def test_include(self):
soap = SOAP(
species=[1, 6, 8],
rcut=3,
nmax=2,
lmax=1,
rbf="gto",
sparse=False,
periodic=False,
)
for method in ["numerical", "analytical"]:
# Invalid include options
with self.assertRaises(ValueError):
soap.derivatives(H2O, include=[], method=method)
with self.assertRaises(ValueError):
soap.derivatives(H2O, include=[3], method=method)
with self.assertRaises(ValueError):
soap.derivatives(H2O, include=[-1], method=method)
# Test that correct atoms are included and in the correct order
D1, d1 = soap.derivatives(H2O, include=[2, 0], method=method)
D2, d2 = soap.derivatives(H2O, method=method)
self.assertTrue(np.array_equal(D1[:, 0], D2[:, 2]))
self.assertTrue(np.array_equal(D1[:, 1], D2[:, 0]))
# Test that using single list and multiple samples works
D1, d1 = soap.derivatives([H2O, CO2],
include=[1, 0],
method=method)
D2, d2 = soap.derivatives([H2O, CO2], method=method)
self.assertTrue(np.array_equal(D1[:, :, 0], D2[:, :, 1]))
self.assertTrue(np.array_equal(D1[:, :, 1], D2[:, :, 0]))
def test_return_descriptor(self):
soap = SOAP(
species=[1, 8],
rcut=3,
nmax=2,
lmax=0,
rbf="gto",
sparse=False,
periodic=False,
)
s = soap.derivatives(H2O, method="analytical", return_descriptor=False)
D, d = soap.derivatives(H2O,
method="analytical",
return_descriptor=True)
s = soap.derivatives(H2O, method="numerical", return_descriptor=False)
D, d = soap.derivatives(H2O,
method="numerical",
return_descriptor=True)
def test_stratification(self):
"""Tests that the ordering of the output works, especially when the
total chemical space is larger than the chemical space of individual
samples.
"""
soap = SOAP(
species=[1, 6, 5, 8, 9],
rcut=3,
nmax=1,
lmax=1,
rbf="gto",
average="off",
crossover=True,
)
derivatives_n, d_n = soap.derivatives(CO2, method="numerical")
derivatives_a, d_a = soap.derivatives(CO2, method="analytical")
self.assertTrue(
np.allclose(derivatives_n, derivatives_a, rtol=1e-6, atol=1e-6))
self.assertTrue(np.allclose(d_n, d_a, rtol=1e-6, atol=1e-6))
def test_descriptor_output(self):
"""Tests that the descriptor is output correctly both for numerical and
analytical version.
"""
soap = SOAP(
species=["H", "O"],
rcut=3,
nmax=3,
lmax=3,
crossover=True,
)
positions = H2O.get_positions()
_, d_num = soap.derivatives(H2O,
positions=positions,
method="numerical")
_, d_anal = soap.derivatives(H2O,
positions=positions,
method="analytical")
d = soap.create(H2O, positions=positions)
self.assertTrue(np.allclose(d, d_num))
self.assertTrue(np.allclose(d, d_anal))
def test_sparse(self):
"""Test that the sparse values are identical to the dense ones."""
positions = H2O.get_positions()
soap = SOAP(
species=["H", "O"],
rcut=3,
nmax=1,
lmax=1,
sparse=False,
crossover=False,
)
D_dense, d_dense = soap.derivatives(H2O,
positions=positions,
method="analytical")
soap.sparse = True
D_sparse, d_sparse = soap.derivatives(H2O,
positions=positions,
method="analytical")
self.assertTrue(np.allclose(D_dense, D_sparse.todense()))
self.assertTrue(np.allclose(d_dense, d_sparse.todense()))
def test_dtype(self):
"""Tests that the the specified data type is respected."""
# Dense, float32
soap = SOAP(species=[1, 8], rcut=3, nmax=1, lmax=1, dtype="float32")
desc1 = soap.create(H2O)
der, desc2 = soap.derivatives(H2O)
self.assertTrue(desc1.dtype == np.float32)
self.assertTrue(desc2.dtype == np.float32)
self.assertTrue(der.dtype == np.float32)
# Sparse, float32
soap = SOAP(
species=[1, 8], rcut=3, nmax=1, lmax=1, sparse=True, dtype="float32"
)
desc1 = soap.create(H2O)
der, desc2 = soap.derivatives(H2O)
self.assertTrue(desc1.dtype == np.float32)
self.assertTrue(desc2.dtype == np.float32)
self.assertTrue(der.dtype == np.float32)
# Dense, float64
soap = SOAP(species=[1, 8], rcut=3, nmax=1, lmax=1, dtype="float64")
desc1 = soap.create(H2O)
der, desc2 = soap.derivatives(H2O)
self.assertTrue(desc1.dtype == np.float64)
self.assertTrue(desc2.dtype == np.float64)
self.assertTrue(der.dtype == np.float64)
# Sparse, float64
soap = SOAP(
species=[1, 8], rcut=3, nmax=1, lmax=1, sparse=True, dtype="float64"
)
desc1 = soap.create(H2O)
der, desc2 = soap.derivatives(H2O)
self.assertTrue(desc1.dtype == np.float64)
self.assertTrue(desc2.dtype == np.float64)
self.assertTrue(der.dtype == np.float64)
def test_crossover(self):
"""Tests the analytical soap derivatives implementation with crossover
against the numerical implementation.
"""
soap = SOAP(
species=["H", "O"],
rcut=3,
nmax=9,
lmax=9,
sparse=False,
crossover=True,
)
positions = H2O.get_positions()
derivatives_cpp, d_num = soap.derivatives(H2O,
positions=positions,
method="numerical")
derivatives_anal, d_anal = soap.derivatives(H2O,
positions=positions,
method="analytical")
self.assertTrue(
np.allclose(derivatives_cpp,
derivatives_anal,
rtol=1e-6,
atol=1e-6))
def soap_sparse_vs_dense(version):
"""Tests sparse vs. dense derivatives calculation.
"""
nmax = 4
lmax = 4
fig = mpl.figure(figsize=[9, 7])
ax = fig.add_subplot(111)
ax.set_title("SOAP derivatives nmax={}, lmax={}, version={}".format(
nmax, lmax, version))
ax.set_xlabel("Number of atoms")
ax.set_ylabel("Time (s)")
system = system_periodic * (5, 5, 5)
# Loop over different system sizes
vals = []
for sparse in [True, False]:
N = []
t = []
for ncells in tqdm(range(1, 6)):
soap_generator = SOAP(
rcut=3.0,
nmax=nmax,
lmax=lmax,
species=["Ni", "Ti"],
rbf="gto",
crossover=True,
periodic=False,
sparse=sparse,
)
i_system = system.copy() * [ncells, 1, 1]
t0 = time()
der, des = soap_generator.derivatives(i_system,
method="analytical")
vals.append(der)
t1 = time()
N.append(len(i_system))
t.append(t1 - t0)
ax.plot(N, t, "o--", label="sparse={}".format(sparse))
mpl.legend()
mpl.show()
def soap_derivatives(version):
"""Tests how the SOAP derivative calculation (numerical+analytical) scales
with system size.
"""
nmax = 4
lmax = 4
fig = mpl.figure(figsize=[9, 7])
ax = fig.add_subplot(111)
ax.set_title("SOAP derivatives nmax={}, lmax={}, version={}".format(nmax, lmax, version))
ax.set_xlabel("lmax")
ax.set_ylabel("Time (s)")
system = system_periodic*(5,5,5)
for method in ["numerical", "analytical"]:
N = []
t = []
for ncells in tqdm(range(1, 5)):
i_system = system.copy() * [ncells, 1, 1]
soap_generator = SOAP(
rcut=3.0,
nmax=nmax,
lmax=lmax,
species=["Ni", "Ti"],
rbf="gto",
crossover=True,
periodic=False
)
t0 = time()
der, des = soap_generator.derivatives(i_system, method=method)
t1 = time()
N.append(len(i_system))
t.append(t1 - t0)
ax.plot(N, t, "o--", label="{}".format(method))
mpl.legend()
mpl.show()
import numpy as np
from ase.build import molecule
from dscribe.descriptors import SOAP
from dscribe.descriptors import CoulombMatrix
# Define atomic structures
samples = [molecule("H2O"), molecule("NO2"), molecule("CO2")]
# Setup descriptors
cm_desc = CoulombMatrix(n_atoms_max=3, permutation="sorted_l2")
soap_desc = SOAP(species=["C", "H", "O", "N"], rcut=5, nmax=8, lmax=6, crossover=True)
# Create descriptors as numpy arrays or sparse arrays
water = samples[0]
coulomb_matrix = cm_desc.create(water)
soap = soap_desc.create(water, positions=[0])
# Easy to use also on multiple systems, can be parallelized across processes
coulomb_matrices = cm_desc.create(samples)
coulomb_matrices = cm_desc.create(samples, n_jobs=3)
oxygen_indices = [np.where(x.get_atomic_numbers() == 8)[0] for x in samples]
oxygen_soap = soap_desc.create(samples, oxygen_indices, n_jobs=3)
# Some descriptors also allow calculating derivatives with respect to atomic
# positions
der, des = soap_desc.derivatives(samples, method="auto", return_descriptor=True)
def test_combinations(self):
"""Tests that different combinations of centers/atoms work as intended
and are equal between analytical/numerical code.
"""
# Elaborate test system with multiple species, non-cubic cell, and
# close-by atoms.
a = 1
system = (Atoms(
symbols=["C", "C", "C"],
cell=[[0, a, a], [a, 0, a], [a, a, 0]],
scaled_positions=[
[0, 0, 0],
[1 / 3, 1 / 3, 1 / 3],
[2 / 3, 2 / 3, 2 / 3],
],
pbc=[True, True, True],
) * (3, 3, 3))
soap = SOAP(
species=[6],
rcut=3,
nmax=1,
lmax=1,
rbf="gto",
sparse=False,
average="off",
crossover=True,
periodic=False,
)
centers = [5, 3, 4]
include = [3, 0, 2]
# The typical full set: derivatives for all atoms, all atoms act as
# centers.
derivatives_n, d_n = soap.derivatives(system, method="numerical")
derivatives_a, d_a = soap.derivatives(system, method="analytical")
self.assertTrue(
np.allclose(derivatives_n, derivatives_a, rtol=1e-6, atol=1e-6))
self.assertTrue(np.allclose(d_n, d_a, rtol=1e-6, atol=1e-6))
# Derivatives for all atoms, only some atoms act as centers
derivatives_n, d_n = soap.derivatives(system,
positions=centers,
method="numerical")
derivatives_a, d_a = soap.derivatives(system,
positions=centers,
method="analytical")
self.assertTrue(
np.allclose(derivatives_n, derivatives_a, rtol=1e-6, atol=1e-6))
self.assertTrue(np.allclose(d_n, d_a, rtol=1e-6, atol=1e-6))
# Derivatives for some atoms, all atoms act as centers
derivatives_n, d_n = soap.derivatives(system,
include=include,
method="numerical")
derivatives_a, d_a = soap.derivatives(system,
include=include,
method="analytical")
self.assertTrue(
np.allclose(derivatives_n, derivatives_a, rtol=1e-6, atol=1e-6))
self.assertTrue(np.allclose(d_n, d_a, rtol=1e-6, atol=1e-6))
# Mixed set of derivatives and centers
derivatives_n, d_n = soap.derivatives(system,
positions=centers,
include=include,
method="numerical")
derivatives_a, d_a = soap.derivatives(system,
positions=centers,
include=include,
method="analytical")
self.assertTrue(
np.allclose(derivatives_n, derivatives_a, rtol=1e-6, atol=1e-6))
self.assertTrue(np.allclose(d_n, d_a, rtol=1e-6, atol=1e-6))
def test_exceptions(self):
"""Test the derivative interface."""
soap = SOAP(
species=[1, 8],
rcut=3,
nmax=2,
lmax=0,
sparse=False,
)
positions = [[0.0, 0.0, 0.0]]
# Test that trying to get analytical derivatives with averaged output
# raises an exception
soap.sparse = False
soap.average = "inner"
with self.assertRaises(ValueError):
soap.derivatives(H2, positions=positions, method="analytical")
soap.average = "off"
# Test that trying to get analytical derivatives with polynomial basis
# raises an exception, but the numerical ones work.
soap_poly = SOAP(
species=[1, 8],
rcut=3,
nmax=2,
lmax=0,
rbf="polynomial",
sparse=False,
)
with self.assertRaises(ValueError):
soap_poly.derivatives(H2, positions=positions, method="analytical")
soap_poly.derivatives(H2, positions=positions, method="numerical")
# Test that trying to provide both include and exclude raises an error
with self.assertRaises(ValueError):
soap.derivatives(H2, include=[0], exclude=[1])
# Test that trying to get derivatives with periodicicity on raises an
# exception
soap = SOAP(
species=[1, 8],
rcut=3,
nmax=2,
lmax=0,
rbf="gto",
sparse=False,
periodic=True,
)
with self.assertRaises(ValueError):
soap.derivatives(H2, positions=positions, method="analytical")
with self.assertRaises(ValueError):
soap.derivatives(H2, positions=positions, method="numerical")
def test_numerical(self):
"""Test numerical values against a naive python implementation."""
# Elaborate test system with multiple species, non-cubic cell, and
# close-by atoms.
a = 1
system = (Atoms(
symbols=["C", "H", "O"],
cell=[[0, a, a], [a, 0, a], [a, a, 0]],
scaled_positions=[
[0, 0, 0],
[1 / 3, 1 / 3, 1 / 3],
[2 / 3, 2 / 3, 2 / 3],
],
pbc=[True, True, True],
) * (3, 3, 3))
# view(system)
# Two centers: one in the middle, one on the edge.
centers = [np.sum(system.get_cell(), axis=0) / 2, [0, 0, 0]]
h = 0.0001
n_atoms = len(system)
n_comp = 3
# The maximum error depends on how big the system is. With a small
# system the error is smaller for non-periodic systems than the
# corresponding error when periodicity is turned on. The errors become
# equal (~1e-5) when the size of the system is increased.
for periodic in [False]:
for rbf in ["gto", "polynomial"]:
for average in ["off", "outer", "inner"]:
soap = SOAP(
species=[1, 8, 6],
rcut=3,
nmax=4,
lmax=4,
rbf=rbf,
sparse=False,
average=average,
crossover=True,
periodic=periodic,
dtype=
"float64", # The numerical derivatives require double precision
)
n_features = soap.get_number_of_features()
if average != "off":
n_centers = 1
derivatives_python = np.zeros(
(n_atoms, n_comp, n_features))
else:
n_centers = len(centers)
derivatives_python = np.zeros(
(n_centers, n_atoms, n_comp, n_features))
d0 = soap.create(system, centers)
coeffs = [-1.0 / 2.0, 1.0 / 2.0]
deltas = [-1.0, 1.0]
for i_atom in range(len(system)):
for i_center in range(n_centers):
for i_comp in range(3):
for i_stencil in range(2):
if average == "off":
i_cent = [centers[i_center]]
else:
i_cent = centers
system_disturbed = system.copy()
i_pos = system_disturbed.get_positions()
i_pos[i_atom,
i_comp] += h * deltas[i_stencil]
system_disturbed.set_positions(i_pos)
d1 = soap.create(system_disturbed, i_cent)
if average != "off":
derivatives_python[
i_atom,
i_comp, :] += (coeffs[i_stencil] *
d1 / h)
else:
derivatives_python[
i_center, i_atom,
i_comp, :] += (coeffs[i_stencil] *
d1[0, :] / h)
# Calculate with central finite difference implemented in C++.
# Try both cartesian centers and indices.
for c in [centers]:
derivatives_cpp, d_cpp = soap.derivatives(
system, positions=c, method="numerical")
# Test that descriptor values are correct
self.assertTrue(np.allclose(d0, d_cpp, atol=1e-6))
# Compare values
# print(np.abs(derivatives_python).max())
# print(derivatives_python[0,1,:,:])
# print(derivatives_cpp[0,0,:,:])
self.assertTrue(
np.allclose(derivatives_python,
derivatives_cpp,
atol=2e-5))
def test_parallel(self):
"""Tests parallel output validity for both dense and sparse output."""
for sparse in [False, True]:
desc = SOAP(
species=[1, 6, 7, 8],
rcut=5,
nmax=3,
lmax=3,
sigma=1,
periodic=False,
crossover=True,
average="off",
sparse=sparse,
)
n_features = desc.get_number_of_features()
samples = [molecule("CO"), molecule("NO"), molecule("OH")]
centers = [[0], [0], [0]]
# Determining number of jobs based on the amount of CPUs
# desc.derivatives(system=samples, n_jobs=-1, only_physical_cores=False)
# desc.derivatives(system=samples, n_jobs=-1, only_physical_cores=True)
# Perhaps most common scenario: more systems than jobs, using all
# centers and indices
der, des = desc.derivatives(
system=samples,
n_jobs=2,
)
self.assertTrue(der.shape == (3, 2, 2, 3, n_features))
self.assertTrue(des.shape == (3, 2, n_features))
assumed_der = np.empty((3, 2, 2, 3, n_features))
assumed_des = np.empty((3, 2, n_features))
desc.sparse = False
assumed_der[0, :], assumed_des[0, :] = desc.derivatives(samples[0],
n_jobs=1)
assumed_der[1, :], assumed_des[1, :] = desc.derivatives(samples[1],
n_jobs=1)
assumed_der[2, :], assumed_des[2, :] = desc.derivatives(samples[2],
n_jobs=1)
desc._sparse = sparse
if sparse:
der = der.todense()
des = des.todense()
self.assertTrue(np.allclose(assumed_der, der))
self.assertTrue(np.allclose(assumed_des, des))
# More systems than jobs, using all centers and indices, not requesting
# descriptors
der = desc.derivatives(
system=samples,
return_descriptor=False,
n_jobs=2,
)
self.assertTrue(der.shape == (3, 2, 2, 3, n_features))
assumed_der = np.empty((3, 2, 2, 3, n_features))
desc._sparse = False
assumed_der[0, :] = desc.derivatives(samples[0],
n_jobs=1,
return_descriptor=False)
assumed_der[1, :] = desc.derivatives(samples[1],
n_jobs=1,
return_descriptor=False)
assumed_der[2, :] = desc.derivatives(samples[2],
n_jobs=1,
return_descriptor=False)
desc._sparse = sparse
if sparse:
der = der.todense()
self.assertTrue(np.allclose(assumed_der, der))
# More systems than jobs, using custom indices as centers
der, des = desc.derivatives(
system=samples,
positions=centers,
n_jobs=2,
)
self.assertTrue(der.shape == (3, 1, 2, 3, n_features))
self.assertTrue(des.shape == (3, 1, n_features))
assumed_der = np.empty((3, 1, 2, 3, n_features))
assumed_des = np.empty((3, 1, n_features))
desc._sparse = False
assumed_der[0, :], assumed_des[0, :] = desc.derivatives(samples[0],
centers[0],
n_jobs=1)
assumed_der[1, :], assumed_des[1, :] = desc.derivatives(samples[1],
centers[1],
n_jobs=1)
assumed_der[2, :], assumed_des[2, :] = desc.derivatives(samples[2],
centers[2],
n_jobs=1)
desc._sparse = sparse
if sparse:
der = der.todense()
des = des.todense()
self.assertTrue(np.allclose(assumed_der, der))
self.assertTrue(np.allclose(assumed_des, des))
# More systems than jobs, using custom cartesian centers
centers = [[[0, 1, 2]], [[2, 1, 0]], [[1, 2, 0]]]
der, des = desc.derivatives(
system=samples,
positions=centers,
n_jobs=2,
)
self.assertTrue(der.shape == (3, 1, 2, 3, n_features))
self.assertTrue(des.shape == (3, 1, n_features))
assumed_der = np.empty((3, 1, 2, 3, n_features))
assumed_des = np.empty((3, 1, n_features))
desc._sparse = False
assumed_der[0, :], assumed_des[0, :] = desc.derivatives(samples[0],
centers[0],
n_jobs=1)
assumed_der[1, :], assumed_des[1, :] = desc.derivatives(samples[1],
centers[1],
n_jobs=1)
assumed_der[2, :], assumed_des[2, :] = desc.derivatives(samples[2],
centers[2],
n_jobs=1)
desc._sparse = sparse
if sparse:
der = der.todense()
des = des.todense()
self.assertTrue(np.allclose(assumed_der, der))
self.assertTrue(np.allclose(assumed_des, des))
# Includes
includes = [[0], [0], [0]]
der, des = desc.derivatives(
system=samples,
include=includes,
n_jobs=2,
)
self.assertTrue(der.shape == (3, 2, 1, 3, n_features))
self.assertTrue(des.shape == (3, 2, n_features))
assumed_der = np.empty((3, 2, 1, 3, n_features))
assumed_des = np.empty((3, 2, n_features))
desc._sparse = False
assumed_der[0, :], assumed_des[0, :] = desc.derivatives(
samples[0], include=includes[0], n_jobs=1)
assumed_der[1, :], assumed_des[1, :] = desc.derivatives(
samples[1], include=includes[1], n_jobs=1)
assumed_der[2, :], assumed_des[2, :] = desc.derivatives(
samples[2], include=includes[2], n_jobs=1)
desc._sparse = sparse
if sparse:
der = der.todense()
des = des.todense()
self.assertTrue(np.allclose(assumed_der, der))
self.assertTrue(np.allclose(assumed_des, des))
# Excludes
excludes = [[0], [0], [0]]
der, des = desc.derivatives(
system=samples,
exclude=excludes,
n_jobs=2,
)
self.assertTrue(der.shape == (3, 2, 1, 3, n_features))
self.assertTrue(des.shape == (3, 2, n_features))
assumed_der = np.empty((3, 2, 1, 3, n_features))
assumed_des = np.empty((3, 2, n_features))
desc._sparse = False
assumed_der[0, :], assumed_des[0, :] = desc.derivatives(
samples[0], exclude=excludes[0], n_jobs=1)
assumed_der[1, :], assumed_des[1, :] = desc.derivatives(
samples[1], exclude=excludes[1], n_jobs=1)
assumed_der[2, :], assumed_des[2, :] = desc.derivatives(
samples[2], exclude=excludes[2], n_jobs=1)
desc._sparse = sparse
if sparse:
der = der.todense()
des = des.todense()
self.assertTrue(np.allclose(assumed_der, der))
self.assertTrue(np.allclose(assumed_des, des))
# Test averaged output
desc.average = "inner"
positions = [[0], [0, 1], [1]]
der, des = desc.derivatives(
system=samples,
positions=positions,
n_jobs=2,
)
self.assertTrue(der.shape == (3, 1, 2, 3, n_features))
self.assertTrue(des.shape == (3, 1, n_features))
desc._sparse = False
assumed_der = np.empty((3, 1, 2, 3, n_features))
assumed_des = np.empty((3, 1, n_features))
assumed_der[0, :], assumed_des[0, :] = desc.derivatives(
samples[0], positions=positions[0], n_jobs=1)
assumed_der[1, :], assumed_des[1, :] = desc.derivatives(
samples[1], positions=positions[1], n_jobs=1)
assumed_der[2, :], assumed_des[2, :] = desc.derivatives(
samples[2], positions=positions[2], n_jobs=1)
desc._sparse = sparse
if sparse:
der = der.todense()
des = des.todense()
self.assertTrue(np.allclose(assumed_der, der))
self.assertTrue(np.allclose(assumed_des, des))
# Variable size list output, as the systems have a different size
desc.average = "off"
samples = [molecule("CO"), molecule("NO2"), molecule("OH")]
der, des = desc.derivatives(
system=samples,
n_jobs=2,
)
self.assertTrue(isinstance(der, list))
self.assertTrue(der[0].shape == (2, 2, 3, n_features))
self.assertTrue(der[1].shape == (3, 3, 3, n_features))
self.assertTrue(der[2].shape == (2, 2, 3, n_features))
desc._sparse = False
for i in range(len(samples)):
assumed_der, assumed_des = desc.derivatives(samples[i],
n_jobs=1)
i_der = der[i]
i_des = des[i]
if sparse:
i_der = i_der.todense()
i_des = i_des.todense()
self.assertTrue(np.allclose(assumed_der, i_der))
self.assertTrue(np.allclose(assumed_des, i_des))
desc._sparse = sparse
energies = np.zeros(n_samples)
forces = np.zeros((n_samples, n_atoms, 3))
r = np.linspace(2.5, 5.0, n_samples)
for i, d in enumerate(r):
a = ase.Atoms('HH', positions=[[-0.5 * d, 0, 0], [0.5 * d, 0, 0]])
a.set_calculator(LennardJones(epsilon=1.0, sigma=2.9))
traj.append(a)
energies[i] = a.get_total_energy()
forces[i, :, :] = a.get_forces()
# Plot the energies to validate them
fig, ax = plt.subplots(figsize=(8, 5))
plt.subplots_adjust(left=0.1, right=0.95, top=0.95, bottom=0.1)
line, = ax.plot(r, energies)
plt.xlabel("Distance (Å)")
plt.ylabel("Energy (eV)")
plt.show()
# Create the SOAP desciptors and their derivatives for all samples. One center
# is chosen to be directly between the atoms.
derivatives, descriptors = soap.derivatives(traj,
positions=[[[0, 0, 0]]] * len(r),
method="analytical")
# Save to disk for later training
np.save("r.npy", r)
np.save("E.npy", energies)
np.save("D.npy", descriptors)
np.save("dD_dr.npy", derivatives)
np.save("F.npy", forces)