\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)

poly.hpp

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Source: Poly

# ifndef CPPAD_POLY_HPP

# define CPPAD_POLY_HPP

# include <cstddef>  // used to defined size_t
# include <cppad/utility/check_simple_vector.hpp>

namespace CppAD {    // BEGIN CppAD namespace

template <class Type, class Vector>
Type Poly(size_t k, const Vector &a, const Type &z)
{  size_t i;
   size_t d = a.size() - 1;

   Type tmp;

   // check Vector is Simple Vector class with Type elements
   CheckSimpleVector<Type, Vector>();

   // case where derivative order greater than degree of polynomial
   if( k > d )
   {  tmp = 0;
      return tmp;
   }
   // case where we are evaluating a derivative
   if( k > 0 )
   {  // initialize factor as (k-1) !
      size_t factor = 1;
      for(i = 2; i < k; i++)
         factor *= i;

      // set b to coefficient vector corresponding to derivative
      Vector b(d - k + 1);
      for(i = k; i <= d; i++)
      {  factor   *= i;
         tmp       = double( factor );
         b[i - k]  = a[i] * tmp;
         factor   /= (i - k + 1);
      }
      // value of derivative polynomial
      return Poly(0, b, z);
   }
   // case where we are evaluating the original polynomial
   Type sum = a[d];
   i        = d;
   while(i > 0)
   {  sum *= z;
      sum += a[--i];
   }
   return sum;
}
} // END CppAD namespace

# endif