org.openimaj.math.matrix

Class GeneralisedEigenvalueProblem

java.lang.Object

org.openimaj.math.matrix.GeneralisedEigenvalueProblem

public class GeneralisedEigenvalueProblem
extends Object

Methods for solving the Generalised Eigenvalue Problem: A x = L B x.

Internally the methods in this class use LAPACK to compute the solutions.

Author:

Jonathon Hare (jsh2@ecs.soton.ac.uk)

Constructor Summary

Constructors

Constructor and Description
GeneralisedEigenvalueProblem()

Method Summary

Modifier and Type	Method and Description
static no.uib.cipr.matrix.DenseVector	symmetricGeneralisedEigenvalues(no.uib.cipr.matrix.DenseMatrix A, no.uib.cipr.matrix.DenseMatrix B) Compute the generalised eigenvalues, L, of the problem A x = L B x.
static double[]	symmetricGeneralisedEigenvalues(Jama.Matrix A, Jama.Matrix B) Compute the generalised eigenvalues, L, of the problem A x = L B x.
static IndependentPair<no.uib.cipr.matrix.DenseMatrix,no.uib.cipr.matrix.DenseVector>	symmetricGeneralisedEigenvectors(no.uib.cipr.matrix.DenseMatrix A, no.uib.cipr.matrix.DenseMatrix B) Solve the general problem A x = L B x.
static IndependentPair<Jama.Matrix,double[]>	symmetricGeneralisedEigenvectors(Jama.Matrix A, Jama.Matrix B) Solve the general problem A x = L B x.
static IndependentPair<Jama.Matrix,double[]>	symmetricGeneralisedEigenvectorsSorted(Jama.Matrix A, Jama.Matrix B) Solve the general problem A x = L B x.
static IndependentPair<Jama.Matrix,double[]>	symmetricGeneralisedEigenvectorsSorted(Jama.Matrix A, Jama.Matrix B, int numVecs) Solve the general problem A x = L B x.

Methods inherited from class java.lang.Object

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

Constructor Detail

GeneralisedEigenvalueProblem

public GeneralisedEigenvalueProblem()

Method Detail

symmetricGeneralisedEigenvalues

public static no.uib.cipr.matrix.DenseVector symmetricGeneralisedEigenvalues(no.uib.cipr.matrix.DenseMatrix A,
                                                                             no.uib.cipr.matrix.DenseMatrix B)

Compute the generalised eigenvalues, L, of the problem A x = L B x. The returned eigenvalues are not ordered.

Parameters:

A - symmetric Matrix A; only the upper triangle is used.

B - symmetric Matrix B; only the upper triangle is used.

Returns:

the eigenvalues L.

symmetricGeneralisedEigenvectors

public static IndependentPair<no.uib.cipr.matrix.DenseMatrix,no.uib.cipr.matrix.DenseVector> symmetricGeneralisedEigenvectors(no.uib.cipr.matrix.DenseMatrix A,
                                                                                                                              no.uib.cipr.matrix.DenseMatrix B)

Solve the general problem A x = L B x. The returned eigenvalues are not ordered.

Parameters:

A - symmetric matrix A

B - symmetric matrix B

Returns:

The eigenvectors x and eigenvalues L.

symmetricGeneralisedEigenvalues

public static double[] symmetricGeneralisedEigenvalues(Jama.Matrix A,
                                                       Jama.Matrix B)

Compute the generalised eigenvalues, L, of the problem A x = L B x. The returned eigenvalues are not ordered.

Parameters:

A - symmetric Matrix A; only the upper triangle is used.

B - symmetric Matrix B; only the upper triangle is used.

Returns:

the eigenvalues L.

symmetricGeneralisedEigenvectors

public static IndependentPair<Jama.Matrix,double[]> symmetricGeneralisedEigenvectors(Jama.Matrix A,
                                                                                     Jama.Matrix B)

Solve the general problem A x = L B x. The returned eigenvalues are not ordered.

Parameters:

A - symmetric matrix A

B - symmetric matrix B

Returns:

The eigenvectors x and eigenvalues L.

symmetricGeneralisedEigenvectorsSorted

public static IndependentPair<Jama.Matrix,double[]> symmetricGeneralisedEigenvectorsSorted(Jama.Matrix A,
                                                                                           Jama.Matrix B)

Solve the general problem A x = L B x. The returned eigenvalues ordered in a decreasing manner.

Parameters:

A - symmetric matrix A

B - symmetric matrix B

Returns:

The eigenvectors x and eigenvalues L.

symmetricGeneralisedEigenvectorsSorted

public static IndependentPair<Jama.Matrix,double[]> symmetricGeneralisedEigenvectorsSorted(Jama.Matrix A,
                                                                                           Jama.Matrix B,
                                                                                           int numVecs)

Solve the general problem A x = L B x. The returned eigenvalues ordered in a decreasing manner. Only the top numVecs eigenvalues and vectors are returned.

Parameters:

A - symmetric matrix A

B - symmetric matrix B

numVecs - number of eigenvalues/eigenvectors

Returns:

The eigenvectors x and eigenvalues L.