CCCoreLib::Jacobi< Scalar > Class Template Reference

Jacobi eigen vectors/values decomposition. More...

#include <Jacobi.h>

Public Types
using	SquareMatrix = 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)
	Sorts the eigenvectors in the decreasing order of their associated eigenvalues. More...
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 CCCoreLib::Jacobi< Scalar >

Jacobi eigen vectors/values decomposition.

Member Function Documentation

ComputeEigenValuesAndVectors()

template<typename Scalar >

static bool CCCoreLib::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.

ComputeEigenValuesAndVectors2()

template<typename Scalar >

static bool CCCoreLib::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!!!

Parameters

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

Returns

success

GetEigenVector()

template<typename Scalar >

static bool CCCoreLib::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

GetMaxEigenValueAndVector()

template<typename Scalar >

static bool CCCoreLib::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

GetMinEigenValueAndVector()

template<typename Scalar >

static bool CCCoreLib::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

SortEigenValuesAndVectors()

template<typename Scalar >

static bool CCCoreLib::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

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

• Jacobi.h