def spherical_harmonics_and_derivatives(R_c, lmax=LMAX):
R_c = np.asarray(R_c)
drlYdR_lmc = []
rlY_lm = spherical_harmonics(R_c, lmax)
for l, rlY_m in enumerate(rlY_lm):
drlYdR_mc = np.empty((2 * l + 1, 3))
for m in range(2 * l + 1):
L = l**2 + m
drlYdR_mc[m, :] = nablarlYL(L, R_c)
drlYdR_lmc.append(drlYdR_mc)
return rlY_lm, drlYdR_lmc
def spherical_harmonics_and_derivatives(R_c, lmax=LMAX):
R_c = np.asarray(R_c)
drlYdR_lmc = []
rlY_lm = spherical_harmonics(R_c, lmax)
for l, rlY_m in enumerate(rlY_lm):
drlYdR_mc = np.empty((2 * l + 1, 3))
for m in range(2 * l + 1):
L = l**2 + m
drlYdR_mc[m, :] = nablarlYL(L, R_c)
drlYdR_lmc.append(drlYdR_mc)
return rlY_lm, drlYdR_lmc
def _stress_tensor_contribution(self, v1, v2, cache, G1, G2,
G_Gv, a_xG, c_axi, q):
f_IG = np.empty((self.nI, G2 - G1), complex)
K_v = self.pd.K_qv[q]
for a, j, i1, i2, I1, I2 in self:
l = self.lf_aj[a][j][0]
spline = self.spline_aj[a][j]
f_G, dfdGoG_G = cache[spline]
emiGR_G = np.exp(-1j * np.dot(G_Gv, self.pos_av[a]))
f_IG[I1:I2] = (emiGR_G * (-1.0j)**l *
np.exp(1j * np.dot(K_v, self.pos_av[a])) * (
dfdGoG_G[G1:G2] * G_Gv[:, v1] * G_Gv[:, v2] *
self.Y_qLG[q][l**2:(l + 1)**2, G1:G2] +
f_G[G1:G2] * G_Gv[:, v1] *
[nablarlYL(L, G_Gv.T)[v2]
for L in range(l**2, (l + 1)**2)]))
c_xI = np.zeros(a_xG.shape[:-1] + (self.nI,), self.pd.dtype)
b_xI = c_xI.reshape((np.prod(c_xI.shape[:-1], dtype=int), self.nI))
a_xG = a_xG.reshape((-1, a_xG.shape[-1]))
alpha = 1.0 / self.pd.gd.N_c.prod()
if self.pd.dtype == float:
alpha *= 2
if G1 == 0:
f_IG[:, 0] *= 0.5
f_IG = f_IG.view(float)
a_xG = a_xG.view(float)
gemm(alpha, f_IG, a_xG, 0.0, b_xI, 'c')
stress = 0.0
for a, I1, I2 in self.indices:
stress -= self.eikR_qa[q][a] * (c_axi[a] * c_xI[..., I1:I2]).sum()
return stress.real
def evaluate(self, l):
drlYdR_mc = np.empty((2 * l + 1, 3))
L0 = l**2
for m in range(2 * l + 1):
drlYdR_mc[m, :] = nablarlYL(L0 + m, self.R_c)
return drlYdR_mc
L v=1 L
dY
L
A = --- r
Lv dr
v
"""
# A_nvL is defined as above, n is an expansion point index (50 Lebedev points).
rnablaY_nLv = np.empty((len(R_nv), 25, 3))
for rnablaY_Lv, Y_L, R_v in zip(rnablaY_nLv, Y_nL, R_nv):
for l in range(5):
for L in range(l**2, (l + 1)**2):
rnablaY_Lv[L] = nablarlYL(L, R_v) - l * R_v * Y_L[L]
class PAWXCCorrection:
def __init__(
self,
w_jg, # all-lectron partial waves
wt_jg, # pseudo partial waves
nc_g, # core density
nct_g, # smooth core density
rgd, # radial grid descriptor
jl, # ?
lmax, # maximal angular momentum to consider
Exc0, # xc energy of reference atom
phicorehole_g, # ?
fcorehole, # ?
def evaluate(self, l):
drlYdR_mc = np.empty((2 * l + 1, 3))
L0 = l**2
for m in range(2 * l + 1):
drlYdR_mc[m, :] = nablarlYL(L0 + m, self.R_c)
return drlYdR_mc
L v=1 L
dY
L
A = --- r
Lv dr
v
"""
# A_nvL is defined as above, n is an expansion point index (50 Lebedev points).
rnablaY_nLv = np.empty((len(R_nv), 25, 3))
for rnablaY_Lv, Y_L, R_v in zip(rnablaY_nLv, Y_nL, R_nv):
for l in range(5):
for L in range(l**2, (l + 1)**2):
rnablaY_Lv[L] = nablarlYL(L, R_v) - l * R_v * Y_L[L]
class PAWXCCorrection:
def __init__(self,
w_jg, # all-lectron partial waves
wt_jg, # pseudo partial waves
nc_g, # core density
nct_g, # smooth core density
rgd, # radial grid descriptor
jl, # ?
lmax, # maximal angular momentum to consider
Exc0, # xc energy of reference atom
phicorehole_g, # ?
fcorehole, # ?
tauc_g, # kinetic core energy array