codac2_AnalyticFunction.h

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#pragma once
 
#include <map>
#include "codac2_AnalyticExpr.h"
#include "codac2_Domain.h"
#include "codac2_analytic_variables.h"
#include "codac2_FunctionBase.h"
#include "codac2_template_tools.h"
#include "codac2_AnalyticExprWrapper.h"
#include "codac2_operators.h"
#include "codac2_cart_prod.h"
#include "codac2_vec.h"
#include "codac2_Wrapper.h"
#include "codac2_Parallelepiped.h"
#include "codac2_peibos_tools.h"
 
namespace codac2
{
  enum class EvalMode
  {
    NATURAL = 0x01,
    CENTERED = 0x02,
    DEFAULT = 0x03 // corresponds to (NATURAL|CENTERED)
  };
 
  inline EvalMode operator&(EvalMode a, EvalMode b)
  { return static_cast<EvalMode>(static_cast<int>(a) & static_cast<int>(b)); }
 
  inline EvalMode operator|(EvalMode a, EvalMode b)
  { return static_cast<EvalMode>(static_cast<int>(a) | static_cast<int>(b)); }
 
  struct ScalarExprList : public AnalyticExprWrapper<VectorType>
  {
    // Mainly used to take advantage of initializer lists in AnalyticFunction constructors.
    template<typename... S>
      requires (std::is_same_v<typename ExprType<S>::Type,ScalarType> && ...)
    ScalarExprList(const S&... y)
      : AnalyticExprWrapper<VectorType>(vec(y...))
    { }
  };
 
  template<typename T>
  class SampledTraj;
 
  template<typename T>
  class SlicedTube;
 
  template<typename T>
    requires std::is_base_of_v<AnalyticTypeBase,T>
  class AnalyticFunction : public FunctionBase<AnalyticExpr<T>>
  {
    public:
 
      AnalyticFunction(const FunctionArgsList& args, const ScalarExprList& y)
        requires(std::is_same_v<T,VectorType>)
        : FunctionBase<AnalyticExpr<T>>(args, y)
      {
        assert_release(y->belongs_to_args_list(this->args()) && 
          "Invalid argument: variable not present in input arguments");
        update_var_names();
      }
 
      AnalyticFunction(const FunctionArgsList& args, const AnalyticExprWrapper<T>& y)
        : FunctionBase<AnalyticExpr<T>>(args, y)
      {
        assert_release(y->belongs_to_args_list(this->args()) && 
          "Invalid argument: variable not present in input arguments");
        update_var_names();
      }
 
      AnalyticFunction(const AnalyticFunction<T>& f)
        : FunctionBase<AnalyticExpr<T>>(f)
      { }
 
      template<typename... X>
      AnalyticExprWrapper<T> operator()(const X&... x) const
      {
        return { this->FunctionBase<AnalyticExpr<T>>::operator()(x...) };
      }
 
      template<typename... Args>
      auto real_eval(const Args&... x) const
      {
        return eval(x...).mid();
      }
 
      template<typename... Args>
      typename T::Domain eval(const EvalMode& m, const Args&... x) const
      {
        check_valid_inputs(x...);
 
        switch(m)
        {
          case EvalMode::NATURAL:
          {
            return eval_<true>(x...).a;
          }
 
          case EvalMode::CENTERED:
          {
            auto x_ = eval_<false>(x...);
            auto flatten_x = IntervalVector(cart_prod(x...));
            assert(x_.da.rows() == x_.a.size() && x_.da.cols() == flatten_x.size());
            
            if constexpr(std::is_same_v<T,ScalarType>)
              return x_.m + (x_.da*(flatten_x-flatten_x.mid()))[0];
 
            else if constexpr(std::is_same_v<T,VectorType>)
              return x_.m + (x_.da*(flatten_x-flatten_x.mid())).col(0);
 
            else
            {
              static_assert(std::is_same_v<T,MatrixType>);
              return x_.m + (x_.da*(flatten_x-flatten_x.mid()))
                .reshaped(x_.m.rows(), x_.m.cols());
            }
          }
 
          case EvalMode::DEFAULT:
          default:
          {
            auto x_ = eval_<false>(x...);
 
            // If the centered form is not available for this expression...
            if(x_.da.size() == 0 // .. because some parts have not yet been implemented,
              || !x_.def_domain) // .. or due to restrictions in the derivative definition domain
              return eval(EvalMode::NATURAL, x...);
 
            else
            {
              auto flatten_x = IntervalVector(cart_prod(x...));
 
              if constexpr(std::is_same_v<T,ScalarType>)
                return x_.a & (x_.m + (x_.da*(flatten_x-flatten_x.mid()))[0]);
 
              else if constexpr(std::is_same_v<T,VectorType>)
              {
                assert(x_.da.rows() == x_.a.size() && x_.da.cols() == flatten_x.size());
                return x_.a & (x_.m + (x_.da*(flatten_x-flatten_x.mid())).col(0));
              }
 
              else
              {
                static_assert(std::is_same_v<T,MatrixType>);
                assert(x_.da.rows() == x_.a.size() && x_.da.cols() == flatten_x.size());
                return x_.a & (x_.m +(x_.da*(flatten_x-flatten_x.mid()))
                  .reshaped(x_.m.rows(),x_.m.cols()));
              }
            }
          }
        }
      }
 
      template<typename... Args>
      auto diff(const Args&... x) const
      {
        check_valid_inputs(x...);
        return eval_<false>(x...).da;
      }
 
      template<typename... Args>
      typename T::Domain eval(const Args&... x) const
      {
        return eval(EvalMode::NATURAL | EvalMode::CENTERED, x...);
      }
 
      template<typename... Args>
      auto traj_eval(const SampledTraj<Args>&... x) const
      {
        SampledTraj<typename T::Scalar> y;
        for(const auto& [ti,xi] : std::get<0>(std::tie(x...)))
          y.set(this->real_eval(x(ti)...),ti);
        return y;
      }
 
      template<typename... Args>
      auto tube_eval(const SlicedTube<Args>&... x) const
      {
        auto tdomain = std::get<0>(std::tie(x...)).tdomain();
 
        SlicedTube<typename T::Domain> y(
          tdomain, (typename T::Domain)(this->output_size())
        );
 
        for(auto it = tdomain->begin() ; it != tdomain->end() ; it++)
          y.slice(it)->codomain() = this->eval(x.slice(it)->codomain()...);
 
        return y;
      }
 
      template<typename... Args>
        requires std::is_same_v<VectorType,T> && ((!std::is_same_v<MatrixType,typename ExprType<Args>::Type>) && ...)
      Parallelepiped parallelepiped_eval(const Args&... x) const
      {
        this->check_valid_inputs(x...);
        assert_release(this->input_size() < this->output_size() &&
                      "Parallelepiped evaluation requires more outputs than inputs.");
        assert_release(this->input_size() > 0 &&
                    "Parallelepiped evaluation requires at least one input.");
 
        IntervalVector Y = this->eval(((typename Wrapper<Args>::Domain)(x)).mid()...);
        Vector z = Y.mid();
 
        Matrix A = this->diff(((typename Wrapper<Args>::Domain)(x)).mid()...).mid();
 
        // Maximum error computation
        double rho = error_peibos(Y, z, this->diff(x...), A, cart_prod(x...));
 
        // Inflation of the parallelepiped
        Matrix A_inf = inflate_flat_parallelepiped(A, (cart_prod(x...).template cast<Interval>()).rad(), rho);
 
        return Parallelepiped(z, A_inf);
      }
 
      Index output_size() const
      {
        if constexpr(std::is_same_v<T,ScalarType>)
          return 1;
 
        else {
          std::pair<Index,Index> oshape = output_shape();
          return oshape.first * oshape.second;
        }
      }
 
      std::pair<Index,Index> output_shape() const 
      {
        if constexpr(std::is_same_v<T,ScalarType>)
          return {1,1};
        else return this->expr()->output_shape();
      }
 
      friend std::ostream& operator<<(std::ostream& os, [[maybe_unused]] const AnalyticFunction<T>& f)
      {
        os << "(";
        for(size_t i = 0 ; i < f.args().size() ; i++)
          os << (i!=0 ? "," : "") << f.args()[i]->name();
        os << ") ↦ " << f.expr()->str();
        return os;
      }
 
      // not working with Clang: template<typename Y, typename... X>
      // not working with Clang:   requires (sizeof...(X) > 0)
      // not working with Clang: friend class CtcInverse;
 
      // So, the following methods are temporarily public
 
      // protected:
 
      template<typename... Args>
      void fill_from_args(ValuesMap& v, const Args&... x) const
      {
        Index i = 0;
        (add_value_to_arg_map(v, x, i++), ...);
      }
 
      template<typename... Args>
      void intersect_from_args(const ValuesMap& v, Args&... x) const
      {
        Index i = 0;
        (intersect_value_from_arg_map(v, x, i++), ...);
      }
 
    protected:
 
      template<typename D>
      void add_value_to_arg_map(ValuesMap& v, const D& x, Index i) const
      {
        assert(i >= 0 && i < (Index)this->args().size());
        assert_release(size_of(x) == this->args()[i]->size() && "provided arguments do not match function inputs");
 
        using D_TYPE = typename ExprType<D>::Type;
 
        IntervalMatrix d = IntervalMatrix::zero(size_of(x), this->args().total_size());
        
        Index p = 0;
        for(Index j = 0 ; j < i ; j++)
          p += this->args()[j]->size();
 
        for(Index k = p ; k < p+size_of(x) ; k++)
          d(k-p,k) = 1.;
 
        v[this->args()[i]->unique_id()] = 
          std::make_shared<D_TYPE>(typename D_TYPE::Domain(x).mid(), x, d, true);
      }
 
      template<typename D>
      void intersect_value_from_arg_map(const ValuesMap& v, D& x, Index i) const
      {
        assert(v.find(this->args()[i]->unique_id()) != v.end() && "argument cannot be found");
        x &= std::dynamic_pointer_cast<typename ExprType<D>::Type>(v.at(this->args()[i]->unique_id()))->a;
      }
 
      template<bool NATURAL_EVAL,typename... Args>
      auto eval_(const Args&... x) const
      {
        ValuesMap v;
 
        if constexpr(sizeof...(Args) == 0)
          return this->expr()->fwd_eval(v, 0, NATURAL_EVAL);
 
        else
        {
          fill_from_args(v, x...);
          return this->expr()->fwd_eval(v, cart_prod(x...).size(), NATURAL_EVAL); // todo: improve size computation
        }
      }
 
      template<typename... Args>
      void check_valid_inputs(const Args&... x) const
      {
        [[maybe_unused]] Index n = 0;
        ((n += size_of(x)), ...);
 
        assert_release(this->_args.total_size() == n && 
          "Invalid arguments: wrong number of input arguments");
      }
      
      inline void update_var_names()
      {
        for(const auto& v : this->_args) // variable names are automatically computed in FunctionArgsList,
          // so we propagate them to the expression
          this->_y->replace_arg(v->unique_id(), std::dynamic_pointer_cast<ExprBase>(v));
      }
  };
 
  AnalyticFunction(const FunctionArgsList&, std::initializer_list<ScalarExpr>) -> 
    AnalyticFunction<VectorType>;
 
  template<typename T>
  AnalyticFunction(const FunctionArgsList&, const T&) -> 
    AnalyticFunction<typename ExprType<T>::Type>;
 
}