Subject: LAPACK performance (was: Definitions of LAPACK)
From: Valery Pipin
Date: Wed, 23 May 2007 01:09:43 +0900
On ??????? 22 ??? 2007, Detlef Schmicker wrote:
> Hi Raymond,
>
> I just got some experience with LAPACK, which I want to share. I used
> dgeev to get the eigenvalues of a 200x200 Matrix. Using gcl (Debian
> unstable maxima 5.12) it was impossble to do, as it took a day and
> crashed. Using sbcl (compiled from 5.11.99rc3) was by a factor of at
> least 50 faster (Tested with 50x50 Matrix) and it solved the (200x200)
> eigenvector problems.
> Just in case, anybody is frustrated with this.
Depends on matrix perhaps. How did you form the matrix?
I've made the 2D Galerkin code for eigen value dynamo problem (large-scale
magnetic field generation on the Sun and convective stars).
Matrix 234x234 is solved on 3-4 seconds with dgeev.
The bifurcation diagram with 25 points is ready within a minute or so.
Moreover the pure diffusion matrix (though it is not a diagonal one because
diffusion is anisotropic and dependent of coordinates) is calculated much
faster.
This is on celeron 1.6Ghz with 512 mb Ram notebook toshiba satelite l-113.
I would recomend to check the matrix itself to make it better.
Note, if I would solve the same task with pseudospectral approach I would have
the dense and not well-conditioned matrix and dgeev would work much longer.