ARPACK
Eigenvalues and Eigenvectors of Large Matrices

ARPACK is a FORTRAN90 program which can compute eigenvalues and eigenvectors of large matrices.

ARPACK supports single and double precision, real or complex arithmetic. The matrices involved can be symmetric or nonsymmetric. The user can request just a few eigenvalues, or all of them. There are special routines for banded matrices.

Because the package uses reverse communication, the user is free to store the matrix in any way suitable. ARPACK will never require direct access to the matrix, only to the value of certain matrix-vector products such as A*x or A'*x.

ARPACK includes calls to the LAPACK and BLAS libraries.

There is an ARPACK home page at: http://www.caam.rice.edu/software/ARPACK/index.html.

Related Data and Programs:

ARPACK is also built into MATLAB, and is accessible through the EIGS command.

BLAS1 is a FORTRAN90 library of vector-vector routines used by LAPACK and hence ARPACK.

BLAS2 is a FORTRAN90 library of matrix-vector routines used by LAPACK and hence ARPACK.

BLAS3 is a FORTRAN90 library of matrix-matrix routines used by LAPACK and hence ARPACK.

EISPACK is a FORTRAN90 library of eigenvalue routines, that was replaced by LAPACK.

LAPACK is a FORTRAN90 library of modern linear algebra routines which includes many eigenvalue routines.

TEST_EIGEN is a FORTRAN90 library of routines that define various eigenvalue test cases.

TEST_MAT is a FORTRAN90 library of routines which define test matrices, some of which have known eigenvalues and eigenvectors.

Reference:

1. Richard Lehoucq, Danny Sorensen, Chao Yang,
   ARPACK User's Guide:
   Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods,
   available as a PDF file
2. Danny Sorensen,
   Implicitly Restarted Arnoldi/Lanczos Methods for Large Scale Eigenvalue Calculations,
   Department of Computational and Applied Mathematics,
   Rice University,
   TR-96-40,
   available as a PDF file
3. Information about the use of the ARPACK execution trace facilities available through "debug.h" is given in arpack_debug.txt
4. Information about the use of the ARPACK operation count and timing statistics available through "stat.h" is given in arpack_stat.txt

Source Code:

• arpack.f90, the source code for the single precision real version.
• debug.h, an INCLUDE file needed for debugging.
• stat.h, an INCLUDE file needed for program performance statistics.
• blas.f90, the source code for all the single precision BLAS routines needed by ARPACK.
• lapack.f90, the source code for all the single precision LAPACK routines needed by ARPACK.
• arpack.csh, commands to compile the source code.

Examples and Tests:

SSSIMP is a simple symmetric test problem:

• sssimp.f90, a sample calling program.
• sssimp.csh, commands to compile and run the sample program.
• sssimp_output.txt, the output file.

SNSIMP is a simple nonsymmetric test problem:

• snsimp.f90, a sample calling program.
• snsimp.csh, commands to compile and run the sample program.
• snsimp_output.txt, the output file.

You can go up one level to the FORTRAN90 source codes.