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 swap(self, mat, qnbigl, qnbigr, direction):
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)
dag_qnmat = inter_change(mat)
if self.method == "1site":
dag_qnmat = np.moveaxis(dag_qnmat, [1, 2], [2, 1])
dag_qnbigl = inter_change(qnbigl)
dag_qnbigr = inter_change(qnbigr)
if direction == "left":
dag_qnbigr = np.moveaxis(dag_qnbigr, [0, 1], [1, 0])
else:
dag_qnbigl = np.moveaxis(dag_qnbigl, [1, 2], [2, 1])
else:
raise NotImplementedError
# we don't recommend 2-site CV-DMRG, which is a huge cost
return dag_qnmat, dag_qnbigl, dag_qnbigr
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 moveaxis(a: Matrix, source, destination):
return Matrix(np.moveaxis(a.array, source, destination))
def optimize_cv(self, lr_group, isite, 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)
dag_qnmat, dag_qnbigl, dag_qnbigr = self.swap(xqnmat, xqnbigl, xqnbigr)
nonzeros = int(
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])]
if self.method == "1site":
# define dot path
path_1 = [([0, 1], "abcd, aefg -> bcdefg"),
([3, 0], "bcdefg, bfhi -> cdeghi"),
([2, 0], "cdeghi, chjk -> degijk"),
([1, 0], "degijk, gikl -> dejl")]
path_2 = [([0, 1], "abcd, aefg -> bcdefg"),
([3, 0], "bcdefg, bfhi -> cdeghi"),
([2, 0], "cdeghi, djek -> cghijk"),
([1, 0], "cghijk, gilk -> chjl")]
path_3 = [([0, 1], "ab, acde -> bcde"), ([1,
0], "bcde, ef -> bcdf")]
vecb = multi_tensor_contract(
path_3, forth_L, moveaxis(self.b_mpo[isite - 1], (1, 2),
(2, 1)),
forth_R)[self.condition(dag_qnmat, [down_exciton, up_exciton])]
a_oper_isite = asxp(self.a_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('abca->abc', first_L)
path_m1 = [([0, 1], "abc, bdef->acdef"), ([1,
0], "acdef, cegh->adfgh")]
M1_2 = multi_tensor_contract(path_m1, M1_1, a_oper_isite, a_oper_isite)
M1_2 = xp.einsum("abcbd->abcd", M1_2)
M1_3 = xp.einsum('ecde->ecd', first_R)
M1_4 = xp.einsum('ff->f', Idt)
path_m1 = [([0, 1], "abcd,ecd->abe"), ([1, 0], "abe,f->abef")]
pre_M1 = multi_tensor_contract(path_m1, M1_2, M1_3, M1_4)
pre_M1 = xp.moveaxis(pre_M1, [-2, -1], [-1, -2])[self.condition(
dag_qnmat, [down_exciton, up_exciton])]
M2_1 = xp.einsum('aeag->aeg', second_L)
M2_2 = xp.einsum('eccf->ecf', a_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])]
M_x = lambda x: asnumpy(
asxp(x) /
(pre_M1 + 2 * pre_M2 + pre_M4 + xp.ones(nonzeros) * self.eta**2))
pre_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))
if self.method == "1site":
M1 = multi_tensor_contract(path_1, first_L, dag_struct,
a_oper_isite, a_oper_isite, first_R)
M2 = multi_tensor_contract(path_2, second_L, dag_struct,
a_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 + dag_struct * self.eta**2
cout = cout[self.condition(dag_qnmat, [down_exciton, up_exciton])]
return asnumpy(cout)
# Matrix A
mat_a = scipy.sparse.linalg.LinearOperator((nonzeros, nonzeros),
matvec=hop)
x, info = scipy.sparse.linalg.cg(mat_a,
asnumpy(vecb),
tol=1.e-5,
x0=asnumpy(guess),
maxiter=500,
M=pre_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:{xp.linalg.norm(vecb)}")
l_value = xp.dot(asxp(hop(x)), asxp(x)) - 2 * xp.dot(vecb, asxp(x))
x = self.dag2mat(xshape, x, dag_qnmat)
if self.method == "1site":
x = np.moveaxis(x, [1, 2], [2, 1])
x, xdim, xqn, compx = self.x_svd(x,
xqnbigl,
xqnbigr,
nexciton,
percent=percent)
if self.method == "1site":
self.cv_mpo[isite - 1] = x
if not self.cv_mpo.to_right:
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
self.cv_mpo.qnidx = isite - 2
else:
self.cv_mpo[isite - 1] = \
tensordot(compx, self.cv_mpo[isite - 1], axes=(-1, 0))
self.cv_mpo.qnidx = 0
else:
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
self.cv_mpo.qnidx = isite
else:
self.cv_mpo[isite - 1] = \
tensordot(self.cv_mpo[isite - 1], compx, axes=(-1, 0))
self.cv_mpo.qnidx = self.cv_mpo.site_num - 1
else:
if not self.cv_mpo.to_right:
self.cv_mpo[isite - 2] = compx
self.cv_mpo[isite - 1] = x
self.cv_mpo.qnidx = isite - 2
else:
self.cv_mpo[isite - 2] = x
self.cv_mpo[isite - 1] = compx
self.cv_mpo.qnidx = isite - 1
self.cv_mpo.qn[isite - 1] = xqn
return float(l_value)