def SimpleUpdate_down(A, B, C, R, la, lb, lc, U):
#
# 0 1
# \| |/ \|
# A B A index 0: outgoing
# \ | / \2 index 2: ingoint
# R
# | 0 1
# C/ \R/
# | |
# 2
#
#
A = A * la[:, None, None]
B = B * lb[:, None, None]
C = C * lc[:, None, None]
T = np.transpose(
np.tensordot(
A, np.tensordot(B, np.tensordot(C, R, ([2], [2])), ([2], [3])),
([2], [4])), [0, 2, 4, 1, 3, 5])
V = np.tensordot(T, U, ([3, 4, 5], [3, 4, 5]))
Tmp = np.tensordot(V, V, ([1, 2, 4, 5], [1, 2, 4, 5])) ## (0,3)
#uA, la_new = tensor_eigh(Tmp, (0,1),(2,3),D_cut)
uA, la_new, _ = tensor_svd(Tmp, (0, 1), (2, 3), D_cut)
la_new = np.sqrt(la_new)
la_new = la_new / np.sqrt(np.dot(la_new, la_new))
A = uA * (1 / la)[:, None, None]
Tmp = np.tensordot(V, V, ([0, 2, 3, 5], [0, 2, 3, 5])) ## (1,4)
#uB, lb_new = tensor_eigh(Tmp, (0,1),(2,3),D_cut)
uB, lb_new, _ = tensor_svd(Tmp, (0, 1), (2, 3), D_cut)
lb_new = np.sqrt(lb_new)
lb_new = lb_new / np.sqrt(np.dot(lb_new, lb_new))
B = uB * (1 / lb)[:, None, None]
Tmp = np.tensordot(V, V, ([0, 1, 3, 4], [0, 1, 3, 4])) ## (2,5)
#uC, lc_new = tensor_eigh(Tmp, (0,1),(2,3),D_cut)
uC, lc_new, _ = tensor_svd(Tmp, (0, 1), (2, 3), D_cut)
lc_new = np.sqrt(lc_new)
lc_new = lc_new / np.sqrt(np.dot(lc_new, lc_new))
C = uC * (1 / lc)[:, None, None]
R_new = np.tensordot(
uA,
np.tensordot(uB, np.tensordot(V, uC, ([2, 5], [0, 1])),
([0, 1], [1, 3])), ([0, 1], [1, 2]))
R_new /= np.max(abs(R_new))
return A, B, C, R_new, la_new, lb_new, lc_new
def SimpleUpdate_up(B,C,A,R,lb,lc,la,U):
#
B =B*lb[None,None,:]
C =C*lc[None,None,:]
A =A*la[None,None,:]
T = np.transpose(
np.tensordot(
B, np.tensordot(
C, np.tensordot(
A, R, ([0], [2])
), ([0], [3])
), ([0], [4])
), [1, 3, 5, 0, 2, 4]
)
V = np.tensordot(
T, U, ([3, 4, 5], [3, 4, 5])
)
Tmp = np.tensordot(V, V.conj(),([1,2,4,5], [1,2,4,5]) ) ## (0,3)
uB, lb_new, _ = tensor_svd(Tmp,(0,1),(2,3),D)
lb_new = np.sqrt(lb_new)
lb_new = lb_new/np.sqrt(np.dot(lb_new,lb_new))
B = np.transpose(uB*(1/lb)[:,None,None],[2,1,0])
Tmp = np.tensordot(V, V.conj(),([0,2,3,5], [0,2,3,5]) ) ## (1,4)
uC, lc_new, _ = tensor_svd(Tmp,(0,1),(2,3),D)
lc_new = np.sqrt(lc_new)
lc_new = lc_new/np.sqrt(np.dot(lc_new,lc_new))
C = np.transpose(uC*(1/lc)[:,None,None],[2,1,0])
Tmp = np.tensordot(V, V.conj(),([0,1,3,4], [0,1,3,4]) ) ## (2,5)
uA, la_new, _ = tensor_svd(Tmp,(0,1),(2,3),D)
la_new = np.sqrt(la_new)
la_new = la_new/np.sqrt(np.dot(la_new,la_new))
A = np.transpose(uA*(1/la)[:,None,None] ,[2,1,0])
R_new = np.tensordot(
uB.conj(), np.tensordot(
uC.conj(), np.tensordot(
V, uA.conj(), ([2, 5], [0, 1])
), ([0, 1], [1, 3])
), ([0, 1], [1, 2])
)
R_new /=np.max(abs(R_new))
return B, C, A, R_new, lb_new, lc_new, la_new
def SimpleUpdate_up(B, C, A, R, lb, lc, la, U):
#
B = B * lb[None, None, :, None]
C = C * lc[None, None, :, None]
A = A * la[None, None, :, None]
T = np.transpose(
np.tensordot(
B, np.tensordot(C, np.tensordot(A, R, ([0], [2])), ([0], [4])),
([0], [6])), [0, 3, 6, 2, 5, 8, 1, 4, 7])
V = np.tensordot(U, T, ([3, 4, 5], [0, 1, 2]))
Tmp = np.tensordot(V, V.conj(),
([1, 2, 4, 5, 7, 8], [1, 2, 4, 5, 7, 8])) ## (0,3,6)
uB, lb_new, _ = tensor_svd(Tmp, (0, 1, 2), (3, 4, 5), D)
lb_new = lb_new / np.sqrt(np.dot(lb_new, lb_new))
lb_new = lb_new[~(lb_new < args.eps_TEBD)]
uB = uB[:, :, :, :lb_new.shape[0]]
B = np.transpose(uB * (1 / lb)[None, None, :, None], [3, 0, 2, 1])
Tmp = np.tensordot(V, V.conj(),
([0, 2, 3, 5, 6, 8], [0, 2, 3, 5, 6, 8])) ## (1,4,7)
uC, lc_new, _ = tensor_svd(Tmp, (0, 1, 2), (3, 4, 5), D)
lc_new = np.sqrt(lc_new)
lc_new = lc_new / np.sqrt(np.dot(lc_new, lc_new))
lc_new = lc_new[~(lc_new < args.eps_TEBD)]
uC = uC[:, :, :, :lc_new.shape[0]]
C = np.transpose(uC * (1 / lc)[None, None, :, None], [3, 0, 2, 1])
Tmp = np.tensordot(V, V.conj(),
([0, 1, 3, 4, 6, 7], [0, 1, 3, 4, 6, 7])) ## (2,5,8)
uA, la_new, _ = tensor_svd(Tmp, (0, 1, 2), (3, 4, 5), D)
la_new = la_new / np.sqrt(np.dot(la_new, la_new))
la_new = la_new[~(la_new < args.eps_TEBD)]
uA = uA[:, :, :, :la_new.shape[0]]
A = np.transpose(uA * (1 / la)[None, None, :, None], [3, 0, 2, 1])
R_new = np.tensordot(
uB.conj(),
np.tensordot(uC.conj(),
np.tensordot(uA.conj(), V, ([0, 1, 2], [2, 5, 8])),
([0, 1, 2], [2, 4, 6])), ([0, 1, 2], [2, 3, 4]))
R_new /= np.max(abs(R_new))
return B, C, A, R_new, lb_new, lc_new, la_new
def SimpleUpdate_down(A, B, C, R, la, lb, lc, U):
#
# 0 1
# \| |/ \|
# A B A index 0: outgoing
# \ | / \2 index 2: ingoint
# R
# | 0 1
# C/ \R/
# | |
# 2
#
#
A = A * la[:, None, None, None]
B = B * lb[:, None, None, None]
C = C * lc[:, None, None, None]
T = np.transpose(
np.tensordot(
A, np.tensordot(B, np.tensordot(C, R, ([2], [2])), ([2], [4])),
([2], [6])), [1, 4, 7, 2, 5, 8, 0, 3, 6])
V = np.tensordot(U, T, ([3, 4, 5], [0, 1, 2]))
Tmp = np.tensordot(V, V.conj(),
([1, 2, 4, 5, 7, 8], [1, 2, 4, 5, 7, 8])) ## (0,3,6)
#uA, la_new = tensor_eigh(Tmp, (0,1),(2,3),D)
uA, la_new, _ = tensor_svd(Tmp, (0, 1, 2), (3, 4, 5), D)
la_new = la_new / np.sqrt(np.dot(la_new, la_new))
la_new = la_new[~(la_new < 1e-8)]
uA = uA[:, :, :, :la_new.shape[0]]
A = uA * (1 / la)[None, None, :, None]
A = A.transpose(2, 0, 3, 1)
Tmp = np.tensordot(V, V.conj(),
([0, 2, 3, 5, 6, 8], [0, 2, 3, 5, 6, 8])) ## (1,4,7)
#uB, lb_new = tensor_eigh(Tmp, (0,1),(2,3),D)
uB, lb_new, _ = tensor_svd(Tmp, (0, 1, 2), (3, 4, 5), D)
lb_new = lb_new / np.sqrt(np.dot(lb_new, lb_new))
lb_new = lb_new[~(lb_new < 1e-8)]
uB = uB[:, :, :, :lb_new.shape[0]]
B = uB * (1 / lb)[None, None, :, None]
B = B.transpose(2, 0, 3, 1)
Tmp = np.tensordot(V, V.conj(),
([0, 1, 3, 4, 6, 7], [0, 1, 3, 4, 6, 7])) ## (2,5,8)
#uC, lc_new = tensor_eigh(Tmp, (0,1),(2,3),D)
uC, lc_new, _ = tensor_svd(Tmp, (0, 1, 2), (3, 4, 5), D)
lc_new = lc_new / np.sqrt(np.dot(lc_new, lc_new))
lc_new = lc_new[~(lc_new < 1e-8)]
uC = uC[:, :, :, :lc_new.shape[0]]
C = uC * (1 / lc)[None, None, :, None]
C = C.transpose(2, 0, 3, 1)
R_new = np.tensordot(
uA,
np.tensordot(uB, np.tensordot(V, uC, ([2, 5, 8], [0, 1, 2])),
([0, 1, 2], [1, 3, 5])), ([0, 1, 2], [1, 2, 3]))
R_new /= np.max(abs(R_new))
return A, B, C, R_new, la_new, lb_new, lc_new
