Programs in Physics & Physical Chemistry
|[Licence| Download | New Version Template] aari_v1_0.gz(17 Kbytes)|
|Manuscript Title: A vectorizable eigenvalue solver for sparse matrices.|
|Authors: L.C. Bernard, F.J. Helton|
|Program title: EIGVEC|
|Catalogue identifier: AARI_v1_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 25(1982)73|
|Programming language: Fortran, CAL Assembler.|
|Operating system: LTSS.|
|RAM: 22K words|
|Word size: 64|
|Keywords: General purpose, Matrix, Numerical mathematics, Eigenvalue problem, Inverse vector iteration, Block matrix, Symmetric matrix, Sparse matrix, Pattern recognition, Vectorization.|
Nature of problem:
This package solves the generalized eigenvalue problem Ax = lambdaBx, a problem which arises often, for example, in: physics, mechanics, and chemistry. Here A and B have a global block diagonal form and fine sparse structure as found in two-dimensional problems with a finite element approach.
Any mode can be obatined by first shifting the spectrum, then using inverse vector iteration to converge toward the lowest eigenvalue in absolute value. The Cholesky decomposition of A is efficiently done using vectorization. Sparse matrix techniques reduce I/O requirements and improve the Cholesky decomposition in some cases.
Both matrices, A and B, must be real symmetric, and B must be positive- definite. Both must have the same sparsity pattern.
The program uses two subroutines written in assembly language for vectorization. The nonstandard FORTR AN statement, NAMELIST, is used.
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