def test_return_stats():
A, _ = diagonal(100)
evals, evecs, stats = primme.eigsh(A, 3, tol=1e-6, which='LA',
return_stats=True, return_history=True)
assert(stats["hist"]["numMatvecs"])
svecs_left, svals, svecs_right, stats = primme.svds(A, 3, tol=1e-6,
which='SM', return_stats=True, return_history=True)
assert(stats["hist"]["numMatvecs"])
# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#
# PRIMME: https://github.com/primme/primme
# Contact: Andreas Stathopoulos, a n d r e a s _at_ c s . w m . e d u
import numpy as np
from numpy.testing import assert_allclose
import scipy.sparse
import primme
# Sparse diagonal matrix of size 100
A = scipy.sparse.spdiags(np.asarray(range(100), dtype=np.float32), [0], 100,
100)
# Compute the three largest eigenvalues of A with a residual norm tolerance of 1e-6
evals, evecs = primme.eigsh(A, 3, tol=1e-6, which='LA')
assert_allclose(evals, [99., 98., 97.], atol=1e-6 * 100)
print(evals) # [ 99., 98., 97.]
# Compute the three largest eigenvalues of A orthogonal to the previous computed
# eigenvectors, i.e., the next three eigenvalues
evals, evecs = primme.eigsh(A, 3, tol=1e-6, which='LA', lock=evecs)
assert_allclose(evals, [96., 95., 94.], atol=1e-6 * 100)
print(evals) # [ 96., 95., 94.]
# Compute the three closest eigenvalues to 50.1
evals, evecs = primme.eigsh(A, 3, tol=1e-6, which=50.1)
assert_allclose(evals, [50., 51., 49.], atol=1e-6 * 100)
print(evals) # [ 50., 51., 49.]
def main(total, cmdargs):
if total != 2:
print(" ".join(str(x) for x in cmdargs))
raise ValueError('Missing arguments')
inputname = cmdargs[1]
sys.stdout = Logger() # for exporting the logfile
# ----------------------- Build and Diagonalize ---------------------------------
para = Parameter(inputname) # import parameters from input.inp
Lat = Lattice(para) # Build lattice
ob = Observ(Lat) # initialize observables
tic = time.perf_counter()
Hamil = Hamiltonian(Lat) # Build Hamiltonian
ham = Hamil.Ham # Hamiltonian as sparse matrix
toc = time.perf_counter()
print(f"Hamiltonian construction time = {toc - tic:0.4f} sec")
tic = time.perf_counter()
evals, evecs = primme.eigsh(ham, para.Nstates, tol=1e-12, which='SA')
evals, evecs = sort(evals, evecs)
toc = time.perf_counter()
evals = np.round(evals, 10)
print("\n-----------Beg of Eigen Values-----------\n", *evals, sep='\n')
print("\n-----------End of Eigen Values-----------")
print(f"Diagonalization time = {toc - tic:0.4f} sec \n\n")
# -------------- Entanglement properties of GS -----------
if para.Option is not None:
if "EE" in para.Option:
EntS, Entvec = ob.EntSpec(
evecs[:, 0]) # Entanglement spectrum and vector
EntS = np.round(EntS, decimals=10)
EntS_log = np.zeros(len(EntS))
for i in range(len(EntS)):
if EntS[i] <= 0:
EntS_log[i] = 0
else:
EntS_log[i] = math.log(EntS[i])
EE = -np.around(np.dot(EntS, EntS_log), decimals=8)
print("Entanglement Spectrum=\n", EntS)
print("Entanglement Entropy=", EE)
# ------------------------ Ascii Ostream for EE--------
file = open("entspec.dat", "w")
# For a U-scan of Bose-Hubbard model
if para.Model == "Bose_Hubbard":
for i in range(EntS.size):
file.write(str(abs(para.U)) + " " + str(EntS[i]))
file.write("\n")
else:
for i in range(EntS.size):
file.write(str(abs(para.Hx)) + " " + str(EntS[i]))
file.write("\n")
# ------------------------ Hdf5 Ostream (Big Data Storage) ------------------------------
# ------------------------ Hdf5 Ostream (Big Data Storage) ------------------------------
# ------------------------ Hdf5 Ostream (Big Data Storage) ------------------------------
tic = time.perf_counter()
file = h5py.File('dataSpec.hdf5', 'w')
file.attrs["LLX"] = para.LLX
file.attrs["LLY"] = para.LLY
file.attrs["IsPeriodicX"] = para.IsPeriodicX
file.attrs["IsPeriodicY"] = para.IsPeriodicY
file.attrs["Kx"] = para.Kxx
file.attrs["Ky"] = para.Kyy
file.attrs["Kz"] = para.Kzz
file.attrs["Hx"] = para.Hz
file.attrs["Hy"] = para.Hy
file.attrs["Hz"] = para.Hz
file.attrs["#States2Keep"] = para.Nstates
file.attrs["Model"] = para.Model
file.attrs["Nsites"] = Lat.Nsite
LatGrp = file.create_group("1.Lattice")
LatGrp.create_dataset("Mesh", data=Lat.mesh_)
LatGrp.create_dataset("Nearest Neighbors", data=Lat.nn_)
ConnGrp = file.create_group("2.Connectors")
if para.Model == "Heisenberg_Square" or para.Model == "Kitaev":
ConnGrp.create_dataset("KxxGraph", data=Hamil.KxxGraph_)
ConnGrp.create_dataset("KyyGraph", data=Hamil.KyyGraph_)
ConnGrp.create_dataset("KzzGraph", data=Hamil.KzzGraph_)
elif para.Model == "AKLT":
ConnGrp.create_dataset("Kxx1Graph", data=Hamil.Kxx1Graph_)
ConnGrp.create_dataset("Kyy1Graph", data=Hamil.Kyy1Graph_)
ConnGrp.create_dataset("Kzz1Graph", data=Hamil.Kzz1Graph_)
ConnGrp.create_dataset("Kxx2Graph", data=Hamil.Kxx2Graph_)
ConnGrp.create_dataset("Kyy2Graph", data=Hamil.Kyy2Graph_)
ConnGrp.create_dataset("Kzz2Graph", data=Hamil.Kzz2Graph_)
elif para.Model == "Bose_Hubbard":
ConnGrp.create_dataset("tGraph", data=Hamil.tGraph_)
EigGrp = file.create_group("3.Eigen")
EigGrp.create_dataset("Eigen Values", data=evals)
EigGrp.create_dataset("Wavefunctions", data=evecs)
if para.Option is not None:
if "EE" in para.Option:
EigGrp = file.create_group("4.Entanglment")
EigGrp.create_dataset("ES", data=EntS)
EigGrp.create_dataset("ESlog", data=EntS_log)
EigGrp.create_dataset("EE", data=EE)
file.close()
toc = time.perf_counter()
print(f"\nHDF5 time = {toc - tic:0.4f} sec")
# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#
# PRIMME: https://github.com/primme/primme
# Contact: Andreas Stathopoulos, a n d r e a s _at_ c s . w m . e d u
import numpy as np
from numpy.testing import assert_allclose
import scipy.sparse
import primme
# Sparse diagonal matrix of size 100
A = scipy.sparse.spdiags(np.asarray(range(100), dtype=np.float32), [0], 100,
100)
# Compute the three largest eigenvalues of A with a residual norm tolerance of 1e-6
evals, evecs = primme.eigsh(A, 3, tol=1e-6, which='LA')
assert_allclose(evals, [99., 98., 97.], atol=1e-6 * 100)
print(evals) # [ 99., 98., 97.]
# Compute the three largest eigenvalues of A orthogonal to the previous computed
# eigenvectors, i.e., the next three eigenvalues
evals, evecs = primme.eigsh(A, 3, tol=1e-6, which='LA', lock=evecs)
assert_allclose(evals, [96., 95., 94.], atol=1e-6 * 100)
print(evals) # [ 96., 95., 94.]
# Sparse rectangular matrix 100x10 with non-zeros on the main diagonal
A = scipy.sparse.spdiags(range(10), [0], 100, 10)
# Compute the three closest to 4.1 singular values and the left and right corresponding
# singular vectors
svecs_left, svals, svecs_right = primme.svds(A, 3, tol=1e-6, which=4.1)
def kernel(self, restart=False, include_psi0=False):
r"""calculate the roots
Parameters
----------
restart: bool, optional
if restart from the former converged root. Default is ``False``.
If ``restart = True``, ``include_psi0`` must be the same as the
former calculation.
include_psi0: bool, optional
if the basis of Hamiltonian includes the ground state
:math:`\Psi_0`. Default is ``False``.
Returns
-------
e: np.ndarray
the energy of the states, if ``include_psi0 = True``, the first
element is the ground state energy, otherwise, it is the energy of
the first excited state.
"""
# right canonical mps
mpo = self.hmpo
nroots = self.nroots
algo = self.algo
site_num = mpo.site_num
if not restart:
# make sure that M is not redundant near the edge
mps = self.mps.ensure_right_canon().canonicalise().normalize().canonicalise()
logger.debug(f"reference mps shape, {mps}")
mps_r_cano = mps.copy()
assert mps.to_right
tangent_u = []
for ims, ms in enumerate(mps):
shape = list(ms.shape)
u, s, vt = scipy.linalg.svd(ms.l_combine(), full_matrices=True)
rank = len(s)
if include_psi0 and ims == site_num-1:
tangent_u.append(u.reshape(shape[:-1]+[-1]))
else:
if rank < u.shape[1]:
tangent_u.append(u[:,rank:].reshape(shape[:-1]+[-1]))
else:
tangent_u.append(None) # the tangent space is None
mps[ims] = u[:,:rank].reshape(shape[:-1]+[-1])
vt = xp.einsum("i, ij -> ij", asxp(s), asxp(vt))
if ims == site_num-1:
assert vt.size == 1 and xp.allclose(vt, 1)
else:
mps[ims+1] = asnumpy(tensordot(vt, mps[ims+1], ([-1],[0])))
mps_l_cano = mps.copy()
mps_l_cano.to_right = False
mps_l_cano.qnidx = site_num-1
else:
mps_l_cano, mps_r_cano, tangent_u, tda_coeff_list = self.wfn
cguess = []
for iroot in range(len(tda_coeff_list)):
tda_coeff = tda_coeff_list[iroot]
x = [c.flatten() for c in tda_coeff if c is not None]
x = np.concatenate(x,axis=None)
cguess.append(x)
cguess = np.stack(cguess, axis=1)
xshape = []
xsize = 0
for ims in range(site_num):
if tangent_u[ims] is None:
xshape.append((0,0))
else:
if ims == site_num-1:
xshape.append((tangent_u[ims].shape[-1], 1))
else:
xshape.append((tangent_u[ims].shape[-1], mps_r_cano[ims+1].shape[0]))
xsize += np.prod(xshape[-1])
logger.debug(f"DMRG-TDA H dimension: {xsize}")
if USE_GPU:
oe_backend = "cupy"
else:
oe_backend = "numpy"
mps_tangent = mps_r_cano.copy()
environ = Environ(mps_tangent, mpo, "R")
hdiag = []
for ims in range(site_num):
ltensor = environ.GetLR(
"L", ims-1, mps_tangent, mpo, itensor=None,
method="System"
)
rtensor = environ.GetLR(
"R", ims+1, mps_tangent, mpo, itensor=None,
method="Enviro"
)
if tangent_u[ims] is not None:
u = asxp(tangent_u[ims])
tmp = oe.contract("abc, ded, bghe, agl, chl -> ld", ltensor, rtensor,
asxp(mpo[ims]), u, u, backend=oe_backend)
hdiag.append(asnumpy(tmp))
mps_tangent[ims] = mps_l_cano[ims]
hdiag = np.concatenate(hdiag, axis=None)
count = 0
# recover the vector-like x back to the ndarray tda_coeff
def reshape_x(x):
tda_coeff = []
offset = 0
for shape in xshape:
if shape == (0,0):
tda_coeff.append(None)
else:
size = np.prod(shape)
tda_coeff.append(x[offset:size+offset].reshape(shape))
offset += size
assert offset == xsize
return tda_coeff
def hop(x):
# H*X
nonlocal count
count += 1
assert len(x) == xsize
tda_coeff = reshape_x(x)
res = [np.zeros_like(coeff) if coeff is not None else None for coeff in tda_coeff]
# fix ket and sweep bra and accumulate into res
for ims in range(site_num):
if tda_coeff[ims] is None:
assert tangent_u[ims] is None
continue
# mix-canonical mps
mps_tangent = merge(mps_l_cano, mps_r_cano, ims+1)
mps_tangent[ims] = tensordot(tangent_u[ims], tda_coeff[ims], (-1, 0))
mps_tangent_conj = mps_r_cano.copy()
environ = Environ(mps_tangent, mpo, "R", mps_conj=mps_tangent_conj)
for ims_conj in range(site_num):
ltensor = environ.GetLR(
"L", ims_conj-1, mps_tangent, mpo, itensor=None,
mps_conj=mps_tangent_conj,
method="System"
)
rtensor = environ.GetLR(
"R", ims_conj+1, mps_tangent, mpo, itensor=None,
mps_conj=mps_tangent_conj,
method="Enviro"
)
if tda_coeff[ims_conj] is not None:
# S-a l-S
# d
# O-b-O-f-O
# e
# S-c k-S
path = [
([0, 1], "abc, cek -> abek"),
([2, 0], "abek, bdef -> akdf"),
([1, 0], "akdf, lfk -> adl"),
]
out = multi_tensor_contract(
path, ltensor, asxp(mps_tangent[ims_conj]),
asxp(mpo[ims_conj]), rtensor
)
res[ims_conj] += asnumpy(tensordot(tangent_u[ims_conj], out,
([0,1], [0,1])))
# mps_conj combine
mps_tangent_conj[ims_conj] = mps_l_cano[ims_conj]
res = [mat for mat in res if mat is not None]
return np.concatenate(res, axis=None)
if algo == "davidson":
if restart:
cguess = [cguess[:,i] for i in range(cguess.shape[1])]
else:
cguess = [np.random.random(xsize) - 0.5]
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 nroots == 1:
c = [c]
c = np.stack(c, axis=1)
elif algo == "primme":
if not restart:
cguess = None
def multi_hop(x):
if x.ndim == 1:
return hop(x)
elif x.ndim == 2:
return np.stack([hop(x[:,i]) for i in range(x.shape[1])],axis=1)
else:
assert False
def precond(x):
if x.ndim == 1:
return np.einsum("i, i -> i", 1/(hdiag+1e-4), x)
elif x.ndim ==2:
return np.einsum("i, ij -> ij", 1/(hdiag+1e-4), x)
else:
assert False
A = scipy.sparse.linalg.LinearOperator((xsize,xsize),
matvec=multi_hop, matmat=multi_hop)
M = scipy.sparse.linalg.LinearOperator((xsize,xsize),
matvec=precond, matmat=precond)
e, c = primme.eigsh(A, k=min(nroots,xsize), which="SA",
v0=cguess,
OPinv=M,
method="PRIMME_DYNAMIC",
tol=1e-6)
else:
assert False
logger.debug(f"H*C times: {count}")
tda_coeff_list = []
for iroot in range(nroots):
tda_coeff_list.append(reshape_x(c[:,iroot]))
self.e = np.array(e)
self.wfn = [mps_l_cano, mps_r_cano, tangent_u, tda_coeff_list]
return self.e
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
# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#
# PRIMME: https://github.com/primme/primme
# Contact: Andreas Stathopoulos, a n d r e a s _at_ c s . w m . e d u
import numpy as np
from numpy.testing import assert_allclose
import scipy.sparse
import primme
# Sparse diagonal matrix of size 100
A = scipy.sparse.spdiags(np.asarray(range(100), dtype=np.float32), [0], 100,
100)
# Compute the three largest eigenvalues of A with a residual norm tolerance of 1e-6
evals, evecs = primme.eigsh(A, 3, tol=1e-6, which='LA')
assert_allclose(evals, [99., 98., 97.], atol=1e-6 * 100)
print(evals) # [ 99., 98., 97.]
# Compute the three largest eigenvalues of A orthogonal to the previous computed
# eigenvectors, i.e., the next three eigenvalues
evals, evecs = primme.eigsh(A, 3, tol=1e-6, which='LA', lock=evecs)
assert_allclose(evals, [96., 95., 94.], atol=1e-6 * 100)
print(evals) # [ 96., 95., 94.]
# Compute the three closest eigenvalues to 50.1
evals, evecs = primme.eigsh(A, 3, tol=1e-6, which=50.1)
assert_allclose(evals, [50., 51., 49.], atol=1e-6 * 100)
print(evals) # [ 50., 51., 49.]