PseudoInverse Class Reference

handles (weighted) pseudo-inverses and related operations. More...

#include <pinv.hpp>

Public Member Functions
double	derivsv (const double *Adot, int strideAdot, int svnr)
void	inverse (const double y, double x, double eps)
void	inverseWithNullSpace (const double y, double x, const double *xd, double eps)
int	prepare (const double _A, int _strideA, int _m, int _n, const double _Ly, const double *_Lx, int nrOfIts)
	prepares for solving Ax=y by calculating the singular value decomposition.
	PseudoInverse (int _maxsize)
int	smallestSV (double eps)
	Smallest eigenvalue larger then eps.
	~PseudoInverse ()
Public Attributes
const double *	A
const double *	Lx
const double *	Ly
int	m
int	n
int *	ndx
bool	prepared
	the prepare method() has been called
double *	S
int	strideA
int	strideU
	the stride for U.
int	strideV
	the stride for V
double *	U
	left orthonormal matrix when prepare() is called, U contains the left orthonormal matrix of the singular value decomposition.
double *	V
	right orthonormal matrix when prepare is called, V contains the right orthonormal matrix of the singular value decomposition.
Private Attributes
int	maxsize
double *	tmp
double *	y2

Detailed Description

handles (weighted) pseudo-inverses and related operations.

Definition at line 49 of file pinv.hpp.

Constructor & Destructor Documentation

PseudoInverse::PseudoInverse ( int _maxsize )

Allocate temporary space for calculating the pseudo-inverse of a matrix with maxrows rows or less , and maxcols collumns or less. maxrows > maxcols, because if nrofrows < nrofcols, extra rows have to be added to the matrix.

Definition at line 304 of file pinv.cpp.

PseudoInverse::~PseudoInverse ( )

Definition at line 318 of file pinv.cpp.

Member Function Documentation

double PseudoInverse::derivsv	(	const double *	Adot,
		int	strideAdot,
		int	svnr
	)

function to calculate :

$\frac{\partial \tilde{\sigma}_r }{\partial x_i} = u^T_r L_y \frac{\partial A }{\partial x_i} L^{-1}_x v_r$

Parameters:

`[in]`	Adot	the derivative (towards some variable) of the A matrix
`[in]`	strideAdot
`[in]`	svnr	indicates for which singular value the derivative is taken.

Warning:: prepare() should have been called

Definition at line 460 of file pinv.cpp.

void PseudoInverse::inverse	(	const double *	y,
		double *	x,
		double	eps
	)

solves an equation with the weighted pseudo-inverse
given : A.x = y

Calculates x = A# y for the prepared matrix and weights.

Warning:: first call prepare()

Parameters:

`[in]`	y	right hand side of the equations
`[out]`	x
`[in]`	eps	tollerance for determining the nullspace. This is lowest value a singular value may have without entering the nullspace.

Warning:: uses the U, V, S members; changes the tmp member

Definition at line 327 of file pinv.cpp.

void PseudoInverse::inverseWithNullSpace	(	const double *	y,
		double *	x,
		const double *	xd,
		double	eps
	)

given : y = A.x
Calculates x = A# y + (I-A# A) xd with A the weighted inverse
A is specified with the prepare() method.
Method : uses x = A# ( y -A.xd) + xd and calculates this via S.V.D.
Parameters:

[in] y

[out] x

[in] xd

[in] eps tollerance for determining the nullspace. This is lowest value a singular value may have without entering the nullspace.

Warning:
prepare() has to be called first.

uses inverse method;

changes y2 members;

Definition at line 356 of file pinv.cpp.

int PseudoInverse::prepare	(	const double *	_A,
		int	_strideA,
		int	_m,
		int	_n,
		const double *	_Ly,
		const double *	_Lx,
		int	nrOfIts
	)

prepares for solving Ax=y by calculating the singular value decomposition.

prepare calculations for solving equations A.x = y.

Parameters:

`[in]`	A
`[in]`	strideA	: stride of A, i.e. the amount of elements in the array between each row of A
`[in]`	m	number of rows of A.
`[in]`	n	number of columns of A.
`[in]`	Ly	vector describing the square root of the diagonal weight matrix in y-space, has m elements.
`[in]`	Lx	vector describing the square root of the diagonal weight matrix in x-space, has n elements.
`[in]`	nrOfIts	maximal number of iterations while calculating the singular value decomposition of A.

Returns:: 0 if successfull.

Warning:: a REFERENCE to _A,_Lx,_Ly is kept. So do not change these variables as long as you want to perform additional operations.

prepare calculations for solving equations A.x = y.

Parameters:

`[in]`	A
`[in]`	strideA	: stride of A, i.e. the amount of elements in the array between each row of A
`[in]`	m	number of rows of A.
`[in]`	n	number of columns of A.
`[in]`	Lx	vector describing the square root of the diagonal weight matrix in x-space, has n elements.
`[in]`	Ly	vector describing the square root of the diagonal weight matrix in y-space, has m elements.

Returns:: 0 if successfull.

Warning:: changes the U, V, S, tmp members

Definition at line 409 of file pinv.cpp.

int PseudoInverse::smallestSV ( double eps )

Smallest eigenvalue larger then eps.

Parameters:

eps

: tollerance level, singular values smaller than eps are considered to be zero.

Returns:: the index into S of the smallest eigenvalue larger then eps.

Definition at line 451 of file pinv.cpp.

Member Data Documentation

const double* PseudoInverse::A

a reference to the matrix of which you take the pseudo-inverse

Definition at line 58 of file pinv.hpp.

const double* PseudoInverse::Lx

weights in x-space

Definition at line 68 of file pinv.hpp.

const double* PseudoInverse::Ly

weights in y-space

Definition at line 73 of file pinv.hpp.

int PseudoInverse::m

nr of rows

Definition at line 78 of file pinv.hpp.

int PseudoInverse::maxsize [private]

Definition at line 50 of file pinv.hpp.

int PseudoInverse::n

nr of columns

Definition at line 83 of file pinv.hpp.

int* PseudoInverse::ndx

index to determine the sorted singular values : i = ndx[j], where j==1 corresponds to the largest, and j==n corresponds to the smallest singular value and where i corresponds to the index in S.

Definition at line 118 of file pinv.hpp.

bool PseudoInverse::prepared

the prepare method() has been called

Definition at line 88 of file pinv.hpp.

double* PseudoInverse::S

array containing the diagonal elements of $\Sigma$