Essentia  2.1-beta6-dev
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).

## ◆ SVD()

 SVD ( const Array2D< Real > & Arg )
inline

## ◆ 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().

 int m
private

 int n
private

## ◆ s

 Array1D s
private

## ◆ U

 Array2D U
private

## ◆ V

 Array2D V
private

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