def dotMPS(self, mps, debug=False):
if debug: print '\n[mpo_class.dotMPS]'
assert self.nsite == mps.nsite
mps2 = mps.torank2()
tmps = self.dot(mps2)
#
# Quantum number operations if Qnums exist
#
qnums = None
if self.qnums is not None and mps.qnums is not None:
if debug: print 'Merge quantum numbers:'
q1 = self.qnums
q2 = mps.qnums
b1 = self.bdim()
b2 = mps.bdim()
qnums = [0] * self.nsite
for ibond in range(self.nsite):
q1i = self.qnums[ibond]
q2i = mps.qnums[ibond]
q12 = mpo_qphys.dpt(q1i, q2i)
if debug: print 'q12=', q12
# Some compressions are required to remove negative
# and large q12 that exceed the allowed qnums.
qnums[ibond] = copy.deepcopy(q12)
# Product new MPS
mps2 = mps_class.class_mps(self.nsite,
sites=tmps,
qphys=mps.qphys,
qnums=qnums)
return mps2
def qrightCanon(self, thresh=-1.e-12, Dcut=-1, debug=False):
print '\n[mps_class.qrightCanon]'
print ' Bdim before: ', self.bdim()
assert abs(self.norm() - 1.0) < 1.e-8
sites = self.sites
nsite = len(sites)
link = [0] * (nsite - 1)
sval = [0] * (nsite - 1)
rmps = [0] * nsite
qnums = [0] * nsite
# Current object
tsite = sites[nsite - 1].copy()
# Now the symmetry is purely determined from qphys
qnumr = [copy.deepcopy(self.qphys[0][0])]
qnums[nsite - 1] = copy.deepcopy(qnumr)
qphys = copy.deepcopy(self.qphys)
# rk3
for isite in range(nsite - 1, -1, -1):
s = tsite.shape
d1 = s[0]
d2 = s[1] * s[2]
# Combine quantum numbers
qphys_isite = qphys[isite]
qnum1 = mpo_qphys.dpt(qphys_isite, qnumr)
mat = tsite.reshape((d1, d2)).copy()
classes = qnum1
if isite != 0:
dwts, qred, u, sigs, vt = qparser.row_svd(
mat.T.copy(), classes, thresh, Dcut)
bdim = len(sigs)
print ' isite/bdim=', isite, bdim
rmps[isite] = u.T.reshape((bdim, s[1], s[2])).copy()
qnumr = numpy.array(copy.deepcopy(qred))
qnums[isite - 1] = qnumr.copy()
# Update next tsite
tmp = numpy.diag(sigs).dot(vt).T.copy()
link[isite - 1] = tmp.copy()
#tsite = numpy.einsum('lur,rs->lus',sites[isite-1],tmp)
tsite = numpy.tensordot(sites[isite - 1], tmp, axes=([2], [0]))
sval[isite - 1] = sigs.copy()
else:
# Always cut the last one
dwts, qred, u, sigs, vt = qparser.row_svd(
mat.T.copy(), classes, thresh, 1)
bdim = len(sigs)
print ' isite/bdim=', isite, bdim
assert bdim == 1
rmps[isite] = u.T.reshape((bdim, s[1], s[2])).copy()
if debug:
print '-' * 80
print ' Results[i]:', isite
print '-' * 80
print ' dimension:', (d1, d2), '->', bdim
print ' qred:', qred
print ' sum of sigs2:', numpy.sum(
numpy.array(sigs)**2), ' dwts:', dwts
print ' sigs:\n', sigs
# Final
self.sites = copy.deepcopy(rmps)
self.qnums = copy.deepcopy(qnums)
if debug: self.prt()
print ' Bdim after: ', self.bdim()
return link, sval
def qleftCanon(self, thresh=-1.e-12, Dcut=-1, debug=False):
print '\n[mps_class.qleftCanon]'
print ' Bdim before: ', self.bdim()
assert abs(self.norm() - 1.0) < 1.e-8
sites = self.sites
nsite = len(sites)
link = [0] * (nsite - 1)
sval = [0] * (nsite - 1)
lmps = [0] * nsite
qnums = [0] * nsite
# Current object
tsite = sites[0].copy()
# Now the symmetry is purely determined from qphys
qnuml = [copy.deepcopy(self.qphys[0][0])]
qphys = copy.deepcopy(self.qphys)
# rk3
for isite in range(nsite):
s = tsite.shape
d1 = s[0] * s[1]
d2 = s[2]
# Combine quantum numbers
qphys_isite = qphys[isite]
qnum1 = mpo_qphys.dpt(qnuml, qphys_isite)
mat = tsite.reshape((d1, d2)).copy()
classes = qnum1
if isite != nsite - 1:
dwts, qred, u, sigs, vt = qparser.row_svd(
mat, classes, thresh, Dcut)
bdim = len(sigs)
print ' isite/bdim=', isite, bdim
lmps[isite] = u.reshape((s[0], s[1], bdim)).copy()
qnuml = numpy.array(copy.deepcopy(qred))
qnums[isite] = qnuml.copy()
# Update next tsite
tmp = numpy.diag(sigs).dot(vt)
link[isite] = tmp.copy()
#tsite = numpy.einsum('sl,lur->sur',tmp,sites[isite+1])
tsite = numpy.tensordot(tmp, sites[isite + 1], axes=([1], [0]))
sval[isite] = sigs.copy()
else:
# Otherwise the MPS is zero, or have multiple qnumbers
# (particle number breaking!)
dwts, qred, u, sigs, vt = qparser.row_svd(
mat, classes, thresh, 1)
bdim = len(sigs)
print ' isite/bdim=', isite, bdim
assert bdim == 1
lmps[isite] = u.reshape((s[0], s[1], bdim)).copy()
qnuml = numpy.array(copy.deepcopy(qred))
qnums[isite] = qnuml.copy()
if debug:
print '-' * 80
print ' Results[i]:', isite
print '-' * 80
print ' dimension:', (d1, d2), '->', bdim
print ' qred:', qred
print ' sum of sigs2:', numpy.sum(
numpy.array(sigs)**2), ' dwts:', dwts
print ' sigs:\n', sigs
# Final
self.sites = copy.deepcopy(lmps)
self.qnums = copy.deepcopy(qnums)
if debug: self.prt()
print ' Bdim after: ', self.bdim()
return link, sval