Tricks for stopping criterion

[haampie]

WIP towards efficient computation of residual estimate of Ritz vectors

Steps:

• [x] Compute jth normalized eigenvector of quasi-upper triangular, real matrix
• [x] Compute the quantities abs(sum(Q[1:i, end] * y[i] for i = 1 : j)) for the jth pre-ritz vector as they appear in the estimate.
• [x] Use this info in the shifts, somehow.
• [x] Implement early exit when the Ritz vectors have converged, even if deflation in the Hessenberg matrix is not detected (sometimes off-diagonal values are large even when all eigenvalues are converged).
• [x] ~Fix deflation detection; it is currently a different criterion from the convergence detection stuff.~ for later

[haampie]

This is close to being finished now! This PR makes sure that we never shift converged eigenvalues. Further it seems that Ritz vectors converge according to the new criterion, yet they are not detected by the deflation bit. Not entirely sure how to handle this.

One idea: once nev eigenvalues have converged, reduce the size of the Kyrlov subspace exactly to nev, then most probably we can just set H[nev+1,nev] to 0 and have a partial Schur form (?).

Additional TODO:

• [x] Add back the search targets / for now it is just LM()

[haampie]

One idea: once nev eigenvalues have converged ...

Simple example shows that this idea works 🎉 , I'll try and implement it soon.