def genHfacSpatialQt(p, nsite, isite, hq, vqrs):
iop = 1
isym = 2
status = 'L'
isz = p % 2
site = mpo_dmrg_opers.genHfacSpatial(p, nsite, isite, hq, vqrs)
# Status
qt = qtensor.qtensor([False, True, False, True])
# 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)]
# Combine
qt.fromDenseTensor(site, [ql, qr, qu, qd])
return qt
def testHfacSpatial():
#
# ta = 29.8947856426
# tb = 34.9535117149
# tc = 27.4478466511 [again for large nsite=100, contraction based is better.]
#
# p,isz,isite= 1 1 50
# hop= (402, 402, 4, 4)
# site0.shape= (402, 402, 4, 4) sum= 763.35358861
# Basic information:
# rank = 4 shape= [402 402 4 4] nsyms= [8 8 4 4]
# nblks_allowed = 84 nblks = 1024
# size_allowed = 212812 size = 2585664 savings= 0.0823045840449
# site1a.shape= (402, 402, 4, 4) sum= 763.35358861
# isz,isite,diffa= 1 50 0.0
# Basic information:
# rank = 4 shape= [402 402 4 4] nsyms= [8 8 4 4]
# nblks_allowed = 84 nblks = 1024
# size_allowed = 212812 size = 2585664 savings= 0.0823045840449
# site1b.shape= (402, 402, 4, 4) sum= 763.35358861
# isz,isite,diffb= 1 50 0.0
# isz,isite,diffab= 1 50 0.0
# t1[mat]= 0.183460950851
# t2[Qt ]= 0.20934510231
# t3[Qt0]= 0.174911975861
# equalSym= True
#
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.
tc = 0.
for p in range(nbas):
isz = p % 2
hq = hmo[isz]
vqrs = eri[isz]
for isite in range(nsite):
print '\np,isz,isite=', p, isz, isite
t0 = time.time()
site0 = mpo_dmrg_opers.genHfacSpatial(p, nbas, isite, hq, vqrs)
t1 = time.time()
print 'hop=', site0.shape
print 'site0.shape=', site0.shape, ' sum=', numpy.sum(site0)
# Wsite
qt12a = genHfacSpatialQt(p, nbas, isite, hq, vqrs)
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
t3 = time.time()
qt12e = genHfacSpinQt(p, nbas, 2 * isite, hq, vqrs)
qt12o = genHfacSpinQt(p, nbas, 2 * isite + 1, hq, vqrs)
qt12b = linkTwoOpers(qt12e, qt12o)
qt12b.prt()
site1b = qt12b.toDenseTensor()
t4 = time.time()
print 'site1b.shape=', site1b.shape, ' sum=', numpy.sum(site1b)
assert site0.shape == site1b.shape
diffb = numpy.linalg.norm(site0 - site1b)
print 'isz,isite,diffb=', isz, isite, diffb
ta += t1 - t0
tb += t2 - t1
tc += t4 - t3
diffab = numpy.linalg.norm(site1a - site1b)
print 'isz,isite,diffab=', isz, isite, diffab
print ' t1[mat]=', t1 - t0
print ' t2[Qt ]=', t2 - t1
print ' t3[Qt0]=', t4 - t3
assert diffa < 1.e-10
assert diffb < 1.e-10
assert diffab < 1.e-10
print ' equalSym=', qt12a.equalSym(qt12b)
assert qt12a.equalSym(qt12b)
print
print 'ta =', ta
print 'tb =', tb
print 'tc =', tc
return 0
def test_Hfac():
#
#------------------------------------------------------------------------
# The large memory cost of Wop*|Psi> [O(K2D2)] requires, for large Dmps
# and Dwop, a sequential compression should be implemented as a sweep,
# such that the [Wsite*MPSsite] can be avoided partially.
#------------------------------------------------------------------------
#
# isite,diff= 0 (1, 4, 232) 0.0 t0= 0.0527150630951 t1= 0.0431280136108
# isite,diff= 1 (232, 4, 928) 0.0 t0= 0.0108029842377 t1= 0.050961971283
# isite,diff= 2 (928, 4, 3712) 0.0 t0= 0.146265029907 t1= 0.182390928268
# isite,diff= 3 (3712, 4, 14848) 0.0 t0= 2.27565908432 t1= 1.25626206398
# isite= 4 [14848 4 58870] t1= 3.11030101776
# isite= 5 [ 58870 4 105676] t1= 30.1744351387
# isite= 6 [105676 4 162806] t1= 101.686741114
# isite= 7 [162806 4 76966] t1= 75.6775298119
# isite= 8 [76966 4 29638] t1= 8.44200801849
# isite= 9 [29638 4 9976] t1= 1.69688081741
# isite= 10 [9976 4 3074] t1= 0.343852996826
# isite= 11 [3074 4 870] t1= 0.101953983307
# isite= 12 [870 4 232] t1= 0.044182062149
# isite= 13 [232 4 1] t1= 0.00591492652893
#
# 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
hq = hmo[isz]
vqrs = eri[isz]
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:
t0 = time.time()
#op = mpo_dmrg_opers.genWfacSpatial(nbas,isite,hq,vqrs)
op = mpo_dmrg_opers.genHfacSpatial(p, nbas, isite, hq, vqrs)
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)
#qop = qtensor_opers.genWfacSpatialQt(nbas,isite,hq,vqrs,isz)
qop = qtensor_opers.genHfacSpatialQt(p, nbas, isite, hq, vqrs)
tmps2 = qtensor.tensordot(qop, tmps, 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:
if isite == maxn: print('>>> Check internal consistency <<<')
t0 = time.time()
#qop = qtensor_opers.genWfacSpatialQt(nbas,isite,hq,vqrs,isz)
qop = qtensor_opers.genHfacSpatialQt(p, nbas, isite, hq, vqrs)
tmps2 = qtensor.tensordot(qop, tmps, axes=([3], [1]))
tmps2 = tmps2.transpose(0, 3, 2, 1, 4)
tmps2 = tmps2.merge([[0, 1], [2], [3, 4]])
tmps2.prt()
t1 = time.time()
sum1 = numpy.sum(tmps2.value)
print('isite=', isite, tmps.shape, ' t0=', t1 - t0, ' sum=',
sum1)
tmps2 = None
qop = qtensor_opers.genHfacSpatialQt0(p, nbas, isite, hq, vqrs)
tmps2 = qtensor.tensordot(qop, tmps, axes=([3], [1]))
tmps2 = tmps2.transpose(0, 3, 2, 1, 4)
tmps2 = tmps2.merge([[0, 1], [2], [3, 4]])
tmps2.prt()
t2 = time.time()
sum2 = numpy.sum(tmps2.value)
print('isite=', isite, tmps2.shape, ' t1=', t2 - t1, ' sum=',
sum2)
tmps2 = None
diff = abs(sum1 - sum2)
print('diff =', diff)
assert diff < 1.e-10
print()
print('ta=', ta)
print('tb=', tb)
print()
return 0