Jacobi eigen vectors/values decomposition. More...

#include <Jacobi.h>

Public Types
using	SquareMatrix = cloudViewer::SquareMatrixTpl< Scalar >

using	EigenValues = std::vector< Scalar >

Static Public Member Functions
static bool	ComputeEigenValuesAndVectors2 (const SquareMatrix &matrix, SquareMatrix &eigenVectors, EigenValues &eigenValues, unsigned maxIterationCount=50)
	Computes the eigenvalues and eigenvectors of a given square matrix. More...

static bool	ComputeEigenValuesAndVectors (const SquareMatrix &matrix, SquareMatrix &eigenVectors, EigenValues &eigenValues, bool absoluteValues=true, unsigned maxIterationCount=50)
	Computes eigen vectors (and values) with the Jacobian method. More...

static bool	SortEigenValuesAndVectors (SquareMatrix &eigenVectors, EigenValues &eigenValues)

static bool	GetEigenVector (const SquareMatrix &eigenVectors, unsigned index, Scalar eigenVector[])
	Returns the given eigenvector. More...

static bool	GetMaxEigenValueAndVector (const SquareMatrix &eigenVectors, const EigenValues &eigenValues, Scalar &maxEigenValue, Scalar maxEigenVector[])
	Returns the biggest eigenvalue and its associated eigenvector. More...

static bool	GetMinEigenValueAndVector (const SquareMatrix &eigenVectors, const EigenValues &eigenValues, Scalar &minEigenValue, Scalar minEigenVector[])
	Returns the smallest eigenvalue and its associated eigenvector. More...

Detailed Description

template<typename Scalar>
class Jacobi< Scalar >

Jacobi eigen vectors/values decomposition.

Definition at line 23 of file Jacobi.h.

Member Typedef Documentation

◆ EigenValues

template<typename Scalar >

using Jacobi< Scalar >::EigenValues = std::vector<Scalar>

Definition at line 26 of file Jacobi.h.

◆ SquareMatrix

template<typename Scalar >

using Jacobi< Scalar >::SquareMatrix = cloudViewer::SquareMatrixTpl<Scalar>

Definition at line 25 of file Jacobi.h.

Member Function Documentation

◆ ComputeEigenValuesAndVectors()

template<typename Scalar >

static bool Jacobi< Scalar >::ComputeEigenValuesAndVectors	(	const SquareMatrix &	matrix,
		SquareMatrix &	eigenVectors,
		EigenValues &	eigenValues,
		bool	absoluteValues = `true`,
		unsigned	maxIterationCount = `50`
	)

inlinestatic

Computes eigen vectors (and values) with the Jacobian method.

See the Numerical Recipes.

Definition at line 183 of file Jacobi.h.

References abs(), cloudViewer::SquareMatrixTpl< Scalar >::isValid(), cloudViewer::SquareMatrixTpl< Scalar >::m_values, ROTATE, cloudViewer::SquareMatrixTpl< Scalar >::size(), and cloudViewer::SquareMatrixTpl< Scalar >::toIdentity().

Referenced by ccCompass::estimateStrain(), and ccCompass::estimateStructureNormals().

◆ ComputeEigenValuesAndVectors2()

template<typename Scalar >

static bool Jacobi< Scalar >::ComputeEigenValuesAndVectors2	(	const SquareMatrix &	matrix,
		SquareMatrix &	eigenVectors,
		EigenValues &	eigenValues,
		unsigned	maxIterationCount = `50`
	)

inlinestatic

Computes the eigenvalues and eigenvectors of a given square matrix.

It uses Rutishauser's modfications of the classical Jacobi rotation method with threshold pivoting.

 Note: this code is inspired from John Burkardt's 'jacobi_eigenvalue'

code See https://people.sc.fsu.edu/~jburkardt/cpp_src/jacobi_eigenvalue/jacobi_eigenvalue.cpp

 \warning DGM: this method gives strange results in some particular

cases!!!

 \param[in] matrix input square matrix
 \param[out] eigenVectors eigenvectors (as a square matrix)
 \param[out] eigenValues eigenvalues
 \param[in] maxIterationCount max number of iteration (optional)
 \return success

Definition at line 45 of file Jacobi.h.

References cloudViewer::SquareMatrixTpl< Scalar >::isValid(), cloudViewer::SquareMatrixTpl< Scalar >::m_values, cloudViewer::SquareMatrixTpl< Scalar >::size(), and cloudViewer::SquareMatrixTpl< Scalar >::toIdentity().

◆ GetEigenVector()

template<typename Scalar >

static bool Jacobi< Scalar >::GetEigenVector	(	const SquareMatrix &	eigenVectors,
		unsigned	index,
		Scalar	eigenVector[]
	)

inlinestatic

Returns the given eigenvector.

Parameters

eigenVectors	eigenvectors (as a square matrix)
index	requested eigenvector index (< eigenvectors matrix size)
eigenVector	output vector (size = matrix size)

Returns: success

Definition at line 364 of file Jacobi.h.

References cloudViewer::SquareMatrixTpl< Scalar >::m_values, and cloudViewer::SquareMatrixTpl< Scalar >::size().

Referenced by cloudViewer::Neighbourhood::computeMomentOrder1(), Jacobi< Scalar >::GetMaxEigenValueAndVector(), and Jacobi< Scalar >::GetMinEigenValueAndVector().

◆ GetMaxEigenValueAndVector()

template<typename Scalar >

static bool Jacobi< Scalar >::GetMaxEigenValueAndVector	(	const SquareMatrix &	eigenVectors,
		const EigenValues &	eigenValues,
		Scalar &	maxEigenValue,
		Scalar	maxEigenVector[]
	)

inlinestatic

Returns the biggest eigenvalue and its associated eigenvector.

Parameters

eigenVectors	eigenvectors (as a square matrix)
eigenValues	eigenvalues
maxEigenValue	biggest eigenvalue
maxEigenVector	eigenvector vector corresponding to the biggest eigenvalue

Returns: success

Definition at line 385 of file Jacobi.h.

References Jacobi< Scalar >::GetEigenVector(), cloudViewer::SquareMatrixTpl< Scalar >::isValid(), and cloudViewer::SquareMatrixTpl< Scalar >::size().

Referenced by cloudViewer::Neighbourhood::computeLeastSquareBestFittingPlane(), and cloudViewer::RegistrationTools::RegistrationProcedure().

◆ GetMinEigenValueAndVector()

template<typename Scalar >

static bool Jacobi< Scalar >::GetMinEigenValueAndVector	(	const SquareMatrix &	eigenVectors,
		const EigenValues &	eigenValues,
		Scalar &	minEigenValue,
		Scalar	minEigenVector[]
	)

inlinestatic

Returns the smallest eigenvalue and its associated eigenvector.

Parameters

eigenVectors	eigenvectors (as a square matrix)
eigenValues	eigenvalues
minEigenValue	smallest eigenvalue
minEigenVector	eigenvector vector corresponding to the smallest eigenvalue

Returns: success

Definition at line 410 of file Jacobi.h.

References Jacobi< Scalar >::GetEigenVector(), cloudViewer::SquareMatrixTpl< Scalar >::isValid(), and cloudViewer::SquareMatrixTpl< Scalar >::size().

Referenced by ComputeCorePointNormal(), and cloudViewer::Neighbourhood::computeLeastSquareBestFittingPlane().

◆ SortEigenValuesAndVectors()

template<typename Scalar >

static bool Jacobi< Scalar >::SortEigenValuesAndVectors	(	SquareMatrix &	eigenVectors,
		EigenValues &	eigenValues
	)

inlinestatic

Sorts the eigenvectors in the decreasing order of their associated eigenvalues

Parameters

eigenVectors	eigenvectors (as a square matrix)
eigenValues	eigenvalues

Returns: success

Definition at line 333 of file Jacobi.h.

References cloudViewer::SquareMatrixTpl< Scalar >::isValid(), cloudViewer::SquareMatrixTpl< Scalar >::m_values, cloudViewer::SquareMatrixTpl< Scalar >::size(), and std::swap().

Referenced by cloudViewer::Neighbourhood::computeFeature(), cloudViewer::Neighbourhood::computeMomentOrder1(), DimensionalityScaleParamsComputer::computeScaleParams(), ccCompass::estimateStrain(), and ccCompass::estimateStructureNormals().

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

/root/ACloudViewer/core/include/Jacobi.h

Public Types

Static Public Member Functions

Detailed Description

template<typename Scalar> class Jacobi< Scalar >

Member Typedef Documentation

◆ EigenValues

◆ SquareMatrix

Member Function Documentation

◆ ComputeEigenValuesAndVectors()

◆ ComputeEigenValuesAndVectors2()

◆ GetEigenVector()

◆ GetMaxEigenValueAndVector()

◆ GetMinEigenValueAndVector()

◆ SortEigenValuesAndVectors()

template<typename Scalar>
class Jacobi< Scalar >