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<center><b><big><big>Source: ode_evaluate</big></big></b></center>
<code><font color="blue"># ifndef CPPAD_ODE_EVALUATE_INCLUDED 
<code><span style='white-space: nowrap'><br/>
</span></code># define CPPAD_ODE_EVALUATE_INCLUDED 

<pre style='display:inline'> 
# include &lt;cppad/vector.hpp&gt;
# include &lt;cppad/ode_err_control.hpp&gt;
# include &lt;cppad/runge_45.hpp&gt;

namespace CppAD { 

	template &lt;class Float&gt;
	class ode_evaluate_fun {
	public:
		// Given that y_i (0) = x_i, 
		// the following y_i (t) satisfy the ODE below:
		// y_0 (t) = x[0]
		// y_1 (t) = x[1] + x[0] * t 
		// y_2 (t) = x[2] + x[1] * t + x[0] * t^2/2
		// y_3 (t) = x[3] + x[2] * t + x[1] * t^2/2 + x[0] * t^3 / 3!
		// ...
		void Ode(
			const Float&amp;                    t, 
			const CppAD::vector&lt;Float&gt;&amp;     y, 
			CppAD::vector&lt;Float&gt;&amp;           f)
		{	size_t n  = y.size();	
			f[0]      = 0.;
			for(size_t k = 1; k &lt; n; k++)
				f[k] = y[k-1];
		}
	};
	//
	template &lt;class Float&gt;
	void ode_evaluate(
		const CppAD::vector&lt;Float&gt;&amp; x  , 
		size_t                      p  , 
		CppAD::vector&lt;Float&gt;&amp;       fp )
	{	using CppAD::vector;
		typedef vector&lt;Float&gt; VectorFloat;

		size_t n = x.size();
		CPPAD_ASSERT_KNOWN( p == 0 || p == 1,
			&quot;ode_evaluate: p is not zero or one&quot;
		);
		CPPAD_ASSERT_KNOWN( 
			((p==0) &amp; (fp.size()==n)) || ((p==1) &amp; (fp.size()==n*n)),
			&quot;ode_evaluate: the size of fp is not correct&quot;
		);
		if( p == 0 )
		{	// function that defines the ode
			ode_evaluate_fun&lt;Float&gt; F;

			// number of Runge45 steps to use
			size_t M = 10;

			// initial and final time
			Float ti = 0.0;
			Float tf = 1.0;

			// initial value for y(x, t); i.e. y(x, 0)
			// (is a reference to x)
			const VectorFloat&amp; yi = x;

			// final value for y(x, t); i.e., y(x, 1)
			// (is a reference to fp)
			VectorFloat&amp; yf = fp;
			
			// Use fourth order Runge-Kutta to solve ODE
			yf = CppAD::Runge45(F, M, ti, tf, yi);

			return;
		}
		/* Compute derivaitve of y(x, 1) w.r.t x
		y_0 (x, t) = x[0]
		y_1 (x, t) = x[1] + x[0] * t 
		y_2 (x, t) = x[2] + x[1] * t + x[0] * t^2/2
		y_3 (x, t) = x[3] + x[2] * t + x[1] * t^2/2 + x[0] * t^3 / 3!
		...
		*/
		size_t i, j, k;
		for(i = 0; i &lt; n; i++)
		{	for(j = 0; j &lt; n; j++)
				fp[ i * n + j ] = 0.0;
		}
		size_t factorial = 1;
		for(k = 0; k &lt; n; k++)
		{	if( k &gt; 1 )
				factorial *= k; 
			for(i = k; i &lt; n; i++)
			{	// partial w.r.t x[i-k] of x[i-k] * t^k / k!
				j = i - k;
				fp[ i * n + j ] += 1.0 / Float(factorial);
			}
		}
	}
}
</pre>


# endif
</font></code>


<hr/>Input File: omh/ode_evaluate.omh

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