BIAS::Quadric3D Class Reference

A quadric as a 4x4 matrix describing a surface in 3d projective space defined by a quadratic equation, e.g. More...

#include <Geometry/Quadric3D.hh>

Inheritance diagram for BIAS::Quadric3D:

Collaboration diagram for BIAS::Quadric3D:

Public Types
typedef const T *	const_iterator
typedef const T &	const_reference
typedef T	element_type
typedef T *	iterator
typedef T *	pointer
typedef T &	reference
typedef Subscript	size_type
typedef T	value_type

Public Member Functions
void	AbsIP ()
	absolute values of all elements of the matrix (in place) More...
Matrix< QUADRIC3D_TYPE >	Adjoint () const
	computes the adjoint matrix More...
void	clear ()
	stl conform interface More...
QUADRIC3D_TYPE	det () const
	calculate the determinant recursively using sub matrices of size 3x3 More...
Subscript	dim (Subscript d) const
void	GaussJordan ()
	use the Gauss Jordan Algrithm to transform the matrix to reduced row echelon form. More...
Quadric3D	GetDualQuadric (bool UseSVD=false) const
	computes the dual quadric (points <-> planes) More...
Matrix< QUADRIC3D_TYPE >	GetMax (Matrix< QUADRIC3D_TYPE > &m)
	returns an matrix the same size as the matrix n and m with the largest elements taken from n or m More...
Matrix< QUADRIC3D_TYPE >	GetMin (Matrix< QUADRIC3D_TYPE > &m)
	returns an matrix the same size as the matrix n and m with the smallest elements taken from n or m More...
unsigned int	GetSignature ()
	computes signature of matrix, (no. More...
	initialize (M, N)
bool	IsIdentity (double eps=0.0) const
	Checks if the matrix a an identity. More...
bool	IsZero (double eps=0.0) const
	Checks if the matrix is a null matrix. More...
void	Kronecker (Matrix< QUADRIC3D_TYPE > const B, Matrix< QUADRIC3D_TYPE > &dest) const
	Kronecker-product with matrix, result in dest. More...
Subscript	lbound () const
double	LocatePoint (const HomgPoint3D &point3D) const
	determines if point3D is inside/on/outside the surface More...
void	Mult (const Vector4< QUADRIC3D_TYPE > &argvec, Vector4< QUADRIC3D_TYPE > &destvec) const
	matrix - vector multiplicate this matrix with Vector4, storing the result in destvec, calculates: destvec = (this Matrix) * argvec More...
void	Mult (const Matrix4x4< QUADRIC3D_TYPE > &argmat, Matrix4x4< QUADRIC3D_TYPE > &destmat) const
	matrix-matrix multiplication with other Matrix4x4, storing the result in destmat using 'manual inlining' More...
Matrix< T > &	newsize (Subscript M, Subscript N)
Matrix4x4 &	newsize (int rows, int cols)
	just neccessary to avoid resizing of this 'fixed size' matrix because it is derived from the resizable Matrix Should be removed if Matrix4x4 becomes a base class. More...
bool	Normalize ()
	sets trace of upperleft submatrix3x3 to unity More...
Subscript	num_cols () const
Subscript	num_rows () const
reference	operator() (Subscript i)
const_reference	operator() (Subscript i) const
reference	operator() (Subscript i, Subscript j)
const_reference	operator() (Subscript i, Subscript j) const
Quadric3D &	operator= (const Matrix< QUADRIC3D_TYPE > &M)
T *	operator[] (Subscript i)
const T *	operator[] (Subscript i) const
std::ostream &	Print (std::ostream &s, const int width, const int precision, bool scientific=true) const
std::ostream &	Print (std::ostream &s, const bool intCastOutput=false, const bool binaryOutput=false, const bool forceFullPrecision=false) const
std::ostream &	PrintPretty (std::ostream &s, const std::string &name="", const int width=8, const bool alignLeft=true) const
	Quadric3D ()
	Quadric3D (const MatrixInitType &i)
	set default matrix values More...
	Quadric3D (const Matrix< QUADRIC3D_TYPE > &M)
	Quadric3D (const HomgPoint3D &C, const CovMatrix3x3 &cov, const double &dScale=GAUSS3D_CONFIDENCE_20_PERCENT)
	constructs an ellipsoid around the center C More...
std::istream &	Read (std::istream &s, const bool intCastInput=false, const bool binaryInput=false)
	JW. More...
	set (value)
void	SetIdentity ()
	set the elements of this matrix to the identity matrix (posisbly overriding the inherited method) More...
Subscript	size () const
void	SwapRows (const int i, const int r)
	swaps two rows More...
Matrix4x4	Transpose () const
void	TransposeIP ()
	tranpose this matrix "in place" example: 0 1 2 3 –> 0 4 8 12 4 5 6 7 –> 1 5 9 13 8 9 10 11 –> 2 6 10 14 12 13 14 15 –> 3 7 11 15 More...
void	Vec (Vector< QUADRIC3D_TYPE > &dest) const
	vec-operator returns the elements of the matrix columwise as vector More...
Arithmetic
void	Mult (const Matrix< QUADRIC3D_TYPE > &arg, Matrix< QUADRIC3D_TYPE > &result) const
	matrix multiplication, result is not allocated More...
void	Mult (const Matrix< QUADRIC3D_TYPE > &arg)
	in Place matrix multiplication this is equal to M = M * arg, but faster More...
void	Mult (const Vector< QUADRIC3D_TYPE > &arg, Vector< QUADRIC3D_TYPE > &result) const
	matrix vector multiplication, result is not allocated More...
void	AddIP (const QUADRIC3D_TYPE &scalar)
	in place addition function More...
void	AddIP (const Matrix< QUADRIC3D_TYPE > &arg)
	Adds arg to this. More...
void	SubIP (const Matrix< QUADRIC3D_TYPE > &arg)
	Subtracts arg from this this -= arg. More...
void	SubIP (const QUADRIC3D_TYPE &scalar)
	in place subtraction function More...
void	Add (const QUADRIC3D_TYPE &scalar, Matrix< QUADRIC3D_TYPE > &dest) const
	addition function, storing data destination matrix More...
void	Sub (const QUADRIC3D_TYPE &scalar, Matrix< QUADRIC3D_TYPE > &dest) const
	substraction function, storing data destination matrix More...
void	MultiplyIP (const QUADRIC3D_TYPE &scalar)
	in place multiplication function More...
void	Multiply (const QUADRIC3D_TYPE &scalar, Matrix< QUADRIC3D_TYPE > &dest) const
	multiplication function, storing data destination matrix More...
void	MultLeft (const Matrix< QUADRIC3D_TYPE > &arg)
	in Place matrix multiplication this is equal to M = arg*M, but faster More...
void	MultLeft (const Vector< QUADRIC3D_TYPE > &arg, Vector< QUADRIC3D_TYPE > &result) const
	vector matrix multiplication result=arg*this. More...
void	MultiplyWithTransposeOf (const Matrix< QUADRIC3D_TYPE > &arg, Matrix< QUADRIC3D_TYPE > &result) const
	matrix matrix multiplication for multiplication with the transpose of the given matrix, result=this*arg^T. More...
void	DivideIP (const QUADRIC3D_TYPE &scalar)
	in place division function More...
void	Divide (const QUADRIC3D_TYPE &scalar, Matrix< QUADRIC3D_TYPE > &dest) const
	division function, storing data destination matrix More...
void	DivideElementwise (const Matrix< QUADRIC3D_TYPE > &arg)
	elementwise division function in place More...
void	GetSystemMatrix (Matrix< QUADRIC3D_TYPE > &dest) const
	compute square system matrix dest = A^T * A More...
Get Functions
QUADRIC3D_TYPE	GetMax () const
	Returns the maximum value of the matrix elements. More...
QUADRIC3D_TYPE	GetMin () const
	Returns the minimum value of the matrix elements. More...
QUADRIC3D_TYPE *	GetData ()
	get the pointer to the data array of the matrix (for faster direct memeory access) More...
const QUADRIC3D_TYPE *	GetData () const
const QUADRIC3D_TYPE **	GetDataArray () const
	returns zero based arry for data access More...
QUADRIC3D_TYPE **	GetDataArray ()
QUADRIC3D_TYPE **	GetDataArray1 () const
	returns 1 based array to data access More...
unsigned int	GetRows () const
unsigned int	GetCols () const
const QUADRIC3D_TYPE *	GetDataLast () const
	Get a pointer to the last data element Do not use this on unitilized matrices with <= on pointers because on an unitilized matrix GetData() will be NULL and last Element < (typically FFFFF8) We don't want an if here for performance reasons of the innerst loop. More...
QUADRIC3D_TYPE *	GetDataLast ()
Vector< QUADRIC3D_TYPE >	GetRow (const int &row) const
	return a copy of row "row" of this matrix, zero based counting More...
Vector< QUADRIC3D_TYPE >	GetCol (const int &col) const
	return a copy of column "col", zero based counting More...
void	GetSubMatrix (const size_t startRow, const size_t startCol, const size_t numRows, const size_t numCols, Matrix< QUADRIC3D_TYPE > &submatrix) const
	return a submatrix from this. More...
void	GetSubMatrix (const Vector< int > &rows, const Vector< int > &cols, Matrix< QUADRIC3D_TYPE > &submatrix) const
	return a submatrix from this. More...
Matrix< QUADRIC3D_TYPE >	GetSubMatrix (const Vector< int > &rows, const Vector< int > &cols) const
	return a submatrix from this. More...
void	SetSubMatrix (const size_t startRowInThis, const size_t startColInThis, const Matrix< QUADRIC3D_TYPE > &submatrix, const size_t startRowInSub, const size_t startColInSub, const size_t numRows, const size_t numCols)
	sets a submatrix in this. More...
void	SetSubMatrix (const size_t startRowInThis, const size_t startColInThis, const Matrix3x3< QUADRIC3D_TYPE > &submatrix)
	sets a 3x3 submatrix in this. More...
void	SetSubMatrix (const size_t startRowInThis, const size_t startColInThis, const Vector3< QUADRIC3D_TYPE > &subvector)
	sets a 3x1 submatrix in this. More...
void	SetRow (const int row, const Vector< QUADRIC3D_TYPE > &data)
	set a row of matrix from vector More...
void	SetCol (const int row, const Vector< QUADRIC3D_TYPE > &data)
	set a col of matrix from vector More...
void	Set (const int row, const int col, const Matrix< QUADRIC3D_TYPE > &data)
	Copies the contents of data into this at the position indicated by row and col. More...
void	Set (const int row, const int col, const Vector< QUADRIC3D_TYPE > &data)
	Copies the contents of data into this at the position indicated by row and col. More...
void	SetTranspose (const int row, const int col, const Vector< QUADRIC3D_TYPE > &data)
	Copies the contents of data into this at the position indicated by row and col. More...
int	GetNumElements () const
	Returns the total number of elements. More...
void	GetMaxMin (QUADRIC3D_TYPE &max, QUADRIC3D_TYPE &min) const
	return biggest and smallest entry More...
void	GetAbsMaxMin (QUADRIC3D_TYPE &max, QUADRIC3D_TYPE &min) const
	return biggest and smallest absolute values More...
QUADRIC3D_TYPE	GetMean () const
	Returns the mean value of the matrix elements. More...
QUADRIC3D_TYPE	NormL1 () const
	Return the L1 norm: |a| + |b| + |c| + ... More...
double	NormL2 () const
	Return the L2 norm: a^2 + b^2 + c^2 + ... More...
double	NormFrobenius () const
	Return Frobenius norm = sqrt(trace(A^t * A)). More...
QUADRIC3D_TYPE	Trace () const
QUADRIC3D_TYPE	DetSquare () const
Set Functions
void	SetZero ()
	Sets all values to zero. More...
void	MakeSymmetric ()
	componentwise: this = 0.5(this + this^T) yields symmetric matrix only allowed for square shaped matrices More...
void	Fill (const QUADRIC3D_TYPE &scalar)
	Takes the elements of a Vector and put them as diagonal elements into a matrix. More...
Scaling and Normalization
void	NormalizeColsToOne (const int norm_row_index)
	divides each column of the matrix through the element norm_row_index. More...
void	NormalizeRowsToOne (const int norm_col_index)
	divides each row of the matrix through the element norm_col_index. More...
void	NormalizeRows ()
	Normalizes each row to L2 norm one. More...
void	NormalizeCols ()
	Normalizes each coloumn to L_2 norm one. More...
void	ScaleRow (int NoRow, QUADRIC3D_TYPEscale)
	Scales row NoRow with scale. More...
void	ScaleCol (int NoCol, QUADRIC3D_TYPEscale)
	Scales column NoCol with scale. More...
Input / Output
bool	Load (const std::string &filename)
	method to load directly from a given filename. More...
bool	Save (const std::string &filename) const
	method to save directly to a given filename. More...
int	WriteMatlab (std::ostream &ostr, const std::string &name) const
	Write the matrix in Matlab format to the given stream. More...
bool	BinRead (const char *filename) const
	This method reads a matrix from a given file in binary format. More...
bool	BinWrite (const char *filename) const
	This method writes a matrix to a given file in binary format. More...

Protected Member Functions
void	copy (const T *v)
void	destroy ()
void	initialize (Subscript M, Subscript N)
void	set (const T &val)

Protected Attributes
Subscript	m_
Subscript	mn_
Subscript	n_
T **	row_
T **	rowm1_
T *	v_
T *	vm1_

Related Functions
(Note that these are not member functions.)
template<class T >
Matrix< T >	operator* (const Matrix< T > &A, const Matrix< T > &B)
template<class T >
Vector< T >	operator* (const Matrix< T > &A, const Vector< T > &x)
template<class T >
Matrix< T >	operator+ (const Matrix< T > &A, const Matrix< T > &B)
template<class T >
Matrix< T >	operator- (const Matrix< T > &A, const Matrix< T > &B)
std::ostream &	operator<< (std::ostream &s, const Matrix< char > &A)
std::ostream &	operator<< (std::ostream &s, const Matrix< unsigned char > &A)
template<class T >
std::ostream &	operator<< (std::ostream &s, const Matrix< T > &A)
std::istream &	operator>> (std::istream &s, Matrix< unsigned char > &A)
std::istream &	operator>> (std::istream &s, Matrix< char > &A)
template<class T >
std::istream &	operator>> (std::istream &s, Matrix< T > &A)

Detailed Description

A quadric as a 4x4 matrix describing a surface in 3d projective space defined by a quadratic equation, e.g.

a sphere.

Quadric3D is a 4x4 matrix Q, which describes a surface in 3d. All points x that lie on this surface, fulfill x^T Q x = 0, which is a quadratic equation in the components of x. For quadrics such as spheres or ellipsoids you can check if a point is inside or outside the quadric using LocatePoint(), for others you can also get the "side" the point lies relative to the Quadric. If the Quadric is a normalized ellipsoid, points inside yield negative values while LocatePoint computes positive ones for points ouside.

Projective cameras map quadrics to conics (see Conic2D) in the image plane.

Construction of Quadrics (i.e. ellipsoids) from covariance matrices: You can construct a Quadric3D from a CovMatrix3x3, the 3d surface will then represent all points of some constant probability of the 3d-normal distribution. The decision which probability to choose as a threshold, and thus how large the ellipsoid should become, depends on the desired probability for a new measurement to lie inside the quadric.

The standard confidence region is the set of points which lie inside the ellipsoid defined by main axes' length = sigma_i The probability that a measurement falls into this region is only 20%. If you want to increase the confidence that a point falls into your ellipsoid, you may enlarge the main axes by multiplication with a constant factor (see 3D column in subsequent table). For comparison purposes, the coresponding factors for 1D/2D are also given in the table:

• 1-D 2-D 3-D Conf(%)
• 0.01 0.14 0.33 .. 01
• 0.06 0.32 0.59 .. 05
• 0.14 0.46 0.76 .. 10
• 0.25 0.66 1.00 .. 20
• 0.52 1.00 1.36 .. 39
• 0.68 1.18 1.54 .. 50
• 1.00 1.52 1.88 .. 68
• 1.64 2.15 2.50 .. 90
• 1.96 2.45 2.79 .. 95
• 2.58 3.04 3.37 .. 99
• 2.81 3.26 3.58 .. 99.5

Suppose you have a covariance matrix and want to create an ellipsoid, where 99% of new measurements will fall in. In that case you have to use main axes of length (sigma_i*3.37)

Author

koeser 10/2003

Examples:

ExampleConic.cpp.

Definition at line 106 of file Quadric3D.hh.

Member Typedef Documentation

template<class T>

typedef const T* TNT::Matrix< T >::const_iterator

inherited

Definition at line 78 of file cmat.h.

template<class T>

typedef const T& TNT::Matrix< T >::const_reference

inherited

Definition at line 79 of file cmat.h.

template<class T>

typedef T TNT::Matrix< T >::element_type

inherited

Definition at line 74 of file cmat.h.

template<class T>

typedef T* TNT::Matrix< T >::iterator

inherited

Definition at line 76 of file cmat.h.

template<class T>

typedef T* TNT::Matrix< T >::pointer

inherited

Definition at line 75 of file cmat.h.

template<class T>

typedef T& TNT::Matrix< T >::reference

inherited

Definition at line 77 of file cmat.h.

template<class T>

typedef Subscript TNT::Matrix< T >::size_type

inherited

Definition at line 72 of file cmat.h.

template<class T>

typedef T TNT::Matrix< T >::value_type

inherited

Definition at line 73 of file cmat.h.

Constructor & Destructor Documentation

BIAS::Quadric3D::Quadric3D ( )

inline

Definition at line 110 of file Quadric3D.hh.

BIAS::Quadric3D::Quadric3D ( const MatrixInitType &  i )

inlineexplicit

set default matrix values

Definition at line 113 of file Quadric3D.hh.

BIAS::Quadric3D::Quadric3D ( const Matrix< QUADRIC3D_TYPE > &  M )

inline

Definition at line 116 of file Quadric3D.hh.

Quadric3D::Quadric3D	(	const HomgPoint3D &	C,
		const CovMatrix3x3 &	cov,
		const double &	dScale = GAUSS3D_CONFIDENCE_20_PERCENT
	)

constructs an ellipsoid around the center C

The covariance matrix's stddevs along the main axes (multiplied by dSize) are used as the ellipsoid's radii for dsize==1 this is the standard confidence region (SCR) see Kanatani: "Statistical optimization ...", p.122 The probability that the point is in the SCR is about 20% See doc above for values for other probabilities

Definition at line 36 of file Quadric3D.cpp.

References BIAS::Matrix3x3< T >::GetInverse(), BIAS::SVD::GetS(), BIAS::SVD::GetU(), BIAS::SVD::GetV(), BIAS::Matrix4x4< T >::SetIdentity(), BIAS::Matrix3x3< T >::SetZero(), BIAS::Matrix< T >::Transpose(), and BIAS::Matrix4x4< T >::Transpose().

Member Function Documentation

void BIAS::Matrix< QUADRIC3D_TYPE >::AbsIP ( )

inherited

absolute values of all elements of the matrix (in place)

Author

bangerer 01/2009

void BIAS::Matrix< QUADRIC3D_TYPE >::Add ( const QUADRIC3D_TYPE &  scalar, Matrix< QUADRIC3D_TYPE > &  dest  ) const

inlineinherited

addition function, storing data destination matrix

implementation

Author

Ingo Thomsen tested

void BIAS::Matrix< QUADRIC3D_TYPE >::AddIP ( const QUADRIC3D_TYPE &  scalar )

inlineinherited

in place addition function

Author

Ingo Thomsen tested

Definition at line 415 of file Matrix.hh.

void BIAS::Matrix< QUADRIC3D_TYPE >::AddIP ( const Matrix< QUADRIC3D_TYPE > &  arg )

inlineinherited

Adds arg to this.

Author

grest,2004

Matrix<QUADRIC3D_TYPE > BIAS::Matrix< QUADRIC3D_TYPE >::Adjoint ( ) const

inlineinherited

computes the adjoint matrix

Author

Christian Beder

bool BIAS::Matrix< QUADRIC3D_TYPE >::BinRead ( const char *  filename ) const

inherited

This method reads a matrix from a given file in binary format.

The file is not human read-/editable but provides full precision. A dimension check is performed.

Returns

true on success

Author

mdunda 04 2004

bool BIAS::Matrix< QUADRIC3D_TYPE >::BinWrite ( const char *  filename ) const

inherited

This method writes a matrix to a given file in binary format.

The file is not human read-/editable but provides full precision.

Returns

true on success

Author

mdunda 04 2004

void BIAS::Matrix4x4< QUADRIC3D_TYPE >::clear ( )

inlinevirtualinherited

stl conform interface

Reimplemented from BIAS::Matrix< QUADRIC3D_TYPE >.

Definition at line 281 of file Matrix4x4.hh.

template<class T>

void TNT::Matrix< T >::copy ( const T *  v )

inlineprotectedinherited

Definition at line 122 of file cmat.h.

Referenced by TNT::Matrix< BIAS::BIAS::Vector< int > >::Matrix(), and TNT::Matrix< BIAS::BIAS::Vector< int > >::operator=().

template<class T>

void TNT::Matrix< T >::destroy ( )

inlineprotectedinherited

Definition at line 181 of file cmat.h.

Referenced by TNT::Matrix< BIAS::BIAS::Vector< int > >::newsize(), TNT::Matrix< BIAS::BIAS::Vector< int > >::operator=(), and TNT::Matrix< BIAS::BIAS::Vector< int > >::~Matrix().

QUADRIC3D_TYPE BIAS::Matrix4x4< QUADRIC3D_TYPE >::det ( ) const

inlineinherited

calculate the determinant recursively using sub matrices of size 3x3

Author

koeser 10/2003 experimental, slow implementation, not yet heavily tested

Definition at line 164 of file Matrix4x4.hh.

QUADRIC3D_TYPE BIAS::Matrix< QUADRIC3D_TYPE >::DetSquare ( ) const

inlineinherited

Author

koeser

Warning

very slow, generic implementation (order "n!"), better to use matrix decomposition (see BIAS/MathAlgo/Lapack.hh)

Definition at line 369 of file Matrix.hh.

template<class T>

Subscript TNT::Matrix< T >::dim ( Subscript  d ) const

inlineinherited

Definition at line 310 of file cmat.h.

void BIAS::Matrix< QUADRIC3D_TYPE >::Divide ( const QUADRIC3D_TYPE &  scalar, Matrix< QUADRIC3D_TYPE > &  dest  ) const

inlineinherited

division function, storing data destination matrix

Author

Ingo Thomsen tested

void BIAS::Matrix< QUADRIC3D_TYPE >::DivideElementwise ( const Matrix< QUADRIC3D_TYPE > &  arg )

inlineinherited

elementwise division function in place

Author

Ingo Schiller tested

void BIAS::Matrix< QUADRIC3D_TYPE >::DivideIP ( const QUADRIC3D_TYPE &  scalar )

inlineinherited

in place division function

Author

Ingo Thomsen tested

Definition at line 486 of file Matrix.hh.

void BIAS::Matrix< QUADRIC3D_TYPE >::Fill ( const QUADRIC3D_TYPE &  scalar )

inherited

Takes the elements of a Vector and put them as diagonal elements into a matrix.

The size of this Vector must be exactly min( matrix.width, matrix.height). Optionally all other elements may be set to zero

Author

Ingo Thomsen

Parameters

zero_others

Must be true, if all non-diagonal elements shall be set to zero

void BIAS::Matrix< QUADRIC3D_TYPE >::GaussJordan ( )

inherited

use the Gauss Jordan Algrithm to transform the matrix to reduced row echelon form.

Author

woelk 05/2008 www.vision-n.de

void BIAS::Matrix< QUADRIC3D_TYPE >::GetAbsMaxMin ( QUADRIC3D_TYPE &  max, QUADRIC3D_TYPE &  min  ) const

inherited

return biggest and smallest absolute values

Vector<QUADRIC3D_TYPE > BIAS::Matrix< QUADRIC3D_TYPE >::GetCol ( const int &  col ) const

inherited

return a copy of column "col", zero based counting

Author

Jan Woetzel

unsigned int BIAS::Matrix< QUADRIC3D_TYPE >::GetCols ( ) const

inlineinherited

Definition at line 204 of file Matrix.hh.

QUADRIC3D_TYPE * BIAS::Matrix< QUADRIC3D_TYPE >::GetData ( )

inlineinherited

get the pointer to the data array of the matrix (for faster direct memeory access)

the order of the data is linewise, which means an elemnt sequence of e.g. [0] = M(0,0) [1] = M(0,1) [2] = M(0,2) [3] = M(1,0) // next line [4] = M(1,1) ...

Author

Jan Woetzel

Returns

a pointer to the data array (beginning with GetData[0]) alpha (02/27/2002) -added const (jw) 03/12/2002

Definition at line 185 of file Matrix.hh.

const QUADRIC3D_TYPE * BIAS::Matrix< QUADRIC3D_TYPE >::GetData ( ) const

inlineinherited

Definition at line 188 of file Matrix.hh.

const QUADRIC3D_TYPE ** BIAS::Matrix< QUADRIC3D_TYPE >::GetDataArray ( ) const

inlineinherited

returns zero based arry for data access

Definition at line 192 of file Matrix.hh.

QUADRIC3D_TYPE ** BIAS::Matrix< QUADRIC3D_TYPE >::GetDataArray ( )

inlineinherited

Definition at line 195 of file Matrix.hh.

QUADRIC3D_TYPE ** BIAS::Matrix< QUADRIC3D_TYPE >::GetDataArray1 ( ) const

inlineinherited

returns 1 based array to data access

Definition at line 199 of file Matrix.hh.

const QUADRIC3D_TYPE * BIAS::Matrix< QUADRIC3D_TYPE >::GetDataLast ( ) const

inlineinherited

Get a pointer to the last data element Do not use this on unitilized matrices with <= on pointers because on an unitilized matrix GetData() will be NULL and last Element < (typically FFFFF8) We don't want an if here for performance reasons of the innerst loop.

Author

Ingo Thomsen, Jan Woetzel

Date

04/11/2002

Definition at line 213 of file Matrix.hh.

QUADRIC3D_TYPE * BIAS::Matrix< QUADRIC3D_TYPE >::GetDataLast ( )

inlineinherited

Definition at line 219 of file Matrix.hh.

Quadric3D Quadric3D::GetDualQuadric

(

bool

UseSVD = false

)

const

computes the dual quadric (points <-> planes)

Parameters

UseSVD

use numerically robust svd or fast analytic inverse

Author

koeser 03/2005

Definition at line 121 of file Quadric3D.cpp.

References BIAS::SVD::Invert().

Referenced by BIAS::Conic2D::SetQuadricProjection().

Matrix<QUADRIC3D_TYPE > BIAS::Matrix< QUADRIC3D_TYPE >::GetMax ( Matrix< QUADRIC3D_TYPE > &  m )

inherited

returns an matrix the same size as the matrix n and m with the largest elements taken from n or m

Author

bangerer 01/2009

QUADRIC3D_TYPE BIAS::Matrix< QUADRIC3D_TYPE >::GetMax ( ) const

inherited

Returns the maximum value of the matrix elements.

Author

Ingo Thomsen

Date

04/11/2002 tested

void BIAS::Matrix< QUADRIC3D_TYPE >::GetMaxMin ( QUADRIC3D_TYPE &  max, QUADRIC3D_TYPE &  min  ) const

inherited

return biggest and smallest entry

QUADRIC3D_TYPE BIAS::Matrix< QUADRIC3D_TYPE >::GetMean ( void  ) const

inherited

Returns the mean value of the matrix elements.

Author

Ingo Thomsen

Date

04/11/2002 tested

Matrix<QUADRIC3D_TYPE > BIAS::Matrix< QUADRIC3D_TYPE >::GetMin ( Matrix< QUADRIC3D_TYPE > &  m )

inherited

returns an matrix the same size as the matrix n and m with the smallest elements taken from n or m

Author

bangerer 01/2009

QUADRIC3D_TYPE BIAS::Matrix< QUADRIC3D_TYPE >::GetMin ( ) const

inherited

Returns the minimum value of the matrix elements.

Author

Ingo Thomsen

Date

04/11/2002 tested

int BIAS::Matrix< QUADRIC3D_TYPE >::GetNumElements ( ) const

inlineinherited

Returns the total number of elements.

Author

Ingo Thomsen

Date

04/11/2002 tested

Definition at line 321 of file Matrix.hh.

Vector<QUADRIC3D_TYPE > BIAS::Matrix< QUADRIC3D_TYPE >::GetRow ( const int &  row ) const

inherited

return a copy of row "row" of this matrix, zero based counting

Author

Jan Woetzel

unsigned int BIAS::Matrix< QUADRIC3D_TYPE >::GetRows ( ) const

inlineinherited

Definition at line 202 of file Matrix.hh.

unsigned int Quadric3D::GetSignature

(

)

computes signature of matrix, (no.

of neg. eigenvalues) - (no. of pos. eigenvalues) or vice versa if there are more pos. eigenvalues

Definition at line 91 of file Quadric3D.cpp.

References BIAS::SVD::GetS(), and BIAS::SVD::GetVT().

void BIAS::Matrix< QUADRIC3D_TYPE >::GetSubMatrix ( const size_t  startRow, const size_t  startCol, const size_t  numRows, const size_t  numCols, Matrix< QUADRIC3D_TYPE > &  submatrix  ) const

inherited

return a submatrix from this.

Start index is [startRow][startCol] end index is [startRow+numRows-1][startCol+numCols-1]. submatrix is resized to numRows/numCols if necessary.

Author

apetersen 12/2010

void BIAS::Matrix< QUADRIC3D_TYPE >::GetSubMatrix ( const Vector< int > &  rows, const Vector< int > &  cols, Matrix< QUADRIC3D_TYPE > &  submatrix  ) const

inherited

return a submatrix from this.

Similar to matlab notation (except indexing, starts with 0 of course!). Vectors rows = '1 3' and cols = '1 2' for matrix: / 1 2 3 \ | 4 5 6 | \ 7 8 9 / results in: / 1 2 \ \ 7 8 / Matrix has to be initialized!!!

Author

apetersen 7/2011

Matrix<QUADRIC3D_TYPE > BIAS::Matrix< QUADRIC3D_TYPE >::GetSubMatrix ( const Vector< int > &  rows, const Vector< int > &  cols  ) const

inherited

return a submatrix from this.

Similar to matlab notation (except indexing, starts with 0 of course!), see GetSubMatrix(const Vector<int> &rows, const Vector<int> &cols, Matrix<T> &submatrix)

Author

apetersen 7/2011

void BIAS::Matrix< QUADRIC3D_TYPE >::GetSystemMatrix ( Matrix< QUADRIC3D_TYPE > &  dest ) const

inlineinherited

compute square system matrix dest = A^T * A

Parameters

dest	holds result of this->Transpose * this

If you want to solve A * x = b, where A has more rows than columns, a common technique is to solve x = (A^T * A)^-1 * A^T * b. This function provides a fast way to compute A^T*A from A.

Author

grest/koeser

template<class T>

void TNT::Matrix< T >::initialize ( Subscript  M, Subscript  N  )

inlineprotectedinherited

Definition at line 95 of file cmat.h.

Referenced by TNT::Matrix< BIAS::BIAS::Vector< int > >::Matrix(), TNT::Matrix< BIAS::BIAS::Vector< int > >::newsize(), and TNT::Matrix< BIAS::BIAS::Vector< int > >::operator=().

template<class T>

TNT::Matrix< T >::initialize ( M  , N    )

inherited

bool BIAS::Matrix< QUADRIC3D_TYPE >::IsIdentity ( double  eps = 0.0 ) const

inherited

Checks if the matrix a an identity.

I.e. all elements with index i==j are equal 1 and all others are zero.

Author

mdunda 12 2003

Returns

true if matrix is identity

bool BIAS::Matrix< QUADRIC3D_TYPE >::IsZero ( double  eps = 0.0 ) const

inherited

Checks if the matrix is a null matrix.

Author

mdunda 12 2003

Returns

true if all elements are zero

void BIAS::Matrix< QUADRIC3D_TYPE >::Kronecker ( Matrix< QUADRIC3D_TYPE > const  B, Matrix< QUADRIC3D_TYPE > &  dest  ) const

inherited

Kronecker-product with matrix, result in dest.

Kronecker-product with matrix B, result in dest.

template<class T>

Subscript TNT::Matrix< T >::lbound ( ) const

inlineinherited

Definition at line 81 of file cmat.h.

bool BIAS::Matrix< QUADRIC3D_TYPE >::Load ( const std::string &  filename )

inherited

method to load directly from a given filename.

internally using stream operator

Author

Jan Woetzel 05/2003

Returns

false in case of error, true in case of success

double BIAS::Quadric3D::LocatePoint ( const HomgPoint3D &  point3D ) const

inline

determines if point3D is inside/on/outside the surface

For a normalized ellipsoid, a negative return value means the point is inside, a positive value means outside and 0 means exactly on the surface (you have to use epsilon environments for all tests) LocatePoint internally computes the difference of Mahalanobis distances of point3D from the center and a surface point from the center

Examples:

ExampleConic.cpp.

Definition at line 137 of file Quadric3D.hh.

void BIAS::Matrix< QUADRIC3D_TYPE >::MakeSymmetric ( )

inlineinherited

componentwise: this = 0.5(this + this^T) yields symmetric matrix only allowed for square shaped matrices

Author

koeser 01/2007

Definition at line 522 of file Matrix.hh.

void BIAS::Matrix4x4< QUADRIC3D_TYPE >::Mult ( const Vector4< QUADRIC3D_TYPE > &  argvec, Vector4< QUADRIC3D_TYPE > &  destvec  ) const

inlineinherited

matrix - vector multiplicate this matrix with Vector4, 

storing the result in destvec, calculates: destvec = (this Matrix) * argvec

Author

Jan Woetzel untested (04/17/2002)

Definition at line 121 of file Matrix4x4.hh.

void BIAS::Matrix4x4< QUADRIC3D_TYPE >::Mult ( const Matrix4x4< QUADRIC3D_TYPE > &  argmat, Matrix4x4< QUADRIC3D_TYPE > &  destmat  ) const

inlineinherited

matrix-matrix multiplication with other Matrix4x4, 

storing the result in destmat using 'manual inlining'

Author

Jan Woetzel untested (04/17/2002)

Definition at line 190 of file Matrix4x4.hh.

void BIAS::Matrix< QUADRIC3D_TYPE >::Mult ( const Matrix< QUADRIC3D_TYPE > &  arg, Matrix< QUADRIC3D_TYPE > &  result  ) const

inlineinherited

matrix multiplication, result is not allocated

Author

Felix Woelk

void BIAS::Matrix< QUADRIC3D_TYPE >::Mult ( const Matrix< QUADRIC3D_TYPE > &  arg )

inlineinherited

in Place matrix multiplication this is equal to M = M * arg, but faster

Author

Daniel Grest

void BIAS::Matrix< QUADRIC3D_TYPE >::Mult ( const Vector< QUADRIC3D_TYPE > &  arg, Vector< QUADRIC3D_TYPE > &  result  ) const

inlineinherited

matrix vector multiplication, result is not allocated

Author

Felix Woelk

void BIAS::Matrix< QUADRIC3D_TYPE >::Multiply ( const QUADRIC3D_TYPE &  scalar, Matrix< QUADRIC3D_TYPE > &  dest  ) const

inlineinherited

multiplication function, storing data destination matrix

Author

Ingo Thomsen tested

void BIAS::Matrix< QUADRIC3D_TYPE >::MultiplyIP ( const QUADRIC3D_TYPE &  scalar )

inlineinherited

in place multiplication function

Author

Ingo Thomsen tested

Definition at line 448 of file Matrix.hh.

void BIAS::Matrix< QUADRIC3D_TYPE >::MultiplyWithTransposeOf ( const Matrix< QUADRIC3D_TYPE > &  arg, Matrix< QUADRIC3D_TYPE > &  result  ) const

inlineinherited

matrix matrix multiplication for multiplication with the transpose of the given matrix, result=this*arg^T.

Author

Arne Petersen

void BIAS::Matrix< QUADRIC3D_TYPE >::MultLeft ( const Matrix< QUADRIC3D_TYPE > &  arg )

inlineinherited

in Place matrix multiplication this is equal to M = arg*M, but faster

Author

Daniel Grest

void BIAS::Matrix< QUADRIC3D_TYPE >::MultLeft ( const Vector< QUADRIC3D_TYPE > &  arg, Vector< QUADRIC3D_TYPE > &  result  ) const

inlineinherited

vector matrix multiplication result=arg*this.

Author

Marcel Lilienthal

template<class T>

Matrix<T>& TNT::Matrix< T >::newsize ( Subscript  M, Subscript  N  )

inlineinherited

Examples:

EvaluateAlignment.cpp, ExampleAlignment.cpp, ExampleIEKF.cpp, ExampleLeastSquares.cpp, ExampleRegressionPlane.cpp, and ExampleUncertaintyTransform.cpp.

Definition at line 269 of file cmat.h.

Referenced by BIAS::Matrix< T >::Add(), BIAS::RegionMatcher::BilinearRegion(), BIAS::RegionMatcher::BilinearRegionColor3(), BIAS::ComputeCovariance(), BIAS::LDA::ComputeReductionMatrix(), BIAS::PCA::ComputeReductionMatrix(), BIAS::ContourBSplineShapeMatrix::ComputeRegularisationMatrix(), BIAS::ContourBSplineData::ComputeSplineMetricMatrix_(), BIAS::Matrix< T >::Conv(), BIAS::CamPoseCalib::CreateSecDMatrix_(), BIAS::Matrix< T >::Divide(), Eigenproblem_quadratic_matrix(), BIAS::CamPoseCalib::Estimate(), BIAS::TrackerBaseAffine< StorageType >::EvaluateResult_(), BIAS::TrackerBaseAffine2< StorageType >::EvaluateResult_(), BIAS::TrackerBaseInterface< StorageType >::EvaluateResult_(), BIAS::TrackerBaseInterface< StorageType >::Filter_ByMask(), BIAS::TrackerBaseInterface< StorageType >::Filter_BySeparableMask(), BIAS::TrackerBaseInterface< StorageType >::Filter_GradXSobel3x3(), BIAS::TrackerBaseInterface< StorageType >::Filter_GradYSobel3x3(), BIAS::TrackerBaseInterface< StorageType >::FilterLowpass_Binomial3x3(), BIAS::TrackerBaseInterface< StorageType >::FilterLowpass_ByMask(), BIAS::TrackerBaseInterface< StorageType >::FilterLowpass_BySeparableMask(), Fortran_Matrix_to_Matrix(), generalised_eigenvalue_matrix_solve(), BIAS::LDA::GenerateRandomTestData(), BIAS::SparseMatrix::GetAsDense(), BIAS::Random::GetMeanAndCovariance(), BIAS::PMatrixLinear::GetPEstSystemHom(), BIAS::PMatrixLinear::GetPEstSystemInHom(), BIAS::Matrix< T >::GetSystemMatrix(), BIAS::Kalman::Init(), BIAS::IteratedExtendedKalman::Init(), BIAS::SparseMatrix::Invert(), BIAS::SparseMatrix::InvertAndSolve(), BIAS::Matrix< T >::Kronecker(), Lapack_Cholesky_SymmetricPositiveDefinit(), BIAS::RegionMatcher::LinearRegionX(), BIAS::LevenbergMarquardtBase::LM_Compute(), BIAS::LevenbergMarquardtBase::LM_ComputeWithoutJacobian(), TNT::matmult(), BIAS::Matrix< T >::Mult(), BIAS::Matrix< T >::Multiply(), BIAS::Matrix< T >::MultiplyWithTransposeOf(), BIAS::MxArrToBIASMatrix(), BIAS::Matrix3x4< T >::newsize(), BIAS::Matrix4x4< T >::newsize(), BIAS::TextureTransformHomography::ParameterInversionJacobian(), BIAS::TextureTransformAffine::ParameterInversionJacobian(), BIAS::TextureTransformDisparity::ParameterInversionJacobian(), BIAS::TextureTransformDisplacement::ParameterInversionJacobian(), BIAS::TextureTransformRotation::ParameterInversionJacobian(), BIAS::TextureTransformEuclidian::ParameterInversionJacobian(), BIAS::TextureTransformHomography::ParameterJacobianBackward(), BIAS::TextureTransformAffine::ParameterJacobianBackward(), BIAS::TextureTransformDisparity::ParameterJacobianBackward(), BIAS::TextureTransformDisplacement::ParameterJacobianBackward(), BIAS::TextureTransformRotation::ParameterJacobianBackward(), BIAS::TextureTransformEuclidian::ParameterJacobianBackward(), BIAS::TextureTransformSimilar::ParameterJacobianBackward(), BIAS::TextureTransform::ParameterJacobianBackward(), BIAS::TextureTransformAffine::ParameterJacobianForward(), BIAS::TextureTransformHomography::ParameterJacobianForward(), BIAS::TextureTransformDisparity::ParameterJacobianForward(), BIAS::TextureTransformDisplacement::ParameterJacobianForward(), BIAS::TextureTransformRotation::ParameterJacobianForward(), BIAS::TextureTransformSimilar::ParameterJacobianForward(), BIAS::TextureTransformEuclidian::ParameterJacobianForward(), BIAS::TextureTransform::ParameterJacobianForward(), BIAS::IteratedExtendedKalman::Predict(), BIAS::Covariance3Dto2D::Project(), BIAS::Covariance3Dto2DHomg::Project(), BIAS::QRFrac(), BIAS::RegionMatcher::RegionMatcher(), BIAS::ContourBSplineShapeMatrix::SetShapeSpaceEuclidian(), BIAS::ContourBSplineShapeMatrix::SetShapeSpaceIdentity(), BIAS::ContourBSplineShapeMatrix::SetShapeSpaceMatrix(), BIAS::ContourBSplineShapeMatrix::SetShapeSpacePlanarAffin(), BIAS::ContourBSplineShapeMatrix::SetSubShapeSpaceZero(), BIAS::Matrix< T >::Sub(), BIAS::TrackerBaseAffine< StorageType >::TrackAffine_(), BIAS::MonteCarloTransform::Transform(), BIAS::UnscentedTransform::Transform(), BIAS::IteratedExtendedKalman::Update(), and BIAS::Tracker< StorageType, CalculationType >::Vector2FilterMask_().

Matrix4x4& BIAS::Matrix4x4< QUADRIC3D_TYPE >::newsize ( int  rows, int  cols  )

inherited

just neccessary to avoid resizing of this 'fixed size' matrix because it is derived from the resizable Matrix

Should be removed if Matrix4x4 becomes a base class.

(04/17/2002) Jan Woetzel

bool BIAS::Quadric3D::Normalize ( )

inline

sets trace of upperleft submatrix3x3 to unity

Definition at line 141 of file Quadric3D.hh.

void BIAS::Matrix< QUADRIC3D_TYPE >::NormalizeCols ( )

inherited

Normalizes each coloumn to L_2 norm one.

Attention each column is normaized by its own scale!

void BIAS::Matrix< QUADRIC3D_TYPE >::NormalizeColsToOne ( const int  norm_row_index )

inherited

divides each column of the matrix through the element norm_row_index.

index runs [0..num_rows-1] for example: 2 3 4 5 normalized with row '1' will be 2/4 3/5 1 1

void BIAS::Matrix< QUADRIC3D_TYPE >::NormalizeRows ( )

inherited

Normalizes each row to L2 norm one.

Attention each row is normaized by its own scale!

void BIAS::Matrix< QUADRIC3D_TYPE >::NormalizeRowsToOne ( const int  norm_col_index )

inherited

divides each row of the matrix through the element norm_col_index.

index runs [0..num_cols-1] for example: 2 3 4 5 normalized with row '1' will be 2/3 1 4/5 1

double BIAS::Matrix< QUADRIC3D_TYPE >::NormFrobenius ( ) const

inlineinherited

Return Frobenius norm = sqrt(trace(A^t * A)).

this method is deprecated because it is equivalent to NormL2

This function is deprecated, because it is equivalent to NormL2.

Author

koeser 02/2004

QUADRIC3D_TYPE BIAS::Matrix< QUADRIC3D_TYPE >::NormL1 ( ) const

inlineinherited

Return the L1 norm: |a| + |b| + |c| + ...

Author

Ingo Thomsen

Date

04/11/2002 untested

double BIAS::Matrix< QUADRIC3D_TYPE >::NormL2 ( ) const

inlineinherited

Return the L2 norm: a^2 + b^2 + c^2 + ...

Author

woelk 07/2004

template<class T>

Subscript TNT::Matrix< T >::num_cols ( ) const

inlineinherited

Examples:

ExampleGenerateGauss.cpp.

Definition at line 320 of file cmat.h.

Referenced by BIAS::Matrix< T >::Add(), BIAS::Matrix< T >::AddIP(), BIAS::ImageAlignment::Align(), BIAS::CamPoseCalib::ApplyCoVariances_(), BIAS::ImageAlignment::AutoAlign(), BIAS::TFTensorEstimation::Compute(), BIAS::SVD3x3::Compute(), BIAS::GaussHelmert::ComputeNormalSystem_(), BIAS::LDA::ComputeReductionMatrix(), BIAS::PCA::ComputeReductionMatrix(), BIAS::ContourBSplineShapeMatrix::ComputeRegularisationMatrix(), BIAS::PCA::ComputeScatter(), BIAS::UnscentedTransform::ComputeSigmaPoints_(), BIAS::LDA::ComputeWithinAndInterClassCovs(), BIAS::Matrix< T >::Conv(), BIAS::Matrix< T >::Divide(), BIAS::Matrix< T >::DivideElementwise(), Eigenproblem_quadratic_matrix(), Eigenvalue_solve(), BIAS::CamPoseCalib::Estimate(), Fortran_Matrix_to_Matrix(), General_singular_value_decomposition(), generalised_eigenvalue_matrix_solve(), BIAS::CamPoseCalib::GetCov(), BIAS::CamPoseCalib::GetCoVarMatrix(), BIAS::SVD::GetNullvector(), BIAS::Matrix< T >::Kronecker(), Lapack_Cholesky_SymmetricPositiveDefinit(), Lapack_LLS_QR_linear_solve(), Lapack_LU_linear_solve(), Lapack_WLLS_solve(), TNT::matmult(), BIAS::Matrix2x2< T >::Matrix2x2(), BIAS::Matrix3x3< T >::Matrix3x3(), BIAS::Matrix4x4< T >::Matrix4x4(), BIAS::Matrix< T >::Mult(), TNT::mult_element(), BIAS::Matrix< T >::Multiply(), BIAS::Matrix< T >::MultiplyWithTransposeOf(), TNT::Matrix< BIAS::BIAS::Vector< int > >::newsize(), BIAS::TrackerBaseInterface< StorageType >::NormalizeRegion_(), BIAS::Vector< T >::operator*(), BIAS::Vector3< T >::operator*(), BIAS::Vector4< T >::operator*(), TNT::Matrix< T >::operator+(), TNT::Matrix< T >::operator-(), BIAS::Matrix3x4< T >::operator=(), BIAS::Matrix4x4< T >::operator=(), BIAS::PMatrix::PMatrix(), BIAS::PMatrixBase::PMatrixBase(), BIAS::CovTransformPose::PoseEulerZYXToQuat(), BIAS::CovTransformPose::PoseQuatToEulerZYX(), BIAS::IteratedExtendedKalman::Predict(), BIAS::Covariance3Dto2DHomg::Project(), BIAS::RMatrix::RMatrix(), BIAS::RMatrixBase::RMatrixBase(), BIAS::Matrix< T >::Set(), BIAS::RParametrization::SetCovarianceMatrix(), BIAS::PoseParametrization::SetCovarianceMatrix(), BIAS::EParametrization::SetCovarianceMatrix(), BIAS::LocalAffineFrame::SetFromMatrix(), BIAS::IteratedExtendedKalman::SetProcessCov(), BIAS::ContourBSplineShapeMatrix::SetShapeSpaceMatrix(), BIAS::IteratedExtendedKalman::SetState(), BIAS::ContourBSplineShapeMatrix::SetSubShapeSpaceZero(), BIAS::GaussHelmert::Solve(), BIAS::LeastSquaresSVD::Solve(), BIAS::SVD::Solve(), BIAS::CamPoseCalib::SolveLM_(), BIAS::ImageAlignment::StrictPyramidAlign(), BIAS::Matrix< T >::Sub(), BIAS::Matrix< T >::SubIP(), BIAS::SymmetricMatrix3x3< T >::SymmetricMatrix3x3(), BIAS::TrackerBaseAffine< StorageType >::TrackAffine_(), BIAS::MonteCarloTransform::Transform(), BIAS::UnscentedTransform::Transform(), BIAS::CovTransformPose::TransformPoint3D(), BIAS::CovTransformPose::TransformPose(), TNT::transpose(), BIAS::Kalman::Update(), BIAS::IteratedExtendedKalman::Update(), and Upper_symmetric_eigenvalue_solve().

template<class T>

Subscript TNT::Matrix< T >::num_rows ( ) const

inlineinherited

Examples:

ExampleGenerateGauss.cpp.

Definition at line 319 of file cmat.h.

Referenced by BIAS::Matrix< T >::Add(), BIAS::Matrix< T >::AddIP(), BIAS::ImageAlignment::Align(), BIAS::ImageAlignment::AutoAlign(), BIAS::SVD3x3::Compute(), BIAS::ImageBlender::ComputeCylCamGeometry(), BIAS::ImageBlenderIncremental::ComputeCylCamGeometry_(), BIAS::LDA::ComputeReductionMatrix(), BIAS::PCA::ComputeReductionMatrix(), BIAS::ContourBSplineShapeMatrix::ComputeRegularisationMatrix(), BIAS::PCA::ComputeScatter(), BIAS::UnscentedTransform::ComputeSigmaPoints_(), BIAS::LDA::ComputeWithinAndInterClassCovs(), BIAS::Matrix< T >::Conv(), BIAS::Matrix< T >::Divide(), BIAS::Matrix< T >::DivideElementwise(), Eigenproblem_quadratic_matrix(), Eigenvalue_solve(), BIAS::CamPoseCalib::Estimate(), Fortran_Matrix_to_Matrix(), General_singular_value_decomposition(), generalised_eigenvalue_matrix_solve(), BIAS::CamPoseCalib::GetCov(), BIAS::CamPoseCalib::GetCoVarMatrix(), BIAS::SVD::GetLeftNullvector(), BIAS::Kalman::Init(), BIAS::IteratedExtendedKalman::Init(), BIAS::Matrix< T >::Kronecker(), Lapack_Cholesky_SymmetricPositiveDefinit(), Lapack_LLS_QR_linear_solve(), Lapack_LU_linear_solve(), Lapack_WLLS_solve(), TNT::matmult(), BIAS::Matrix2x2< T >::Matrix2x2(), BIAS::Matrix3x3< T >::Matrix3x3(), BIAS::Matrix4x4< T >::Matrix4x4(), BIAS::Matrix< T >::Mult(), TNT::mult_element(), BIAS::Matrix< T >::Multiply(), BIAS::Matrix< T >::MultiplyWithTransposeOf(), BIAS::Matrix< T >::MultLeft(), TNT::Matrix< BIAS::BIAS::Vector< int > >::newsize(), BIAS::TrackerBaseInterface< StorageType >::NormalizeRegion_(), BIAS::Vector< T >::operator*(), BIAS::Vector3< T >::operator*(), BIAS::Vector4< T >::operator*(), TNT::Matrix< T >::operator+(), TNT::Matrix< T >::operator-(), BIAS::Matrix3x4< T >::operator=(), BIAS::Matrix4x4< T >::operator=(), BIAS::PMatrix::PMatrix(), BIAS::PMatrixBase::PMatrixBase(), BIAS::CovTransformPose::PoseEulerZYXToQuat(), BIAS::CovTransformPose::PoseQuatToEulerZYX(), BIAS::IteratedExtendedKalman::Predict(), BIAS::RMatrix::RMatrix(), BIAS::RMatrixBase::RMatrixBase(), BIAS::Matrix< T >::Set(), BIAS::RParametrization::SetCovarianceMatrix(), BIAS::PoseParametrization::SetCovarianceMatrix(), BIAS::EParametrization::SetCovarianceMatrix(), BIAS::LocalAffineFrame::SetFromMatrix(), BIAS::IteratedExtendedKalman::SetProcessCov(), BIAS::ContourBSplineShapeMatrix::SetShapeSpaceMatrix(), BIAS::IteratedExtendedKalman::SetState(), BIAS::ContourBSplineShapeMatrix::SetSubShapeSpaceZero(), BIAS::GaussHelmert::Solve(), BIAS::LeastSquaresSVD::Solve(), BIAS::SVD::Solve(), BIAS::CamPoseCalib::SolveLM_(), SquaredMahalanobisDistance(), BIAS::ImageAlignment::StrictPyramidAlign(), BIAS::Matrix< T >::Sub(), BIAS::Matrix< T >::SubIP(), BIAS::SymmetricMatrix3x3< T >::SymmetricMatrix3x3(), BIAS::TrackerBaseAffine2< StorageType >::TrackAffine_(), BIAS::MonteCarloTransform::Transform(), BIAS::UnscentedTransform::Transform(), BIAS::CovTransformPose::TransformPoint3D(), BIAS::CovTransformPose::TransformPose(), TNT::transpose(), BIAS::Kalman::Update(), BIAS::IteratedExtendedKalman::Update(), Upper_symmetric_eigenvalue_solve(), and BIAS::LeastSquaresLapack::WeightedSolve().

template<class T>

reference TNT::Matrix< T >::operator() ( Subscript  i )

inlineinherited

Definition at line 343 of file cmat.h.

template<class T>

const_reference TNT::Matrix< T >::operator() ( Subscript  i ) const

inlineinherited

Definition at line 352 of file cmat.h.

template<class T>

reference TNT::Matrix< T >::operator() ( Subscript  i, Subscript  j  )

inlineinherited

Definition at line 363 of file cmat.h.

template<class T>

const_reference TNT::Matrix< T >::operator() ( Subscript  i, Subscript  j  ) const

inlineinherited

Definition at line 376 of file cmat.h.

Quadric3D& BIAS::Quadric3D::operator= ( const Matrix< QUADRIC3D_TYPE > &  M )

inline

Definition at line 146 of file Quadric3D.hh.

References BIAS::Matrix4x4< T >::operator=().

template<class T>

T* TNT::Matrix< T >::operator[] ( Subscript  i )

inlineinherited

Definition at line 325 of file cmat.h.

template<class T>

const T* TNT::Matrix< T >::operator[] ( Subscript  i ) const

inlineinherited

Definition at line 334 of file cmat.h.

template<class T>

std::ostream& TNT::Matrix< T >::Print ( std::ostream &  s, const int  width, const int  precision, bool  scientific = true  ) const

inlineinherited

Author

Ingo Schiller

Examples:

ExampleSparseMatrix.cpp.

template<class T>

std::ostream& TNT::Matrix< T >::Print ( std::ostream &  s, const bool  intCastOutput = false, const bool  binaryOutput = false, const bool  forceFullPrecision = false  ) const

inlineinherited

Author

Jan Woetzel

template<class T>

std::ostream& TNT::Matrix< T >::PrintPretty ( std::ostream &  s, const std::string &  name = "", const int  width = 8, const bool  alignLeft = true  ) const

inlineinherited

Author

Sandro Esquivel

Examples:

ExampleSVD.cpp, and ExampleSVD3x3.cpp.

template<class T >

std::istream & TNT::Matrix< T >::Read ( std::istream &  s, const bool  intCastInput = false, const bool  binaryInput = false  )

inlineinherited

JW.

Author

Jan Woetzel

Definition at line 605 of file cmat.h.

Referenced by TNT::Matrix< T >::operator>>().

bool BIAS::Matrix< QUADRIC3D_TYPE >::Save ( const std::string &  filename ) const

inherited

method to save directly to a given filename.

internally using stream operator

Author

Jan Woetzel 05/2003

Returns

false in case of error, true in case of success

void BIAS::Matrix< QUADRIC3D_TYPE >::ScaleCol ( int  NoCol, QUADRIC3D_TYPE  scale  )

inherited

Scales column NoCol with scale.

void BIAS::Matrix< QUADRIC3D_TYPE >::ScaleRow ( int  NoRow, QUADRIC3D_TYPE  scale  )

inherited

Scales row NoRow with scale.

template<class T>

void TNT::Matrix< T >::set ( const T &  val )

inlineprotectedinherited

Definition at line 152 of file cmat.h.

Referenced by TNT::Matrix< BIAS::BIAS::Vector< int > >::operator=().

template<class T>

TNT::Matrix< T >::set ( value  )

inherited

void BIAS::Matrix< QUADRIC3D_TYPE >::Set ( const int  row, const int  col, const Matrix< QUADRIC3D_TYPE > &  data  )

inherited

Copies the contents of data into this at the position indicated by row and col.

The size of *this must be big enought to carry data

Author

woelk 05/2008 (c) www.vision-n.de

void BIAS::Matrix< QUADRIC3D_TYPE >::Set ( const int  row, const int  col, const Vector< QUADRIC3D_TYPE > &  data  )

inherited

Copies the contents of data into this at the position indicated by row and col.

The size of *this must be big enought to carry data. Data i interpreted as column vector

Author

woelk 05/2008 (c) www.vision-n.de

void BIAS::Matrix< QUADRIC3D_TYPE >::SetCol ( const int  row, const Vector< QUADRIC3D_TYPE > &  data  )

inherited

set a col of matrix from vector

Author

woelk 08/2004

void BIAS::Matrix4x4< QUADRIC3D_TYPE >::SetIdentity ( )

inlineinherited

set the elements of this matrix to the identity matrix

(posisbly overriding the inherited method)

Author

, Jan Woetzel

Date

04/17/2002 untested

Definition at line 260 of file Matrix4x4.hh.

void BIAS::Matrix< QUADRIC3D_TYPE >::SetRow ( const int  row, const Vector< QUADRIC3D_TYPE > &  data  )

inherited

set a row of matrix from vector

Author

woelk 08/2004

void BIAS::Matrix< QUADRIC3D_TYPE >::SetSubMatrix ( const size_t  startRowInThis, const size_t  startColInThis, const Matrix< QUADRIC3D_TYPE > &  submatrix, const size_t  startRowInSub, const size_t  startColInSub, const size_t  numRows, const size_t  numCols  )

inherited

sets a submatrix in this.

Start index in this is [startRowInThis][startColInThis] end index is [startRowInThis+numRows-1][startColInThis+numCols-1]. Entries copyed from submatrix beginning at [startRowInSub][startColInSub] and stop at [startRowInSub+numRows-1][startColInSub+numCols-1]

Author

apetersen 12/2010

void BIAS::Matrix< QUADRIC3D_TYPE >::SetSubMatrix ( const size_t  startRowInThis, const size_t  startColInThis, const Matrix3x3< QUADRIC3D_TYPE > &  submatrix  )

inherited

sets a 3x3 submatrix in this.

Start index in this is [startRowInThis][startColInThis] end index is [startRowInThis+2][startColInThis+2].

Author

apetersen 12/2010

void BIAS::Matrix< QUADRIC3D_TYPE >::SetSubMatrix ( const size_t  startRowInThis, const size_t  startColInThis, const Vector3< QUADRIC3D_TYPE > &  subvector  )

inherited

sets a 3x1 submatrix in this.

Start index in this is [startRowInThis][startColInThis] end index is [startRowInThis+2][startColInThis].

Author

apetersen 12/2010

void BIAS::Matrix< QUADRIC3D_TYPE >::SetTranspose ( const int  row, const int  col, const Vector< QUADRIC3D_TYPE > &  data  )

inherited

Copies the contents of data into this at the position indicated by row and col.

The size of *this must be big enought to carry data. Data is interpreted as row vector.

Author

woelk 05/2008 (c) www.vision-n.de

void BIAS::Matrix< QUADRIC3D_TYPE >::SetZero ( )

inlineinherited

Sets all values to zero.

Author

Ingo Thomsen, JW

Date

04/11/2002 tested

template<class T>

Subscript TNT::Matrix< T >::size ( ) const

inlineinherited

Definition at line 212 of file cmat.h.

Referenced by Eigenproblem_quadratic_matrix(), BIAS::Random::GetMeanAndCovariance(), BIAS::Matrix< T >::operator==(), and BIAS::IteratedExtendedKalman::SetState().

void BIAS::Matrix< QUADRIC3D_TYPE >::Sub ( const QUADRIC3D_TYPE &  scalar, Matrix< QUADRIC3D_TYPE > &  dest  ) const

inlineinherited

substraction function, storing data destination matrix

Author

Ingo Thomsen tested

void BIAS::Matrix< QUADRIC3D_TYPE >::SubIP ( const Matrix< QUADRIC3D_TYPE > &  arg )

inlineinherited

Subtracts arg from this
this -= arg.

Author

grest, 2004

void BIAS::Matrix< QUADRIC3D_TYPE >::SubIP ( const QUADRIC3D_TYPE &  scalar )

inlineinherited

in place subtraction function

Author

Ingo Thomsen tested

Definition at line 437 of file Matrix.hh.

void BIAS::Matrix< QUADRIC3D_TYPE >::SwapRows ( const int  i, const int  r  )

inherited

swaps two rows

Author

woelk 05/2008 www.vision-n.de

QUADRIC3D_TYPE BIAS::Matrix< QUADRIC3D_TYPE >::Trace ( ) const

inlineinherited

Author

koeser

Matrix4x4 BIAS::Matrix4x4< QUADRIC3D_TYPE >::Transpose ( ) const

inlineinherited

Definition at line 315 of file Matrix4x4.hh.

void BIAS::Matrix4x4< QUADRIC3D_TYPE >::TransposeIP ( )

inlineinherited

tranpose this matrix "in place"

example: 0 1 2 3 –> 0 4 8 12 4 5 6 7 –> 1 5 9 13 8 9 10 11 –> 2 6 10 14 12 13 14 15 –> 3 7 11 15

Author

Jan-Friso Evers-Senne untested (07/08/2002)

Definition at line 302 of file Matrix4x4.hh.

void BIAS::Matrix< QUADRIC3D_TYPE >::Vec ( Vector< QUADRIC3D_TYPE > &  dest ) const

inherited

vec-operator returns the elements of the matrix columwise as vector

vec-operator returns the elements of the matrix columnwise as vector

int BIAS::Matrix< QUADRIC3D_TYPE >::WriteMatlab ( std::ostream &  ostr, const std::string &  name  ) const

inherited

Write the matrix in Matlab format to the given stream.

Parameters

name	Is the name of the Matlab variable

Author

streckel 08/2006

Returns

negativev if error

Friends And Related Function Documentation

template<class T >

Matrix< T > operator* ( const Matrix< T > &  A, const Matrix< T > &  B  )

related

Definition at line 842 of file cmat.h.

References TNT::matmult().

template<class T >

Vector< T > operator* ( const Matrix< T > &  A, const Vector< T > &  x  )

related

Definition at line 915 of file cmat.h.

References TNT::matmult().

template<class T >

Matrix< T > operator+ ( const Matrix< T > &  A, const Matrix< T > &  B  )

related

Definition at line 730 of file cmat.h.

References TNT::Matrix< T >::num_cols(), and TNT::Matrix< T >::num_rows().

template<class T >

Matrix< T > operator- ( const Matrix< T > &  A, const Matrix< T > &  B  )

related

Definition at line 752 of file cmat.h.

References TNT::Matrix< T >::num_cols(), and TNT::Matrix< T >::num_rows().

template<class T>

std::ostream & operator<< ( std::ostream &  s, const Matrix< char > &  A  )

related

Author

Jan Woetzel

Definition at line 663 of file cmat.h.

template<class T>

std::ostream & operator<< ( std::ostream &  s, const Matrix< unsigned char > &  A  )

related

Author

Jan Woetzel

Definition at line 670 of file cmat.h.

template<class T >

std::ostream & operator<< ( std::ostream &  s, const Matrix< T > &  A  )

related

Author

Jan Woetzel

Definition at line 695 of file cmat.h.

template<class T>

std::istream & operator>> ( std::istream &  s, Matrix< unsigned char > &  A  )

related

Author

Jan Woetzel

Definition at line 703 of file cmat.h.

References TNT::Matrix< T >::Read().

template<class T>

std::istream & operator>> ( std::istream &  s, Matrix< char > &  A  )

related

Author

Jan Woetzel

Definition at line 711 of file cmat.h.

References TNT::Matrix< T >::Read().

template<class T >

std::istream & operator>> ( std::istream &  s, Matrix< T > &  A  )

related

Author

Jan Woetzel

Definition at line 719 of file cmat.h.

References TNT::Matrix< T >::Read().

Member Data Documentation

template<class T>

Subscript TNT::Matrix< T >::m_

protectedinherited

Definition at line 84 of file cmat.h.

Referenced by TNT::Matrix< BIAS::BIAS::Vector< int > >::copy(), TNT::Matrix< BIAS::BIAS::Vector< int > >::destroy(), TNT::Matrix< BIAS::BIAS::Vector< int > >::dim(), TNT::Matrix< BIAS::BIAS::Vector< int > >::initialize(), TNT::Matrix< BIAS::BIAS::Vector< int > >::Matrix(), TNT::Matrix< BIAS::BIAS::Vector< int > >::num_rows(), TNT::Matrix< BIAS::BIAS::Vector< int > >::operator()(), TNT::Matrix< BIAS::BIAS::Vector< int > >::operator=(), TNT::Matrix< BIAS::BIAS::Vector< int > >::operator[](), and TNT::Matrix< BIAS::BIAS::Vector< int > >::set().

template<class T>

Subscript TNT::Matrix< T >::mn_

protectedinherited

Definition at line 86 of file cmat.h.

Referenced by TNT::Matrix< BIAS::BIAS::Vector< int > >::destroy(), TNT::Matrix< BIAS::BIAS::Vector< int > >::initialize(), TNT::Matrix< BIAS::BIAS::Vector< int > >::operator()(), and TNT::Matrix< BIAS::BIAS::Vector< int > >::size().

template<class T>

Subscript TNT::Matrix< T >::n_

protectedinherited

Definition at line 85 of file cmat.h.

Referenced by TNT::Matrix< BIAS::BIAS::Vector< int > >::copy(), TNT::Matrix< BIAS::BIAS::Vector< int > >::destroy(), TNT::Matrix< BIAS::BIAS::Vector< int > >::dim(), TNT::Matrix< BIAS::BIAS::Vector< int > >::initialize(), TNT::Matrix< BIAS::BIAS::Vector< int > >::Matrix(), TNT::Matrix< BIAS::BIAS::Vector< int > >::num_cols(), TNT::Matrix< BIAS::BIAS::Vector< int > >::operator()(), TNT::Matrix< BIAS::BIAS::Vector< int > >::operator=(), and TNT::Matrix< BIAS::BIAS::Vector< int > >::set().

template<class T>

T** TNT::Matrix< T >::row_

protectedinherited

Definition at line 88 of file cmat.h.

Referenced by TNT::Matrix< BIAS::BIAS::Vector< int > >::destroy(), TNT::Matrix< BIAS::BIAS::Vector< int > >::initialize(), TNT::Matrix< BIAS::BIAS::Vector< int > >::Matrix(), BIAS::PMatrix::Normalize(), and TNT::Matrix< BIAS::BIAS::Vector< int > >::operator[]().

template<class T>

T** TNT::Matrix< T >::rowm1_

protectedinherited

Definition at line 90 of file cmat.h.

Referenced by TNT::Matrix< BIAS::BIAS::Vector< int > >::destroy(), TNT::Matrix< BIAS::BIAS::Vector< int > >::initialize(), and TNT::Matrix< BIAS::BIAS::Vector< int > >::operator()().

template<class T>

T* TNT::Matrix< T >::v_

protectedinherited

Definition at line 87 of file cmat.h.

Referenced by TNT::Matrix< BIAS::BIAS::Vector< int > >::copy(), TNT::Matrix< BIAS::BIAS::Vector< int > >::destroy(), TNT::Matrix< BIAS::BIAS::Vector< int > >::initialize(), TNT::Matrix< BIAS::BIAS::Vector< int > >::Matrix(), BIAS::AffineTransf::Mult(), BIAS::AffineTransf::operator=(), TNT::Matrix< BIAS::BIAS::Vector< int > >::operator=(), TNT::Matrix< BIAS::BIAS::Vector< int > >::set(), and BIAS::AffineTransf::SetAsRotationMatrix().

template<class T>

T* TNT::Matrix< T >::vm1_

protectedinherited

Definition at line 89 of file cmat.h.

Referenced by TNT::Matrix< BIAS::BIAS::Vector< int > >::initialize(), and TNT::Matrix< BIAS::BIAS::Vector< int > >::operator()().

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

• Geometry/Quadric3D.hh
• Geometry/Quadric3D.cpp