def P_irrep_o_l(shell, l, I, lblock=False):
nnk_list = defns.shell_nnk_list(shell)
Lk = GT.little_group(shell)
d_I = GT.irrep_dim(I)
P_shell = []
for k2 in nnk_list:
R20 = GT.Rvec(k2, shell)
P_k2 = []
for k1 in nnk_list:
R01 = GT.Rvec(shell, k1)
P_block = np.zeros((6, 6))
for R in Lk:
RRR = GT.R_prod(R20, R, R01)
if l == 0:
P_block[0, 0] += GT.chi(RRR, I)
elif l == 2:
P_block[1:, 1:] += GT.chi(RRR, I) * GT.Dmat(RRR)[1:, 1:]
P_block = defns.chop(P_block)
P_k2.append(P_block)
P_shell.append(P_k2)
out = d_I / 48 * np.block(P_shell)
if lblock == True:
if l == 0:
return l0_proj(out)
elif l == 2:
return l2_proj(out)
else:
return out
def A1_little_group_sum(shell):
Lk = GT.little_group(shell)
Usum = np.zeros((6, 6))
for R in Lk:
Usum += GT.Dmat(R)
Usum = defns.chop(Usum / len(Lk))
return Usum
def P_A1_o_naive(shell):
Nk = len(defns.shell_nnk_list(shell))
P_shell = np.zeros((6 * Nk, 6 * Nk))
for R in GT.Oh_list():
P_shell += np.kron(GT.Smat(R, shell).T, GT.Dmat(R))
P_shell = P_shell / 48
return P_shell
def P_A1_o(shell):
shell = list(shell)
No = len(defns.shell_nnk_list(shell))
one_mat = np.ones((No, No)) / No
Pk = A1_little_group_sum(shell)
U_block_list = []
for p in defns.shell_nnk_list(shell):
p = list(p)
U_block_list.append(GT.Dmat(GT.Rvec(p, shell)))
U = block_diag(*U_block_list)
return U @ np.kron(one_mat, Pk) @ U.T