def F3i_I_eigs_list(E_list, L, F3_list, I, flip=False):
out = []
for i in range(len(E_list)):
E = E_list[i]
F3 = F3_list[i]
if flip == False: # project before inverting F3
F3_I = proj.irrep_proj(F3, E, L, I) # works for all shells
if F3_I.shape == ():
F3i_I = 1 / F3_I
F3i_I_eigs = F3i_I
else:
F3_I_eigs = defns.chop(
np.array(sorted(LA.eigvals(F3_I), key=abs,
reverse=True)).real)
#F3i_I = defns.chop(LA.inv(F3_I))
if F3_I_eigs[-1] == 0:
print(E, F3_I_eigs)
sys.exit()
else:
F3i_I_eigs = np.array([1 / x for x in F3_I_eigs])
elif flip == True: # invert F3 before projecting
F3i = defns.chop(LA.inv(F3))
F3i_I = proj.irrep_proj(F3i, E, L, I)
F3i_I_eigs = defns.chop(np.array(sorted(LA.eigvals(F3i_I))).real)
out.append(F3i_I_eigs)
return out
def F3mat00iso(E, L, Lista0, r0, P0, a2, alpha, IPV=0):
F00 = Fmat00(E, L, alpha, IPV)
F00o3 = 1. / 3 * F00
Gt00 = Gmatrix.Gmat00(E, L)
res = []
ones = np.ones(len(F00))
for a0 in Lista0:
K2it00 = K2i_mat.K2inv_mat00(E, L, a0, r0, P0, IPV)
Hi00 = chop(LAinv(K2it00 + F00 + Gt00))
f3mat = 1 / L**3 * chop((F00o3 - F00 @ Hi00 @ F00))
res.append(1. / (ones @ f3mat @ ones))
return res
def K33Bmat(E, L, a0, a2):
nnk_list = list_nnk(E, L)
N = len(nnk_list)
#print(nnk_list)
#print(N)
Gfull = []
for p in range(N):
nnp = list(nnk_list[p])
Gp = []
for k in range(N):
nnk = list(nnk_list[k])
Gpk = np.zeros((6, 6))
for i1 in range(6):
[l1, m1] = Gmatrix.lm_idx(i1)
for i2 in range(6):
[l2, m2] = Gmatrix.lm_idx(i2)
Gpk[i1,
i2] = K33B.K3cubicB(E, 2 * math.pi / L * np.array(nnp),
l1, m1,
2 * math.pi / L * np.array(nnk),
l2, m2)
Gp.append(Gpk)
Gfull.append(Gp)
matrix = np.ones_like(chop(np.block(Gfull)))
print(matrix.shape)
return pr.irrep_proj(matrix, E, L, "A1")
def Gmat(E, L):
nnk_list = list_nnk(E, L)
N = len(nnk_list)
#print(nnk_list)
#print(N)
Gfull = []
for p in range(N):
nnp = list(nnk_list[p])
Gp = []
for k in range(N):
nnk = list(nnk_list[k])
Gpk = np.zeros((6, 6))
for i1 in range(6):
[l1, m1] = lm_idx(i1)
for i2 in range(6):
[l2, m2] = lm_idx(i2)
Gpk[i1, i2] = G(E, L, nnp, nnk, l1, m1, l2, m2)
Gp.append(Gpk)
Gfull.append(Gp)
return chop(np.block(Gfull))
def F3i_iso_mat(E, L, a0, r0, P0, a2, alpha):
F3_iso = F3_iso_mat(E, L, a0, r0, P0, a2, alpha)
if F3_iso.shape == ():
return 1 / F3_iso
else:
return chop(LA.inv(F3_iso))
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 K3mat(E, L, K0, K1, K2, A, B, Ytype):
nnk_list = list_nnk(E, L)
N = len(nnk_list)
K3full = []
for p in range(N):
pvec = [i * 2 * pi / L for i in nnk_list[p]]
K3p = []
for k in range(N):
kvec = [i * 2 * pi / L for i in nnk_list[k]]
K3pk = np.zeros((6, 6))
for i1 in range(6):
[lp, mp] = lm_idx(i1)
for i2 in range(6):
[l, m] = lm_idx(i2)
K3pk[i1][i2] = K3quad(E, pvec, lp, mp, kvec, l, m, K0, K1,
K2, A, B, Ytype)
K3p.append(K3pk)
K3full.append(K3p)
return chop(np.block(K3full))
def F3i_A1_mat(E, L, a0, r0, P0, a2, alpha):
F3_A1 = F3_A1_mat(E, L, a0, r0, P0, a2, alpha)
if F3_A1.shape == ():
return 1 / F3_A1
else:
return chop(LA.inv(F3_A1))
def F3i_I_mat(E, L, a0, r0, P0, a2, alpha, I):
F3_I = F3_I_mat(E, L, a0, r0, P0, a2, alpha, I)
if F3_I.shape == ():
return 1 / F3_I
else:
return chop(LA.inv(F3_I))
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 Rmat(n, t):
N = LA.norm(n)
n = [i / N for i in n]
n_sin = np.array([[0, -n[2], n[1]], [n[2], 0, -n[0]], [-n[1], n[0], 0]])
return defns.chop(
np.cos(t) * np.identity(3) + np.sin(t) * n_sin +
(1 - np.cos(t)) * np.outer(n, n))
def F3i_A1_eigs_list(E_list, L, F3_list):
out = []
for i in range(len(E_list)):
E = E_list[i]
F3 = F3_list[i]
#F3_A1 = proj.A1_proj_old(F3,E,L) # only works for 2 shells
F3_A1 = proj.A1_proj(F3, E, L) # works for all shells
if F3_A1.shape == ():
F3i_A1 = 1 / F3_A1
F3i_A1_eigs = F3i_A1
else:
F3i_A1 = defns.chop(LA.inv(F3_A1))
F3i_A1_eigs = defns.chop(np.array(sorted(LA.eigvals(F3i_A1))).real)
out.append(F3i_A1_eigs)
return out
def P_A1_subspace(E, L):
P_A1 = P_A1_full(E, L)
elist, vlist = LA.eig(P_A1)
# eigenvalues should all be 0 or 1; only want 1's
ivec = [i for i, e in enumerate(elist) if abs(e - 1) < 1e-13]
if len(ivec) != int(round(np.trace(P_A1))):
print('Error in P_A1_subspace: wrong subspace dimension')
return defns.chop(vlist[:, ivec].real)
def F3i_I_eigs_o(E, L, a0, r0, P0, a2, alpha, I, shell):
F3 = F3mat(E, L, a0, r0, P0, a2, alpha)
F3_I_o = proj.irrep_proj_o(F3, E, L, I, shell)
F3i_I_o = chop(LA.inv(F3_I_o))
# F3i = chop(LA.inv(F3)) # temporary BLEH
# F3i_I_o = proj.irrep_proj_o( F3i,E,L,I,shell ) # temporary BLEH
return np.array(sorted(LA.eigvals(F3i_I_o))).real
def F3i_eigs_list(E_list, L, F3_list):
out = []
for i in range(len(E_list)):
F3 = F3_list[i]
F3i = defns.chop(LA.inv(F3))
F3i_eigs = np.array(sorted(LA.eigvals(F3i))).real
out.append(F3i_eigs)
return out
def F3i_I_eigs_list_o(E_list, L, F3_list, I, shell):
out = []
for i in range(len(E_list)):
E = E_list[i]
F3 = F3_list[i]
F3_I = proj.irrep_proj_o(F3, E, L, I, shell) # works for all shells
if F3_I.shape == ():
F3i_I = 1 / F3_I
F3i_I_eigs = F3i_I
else:
F3i_I = defns.chop(LA.inv(F3_I))
F3i_I_eigs = defns.chop(np.array(sorted(LA.eigvals(F3i_I))).real)
# F3i = defns.chop(LA.inv(F3)) # temporary BLEH
# F3i_I = proj.irrep_proj_o(F3i,E,L,I,shell) # temporary BLEH
# F3i_I_eigs = defns.chop(np.array(sorted(LA.eigvals(F3i_I))).real) # temporary BLEH
out.append(F3i_I_eigs)
return out
def P_irrep_subspace_o_l(E, L, I, shell, l, lblock=False):
P_block_list = []
for nk in defns.shell_list(E, L):
if list(nk) == list(shell):
P_block_list.append(P_irrep_o_l(shell, l, I, lblock))
else:
P_block_list.append(np.zeros(P_irrep_o_l(nk, l, I, lblock).shape))
P_I = block_diag(*P_block_list)
elist, vlist = LA.eig(P_I)
# eigenvalues should all be 0 or 1; only want 1's
ivec = [i for i, e in enumerate(elist) if abs(e - 1) < 1e-13]
if len(ivec) != int(round(np.trace(P_I))):
print('Error in P_irrep_subspace: wrong subspace dimension')
Psub = defns.chop(vlist[:, ivec].real)
if ivec == []:
return Psub
else:
return defns.chop(LA.qr(Psub)[0])
def F3i_22_I_eigs_list(E_list, L, F3_22_list, I, flip=False):
out = []
for i in range(len(E_list)):
E = E_list[i]
F3 = F3_22_list[i]
if flip == False: # project before inverting F3
F3_I = proj.irrep_proj_22(F3, E, L, I) # works for all shells
if F3_I.shape == ():
F3i_I = 1 / F3_I
F3i_I_eigs = F3i_I
else:
F3i_I = defns.chop(LA.inv(F3_I))
elif flip == True: # invert F3 before projecting
F3i = defns.chop(LA.inv(F3))
F3i_I = proj.irrep_proj_22(F3i, E, L, I)
F3i_I_eigs = defns.chop(np.array(sorted(LA.eigvals(F3i_I))).real)
out.append(F3i_I_eigs)
return out
def Gmat00(E, L):
nnk_list = list_nnk(E, L)
N = len(nnk_list)
Gfull = np.zeros((N, N))
for p in range(N):
nnp = list(nnk_list[p])
for k in range(N):
nnk = list(nnk_list[k])
Gfull[p][k] = G(E, L, nnp, nnk, 0, 0, 0, 0)
return chop(Gfull)
def F3_iso_fast(E, L, a0, r0, P0, a2, alpha):
Ft00_A1 = Fmat00_A1(E, L, alpha)
Gt00_A1 = Gmatrix.Gmat00_A1(E, L)
K2it00_A1 = K2i_mat.K2inv_mat00_A1(E, L, a0, r0, P0)
Hi_00_A1 = chop(LA.inv(K2it00_A1 + Ft00_A1 + Gt00_A1))
F3_00_A1 = 1 / L**3 * (1 / 3 * Ft00_A1 - Ft00_A1 @ Hi_00_A1 @ Ft00_A1)
shells = shell_list(E, L)
F3_iso = 0
for ip in range(len(shells)):
for ik in range(len(shells)):
F3_iso += F3_00_A1[ip, ik] * sqrt(
len(shell_nnk_list(shells[ip])) *
len(shell_nnk_list(shells[ik])))
return F3_iso
def F3i_iso_eigs_list_bad(E_list, L, F3_list):
out = []
for i in range(len(E_list)):
E = E_list[i]
F3 = F3_list[i]
F3_iso = proj.iso_proj_bad(F3, E, L)
if F3_iso.shape == ():
F3i_iso = 1 / F3_iso
F3i_iso_eigs = F3i_iso
else:
F3i_iso = defns.chop(LA.inv(F3_iso))
F3i_iso_eigs = np.array(sorted(LA.eigvals(F3i_iso))).real
out.append(F3i_iso_eigs)
return out
def Gmat00(E, L):
nnk_list = list_nnk(E, L)
N = len(nnk_list)
# print(nnk_list)
# print(list(nnk_list[0]))
Gfull = np.zeros((N, N))
for p in range(N):
# nnp = list(nnk_list[p])
nnp = nnk_list[p]
for k in range(N):
# nnk = list(nnk_list[k])
nnk = nnk_list[k]
Gfull[p, k] = G(E, L, np.array(nnp), np.array(nnk), 0, 0, 0, 0)
return chop(Gfull)
def Gmat22(E, L):
nnk_list = list_nnk(E, L)
N = len(nnk_list)
Gfull = []
for p in range(N):
nnp = list(nnk_list[p])
Gp = []
for k in range(N):
nnk = list(nnk_list[k])
Gpk = np.zeros((5, 5))
for mp in range(-2, 3):
for m in range(-2, 3):
Gpk[mp, m] = G(E, L, nnp, nnk, 2, mp, 2, m)
Gp.append(Gpk)
Gfull.append(Gp)
return chop(np.block(Gfull))
def Gmat22(E, L):
nnk_list = list_nnk(E, L)
N = len(nnk_list)
Gfull = []
for p in range(N):
nnp = list(nnk_list[p])
Gp = []
for k in range(N):
nnk = list(nnk_list[k])
Gpk = np.zeros((5, 5))
for i in range(5):
for j in range(5):
mp = i - 2
m = j - 2
Gpk[i, j] = G(E, L, nnp, nnk, 2, mp, 2, m)
Gp.append(Gpk)
Gfull.append(Gp)
return chop(np.block(Gfull))
def Gmat00_A1(E, L):
shells = shell_list(E, L)
Nshells = len(shells)
out = np.zeros((Nshells, Nshells))
# Each row/column corresponds to a different shell
for ip in range(Nshells):
op = shell_nnk_list(
shells[ip]) # list of nnp's in shell op (index = ip)
for ik in range(ip, Nshells):
ok = shell_nnk_list(
shells[ik]) # list of nnk's in shell ok (index = ik)
# Sum over G(p,k) for p in op & k in ok (part of A1+ projection)
for nnp in op:
for nnk in ok:
out[ip, ik] += G(E, L, nnp, nnk, 0, 0, 0, 0)
out[ip,
ik] *= 1 / npsqrt(len(op) * len(ok)) # normalization factor
if ip != ik:
out[ik, ip] = out[ip, ik] # take advantage of symmetry
return chop(out)
def F3imat22(E, L, a0, r0, P0, a2, alpha):
return chop(LA.inv(F3mat22(E, L, a0, r0, P0, a2, alpha)))
def F3mat22(E, L, a0, r0, P0, a2, alpha):
F22 = Fmat22(E, L, alpha)
Hi22 = chop(LA.inv(Hmat22(E, L, a2, alpha)))
return 1 / L**3 * chop((1 / 3 * F22 - F22 @ Hi22 @ F22))
def F3imat00(E, L, a0, r0, P0, a2, alpha, IPV=0):
return chop(LA.inv(F3mat00(E, L, a0, r0, P0, a2, alpha, IPV)))
def F3mat00(E, L, a0, r0, P0, a2, alpha, IPV=0):
F00 = Fmat00(E, L, alpha, IPV)
Gt00 = Gmatrix.Gmat00(E, L)
K2it00 = K2i_mat.K2inv_mat00(E, L, a0, r0, P0, IPV)
Hi00 = chop(LA.inv(K2it00 + F00 + Gt00))
return 1 / L**3 * chop((1 / 3 * F00 - F00 @ Hi00 @ F00))
def F3mat(E, L, a0, r0, P0, a2, alpha):
F = Fmat(E, L, alpha)
Hi = chop(LA.inv(Hmat(E, L, a0, r0, P0, a2, alpha)))
return 1 / L**3 * chop((1 / 3 * F - F @ Hi @ F))
