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Diffstat (limited to 'src/Coxeter_triangulation/include/gudhi/Functions/Embed_in_Rd.h')
-rw-r--r-- | src/Coxeter_triangulation/include/gudhi/Functions/Embed_in_Rd.h | 93 |
1 files changed, 93 insertions, 0 deletions
diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/Embed_in_Rd.h b/src/Coxeter_triangulation/include/gudhi/Functions/Embed_in_Rd.h new file mode 100644 index 00000000..e1fe868f --- /dev/null +++ b/src/Coxeter_triangulation/include/gudhi/Functions/Embed_in_Rd.h @@ -0,0 +1,93 @@ +/* This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT. + * See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details. + * 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> // for std::size_t + +#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. + */ +template <class Function_> +struct Embed_in_Rd { + /** + * \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) {} + + private: + 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 |