def restore_RCF(self, use_QR=True, update_l=True, diag_l=True):
"""Use a gauge-transformation to restore right canonical form.
Implements the conditions for right canonical form from sub-section
3.1, theorem 1 of arXiv:quant-ph/0608197v2.
It is possible to skip the diagonalization of the l's, such that
only the right orthonormalization condition (r_n = eye) is met.
By default, the l's are updated even if diag_l=False.
Parameters
----------
update_l : bool
Whether to call calc_l() after completion (defaults to True)
diag_l : bool
Whether to put l in diagonal form (defaults to True)
"""
if use_QR:
tm.restore_RCF_r_seq(self.A, self.r, sanity_checks=self.sanity_checks,
sc_data="restore_RCF_r")
else:
G_n_i = sp.eye(self.D[self.N], dtype=self.typ) #This is actually just the number 1
for n in xrange(self.N, 0, -1):
self.r[n - 1], G_n, G_n_i = tm.restore_RCF_r(self.A[n], self.r[n],
G_n_i, sc_data=('site', n),
zero_tol=self.zero_tol,
sanity_checks=self.sanity_checks)
if self.sanity_checks:
if not sp.allclose(self.r[0].A, 1, atol=1E-12, rtol=1E-12):
log.warning("Sanity Fail in restore_RCF!: r_0 is bad / norm failure")
if diag_l:
tm.restore_RCF_l_seq(self.A, self.l, sanity_checks=self.sanity_checks,
sc_data="restore_RCF_l")
if self.sanity_checks:
if not sp.allclose(self.l[self.N].A, 1, atol=1E-12, rtol=1E-12):
log.warning("Sanity Fail in restore_RCF!: l_N is bad / norm failure")
log.warning("l_N = %s", self.l[self.N].squeeze().real)
for n in xrange(1, self.N + 1):
r_nm1 = tm.eps_r_noop(self.r[n], self.A[n], self.A[n])
#r_nm1 = tm.eps_r_noop(m.eyemat(self.D[n], self.typ), self.A[n], self.A[n])
if not sp.allclose(r_nm1, self.r[n - 1], atol=1E-11, rtol=1E-11):
log.warning("Sanity Fail in restore_RCF!: r_%u is bad (off by %g)", n, la.norm(r_nm1 - self.r[n - 1]))
elif update_l:
self.calc_l()
def _restore_CF_ONR(self):
nc = self.N_centre
#Want: r[n >= nc] = eye
#First do uni_r
uGs, uG_is = self.uni_r.restore_RCF(
zero_tol=self.zero_tol, diag_l=False,
ret_g=True) #FIXME: Don't always to all!
Gi = uGs[-1] #Inverse is on the other side in the uniform code.
self.r[self.N] = self.uni_r.r[-1]
for n in xrange(self.N, nc, -1):
self.r[n - 1], Gm1, Gm1_i = tm.restore_RCF_r(
self.A[n],
self.r[n],
Gi,
zero_tol=self.zero_tol,
sanity_checks=self.sanity_checks)
Gi = Gm1_i
self.r[self.N + 1] = self.r[self.N]
#G is now G_nc
for s in xrange(self.q[nc]):
self.A[nc][s] = self.A[nc][s].dot(Gi)
#Now want: l[n < nc] = eye
uGs, uG_is = self.uni_l.restore_LCF(zero_tol=self.zero_tol,
diag_r=False,
ret_g=True)
Gm1 = uG_is[-1]
self.l[0] = self.uni_l.l[-1]
lm1 = self.l[0]
for n in xrange(1, nc):
self.l[n], G, Gi = tm.restore_LCF_l(
self.A[n],
lm1,
Gm1,
zero_tol=self.zero_tol,
sanity_checks=self.sanity_checks)
lm1 = self.l[n]
Gm1 = G
#Gm1 is now G_nc-1
for s in xrange(self.q[nc]):
self.A[nc][s] = Gm1.dot(self.A[nc][s])
def restore_RCF(self, use_QR=True, update_l=True, diag_l=True):
"""Use a gauge-transformation to restore right canonical form.
Implements the conditions for right canonical form from sub-section
3.1, theorem 1 of arXiv:quant-ph/0608197v2.
It is possible to skip the diagonalization of the l's, such that
only the right orthonormalization condition (r_n = eye) is met.
By default, the l's are updated even if diag_l=False.
Parameters
----------
update_l : bool
Whether to call calc_l() after completion (defaults to True)
diag_l : bool
Whether to put l in diagonal form (defaults to True)
"""
if use_QR:
tm.restore_RCF_r_seq(self.A, self.r, sanity_checks=self.sanity_checks,
sc_data="restore_RCF_r")
else:
G_n_i = sp.eye(self.D[self.N], dtype=self.typ) #This is actually just the number 1
for n in xrange(self.N, 0, -1):
self.r[n - 1], G_n, G_n_i = tm.restore_RCF_r(self.A[n], self.r[n],
G_n_i, sc_data=('site', n),
zero_tol=self.zero_tol,
sanity_checks=self.sanity_checks)
if self.sanity_checks:
if not sp.allclose(self.r[0].A, 1, atol=1E-12, rtol=1E-12):
log.warning("Sanity Fail in restore_RCF!: r_0 is bad / norm failure")
if diag_l:
tm.restore_RCF_l_seq(self.A, self.l, sanity_checks=self.sanity_checks,
sc_data="restore_RCF_l")
if self.sanity_checks:
if not sp.allclose(self.l[self.N].A, 1, atol=1E-12, rtol=1E-12):
log.warning("Sanity Fail in restore_RCF!: l_N is bad / norm failure")
log.warning("l_N = %s", self.l[self.N].squeeze().real)
for n in xrange(1, self.N + 1):
r_nm1 = tm.eps_r_noop(self.r[n], self.A[n], self.A[n])
#r_nm1 = tm.eps_r_noop(m.eyemat(self.D[n], self.typ), self.A[n], self.A[n])
if not sp.allclose(r_nm1, self.r[n - 1], atol=1E-11, rtol=1E-11):
log.warning("Sanity Fail in restore_RCF!: r_%u is bad (off by %g)", n, la.norm(r_nm1 - self.r[n - 1]))
elif update_l:
self.calc_l()
def _restore_CF_ONR(self):
nc = self.N_centre
#Want: r[n >= nc] = eye
#First do uni_r
uGs, uG_is = self.uni_r.restore_RCF(zero_tol=self.zero_tol, diag_l=False, ret_g=True) #FIXME: Don't always to all!
Gi = uGs[-1] #Inverse is on the other side in the uniform code.
self.r[self.N] = self.uni_r.r[-1]
for n in xrange(self.N, nc, -1):
self.r[n - 1], Gm1, Gm1_i = tm.restore_RCF_r(self.A[n], self.r[n],
Gi, zero_tol=self.zero_tol,
sanity_checks=self.sanity_checks)
Gi = Gm1_i
self.r[self.N + 1] = self.r[self.N]
#G is now G_nc
for s in xrange(self.q[nc]):
self.A[nc][s] = self.A[nc][s].dot(Gi)
#Now want: l[n < nc] = eye
uGs, uG_is = self.uni_l.restore_LCF(zero_tol=self.zero_tol, diag_r=False, ret_g=True)
Gm1 = uG_is[-1]
self.l[0] = self.uni_l.l[-1]
lm1 = self.l[0]
for n in xrange(1, nc):
self.l[n], G, Gi = tm.restore_LCF_l(self.A[n], lm1, Gm1,
zero_tol=self.zero_tol,
sanity_checks=self.sanity_checks)
lm1 = self.l[n]
Gm1 = G
#Gm1 is now G_nc-1
for s in xrange(self.q[nc]):
self.A[nc][s] = Gm1.dot(self.A[nc][s])
def _restore_CF_ONR(self):
nc = self.N_centre
#Want: r[n >= nc] = eye
Gi = None
for n in xrange(self.N + 1, nc, -1):
self.r[n - 1], Gm1, Gm1_i = tm.restore_RCF_r(self.A[n], self.r[n],
Gi, zero_tol=self.zero_tol,
sanity_checks=self.sanity_checks)
if n == self.N + 1:
self.uni_r.l = Gm1_i.conj().T.dot(self.uni_r.l.dot(Gm1_i))
Gi = Gm1_i
self.r[self.N + 1] = self.r[self.N]
#G is now G_nc
for s in xrange(self.q[nc]):
self.A[nc][s] = self.A[nc][s].dot(Gi)
#Now want: l[n < nc] = eye
Gm1 = None
lm1 = self.l[0]
for n in xrange(nc):
self.l[n], G, Gi = tm.restore_LCF_l(self.A[n], lm1, Gm1,
zero_tol=self.zero_tol,
sanity_checks=self.sanity_checks)
if n == 0:
self.uni_l.r = G.dot(self.uni_l.r.dot(G.conj().T))
lm1 = self.l[n]
Gm1 = G
#Gm1 is now G_nc-1
for s in xrange(self.q[nc]):
self.A[nc][s] = Gm1.dot(self.A[nc][s])
def restore_RCF(self, update_l=True, normalize=True, diag_l=True):
"""Use a gauge-transformation to restore right canonical form.
Implements the conditions for right canonical form from sub-section
3.1, theorem 1 of arXiv:quant-ph/0608197v2.
This performs two 'almost' gauge transformations, where the 'almost'
means we allow the norm to vary (if "normalize" = True).
The last step (A[1]) is done diffently to the others since G[0],
the gauge-transf. matrix, is just a number, which can be found more
efficiently and accurately without using matrix methods.
The last step (A[1]) is important because, if we have successfully made
r[1] = 1 in the previous steps, it fully determines the normalization
of the state via r[0] ( = l[N]).
Optionally (normalize=False), the function will not attempt to make
A[1] satisfy the orthonorm. condition, and will take G[0] = 1 = G[N],
thus performing a pure gauge-transformation, but not ensuring complete
canonical form.
It is also possible to begin the process from a site n other than N,
in case the sites > n are known to be in the desired form already.
It is also possible to skip the diagonalization of the l's, such that
only the right orthonormalization condition (r_n = eye) is met.
By default, the l's are updated even if diag_l=False.
Parameters
----------
update_l : bool
Whether to call calc_l() after completion (defaults to True)
normalize : bool
Whether to also attempt to normalize the state.
diag_l : bool
Whether to put l in diagonal form (defaults to True)
"""
start = self.N
G_n_i = sp.eye(self.D[start], dtype=self.typ) #This is actually just the number 1
for n in xrange(start, 1, -1):
self.r[n - 1], G_n, G_n_i = tm.restore_RCF_r(self.A[n], self.r[n],
G_n_i, sc_data=('site', n),
zero_tol=self.zero_tol,
sanity_checks=self.sanity_checks)
#Now do A[1]...
#Apply the remaining G[1]^-1 from the previous step.
for s in xrange(self.q[1]):
self.A[1][s] = m.mmul(self.A[1][s], G_n_i)
#Now finish off
tm.eps_r_noop_inplace(self.r[1], self.A[1], self.A[1], out=self.r[0])
if normalize:
G0 = 1. / sp.sqrt(self.r[0].squeeze().real)
self.A[1] *= G0
self.r[0][:] = 1
if self.sanity_checks:
r0 = tm.eps_r_noop(self.r[1], self.A[1], self.A[1])
if not sp.allclose(r0, 1, atol=1E-12, rtol=1E-12):
log.warning("Sanity Fail in restore_RCF!: r_0 is bad / norm failure")
if diag_l:
G_nm1 = sp.eye(self.D[0], dtype=self.typ)
for n in xrange(1, self.N):
self.l[n], G_nm1, G_nm1_i = tm.restore_RCF_l(self.A[n],
self.l[n - 1],
G_nm1,
self.sanity_checks)
#Apply remaining G_Nm1 to A[N]
n = self.N
for s in xrange(self.q[n]):
self.A[n][s] = m.mmul(G_nm1, self.A[n][s])
#Deal with final, scalar l[N]
tm.eps_l_noop_inplace(self.l[n - 1], self.A[n], self.A[n], out=self.l[n])
if self.sanity_checks:
if not sp.allclose(self.l[self.N].real, 1, atol=1E-12, rtol=1E-12):
log.warning("Sanity Fail in restore_RCF!: l_N is bad / norm failure")
log.warning("l_N = %s", self.l[self.N].squeeze().real)
for n in xrange(1, self.N + 1):
r_nm1 = tm.eps_r_noop(self.r[n], self.A[n], self.A[n])
#r_nm1 = tm.eps_r_noop(m.eyemat(self.D[n], self.typ), self.A[n], self.A[n])
if not sp.allclose(r_nm1, self.r[n - 1], atol=1E-11, rtol=1E-11):
log.warning("Sanity Fail in restore_RCF!: r_%u is bad (off by %g)", n, la.norm(r_nm1 - self.r[n - 1]))
elif update_l:
self.calc_l()
def restore_RCF(self, update_l=True, normalize=True, diag_l=True):
"""Use a gauge-transformation to restore right canonical form.
Implements the conditions for right canonical form from sub-section
3.1, theorem 1 of arXiv:quant-ph/0608197v2.
This performs two 'almost' gauge transformations, where the 'almost'
means we allow the norm to vary (if "normalize" = True).
The last step (A[1]) is done diffently to the others since G[0],
the gauge-transf. matrix, is just a number, which can be found more
efficiently and accurately without using matrix methods.
The last step (A[1]) is important because, if we have successfully made
r[1] = 1 in the previous steps, it fully determines the normalization
of the state via r[0] ( = l[N]).
Optionally (normalize=False), the function will not attempt to make
A[1] satisfy the orthonorm. condition, and will take G[0] = 1 = G[N],
thus performing a pure gauge-transformation, but not ensuring complete
canonical form.
It is also possible to begin the process from a site n other than N,
in case the sites > n are known to be in the desired form already.
It is also possible to skip the diagonalization of the l's, such that
only the right orthonormalization condition (r_n = eye) is met.
By default, the l's are updated even if diag_l=False.
Parameters
----------
update_l : bool
Whether to call calc_l() after completion (defaults to True)
normalize : bool
Whether to also attempt to normalize the state.
diag_l : bool
Whether to put l in diagonal form (defaults to True)
"""
start = self.N
G_n_i = sp.eye(self.D[start],
dtype=self.typ) #This is actually just the number 1
for n in xrange(start, 1, -1):
self.r[n - 1], G_n, G_n_i = tm.restore_RCF_r(
self.A[n],
self.r[n],
G_n_i,
sc_data=('site', n),
zero_tol=self.zero_tol,
sanity_checks=self.sanity_checks)
#Now do A[1]...
#Apply the remaining G[1]^-1 from the previous step.
for s in xrange(self.q[1]):
self.A[1][s] = m.mmul(self.A[1][s], G_n_i)
#Now finish off
tm.eps_r_noop_inplace(self.r[1], self.A[1], self.A[1], out=self.r[0])
if normalize:
G0 = 1. / sp.sqrt(self.r[0].squeeze().real)
self.A[1] *= G0
self.r[0][:] = 1
if self.sanity_checks:
r0 = tm.eps_r_noop(self.r[1], self.A[1], self.A[1])
if not sp.allclose(r0, 1, atol=1E-12, rtol=1E-12):
log.warning(
"Sanity Fail in restore_RCF!: r_0 is bad / norm failure"
)
if diag_l:
G_nm1 = sp.eye(self.D[0], dtype=self.typ)
for n in xrange(1, self.N):
self.l[n], G_nm1, G_nm1_i = tm.restore_RCF_l(
self.A[n], self.l[n - 1], G_nm1, self.sanity_checks)
#Apply remaining G_Nm1 to A[N]
n = self.N
for s in xrange(self.q[n]):
self.A[n][s] = m.mmul(G_nm1, self.A[n][s])
#Deal with final, scalar l[N]
tm.eps_l_noop_inplace(self.l[n - 1],
self.A[n],
self.A[n],
out=self.l[n])
if self.sanity_checks:
if not sp.allclose(
self.l[self.N].real, 1, atol=1E-12, rtol=1E-12):
log.warning(
"Sanity Fail in restore_RCF!: l_N is bad / norm failure"
)
log.warning("l_N = %s", self.l[self.N].squeeze().real)
for n in xrange(1, self.N + 1):
r_nm1 = tm.eps_r_noop(self.r[n], self.A[n], self.A[n])
#r_nm1 = tm.eps_r_noop(m.eyemat(self.D[n], self.typ), self.A[n], self.A[n])
if not sp.allclose(
r_nm1, self.r[n - 1], atol=1E-11, rtol=1E-11):
log.warning(
"Sanity Fail in restore_RCF!: r_%u is bad (off by %g)",
n, la.norm(r_nm1 - self.r[n - 1]))
elif update_l:
self.calc_l()