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

#include <vnl_algo_fwd.h>

Public Member Functions
	vnl_symmetric_eigensystem (vnl_matrix< T > const &M)
	Solve real symmetric eigensystem $A x = \lambda x$. More...

vnl_vector< T >	get_eigenvector (int i) const
	Recover specified eigenvector after computation. More...

T	get_eigenvalue (int i) const
	Recover specified eigenvalue after computation. More...

vnl_vector< T >	nullvector () const
	Convenience method to get least-squares nullvector. More...

vnl_matrix< T >	recompose () const
	Return the matrix $V D V^\top$. More...

T	determinant () const
	return product of eigenvalues. More...

vnl_matrix< T >	pinverse () const
	return the pseudoinverse. More...

vnl_matrix< T >	square_root () const
	return the square root, if positive semi-definite. More...

vnl_matrix< T >	inverse_square_root () const
	return the inverse of the square root, if positive semi-definite. More...

vnl_vector< T >	solve (vnl_vector< T > const &b)
	Solve LS problem M x = b. More...

void	solve (vnl_vector< T > const &b, vnl_vector< T > *x)
	Solve LS problem M x = b. More...

Public Attributes
vnl_matrix< T >	V
	Public eigenvectors. More...

vnl_diag_matrix< T >	D
	Public eigenvalues. More...

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 9 of file vnl_algo_fwd.h.

Constructor & Destructor Documentation

◆ vnl_symmetric_eigensystem()

template<class T >

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

Solve real symmetric eigensystem $A x = \lambda x$.

Definition at line 140 of file vnl_symmetric_eigensystem.hxx.

Member Function Documentation

◆ determinant()

template<class T >

T vnl_symmetric_eigensystem< T >::determinant ( ) const

return product of eigenvalues.

Definition at line 178 of file vnl_symmetric_eigensystem.hxx.

◆ get_eigenvalue()

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.hxx.

◆ get_eigenvector()

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.hxx.

◆ inverse_square_root()

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.hxx.

◆ nullvector()

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 109 of file vnl_symmetric_eigensystem.h.

◆ pinverse()

template<class T >

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

return the pseudoinverse.

Definition at line 188 of file vnl_symmetric_eigensystem.hxx.

◆ recompose()

template<class T>

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

inline

Return the matrix $V D V^\top$.

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 119 of file vnl_symmetric_eigensystem.h.

◆ solve() [1/2]

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.hxx.

◆ solve() [2/2]

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 137 of file vnl_symmetric_eigensystem.h.

◆ square_root()

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.hxx.

Member Data Documentation

◆ D

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 std::vector while behaving as a matrix.

Definition at line 99 of file vnl_symmetric_eigensystem.h.