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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_EMBED_IN_RD_H_
#define FUNCTIONS_EMBED_IN_RD_H_
#include <cstdlib>
#include <random>
#include <gudhi/Functions/Function.h>
#include <Eigen/Dense>
namespace Gudhi {
namespace coxeter_triangulation {
/**
* \class Embed_in_Rd
* \brief Embedding of an implicit manifold in a higher dimension.
*
* \tparam Function_ The function template parameter. Should be a model of
* the concept FunctionForImplicitManifold.
*
* \ingroup coxeter_triangulation
*/
template <class Function_>
struct Embed_in_Rd : 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 {
Eigen::VectorXd x = p;
Eigen::VectorXd x_k(fun_.amb_d()), x_rest(d_ - fun_.amb_d());
for (std::size_t i = 0; i < fun_.amb_d(); ++i)
x_k(i) = x(i);
for (std::size_t i = fun_.amb_d(); i < d_; ++i)
x_rest(i - fun_.amb_d()) = x(i);
Eigen::VectorXd result = fun_(x_k);
result.conservativeResize(this->cod_d());
for (std::size_t i = fun_.cod_d(); i < this->cod_d(); ++i)
result(i) = x_rest(i - fun_.cod_d());
return result;
}
/** \brief Returns the domain (ambient) dimension. */
std::size_t amb_d() const {return d_;}
/** \brief Returns the codomain dimension. */
std::size_t cod_d() const {return d_-(fun_.amb_d() - fun_.cod_d());}
/** \brief Returns a point on the zero-set of the embedded function. */
Eigen::VectorXd seed() const {
Eigen::VectorXd result = fun_.seed();
result.conservativeResize(d_);
for (std::size_t l = fun_.amb_d(); l < d_; ++l)
result(l) = 0;
return result;
}
/**
* \brief Constructor of the embedding function.
*
* @param[in] function The function to be embedded in higher dimension.
* @param[in] d Embedding dimension.
*/
Embed_in_Rd(const Function_& function, std::size_t d) :
fun_(function), d_(d) {
}
Function_ fun_;
std::size_t d_;
};
/**
* \brief Static constructor of an embedding function.
*
* @param[in] function The function to be embedded in higher dimension.
* @param[in] d Embedding dimension.
*
* \tparam Function_ The function template parameter. Should be a model of
* the concept FunctionForImplicitManifold.
*
* \ingroup coxeter_triangulation
*/
template <class Function_>
Embed_in_Rd<Function_> make_embedding(const Function_& function, std::size_t d) {
return Embed_in_Rd<Function_>(function, d);
}
} // namespace coxeter_triangulation
} // namespace Gudhi
#endif
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