vnl_matrix_inverse< T > Struct Template Reference

#include <vnl_matrix_inverse.h>

Inheritance diagram for vnl_matrix_inverse< T >:

List of all members.

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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 34 of file vnl_matrix_inverse.h.

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>.
Public Member Functions
	vnl_matrix_inverse (vnl_matrix< T > const &M)
	~vnl_matrix_inverse ()
	operator vnl_matrix () const
void	zero_out_absolute (double tol=1e-8)
	find weights below threshold tol, zero them out, and update W_ and Winverse_.
void	zero_out_relative (double tol=1e-8)
	find weights below tol*max(w) and zero them out.
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.
singval_t	norm () const
vnl_matrix< T > &	U ()
	Return the matrix U.
vnl_matrix< T > const &	U () const
	Return the matrix U.
T	U (int i, int j) const
	Return the matrix U's (i,j)th entry (to avoid svd.U()(i,j); ).
vnl_diag_matrix< singval_t > &	W ()
	Get at DiagMatrix (q.v.
vnl_diag_matrix< singval_t > const &	W () const
	Get at DiagMatrix (q.v.
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.
vnl_matrix< T > const &	V () const
	Return the matrix V.
T	V (int i, int j) const
	Return the matrix V's (i,j)th entry (to avoid svd.V()(i,j); ).
vnl_matrix< T >	inverse () const
vnl_matrix< T >	pinverse (unsigned int rank=~0u) const
	pseudo-inverse (for non-square matrix) of desired rank.
vnl_matrix< T >	tinverse (unsigned int rank=~0u) const
	Calculate inverse of transpose, using desired rank.
vnl_matrix< T >	recompose (unsigned int rank=~0u) const
	Recompose SVD to U*W*V', using desired rank.
vnl_matrix< T >	solve (vnl_matrix< T > const &B) const
	Solve the matrix equation M X = B, returning X.
vnl_vector< T >	solve (vnl_vector< T > const &y) const
	Solve the matrix-vector system M x = y, returning x.
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.
vnl_matrix< T >	nullspace () const
	Return N such that M * N = 0.
vnl_matrix< T >	nullspace (int required_nullspace_dimension) const
	Return N such that M * N = 0.
vnl_matrix< T >	left_nullspace () const
	Return N such that M' * N = 0.
vnl_matrix< T >	left_nullspace (int required_nullspace_dimension) const
	Implementation to be done yet; currently returns left_nullspace(). - PVR.
vnl_vector< T >	nullvector () const
	Return the rightmost column of V.
vnl_vector< T >	left_nullvector () const
	Return the rightmost column of U.
bool	valid () const

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Member Typedef Documentation

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 66 of file vnl_svd.h.

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Constructor & Destructor Documentation

template<class T> vnl_matrix_inverse< T >::vnl_matrix_inverse (  vnl_matrix< T > const &  M  )  [inline]

Definition at line 36 of file vnl_matrix_inverse.h.

template<class T> vnl_matrix_inverse< T >::~vnl_matrix_inverse (   )  [inline]

Definition at line 37 of file vnl_matrix_inverse.h.

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Member Function Documentation

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 209 of file vnl_svd.txx.

template<class T> vnl_matrix<T> vnl_svd< T >::inverse (   )  const [inline, inherited]

Definition at line 132 of file vnl_svd.h.

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: . Definition at line 388 of file vnl_svd.txx.

template<class T> vnl_matrix< T > vnl_svd< T >::left_nullspace (   )  const [inherited]

Return N such that M' * N = 0. Definition at line 378 of file vnl_svd.txx.

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 411 of file vnl_svd.txx.

template<class T> vnl_svd< T >::singval_t vnl_svd< T >::norm (   )  const [inherited]

Definition at line 222 of file vnl_svd.txx.

template<class T> vnl_matrix< T > vnl_svd< T >::nullspace (  int  required_nullspace_dimension  )  const [inherited]

Return N such that M * N = 0. Definition at line 370 of file vnl_svd.txx.

template<class T> vnl_matrix< T > vnl_svd< T >::nullspace (   )  const [inherited]

Return N such that M * N = 0. Definition at line 359 of file vnl_svd.txx.

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 399 of file vnl_svd.txx.

template<class T> vnl_matrix_inverse< T >::operator vnl_matrix (   )  const [inline]

Definition at line 39 of file vnl_matrix_inverse.h.

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. Definition at line 243 of file vnl_svd.txx.

template<class T> unsigned int vnl_svd< T >::rank (   )  const [inline, inherited]

Definition at line 94 of file vnl_svd.h.

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. Definition at line 229 of file vnl_svd.txx.

template<class T> singval_t vnl_svd< T >::sigma_max (   )  const [inline, inherited]

Definition at line 119 of file vnl_svd.h.

template<class T> singval_t vnl_svd< T >::sigma_min (   )  const [inline, inherited]

Definition at line 120 of file vnl_svd.h.

template<class T> int vnl_svd< T >::singularities (   )  const [inline, inherited]

Definition at line 93 of file vnl_svd.h.

template<class T> void vnl_svd< T >::solve (  T const *  rhs, T *  lhs )  const [inherited]

Definition at line 332 of file vnl_svd.txx.

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 293 of file vnl_svd.txx.

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 271 of file vnl_svd.txx.

template<class T> void vnl_svd< T >::solve_preinverted (  vnl_vector< T > const &  rhs, vnl_vector< T > *  out )  const [inherited]

Solve the matrix-vector system M x = y. Assuming that the singular values W have been preinverted by the caller. Definition at line 340 of file vnl_svd.txx.

template<class T> vnl_matrix< T > vnl_svd< T >::tinverse (  unsigned int  rank = ~0u  )  const [inherited]

Calculate inverse of transpose, using desired rank. Definition at line 257 of file vnl_svd.txx.

template<class T> T vnl_svd< T >::U (  int  i, int  j )  const [inline, inherited]

Return the matrix U's (i,j)th entry (to avoid svd.U()(i,j); ). Definition at line 108 of file vnl_svd.h.

template<class T> vnl_matrix<T> const& vnl_svd< T >::U (   )  const [inline, inherited]

Return the matrix U. Definition at line 105 of file vnl_svd.h.

template<class T> vnl_matrix<T>& vnl_svd< T >::U (   )  [inline, inherited]

Return the matrix U. Definition at line 102 of file vnl_svd.h.

template<class T> T vnl_svd< T >::V (  int  i, int  j )  const [inline, inherited]

Return the matrix V's (i,j)th entry (to avoid svd.V()(i,j); ). Definition at line 129 of file vnl_svd.h.

template<class T> vnl_matrix<T> const& vnl_svd< T >::V (   )  const [inline, inherited]

Return the matrix V. Definition at line 126 of file vnl_svd.h.

template<class T> vnl_matrix<T>& vnl_svd< T >::V (   )  [inline, inherited]

Return the matrix V. Definition at line 123 of file vnl_svd.h.

template<class T> bool vnl_svd< T >::valid (   )  const [inline, inherited]

Definition at line 175 of file vnl_svd.h.

template<class T> singval_t& vnl_svd< T >::W (  int  i  )  [inline, inherited]

Definition at line 118 of file vnl_svd.h.

template<class T> singval_t& vnl_svd< T >::W (  int  i, int  j )  [inline, inherited]

Definition at line 117 of file vnl_svd.h.

template<class T> vnl_diag_matrix<singval_t> const& vnl_svd< T >::W (   )  const [inline, inherited]

Get at DiagMatrix (q.v. ) of singular values, sorted from largest to smallest. Definition at line 114 of file vnl_svd.h.

template<class T> vnl_diag_matrix<singval_t>& vnl_svd< T >::W (   )  [inline, inherited]

Get at DiagMatrix (q.v. ) of singular values, sorted from largest to smallest. Definition at line 111 of file vnl_svd.h.

template<class T> singval_t vnl_svd< T >::well_condition (   )  const [inline, inherited]

Definition at line 95 of file vnl_svd.h.

template<class T> vnl_diag_matrix<singval_t> const& vnl_svd< T >::Winverse (   )  const [inline, inherited]

Definition at line 116 of file vnl_svd.h.

template<class T> vnl_diag_matrix<singval_t>& vnl_svd< T >::Winverse (   )  [inline, inherited]

Definition at line 115 of file vnl_svd.h.

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 179 of file vnl_svd.txx.

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 199 of file vnl_svd.txx.

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

• core/vnl/algo/vnl_matrix_inverse.h

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