edu.umich.eecs.april.jmat

Class SingularValueDecomposition

java.lang.Object

edu.umich.eecs.april.jmat.SingularValueDecomposition

public class SingularValueDecomposition
extends java.lang.Object

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.

FIXME: This code has not been optimized AT ALL.

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
(package private) class	SingularValueDecomposition.SVDImpl

Constructor Summary

Constructors

Constructor and Description
SingularValueDecomposition(Matrix A) Construct the singular value decomposition

Method Summary

Modifier and Type	Method and Description
double	cond() Two norm condition number
Matrix	getS()
double[]	getSingularValues()
Matrix	getU()
Matrix	getV()
(package private) static double	hypot(double a, double b)
static void	main(java.lang.String[] args)
double	norm2()
int	rank() 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 A)

Construct the singular value decomposition

Parameters:

A - Rectangular matrix

Method Detail

getU

public Matrix getU()

getV

public Matrix getV()

getSingularValues

public double[] getSingularValues()

getS

public Matrix getS()

norm2

public double norm2()

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.

hypot

static final double hypot(double a,
                          double b)

main

public static void main(java.lang.String[] args)