Re: [eigen] Eigenvalues of (lower) Hessenberg matrix

[Yixuan Qiu <yixuanq@xxxxxxxxx>]

There is a parameter you can set in the constructor: http://eigen.tuxfamily.org/dox/classEigen_1_1EigenSolver.html#a7e8ab3d89ea525af5f27f1a8e805fae1

Best,

Yixuan

2017-04-04 18:07 GMT-04:00 Ian Bell <ian.h.bell@xxxxxxxxx>:

Yixuan,

That's certainly much better - on par at these sizes now with the naive eigenvalues() function in Eigen.  I guess if you are focused on larger matrices (as most people seem to be), my matrices are rather tiny, and perhaps, less interesting.

For sure I took many replicates - the timings were actually carried out in a python library built with pybind11 on top of your code, Eigen, and some of my own code.  The library is actually for working with Chebyshev expansions of continuous functions and doing rootfinding with them.  I'm relatively familiar with the pitfalls of profiling, so I think this is a pretty fair test.

For these sizes, there just isn't much more to do in Eigen-based eigenvalue solving.  The solver in LAPACK for Hessenberg matrices is about two times (very roughly) faster for 16 x 16 matrices.  So this is not the end, I guess, but it might be the end of my capabilities in the world of linear algebra.

For future reference, how does one "select "computeEigenvectors = false" in EigenSolve"?

Kind Regards, and thanks for your help,

Ian

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Yixuan Qiu <yixuanq@xxxxxxxxx>
Department of Statistics,
Purdue University