Unexpected determinant for 4X4 matrix

[ja-b]

When upgrading to 0.10.0 we run into an expected 0 determinant for the following matrix

tensor = Nx.tensor([
  [-1.0, 1.0, -1.0, 0.0],
  [1.0, 0.0, 0.0, 0.0],
  [0.0, 0.0, 0.0, 1.0],
  [0.0, 1.0, 0.0, 0.0]
], type: :f64)

result = Nx.LinAlg.determinant(tensor)

IO.inspect(result)

With result

#Nx.Tensor<
  f64
  0.0
>

We had this trigger in our unit tests when upgrading to 0.10.0, but I'm having trouble at the moment reverting to a prior version to get a different value. Trying to figure this out at the moment.

But in the meantime -- numpy arrives at a 1.0 determinant for this matrix.

import numpy as np

if __name__ == "__main__":

    arr = np.array([
        [-1.0, 1.0, -1.0, 0.0],
        [1.0, 0.0, 0.0, 0.0],
        [0.0, 0.0, 0.0, 1.0],
        [0.0, 1.0, 0.0, 0.0]
    ])

    det = np.linalg.det(arr)

    print("Array:")
    print(arr)
    print("\nDeterminant:", det)

Determinant: 1.0

And I think 1.0 is correct, the matrix certainly doesn't seem ill-formed.

[polvalente]

Yeah, a quick look at the matrix does seem like 1 is the correct answer.

Is this happening on the binary backend?

[ja-b]

We encountered it initially on the Exla backend -- but that isolated test should be on the binary backend.

[polvalente]

Thanks, that helps determine where to look

[ja-b]

IO.inspect(Nx.default_backend())
result = Nx.LinAlg.determinant(tensor)

{Nx.BinaryBackend, []}

[ja-b]

Was able to boil down a little more -- it looks like

• Nx <=0.9.2 -- the determinant is still 0 for the binary backend case, in EXLA its 1.
• Nx ==0.10.0 -- the determinant is 0 between the two backends.

[polvalente]

The problem is Nx.LinAlg.lu. The new defn implementation has a problem handling that matrix, and this propagates to det.
With EXLA < 0.10 this was handled by a custom implementation, which is why this didn't show before