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// Copyright (c) 2014 INRIA Sophia-Antipolis (France). // All rights reserved. // // This file is part of CGAL (www.cgal.org) // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Solver_interface/include/CGAL/Eigen_diagonalize_traits.h $ // $Id: include/CGAL/Eigen_diagonalize_traits.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // Author(s) : Jocelyn Meyron and Quentin Mérigot // #ifndef CGAL_EIGEN_DIAGONALIZE_TRAITS_H #define CGAL_EIGEN_DIAGONALIZE_TRAITS_H #include #include // If the matrix to diagonalize is of dimension 2x2 or 3x3, Eigen // provides a faster implementation using a closed-form // algorithm. However, it offers less precision. See: // https://eigen.tuxfamily.org/dox/classEigen_1_1SelfAdjointEigenSolver.html // This is usually acceptable for CGAL algorithms but one might want // to use the slower but more accurate version. In that case, just // uncomment the following line: //#define DO_NOT_USE_EIGEN_COMPUTEDIRECT_FOR_DIAGONALIZATION #include #include namespace CGAL { namespace internal { template struct Restricted_FT { typedef double type; }; template <> struct Restricted_FT { typedef float type; }; } /// \ingroup PkgSolverInterfaceLS /// /// The class `Eigen_diagonalize_traits` provides an interface to the /// diagonalization of covariance matrices of \ref thirdpartyEigen /// "Eigen". /// /// \ref thirdpartyEigen "Eigen" version 3.1 (or later) must be available on the system. /// /// \tparam FT Number type /// \tparam dim Dimension of the matrices and vectors /// /// \cgalModels{DiagonalizeTraits} /// /// \sa https://eigen.tuxfamily.org/index.php?title=Main_Page template class Eigen_diagonalize_traits { typedef typename internal::Restricted_FT::type RFT; public: typedef std::array Vector; typedef std::array Matrix; typedef std::array Covariance_matrix; private: typedef Eigen::Matrix EigenMatrix; typedef Eigen::Matrix EigenVector; /// Construct the covariance matrix static EigenMatrix construct_covariance_matrix(const Covariance_matrix& cov) { EigenMatrix m; for(std::size_t i=0; i(CGAL::to_double(cov[(dim * i) + j - ((i * (i+1)) / 2)])); if(i != j) m(j,i) = m(i,j); } } return m; } /// Fill `eigenvalues` with the eigenvalues and `eigenvectors` with /// the eigenvectors of the selfadjoint matrix represented by `m`. /// Eigenvalues are sorted by increasing order. /// \return `true` if the operation was successful and `false` otherwise. static bool diagonalize_selfadjoint_matrix(EigenMatrix& m, EigenMatrix& eigenvectors, EigenVector& eigenvalues) { Eigen::SelfAdjointEigenSolver eigensolver; #ifndef DO_NOT_USE_EIGEN_COMPUTEDIRECT_FOR_DIAGONALIZATION if(dim == 2 || dim == 3) eigensolver.computeDirect(m); else #endif eigensolver.compute(m); if(eigensolver.info() != Eigen::Success) return false; eigenvalues = eigensolver.eigenvalues(); eigenvectors = eigensolver.eigenvectors(); return true; } public: /// Fill `eigenvalues` with the eigenvalues of the covariance matrix represented by `cov`. /// Eigenvalues are sorted by increasing order. /// \return `true` if the operation was successful and `false` otherwise. static bool diagonalize_selfadjoint_covariance_matrix(const Covariance_matrix& cov, Vector& eigenvalues) { EigenMatrix m = construct_covariance_matrix(cov); // Diagonalizing the matrix EigenVector eigenvalues_; EigenMatrix eigenvectors_; bool res = diagonalize_selfadjoint_matrix(m, eigenvectors_, eigenvalues_); if(res) { for(std::size_t i=0; i(eigenvalues_[i]); } return res; } /// Fill `eigenvalues` with the eigenvalues and `eigenvectors` with /// the eigenvectors of the covariance matrix represented by `cov`. /// Eigenvalues are sorted by increasing order. /// \return `true` if the operation was successful and `false` otherwise. static bool diagonalize_selfadjoint_covariance_matrix(const Covariance_matrix& cov, Vector& eigenvalues, Matrix& eigenvectors) { EigenMatrix m = construct_covariance_matrix(cov); // Diagonalizing the matrix EigenVector eigenvalues_; EigenMatrix eigenvectors_; bool res = diagonalize_selfadjoint_matrix(m, eigenvectors_, eigenvalues_); if(res) { for(std::size_t i=0; i(eigenvalues_[i]); for(std::size_t j=0; j(eigenvectors_(j,i)); } } else{ for(std::size_t i=0; i(0.); for(std::size_t j=0; j(0.); } } return res; } /// Extract the eigenvector associated to the largest eigenvalue /// of the covariance matrix represented by `cov`. /// \return `true` if the operation was successful and `false` otherwise. static bool extract_largest_eigenvector_of_covariance_matrix(const Covariance_matrix& cov, Vector& normal) { // Construct covariance matrix EigenMatrix m = construct_covariance_matrix(cov); // Diagonalizing the matrix EigenVector eigenvalues; EigenMatrix eigenvectors; if(! diagonalize_selfadjoint_matrix(m, eigenvectors, eigenvalues)) return false; // Eigenvalues are sorted by increasing order for(unsigned int i=0; i (eigenvectors(i, dim-1)); return true; } }; } // namespace CGAL #endif // CGAL_EIGEN_DIAGONALIZE_TRAITS_H