codac2_Slice.h

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#pragma once
 
#include "codac2_SliceBase.h"
#include "codac2_ConvexPolygon.h"
#include "codac2_CtcDeriv.h"
#include "codac2_cart_prod.h"
#include "codac2_trunc.h"
 
namespace codac2
{
  template<class T>
  class Slice : public SliceBase,
    protected T
    // T class inheritance is protected, because modifying a
    // Slice's codomain can affect adjacent gates if they exist
  {
    public:

      explicit Slice(const SlicedTubeBase& tube, const std::list<TSlice>::iterator& it_tslice, const T& codomain)
        : SliceBase(tube, it_tslice), T(codomain)
      { }

      Slice(const Slice& s, const SlicedTubeBase& tube)
        : SliceBase(tube, s._it_tslice), T(s.codomain())
      { }
 
      // Slice objects cannot be copyable or movable,
      // as they are supposed to be connected to other Slice objects
      Slice(const Slice& s) = delete;
      Slice& operator=(const Slice&) = delete;
      Slice(Slice&&) = delete;
      Slice& operator=(Slice&&) = delete;

      inline const SlicedTube<T>& tube() const
      {
        return static_cast<const SlicedTube<T>&>(_tube);
      }

      inline std::shared_ptr<SliceBase> copy() const override
      {
        return std::make_shared<Slice>(*this, this->_tube);
      }

      inline Index size() const
      {
        return this->T::size();
      }

      inline T& codomain()
      {
        return static_cast<T&>(*this);
      }

      inline const T& codomain() const
      {
        return static_cast<const T&>(*this);
      }

      inline bool is_gate() const
      {
        return t0_tf().is_degenerated();
      }

      inline std::shared_ptr<const Slice<T>> prev_slice() const
      {
        return std::static_pointer_cast<const Slice<T>>(
          this->SliceBase::prev_slice());
      }

      inline std::shared_ptr<Slice<T>> prev_slice()
      {
        return std::const_pointer_cast<Slice<T>>(
          static_cast<const Slice<T>&>(*this).prev_slice());
      }

      inline std::shared_ptr<const Slice<T>> next_slice() const
      {
        return std::static_pointer_cast<const Slice<T>>(
          this->SliceBase::next_slice());
      }

      inline std::shared_ptr<Slice<T>> next_slice()
      {
        return std::const_pointer_cast<Slice<T>>(
          static_cast<const Slice<T>&>(*this).next_slice());
      }

      inline T input_gate() const
      {
        if(!prev_slice())
          return codomain();
 
        else
        {
          if(prev_slice()->is_gate())
            return prev_slice()->codomain();
          else
            return codomain() & prev_slice()->codomain();
        }
      }

      inline T output_gate() const
      {
        if(!next_slice())
          return codomain();
 
        else
        {
          if(next_slice()->is_gate())
            return next_slice()->codomain();
          else
            return codomain() & next_slice()->codomain();
        }
      }

      inline std::pair<T,T> enclosed_bounds(const Interval& t) const
      {
        T x = *this; x.set_empty(); 
        auto bounds = std::make_pair(x,x);
 
        if(t.lb() < t0_tf().lb() || t.ub() > t0_tf().ub())
        {
          x.init(Interval(-oo,0));
          bounds.first |= x;
          x.init(Interval(0,oo));
          bounds.second |= x;
        }
 
        if(t.contains(t0_tf().lb()))
        {
          bounds.first |= input_gate().lb();
          bounds.second |= input_gate().ub();
        }
 
        if(t.contains(t0_tf().ub()))
        {
          bounds.first |= output_gate().lb();
          bounds.second |= output_gate().ub();
        }
 
        if(t.is_subset(t0_tf()) && t != t0_tf().lb() && t != t0_tf().ub())
        {
          bounds.first |= this->lb();
          bounds.second |= this->ub();
        }
 
        return bounds;
      }

      inline void set(const T& x, bool propagate = true)
      {
        assert_release(x.size() == this->size());
        codomain() = x;
        if(propagate)
          update_adjacent_codomains();
      }

      inline void init()
      {
        this->T::init();
        // Nothing to propagate to adjacent codomains
      }

      inline void set_empty()
      {
        set_empty(true);
      }

      inline bool operator==(const Slice& x) const
      {
        return codomain() == x.codomain();
      }

      inline ConvexPolygon polygon_slice(const Slice<T>& v) const
        requires std::is_same_v<T,Interval>
      {
        const Interval& t = this->t0_tf();
        Interval input = this->input_gate(), output = this->output_gate();
 
        // /!\ .diam() method is not reliable (floating point result)
        // -> We need to compute the diameter with intervals
        Interval d = Interval(t.ub())-Interval(t.lb());
 
        Interval proj_output =  input + d * v;
        Interval proj_input  = output - d * v;
 
        return CtcDeriv::polygon_slice(
          t, *this,
          input, proj_input,
          output, proj_output,
          v);
      }

      inline ConvexPolygon polygon_slice_i(const Slice<T>& v, Index i) const
        requires std::is_same_v<T,IntervalVector>
      {
        const Interval& t = this->t0_tf();
 
        // /!\ .diam() method is not reliable (floating point result)
        // -> We need to compute the diameter with intervals
        Interval d = Interval(t.ub())-Interval(t.lb());
 
        Interval input = this->input_gate()[i], output = this->output_gate()[i];
        Interval proj_output =  input + d * v[i];
        Interval proj_input  = output - d * v[i];
 
        return CtcDeriv::polygon_slice(
          t, (*this)[i],
          input, proj_input,
          output, proj_output,
          v[i]);
      }

      inline T operator()(double t) const
      {
        if(t == t0_tf().lb())
          return input_gate();
 
        else if(t == t0_tf().ub())
          return output_gate();
 
        else if(t0_tf().contains(t))
          return codomain();
 
        else
          return all_reals_value();
      }

      inline T operator()(const Interval& t) const
      {
        if(t.is_degenerated())
          return operator()(t.lb());
 
        else if(t.is_subset(t0_tf()))
          return codomain();
 
        else
          return all_reals_value();
      }

      inline T operator()(double t, const Slice<T>& v) const
        requires (std::is_same_v<T,Interval> || std::is_same_v<T,IntervalVector>)
      {
        return operator()(Interval(t),v);
      }

      inline T operator()(const Interval& t, const Slice<T>& v) const
        requires (std::is_same_v<T,Interval> || std::is_same_v<T,IntervalVector>)
      {
        if constexpr(std::is_same_v<T,Interval>)
          return untrunc((polygon_slice(v) & ConvexPolygon(cart_prod(t,trunc(codomain())))).box()[1]);
 
        else if constexpr(std::is_same_v<T,IntervalVector>)
        {
          T y = all_reals_value();
          IntervalVector codom = codomain();
          for(Index i = 0 ; i < size() ; i++)
            y[i] &= untrunc((polygon_slice_i(v,i) & ConvexPolygon(cart_prod(t,trunc(codom[i])))).box()[1]);
          return y;
        }
      }

      inline Interval invert(const T& y, const Interval& t = Interval()) const
      {
        if(t.is_empty())
          return Interval::empty();
 
        else if(t.is_strict_superset(t0_tf()))
          return Interval();
 
        else if((t0_tf() & t) == t0_tf() && codomain().is_subset(y))
          return t0_tf();
 
        else if(t == t0_tf().lb())
        {
          if(y.intersects(input_gate()))
            return t0_tf().lb();
          else
            return Interval::empty();
        }
 
        else if(t == t0_tf().ub())
        {
          if(y.intersects(output_gate()))
            return t0_tf().ub();
          else
            return Interval::empty();
        }
 
        else
        {
          if(y.intersects(codomain()))
            return t & t0_tf();
          else
            return Interval::empty();
        }
      }

      inline Interval invert(const T& y, const Slice<T>& v, const Interval& t = Interval()) const
        requires (std::is_same_v<T,Interval> || std::is_same_v<T,IntervalVector>)
      {
        if(t.is_empty() || y.is_empty())
          return Interval::empty();
 
        else if(!t.is_subset(t0_tf()))
          return Interval();
 
        else
        {
          if constexpr(std::is_same_v<T,Interval>)
            return untrunc((polygon_slice(v) & ConvexPolygon(cart_prod(t,trunc(y)))).box()[0]);
 
          else if constexpr(std::is_same_v<T,IntervalVector>)
          {
            Interval t_(t);
            for(Index i = 0 ; i < size() ; i++)
              if(!t_.is_empty())
                t_ &= untrunc((polygon_slice_i(v,i) & ConvexPolygon(cart_prod(t_,trunc(y[i])))).box()[0]);
            return t_;
          }
        }
      }

      friend inline std::ostream& operator<<(std::ostream& os, const Slice& x)
      {
        os << x.t0_tf()
           << "↦" << x.codomain()
           << std::flush;
        return os;
      }

      inline T all_reals_value() const
      {
        T x = codomain();
        x.init();
        return x;
      }

      inline T empty_value() const
      {
        T x = codomain();
        x.set_empty();
        return x;
      }
      
 
    protected:
 
      template<typename T_>
      friend class SlicedTube;

      inline void set_empty(bool propagate)
      {
        this->T::set_empty();
        if(propagate)
          update_adjacent_codomains();
      }

      inline void update_adjacent_codomains()
      {
        if(prev_slice())
        {
          assert(prev_slice()->size() == this->size());
          if(is_gate())
            codomain() &= prev_slice()->codomain();
          else if(prev_slice()->is_gate())
            prev_slice()->codomain() &= codomain();
        }
 
        if(next_slice())
        {
          assert(next_slice()->size() == this->size());
          if(is_gate())
            codomain() &= next_slice()->codomain();
          else if(next_slice()->is_gate())
            next_slice()->codomain() &= codomain();
        }
      }
  };
}