EigenSolver< _MatrixType > Class Template Reference

Eigen values/vectors solver for non selfadjoint matrices. More...

#include <EigenSolver.h>

Public Types
typedef std::complex< RealScalar >	Complex
typedef Matrix< Complex, MatrixType::ColsAtCompileTime, 1 >	EigenvalueType
typedef Matrix< Complex, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime >	EigenvectorType
typedef _MatrixType	MatrixType
typedef NumTraits< Scalar >::Real	RealScalar
typedef Matrix< RealScalar, MatrixType::ColsAtCompileTime, 1 >	RealVectorType
typedef Matrix< RealScalar, Dynamic, 1 >	RealVectorTypeX
typedef MatrixType::Scalar	Scalar
Public Member Functions
void	compute (const MatrixType &matrix)
	EigenSolver (const MatrixType &matrix)
	EigenSolver ()
	Default Constructor.
EigenvalueType	eigenvalues () const
EigenvectorType	eigenvectors (void) const
MatrixType	pseudoEigenvalueMatrix () const
const MatrixType &	pseudoEigenvectors () const
Protected Attributes
EigenvalueType	m_eivalues
MatrixType	m_eivec
bool	m_isInitialized
Private Member Functions
void	hqr2 (MatrixType &matH)
void	orthes (MatrixType &matH, RealVectorType &ort)

Detailed Description

template<typename _MatrixType>
class EigenSolver< _MatrixType >

Eigen values/vectors solver for non selfadjoint matrices.

Parameters:

MatrixType

the type of the matrix of which we are computing the eigen decomposition

Currently it only support real matrices.

Note:: this code was adapted from JAMA (public domain)

See also:: MatrixBase::eigenvalues(), SelfAdjointEigenSolver

Definition at line 43 of file EigenSolver.h.

Member Typedef Documentation

template<typename _MatrixType >

typedef std::complex<RealScalar> EigenSolver< _MatrixType >::Complex

Definition at line 50 of file EigenSolver.h.

template<typename _MatrixType >

typedef Matrix<Complex, MatrixType::ColsAtCompileTime, 1> EigenSolver< _MatrixType >::EigenvalueType

Definition at line 51 of file EigenSolver.h.

template<typename _MatrixType >

typedef Matrix<Complex, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime> EigenSolver< _MatrixType >::EigenvectorType

Definition at line 52 of file EigenSolver.h.

template<typename _MatrixType >

typedef _MatrixType EigenSolver< _MatrixType >::MatrixType

Definition at line 47 of file EigenSolver.h.

template<typename _MatrixType >

typedef NumTraits<Scalar>::Real EigenSolver< _MatrixType >::RealScalar

Definition at line 49 of file EigenSolver.h.

template<typename _MatrixType >

typedef Matrix<RealScalar, MatrixType::ColsAtCompileTime, 1> EigenSolver< _MatrixType >::RealVectorType

Definition at line 53 of file EigenSolver.h.

template<typename _MatrixType >

typedef Matrix<RealScalar, Dynamic, 1> EigenSolver< _MatrixType >::RealVectorTypeX

Definition at line 54 of file EigenSolver.h.

template<typename _MatrixType >

typedef MatrixType::Scalar EigenSolver< _MatrixType >::Scalar

Definition at line 48 of file EigenSolver.h.

Constructor & Destructor Documentation

template<typename _MatrixType >

EigenSolver< _MatrixType >::EigenSolver ( ) [inline]

Default Constructor.

The default constructor is useful in cases in which the user intends to perform decompositions via EigenSolver::compute(const MatrixType&).

Definition at line 62 of file EigenSolver.h.

template<typename _MatrixType >

EigenSolver< _MatrixType >::EigenSolver ( const MatrixType & matrix ) [inline]

Definition at line 64 of file EigenSolver.h.

Member Function Documentation

template<typename MatrixType >

void EigenSolver< MatrixType >::compute ( const MatrixType & matrix ) [inline]

Definition at line 192 of file EigenSolver.h.

template<typename _MatrixType >

EigenvalueType EigenSolver< _MatrixType >::eigenvalues ( ) const [inline]

Returns:: the eigenvalues as a column vector

Definition at line 115 of file EigenSolver.h.

template<typename MatrixType >

EigenSolver< MatrixType >::EigenvectorType EigenSolver< MatrixType >::eigenvectors ( void ) const [inline]

Returns:: the normalized complex eigenvectors as a matrix of column vectors.

See also:: eigenvalues(), pseudoEigenvectors()

Definition at line 163 of file EigenSolver.h.

template<typename MatrixType >

void EigenSolver< MatrixType >::hqr2 ( MatrixType & matH ) [inline, private]

Definition at line 295 of file EigenSolver.h.

template<typename MatrixType >

void EigenSolver< MatrixType >::orthes	(	MatrixType &	matH,
		RealVectorType &	ort
	)			`[inline, private]`

Definition at line 212 of file EigenSolver.h.

template<typename MatrixType >

MatrixType EigenSolver< MatrixType >::pseudoEigenvalueMatrix ( ) const [inline]

Returns:: the real block diagonal matrix D of the eigenvalues.

See pseudoEigenvectors() for the details.

Definition at line 139 of file EigenSolver.h.

template<typename _MatrixType >

const MatrixType& EigenSolver< _MatrixType >::pseudoEigenvectors ( ) const [inline]

Returns:: a real matrix V of pseudo eigenvectors.

Let D be the block diagonal matrix with the real eigenvalues in 1x1 blocks, and any complex values u+iv in 2x2 blocks [u v ; -v u]. Then, the matrices D and V satisfy A*V = V*D.

More precisely, if the diagonal matrix of the eigen values is:
$\left[ \begin{array}{cccccc} u+iv & & & & & \\ & u-iv & & & & \\ & & a+ib & & & \\ & & & a-ib & & \\ & & & & x & \\ & & & & & y \\ \end{array} \right]$
then, we have:
$D =\left[ \begin{array}{cccccc} u & v & & & & \\ -v & u & & & & \\ & & a & b & & \\ & & -b & a & & \\ & & & & x & \\ & & & & & y \\ \end{array} \right]$