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<?xml version='1.0'?>
<html xmlns='http://www.w3.org/1999/xhtml'
      xmlns:math='http://www.w3.org/1998/Math/MathML'
>
<head>
<title>ODE Fitting Using Simple Representation</title>
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<meta name="description" id="description" content="ODE Fitting Using Simple Representation"/>
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<center><b><big><big>ODE Fitting Using Simple Representation</big></big></b></center>
<code><font color="blue"><pre style='display:inline'> 
# include &quot;ode_problem.hpp&quot;

// define in the empty namespace
namespace {
	using namespace cppad_ipopt;

	class FG_simple : public cppad_ipopt_fg_info
	{
	private:
		bool       retape_;
		SizeVector N_;
		SizeVector S_;
	public:
		// derived class part of constructor
		FG_simple(bool retape_in, const SizeVector&amp; N)
		: retape_ (retape_in), N_(N)
		{	assert( N_[0] == 0 );
			S_.resize( N.size() );
			S_[0] = 0;
			for(size_t i = 1; i &lt; N_.size(); i++)
				S_[i] = S_[i-1] + N_[i];
		}
		// Evaluation of the objective f(x), and constraints g(x)
		// using an Algorithmic Differentiation (AD) class.
		ADVector eval_r(size_t not_used, const ADVector&amp;  x)
		{	count_eval_r();

			// temporary indices
			size_t i, j, k;
			// # of components of x corresponding to values for y
			size_t ny_inx = (S_[Nz] + 1) * Ny;
			// # of constraints (range dimension of g)
			size_t m = ny_inx;
			// # of components in x (domain dimension for f and g)
			assert ( x.size() == ny_inx + Na );
			// vector for return value
			ADVector fg(m + 1);
			// vector of parameters
			ADVector a(Na);
			for(j = 0; j &lt; Na; j++)
				a[j] = x[ny_inx + j];
			// vector for value of y(t)
			ADVector y(Ny);
			// objective function -------------------------------
			fg[0] = 0.;
			for(k = 0; k &lt; Nz; k++)
			{	for(j = 0; j &lt; Ny; j++)
					y[j] = x[Ny*S_[k+1] + j];
				fg[0] += eval_H&lt;ADNumber&gt;(k+1, y, a);
			}
			// initial condition ---------------------------------
			ADVector F = eval_F(a);
			for(j = 0; j &lt; Ny; j++)
			{	y[j]    = x[j];
				fg[1+j] = y[j] - F[j];
			}
			// trapezoidal approximation --------------------------
			ADVector ym(Ny), G(Ny), Gm(Ny);
			G = eval_G(y, a);
			ADNumber dy;
			for(k = 0; k &lt; Nz; k++)
			{	// interval between data points
				Number T  = s[k+1] - s[k];
				// integration step size
				Number dt = T / Number( N_[k+1] );
				for(j = 0; j &lt; N_[k+1]; j++)
				{	size_t Index = (j + S_[k]) * Ny;
				 	// y(t) at end of last step
					ym = y;
					// G(y, a) at end of last step
					Gm = G;
					// value of y(t) at end of this step
					for(i = 0; i &lt; Ny; i++)
						y[i] = x[Ny + Index + i];
					// G(y, a) at end of this step
					G = eval_G(y, a);
					// trapezoidal approximation residual
					for(i = 0; i &lt; Ny; i++)
					{	dy = (G[i] + Gm[i]) * dt / 2;
						fg[1+Ny+Index+i] =
							y[i] - ym[i] - dy;
					}
				}
			}
			return fg;
		}
		// The operations sequence for r_eval does not depend on u,
		// hence retape = false should work and be faster.
		bool retape(size_t k)
		{	return retape_; }
	};

}
</pre>

</font></code>


<hr/>Input File: cppad_ipopt/example/ode_simple.hpp

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