org.jquantlib.math.matrixutilities

Class SVD

java.lang.Object

org.jquantlib.math.matrixutilities.SVD

public class SVD
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.data[S.addr.op(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:

JAMA

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
double	cond() Two norm condition number
double	norm2() Two norm
int	rank() Effective numerical matrix rank
Matrix	S() Return the diagonal matrix of singular values
Array	singularValues() Return the one-dimensional array of singular values
Matrix	U() Return the left singular vectors
Matrix	V() Return the right singular vectors

Methods inherited from class java.lang.Object

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

Constructor Detail

SVD

public SVD(Matrix A)

Construct the singular value decomposition

Parameters:

A - is a rectangular matrix

Method Detail

U

public Matrix U()

Return the left singular vectors

Returns:

U

V

public Matrix V()

Return the right singular vectors

Returns:

V

singularValues

public Array singularValues()

Return the one-dimensional array of singular values

Returns:

diagonal of S.

S

public Matrix S()

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.