def genHfacSpinQt0(p, nsite, isite, hq, vqrs):
isz = p % 2
elem = genElemSpinQt(p, isite, iop=1)
wfac = genWfacSpinQt(nsite, isite, hq, vqrs, isz)
# lrij,abjk-> lriabk ->larbik
hfac = qtensor.tensordot(elem, wfac, axes=([3], [2]))
hfac = hfac.transpose(0, 3, 1, 4, 2, 5)
hfac = hfac.merge([[0, 1], [2, 3], [4], [5]])
return hfac
def mps_dot(bmps, kmps, status='L'):
nsite1 = len(bmps)
nsite2 = len(kmps)
assert nsite1 == nsite2
nsite = nsite1
if status == 'L':
tmp = qtensor.tensordot(bmps[0], kmps[0], axes=([1], [1]))
tmp.status[0] = ~tmp.status[0]
tmp.status[2] = ~tmp.status[2]
tmp = tmp.merge([[0, 1], [2, 3]])
for i in range(1, nsite):
# t[l,r]*k[r,n,r'] = t[l,n,r']
# b[l,n,l']*t[l,n,r'] = t[l',r']
tmp = qtensor.tensordot(tmp, kmps[i], axes=([1], [0]))
tmp = qtensor.tensordot(bmps[i], tmp, axes=([0, 1], [0, 1]))
elif status == 'R':
tmp = qtensor.tensordot(bmps[nsite - 1],
kmps[nsite - 1],
axes=([1], [1]))
tmp.status[1] = ~tmp.status[1]
tmp.status[3] = ~tmp.status[3]
tmp = tmp.merge([[0, 1], [2, 3]])
for i in range(nsite - 2, -1, -1):
# b[l,n,l']*t[l',r'] = t[l,n,r']
# t[l,n,r']*k[r,n,r'] = t[l,r]
tmp = qtensor.tensordot(bmps[i], tmp, axes=([2], [0]))
tmp = qtensor.tensordot(tmp, kmps[i], axes=([1, 2], [1, 2]))
assert len(tmp.value) == 1
ovlp = tmp.value[0]
return ovlp
def test_creann():
# LOAD MPS
fname = './mps.h5'
mps, qnum = mps_io.loadMPS(fname)
lmps = [mps, qnum]
bdim = map(lambda x: len(x), 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 linkTwoOpers(qt1, qt2):
# (abij),(bckl)-> (aij,ckl)
qt12 = qtensor.tensordot(qt1, qt2, axes=([1], [0]))
qt12 = qt12.transpose(0, 3, 1, 4, 2, 5)
qt12 = qt12.merge([[0], [1], [2, 3], [4, 5]])
return qt12
def test_HRfac():
# LOAD MPS
fname = './mps.h5'
mps, qnum = mps_io.loadMPS(fname)
lmps = [mps, qnum]
bdim = map(lambda x: len(x), 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 = map(lambda x: len(x), 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 = map(lambda x: len(x), 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 = map(lambda x: len(x), 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