edu.northwestern.at.utils.math.matrix
Class SingularValueDecomposition

java.lang.Object
  edu.northwestern.at.utils.math.matrix.SingularValueDecomposition

public class SingularValueDecomposition
extends java.lang.Object

Singular Value Decomposition of a matrix.

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 slight modification of the JAMA code, which in turn is based on the Linpack code.

Constructor Summary

SingularValueDecomposition(Matrix matrix)
Construct the singular value decomposition.

Method Summary

double	cond() Return two norm condition number.
Matrix	getS() Return diagonal matrix of singular values.
double[]	getSingularValues() Return singular values.
Matrix	getU() Return the left singular vectors
Matrix	getV() Return the right singular vectors
double	norm2() Return two norm.
int	rank() Return effective numerical matrix rank.

Methods inherited from class java.lang.Object

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

Constructor Detail

SingularValueDecomposition

public SingularValueDecomposition(Matrix matrix)

Construct the singular value decomposition.

Parameters:

matrix - Rectangular matrix to decompose.

Method Detail

getU

public Matrix getU()

Return the left singular vectors

Returns:

U (left singular vectors) as a matrix.

getV

public Matrix getV()

Return the right singular vectors

Returns:

V (right singular vectors) as a matrix.

getSingularValues

public double[] getSingularValues()

Return singular values.

Returns:

double[] vector of singular values.

getS

public Matrix getS()

Return diagonal matrix of singular values.

Returns:

S as a diagonal matrix.

norm2

public double norm2()

Return two norm.

Returns:

Maximum singular value.

cond

public double cond()

Return two norm condition number.

Returns:

maximum singular value / minimum singular value.

rank

public int rank()

Return effective numerical matrix rank.

Returns:

Number of nonnegligible singular values.