Eigendecomposition. Decomposes any square (n x n) symmetric matrix $(A = A^T)$ into eigenvalues and eigenvectors. More...

#include <Eigen.h>

Public Types
typedef Matrix< matrix::dynamic, matrix::dynamic, Real >	Matrix

typedef Vec< matrix::dynamic, Real >	Vec

Public Member Functions
	Eigen ()

template<class T >
	Eigen (const MatrixBase< T > &a)
	Calculate the eigendecomposition of symmetric matrix A. More...

template<class T >
Eigen &	calc (const MatrixBase< T > &a)
	Calculate the eigendecomposition of symmetric matrix A. The eigenvalues/vectors are sorted from largest to smallest. More...

template<class T >
Eigen &	calcValues (const MatrixBase< T > &a)
	Calculate the eigenvalues of symmetric matrix A. This is a fast method for when the eigenvectors are not needed. More...

template<class B , class X >
void	solve (const MatrixBase< B > &b, MatrixBase< X > &x)
	Solve the linear system where A is the decomposed matrix. A and B row sizes must match. More...

template<class T >
void	inverse (MatrixBase< T > &res)
	Calculate the inverse of A, the decomposed matrix. More...

const Vec &	w () const
	Get the eigenvalues of the decomposition. More...

const Matrix &	v () const
	Get the column eigenvectors of the decomposition. More...

const Matrix &	vt () const
	Get the row eigenvectors of the decomposition. More...

Detailed Description

template<class Real>
class honey::Eigen< Real >

Eigendecomposition. Decomposes any square (n x n) symmetric matrix $(A = A^T)$ into eigenvalues and eigenvectors.

An eigenvector of a square matrix is a non-zero vector that when multiplied by the matrix remains parallel to the original.
An eigenvector $\vec{v}$ satisfies: $A \vec{v} = w \vec{v}$ , where w is a scalar that elongates or shrinks the vector.

The eigendecomposition of a symmetric matrix A is: $ A = V W V^T $ where V is an orthonormal matrix of column eigenvectors and W is a diagonal of eigenvalues.

Complexity: $ O(n^3) $

Member Typedef Documentation

template<class Real >

typedef Matrix<matrix::dynamic, matrix::dynamic, Real> honey::Eigen< Real >::Matrix

template<class Real >

typedef Vec<matrix::dynamic, Real> honey::Eigen< Real >::Vec

Constructor & Destructor Documentation

template<class Real >

honey::Eigen< Real >::Eigen ( )

inline

template<class Real >

template<class T >

honey::Eigen< Real >::Eigen ( const MatrixBase< T > & a )

inline

Calculate the eigendecomposition of symmetric matrix A.

Member Function Documentation

template<class Real >

template<class T >

Eigen& honey::Eigen< Real >::calc ( const MatrixBase< T > & a )

inline

Calculate the eigendecomposition of symmetric matrix A. The eigenvalues/vectors are sorted from largest to smallest.

template<class Real >

template<class T >

Eigen& honey::Eigen< Real >::calcValues ( const MatrixBase< T > & a )

inline

Calculate the eigenvalues of symmetric matrix A. This is a fast method for when the eigenvectors are not needed.

template<class Real >

template<class T >

void honey::Eigen< Real >::inverse ( MatrixBase< T > & res )

inline

Calculate the inverse of A, the decomposed matrix.

template<class Real >

template<class B , class X >

void honey::Eigen< Real >::solve	(	const MatrixBase< B > &	b,
		MatrixBase< X > &	x
	)

inline

Solve the linear system $ Ax = B $ where A is the decomposed matrix. A and B row sizes must match.

template<class Real >

const Matrix& honey::Eigen< Real >::v ( ) const

inline

Get the column eigenvectors of the decomposition.

template<class Real >

const Matrix& honey::Eigen< Real >::vt ( ) const

inline

Get the row eigenvectors $ V^T $ of the decomposition.

template<class Real >

const Vec& honey::Eigen< Real >::w ( ) const

inline

Get the eigenvalues of the decomposition.

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

src/common/Honey/Math/NumAnalysis/Eigen.h
src/common/Honey/Math/NumAnalysis/Eigen.cpp

Public Types

Public Member Functions

Detailed Description

template<class Real> class honey::Eigen< Real >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

template<class Real>
class honey::Eigen< Real >