Computes and stores the eigensystem decomposition of a symmetric matrix. More...

#include <vnl_symmetric_eigensystem.h>

Public Member Functions
	vnl_symmetric_eigensystem (vnl_matrix< T > const &M)
	Solve real symmetric eigensystem $A x = x$.
vnl_vector< T >	get_eigenvector (int i) const
	Recover specified eigenvector after computation.
T	get_eigenvalue (int i) const
	Recover specified eigenvalue after computation.
vnl_vector< T >	nullvector () const
	Convenience method to get least-squares nullvector.
vnl_matrix< T >	recompose () const
	Return the matrix $V D V^$.
T	determinant () const
	return product of eigenvalues.
vnl_matrix< T >	pinverse () const
	return the pseudoinverse.
vnl_matrix< T >	square_root () const
	return the square root, if positive semi-definite.
vnl_matrix< T >	inverse_square_root () const
	return the inverse of the square root, if positive semi-definite.
vnl_vector< T >	solve (vnl_vector< T > const &b)
	Solve LS problem M x = b.
void	solve (vnl_vector< T > const &b, vnl_vector< T > *x)
	Solve LS problem M x = b.
Public Attributes
vnl_matrix< T >	V
	Public eigenvectors.
vnl_diag_matrix< T >	D
	Public eigenvalues.
Protected Attributes
int	n_

Detailed Description

template<class T>
class vnl_symmetric_eigensystem< T >

Computes and stores the eigensystem decomposition of a symmetric matrix.

Definition at line 81 of file vnl_symmetric_eigensystem.h.

Constructor & Destructor Documentation

template<class T >

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

Solve real symmetric eigensystem $A x = x$.

Definition at line 140 of file vnl_symmetric_eigensystem.txx.

Member Function Documentation

template<class T >

T vnl_symmetric_eigensystem< T >::determinant ( ) const

return product of eigenvalues.

Definition at line 178 of file vnl_symmetric_eigensystem.txx.

template<class T >

T vnl_symmetric_eigensystem< T >::get_eigenvalue ( int i ) const

Recover specified eigenvalue after computation.

Definition at line 159 of file vnl_symmetric_eigensystem.txx.

template<class T >

vnl_vector< T > vnl_symmetric_eigensystem< T >::get_eigenvector ( int i ) const

Recover specified eigenvector after computation.

Definition at line 153 of file vnl_symmetric_eigensystem.txx.

template<class T >

vnl_matrix< T > vnl_symmetric_eigensystem< T >::inverse_square_root ( ) const

return the inverse of the square root, if positive semi-definite.

Definition at line 219 of file vnl_symmetric_eigensystem.txx.

template<class T>

vnl_vector<T> vnl_symmetric_eigensystem< T >::nullvector ( ) const [inline]

Convenience method to get least-squares nullvector.

It is deliberate that the signature is the same as on vnl_svd<T>.

Definition at line 111 of file vnl_symmetric_eigensystem.h.

template<class T >

vnl_matrix< T > vnl_symmetric_eigensystem< T >::pinverse ( ) const

return the pseudoinverse.

Definition at line 188 of file vnl_symmetric_eigensystem.txx.

template<class T>

vnl_matrix<T> vnl_symmetric_eigensystem< T >::recompose ( ) const [inline]

Return the matrix $V D V^$.

This can be useful if you've modified $D$ . So an inverse is obtained using

   vnl_symmetric_eigensystem} eig(A);
   eig.D.invert_in_place}();
   vnl_matrix<double> Ainverse = eig.recompose();

Definition at line 121 of file vnl_symmetric_eigensystem.h.

template<class T >

vnl_vector< T > vnl_symmetric_eigensystem< T >::solve ( vnl_vector< T > const & b )

Solve LS problem M x = b.

Definition at line 165 of file vnl_symmetric_eigensystem.txx.

template<class T>

void vnl_symmetric_eigensystem< T >::solve	(	vnl_vector< T > const &	b,
		vnl_vector< T > *	x
	)		`[inline]`

Solve LS problem M x = b.

Definition at line 139 of file vnl_symmetric_eigensystem.h.

template<class T >

vnl_matrix< T > vnl_symmetric_eigensystem< T >::square_root ( ) const

return the square root, if positive semi-definite.

Definition at line 203 of file vnl_symmetric_eigensystem.txx.

Member Data Documentation

template<class T>

vnl_diag_matrix<T> vnl_symmetric_eigensystem< T >::D

Public eigenvalues.

After construction, D contains the eigenvalues, sorted as described above. Note that D is a vnl_diag_matrix, and is therefore stored as a vcl_vector while behaving as a matrix.

Definition at line 101 of file vnl_symmetric_eigensystem.h.

template<class T>

int vnl_symmetric_eigensystem< T >::n_ [protected]

Definition at line 90 of file vnl_symmetric_eigensystem.h.

template<class T>

vnl_matrix<T> vnl_symmetric_eigensystem< T >::V

Public eigenvectors.

After construction, the columns of V are the eigenvectors, sorted by increasing eigenvalue, from most negative to most positive.

Definition at line 96 of file vnl_symmetric_eigensystem.h.

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