This class finds eigenvalues and eigenvectors of real symmetric tridiagonal matrices. More...

#include <math_EigenValuesSearcher.hxx>

Public Member Functions
	math_EigenValuesSearcher (const NCollection_Array1< double > &theDiagonal, const NCollection_Array1< double > &theSubdiagonal)
bool	IsDone () const
	Returns true if computation is performed successfully. Computation may fail due to numerical issues or invalid input.
int	Dimension () const
	Returns the dimension of the tridiagonal matrix.
double	EigenValue (const int theIndex) const
	Returns the specified eigenvalue. Eigenvalues are returned in the order they were computed by the algorithm, which may not be sorted. Use sorting if ordered eigenvalues are needed.
math_Vector	EigenVector (const int theIndex) const
	Returns the specified eigenvector. The returned eigenvector is normalized and orthogonal to all other eigenvectors. The eigenvector satisfies: A * v = lambda * v, where A is the original matrix, v is the eigenvector, and lambda is the corresponding eigenvalue.

Detailed Description

This class finds eigenvalues and eigenvectors of real symmetric tridiagonal matrices.

The implementation uses the QR algorithm with implicit shifts for numerical stability. All computed eigenvalues are real (since the matrix is symmetric), and eigenvectors are orthonormal. The class handles the complete eigendecomposition: A * V = V * D, where A is the input matrix, V contains eigenvectors as columns, and D is diagonal with eigenvalues.

Key features:

Robust QR algorithm implementation
Numerical stability through implicit shifts
Complete eigenvalue/eigenvector computation
Proper handling of degenerate cases

Constructor & Destructor Documentation

◆ math_EigenValuesSearcher()

math_EigenValuesSearcher::math_EigenValuesSearcher	(	const NCollection_Array1< double > &	theDiagonal,
		const NCollection_Array1< double > &	theSubdiagonal )

Member Function Documentation

◆ Dimension()

int math_EigenValuesSearcher::Dimension ( ) const

Returns the dimension of the tridiagonal matrix.

◆ EigenValue()

double math_EigenValuesSearcher::EigenValue ( const int theIndex ) const

Returns the specified eigenvalue. Eigenvalues are returned in the order they were computed by the algorithm, which may not be sorted. Use sorting if ordered eigenvalues are needed.

Parameters

theIndex index of the desired eigenvalue (1-based indexing)

Returns: the eigenvalue at the specified index

◆ EigenVector()

math_Vector math_EigenValuesSearcher::EigenVector ( const int theIndex ) const

Returns the specified eigenvector. The returned eigenvector is normalized and orthogonal to all other eigenvectors. The eigenvector satisfies: A * v = lambda * v, where A is the original matrix, v is the eigenvector, and lambda is the corresponding eigenvalue.

Parameters

theIndex index of the desired eigenvector (1-based indexing)

Returns: the normalized eigenvector corresponding to EigenValue(theIndex)

◆ IsDone()

bool math_EigenValuesSearcher::IsDone ( ) const

Returns true if computation is performed successfully. Computation may fail due to numerical issues or invalid input.

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

math_EigenValuesSearcher.hxx

Public Member Functions