no.uib.cipr.matrix.sparse

Class ArpackGen

java.lang.Object

no.uib.cipr.matrix.sparse.ArpackGen

public class ArpackGen
extends Object

Uses ARPACK to partially solve general eigensystems (ARPACK is designed to compute a subset of eigenvalues/eigenvectors).

Author:

Andreas Solti adopted from the class ArpackSym by Sam Halliday

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	ArpackGen.Ritz

Field Summary

Fields

Modifier and Type	Field and Description
static double	convergedTolerance
static int	maxIterations The maximum iterations allowed to perform until we decide that convergence is not attained.
static double	tolerance The tolerance at which the iterations are allowed to stop.

Constructor Summary

Constructors

Constructor and Description
ArpackGen(Matrix matrix) If the matrix is symmetric, ArpackSym is the better choice, as this property can be exploited in computation.

Method Summary

Methods

Modifier and Type	Method and Description
void	setComputeOnlyEigenvalues(boolean computeOnlyEigenvalues)
Map<Double,DenseVectorSub>	solve(int eigenvalues, ArpackGen.Ritz ritz) Solve the eigensystem for the number of eigenvalues requested.
Map<Double,DenseVectorSub>	solve(int eigenvalues, ArpackGen.Ritz ritz, double tolerance) Solve the eigensystem for the number of eigenvalues requested.
Map<Double,DenseVectorSub>	solve(int eigenvalues, ArpackGen.Ritz ritz, double tolerance, int ncvModification)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

tolerance

public static double tolerance

The tolerance at which the iterations are allowed to stop.

convergedTolerance

public static double convergedTolerance

maxIterations

public static int maxIterations

The maximum iterations allowed to perform until we decide that convergence is not attained.

Constructor Detail

ArpackGen

public ArpackGen(Matrix matrix)

If the matrix is symmetric, ArpackSym is the better choice, as this property can be exploited in computation.

Parameters:

matrix -

Method Detail

setComputeOnlyEigenvalues

public void setComputeOnlyEigenvalues(boolean computeOnlyEigenvalues)

solve

public Map<Double,DenseVectorSub> solve(int eigenvalues,
                               ArpackGen.Ritz ritz)

Solve the eigensystem for the number of eigenvalues requested.

NOTE: The references to the eigenvectors will keep alive a reference to a nev * n double array, so use the copy() method to free it up if only a subset is required.

Parameters:

eigenvalues -

ritz - preference for solutions

Returns:

a map from eigenvalues to corresponding eigenvectors.

solve

public Map<Double,DenseVectorSub> solve(int eigenvalues,
                               ArpackGen.Ritz ritz,
                               double tolerance)

Solve the eigensystem for the number of eigenvalues requested.

NOTE: The references to the eigenvectors will keep alive a reference to a nev * n double array, so use the copy() method to free it up if only a subset is required.

Parameters:

eigenvalues -

ritz - preference for solutions

Returns:

a map from eigenvalues to corresponding eigenvectors.

solve

public Map<Double,DenseVectorSub> solve(int eigenvalues,
                               ArpackGen.Ritz ritz,
                               double tolerance,
                               int ncvModification)

Parameters:

eigenvalues - NEV Integer. (INPUT) Number of eigenvalues of OP to be computed. 0 < NEV < N-1. (Where N is the matrix dimension)

ritz -

tolerance -

ncvModification - At present there is no a-priori analysis to guide the selection of NCV relative to NEV. The only formal requirement is that NCV > NEV + 2. However, it is recommended that NCV .ge. 2*NEV+1. If many problems of the same type are to be solved, one should experiment with increasing NCV while keeping NEV fixed for a given test problem. This will usually decrease the required number of OP*x operations but it also increases the work and storage required to maintain the orthogonal basis vectors. The optimal "cross-over" with respect to CPU time is problem dependent and must be determined empirically. See Chapter 8 of Reference 2 for further information.