| Prev | Next |  |  |  |  |  | ipopt_nlp_ode_problem.hpp | Headings

ODE Inverse Problem Definitions: Source Code
`

    # include "../src/cppad_ipopt_nlp.hpp"

    namespace {
         //------------------------------------------------------------------
         typedef Ipopt::Number Number;
         Number a0 = 1.;  // simulation value for a[0]
         Number a1 = 2.;  // simulation value for a[1]
         Number a2 = 1.;  // simulatioln value for a[2]

         // function used to simulate data
         Number y_one(Number t)
         {     Number y_1 =  a0*a1 * (exp(-a2*t) - exp(-a1*t)) / (a1 - a2);
              return y_1;
         }

         // time points were we have data (no data at first point)
         double s[] = { 0.0,        0.5,        1.0,        1.5,        2.0 };
         // Simulated data for case with no noise (first point is not used)
         double z[] = { 0.0,  y_one(0.5), y_one(1.0), y_one(1.5), y_one(2.0) };
         // Number of measurement values
         size_t Nz  = sizeof(z) / sizeof(z[0]) - 1;
         // Number of components in the function y(t, a)
         size_t Ny  = 2;
         // Number of components in the vectro a
         size_t Na  = 3;

         // Initial Condition function, F(a) = y(t, a) at t = 0
         // (for this particular example)
         template <class Vector>
         Vector eval_F(const Vector &a)
         {     Vector F(Ny);
              // y_0 (t) = a[0]*exp(-a[1] * t)
              F[0] = a[0];
              // y_1 (t) =
              // a[0]*a[1]*(exp(-a[2] * t) - exp(-a[1] * t))/(a[1] - a[2])
              F[1] = 0.;
              return F;
         }
         // G(y, a) =  \partial_t y(t, a); i.e. the differential equation
         // (for this particular example)
         template <class Vector>
         Vector eval_G(const Vector &y , const Vector &a)
         {     Vector G(Ny);
              // y_0 (t) = a[0]*exp(-a[1] * t)
              G[0] = -a[1] * y[0];
              // y_1 (t) =
              // a[0]*a[1]*(exp(-a[2] * t) - exp(-a[1] * t))/(a[1] - a[2])
              G[1] = +a[1] * y[0] - a[2] * y[1];
              return G;
         }
         // H(i, y, a) = contribution to objective at i-th data point
         // (for this particular example)
         template <class Scalar, class Vector>
         Scalar eval_H(size_t i, const Vector &y, const Vector &a)
         {     // This particular H is for a case where y_1 (t) is measured
              Scalar diff = z[i] - y[1];
              return diff * diff;
         }
         // function used to count the number of calls to eval_r
         size_t count_eval_r(void)
         {     static size_t count = 0;
              ++count;
              return count;
         }
    }

`

Input File: cppad_ipopt/example/ode_problem.hpp