Re: nonsymmetric nondefective matrix eigenvalues and eigenvectors

[Brian Gough <bjg at network-theory dot co dot uk>]

jdwright@wesleyan.edu writes:
 > Dear GSL-users,
 >  Can GSL provide the eigen-values and eigen-vectors of a
 > non-defective, non-symmetric matrix?  As far as I can tell, GSL
 > lacks this ability.

Hi,

GSL doesn't provide any routines for non-symmetric eigensystems.  The
Schur decomposition used to compute them is a complicated algorithm to
program.

 >  I did find a complete routine in "Numerical Recipes in C".
 > However, this routine merely provides the eigen-vectors.
 > Nonetheless, I will try to use it as a first step.  Now comes a
 > more concrete question.  If I have a variable H defined with the
 > statement "gsl_matrix * H = gsl_matrix_alloc(100,100)" how can I
 > pass this object into a function with the prototype "void hqr(float
 > **a, int n, float wr[], float wi[])"?  Is it possible or do I have
 > to modify the routine to use gsl functions like gsl_matrix_get and
 > gsl_matrix_set?

I think there's a discussion of how the Numerical Recipes authors
interface arrays and float ** pointers in their book.

For linear algebra routines not in GSL I'd recommend using LAPACK or
its C version CLAPACK, since it is free software and very well tested.

regards
Brian Gough