TOMS343
Eigenvalues and Eigenvectors of a Real General Matrix

TOMS343 is a FORTRAN77 library which implements ACM TOMS algorithm 343, for computing the eigenvalues and eigenvectors of a real general matrix.

The text of many ACM TOMS algorithms is available online through ACM: http://www.acm.org/pubs/calgo or NETLIB: http://www.netlib.org/toms/index.html.

Usage:

call eigenp ( n, nm, a, t, evr, evi, vecr, veci, indic )

N is the order of the matrix, NM is the leading dimension of the two dimensional arrays (which must be at least equal to N), A(NM,N) contains the matrix on input, but the contents are destroyed on output, t is a real value equal to the number of binary digits of a single precision floating point number (23, for instance); EVR and EVI contain the real and imaginary parts of the eigenvalues, while the columns of VECR and VECI contain the real and imaginary parts of the eigenvectors, and INDIC is an integer vector of length N which indicates success or failure for each of the N eigenvalue/eigenvector computations.

Languages:

TOMS343 is available in a FORTRAN77 version.

Related Data and Programs:

EISPACK, a FORTRAN90 library which handle eigenvalue and eigenvector computations.

LAPACK_EXAMPLES, a FORTRAN90 program which demonstrates the use of the LAPACK linear algebra library.

TOMS384, a FORTRAN77 routine which computes the eigenvalues and eigenvectors of a symmetric matrix.

Reference:

1. J Grad, MA Brebner,
   Algorithm 343: Eigenvalues and Eigenvectors of a Real General Matrix,
   Communications of the ACM,
   Volume 11, Number 12, December 1968, pages 820-826.

Source Code:

• toms343.f, the source code.
• toms343.sh, commands to compile the source code.

Examples and Tests:

• toms343_prb.f, a sample calling program.
• toms343_prb.sh, commands to compile and run the sample program.
• toms343_prb_output.txt, the output file.

List of Routines:

• EIGENP computes the eigenvalues and eigenvectors of a real general matrix;
• SCALE scales the matrix so that it is balanced;
• HESQR applies the QR method to the matrix to find the eigenvalues;
• REALVE computes eigenvectors associated with a real eigenvalue;
• COMPVE computes eigenvectors associated with a complex eigenvalue;

You can go up one level to the FORTRAN77 source codes.