TNT::Linear_Algebra::SVD< Real > Class Template Reference

#include <tnt_linalg.h>

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

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Detailed Description

template<class Real>
class TNT::Linear_Algebra::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).

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Member Function Documentation

template<class Real >

double TNT::Linear_Algebra::SVD< Real >::cond

(

)

[inline]

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

template<class Real >

void TNT::Linear_Algebra::SVD< Real >::getS

(

Matrix< Real > &

A

)

[inline]

Return the diagonal matrix of singular values

Returns:

S

template<class Real >

void TNT::Linear_Algebra::SVD< Real >::getSingularValues

(

Vector< Real > &

x

)

[inline]

Return the one-dimensional array of singular values

template<class Real >

double TNT::Linear_Algebra::SVD< Real >::norm2

(

)

[inline]

Two norm (max(S))

template<class Real >

int TNT::Linear_Algebra::SVD< Real >::rank

(

)

[inline]

Effective numerical matrix rank

Returns:

Number of nonnegligible singular values.

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

• tnt/tnt_linalg.h