# -*- 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 numpy as np
from ase import Atoms
from dscribe.core import System
from dscribe.descriptors.descriptormatrix import DescriptorMatrix
[docs]class SineMatrix(DescriptorMatrix):
"""Calculates the zero padded Sine matrix for different systems.
The Sine matrix is defined as:
Cij = 0.5 Zi**exponent | i = j
= (Zi*Zj)/phi(Ri, Rj) | i != j
where phi(r1, r2) = | B * sum(k = x,y,z)[ek * sin^2(pi * ek * B^-1
(r2-r1))] | (B is the matrix of basis cell vectors, ek are the unit
vectors)
The matrix is padded with invisible atoms, which means that the matrix is
padded with zeros until the maximum allowed size defined by n_max_atoms is
reached.
For reference, see:
"Crystal Structure Representations for Machine Learning Models of
Formation Energies", Felix Faber, Alexander Lindmaa, Anatole von
Lilienfeld, and Rickard Armiento, International Journal of Quantum
Chemistry, (2015),
https://doi.org/10.1002/qua.24917
"""
[docs] def create(self, system, n_jobs=1, only_physical_cores=False, verbose=False):
"""Return the Sine matrix for the given systems.
Args:
system (:class:`ase.Atoms` or list of :class:`ase.Atoms`): One or
many atomic structures.
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: Sine matrix for the given systems. The
return type depends on the 'sparse'-attribute. The first dimension
is determined by the amount of systems.
"""
# Combine input arguments / check input validity
system = [system] if isinstance(system, Atoms) else system
for s in system:
if len(s) > self.n_atoms_max:
raise ValueError(
"One of the given systems has more atoms ({}) than allowed "
"by n_atoms_max ({}).".format(len(s), self.n_atoms_max)
)
inp = [(i_sys,) for i_sys in system]
# Determine if the outputs have a fixed size
n_features = self.get_number_of_features()
static_size = [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 get_matrix(self, system):
"""Creates the Sine matrix for the given system.
Args:
system (:class:`ase.Atoms` | :class:`.System`): Input system.
Returns:
np.ndarray: Sine matrix as a 2D array.
"""
# Force the use of periodic boundary conditions
system = System.from_atoms(system)
system.set_pbc(True)
# Cell and inverse cell
B = system.get_cell()
try:
B_inv = system.get_cell_inverse()
except:
raise ValueError(
"The given system has a non-invertible cell matrix: {}.".format(B)
)
# Difference vectors as a 3D tensor
diff_tensor = system.get_displacement_tensor()
# Calculate phi
arg_to_sin = np.pi * np.dot(diff_tensor, B_inv)
phi = np.linalg.norm(np.dot(np.sin(arg_to_sin) ** 2, B), axis=2)
with np.errstate(divide="ignore"):
phi = np.reciprocal(phi)
# Calculate Z_i*Z_j
q = system.get_atomic_numbers()
qiqj = q[None, :] * q[:, None]
np.fill_diagonal(phi, 0)
# Multiply by charges
smat = qiqj * phi
# Set diagonal
np.fill_diagonal(smat, 0.5 * q**2.4)
return smat