def leftorth(A, C=None, tol=1E-13, maxiter=100):
if C is None:
C = np.eye(A.shape[1], dtype=A.dtype)
#print(np.trace(ct.XopL(A))/A.shape[1])
lam2, rho = tmeigs(A,
which="LM",
tol=tol,
direction="left",
v0=np.dot(np.conj(C.T), C),
nev=1)
rho = rho + np.conj(rho.T)
rho /= np.trace(rho)
U, S, VH = np.linalg.svd(rho)
C = ct.leftmult(np.sqrt(S), np.conj(VH))
_, C = qrmat(C)
AL, R = qrpos(ct.leftmult(C, A))
lam = np.linalg.norm(R)
R /= lam
numiter = 1
ldelt = np.abs(np.abs(np.trace(ct.XopL(AL)) / A.shape[1]) - 1)
while ldelt > tol and numiter < maxiter:
_, C = tmeigs(A, B=np.conj(AL), v0=R, tol=ldelt / 10, nev=1)
_, C = qrpos(C)
C /= np.linalg.norm(C)
AL, R = qrpos(ct.leftmult(C, A))
lam = np.linalg.norm(R)
R = R / lam
numiter += 1
ldelt = np.abs(np.abs(np.trace(ct.XopL(AL)) / A.shape[1]) - 1)
C = R
return (AL, C, lam)
def matvec(v):
v = v.reshape((chi, chi))
Th_v = ct.XopL(A_L, X=v)
vR = proj(v, lR) * I
v = v - Th_v + vR
v = v.flatten()
return v
def B2_tensor(oldlist, newlist):
NL, NR = null_spaces(oldlist)
AL, C, AR = newlist
AC = ct.rightmult(AL, C)
L = ct.XopL(AC, B=np.conj(NL))
R = ct.XopR(AR, B=np.conj(NR))
return np.dot(L, R.T)
def is_right_canonical(A_R, L, rtol=1E-5, atol=1E-8, verbose=False):
is_iso = is_right_isometric(A_R, rtol=rtol, atol=atol, verbose=verbose)
contracted = ct.XopL(A_R, X=L)
passed = is_iso and np.allclose(contracted, L, rtol=rtol, atol=atol)
if verbose:
print("Testing if right canonical.")
check(verbose, passed)
return passed
def is_left_isometric(A_L, rtol=1E-5, atol=1E-8, verbose=False):
contracted = ct.XopL(A_L)
eye = np.eye(contracted.shape[0], dtype=A_L.dtype)
passed = np.allclose(contracted, eye, rtol=rtol, atol=atol)
if verbose:
print("Testing if left isometric.")
check(verbose, passed)
return passed
def tmmatvec(xvec):
xmat = xvec.reshape(outshape)
xmat = ct.XopL(A, B=B, X=xmat)
xvec = xmat.flatten()
return xvec
