def test_k3_peaks_periodic(self):
"""Tests that the final spectra does not change when translating atoms
in a periodic cell. This is not trivially true unless the weight of
angles is weighted according to the cell indices of the involved three
atoms. Notice that the values of the geometry and weight functions are
not equal before summing them up in the final graph.
"""
scale = 0.85
desc = MBTR(
species=["H"],
k3={
"geometry": {"function": "angle"},
"grid": {"min": 0, "max": 180, "sigma": 5, "n": 2000},
"weighting": {"function": "exp", "scale": scale, "cutoff": 1e-3},
},
normalize_gaussians=False,
periodic=True,
flatten=True,
sparse=False
)
atoms = Atoms(
cell=[
[10, 0, 0],
[0, 10, 0],
[0, 0, 10],
],
symbols=3*["H"],
scaled_positions=[
[0.05, 0.40, 0.5],
[0.05, 0.60, 0.5],
[0.95, 0.5, 0.5],
],
pbc=True
)
features = desc.create(atoms)[0, :]
x = desc.get_k3_axis()
# Calculate assumed locations and intensities.
assumed_locs = np.array([45, 90])
dist = 2+2*np.sqrt(2) # The total distance around the three atoms
weight = np.exp(-scale*dist)
assumed_ints = np.array([4*weight, 2*weight])
assumed_ints /= 2 # The periodic distances ar halved because they belong to different cells
# Check the H-H-H peaks
hhh_feat = features[desc.get_location(("H", "H", "H"))]
hhh_peak_indices = find_peaks(hhh_feat, prominence=0.01)[0]
hhh_peak_locs = x[hhh_peak_indices]
hhh_peak_ints = hhh_feat[hhh_peak_indices]
self.assertTrue(np.allclose(hhh_peak_locs, assumed_locs, rtol=0, atol=1e-1))
self.assertTrue(np.allclose(hhh_peak_ints, assumed_ints, rtol=0, atol=1e-1))
# Check that everything else is zero
features[desc.get_location(("H", "H", "H"))] = 0
self.assertEqual(features.sum(), 0)
def test_k3_peaks_finite(self):
"""Tests that all the correct angles are present in finite systems.
There should be n*(n-1)*(n-2)/2 unique angles where the division by two
gets rid of duplicate angles.
"""
desc = MBTR(
species=["H", "O"],
k3={
"geometry": {"function": "angle"},
"grid": {"min": -10, "max": 180, "sigma": 5, "n": 2000},
"weighting": {"function": "unity"},
},
normalize_gaussians=False,
periodic=False,
flatten=True,
sparse=False
)
features = desc.create(H2O)[0, :]
x = desc.get_k3_axis()
# Check the H-H-O peaks
hho_assumed_locs = np.array([38])
hho_assumed_ints = np.array([2])
hho_feat = features[desc.get_location(("H", "H", "O"))]
hho_peak_indices = find_peaks(hho_feat, prominence=0.5)[0]
hho_peak_locs = x[hho_peak_indices]
hho_peak_ints = hho_feat[hho_peak_indices]
self.assertTrue(np.allclose(hho_peak_locs, hho_assumed_locs, rtol=0, atol=5e-2))
self.assertTrue(np.allclose(hho_peak_ints, hho_assumed_ints, rtol=0, atol=5e-2))
# Check the H-O-H peaks
hoh_assumed_locs = np.array([104])
hoh_assumed_ints = np.array([1])
hoh_feat = features[desc.get_location(("H", "O", "H"))]
hoh_peak_indices = find_peaks(hoh_feat, prominence=0.5)[0]
hoh_peak_locs = x[hoh_peak_indices]
hoh_peak_ints = hoh_feat[hoh_peak_indices]
self.assertTrue(np.allclose(hoh_peak_locs, hoh_assumed_locs, rtol=0, atol=5e-2))
self.assertTrue(np.allclose(hoh_peak_ints, hoh_assumed_ints, rtol=0, atol=5e-2))
# Check that everything else is zero
features[desc.get_location(("H", "H", "O"))] = 0
features[desc.get_location(("H", "O", "H"))] = 0
self.assertEqual(features.sum(), 0)
def test_periodic_images(self):
"""Tests that periodic images are handled correctly.
"""
decay = 1
desc = MBTR(
species=[1],
periodic=True,
k1={
"geometry": {"function": "atomic_number"},
"grid": {"min": 0, "max": 2, "sigma": 0.1, "n": 21}
},
k2={
"geometry": {"function": "inverse_distance"},
"grid": {"min": 0, "max": 1.0, "sigma": 0.02, "n": 21},
"weighting": {"function": "exp", "scale": decay, "cutoff": 1e-4}
},
k3={
"geometry": {"function": "cosine"},
"grid": {"min": -1.0, "max": 1.0, "sigma": 0.02, "n": 21},
"weighting": {"function": "exp", "scale": decay, "cutoff": 1e-4},
},
normalization="l2_each", # This normalizes the spectrum
flatten=True
)
# Tests that a system has the same spectrum as the supercell of
# the same system.
molecule = H.copy()
a = 1.5
molecule.set_cell([
[a, 0.0, 0.0],
[0.0, a, 0.0],
[0.0, 0.0, a]
])
cubic_cell = desc.create(molecule)
suce = molecule * (2, 1, 1)
cubic_suce = desc.create(suce)
diff = abs(np.sum(cubic_cell[0, :] - cubic_suce[0, :]))
cubic_sum = abs(np.sum(cubic_cell[0, :]))
self.assertTrue(diff/cubic_sum < 0.05) # A 5% error is tolerated
# Same test but for triclinic cell
molecule.set_cell([
[0.0, 2.0, 1.0],
[1.0, 0.0, 1.0],
[1.0, 2.0, 0.0]
])
triclinic_cell = desc.create(molecule)
suce = molecule * (2, 1, 1)
triclinic_suce = desc.create(suce)
diff = abs(np.sum(triclinic_cell[0, :] - triclinic_suce[0, :]))
tricl_sum = abs(np.sum(triclinic_cell[0, :]))
self.assertTrue(diff/tricl_sum < 0.05)
# Testing that the same crystal, but different unit cells will have a
# similar spectrum when they are normalized. There will be small
# differences in the shape (due to not double counting distances)
a1 = bulk('H', 'fcc', a=2.0)
a2 = bulk('H', 'fcc', a=2.0, orthorhombic=True)
a3 = bulk('H', 'fcc', a=2.0, cubic=True)
triclinic_cell = desc.create(a1)
orthorhombic_cell = desc.create(a2)
cubic_cell = desc.create(a3)
diff1 = abs(np.sum(triclinic_cell[0, :] - orthorhombic_cell[0, :]))
diff2 = abs(np.sum(triclinic_cell[0, :] - cubic_cell[0, :]))
tricl_sum = abs(np.sum(triclinic_cell[0, :]))
self.assertTrue(diff1/tricl_sum < 0.05)
self.assertTrue(diff2/tricl_sum < 0.05)
# Tests that the correct peak locations are present in a cubic periodic
desc = MBTR(
species=["H"],
periodic=True,
k3={
"geometry": {"function": "cosine"},
"grid": {"min": -1.1, "max": 1.1, "sigma": 0.010, "n": 600},
"weighting": {"function": "exp", "scale": decay, "cutoff": 1e-4}
},
normalization="l2_each", # This normalizes the spectrum
flatten=True
)
a = 2.2
system = Atoms(
cell=[
[a, 0.0, 0.0],
[0.0, a, 0.0],
[0.0, 0.0, a]
],
positions=[
[0, 0, 0],
],
symbols=["H"],
)
cubic_spectrum = desc.create(system)[0, :]
x3 = desc.get_k3_axis()
peak_ids = find_peaks_cwt(cubic_spectrum, [2])
peak_locs = x3[peak_ids]
assumed_peaks = np.cos(np.array(
[
180,
90,
np.arctan(np.sqrt(2))*180/np.pi,
45,
np.arctan(np.sqrt(2)/2)*180/np.pi,
0
])*np.pi/180
)
self.assertTrue(np.allclose(peak_locs, assumed_peaks, rtol=0, atol=5*np.pi/180))
# Tests that the correct peak locations are present in a system with a
# non-cubic basis
desc = MBTR(
species=["H"],
periodic=True,
k3={
"geometry": {"function": "cosine"},
"grid": {"min": -1.0, "max": 1.0, "sigma": 0.030, "n": 200},
"weighting": {"function": "exp", "scale": 1.5, "cutoff": 1e-4}
},
normalization="l2_each", # This normalizes the spectrum
flatten=True,
sparse=False
)
a = 2.2
system = Atoms(
cell=[
[a, 0.0, 0.0],
[0.0, a, 0.0],
[0.0, 0.0, a]
],
positions=[
[0, 0, 0],
],
symbols=["H"],
)
angle = 30
system = Atoms(
cell=ase.geometry.cellpar_to_cell([3*a, a, a, angle, 90, 90]),
positions=[
[0, 0, 0],
],
symbols=["H"],
)
tricl_spectrum = desc.create(system)
x3 = desc.get_k3_axis()
peak_ids = find_peaks_cwt(tricl_spectrum[0, :], [3])
peak_locs = x3[peak_ids]
angle = (6)/(np.sqrt(5)*np.sqrt(8))
assumed_peaks = np.cos(np.array([180, 105, 75, 51.2, 30, 0])*np.pi/180)
self.assertTrue(np.allclose(peak_locs, assumed_peaks, rtol=0, atol=5*np.pi/180))
