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In this section, the simple code dssimp is discussed.
All of the other example drivers are similar in nature.
This particular example program illustrates the simplest computational
mode of using ARPACK in considerable detail.
dssimp shows how to use ARPACK to find a few eigenvalues
and corresponding eigenvectors for the standard
eigenvalue problem:
where
is an n by n real symmetric matrix.
The main points illustrated are:
-
How to declare sufficient memory to find nev
eigenvalues. dssimp is set up to find nev eigenvalues of largest
magnitude LM. This may be reset to any one of the additional
options (SM, LA, SA, BE) to find other eigenvalues of interest.
-
Illustration of the reverse communication interface
needed to utilize the top level ARPACK routine dsaupd.
This routine computes the quantities needed to construct
the desired eigenvalues and the corresponding eigenvectors.
-
How to extract the desired eigenvalues and eigenvectors
from the quantities computed with dsaupd by
using the ARPACK routine dseupd.
This dssimp program is a driver for the subroutine
dsaupd and it is set up to solve the following problem:
-
Solve in regular mode.
Regular mode only uses matrix vector products involving
- The matrix
for this example is derived from the central
difference discretization of the 2-dimensional Laplacian on the
unit square with zero Dirichlet boundary conditions.
- The goal is to compute nev eigenvalues of largest
magnitude and corresponding eigenvectors.
The only thing that must be supplied in order to use this
routine on your problem is to change the array dimensions
and to supply a means to compute the matrix-vector product
on request from dsaupd.
The selection of which eigenvalues to compute
may be altered by changing the parameter which.
Once usage of dsaupd in the simplest mode is understood, you may
wish to explore the other available options such as
solving generalized eigenvalue problems using a shift-invert
computational mode.
Some of these additional modes are described in the latter
sections of this chapter and also in the file ex-sym.doc
in DOCUMENTS directory.
Next: The Reverse Communication Interface
Up: Getting Started with ARPACK
Previous: Getting Started
Chao Yang
11/7/1997