mapar = mbpar
for ma in range(0, l + 1, 1):
if mapar == 1:
ulist[llup] = np.conj(ulist[llu])
else:
ulist[llup] = -np.conj(ulist[llu])
mapar = -mapar
llu += 1
llup -= 1
mbpar = -mbpar
mb += 1
return
@nb.njit(nb.c16(nb.c16, nb.c16, nb.i8, nb.i8),
cache=True,
fastmath=True,
nogil=True)
def sph_harm(Ra, Rb, l, m):
'''
Spherical harmonics from Wigner-D functions
args:
Ra: complex, Cayley-Klein parameter for spherical harmonic
Rb: complex, Cayley-Klein parameter for spherical harmonic
l: int, index of spherical harmonic l >= 0
m: int, index of spherical harmonic -l <= m <= l
The spherical harmonics are a subset of Wigner-D matrices,
and can be calculated in the same manner
3.28721858553429e+293, 5.42391066613159e+295, 9.00369170577843e+297,
1.503616514865e+300
],
dtype=np.float64)
return fac_arr[n]
@nb.njit(nb.f8(nb.i8, nb.i8, nb.i8), cache=True, fastmath=True, nogil=True)
def deltacg(l1, l2, l):
sfaccg = factorial((l1 + l2 + l) // 2 + 1)
return np.sqrt(
factorial((l1 + l2 - l) // 2) * factorial(
(l1 - l2 + l) // 2) * factorial((-l1 + l2 + l) // 2) / sfaccg)
@nb.njit(nb.c16(nb.c16, nb.c16, nb.i8, nb.i8, nb.i8),
cache=True,
fastmath=True,
nogil=True)
def Wigner_D(Ra, Rb, twol, twomp, twom):
ra, phia = cmath.polar(Ra)
rb, phib = cmath.polar(Rb)
epsilon = 10**(-15)
if ra <= epsilon:
if twomp != -twom or abs(twomp) > twol or abs(twom) > twol:
return 0.0j
else:
if (twol - twom) % 4 == 0:
if m < 0 or m > j:
continue
# convert array arguments to CG args
J1 = j1 / 2
J2 = j2 / 2
J = j / 2
M1 = m1 - J1
M2 = m2 - J2
M = m - J
# add CG coef to cgs array
cgs[j1, j2, j, m1, m2] = CG(J1, M1, J2, M2, J, M)
@numba.njit(numba.c16(numba.i8, numba.i8, numba.i8, numba.f8, numba.f8,
numba.f8),
cache=True,
fastmath=True,
nogil=True)
def U(j, m, m_prime, psi, theta, phi):
'''
Computes the 4-D hyperspherical harmonic given the three angular coordinates
and indices
args:
j: free integer parameter, used to index arrays, corresponds to free half integral/
integral constants used for calculation, int
m, mp: free integer parameter, used to index arrays, cooresponds to free half integral/
integral constants used for calculation, int
atm_nums[i, j] = neighbor[0].specie.number
else:
raise NotImplementedError('Specified backend not supported')
# assign these arrays to attributes
self.center_atoms = center_atoms
self.neighborlist = neighborlist
self.neighbor_indices = neighbor_inds
self.atomic_numbers = atm_nums
self.site_atomic_numbers = site_atomic_numbers
return
@nb.njit(nb.c16(nb.c16, nb.c16, nb.i8, nb.i8), cache=True,
fastmath=True, nogil=True)
def sph_harm(Ra, Rb, l, m):
'''
Spherical harmonics from Wigner-D functions
args:
Ra: complex, Cayley-Klein parameter for spherical harmonic
Rb: complex, Cayley-Klein parameter for spherical harmonic
l: int, index of spherical harmonic l >= 0
layer: int, index of spherical harmonic -l <= layer <= l
The spherical harmonics are a subset of Wigner-D matrices,
and can be calculated in the same manner
'''
if m % 2 == 0:
np.sin(beta / 2)**(2 * J - M - MP - 2 * k) / factorial(k) /
factorial(J - M - k) / factorial(J - MP - k) /
factorial(M + MP + k))
if derivative == True:
temp *= ((2 * J - M - MP - 2 * k) / np.tan(beta / 2) -
(M + MP + 2 * k) * np.tan(beta / 2))
d += temp
d *= constant
return d
@numba.njit(numba.c16(numba.f8, numba.f8, numba.f8, numba.f8, numba.f8,
numba.f8, numba.b1),
cache=True,
fastmath=True,
nogil=True)
def wigner_D(J, M, MP, alpha, beta, gamma, derivative):
'''
Large Wigner D function
Ref: Quantum theory of angular momentum D.A. Varshalovich 1988
Args:
alpha: float
First euler angle of rotation
beta: float
Second euler angle of rotation
gamma: float
