RBFWithLinear.hpp

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#pragma once
 
#include <polyfem/quadrature/Quadrature.hpp>
#include <Eigen/Dense>
 
namespace polyfem
{
    namespace basis
    {
        class RBFWithLinear
        {
        public:
            RBFWithLinear(const Eigen::MatrixXd &centers, const Eigen::MatrixXd &collocation_points,
                          const Eigen::MatrixXd &local_basis_integral, const quadrature::Quadrature &quadr,
                          Eigen::MatrixXd &rhs, bool with_constraints = true);
 
            void basis(const int local_index, const Eigen::MatrixXd &uv, Eigen::MatrixXd &val) const;
 
            void grad(const int local_index, const Eigen::MatrixXd &uv, Eigen::MatrixXd &val) const;
 
            void bases_values(const Eigen::MatrixXd &samples, Eigen::MatrixXd &val) const;
 
            void bases_grads(const int axis, const Eigen::MatrixXd &samples, Eigen::MatrixXd &val) const;
 
        private:
            bool is_volume() const { return centers_.cols() == 3; }
 
            // Computes the matrix that evaluates the kernels + polynomial terms on the given sample points
            void compute_kernels_matrix(const Eigen::MatrixXd &samples, Eigen::MatrixXd &A) const;
 
            // Computes the relationship w = L v + t between the unknowns (v) and the weights w
            void compute_constraints_matrix(const int num_bases, const quadrature::Quadrature &quadr,
                                            const Eigen::MatrixXd &local_basis_integral, Eigen::MatrixXd &L, Eigen::MatrixXd &t) const;
 
            // Computes the weights by solving a (possibly constrained) linear least square
            void compute_weights(const Eigen::MatrixXd &collocation_points,
                                 const Eigen::MatrixXd &local_basis_integral, const quadrature::Quadrature &quadr,
                                 Eigen::MatrixXd &rhs, bool with_constraints);
 
        private:
            // #C x dim matrix of kernel center positions
            Eigen::MatrixXd centers_;
 
            // (#C + dim + 1) x #B matrix of weights extending the #B bases that are non-vanishing on the polytope
            Eigen::MatrixXd weights_;
        };
    } // namespace basis
} // namespace polyfem