SVD< Real > Class Template Reference

#include <jama_svd.h>

Public Member Functions
	SVD (const Array2D< Real > &Arg)
void	getU (Array2D< Real > &A)
void	getV (Array2D< Real > &A)
void	getSingularValues (Array1D< Real > &x)
void	getS (Array2D< Real > &A)
double	norm2 ()
double	cond ()
int	rank ()

Private Attributes
Array2D< Real >	U
Array2D< Real >	V
Array1D< Real >	s
int	m
int	n

Detailed Description

template<class Real>
class JAMA::SVD< Real >

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.

(Adapted from JAMA, a Java Matrix Library, developed by jointly by the Mathworks and NIST; see http://math.nist.gov/javanumerics/jama).

Constructor & Destructor Documentation

SVD()

SVD ( const Array2D< Real > &  Arg )

inline

References Array2D< T >::copy(), Array2D< T >::dim1(), Array2D< T >::dim2(), and TNT::hypot().

Member Function Documentation

cond()

double cond ( )

inline

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

getS()

void getS ( Array2D< Real > &  A )

inline

Return the diagonal matrix of singular values

Returns

S

getSingularValues()

void getSingularValues ( Array1D< Real > &  x )

inline

Return the one-dimensional array of singular values

getU()

void getU ( Array2D< Real > &  A )

inline

getV()

void getV ( Array2D< Real > &  A )

inline

norm2()

double norm2 ( )

inline

Two norm (max(S))

rank()

int rank ( )

inline

Effective numerical matrix rank

Returns

Number of nonnegligible singular values.

References Array1D< T >::dim().

Member Data Documentation

m

int m

private

n

int n

private

s

Array1D<Real> s

private

U

Array2D<Real> U

private

V

Array2D<Real> V

private

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The documentation for this class was generated from the following file:

• src/essentia/utils/tnt/jama_svd.h