Definition at line 30 of file TMatrixDEigen.h.

Public Types
enum	{ kWorkMax = 100 }

Public Member Functions
	TMatrixDEigen ()

	TMatrixDEigen (const TMatrixD &a)

	TMatrixDEigen (const TMatrixDEigen &another)
	Copy constructor. More...

virtual	~TMatrixDEigen ()

const TMatrixD &	GetEigenVectors () const

const TVectorD &	GetEigenValuesRe () const

const TVectorD &	GetEigenValuesIm () const

const TMatrixD	GetEigenValues () const
	Computes the block diagonal eigenvalue matrix. More...

TMatrixDEigen &	operator= (const TMatrixDEigen &source)
	Assignment operator. More...

Static Protected Member Functions
static void	MakeHessenBerg (TMatrixD &v, TVectorD &ortho, TMatrixD &H)
	Nonsymmetric reduction to Hessenberg form. More...

static void	MakeSchurr (TMatrixD &v, TVectorD &d, TVectorD &e, TMatrixD &H)
	Nonsymmetric reduction from Hessenberg to real Schur form. More...

static void	Sort (TMatrixD &v, TVectorD &d, TVectorD &e)
	Sort eigenvalues and corresponding vectors in descending order of Re^2+Im^2 of the complex eigenvalues . More...

Protected Attributes
TMatrixD	fEigenVectors

TVectorD	fEigenValuesRe

TVectorD	fEigenValuesIm

#include <TMatrixDEigen.h>

Collaboration diagram for TMatrixDEigen:

Member Enumeration Documentation

anonymous enum

Enumerator
kWorkMax

Definition at line 44 of file TMatrixDEigen.h.

Constructor & Destructor Documentation

TMatrixDEigen::TMatrixDEigen ( )

inline

Definition at line 46 of file TMatrixDEigen.h.

TMatrixDEigen::TMatrixDEigen ( const TMatrixD & a )

TMatrixDEigen::TMatrixDEigen ( const TMatrixDEigen & another )

Copy constructor.

Definition at line 93 of file TMatrixDEigen.cxx.

virtual TMatrixDEigen::~TMatrixDEigen ( )

inlinevirtual

Definition at line 50 of file TMatrixDEigen.h.

Member Function Documentation

const TMatrixD TMatrixDEigen::GetEigenValues ( ) const

Computes the block diagonal eigenvalue matrix.

If the original matrix A is not symmetric, then the eigenvalue matrix D is block diagonal with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues, a + i*b, in 2-by-2 blocks, [a, b; -b, a]. That is, if the complex eigenvalues look like

u + iv . . . . . . u - iv . . . . . . a + ib . . . . . . a - ib . . . . . . x . . . . . . y

then D looks like

u        v        .          .      .    .

-v u . . . . . . a b . . . . -b a . . . . . . x . . . . . . y

This keeps V a real matrix in both symmetric and non-symmetric cases, and A*V = V*D.

Indexing: If matrix A has the index/shape (rowLwb,rowUpb,rowLwb,rowUpb) each eigen-vector must have the shape (rowLwb,rowUpb) . For convinience, the column index of the eigen-vector matrix also runs from rowLwb to rowUpb so that the returned matrix has also index/shape (rowLwb,rowUpb,rowLwb,rowUpb) .

Definition at line 780 of file TMatrixDEigen.cxx.

const TVectorD& TMatrixDEigen::GetEigenValuesIm ( ) const

inline

Definition at line 61 of file TMatrixDEigen.h.

const TVectorD& TMatrixDEigen::GetEigenValuesRe ( ) const

inline

Definition at line 60 of file TMatrixDEigen.h.

Referenced by TMatrixT< Element >::EigenVectors().

const TMatrixD& TMatrixDEigen::GetEigenVectors ( ) const

inline

Definition at line 59 of file TMatrixDEigen.h.

Referenced by TMatrixT< Element >::EigenVectors().

void TMatrixDEigen::MakeHessenBerg	(	TMatrixD &	v,
		TVectorD &	ortho,
		TMatrixD &	H
	)

staticprotected

Nonsymmetric reduction to Hessenberg form.

This is derived from the Algol procedures orthes and ortran, by Martin and Wilkinson, Handbook for Auto. Comp., Vol.ii-Linear Algebra, and the corresponding Fortran subroutines in EISPACK.

Definition at line 104 of file TMatrixDEigen.cxx.

void TMatrixDEigen::MakeSchurr	(	TMatrixD &	v,
		TVectorD &	d,
		TVectorD &	e,
		TMatrixD &	H
	)

staticprotected

Nonsymmetric reduction from Hessenberg to real Schur form.

This is derived from the Algol procedure hqr2, by Martin and Wilkinson, Handbook for Auto. Comp., Vol.ii-Linear Algebra, and the corresponding Fortran subroutine in EISPACK.

Definition at line 229 of file TMatrixDEigen.cxx.

TMatrixDEigen & TMatrixDEigen::operator= ( const TMatrixDEigen & source )

Assignment operator.

Definition at line 735 of file TMatrixDEigen.cxx.

void TMatrixDEigen::Sort	(	TMatrixD &	v,
		TVectorD &	d,
		TVectorD &	e
	)

staticprotected

Sort eigenvalues and corresponding vectors in descending order of Re^2+Im^2 of the complex eigenvalues .

Definition at line 694 of file TMatrixDEigen.cxx.

Member Data Documentation

TVectorD TMatrixDEigen::fEigenValuesIm

protected

Definition at line 40 of file TMatrixDEigen.h.

Referenced by GetEigenValues(), GetEigenValuesIm(), and operator=().

TVectorD TMatrixDEigen::fEigenValuesRe

protected

Definition at line 39 of file TMatrixDEigen.h.

Referenced by GetEigenValues(), GetEigenValuesRe(), and operator=().

TMatrixD TMatrixDEigen::fEigenVectors

protected

Definition at line 38 of file TMatrixDEigen.h.

Referenced by GetEigenValues(), GetEigenVectors(), and operator=().

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

math/matrix/inc/TMatrixDEigen.h
math/matrix/src/TMatrixDEigen.cxx

Public Types

Public Member Functions

Static Protected Member Functions

Protected Attributes

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation