org.jeometry.math.decomposition.SVDDecomposition Maven / Gradle / Ivy

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package org.jeometry.math.decomposition;

import org.jeometry.Geometry;
import org.jeometry.math.Matrix;

/**
 * This interface describes a Singular Values Decomposition (SVD).

 * 

 * Let A be a real matrix that has a matrix of {@link EigenDecomposition Eigen vectors} P that is not invertible 
 * (no {@link EigenDecomposition Eigen decomposition} can be computed). 
 * 


 * If A is an m × n real matrix with m > n, then A can be written using a so-called singular value decomposition of the form 
 * A = UDV^T

 * 

 * where:

 * 
 * U is a m × m matrix with orthogonal columns (U^TU = I)
 * 
D is a m × n diagonal matrix
 * 
V is a n × n matrix with orthogonal columns (V^TV = I)
 * 
 * 

 * 

 * source: Wolfram math
 * @author Julien Seinturier - COMEX S.A. - [email protected] - https://github.com/jorigin/jeometry
 * @version {@value Geometry#version} b{@value Geometry#BUILD}
 * @since 1.0.0
 */
public interface SVDDecomposition extends Decomposition {

	/**
	 * Get the U matrix that is a m × m matrix with orthogonal columns (U^TU = I).
	 * @return the U matrix
	 * @see #getD()
	 * @see #getV()
	 */
	public Matrix getU();
	
	/**
	 * Get the D matrix that is is a m × n diagonal matrix.
	 * @return the D matrix
	 * @see #getU()
	 * @see #getV()
	 */
	public Matrix getD();
	
	/**
	 * Get the V matrix that is a n × n matrix with orthogonal columns (V^TV = I).
	 * @return the V matrix
	 * @see #getU()
	 * @see #getD()
	 */
	public Matrix getV();
}