MathKeisan User's Guide

ARPACK and PARPACK

Introduction

ARPACK (ARnoldi PACKage) is a collection of Fortran subprograms designed to solve large-scale eigenvalue problems. It is capable of solving standard or generalized eigenvalue problems for symmetric (Hermitian) and non-symmetric (non-Hermitian) systems. The ARPACK library is designed to compute a few, say k, eigenvalues with user-specified features such as those of largest real part or largest magnitude using O(nk+k²) storage. No auxiliary storage is required. A set of Schur basis vectors for the desired k-dimensional eigenspace is computed, and is numerically orthogonal within the working precision. Eigenvectors are also available upon request. ARPACK is dependent upon a number of subprograms from LAPACK and BLAS. The performance scales asymptotically to the Level 2 BLAS operation GEMV.

PARPACK (Parallel ARPACK) is an extension of the ARPACK software package, used for solving large scale eigenvalue problems on distributed memory parallel architectures. The PARPACK in MathKeisan supports the MPI message passing layer.

User Interface

User interface information is available from several sources:

The ARPACK Routine List and PARPACK Routine List contains one-line summaries of the subprograms in ARPACK and PARPACK.
There are ARPACK Man Pages and PARPACK Man Pages which have user interface information for individual subroutines. To view information on subroutine DNAUPD from the command line, type man dnaupd. If you have difficulty viewing man pages, please see the Man Pages Chapter.
The Linking Chapter tells how to link with the ARPACK and PARPACK libraries.

ARPACK Routine List

^† `?` indicates prefix which must be filled with a combination of:
`S = REAL(kind=4)`, `D = REAL(kind=8)`, `C = COMPLEX(kind=4)`, `Z = COMPLEX(kind=8)`
Name^†	Prefixes	Description
`?NAUPD`	`S D C Z`	Non-symmetric implicitly restarted Arnoldi method.
`?NEUPD`	`S D C Z`	Computes eigen/Schur vector for eigenvalue from `?NAUPD`.
`?SAUPD`	`S D`	Symmetric implicitly restarted Arnoldi method.
`?SEUPD`	`S D`	Computes eigen/Schur vector for eigenvalue from `?SAUPD`.

PARPACK Routine List