Catalano.Math.Decompositions

Class SingularValueDecomposition

java.lang.Object

Catalano.Math.Decompositions.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'.

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.

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
SingularValueDecomposition(double[][] matrix) Initializes a new instance of the SingularValueDecomposition class.
SingularValueDecomposition(double[][] matrix, boolean wantU, boolean wantV) Initializes a new instance of the SingularValueDecomposition class.

Method Summary

Modifier and Type	Method and Description
double	cond() Two norm condition number.
double[][]	getS() Get Diagonal matrix of singular values.
double[]	getSingularValues() Return the one-dimensional array of singular values
double[][]	getU() Get Left singular vectors.
double[][]	getV() Get Right singular vectors.
double[][]	inverse()
boolean	isWantU() Check if need to compute U.
boolean	isWantV() Check if need to compute V.
double	norm2() Two norm.
int	rank() Effective numerical matrix rank.
void	setWantU(boolean wantu) Compute U.
void	setWantV(boolean wantv) Compute V.
double	threshold()

Methods inherited from class java.lang.Object

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

Constructor Detail

SingularValueDecomposition

public SingularValueDecomposition(double[][] matrix,
                                  boolean wantU,
                                  boolean wantV)

Initializes a new instance of the SingularValueDecomposition class.

Parameters:

matrix - Matrix.

wantU - Compute U.

wantV - Compute V.

SingularValueDecomposition

public SingularValueDecomposition(double[][] matrix)

Initializes a new instance of the SingularValueDecomposition class.

Parameters:

matrix - The matrix to be decomposed.

Throws:

java.lang.IllegalArgumentException - Matrix does not have any rows or columns.

Method Detail

isWantU

public boolean isWantU()

Check if need to compute U.

Returns:

True if the U is computed, otherwise false.

setWantU

public void setWantU(boolean wantu)

Compute U.

Parameters:

wantu - True if need to compute U, otherwise false.

isWantV

public boolean isWantV()

Check if need to compute V.

Returns:

True if the V is computed, otherwise false.

setWantV

public void setWantV(boolean wantv)

Compute V.

Parameters:

wantv - True if need to compute V, otherwise false.

getU

public double[][] getU()

Get Left singular vectors.

Returns:

Left singular vectors.

getV

public double[][] getV()

Get Right singular vectors.

Returns:

Right singular vectors.

getSingularValues

public double[] getSingularValues()

Return the one-dimensional array of singular values

Returns:

diagonal of S.

getS

public double[][] getS()

Get Diagonal matrix of singular values.

Returns:

Diagonal matrix of singular values.

norm2

public double norm2()

Two norm. max(S).

Returns:

Two norm.

cond

public double cond()

Two norm condition number. max(S)/min(S)

Returns:

Two norm condition number.

rank

public int rank()

Effective numerical matrix rank.

Returns:

Number of nonnegligible singular values.

threshold

public double threshold()

inverse

public double[][] inverse()