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/* This file is part of the Gudhi Library. The Gudhi library
* (Geometric Understanding in Higher Dimensions) is a generic C++
* library for computational topology.
*
* Author(s): Siargey Kachanovich
*
* Copyright (C) 2019 Inria
*
* Modification(s):
* - YYYY/MM Author: Description of the modification
*/
#ifndef FUNCTIONS_PL_APPROXIMATION_H_
#define FUNCTIONS_PL_APPROXIMATION_H_
#include <cstdlib>
#include <gudhi/Functions/Function.h>
#include <Eigen/Dense>
namespace Gudhi {
namespace coxeter_triangulation {
/**
* \class PL_approximation
* \brief Constructs a piecewise-linear approximation of a function induced by
* an ambient triangulation.
*
* \tparam Function The function template parameter. Should be a model of
* the concept FunctionForImplicitManifold.
* \tparam Triangulation The triangulation template parameter. Should be a model of
* the concept TriangulationForManifoldTracing.
*
* \ingroup coxeter_triangulation
*/
template <class Function_,
class Triangulation_>
struct PL_approximation : public Function {
/**
* \brief Value of the function at a specified point.
* @param[in] p The input point. The dimension needs to coincide with the ambient dimension.
*/
Eigen::VectorXd operator()(const Eigen::VectorXd& p) const {
std::size_t cod_d = this->cod_d();
std::size_t amb_d = this->amb_d();
auto s = tr_.locate_point(p);
Eigen::MatrixXd matrix(cod_d, s.dimension() + 1);
Eigen::MatrixXd vertex_matrix(amb_d + 1, s.dimension() + 1);
for (std::size_t i = 0; i < s.dimension() + 1; ++i)
vertex_matrix(0, i) = 1;
std::size_t j = 0;
for (auto v: s.vertex_range()) {
Eigen::VectorXd pt_v = tr_.cartesian_coordinates(v);
Eigen::VectorXd fun_v = fun_(pt_v);
for (std::size_t i = 1; i < amb_d + 1; ++i)
vertex_matrix(i, j) = pt_v(i-1);
for (std::size_t i = 0; i < cod_d; ++i)
matrix(i, j) = fun_v(i);
j++;
}
assert(j == s.dimension()+1);
Eigen::VectorXd z(amb_d + 1);
z(0) = 1;
for (std::size_t i = 1; i < amb_d + 1; ++i)
z(i) = p(i-1);
Eigen::VectorXd lambda = vertex_matrix.colPivHouseholderQr().solve(z);
Eigen::VectorXd result = matrix * lambda;
return result;
}
/** \brief Returns the domain (ambient) dimension. */
std::size_t amb_d() const {return fun_.amb_d();}
/** \brief Returns the codomain dimension. */
std::size_t cod_d() const {return fun_.cod_d();}
/** \brief Returns a point on the zero-set. */
Eigen::VectorXd seed() const {
// TODO: not finished. Should use an oracle.
return Eigen::VectorXd(amb_d());
}
/**
* \brief Constructor of the piecewise-linear approximation of a function
* induced by an ambient triangulation.
*
* @param[in] function The function.
* @param[in] triangulation The ambient triangulation.
*/
PL_approximation(const Function_& function, const Triangulation_& triangulation)
: fun_(function), tr_(triangulation) {}
private:
Function_ fun_;
Triangulation_ tr_;
};
/**
* \brief Static constructor of the piecewise-linear approximation of a function
* induced by an ambient triangulation.
*
* @param[in] function The function.
* @param[in] triangulation The ambient triangulation.
*
* \tparam Function_ The function template parameter. Should be a model of
* the concept FunctionForImplicitManifold.
*
* \ingroup coxeter_triangulation
*/
template <class Function_,
class Triangulation_>
PL_approximation<Function_, Triangulation_>
make_pl_approximation(const Function_& function,
const Triangulation_& triangulation) {
return PL_approximation<Function_, Triangulation_>(function, triangulation);
}
} // namespace coxeter_triangulation
} // namespace Gudhi
#endif
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