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

ode_evaluate.cpp

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ode_evaluate: Example and test

# include <cppad/speed/ode_evaluate.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/cppad.hpp>

bool ode_evaluate(void)
{  using CppAD::NearEqual;
   using CppAD::AD;

   bool ok = true;

   size_t n = 3;
   CppAD::vector<double>       x(n);
   CppAD::vector<double>       ym(n * n);
   CppAD::vector< AD<double> > X(n);
   CppAD::vector< AD<double> > Ym(n);

   // choose x
   size_t j;
   for(j = 0; j < n; j++)
   {  x[j] = double(j + 1);
      X[j] = x[j];
   }

   // declare independent variables
   Independent(X);

   // evaluate function
   size_t m = 0;
   CppAD::ode_evaluate(X, m, Ym);

   // evaluate derivative
   m = 1;
   CppAD::ode_evaluate(x, m, ym);

   // use AD to evaluate derivative
   CppAD::ADFun<double>   F(X, Ym);
   CppAD::vector<double>  dy(n * n);
   dy = F.Jacobian(x);

   size_t k;
   for(k = 0; k < n * n; k++)
      ok &= NearEqual(ym[k], dy[k] , 1e-7, 1e-7);

   return ok;
}