cvr::symmetricEigenSystem< T > Class Template Reference
[Linear Algebra, Statistics]

Computes the Eigenvectors and Eigenvalues of a symmetric, positive definite, real matrix. More...

#include <cvrSymmetricEigenSystem.h>

Inheritance diagram for cvr::symmetricEigenSystem< T >:

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List of all members.

Classes
class	parameters
	eigenSystem parameter class More...
Public Member Functions
	symmetricEigenSystem ()
	symmetricEigenSystem (const parameters &params)
virtual bool	apply (const matrix< T > &theMatrix, vector< T > &eigenvalues, matrix< T > &eigenvectors) const
virtual bool	reducedEigenSystem (const matrix< T > &theMatrix, vector< T > &eigenvalues, matrix< T > &eigenvectors, const int dimensions) const
const std::string &	name () const
virtual symmetricEigenSystem *	clone () const
virtual symmetricEigenSystem *	newInstance () const
const parameters &	getParameters () const

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Detailed Description

template<typename T>
class cvr::symmetricEigenSystem< T >

Computes the Eigenvectors and Eigenvalues of a symmetric, positive definite, real matrix.

The most common source of such matrices is a covariance matrix (see cvr::secondOrderStatistics).

This class uses the LAPACK functions by default if they are installed on your system. Otherwise a simple Jacobi algorithm is used. This can also be chosen deliberately by setting parameters::useLapack to false.

The eigenvectors can be sorted according to their eigenvalues by setting parameters::sort. A fixed number of eigenvectors can be set via parameters::dimension. For LAPACK this also reduces computation time.

Please note that the eigenvector matrices will contain the eigenvectors in the COLUMNS and not in the rows, as could be expected. This avoids the requirement of transposing matrices in eigenvector-based transformations like PCA!

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Constructor & Destructor Documentation

template<typename T >

cvr::symmetricEigenSystem< T >::symmetricEigenSystem

(

)

Default constructor.

template<typename T >

cvr::symmetricEigenSystem< T >::symmetricEigenSystem

(

const parameters &

params

)

Default constructor with parameters.

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Member Function Documentation

template<typename T >

virtual bool cvr::symmetricEigenSystem< T >::apply	(	const matrix< T > &	theMatrix,
		vector< T > &	eigenvalues,
		matrix< T > &	eigenvectors
	)			const [virtual]

Calculate the Eigensystem with eigenvalues and eigenvalues from the given data in theMatrix (Samples in rows).

Due to the symmetricity of the data it suffices if theMatrix is upper triangular.

Parameters:

	theMatrix	Real symmetric matrix to be transformed. Only the diagonal and above diagonal elements have to be set.
	eigenvalues	Elements will contain the eigenvalues.
	eigenvectors	Columns will contain the eigenvectors corresponding to the eigenvalues. returns true if successful, false otherwise.

template<typename T >

virtual symmetricEigenSystem* cvr::symmetricEigenSystem< T >::clone

(

)

const [virtual]

Returns a pointer to a clone of this functor.

Implements cvr::functor.

template<typename T >

const parameters& cvr::symmetricEigenSystem< T >::getParameters

(

)

const

returns the current parameters.

Reimplemented from cvr::linearAlgebraFunctor.

template<typename T >

const std::string& cvr::symmetricEigenSystem< T >::name

(

)

const [virtual]

Returns the name of this class.

Reimplemented from cvr::lapackInterface.

template<typename T >

virtual symmetricEigenSystem* cvr::symmetricEigenSystem< T >::newInstance

(

)

const [virtual]

Returns a pointer to a new instance of this functor.

Implements cvr::functor.

template<typename T >

virtual bool cvr::symmetricEigenSystem< T >::reducedEigenSystem	(	const matrix< T > &	theMatrix,
		vector< T > &	eigenvalues,
		matrix< T > &	eigenvectors,
		const int	dimensions
	)			const [virtual]

Convenience function that calculates the Eigensystem like apply, but uses the given argument dimensions instead of those given in parameters::dimensions.

Parameters:

	theMatrix	Real symmetric matrix to be transformed. Only the diagonal and above diagonal elements have to be set.
	eigenvalues	Elements will contain the eigenvalues.
	eigenvectors	Columns will contain the eigenvectors corresponding to the eigenvalues.
	dimensions	number of dimensions in eigenspace returns true if successful, false otherwise.

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

• cvrSymmetricEigenSystem.h