def matvec(v):
v = v.reshape((chi, chi))
Th_v = ct.XopL(A_L, X=v)
vR = ct.proj(v, lR) * Id
v = v - Th_v + vR
v = v.flatten()
return v
def is_left_isometric(A_L, rtol=1E-5, atol=1E-8, verbose=False):
"""
Passes if A_L is left-isometric.
"""
contracted = ct.XopL(A_L)
eye = np.eye(contracted.shape[0], dtype=A_L.dtype)
passed, err = check(verbose, contracted, eye, thresh=atol)
return (passed, err)
def is_right_canonical(A_R, L, rtol=1E-5, atol=1E-8, verbose=False):
"""
Passes if A_R is right-canonical.
"""
if verbose:
print("Testing if right isometric.")
is_iso, iso_err = is_right_isometric(A_R, rtol=rtol, atol=atol,
verbose=verbose)
contracted = ct.XopL(A_R, X=L)
if verbose:
print("Testing if right canonical.")
is_can, can_err = check(verbose, contracted, L, thresh=atol)
passed = is_iso and is_can
err = iso_err + can_err
return (passed, err)
def B2_variance(oldlist, newlist):
"""
Given two MPS tensors in mixed canonical form, estimate the gradient
variance.
PARAMETERS
----------
oldlist, newlist: Both lists [A_L, C, A_R] representing two MPS in
mixed canonical form.
RETURNS
------
B2 (float) : The gradient variance.
"""
NL, NR = mps_null_spaces(oldlist)
AL, C, AR = newlist
AC = ct.rightmult(AL, C)
L = ct.XopL(AC, B=NL)
R = ct.XopR(AR, B=NR)
B2_tensor = L @ R.T
B2 = norm(B2_tensor)
return B2
def tmmatvec(xvec):
xmat = xvec.reshape(outshape)
xmat = ct.XopL(A, B=B, X=xmat)
xvec = xmat.flatten()
return xvec