Optimise solvers

[eprovst]

PR description

Overall improvements of Legolas, mainly with respect to optimising the eigensolvers.

To do

• Rebase on develop, so a merge is possible.
• Computation of residuals needs to be optimised.
• Documentation needs to be updated.
• Tests need to be added for inverse vector iteration.
• Tests need to be added for QR-cholesky.
• QR-cholesky's results have to be normalized.
• QR-invert and QR-cholesky need to be merged.
• Techniques of QR-cholesky need to be applied to Arnoldi.
• Sparse matrices need to be immediately converted to banded, instead of going through dense.

New features

Legolas

• More compile time optimizations for release builds.
• Faster QZ-direct.
• QZ-direct now gives eigenvectors.
• Faster QR-invert.
• New QR-cholesky.
• New inverse-iteration.
• Much faster Arnoldi.
• Output of eigenvectors.
• Computation and output of residuals.
• Timing logs of eigensolvers.
• Some ease of use fixes with regard to parfiles.
• Tolerance of iterative methods can now be set.

Pylbo

• Reading eigenvectors.
• Reading residuals.

Bugfixes

Legolas

• Arnoldi now works for only a couple of eigenvalues.
• Greatly reduced numerical error in some cases.

Checklist

• all tests pass (and for new features, new tests are added)
• documentation has been updated (if applicable)

[eprovst]

Note: I'm currently rebasing my changes on the develop branch. This will likely involve some forced pushes. Arnoldi diverged the most and hence will see the most changes.

[codecov]

Codecov Report

Merging #106 (7c39a20) into develop (2819e9e) will decrease coverage by 0.85%.
The diff coverage is 81.91%.

Additional details and impacted files

@@             Coverage Diff             @@
##           develop     #106      +/-   ##
===========================================
- Coverage    88.74%   87.89%   -0.86%     
===========================================
  Files          112      115       +3     
  Lines         6470     6659     +189     
===========================================
+ Hits          5742     5853     +111     
- Misses         728      806      +78     

Flag	Coverage Δ
legolas	90.53% <90.43%> (-0.52%)	⬇️
pylbo	81.89% <28.84%> (-1.66%)	⬇️

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[n-claes]

Open todo-tasks can go in a separate PR, merging this so we can start rebasing and integrating other branches into develop as well.