def construct_X_qnmat(self, addlist):
pbond = self.model.pbond_list
xqnl = np.array(self.cv_mpo.qn[addlist[0]])
xqnr = np.array(self.cv_mpo.qn[addlist[-1] + 1])
xqnmat = xqnl.copy()
xqnsigmalist = []
for idx in addlist:
sigmaqn = self.model.basis[idx].sigmaqn
xqnsigma = np.array(list(product(sigmaqn, repeat=2)))
xqnsigma = xqnsigma.reshape(pbond[idx], pbond[idx], 2)
xqnmat = self.qnmat_add(xqnmat, xqnsigma)
xqnsigmalist.append(xqnsigma)
xqnmat = self.qnmat_add(xqnmat, xqnr)
matshape = list(xqnmat.shape)
if self.method == "1site":
if xqnmat.ndim == 4:
if not self.cv_mpo.to_right:
xqnmat = np.moveaxis(xqnmat.reshape(matshape + [1]), -1,
-2)
else:
xqnmat = xqnmat.reshape([1] + matshape)
if not self.cv_mpo.to_right:
xqnbigl = xqnl.copy()
xqnbigr = self.qnmat_add(xqnsigmalist[0], xqnr)
if xqnbigr.ndim == 3:
rshape = list(xqnbigr.shape)
xqnbigr = np.moveaxis(xqnbigr.reshape(rshape + [1]), -1,
-2)
else:
xqnbigl = self.qnmat_add(xqnl, xqnsigmalist[0])
xqnbigr = xqnr.copy()
if xqnbigl.ndim == 3:
lshape = list(xqnbigl.shape)
xqnbigl = xqnbigl.reshape([1] + lshape)
else:
if xqnmat.ndim == 6:
if addlist[0] != 0:
xqnmat = np.moveaxis(xqnmat.resahpe(matshape + [1]), -1,
-2)
else:
xqnmat = xqnmat.reshape([1] + matshape)
xqnbigl = self.qnmat_add(xqnl, xqnsigmalist[0])
if xqnbigl.ndim == 3:
lshape = list(xqnbigl.shape)
xqnbigl = xqnbigl.reshape([1] + lshape)
xqnbigr = self.qnmat_add(xqnsigmalist[-1], xqnr)
if xqnbigr.ndim == 3:
rshape = list(xqnbigr.shape)
xqnbigr = np.moveaxis(xqnbigr.reshape(rshape + [1]), -1, -2)
xshape = list(xqnmat.shape)
del xshape[-1]
if len(xshape) == 3:
if not self.cv_mpo.to_right:
xshape = xshape + [1]
else:
xshape = [1] + xshape
return xqnmat, xqnbigl, xqnbigr, xshape
def construct_qnmat(mps, pbond, addlist, method, system):
"""
construct the quantum number pattern, the structure is as the coefficient
QN: quantum number list at each bond
pbond : physical pbond
addlist : the sigma orbital set
"""
# print(method)
assert method in ["1site", "2site"]
assert system in ["L", "R"]
qnl = np.array(mps.qn[addlist[0]])
qnr = np.array(mps.qn[addlist[-1] + 1])
qnmat = qnl.copy()
qnsigmalist = []
for idx in addlist:
qnsigma = mps[idx].sigmaqn
qnmat = np.add.outer(qnmat, qnsigma)
qnsigmalist.append(qnsigma)
qnmat = np.add.outer(qnmat, qnr)
if method == "1site":
if system == "R":
qnbigl = qnl
qnbigr = np.add.outer(qnsigmalist[-1], qnr)
else:
qnbigl = np.add.outer(qnl, qnsigmalist[0])
qnbigr = qnr
else:
qnbigl = np.add.outer(qnl, qnsigmalist[0])
qnbigr = np.add.outer(qnsigmalist[-1], qnr)
return qnmat, qnbigl, qnbigr
def auto_corr(self) -> np.ndarray:
"""
Correlation function :math:`C(t)`.
:returns: 1-d numpy array containing the correlation function evaluated at each time step.
"""
return np.array(self._auto_corr)
def inter_change(ori_mat):
matshape = ori_mat.shape
len_mat = int(np.prod(np.array(matshape[:-1])))
ori_mat = ori_mat.reshape(len_mat, 2)
change_mat = copy.deepcopy(ori_mat)
change_mat[:, 0], change_mat[:, 1] = ori_mat[:, 1], ori_mat[:, 0]
return change_mat.reshape(matshape)
def qnmat_add(self, mat_l, mat_r):
lshape, rshape = mat_l.shape, mat_r.shape
lena = int(np.prod(np.array(lshape)) / 2)
lenb = int(np.prod(np.array(rshape)) / 2)
matl = mat_l.reshape(lena, 2)
matr = mat_r.reshape(lenb, 2)
lr1 = np.add.outer(matl[:, 0], matr[:, 0]).flatten()
lr2 = np.add.outer(matl[:, 1], matr[:, 1]).flatten()
lr = np.zeros((len(lr1), 2))
lr[:, 0] = lr1
lr[:, 1] = lr2
shapel = list(mat_l.shape)
del shapel[-1]
shaper = list(mat_r.shape)
del shaper[-1]
lr = lr.reshape(shapel + shaper + [2])
return lr
def _get_big_qn(self, idx):
assert self.qnidx == idx
mt: Matrix = self[idx]
sigmaqn = np.array(mt.sigmaqn)
qnl = np.array(self.qn[idx])
qnr = np.array(self.qn[idx + 1])
assert qnl.size == mt.shape[0]
assert qnr.size == mt.shape[-1]
assert sigmaqn.size == mt.pdim_prod
if self.to_right:
qnbigl = np.add.outer(qnl, sigmaqn)
qnbigr = qnr
else:
qnbigl = qnl
qnbigr = np.add.outer(sigmaqn, qnr)
qnmat = np.add.outer(qnbigl, qnbigr)
return qnbigl, qnbigr, qnmat
def _get_big_qn(self, cidx: List[int]):
r""" get the quantum number of L-block and R-block renormalized basis
Parameters
----------
cidx : list
a list of center(active) site index. For 1site/2site algorithm, cidx
has one/two elements.
Returns
-------
qnbigl : np.ndarray
super-L-block (L-block + active site if necessary) quantum number
qnbigr : np.ndarray
super-R-block (active site + R-block if necessary) quantum number
qnmat : np.ndarray
L-block + active site + R-block quantum number
"""
if len(cidx) == 2:
cidx = sorted(cidx)
assert cidx[0] + 1 == cidx[1]
elif len(cidx) > 2:
assert False
assert self.qnidx in cidx
sigmaqn = [np.array(self[idx].sigmaqn) for idx in cidx]
qnl = np.array(self.qn[cidx[0]])
qnr = np.array(self.qn[cidx[-1] + 1])
if len(cidx) == 1:
if self.to_right:
qnbigl = np.add.outer(qnl, sigmaqn[0])
qnbigr = qnr
else:
qnbigl = qnl
qnbigr = np.add.outer(sigmaqn[0], qnr)
else:
qnbigl = np.add.outer(qnl, sigmaqn[0])
qnbigr = np.add.outer(sigmaqn[1], qnr)
qnmat = np.add.outer(qnbigl, qnbigr)
return qnbigl, qnbigr, qnmat
def auto_corr_decomposition(self) -> np.ndarray:
r"""
Correlation function :math:`C(t)` decomposed into contributions from different parts
of the current operator. Generally, the current operator can be split into two parts:
current without phonon assistance and current with phonon assistance.
For example, if the Holstein-Peierls model is considered:
.. math::
\hat H = \sum_{mn} [\epsilon_{mn} + \sum_\lambda \hbar g_{mn\lambda} \omega_\lambda
(b^\dagger_\lambda + b_\lambda) ] a^\dagger_m a_n
+ \sum_\lambda \hbar \omega_\lambda b^\dagger_\lambda b_\lambda
Then current operator without phonon assistance is defined as:
.. math::
\hat j_1 = \frac{e_0}{i\hbar} \sum_{mn} (R_m - R_n) \epsilon_{mn} a^\dagger_m a_n
and the current operator with phonon assistance is defined as:
.. math::
\hat j_2 = \frac{e_0}{i\hbar} \sum_{mn} (R_m - R_n) \hbar g_{mn\lambda} \omega_\lambda
(b^\dagger_\lambda + b_\lambda) a^\dagger_m a_n
With :math:`\hat j = \hat j_1 + \hat j_2`, the correlation function can be
decomposed into four parts:
.. math::
\begin{align}
C(t) & = \langle \hat j(t) \hat j(0) \rangle \\
& = \langle ( \hat j_1(t) + \hat j_2(t) ) (\hat j_1(0) + \hat j_2(0) ) \rangle \\
& = \langle \hat j_1(t) \hat j_1(0) \rangle + \langle \hat j_1(t) \hat j_2(0) \rangle
+ \langle \hat j_2(t) \hat j_1(0) \rangle + \langle \hat j_2(t) \hat j_2(0) \rangle
\end{align}
:return: :math:`n \times 4` array for the decomposed correlation function defined as above
where :math:`n` is the number of time steps.
"""
return np.array(self._auto_corr_deomposition)
def Csvd(
cstruct: np.ndarray,
qnbigl,
qnbigr,
nexciton,
QR=False,
system=None,
full_matrices=True,
ddm=False,
):
"""
block svd the coefficient matrix (l, sigmal, sigmar, r) or (l,sigma,r)
according to the quantum number
ddm is the direct diagonalization the reduced density matrix
"""
Gamma = cstruct.reshape((np.prod(qnbigl.shape), np.prod(qnbigr.shape)))
localqnl = qnbigl.ravel()
localqnr = qnbigr.ravel()
Uset = [] # corresponds to nonzero svd value
Uset0 = [] # corresponds to zero svd value
Vset = []
Vset0 = []
Sset = []
SUset0 = []
SVset0 = []
qnlset = []
qnlset0 = []
qnrset = []
qnrset0 = []
if not ddm:
# different combination
if cstruct.ndim == 4: # density matrix
combine = [[x, nexciton - x] for x in range(nexciton + 1)]
else:
min0 = min(np.min(localqnl), np.min(localqnr))
max0 = max(np.max(localqnl), np.max(localqnr))
combine = [[x, nexciton - x] for x in range(min0, max0 + 1)]
else:
# ddm is for diagonlize the reduced density matrix for multistate
combine = [[x, x] for x in range(nexciton + 1)]
for nl, nr in combine:
lset = np.where(localqnl == nl)[0]
rset = np.where(localqnr == nr)[0]
if len(lset) == 0 or len(rset) == 0:
continue
# Gamma_block = Gamma[np.ix_(lset,rset)]
Gamma_block = Gamma.ravel().take((lset *
Gamma.shape[1]).reshape(-1, 1) +
rset)
if not ddm:
if not QR:
try:
U, S, Vt = scipy.linalg.svd(
Gamma_block,
full_matrices=full_matrices,
lapack_driver="gesdd",
)
except:
# print "Csvd converge failed"
U, S, Vt = scipy.linalg.svd(
Gamma_block,
full_matrices=full_matrices,
lapack_driver="gesvd",
)
dim = S.shape[0]
Sset.append(S)
else:
if full_matrices:
mode = "full"
else:
mode = "economic"
if system == "R":
U, Vt = scipy.linalg.rq(Gamma_block, mode=mode)
elif system == "L":
U, Vt = scipy.linalg.qr(Gamma_block, mode=mode)
else:
assert False
dim = min(Gamma_block.shape)
Uset, Uset0, qnlset, qnlset0, SUset0 = blockappend(
Uset,
Uset0,
qnlset,
qnlset0,
SUset0,
U,
nl,
dim,
lset,
Gamma.shape[0],
full_matrices=full_matrices,
)
Vset, Vset0, qnrset, qnrset0, SVset0 = blockappend(
Vset,
Vset0,
qnrset,
qnrset0,
SVset0,
Vt.T,
nr,
dim,
rset,
Gamma.shape[1],
full_matrices=full_matrices,
)
else:
S, U = scipy.linalg.eigh(Gamma_block)
# numerical error for eigenvalue < 0
for ss in range(len(S)):
if S[ss] < 0:
S[ss] = 0.0
S = np.sqrt(S)
dim = S.shape[0]
Sset.append(S)
Uset, Uset0, qnlset, qnlset0, SUset0 = blockappend(
Uset,
Uset0,
qnlset,
qnlset0,
SUset0,
U,
nl,
dim,
lset,
Gamma.shape[0],
full_matrices=False,
)
if not ddm:
if full_matrices:
Uset = np.concatenate(Uset + Uset0, axis=1)
Vset = np.concatenate(Vset + Vset0, axis=1)
qnlset = qnlset + qnlset0
qnrset = qnrset + qnrset0
if not QR:
# not sorted
SUset = np.concatenate(Sset + SUset0)
SVset = np.concatenate(Sset + SVset0)
return Uset, SUset, qnlset, Vset, SVset, qnrset
else:
return Uset, qnlset, Vset, qnrset
else:
Uset = np.concatenate(Uset, axis=1)
Vset = np.concatenate(Vset, axis=1)
if not QR:
Sset = np.concatenate(Sset)
# sort the singular value in descending order
order = np.argsort(Sset)[::-1]
Uset_order = Uset[:, order]
Vset_order = Vset[:, order]
Sset_order = Sset[order]
qnlset_order = np.array(qnlset)[order].tolist()
qnrset_order = np.array(qnrset)[order].tolist()
return (
Uset_order,
Sset_order,
qnlset_order,
Vset_order,
Sset_order,
qnrset_order,
)
else:
return Uset, qnlset, Vset, qnrset
else:
Uset = np.concatenate(Uset, axis=1)
Sset = np.concatenate(Sset)
return Uset, Sset, qnlset
def x_svd(self, xstruct, xqnbigl, xqnbigr, nexciton, direction, percent=0):
Gamma = xstruct.reshape(
np.prod(xqnbigl.shape) // 2,
np.prod(xqnbigr.shape) // 2)
localXqnl = xqnbigl.ravel()
localXqnr = xqnbigr.ravel()
list_locall = []
list_localr = []
for i in range(0, len(localXqnl), 2):
list_locall.append([localXqnl[i], localXqnl[i + 1]])
for i in range(0, len(localXqnr), 2):
list_localr.append([localXqnr[i], localXqnr[i + 1]])
localXqnl = copy.deepcopy(list_locall)
localXqnr = copy.deepcopy(list_localr)
xuset = []
xuset0 = []
xvset = []
xvset0 = []
xsset = []
xsuset0 = []
xsvset0 = []
xqnlset = []
xqnlset0 = []
xqnrset = []
xqnrset0 = []
if self.spectratype == "abs":
combine = [[[y, 0], [nexciton - y, 0]]
for y in range(nexciton + 1)]
elif self.spectratype == "emi":
combine = [[[0, y], [0, nexciton - y]]
for y in range(nexciton + 1)]
for nl, nr in combine:
lset = np.where(self.condition(np.array(localXqnl), [nl]))[0]
rset = np.where(self.condition(np.array(localXqnr), [nr]))[0]
if len(lset) != 0 and len(rset) != 0:
Gamma_block = Gamma.ravel().take(
(lset * Gamma.shape[1]).reshape(-1, 1) + rset)
try:
U, S, Vt = \
scipy.linalg.svd(Gamma_block, full_matrices=True,
lapack_driver='gesdd')
except:
U, S, Vt = \
scipy.linalg.svd(Gamma_block, full_matrices=True,
lapack_driver='gesvd')
dim = S.shape[0]
xsset.append(S)
# U part quantum number
xuset.append(
svd_qn.blockrecover(lset, U[:, :dim], Gamma.shape[0]))
xqnlset += [nl] * dim
xuset0.append(
svd_qn.blockrecover(lset, U[:, dim:], Gamma.shape[0]))
xqnlset0 += [nl] * (U.shape[0] - dim)
xsuset0.append(np.zeros(U.shape[0] - dim))
# V part quantum number
VT = Vt.T
xvset.append(
svd_qn.blockrecover(rset, VT[:, :dim], Gamma.shape[1]))
xqnrset += [nr] * dim
xvset0.append(
svd_qn.blockrecover(rset, VT[:, dim:], Gamma.shape[1]))
xqnrset0 += [nr] * (VT.shape[0] - dim)
xsvset0.append(np.zeros(VT.shape[0] - dim))
xuset = np.concatenate(xuset + xuset0, axis=1)
xvset = np.concatenate(xvset + xvset0, axis=1)
xsuset = np.concatenate(xsset + xsuset0)
xsvset = np.concatenate(xsset + xsvset0)
xqnlset = xqnlset + xqnlset0
xqnrset = xqnrset + xqnrset0
bigl_shape = list(xqnbigl.shape)
del bigl_shape[-1]
bigr_shape = list(xqnbigr.shape)
del bigr_shape[-1]
if direction == "left":
x, xdim, xqn, compx = update_cv(xvset,
xsvset,
xqnrset,
xuset,
nexciton,
self.m_max,
self.spectratype,
percent=percent)
if (self.method == "1site") and (len(bigr_shape + [xdim]) == 3):
return np.moveaxis(
x.reshape(bigr_shape + [1] + [xdim]), -1, 0),\
xdim, xqn, compx.reshape(bigl_shape + [xdim])
else:
return np.moveaxis(x.reshape(bigr_shape + [xdim]), -1, 0),\
xdim, xqn, compx.reshape(bigl_shape + [xdim])
elif direction == "right":
x, xdim, xqn, compx = update_cv(xuset,
xsuset,
xqnlset,
xvset,
nexciton,
self.m_max,
self.spectratype,
percent=percent)
if (self.method == "1site") and (len(bigl_shape + [xdim]) == 3):
return x.reshape([1] + bigl_shape + [xdim]), xdim, xqn, \
np.moveaxis(compx.reshape(bigr_shape + [xdim]), -1, 0)
else:
return x.reshape(bigl_shape + [xdim]), xdim, xqn, \
np.moveaxis(compx.reshape(bigr_shape + [xdim]), -1, 0)
def construct_X_qnmat(self, addlist, direction):
pbond = self.mol_list.pbond_list
xqnl = np.array(self.cv_mpo.qn[addlist[0]])
xqnr = np.array(self.cv_mpo.qn[addlist[-1] + 1])
xqnmat = xqnl.copy()
xqnsigmalist = []
for idx in addlist:
if self.mol_list.ephtable.is_electron(idx):
xqnsigma = np.array([[[0, 0], [0, 1]], [[1, 0], [1, 1]]])
else:
xqnsigma = []
for i in range((pbond[idx])**2):
xqnsigma.append([0, 0])
xqnsigma = np.array(xqnsigma)
xqnsigma = xqnsigma.reshape(pbond[idx], pbond[idx], 2)
xqnmat = self.qnmat_add(xqnmat, xqnsigma)
xqnsigmalist.append(xqnsigma)
xqnmat = self.qnmat_add(xqnmat, xqnr)
matshape = list(xqnmat.shape)
if self.method == "1site":
if xqnmat.ndim == 4:
if direction == "left":
xqnmat = np.moveaxis(xqnmat.reshape(matshape + [1]), -1,
-2)
else:
xqnmat = xqnmat.reshape([1] + matshape)
if direction == "left":
xqnbigl = xqnl.copy()
xqnbigr = self.qnmat_add(xqnsigmalist[0], xqnr)
if xqnbigr.ndim == 3:
rshape = list(xqnbigr.shape)
xqnbigr = np.moveaxis(xqnbigr.reshape(rshape + [1]), -1,
-2)
else:
xqnbigl = self.qnmat_add(xqnl, xqnsigmalist[0])
xqnbigr = xqnr.copy()
if xqnbigl.ndim == 3:
lshape = list(xqnbigl.shape)
xqnbigl = xqnbigl.reshape([1] + lshape)
else:
if xqnmat.ndim == 6:
if addlist[0] != 0:
xqnmat = np.moveaxis(xqnmat.resahpe(matshape + [1]), -1,
-2)
else:
xqnmat = xqnmat.reshape([1] + matshape)
xqnbigl = self.qnmat_add(xqnl, xqnsigmalist[0])
if xqnbigl.ndim == 3:
lshape = list(xqnbigl.shape)
xqnbigl = xqnbigl.reshape([1] + lshape)
xqnbigr = self.qnmat_add(xqnsigmalist[-1], xqnr)
if xqnbigr.ndim == 3:
rshape = list(xqnbigr.shape)
xqnbigr = np.moveaxis(xqnbigr.reshape(rshape + [1]), -1, -2)
xshape = list(xqnmat.shape)
del xshape[-1]
if len(xshape) == 3:
if direction == "left":
xshape = xshape + [1]
elif direction == "right":
xshape = [1] + xshape
return xqnmat, xqnbigl, xqnbigr, xshape
def optimize_cv(self, lr_group, direction, isite, num, percent=0):
if self.spectratype == "abs":
# quantum number restriction, |1><0|
up_exciton, down_exciton = 1, 0
elif self.spectratype == "emi":
# quantum number restriction, |0><1|
up_exciton, down_exciton = 0, 1
nexciton = 1
first_LR, second_LR, third_LR, forth_LR = lr_group
if self.method == "1site":
add_list = [isite - 1]
first_L = asxp(first_LR[isite - 1])
first_R = asxp(first_LR[isite])
second_L = asxp(second_LR[isite - 1])
second_R = asxp(second_LR[isite])
third_L = asxp(third_LR[isite - 1])
third_R = asxp(third_LR[isite])
forth_L = asxp(forth_LR[isite - 1])
forth_R = asxp(forth_LR[isite])
else:
add_list = [isite - 2, isite - 1]
first_L = asxp(first_LR[isite - 2])
first_R = asxp(first_LR[isite])
second_L = asxp(second_LR[isite - 2])
second_R = asxp(second_LR[isite])
third_L = asxp(third_LR[isite - 2])
third_R = asxp(third_LR[isite])
forth_L = asxp(forth_LR[isite - 2])
forth_R = asxp(forth_LR[isite])
xqnmat, xqnbigl, xqnbigr, xshape = \
self.construct_X_qnmat(add_list, direction)
dag_qnmat, dag_qnbigl, dag_qnbigr = self.swap(xqnmat, xqnbigl, xqnbigr,
direction)
nonzeros = np.sum(self.condition(dag_qnmat,
[down_exciton, up_exciton]))
if self.method == "1site":
guess = moveaxis(self.cv_mpo[isite - 1], (1, 2), (2, 1))
else:
guess = tensordot(moveaxis(self.cv_mpo[isite - 2], (1, 2), (2, 1)),
moveaxis(self.cv_mpo[isite - 1]),
axes=(-1, 0))
guess = guess[self.condition(dag_qnmat,
[down_exciton, up_exciton])].reshape(
nonzeros, 1)
if self.method == "1site":
# define dot path
path_1 = [([0, 1], "abc, adef -> bcdef"),
([2, 0], "bcdef, begh -> cdfgh"),
([1, 0], "cdfgh, fhi -> cdgi")]
path_2 = [([0, 1], "abcd, aefg -> bcdefg"),
([3, 0], "bcdefg, bfhi -> cdeghi"),
([2, 0], "cdeghi, djek -> cghijk"),
([1, 0], "cghijk, gilk -> chjl")]
path_4 = [([0, 1], "ab, acde -> bcde"), ([1,
0], "bcde, ef -> bcdf")]
vecb = multi_tensor_contract(
path_4, forth_L,
moveaxis(self.a_ket_mpo[isite - 1], (1, 2), (2, 1)), forth_R)
vecb = -self.eta * vecb
a_oper_isite = asxp(self.a_oper[isite - 1])
b_oper_isite = asxp(self.b_oper[isite - 1])
h_mpo_isite = asxp(self.h_mpo[isite - 1])
# construct preconditioner
Idt = xp.identity(h_mpo_isite.shape[1])
M1_1 = xp.einsum('aea->ae', first_L)
M1_2 = xp.einsum('eccf->ecf', a_oper_isite)
M1_3 = xp.einsum('dfd->df', first_R)
M1_4 = xp.einsum('bb->b', Idt)
path_m1 = [([0, 1], "ae,b->aeb"), ([2, 0], "aeb,ecf->abcf"),
([1, 0], "abcf, df->abcd")]
pre_M1 = multi_tensor_contract(path_m1, M1_1, M1_4, M1_2, M1_3)
pre_M1 = pre_M1[self.condition(dag_qnmat, [down_exciton, up_exciton])]
M2_1 = xp.einsum('aeag->aeg', second_L)
M2_2 = xp.einsum('eccf->ecf', b_oper_isite)
M2_3 = xp.einsum('gbbh->gbh', h_mpo_isite)
M2_4 = xp.einsum('dfdh->dfh', second_R)
path_m2 = [([0, 1], "aeg,gbh->aebh"), ([2, 0], "aebh,ecf->abchf"),
([1, 0], "abhcf,dfh->abcd")]
pre_M2 = multi_tensor_contract(path_m2, M2_1, M2_3, M2_2, M2_4)
pre_M2 = pre_M2[self.condition(dag_qnmat, [down_exciton, up_exciton])]
M4_1 = xp.einsum('faah->fah', third_L)
M4_4 = xp.einsum('gddi->gdi', third_R)
M4_5 = xp.einsum('cc->c', Idt)
M4_path = [([0, 1], "fah,febg->ahebg"), ([2, 0], "ahebg,hjei->abgji"),
([1, 0], "abgji,gdi->abjd")]
pre_M4 = multi_tensor_contract(M4_path, M4_1, h_mpo_isite, h_mpo_isite,
M4_4)
pre_M4 = xp.einsum('abbd->abd', pre_M4)
pre_M4 = xp.tensordot(pre_M4, M4_5, axes=0)
pre_M4 = xp.moveaxis(pre_M4, [2, 3], [3, 2])[self.condition(
dag_qnmat, [down_exciton, up_exciton])]
pre_M = (pre_M1 + 2 * pre_M2 + pre_M4)
indices = np.array(range(nonzeros))
indptr = np.array(range(nonzeros + 1))
pre_M = scipy.sparse.csc_matrix((asnumpy(pre_M), indices, indptr),
shape=(nonzeros, nonzeros))
M_x = lambda x: scipy.sparse.linalg.spsolve(pre_M, x)
M = scipy.sparse.linalg.LinearOperator((nonzeros, nonzeros), M_x)
count = 0
def hop(x):
nonlocal count
count += 1
dag_struct = asxp(self.dag2mat(xshape, x, dag_qnmat, direction))
if self.method == "1site":
M1 = multi_tensor_contract(path_1, first_L, dag_struct,
a_oper_isite, first_R)
M2 = multi_tensor_contract(path_2, second_L, dag_struct,
b_oper_isite, h_mpo_isite, second_R)
M2 = xp.moveaxis(M2, (1, 2), (2, 1))
M3 = multi_tensor_contract(path_2, third_L, h_mpo_isite,
dag_struct, h_mpo_isite, third_R)
M3 = xp.moveaxis(M3, (1, 2), (2, 1))
cout = M1 + 2 * M2 + M3
cout = cout[self.condition(dag_qnmat,
[down_exciton, up_exciton])].reshape(
nonzeros, 1)
return asnumpy(cout)
# Matrix A and Vector b
vecb = asnumpy(vecb)[self.condition(
dag_qnmat, [down_exciton, up_exciton])].reshape(nonzeros, 1)
mata = scipy.sparse.linalg.LinearOperator((nonzeros, nonzeros),
matvec=hop)
# conjugate gradient method
# x, info = scipy.sparse.linalg.cg(MatA, VecB, atol=0)
if num == 1:
x, info = scipy.sparse.linalg.cg(mata,
vecb,
tol=1.e-5,
maxiter=500,
M=M,
atol=0)
else:
x, info = scipy.sparse.linalg.cg(mata,
vecb,
tol=1.e-5,
x0=guess,
maxiter=500,
M=M,
atol=0)
# logger.info(f"linear eq dim: {nonzeros}")
# logger.info(f'times for hop:{count}')
self.hop_time.append(count)
if info != 0:
logger.warning(
f"cg not converged, vecb.norm:{np.linalg.norm(vecb)}")
l_value = np.inner(
hop(x).reshape(1, nonzeros), x.reshape(1, nonzeros)) - \
2 * np.inner(vecb.reshape(1, nonzeros), x.reshape(1, nonzeros))
x = self.dag2mat(xshape, x, dag_qnmat, direction)
if self.method == "1site":
x = np.moveaxis(x, [1, 2], [2, 1])
x, xdim, xqn, compx = self.x_svd(x,
xqnbigl,
xqnbigr,
nexciton,
direction,
percent=percent)
if self.method == "1site":
self.cv_mpo[isite - 1] = x
if direction == "left":
if isite != 1:
self.cv_mpo[isite - 2] = \
tensordot(self.cv_mpo[isite - 2], compx, axes=(-1, 0))
self.cv_mpo.qn[isite - 1] = xqn
else:
self.cv_mpo[isite - 1] = \
tensordot(compx, self.cv_mpo[isite - 1], axes=(-1, 0))
elif direction == "right":
if isite != len(self.cv_mpo):
self.cv_mpo[isite] = \
tensordot(compx, self.cv_mpo[isite], axes=(-1, 0))
self.cv_mpo.qn[isite] = xqn
else:
self.cv_mpo[isite - 1] = \
tensordot(self.cv_mpo[isite - 1], compx, axes=(-1, 0))
else:
if direction == "left":
self.cv_mpo[isite - 2] = compx
self.cv_mpo[isite - 1] = x
else:
self.cv_mpo[isite - 2] = x
self.cv_mpo[isite - 1] = compx
self.cv_mpo.qn[isite - 1] = xqn
return l_value[0][0]
def auto_corr(self):
return np.array(self._auto_corr)
def to_complex(self):
# `xp.array` always creates new array, so to_complex means copy, which is
# in accordance with NumPy
return np.array(self.array, dtype=backend.complex_dtype)
