def efs_force(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, sig, ls,
r_cut, cutoff_func):
energy_kernels = np.zeros(3)
force_kernels = np.zeros((3, 3))
stress_kernels = np.zeros((6, 3))
ls1 = 1 / (2 * ls * ls)
ls2 = 1 / (ls * ls)
ls3 = ls2 * ls2
sig2 = sig * sig
for m in range(bond_array_1.shape[0]):
ri = bond_array_1[m, 0]
fi, _ = cutoff_func(r_cut, ri, 0)
e1 = etypes1[m]
for n in range(bond_array_2.shape[0]):
e2 = etypes2[n]
# check if bonds agree
if (c1 == c2 and e1 == e2) or (c1 == e2 and c2 == e1):
rj = bond_array_2[n, 0]
fj, _ = cutoff_func(r_cut, rj, 0)
r11 = ri - rj
D = r11 * r11
for d1 in range(3):
cj = bond_array_2[n, d1 + 1]
_, fdj = cutoff_func(r_cut, rj, cj)
C = r11 * cj
energy_kernels[d1] += \
force_energy_helper(-C, D, fj, fi, fdj, ls1, ls2,
sig2) / 2
stress_count = 0
for d3 in range(3):
ci = bond_array_1[m, d3 + 1]
_, fdi = cutoff_func(r_cut, ri, ci)
A = ci * cj
B = r11 * ci
force_kern = \
force_helper(A, B, C, D, fi, fj, fdi, fdj,
ls1, ls2, ls3, sig2)
force_kernels[d3, d1] += force_kern
for d2 in range(d3, 3):
coordinate = bond_array_1[m, d2 + 1] * ri
stress_kernels[stress_count, d1] -= \
force_kern * coordinate / 2
stress_count += 1
return energy_kernels, force_kernels, stress_kernels
def efs_self(bond_array_1, c1, etypes1, sig, ls, r_cut, cutoff_func):
energy_kernel = 0
force_kernels = np.zeros(3)
stress_kernels = np.zeros(6)
ls1 = 1 / (2 * ls * ls)
ls2 = 1 / (ls * ls)
ls3 = ls2 * ls2
sig2 = sig * sig
for m in range(bond_array_1.shape[0]):
ri = bond_array_1[m, 0]
fi, _ = cutoff_func(r_cut, ri, 0)
e1 = etypes1[m]
for n in range(bond_array_1.shape[0]):
e2 = etypes1[n]
# check if bonds agree
if (e1 == e2) or (c1 == e2 and c1 == e1):
rj = bond_array_1[n, 0]
fj, _ = cutoff_func(r_cut, rj, 0)
r11 = ri - rj
D = r11 * r11
energy_kernel += fi * fj * sig2 * exp(-D * ls1) / 4
stress_count = 0
for d1 in range(3):
cj = bond_array_1[n, d1 + 1]
_, fdj = cutoff_func(r_cut, rj, cj)
C = r11 * cj
ci = bond_array_1[m, d1 + 1]
_, fdi = cutoff_func(r_cut, ri, ci)
A = ci * cj
B = r11 * ci
force_kern = \
force_helper(A, B, C, D, fi, fj, fdi, fdj,
ls1, ls2, ls3, sig2)
force_kernels[d1] += force_kern
for d2 in range(d1, 3):
coord1 = bond_array_1[m, d2 + 1] * ri
coord2 = bond_array_1[n, d2 + 1] * rj
stress_kernels[stress_count] += \
force_kern * coord1 * coord2 / 4
stress_count += 1
return energy_kernel, force_kernels, stress_kernels
def self_two_body_mc_jit(bond_array, c, etypes,
d, sig, ls, r_cut, cutoff_func):
"""Multicomponent two-body force/force kernel accelerated with Numba's
njit decorator.
Loops over bonds in two environments and adds to the kernel if bonds are
of the same type.
"""
kern = 0
ls1 = 1 / (2 * ls * ls)
ls2 = 1 / (ls * ls)
ls3 = ls2 * ls2
sig2 = sig * sig
for m in range(bond_array.shape[0]):
ri = bond_array[m, 0]
ci = bond_array[m, d]
fi, fdi = cutoff_func(r_cut, ri, ci)
e1 = etypes[m]
for n in range(m, bond_array.shape[0]):
e2 = etypes[n]
# check if bonds agree
if (c == c and e1 == e2) or (c == e2 and c == e1):
rj = bond_array[n, 0]
cj = bond_array[n, d]
fj, fdj = cutoff_func(r_cut, rj, cj)
r11 = ri - rj
A = ci * cj
B = r11 * ci
C = r11 * cj
D = r11 * r11
kern0 = force_helper(A, B, C, D, fi, fj, fdi, fdj,
ls1, ls2, ls3, sig2)
kern += kern0 if m == n else 2 * kern0
return kern
def stress_stress(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, sig,
ls, r_cut, cutoff_func):
"""2-body multi-element kernel between two partial stress components
accelerated with Numba.
Args:
bond_array_1 (np.ndarray): 2-body bond array of the first local
environment.
c1 (int): Species of the central atom of the first local environment.
etypes1 (np.ndarray): Species of atoms in the first local
environment.
bond_array_2 (np.ndarray): 2-body bond array of the second local
environment.
c2 (int): Species of the central atom of the second local environment.
etypes2 (np.ndarray): Species of atoms in the second local
environment.
sig (float): 2-body signal variance hyperparameter.
ls (float): 2-body length scale hyperparameter.
r_cut (float): 2-body cutoff radius.
cutoff_func (Callable): Cutoff function.
Return:
float: Value of the 2-body kernel.
"""
kernel_matrix = np.zeros((6, 6))
ls1 = 1 / (2 * ls * ls)
ls2 = 1 / (ls * ls)
ls3 = ls2 * ls2
sig2 = sig * sig
for m in range(bond_array_1.shape[0]):
ri = bond_array_1[m, 0]
e1 = etypes1[m]
for n in range(bond_array_2.shape[0]):
e2 = etypes2[n]
# check if bonds agree
if (c1 == c2 and e1 == e2) or (c1 == e2 and c2 == e1):
rj = bond_array_2[n, 0]
r11 = ri - rj
D = r11 * r11
s1 = 0
for d1 in range(3):
ci = bond_array_1[m, d1 + 1]
B = r11 * ci
fi, fdi = cutoff_func(r_cut, ri, ci)
for d2 in range(d1, 3):
coordinate_1 = bond_array_1[m, d2 + 1] * ri
s2 = 0
for d3 in range(3):
cj = bond_array_2[n, d3 + 1]
A = ci * cj
C = r11 * cj
fj, fdj = cutoff_func(r_cut, rj, cj)
for d4 in range(d3, 3):
coordinate_2 = bond_array_2[n, d4 + 1] * rj
force_kern = \
force_helper(A, B, C, D, fi, fj, fdi, fdj,
ls1, ls2, ls3, sig2)
kernel_matrix[s1, s2] += \
force_kern * coordinate_1 * \
coordinate_2
s2 += 1
s1 += 1
return kernel_matrix / 4
def force_force(bond_array_1, c1, etypes1, bond_array_2, c2, etypes2, sig, ls,
r_cut, cutoff_func):
"""2-body multi-element kernel between two force components accelerated
with Numba.
Args:
bond_array_1 (np.ndarray): 2-body bond array of the first local
environment.
c1 (int): Species of the central atom of the first local environment.
etypes1 (np.ndarray): Species of atoms in the first local
environment.
bond_array_2 (np.ndarray): 2-body bond array of the second local
environment.
c2 (int): Species of the central atom of the second local environment.
etypes2 (np.ndarray): Species of atoms in the second local
environment.
d1 (int): Force component of the first environment (1=x, 2=y, 3=z).
d2 (int): Force component of the second environment (1=x, 2=y, 3=z).
sig (float): 2-body signal variance hyperparameter.
ls (float): 2-body length scale hyperparameter.
r_cut (float): 2-body cutoff radius.
cutoff_func (Callable): Cutoff function.
Return:
float: Value of the 2-body kernel.
"""
kernel_matrix = np.zeros((3, 3))
ls1 = 1 / (2 * ls * ls)
ls2 = 1 / (ls * ls)
ls3 = ls2 * ls2
sig2 = sig * sig
for m in range(bond_array_1.shape[0]):
ri = bond_array_1[m, 0]
e1 = etypes1[m]
for n in range(bond_array_2.shape[0]):
e2 = etypes2[n]
# check if bonds agree
if (c1 == c2 and e1 == e2) or (c1 == e2 and c2 == e1):
rj = bond_array_2[n, 0]
r11 = ri - rj
D = r11 * r11
# Note: Some redundancy here; can move this higher up.
for d1 in range(3):
ci = bond_array_1[m, d1 + 1]
fi, fdi = cutoff_func(r_cut, ri, ci)
for d2 in range(3):
cj = bond_array_2[n, d2 + 1]
fj, fdj = cutoff_func(r_cut, rj, cj)
A = ci * cj
B = r11 * ci
C = r11 * cj
kernel_matrix[d1, d2] += \
force_helper(A, B, C, D, fi, fj, fdi, fdj,
ls1, ls2, ls3, sig2)
return kernel_matrix