Public Member Functions | Public Attributes | Private Attributes
PseudoInverse Class Reference

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

#include <pinv.hpp>

List of all members.

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]Adotthe derivative (towards some variable) of the A matrix
[in]strideAdot
[in]svnrindicates 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]yright hand side of the equations
    [out]x
    [in]epstollerance 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]epstollerance 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]mnumber of rows of A.
    [in]nnumber of columns of A.
    [in]Lyvector describing the square root of the diagonal weight matrix in y-space, has m elements.
    [in]Lxvector describing the square root of the diagonal weight matrix in x-space, has n elements.
    [in]nrOfItsmaximal 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]mnumber of rows of A.
    [in]nnumber of columns of A.
    [in]Lxvector describing the square root of the diagonal weight matrix in x-space, has n elements.
    [in]Lyvector 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 $

Definition at line 112 of file pinv.hpp.

int PseudoInverse::strideA

stride A

Definition at line 63 of file pinv.hpp.

int PseudoInverse::strideU

the stride for U.

Definition at line 98 of file pinv.hpp.

int PseudoInverse::strideV

the stride for V

Definition at line 108 of file pinv.hpp.

double* PseudoInverse::tmp [private]

Definition at line 51 of file pinv.hpp.

double* PseudoInverse::U

left orthonormal matrix when prepare() is called, U contains the left orthonormal matrix of the singular value decomposition.

Definition at line 94 of file pinv.hpp.

double* PseudoInverse::V

right orthonormal matrix when prepare is called, V contains the right orthonormal matrix of the singular value decomposition.

Definition at line 104 of file pinv.hpp.

double* PseudoInverse::y2 [private]

Definition at line 52 of file pinv.hpp.

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

orocos_kdl
Author(s): Ruben Smits, Erwin Aertbelien, Orocos Developers
autogenerated on Sat Dec 28 2013 17:17:26