Prev Next sacado_poly.cpp

Sacado Speed: Second Derivative of a Polynomial

link_poly
Routine that computes the derivative of a polynomial using Sacado:
# include <cppad/vector.hpp>
# include <cppad/poly.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <Sacado.hpp>

bool link_poly(
     size_t                     size     , 
     size_t                     repeat   , 
     bool                       retape   ,
     CppAD::vector<double>     &a        ,  // coefficients of polynomial
     CppAD::vector<double>     &z        ,  // polynomial argument value
     CppAD::vector<double>     &ddp      )  // second derivative w.r.t z  
{
     // -----------------------------------------------------
     // setup
     typedef Sacado::Tay::Taylor<double>  ADScalar;
     CppAD::vector<ADScalar>              A(size);

     size_t i;               // temporary index     
     ADScalar   Z;           // domain space AD value
     ADScalar   P;           // range space AD value 
     unsigned int order = 2; // order of Taylor coefficients
     Z.resize(order+1, false);
     P.resize(order+1, false);

     // choose the polynomial coefficients
     CppAD::uniform_01(size, a);

     // AD copy of the polynomial coefficients
     for(i = 0; i < size; i++)
          A[i] = a[i];

     // ------------------------------------------------------
     while(repeat--)
     {    // get the next argument value
          CppAD::uniform_01(1, z);

          // independent variable value
          Z.fastAccessCoeff(0)   = z[0]; // argument value
          Z.fastAccessCoeff(1)   = 1.;   // first order coefficient
          Z.fastAccessCoeff(2)   = 0.;   // second order coefficient

          // AD computation of the dependent variable
          P = CppAD::Poly(0, A, Z);

          // second derivative is twice second order Taylor coefficient
          ddp[0] = 2. * P.fastAccessCoeff(2);
     }
     // ------------------------------------------------------
     return true;
}

Input File: speed/sacado/poly.cpp