BIAS::SVD Class Reference

computes and holds the singular value decomposition of a rectangular (not necessarily quadratic) Matrix A More...

#include <MathAlgo/SVD.hh>

Inheritance diagram for BIAS::SVD:

Collaboration diagram for BIAS::SVD:

Public Member Functions
const int	AbsLeftNullspaceDim () const
	returns the dim of the matrix's left nullspace, using absolute threshold criterion More...
const int	AbsNullspaceDim () const
	returns dim of nullspace using the absolute threshold criterion More...
const int	AbsRightNullspaceDim () const
	returns the dim of the matrix's right nullspace, using absolute threshold criterion More...
void	AddDebugLevel (const long int lv)
void	AddDebugLevel (const std::string &name)
int	Compute (const Matrix< double > &M, double ZeroThreshold=DEFAULT_DOUBLE_ZERO_THRESHOLD)
	set a new matrix and compute its decomposition. More...
int	compute (const Matrix< double > &M, double ZeroThreshold=DEFAULT_DOUBLE_ZERO_THRESHOLD)
	use our naming convention More...
int	ComputeOpenCV (const Matrix< double > &M, double ZeroThreshold=DEFAULT_DOUBLE_ZERO_THRESHOLD)
	Use OpenCV for decomposition as Lapack frequently leads to crashes under windows. More...
bool	DebugLevelIsSet (const long int lv) const
bool	DebugLevelIsSet (const std::string &name) const
int	General_Eigenproblem_GeneralMatrix_Lapack (const Matrix< double > &M)
	solve the general (non-special) eigenvalue/eigenvector problem of a general (non-symmetric) matrix M calls the extern liblapack routine dgesvd . More...
int	GetDebugLevel () const
std::ostream &	GetDebugStream () const
void	GetDebugStream (std::ostream &os) const
BIAS::Vector< double >	GetEigenValues ()
	Call this after Compute(), returns the eigenvalues of the matrix in ascending order (smallest first), which are NOT the singular values! Works only, if the original Matrix was symmetric. More...
bool	GetLeftNullvector (Vector< double > &nv, const int last_offset=0)
	Return one of the left nullvectors. More...
Vector< double >	GetLeftNullvector (const int last_offset=0)
	same as above but returning vector More...
Vector< double >	GetNullvector (const int last_offset=0)
	return one of the nullvectors. More...
bool	GetNullvector (Vector< double > &NullVec, const int last_offset=0)
	Returns one of the nullvectors in argument and true if Nullvector exists. More...
const Vector< double > &	GetS () const
	return S which is a vector of the singular values of A in descending order. More...
const double	GetSingularValue (int index) const
	return one singular value (which may be zero). More...
const Matrix< double > &	GetU () const
	return U U is a m x m orthogonal matrix More...
Matrix< double >	GetV () const
	return V More...
const Matrix< double > &	GetVT () const
	return VT (=transposed(V)) More...
double	GetZeroThreshold () const
	return zerothresh currently used More...
Matrix< double >	Invert ()
	returns pseudoinverse of A = U * S * V^T A^+ = V * S^+ * U^T More...
Matrix< double >	Invert (int rank)
	returns pseudoinverse of A = U * S * V^T A^+ = V * S^+ * U^T the first "rank" elements of S are inverted the others are set to zero More...
Matrix< double >	Invert (Matrix< double > A)
	as above, but compute new svd for a More...
Matrix< double >	InvertOpenCV (const Matrix< double > &A)
	Calculates new inverse with OpenCV cvInvert. More...
const int	LeftNullspaceDim () const
	returns the dim of the matrix's left nullspace More...
long int	Name2DebugLevel (const std::string &name) const
	looks up a debuglevel in the internal map, returns 0 if not found More...
long int	NewDebugLevel (const std::string &name)
	creates a new debuglevel More...
const int	NullspaceDim () const
	return the dim of the nullspace. More...
void	PrintDebugLevel (std::ostream &os=std::cout) const
unsigned int	Rank ()
	returns the rank of A_ More...
const int	RelLeftNullspaceDim () const
const int	RelNullspaceDim () const
	compare singular values against greatest, not absolute More...
const int	RelRightNullspaceDim () const
void	RemoveDebugLevel (const long int lv)
void	RemoveDebugLevel (const std::string &name)
const int	RightNullspaceDim () const
	returns the dim of the matrix's right nullspace More...
void	SetDebugLevel (const long int lv)
void	SetDebugLevel (const std::string &name)
void	SetDebugStream (const std::ostream &os)
void	ShowDebugLevel (std::ostream &os=std::cout) const
	prints all internally known debuglevels More...
int	size () const
	return the length of the singular value vector inline const int size() const More...
Vector< double >	Solve (const Vector< double > &y) const
Vector< double >	solve (const Vector< double > &y) const
	use our naming convention More...
int	Solve (Matrix< double > &A, Vector< double > &B, Vector< double > &X)
	solves the overdetermined linear system $AX=B$ with the unknown $X$, where $A$ is an $m x n$ matrix ($m>n$)and B is a vector of size $m$. More...
Matrix< double >	Sqrt ()
	returns the square root of a symmetric positive definite matrix M A = sqrt(M) = U * sqrt(S) * V_T, such that A*A = M. More...
Matrix< double >	Sqrt (const Matrix< double > &A)
	as above, but compute new svd for More...
Matrix< double >	SqrtT ()
	returns the square root of a symmetric positive definite matrix M A = sqrt(M) = U * sqrt(S), such that A*A^T = M. More...
Matrix< double >	SqrtT (const Matrix< double > &A)
	as above, but compute new svd for More...
	SVD (const Matrix< double > &M, double ZeroThreshold=DEFAULT_DOUBLE_ZERO_THRESHOLD, bool AbsoluteZeroThreshold=true)
	solve the general eigenproblem of the rectangular matrix M or with other words, make the U*S*V^T decomposition More...
	SVD (bool AbsoluteZeroThreshold=true)
	creates an empty svd without automatically decomposing any matrix More...
virtual	~SVD ()

Static Public Member Functions
static long int	GetGlobalDebugLevel ()
static void	SetGlobalDebugLevel (long int lev)

Protected Member Functions
long	ConsumeNextFreeDebuglevel_ ()
	returns the next available debuglevel More...

Protected Attributes
long int	_liDebugLevel
long int	_liNextDebugLevel
	new concept, debuglevel are managed here in the debug class More...
std::map< std::string, long int >	_String2Debuglevel
Matrix< double >	A_
	data members: original matrix (to be decomposed) More...
bool	AbsoluteZeroThreshold_
	determines whether we compare singular-values directly (absolute) to the zero threshold or whether we compare the ratio of the sing-value under inspection and the largest one to the threshold (relative) More...
bool	Decomposed_
	flag for holding decomposed matrix More...
Vector< double >	S_
	contains the singular values of A_ corresponding to the i'th column in descending order. More...
Matrix< double >	U_
	contains columnwise the left singular vectors of A_ corresponding to the i'th singular value More...
Matrix< double >	VT_
	contains the right singular vectors of A- in rows [because VT is transpose(V) ] More...
double	ZeroThreshold_
	values below this threshold are treated as zero More...

Static Protected Attributes
static std::ostream	_zDebugStream
static long int	GlobalDebugLevel = 0

Detailed Description

computes and holds the singular value decomposition of a rectangular (not necessarily quadratic) Matrix A

M = U S V't.

The singular vectors vi and (right) singular values sigma_i satisfy the equation: A vi = sigma_i vi

The Vector S_ stores the singular values of A in decreasing order (smallest is last)

The columns of U are the left singular vectors of A and form an orthonormal basis of A which corresponds to the nonzero singular values. while the columns of U corresponding to (nearly) zero values are the nullspace.

This function is a base class and not a member in Matrix because:

• holding the U,S,V matrices allows repeated queries of the same SVD results. -avoid namespace clutter in the Matrix class. There are many other decompositions that might be of interest, and adding them all would make for a very large Matrix class with extra members which are irrelevant for the Matrix itself.

You can create the svd object either in relative or in absolute mode: if AbsoluteZeroThreshold is true, a singular value is compared to the threshold "absolutely", otherwise the ratio of the largest and the current singular value is compared against the threshold. Usually you want AbsoluteZeroThreshold = false, but for the sake of interface stability/downwards compatibility, the default is true

Author

Jan Woetzel

Examples:

Example7Point.cpp, ExampleHdr.cpp, ExampleLapack.cpp, ExampleRegressionPlane.cpp, ExampleSparseMatrix.cpp, ExampleSparseMatrix2.cpp, ExampleSVD.cpp, ExampleSVD3x3.cpp, and InvestigatePRelations.cpp.

Definition at line 92 of file SVD.hh.

Constructor & Destructor Documentation

SVD::SVD	(	const Matrix< double > &	M,
		double	ZeroThreshold = DEFAULT_DOUBLE_ZERO_THRESHOLD,
		bool	AbsoluteZeroThreshold = true
	)

solve the general eigenproblem of the rectangular matrix M or with other words, make the U*S*V^T decomposition

Parameters

M	matrix to decompose
ZeroThreshold	for nullspace determination, if a singular value is lower than ZeroThreshold, define the corresponding vector in V^T to be a null-vector (also sing.vals are treated this way)
AbsoluteZeroThreshold	if true, a singular value is compared to the threshold "absoultely", otherwise the ratio of the largest and the current singular value is compared against the threshold. Usually you want AbsoluteZeroThreshold = false, but for the sake of interface stability/downwards compatibility, the default is true

Author

Jan Woetzel

Definition at line 43 of file SVD.cpp.

BIAS::SVD::SVD ( bool  AbsoluteZeroThreshold = true )

inline

creates an empty svd without automatically decomposing any matrix

Parameters

AbsoluteZeroThreshold

if true, a singular value is compared to the threshold "absolutely", otherwise the ratio of the largest and the current singular value is compared against the threshold. Usually you want AbsoluteZeroThreshold = false, but for the sake of interface stability/downwards compatibility, the default is true

Definition at line 117 of file SVD.hh.

virtual BIAS::SVD::~SVD ( )

inlinevirtual

Definition at line 123 of file SVD.hh.

Member Function Documentation

const int SVD::AbsLeftNullspaceDim

(

)

const

returns the dim of the matrix's left nullspace, using absolute threshold criterion

Author

woelk 04 2003

Definition at line 467 of file SVD.cpp.

const int SVD::AbsNullspaceDim

(

)

const

returns dim of nullspace using the absolute threshold criterion

For rectangular matrices this is the number of singular values which are (about) zero. The nullspace is spaned by the singular vectors corresponding to the zero singular values. woelk 4 2003: changed API, diffentiate between Left and Right Nullspace

Author

Jan Woetzel 04/04/2002

Definition at line 415 of file SVD.cpp.

const int SVD::AbsRightNullspaceDim

(

)

const

returns the dim of the matrix's right nullspace, using absolute threshold criterion

Author

woelk 04 2003

Definition at line 459 of file SVD.cpp.

void BIAS::Debug::AddDebugLevel ( const long int  lv )

inlineinherited

Examples:

EvaluateAlignment.cpp, ExampleAlignment.cpp, ExampleMinMax.cpp, ExampleRANSAC_double.cpp, ExampleRANSACPlane.cpp, and ExampleTriangulateOptimal.cpp.

Definition at line 355 of file Debug.hh.

Referenced by BIAS::GLProjectionParametersBase::AddDebugLevel(), BIAS::Triangulation::CorrectCorrespondences(), BIAS::FilterBase< InputStorageType, OutputStorageType >::FilterBase(), BIAS::ShowCamWxVideoSourceFactory::OpenDevice(), and BIAS::SceneOpenSceneGraph::SceneOpenSceneGraph().

void BIAS::Debug::AddDebugLevel ( const std::string &  name )

inlineinherited

Definition at line 362 of file Debug.hh.

int SVD::Compute	(	const Matrix< double > &	M,
		double	ZeroThreshold = DEFAULT_DOUBLE_ZERO_THRESHOLD
	)

set a new matrix and compute its decomposition.

solves the general eigenproblem of the rectangular matrix M

Author

Jan Woetzel 05/142002)

Examples:

Example7Point.cpp, and ExampleSVD.cpp.

Definition at line 102 of file SVD.cpp.

Referenced by BIAS::CovMatrix3x3::_Decompose(), BIAS::ImageAlignment::Align(), BIAS::LDA::ComputeReductionMatrix(), BIAS::HMatrix::FactorizeAffineMatrixRLeft(), BIAS::HMatrix::FactorizeAffineMatrixRRight(), BIAS::LDA::GenerateRandomTestData(), BIAS::EMatrix::GetRotationTranslation(), and BIAS::Interpolator::InitSpline3().

int BIAS::SVD::compute ( const Matrix< double > &  M, double  ZeroThreshold = DEFAULT_DOUBLE_ZERO_THRESHOLD  )

inline

use our naming convention

Definition at line 132 of file SVD.hh.

Referenced by BIAS::PMatrix::MakeSVD_().

int SVD::ComputeOpenCV	(	const Matrix< double > &	M,
		double	ZeroThreshold = DEFAULT_DOUBLE_ZERO_THRESHOLD
	)

Use OpenCV for decomposition as Lapack frequently leads to crashes under windows.

Attention

This does not deliver the same results as Compute(). The columns of U and VT differ in sign.

Author

Ingo Schiller

Examples:

ExampleSVD.cpp.

Definition at line 51 of file SVD.cpp.

References BIAS::Matrix< T >::GetCols(), and BIAS::Matrix< T >::GetRows().

long BIAS::Debug::ConsumeNextFreeDebuglevel_ ( )

inlineprotectedinherited

returns the next available debuglevel

Author

woelk 09/2006

Definition at line 521 of file Debug.hh.

bool BIAS::Debug::DebugLevelIsSet ( const long int  lv ) const

inlineinherited

Examples:

ExampleTriangulateOptimal.cpp.

Definition at line 341 of file Debug.hh.

Referenced by BIAS::GenSynthMatches::_AddUniformDistributedOutliers(), BIAS::GenSynthMatches::_CreateCamMovement(), BIAS::GenSynthMatches::_CreateStatic2DPoints(), BIAS::UnscentedTransform::ComputeSigmaPoints_(), BIAS::Triangulation::CorrectCorrespondences(), BIAS::GenSynthMatches::GetGTNormalizedF(), BIAS::MonteCarloTransform::GetSamples_(), and BIAS::MonteCarloTransform::Transform().

bool BIAS::Debug::DebugLevelIsSet ( const std::string &  name ) const

inlineinherited

Definition at line 350 of file Debug.hh.

int SVD::General_Eigenproblem_GeneralMatrix_Lapack

(

const Matrix< double > &

M

)

solve the general (non-special) eigenvalue/eigenvector problem of a general (non-symmetric) matrix M calls the extern liblapack routine dgesvd .

computes the genral singular value decomposition with M = U * Sigma(S) * VT with Sigma(S) is the qudratic, symmetric matrix which contains the singular vales in the diagonal and zero and zero else. U, VT as described in the data mambers.

Author

Jan Woetzel (04/04/2002)

Definition at line 110 of file SVD.cpp.

References General_singular_value_decomposition().

int BIAS::Debug::GetDebugLevel ( ) const

inlineinherited

Examples:

ExampleCamera.cpp, ExampleCamPoseCalib.cpp, ExampleCopy.cpp, and ExampleParabola.cpp.

Definition at line 332 of file Debug.hh.

Referenced by BIAS::listenthread(), BIAS::Image< StorageType >::operator=(), and BIAS::ImageBase::operator=().

std::ostream& BIAS::Debug::GetDebugStream ( ) const

inlineinherited

Definition at line 405 of file Debug.hh.

void BIAS::Debug::GetDebugStream ( std::ostream &  os ) const

inlineinherited

Definition at line 414 of file Debug.hh.

BIAS::Vector< double > SVD::GetEigenValues

(

)

Call this after Compute(), returns the eigenvalues of the matrix in ascending order (smallest first), which are NOT the singular values! Works only, if the original Matrix was symmetric.

Author

grest, July 2006

Definition at line 573 of file SVD.cpp.

Referenced by BIAS::CamPoseCalib::SolveLM_().

static long int BIAS::Debug::GetGlobalDebugLevel ( )

inlinestaticinherited

Definition at line 431 of file Debug.hh.

bool BIAS::SVD::GetLeftNullvector ( Vector< double > &  nv, const int  last_offset = 0  )

inline

Return one of the left nullvectors.

If last_offset=0 then the last nullvector (corresponding to the smallest singular value) is returned, if last_offset=1 then the last but one nullvector is returned, and so on. The last_offset must be in [0..NullspaceDim-1] otherwise 0 is returned

Author

JMF/koeser

Definition at line 443 of file SVD.hh.

References TNT::Vector< T >::newsize(), NullspaceDim(), TNT::Matrix< T >::num_rows(), S_, U_, and VT_.

Referenced by BIAS::TrifocalTensor::ComputeEpipoles(), BIAS::TrifocalTensor::GetEpipolarLines(), BIAS::FMatrix::GetEpipoles(), and GetLeftNullvector().

Vector< double > BIAS::SVD::GetLeftNullvector ( const int  last_offset = 0 )

inline

same as above but returning vector

Definition at line 434 of file SVD.hh.

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

Vector< double > BIAS::SVD::GetNullvector ( const int  last_offset = 0 )

inline

return one of the nullvectors.

if last_offset=0 then the last nullvector (corresponding to the smallest singular value) is returned, if last_offset=1 then the last but one nullvector is returned, and so on. The last_offset must be in [0..NullspaceDim-1].

Author

Jan Woetzel(08/08/2002), JMF

Definition at line 404 of file SVD.hh.

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

Referenced by BIAS::TFTensorEstimation::Compute(), BIAS::TrifocalTensor::ComputeEpipoles(), BIAS::ProjectionParametersProjective::GetC(), BIAS::TrifocalTensor::GetEpipolarLines(), BIAS::FMatrix::GetEpipoles(), BIAS::PMatrix::GetNullVector(), BIAS::Conic2D::GetPoint(), BIAS::PlaneRANSAC::RefineSolution(), and BIAS::FMatrixEstimation::SevenPoint().

bool BIAS::SVD::GetNullvector ( Vector< double > &  NullVec, const int  last_offset = 0  )

inline

Returns one of the nullvectors in argument and true if Nullvector exists.

if last_offset=0 then the last nullvector (corresponding to the smallest singular value) is returned, if last_offset=1 then the last but one nullvector is returned, and so on. The last_offset must be in [0..NullspaceDim-1].

Author

Jan Woetzel (08/08/2002), JMF

Definition at line 413 of file SVD.hh.

References TNT::Vector< T >::newsize(), NullspaceDim(), TNT::Matrix< T >::num_cols(), and VT_.

const Vector<double>& BIAS::SVD::GetS ( ) const

inline

return S which is a vector of the singular values of A in descending order.

The diagonalelements of Sigma are the singular values of A.

Author

Jan Woetzel 04/04/2002

Examples:

Example7Point.cpp, ExampleSVD.cpp, and ExampleSVD3x3.cpp.

Definition at line 167 of file SVD.hh.

Referenced by BIAS::CovMatrix3x3::_Decompose(), BIAS::ImageAlignment::Align(), BIAS::PMatrixLinear::Compute(), BIAS::PMatrixLinear::ComputeCalibrated(), BIAS::PMatrixEstimation::ComputeFromFDirect(), BIAS::LDA::ComputeReductionMatrix(), BIAS::PCA::ComputeReductionMatrix(), BIAS::FMatrixEstimation::EnforceMaxRank2(), BIAS::HMatrix::FactorizeAffineMatrixRLeft(), BIAS::HMatrix::FactorizeAffineMatrixRRight(), BIAS::LDA::GenerateRandomTestData(), BIAS::GetBaseLevel(), BIAS::FMatrix::GetEpipoles(), BIAS::PMatrix::GetPseudoInverse(), BIAS::Quadric3D::GetSignature(), BIAS::Conic2D::GetSignature(), BIAS::PMatrix::GetSVD(), BIAS::EMatrix::InitFromF(), Lapack_LLS_QR_linear_solve(), and BIAS::Quadric3D::Quadric3D().

const double BIAS::SVD::GetSingularValue ( int  index ) const

inline

return one singular value (which may be zero).

inline implementations

the index runs from 0.. (size-1)

Author

Jan Woetzel 04/04/2002

Definition at line 386 of file SVD.hh.

References S_, size(), and TNT::Vector< T >::size().

Referenced by BIAS::CamPoseCalib::outputPose_().

const Matrix<double>& BIAS::SVD::GetU ( ) const

inline

return U U is a m x m orthogonal matrix

Author

Jan Woetzel (04/04/2002)

Examples:

ExampleSVD.cpp, and ExampleSVD3x3.cpp.

Definition at line 187 of file SVD.hh.

Referenced by BIAS::CovMatrix3x3::_Decompose(), BIAS::PMatrixLinear::ComputeCalibrated(), BIAS::RMatrix::EnforceConstraints(), BIAS::FMatrixEstimation::EnforceMaxRank2(), BIAS::HMatrix::FactorizeAffineMatrixRLeft(), BIAS::HMatrix::FactorizeAffineMatrixRRight(), BIAS::LDA::GenerateRandomTestData(), BIAS::Conic2D::GetDualConic(), BIAS::FMatrix::GetEpipoles(), BIAS::PMatrix::GetPseudoInverse(), BIAS::EMatrix::GetRotationTranslation(), BIAS::PMatrix::GetSVD(), BIAS::EMatrix::InitFromF(), and BIAS::Quadric3D::Quadric3D().

Matrix< double > BIAS::SVD::GetV ( ) const

inline

return V

Author

Jan Woetzel (04/04/2002)

Definition at line 396 of file SVD.hh.

References BIAS::Matrix< T >::Transpose(), and VT_.

Referenced by BIAS::RotationAveraging::ChordalL2Mean(), BIAS::LDA::ComputeReductionMatrix(), BIAS::Conic2D::GetDualConic(), BIAS::PMatrix::GetPseudoInverse(), and BIAS::Quadric3D::Quadric3D().

const Matrix<double>& BIAS::SVD::GetVT ( ) const

inline

return VT (=transposed(V))

Author

Jan Woetzel (04/04/2002)

Examples:

ExampleSVD.cpp, and ExampleSVD3x3.cpp.

Definition at line 177 of file SVD.hh.

Referenced by BIAS::CovMatrix3x3::_Decompose(), BIAS::TFTensorEstimation::Compute(), BIAS::PMatrixLinear::Compute(), BIAS::PMatrixLinear::ComputeCalibrated(), BIAS::ImageBlender::ComputeCylCamGeometry(), BIAS::ImageBlenderIncremental::ComputeCylCamGeometry_(), BIAS::clfTrimmedICP::ComputeOptimalMotion_(), BIAS::LDA::ComputeReductionMatrix(), BIAS::PCA::ComputeReductionMatrix(), BIAS::RMatrix::EnforceConstraints(), BIAS::FMatrixEstimation::EnforceMaxRank2(), BIAS::HMatrix::FactorizeAffineMatrixRLeft(), BIAS::HMatrix::FactorizeAffineMatrixRRight(), BIAS::LDA::GenerateRandomTestData(), BIAS::Triangulation::GetCovarianceProjective(), BIAS::FMatrix::GetEpipoles(), BIAS::EMatrix::GetRotationTranslation(), BIAS::Quadric3D::GetSignature(), BIAS::Conic2D::GetSignature(), BIAS::PMatrix::GetSVD(), BIAS::EMatrix::InitFromF(), BIAS::FMatrixEstimation::Linear(), and BIAS::Triangulation::TriangulateLinear().

double BIAS::SVD::GetZeroThreshold ( ) const

inline

return zerothresh currently used

Author

koeser

Definition at line 160 of file SVD.hh.

Referenced by BIAS::PMatrixLinear::Compute().

Matrix< double > SVD::Invert

(

)

returns pseudoinverse of A = U * S * V^T A^+ = V * S^+ * U^T

Author

F Woelk

Examples:

ExampleLapack.cpp, ExampleSparseMatrix2.cpp, ExampleSVD.cpp, and InvestigatePRelations.cpp.

Definition at line 214 of file SVD.cpp.

References BIAS::Matrix< T >::SetZero().

Referenced by BIAS::ImageAlignment::Align(), BIAS::TextureTransformAffine::ComposeWithInverseDeltaP(), BIAS::ImageBlender::ComputeCylCamGeometry(), BIAS::ImageBlenderIncremental::ComputeCylCamGeometry_(), BIAS::ProjectionError::ComputeDiff(), BIAS::GaussHelmert::ComputeNormalSystem_(), BIAS::LDA::ComputeReductionMatrix(), BIAS::ContourBSplineShapeMatrix::ComputeRegularisationMatrix(), BIAS::ContourDetectorBSpline< StorageType >::Fit_(), BIAS::PMatrix::GetCanonicalH(), BIAS::Triangulation::GetCovarianceProjective(), BIAS::CamPoseCalib::GetCoVarMatrix(), BIAS::Conic2D::GetDualConic(), BIAS::Quadric3D::GetDualQuadric(), BIAS::Interpolator::InitSpline3(), BIAS::CoordinateTransform3D::SetFromMatrix3x4(), BIAS::GaussHelmert::Solve(), BIAS::TrackerBaseAffine< StorageType >::TrackAffine_(), BIAS::TrackerBaseAffine2< StorageType >::TrackAffine_(), and BIAS::IteratedExtendedKalman::Update().

Matrix< double > SVD::Invert

(

int

rank

)

returns pseudoinverse of A = U * S * V^T A^+ = V * S^+ * U^T the first "rank" elements of S are inverted the others are set to zero

Author

Christian Beder

Definition at line 243 of file SVD.cpp.

References BIAS::Matrix< T >::SetZero().

Matrix< double > SVD::Invert

(

Matrix< double >

A

)

as above, but compute new svd for a

Definition at line 268 of file SVD.cpp.

Matrix< double > SVD::InvertOpenCV

(

const Matrix< double > &

A

)

Calculates new inverse with OpenCV cvInvert.

Attention

This does not deliver the same results as Invert().

Examples:

ExampleSVD.cpp.

Definition at line 182 of file SVD.cpp.

References BIAS::Matrix< T >::GetCols(), and BIAS::Matrix< T >::GetRows().

const int BIAS::SVD::LeftNullspaceDim ( ) const

inline

returns the dim of the matrix's left nullspace

Author

woelk 04 2003

Definition at line 223 of file SVD.hh.

Referenced by BIAS::TFTensorEstimation::Compute().

long int BIAS::Debug::Name2DebugLevel ( const std::string &  name ) const

inlineinherited

looks up a debuglevel in the internal map, returns 0 if not found

Author

woelk 09/2006

Definition at line 454 of file Debug.hh.

long int BIAS::Debug::NewDebugLevel ( const std::string &  name )

inlineinherited

creates a new debuglevel

Author

woelk 09/2006

Definition at line 474 of file Debug.hh.

Referenced by BIAS::COSAC< SolutionType >::COSAC(), BIAS::ProjectionParametersPerspectiveDepth::Init(), BIAS::MonteCarloTransform::MonteCarloTransform(), BIAS::PMatrixEstimation::PMatrixEstimation(), BIAS::PreemptiveRANSAC< SolutionType >::PreemptiveRANSAC(), BIAS::RANSACPreKnowledge< SolutionType >::RANSACPreKnowledge(), BIAS::ROI::ROI(), BIAS::RotationAveraging::RotationAveraging(), BIAS::SceneOpenSceneGraph::SceneOpenSceneGraph(), BIAS::ThreeDOutOpenSceneGraph::ThreeDOutOpenSceneGraph(), BIAS::Triangulation::Triangulation(), and BIAS::UnscentedTransform::UnscentedTransform().

const int BIAS::SVD::NullspaceDim ( ) const

inline

return the dim of the nullspace.

For rectangular matrices this is the number of singular values which are (about) zero. The nullspace is spaned by the singular vectors corresponding to the zero singular values. woelk 4 2003: changed API, diffentiate between Left and Right Nullspace koeser 01/2005: rel/abs handled by flag: AbsoluteZeroThreshold_ determines whther we compare absolute or relative singular values against the threshold

Author

Jan Woetzel 04/04/2002

Examples:

ExampleSVD3x3.cpp.

Definition at line 209 of file SVD.hh.

Referenced by BIAS::FMatrix::GetEpipoles(), GetLeftNullvector(), GetNullvector(), and BIAS::FMatrix::IsValid().

void BIAS::Debug::PrintDebugLevel ( std::ostream &  os = std::cout ) const

inlineinherited

Definition at line 383 of file Debug.hh.

unsigned int SVD::Rank

(

)

returns the rank of A_

Definition at line 506 of file SVD.cpp.

Referenced by BIAS::LDA::ComputeReductionMatrix(), Lapack_LLS_QR_linear_solve(), and BIAS::PlaneRANSAC::RefineSolution().

const int SVD::RelLeftNullspaceDim

(

)

const

Definition at line 485 of file SVD.cpp.

const int SVD::RelNullspaceDim

(

)

const

compare singular values against greatest, not absolute

Author

Christian Buck changed criterion for insignificant singular values according to hartley/zisserman from s_i<ZeroThreshold to s_i/s_0<ZeroThreshold. fallback to old criterion iff s_0=0.

Definition at line 433 of file SVD.cpp.

Referenced by BIAS::PMatrixLinear::Compute(), BIAS::PMatrixLinear::ComputeCalibrated(), and BIAS::Conic2D::GetDualConic().

const int SVD::RelRightNullspaceDim

(

)

const

Definition at line 463 of file SVD.cpp.

void BIAS::Debug::RemoveDebugLevel ( const long int  lv )

inlineinherited

Definition at line 369 of file Debug.hh.

void BIAS::Debug::RemoveDebugLevel ( const std::string &  name )

inlineinherited

Definition at line 376 of file Debug.hh.

const int BIAS::SVD::RightNullspaceDim ( ) const

inline

returns the dim of the matrix's right nullspace

Author

woelk 04 2003

Definition at line 216 of file SVD.hh.

Referenced by BIAS::TFTensorEstimation::Compute().

void BIAS::Debug::SetDebugLevel ( const long int  lv )

inlineinherited

Examples:

ExampleCamera.cpp, ExampleCamPoseCalib.cpp, ExampleCopy.cpp, ExampleDcam.cpp, ExampleDcamImageConvert.cpp, ExampleDirectToDisk.cpp, ExampleGrabTrippleFromXB3.cpp, ExampleHarrisColor.cpp, ExampleLDA.cpp, ExampleLineMatcher.cpp, ExampleMDCamToShm.cpp, ExampleParabola.cpp, ExamplePMatrix.cpp, ExamplePtGreyHiresColor.cpp, ExampleVideoSource_Shm.cpp, and Scan1394Bus.cpp.

Definition at line 318 of file Debug.hh.

Referenced by BIAS::ShowCamWxVideoSourceFactory::CreateBumbleBee(), BIAS::ShowCamWxVideoSourceFactory::CreateDCAM(), BIAS::VideoSource_MDcam::ScanBus(), BIAS::GLProjectionParametersBase::SetDebugLevel(), BIAS::VideoSource_Disk::VideoSource_Disk(), BIAS::VideoSource_DV2::VideoSource_DV2(), BIAS::VideoSource_DV::VideoSource_DV_Internal_Init_(), and BIAS::VideoSource_V4L::VideoSource_V4L().

void BIAS::Debug::SetDebugLevel ( const std::string &  name )

inlineinherited

Definition at line 325 of file Debug.hh.

void BIAS::Debug::SetDebugStream ( const std::ostream &  os )

inlineinherited

Definition at line 398 of file Debug.hh.

static void BIAS::Debug::SetGlobalDebugLevel ( long int  lev )

inlinestaticinherited

Definition at line 424 of file Debug.hh.

void BIAS::Debug::ShowDebugLevel ( std::ostream &  os = std::cout ) const

inlineinherited

prints all internally known debuglevels

Author

woelk 09/2006

Definition at line 496 of file Debug.hh.

int BIAS::SVD::size ( ) const

inline

return the length of the singular value vector inline const int size() const

Definition at line 192 of file SVD.hh.

Referenced by GetSingularValue().

Vector< double > SVD::Solve

(

const Vector< double > &

y

)

const

Bug:

bug in this function (woelk)

Examples:

ExampleHdr.cpp.

Definition at line 135 of file SVD.cpp.

References TNT::Vector< T >::size(), and BIAS::Matrix< T >::Transpose().

Referenced by BIAS::CamPoseCalib::Estimate(), BIAS::PolynomialSolve::FitPolynomial(), BIAS::ProjectionParametersSphericalFast::FitPolynomial(), BIAS::ProjectionParametersSpherical::FitPolynomialWithoutLinearMonomial_(), BIAS::PMatrix::GetCanonicalH(), BIAS::GaussHelmert::Solve(), BIAS::CamPoseCalib::Solve_(), and BIAS::TrackerBaseAffine< StorageType >::TrackAffine_().

Vector<double> BIAS::SVD::solve ( const Vector< double > &  y ) const

inline

use our naming convention

Definition at line 292 of file SVD.hh.

int SVD::Solve	(	Matrix< double > &	A,
		Vector< double > &	B,
		Vector< double > &	X
	)

solves the overdetermined linear system $AX=B$ with the unknown $X$, where $A$ is an $m x n$ matrix ($m>n$)and B is a vector of size $m$.

Author

woelk 07/2004

Definition at line 516 of file SVD.cpp.

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

Matrix< double > SVD::Sqrt

(

)

returns the square root of a symmetric positive definite matrix M A = sqrt(M) = U * sqrt(S) * V_T, such that A*A = M.

The result is only valid when the M is symmetric positive definite.

Author

woelk 01/2006

Examples:

ExampleSVD.cpp.

Definition at line 276 of file SVD.cpp.

References BIAS::Equal(), BIAS::GreaterEqual(), BIAS::MatrixZero, BIAS::Matrix< T >::SetZero(), TNT::Vector< T >::size(), and Upper_symmetric_eigenvalue_solve().

Matrix< double > SVD::Sqrt

(

const Matrix< double > &

A

)

as above, but compute new svd for

Parameters

A

Definition at line 337 of file SVD.cpp.

Matrix< double > SVD::SqrtT

(

)

returns the square root of a symmetric positive definite matrix M A = sqrt(M) = U * sqrt(S), such that A*A^T = M.

The result is only valid when the M is symmetric positive definite.

Author

woelk 01/2006

Definition at line 344 of file SVD.cpp.

References BIAS::Equal(), BIAS::GreaterEqual(), BIAS::MatrixZero, TNT::Vector< T >::size(), and Upper_symmetric_eigenvalue_solve().

Referenced by BIAS::LDA::ComputeReductionMatrix(), and BIAS::UnscentedTransform::ComputeSigmaPoints_().

Matrix< double > SVD::SqrtT

(

const Matrix< double > &

A

)

as above, but compute new svd for

Parameters

A

Definition at line 407 of file SVD.cpp.

Member Data Documentation

long int BIAS::Debug::_liDebugLevel

protectedinherited

Definition at line 510 of file Debug.hh.

Referenced by BIAS::Debug::operator=(), and BIAS::ImageBase::operator=().

long int BIAS::Debug::_liNextDebugLevel

protectedinherited

new concept, debuglevel are managed here in the debug class

Definition at line 516 of file Debug.hh.

Referenced by BIAS::Debug::operator=().

std::map<std::string, long int> BIAS::Debug::_String2Debuglevel

protectedinherited

Definition at line 517 of file Debug.hh.

Referenced by BIAS::Debug::operator=().

std::ostream BIAS::Debug::_zDebugStream

staticprotectedinherited

Definition at line 511 of file Debug.hh.

Referenced by BIAS::Debug::operator=().

Matrix<double> BIAS::SVD::A_

protected

data members: original matrix (to be decomposed)

Definition at line 355 of file SVD.hh.

bool BIAS::SVD::AbsoluteZeroThreshold_

protected

determines whether we compare singular-values directly (absolute) to the zero threshold or whether we compare the ratio of the sing-value under inspection and the largest one to the threshold (relative)

Definition at line 372 of file SVD.hh.

bool BIAS::SVD::Decomposed_

protected

flag for holding decomposed matrix

Definition at line 378 of file SVD.hh.

long int BIAS::Debug::GlobalDebugLevel = 0

staticprotectedinherited

Definition at line 513 of file Debug.hh.

Vector<double> BIAS::SVD::S_

protected

contains the singular values of A_ corresponding to the i'th column in descending order.

Definition at line 359 of file SVD.hh.

Referenced by GetLeftNullvector(), and GetSingularValue().

Matrix<double> BIAS::SVD::U_

protected

contains columnwise the left singular vectors of A_ corresponding to the i'th singular value

Definition at line 363 of file SVD.hh.

Referenced by GetLeftNullvector().

Matrix<double> BIAS::SVD::VT_

protected

contains the right singular vectors of A- in rows [because VT is transpose(V) ]

Definition at line 367 of file SVD.hh.

Referenced by GetLeftNullvector(), GetNullvector(), and GetV().

double BIAS::SVD::ZeroThreshold_

protected

values below this threshold are treated as zero

Definition at line 375 of file SVD.hh.

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

• MathAlgo/SVD.hh
• MathAlgo/SVD.cpp