SemiExplicit.hxx

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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_SEMIEXPLICIT_SYSTEM_HXX
#define SANDALS_SEMIEXPLICIT_SYSTEM_HXX
 
namespace Sandals {
 
  /*\
   |   ____                 _ _____            _ _      _ _
   |  / ___|  ___ _ __ ___ (_) ____|_  ___ __ | (_) ___(_) |_
   |  \___ \ / _ \ '_ ` _ \| |  _| \ \/ / '_ \| | |/ __| | __|
   |   ___) |  __/ | | | | | | |___ >  <| |_) | | | (__| | |_
   |  |____/ \___|_| |_| |_|_|_____/_/\_\ .__/|_|_|\___|_|\__|
   |                                    |_|
  \*/

  template <Integer N, Integer M = 0>
  class SemiExplicit : public Explicit<N, M>
  {
  public:
    using Pointer  = std::shared_ptr<SemiExplicit<N, M>>; 
    using VectorF  = typename Explicit<N, M>::VectorF;    
    using MatrixJF = typename Explicit<N, M>::MatrixJF;   
    using MatrixA  = typename Explicit<N, M>::MatrixJF;   
    using TensorTA = typename std::vector<MatrixJF>;      
    using VectorB  = typename Explicit<N, M>::VectorF;    
    using MatrixJB = typename Explicit<N, M>::MatrixJF;   
    using Type     = typename Explicit<N, M>::Type;       
 
  private:
    mutable Eigen::FullPivLU<MatrixA> m_lu; 
 
  public:

    SemiExplicit() : Explicit<N, M>(Type::SEMIEXPLICIT, "(missing name)") {}

    SemiExplicit(std::string t_name) : Explicit<N, M>(Type::SEMIEXPLICIT, t_name) {}

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

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

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

    VectorF f(VectorF const &x, Real t) const override
    {
      this->m_lu.compute(this->A(x, t));
      SANDALS_ASSERT(this->m_lu.rank() == N,
        "Sandals:SemiExplicit::f(...): singular mass matrix A detected.");
      return this->m_lu.solve(this->b(x, t));
    }

    MatrixJF Jf_x(VectorF const &x, VectorF const &x_dot, Real t) const
    {
      TensorTA TA_x{this->TA_x(x, t)};
      MatrixJF tAp{MatrixJF::Zero()};
      for (Integer i{0}; i < N; ++i) {tAp.col(i) = TA_x[i] * x_dot;} // TODO: Check if TA_x.size() = N
      this->m_lu.compute(this->A(x, t));
      SANDALS_ASSERT(this->m_lu.rank() == N,
        "Sandals:SemiExplicit::Jf_x(...): singular mass matrix A detected.");
      return this->m_lu.solve(this->Jb_x(x, t) - tAp);
    }

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

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

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

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

    virtual MatrixJB Jb_x(VectorF const &x, Real t) const = 0;
 
  }; // class SemiExplicit
 
} // namespace Sandals
 
#endif // SANDALS_SEMIEXPLICIT_SYSTEM_HXX