codac2_pow.h

Go to the documentation of this file.

 
#pragma once
 
#include "codac2_Interval.h"
#include "codac2_AnalyticType.h"
#include "codac2_AnalyticExprWrapper.h"
 
namespace codac2
{
  struct PowOp
  {
    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, int 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
  pow(const ScalarExpr& x1, const ScalarExpr& x2)
  {
    return { std::make_shared<AnalyticOperationExpr<PowOp,ScalarType,ScalarType,ScalarType>>(x1,x2) };
  }
 
  inline ScalarExpr
  operator^(const ScalarExpr& x1, const ScalarExpr& x2)
  {
    return { std::make_shared<AnalyticOperationExpr<PowOp,ScalarType,ScalarType,ScalarType>>(x1,x2) };
  }
 
  // Inline functions
 
  inline Interval PowOp::fwd(const Interval& x1, const Interval& x2)
  {
    return pow(x1,x2);
  }
 
  inline ScalarType PowOp::fwd_natural(const ScalarType& x1, const ScalarType& x2)
  {
    return {
      fwd(x1.a, x2.a),
      x1.def_domain && x2.def_domain
    };
  }
 
  inline ScalarType PowOp::fwd_centered(const ScalarType& x1, const ScalarType& x2)
  {
    if(centered_form_not_available_for_args(x1,x2))
      return fwd_natural(x1,x2);
 
    IntervalMatrix d(1,x1.da.size());
    for(Index i = 0 ; i < d.size() ; i++)
      d(0,i) = x2.a*x1.da(0,i)*pow(x1.a,x2.a-1.);
 
    return {
      fwd(x1.m, x2.m),
      fwd(x1.a, x2.a),
      d,
      x1.def_domain && x2.def_domain
    };
  }
 
  inline void PowOp::bwd(const Interval& y, Interval& x1, int 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
 
    if(x2 % 2 == 0)
    {
      Interval proj = root(y, x2);
      Interval pos_proj = proj & x1;
      Interval neg_proj = (-proj) & x1;
      x1 = pos_proj | neg_proj;
    }
 
    else
      x1 &= root(y, x2);
  }
 
  inline void PowOp::bwd(const Interval& y, Interval& x1, Interval& x2)
  {
    assert_release(x2.is_degenerated() && "PowOp::bwd(y,x1,x2) (with x1 and x2 intervals) not implemented yet with Gaol");
    assert_release(x2 == (int)(x2.mid()) && "PowOp::bwd(y,x1,x2) (x2 not integer) not implemented yet with Gaol");
    PowOp::bwd(y, x1, x2.mid());
  }
}