JMSLTM Numerical Library 6.1

com.imsl.math
Class Eigen

java.lang.Object
  extended by com.imsl.math.Eigen

public class Eigen
extends Object

Collection of Eigen System functions.

Eigen computes the eigenvalues and eigenvectors of a real matrix. The matrix is first balanced. Orthogonal similarity transformations are used to reduce the balanced matrix to a real upper Hessenberg matrix. The implicit double-shifted QR algorithm is used to compute the eigenvalues and eigenvectors of this Hessenberg matrix. The eigenvectors are normalized such that each has Euclidean length of value one. The largest component is real and positive.

The balancing routine is based on the EISPACK routine BALANC. The reduction routine is based on the EISPACK routines ORTHES and ORTRAN. The QR algorithm routine is based on the EISPACK routine HQR2. See Smith et al. (1976) for the EISPACK routines. Further details, some timing data, and credits are given in Hanson et al. (1990).

While the exact value of the performance index, tau, is highly machine dependent, the performance of Eigen is considered excellent if tau lt 1, good if 1 le  tau le  100, and poor if tau gt 100.

The performance index was first developed by the EISPACK project at Argonne National Laboratory; see Smith et al. (1976, pages 124-125).

See Also:
Example

Nested Class Summary
static class Eigen.DidNotConvergeException
          The iteration did not converge
 
Constructor Summary
Eigen()
          Constructs the eigenvalues and the eigenvectors of a real square matrix.
 
Method Summary
 int getMaxIterations()
          Returns the maximum number of iterations.
 Complex[] getValues()
          Returns the eigenvalues of a matrix of type double.
 Complex[][] getVectors()
          Returns the eigenvectors.
 double performanceIndex(double[][] a)
          Returns the performance index of a real eigensystem.
 void setMaxIterations(int maxIterations)
          Set the maximum number of iterations allowed.
 void solve(double[][] a, boolean computeVectors)
          Solves for the eigenvalues and (optionally) the eigenvectors of a real square matrix.
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

Eigen

public Eigen()
Constructs the eigenvalues and the eigenvectors of a real square matrix.

Method Detail

getMaxIterations

public int getMaxIterations()
Returns the maximum number of iterations.

Returns:
an int containing the maximum number of iterations.

getValues

public Complex[] getValues()
Returns the eigenvalues of a matrix of type double.

Returns:
a Complex array containing the eigenvalues of this matrix in descending order

getVectors

public Complex[][] getVectors()
Returns the eigenvectors.

Returns:
A Complex matrix containing the eigenvectors. The eigenvector corresponding to the j-th eigenvalue is stored in the j-th column. Each vector is normalized to have Euclidean length one.

performanceIndex

public double performanceIndex(double[][] a)
Returns the performance index of a real eigensystem.

Parameters:
a - a double matrix
Returns:
A double scalar value indicating how well the algorithms which have computed the eigenvalue and eigenvector pairs have performed. A performance index less than 1 is considered excellent, 1 to 100 is good, while greater than 100 is considered poor.

setMaxIterations

public void setMaxIterations(int maxIterations)
Set the maximum number of iterations allowed.

Parameters:
maxIterations - an int specifying the maximum number of iterations allowed. maxIterations must be greater than 0. By default, maxIterations = 50.

solve

public void solve(double[][] a,
                  boolean computeVectors)
           throws Eigen.DidNotConvergeException
Solves for the eigenvalues and (optionally) the eigenvectors of a real square matrix.

Parameters:
a - is the double square matrix for which the eigenvalues and (optionally) eigenvectors are to be found
computeVectors - is true if the eigenvectors are to be computed
Throws:
Eigen.DidNotConvergeException - is thrown when the algorithm fails to converge on the eigenvalues of the matrix.

JMSLTM Numerical Library 6.1

Copyright © 1970-2010 Visual Numerics, Inc.
Built July 30 2010.