org.ejml.interfaces.decomposition.EigenDecomposition Maven / Gradle / Ivy
/*
* Copyright (c) 2009-2014, Peter Abeles. All Rights Reserved.
*
* This file is part of Efficient Java Matrix Library (EJML).
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.ejml.interfaces.decomposition;
import org.ejml.data.Complex64F;
import org.ejml.data.Matrix64F;
/**
*
* This is a generic interface for computing the eigenvalues and eigenvectors of a matrix.
* Eigenvalues and eigenvectors have the following property:
*
* A*v=λ*v
*
* where A is a square matrix and v is an eigenvector associated with the eigenvalue λ.
*
*
*
* In general, both eigenvalues and eigenvectors can be complex numbers. For symmetric matrices the
* eigenvalues and eigenvectors are always real numbers. EJML does not support complex matrices but
* it does have minimal support for complex numbers. As a result complex eigenvalues are found, but only
* the real eigenvectors are computed.
*
*
*
* To create a new instance of {@link EigenDecomposition} use {@link org.ejml.factory.DecompositionFactory}. If the matrix
* is known to be symmetric be sure to use the symmetric decomposition, which is much faster and more accurate
* than the general purpose one.
*
* @author Peter Abeles
*/
public interface EigenDecomposition
extends DecompositionInterface {
/**
* Returns the number of eigenvalues/eigenvectors. This is the matrix's dimension.
*
* @return number of eigenvalues/eigenvectors.
*/
public int getNumberOfEigenvalues();
/**
*
* Returns an eigenvalue as a complex number. For symmetric matrices the returned eigenvalue will always be a real
* number, which means the imaginary component will be equal to zero.
*
*
*
* NOTE: The order of the eigenvalues is dependent upon the decomposition algorithm used. This means that they may
* or may not be ordered by magnitude. For example the QR algorithm will returns results that are partially
* ordered by magnitude, but this behavior should not be relied upon.
*
*
* @param index Index of the eigenvalue eigenvector pair.
* @return An eigenvalue.
*/
public Complex64F getEigenvalue( int index );
/**
*
* Used to retrieve real valued eigenvectors. If an eigenvector is associated with a complex eigenvalue
* then null is returned instead.
*
*
* @param index Index of the eigenvalue eigenvector pair.
* @return If the associated eigenvalue is real then an eigenvector is returned, null otherwise.
*/
public MatrixType getEigenVector( int index );
}