TMatrixDEigen Class Reference

TMatrixDEigen.

Eigenvalues and eigenvectors of a real matrix.

If 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.

Definition at line 26 of file TMatrixDEigen.h.

Public Types
enum	{ kWorkMax = 100 }

Public Member Functions
	TMatrixDEigen ()
	TMatrixDEigen (const TMatrixD &a)
	Constructor for eigen-problem of matrix A . More...
	TMatrixDEigen (const TMatrixDEigen &another)
	Copy constructor. More...
virtual	~TMatrixDEigen ()
const TMatrixD	GetEigenValues () const
	Computes the block diagonal eigenvalue matrix. More...
const TVectorD &	GetEigenValuesIm () const
const TVectorD &	GetEigenValuesRe () const
const TMatrixD &	GetEigenVectors () const
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
TVectorD	fEigenValuesIm
TVectorD	fEigenValuesRe
TMatrixD	fEigenVectors

#include <TMatrixDEigen.h>

Member Enumeration Documentation

anonymous enum

anonymous enum

Enumerator
kWorkMax

Definition at line 40 of file TMatrixDEigen.h.

Constructor & Destructor Documentation

TMatrixDEigen() [1/3]

TMatrixDEigen::TMatrixDEigen ( )

inline

Definition at line 42 of file TMatrixDEigen.h.

TMatrixDEigen() [2/3]

TMatrixDEigen::TMatrixDEigen

(

const TMatrixD &

a

)

Constructor for eigen-problem of matrix A .

Definition at line 57 of file TMatrixDEigen.cxx.

TMatrixDEigen() [3/3]

TMatrixDEigen::TMatrixDEigen

(

const TMatrixDEigen &

another

)

Copy constructor.

Definition at line 98 of file TMatrixDEigen.cxx.

~TMatrixDEigen()

virtual TMatrixDEigen::~TMatrixDEigen ( )

inlinevirtual

Definition at line 46 of file TMatrixDEigen.h.

Member Function Documentation

GetEigenValues()

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 convenience, 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 789 of file TMatrixDEigen.cxx.

GetEigenValuesIm()

const TVectorD& TMatrixDEigen::GetEigenValuesIm ( ) const

inline

Definition at line 57 of file TMatrixDEigen.h.

GetEigenValuesRe()

const TVectorD& TMatrixDEigen::GetEigenValuesRe ( ) const

inline

Definition at line 56 of file TMatrixDEigen.h.

GetEigenVectors()

const TMatrixD& TMatrixDEigen::GetEigenVectors ( ) const

inline

Definition at line 55 of file TMatrixDEigen.h.

MakeHessenBerg()

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 109 of file TMatrixDEigen.cxx.

MakeSchurr()

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 234 of file TMatrixDEigen.cxx.

operator=()

TMatrixDEigen & TMatrixDEigen::operator=

(

const TMatrixDEigen &

source

)

Assignment operator.

Definition at line 740 of file TMatrixDEigen.cxx.

Sort()

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 699 of file TMatrixDEigen.cxx.

Member Data Documentation

fEigenValuesIm

TVectorD TMatrixDEigen::fEigenValuesIm

protected

Definition at line 36 of file TMatrixDEigen.h.

fEigenValuesRe

TVectorD TMatrixDEigen::fEigenValuesRe

protected

Definition at line 35 of file TMatrixDEigen.h.

fEigenVectors

TMatrixD TMatrixDEigen::fEigenVectors

protected

Definition at line 34 of file TMatrixDEigen.h.

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

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