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  3. User's Guide: ARPACK and PARPACK

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:

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

 ? 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
P?NAUPD S D C Z Non-symmetric implicitly restarted Arnoldi method.
P?NEUPD S D C Z Computes eigen/Schur vector for eigenvalue from P?NAUPD.
P?SAUPD S D Symmetric implicitly restarted Arnoldi method.
P?SEUPD S D Computes eigen/Schur vector for eigenvalue from P?SAUPD.

Further Reading

  1. ARPACK User's Guide
  2. A hardcopy ARPACK User's Guide may be ordered from SIAM:

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    http://www.siam.org/

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