# -*- coding: utf-8 -*-
"""Copyright 2019 DScribe developers
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
"""
import time
import numpy as np
from scipy.special import gamma
from scipy.linalg import sqrtm, inv
from ase import Atoms
import ase.geometry.cell
import ase.data
import sparse as sp
from dscribe.descriptors import Descriptor
from dscribe.core import System
from dscribe.utils.dimensionality import is1d
import dscribe.ext
[docs]class SOAP(Descriptor):
"""Class for generating a partial power spectrum from Smooth Overlap of
Atomic Orbitals (SOAP). This implementation uses real (tesseral) spherical
harmonics as the angular basis set and provides two orthonormalized
alternatives for the radial basis functions: spherical primitive gaussian
type orbitals ("gto") or the polynomial basis set ("polynomial").
For reference, see:
"On representing chemical environments, Albert P. Bartók, Risi Kondor, and
Gábor Csányi, Phys. Rev. B 87, 184115, (2013),
https://doi.org/10.1103/PhysRevB.87.184115
"Comparing molecules and solids across structural and alchemical space",
Sandip De, Albert P. Bartók, Gábor Csányi and Michele Ceriotti, Phys.
Chem. Chem. Phys. 18, 13754 (2016), https://doi.org/10.1039/c6cp00415f
"Machine learning hydrogen adsorption on nanoclusters through structural
descriptors", Marc O. J. Jäger, Eiaki V. Morooka, Filippo Federici Canova,
Lauri Himanen & Adam S. Foster, npj Comput. Mater., 4, 37 (2018),
https://doi.org/10.1038/s41524-018-0096-5
"""
[docs] def __init__(
self,
rcut,
nmax,
lmax,
sigma=1.0,
rbf="gto",
species=None,
periodic=False,
crossover=True,
average="off",
sparse=False,
dtype="float32",
):
"""
Args:
rcut (float): A cutoff for local region in angstroms. Should be
bigger than 1 angstrom.
nmax (int): The number of radial basis functions.
lmax (int): The maximum degree of spherical harmonics.
species (iterable): The chemical species as a list of atomic
numbers or as a list of chemical symbols. Notice that this is not
the atomic numbers that are present for an individual system, but
should contain all the elements that are ever going to be
encountered when creating the descriptors for a set of systems.
Keeping the number of chemical species as low as possible is
preferable.
sigma (float): The standard deviation of the gaussians used to expand the
atomic density.
rbf (str): The radial basis functions to use. The available options are:
* "gto": Spherical gaussian type orbitals defined as :math:`g_{nl}(r) = \sum_{n'=1}^{n_\mathrm{max}}\,\\beta_{nn'l} r^l e^{-\\alpha_{n'l}r^2}`
* "polynomial": Polynomial basis defined as :math:`g_{n}(r) = \sum_{n'=1}^{n_\mathrm{max}}\,\\beta_{nn'} (r-r_\mathrm{cut})^{n'+2}`
periodic (bool): Set to true if you want the descriptor output to
respect the periodicity of the atomic systems (see the
pbc-parameter in the constructor of ase.Atoms).
crossover (bool): Determines if crossover of atomic types should
be included in the power spectrum. If enabled, the power
spectrum is calculated over all unique species combinations Z
and Z'. If disabled, the power spectrum does not contain
cross-species information and is only run over each unique
species Z. Turned on by default to correspond to the original
definition
average (str): The averaging mode over the centers of interest.
Valid options are:
* "off": No averaging.
* "inner": Averaging over sites before summing up the magnetic quantum numbers: :math:`p_{nn'l}^{Z_1,Z_2} \sim \sum_m (\\frac{1}{n} \sum_i c_{nlm}^{i, Z_1})^{*} (\\frac{1}{n} \sum_i c_{n'lm}^{i, Z_2})`
* "outer": Averaging over the power spectrum of different sites: :math:`p_{nn'l}^{Z_1,Z_2} \sim \\frac{1}{n} \sum_i \sum_m (c_{nlm}^{i, Z_1})^{*} (c_{n'lm}^{i, Z_2})`
sparse (bool): Whether the output should be a sparse matrix or a
dense numpy array.
dtype (string): The data type of the output. Valid options are:
* "float32": Single precision floating point numbers.
* "float64": Double precision floating point numbers.
"""
supported_dtype = set(("float32", "float64"))
if dtype not in supported_dtype:
raise ValueError(
"Invalid output data type '{}' given. Please use "
"one of the following: {}".format(dtype, supported_dtype)
)
super().__init__(periodic=periodic, flatten=True, sparse=sparse, dtype=dtype)
# Setup the involved chemical species
self.species = species
# Test that general settings are valid
if sigma <= 0:
raise ValueError(
"Only positive gaussian width parameters 'sigma' are allowed."
)
self._eta = 1 / (2 * sigma ** 2)
self._sigma = sigma
if lmax < 0:
raise ValueError("lmax cannot be negative. lmax={}".format(lmax))
supported_rbf = set(("gto", "polynomial"))
if rbf not in supported_rbf:
raise ValueError(
"Invalid radial basis function of type '{}' given. Please use "
"one of the following: {}".format(rbf, supported_rbf)
)
if nmax < 1:
raise ValueError(
"Must have at least one radial basis function." "nmax={}".format(nmax)
)
supported_average = set(("off", "inner", "outer"))
if average not in supported_average:
raise ValueError(
"Invalid average mode '{}' given. Please use "
"one of the following: {}".format(average, supported_average)
)
# Test that radial basis set specific settings are valid
if rbf == "gto":
if rcut <= 1:
raise ValueError(
"When using the gaussian radial basis set (gto), the radial "
"cutoff should be bigger than 1 angstrom."
)
if lmax > 9:
raise ValueError(
"When using the gaussian radial basis set (gto), lmax "
"cannot currently exceed 9. lmax={}".format(lmax)
)
# Precalculate the alpha and beta constants for the GTO basis
self._alphas, self._betas = self.get_basis_gto(rcut, nmax)
elif rbf == "polynomial":
if lmax > 20:
raise ValueError(
"When using the polynomial radial basis set, lmax "
"cannot currently exceed 20. lmax={}".format(lmax)
)
self._rcut = rcut
self._nmax = nmax
self._lmax = lmax
self._rbf = rbf
self.average = average
self.crossover = crossover
[docs] def prepare_centers(self, system, cutoff_padding, positions=None):
"""Validates and prepares the centers for the C++ extension."""
# Transform the input system into the internal System-object
system = self.get_system(system)
# Check that the system does not have elements that are not in the list
# of atomic numbers
self.check_atomic_numbers(system.get_atomic_numbers())
# Check if periodic is valid
if self.periodic:
cell = system.get_cell()
if np.cross(cell[0], cell[1]).dot(cell[2]) == 0:
raise ValueError("System doesn't have cell to justify periodicity.")
# Setup the local positions
if positions is None:
list_positions = system.get_positions()
indices = np.arange(len(system))
else:
# Check validity of position definitions and create final cartesian
# position list
error = ValueError(
"The argument 'positions' should contain a non-empty "
"one-dimensional list of"
" atomic indices or a two-dimensional "
"list of cartesian coordinates with x, y and z components."
)
if (
not isinstance(positions, (list, tuple, np.ndarray))
or len(positions) == 0
):
raise error
list_positions = []
indices = np.full(len(positions), -1, dtype=np.int)
for idx, i in enumerate(positions):
if np.issubdtype(type(i), np.integer):
list_positions.append(system.get_positions()[i])
indices[idx] = i
elif isinstance(i, (list, tuple, np.ndarray)):
if len(i) != 3:
raise error
list_positions.append(i)
else:
raise error
return np.asarray(list_positions), indices
[docs] def get_cutoff_padding(self):
"""The radial cutoff is extended by adding a padding that depends on
the used used sigma value. The padding is chosen so that the gaussians
decay to the specified threshold value at the cutoff distance.
"""
threshold = 0.001
cutoff_padding = self._sigma * np.sqrt(-2 * np.log(threshold))
return cutoff_padding
[docs] def init_descriptor_array(self, n_centers, n_features):
"""Return a zero-initialized numpy array for the descriptor."""
if self.average == "inner" or self.average == "outer":
c = np.zeros((1, n_features), dtype=np.float64)
else:
c = np.zeros((n_centers, n_features), dtype=np.float64)
return c
[docs] def init_derivatives_array(self, n_centers, n_atoms, n_features):
"""Return a zero-initialized numpy array for the derivatives."""
if self.average == "inner" or self.average == "outer":
return np.zeros((1, n_atoms, 3, n_features), dtype=np.float64)
else:
return np.zeros((n_centers, n_atoms, 3, n_features), dtype=np.float64)
[docs] def init_internal_dev_array(self, n_centers, n_atoms, n_types, n, lMax):
d = np.zeros(
(n_atoms, n_centers, n_types, n, (lMax + 1) * (lMax + 1)), dtype=np.float64
)
return d
[docs] def init_internal_array(self, n_centers, n_types, n, lMax):
d = np.zeros((n_centers, n_types, n, (lMax + 1) * (lMax + 1)), dtype=np.float64)
return d
[docs] def create(
self, system, positions=None, n_jobs=1, only_physical_cores=False, verbose=False
):
"""Return the SOAP output for the given systems and given positions.
Args:
system (:class:`ase.Atoms` or list of :class:`ase.Atoms`): One or
many atomic structures.
positions (list): Positions where to calculate SOAP. Can be
provided as cartesian positions or atomic indices. If no
positions are defined, the SOAP output will be created for all
atoms in the system. When calculating SOAP for multiple
systems, provide the positions as a list for each system.
n_jobs (int): Number of parallel jobs to instantiate. Parallellizes
the calculation across samples. Defaults to serial calculation
with n_jobs=1. If a negative number is given, the used cpus
will be calculated with, n_cpus + n_jobs, where n_cpus is the
amount of CPUs as reported by the OS. With only_physical_cores
you can control which types of CPUs are counted in n_cpus.
only_physical_cores (bool): If a negative n_jobs is given,
determines which types of CPUs are used in calculating the
number of jobs. If set to False (default), also virtual CPUs
are counted. If set to True, only physical CPUs are counted.
verbose(bool): Controls whether to print the progress of each job
into to the console.
Returns:
np.ndarray | sparse.COO: The SOAP output for the given systems and
positions. The return type depends on the 'sparse'-attribute. The
first dimension is determined by the amount of positions and
systems and the second dimension is determined by the
get_number_of_features()-function. When multiple systems are
provided the results are ordered by the input order of systems and
their positions.
"""
# If single system given, skip the parallelization
if isinstance(system, (Atoms, System)):
return self.create_single(system, positions)
else:
self._check_system_list(system)
# Combine input arguments
n_samples = len(system)
if positions is None:
inp = [(i_sys,) for i_sys in system]
else:
n_pos = len(positions)
if n_pos != n_samples:
raise ValueError(
"The given number of positions does not match the given"
"number of systems."
)
inp = list(zip(system, positions))
# Determine if the outputs have a fixed size
n_features = self.get_number_of_features()
static_size = None
if self.average == "outer" or self.average == "inner":
static_size = [n_features]
else:
if positions is None:
n_centers = len(inp[0][0])
else:
first_sample, first_pos = inp[0]
if first_pos is not None:
n_centers = len(first_pos)
else:
n_centers = len(first_sample)
def is_static():
for i_job in inp:
if positions is None:
if len(i_job[0]) != n_centers:
return False
else:
if i_job[1] is not None:
if len(i_job[1]) != n_centers:
return False
else:
if len(i_job[0]) != n_centers:
return False
return True
if is_static():
static_size = [n_centers, n_features]
# Create in parallel
output = self.create_parallel(
inp,
self.create_single,
n_jobs,
static_size,
only_physical_cores,
verbose=verbose,
)
return output
[docs] def create_single(self, system, positions=None):
"""Return the SOAP output for the given system and given positions.
Args:
system (:class:`ase.Atoms` | :class:`.System`): Input system.
positions (list): Cartesian positions or atomic indices. If
specified, the SOAP spectrum will be created for these points.
If no positions are defined, the SOAP output will be created
for all atoms in the system.
Returns:
np.ndarray | sparse.COO: The SOAP output for the
given system and positions. The return type depends on the
'sparse'-attribute. The first dimension is given by the number of
positions and the second dimension is determined by the
get_number_of_features()-function.
"""
cutoff_padding = self.get_cutoff_padding()
centers, _ = self.prepare_centers(system, cutoff_padding, positions)
n_centers = centers.shape[0]
n_species = self._atomic_numbers.shape[0]
pos = system.get_positions()
Z = system.get_atomic_numbers()
n_features = self.get_number_of_features()
n_atoms = Z.shape[0]
soap_mat = self.init_descriptor_array(n_centers, n_features)
# Determine the function to call based on rbf
if self._rbf == "gto":
# Orthonormalized RBF coefficients
alphas = self._alphas.flatten()
betas = self._betas.flatten()
# Determine shape
n_features = self.get_number_of_features()
soap_mat = self.init_descriptor_array(n_centers, n_features)
# Calculate with extension
soap_gto = dscribe.ext.SOAPGTO(
self._rcut,
self._nmax,
self._lmax,
self._eta,
self._atomic_numbers,
self.periodic,
self.crossover,
self.average,
cutoff_padding,
alphas,
betas,
)
soap_gto.create(
soap_mat,
pos,
Z,
ase.geometry.cell.complete_cell(system.get_cell()),
np.asarray(system.get_pbc(), dtype=bool),
centers,
)
elif self._rbf == "polynomial":
# Get the discretized and orthogonalized polynomial radial basis
# function values
rx, gss = self.get_basis_poly(self._rcut, self._nmax)
gss = gss.flatten()
# Calculate with extension
soap_poly = dscribe.ext.SOAPPolynomial(
self._rcut,
self._nmax,
self._lmax,
self._eta,
self._atomic_numbers,
self.periodic,
self.crossover,
self.average,
cutoff_padding,
rx,
gss,
)
soap_poly.create(
soap_mat,
pos,
Z,
ase.geometry.cell.complete_cell(system.get_cell()),
np.asarray(system.get_pbc(), dtype=bool),
centers,
)
# Averaged output is a global descriptor, and thus the first dimension
# is squeezed out to keep the output size consistent with the size of
# other global descriptors.
if self.average != "off":
soap_mat = np.squeeze(soap_mat, axis=0)
# Convert to the final output precision.
if self.dtype == "float32":
soap_mat = soap_mat.astype(self.dtype)
# Make into a sparse array if requested
if self._sparse:
soap_mat = sp.COO.from_numpy(soap_mat)
return soap_mat
def _cartesian(self, system, positions=None):
"""Internal test function."""
cutoff_padding = self.get_cutoff_padding()
centers, center_indices = self.prepare_centers(
system, cutoff_padding, positions
)
n_centers = centers.shape[0]
n_species = self._atomic_numbers.shape[0]
pos = system.get_positions()
Z = system.get_atomic_numbers()
n_features = self.get_number_of_features()
n_atoms = Z.shape[0]
soap_mat = self.init_descriptor_array(n_centers, n_features)
# Determine the function to call based on rbf
if self._rbf == "gto":
# Orthonormalized RBF coefficients
alphas = self._alphas.flatten()
betas = self._betas.flatten()
# Determine shape
n_features = self.get_number_of_features()
soap_mat = self.init_descriptor_array(n_centers, n_features)
# Calculate with extension
soap_gto = dscribe.ext.SOAPGTO(
self._rcut,
self._nmax,
self._lmax,
self._eta,
self._atomic_numbers,
self.periodic,
self.crossover,
self.average,
cutoff_padding,
alphas,
betas,
)
# Calculate analytically with extension
xd = np.empty((1, 1, 1, 1, 1))
yd = np.empty((1, 1, 1, 1, 1))
zd = np.empty((1, 1, 1, 1, 1))
cd = self.init_internal_array(n_centers, n_species, self._nmax, self._lmax)
d = np.empty((1, 1, 1, 1))
soap_gto.create_cartesian(
d,
soap_mat,
xd,
yd,
zd,
cd,
pos,
Z,
ase.geometry.cell.complete_cell(system.get_cell()),
np.asarray(system.get_pbc(), dtype=bool),
centers,
center_indices,
[],
True,
)
# Convert to the final output precision.
if self.dtype == "float32":
soap_mat = soap_mat.astype(self.dtype)
# Make into a sparse array if requested
if self.sparse:
soap_mat = coo_matrix(soap_mat)
return soap_mat
[docs] def derivatives(
self,
system,
positions=None,
include=None,
exclude=None,
method="auto",
return_descriptor=True,
n_jobs=1,
only_physical_cores=False,
verbose=False,
):
"""Return the descriptor derivatives for the given systems and given positions.
Args:
system (:class:`ase.Atoms` or list of :class:`ase.Atoms`): One or
many atomic structures.
positions (list): Positions where to calculate the descriptor. Can be
provided as cartesian positions or atomic indices. If no
positions are defined, the descriptor output will be created for all
atoms in the system. When calculating descriptor for multiple
systems, provide the positions as a list for each system.
include (list): Indices of atoms to compute the derivatives on.
When calculating descriptor for multiple systems, provide
either a one-dimensional list that if applied to all systems or
a two-dimensional list of indices. Cannot be provided together
with 'exclude'.
exclude (list): Indices of atoms not to compute the derivatives on.
When calculating descriptor for multiple systems, provide
either a one-dimensional list that if applied to all systems or
a two-dimensional list of indices. Cannot be provided together
with 'include'.
method (str): The method for calculating the derivatives. Provide
either 'numerical', 'analytical' or 'auto'. If using 'auto',
the most efficient available method is automatically chosen.
return_descriptor (bool): Whether to also calculate the descriptor
in the same function call. Notice that it typically is faster
to calculate both in one go.
n_jobs (int): Number of parallel jobs to instantiate. Parallellizes
the calculation across samples. Defaults to serial calculation
with n_jobs=1. If a negative number is given, the number of jobs
will be calculated with, n_cpus + n_jobs, where n_cpus is the
amount of CPUs as reported by the OS. With only_physical_cores
you can control which types of CPUs are counted in n_cpus.
only_physical_cores (bool): If a negative n_jobs is given,
determines which types of CPUs are used in calculating the
number of jobs. If set to False (default), also virtual CPUs
are counted. If set to True, only physical CPUs are counted.
verbose(bool): Controls whether to print the progress of each job
into to the console.
Returns:
If return_descriptor is True, returns a tuple, where the first item
is the derivative array and the second is the descriptor array.
Otherwise only returns the derivatives array. The derivatives array
is a either a 4D or 5D array, depending on whether you have
provided a single or multiple systems. If the output shape for each
system is the same, a single monolithic numpy array is returned.
For variable sized output (e.g. differently sized systems,
different number of centers or different number of included atoms),
a regular python list is returned. The dimensions are:
[(n_systems,) n_positions, n_atoms, 3, n_features]. The first
dimension goes over the different systems in case multiple were
given. The second dimension goes over the descriptor centers in
the same order as they were given in the argument. The third
dimension goes over the included atoms. The order is same as the
order of atoms in the given system. The fourth dimension goes over
the cartesian components, x, y and z. The fifth dimension goes over
the features in the default order.
"""
methods = {"numerical", "analytical", "auto"}
if method not in methods:
raise ValueError(
"Invalid method specified. Please choose from: {}".format(methods)
)
if self.average != "off" and method == "analytical":
raise ValueError(
"Analytical derivatives not currently available for averaged output."
)
if self.periodic:
raise ValueError(
"Derivatives are currently not available for periodic systems."
)
if self._rbf == "polynomial" and method == "analytical":
raise ValueError(
"Analytical derivatives not currently available for polynomial "
"radial basis set."
)
# Determine the appropriate method if not given explicitly.
if method == "auto":
if self._rbf == "polynomial" or self.average != "off":
method = "numerical"
else:
method = "analytical"
# If single system given, skip the parallelization
if isinstance(system, (Atoms, System)):
n_atoms = len(system)
indices = self._get_indices(n_atoms, include, exclude)
return self.derivatives_single(
system,
positions,
indices,
method=method,
return_descriptor=return_descriptor,
)
# Check input validity
self._check_system_list(system)
n_samples = len(system)
if positions is None:
positions = [None] * n_samples
if include is None:
include = [None] * n_samples
elif is1d(include, np.integer):
include = [include] * n_samples
if exclude is None:
exclude = [None] * n_samples
elif is1d(exclude, np.integer):
exclude = [exclude] * n_samples
n_pos = len(positions)
if n_pos != n_samples:
raise ValueError(
"The given number of positions does not match the given "
"number of systems."
)
n_inc = len(include)
if n_inc != n_samples:
raise ValueError(
"The given number of includes does not match the given "
"number of systems."
)
n_exc = len(exclude)
if n_exc != n_samples:
raise ValueError(
"The given number of excludes does not match the given "
"number of systems."
)
# Determine the atom indices that are displaced
indices = []
for sys, inc, exc in zip(system, include, exclude):
n_atoms = len(sys)
indices.append(self._get_indices(n_atoms, inc, exc))
# Combine input arguments
inp = list(
zip(
system,
positions,
indices,
[method] * n_samples,
[return_descriptor] * n_samples,
)
)
# For the descriptor, the output size for each job depends on the exact arguments.
# Here we precalculate the size for each job to preallocate memory and
# make the process faster.
n_features = self.get_number_of_features()
def get_shapes(job):
centers = job[1]
if centers is None:
n_positions = len(job[0])
else:
n_positions = 1 if self.average != "off" else len(centers)
n_indices = len(job[2])
return (n_positions, n_indices, 3, n_features), (n_positions, n_features)
derivatives_shape, descriptor_shape = get_shapes(inp[0])
def is_variable(inp):
for job in inp[1:]:
i_der_shape, i_desc_shape = get_shapes(job)
if i_der_shape != derivatives_shape or i_desc_shape != descriptor_shape:
return True
return False
if is_variable(inp):
derivatives_shape = None
descriptor_shape = None
# Create in parallel
output = self.derivatives_parallel(
inp,
self.derivatives_single,
n_jobs,
derivatives_shape,
descriptor_shape,
return_descriptor,
only_physical_cores,
verbose=verbose,
)
return output
[docs] def derivatives_single(
self, system, positions, indices, method="numerical", return_descriptor=True
):
"""Return the SOAP output for the given system and given positions.
Args:
system (:class:`ase.Atoms`): Atomic structure.
positions (list): Positions where to calculate SOAP. Can be
provided as cartesian positions or atomic indices. If no
positions are defined, the SOAP output will be created for all
atoms in the system. When calculating SOAP for multiple
systems, provide the positions as a list for each system.
indices (list): Indices of atoms for which the derivatives will be
computed for.
method (str): 'numerical' or 'analytical' derivatives. Numerical
derivatives are implemented with central finite difference. If
not specified, analytical derivatives are used when available.
return_descriptor (bool): Whether to also calculate the descriptor
in the same function call. This is true by default as it
typically is faster to calculate both in one go.
Returns:
If return_descriptor is True, returns a tuple, where the first item
is the derivative array and the second is the descriptor array.
Otherwise only returns the derivatives array. The derivatives array
is a 4D numpy array. The dimensions are: [n_positions, n_atoms, 3,
n_features]. The first dimension goes over the SOAP centers in the
same order as they were given in the argument. The second dimension
goes over the included atoms. The order is same as the order of
atoms in the given system. The third dimension goes over the
cartesian components, x, y and z. The last dimension goes over the
features in the default order.
"""
cutoff_padding = self.get_cutoff_padding()
centers, center_indices = self.prepare_centers(
system, cutoff_padding, positions
)
pos = system.get_positions()
Z = system.get_atomic_numbers()
sorted_species = self._atomic_numbers
n_species = len(sorted_species)
n_centers = centers.shape[0]
n_indices = len(indices)
n_atoms = len(system)
n_features = self.get_number_of_features()
if return_descriptor:
c = self.init_descriptor_array(n_centers, n_features)
else:
c = np.empty(0)
d = self.init_derivatives_array(n_centers, n_indices, n_features)
if self._rbf == "gto":
alphas = self._alphas.flatten()
betas = self._betas.flatten()
soap_gto = dscribe.ext.SOAPGTO(
self._rcut,
self._nmax,
self._lmax,
self._eta,
self._atomic_numbers,
self.periodic,
self.crossover,
self.average,
cutoff_padding,
alphas,
betas,
)
# Calculate numerically with extension
if method == "numerical":
soap_gto.derivatives_numerical(
d,
c,
pos,
Z,
ase.geometry.cell.complete_cell(system.get_cell()),
np.asarray(system.get_pbc(), dtype=bool),
centers,
center_indices,
indices,
return_descriptor,
)
# Calculate analytically with extension
elif method == "analytical":
# These arrays are only used internally by the C++ code.
# Allocating them here with python is much faster than
# allocating similarly sized arrays within C++. It seems
# that numpy does some kind of lazy allocation that is
# highly efficient for zero-initialized arrays. Similar
# performace could not be achieved even with calloc.
cd = self.init_internal_array(
n_centers, n_species, self._nmax, self._lmax
)
xd = self.init_internal_dev_array(
n_centers, n_atoms, n_species, self._nmax, self._lmax
)
yd = self.init_internal_dev_array(
n_centers, n_atoms, n_species, self._nmax, self._lmax
)
zd = self.init_internal_dev_array(
n_centers, n_atoms, n_species, self._nmax, self._lmax
)
soap_gto.derivatives_analytical(
d,
c,
xd,
yd,
zd,
cd,
pos,
Z,
ase.geometry.cell.complete_cell(system.get_cell()),
np.asarray(system.get_pbc(), dtype=bool),
centers,
center_indices,
indices,
return_descriptor,
)
elif self._rbf == "polynomial":
rx, gss = self.get_basis_poly(self._rcut, self._nmax)
gss = gss.flatten()
# Calculate numerically with extension
if method == "numerical":
soap_poly = dscribe.ext.SOAPPolynomial(
self._rcut,
self._nmax,
self._lmax,
self._eta,
self._atomic_numbers,
self.periodic,
self.crossover,
self.average,
cutoff_padding,
rx,
gss,
)
soap_poly.derivatives_numerical(
d,
c,
pos,
Z,
ase.geometry.cell.complete_cell(system.get_cell()),
np.asarray(system.get_pbc(), dtype=bool),
centers,
center_indices,
indices,
return_descriptor,
)
# Convert to the final output precision.
if self.dtype == "float32":
d = d.astype(self.dtype)
c = c.astype(self.dtype)
# Convert to sparse here. Currently everything up to this point is
# calculated with dense matrices. This imposes some memory limitations.
if self.sparse:
d = sp.COO.from_numpy(d)
c = sp.COO.from_numpy(c)
if return_descriptor:
return (d, c)
return d
@property
def species(self):
return self._species
@species.setter
def species(self, value):
"""Used to check the validity of given atomic numbers and to initialize
the C-memory layout for them.
Args:
value(iterable): Chemical species either as a list of atomic
numbers or list of chemical symbols.
"""
# The species are stored as atomic numbers for internal use.
self._set_species(value)
# Setup mappings between atom indices and types
self.atomic_number_to_index = {}
self.index_to_atomic_number = {}
for i_atom, atomic_number in enumerate(self._atomic_numbers):
self.atomic_number_to_index[atomic_number] = i_atom
self.index_to_atomic_number[i_atom] = atomic_number
self.n_elements = len(self._atomic_numbers)
[docs] def get_number_of_features(self):
"""Used to inquire the final number of features that this descriptor
will have.
Returns:
int: Number of features for this descriptor.
"""
n_elem = len(self._atomic_numbers)
if self.crossover:
n_elem_radial = n_elem * self._nmax
return int((n_elem_radial) * (n_elem_radial + 1) / 2 * (self._lmax + 1))
else:
return int(n_elem * self._nmax * (self._nmax + 1) / 2 * (self._lmax + 1))
[docs] def get_location(self, species):
"""Can be used to query the location of a species combination in the
the flattened output.
Args:
species(tuple): A tuple containing a pair of species as chemical
symbols or atomic numbers. The tuple can be for example ("H", "O").
Returns:
slice: slice containing the location of the specified species
combination. The location is given as a python slice-object, that
can be directly used to target ranges in the output.
Raises:
ValueError: If the requested species combination is not in the
output or if invalid species defined.
"""
# Check that the corresponding part is calculated
if len(species) != 2:
raise ValueError("Please use a pair of atomic numbers or chemical symbols.")
# Change chemical elements into atomic numbers
numbers = []
for specie in species:
if isinstance(specie, str):
try:
specie = ase.data.atomic_numbers[specie]
except KeyError:
raise ValueError("Invalid chemical species: {}".format(specie))
numbers.append(specie)
# See if species defined
for number in numbers:
if number not in self._atomic_number_set:
raise ValueError(
"Atomic number {} was not specified in the species.".format(number)
)
# Change into internal indexing
numbers = [self.atomic_number_to_index[x] for x in numbers]
n_elem = self.n_elements
if numbers[0] > numbers[1]:
numbers = list(reversed(numbers))
i = numbers[0]
j = numbers[1]
n_elem_feat_symm = self._nmax * (self._nmax + 1) / 2 * (self._lmax + 1)
if self.crossover:
n_elem_feat_unsymm = self._nmax * self._nmax * (self._lmax + 1)
n_elem_feat = n_elem_feat_symm if i == j else n_elem_feat_unsymm
# The diagonal terms are symmetric and off-diagonal terms are
# unsymmetric
m_symm = i + int(j > i)
m_unsymm = j + i * n_elem - i * (i + 1) / 2 - m_symm
start = int(m_symm * n_elem_feat_symm + m_unsymm * n_elem_feat_unsymm)
end = int(start + n_elem_feat)
else:
if i != j:
raise ValueError(
"Crossover is set to False. No cross-species output " "available"
)
start = int(i * n_elem_feat_symm)
end = int(start + n_elem_feat_symm)
return slice(start, end)
[docs] def get_basis_gto(self, rcut, nmax):
"""Used to calculate the alpha and beta prefactors for the gto-radial
basis.
Args:
rcut(float): Radial cutoff.
nmax(int): Number of gto radial bases.
Returns:
(np.ndarray, np.ndarray): The alpha and beta prefactors for all bases
up to a fixed size of l=10.
"""
# These are the values for where the different basis functions should decay
# to: evenly space between 1 angstrom and rcut.
a = np.linspace(1, rcut, nmax)
threshold = 1e-3 # This is the fixed gaussian decay threshold
alphas_full = np.zeros((10, nmax))
betas_full = np.zeros((10, nmax, nmax))
for l in range(0, 10):
# The alphas are calculated so that the GTOs will decay to the set
# threshold value at their respective cutoffs
alphas = -np.log(threshold / np.power(a, l)) / a ** 2
# Calculate the overlap matrix
m = np.zeros((alphas.shape[0], alphas.shape[0]))
m[:, :] = alphas
m = m + m.transpose()
S = 0.5 * gamma(l + 3.0 / 2.0) * m ** (-l - 3.0 / 2.0)
# Get the beta factors that orthonormalize the set with Löwdin
# orthonormalization
betas = sqrtm(inv(S))
# If the result is complex, the calculation is currently halted.
if betas.dtype == np.complex128:
raise ValueError(
"Could not calculate normalization factors for the radial "
"basis in the domain of real numbers. Lowering the number of "
"radial basis functions (nmax) or increasing the radial "
"cutoff (rcut) is advised."
)
alphas_full[l, :] = alphas
betas_full[l, :, :] = betas
return alphas_full, betas_full
[docs] def get_basis_poly(self, rcut, nmax):
"""Used to calculate discrete vectors for the polynomial basis functions.
Args:
rcut(float): Radial cutoff.
nmax(int): Number of polynomial radial bases.
Returns:
(np.ndarray, np.ndarray): Tuple containing the evaluation points in
radial direction as the first item, and the corresponding
orthonormalized polynomial radial basis set as the second item.
"""
# Calculate the overlap of the different polynomial functions in a
# matrix S. These overlaps defined through the dot product over the
# radial coordinate are analytically calculable: Integrate[(rc - r)^(a
# + 2) (rc - r)^(b + 2) r^2, {r, 0, rc}]. Then the weights B that make
# the basis orthonormal are given by B=S^{-1/2}
S = np.zeros((nmax, nmax), dtype=np.float64)
for i in range(1, nmax + 1):
for j in range(1, nmax + 1):
S[i - 1, j - 1] = (2 * (rcut) ** (7 + i + j)) / (
(5 + i + j) * (6 + i + j) * (7 + i + j)
)
# Get the beta factors that orthonormalize the set with Löwdin
# orthonormalization
betas = sqrtm(np.linalg.inv(S))
# If the result is complex, the calculation is currently halted.
if betas.dtype == np.complex128:
raise ValueError(
"Could not calculate normalization factors for the radial "
"basis in the domain of real numbers. Lowering the number of "
"radial basis functions (nmax) or increasing the radial "
"cutoff (rcut) is advised."
)
# The radial basis is integrated in a very specific nonlinearly spaced
# grid given by rx
x = np.zeros(100)
x[0] = -0.999713726773441234
x[1] = -0.998491950639595818
x[2] = -0.996295134733125149
x[3] = -0.99312493703744346
x[4] = -0.98898439524299175
x[5] = -0.98387754070605702
x[6] = -0.97780935848691829
x[7] = -0.97078577576370633
x[8] = -0.962813654255815527
x[9] = -0.95390078292549174
x[10] = -0.94405587013625598
x[11] = -0.933288535043079546
x[12] = -0.921609298145333953
x[13] = -0.90902957098252969
x[14] = -0.895561644970726987
x[15] = -0.881218679385018416
x[16] = -0.86601468849716462
x[17] = -0.849964527879591284
x[18] = -0.833083879888400824
x[19] = -0.815389238339176254
x[20] = -0.79689789239031448
x[21] = -0.77762790964949548
x[22] = -0.757598118519707176
x[23] = -0.736828089802020706
x[24] = -0.715338117573056447
x[25] = -0.69314919935580197
x[26] = -0.670283015603141016
x[27] = -0.64676190851412928
x[28] = -0.622608860203707772
x[29] = -0.59784747024717872
x[30] = -0.57250193262138119
x[31] = -0.546597012065094168
x[32] = -0.520158019881763057
x[33] = -0.493210789208190934
x[34] = -0.465781649773358042
x[35] = -0.437897402172031513
x[36] = -0.409585291678301543
x[37] = -0.380872981624629957
x[38] = -0.351788526372421721
x[39] = -0.322360343900529152
x[40] = -0.292617188038471965
x[41] = -0.26258812037150348
x[42] = -0.23230248184497397
x[43] = -0.201789864095735997
x[44] = -0.171080080538603275
x[45] = -0.140203137236113973
x[46] = -0.109189203580061115
x[47] = -0.0780685828134366367
x[48] = -0.046871682421591632
x[49] = -0.015628984421543083
x[50] = 0.0156289844215430829
x[51] = 0.046871682421591632
x[52] = 0.078068582813436637
x[53] = 0.109189203580061115
x[54] = 0.140203137236113973
x[55] = 0.171080080538603275
x[56] = 0.201789864095735997
x[57] = 0.23230248184497397
x[58] = 0.262588120371503479
x[59] = 0.292617188038471965
x[60] = 0.322360343900529152
x[61] = 0.351788526372421721
x[62] = 0.380872981624629957
x[63] = 0.409585291678301543
x[64] = 0.437897402172031513
x[65] = 0.465781649773358042
x[66] = 0.49321078920819093
x[67] = 0.520158019881763057
x[68] = 0.546597012065094168
x[69] = 0.572501932621381191
x[70] = 0.59784747024717872
x[71] = 0.622608860203707772
x[72] = 0.64676190851412928
x[73] = 0.670283015603141016
x[74] = 0.693149199355801966
x[75] = 0.715338117573056447
x[76] = 0.736828089802020706
x[77] = 0.75759811851970718
x[78] = 0.77762790964949548
x[79] = 0.79689789239031448
x[80] = 0.81538923833917625
x[81] = 0.833083879888400824
x[82] = 0.849964527879591284
x[83] = 0.866014688497164623
x[84] = 0.881218679385018416
x[85] = 0.89556164497072699
x[86] = 0.90902957098252969
x[87] = 0.921609298145333953
x[88] = 0.933288535043079546
x[89] = 0.94405587013625598
x[90] = 0.953900782925491743
x[91] = 0.96281365425581553
x[92] = 0.970785775763706332
x[93] = 0.977809358486918289
x[94] = 0.983877540706057016
x[95] = 0.98898439524299175
x[96] = 0.99312493703744346
x[97] = 0.99629513473312515
x[98] = 0.998491950639595818
x[99] = 0.99971372677344123
rx = rcut * 0.5 * (x + 1)
# Calculate the value of the orthonormalized polynomial basis at the rx
# values
fs = np.zeros([nmax, len(x)])
for n in range(1, nmax + 1):
fs[n - 1, :] = (rcut - np.clip(rx, 0, rcut)) ** (n + 2)
gss = np.dot(betas, fs)
return rx, gss