1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
|
"""MIT License
Copyright (c) 2019 David Luevano Alvarado
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.
"""
import time
import math
import numpy as np
from numpy.linalg import eig
from ml_exp.misc import printc
def lj_matrix(mol_data,
nc_data,
diag_value=None,
sigma=1.0,
epsilon=1.0,
max_len=25,
as_eig=True,
bohr_radius_units=False):
"""
Creates the Lennard-Jones Matrix from the molecule data given.
mol_data: molecule data, matrix of atom coordinates.
nc_data: nuclear charge data, array of atom data.
diag_value: if special diagonal value is to be used.
sigma: sigma value.
epsilon: epsilon value.
max_len: maximum amount of atoms in molecule.
as_eig: if data should be returned as matrix or array of eigenvalues.
bohr_radius_units: if units should be in bohr's radius units.
"""
if bohr_radius_units:
conversion_rate = 0.52917721067
else:
conversion_rate = 1
mol_n = len(mol_data)
mol_nr = range(mol_n)
if not mol_n == len(nc_data):
print(''.join(['Error. Molecule matrix dimension is different ',
'than the nuclear charge array dimension.']))
else:
if max_len < mol_n:
print(''.join(['Error. Molecule matrix dimension (mol_n) is ',
'greater than max_len. Using mol_n.']))
max_len = None
if max_len:
lj = np.zeros((max_len, max_len))
ml_r = range(max_len)
# Actual calculation of the coulomb matrix.
for i in ml_r:
if i < mol_n:
x_i = mol_data[i, 0]
y_i = mol_data[i, 1]
z_i = mol_data[i, 2]
Z_i = nc_data[i]
else:
break
for j in ml_r:
if j < mol_n:
x_j = mol_data[j, 0]
y_j = mol_data[j, 1]
z_j = mol_data[j, 2]
x = (x_i-x_j)**2
y = (y_i-y_j)**2
z = (z_i-z_j)**2
if i == j:
if diag_value is None:
lj[i, j] = (0.5*Z_i**2.4)
else:
lj[i, j] = diag_value
else:
# Calculations are done after i==j is checked
# so no division by zero is done.
# A little play with r exponents
# so no square root is calculated.
# Conversion factor is included in r^2.
# 1/r^2
r_2 = sigma**2/(conversion_rate**2*(x + y + z))
r_6 = math.pow(r_2, 3)
r_12 = math.pow(r_6, 2)
lj[i, j] = (4*epsilon*(r_12 - r_6))
else:
break
# Now the value will be returned.
if as_eig:
lj_sorted = np.sort(eig(lj)[0])[::-1]
# Thanks to SO for the following lines of code.
# https://stackoverflow.com/a/43011036
# Keep zeros at the end.
mask = lj_sorted != 0.
f_mask = mask.sum(0, keepdims=1) >\
np.arange(lj_sorted.shape[0]-1, -1, -1)
f_mask = f_mask[::-1]
lj_sorted[f_mask] = lj_sorted[mask]
lj_sorted[~f_mask] = 0.
return lj_sorted
else:
return lj
else:
lj_temp = []
# Actual calculation of the coulomb matrix.
for i in mol_nr:
x_i = mol_data[i, 0]
y_i = mol_data[i, 1]
z_i = mol_data[i, 2]
Z_i = nc_data[i]
lj_row = []
for j in mol_nr:
x_j = mol_data[j, 0]
y_j = mol_data[j, 1]
z_j = mol_data[j, 2]
x = (x_i-x_j)**2
y = (y_i-y_j)**2
z = (z_i-z_j)**2
if i == j:
if not diag_value:
lj_row.append(0.5*Z_i**2.4)
else:
lj_row.append(diag_value)
else:
# Calculations are done after i==j is checked
# so no division by zero is done.
# A little play with r exponents
# so no square root is calculated.
# Conversion factor is included in r^2.
# 1/r^2
r_2 = sigma**2/(conversion_rate**2*(x + y + z))
r_6 = math.pow(r_2, 3)
r_12 = math.pow(r_6, 2)
lj_row.append(4*epsilon*(r_12 - r_6))
lj_temp.append(np.array(lj_row))
lj = np.array(lj_temp)
# Now the value will be returned.
if as_eig:
return np.sort(eig(lj)[0])[::-1]
else:
return lj
def lj_matrix_multiple(mol_data,
nc_data,
pipe=None,
diag_value=None,
sigma=1.0,
epsilon=1.0,
max_len=25,
as_eig=True,
bohr_radius_units=False):
"""
Calculates the Lennard-Jones Matrix of multiple molecules.
mol_data: molecule data, matrix of atom coordinates.
nc_data: nuclear charge data, array of atom data.
pipe: for multiprocessing purposes. Sends the data calculated
through a pipe.
diag_value: if special diagonal value is to be used.
sigma: sigma value.
epsilon: epsilon value.
max_len: maximum amount of atoms in molecule.
as_eig: if data should be returned as matrix or array of eigenvalues.
bohr_radius_units: if units should be in bohr's radius units.
"""
printc('L-J Matrices calculation started.', 'CYAN')
tic = time.perf_counter()
ljm_data = np.array([lj_matrix(mol,
nc,
diag_value,
sigma,
epsilon,
max_len,
as_eig,
bohr_radius_units)
for mol, nc in zip(mol_data, nc_data)])
toc = time.perf_counter()
printc('\tL-JM calculation took {:.4f} seconds.'.format(toc-tic), 'GREEN')
if pipe:
pipe.send(ljm_data)
return ljm_data
|
