How to do THIS in python?
Currently, I can transform a 4X4 matrix 'A' into its bipartite shape [2,2,2,2], as described in here. Once performing the SVD on the latter (the transformed version of 'A') using python via:
- NumPy SVD:
U, S, Vh = numpy.linalg.svd(A) - PyTorch SVD:
U, S, Vh = torch.linalg.svd(A)
and it turns out (in both cases):
U.shape = Vh.shape = [2,2,2,2]S.shape = [2,2,2]
I want to write a function:
def to_schmidt(A):
U, S, Vh = torch.linalg.svd(A)
#
# Do stuff with U, S, and Vh
#
return [[s1, ..., s4], [B1, ..., B4], [C1, ..., C4]]
Which returns a list of the s's' B's, and C's just as described in here. Just to clarify (using PyTorch in the example):
should_be_the_original_matrix_A = None
for i in range(4):
if should_be_the_original_matrix_A = None:
should_be_the_original_matrix_A = s[i] * torch.kron(B[i], C[i])
else:
should_be_the_original_matrix_A += s[i] * torch.kron(B[i], C[i])
#
# The one with A_{i}{j} with i,j = 0, 1, 2, 3
# or alternatively A.shape= [4,4], i.e.
# before the transformation to the bipartite rep.
#
The answer given there uses Mathematica, but as I'm not familiar with it:
How to complete this function?
Hopefully, using PyTorch, NumPy, or anything convertible to them, fairly trivially.
