#include <itkBridgeMathSVD.h>

Detailed Description

template<typename TReal, unsigned int VRows, unsigned int VCols>
struct itk::bridge::Math::FixedRectangularSVDResult< TReal, VRows, VCols >

Result of a fixed-size rectangular SVD with thin factors: A (VRows x VCols) == U diag(W) V^T, where U is VRows x K, V is VCols x K and K = min(VRows, VCols); W is descending. rcond < 0 auto-selects a K*epsilon threshold.

Definition at line 321 of file itkBridgeMathSVD.h.

Public Member Functions
TReal	DeterminantMagnitude () const

vnl_vector_fixed< TReal, VCols >	NullVector () const

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

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

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

vnl_matrix_fixed< TReal, VRows, VCols >	RecomposeWith (const vnl_vector_fixed< TReal, K > &modifiedW) const

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

TReal	WellCondition () const

Public Attributes
vnl_matrix_fixed< TReal, VRows, K >	U {}

vnl_matrix_fixed< TReal, VCols, K >	V {}

vnl_vector_fixed< TReal, K >	W {}

Static Public Attributes
static constexpr unsigned int	K = (VRows < VCols) ? VRows : VCols

Member Function Documentation

◆ DeterminantMagnitude()

template<typename TReal, unsigned int VRows, unsigned int VCols>

TReal itk::bridge::Math::FixedRectangularSVDResult< TReal, VRows, VCols >::DeterminantMagnitude ( ) const

inline

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

Definition at line 383 of file itkBridgeMathSVD.h.

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

◆ NullVector()

template<typename TReal, unsigned int VRows, unsigned int VCols>

vnl_vector_fixed< TReal, VCols > itk::bridge::Math::FixedRectangularSVDResult< TReal, VRows, VCols >::NullVector ( ) const

inline

Singular vector for the smallest singular value (last column of V); spans the nullspace when A is rank-deficient. Overdetermined shapes only: the thin V of an underdetermined input does not span the nullspace.

Definition at line 368 of file itkBridgeMathSVD.h.

References K, and V.

◆ PseudoInverse()

template<typename TReal, unsigned int VRows, unsigned int VCols>

vnl_matrix_fixed< TReal, VCols, VRows > itk::bridge::Math::FixedRectangularSVDResult< TReal, VRows, VCols >::PseudoInverse ( TReal rcond = TReal{ -1 } ) const

inline

Moore-Penrose pseudo-inverse A^+ (VCols x VRows).

Definition at line 331 of file itkBridgeMathSVD.h.

◆ Rank()

template<typename TReal, unsigned int VRows, unsigned int VCols>

unsigned int itk::bridge::Math::FixedRectangularSVDResult< TReal, VRows, VCols >::Rank ( TReal rcond = TReal{ -1 } ) const

inline

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

Definition at line 345 of file itkBridgeMathSVD.h.

◆ Recompose()

template<typename TReal, unsigned int VRows, unsigned int VCols>

vnl_matrix_fixed< TReal, VRows, VCols > itk::bridge::Math::FixedRectangularSVDResult< TReal, VRows, VCols >::Recompose ( TReal rcond = TReal{ -1 } ) const

inline

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

Definition at line 352 of file itkBridgeMathSVD.h.

◆ RecomposeWith()

template<typename TReal, unsigned int VRows, unsigned int VCols>

vnl_matrix_fixed< TReal, VRows, VCols > itk::bridge::Math::FixedRectangularSVDResult< TReal, VRows, VCols >::RecomposeWith ( const vnl_vector_fixed< TReal, K > & modifiedW ) const

inline

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

Definition at line 359 of file itkBridgeMathSVD.h.

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

◆ Solve()

template<typename TReal, unsigned int VRows, unsigned int VCols>

vnl_vector_fixed< TReal, VCols > itk::bridge::Math::FixedRectangularSVDResult< TReal, VRows, VCols >::Solve	(	const vnl_vector_fixed< TReal, VRows > &	b,
		TReal	rcond = TReal{ -1 } ) const