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Refactor and test Structure Factor (#4205)
Fixes #270, closes #4182 Description of changes: - fix undefined behavior (access out of bounds) - simplify structure factor code: use an exception instead of `errexit()`, combine the two C++ functions into a single function - check structure factor against analytical solutions for simple tetragonal lattices
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,181 @@ | ||
| # | ||
| # Copyright (C) 2017-2021 The ESPResSo project | ||
| # | ||
| # This file is part of ESPResSo. | ||
| # | ||
| # ESPResSo is free software: you can redistribute it and/or modify | ||
| # it under the terms of the GNU General Public License as published byss | ||
| # the Free Software Foundation, either version 3 of the License, or | ||
| # (at your option) any later version. | ||
| # | ||
| # ESPResSo 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/>. | ||
| # | ||
|
|
||
| import unittest as ut | ||
| import espressomd | ||
| import numpy as np | ||
| import itertools | ||
|
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|
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| class StructureFactorTest(ut.TestCase): | ||
| ''' | ||
| Test structure factor analysis against rectangular lattices. | ||
| We do not check the wavevectors directly, but rather the | ||
| corresponding SF order, which is more readable (integer value). | ||
| ''' | ||
|
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||
| box_l = 16 | ||
| part_ty = 0 | ||
| sf_order = 16 | ||
| system = espressomd.System(box_l=[box_l, box_l, box_l]) | ||
|
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||
| def tearDown(self): | ||
| self.system.part.clear() | ||
|
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| def order(self, wavevectors, a): | ||
| """ | ||
| Square and rescale wavevectors to recover the corresponding | ||
| SF order, which is an integer between 0 and ``self.sf_order``. | ||
| """ | ||
| return (wavevectors * a / (2 * np.pi))**2 | ||
|
|
||
| def generate_peaks(self, a, b, c, conditions): | ||
| ''' | ||
| Generate the main diffraction peaks for crystal structures. | ||
| Parameters | ||
| ---------- | ||
| a: :obj:`float` | ||
| Length of the unit cell on the x-axis. | ||
| b: :obj:`float` | ||
| Length of the unit cell on the y-axis. | ||
| c: :obj:`float` | ||
| Length of the unit cell on the z-axis. | ||
| conditions: :obj:`function` | ||
| Reflection conditions for the crystal lattice. | ||
| ''' | ||
| hkl_ranges = [ | ||
| range(0, self.sf_order + 1), | ||
| range(-self.sf_order, self.sf_order + 1), | ||
| range(-self.sf_order, self.sf_order + 1), | ||
| ] | ||
| reflections = [np.linalg.norm([h / a, k / b, l / c]) * 2 * np.pi | ||
| for (h, k, l) in itertools.product(*hkl_ranges) | ||
| if conditions(h, k, l) and (h + k + l != 0) and | ||
| (h**2 + k**2 + l**2) <= self.sf_order**2] | ||
| return np.unique(reflections) | ||
|
|
||
| def test_tetragonal(self): | ||
| """Check tetragonal lattice.""" | ||
| a = 2 | ||
| b = 4 | ||
| c = 8 | ||
| xen = range(0, self.box_l, a) | ||
| yen = range(0, self.box_l, b) | ||
| zen = range(0, self.box_l, c) | ||
| for i, j, k in itertools.product(xen, yen, zen): | ||
| self.system.part.add(type=self.part_ty, pos=(i, j, k)) | ||
| wavevectors, intensities = self.system.analysis.structure_factor( | ||
| sf_types=[self.part_ty], sf_order=self.sf_order) | ||
| intensities = np.around(intensities, 8) | ||
| # no reflection conditions on (h,k,l) | ||
| peaks_ref = self.generate_peaks(a, b, c, lambda h, k, l: True) | ||
| peaks = wavevectors[np.nonzero(intensities)] | ||
| np.testing.assert_array_almost_equal( | ||
| self.order(peaks, a), self.order(peaks_ref[:len(peaks)], a)) | ||
|
|
||
| def test_sc(self): | ||
| """Check simple cubic lattice.""" | ||
| l0 = 4 | ||
| xen = range(0, self.box_l, l0) | ||
| for i, j, k in itertools.product(xen, repeat=3): | ||
| self.system.part.add(type=self.part_ty, pos=(i, j, k)) | ||
| wavevectors, intensities = self.system.analysis.structure_factor( | ||
| sf_types=[self.part_ty], sf_order=self.sf_order) | ||
| intensities = np.around(intensities, 8) | ||
| np.testing.assert_array_equal( | ||
| intensities[np.nonzero(intensities)], len(self.system.part)) | ||
| # no reflection conditions on (h,k,l) | ||
| peaks = wavevectors[np.nonzero(intensities)] | ||
| peaks_ref = self.generate_peaks(l0, l0, l0, lambda h, k, l: True) | ||
| np.testing.assert_array_almost_equal( | ||
| self.order(peaks, l0), self.order(peaks_ref[:len(peaks)], l0)) | ||
|
|
||
| def test_bcc(self): | ||
| """Check body-centered cubic lattice.""" | ||
| l0 = 4 | ||
| m = l0 / 2 | ||
| xen = range(0, self.box_l, l0) | ||
| for i, j, k in itertools.product(xen, repeat=3): | ||
| self.system.part.add(type=self.part_ty, pos=(i, j, k)) | ||
| self.system.part.add(type=self.part_ty, pos=(i + m, j + m, k + m)) | ||
| wavevectors, intensities = self.system.analysis.structure_factor( | ||
| sf_types=[self.part_ty], sf_order=self.sf_order) | ||
| intensities = np.around(intensities, 8) | ||
| np.testing.assert_array_equal( | ||
| intensities[np.nonzero(intensities)], len(self.system.part)) | ||
| # reflection conditions | ||
| # (h+k+l) even => F = 2f, otherwise F = 0 | ||
| peaks_ref = self.generate_peaks( | ||
| l0, l0, l0, lambda h, k, l: (h + k + l) % 2 == 0) | ||
| peaks = wavevectors[np.nonzero(intensities)] | ||
| np.testing.assert_array_almost_equal( | ||
| self.order(peaks, l0), self.order(peaks_ref[:len(peaks)], l0)) | ||
|
|
||
| def test_fcc(self): | ||
| """Check face-centered cubic lattice.""" | ||
| l0 = 4 | ||
| m = l0 / 2 | ||
| xen = range(0, self.box_l, l0) | ||
| for i, j, k in itertools.product(xen, repeat=3): | ||
| self.system.part.add(type=self.part_ty, pos=(i, j, k)) | ||
| self.system.part.add(type=self.part_ty, pos=(i + m, j + m, k)) | ||
| self.system.part.add(type=self.part_ty, pos=(i + m, j, k + m)) | ||
| self.system.part.add(type=self.part_ty, pos=(i, j + m, k + m)) | ||
| wavevectors, intensities = self.system.analysis.structure_factor( | ||
| sf_types=[self.part_ty], sf_order=self.sf_order) | ||
| intensities = np.around(intensities, 8) | ||
| np.testing.assert_array_equal( | ||
| intensities[np.nonzero(intensities)], len(self.system.part)) | ||
| # reflection conditions | ||
| # (h,k,l) all even or odd => F = 4f, otherwise F = 0 | ||
| peaks_ref = self.generate_peaks( | ||
| l0, l0, l0, lambda h, k, l: | ||
| h % 2 == 0 and k % 2 == 0 and l % 2 == 0 or | ||
| h % 2 == 1 and k % 2 == 1 and l % 2 == 1) | ||
| peaks = wavevectors[np.nonzero(intensities)] | ||
| np.testing.assert_array_almost_equal( | ||
| self.order(peaks, l0), self.order(peaks_ref[:len(peaks)], l0)) | ||
|
|
||
| def test_cco(self): | ||
| """Check c-centered orthorhombic lattice.""" | ||
| l0 = 4 | ||
| m = l0 / 2 | ||
| xen = range(0, self.box_l, l0) | ||
| for i, j, k in itertools.product(xen, repeat=3): | ||
| self.system.part.add(type=self.part_ty, pos=(i, j, k)) | ||
| self.system.part.add(type=self.part_ty, pos=(i + m, j + m, k)) | ||
| wavevectors, intensities = self.system.analysis.structure_factor( | ||
| sf_types=[self.part_ty], sf_order=self.sf_order) | ||
| intensities = np.around(intensities, 8) | ||
| # reflection conditions | ||
| # (h+k) even => F = 2f, otherwise F = 0 | ||
| peaks_ref = self.generate_peaks( | ||
| l0, l0, l0, lambda h, k, l: (h + k) % 2 == 0) | ||
| peaks = wavevectors[np.nonzero(intensities)] | ||
| np.testing.assert_array_almost_equal( | ||
| self.order(peaks, l0), self.order(peaks_ref[:len(peaks)], l0)) | ||
|
|
||
| def test_exceptions(self): | ||
| with self.assertRaisesRegex(ValueError, 'order has to be a strictly positive number'): | ||
| self.system.analysis.structure_factor(sf_types=[0], sf_order=0) | ||
|
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||
|
|
||
| if __name__ == "__main__": | ||
| ut.main() |