def iterate(self,
log,
info='',
sp=True,
nmax=200,
tol=10**-6,
divisor=None,
piechart=True):
'''
The two site dmrg step.
Parameters
----------
log : Log
The log file.
info : str, optional
The information string passed to self.log.
sp : logical, optional
True for state prediction False for not.
nmax : int, optional
The maximum singular values to be kept.
tol : float, optional
The tolerance of the singular values.
divisor : int/None, optional
* When int, it is used as the divisor to calculated the ground state energy per site;
* When None, the default divisor will be used to calculated the ground state energy per site.
piechart : logical, optional
True for showing the piechart of self.timers while False for not.
'''
log << '%s(%s)\n%s\n' % (info, self.ttype, self.graph)
with self.timers.get('Preparation'):
Ha, Hasite = self.lcontracts[self.cut - 1], self.mpo[self.cut - 1]
Hb, Hbsite = self.rcontracts[self.cut + 1], self.mpo[self.cut]
Oa, (La, Sa,
Ra) = Hasite.labels[MPO.R], self.mps[self.cut - 1].labels
Ob, (Lb, Sb, Rb) = Hbsite.labels[MPO.L], self.mps[self.cut].labels
assert Ra == Lb and Oa == Ob
Lsys, sysinfo = Label.union([La, Sa],
'__DMRG_ITERATE_SYS__',
flow=+1 if self.mps.qnon else 0,
mode=+2 if self.ttype == 'S' else +1)
Lenv, envinfo = Label.union([Sb, Rb],
'__DMRG_ITERATE_ENV__',
flow=-1 if self.mps.qnon else 0,
mode=+2 if self.ttype == 'S' else +1)
subslice = QuantumNumbers.kron(
[Lsys.qns, Lenv.qns], signs=[1, -1]).subslice(targets=(
self.target.zero(), )) if self.mps.qnon else slice(None)
shape = (len(subslice),
len(subslice)) if self.mps.qnon else (Lsys.qns * Lenv.qns,
Lsys.qns * Lenv.qns)
Hsys = (Ha * Hasite).transpose([Oa, La.P, Sa.P, La, Sa]).merge(
([La.P, Sa.P], Lsys.P.inverse, sysinfo),
([La, Sa], Lsys.inverse, sysinfo))
Henv = (Hbsite * Hb).transpose([Ob, Sb.P, Rb.P, Sb, Rb]).merge(
([Sb.P, Rb.P], Lenv.P.inverse, envinfo),
([Sb, Rb], Lenv.inverse, envinfo))
matvec = DMRGMatVec(Hsys, Henv)
def timedmatvec(v):
with self.timers.get('matvec'):
return matvec(v)
matrix = hm.LinearOperator(shape=shape,
matvec=timedmatvec,
dtype=Hsys.dtype)
with self.timers.get('Diagonalization'):
u, s, v = self.mps[self.cut -
1], self.mps.Lambda, self.mps[self.cut]
v0 = (u * s * v).merge(
([La, Sa], Lsys, sysinfo),
([Sb, Rb], Lenv, envinfo)).toarray().reshape(
-1)[subslice] if sp and s.norm > RZERO else None
es, vs = hm.eigsh(matrix, which='SA', v0=v0, k=1, tol=tol * 10**-2)
energy, Psi = es[0], vs[:, 0]
self.info['Etotal'] = energy, '%.6f'
self.info['Esite'] = energy / (divisor or self.nsite), '%.8f'
self.info['nmatvec'] = matrix.count
self.info['overlap'] = np.inf if v0 is None else np.abs(
Psi.conjugate().dot(v0) / norm(v0) / norm(Psi)), '%.6f'
with self.timers.get('Truncation'):
sysantiinfo = sysinfo if self.ttype == 'S' else np.argsort(
sysinfo) if self.mps.qnon else None
envantiinfo = envinfo if self.ttype == 'S' else np.argsort(
envinfo) if self.mps.qnon else None
qns = QuantumNumbers.mono(
self.target.zero(),
count=len(subslice)) if self.mps.qnon else Lsys.qns * Lenv.qns
Lgs, new = Label('__DMRG_ITERATE_GS__',
qns=qns), Ra.replace(qns=None)
u, s, v, err = partitionedsvd(Tensor(Psi, labels=[Lgs]),
Lsys,
new,
Lenv,
nmax=nmax,
tol=tol,
ttype=self.ttype,
returnerr=True)
self.mps[self.cut - 1] = u.split((Lsys, [La, Sa], sysantiinfo))
self.mps[self.cut] = v.split((Lenv, [Sb, Rb], envantiinfo))
self.mps.Lambda = s
self.setlcontract(self.cut)
self.setrcontract(self.cut)
self.info['nslice'] = Lgs.dim
self.info['nbasis'] = s.shape[0]
self.info['err'] = err, '%.1e'
self.timers.record()
log << 'timers of the dmrg:\n%s\n' % self.timers.tostr(Timers.ALL)
log << 'info of the dmrg:\n%s\n\n' % self.info
if piechart: self.timers.graph(parents=Timers.ALL)
def iterate(self, info='', sp=True, nmax=200, tol=hm.TOL, piechart=True):
'''
The two site dmrg step.
Parameters
----------
info : str, optional
The information string passed to self.log.
sp : logical, optional
True for state prediction False for not.
nmax : integer, optional
The maximum singular values to be kept.
tol : np.float64, optional
The tolerance of the singular values.
piechart : logical, optional
True for showing the piechart of self.timers while False for not.
'''
self.log << '%s%s\n%s\n' % (self.state, info, self.graph)
eold = self.info['Esite']
with self.timers.get('Preparation'):
Ha, Hb = self._Hs_['L'][self.mps.cut -
1], self._Hs_['R'][self.mps.nsite -
self.mps.cut - 1]
Hasite, Hbsite = self.mpo[self.mps.cut - 1], self.mpo[self.mps.cut]
La, Sa, Ra = self.mps[self.mps.cut - 1].labels
Lb, Sb, Rb = self.mps[self.mps.cut].labels
Oa, Ob = Hasite.labels[MPO.R], Hbsite.labels[MPO.L]
assert Ra == Lb
if self.mps.mode == 'QN':
sysqns, syspt = QuantumNumbers.kron(
[La.qns, Sa.qns], signs='++').sort(history=True)
envqns, envpt = QuantumNumbers.kron(
[Sb.qns, Rb.qns], signs='-+').sort(history=True)
sysantipt, envantipt = np.argsort(syspt), np.argsort(envpt)
subslice = QuantumNumbers.kron(
[sysqns, envqns],
signs='+-').subslice(targets=(self.target.zero(), ))
qns = QuantumNumbers.mono(self.target.zero(),
count=len(subslice))
self.info['nslice'] = len(subslice)
else:
sysqns, syspt, sysantipt = np.product([La.qns,
Sa.qns]), None, None
envqns, envpt, envantipt = np.product([Sb.qns,
Rb.qns]), None, None
subslice, qns = slice(None), sysqns * envqns
self.info['nslice'] = qns
Lpa, Spa, Spb, Rpb = La.prime, Sa.prime, Sb.prime, Rb.prime
Lsys, Lenv, new = Label('__DMRG_TWO_SITE_STEP_SYS__',
qns=sysqns), Label(
'__DMRG_TWO_SITE_STEP_ENV__',
qns=envqns), Ra.replace(qns=None)
Lpsys, Lpenv = Lsys.prime, Lenv.prime
Hsys = contract([Ha, Hasite], engine='tensordot').transpose(
[Oa, Lpa, Spa, La, Sa]).merge(([Lpa, Spa], Lpsys, syspt),
([La, Sa], Lsys, syspt))
Henv = contract([Hbsite, Hb], engine='tensordot').transpose(
[Ob, Spb, Rpb, Sb, Rb]).merge(([Spb, Rpb], Lpenv, envpt),
([Sb, Rb], Lenv, envpt))
if self.matvec == 'csr':
with self.timers.get('Hamiltonian'):
if isinstance(subslice, slice):
rcs = None
else:
rcs = (np.divide(subslice, Henv.shape[1]),
np.mod(subslice, Henv.shape[1]),
np.zeros(Hsys.shape[1] * Henv.shape[1],
dtype=np.int64))
rcs[2][subslice] = xrange(len(subslice))
matrix = 0
for hsys, henv in zip(Hsys, Henv):
with self.timers.get('kron'):
temp = hm.kron(hsys, henv, rcs=rcs, timers=self.timers)
with self.timers.get('sum'):
matrix += temp
self.info['nnz'] = matrix.nnz
self.info['nz'] = (
len(np.argwhere(np.abs(matrix.data) < tol)) * 100.0 /
matrix.nnz) if matrix.nnz > 0 else 0, '%1.1f%%'
self.info['density'] = 1.0 * self.info['nnz'] / self.info[
'nslice']**2, '%.1e'
matrix = hm.LinearOperator(shape=matrix.shape,
matvec=matrix.dot,
dtype=self.dtype)
else:
with self.timers.get('Preparation'):
if self.mps.mode == 'QN':
sysod, envod = sysqns.to_ordereddict(
), envqns.to_ordereddict()
qnpairs = [[
(tuple(qn), tuple(qn - oqn)) for qn in sysqns
if tuple(qn) in envod and tuple(qn - oqn) in sysod
and tuple(qn - oqn) in envod
] for oqn in Oa.qns]
assert len(qnpairs) == len(Hsys)
self.cache['vecold'] = np.zeros(Hsys.shape[1] *
Henv.shape[1],
dtype=self.dtype)
self.cache['vecnew'] = np.zeros(
(Hsys.shape[1], Henv.shape[1]), dtype=self.dtype)
def matvec(v):
with self.timers.get('matvec'):
vec, result = self.cache['vecold'], self.cache[
'vecnew']
vec[subslice] = v
result[...] = 0.0
vec = vec.reshape((Hsys.shape[1], Henv.shape[1]))
for hsys, henv, pairs in zip(Hsys, Henv, qnpairs):
for qn1, qn2 in pairs:
result[sysod[qn1], envod[qn1]] += hsys[
sysod[qn1], sysod[qn2]].dot(
vec[sysod[qn2], envod[qn2]]).dot(
henv.T[envod[qn2], envod[qn1]])
return result.reshape(-1)[subslice]
matrix = hm.LinearOperator(shape=(len(subslice),
len(subslice)),
matvec=matvec,
dtype=self.dtype)
else:
def matvec(v):
v = v.reshape((Hsys.shape[1], Henv.shape[1]))
result = np.zeros_like(v)
for hsys, henv in zip(Hsys, Henv):
result += hsys.dot(v).dot(henv.T)
return result.reshape(-1)
matrix = hm.LinearOperator(
shape=(Hsys.shape[1] * Henv.shape[1],
Hsys.shape[1] * Henv.shape[1]),
matvec=matvec,
dtype=self.dtype)
with self.timers.get('Diagonalization'):
u, s, v = self.mps[self.mps.cut -
1], self.mps.Lambda, self.mps[self.mps.cut]
if sp and norm(s) > RZERO:
v0 = np.asarray(
contract([u, s, v], engine='einsum').merge(
([La, Sa], Lsys, syspt),
([Sb, Rb], Lenv, envpt))).reshape(-1)[subslice]
else:
v0 = None
es, vs = hm.eigsh(matrix, which='SA', v0=v0, k=1)
energy, Psi = es[0], vs[:, 0]
self.info['Etotal'] = energy, '%.6f'
self.info['Esite'] = energy / self.mps.nsite, '%.8f'
self.info['dE/E'] = None if eold is None else (
norm(self.info['Esite'] - eold) /
norm(self.info['Esite'] + eold), '%.1e')
self.info['nmatvec'] = matrix.count
self.info['overlap'] = np.inf if v0 is None else np.abs(
Psi.conjugate().dot(v0) / norm(v0) / norm(Psi)), '%.6f'
with self.timers.get('Truncation'):
u, s, v, err = Tensor(
Psi, labels=[Label('__DMRG_TWO_SITE_STEP__', qns=qns)
]).partitioned_svd(Lsys,
new,
Lenv,
nmax=nmax,
tol=tol,
return_truncation_err=True)
self.mps[self.mps.cut - 1] = u.split((Lsys, [La, Sa], sysantipt))
self.mps[self.mps.cut] = v.split((Lenv, [Sb, Rb], envantipt))
self.mps.Lambda = s
self.set_HL_(self.mps.cut - 1, tol=tol)
self.set_HR_(self.mps.cut, tol=tol)
self.info['nbasis'] = len(s)
self.info['err'] = err, '%.1e'
self.timers.record()
self.log << 'timers of the dmrg:\n%s\n' % self.timers.tostr(Timers.ALL)
self.log << 'info of the dmrg:\n%s\n\n' % self.info
if piechart: self.timers.graph(parents=Timers.ALL)