Failure to raise error for ill-posed system if using LU and 32-bit

[johannahaffner]

When using AutoLinearOperator with well_posed=True and no tags specifying some structure, the LU solver is used.

LU wraps the jax.scipy implementation and raises an error if the output has NaN or +/- inf values. However, jsp.linalg.lu_solve will not necessarily return a vector with such values for an ill-posed problem, unless one uses double-precision: jax-ml/jax#23626
If there is no fix in JAX itself, then we could check if the solution is valid and throw an error if it's not.

I am using SVD for that particular problem anyway, but wanted to note this here since AutoLinearSolver promises to raise an error for ill-posed problems.

[patrick-kidger]

For this one I think let's aim to get this fixed upstream in JAX itself. I think it'd be really hard for us to work around this issue here in a reliable way. I'm following the discussion there; let me know if you need any input. :)

[johannahaffner]

Alright!