def test_skewed(self):
# Make sure that highly distorted cells evaluate properly
energy_1, jacobian_1 = potential._evaluate_fast(
*EvaluateTests._cases[10][:3])
energy_2, jacobian_2 = potential._evaluate_fast(
*EvaluateTests._cases[11][:3])
self.assertTrue(numpy.all(numpy.isclose(energy_1, energy_2)))
self.assertTrue(numpy.all(numpy.isclose(jacobian_1, jacobian_2)))
def test_translated(self):
# Make sure that an arbitrary translation does not affect anything
energy_1, jacobian_1 = potential._evaluate_fast(
*EvaluateTests._cases[12][:3])
energy_2, jacobian_2 = potential._evaluate_fast(
*EvaluateTests._cases[13][:3])
self.assertTrue(numpy.all(numpy.isclose(energy_1, energy_2)))
self.assertTrue(numpy.all(numpy.isclose(jacobian_1, jacobian_2)))
def test_histogram_binning(self):
# Check for proper binning (number of bins)
cell = crystal.Cell(
numpy.eye(3),
[numpy.zeros((1, 3)),
numpy.array([[0.3] * 3, [0.65] * 3])])
self.assertEqual(
potential._evaluate_fast(cell, None, 6, 0.25)[2].shape[2], 24)
self.assertEqual(
potential._evaluate_fast(cell, None, 6.01, 0.25)[2].shape[2], 25)
self.assertEqual(
potential._evaluate_fast(cell, None, 4, 5)[2].shape[2], 1)
def test_filter_actual_energy(self):
generator = wallpaper.generate_wallpaper((1, 1),
place_max=5,
sample_count=100)
result = [None]
def callback(energies):
result[0] = energies
potentials = {
(0, 0): potential.LennardJonesType(lambda_=-1),
(1, 1): potential.LennardJonesType(lambda_=-1),
(0, 1): potential.LennardJonesType(lambda_=1)
}
distance = 4.0
filter = minimization.filter(generator,
potentials,
distance,
20,
histogram_callback=callback)
# Make sure true energies are actually less than cutoff
filter_results = list(filter) # Exhaust generator to trigger callback
energies = result[0]
for cell in filter_results:
self.assertLessEqual(
potential._evaluate_fast(cell[1], potentials, distance)[0],
min(energies[20:]))
def test_histogram_correct(self):
# Construct a histogram manually using cell RDF method
cell = crystal.Cell(
numpy.eye(3),
[numpy.zeros((1, 3)),
numpy.array([[0.3] * 3, [0.65] * 3])])
histogram = numpy.zeros((2, 2, 20))
for source in range(2):
for target in range(2):
for key, value in cell.rdf(source, target, 5).items():
factor = 0.5 + (4 * key) - int(numpy.round(4 * key))
histogram[source, target,
max(0,
int(numpy.round(4 * key)) -
1)] += value * (1 - factor)
histogram[source, target,
min(19, int(numpy.round(4 *
key)))] += value * factor
# Construct a fast histogram and compare
self.assertTrue(
numpy.all(
numpy.isclose(histogram,
potential._evaluate_fast(cell, None, 5,
0.25)[2])))
def test_methods_jacobian(self):
for cell, potentials, cutoff, expected in EvaluateTests._cases:
# First, make sure Python and Cython algorithms give identical answers
cell = crystal.CellTools.reduce(cell)
energy_slow = crystal.CellTools.energy(cell, potentials, cutoff)
energy_fast, jacobian_fast = potential._evaluate_fast(
cell, potentials, cutoff)
self.assertAlmostEqual(energy_slow, energy_fast)
if expected is not None:
self.assertTrue(numpy.isclose(energy_fast, expected))
# Now use second-order finite differences to make sure gradient is correct
delta = 2.0**-26.0
index = 0
for type_index in range(cell.atom_types):
for atom_index in range(cell.atom_count(type_index)):
for component_index in range(cell.dimensions):
low_lists, high_lists = cell.atom_lists, cell.atom_lists
low_lists[type_index][atom_index][
component_index] -= delta
high_lists[type_index][atom_index][
component_index] += delta
low_energy = potential._evaluate_fast(
crystal.CellTools.wrap(
crystal.Cell(cell.vectors, low_lists)),
potentials, cutoff)[0]
high_energy = potential._evaluate_fast(
crystal.CellTools.wrap(
crystal.Cell(cell.vectors, high_lists)),
potentials, cutoff)[0]
derivative = (high_energy - low_energy) / (delta * 2)
self.assertTrue(
numpy.isclose(derivative,
jacobian_fast[index],
atol=1e-4,
rtol=1e-4))
index += 1
def test_filter_generator(self):
count = 100
distance = 3.0
radii = (2.**(1. / 6.) / 2., 2.**(1. / 6.) / 2.)
potentials = {
(0, 0): potential.LennardJonesType(epsilon=0),
(1, 1): potential.LennardJonesType(epsilon=1),
(0, 1): potential.LennardJonesType(epsilon=0.5)
}
mm = similarity.Histogram(distance,
0.05,
0.99,
norm=similarity.Minimum())
# Generate an ensemble of candidates
generator = wallpaper.generate_wallpaper(
(1, 1),
place_max=4,
random_seed=0,
sample_count=count,
merge_sets=False,
sample_groups=[wallpaper.WallpaperGroup(name="p3")])
results = list(generator)
# All "count" structures should be provided
self.assertEqual(len(results), count)
# Scale cells to "contact"
scale_cell = lambda cell: crystal.CellTools.scale(
cell, cell.vectors / cell.scale_factor(radii))
cells = [scale_cell(c) for g, c in results]
energies = numpy.array([
potential._evaluate_fast(c, potentials, distance)[0] for c in cells
])
res = zip(cells, energies)
# Find "unique" ones
reduced_cells = similarity.reduce(res, mm)
manually_reduced = len(reduced_cells)
self.assertEqual(manually_reduced, 89)
# Do in an automated fashion to compare
generator2 = wallpaper.generate_wallpaper(
(1, 1),
place_max=4,
random_seed=0,
sample_count=count,
merge_sets=False,
sample_groups=[wallpaper.WallpaperGroup(name="p3")])
filter2 = minimization.filter(generator2,
potentials,
distance,
count,
radii,
similarity_metric=mm)
self.assertEqual(len(list(filter2)), manually_reduced)
# Confirm that cells from automatic reduction have not been rescaled
for idx, (g, c) in enumerate(list(filter2)):
self.assertTrue(c != reduced_cells[idx][0])
self.assertTrue(scale_cell(c) == reduced_cells[idx][0])
self.assertTrue(
potential._evaluate_fast(scale_cell(c), potentials, distance)
[0] == reduced_cells[idx][1])
def test_double_wrap(self):
# Make sure wrapping is working properly
energy, jacobian = potential._evaluate_fast(
*EvaluateTests._cases[4][:3])
self.assertLess(jacobian[0], 0)
self.assertGreater(jacobian[3], 0)
def test_double(self):
# Simple check with pairwise interaction direction
energy, jacobian = potential._evaluate_fast(
*EvaluateTests._cases[2][:3])
self.assertLess(jacobian[0], 0)
self.assertGreater(jacobian[3], 0)
