itk::bridge::Math::detail Namespace Reference

Typedefs
template<typename TReal>
using	CholeskyRowMajor = Eigen::Matrix<TReal, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>
template<typename TReal>
using	CholeskyVector = Eigen::Matrix<TReal, Eigen::Dynamic, 1>

Functions
template<unsigned int VDim, typename TReal>
TReal	DeterminantEigen (const TReal *inData)
template<typename TVector>
auto	DeterminantMagnitude (const TVector &W) -> std::decay_t< decltype(W[0])>
template<typename TReal>
TReal	DynamicDeterminantEigen (const TReal *inData, unsigned int n)
template<typename TReal>
void	DynamicSquareSVDEigen (const TReal *inData, unsigned int n, TReal *uData, TReal *wData, TReal *vData)
template void	DynamicSquareSVDEigen< double > (const double *, unsigned int, double *, double *, double *)
template void	DynamicSquareSVDEigen< float > (const float *, unsigned int, float *, float *, float *)
template<typename TReal>
void	InverseSymmetricLDLTEigen (const TReal *aData, unsigned int n, TReal *invData)
template<typename TVector, typename TReal>
unsigned int	NumericalRank (const TVector &W, TReal rcond)
template<typename TMatrixU, typename TVector, typename TMatrixV, typename TReal>
auto	PseudoInverse (const TMatrixU &U, const TVector &W, const TMatrixV &V, TReal rcond)
template<typename TMatrixU, typename TVector, typename TMatrixV, typename TReal>
auto	Recompose (const TMatrixU &U, const TVector &W, const TMatrixV &V, TReal rcond)
template<typename TMatrixU, typename TVector, typename TMatrixV>
auto	RecomposeWith (const TMatrixU &U, const TVector &modifiedW, const TMatrixV &V)
template<typename TReal>
void	RectangularSVDEigen (const TReal *inData, unsigned int rows, unsigned int cols, TReal *uData, TReal *wData, TReal *vData)
template void	RectangularSVDEigen< double > (const double *, unsigned int, unsigned int, double *, double *, double *)
template void	RectangularSVDEigen< float > (const float *, unsigned int, unsigned int, float *, float *, float *)
template<typename TReal>
TReal	ResolveRcond (TReal rcond, unsigned int n)
template<typename TMatrixU, typename TVector, typename TMatrixV, typename TVectorB, typename TReal>
auto	SolveLinear (const TMatrixU &U, const TVector &W, const TMatrixV &V, const TVectorB &b, TReal rcond)
template<typename TReal>
void	SolveSymmetricLDLTEigen (const TReal *aData, const TReal *bData, unsigned int n, TReal *xData)
template<typename TReal>
void	SolveSymmetricMatrixLDLTEigen (const TReal *aData, const TReal *bData, unsigned int n, unsigned int m, TReal *xData)
template<unsigned int VDim, typename TReal>
void	SquareSVDEigen (const TReal *inData, TReal *uData, TReal *wData, TReal *vData)
template<typename TVector>
auto	WellCondition (const TVector &W) -> std::decay_t< decltype(W[0])>

Variables
constexpr unsigned int	kFixedSVDMaxDim = 16
constexpr unsigned int	kJacobiMaxDim = 6

Detailed Description

Cholesky-based linear algebra for symmetric matrices, backed by Eigen.

SolveSymmetricPositiveDefinite() uses Eigen's robust LDL^T (pivoted) factor, which handles near-semidefinite regularized Gram matrices. CholeskyLowerTriangle() returns the L of A = L L^T via Eigen's LLT.

Typedef Documentation

CholeskyRowMajor

template<typename TReal>

using itk::bridge::Math::detail::CholeskyRowMajor = Eigen::Matrix<TReal, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>

Definition at line 44 of file itkBridgeCholeskySolve.h.

CholeskyVector

template<typename TReal>

using itk::bridge::Math::detail::CholeskyVector = Eigen::Matrix<TReal, Eigen::Dynamic, 1>

Definition at line 46 of file itkBridgeCholeskySolve.h.

Function Documentation

DeterminantEigen()

template<unsigned int VDim, typename TReal>

TReal itk::bridge::Math::detail::DeterminantEigen

(

const TReal *

inData

)

Definition at line 47 of file itkBridgeMathDeterminant.h.

Referenced by itk::bridge::Math::Determinant(), and DynamicDeterminantEigen().

DeterminantMagnitude()

template<typename TVector>

auto itk::bridge::Math::detail::DeterminantMagnitude

(

const TVector &

W

)

-> std::decay_t<decltype(W[0])>

Definition at line 164 of file itkBridgeMathSVD.h.

Referenced by itk::bridge::Math::FixedRectangularSVDResult< TReal, VRows, VCols >::DeterminantMagnitude(), itk::bridge::Math::FixedSquareSVDResult< TReal, VDim >::DeterminantMagnitude(), and itk::bridge::Math::SVDResult< TReal >::DeterminantMagnitude().

DynamicDeterminantEigen()

template<typename TReal>

TReal itk::bridge::Math::detail::DynamicDeterminantEigen	(	const TReal *	inData,
		unsigned int	n )

Definition at line 55 of file itkBridgeMathDeterminant.h.

References DeterminantEigen().

Referenced by itk::bridge::Math::Determinant().

DynamicSquareSVDEigen()

template<typename TReal>

void itk::bridge::Math::detail::DynamicSquareSVDEigen	(	const TReal *	inData,
		unsigned int	n,
		TReal *	uData,
		TReal *	wData,
		TReal *	vData )

Definition at line 403 of file itkBridgeMathSVD.h.

References kJacobiMaxDim.

Referenced by SquareSVDEigen(), and itk::bridge::Math::SVD().

DynamicSquareSVDEigen< double >()

template void itk::bridge::Math::detail::DynamicSquareSVDEigen< double > ( const double * , unsigned int , double * , double * , double *  )

extern

References ITKCommon_EXPORT_EXPLICIT.

DynamicSquareSVDEigen< float >()

template void itk::bridge::Math::detail::DynamicSquareSVDEigen< float > ( const float * , unsigned int , float * , float * , float *  )

extern

References ITKCommon_EXPORT_EXPLICIT.

InverseSymmetricLDLTEigen()

template<typename TReal>

void itk::bridge::Math::detail::InverseSymmetricLDLTEigen	(	const TReal *	aData,
		unsigned int	n,
		TReal *	invData )

Definition at line 105 of file itkBridgeMathLDLT.h.

Referenced by itk::bridge::Math::InverseSymmetric(), and itk::bridge::Math::InverseSymmetric().

NumericalRank()

template<typename TVector, typename TReal>

unsigned int itk::bridge::Math::detail::NumericalRank	(	const TVector &	W,
		TReal	rcond )

Definition at line 96 of file itkBridgeMathSVD.h.

References ResolveRcond().

PseudoInverse()

template<typename TMatrixU, typename TVector, typename TMatrixV, typename TReal>

auto itk::bridge::Math::detail::PseudoInverse	(	const TMatrixU &	U,
		const TVector &	W,
		const TMatrixV &	V,
		TReal	rcond )

Definition at line 62 of file itkBridgeMathSVD.h.

References ResolveRcond().

Recompose()

template<typename TMatrixU, typename TVector, typename TMatrixV, typename TReal>

auto itk::bridge::Math::detail::Recompose	(	const TMatrixU &	U,
		const TVector &	W,
		const TMatrixV &	V,
		TReal	rcond )

Definition at line 115 of file itkBridgeMathSVD.h.

References ResolveRcond().

RecomposeWith()

template<typename TMatrixU, typename TVector, typename TMatrixV>

auto itk::bridge::Math::detail::RecomposeWith	(	const TMatrixU &	U,
		const TVector &	modifiedW,
		const TMatrixV &	V )

Definition at line 135 of file itkBridgeMathSVD.h.

Referenced by itk::bridge::Math::FixedRectangularSVDResult< TReal, VRows, VCols >::RecomposeWith(), itk::bridge::Math::FixedSquareSVDResult< TReal, VDim >::RecomposeWith(), and itk::bridge::Math::SVDResult< TReal >::RecomposeWith().

RectangularSVDEigen()

template<typename TReal>

void itk::bridge::Math::detail::RectangularSVDEigen	(	const TReal *	inData,
		unsigned int	rows,
		unsigned int	cols,
		TReal *	uData,
		TReal *	wData,
		TReal *	vData )

Definition at line 478 of file itkBridgeMathSVD.h.

Referenced by itk::bridge::Math::SVD(), and itk::bridge::Math::SVD().

RectangularSVDEigen< double >()

template void itk::bridge::Math::detail::RectangularSVDEigen< double > ( const double * , unsigned int , unsigned int , double * , double * , double *  )

extern

References ITKCommon_EXPORT_EXPLICIT.

RectangularSVDEigen< float >()

template void itk::bridge::Math::detail::RectangularSVDEigen< float > ( const float * , unsigned int , unsigned int , float * , float * , float *  )

extern

References ITKCommon_EXPORT_EXPLICIT.

ResolveRcond()

template<typename TReal>

TReal itk::bridge::Math::detail::ResolveRcond	(	TReal	rcond,
		unsigned int	n )

Definition at line 53 of file itkBridgeMathSVD.h.

Referenced by NumericalRank(), PseudoInverse(), Recompose(), and SolveLinear().

SolveLinear()

template<typename TMatrixU, typename TVector, typename TMatrixV, typename TVectorB, typename TReal>

auto itk::bridge::Math::detail::SolveLinear	(	const TMatrixU &	U,
		const TVector &	W,
		const TMatrixV &	V,
		const TVectorB &	b,
		TReal	rcond )

Definition at line 82 of file itkBridgeMathSVD.h.

References ResolveRcond().

SolveSymmetricLDLTEigen()

template<typename TReal>

void itk::bridge::Math::detail::SolveSymmetricLDLTEigen	(	const TReal *	aData,
		const TReal *	bData,
		unsigned int	n,
		TReal *	xData )

Definition at line 63 of file itkBridgeMathLDLT.h.

Referenced by itk::bridge::Math::SolveSymmetric(), itk::bridge::Math::SolveSymmetric(), itk::bridge::Math::SolveSymmetric(), and itk::bridge::Math::SolveSymmetric().

SolveSymmetricMatrixLDLTEigen()

template<typename TReal>

void itk::bridge::Math::detail::SolveSymmetricMatrixLDLTEigen	(	const TReal *	aData,
		const TReal *	bData,
		unsigned int	n,
		unsigned int	m,
		TReal *	xData )

Definition at line 85 of file itkBridgeMathLDLT.h.

Referenced by itk::bridge::Math::SolveSymmetric(), and itk::bridge::Math::SolveSymmetric().

SquareSVDEigen()

template<unsigned int VDim, typename TReal>

void itk::bridge::Math::detail::SquareSVDEigen	(	const TReal *	inData,
		TReal *	uData,
		TReal *	wData,
		TReal *	vData )

Definition at line 440 of file itkBridgeMathSVD.h.

References DynamicSquareSVDEigen(), and kFixedSVDMaxDim.

Referenced by itk::bridge::Math::SVD().

WellCondition()

template<typename TVector>

auto itk::bridge::Math::detail::WellCondition

(

const TVector &

W

)

-> std::decay_t<decltype(W[0])>

Definition at line 151 of file itkBridgeMathSVD.h.

Referenced by itk::bridge::Math::FixedRectangularSVDResult< TReal, VRows, VCols >::WellCondition(), itk::bridge::Math::FixedSquareSVDResult< TReal, VDim >::WellCondition(), and itk::bridge::Math::SVDResult< TReal >::WellCondition().

Variable Documentation

kFixedSVDMaxDim

unsigned int itk::bridge::Math::detail::kFixedSVDMaxDim = 16

constexpr

Definition at line 393 of file itkBridgeMathSVD.h.

Referenced by SquareSVDEigen().

kJacobiMaxDim

unsigned int itk::bridge::Math::detail::kJacobiMaxDim = 6

constexpr

Definition at line 397 of file itkBridgeMathSVD.h.

Referenced by DynamicSquareSVDEigen().