def normalize_tensor(tensor, if_flatten=False, is_enforce=False):
"""
Normalize a tensor
:param tensor: a tensor
:param if_flatten: if flat the tensor into a vector
:return: a tensor or a vector, and the norm
Example:
>>>T = np.array([[[1, 1], [1, 1]],[[1, 1], [1, 1]]])
>>>print(normalize_tensor(T))
(array([[[0.35355339, 0.35355339],
[0.35355339, 0.35355339]],
[[0.35355339, 0.35355339],
[0.35355339, 0.35355339]]]), 2.8284271247461903)
"""
v = tensor.reshape(-1, )
norm = np.linalg.norm(v)
if norm < 1e-30 and not is_enforce:
cprint('InfWarning: norm is too small to normalize', 'magenta')
trace_stack()
if if_flatten:
return v, norm
else:
return tensor, norm
else:
if if_flatten:
return v / norm, norm
else:
return tensor / norm, norm
def bound_vec_operator_right2left(tensor,
op=np.zeros(0),
v=np.zeros(0),
normalize=False,
symme=False):
"""
Contract right boundary vector with transfer matrix of MPS
:param tensor: a tensor of MPS
:param op: operator on physical bonds
:param v: left boundary
:param normalize: if normalized the outcome vector
:param symme: if symmertrized the outcome vector
:return: the outcome vector
Notes: 1.if v leaves empty, this function will use identity as default
Examples:
>>>T = np.array([[[1, 2, 1], [2, 1, 2]], [[2, 0, 2], [1, 3, 1]], [[3, 1, 0], [2, 2, 1]]])
>>>print(bound_vec_operator_right2left(T))
[[15 11 13]
[11 19 15]
[13 15 19]]
>>>print(bound_vec_operator_right2left(T, v = np.array([[1, 1, 1], [1, 2, 1], [2, 2, 1]])))
[[55 54 57]
[53 58 59]
[48 51 50]]
"""
s = tensor.shape
if op.size != 0: # deal with the operator
tensor1 = absorb_matrix2tensor(tensor, op.T, 1)
else: # no operator
tensor1 = tensor.copy()
if v.size == 0: # no input boundary vector v
tensor = tensor.reshape(s[0], s[1] * s[2]).conj()
tensor1 = tensor1.reshape(s[0], s[1] * s[2])
v1 = tensor.dot(tensor1.T)
else: # there is an input boundary vector v
if is_debug:
if v.shape[0] != s[2]:
cprint(
'BondDimError: the v_right has inconsistent dimension with the tensor',
'magenta')
cprint('v.shape = ' + str(v.shape) + '; T.shape = ' + str(s))
trace_stack()
tensor = tensor.reshape(s[0] * s[1], s[2]).conj().dot(v)
v1 = tensor.reshape(s[0], s[1] * s[2]).dot(
tensor1.reshape(s[0], s[1] * s[2]).T)
if normalize:
v1 = normalize_tensor(v1)[0]
if symme:
v1 = (v1 + v1.conj().T) / 2
return v1
def absorb_matrices2tensor_full_fast(tensor, mats):
"""
Absorb tensor with matrices on all bonds
:param tensor: a tensor
:param mats: matrices to contracted on all bonds
:return: tensor after absorb matrices
Example:
>>>T = np.array([[[1, 1], [1, 1]],[[1, 1], [1, 1]]])
>>>M = [np.array([[1, 2], [2, 3]]), np.array([[2, 3], [3, 4]]), np.array([[3, 4], [4, 5]])]
>>>print(absorb_matrices2tensor_full_fast(T, M))
[[[105 135]
[147 189]]
[[175 225]
[245 315]]]
"""
# generally, recommend to use the function 'absorb_matrices2tensor'
# each bond will have a matrix to contract with
# the matrices must be in the right order
# contract the 1st bond of mat with tensor
nb = tensor.ndim
s = np.array(tensor.shape)
is_bug = False
if is_debug:
for n in range(0, nb):
if mats[n].shape[1] != s[n]:
cprint(
'Error: the %d-th matrix has inconsistent dimension with the tensor'
% n, 'magenta')
cprint(
'T.shape = ' + str(s) + ', mat.shape = ' +
str(mats[n].shape), 'magenta')
is_bug = True
for n in range(nb - 1, -1, -1):
tensor = tensor.reshape(np.prod(s[:nb - 1]), s[nb - 1]).dot(mats[n])
s[-1] = mats[n].shape[1]
ind = [nb - 1] + list(range(0, nb - 1))
tensor = tensor.reshape(s).transpose(ind)
s = s[ind]
if is_debug and is_bug:
trace_stack()
# tensor = CONT([tensor] + mats, [[1, 2, 3], [1, -1], [2, -2], [3, -3]])
return tensor