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# ifndef CPPAD_CPPAD_IPOPT_EXAMPLE_ODE_PROBLEM_HPP
# define CPPAD_CPPAD_IPOPT_EXAMPLE_ODE_PROBLEM_HPP
// SPDX-License-Identifier: EPL-2.0 OR GPL-2.0-or-later
// SPDX-FileCopyrightText: Bradley M. Bell <bradbell@seanet.com>
// SPDX-FileContributor: 2003-22 Bradley M. Bell
// ----------------------------------------------------------------------------
/*
{xrst_begin ipopt_nlp_ode_problem.hpp dev}
ODE Inverse Problem Definitions: Source Code
############################################
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end ipopt_nlp_ode_problem.hpp}
------------------------------------------------------------------------------
*/
// BEGIN C++
# 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;
}
}
// END C++
# endif
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