math.matrix
Class SingularValueDecomposition

java.lang.Object
  |
  +--math.matrix.SingularValueDecomposition

All Implemented Interfaces:

java.io.Serializable

public class SingularValueDecomposition

extends java.lang.Object

implements java.io.Serializable

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'.

This class also allows for the SVD of an m-by-n matrix B where the number of rows is less than the number of columns (m The singular values, sigma[k] = S[k][k], are ordered so that sigma[0] >= sigma[1] >= ... >= sigma[n-1].

The singular value decomposition always exists for healthy matrices, so the constructor will never fail. (An unhealthy matrix is null, or with number of rows or columns < 1. In this case the constructor will throw an IllegalArgumentException runtime exception). The matrix condition number and the effective numerical rank can be computed from this decomposition.

See Also:

Serialized Form

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

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

Constructor Detail

SingularValueDecomposition

public SingularValueDecomposition(Matrix Arg)

Construct the singular value decomposition. The structure returned allows user to access U, S and V.

Parameters:

Arg - the rectangular matrix to be decomposed

Method Detail

getU

public Matrix getU()

Return the left singular vectors

Returns:

U

getV

public Matrix getV()

Return the right singular vectors

Returns:

V

getSingularValues

public double[] getSingularValues()

Return the one-dimensional array of singular values

Returns:

diagonal of S.

getS

public Matrix getS()

Return the diagonal matrix of singular values

Returns:

S

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.