[feature req. for torch.inverse] optional return for indicating that whether input is not invertable or not.

[7starsea]

🚀 Feature

torch.inverse(input) -> (output, indicator)
dimension of input: (*, n, n),
dimension of (output, indicator): (*, n, n), (*,)

output is the inverse of input, and indicator indicate whether the input is invertable or not.
If (some of) the input is not invertable, do not incur a RuntimeError.

Motivation

torch.inverse will incur a RuntimeError when (some of) input is not invertable. If we want to invert a batch of matrices, a single singular matrix will ruin the whole inverting task.

Pitch

Alternatives

Additional context

cc @vincentqb @vishwakftw @jianyuh @nikitaved @pearu @mruberry @heitorschueroff @ssnl

[vishwakftw]

In CPU, this should be possible since we execute getrf / getri sequentially.

I'm not sure about CUDA, because both getrf and getri call batched kernels.

[7starsea]

Thanks for your response. I then guess we need to dive into the cuda kernels: getrf and getri.

If we had found a solution to torch.inverse, we probably could also have a similar solution for torch.cholesky which has the same problem (singular matrix will incur a RuntimeError during decomposition).

Thanks.