MATRIX commands


PROGRAM NAME

meigen - Compute Eigenvectors and Eigenvalues of a Square Matrix

DESCRIPTION

meigen computes the eigenvalues and right eigenvectors of a square matrix. The input matrix can be nonsymmetric. The input matrix is caste to KDCOMPLEX for reading, and all output matrices are of type KDCOMPLEX.

The eigenvectors are stored as columns of the eigenvector output matrix. The eigenvectors are all normalized to have unit 2-norm and a purely real largest component.

The eigenvalues are stored as a diagonal matrix with the i'th diagonal being the eigenvalue corresponding the the eigenvector in column i of the eigenvector output matrix.

The eigenvalues (and thier associated eigenvectors) appear in decreasing order. They are explicitly sorted (while keeping track of the associated eigenvectors).

meigen uses the LAPACK routine ZGEEV to perform the calculations.

REQUIRED ARGUMENTS

-i
type: infile
desc: Input Matrix

OPTIONAL ARGUMENTS

-o1
type: outfile
desc: Eigenvector output matrix
default: {none}
-o2
type: outfile
desc: Eigenvalue output matrix
default: {none}

EXAMPLES

SEE ALSO

MATRIX:zlapack:zgeev

RESTRICTIONS

It has been observed that LAPACK generally gets the eigenvalues sorted in decending order, but occasionally will return with some of the smaller eigenvalues out of order. This is not a bug in meigen, although a sort may be inserted at some future date to make sure that the eigenvalues and thier associated eigenvectors are sorted. The 1992 version of the LAPACK USERS' GUIDE doesn't specify an ordering for the eigenvalues.

REFERENCES

LAPACK Users' Guide, E. Anderson et. al., SIAM 1992. ISBN 0-89871-294-7

COPYRIGHT

Copyright (C) 1993 - 1997, Khoral Research, Inc. ("KRI") All rights reserved.