Increase gram_schmidt default reiteration_tol to 9e-1

[sdrave]

See discussion in #1067

Fixes #1067.

[sdrave]

@lbalicki, the CI build for this PR should fail with test failures for the samdp algorithm. Can you take a look at what is happening?

[lbalicki]

There seems to be an Inversion error (RuntimeError: Factor is exactly singular) when executing one of the samdp tests. It only happens on the pip_installed test and unfortunately I was not able to recreate this type of behaviour on my machine. Is it possible to either get the data of the CI test or recreate the pip_installed test pipeline on my machine?

Looking at the CI output I can not really tell what the problem is. Especially the inversion error occurs when calling tEmA.apply_inverse_adjoint(...) and one line before that the line tEmA.apply_inverse(...) is executed succesfully. How can the numpy operator tEmA be invertible during the apply_inverse function call and its adjoint be singular in the apply_inverse_adjoint call?

[sdrave]

There seems to be an Inversion error (RuntimeError: Factor is exactly singular) when executing one of the samdp tests. It only happens on the pip_installed test and unfortunately I was not able to recreate this type of behaviour on my machine.

That's rather strange. @renefritze, do you have an idea where this comes from?

I can reproduce the failure on my system. I have attached the non-invertible operator and backtrace. (Load the operator using pickle.) The parameters for the test were test_samdp[False-LR-15-2-2-50].

backtrace.txt operator.dat.gz

How can the numpy operator tEmA be invertible during the apply_inverse function call and its adjoint be singular in the apply_inverse_adjoint call?

I guess both operators will be singular, but the linear solver doesn't notice in one case (even for direct solvers, floating-point arithmetic may make the operator appear non-singular).

[renefritze]

The PR build is fine btw. All pip installed * there ran on openstack machines, in the push build all pip installed * failed on our local machine.

[lbalicki]

I think I found the issue. If an exact eigenvalue theta of (A, E) is passed to the _twosided_rqi method, the linear combination of operators theta * E - A will become singular. With #1156 the check if theta is an eigenvalue is improved, so it will hopefully take the case into account where the test fails here.

[codecov]

Codecov Report

Merging #1154 (3a89ce4) into master (c602a0a) will decrease coverage by 0.01%.
The diff coverage is n/a.

Impacted Files	Coverage Δ
src/pymor/algorithms/gram_schmidt.py	97.93% <ø> (ø)
src/pymor/bindings/fenics.py	84.30% <0.00%> (-0.80%)	⬇️
src/pymor/vectorarrays/numpy.py	84.29% <0.00%> (-0.25%)	⬇️
src/pymor/vectorarrays/list.py	82.18% <0.00%> (ø)
src/pymor/bindings/ngsolve.py	84.61% <0.00%> (+0.76%)	⬆️

[sdrave]

@lbalicki, good to merge?