Explicit.hh

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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\
 * Copyright (c) 2025, Davide Stocco and Enrico Bertolazzi.                                      *
 *                                                                                               *
 * The Sandals project is distributed under the BSD 2-Clause License.                            *
 *                                                                                               *
 * Davide Stocco                                                               Enrico Bertolazzi *
 * University of Trento                                                     University of Trento *
 * e-mail: davide.stocco@unitn.it                             e-mail: enrico.bertolazzi@unitn.it *
\* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
 
#pragma once
 
#ifndef SANDALS_EXPLICIT_SYSTEM_HH
#define SANDALS_EXPLICIT_SYSTEM_HH
 
#include <Sandals.hh>
#include <Sandals/System/Implicit.hh>
 
namespace Sandals {
 
  /*\
   |   _____            _ _      _ _
   |  | ____|_  ___ __ | (_) ___(_) |_
   |  |  _| \ \/ / '_ \| | |/ __| | __|
   |  | |___ >  <| |_) | | | (__| | |_
   |  |_____/_/\_\ .__/|_|_|\___|_|\__|
   |             |_|
  \*/

  template <typename Real, Integer N, Integer M = 0>
  class Explicit : public Implicit<Real, N, M>
  {
  public:
    SANDALS_BASIC_CONSTANTS(Real) 
 
    using Pointer = std::shared_ptr<Explicit<Real, N, M>>; 
    using VectorF = typename Implicit<Real, N, M>::VectorF; 
    using MatrixJF = typename Implicit<Real, N, M>::MatrixJF; 
    using Type = typename Implicit<Real, N, M>::Type; 
 
  protected:
    Explicit(Type t_type, std::string t_name) : Implicit<Real, N, M>(t_type, t_name) {}
 
  public:
    Explicit() : Implicit<Real, N, M>(Type::EXPLICIT, "(missing name)") {}

    Explicit(std::string t_name) : Implicit<Real, N, M>(Type::EXPLICIT, t_name) {}

    VectorF F(VectorF const & x, VectorF const & x_dot, Real const t) const override
    {
      return x_dot - this->f(x, t);
    }

    MatrixJF JF_x(VectorF const & x, VectorF const &/*x_dot*/, Real const t) const override
    {
      return -this->Jf_x(x, t);
    }

    MatrixJF JF_x_dot(VectorF const &/*x*/, VectorF const &/*x_dot*/, Real /*t*/) const override
    {
      return MatrixJF::Identity();
    }

    virtual VectorF f(VectorF const & x, Real const t) const = 0;

    virtual MatrixJF Jf_x(VectorF const & x, Real const t) const = 0;

    VectorF f_reverse(VectorF const & x, Real const t) const
    {
      return -this->f(x, -t);
    }

    MatrixJF Jf_x_reverse(VectorF const & x, Real const t) const
    {
      return -this->Jf_x(x, -t);
    }

    VectorF F_reverse(VectorF const & x, VectorF const & x_dot, Real const t) const
    {
      return -x_dot - this->f(x, -t);
    }

    MatrixJF JF_x_reverse(VectorF const & x, VectorF const &/*x_dot*/, Real const t) const
    {
      return -this->Jf_x(x, -t);
    }

    MatrixJF JF_x_dot_reverse(VectorF const &/*x*/, VectorF const &/*x_dot*/, Real /*t*/) const
    {
      return -MatrixJF::Identity();
    }
 
  }; // class Explicit
 
  /*\
   |   _____            _ _      _ _ __        __
   |  | ____|_  ___ __ | (_) ___(_) |\ \      / / __ __ _ _ __  _ __   ___ _ __
   |  |  _| \ \/ / '_ \| | |/ __| | __\ \ /\ / / '__/ _` | '_ \| '_ \ / _ \ '__|
   |  | |___ >  <| |_) | | | (__| | |_ \ V  V /| | | (_| | |_) | |_) |  __/ |
   |  |_____/_/\_\ .__/|_|_|\___|_|\__| \_/\_/ |_|  \__,_| .__/| .__/ \___|_|
   |             |_|                                     |_|   |_|
  \*/

  template <typename Real, Integer N, Integer M = 0>
  class ExplicitWrapper : public Explicit<Real, N, M>
  {
  public:
    SANDALS_BASIC_CONSTANTS(Real) 
 
    using Pointer = std::shared_ptr<ExplicitWrapper<Real, N, M>>; 
    using VectorF = typename Explicit<Real, N, M>::VectorF; 
    using MatrixJF = typename Explicit<Real, N, M>::MatrixJF; 
    using VectorH = typename Explicit<Real, N, M>::VectorH; 
    using MatrixJH = typename Explicit<Real, N, M>::MatrixJH; 
    using FunctionF = std::function<VectorF(VectorF const &, Real const)>; 
    using FunctionJF = std::function<MatrixJF(VectorF const &, Real const)>; 
    using FunctionH = std::function<VectorH(VectorF const &, Real const)>; 
    using FunctionJH = std::function<MatrixJH(VectorF const &, Real const)>; 
    using FunctionID = std::function<bool(VectorF const &, Real const)>; 
 
    inline const static FunctionH DefaultH = [](VectorF const &, Real const) {return VectorH::Zero();}; 
    inline const static FunctionJH DefaultJH = [](VectorF const &, Real const) {return MatrixJH::Zero();}; 
    inline const static FunctionID DefaultID = [](VectorF const &, Real const) {return true;}; 
 
  private:
    FunctionF m_f{nullptr}; 
    FunctionJF m_Jf_x{nullptr}; 
    FunctionH m_h{nullptr}; 
    FunctionJH m_Jh_x{nullptr}; 
    FunctionID m_in_domain{nullptr}; 
 
  public:
    ExplicitWrapper(FunctionF t_f, FunctionJF t_Jf_x, FunctionH t_h = DefaultH, FunctionJH t_Jh_x = DefaultJH,
      FunctionID t_in_domain = DefaultID) : Explicit<Real, N, M>(), m_f(t_f), m_Jf_x(t_Jf_x), m_h(t_h),
      m_Jh_x(t_Jh_x), m_in_domain(t_in_domain)
    {}

    ExplicitWrapper(std::string t_name, FunctionF t_f, FunctionJF t_Jf_x, FunctionH t_h = DefaultH,
      FunctionJH t_Jh_x = DefaultJH, FunctionID t_in_domain = DefaultID) : Explicit<Real, N, M>(t_name),
      m_f(t_f), m_Jf_x(t_Jf_x), m_h(t_h), m_Jh_x(t_Jh_x), m_in_domain(t_in_domain)
    {}

    ~ExplicitWrapper() {}

    FunctionF & f() {return this->m_f;}

    FunctionJF & Jf_x() {return this->m_Jf_x;}

    FunctionH & h() {return this->m_h;}

    FunctionJH & Jh_x() {return this->m_Jh_x;}

    FunctionID & in_domain() {return this->m_in_domain;}

    VectorF f(VectorF const & x, Real const t) const override
    {
      return this->m_f(x, t);
    }

    MatrixJF Jf_x(VectorF const & x, Real const t) const override
    {
      return this->m_Jf_x(x, t);
    }

    VectorH h(VectorF const & x, Real const t) const override
    {
      return this->m_h(x, t);
    }

    MatrixJH Jh_x(VectorF const & x, Real const t) const override
    {
      return this->m_Jh_x(x, t);
    }

    bool in_domain(VectorF const & x, Real const t) const override
    {
      return this->m_in_domain(x, t);
    }
 
  }; // class ExplicitWrapper
 
} // namespace Sandals
 
#endif // SANDALS_EXPLICIT_SYSTEM_HH