edu.stanford.rsl.conrad.numerics

Class DecompositionSVD

java.lang.Object

edu.stanford.rsl.conrad.numerics.DecompositionSVD

All Implemented Interfaces:

java.io.Serializable

public class DecompositionSVD
extends java.lang.Object
implements java.io.Serializable

Singular Value Decomposition.

For an m-by-n matrix A, the singular value decomposition is an m-by-(m or n) orthogonal matrix U, a (m or 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 class is mainly based on SingularValueDecomposition class in Jama in which SVD sometimes fails on cases m < n. The bug has been fixed by Ron Boisvert . Details of what were fixed can be found below: http://cio.nist.gov/esd/emaildir/lists/jama/msg01431.html http://cio.nist.gov/esd/emaildir/lists/jama/msg01430.html http://metamerist.blogspot.com/2008/04/svd-for-vertically-challenged.html Then, small changes were made to be compatible with CONRAD.

Author:

Jang-Hwan Choi

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
DecompositionSVD(SimpleMatrix Arg) Old Constructor Construct the singular value decomposition Structure to access U, S and V.
DecompositionSVD(SimpleMatrix Arg, boolean thin, boolean wantu, boolean wantv) Construct the singular value decomposition, i.e.

Method Summary

Methods

Modifier and Type	Method and Description
double	cond() Two norm condition number
SimpleMatrix	getreciprocalS() Return the diagonal matrix of the reciprocals of the singular values
SimpleMatrix	getS() Return the diagonal matrix of singular values
double[]	getSingularValues() Return the one-dimensional array of singular values
SimpleMatrix	getU() Return the left singular vectors
SimpleMatrix	getV() Return the right singular vectors
SimpleMatrix	inverse(boolean omit) Return the Moore-Penrose (generalized) inverse Slightly modified version of Kim van der Linde's code
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

DecompositionSVD

public DecompositionSVD(SimpleMatrix Arg)

Old Constructor
Construct the singular value decomposition Structure to access U, S and V.

Parameters:

Arg - Rectangular matrix

DecompositionSVD

public DecompositionSVD(SimpleMatrix Arg,
                boolean thin,
                boolean wantu,
                boolean wantv)

Construct the singular value decomposition, i.e. a structure to access U, S and V.

Parameters:

Arg - Rectangular matrix

thin - If true U is economy sized

wantu - If true generate the U matrix

wantv - If true generate the V matrix

Method Detail

getU

public SimpleMatrix getU()

Return the left singular vectors

Returns:

U

getV

public SimpleMatrix 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 SimpleMatrix getS()

Return the diagonal matrix of singular values

Returns:

S

getreciprocalS

public SimpleMatrix getreciprocalS()

Return the diagonal matrix of the reciprocals of the singular values

Returns:

S+

inverse

public SimpleMatrix inverse(boolean omit)

Return the Moore-Penrose (generalized) inverse Slightly modified version of Kim van der Linde's code

Parameters:

omit - if true tolerance based omitting of negligible singular values

Returns:

A+

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.