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 TMatrixDGetEigenValues() const
const TVectorD&GetEigenValuesIm() const
const TVectorD&GetEigenValuesRe() const
const TMatrixD&GetEigenVectors() const
virtual TClass*IsA() const
TMatrixDEigen&operator=(const TMatrixDEigen& source)
virtual voidShowMembers(TMemberInspector& insp, char* parent)
virtual voidStreamer(TBuffer& b)
voidStreamerNVirtual(TBuffer& b)
protected:
static voidMakeHessenBerg(TMatrixD& v, TVectorD& ortho, TMatrixD& H)
static voidMakeSchurr(TMatrixD& v, TVectorD& d, TVectorD& e, TMatrixD& H)
static voidSort(TMatrixD& v, TVectorD& d, TVectorD& e)

Data Members

public:
enum { kWorkMax
};
protected:
TVectorDfEigenValuesImEigen-values
TVectorDfEigenValuesReEigen-values
TMatrixDfEigenVectorsEigen-vectors of matrix

Class Charts

Inheritance Inherited Members Includes Libraries
Class Charts

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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