def oper_prepare(self, omega):
# set up a_oper = (H_0 - e0 - omega)
identity = Mpo.identity(self.model).scale(-self.e0 - omega)
self.a_oper = self.h_mpo.add(identity)
def test_identity():
identity = Mpo.identity(mol_list)
mps = Mps.random(mol_list, nexciton=1, m_max=5)
assert mps.expectation(identity) == pytest.approx(mps.dmrg_norm) == pytest.approx(1)
def test_identity():
identity = Mpo.identity(holstein_model)
mps = Mps.random(holstein_model, nexciton=1, m_max=5)
assert mps.expectation(identity) == pytest.approx(
mps.dmrg_norm) == pytest.approx(1)
def oper_prepare(self, omega):
identity = Mpo.identity(self.model).scale(omega)
self.a_oper = identity.add(self.h_mpo.scale(-1, inplace=False))
def optimize_mps(mps: Mps, mpo: Mpo, omega: float = None) -> Tuple[List, Mps]:
r""" DMRG ground state algorithm and state-averaged excited states algorithm
Parameters
----------
mps : renormalizer.mps.Mps
initial guess of mps
mpo : renormalizer.mps.Mpo
mpo of Hamiltonian
omega: float, optional
target the eigenpair near omega with special variational function
:math:(\hat{H}-\omega)^2. Default is `None`.
Returns
-------
energy : list
list of energy of each marco sweep.
:math:`[e_0, e_0, \cdots, e_0]` if ``nroots=1``.
:math:`[[e_0, \cdots, e_n], \dots, [e_0, \cdots, e_n]]` if ``nroots=n``.
mps : renormalizer.mps.Mps
optimized ground state mps. The input mps is overwritten and could not
be used anymore.
See Also
--------
renormalizer.utils.configs.OptimizeConfig : The optimization configuration.
"""
algo = mps.optimize_config.algo
method = mps.optimize_config.method
procedure = mps.optimize_config.procedure
inverse = mps.optimize_config.inverse
nroots = mps.optimize_config.nroots
assert method in ["2site", "1site"]
logger.info(f"optimization method: {method}")
logger.info(f"e_rtol: {mps.optimize_config.e_rtol}")
logger.info(f"e_atol: {mps.optimize_config.e_atol}")
if USE_GPU:
oe_backend = "cupy"
else:
oe_backend = "numpy"
# ensure that mps is left or right-canonical
# TODO: start from a mix-canonical MPS
if mps.is_left_canon:
mps.ensure_right_canon()
env = "R"
else:
mps.ensure_left_canon()
env = "L"
# in state-averged calculation, contains C of each state for better initial
# guess
averaged_ms = None
# the index of active site of the returned mps
res_mps_idx = None
# target eigenstate close to omega with (H-omega)^2
# construct the environment matrix
if omega is not None:
identity = Mpo.identity(mpo.model)
mpo = mpo.add(identity.scale(-omega))
environ = Environ(mps, [mpo, mpo], env)
else:
environ = Environ(mps, mpo, env)
macro_iteration_result = []
converged = False
for isweep, (mmax, percent) in enumerate(procedure):
logger.debug(f"isweep: {isweep}")
logger.debug(f"mmax, percent: {mmax}, {percent}")
logger.debug(f"{mps}")
micro_iteration_result = []
for imps in mps.iter_idx_list(full=True):
if method == "2site" and \
((mps.to_right and imps == mps.site_num-1)
or ((not mps.to_right) and imps == 0)):
break
if mps.to_right:
lmethod, rmethod = "System", "Enviro"
else:
lmethod, rmethod = "Enviro", "System"
if method == "1site":
lidx = imps - 1
cidx = [imps]
ridx = imps + 1
elif method == "2site":
if mps.to_right:
lidx = imps - 1
cidx = [imps, imps + 1]
ridx = imps + 2
else:
lidx = imps - 2
cidx = [imps - 1, imps] # center site
ridx = imps + 1
else:
assert False
logger.debug(f"optimize site: {cidx}")
if omega is None:
operator = mpo
else:
operator = [mpo, mpo]
ltensor = environ.GetLR("L",
lidx,
mps,
operator,
itensor=None,
method=lmethod)
rtensor = environ.GetLR("R",
ridx,
mps,
operator,
itensor=None,
method=rmethod)
# get the quantum number pattern
qnbigl, qnbigr, qnmat = mps._get_big_qn(cidx)
cshape = qnmat.shape
nonzeros = np.sum(qnmat == mps.qntot)
logger.debug(f"Hmat dim: {nonzeros}")
# center mo
cmo = [asxp(mpo[idx]) for idx in cidx]
if qnmat.size > 1000 and algo != "direct":
# iterative algorithm
# diagonal elements of H
if omega is None:
tmp_ltensor = xp.einsum("aba -> ba", ltensor)
tmp_cmo0 = xp.einsum("abbc -> abc", cmo[0])
tmp_rtensor = xp.einsum("aba -> ba", rtensor)
if method == "1site":
# S-a c f-S
# O-b-O-g-O
# S-a c f-S
path = [([0, 1], "ba, bcg -> acg"),
([1, 0], "acg, gf -> acf")]
hdiag = multi_tensor_contract(
path, tmp_ltensor, tmp_cmo0,
tmp_rtensor)[(qnmat == mps.qntot)]
else:
# S-a c d f-S
# O-b-O-e-O-g-O
# S-a c d f-S
tmp_cmo1 = xp.einsum("abbc -> abc", cmo[1])
path = [
([0, 1], "ba, bce -> ace"),
([0, 1], "edg, gf -> edf"),
([0, 1], "ace, edf -> acdf"),
]
hdiag = multi_tensor_contract(
path, tmp_ltensor, tmp_cmo0, tmp_cmo1,
tmp_rtensor)[(qnmat == mps.qntot)]
else:
if method == "1site":
# S-a d h-S
# O-b-O-f-O
# | e |
# O-c-O-g-O
# S-a d h-S
hdiag = oe.contract(
"abca, bdef, cedg, hfgh -> adh",
ltensor,
cmo[0],
cmo[0],
rtensor,
backend=oe_backend)[(qnmat == mps.qntot)]
else:
# S-a d h l-S
# O-b-O-f-O-j-O
# | e i |
# O-c-O-g-O-k-O
# S-a d h l-S
hdiag = oe.contract(
"abca, bdef, cedg, fhij, gihk, ljkl -> adhl",
ltensor,
cmo[0],
cmo[0],
cmo[1],
cmo[1],
rtensor,
backend=oe_backend)[(qnmat == mps.qntot)]
hdiag = asnumpy(hdiag * inverse)
# initial guess
if method == "1site":
# initial guess b-S-c
# a
if nroots == 1:
cguess = [asnumpy(mps[cidx[0]])[qnmat == mps.qntot]]
else:
cguess = []
if averaged_ms is not None:
for ms in averaged_ms:
cguess.append(asnumpy(ms)[qnmat == mps.qntot])
else:
# initial guess b-S-c-S-e
# a d
if nroots == 1:
cguess = [
asnumpy(
tensordot(mps[cidx[0]], mps[cidx[1]],
axes=1)[qnmat == mps.qntot])
]
else:
cguess = []
if averaged_ms is not None:
for ms in averaged_ms:
if mps.to_right:
cguess.append(
asnumpy(
tensordot(
ms, mps[cidx[1]],
axes=1)[qnmat == mps.qntot]))
else:
cguess.append(
asnumpy(
tensordot(
mps[cidx[0]], ms,
axes=1)[qnmat == mps.qntot]))
if omega is not None:
if method == "1site":
# S-a e j-S
# O-b-O-g-O
# | f |
# O-c-O-i-O
# S-d h k-S
expr = oe.contract_expression(
"abcd, befg, cfhi, jgik, aej -> dhk",
ltensor,
cmo[0],
cmo[0],
rtensor,
cshape,
constants=[0, 1, 2, 3])
else:
# S-a e j o-S
# O-b-O-g-O-l-O
# | f k |
# O-c-O-i-O-n-O
# S-d h m p-S
expr = oe.contract_expression(
"abcd, befg, cfhi, gjkl, ikmn, olnp, aejo -> dhmp",
ltensor,
cmo[0],
cmo[0],
cmo[1],
cmo[1],
rtensor,
cshape,
constants=[0, 1, 2, 3, 4, 5])
count = 0
def hop(x):
nonlocal count
count += 1
clist = []
if x.ndim == 1:
clist.append(x)
else:
for icol in range(x.shape[1]):
clist.append(x[:, icol])
res = []
for c in clist:
# convert c to initial structure according to qn pattern
cstruct = asxp(cvec2cmat(cshape, c, qnmat, mps.qntot))
if omega is None:
if method == "1site":
# S-a l-S
# d
# O-b-O-f-O
# e
# S-c k-S
path = [
([0, 1], "abc, adl -> bcdl"),
([2, 0], "bcdl, bdef -> clef"),
([1, 0], "clef, lfk -> cek"),
]
cout = multi_tensor_contract(
path, ltensor, cstruct, cmo[0], rtensor)
else:
# S-a l-S
# d g
# O-b-O-f-O-j-O
# e h
# S-c k-S
path = [
([0, 1], "abc, adgl -> bcdgl"),
([3, 0], "bcdgl, bdef -> cglef"),
([2, 0], "cglef, fghj -> clehj"),
([1, 0], "clehj, ljk -> cehk"),
]
cout = multi_tensor_contract(
path,
ltensor,
cstruct,
cmo[0],
cmo[1],
rtensor,
)
else:
cout = expr(cstruct, backend=oe_backend)
# convert structure c to 1d according to qn
res.append(asnumpy(cout)[qnmat == mps.qntot])
if len(res) == 1:
return inverse * res[0]
else:
return inverse * np.stack(res, axis=1)
if len(cguess) < nroots:
cguess.extend([
np.random.random([nonzeros]) - 0.5
for i in range(len(cguess), nroots)
])
if algo == "davidson":
precond = lambda x, e, *args: x / (hdiag - e + 1e-4)
e, c = davidson(hop,
cguess,
precond,
max_cycle=100,
nroots=nroots,
max_memory=64000)
# if one root, davidson return e as np.float
#elif algo == "arpack":
# # scipy arpack solver : much slower than pyscf/davidson
# A = scipy.sparse.linalg.LinearOperator((nonzeros,nonzeros), matvec=hop)
# e, c = scipy.sparse.linalg.eigsh(A, k=nroots, which="SA", v0=cguess)
# # scipy return numpy.array
# if nroots == 1:
# e = e[0]
#elif algo == "lobpcg":
# precond = lambda x: scipy.sparse.diags(1/(hdiag+1e-4)) @ x
# A = scipy.sparse.linalg.LinearOperator((nonzeros,nonzeros),
# matvec=hop, matmat=hop)
# M = scipy.sparse.linalg.LinearOperator((nonzeros,nonzeros),
# matvec=precond, matmat=hop)
# e, c = scipy.sparse.linalg.lobpcg(A, np.array(cguess).T,
# M=M, largest=False)
elif algo == "primme":
precond = lambda x: scipy.sparse.diags(1 /
(hdiag + 1e-4)) @ x
A = scipy.sparse.linalg.LinearOperator(
(nonzeros, nonzeros), matvec=hop, matmat=hop)
M = scipy.sparse.linalg.LinearOperator(
(nonzeros, nonzeros), matvec=precond, matmat=hop)
e, c = primme.eigsh(A,
k=min(nroots, nonzeros),
which="SA",
v0=np.array(cguess).T,
OPinv=M,
method="PRIMME_DYNAMIC",
tol=1e-6)
else:
assert False
logger.debug(f"use {algo}, HC hops: {count}")
else:
logger.debug(f"use direct eigensolver")
# direct algorithm
if omega is None:
if method == "1site":
# S-a l-S
# d
# O-b-O-f-O
# e
# S-c k-S
ham = oe.contract("abc,bdef,lfk->adlcek",
ltensor,
cmo[0],
rtensor,
backend=oe_backend)
ham = ham[:, :, :, qnmat == mps.qntot][
qnmat == mps.qntot, :] * inverse
else:
# S-a l-S
# d g
# O-b-O-f-O-j-O
# e h
# S-c k-S
ham = oe.contract("abc,bdef,fghj,ljk->adglcehk",
ltensor, cmo[0], cmo[1], rtensor)
ham = ham[:, :, :, :, qnmat == mps.qntot][
qnmat == mps.qntot, :] * inverse
else:
if method == "1site":
# S-a e j-S
# O-b-O-g-O
# | f |
# O-c-O-i-O
# S-d h k-S
ham = oe.contract("abcd, befg, cfhi, jgik -> aejdhk",
ltensor, cmo[0], cmo[0], rtensor)
ham = ham[:, :, :, qnmat == mps.qntot][
qnmat == mps.qntot, :] * inverse
else:
# S-a e j o-S
# O-b-O-g-O-l-O
# | f k |
# O-c-O-i-O-n-O
# S-d h m p-S
ham = oe.contract(
"abcd, befg, cfhi, gjkl, ikmn, olnp -> aejodhmp",
ltensor, cmo[0], cmo[0], cmo[1], cmo[1], rtensor)
ham = ham[:, :, :, :, qnmat == mps.qntot][
qnmat == mps.qntot, :] * inverse
w, v = scipy.linalg.eigh(asnumpy(ham))
if nroots == 1:
e = w[0]
c = v[:, 0]
else:
e = w[:nroots]
c = [
v[:, iroot] for iroot in range(min(nroots, v.shape[1]))
]
# if multi roots, both davidson and primme return np.ndarray
if nroots > 1:
e = e.tolist()
logger.debug(f"energy: {e}")
micro_iteration_result.append(e)
cstruct = cvec2cmat(cshape, c, qnmat, mps.qntot, nroots=nroots)
# store the "optimal" mps (usually in the middle of each sweep)
if res_mps_idx is not None and res_mps_idx == imps:
if nroots == 1:
res_mps = mps.copy()
res_mps._update_mps(cstruct, cidx, qnbigl, qnbigr, mmax,
percent)
else:
res_mps = [mps.copy() for i in range(len(cstruct))]
for iroot in range(len(cstruct)):
res_mps[iroot]._update_mps(cstruct[iroot], cidx,
qnbigl, qnbigr, mmax,
percent)
averaged_ms = mps._update_mps(cstruct, cidx, qnbigl, qnbigr, mmax,
percent)
mps._switch_direction()
res_mps_idx = micro_iteration_result.index(min(micro_iteration_result))
macro_iteration_result.append(micro_iteration_result[res_mps_idx])
# check if convergence
if isweep > 0 and percent == 0:
v1, v2 = sorted(macro_iteration_result)[:2]
if np.allclose(v1,
v2,
rtol=mps.optimize_config.e_rtol,
atol=mps.optimize_config.e_atol):
converged = True
break
logger.debug(
f"{isweep+1} sweeps are finished, lowest energy = {sorted(macro_iteration_result)[0]}"
)
if converged:
logger.info("DMRG is converged!")
else:
logger.warning("DMRG is not converged! Please increase the procedure!")
logger.info(
f"The lowest two energies: {sorted(macro_iteration_result)[:2]}.")
# remove the redundant basis near the edge
if nroots == 1:
res_mps = res_mps.normalize().ensure_left_canon().canonicalise()
logger.info(f"{res_mps}")
else:
res_mps = [
mp.normalize().ensure_left_canon().canonicalise() for mp in res_mps
]
logger.info(f"{res_mps[0]}")
return macro_iteration_result, res_mps
def mpdm_norm(self):
# the trace
i = Mpo.identity(self.mol_list)
return self.expectation(i, i)
def _expectation_conj(self):
i = Mpo.identity(self.mol_list)
i.scale(1 / self.mpdm_norm(), inplace=True)
return i