#include <itkSymmetricEigenDecomposition.h>

Detailed Description

template<typename T>
class itk::SymmetricEigenDecomposition< T >

Stored eigendecomposition of a real symmetric matrix, Eigen-backed.

Computes A = V D V^T for symmetric A in the constructor and stores the result. Eigenvalues (D) are real and ascending; the columns of V are the orthonormal eigenvectors, sign-canonicalized (each column's largest-magnitude entry is positive) for cross-platform reproducibility. The public V / D members and the get_eigenvector / get_eigenvalue accessors mirror the legacy vnl_symmetric_eigensystem layout, so its call sites port by changing only the type name, with no Eigen type in the interface.

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

Note: Distinct from itk::SymmetricEigenAnalysis, which is a configurable solver object (SetDimension / SetOrderEigenValues) that writes results into caller-supplied output arguments and is tuned for repeated per-pixel tensor eigenanalysis; it does not canonicalize eigenvector signs. This class is a single-shot stored decomposition. Prefer SymmetricEigenAnalysis for high-throughput fixed-size tensor work; prefer this for vnl_symmetric_eigensystem-style usage.

See also: SymmetricEigenAnalysis

Definition at line 60 of file itkSymmetricEigenDecomposition.h.

Public Member Functions
T	get_eigenvalue (int i) const

vnl_vector< T >	get_eigenvector (int i) const

vnl_vector< T >	nullvector () const

vnl_matrix< T >	recompose () const

	SymmetricEigenDecomposition (const vnl_matrix< T > &M, bool canonicalizeSigns=true)

Public Attributes
vnl_diag_matrix< T >	D

vnl_matrix< T >	V

Constructor & Destructor Documentation

◆ SymmetricEigenDecomposition()

template<typename T>

itk::SymmetricEigenDecomposition< T >::SymmetricEigenDecomposition	(	const vnl_matrix< T > &	M,
		bool	canonicalizeSigns = true )

inlineexplicit

Compute the decomposition of symmetric M. 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 67 of file itkSymmetricEigenDecomposition.h.

References itk::detail::CanonicalizeEigenvectorColumnSigns(), D, itk::detail::EigenComputationInfoString(), and V.