itk::bridge::Math::SVDResult< TReal > Struct Template Reference

#include <itkBridgeMathSVD.h>

Detailed Description

template<typename TReal>
struct itk::bridge::Math::SVDResult< TReal >

Result of a runtime-sized SVD (square or rectangular): A == U diag(W) V^T, W descending. For an m x n input, U is m x k, V is n x k and W has length k = min(m, n) (thin factors). rcond < 0 auto-selects a k*epsilon threshold.

Definition at line 246 of file itkBridgeMathSVD.h.

Public Member Functions
TReal	DeterminantMagnitude () const
vnl_vector< TReal >	NullVector () const
vnl_matrix< TReal >	PseudoInverse (TReal rcond=TReal{ -1 }) const
unsigned int	Rank (TReal rcond=TReal{ -1 }) const
vnl_matrix< TReal >	Recompose (TReal rcond=TReal{ -1 }) const
vnl_matrix< TReal >	RecomposeWith (const vnl_vector< TReal > &modifiedW) const
vnl_vector< TReal >	Solve (const vnl_vector< TReal > &b, TReal rcond=TReal{ -1 }) const
TReal	WellCondition () const

Public Attributes
vnl_matrix< TReal >	U {}
vnl_matrix< TReal >	V {}
vnl_vector< TReal >	W {}

Member Function Documentation

DeterminantMagnitude()

template<typename TReal>

TReal itk::bridge::Math::SVDResult< TReal >::DeterminantMagnitude ( ) const

inline

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

Definition at line 311 of file itkBridgeMathSVD.h.

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

NullVector()

template<typename TReal>

vnl_vector< TReal > itk::bridge::Math::SVDResult< TReal >::NullVector ( ) const

inline

Singular vector for the smallest singular value (last column of V); spans the nullspace when A is rank-deficient. Defined only for rows >= cols: an underdetermined input's thin V (cols x min(rows,cols)) cannot span the nullspace, so this throws rather than return a misleading direction.

Definition at line 292 of file itkBridgeMathSVD.h.

References U, and V.

PseudoInverse()

template<typename TReal>

vnl_matrix< TReal > itk::bridge::Math::SVDResult< TReal >::PseudoInverse ( TReal rcond = TReal{ -1 } ) const

inline

Moore-Penrose pseudo-inverse A^+.

Definition at line 254 of file itkBridgeMathSVD.h.

Rank()

template<typename TReal>

unsigned int itk::bridge::Math::SVDResult< TReal >::Rank ( TReal rcond = TReal{ -1 } ) const

inline

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

Definition at line 268 of file itkBridgeMathSVD.h.

Recompose()

template<typename TReal>

vnl_matrix< TReal > itk::bridge::Math::SVDResult< TReal >::Recompose ( TReal rcond = TReal{ -1 } ) const

inline

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

Definition at line 275 of file itkBridgeMathSVD.h.

RecomposeWith()

template<typename TReal>

vnl_matrix< TReal > itk::bridge::Math::SVDResult< TReal >::RecomposeWith ( const vnl_vector< TReal > & modifiedW ) const

inline

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

Definition at line 282 of file itkBridgeMathSVD.h.

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

Solve()

template<typename TReal>

vnl_vector< TReal > itk::bridge::Math::SVDResult< TReal >::Solve ( const vnl_vector< TReal > & b, TReal rcond = TReal{ -1 } ) const

inline

Least-squares / minimum-norm solution of A x = b.

Definition at line 261 of file itkBridgeMathSVD.h.

WellCondition()

template<typename TReal>

TReal itk::bridge::Math::SVDResult< TReal >::WellCondition ( ) const

inline

Reciprocal condition number sigma_min/sigma_max (0 = singular, 1 = perfect).

Definition at line 304 of file itkBridgeMathSVD.h.

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

Member Data Documentation

U

template<typename TReal>

vnl_matrix<TReal> itk::bridge::Math::SVDResult< TReal >::U {}

Definition at line 248 of file itkBridgeMathSVD.h.

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

V

template<typename TReal>

vnl_matrix<TReal> itk::bridge::Math::SVDResult< TReal >::V {}

Definition at line 250 of file itkBridgeMathSVD.h.

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

W

template<typename TReal>

vnl_vector<TReal> itk::bridge::Math::SVDResult< TReal >::W {}

Definition at line 249 of file itkBridgeMathSVD.h.

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

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The documentation for this struct was generated from the following file:

• itkBridgeMathSVD.h