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# coding: utf-8
# /*##########################################################################
# Copyright (C) 2016 European Synchrotron Radiation Facility
#
# 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.
#
# ############################################################################*/
"""
Tests for functions module
"""
import unittest
import numpy
import math
from silx.math.fit import functions
__authors__ = ["P. Knobel"]
__license__ = "MIT"
__date__ = "21/07/2016"
class Test_functions(unittest.TestCase):
"""
Unit tests of multi-peak functions.
"""
def setUp(self):
self.x = numpy.arange(11)
# height, center, sigma1, sigma2
(h, c, s1, s2) = (7., 5., 3., 2.1)
self.g_params = {
"height": h,
"center": c,
#"sigma": s,
"fwhm1": 2 * math.sqrt(2 * math.log(2)) * s1,
"fwhm2": 2 * math.sqrt(2 * math.log(2)) * s2,
"area1": h * s1 * math.sqrt(2 * math.pi)
}
# result of `7 * scipy.signal.gaussian(11, 3)`
self.scipy_gaussian = numpy.array(
[1.74546546, 2.87778603, 4.24571462, 5.60516182, 6.62171628,
7., 6.62171628, 5.60516182, 4.24571462, 2.87778603,
1.74546546]
)
# result of:
# numpy.concatenate((7 * scipy.signal.gaussian(11, 3)[0:5],
# 7 * scipy.signal.gaussian(11, 2.1)[5:11]))
self.scipy_asym_gaussian = numpy.array(
[1.74546546, 2.87778603, 4.24571462, 5.60516182, 6.62171628,
7., 6.24968751, 4.44773692, 2.52313452, 1.14093853, 0.41124877]
)
def tearDown(self):
pass
def testGauss(self):
"""Compare sum_gauss with scipy.signals.gaussian"""
y = functions.sum_gauss(self.x,
self.g_params["height"],
self.g_params["center"],
self.g_params["fwhm1"])
for i in range(11):
self.assertAlmostEqual(y[i], self.scipy_gaussian[i])
def testAGauss(self):
"""Compare sum_agauss with scipy.signals.gaussian"""
y = functions.sum_agauss(self.x,
self.g_params["area1"],
self.g_params["center"],
self.g_params["fwhm1"])
for i in range(11):
self.assertAlmostEqual(y[i], self.scipy_gaussian[i])
def testFastAGauss(self):
"""Compare sum_fastagauss with scipy.signals.gaussian
Limit precision to 3 decimal places."""
y = functions.sum_fastagauss(self.x,
self.g_params["area1"],
self.g_params["center"],
self.g_params["fwhm1"])
for i in range(11):
self.assertAlmostEqual(y[i], self.scipy_gaussian[i], 3)
def testSplitGauss(self):
"""Compare sum_splitgauss with scipy.signals.gaussian"""
y = functions.sum_splitgauss(self.x,
self.g_params["height"],
self.g_params["center"],
self.g_params["fwhm1"],
self.g_params["fwhm2"])
for i in range(11):
self.assertAlmostEqual(y[i], self.scipy_asym_gaussian[i])
def testErf(self):
"""Compare erf with math.erf"""
# scalars
self.assertAlmostEqual(functions.erf(0.14), math.erf(0.14), places=5)
self.assertAlmostEqual(functions.erf(0), math.erf(0), places=5)
self.assertAlmostEqual(functions.erf(-0.74), math.erf(-0.74), places=5)
# lists
x = [-5, -2, -1.5, -0.6, 0, 0.1, 2, 3]
erfx = functions.erf(x)
for i in range(len(x)):
self.assertAlmostEqual(erfx[i],
math.erf(x[i]),
places=5)
# ndarray
x = numpy.array([[0.1, 0.2, 0.3], [0.4, 0.5, 0.6]])
erfx = functions.erf(x)
for i in range(x.shape[0]):
for j in range(x.shape[1]):
self.assertAlmostEqual(erfx[i, j],
math.erf(x[i, j]),
places=5)
def testErfc(self):
"""Compare erf with math.erf"""
# scalars
self.assertAlmostEqual(functions.erfc(0.14), math.erfc(0.14), places=5)
self.assertAlmostEqual(functions.erfc(0), math.erfc(0), places=5)
self.assertAlmostEqual(functions.erfc(-0.74), math.erfc(-0.74), places=5)
# lists
x = [-5, -2, -1.5, -0.6, 0, 0.1, 2, 3]
erfcx = functions.erfc(x)
for i in range(len(x)):
self.assertAlmostEqual(erfcx[i], math.erfc(x[i]), places=5)
# ndarray
x = numpy.array([[0.1, 0.2, 0.3], [0.4, 0.5, 0.6]])
erfcx = functions.erfc(x)
for i in range(x.shape[0]):
for j in range(x.shape[1]):
self.assertAlmostEqual(erfcx[i, j], math.erfc(x[i, j]), places=5)
def testAtanStepUp(self):
"""Compare atan_stepup with math.atan
atan_stepup(x, a, b, c) = a * (0.5 + (arctan((x - b) / c) / pi))"""
x0 = numpy.arange(100) / 6.33
y0 = functions.atan_stepup(x0, 11.1, 22.2, 3.33)
for x, y in zip(x0, y0):
self.assertAlmostEqual(
11.1 * (0.5 + math.atan((x - 22.2) / 3.33) / math.pi),
y
)
def testStepUp(self):
"""sanity check for step up:
- derivative must be largest around the step center
- max value must be close to height parameter
"""
x0 = numpy.arange(1000)
center = 444
height = 1234
fwhm = 210
y0 = functions.sum_stepup(x0, height, center, fwhm)
self.assertLess(max(y0), height)
self.assertAlmostEqual(max(y0), height, places=1)
self.assertAlmostEqual(min(y0), 0, places=1)
deriv0 = _numerical_derivative(functions.sum_stepup, x0, [height, center, fwhm])
# Test center position within +- 1 sample of max derivative
index_max_deriv = numpy.argmax(deriv0)
self.assertLess(abs(index_max_deriv - center),
1)
def testStepDown(self):
"""sanity check for step down:
- absolute value of derivative must be largest around the step center
- max value must be close to height parameter
"""
x0 = numpy.arange(1000)
center = 444
height = 1234
fwhm = 210
y0 = functions.sum_stepdown(x0, height, center, fwhm)
self.assertLess(max(y0), height)
self.assertAlmostEqual(max(y0), height, places=1)
self.assertAlmostEqual(min(y0), 0, places=1)
deriv0 = _numerical_derivative(functions.sum_stepdown, x0, [height, center, fwhm])
# Test center position within +- 1 sample of max derivative
index_min_deriv = numpy.argmax(-deriv0)
self.assertLess(abs(index_min_deriv - center),
1)
def testSlit(self):
"""sanity check for slit:
- absolute value of derivative must be largest around the step center
- max value must be close to height parameter
"""
x0 = numpy.arange(1000)
center = 444
height = 1234
fwhm = 210
beamfwhm = 30
y0 = functions.sum_slit(x0, height, center, fwhm, beamfwhm)
self.assertAlmostEqual(max(y0), height, places=1)
self.assertAlmostEqual(min(y0), 0, places=1)
deriv0 = _numerical_derivative(functions.sum_slit, x0, [height, center, fwhm, beamfwhm])
# Test step up center position (center - fwhm/2) within +- 1 sample of max derivative
index_max_deriv = numpy.argmax(deriv0)
self.assertLess(abs(index_max_deriv - (center - fwhm/2)),
1)
# Test step down center position (center + fwhm/2) within +- 1 sample of min derivative
index_min_deriv = numpy.argmin(deriv0)
self.assertLess(abs(index_min_deriv - (center + fwhm/2)),
1)
def _numerical_derivative(f, x, params=[], delta_factor=0.0001):
"""Compute the numerical derivative of ``f`` for all values of ``x``.
:param f: function
:param x: Array of evenly spaced abscissa values
:param params: list of additional parameters
:return: Array of derivative values
"""
deltax = (x[1] - x[0]) * delta_factor
y_plus = f(x + deltax, *params)
y_minus = f(x - deltax, *params)
return (y_plus - y_minus) / (2 * deltax)
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