codac2_min.h

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#pragma once
 
#include "codac2_Interval.h"
#include "codac2_AnalyticType.h"
#include "codac2_AnalyticExprWrapper.h"
 
namespace codac2
{
  struct MinOp
  {
    template<typename X1,typename X2>
    static std::string str(const X1& x1, const X2& x2)
    {
      return "min(" +  x1->str() + "," + x2->str() + ")";
    }
 
    template<typename X1, typename X2>
    static std::pair<Index,Index> output_shape([[maybe_unused]] const X1& s1, [[maybe_unused]] const X2& s2)
    {
      return {1,1};
    }
 
    static Interval fwd(const Interval& x1, const Interval& x2);
    static ScalarType fwd_natural(const ScalarType& x1, const ScalarType& x2);
    static ScalarType fwd_centered(const ScalarType& x1, const ScalarType& x2);
    static void bwd(const Interval& y, Interval& x1, Interval& x2);
  };
 
  // Analytic operator
  // The following function can be used to build analytic expressions.
 
  inline ScalarExpr
  min(const ScalarExpr& x1, const ScalarExpr& x2)
  {
    return { std::make_shared<AnalyticOperationExpr<MinOp,ScalarType,ScalarType,ScalarType>>(x1,x2) };
  }
 
  // Inline functions
 
  inline Interval MinOp::fwd(const Interval& x1, const Interval& x2)
  {
    return min(x1,x2);
  }
 
  inline ScalarType MinOp::fwd_natural(const ScalarType& x1, const ScalarType& x2)
  {
    return {
      fwd(x1.a, x2.a),
      x1.def_domain && x2.def_domain
    };
  }
 
  inline ScalarType MinOp::fwd_centered(const ScalarType& x1, const ScalarType& x2)
  {
    if(centered_form_not_available_for_args(x1,x2))
      return fwd_natural(x1,x2);
    
    assert(x1.da.rows() == 1);
    assert(x1.da.rows() == x2.da.rows() && x1.da.cols() == x2.da.cols());
 
    IntervalMatrix d(1,x1.da.cols());
    for(Index i = 0 ; i < d.size() ; i++)
      d(0,i) = chi(x1.a-x2.a, x1.da(0,i), x2.da(0,i));
 
    return {
      fwd(x1.m, x2.m),
      fwd(x1.a, x2.a),
      d,
      x1.def_domain && x2.def_domain
        && (x1.a != x2.a) // def domain of the derivative of min
    };
  }
 
  inline void MinOp::bwd(const Interval& y, Interval& x1, Interval& x2)
  {
    // The content of this function comes from the IBEX library.
    // See ibex::Interval (IBEX lib, main author: Gilles Chabert)
    //   https://ibex-lib.readthedocs.io
 
    Interval mx1 = -x1;
    Interval mx2 = -x2;
 
    MaxOp::bwd(-y,mx1,mx2);
 
    if(mx1.is_empty() || mx2.is_empty())
    {
      x1.set_empty();
      x2.set_empty();
    }
 
    else
    {
      x1 = -mx1;
      x2 = -mx2;
    }
  }
}