def genWfacSpatialQt(nsite, isite, hq, vqrs, isz):
isym = 2
status = 'L'
site = mpo_dmrg_opers.genWfacSpatial(nsite, isite, hq, vqrs)
qt = qtensor.qtensor([False, True, False, True])
# Site physical indices
qu, qd = genQphys(isym, isite)
# Quantum numbers
ql1, qr1 = genWfacQnums(nsite, 2 * isite, isz, status)
ql2, qr2 = genWfacQnums(nsite, 2 * isite + 1, isz, status)
ql = ql1
qr = qr2
qt.fromDenseTensor(site, [ql, qr, qu, qd])
return qt
def testWfacSpatial():
#
# Time for tc becomes smaller for nsite=100,
# due to the saving in contraction two sites.
#
# ta = 14.3027746677
# tb = 16.9804520607 averaged(/100) = 0.16s.
# tc = 13.7098605633
#
# isz,isite= 0 46
# wop= (402, 402, 4, 4)
# Basic information:
# rank = 4 shape= [402 402 4 4] nsyms= [8 8 4 4]
# nblks_allowed = 84 nblks = 1024
# size_allowed = 212956 size = 2585664 savings= 0.0823602757357
# isz,isite,diff= 0 46 0.0
# Basic information:
# rank = 4 shape= [402 402 4 4] nsyms= [8 8 4 4]
# nblks_allowed = 84 nblks = 1024
# size_allowed = 212956 size = 2585664 savings= 0.0823602757357
# isz,isite,diff= 0 46 0.0
# equalSym= True
# t1= 0.189389944077
# t2= 0.212503194809
# t3= 0.176101922989
#
nsite = 40
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))
for isz in [0, 1]:
hq = hmo[isz]
vqrs = eri[isz]
ta = 0.
tb = 0.
tc = 0.
for isite in range(nsite):
print '\nisz,isite=', isz, isite
t0 = time.time()
site0 = mpo_dmrg_opers.genWfacSpatial(nbas, isite, hq, vqrs)
t1 = time.time()
print 'wop=', site0.shape
# Wsite
qt12 = genWfacSpatialQt(nbas, isite, hq, vqrs, isz)
qt12.prt()
site1 = qt12.toDenseTensor()
t2 = time.time()
ta += t1 - t0
tb += t2 - t1
assert site0.shape == site1.shape
diff = numpy.linalg.norm(site0 - site1)
print 'isz,isite,diff=', isz, isite, diff
assert diff < 1.e-10
t3 = time.time()
qt12a = genWfacSpinQt(nbas, 2 * isite, hq, vqrs, isz)
qt12b = genWfacSpinQt(nbas, 2 * isite + 1, hq, vqrs, isz)
qt12l = linkTwoOpers(qt12a, qt12b)
qt12l.prt()
site2 = qt12l.toDenseTensor()
t4 = time.time()
tc += t4 - t3
assert site1.shape == site2.shape
diff = numpy.linalg.norm(site1 - site2)
print 'isz,isite,diff=', isz, isite, diff
assert diff < 1.e-10
print ' equalSym=', qt12l.equalSym(qt12)
print ' t1=', t1 - t0
print ' t2=', t2 - t1
print ' t3=', t4 - t3
print
print 'ta =', ta
print 'tb =', tb
print 'tc =', tc
return 0
def test_Wfac():
#
# Wop*Site = [256*30,4,30*1015] = [935424000] - 7G
#
# isite/nsite= 4 14
# Basic information:
# rank = 3 shape= [ 256 4 1015] nsyms= [25 4 36]
# nblks_allowed = 100 nblks = 3600
# size_allowed = 62804 size = 1039360 savings= 0.0604256465517
# wop= (30, 30, 4, 4)
# t1= 13.3494501114
# t2= 2.59876251221e-05
#
# isite/nsite= 5 14 --- 50G for storage.
# Basic information:
# rank = 3 shape= [1015 4 1822] nsyms= [36 4 44]
# nblks_allowed = 136 nblks = 6336
# size_allowed = 376882 size = 7397320 savings= 0.0509484516014
# wop= (30, 30, 4, 4)
#
#>>> Sparse op becomes better for D~500 for computational time.
#
#isite/nsite= 3 14
#Basic information:
# rank = 3 shape= [ 64 4 256] nsyms= [16 4 25]
# nblks_allowed = 64 nblks = 1600
# size_allowed = 4900 size = 65536 savings= 0.0747680664062
# wop= (30, 30, 4, 4)
# t1= 0.615185976028
# t2= 0.715934991837
#isite,diff= 3 (1920, 4, 7680) 0.0 t0= 0.615185976028 t1= 0.715934991837
#
#isite/nsite= 4 14
#Basic information:
# rank = 3 shape= [ 256 4 1015] nsyms= [25 4 36]
# nblks_allowed = 100 nblks = 3600
# size_allowed = 62804 size = 1039360 savings= 0.0604256465517
# wop= (30, 30, 4, 4)
# t1= 10.8923699856
# t2= 3.5177989006
#isite,diff= 4 (7680, 4, 30450) 0.0 t0= 10.8923699856 t1= 3.5177989006
#
#ta= 11.5469501019
#tb= 4.54184865952
#
# 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.
isz = 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)
hq = hmo[isz]
vqrs = eri[isz]
maxn = 3
for isite in range(min(nsite, maxn)):
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])
tmps.prt()
t0 = time.time()
op = mpo_dmrg_opers.genWfacSpatial(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)
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
print()
print('ta=', ta)
print('tb=', tb)
print()
return 0