[Maxima] matrix 2-norm and associated matrix condition number
toy.raymond at gmail.com
Thu Apr 26 16:15:23 CDT 2007
Barton Willis wrote:
> For matrices larger that 3 x 3, it's unlikely that your function will
> work. If you are interested in floating point, maybe you could
> use eigens_by_jacobi. Also, there is a recently added function (not
> sure of its name) for numerical eigenvalue problems that should be
> faster than eigens_by_jacobi.
You need to load the lapack package first, via load("lapack").
dgeev computes the eigenvalues of a real matrix: dgeev(matrix,
right-vec, left-vec), where right-vec and left-vec are optional args
indicating if you want the right or left eigenvectors to be computed.
The result is a list of three items. The first is the list of
eigenvalues. The second and third, if requested, the right and left
dlange computes some matrix norms: dlange(norm, matrix). norm should
be 'max, 'one_norm, 'inf_norm, or 'frobenius to choose the desired norm.
LAPACK has routines to compute matrix condition numbers, but I can't
remember what they're called and there is currently no interface for
maxima to these functions.
These functions are currently documented because its not clear what the
right interface should be. When that is decided, some documentation
will be written.
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