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test_fchl_scalar.py
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# MIT License
#
# Copyright (c) 2018 Anders Steen Christensen
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in all
# copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.
from __future__ import print_function
import os
import numpy as np
import scipy
from scipy.special import jn
from scipy.special import binom
from scipy.special import factorial
from qml.data import Compound
from qml.math import cho_solve
from qml.fchl import generate_representation
from qml.fchl import get_local_symmetric_kernels
from qml.fchl import get_local_kernels
from qml.fchl import get_global_symmetric_kernels
from qml.fchl import get_global_kernels
from qml.fchl import get_atomic_kernels
from qml.fchl import get_atomic_symmetric_kernels
def get_energies(filename):
""" Returns a dictionary with heats of formation for each xyz-file.
"""
f = open(filename, "r")
lines = f.readlines()
f.close()
energies = dict()
for line in lines:
tokens = line.split()
xyz_name = tokens[0]
hof = float(tokens[1])
energies[xyz_name] = hof
return energies
def test_krr_fchl_local():
# Test that all kernel arguments work
kernel_args = {
"cut_distance": 1e6,
"cut_start": 0.5,
"two_body_width": 0.1,
"two_body_scaling": 2.0,
"two_body_power": 6.0,
"three_body_width": 3.0,
"three_body_scaling": 2.0,
"three_body_power": 3.0,
"alchemy": "periodic-table",
"alchemy_period_width": 1.0,
"alchemy_group_width": 1.0,
"fourier_order": 2,
"kernel": "gaussian",
"kernel_args": {
"sigma": [2.5],
},
}
test_dir = os.path.dirname(os.path.realpath(__file__))
# Parse file containing PBE0/def2-TZVP heats of formation and xyz filenames
data = get_energies(test_dir + "/data/hof_qm7.txt")
# Generate a list of Compound() objects"
mols = []
for xyz_file in sorted(data.keys())[:100]:
# Initialize the Compound() objects
mol = Compound(xyz=test_dir + "/qm7/" + xyz_file)
# Associate a property (heat of formation) with the object
mol.properties = data[xyz_file]
# This is a Molecular Coulomb matrix sorted by row norm
mol.generate_fchl_representation(cut_distance=1e6)
mols.append(mol)
# Shuffle molecules
np.random.seed(666)
np.random.shuffle(mols)
# Make training and test sets
n_test = len(mols) // 3
n_train = len(mols) - n_test
training = mols[:n_train]
test = mols[-n_test:]
X = np.array([mol.representation for mol in training])
Xs = np.array([mol.representation for mol in test])
# List of properties
Y = np.array([mol.properties for mol in training])
Ys = np.array([mol.properties for mol in test])
# Set hyper-parameters
llambda = 1e-8
K_symmetric = get_local_symmetric_kernels(X, **kernel_args)[0]
K = get_local_kernels(X, X, **kernel_args)[0]
assert np.allclose(K, K_symmetric), "Error in FCHL symmetric local kernels"
assert np.invert(np.all(np.isnan(K_symmetric))), "FCHL local symmetric kernel contains NaN"
assert np.invert(np.all(np.isnan(K))), "FCHL local kernel contains NaN"
# Solve alpha
K[np.diag_indices_from(K)] += llambda
alpha = cho_solve(K,Y)
# Calculate prediction kernel
Ks = get_local_kernels(Xs, X, **kernel_args)[0]
assert np.invert(np.all(np.isnan(Ks))), "FCHL local testkernel contains NaN"
Yss = np.dot(Ks, alpha)
mae = np.mean(np.abs(Ys - Yss))
assert abs(2 - mae) < 1.0, "Error in FCHL local kernel-ridge regression"
def test_krr_fchl_global():
# Test that all kernel arguments work
kernel_args = {
"kernel": "gaussian",
"kernel_args": {
"sigma": [100.0],
},
}
test_dir = os.path.dirname(os.path.realpath(__file__))
# Parse file containing PBE0/def2-TZVP heats of formation and xyz filenames
data = get_energies(test_dir + "/data/hof_qm7.txt")
# Generate a list of Compound() objects"
mols = []
for xyz_file in sorted(data.keys())[:100]:
# Initialize the Compound() objects
mol = Compound(xyz=test_dir + "/qm7/" + xyz_file)
# Associate a property (heat of formation) with the object
mol.properties = data[xyz_file]
# This is a Molecular Coulomb matrix sorted by row norm
mol.representation = generate_representation(mol.coordinates, \
mol.nuclear_charges, cut_distance=1e6)
mols.append(mol)
# Shuffle molecules
np.random.seed(666)
np.random.shuffle(mols)
# Make training and test sets
n_test = len(mols) // 3
n_train = len(mols) - n_test
training = mols[:n_train]
test = mols[-n_test:]
X = np.array([mol.representation for mol in training])
Xs = np.array([mol.representation for mol in test])
# List of properties
Y = np.array([mol.properties for mol in training])
Ys = np.array([mol.properties for mol in test])
# Set hyper-parameters
# sigma = 100.0
llambda = 1e-8
K_symmetric = get_global_symmetric_kernels(X, **kernel_args)[0]
K = get_global_kernels(X, X, **kernel_args)[0]
assert np.allclose(K, K_symmetric), "Error in FCHL symmetric global kernels"
assert np.invert(np.all(np.isnan(K_symmetric))), "FCHL global symmetric kernel contains NaN"
assert np.invert(np.all(np.isnan(K))), "FCHL global kernel contains NaN"
# Solve alpha
K[np.diag_indices_from(K)] += llambda
alpha = cho_solve(K,Y)
Ks = get_global_kernels(Xs, X, **kernel_args)[0]
assert np.invert(np.all(np.isnan(Ks))), "FCHL global testkernel contains NaN"
Yss = np.dot(Ks, alpha)
print(Ys, Yss)
mae = np.mean(np.abs(Ys - Yss))
assert abs(2 - mae) < 1.0, "Error in FCHL global kernel-ridge regression"
def test_krr_fchl_atomic():
kernel_args = {
"kernel": "gaussian",
"kernel_args": {
"sigma": [2.5],
},
}
test_dir = os.path.dirname(os.path.realpath(__file__))
# Parse file containing PBE0/def2-TZVP heats of formation and xyz filenames
data = get_energies(test_dir + "/data/hof_qm7.txt")
# Generate a list of Compound() objects"
mols = []
for xyz_file in sorted(data.keys())[:10]:
# Initialize the Compound() objects
mol = Compound(xyz=test_dir + "/qm7/" + xyz_file)
# Associate a property (heat of formation) with the object
mol.properties = data[xyz_file]
# This is a Molecular Coulomb matrix sorted by row norm
mol.representation = generate_representation(mol.coordinates, \
mol.nuclear_charges, cut_distance=1e6)
mols.append(mol)
X = np.array([mol.representation for mol in mols])
K = get_local_symmetric_kernels(X, **kernel_args)[0]
K_test = np.zeros((len(mols),len(mols)))
for i, Xi in enumerate(X):
for j, Xj in enumerate(X):
K_atomic = get_atomic_kernels(Xi[:mols[i].natoms], Xj[:mols[j].natoms], **kernel_args)[0]
K_test[i,j] = np.sum(K_atomic)
assert np.invert(np.all(np.isnan(K_atomic))), "FCHL atomic kernel contains NaN"
if (i == j):
K_atomic_symmetric = get_atomic_symmetric_kernels(Xi[:mols[i].natoms], **kernel_args)[0]
assert np.allclose(K_atomic, K_atomic_symmetric), "Error in FCHL symmetric atomic kernels"
assert np.invert(np.all(np.isnan(K_atomic_symmetric))), "FCHL atomic symmetric kernel contains NaN"
assert np.allclose(K, K_test), "Error in FCHL atomic kernels"
def test_fchl_local_periodic():
kernel_args = {
"cut_distance": 7.0,
"cut_start": 0.7,
"kernel": "gaussian",
"kernel_args": {
"sigma": [2.5],
},
}
nuclear_charges = [
np.array([13, 13, 58, 58, 58, 58, 58, 58, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 23, 23]),
np.array([34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 73, 73, 73, 73, 81, 81, 81, 81]),
np.array([48, 8, 8, 8, 8, 8, 8, 51, 51]),
np.array([16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30]),
np.array([58, 58, 8, 8, 8, 8, 8, 8, 8, 8, 23, 23])]
cells = np.array([
[[ 1.01113290e+01, -1.85000000e-04, 0.00000000e+00],
[ -5.05582400e+00, 8.75745400e+00, 0.00000000e+00],
[ 0.00000000e+00, 0.00000000e+00, 6.15100100e+00]],
[[ 9.672168, 0. , 0. ],
[ 0. , 3.643786, 0. ],
[ 0. , 0. , 14.961818]],
[[ 5.28208000e+00, -1.20000000e-05, 1.50000000e-05],
[ -2.64105000e+00, 4.57443400e+00, -3.00000000e-05],
[ 1.40000000e-05, -2.40000000e-05, 4.77522000e+00]],
[[ -1.917912, 3.321921, 0. ],
[ 3.835824, 0. , 0. ],
[ 1.917912, -1.107307, -56.423542]],
[[ 3.699168, 3.699168, -3.255938],
[ 3.699168, -3.699168, 3.255938],
[-3.699168, -3.699168, -3.255938]]])
fractional_coordinates = [
[[ 0.6666706 , 0.33333356, 0.15253127],
[ 0.33332896, 0.66666655, 0.65253119],
[ 0.14802736, 0.375795 , 0.23063888],
[ 0.62422269, 0.77225019, 0.23063888],
[ 0.22775607, 0.85196133, 0.23063888],
[ 0.77224448, 0.14803879, 0.7306388 ],
[ 0.37577687, 0.22774993, 0.7306388 ],
[ 0.8519722 , 0.62420512, 0.7306388 ],
[ 0.57731818, 0.47954083, 0.0102715 ],
[ 0.52043884, 0.09777799, 0.01028288],
[ 0.90211803, 0.4226259 , 0.01032677],
[ 0.33335216, 0.6666734 , 0.01482035],
[ 0.90959766, 0.77585201, 0.30637615],
[ 0.86626106, 0.09040873, 0.3063794 ],
[ 0.22415808, 0.13374794, 0.30638265],
[ 0.42268138, 0.52045928, 0.51027142],
[ 0.47956114, 0.90222098, 0.5102828 ],
[ 0.09788153, 0.57737421, 0.51032669],
[ 0.6666474 , 0.33332671, 0.51482027],
[ 0.09040133, 0.22414696, 0.80637769],
[ 0.13373793, 0.90959025, 0.80637932],
[ 0.77584247, 0.86625217, 0.80638257],
[ 0. , 0. , 0.05471142],
[ 0. , 0. , 0.55471134]],
[[ 0.81615001, 0.75000014, 0.00116296],
[ 0.52728096, 0.25000096, 0.0993275 ],
[ 0.24582596, 0.75000014, 0.2198563 ],
[ 0.74582658, 0.75000014, 0.28014376],
[ 0.02728137, 0.25000096, 0.40067257],
[ 0.31615042, 0.75000014, 0.49883711],
[ 0.68384978, 0.25000096, 0.50116236],
[ 0.97271884, 0.75000014, 0.59932757],
[ 0.25417362, 0.25000096, 0.71985637],
[ 0.75417321, 0.25000096, 0.78014383],
[ 0.47271925, 0.75000014, 0.90067263],
[ 0.1838502 , 0.25000096, 0.99883717],
[ 0.33804831, 0.75000014, 0.07120258],
[ 0.83804789, 0.75000014, 0.42879749],
[ 0.16195232, 0.25000096, 0.57120198],
[ 0.6619519 , 0.25000096, 0.92879756],
[ 0.98245812, 0.25000096, 0.17113829],
[ 0.48245853, 0.25000096, 0.32886177],
[ 0.51754167, 0.75000014, 0.67113836],
[ 0.01754209, 0.75000014, 0.82886184]],
[[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 3.66334233e-01, 1.96300000e-07, 2.70922493e-01],
[ 6.33665197e-01, 6.33666177e-01, 2.70923540e-01],
[ 3.62000000e-08, 3.66333081e-01, 2.70923851e-01],
[ 6.70000000e-09, 6.33664733e-01, 7.29076149e-01],
[ 6.33664135e-01, 9.99998055e-01, 7.29076460e-01],
[ 3.66336157e-01, 3.66334260e-01, 7.29077507e-01],
[ 3.33333635e-01, 6.66667395e-01, 4.99998953e-01],
[ 6.66667720e-01, 3.33333042e-01, 5.00000000e-01]],
[[ 0.3379644 , 0.66203644, 0.01389048],
[ 0.02316309, 0.97683587, 0.06948926],
[ 0.70833843, 0.29165976, 0.12501892],
[ 0.39352259, 0.60647824, 0.18056506],
[ 0.74538243, 0.25461577, 0.2361509 ],
[ 0.09722803, 0.90277092, 0.2916841 ],
[ 0.44907919, 0.55092165, 0.34723485],
[ 0.8009281 , 0.1990701 , 0.4027879 ],
[ 0.15278103, 0.84721793, 0.45834308],
[ 0.83797345, 0.16202475, 0.51392396],
[ 0.52315813, 0.4768427 , 0.56947169],
[ 0.20833916, 0.7916598 , 0.62501748],
[ 0.89352691, 0.10647128, 0.68058436],
[ 0.57870427, 0.42129656, 0.73611012],
[ 0.93056329, 0.06943491, 0.79169347],
[ 0.28241704, 0.71758191, 0.84725114],
[ 0.63426956, 0.36573128, 0.90280596],
[ 0.98611817, 0.01388002, 0.95835813],
[ 0. , 0. , 0. ],
[ 0.35185434, 0.64814649, 0.05556032],
[ 0.03704151, 0.96295744, 0.11112454],
[ 0.72221887, 0.27777932, 0.16666022],
[ 0.40741437, 0.59258647, 0.22224039],
[ 0.75926009, 0.24073811, 0.27778387],
[ 0.11111195, 0.888887 , 0.33333586],
[ 0.46296234, 0.53703849, 0.38888431],
[ 0.81480954, 0.18518866, 0.44443222],
[ 0.16667233, 0.83332662, 0.500017 ],
[ 0.85185117, 0.14814703, 0.55555711],
[ 0.53704217, 0.46295866, 0.61112381],
[ 0.22222196, 0.777777 , 0.66666587],
[ 0.90740847, 0.09258972, 0.72222903],
[ 0.59259328, 0.40740756, 0.77777712],
[ 0.94444213, 0.05555607, 0.83333 ],
[ 0.29630132, 0.70369764, 0.88890396],
[ 0.64815247, 0.35184836, 0.94445471]],
[[ 0. , 0. , 0. ],
[ 0.75000042, 0.50000027, 0.25000015],
[ 0.15115386, 0.81961403, 0.33154037],
[ 0.51192691, 0.18038651, 0.3315404 ],
[ 0.08154025, 0.31961376, 0.40115401],
[ 0.66846017, 0.81961403, 0.48807366],
[ 0.08154025, 0.68038678, 0.76192703],
[ 0.66846021, 0.18038651, 0.84884672],
[ 0.23807355, 0.31961376, 0.91846033],
[ 0.59884657, 0.68038678, 0.91846033],
[ 0.50000031, 0. , 0.50000031],
[ 0.25000015, 0.50000027, 0.75000042]]]
n = 5
X = np.array([generate_representation(fractional_coordinates[i], nuclear_charges[i],
cell=cells[i], max_size=36, neighbors=200, cut_distance=7.0) for i in range(5)])
K = get_local_symmetric_kernels(X, **kernel_args)
K_ref = np.array(
[[ 530.03184304, 435.65196293, 198.61245535, 782.49428327, 263.53562172],
[ 435.65196293, 371.35281119, 163.83766549, 643.99777576, 215.04338938],
[ 198.61245535, 163.83766549, 76.12134823, 295.02739281, 99.89595704],
[ 782.49428327, 643.99777576, 295.02739281, 1199.61736141, 389.31169487],
[ 263.53562172, 215.04338938, 99.89595704, 389.31169487, 133.36920188]]
)
assert np.allclose(K, K_ref), "Error in periodic FCHL"
def test_krr_fchl_alchemy():
test_dir = os.path.dirname(os.path.realpath(__file__))
# Parse file containing PBE0/def2-TZVP heats of formation and xyz filenames
data = get_energies(test_dir + "/data/hof_qm7.txt")
# Generate a list of Compound() objects"
mols = []
for xyz_file in sorted(data.keys())[:20]:
# Initialize the Compound() objects
mol = Compound(xyz=test_dir + "/qm7/" + xyz_file)
# Associate a property (heat of formation) with the object
mol.properties = data[xyz_file]
# This is a Molecular Coulomb matrix sorted by row norm
mol.generate_fchl_representation(cut_distance=1e6)
mols.append(mol)
# Shuffle molecules
np.random.seed(666)
np.random.shuffle(mols)
X = np.array([mol.representation for mol in mols])
np.set_printoptions(edgeitems = 16, linewidth=6666)
overlap = np.array([[ 1. , 0.00835282, 0.90696062, 0.82257756, 0.61368025, 0.37660345, 0.19010927, 0.07894037, 0.02696323, 0.00757568, 0.67663385, 0.61368025, 0.45783336, 0.28096329, 0.14183016, 0.05889311, 0.02011579, 0.0056518 , 0.41523683, 0.37660345],
[ 0.00835282, 1. , 0.00757568, 0.02696323, 0.07894037, 0.19010927, 0.37660345, 0.61368025, 0.82257756, 0.90696062, 0.0056518 , 0.02011579, 0.05889311, 0.14183016, 0.28096329, 0.45783336, 0.61368025, 0.67663385, 0.0034684 , 0.01234467],
[ 0.90696062, 0.00757568, 1. , 0.90696062, 0.67663385, 0.41523683, 0.20961139, 0.08703837, 0.02972922, 0.00835282, 0.90696062, 0.82257756, 0.61368025, 0.37660345, 0.19010927, 0.07894037, 0.02696323, 0.00757568, 0.67663385, 0.61368025],
[ 0.82257756, 0.02696323, 0.90696062, 1. , 0.90696062, 0.67663385, 0.41523683, 0.20961139, 0.08703837, 0.02972922, 0.82257756, 0.90696062, 0.82257756, 0.61368025, 0.37660345, 0.19010927, 0.07894037, 0.02696323, 0.61368025, 0.67663385],
[ 0.61368025, 0.07894037, 0.67663385, 0.90696062, 1. , 0.90696062, 0.67663385, 0.41523683, 0.20961139, 0.08703837, 0.61368025, 0.82257756, 0.90696062, 0.82257756, 0.61368025, 0.37660345, 0.19010927, 0.07894037, 0.45783336, 0.61368025],
[ 0.37660345, 0.19010927, 0.41523683, 0.67663385, 0.90696062, 1. , 0.90696062, 0.67663385, 0.41523683, 0.20961139, 0.37660345, 0.61368025, 0.82257756, 0.90696062, 0.82257756, 0.61368025, 0.37660345, 0.19010927, 0.28096329, 0.45783336],
[ 0.19010927, 0.37660345, 0.20961139, 0.41523683, 0.67663385, 0.90696062, 1. , 0.90696062, 0.67663385, 0.41523683, 0.19010927, 0.37660345, 0.61368025, 0.82257756, 0.90696062, 0.82257756, 0.61368025, 0.37660345, 0.14183016, 0.28096329],
[ 0.07894037, 0.61368025, 0.08703837, 0.20961139, 0.41523683, 0.67663385, 0.90696062, 1. , 0.90696062, 0.67663385, 0.07894037, 0.19010927, 0.37660345, 0.61368025, 0.82257756, 0.90696062, 0.82257756, 0.61368025, 0.05889311, 0.14183016],
[ 0.02696323, 0.82257756, 0.02972922, 0.08703837, 0.20961139, 0.41523683, 0.67663385, 0.90696062, 1. , 0.90696062, 0.02696323, 0.07894037, 0.19010927, 0.37660345, 0.61368025, 0.82257756, 0.90696062, 0.82257756, 0.02011579, 0.05889311],
[ 0.00757568, 0.90696062, 0.00835282, 0.02972922, 0.08703837, 0.20961139, 0.41523683, 0.67663385, 0.90696062, 1. , 0.00757568, 0.02696323, 0.07894037, 0.19010927, 0.37660345, 0.61368025, 0.82257756, 0.90696062, 0.0056518 , 0.02011579],
[ 0.67663385, 0.0056518 , 0.90696062, 0.82257756, 0.61368025, 0.37660345, 0.19010927, 0.07894037, 0.02696323, 0.00757568, 1. , 0.90696062, 0.67663385, 0.41523683, 0.20961139, 0.08703837, 0.02972922, 0.00835282, 0.90696062, 0.82257756],
[ 0.61368025, 0.02011579, 0.82257756, 0.90696062, 0.82257756, 0.61368025, 0.37660345, 0.19010927, 0.07894037, 0.02696323, 0.90696062, 1. , 0.90696062, 0.67663385, 0.41523683, 0.20961139, 0.08703837, 0.02972922, 0.82257756, 0.90696062],
[ 0.45783336, 0.05889311, 0.61368025, 0.82257756, 0.90696062, 0.82257756, 0.61368025, 0.37660345, 0.19010927, 0.07894037, 0.67663385, 0.90696062, 1. , 0.90696062, 0.67663385, 0.41523683, 0.20961139, 0.08703837, 0.61368025, 0.82257756],
[ 0.28096329, 0.14183016, 0.37660345, 0.61368025, 0.82257756, 0.90696062, 0.82257756, 0.61368025, 0.37660345, 0.19010927, 0.41523683, 0.67663385, 0.90696062, 1. , 0.90696062, 0.67663385, 0.41523683, 0.20961139, 0.37660345, 0.61368025],
[ 0.14183016, 0.28096329, 0.19010927, 0.37660345, 0.61368025, 0.82257756, 0.90696062, 0.82257756, 0.61368025, 0.37660345, 0.20961139, 0.41523683, 0.67663385, 0.90696062, 1. , 0.90696062, 0.67663385, 0.41523683, 0.19010927, 0.37660345],
[ 0.05889311, 0.45783336, 0.07894037, 0.19010927, 0.37660345, 0.61368025, 0.82257756, 0.90696062, 0.82257756, 0.61368025, 0.08703837, 0.20961139, 0.41523683, 0.67663385, 0.90696062, 1. , 0.90696062, 0.67663385, 0.07894037, 0.19010927],
[ 0.02011579, 0.61368025, 0.02696323, 0.07894037, 0.19010927, 0.37660345, 0.61368025, 0.82257756, 0.90696062, 0.82257756, 0.02972922, 0.08703837, 0.20961139, 0.41523683, 0.67663385, 0.90696062, 1. , 0.90696062, 0.02696323, 0.07894037],
[ 0.0056518 , 0.67663385, 0.00757568, 0.02696323, 0.07894037, 0.19010927, 0.37660345, 0.61368025, 0.82257756, 0.90696062, 0.00835282, 0.02972922, 0.08703837, 0.20961139, 0.41523683, 0.67663385, 0.90696062, 1. , 0.00757568, 0.02696323],
[ 0.41523683, 0.0034684 , 0.67663385, 0.61368025, 0.45783336, 0.28096329, 0.14183016, 0.05889311, 0.02011579, 0.0056518 , 0.90696062, 0.82257756, 0.61368025, 0.37660345, 0.19010927, 0.07894037, 0.02696323, 0.00757568, 1. , 0.90696062],
[ 0.37660345, 0.01234467, 0.61368025, 0.67663385, 0.61368025, 0.45783336, 0.28096329, 0.14183016, 0.05889311, 0.02011579, 0.82257756, 0.90696062, 0.82257756, 0.61368025, 0.37660345, 0.19010927, 0.07894037, 0.02696323, 0.90696062, 1. ]])
kernel_args = {
"alchemy": "periodic-table",
"kernel": "gaussian",
"kernel_args": {
"sigma": [2.5],
},
}
K_alchemy = get_local_symmetric_kernels(X, **kernel_args)[0]
kernel_args = {
"alchemy": overlap,
"kernel": "gaussian",
"kernel_args": {
"sigma": [2.5],
},
}
K_custom = get_local_symmetric_kernels(X, **kernel_args)[0]
assert np.allclose(K_alchemy, K_custom), "Error in alchemy"
nooverlap = np.eye(100)
kernel_args = {
"alchemy": "off",
"kernel": "gaussian",
"kernel_args": {
"sigma": [2.5],
},
}
K_noalchemy = get_local_symmetric_kernels(X, **kernel_args)[0]
kernel_args = {
"alchemy": nooverlap,
"kernel": "gaussian",
"kernel_args": {
"sigma": [2.5],
},
}
K_custom = get_local_symmetric_kernels(X, **kernel_args)[0]
assert np.allclose(K_noalchemy, K_custom), "Error in no-alchemy"
def test_fchl_linear():
test_dir = os.path.dirname(os.path.realpath(__file__))
# Parse file containing PBE0/def2-TZVP heats of formation and xyz filenames
data = get_energies(test_dir + "/data/hof_qm7.txt")
# Generate a list of qml.Compound() objects"
mols = []
for xyz_file in sorted(data.keys())[:5]:
# Initialize the qml.Compound() objects
mol = Compound(xyz=test_dir + "/qm7/" + xyz_file)
# This is a Molecular Coulomb matrix sorted by row norm
mol.representation = generate_representation(mol.coordinates, \
mol.nuclear_charges, cut_distance=1e6)
mols.append(mol)
X = np.array([mol.representation for mol in mols])
K = get_local_symmetric_kernels(X)[0]
K_test = np.zeros((len(mols),len(mols)))
kernel_args = {
"kernel": "linear",
"kernel_args": {"c": [1.0],},
}
for i, Xi in enumerate(X):
Sii = get_atomic_kernels(Xi[:mols[i].natoms], Xi[:mols[i].natoms], **kernel_args)[0]
for j, Xj in enumerate(X):
Sjj = get_atomic_kernels(Xj[:mols[j].natoms], Xj[:mols[j].natoms], **kernel_args)[0]
Sij = get_atomic_kernels(Xi[:mols[i].natoms], Xj[:mols[j].natoms], **kernel_args)[0]
for ii in range(Sii.shape[0]):
for jj in range(Sjj.shape[0]):
l2 = Sii[ii,ii] + Sjj[jj,jj] - 2 * Sij[ii,jj]
K_test[i,j] += np.exp(- l2 / (2*(2.5**2)))
assert np.allclose(K, K_test), "Error in FCHL linear kernels"
def test_fchl_polynomial():
test_dir = os.path.dirname(os.path.realpath(__file__))
# Parse file containing PBE0/def2-TZVP heats of formation and xyz filenames
data = get_energies(test_dir + "/data/hof_qm7.txt")
# Generate a list of qml.Compound() objects"
mols = []
for xyz_file in sorted(data.keys())[:5]:
# Initialize the qml.Compound() objects
mol = Compound(xyz=test_dir + "/qm7/" + xyz_file)
# This is a Molecular Coulomb matrix sorted by row norm
mol.representation = generate_representation(mol.coordinates, \
mol.nuclear_charges, cut_distance=1e6)
mols.append(mol)
X = np.array([mol.representation for mol in mols])
polynomial_kernel_args = {
"kernel": "polynomial",
"kernel_args": {
"alpha": [2.0],
"c": [3.0],
"d": [4.0],
},
}
linear_kernel_args = {
"kernel": "linear",
"kernel_args": {
"c": [0.0],
},
}
K = get_local_symmetric_kernels(X, **polynomial_kernel_args)[0]
K_test = np.zeros((len(mols),len(mols)))
for i, Xi in enumerate(X):
for j, Xj in enumerate(X):
Sij = get_atomic_kernels(Xi[:mols[i].natoms], Xj[:mols[j].natoms], **linear_kernel_args)[0]
for ii in range(Sij.shape[0]):
for jj in range(Sij.shape[1]):
K_test[i,j] += (2.0 * Sij[ii,jj] + 3.0)**4.0
assert np.allclose(K, K_test), "Error in FCHL polynomial kernels"
def test_fchl_sigmoid():
test_dir = os.path.dirname(os.path.realpath(__file__))
# Parse file containing PBE0/def2-TZVP heats of formation and xyz filenames
data = get_energies(test_dir + "/data/hof_qm7.txt")
# Generate a list of qml.Compound() objects"
mols = []
for xyz_file in sorted(data.keys())[:5]:
# Initialize the qml.Compound() objects
mol = Compound(xyz=test_dir + "/qm7/" + xyz_file)
# This is a Molecular Coulomb matrix sorted by row norm
mol.representation = generate_representation(mol.coordinates, \
mol.nuclear_charges, cut_distance=1e6)
mols.append(mol)
X = np.array([mol.representation for mol in mols])
sigmoid_kernel_args = {
"kernel": "sigmoid",
"kernel_args": {
"alpha": [2.0],
"c": [3.0],
},
}
linear_kernel_args = {
"kernel": "linear",
"kernel_args": {
"c": [0.0],
},
}
K = get_local_symmetric_kernels(X, **sigmoid_kernel_args)[0]
K_test = np.zeros((len(mols),len(mols)))
for i, Xi in enumerate(X):
for j, Xj in enumerate(X):
Sij = get_atomic_kernels(Xi[:mols[i].natoms], Xj[:mols[j].natoms], **linear_kernel_args)[0]
for ii in range(Sij.shape[0]):
for jj in range(Sij.shape[1]):
# K_test[i,j] += (2.0 * Sij[ii,jj] + 3.0)**4.0
K_test[i,j] += np.tanh(2.0 * Sij[ii,jj] + 3.0)
assert np.allclose(K, K_test), "Error in FCHL sigmoid kernels"
def test_fchl_multiquadratic():
test_dir = os.path.dirname(os.path.realpath(__file__))
# Parse file containing PBE0/def2-TZVP heats of formation and xyz filenames
data = get_energies(test_dir + "/data/hof_qm7.txt")
# Generate a list of qml.Compound() objects"
mols = []
for xyz_file in sorted(data.keys())[:5]:
# Initialize the qml.Compound() objects
mol = Compound(xyz=test_dir + "/qm7/" + xyz_file)
# This is a Molecular Coulomb matrix sorted by row norm
mol.representation = generate_representation(mol.coordinates, \
mol.nuclear_charges, cut_distance=1e6)
mols.append(mol)
X = np.array([mol.representation for mol in mols])
kernel_args = {
"kernel": "multiquadratic",
"kernel_args": {
"c": [2.0],
},
}
linear_kernel_args = {
"kernel": "linear",
"kernel_args": {
"c": [0.0],
},
}
K = get_local_symmetric_kernels(X, **kernel_args)[0]
K_test = np.zeros((len(mols),len(mols)))
for i, Xi in enumerate(X):
Sii = get_atomic_kernels(Xi[:mols[i].natoms], Xi[:mols[i].natoms], **linear_kernel_args)[0]
for j, Xj in enumerate(X):
Sjj = get_atomic_kernels(Xj[:mols[j].natoms], Xj[:mols[j].natoms], **linear_kernel_args)[0]
Sij = get_atomic_kernels(Xi[:mols[i].natoms], Xj[:mols[j].natoms], **linear_kernel_args)[0]
for ii in range(Sii.shape[0]):
for jj in range(Sjj.shape[0]):
l2 = Sii[ii,ii] + Sjj[jj,jj] - 2 * Sij[ii,jj]
K_test[i,j] += np.sqrt(l2 + 4.0)
assert np.allclose(K, K_test), "Error in FCHL multiquadratic kernels"
def test_fchl_inverse_multiquadratic():
test_dir = os.path.dirname(os.path.realpath(__file__))
# Parse file containing PBE0/def2-TZVP heats of formation and xyz filenames
data = get_energies(test_dir + "/data/hof_qm7.txt")
# Generate a list of qml.Compound() objects"
mols = []
for xyz_file in sorted(data.keys())[:5]:
# Initialize the qml.Compound() objects
mol = Compound(xyz=test_dir + "/qm7/" + xyz_file)
# This is a Molecular Coulomb matrix sorted by row norm
mol.representation = generate_representation(mol.coordinates, \
mol.nuclear_charges, cut_distance=1e6)
mols.append(mol)
X = np.array([mol.representation for mol in mols])
kernel_args = {
"kernel": "inverse-multiquadratic",
"kernel_args": {
"c": [2.0],
},
}
linear_kernel_args = {
"kernel": "linear",
"kernel_args": {
"c": [0.0],
},
}
K = get_local_symmetric_kernels(X, **kernel_args)[0]
K_test = np.zeros((len(mols),len(mols)))
for i, Xi in enumerate(X):
Sii = get_atomic_kernels(Xi[:mols[i].natoms], Xi[:mols[i].natoms], **linear_kernel_args)[0]
for j, Xj in enumerate(X):
Sjj = get_atomic_kernels(Xj[:mols[j].natoms], Xj[:mols[j].natoms], **linear_kernel_args)[0]
Sij = get_atomic_kernels(Xi[:mols[i].natoms], Xj[:mols[j].natoms], **linear_kernel_args)[0]
for ii in range(Sii.shape[0]):
for jj in range(Sjj.shape[0]):
l2 = Sii[ii,ii] + Sjj[jj,jj] - 2 * Sij[ii,jj]
K_test[i,j] += 1.0 / np.sqrt(l2 + 4.0)
assert np.allclose(K, K_test), "Error in FCHL inverse multiquadratic kernels"
def test_fchl_bessel():
test_dir = os.path.dirname(os.path.realpath(__file__))
# Parse file containing PBE0/def2-TZVP heats of formation and xyz filenames
data = get_energies(test_dir + "/data/hof_qm7.txt")
# Generate a list of qml.Compound() objects"
mols = []
for xyz_file in sorted(data.keys())[:5]:
# Initialize the qml.Compound() objects
mol = Compound(xyz=test_dir + "/qm7/" + xyz_file)
# This is a Molecular Coulomb matrix sorted by row norm
mol.representation = generate_representation(mol.coordinates, \
mol.nuclear_charges, cut_distance=1e6)
mols.append(mol)
X = np.array([mol.representation for mol in mols])
kernel_args = {
"kernel": "bessel",
"kernel_args": {
"sigma": [2.0],
"v": [3.0],
"n": [2.0],
},
}
linear_kernel_args = {
"kernel": "linear",
"kernel_args": {
"c": [0.0],
},
}
K = get_local_symmetric_kernels(X, **kernel_args)[0]
K_test = np.zeros((len(mols),len(mols)))
sigma = 2.0
v = 3
n = 2
for i, Xi in enumerate(X):
Sii = get_atomic_kernels(Xi[:mols[i].natoms], Xi[:mols[i].natoms], **linear_kernel_args)[0]
for j, Xj in enumerate(X):
Sjj = get_atomic_kernels(Xj[:mols[j].natoms], Xj[:mols[j].natoms], **linear_kernel_args)[0]
Sij = get_atomic_kernels(Xi[:mols[i].natoms], Xj[:mols[j].natoms], **linear_kernel_args)[0]
for ii in range(Sii.shape[0]):
for jj in range(Sjj.shape[0]):
l2 = np.sqrt(Sii[ii,ii] + Sjj[jj,jj] - 2 * Sij[ii,jj])
K_test[i,j] += jn(v, sigma * Sij[ii,jj])/ Sij[ii,jj]**(-n*(v+1))
assert np.allclose(K, K_test), "Error in FCHL inverse bessel kernels"
def test_fchl_l2():
test_dir = os.path.dirname(os.path.realpath(__file__))
# Parse file containing PBE0/def2-TZVP heats of formation and xyz filenames
data = get_energies(test_dir + "/data/hof_qm7.txt")
# Generate a list of qml.Compound() objects"
mols = []
for xyz_file in sorted(data.keys())[:5]:
# Initialize the qml.Compound() objects
mol = Compound(xyz=test_dir + "/qm7/" + xyz_file)
# This is a Molecular Coulomb matrix sorted by row norm
mol.representation = generate_representation(mol.coordinates, \
mol.nuclear_charges, cut_distance=1e6)
mols.append(mol)
X = np.array([mol.representation for mol in mols])
l2_kernel_args = {
"kernel": "l2",
"kernel_args": {
"alpha": [1.0],
"c": [0.0],
},
}
K = get_local_symmetric_kernels(X)[0]
K_test = np.zeros((len(mols),len(mols)))
sigma = 2.0
v = 3
n = 2
inv_sigma = -1.0/ (2.0*2.5**2)
for i, Xi in enumerate(X):
for j, Xj in enumerate(X):
Sij = get_atomic_kernels(Xi[:mols[i].natoms], Xj[:mols[j].natoms],
**l2_kernel_args)[0]
for ii in range(Sij.shape[0]):
for jj in range(Sij.shape[1]):
K_test[i,j] += np.exp(Sij[ii,jj] * inv_sigma)
assert np.allclose(K, K_test), "Error in FCHL l2 kernels"
def test_fchl_matern():
test_dir = os.path.dirname(os.path.realpath(__file__))
# Parse file containing PBE0/def2-TZVP heats of formation and xyz filenames
data = get_energies(test_dir + "/data/hof_qm7.txt")
# Generate a list of qml.Compound() objects"
mols = []
for xyz_file in sorted(data.keys())[:5]:
# Initialize the qml.Compound() objects
mol = Compound(xyz=test_dir + "/qm7/" + xyz_file)
# This is a Molecular Coulomb matrix sorted by row norm
mol.representation = generate_representation(mol.coordinates, \
mol.nuclear_charges, cut_distance=1e6)
mols.append(mol)
X = np.array([mol.representation for mol in mols])
kernel_args = {
"kernel": "matern",
"kernel_args": {
"sigma": [5.0],
"n": [2.0],
},
}
linear_kernel_args = {
"kernel": "linear",
"kernel_args": {
"c": [0.0],
},
}
K = get_local_symmetric_kernels(X, **kernel_args)[0]
K_test = np.zeros((len(mols),len(mols)))
sigma = 5.0
n = 2
v = n + 0.5
for i, Xi in enumerate(X):
Sii = get_atomic_kernels(Xi[:mols[i].natoms], Xi[:mols[i].natoms], **linear_kernel_args)[0]
for j, Xj in enumerate(X):
Sjj = get_atomic_kernels(Xj[:mols[j].natoms], Xj[:mols[j].natoms], **linear_kernel_args)[0]
Sij = get_atomic_kernels(Xi[:mols[i].natoms], Xj[:mols[j].natoms], **linear_kernel_args)[0]
for ii in range(Sii.shape[0]):
for jj in range(Sjj.shape[0]):
l2 = np.sqrt(Sii[ii,ii] + Sjj[jj,jj] - 2 * Sij[ii,jj])
rho = (2*np.sqrt(2*v)*l2/sigma)
for k in range(0, n+1):
fact = float(factorial(n+k)) / factorial(2*n) * binom(n,k)
K_test[i,j] += np.exp(-0.5 * rho) * fact * rho**(n-k)
assert np.allclose(K, K_test), "Error in FCHL matern kernels"
def test_fchl_cauchy():
test_dir = os.path.dirname(os.path.realpath(__file__))
# Parse file containing PBE0/def2-TZVP heats of formation and xyz filenames
data = get_energies(test_dir + "/data/hof_qm7.txt")
# Generate a list of qml.Compound() objects"