def test_basic():
print '[test_basic]'
np.random.seed(5)
nr = 4
nc = 4
pdim = 2
bond = 1
auxbond = 8
shape = (nr, nc)
# simple peps
pepsc = peps.zeros(shape, pdim, bond)
pepsc[1, 1].prt()
pepsc[2, 2].prt()
p = einsum('pijkl,pijkl', pepsc[1, 1], pepsc[1, 1])
print p
p = einsum('pijkl,pklmn->ijmn', pepsc[1, 1], pepsc[2, 2])
p.prt()
# random peps
pepsn = peps.random(shape, pdim, bond)
pepsn[1, 1].prt()
# add peps
peps0 = peps.add(pepsn, pepsn)
pepsn[0, 0].prt()
peps0[0, 0].prt()
peps1 = peps.add(peps0, pepsn)
peps1[0, 0].prt()
return 0
def dot(mpsa,mpsb):
"""
dot product of two mps
"""
assert len(mpsa)==len(mpsb)
nsites = len(mpsa)
e0 = PArray([[0],[0]],[[1],[1]])
e0[0,0] = np.ones(1).reshape(1,1)
for i in xrange(nsites):
tmp = einsum('ij,jnr->inr',e0,mpsb[i])
e0 = einsum('inl,inr->lr',mpsa[i],tmp)
return e0[0,0][0,0]
def epeps(pepsa,pepsb):
shape = pepsa.shape
epeps = np.empty(shape, dtype=np.object)
for i in range(shape[0]):
for j in range(shape[1]):
epeps[i,j]=einsum("pludr,pLUDR->lLuUdDrR",pepsa[i,j],pepsb[i,j])
epeps[i,j] = epeps[i,j].merge([[0,1],[2,3],[4,5],[6,7]])
return epeps
def mapply(mpo, mps):
"""
apply mpo to mps, or apply mpo to mpo
"""
nsites = len(mpo)
assert len(mps) == nsites
ret = [None] * nsites
if len(mps[0].shape) == 3:
# mpo x mps
for i in xrange(nsites):
mt = einsum("apqb,cqd->acpbd", mpo[i], mps[i])
ret[i] = mt.merge([[0, 1], [2], [3, 4]])
elif len(mps[0].shape) == 4:
# mpo x mpo
for i in xrange(nsites):
mt = einsum("apqb,cqrd->acprbd", mpo[i], mps[i])
ret[i] = mt.merge([[0, 1], [2], [3], [4, 5]])
return ret
def eval_vbond(pepsa0, pepsa, i, j, auxbond):
debug = False
# Sz*Sz
pepsb = peps.copy(pepsa)
pepsb[i, j] = einsum("pq,qludr->pludr", Sz, pepsa[i, j])
pepsb[i + 1, j] = einsum("pq,qludr->pludr", Sz, pepsa[i + 1, j])
valzz = peps.dot(pepsa0, pepsb, auxbond)
if debug: print(i, j), 'valzz=', valzz
# Sp*Sm
pepsb = peps.copy(pepsa)
pepsb[i, j] = einsum("xpq,qludr->plxudr", Sp,
pepsa[i, j]).merge_adjpair(2, 3)
pepsb[i + 1, j] = einsum("xpq,qludr->pluxdr", Sm,
pepsa[i + 1, j]).merge_adjpair(3, 4)
valpm = peps.dot(pepsa0, pepsb, auxbond)
if debug: print(i, j), 'valpm=', valpm
# Sm*Sp
pepsb = peps.copy(pepsa)
pepsb[i, j] = einsum("xpq,qludr->plxudr", Sm,
pepsa[i, j]).merge_adjpair(2, 3)
pepsb[i + 1, j] = einsum("xpq,qludr->pluxdr", Sp,
pepsa[i + 1, j]).merge_adjpair(3, 4)
valmp = peps.dot(pepsa0, pepsb, auxbond)
if debug: print(i, j), 'valmp=', valmp
return valzz + 0.5 * (valpm + valmp)
def test_conf():
np.random.seed(5)
nr = 3
nc = 3
pdim = 2
bond = 2
auxbond = 4
# Initialization:
# [[0 1 0 1]
# [1 0 1 0]
# [0 1 0 1]
# [1 0 1 0]
# [0 1 0 1]
# [1 0 1 0]]
configa = np.zeros([nr, nc], dtype=np.int)
for i in range(nr):
for j in range(nc):
configa[i, j] = (i + j) % 2
pepsa = peps.create(pdim, configa)
#for i in range(nr):
# for j in range(nc):
# print '(i,j)=',(i,j)
# pepsa[i,j].prt()
print "CEVAL =", peps.ceval(pepsa, configa, auxbond)
PP = peps.dot(pepsa, pepsa, None)
print "<P|P> =", PP
Sp = peps_h.get_Sp()
Sm = peps_h.get_Sm()
Sz = peps_h.get_Sz()
i = j = 0
# Sm*Sp
pepsb = peps.copy(pepsa)
pepsb[i, j] = einsum("xpq,qludr->plxudr", Sm,
pepsa[i, j]).merge_adjpair(2, 3)
pepsb[i, j].prt()
pepsb[i, j + 1] = einsum("xpq,qludr->pluxdr", Sp,
pepsa[i, j + 1]).merge_adjpair(3, 4)
valmp = peps.dot(pepsb, pepsa, auxbond)
print 'valmp=', valmp
# Sz*Sz
pepsb = peps.copy(pepsa)
pepsb[i, j] = einsum("pq,qludr->pludr", Sz, pepsa[i, j])
pepsb[i, j + 1] = einsum("pq,qludr->pludr", Sz, pepsa[i, j + 1])
valzz = peps.dot(pepsb, pepsa, auxbond)
print 'valzz=', valzz
# Sp*Sm
pepsb = peps.copy(pepsa)
pepsb[i, j] = einsum("xpq,qludr->plxudr", Sp,
pepsa[i, j]).merge_adjpair(2, 3)
pepsb[i, j + 1] = einsum("xpq,qludr->pluxdr", Sm,
pepsa[i, j + 1]).merge_adjpair(3, 4)
valpm = peps.dot(pepsb, pepsa, auxbond)
print 'valpm=', valpm
return 0
def compress_left(mps,trunc=1.e-12,debug=False):
nrm2 = dot(mps, mps)
nsites = len(mps)
ret_mps = [None]*nsites
# Note: in EPEPS, the physical dim can be O(D^2);
# auxbond O(D^4) after MPO apply to MPS.
res0 = mps[0]
for i in xrange(1,nsites):
# Merge (l,n,r)
res = res0.merge_adjpair(0,1)
u0,sigma0,vt0 = autograd.numpy.linalg.svd(res[0,0],full_matrices=False)
u1,sigma1,vt1 = autograd.numpy.linalg.svd(res[1,1],full_matrices=False)
assert len(sigma0) == len(sigma1)
if trunc==0:
m_trunc=len(sigma0)
elif trunc<1.:
# count how many sing vals < trunc
total = np.sqrt(np.sum(sigma0**2)+np.sum(sigma1**2))
normed_sigma0=sigma0/total
normed_sigma1=sigma1/total
m_trunc=max(len([s for s in normed_sigma0 if s >trunc]),\
len([s for s in normed_sigma1 if s >trunc]))
else:
m_trunc=int(trunc)
m_trunc=min(m_trunc,len(sigma0))
if debug:
s0r = np.sum(sigma0[0:m_trunc]**2)
s0t = np.sum(sigma0**2)
s1r = np.sum(sigma1[0:m_trunc]**2)
s1t = np.sum(sigma1**2)
print ' i=',i,' len(sig0)=',len(sigma0),' m_trunc=',m_trunc,' trunc=',trunc
print ' sigma0^2[tot,rem,dis] =',(s0t,s0r,s0t-s0r)
print ' sigma1^2[tot,rem,dis] =',(s1t,s1r,s1t-s1r)
u0=u0[:,0:m_trunc]
sigma0=np.diag(sigma0[0:m_trunc])
vt0=vt0[0:m_trunc,:]
u1=u1[:,0:m_trunc]
sigma1=np.diag(sigma1[0:m_trunc])
vt1=vt1[0:m_trunc,:]
# Update site
ptys = res0.ptys
dims = res0.dims
dimr = [m_trunc,m_trunc]
site = PArray([ptys[0],ptys[1],[0,1]],[dims[0],dims[1],dimr])
if len(ptys[0]) == 1:
site[0,0,0] = u0.reshape(site[0,0,0].shape) # parity-0
site[0,1,1] = u1.reshape(site[0,1,1].shape) # parity-1
else:
nblk00 = dims[0][0]*dims[1][0]
nblk01 = dims[0][0]*dims[1][1]
site[0,0,0] = u0[:nblk00,:].reshape(site[0,0,0].shape) # parity-0
site[1,1,0] = u0[nblk00:,:].reshape(site[1,1,0].shape) # parity-0
site[0,1,1] = u1[:nblk01,:].reshape(site[0,1,1].shape) # parity-1
site[1,0,1] = u1[nblk01:,:].reshape(site[1,1,0].shape) # parity-1
ret_mps[i-1] = site
# Assignment of vt
vt = PArray([[0,1],[0,1]],[dimr,dims[2]])
vt[0,0] = np.dot(sigma0,vt0)
vt[1,1] = np.dot(sigma1,vt1)
res0 = einsum('ij,jnr->inr',vt,mps[i])
# Last one
ret_mps[nsites-1] = res0
# Check
fidelity = dot(ret_mps, mps)/(nrm2+1.e-10) # zero-EPES
if debug: print ' nrm2=',nrm2,' fidelity=',fidelity
return fidelity,ret_mps