DiagonalizeTraits< FT, dim > Concept Reference Definition template<typename FT, unsigned int dim = 3> class DiagonalizeTraits< FT, dim >Concept providing functions to extract eigenvectors and eigenvalues from covariance matrices represented by an array a, using symmetric diagonalization. For example, a matrix of dimension 3 is defined as follows: \( \begin{bmatrix} a[0] & a[1] & a[2] \\ a[1] & a[3] & a[4] \\ a[2] & a[4] & a[5] \\ \end{bmatrix}\) Template Parameters FTNumber type dimDimension of the matrices and vectors Has models CGAL::Eigen_diagonalize_traits 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. 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. 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. Member Function Documentation diagonalize_selfadjoint_covariance_matrix() [1/2] template<typename FT, unsigned int dim = 3> bool DiagonalizeTraits< 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. Returnstrue if the operation was successful and false otherwise. diagonalize_selfadjoint_covariance_matrix() [2/2] template<typename FT, unsigned int dim = 3> bool DiagonalizeTraits< 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. Returnstrue if the operation was successful and false otherwise. extract_largest_eigenvector_of_covariance_matrix() template<typename FT, unsigned int dim = 3> bool DiagonalizeTraits< 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. Returnstrue if the operation was successful and false otherwise. DiagonalizeTraits Generated by 1.17.0

Definition

template<typename FT, unsigned int dim = 3>
class DiagonalizeTraits< FT, dim >

Concept providing functions to extract eigenvectors and eigenvalues from covariance matrices represented by an array a, using symmetric diagonalization.

For example, a matrix of dimension 3 is defined as follows:

\( \begin{bmatrix} a[0] & a[1] & a[2] \\ a[1] & a[3] & a[4] \\ a[2] & a[4] & a[5] \\ \end{bmatrix}\)

Template Parameters

FT	Number type
dim	Dimension of the matrices and vectors

Has models

CGAL::Eigen_diagonalize_traits

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.
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.
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.

Member Function Documentation

diagonalize_selfadjoint_covariance_matrix() [1/2]

template<typename FT, unsigned int dim = 3>

bool DiagonalizeTraits< 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>

bool DiagonalizeTraits< 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>

bool DiagonalizeTraits< 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.