Add `on_error` argument to linalg functions

[jessegrabowski]

Description

Our implementation of Cholesky has a nice argument on_error that lets the user get back nan from an bad input instead of halting the program. This would be a nice feature to have in other places where shoving in random matrices (pun intended) can be dangerous. I'm thinking specifically about pt.linalg.solve, but I kept the issue name generic in case we think of others.

The fix itself is trivial: add a try/except around the perform method of e.g. solve. The only wrinkle I foresee is what to do with the gradients.

[ricardoV94]

The only wrinkle I foresee is what to do with the gradients.

Do we do anything on the Solve?

[jessegrabowski]

On CholeskySolve you mean? Or just solve generally?

Right now if pt.linalg.solve fails (for example because you pass a low-rank matrix) the program crashes with a LAPACK error

[ricardoV94]

Sorry I meant on the Cholesky that has this special behavior implemented. Do we do anything different on the gradient in the case of on_error="nan"?

[jessegrabowski]

Yeah it gets replaced with a scalar 1 to allow some intermediate computation, then returns a matrix of nan in the end.

[ricardoV94]

So it returns nan, and it has the work-around for Solve. If Solve returned nan, it wouldn't need the work-around?

[ricardoV94]

This would also allow us to remove this switch logic in the multivariate logp: https://github.com/pymc-devs/pymc/blob/f5517186874107e72440ec9b55cd31ce77cc2a3d/pymc/distributions/multivariate.py#L181-L183