def contract_from_right(R, A, W, B):
r"""Tensor contraction from the right hand side.::
-i- + -i- A -j- +
| |s |
-a- R' = -a- W -b- R
| |t |
-k- + -k- B -l- +
Parameters
----------
R : (b, j, l) ndarray
A : (s, i, j) ndarray
W : (a, b, s, t) ndarray
B : (t, k, l) ndarray
Returns
-------
R' : {(a, i, k) ndarray, (i, k) ndarray}
L'[a, i, k] if ``W`` is not ``None``, otherwise L'[i, k].
"""
if W is not None:
temp = np.einsum('sij,bjl->sbil', A, R)
temp = np.einsum('sbil,abst->tail', temp, W)
temp = np.einsum('tail,tkl->aik', temp, B)
else:
temp = np.einsum('sij,jl->sil', A, R)
temp = np.einsum('sil,skl->ik', temp, B)
return temp
def contract_from_left(L, A, W, B):
r"""Tensor contraction from the left hand side.::
+ -j- + -i- A -j-
| | |s
L'-b- = L -a- W -b-
| | |t
+ -l- + -k- B -l-
Parameters
----------
L : (a, i, k) ndarray
A : (s, i, j) ndarray
W : {(a, b, s, t) ndarray, None}
B : (t, k, l) ndarray
Returns
-------
L' : {(b, j, l) ndarray, (j, l) ndarray}
L'[b, j, l] if ``W`` is not ``None``, otherwise L'[j, l].
"""
if W is not None:
temp = np.einsum('sij,aik->sajk', A, L)
temp = np.einsum('sajk,abst->tbjk', temp, W)
temp = np.einsum('tbjk,tkl->bjl', temp, B)
else:
temp = np.einsum('sij,ik->sjk', A, L)
temp = np.einsum('sjk,skl->jl', temp, B)
return temp
def coarse_grain_mpo(W, X):
"""Coarse-graining of two site MPO into one site.::
|su |s |u
-a- R -c- = -a- W -b- X -c-
|tv |t |v
Parameters
----------
W : (a, b, s, t) ndarray
A MPS matrix.
X : (b, c, u, v) ndarray
A MPS matrix.
Returns
-------
R : (a, c, su, tv) ndarray
A MPS matrix.
"""
R = np.einsum("abst,bcuv->acsutv", W, X)
sh = [
W.shape[0], # a
X.shape[1], # c
W.shape[2] * X.shape[2], # su
W.shape[3] * X.shape[3]
] # tv
return np.reshape(R, sh)
def _move_right(mat, mat_next, _trunc):
shape = np.shape(mat)
# SVD on mat[si, j]
mat = np.reshape(mat, (shape[0] * shape[1], shape[2]))
U, S, V = np.linalg.svd(mat, full_matrices=0)
# truncated to compress.
U, S, V, compress_error = compress_svd(U, S, V, _trunc)
mat = np.reshape(U, (shape[0], shape[1], -1)) # U[si, m]
SV = np.matmul(np.diag(S), V)
mat_next = np.einsum('mj,tjk->tmk', SV, mat_next)
return mat, mat_next
def _move_left(mat, mat_prev, _trunc):
shape = np.shape(mat)
mat = np.reshape(
np.transpose(mat, (1, 0, 2)), # mat[i, s, j]
(shape[1], shape[0] * shape[2])) # SVD on mat[i, sj]
U, S, V = np.linalg.svd(mat, full_matrices=0)
# truncated to compress.
U, S, V, compress_error = compress_svd(U, S, V, _trunc)
mat = np.reshape(V, (-1, shape[0], shape[2])) # V[m, sj]
mat = np.transpose(mat, (1, 0, 2)) # mat[s, m, j]
US = np.matmul(U, np.diag(S))
mat_prev = np.einsum('rhi,im->rhm', mat_prev, US)
return mat, mat_prev
def coarse_grain_mps(A, B):
"""Coarse-graining of two-site MPS into one site.::
|st |s |t
-i- C -k- = -i- A -j- B -k-
Parameters
----------
A : (s, i, j) ndarray
A MPS matrix.
B : (t, j, k) ndarray
A MPS matrix.
Returns
-------
C : (st, i, k) ndarray
A MPS matrix.
"""
shape_C = [A.shape[0] * B.shape[0], A.shape[1], B.shape[2]]
C = np.einsum("sij,tjk->stik", A, B)
return np.reshape(C, shape_C)
def _matvec(self, A):
temp = np.einsum('aij,sik->ajsk', self.L, np.reshape(A, self.io_shape))
temp = np.einsum('ajsk,abst->bjtk', temp, self.W)
temp = np.einsum('bjtk,bkl->tjl', temp, self.R)
return np.reshape(temp, self.size)