jsat.linear

Class EigenValueDecomposition

java.lang.Object

jsat.linear.EigenValueDecomposition

All Implemented Interfaces:

Serializable

public class EigenValueDecomposition
extends Object
implements Serializable

Class for performing the Eigen Value Decomposition of a matrix. The EVD of a real matrix may contain complex results. When this occurs, the EVD is less useful since JSAT only supports real matrices. The SingularValueDecomposition of a real matrix is always real, and may be more useful.

Implementation adapted from the Public Domain work of JAMA: A Java Matrix Package

If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal. V * V' equals the identity matrix.

If A is not symmetric, then the eigenvalue matrix D is block diagonal with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues, lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The columns of V represent the eigenvectors in the sense that A*V = V*D. The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V*D*inverse(V) depends upon the condition of V.
If there are no complex eigen values, which can be checked using isComplex(), then D is a normal diagonal matrix.

Author:

Edward Raff

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
EigenValueDecomposition(Matrix A) Creates a new new Eigen Value Decomposition.
EigenValueDecomposition(Matrix A, double eps) Creates a new new Eigen Value Decomposition.

Method Summary

Modifier and Type	Method and Description
Matrix	getD() Return the block diagonal eigenvalue matrix
double[]	getImagEigenvalues() Return the imaginary parts of the eigenvalues
double[]	getRealEigenvalues() Return the real parts of the eigenvalues
Matrix	getV() Return a copy of the eigenvector matrix
Matrix	getVRaw() Returns the raw eigenvector matrix.
Matrix	getVT() Returns a copy of the transposed eigenvector matrix.
boolean	isComplex() Indicates wether or not the EVD contains complex eigen values.
void	sortByEigenValue(Comparator<Double> cmp) Sorts the eigen values and the corresponding eigenvector columns by the associated eigen value.

Methods inherited from class java.lang.Object

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

Constructor Detail

EigenValueDecomposition

public EigenValueDecomposition(Matrix A)

Creates a new new Eigen Value Decomposition. The input matrix will not be altered. If the input is symmetric, a more efficient algorithm will be used.

Parameters:

A - the square matrix to work on.

EigenValueDecomposition

public EigenValueDecomposition(Matrix A,
                               double eps)

Creates a new new Eigen Value Decomposition. The input matrix will not be altered. If the input is symmetric, a more efficient algorithm will be used.

Parameters:

A - the square matrix to work on.

eps - the numerical tolerance for differences in value to be considered the same.

Method Detail

sortByEigenValue

public void sortByEigenValue(Comparator<Double> cmp)

Sorts the eigen values and the corresponding eigenvector columns by the associated eigen value. Sorting can not occur if complex values are present.

Parameters:

cmp - the comparator to use to sort the eigen values

getV

public Matrix getV()

Return a copy of the eigenvector matrix

Returns:

the eigen vector matrix

getVRaw

public Matrix getVRaw()

Returns the raw eigenvector matrix. Modifying this matrix will effect others using the same matrix.

Returns:

the eigen vector matrix

getVT

public Matrix getVT()

Returns a copy of the transposed eigenvector matrix.

Returns:

the transposed eigen the eigen vector matrix

getRealEigenvalues

public double[] getRealEigenvalues()

Return the real parts of the eigenvalues

Returns:

real(diag(D))

getImagEigenvalues

public double[] getImagEigenvalues()

Return the imaginary parts of the eigenvalues

Returns:

imag(diag(D))

getD

public Matrix getD()

Return the block diagonal eigenvalue matrix

Returns:

D

isComplex

public boolean isComplex()

Indicates wether or not the EVD contains complex eigen values. Because EVD works with real matrices, the complex eigen vectors are lost - and the complex eigen values are in the off diagonal spaces of the D matrix.

Returns:

true if the EVD results in complex eigen values.