codac2_acos.h

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#pragma once
 
#include "codac2_Interval.h"
#include "codac2_AnalyticType.h"
#include "codac2_AnalyticExprWrapper.h"
 
namespace codac2
{
  struct AcosOp
  {
    template<typename X1>
    static std::string str(const X1& x1)
    {
      return "acos(" + x1->str() + ")";
    }
 
    template<typename X1>
    static std::pair<Index,Index> output_shape([[maybe_unused]] const X1& x1)
    {
      return {1,1};
    }
 
    static Interval fwd(const Interval& x1);
    static ScalarType fwd_natural(const ScalarType& x1);
    static ScalarType fwd_centered(const ScalarType& x1);
    static void bwd(const Interval& y, Interval& x1);
  };
 
  // Analytic operator
  // The following function can be used to build analytic expressions.
 
  inline ScalarExpr
  acos(const ScalarExpr& x1)
  {
    return { std::make_shared<AnalyticOperationExpr<AcosOp,ScalarType,ScalarType>>(x1) };
  }
  
  // Inline functions
 
  inline Interval AcosOp::fwd(const Interval& x1)
  {
    return acos(x1);
  }
 
  inline ScalarType AcosOp::fwd_natural(const ScalarType& x1)
  {
    return {
      fwd(x1.a),
      x1.a.is_subset({-1,1}) // def domain of acos
      && x1.a != 1. // def domain of the derivative of acos
      && x1.def_domain
    };
  }
 
  inline ScalarType AcosOp::fwd_centered(const ScalarType& x1)
  {
    if(centered_form_not_available_for_args(x1))
      return fwd_natural(x1);
    
    IntervalMatrix d(1,x1.da.size());
    for(Index i = 0 ; i < d.size() ; i++)
      d(0,i) = -x1.da(0,i)/sqrt(1.-sqr(x1.a));
 
    return {
      fwd(x1.m),
      fwd(x1.a),
      d,
      x1.a.is_subset({-1,1}) // def domain of acos
      && x1.a != 1. // def domain of the derivative of acos
      && x1.def_domain
    };
  }
 
  inline void AcosOp::bwd(const Interval& y, Interval& x1)
  {
    x1 &= cos(y);
  }
 
}