def fmpsQt(fmps0, fmps1, status, isym=2):
print('\n[qtensor_api.fmpsQt] status=', status)
nsite = fmps0['nsite'].value
fmps1['nsite'] = nsite
qphys = mpo_dmrg_qphys.initSpatialOrb(nsite, isym)
# False = In, True = Out
if status == 'L':
sta = [False, False, True]
elif status == 'R':
sta = [True, False, False]
# Check symmetry
lenSym = len(fmps0['qnum0'].value[0])
if lenSym != isym:
print(' error: isym is not consistent!')
print(' qnum0:', fmps0['qnum0'].value[0])
print(' lenSym/isym =', lenSym, isym)
exit()
# Cast into Qt tensor
for isite in range(nsite):
ql = fmps0['qnum' + str(isite)].value
qn = qphys[isite]
qr = fmps0['qnum' + str(isite + 1)].value
site = fmps0['site' + str(isite)].value
print(' isite =', isite, ' shape=', site.shape)
tmps = qtensor.qtensor(sta)
tmps.fromDenseTensor(site, [ql, qn, qr])
tmps.dump(fmps1, 'site' + str(isite))
# Save qnums
for isite in range(nsite + 1):
ql = fmps0['qnum' + str(isite)].value
fmps1['qnum' + str(isite)] = ql
return 0
def mpsQt(mps, qnum, status):
print('\n[qtensor_api.mpsQt] status=', status)
debug = False
nsite = len(mps)
qphys = mpo_dmrg_qphys.initSpatialOrb(nsite, 2)
# False = In, True = Out
if status == 'L':
sta = [False, False, True]
elif status == 'R':
sta = [True, False, False]
qtlst = []
for isite in range(nsite):
ql = qnum[isite]
qn = qphys[isite]
qr = qnum[isite + 1]
site = mps[isite]
tmps = qtensor.qtensor(sta)
tmps.fromDenseTensor(site, [ql, qn, qr])
qtlst.append(tmps)
# Test
if debug:
print('isite=', isite)
tsite = tmps.toDenseTensor()
diffDense = numpy.linalg.norm(tsite - site)
print(' diffDense=', diffDense)
tmps.prt()
assert diffDense < 1.e-12
return qtlst
def test_transpose_merge():
# 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)
for isite in range(nsite):
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)
site = mps[isite]
tsite0 = site.transpose(2, 0, 1)
print('isite=', isite)
tmps = qtensor.qtensor([False, False, True])
tmps.fromDenseTensor(site, [ql, qn, qr])
tmps = tmps.transpose(2, 0, 1)
tsite = tmps.toDenseTensor()
diff1 = numpy.linalg.norm(tsite0 - tsite)
print(' diff1=', diff1)
shape = tsite0.shape
tmp = tsite0.reshape((shape[0], shape[1] * shape[2]))
tmps = tmps.merge([[0], [1, 2]])
tmat = tmps.toDenseTensor()
diff2 = numpy.linalg.norm(tmp - tmat)
print(' diff2=', diff2)
return 0
def test_io():
# LOAD MPS
fname = './mps.h5'
mps, qnum = mps_io.loadMPS(fname)
lmps = [mps, qnum]
bdim = [len(x) for x in qnum]
print(' bdim = ', bdim)
for item in mps:
print(item.shape)
for item in qnum:
print(item)
nsite = len(mps)
print(nsite)
qphys = mpo_dmrg_qphys.initSpatialOrb(nsite, 2)
print(qphys)
print(len(qnum))
f1 = h5py.File("mpsQt.h5", "w")
for isite in range(nsite):
ql = qnum[isite]
qn = qphys[isite]
qr = qnum[isite + 1]
site = mps[isite]
print()
print('isite=', isite)
tmps = qtensor.qtensor([False, False, True])
tmps.fromDenseTensor(site, [ql, qn, qr])
tmps.dump(f1, 'site' + str(isite))
tmps2 = qtensor.qtensor()
tmps2.load(f1, 'site' + str(isite))
tmps2.prt()
f1.close()
return 0
def test_creann():
# 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.
for isite in range(nsite):
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('isite/nsite=', isite, nsite)
site = mps[isite]
tmps = qtensor.qtensor([False, False, True])
tmps.fromDenseTensor(site, [ql, qn, qr])
tmps.prt()
for iop in [1, 0]:
for p in range(2 * nsite):
t0 = time.time()
op = mpo_dmrg_opers.genElemSpatialMat(p, isite, iop)
#csite = numpy.einsum('ij,ajb->aib',op,site)
csite = numpy.tensordot(op, site, axes=([1], [1])) # iab
csite = csite.transpose(1, 0, 2)
t1 = time.time()
qop = qtensor_opers.genElemSpatialQt(p, isite, iop)
# ijab,xby-> ijaxy -> ix,a,jy
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()
assert csite.shape == tsite.shape
diff = numpy.linalg.norm(tsite - csite)
print('iop,p,diff=', iop, p, csite.shape, diff, ' t0=',
t1 - t0, ' t1=', t2 - t1)
assert diff < 1.e-10
ta += t1 - t0
tb += t2 - t1
# In case of large bond dimension, e.g.,
# D=2000, t0/t1~0.21/0.09 due to sparsity!
print()
print('ta=', ta) # ta= 20.7766697407
print('tb=', tb) # tb= 18.2862818241
print()
return 0
def objectMPS(fmps0,icase,thresh=1.e-12,Dcut=-1):
mps0 = mpo_dmrg_io.loadMPS(fmps0,icase)
nsite = fmps0['nsite'].value
# No symmetry - mpslst as a list
if icase == 0:
mps = mps_class.class_mps(nsite,isym=0,sites=mps0,iop=1)
# With qnums and numpy.array
elif icase == 1:
qphys = mpo_dmrg_qphys.initSpatialOrb(nsite,2)
mps = mps_class.class_mps(nsite,isym=2,sites=mps0[0],iop=1,qphys=qphys,qnums=mps0[1])
# With qnums and Qt
elif icase == 2:
mps = mps0 # [sites,qnums]
return mps
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
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
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
def test_tensordot():
# LOAD MPS
fname = './mps.h5'
mps, qnum = mps_io.loadMPS(fname)
lmps = [mps, qnum]
bdim = [len(x) for x in qnum]
print(' bdim = ', bdim)
for item in mps:
print(item.shape)
for item in qnum:
print(item)
nsite = len(mps)
print(nsite)
qphys = mpo_dmrg_qphys.initSpatialOrb(nsite, 2)
print(qphys)
print(len(qnum))
ta = 0.
tb = 0.
for isite in range(nsite):
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)
site = mps[isite]
print()
print('isite=', isite)
#print len(ql),len(qn),len(qr)
#print 'cl',cl
#print 'cn',cn
#print 'cr',cr
tmps = qtensor.qtensor([False, False, True])
tmps.fromDenseTensor(site, [ql, qn, qr])
tsite = tmps.toDenseTensor()
diffDense = numpy.linalg.norm(tsite - site)
print(' diffDense=', diffDense)
assert diffDense < 1.e-12
##
## test-1
##
#print site.shape
#t0 = time.time()
#tmp = numpy.tensordot(site,site,axes=([0,1],[0,1]))
##tmp1 = numpy.einsum('ijk,lmn',site,site)
##print 'outer=',numpy.linalg.norm(tmp-tmp1)
#t1 = time.time()
#print 'norm=',numpy.linalg.norm(tmp),'t1-t0=',t1-t0
#t1 = time.time()
#tmp2 = qtensor.tensordot(tmps,tmps,axes=([0,1],[0,1]),debug=False)
#t2 = time.time()
#print 'norm=',numpy.linalg.norm(tmp2.value),'t2-t1=',t2-t1
#print 'ratio=',(t2-t1)/(t1-t0)
#ta += t1-t0
#tb += t2-t1
## compare
#tmp3 = tmp2.toDenseTensor()
#diffDense2 = numpy.linalg.norm(tmp-tmp3)
#print ' diffDense2=',diffDense2
#assert diffDense2<1.e-12
#
# test-2: full contraction
#
print('full contraction:', site.shape)
t0 = time.time()
tmp = numpy.tensordot(site, site, axes=([0, 1, 2], [0, 1, 2]))
t1 = time.time()
print('norm=', numpy.linalg.norm(tmp), 't1-t0=', t1 - t0)
t1 = time.time()
tmp2 = qtensor.tensordot(tmps,
tmps,
axes=([0, 1, 2], [0, 1, 2]),
debug=False)
t2 = time.time()
print('norm=', numpy.linalg.norm(tmp2), 't2-t1=', t2 - t1)
print('ratio=', (t2 - t1) / (t1 - t0))
ta += t1 - t0
tb += t2 - t1
# compare
diff = numpy.linalg.norm(tmp - tmp2)
print(' diff=', diff)
assert diff < 1.e-10
print()
print('ta=', ta)
print('tb=', tb)
print()
return 0