def genHRfacSpatialQt(pindx, nsite, isite, int1e, int2e, qpts, pdic, maxslc=1):
p, ip = pindx
iop = 1
isym = 2
status = 'L'
isz = p % 2
site = mpo_dmrg_opers.genHRfacSpatial(pindx, nsite, isite, int1e, int2e,
qpts, pdic)
# Site physical indices
qu, qd = genQphys(isym, isite)
# Orbital dependent part
ql1e, qr1e = genElemQnums(p, 2 * isite, iop, status)
ql2e, qr2e = genElemQnums(p, 2 * isite + 1, iop, status)
ql1 = ql1e
qr1 = qr2e
ql1w, qr1w = genWfacQnums(nsite, 2 * isite, isz, status)
ql2w, qr2w = genWfacQnums(nsite, 2 * isite + 1, isz, status)
ql2 = ql1w
qr2 = qr2w
ql = [q1 + q2 for q1, q2 in itertools.product(ql1, ql2)]
qr = [q1 + q2 for q1, q2 in itertools.product(qr1, qr2)]
# Reduce symmetry: local spin rotation do not change particle number
if ip is not None:
ql = qtensor_util.reduceQnumsToN(ql)
qr = qtensor_util.reduceQnumsToN(qr)
qu = qtensor_util.reduceQnumsToN(qu)
qd = qtensor_util.reduceQnumsToN(qd)
#
# We sort the internal quantum number first
#
nql = len(ql)
nqr = len(qr)
idxl = sortQnums(ql)
idxr = sortQnums(qr)
ql = numpy.array(ql)[idxl]
qr = numpy.array(qr)[idxr]
site = site[numpy.ix_(idxl, idxr)].copy()
# Slice operators if necessary
qts = qtensor.Qt(2)
qts.maxslc[0] = min(maxslc, nql)
qts.maxslc[1] = min(maxslc, nqr)
qts.genDic()
for islc in range(qts.maxslc[0]):
slc0 = parallel_util.partitionSites(nql, qts.maxslc[0], islc)
for jslc in range(qts.maxslc[1]):
slc1 = parallel_util.partitionSites(nqr, qts.maxslc[1], jslc)
ijdx = qts.ravel([islc, jslc])
qts.dic[ijdx] = qtensor.qtensor([False, True, False, True])
# Note that the qsyms for the last two dimensions are not collected
qts.dic[ijdx].fromDenseTensor(site[numpy.ix_(slc0, slc1)],
[ql[slc0], qr[slc1], qu, qd],
ifcollect=[1, 1, 0, 0])
qts.size[ijdx] = qts.dic[ijdx].size_allowed
return qts
def testHRfacSpatial():
#
# Savings are slightly reduced due to the nonzero terms
# that mix blocks with different Sz values. [2 times]
#
# [ 1 0 0 0 ]
# R(a) = [ 0 c -s 0 ]
# [ 0 -s c 0 ]
# [ 0 0 0 1 ]
#
# p,isz,isite= 9 1 39
# hop= (162, 1, 4, 4)
# site0.shape= (162, 1, 4, 4) sum= 19.4722422084
# Basic information:
# rank = 4 shape= [162 1 4 4] nsyms= [4 1 3 3]
# nblks_allowed = 8 nblks = 36
# size_allowed = 572 size = 2592 savings= 0.220679012346
# site1a.shape= (162, 1, 4, 4) sum= 19.4722422084
# isz,isite,diffa= 1 39 0.0
#
numpy.random.seed(10)
nsite = 10
nbas = nsite * 2
hmo = numpy.random.uniform(-1, 1, (nbas, nbas))
hmo[::2, 1::2] = hmo[1::2, ::2] = 0.
# [ij|kl]
eri = numpy.random.uniform(-1, 1, (nbas, nbas, nbas, nbas))
eri[::2, 1::2] = eri[1::2, ::2] = eri[:, :, ::2,
1::2] = eri[:, :, 1::2, ::2] = 0.
# The spin symmetry is essential.
# <ij|kl>=[ik|jl]
eri = eri.transpose(0, 2, 1, 3)
# Antisymmetry is not since only r<s is taken.
# # Antisymmetrize V[pqrs]=-1/2*<pq||rs>
# eri = -0.5*(eri-eri.transpose(0,1,3,2))
ta = 0.
tb = 0.
for p in range(nbas):
isz = p % 2
for isite in range(nsite):
print '\np,isz,isite=', p, isz, isite
t0 = time.time()
pindx = (p, 0)
qpts = numpy.array([0.3])
site0 = mpo_dmrg_opers.genHRfacSpatial(pindx, nbas, isite, hmo,
eri, qpts)
t1 = time.time()
print 'hop=', site0.shape
print 'site0.shape=', site0.shape, ' sum=', numpy.sum(site0)
# Wsite
pdic = None #fake
qt12a = genHRfacSpatialQt(pindx, nbas, isite, hmo, eri, pdic, qpts)
qt12a.prt()
site1a = qt12a.toDenseTensor()
t2 = time.time()
print 'site1a.shape=', site1a.shape, ' sum=', numpy.sum(site1a)
assert site0.shape == site1a.shape
diffa = numpy.linalg.norm(site0 - site1a)
print 'isz,isite,diffa=', isz, isite, diffa
ta += t1 - t0
tb += t2 - t1
print
print 'ta =', ta
print 'tb =', tb
qt12a.prt()
print 'qsyms=', qt12a.qsyms
print 'nsyms=', qt12a.nsyms
print 'idlst=', qt12a.idlst
print 'vals =', qt12a.value
return 0
def test_HRfac():
# LOAD MPS
fname = './mps.h5'
mps, qnum = mps_io.loadMPS(fname)
lmps = [mps, qnum]
bdim = [len(x) for x in qnum]
print(' bdim = ', bdim)
nsite = len(mps)
qphys = mpo_dmrg_qphys.initSpatialOrb(nsite, 2)
ta = 0.
tb = 0.
nbas = 2 * nsite
# random
hmo = numpy.random.uniform(-1, 1, (nbas, nbas))
hmo[::2, 1::2] = hmo[1::2, ::2] = 0.
# [ij|kl]
eri = numpy.random.uniform(-1, 1, (nbas, nbas, nbas, nbas))
eri[::2, 1::2] = eri[1::2, ::2] = eri[:, :, ::2,
1::2] = eri[:, :, 1::2, ::2] = 0.
# The spin symmetry is essential.
# <ij|kl>=[ik|jl]
eri = eri.transpose(0, 2, 1, 3)
maxn = 3
for p in [6, 5]:
isz = p % 2
for isite in range(min(nsite, 5)):
ql = qnum[isite]
qn = qphys[isite]
qr = qnum[isite + 1]
cl = qtensor_util.classification(ql)
cn = qtensor_util.classification(qn)
cr = qtensor_util.classification(qr)
print()
print('isite/nsite=', isite, nsite)
site = mps[isite]
tmps = qtensor.qtensor([False, False, True])
tmps.fromDenseTensor(site, [ql, qn, qr])
print('mps site info:')
tmps.prt()
if isite < maxn:
# Reference value:
t0 = time.time()
pindx = (p, 0)
qpts = numpy.array([0.3])
op = mpo_dmrg_opers.genHRfacSpatial(pindx, nbas, isite, hmo,
eri, qpts)
print(' wop=', op.shape)
#csite = numpy.einsum('lrij,ajb->lairb',op,site)
csite = numpy.tensordot(op, site, axes=([3], [1])) # lriab
csite = csite.transpose(0, 3, 2, 1, 4) # lriab->lairb
s = csite.shape
csite = csite.reshape((s[0] * s[1], s[2], s[3] * s[4]))
t1 = time.time()
print(' t1=', t1 - t0)
# Lowering the symmetry of MPS?
qop = qtensor_opers.genHRfacSpatialQt(pindx, nbas, isite, hmo,
eri, qpts)
# We need to change qop construction allowing given qsyms !
tmps2 = tmps.reduceQsymsToN()
#tmps2 = tmps2.projectionNMs(tmps.qsyms)
#diff = numpy.linalg.norm(tmps2.value-tmps.value)
#print ' diff=',diff
tmps2 = qtensor.tensordot(qop, tmps2, axes=([3], [1]))
tmps2 = tmps2.transpose(0, 3, 2, 1, 4)
tmps2 = tmps2.merge([[0, 1], [2], [3, 4]])
tsite = tmps2.toDenseTensor()
t2 = time.time()
print(' t2=', t2 - t1)
assert csite.shape == tsite.shape
diff = numpy.linalg.norm(tsite - csite)
print('isite,diff=', isite, csite.shape, diff, ' t0=', t1 - t0,
' t1=', t2 - t1)
assert diff < 1.e-10
ta += t1 - t0
tb += t2 - t1
else:
# Reference value:
t0 = time.time()
pindx = (p, 0)
qpts = numpy.array([0.3])
t1 = time.time()
qop = qtensor_opers.genHRfacSpatialQt(pindx, nbas, isite, hmo,
eri, qpts)
tmps2 = tmps.reduceQsymsToN()
tmps2 = qtensor.tensordot(qop, tmps2, axes=([3], [1]))
print('before transposing:')
tmps2.prt()
tmps2 = tmps2.transpose(0, 3, 2, 1, 4)
print('after transposing:')
tmps2.prt()
tmps2 = tmps2.merge([[0, 1], [2], [3, 4]])
print('after merging:')
tmps2.prt()
t2 = time.time()
print('isite=', isite, ' t2=', t2 - t1)
print()
print('ta=', ta)
print('tb=', tb)
print()
return 0