Calculates inverse of a matrix (wrapper around vnl_svd<double>). More...

#include <vnl_algo_fwd.h>

Inheritance diagram for vnl_matrix_inverse< T >:

Public Types
typedef vnl_numeric_traits< T >::abs_t	singval_t
	The singular values of a matrix of complex<T> are of type T, not complex<T>. More...

Public Member Functions
	vnl_matrix_inverse (vnl_matrix< T > const &M)

	~vnl_matrix_inverse () override=default

	operator vnl_matrix< T > () const

void	zero_out_absolute (double tol=1e-8)
	find weights below threshold tol, zero them out, and update W_ and Winverse_. More...

void	zero_out_relative (double tol=1e-8)
	find weights below tol*max(w) and zero them out. More...

int	singularities () const

unsigned int	rank () const

singval_t	well_condition () const

singval_t	determinant_magnitude () const
	Calculate determinant as product of diagonals in W. More...

singval_t	norm () const

vnl_matrix< T > &	U ()
	Return the matrix U. More...

vnl_matrix< T > const &	U () const
	Return the matrix U. More...

T	U (int i, int j) const
	Return the matrix U's (i,j)th entry (to avoid svd.U()(i,j); ). More...

vnl_diag_matrix< singval_t > &	W ()
	Get at DiagMatrix (q.v.) of singular values, sorted from largest to smallest. More...

vnl_diag_matrix< singval_t > const &	W () const
	Get at DiagMatrix (q.v.) of singular values, sorted from largest to smallest. More...

singval_t &	W (int i, int j)

singval_t &	W (int i)

vnl_diag_matrix< singval_t > &	Winverse ()

vnl_diag_matrix< singval_t > const &	Winverse () const

singval_t	sigma_max () const

singval_t	sigma_min () const

vnl_matrix< T > &	V ()
	Return the matrix V. More...

vnl_matrix< T > const &	V () const
	Return the matrix V. More...

T	V (int i, int j) const
	Return the matrix V's (i,j)th entry (to avoid svd.V()(i,j); ). More...

vnl_matrix< T >	inverse () const

vnl_matrix< T >	pinverse (unsigned int rank=~0u) const
	pseudo-inverse (for non-square matrix) of desired rank. More...

vnl_matrix< T >	tinverse (unsigned int rank=~0u) const
	Calculate inverse of transpose, using desired rank. More...

vnl_matrix< T >	recompose (unsigned int rank=~0u) const
	Recompose SVD to UWV', using desired rank. More...

vnl_matrix< T >	solve (vnl_matrix< T > const &B) const
	Solve the matrix equation M X = B, returning X. More...

vnl_vector< T >	solve (vnl_vector< T > const &y) const
	Solve the matrix-vector system M x = y, returning x. More...

void	solve (T const rhs, T lhs) const

void	solve_preinverted (vnl_vector< T > const &rhs, vnl_vector< T > *out) const
	Solve the matrix-vector system M x = y. More...

vnl_matrix< T >	nullspace () const
	Return N such that M * N = 0. More...

vnl_matrix< T >	nullspace (int required_nullspace_dimension) const
	Return N such that M * N = 0. More...

vnl_matrix< T >	left_nullspace () const
	Return N such that M' * N = 0. More...

vnl_matrix< T >	left_nullspace (int required_nullspace_dimension) const
	Implementation to be done yet; currently returns left_nullspace(). - PVR. More...

vnl_vector< T >	nullvector () const
	Return the rightmost column of V. More...

vnl_vector< T >	left_nullvector () const
	Return the rightmost column of U. More...

bool	valid () const

Detailed Description

template<class T>
struct vnl_matrix_inverse< T >

Calculates inverse of a matrix (wrapper around vnl_svd<double>).

vnl_matrix_inverse is a wrapper around vnl_svd<double> that allows you to write

x = vnl_matrix_inverse<double>(A) * b;

This is exactly equivalent to

x = vnl_svd<double>(A).solve(b);

but is arguably clearer, and also allows for the vnl_matrix_inverse class to be changed to use vnl_qr, say.

Definition at line 6 of file vnl_algo_fwd.h.

Member Typedef Documentation

◆ singval_t

template<class T>

typedef vnl_numeric_traits<T>::abs_t vnl_svd< T >::singval_t

inherited

The singular values of a matrix of complex<T> are of type T, not complex<T>.

Definition at line 67 of file vnl_svd.h.

Constructor & Destructor Documentation

◆ vnl_matrix_inverse()

template<class T>

vnl_matrix_inverse< T >::vnl_matrix_inverse ( vnl_matrix< T > const & M )

inline

Definition at line 34 of file vnl_matrix_inverse.h.

◆ ~vnl_matrix_inverse()

template<class T>

vnl_matrix_inverse< T >::~vnl_matrix_inverse ( )

overridedefault

Member Function Documentation

◆ determinant_magnitude()

template<class T >

vnl_svd< T >::singval_t vnl_svd< T >::determinant_magnitude ( ) const

inherited

Calculate determinant as product of diagonals in W.

Definition at line 213 of file vnl_svd.hxx.

◆ inverse()

template<class T>

vnl_matrix<T> vnl_svd< T >::inverse ( ) const

inlineinherited

Definition at line 133 of file vnl_svd.h.

◆ left_nullspace() [1/2]

template<class T >

vnl_matrix< T > vnl_svd< T >::left_nullspace ( ) const

inherited

Return N such that M' * N = 0.

Return N s.t. M' * N = 0.

Definition at line 384 of file vnl_svd.hxx.

◆ left_nullspace() [2/2]

template<class T >

vnl_matrix< T > vnl_svd< T >::left_nullspace ( int required_nullspace_dimension ) const

inherited

Implementation to be done yet; currently returns left_nullspace(). - PVR.

Todo:: Implementation to be done yet; currently returns left_nullspace().

- PVr.

Definition at line 395 of file vnl_svd.hxx.

◆ left_nullvector()

template<class T >

vnl_vector< T > vnl_svd< T >::left_nullvector ( ) const

inherited

Return the rightmost column of U.

Does not check to see whether or not the matrix actually was rank-deficient.

Definition at line 418 of file vnl_svd.hxx.

◆ norm()

template<class T >

vnl_svd< T >::singval_t vnl_svd< T >::norm ( ) const

inherited

Definition at line 226 of file vnl_svd.hxx.

◆ nullspace() [1/2]

template<class T >

vnl_matrix< T > vnl_svd< T >::nullspace ( ) const

inherited

Return N such that M * N = 0.

Return N s.t. M * N = 0.

Definition at line 365 of file vnl_svd.hxx.

◆ nullspace() [2/2]

template<class T >

vnl_matrix< T > vnl_svd< T >::nullspace ( int required_nullspace_dimension ) const

inherited

Return N such that M * N = 0.

Return N s.t. M * N = 0.

Definition at line 376 of file vnl_svd.hxx.

◆ nullvector()

template<class T >

vnl_vector< T > vnl_svd< T >::nullvector ( ) const

inherited

Return the rightmost column of V.

Does not check to see whether or not the matrix actually was rank-deficient - the caller is assumed to have examined W and decided that to his or her satisfaction.

Definition at line 406 of file vnl_svd.hxx.

◆ operator vnl_matrix< T >()

template<class T>

vnl_matrix_inverse< T >::operator vnl_matrix< T > ( ) const

inline

Definition at line 37 of file vnl_matrix_inverse.h.

◆ pinverse()

template<class T >

vnl_matrix< T > vnl_svd< T >::pinverse ( unsigned int rank = ~0u ) const

inherited

pseudo-inverse (for non-square matrix) of desired rank.

Calculate pseudo-inverse.

Definition at line 247 of file vnl_svd.hxx.

◆ rank()

template<class T>

unsigned int vnl_svd< T >::rank ( ) const

inlineinherited

Definition at line 95 of file vnl_svd.h.

◆ recompose()

template<class T >

vnl_matrix< T > vnl_svd< T >::recompose ( unsigned int rank = ~0u ) const

inherited

Recompose SVD to U*W*V', using desired rank.

Recompose SVD to U*W*V'.

Definition at line 233 of file vnl_svd.hxx.

◆ sigma_max()

template<class T>

singval_t vnl_svd< T >::sigma_max ( ) const

inlineinherited

Definition at line 120 of file vnl_svd.h.

◆ sigma_min()

template<class T>

singval_t vnl_svd< T >::sigma_min ( ) const

inlineinherited

Definition at line 121 of file vnl_svd.h.

◆ singularities()

template<class T>

int vnl_svd< T >::singularities ( ) const

inlineinherited

Definition at line 94 of file vnl_svd.h.

◆ solve() [1/3]

template<class T>

vnl_matrix< T > vnl_svd< T >::solve ( vnl_matrix< T > const & B ) const

inherited

Solve the matrix equation M X = B, returning X.

Definition at line 275 of file vnl_svd.hxx.

◆ solve() [2/3]

template<class T>

vnl_vector< T > vnl_svd< T >::solve ( vnl_vector< T > const & y ) const

inherited

Solve the matrix-vector system M x = y, returning x.

Definition at line 298 of file vnl_svd.hxx.

◆ solve() [3/3]

template<class T>

void vnl_svd< T >::solve	(	T const *	rhs,
		T *	lhs
	)		const

inherited

Definition at line 337 of file vnl_svd.hxx.

◆ solve_preinverted()

template<class T>

void vnl_svd< T >::solve_preinverted	(	vnl_vector< T > const &	y,
		vnl_vector< T > *	x_out
	)		const

inherited

Solve the matrix-vector system M x = y.

Assuming that the singular values W have been preinverted by the caller.

Assume that the singular values W have been preinverted by the caller.

Definition at line 345 of file vnl_svd.hxx.

◆ tinverse()

template<class T >

vnl_matrix< T > vnl_svd< T >::tinverse ( unsigned int rank = ~0u ) const

inherited

Calculate inverse of transpose, using desired rank.

Calculate (pseudo-)inverse of transpose.

Definition at line 261 of file vnl_svd.hxx.

◆ U() [1/3]

template<class T>

vnl_matrix<T>& vnl_svd< T >::U ( )

inlineinherited

Return the matrix U.

Definition at line 103 of file vnl_svd.h.

◆ U() [2/3]

template<class T>

vnl_matrix<T> const& vnl_svd< T >::U ( ) const

inlineinherited

Return the matrix U.

Definition at line 106 of file vnl_svd.h.

◆ U() [3/3]

template<class T>

T vnl_svd< T >::U	(	int	i,
		int	j
	)		const

inlineinherited

Return the matrix U's (i,j)th entry (to avoid svd.U()(i,j); ).

Definition at line 109 of file vnl_svd.h.

◆ V() [1/3]

template<class T>

vnl_matrix<T>& vnl_svd< T >::V ( )

inlineinherited

Return the matrix V.

Definition at line 124 of file vnl_svd.h.

◆ V() [2/3]

template<class T>

vnl_matrix<T> const& vnl_svd< T >::V ( ) const

inlineinherited

Return the matrix V.

Definition at line 127 of file vnl_svd.h.

◆ V() [3/3]

template<class T>

T vnl_svd< T >::V	(	int	i,
		int	j
	)		const

inlineinherited

Return the matrix V's (i,j)th entry (to avoid svd.V()(i,j); ).

Definition at line 130 of file vnl_svd.h.

◆ valid()

template<class T>

bool vnl_svd< T >::valid ( ) const

inlineinherited

Definition at line 176 of file vnl_svd.h.

◆ W() [1/4]

template<class T>

vnl_diag_matrix<singval_t>& vnl_svd< T >::W ( )

inlineinherited

Get at DiagMatrix (q.v.) of singular values, sorted from largest to smallest.

Definition at line 112 of file vnl_svd.h.

◆ W() [2/4]

template<class T>

vnl_diag_matrix<singval_t> const& vnl_svd< T >::W ( ) const

inlineinherited

Get at DiagMatrix (q.v.) of singular values, sorted from largest to smallest.

Definition at line 115 of file vnl_svd.h.

◆ W() [3/4]

template<class T>

singval_t& vnl_svd< T >::W	(	int	i,
		int	j
	)

inlineinherited

Definition at line 118 of file vnl_svd.h.

◆ W() [4/4]

template<class T>

singval_t& vnl_svd< T >::W ( int i )

inlineinherited

Definition at line 119 of file vnl_svd.h.

◆ well_condition()

template<class T>

singval_t vnl_svd< T >::well_condition ( ) const

inlineinherited

Definition at line 96 of file vnl_svd.h.

◆ Winverse() [1/2]

template<class T>

vnl_diag_matrix<singval_t>& vnl_svd< T >::Winverse ( )

inlineinherited

Definition at line 116 of file vnl_svd.h.

◆ Winverse() [2/2]

template<class T>

vnl_diag_matrix<singval_t> const& vnl_svd< T >::Winverse ( ) const

inlineinherited

Definition at line 117 of file vnl_svd.h.

◆ zero_out_absolute()

template<class T >

void vnl_svd< T >::zero_out_absolute ( double tol = 1e-8 )

inherited

find weights below threshold tol, zero them out, and update W_ and Winverse_.

Definition at line 182 of file vnl_svd.hxx.

◆ zero_out_relative()

template<class T >

void vnl_svd< T >::zero_out_relative ( double tol = 1e-8 )

inherited

find weights below tol*max(w) and zero them out.

Definition at line 203 of file vnl_svd.hxx.

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

core/vnl/algo/vnl_algo_fwd.h
core/vnl/algo/vnl_matrix_inverse.h

Public Types

Public Member Functions

Detailed Description

template<class T> struct vnl_matrix_inverse< T >

Member Typedef Documentation

◆ singval_t

Constructor & Destructor Documentation

◆ vnl_matrix_inverse()

◆ ~vnl_matrix_inverse()

Member Function Documentation

◆ determinant_magnitude()

◆ inverse()

◆ left_nullspace() [1/2]

◆ left_nullspace() [2/2]

◆ left_nullvector()

◆ norm()

◆ nullspace() [1/2]

◆ nullspace() [2/2]

◆ nullvector()

◆ operator vnl_matrix< T >()

◆ pinverse()

◆ rank()

◆ recompose()

◆ sigma_max()

◆ sigma_min()

◆ singularities()

◆ solve() [1/3]

◆ solve() [2/3]

◆ solve() [3/3]

◆ solve_preinverted()

◆ tinverse()

◆ U() [1/3]

◆ U() [2/3]

◆ U() [3/3]

◆ V() [1/3]

◆ V() [2/3]

◆ V() [3/3]

◆ valid()

◆ W() [1/4]

◆ W() [2/4]

◆ W() [3/4]

◆ W() [4/4]

◆ well_condition()

◆ Winverse() [1/2]

◆ Winverse() [2/2]

◆ zero_out_absolute()

◆ zero_out_relative()

template<class T>
struct vnl_matrix_inverse< T >