ProGAL.math
Class SingularValueDecomposition

java.lang.Object
  ProGAL.math.SingularValueDecomposition

public class SingularValueDecomposition
extends java.lang.Object

A class for calculating and representing the singular value decomposition. For an m-by-n matrix A with m >= n, the singular value decomposition is an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and an n-by-n orthogonal matrix V so that A = U*S*V'. The singular values, sigma[k] = S[k][k], are ordered so that sigma[0] >= sigma[1] >= ... >= sigma[n-1]. The singular value decompostion always exists, so the constructor will never fail. The matrix condition number and the effective numerical rank can be computed from this decomposition. This code is a modified version of the JAMA implementation.

Constructor Summary

SingularValueDecomposition(Matrix Arg)
Construct the singular value decomposition

Method Summary

double	cond() Two norm condition number
Matrix	getS() Return the diagonal matrix of singular values
double[]	getSingularValues() Return the one-dimensional array of singular values.
Matrix	getU() Return the left singular vectors
Matrix	getV() Return the right singular vectors.
double	norm2() Two norm
int	rank() Effective numerical matrix rank

Methods inherited from class java.lang.Object

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

Constructor Detail

SingularValueDecomposition

public SingularValueDecomposition(Matrix Arg)

Construct the singular value decomposition

Method Detail

getU

public Matrix getU()

Return the left singular vectors

getV

public Matrix getV()

Return the right singular vectors.

getSingularValues

public double[] getSingularValues()

Return the one-dimensional array of singular values.

getS

public Matrix getS()

Return the diagonal matrix of singular values

norm2

public double norm2()

Two norm

Returns:

max(S)

cond

public double cond()

Two norm condition number

Returns:

max(S)/min(S)

rank

public int rank()

Effective numerical matrix rank

Returns:

Number of nonnegligible singular values.