SLAMflex SE  0.1.0
SLAMflex provides detection and tracking of dominant planes for smartphone devices. This plane can then be used to show AR content relative to the plane orientation. The detection of plane is performed in the field of view of the smartphone camera. In subsequent frames it is tracked. The interface returns the plane position and orientation.
Public Member Functions | Static Public Attributes | Protected Member Functions | Protected Attributes | List of all members
TooN::GR_SVD< M, N, Precision, WANT_U, WANT_V > Class Template Reference

#include <GR_SVD.h>

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)
 Get the pseudo-inverse $M^{\dagger}$. More...
 
void reorder ()
 Reorder the components so the singular values are in descending order. More...
 

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
 

Detailed Description

template<int M, int N, 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.

Definition at line 60 of file GR_SVD.h.

Constructor & Destructor Documentation

template<int M, int N, class Precision , bool WANT_U, bool WANT_V>
template<class Precision2 , class Base >
TooN::GR_SVD< M, N, Precision, WANT_U, WANT_V >::GR_SVD ( const Matrix< M, N, Precision2, Base > &  A)

Definition at line 148 of file GR_SVD.h.

Member Function Documentation

template<int M, int N, class Precision , bool WANT_U, bool WANT_V>
void TooN::GR_SVD< M, N, Precision, WANT_U, WANT_V >::Accumulate_LHS ( )
protected

Definition at line 281 of file GR_SVD.h.

template<int M, int N, class Precision , bool WANT_U, bool WANT_V>
void TooN::GR_SVD< M, N, Precision, WANT_U, WANT_V >::Accumulate_RHS ( )
protected

Definition at line 248 of file GR_SVD.h.

template<int M, int N, class Precision = DefaultPrecision, bool WANT_U = 1, bool WANT_V = 1>
template<int Rows2, int Cols2, typename P2 , typename B2 >
Matrix<N,Cols2, typename Internal::MultiplyType<Precision,P2>::type > TooN::GR_SVD< M, N, Precision, WANT_U, WANT_V >::backsub ( const Matrix< Rows2, Cols2, P2, B2 > &  rhs,
const Precision  condition = 1e9 
)
inline

Calculate result of multiplying the (pseudo-)inverse of M by another matrix. For a matrix $A$, this calculates $M^{\dagger}A$ by back substitution (i.e. without explictly calculating the (pseudo-)inverse). See the detailed description for a description of condition variables.

Definition at line 96 of file GR_SVD.h.

template<int M, int N, class Precision = DefaultPrecision, bool WANT_U = 1, bool WANT_V = 1>
template<int Size, typename P2 , typename B2 >
Vector<N, typename Internal::MultiplyType<Precision,P2>::type > TooN::GR_SVD< M, N, Precision, WANT_U, WANT_V >::backsub ( const Vector< Size, P2, B2 > &  rhs,
const Precision  condition = 1e9 
)
inline

Calculate result of multiplying the (pseudo-)inverse of M by a vector. For a vector $b$, this calculates $M^{\dagger}b$ by back substitution (i.e. without explictly calculating the (pseudo-)inverse). See the detailed description for a description of condition variables.

Definition at line 109 of file GR_SVD.h.

template<int M, int N, class Precision , bool WANT_U, bool WANT_V>
void TooN::GR_SVD< M, N, Precision, WANT_U, WANT_V >::Bidiagonalize ( )
protected

Definition at line 159 of file GR_SVD.h.

template<int M, int N, class Precision , bool WANT_U, bool WANT_V>
void TooN::GR_SVD< M, N, Precision, WANT_U, WANT_V >::Diagonalize ( )
protected

Definition at line 320 of file GR_SVD.h.

template<int M, int N, class Precision , bool WANT_U, bool WANT_V>
bool TooN::GR_SVD< M, N, Precision, WANT_U, WANT_V >::Diagonalize_SubLoop ( int  k,
Precision &  z 
)
protected

Definition at line 347 of file GR_SVD.h.

template<int M, int N, class Precision = DefaultPrecision, bool WANT_U = 1, bool WANT_V = 1>
const Vector<N, Precision>& TooN::GR_SVD< M, N, Precision, WANT_U, WANT_V >::get_diagonal ( )
inline

Definition at line 71 of file GR_SVD.h.

template<int M, int N, class Precision = DefaultPrecision, bool WANT_U = 1, bool WANT_V = 1>
void TooN::GR_SVD< M, N, Precision, WANT_U, WANT_V >::get_inv_diag ( Vector< N > &  inv_diag,
const Precision  condition 
)
inline

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_diagVector in which to return the inverse diagonal.
conditionElements must be larger than this factor times the largest diagonal element to be considered well scaled.

Definition at line 82 of file GR_SVD.h.

template<int M, int N, class Precision , bool WANT_U, bool WANT_V>
Precision TooN::GR_SVD< M, N, Precision, WANT_U, WANT_V >::get_largest_singular_value ( )

Definition at line 461 of file GR_SVD.h.

template<int M, int N, class Precision = DefaultPrecision, bool WANT_U = 1, bool WANT_V = 1>
Matrix<N,M,Precision> TooN::GR_SVD< M, N, Precision, WANT_U, WANT_V >::get_pinv ( const Precision  condition = 1e9)
inline

Get the pseudo-inverse $M^{\dagger}$.

Definition at line 117 of file GR_SVD.h.

template<int M, int N, class Precision , bool WANT_U, bool WANT_V>
Precision TooN::GR_SVD< M, N, Precision, WANT_U, WANT_V >::get_smallest_singular_value ( )

Definition at line 470 of file GR_SVD.h.

template<int M, int N, class Precision , bool WANT_U, bool WANT_V>
int TooN::GR_SVD< M, N, Precision, WANT_U, WANT_V >::get_smallest_singular_value_index ( )

Definition at line 479 of file GR_SVD.h.

template<int M, int N, class Precision = DefaultPrecision, bool WANT_U = 1, bool WANT_V = 1>
const Matrix<M,N,Precision>& TooN::GR_SVD< M, N, Precision, WANT_U, WANT_V >::get_U ( )
inline

Definition at line 69 of file GR_SVD.h.

template<int M, int N, class Precision = DefaultPrecision, bool WANT_U = 1, bool WANT_V = 1>
const Matrix<N,N,Precision>& TooN::GR_SVD< M, N, Precision, WANT_U, WANT_V >::get_V ( )
inline

Definition at line 70 of file GR_SVD.h.

template<int M, int N, class Precision , bool WANT_U, bool WANT_V>
void TooN::GR_SVD< M, N, Precision, WANT_U, WANT_V >::reorder ( )

Reorder the components so the singular values are in descending order.

Definition at line 494 of file GR_SVD.h.

Member Data Documentation

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

Definition at line 141 of file GR_SVD.h.

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

Definition at line 66 of file GR_SVD.h.

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

Definition at line 136 of file GR_SVD.h.

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

Definition at line 137 of file GR_SVD.h.

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

Definition at line 139 of file GR_SVD.h.

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

Definition at line 140 of file GR_SVD.h.

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

Definition at line 67 of file GR_SVD.h.

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

Definition at line 134 of file GR_SVD.h.

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

Definition at line 135 of file GR_SVD.h.

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