vnl_symmetric_eigensystem< T > Class Template Reference

#include <vnl_symmetric_eigensystem.h>

List of all members.

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Detailed Description

template<class T>
class vnl_symmetric_eigensystem< T >

Computes and stores the eigensystem decomposition of a symmetric matrix.

Definition at line 83 of file 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_

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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 152 of file vnl_symmetric_eigensystem.cxx.

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Member Function Documentation

template<class T> T vnl_symmetric_eigensystem< T >::determinant (   )  const

return product of eigenvalues. Definition at line 190 of file vnl_symmetric_eigensystem.cxx.

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

Recover specified eigenvalue after computation. Definition at line 171 of file vnl_symmetric_eigensystem.cxx.

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

Recover specified eigenvector after computation. Definition at line 165 of file vnl_symmetric_eigensystem.cxx.

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 231 of file vnl_symmetric_eigensystem.cxx.

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 113 of file vnl_symmetric_eigensystem.h.

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

return the pseudoinverse. Definition at line 200 of file vnl_symmetric_eigensystem.cxx.

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 . 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 123 of file vnl_symmetric_eigensystem.h.

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 141 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 177 of file vnl_symmetric_eigensystem.cxx.

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

return the square root, if positive semi-definite. Definition at line 215 of file vnl_symmetric_eigensystem.cxx.

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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 103 of file vnl_symmetric_eigensystem.h.

template<class T> int vnl_symmetric_eigensystem< T >::n_ [protected]

Definition at line 92 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 98 of file vnl_symmetric_eigensystem.h.

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

• core/vnl/algo/vnl_symmetric_eigensystem.h
• core/vnl/algo/vnl_symmetric_eigensystem.cxx

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