GR_SVD< M, N, Precision, WANT_U, WANT_V > Class Template Reference

Performs SVD and back substitute to solve equations. More...

#include <TooN/GR_SVD.h>

List of all members.

Public Member Functions
template<class Precision2 , class Base >
	GR_SVD (const Matrix< M, N, Precision2, Base > &A)
const Matrix< M, N, Precision > &	get_U ()
const Matrix< N, N, Precision > &	get_V ()
const Vector< N, Precision > &	get_diagonal ()
Precision	get_largest_singular_value ()
Precision	get_smallest_singular_value ()
int	get_smallest_singular_value_index ()
void	get_inv_diag (Vector< N > &inv_diag, const Precision condition)
template<int Rows2, int Cols2, typename P2 , typename B2 >
Matrix< N, Cols2, typename Internal::MultiplyType < Precision, P2 >::type >	backsub (const Matrix< Rows2, Cols2, P2, B2 > &rhs, const Precision condition=1e9)
template<int Size, typename P2 , typename B2 >
Vector< N, typename Internal::MultiplyType < Precision, P2 >::type >	backsub (const Vector< Size, P2, B2 > &rhs, const Precision condition=1e9)
Matrix< N, M, Precision >	get_pinv (const Precision condition=1e9)
void	reorder ()
Static Public Attributes
static const int	BigDim = M>N?M:N
static const int	SmallDim = M<N?M:N
Protected Member Functions
void	Bidiagonalize ()
void	Accumulate_RHS ()
void	Accumulate_LHS ()
void	Diagonalize ()
bool	Diagonalize_SubLoop (int k, Precision &z)
Protected Attributes
Vector< N, Precision >	vDiagonal
Vector< BigDim, Precision >	vOffDiagonal
Matrix< M, N, Precision >	mU
Matrix< N, N, Precision >	mV
int	nError
int	nIterations
Precision	anorm

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Detailed Description

template<int M, int N = M, class Precision = DefaultPrecision, bool WANT_U = 1, bool WANT_V = 1>
class TooN::GR_SVD< M, N, Precision, WANT_U, WANT_V >

Performs SVD and back substitute to solve equations.

This code is a c++ translation of the FORTRAN routine give in George E. Forsythe et al, Computer Methods for Mathematical Computations, Prentice-Hall 1977. That code itself is a translation of the ALGOL routine by Golub and Reinsch, Num. Math. 14, 403-420, 1970.

N.b. the singular values returned by this routine are not sorted. N.b. this also means that even for MxN matrices with M<N, N singular values are computed and used.

The template parameters WANT_U and WANT_V may be set to false to indicate that U and/or V are not needed for a minor speed-up.

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Member Function Documentation

void get_inv_diag	(	Vector< N > &	inv_diag,
		const Precision	condition
	)

Return the pesudo-inverse diagonal.

The reciprocal of the diagonal elements is returned if the elements are well scaled with respect to the largest element, otherwise 0 is returned.

Parameters:

inv_diag	Vector in which to return the inverse diagonal.
condition	Elements must be larger than this factor times the largest diagonal element to be considered well scaled.

Referenced by GR_SVD< M, N, Precision, WANT_U, WANT_V >::backsub(), and GR_SVD< M, N, Precision, WANT_U, WANT_V >::get_pinv().

Matrix<N,Cols2, typename Internal::MultiplyType<Precision,P2>::type > backsub	(	const Matrix< Rows2, Cols2, P2, B2 > &	rhs,
		const Precision	condition = 1e9
	)

Calculate result of multiplying the (pseudo-)inverse of M by another matrix.

For a matrix , this calculates by back substitution (i.e. without explictly calculating the (pseudo-)inverse). See the detailed description for a description of condition variables.

References GR_SVD< M, N, Precision, WANT_U, WANT_V >::get_inv_diag().

Vector<N, typename Internal::MultiplyType<Precision,P2>::type > backsub	(	const Vector< Size, P2, B2 > &	rhs,
		const Precision	condition = 1e9
	)

Calculate result of multiplying the (pseudo-)inverse of M by a vector.

For a vector , this calculates by back substitution (i.e. without explictly calculating the (pseudo-)inverse). See the detailed description for a description of condition variables.

References GR_SVD< M, N, Precision, WANT_U, WANT_V >::get_inv_diag().