#include <itkGeneralizedEigenDecomposition.h>

Detailed Description

template<typename TReal>
class itk::GeneralizedEigenDecomposition< TReal >

Symmetric-definite generalized eigenproblem A x = lambda B x, Eigen-backed.

Solves A x = lambda B x with A symmetric and B symmetric positive-definite, via Eigen's GeneralizedSelfAdjointEigenSolver. Eigenvalues are real and returned in ascending order; eigenvectors are the B-orthonormal columns, sign-canonicalized (each column's largest-magnitude entry positive) for cross-platform reproducibility. Results are stored in vnl containers so no Eigen type appears in the public interface.

This is the supported Eigen-backed replacement for the now-deprecated vnl_generalized_eigensystem (netlib EISPACK rsg), which emits a deprecation warning under ITK_LEGACY_REMOVE and is removed under ITK_FUTURE_LEGACY_REMOVE.

Definition at line 49 of file itkGeneralizedEigenDecomposition.h.

Public Types
using	MatrixType = vnl_matrix<TReal>

using	VectorType = vnl_vector<TReal>

Public Member Functions
	GeneralizedEigenDecomposition (const MatrixType &A, const MatrixType &B, bool canonicalizeSigns=true)

const VectorType &	GetEigenvalues () const

const MatrixType &	GetEigenvectors () const

Private Attributes
VectorType	m_Eigenvalues

MatrixType	m_Eigenvectors

Member Typedef Documentation

◆ MatrixType

template<typename TReal>

using itk::GeneralizedEigenDecomposition< TReal >::MatrixType = vnl_matrix<TReal>

Definition at line 52 of file itkGeneralizedEigenDecomposition.h.

◆ VectorType

template<typename TReal>

using itk::GeneralizedEigenDecomposition< TReal >::VectorType = vnl_vector<TReal>

Definition at line 53 of file itkGeneralizedEigenDecomposition.h.

Constructor & Destructor Documentation

◆ GeneralizedEigenDecomposition()

template<typename TReal>

itk::GeneralizedEigenDecomposition< TReal >::GeneralizedEigenDecomposition	(	const MatrixType &	A,
		const MatrixType &	B,
		bool	canonicalizeSigns = true )

inline

Solve A x = lambda B x for symmetric A and symmetric-positive-definite B. With canonicalizeSigns (the default) each eigenvector column's largest-magnitude entry is made positive for cross-platform reproducibility; pass false to keep the solver's raw signs.

Definition at line 59 of file itkGeneralizedEigenDecomposition.h.

References itk::detail::CanonicalizeEigenvectorColumnSigns(), itk::detail::EigenComputationInfoString(), m_Eigenvalues, and m_Eigenvectors.