ARPACK/PARPACK Math Library

The ARPACK (ARnoldi PACKage) software package, developed by Rice University CRPC researcher Danny Sorensen and colleagues, is a collection of Fortran 77 subroutines designed to solve large-scale eigenvalue problems. Parallel ARPACK (PARPACK) is the extension of ARPACK on distributed memory architectures. PARPACK message passing layer currently installed is MPI on the IBM SP.

ARPACK package is designed to compute a few eigenvalues and corresponding eigenvectors of a general n by n matrix A. It is most appropriate for large sparse or structured matrices A where structured means that a matrix-vector product w <-- Av requires order n rather than the usual order n**2 floating point operations. This software is based upon an algorithmic variant of the Arnoldi process called the Implicitly Restarted Arnoldi Method (IRAM). When the matrix A is symmetric it reduces to a variant of the Lanczos process called the Implicitly Restarted Lanczos Method (IRLM). These variants may be viewed as a synthesis of the Arnoldi/Lanczos process with the Implicitly Shifted QR technique that is suitable for large scale problems. For many standard problems, a matrix factorization is not required. Only the action of the matrix on a vector is needed.

ARPACK software is capable of solving large scale symmetric, nonsymmetric, and generalized eigenproblems from significant application areas. The software is designed to compute a few (k) eigenvalues with user specified features such as those of largest real part or largest magnitude. Storage requirements are on the order of n*k locations. No auxiliary storage is required. A set of Schur basis vectors for the desired k-dimensional eigen-space is computed which is numerically orthogonal to working precision. Numerically accurate eigenvectors are available on request.

NOTE: Both 32-bit and 64-bit address space ARPACK/PARPACK libraries are available on the IBM SP. It supports all precisions including single, double, complex and double complex.

How to use

32-bit library

% module load parpack 
  For ARPACK...
% xlf    $ARPACK ...   or 
% xlf90  $ARPACK ...   or 
% xlc    $ARPACK -lxlf90 ...    
  For PARPACK ...
% mpxlf_r    $PARPACK ...      or 
% mpxlf90_r  $PARPACK ...      or 
% mpcc_r     $PARPACK -lxlf90 ...    

64-bit library

% module load parpack_64 
	For ARPACK ...
% xlf   -q64  $ARPACK ...  or
% xlf90 -q64  $ARPACK ...   or
% xlc   -q64  $ARPACK -lxlf90 ...    
	For PARPACK ... 

% mpxlf_r   -q64  $PARPACK ...      or
% mpxlf90_r -q64  $PARPACK ...      or
% mpcc_r    -q64  $PARPACK -lxlf90 ...     

Example Programs

Example programs are available in the following directories.

• ARPACK: $(ARPACK_DIR)/EXAMPLES
• PARPACK: $(PARPACK_DIR)/EXAMPLES

Documentation

For full documentation, see

• ARPACK home page
• Parallel ARPACK Home Page