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):
assert mpo[i].shape[2] == mps[i].shape[1]
mt = N.einsum("apqb,cqd->acpbd", mpo[i], mps[i])
mt = N.reshape(mt, [
mpo[i].shape[0] * mps[i].shape[0], mpo[i].shape[1],
mpo[i].shape[-1] * mps[i].shape[-1]
])
ret[i] = mt
elif len(mps[0].shape) == 4:
# mpo x mpo
for i in xrange(nsites):
assert mpo[i].shape[2] == mps[i].shape[1]
mt = N.einsum("apqb,cqrd->acprbd", mpo[i], mps[i])
mt = N.reshape(mt, [
mpo[i].shape[0] * mps[i].shape[0], mpo[i].shape[1],
mps[i].shape[2], mpo[i].shape[-1] * mps[i].shape[-1]
])
ret[i] = mt
return ret
def create(shape, pdim, config):
peps_config = np.reshape(config, shape)
peps0 = zeros(shape, pdim, 1)
for i in range(shape[0]):
for j in range(shape[1]):
peps0[i, j][peps_config[i, j], 0, 0, 0, 0] = 1.
return peps0
def cpeps(peps, config):
shape = peps.shape
cpeps = np.empty(shape, dtype=np.object)
peps_config = np.reshape(config, peps.shape)
for i in range(shape[0]):
for j in range(shape[1]):
cpeps[i, j] = peps[i, j][peps_config[i, j], :, :, :, :]
return cpeps
def aspeps(vec, shape, pdim, bond):
peps0 = empty(shape, pdim, bond)
assert vec.size == size(peps0)
ptr = 0
for i in range(shape[0]):
for j in range(shape[1]):
nelem = peps0[i, j].size
peps0[i, j] = np.reshape(vec[ptr:ptr + nelem], peps0[i, j].shape)
ptr += nelem
return peps0
def create(ops):
"""
Create MPO operator from a
tensor product of single site operators e.g.
I otimes c otimes d otimes ...
"""
pdim = ops[0].shape[0]
assert ops[0].shape[1] == pdim
return [N.reshape(op, [1, pdim, pdim, 1]) for op in ops]
def from_mps(mps):
"""
squaren physical indices of MPS to MPO
"""
pdim = int(math.sqrt(mps[0].shape[1]))
assert pdim * pdim == mps[0].shape[1]
return [
N.reshape(mt, [mt.shape[0], pdim, pdim, mt.shape[2]]) for mt in mps
]
def to_mps(mpo):
"""
flatten physical indices of MPO to MPS
"""
pdim = mpo[0].shape[1]
assert pdim == mpo[0].shape[2]
return [
N.reshape(mt, [mt.shape[0], pdim * pdim, mt.shape[3]]) for mt in mpo
]
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])
eshape = epeps[i, j].shape
epeps[i, j] = np.reshape(
epeps[i, j], (eshape[0] * eshape[1], eshape[2] * eshape[3],
eshape[4] * eshape[5], eshape[6] * eshape[7]))
return epeps
def contract_cpeps(cpeps, auxbond):
cmps0 = [None] * cpeps.shape[1]
for i in range(cpeps.shape[1]):
l, u, d, r = cpeps[0, i].shape
cmps0[i] = np.reshape(cpeps[0, i], (l, u * d, r))
for i in range(1, cpeps.shape[0]):
cmpo = [None] * cpeps.shape[1]
for j in range(cpeps.shape[1]):
cmpo[j] = cpeps[i, j]
cmps0 = mpo.mapply(cmpo, cmps0)
if auxbond is not None: # compress
cmps0 = mps.SVDcompress(cmps0, auxbond)
return mps.ceval(cmps0, [0] * cpeps.shape[1])
def check_lortho(tens):
tensm = N.reshape(tens, [N.prod(tens.shape[:-1]), tens.shape[-1]])
s = N.dot(N.conj(tensm.T), tensm)
return scipy.linalg.norm(s - N.eye(s.shape[0]))
def check_rortho(tens):
tensm = N.reshape(tens, [tens.shape[0], N.prod(tens.shape[1:])])
s = N.dot(tensm, N.conj(tensm.T))
return scipy.linalg.norm(s - N.eye(s.shape[0]))
def compress(mps, side, trunc=1.e-12, check_canonical=False):
"""
inp: canonicalise MPS (or MPO)
trunc=0: just canonicalise
0<trunc<1: sigma threshold
trunc>1: number of renormalised vectors to keep
side='l': compress LEFT-canonicalised MPS
by sweeping from RIGHT to LEFT
output MPS is right canonicalised i.e. CRRR
side='r': reverse of 'l'
returns:
truncated or canonicalised MPS
"""
assert side in ["l", "r"]
# if trunc==0, we are just doing a canonicalisation,
# so skip check, otherwise, ensure mps is canonicalised
if trunc != 0 and check_canonical:
if side == "l":
assert is_left_canonical(mps)
else:
assert is_right_canonical(mps)
ret_mps = []
nsites = len(mps)
if side == "l":
res = mps[-1]
else:
res = mps[0]
for i in xrange(1, nsites):
# physical indices exclude first and last indices
pdim = list(res.shape[1:-1])
if side == "l":
res = N.reshape(res, (res.shape[0], N.prod(res.shape[1:])))
else:
res = N.reshape(res, (N.prod(res.shape[:-1]), res.shape[-1]))
if svd_iop == 0:
u, sigma, vt = svd(res, full_matrices=False, lapack_driver='gesvd')
else:
u, sigma, vt = svd(res, full_matrices=False)
if trunc == 0:
m_trunc = len(sigma)
elif trunc < 1.:
# count how many sing vals < trunc
normed_sigma = sigma / scipy.linalg.norm(sigma)
m_trunc = len([s for s in normed_sigma if s > trunc])
else:
m_trunc = int(trunc)
m_trunc = min(m_trunc, len(sigma))
u = u[:, 0:m_trunc]
sigma = N.diag(sigma[0:m_trunc])
vt = vt[0:m_trunc, :]
if side == "l":
u = N.dot(u, sigma)
res = N.dot(mps[nsites - i - 1], u)
ret_mpsi = N.reshape(vt, [m_trunc] + pdim +
[vt.shape[1] / N.prod(pdim)])
else:
vt = N.dot(sigma, vt)
res = N.tensordot(vt, mps[i], 1)
ret_mpsi = N.reshape(u, [u.shape[0] / N.prod(pdim)] + pdim +
[m_trunc])
ret_mps.append(ret_mpsi)
ret_mps.append(res)
if side == "l":
ret_mps.reverse()
#fidelity = dot(ret_mps, mps)/dot(mps, mps)
#print "compression fidelity:: ", fidelity
return ret_mps