org.ejml.dense.row

Class EigenOps_FDRM

java.lang.Object

org.ejml.dense.row.EigenOps_FDRM

public class EigenOps_FDRM
extends java.lang.Object

Additional functions related to eigenvalues and eigenvectors of a matrix.

Constructor Summary

Constructors

Constructor and Description
EigenOps_FDRM()

Method Summary

Modifier and Type	Method and Description
static float[]	boundLargestEigenValue(org.ejml.data.FMatrixRMaj A, float[] bound) Generates a bound for the largest eigen value of the provided matrix using Perron-Frobenius theorem.
static float	computeEigenValue(org.ejml.data.FMatrixRMaj A, org.ejml.data.FMatrixRMaj eigenVector) Given matrix A and an eigen vector of A, compute the corresponding eigen value.
static org.ejml.data.FEigenpair	computeEigenVector(org.ejml.data.FMatrixRMaj A, float eigenvalue) Given an eigenvalue it computes an eigenvector using inverse iteration: for i=1:MAX { (A - μI)z(i) = q(i-1) q(i) = z(i) / ||z(i)|| λ(i) = q(i)T A q(i) }
static org.ejml.data.FMatrixRMaj	createMatrixD(org.ejml.interfaces.decomposition.EigenDecomposition_F32 eig) A diagonal matrix where real diagonal element contains a real eigenvalue.
static org.ejml.data.FMatrixRMaj	createMatrixV(org.ejml.interfaces.decomposition.EigenDecomposition_F32<org.ejml.data.FMatrixRMaj> eig) Puts all the real eigenvectors into the columns of a matrix.
static org.ejml.data.FEigenpair	dominantEigenpair(org.ejml.data.FMatrixRMaj A) Computes the dominant eigen vector for a matrix.

Methods inherited from class java.lang.Object

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

Constructor Detail

EigenOps_FDRM

public EigenOps_FDRM()

Method Detail

computeEigenValue

public static float computeEigenValue(org.ejml.data.FMatrixRMaj A,
                                      org.ejml.data.FMatrixRMaj eigenVector)

Given matrix A and an eigen vector of A, compute the corresponding eigen value. This is the Rayleigh quotient.

x^TAx / x^Tx

Parameters:

A - Matrix. Not modified.

eigenVector - An eigen vector of A. Not modified.

Returns:

The corresponding eigen value.

computeEigenVector

public static org.ejml.data.FEigenpair computeEigenVector(org.ejml.data.FMatrixRMaj A,
                                                          float eigenvalue)

Given an eigenvalue it computes an eigenvector using inverse iteration:
for i=1:MAX {
(A - μI)z⁽ⁱ⁾ = q^(i-1)
q⁽ⁱ⁾ = z⁽ⁱ⁾ / ||z⁽ⁱ⁾||
λ⁽ⁱ⁾ = q^(i)T A q⁽ⁱ⁾
}

NOTE: If there is another eigenvalue that is very similar to the provided one then there is a chance of it converging towards that one instead. The larger a matrix is the more likely this is to happen.

Parameters:

A - Matrix whose eigenvector is being computed. Not modified.

eigenvalue - The eigenvalue in the eigen pair.

Returns:

The eigenvector or null if none could be found.

dominantEigenpair

public static org.ejml.data.FEigenpair dominantEigenpair(org.ejml.data.FMatrixRMaj A)

Computes the dominant eigen vector for a matrix. The dominant eigen vector is an eigen vector associated with the largest eigen value.

WARNING: This function uses the power method. There are known cases where it will not converge. It also seems to converge to non-dominant eigen vectors some times. Use at your own risk.

Parameters:

A - A matrix. Not modified.

boundLargestEigenValue

public static float[] boundLargestEigenValue(org.ejml.data.FMatrixRMaj A,
                                             float[] bound)

Generates a bound for the largest eigen value of the provided matrix using Perron-Frobenius theorem. This function only applies to non-negative real matrices.

For "stochastic" matrices (Markov process) this should return one for the upper and lower bound.

Parameters:

A - Square matrix with positive elements. Not modified.

bound - Where the results are stored. If null then a matrix will be declared. Modified.

Returns:

Lower and upper bound in the first and second elements respectively.

createMatrixD

public static org.ejml.data.FMatrixRMaj createMatrixD(org.ejml.interfaces.decomposition.EigenDecomposition_F32 eig)

A diagonal matrix where real diagonal element contains a real eigenvalue. If an eigenvalue is imaginary then zero is stored in its place.

Parameters:

eig - An eigenvalue decomposition which has already decomposed a matrix.

Returns:

A diagonal matrix containing the eigenvalues.

createMatrixV

public static org.ejml.data.FMatrixRMaj createMatrixV(org.ejml.interfaces.decomposition.EigenDecomposition_F32<org.ejml.data.FMatrixRMaj> eig)

Puts all the real eigenvectors into the columns of a matrix. If an eigenvalue is imaginary then the corresponding eigenvector will have zeros in its column.

Parameters:

eig - An eigenvalue decomposition which has already decomposed a matrix.

Returns:

An m by m matrix containing eigenvectors in its columns.