def calc_Vsh_l(A, lm1_sqrt, sanity_checks=False):
D = A.shape[2]
Dm1 = A.shape[1]
q = A.shape[0]
L = sp.zeros((D, q, Dm1), dtype=A.dtype, order='C')
for s in xrange(q):
L[:, s, :] = lm1_sqrt.dot(A[s]).conj().T
L = L.reshape((D, q * Dm1))
V = ns.nullspace_qr(L)
if sanity_checks:
if not sp.allclose(L.dot(V), 0):
log.warning("Sanity Fail in calc_Vsh_l!: LV != 0")
if not sp.allclose(V.conj().T.dot(V), sp.eye(V.shape[1])):
log.warning("Sanity Fail in calc_Vsh_l!: V H(V) != eye")
V = V.reshape((q, Dm1, q * Dm1 - D))
Vsh = sp.transpose(V.conj(), axes=(0, 2, 1))
Vsh = sp.asarray(Vsh, order='C')
if sanity_checks:
M = eps_l_noop(lm1_sqrt, A, V)
if not sp.allclose(M, 0):
log.warning("Sanity Fail in calc_Vsh_l!: Bad Vsh")
return Vsh
def calc_Vsh_l(A, lm1_sqrt, sanity_checks=False):
D = A.shape[2]
Dm1 = A.shape[1]
q = A.shape[0]
L = sp.zeros((D, q, Dm1), dtype=A.dtype, order='C')
for s in xrange(q):
L[:,s,:] = lm1_sqrt.dot(A[s]).conj().T
L = L.reshape((D, q * Dm1))
V = ns.nullspace_qr(L)
if sanity_checks:
if not sp.allclose(L.dot(V), 0):
log.warning("Sanity Fail in calc_Vsh_l!: LV != 0")
if not sp.allclose(V.conj().T.dot(V), sp.eye(V.shape[1])):
log.warning("Sanity Fail in calc_Vsh_l!: V H(V) != eye")
V = V.reshape((q, Dm1, q * Dm1 - D))
Vsh = sp.transpose(V.conj(), axes=(0, 2, 1))
Vsh = sp.asarray(Vsh, order='C')
if sanity_checks:
M = eps_l_noop(lm1_sqrt, A, V)
if not sp.allclose(M, 0):
log.warning("Sanity Fail in calc_Vsh_l!: 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_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
