class TMatrixDSymEigen


TMatrixDSymEigen

Eigenvalues and eigenvectors of a real symmetric matrix.

If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is
diagonal and the eigenvector matrix V is orthogonal. That is, the
diagonal values of D are the eigenvalues, and V*V' = I, where I is
the identity matrix.  The columns of V represent the eigenvectors in
the sense that A*V = V*D.


Function Members (Methods)

public:
TMatrixDSymEigen()
TMatrixDSymEigen(const TMatrixDSym& a)
TMatrixDSymEigen(const TMatrixDSymEigen& another)
virtual~TMatrixDSymEigen()
static TClass*Class()
const TVectorD&GetEigenValues() const
const TMatrixD&GetEigenVectors() const
virtual TClass*IsA() const
TMatrixDSymEigen&operator=(const TMatrixDSymEigen& source)
virtual voidShowMembers(TMemberInspector& insp, char* parent)
virtual voidStreamer(TBuffer& b)
voidStreamerNVirtual(TBuffer& b)
protected:
static voidMakeEigenVectors(TMatrixD& v, TVectorD& d, TVectorD& e)
static voidMakeTridiagonal(TMatrixD& v, TVectorD& d, TVectorD& e)

Data Members

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

Class Charts

Inheritance Inherited Members Includes Libraries
Class Charts

Function documentation

TMatrixDSymEigen(const TMatrixDSym &a)
 Constructor for eigen-problem of symmetric matrix A .
TMatrixDSymEigen(const TMatrixDSymEigen &another)
 Copy constructor
void MakeTridiagonal(TMatrixD& v, TVectorD& d, TVectorD& e)
 This is derived from the Algol procedures tred2 by Bowdler, Martin, Reinsch, and
 Wilkinson, Handbook for Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
 Fortran subroutine in EISPACK.
void MakeEigenVectors(TMatrixD& v, TVectorD& d, TVectorD& e)
 Symmetric tridiagonal QL algorithm.
 This is derived from the Algol procedures tql2, by Bowdler, Martin, Reinsch, and
 Wilkinson, Handbook for Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
 Fortran subroutine in EISPACK.
TMatrixDSymEigen & operator=(const TMatrixDSymEigen& source)
 Assignment operator
TMatrixDSymEigen()
{}
virtual ~TMatrixDSymEigen()
{}
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 vector .
{ return fEigenVectors; }
const TVectorD & GetEigenValues()
{ return fEigenValues; }

Last change: root/matrix:$Id: TMatrixDSymEigen.h 22428 2008-03-03 18:17:03Z brun $
Last generated: 2008-06-25 08:49
Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. *

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