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 void	ShowMembers(TMemberInspector&)
virtual void	Streamer(TBuffer&)
void	StreamerNVirtual(TBuffer& ClassDef_StreamerNVirtual_b)

protected:

static void	MakeEigenVectors(TMatrixD& v, TVectorD& d, TVectorD& e)
static void	MakeTridiagonal(TMatrixD& v, TVectorD& d, TVectorD& e)

Data Members

public:

enum {	kWorkMax
};

protected:

TVectorD	fEigenValues	Eigen-values
TMatrixD	fEigenVectors	Eigen-vectors of matrix

Class Charts

Inheritance Inherited Members Includes Libraries

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() const

 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() const

{ return fEigenValues; }