def calc_Vsh(A, r_s, sanity_checks=False):
D = A.shape[2]
Dm1 = A.shape[1]
q = A.shape[0]
R = sp.zeros((D, q, Dm1), dtype=A.dtype, order='C')
for s in xrange(q):
R[:, s, :] = r_s.dot(A[s].conj().T)
R = R.reshape((q * D, Dm1))
Vconj = ns.nullspace_qr(R.conj().T).T
if sanity_checks:
if not sp.allclose(mm.mmul(Vconj.conj(), R), 0):
log.warning("Sanity Fail in calc_Vsh!: VR != 0")
if not sp.allclose(mm.mmul(Vconj,
Vconj.conj().T), sp.eye(Vconj.shape[0])):
log.warning("Sanity Fail in calc_Vsh!: V H(V) != eye")
Vconj = Vconj.reshape((q * D - Dm1, D, q))
Vsh = Vconj.T
Vsh = sp.asarray(Vsh, order='C')
if sanity_checks:
Vs = sp.transpose(Vsh, axes=(0, 2, 1)).conj()
M = eps_r_noop(r_s, Vs, A)
if not sp.allclose(M, 0):
log.warning("Sanity Fail in calc_Vsh!: Bad Vsh")
return Vsh
def calc_Vsh(A, r_s, sanity_checks=False):
D = A.shape[2]
Dm1 = A.shape[1]
q = A.shape[0]
R = sp.zeros((D, q, Dm1), dtype=A.dtype, order='C')
for s in xrange(q):
R[:,s,:] = r_s.dot(A[s].conj().T)
R = R.reshape((q * D, Dm1))
Vconj = ns.nullspace_qr(R.conj().T).T
if sanity_checks:
if not sp.allclose(mm.mmul(Vconj.conj(), R), 0):
log.warning("Sanity Fail in calc_Vsh!: VR != 0")
if not sp.allclose(mm.mmul(Vconj, Vconj.conj().T), sp.eye(Vconj.shape[0])):
log.warning("Sanity Fail in calc_Vsh!: V H(V) != eye")
Vconj = Vconj.reshape((q * D - Dm1, D, q))
Vsh = Vconj.T
Vsh = sp.asarray(Vsh, order='C')
if sanity_checks:
Vs = sp.transpose(Vsh, axes=(0, 2, 1)).conj()
M = eps_r_noop(r_s, Vs, A)
if not sp.allclose(M, 0):
log.warning("Sanity Fail in calc_Vsh!: Bad Vsh")
return Vsh
def _calc_B_r_diss(self, op, K, C, n, set_eta=True):
if self.q[n] * self.D[n] - self.D[n - 1] > 0:
l_sqrt, l_sqrt_inv, r_sqrt, r_sqrt_inv = tm.calc_l_r_roots(self.l[n - 1],
self.r[n],
sanity_checks=self.sanity_checks,
sc_data=("site", n))
Vsh = tm.calc_Vsh(self.A[n], r_sqrt, sanity_checks=self.sanity_checks)
x = self.calc_x(n, Vsh, l_sqrt, r_sqrt, l_sqrt_inv, r_sqrt_inv)
if set_eta:
self.eta[n] = sp.sqrt(mm.adot(x, x))
B = sp.empty_like(self.A[n])
for s in xrange(self.q[n]):
B[s] = mm.mmul(l_sqrt_inv, x, mm.H(Vsh[s]), r_sqrt_inv)
return B
else:
return None
def _calc_B_r_diss(self, op, K, C, n, set_eta=True):
if self.q[n] * self.D[n] - self.D[n - 1] > 0:
l_sqrt, l_sqrt_inv, r_sqrt, r_sqrt_inv = tm.calc_l_r_roots(
self.l[n - 1],
self.r[n],
sanity_checks=self.sanity_checks,
sc_data=("site", n))
Vsh = tm.calc_Vsh(self.A[n],
r_sqrt,
sanity_checks=self.sanity_checks)
x = self.calc_x(n, Vsh, l_sqrt, r_sqrt, l_sqrt_inv, r_sqrt_inv)
if set_eta:
self.eta[n] = sp.sqrt(mm.adot(x, x))
B = sp.empty_like(self.A[n])
for s in xrange(self.q[n]):
B[s] = mm.mmul(l_sqrt_inv, x, mm.H(Vsh[s]), r_sqrt_inv)
return B
else:
return None
def expect_2s_diss(self, op, LC, LK, n, AA=None):
"""Applies a two-site operator to two sites and returns
the value after the change. In contrast to
mps_gen.apply_op_2s, this routine does not change the state itself.
Also, this does not perform self.update().
Parameters
----------
op : ndarray or callable
The two-site operator. See self.expect_2s().
n: int
The site to apply the operator to.
(It's also applied to n-1.)
"""
#No neighbors, no fun.
if n is 1:
return 0
if n is N:
return 0
A = self.A[n - 1]
Ap1 = self.A[n]
if AA is None:
AA = tm.calc_AA(A, Ap1)
if callable(op):
op = sp.vectorize(op, otypes=[sp.complex128])
op = sp.fromfunction(
op, (A.shape[0], Ap1.shape[0], A.shape[0], Ap1.shape[0]))
op = op.reshape(4, 4, 4, 4)
C = tm.calc_C_mat_op_AA(op, AA)
res = tm.eps_r_op_2s_C12_AA34(self.r[n + 1], LC, AA)
operand = self.l[n - 1]
operand = sp.reshape(operand, (1, 16))
operand = sp.reshape(operand, (2, 8))
return mm.mmul(operand, res)
return mm.adot(self.l[n - 1], res)
def expect_2s_diss(self, op, LC, LK, n, AA=None):
"""Applies a two-site operator to two sites and returns
the value after the change. In contrast to
mps_gen.apply_op_2s, this routine does not change the state itself.
Also, this does not perform self.update().
Parameters
----------
op : ndarray or callable
The two-site operator. See self.expect_2s().
n: int
The site to apply the operator to.
(It's also applied to n-1.)
"""
#No neighbors, no fun.
if n is 1:
return 0
if n is N:
return 0
A = self.A[n-1]
Ap1 = self.A[n]
if AA is None:
AA = tm.calc_AA(A, Ap1)
if callable(op):
op = sp.vectorize(op, otypes=[sp.complex128])
op = sp.fromfunction(op, (A.shape[0], Ap1.shape[0], A.shape[0], Ap1.shape[0]))
op = op.reshape(4,4,4,4)
C = tm.calc_C_mat_op_AA(op, AA)
res = tm.eps_r_op_2s_C12_AA34(self.r[n + 1], LC, AA)
operand = self.l[n-1]
operand = sp.reshape(operand, (1,16))
operand = sp.reshape(operand, (2,8))
return mm.mmul(operand,res)
return mm.adot(self.l[n - 1], res)
