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<center><b><big><big>Correctness Check for Both Simple and Fast Representations</big></big></b></center>
<code><font color="blue"><pre style='display:inline'> 
# include &quot;ode_run.hpp&quot;

bool ode_check(const SizeVector&amp; N, const NumberVector&amp; x)
{	bool ok = true;
	size_t i, j;

	// number of components of x corresponding to values for y
	size_t ny_inx = x.size() - Na;

	// compute the partial sums of the number of grid points
	// and the maximum step size for the trapezoidal approximation
	SizeVector S(Nz+1);
	S[0] = 0;
	double max_step = 0.;
	for(i = 1; i &lt;= Nz; i++)
	{	S[i] = S[i-1] + N[i];
		max_step = std::max(max_step, (s[i] - s[i-1]) / N[i] );
	}

	// split out return values
	NumberVector a(Na), y_0(Ny), y_1(Ny), y_2(Ny);
	for(j = 0; j &lt; Na; j++)
		a[j] = x[ny_inx+j];
	for(j = 0; j &lt; Ny; j++)
	{	y_0[j] = x[j];
		y_1[j] = x[Ny + j];
		y_2[j] = x[2 * Ny + j];
	} 

	// Check some of the optimal a value
	Number rel_tol = max_step * max_step;
	Number abs_tol = rel_tol;
	Number check_a[] = {a0, a1, a2}; // see the y_one function
	for(j = 0; j &lt; Na; j++)
	{
		ok &amp;= CppAD::<a href="nearequal.xml" target="_top">NearEqual</a>( 
			check_a[j], a[j], rel_tol, abs_tol
		);
	}

	// check accuarcy of constraint equations
	rel_tol = 1e-9;
	abs_tol = 1e-9;

	// check the initial value constraint
	NumberVector F = eval_F(a);
	for(j = 0; j &lt; Ny; j++)
		ok &amp;= CppAD::<a href="nearequal.xml" target="_top">NearEqual</a>(F[j], y_0[j], rel_tol, abs_tol);

	// check the first trapezoidal equation
	NumberVector G_0 = eval_G(y_0, a);
	NumberVector G_1 = eval_G(y_1, a);
	Number dt = (s[1] - s[0]) / Number(N[1]);
	Number check;
	for(j = 0; j &lt; Ny; j++)
	{	check = y_1[j] - y_0[j] - (G_1[j]+G_0[j])*dt/2;
		ok &amp;= CppAD::<a href="nearequal.xml" target="_top">NearEqual</a>( check, 0., rel_tol, abs_tol);
	}
	//
	// check the second trapezoidal equation
	NumberVector G_2 = eval_G(y_2, a);
	if( N[1] == 1 )
		dt = (s[2] - s[1]) / Number(N[2]);
	for(j = 0; j &lt; Ny; j++)
	{	check = y_2[j] - y_1[j] - (G_2[j]+G_1[j])*dt/2;
		ok &amp;= CppAD::<a href="nearequal.xml" target="_top">NearEqual</a>( check, 0., rel_tol, abs_tol);
	}
	//
	// check the objective function (specialized to this case)
	check = 0.;
	NumberVector y_i(Ny);
	for(size_t k = 0; k &lt; Nz; k++)
	{	for(j = 0; j &lt; Ny; j++)
			y_i[j] =  x[S[k+1] * Ny + j];
		check += eval_H&lt;Number&gt;(k + 1, y_i, a);
	}
	Number obj_value = 0.; // optimal object (no noise in simulation)
	ok &amp;= CppAD::<a href="nearequal.xml" target="_top">NearEqual</a>(check, obj_value, rel_tol, abs_tol);

	return ok;
}
</pre>

</font></code>


<hr/>Input File: cppad_ipopt/example/ode_check.cpp

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