def setUp(self): #TODO: Test rectangular x as well
self.d = [2, 3]
self.D = [2, 4, 3]
self.l0 = sp.rand(self.D[0],
self.D[0]) + 1.j * sp.rand(self.D[0], self.D[0])
self.r1 = sp.rand(self.D[1],
self.D[1]) + 1.j * sp.rand(self.D[1], self.D[1])
self.r2 = sp.rand(self.D[2],
self.D[2]) + 1.j * sp.rand(self.D[2], self.D[2])
self.ld0 = mm.simple_diag_matrix(
sp.rand(self.D[0]) + 1.j * sp.rand(self.D[0]))
self.rd1 = mm.simple_diag_matrix(
sp.rand(self.D[1]) + 1.j * sp.rand(self.D[1]))
self.rd2 = mm.simple_diag_matrix(
sp.rand(self.D[2]) + 1.j * sp.rand(self.D[2]))
self.eye0 = mm.eyemat(self.D[0], dtype=sp.complex128)
self.eye1 = mm.eyemat(self.D[1], dtype=sp.complex128)
self.eye2 = mm.eyemat(self.D[2], dtype=sp.complex128)
self.A0 = sp.rand(self.d[0], self.D[0], self.D[0]) + 1.j * sp.rand(
self.d[0], self.D[0], self.D[0])
self.A1 = sp.rand(self.d[0], self.D[0], self.D[1]) + 1.j * sp.rand(
self.d[0], self.D[0], self.D[1])
self.A2 = sp.rand(self.d[1], self.D[1], self.D[2]) + 1.j * sp.rand(
self.d[1], self.D[1], self.D[2])
self.A3 = sp.rand(self.d[1], self.D[2], self.D[2]) + 1.j * sp.rand(
self.d[1], self.D[2], self.D[2])
self.B1 = sp.rand(self.d[0], self.D[0], self.D[1]) + 1.j * sp.rand(
self.d[0], self.D[0], self.D[1])
self.B2 = sp.rand(self.d[1], self.D[1], self.D[2]) + 1.j * sp.rand(
self.d[1], self.D[1], self.D[2])
self.E1_AB = make_E_noop(self.A1, self.B1)
self.E2_AB = make_E_noop(self.A2, self.B2)
self.op1s_1 = sp.rand(self.d[0],
self.d[0]) + 1.j * sp.rand(self.d[0], self.d[0])
self.E1_op_AB = make_E_1s(self.A1, self.B1, self.op1s_1)
self.op2s = sp.rand(self.d[0], self.d[1],
self.d[0], self.d[1]) + 1.j * sp.rand(
self.d[0], self.d[1], self.d[0], self.d[1])
self.E12_op = make_E_2s(self.A1, self.A2, self.B1, self.B2, self.op2s)
self.AA12 = tc.calc_AA(self.A1, self.A2)
self.BB12 = tc.calc_AA(self.B1, self.B2)
self.C_A12 = tc.calc_C_mat_op_AA(self.op2s, self.AA12)
self.C_conj_B12 = tc.calc_C_conj_mat_op_AA(self.op2s, self.BB12)
self.C01 = sp.rand(self.d[0], self.d[0],
self.D[0], self.D[1]) + 1.j * sp.rand(
self.d[0], self.d[0], self.D[0], self.D[1])
def restore_LCF_l(A, lm1, Gm1, sanity_checks=False, zero_tol=1E-15):
if Gm1 is None:
GhGm1 = lm1
else:
GhGm1 = Gm1.conj().T.dot(lm1.dot(Gm1))
M = eps_l_noop(GhGm1, A, A)
G, Gi, new_D = herm_fac_with_inv(M,
zero_tol=zero_tol,
return_rank=True,
sanity_checks=sanity_checks)
if Gm1 is None:
Gm1 = G
if sanity_checks:
if new_D == A.shape[2]:
eye = sp.eye(A.shape[2])
else:
eye = mm.simple_diag_matrix(np.append(np.zeros(A.shape[2] - new_D),
np.ones(new_D)),
dtype=A.dtype)
if not sp.allclose(G.dot(Gi), eye, atol=1E-13, rtol=1E-13):
log.warning("Sanity Fail in restore_LCF_l!: Bad GT!")
for s in xrange(A.shape[0]):
A[s] = Gm1.dot(A[s]).dot(Gi)
if new_D == A.shape[2]:
l = mm.eyemat(A.shape[2], A.dtype)
else:
l = mm.simple_diag_matrix(np.append(np.zeros(A.shape[2] - new_D),
np.ones(new_D)),
dtype=A.dtype)
if sanity_checks:
lm1_ = mm.eyemat(A.shape[1], A.dtype)
l_ = eps_l_noop(lm1_, A, A)
if not sp.allclose(l_, l.A, atol=1E-13, rtol=1E-13):
log.warning("Sanity Fail in restore_LCF_l!: l is bad")
log.warning(la.norm(l_ - l))
return l, G, Gi
def restore_LCF_l(A, lm1, Gm1, sanity_checks=False, zero_tol=1E-15):
if Gm1 is None:
GhGm1 = lm1
else:
GhGm1 = Gm1.conj().T.dot(lm1.dot(Gm1))
M = eps_l_noop(GhGm1, A, A)
G, Gi, new_D = herm_fac_with_inv(M, zero_tol=zero_tol, return_rank=True,
sanity_checks=sanity_checks)
if Gm1 is None:
Gm1 = G
if sanity_checks:
if new_D == A.shape[2]:
eye = sp.eye(A.shape[2])
else:
eye = mm.simple_diag_matrix(np.append(np.zeros(A.shape[2] - new_D),
np.ones(new_D)), dtype=A.dtype)
if not sp.allclose(G.dot(Gi), eye, atol=1E-13, rtol=1E-13):
log.warning("Sanity Fail in restore_LCF_l!: Bad GT!")
for s in xrange(A.shape[0]):
A[s] = Gm1.dot(A[s]).dot(Gi)
if new_D == A.shape[2]:
l = mm.eyemat(A.shape[2], A.dtype)
else:
l = mm.simple_diag_matrix(np.append(np.zeros(A.shape[2] - new_D),
np.ones(new_D)), dtype=A.dtype)
if sanity_checks:
lm1_ = mm.eyemat(A.shape[1], A.dtype)
l_ = eps_l_noop(lm1_, A, A)
if not sp.allclose(l_, l.A, atol=1E-13, rtol=1E-13):
log.warning("Sanity Fail in restore_LCF_l!: l is bad")
log.warning(la.norm(l_ - l))
return l, G, Gi
def setUp(self): #TODO: Test rectangular x as well
self.d = [2, 3]
self.D = [2, 4, 3]
self.l0 = sp.rand(self.D[0], self.D[0]) + 1.j * sp.rand(self.D[0], self.D[0])
self.r1 = sp.rand(self.D[1], self.D[1]) + 1.j * sp.rand(self.D[1], self.D[1])
self.r2 = sp.rand(self.D[2], self.D[2]) + 1.j * sp.rand(self.D[2], self.D[2])
self.ld0 = mm.simple_diag_matrix(sp.rand(self.D[0]) + 1.j * sp.rand(self.D[0]))
self.rd1 = mm.simple_diag_matrix(sp.rand(self.D[1]) + 1.j * sp.rand(self.D[1]))
self.rd2 = mm.simple_diag_matrix(sp.rand(self.D[2]) + 1.j * sp.rand(self.D[2]))
self.eye0 = mm.eyemat(self.D[0], dtype=sp.complex128)
self.eye1 = mm.eyemat(self.D[1], dtype=sp.complex128)
self.eye2 = mm.eyemat(self.D[2], dtype=sp.complex128)
self.A0 = sp.rand(self.d[0], self.D[0], self.D[0]) + 1.j * sp.rand(self.d[0], self.D[0], self.D[0])
self.A1 = sp.rand(self.d[0], self.D[0], self.D[1]) + 1.j * sp.rand(self.d[0], self.D[0], self.D[1])
self.A2 = sp.rand(self.d[1], self.D[1], self.D[2]) + 1.j * sp.rand(self.d[1], self.D[1], self.D[2])
self.A3 = sp.rand(self.d[1], self.D[2], self.D[2]) + 1.j * sp.rand(self.d[1], self.D[2], self.D[2])
self.B1 = sp.rand(self.d[0], self.D[0], self.D[1]) + 1.j * sp.rand(self.d[0], self.D[0], self.D[1])
self.B2 = sp.rand(self.d[1], self.D[1], self.D[2]) + 1.j * sp.rand(self.d[1], self.D[1], self.D[2])
self.E1_AB = make_E_noop(self.A1, self.B1)
self.E2_AB = make_E_noop(self.A2, self.B2)
self.op1s_1 = sp.rand(self.d[0], self.d[0]) + 1.j * sp.rand(self.d[0], self.d[0])
self.E1_op_AB = make_E_1s(self.A1, self.B1, self.op1s_1)
self.op2s = sp.rand(self.d[0], self.d[1], self.d[0], self.d[1]) + 1.j * sp.rand(self.d[0], self.d[1], self.d[0], self.d[1])
self.E12_op = make_E_2s(self.A1, self.A2, self.B1, self.B2, self.op2s)
self.AA12 = tc.calc_AA(self.A1, self.A2)
self.BB12 = tc.calc_AA(self.B1, self.B2)
self.C_A12 = tc.calc_C_mat_op_AA(self.op2s, self.AA12)
self.C_conj_B12 = tc.calc_C_conj_mat_op_AA(self.op2s, self.BB12)
self.C01 = sp.rand(self.d[0], self.d[0], self.D[0], self.D[1]) + 1.j * sp.rand(self.d[0], self.d[0], self.D[0], self.D[1])
def restore_RCF_r(A,
r,
G_n_i,
zero_tol=1E-15,
sanity_checks=False,
sc_data=''):
"""Transforms a single A[n] to obtain r[n - 1] = eye(D).
Implements the condition for right-orthonormalization from sub-section
3.1, theorem 1 of arXiv:quant-ph/0608197v2.
This function must be called for each n in turn, starting at N + 1,
passing the gauge transformation matrix from the previous step
as an argument.
Finds a G[n-1] such that orthonormalization is fulfilled for n.
If rank-deficiency is encountered, the result fulfills the orthonormality
condition in the occupied subspace with the zeros at the top-left
(for example r = diag([0, 0, 1, 1, 1, 1, 1])).
Parameters
----------
A : ndarray
The parameter tensor for the nth site A[n].
r : ndarray or object with array interface
The matrix r[n].
G_n_i : ndarray
The inverse gauge transform matrix for site n obtained in the previous step (for n + 1).
sanity_checks : bool (False)
Whether to perform additional sanity checks.
zero_tol : float
Tolerance for detecting zeros.
Returns
-------
r_nm1 : ndarray or simple_diag_matrix or eyemat
The new matrix r[n - 1].
G_nm1 : ndarray
The gauge transformation matrix for the site n - 1.
G_n_m1_i : ndarray
The inverse gauge transformation matrix for the site n - 1.
"""
if G_n_i is None:
GGh_n_i = r
else:
GGh_n_i = G_n_i.dot(r.dot(G_n_i.conj().T))
M = eps_r_noop(GGh_n_i, A, A)
X, Xi, new_D = herm_fac_with_inv(M,
zero_tol=zero_tol,
return_rank=True,
sanity_checks=sanity_checks)
G_nm1 = Xi.conj().T
G_nm1_i = X.conj().T
if G_n_i is None:
G_n_i = G_nm1_i
if sanity_checks:
#GiG may not be equal to eye in the case of rank-deficiency,
#but the rest should lie in the null space of A.
GiG = G_nm1_i.dot(G_nm1)
As = np.sum(A, axis=0)
if not sp.allclose(
GiG.dot(As).dot(G_n_i), As.dot(G_n_i), atol=1E-13, rtol=1E-13):
log.warning("Sanity Fail in restore_RCF_r!: Bad GT! %s %s",
la.norm(GiG.dot(As).dot(G_n_i) - As.dot(G_n_i)),
sc_data)
for s in xrange(A.shape[0]):
A[s] = G_nm1.dot(A[s]).dot(G_n_i)
if new_D == A.shape[1]:
r_nm1 = mm.eyemat(A.shape[1], A.dtype)
else:
r_nm1 = sp.zeros((A.shape[1]), dtype=A.dtype)
r_nm1[-new_D:] = 1
r_nm1 = mm.simple_diag_matrix(r_nm1, dtype=A.dtype)
if sanity_checks:
r_nm1_ = G_nm1.dot(M).dot(G_nm1.conj().T)
if not sp.allclose(r_nm1_, r_nm1.A, atol=1E-13, rtol=1E-13):
log.warning(
"Sanity Fail in restore_RCF_r!: r != g old_r gH! %s %s",
la.norm(r_nm1_ - r_nm1), sc_data)
r_nm1_ = eps_r_noop(r, A, A)
if not sp.allclose(r_nm1_, r_nm1.A, atol=1E-13, rtol=1E-13):
log.warning("Sanity Fail in restore_RCF_r!: r is bad! %s %s",
la.norm(r_nm1_ - r_nm1), sc_data)
return r_nm1, G_nm1, G_nm1_i
def restore_RCF_r(A, r, G_n_i, zero_tol=1E-15, sanity_checks=False, sc_data=''):
"""Transforms a single A[n] to obtain r[n - 1] = eye(D).
Implements the condition for right-orthonormalization from sub-section
3.1, theorem 1 of arXiv:quant-ph/0608197v2.
This function must be called for each n in turn, starting at N + 1,
passing the gauge transformation matrix from the previous step
as an argument.
Finds a G[n-1] such that orthonormalization is fulfilled for n.
If rank-deficiency is encountered, the result fulfills the orthonormality
condition in the occupied subspace with the zeros at the top-left
(for example r = diag([0, 0, 1, 1, 1, 1, 1])).
Parameters
----------
A : ndarray
The parameter tensor for the nth site A[n].
r : ndarray or object with array interface
The matrix r[n].
G_n_i : ndarray
The inverse gauge transform matrix for site n obtained in the previous step (for n + 1).
sanity_checks : bool (False)
Whether to perform additional sanity checks.
zero_tol : float
Tolerance for detecting zeros.
Returns
-------
r_nm1 : ndarray or simple_diag_matrix or eyemat
The new matrix r[n - 1].
G_nm1 : ndarray
The gauge transformation matrix for the site n - 1.
G_n_m1_i : ndarray
The inverse gauge transformation matrix for the site n - 1.
"""
if G_n_i is None:
GGh_n_i = r
else:
GGh_n_i = G_n_i.dot(r.dot(G_n_i.conj().T))
M = eps_r_noop(GGh_n_i, A, A)
X, Xi, new_D = herm_fac_with_inv(M, zero_tol=zero_tol, return_rank=True,
sanity_checks=sanity_checks)
G_nm1 = Xi.conj().T
G_nm1_i = X.conj().T
if G_n_i is None:
G_n_i = G_nm1_i
if sanity_checks:
#GiG may not be equal to eye in the case of rank-deficiency,
#but the rest should lie in the null space of A.
GiG = G_nm1_i.dot(G_nm1)
As = np.sum(A, axis=0)
if not sp.allclose(GiG.dot(As).dot(G_n_i),
As.dot(G_n_i), atol=1E-13, rtol=1E-13):
log.warning("Sanity Fail in restore_RCF_r!: Bad GT! %s %s",
la.norm(GiG.dot(As).dot(G_n_i) - As.dot(G_n_i)), sc_data)
for s in xrange(A.shape[0]):
A[s] = G_nm1.dot(A[s]).dot(G_n_i)
if new_D == A.shape[1]:
r_nm1 = mm.eyemat(A.shape[1], A.dtype)
else:
r_nm1 = sp.zeros((A.shape[1]), dtype=A.dtype)
r_nm1[-new_D:] = 1
r_nm1 = mm.simple_diag_matrix(r_nm1, dtype=A.dtype)
if sanity_checks:
r_nm1_ = G_nm1.dot(M).dot(G_nm1.conj().T)
if not sp.allclose(r_nm1_, r_nm1.A, atol=1E-13, rtol=1E-13):
log.warning("Sanity Fail in restore_RCF_r!: r != g old_r gH! %s %s",
la.norm(r_nm1_ - r_nm1), sc_data)
r_nm1_ = eps_r_noop(r, A, A)
if not sp.allclose(r_nm1_, r_nm1.A, atol=1E-13, rtol=1E-13):
log.warning("Sanity Fail in restore_RCF_r!: r is bad! %s %s",
la.norm(r_nm1_ - r_nm1), sc_data)
return r_nm1, G_nm1, G_nm1_i
