[eigen] Plans for EigenSolver

[Jitse Niesen <jitse@xxxxxxxxxxxxxxxxx>]

Hello,

I'm wondering what your immediate plans for EigenSolver are. I'm thinking 
about extending the unsupported MatrixFunctions module, partially because 
of the recent feature request in the bug tracker but also because I might 
need it myself.

The first step is computing the Schur decomposition. According to the 
source file comments, this is already implemented in EigenSolver::hqr 
(except that I need the complex Schur decomposition and EigenSolver 
computes the real Schur decomposition). However, that is a private 
function. Another problem is that the code is fairly messy and does not 
work for complex matrices. The todo page says that Benoit is to "polish 
(partially rewrite) eigensolvers", but I don't know what his plans 
currently are.

I see two possibilities for me to proceed.

1. I change EigenSolver to expose the Schur decomposition, work from 
there, and when Benoit or somebody else rewrites EigenSolver I use the new 
version. This allows me to work independently.

2. I rewrite EigenSolver along the lines of SelfAdjointEigenSolver, 
possibly working with Benoit (and others) to achieve this. This may be 
more useful (there is more interest in eigenvalue problem solvers than 
matrix function), but I'm not sure it's efficient because Benoit works 
much faster than me.

Any preferences?

Cheers,
Jitse