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# This file is part of xrayutilities.
#
# xrayutilities is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, see <http://www.gnu.org/licenses/>.
#
# Copyright (C) 2014-2020 Dominik Kriegner <dominik.kriegner@gmail.com>
import copy
import unittest
import numpy
import xrayutilities as xu
from scipy.integrate import nquad, quad
class TestMathFunctions(unittest.TestCase):
@classmethod
def setUpClass(cls):
amp = numpy.random.rand() + 0.1
fwhm = numpy.random.rand() * 1.5 + 0.1
cls.x = numpy.arange(-3, 3, 0.0003)
cls.p = [0.0, fwhm, amp, 0.0]
cls.p2d = [
0.0,
0.0,
fwhm,
fwhm,
amp,
0.0,
2 * numpy.pi * numpy.random.rand(),
]
cls.sigma = fwhm / (2 * numpy.sqrt(2 * numpy.log(2)))
def test_gauss1dwidth(self):
p = numpy.copy(self.p)
p[1] = self.sigma
f = xu.math.Gauss1d(self.x, *p)
fwhm = xu.math.fwhm_exp(self.x, f)
self.assertAlmostEqual(fwhm, self.p[1], places=4)
def test_lorentz1dwidth(self):
p = numpy.copy(self.p)
f = xu.math.Lorentz1d(self.x, *p)
fwhm = xu.math.fwhm_exp(self.x, f)
self.assertAlmostEqual(fwhm, self.p[1], places=4)
def test_pvoigt1dwidth(self):
p = list(numpy.copy(self.p))
p += [
numpy.random.rand(),
]
f = xu.math.PseudoVoigt1d(self.x, *p)
fwhm = xu.math.fwhm_exp(self.x, f)
self.assertAlmostEqual(fwhm, self.p[1], places=4)
def test_normedgauss1d(self):
p = numpy.copy(self.p)
p[1] = self.sigma
f = xu.math.Gauss1d(self.x, *p) / xu.math.Gauss1dArea(*p)
norm = xu.math.NormGauss1d(self.x, p[0], p[1])
self.assertAlmostEqual(numpy.sum(numpy.abs(f - norm)), 0, places=6)
def test_gauss1darea(self):
p = numpy.copy(self.p)
p[1] = self.sigma
area = xu.math.Gauss1dArea(*p)
(numarea, err) = quad(
xu.math.Gauss1d, -numpy.inf, numpy.inf, args=tuple(p)
)
digits = int(numpy.abs(numpy.log10(err))) - 3
self.assertTrue(digits >= 3)
self.assertAlmostEqual(area, numarea, places=digits)
def test_lorentz1darea(self):
p = numpy.copy(self.p)
area = xu.math.Lorentz1dArea(*p)
(numarea, err) = quad(
xu.math.Lorentz1d, -numpy.inf, numpy.inf, args=tuple(p)
)
digits = int(numpy.abs(numpy.log10(err))) - 3
self.assertTrue(digits >= 3)
self.assertAlmostEqual(area, numarea, places=digits)
def test_pvoigt1darea(self):
p = list(numpy.copy(self.p))
p += [
numpy.random.rand(),
]
area = xu.math.PseudoVoigt1dArea(*p)
(numarea, err) = quad(
xu.math.PseudoVoigt1d, -numpy.inf, numpy.inf, args=tuple(p)
)
digits = int(numpy.abs(numpy.log10(err))) - 3
self.assertTrue(digits >= 3)
self.assertAlmostEqual(area, numarea, places=digits)
def test_gauss2darea(self):
p = numpy.copy(self.p2d)
p[2] = self.sigma
p[3] = (numpy.random.rand() + 0.1) * self.sigma
area = xu.math.Gauss2dArea(*p)
(numarea, err) = nquad(
xu.math.Gauss2d,
[[-numpy.inf, numpy.inf], [-numpy.inf, numpy.inf]],
args=tuple(p),
)
digits = int(numpy.abs(numpy.log10(err))) - 3
self.assertTrue(digits >= 3)
self.assertAlmostEqual(area, numarea, places=digits)
def test_derivatives(self):
eps = 1e-9
# generate test input parameters (valid for Gauss, Lorentz, and Voigt)
p = list(numpy.copy(self.p))
p[1] = self.sigma
p[3] = numpy.random.rand()
p.append(numpy.random.rand())
params = [
self.x,
] + p
functions = [
(xu.math.Gauss1d, xu.math.Gauss1d_der_x, xu.math.Gauss1d_der_p),
(
xu.math.Lorentz1d,
xu.math.Lorentz1d_der_x,
xu.math.Lorentz1d_der_p,
),
(
xu.math.PseudoVoigt1d,
xu.math.PseudoVoigt1d_der_x,
xu.math.PseudoVoigt1d_der_p,
),
]
# test all derivates by benchmarking against a simple finite difference
# calculation
for f, fdx, fdp in functions:
deriv = numpy.vstack((fdx(*params), fdp(*params)))
for argidx in range(len(deriv)):
pmeps = copy.copy(params)
ppeps = copy.copy(params)
pmeps[argidx] = pmeps[argidx] - eps / 2
ppeps[argidx] = ppeps[argidx] + eps / 2
findiff = (f(*ppeps) - f(*pmeps)) / eps
diff = numpy.abs(deriv[argidx] - findiff)
errinfo = (
f"maximum difference, idx/npoints: "
f"{numpy.max(diff)}, {numpy.argmax(diff)}/{len(diff)}\n"
f"parameters: {str(p)}"
)
self.assertTrue(
numpy.allclose(deriv[argidx], findiff, atol=1e3 * eps),
f"{str(f)}, {argidx}, derivatives not close "
f"to numerical approximation ({errinfo})",
)
if __name__ == "__main__":
unittest.main()
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