def restore_RCF(self, ret_g=False, zero_tol=None):
"""Restores right canonical form.
In this form, self.r = sp.eye(self.D) and self.l is diagonal, with
the squared Schmidt coefficients corresponding to the half-chain
decomposition as eigenvalues.
Parameters
----------
ret_g : bool
Whether to return the gauge-transformation matrices used.
Returns
-------
g, g_i : ndarray
Gauge transformation matrix g and its inverse g_i.
"""
if zero_tol is None:
zero_tol = self.zero_tol
#First get G such that r = eye
G, G_i, rank = tm.herm_fac_with_inv(self.r, lower=True, zero_tol=zero_tol,
return_rank=True)
self.l = m.mmul(m.H(G), self.l, G)
#Now bring l into diagonal form, trace = 1 (guaranteed by r = eye..?)
ev, EV = la.eigh(self.l)
G = G.dot(EV)
G_i = m.H(EV).dot(G_i)
for s in xrange(self.q):
self.A[s] = m.mmul(G_i, self.A[s], G)
#ev contains the squares of the Schmidt coefficients,
self.S_hc = - np.sum(ev * sp.log2(ev))
self.l = m.simple_diag_matrix(ev, dtype=self.typ)
r_old = self.r
if rank == self.D:
self.r = m.eyemat(self.D, self.typ)
else:
self.r = sp.zeros((self.D), dtype=self.typ)
self.r[-rank:] = 1
self.r = m.simple_diag_matrix(self.r, dtype=self.typ)
if self.sanity_checks:
r_ = m.mmul(G_i, r_old, m.H(G_i))
if not np.allclose(self.r, r_,
rtol=self.itr_rtol*self.check_fac,
atol=self.itr_atol*self.check_fac):
log.warning("Sanity check failed: RestoreRCF, bad r (bad GT).")
l = tm.eps_l_noop(self.l, self.A, self.A)
r = tm.eps_r_noop(self.r, self.A, self.A)
if not np.allclose(r, self.r,
rtol=self.itr_rtol*self.check_fac,
atol=self.itr_atol*self.check_fac):
log.warning("Sanity check failed: Restore_RCF, r not eigenvector! %s", la.norm(r - self.r))
if not np.allclose(l, self.l,
rtol=self.itr_rtol*self.check_fac,
atol=self.itr_atol*self.check_fac):
log.warning("Sanity check failed: Restore_RCF, l not eigenvector! %s", la.norm(l - self.l))
if ret_g:
return G, G_i
else:
return
def restore_SCF(self, ret_g=False, zero_tol=None):
"""Restores symmetric canonical form.
In this canonical form, self.l == self.r and are diagonal matrices
with the Schmidt coefficients corresponding to the half-chain
decomposition form the diagonal entries.
Parameters
----------
ret_g : bool
Whether to return the gauge-transformation matrices used.
Returns
-------
g, g_i : ndarray
Gauge transformation matrix g and its inverse g_i.
"""
if zero_tol is None:
zero_tol = self.zero_tol
X, Xi = tm.herm_fac_with_inv(self.r, lower=True, zero_tol=zero_tol)
Y, Yi = tm.herm_fac_with_inv(self.l, lower=False, zero_tol=zero_tol)
U, sv, Vh = la.svd(Y.dot(X))
#s contains the Schmidt coefficients,
lam = sv**2
self.S_hc = - np.sum(lam * sp.log2(lam))
S = m.simple_diag_matrix(sv, dtype=self.typ)
Srt = S.sqrt()
g = m.mmul(Srt, Vh, Xi)
g_i = m.mmul(Yi, U, Srt)
for s in xrange(self.q):
self.A[s] = m.mmul(g, self.A[s], g_i)
if self.sanity_checks:
Sfull = np.asarray(S)
if not np.allclose(g.dot(g_i), np.eye(self.D)):
log.warning("Sanity check failed! Restore_SCF, bad GT!")
l = m.mmul(m.H(g_i), self.l, g_i)
r = m.mmul(g, self.r, m.H(g))
if not np.allclose(Sfull, l):
log.warning("Sanity check failed: Restorce_SCF, left failed!")
if not np.allclose(Sfull, r):
log.warning("Sanity check failed: Restorce_SCF, right failed!")
l = tm.eps_l_noop(Sfull, self.A, self.A)
r = tm.eps_r_noop(Sfull, self.A, self.A)
if not np.allclose(Sfull, l, rtol=self.itr_rtol*self.check_fac,
atol=self.itr_atol*self.check_fac):
log.warning("Sanity check failed: Restorce_SCF, left bad!")
if not np.allclose(Sfull, r, rtol=self.itr_rtol*self.check_fac,
atol=self.itr_atol*self.check_fac):
log.warning("Sanity check failed: Restorce_SCF, right bad!")
self.l = S
self.r = S
if ret_g:
return g, g_i
else:
return
