\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 5.0.4 - CGAL and Solvers
CGAL::Eigen_diagonalize_traits< FT, dim > Class Template Reference

#include <CGAL/Eigen_diagonalize_traits.h>

Definition

template<typename FT, unsigned int dim = 3>
class CGAL::Eigen_diagonalize_traits< FT, dim >

The class Eigen_diagonalize_traits provides an interface to the diagonalization of covariance matrices of Eigen.

Eigen version 3.1 (or later) must be available on the system.

Template Parameters
FTNumber type
dimDimension of the matrices and vectors
Is Model Of:
DiagonalizeTraits
See also
http://eigen.tuxfamily.org/index.php?title=Main_Page
Examples:
Solver_interface/diagonalize_matrix.cpp.

Public Types

typedef std::array< FT, dim > Vector
 
typedef std::array< FT, dim *dim > Matrix
 
typedef std::array< FT,(dim *(dim+1)/2)> Covariance_matrix
 

Static Public Member Functions

static bool diagonalize_selfadjoint_covariance_matrix (const Covariance_matrix &cov, Vector &eigenvalues)
 Fill eigenvalues with the eigenvalues of the covariance matrix represented by cov. More...
 
static bool diagonalize_selfadjoint_covariance_matrix (const Covariance_matrix &cov, Vector &eigenvalues, Matrix &eigenvectors)
 Fill eigenvalues with the eigenvalues and eigenvectors with the eigenvectors of the covariance matrix represented by cov. More...
 
static bool extract_largest_eigenvector_of_covariance_matrix (const Covariance_matrix &cov, Vector &normal)
 Extract the eigenvector associated to the largest eigenvalue of the covariance matrix represented by cov. More...
 

Member Function Documentation

◆ diagonalize_selfadjoint_covariance_matrix() [1/2]

template<typename FT , unsigned int dim = 3>
static bool CGAL::Eigen_diagonalize_traits< FT, dim >::diagonalize_selfadjoint_covariance_matrix ( const Covariance_matrix cov,
Vector eigenvalues 
)
static

Fill eigenvalues with the eigenvalues of the covariance matrix represented by cov.

Eigenvalues are sorted by increasing order.

Returns
true if the operation was successful and false otherwise.

◆ diagonalize_selfadjoint_covariance_matrix() [2/2]

template<typename FT , unsigned int dim = 3>
static bool CGAL::Eigen_diagonalize_traits< FT, dim >::diagonalize_selfadjoint_covariance_matrix ( const Covariance_matrix cov,
Vector eigenvalues,
Matrix eigenvectors 
)
static

Fill eigenvalues with the eigenvalues and eigenvectors with the eigenvectors of the covariance matrix represented by cov.

Eigenvalues are sorted by increasing order.

Returns
true if the operation was successful and false otherwise.

◆ extract_largest_eigenvector_of_covariance_matrix()

template<typename FT , unsigned int dim = 3>
static bool CGAL::Eigen_diagonalize_traits< FT, dim >::extract_largest_eigenvector_of_covariance_matrix ( const Covariance_matrix cov,
Vector normal 
)
static

Extract the eigenvector associated to the largest eigenvalue of the covariance matrix represented by cov.

Returns
true if the operation was successful and false otherwise.