def trace(mpo):
"""
\sum_{n1n2...} A[n1n1] A[n2n2] A[nknk]
"""
traced_mts = [N.einsum("innj", mt) for mt in mpo]
val = traced_mts[0]
nsites = len(mpo)
for i in xrange(1, nsites):
val = N.dot(val, traced_mts[i])
return N.trace(val) #[0,0]
def ceval(mps, config):
"""
Evaluates mps at given config
"""
mps_mats = [None] * len(config)
nsites = len(config)
for i, pval in enumerate(config):
mps_mats[i] = mps[i][:, pval, :]
# multiply "backwards" from right to left
val = mps_mats[0]
for i in xrange(1, nsites):
val = N.dot(val, mps_mats[i])
# turn into scalar
return N.trace(val)
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