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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)
-
-test_cases = (Test_functions,)
-
-def suite():
- loader = unittest.defaultTestLoader
- test_suite = unittest.TestSuite()
- for test_class in test_cases:
- tests = loader.loadTestsFromTestCase(test_class)
- test_suite.addTests(tests)
- return test_suite
-
-if __name__ == '__main__':
- unittest.main(defaultTest="suite")
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