PyTorch how to factor a matrix until get 1 matrix that doesn't change?

Question

I'm having a matrix A, I'd like to factor it as A = BC while knowing that C is some matrix which isn't changed over multiple samples of A. How do I find B using PyTorch? A is a known matrix.

A1 = B1 C
A2 = B2 C
A3 = B3 C
...

Answer 1

You could define C, add it to an optimizer (eg. SGD), and then minimize some distance (eg. MSELoss) between Ai = Bi @ C at every iteration. Here is a minimal example:

C = torch.rand(m,n)
optimizer = torch.optim.SGD([C], lr=0.1)

for a, b in zip(A,B):
    loss = F.mse(a, b@C)
    optimizer.zero_grad()    
    loss.backward()
    optimizer.step()