class TMatrixDEigen


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.

Function Members (Methods)

public:

	TMatrixDEigen()
	TMatrixDEigen(const TMatrixD& a)
	TMatrixDEigen(const TMatrixDEigen& another)
virtual	~TMatrixDEigen()
static TClass*	Class()
const TMatrixD	GetEigenValues() const
const TVectorD&	GetEigenValuesIm() const
const TVectorD&	GetEigenValuesRe() const
const TMatrixD&	GetEigenVectors() const
virtual TClass*	IsA() const
TMatrixDEigen&	operator=(const TMatrixDEigen& source)
virtual void	ShowMembers(TMemberInspector& insp, char* parent)
virtual void	Streamer(TBuffer& b)
void	StreamerNVirtual(TBuffer& b)

protected:

static void	MakeHessenBerg(TMatrixD& v, TVectorD& ortho, TMatrixD& H)
static void	MakeSchurr(TMatrixD& v, TVectorD& d, TVectorD& e, TMatrixD& H)
static void	Sort(TMatrixD& v, TVectorD& d, TVectorD& e)

Data Members

public:

enum {	kWorkMax
};

protected:

TVectorD	fEigenValuesIm	Eigen-values
TVectorD	fEigenValuesRe	Eigen-values
TMatrixD	fEigenVectors	Eigen-vectors of matrix

Class Charts

Inheritance Inherited Members Includes Libraries

Function documentation

TMatrixDEigen(const TMatrixD &a)

 Constructor for eigen-problem of matrix A .

TMatrixDEigen(const TMatrixDEigen &another)

 Copy constructor

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

 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.

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

 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.

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 .

TMatrixDEigen & operator=(const TMatrixDEigen& source)

 Assignment operator

const TMatrixD GetEigenValues()

 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) .

TMatrixDEigen()

{}

virtual ~TMatrixDEigen()

{}

const TMatrixD & GetEigenVectors()

 If matrix A has shape (rowLwb,rowUpb,rowLwb,rowUpb), then each eigen-vector
 must have an index running between (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) .
 The same is true for the eigen-value vectors an matrix .

{ return fEigenVectors; }

const TVectorD & GetEigenValuesRe()

{ return fEigenValuesRe; }

const TVectorD & GetEigenValuesIm()

{ return fEigenValuesIm; }

Last change: root/matrix:$Id: TMatrixDEigen.h 20882 2007-11-19 11:31:26Z rdm $
Last generated: 2008-06-25 08:49
Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. *

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