:    2493.41766 +/- 36.16948 (1.45%) (init= 1878.892)
-        g2_fwhm:         32.5128777 +/- 0.439866 (1.35%)  == '2.3548200*g2_sigma'
-        g2_height:       72.0455935 +/- 0.617221 (0.86%)  == '0.3989423*g2_amplitude/max(1.e-15, g2_sigma)'
-    [[Correlations]] (unreported correlations are <  0.500)
-        C(g1_sigma, g1_amplitude)    =  0.824
-        C(g2_sigma, g2_amplitude)    =  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,
+        exp_decay:      90.9508890 +/- 1.10310483 (1.21%) (init = 111.1985)
+        exp_amplitude:  99.0183270 +/- 0.53748905 (0.54%) (init = 94.53724)
+        g1_sigma:       16.6725765 +/- 0.16048227 (0.96%) (init = 14.5)
+        g1_amplitude:   4257.77343 +/- 42.3836432 (1.00%) (init = 3189.648)
+        g1_center:      107.030956 +/- 0.15006873 (0.14%) (init = 106.5)
+        g1_fwhm:        39.2609166 +/- 0.37790686 (0.96%) == '2.3548200*g1_sigma'
+        g1_height:      101.880230 +/- 0.59217233 (0.58%) == '0.3989423*g1_amplitude/max(1.e-15, g1_sigma)'
+        g2_sigma:       13.8069461 +/- 0.18679534 (1.35%) (init = 15)
+        g2_amplitude:   2493.41733 +/- 36.1696911 (1.45%) (init = 2818.337)
+        g2_center:      153.270101 +/- 0.19466905 (0.13%) (init = 150)
+        g2_fwhm:        32.5128728 +/- 0.43986940 (1.35%) == '2.3548200*g2_sigma'
+        g2_height:      72.0455948 +/- 0.61722329 (0.86%) == '0.3989423*g2_amplitude/max(1.e-15, g2_sigma)'
+    [[Correlations]] (unreported correlations are < 0.500)
+        C(g1_sigma, g1_amplitude)   =  0.824
+        C(g2_sigma, g2_amplitude)   =  0.815
+        C(exp_decay, exp_amplitude) = -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_builtinmodels_nistgauss2.py`` in the examples folder,
 and the fit result shown on the right above shows an improved initial
 estimate of the data.