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.