#include <itkMathSVD.h>

Detailed Description

template<typename TReal, unsigned int VDim>
struct itk::Math::FixedSquareSVDResult< TReal, VDim >

Result of a fixed-size square SVD: A == U * diag(W) * V^T, W descending. For all solver methods, rcond < 0 auto-selects a VDim*epsilon threshold.

Definition at line 175 of file itkMathSVD.h.

Public Member Functions
TReal	DeterminantMagnitude () const

vnl_vector_fixed< TReal, VDim >	NullVector () const

vnl_matrix_fixed< TReal, VDim, VDim >	PseudoInverse (TReal rcond=TReal{ -1 }) const

unsigned int	Rank (TReal rcond=TReal{ -1 }) const

vnl_matrix_fixed< TReal, VDim, VDim >	Recompose (TReal rcond=TReal{ -1 }) const

vnl_matrix_fixed< TReal, VDim, VDim >	RecomposeWith (const vnl_vector_fixed< TReal, VDim > &modifiedW) const

vnl_vector_fixed< TReal, VDim >	Solve (const vnl_vector_fixed< TReal, VDim > &b, TReal rcond=TReal{ -1 }) const

TReal	WellCondition () const

Public Attributes
vnl_matrix_fixed< TReal, VDim, VDim >	U {}

vnl_matrix_fixed< TReal, VDim, VDim >	V {}

vnl_vector_fixed< TReal, VDim >	W {}

Member Function Documentation

◆ DeterminantMagnitude()

template<typename TReal, unsigned int VDim>

TReal itk::Math::FixedSquareSVDResult< TReal, VDim >::DeterminantMagnitude ( ) const

inline

Product of the singular values (magnitude of the determinant for a square A).

Definition at line 233 of file itkMathSVD.h.

References itk::Math::detail::DeterminantMagnitude(), and W.

◆ NullVector()

template<typename TReal, unsigned int VDim>

vnl_vector_fixed< TReal, VDim > itk::Math::FixedSquareSVDResult< TReal, VDim >::NullVector ( ) const

inline

Singular vector for the smallest singular value (last column of V); spans the nullspace when A is rank-deficient.

Definition at line 219 of file itkMathSVD.h.

References V.

◆ PseudoInverse()

template<typename TReal, unsigned int VDim>

vnl_matrix_fixed< TReal, VDim, VDim > itk::Math::FixedSquareSVDResult< TReal, VDim >::PseudoInverse ( TReal rcond = TReal{ -1 } ) const

inline

Moore-Penrose pseudo-inverse A^+.

Definition at line 183 of file itkMathSVD.h.

◆ Rank()

template<typename TReal, unsigned int VDim>

unsigned int itk::Math::FixedSquareSVDResult< TReal, VDim >::Rank ( TReal rcond = TReal{ -1 } ) const

inline

Numerical rank (count of singular values above rcond*max(w)).

Definition at line 197 of file itkMathSVD.h.

◆ Recompose()

template<typename TReal, unsigned int VDim>

vnl_matrix_fixed< TReal, VDim, VDim > itk::Math::FixedSquareSVDResult< TReal, VDim >::Recompose ( TReal rcond = TReal{ -1 } ) const

inline

Reconstruct A with singular values at or below rcond*max(w) zeroed.

Definition at line 204 of file itkMathSVD.h.

◆ RecomposeWith()

template<typename TReal, unsigned int VDim>

vnl_matrix_fixed< TReal, VDim, VDim > itk::Math::FixedSquareSVDResult< TReal, VDim >::RecomposeWith ( const vnl_vector_fixed< TReal, VDim > & modifiedW ) const

inline

Reconstruct U diag(modifiedW) V^T with caller-supplied singular values.

Definition at line 211 of file itkMathSVD.h.

References itk::Math::detail::RecomposeWith(), U, and V.

◆ Solve()

template<typename TReal, unsigned int VDim>

vnl_vector_fixed< TReal, VDim > itk::Math::FixedSquareSVDResult< TReal, VDim >::Solve	(	const vnl_vector_fixed< TReal, VDim > &	b,
		TReal	rcond = TReal{ -1 } ) const