Correctness Check for Both Simple and Fast Representations
Keywords: correctness check both simple fast representations

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Correctness Check for Both Simple and Fast Representations
`

    # include "ode_run.hpp"

    bool ode_check(const SizeVector& N, const NumberVector& 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 <= 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 < Na; j++)
    		a[j] = x[ny_inx+j];
    	for(j = 0; j < 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 < Na; j++)
    	{
    		ok &= CppAD::NearEqual(
    			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 < Ny; j++)
    		ok &= CppAD::NearEqual(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 < Ny; j++)
    	{	check = y_1[j] - y_0[j] - (G_1[j]+G_0[j])*dt/2;
    		ok &= CppAD::NearEqual( 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 < Ny; j++)
    	{	check = y_2[j] - y_1[j] - (G_2[j]+G_1[j])*dt/2;
    		ok &= CppAD::NearEqual( 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 < Nz; k++)
    	{	for(j = 0; j < Ny; j++)
    			y_i[j] =  x[S[k+1] * Ny + j];
    		check += eval_H<Number>(k + 1, y_i, a);
    	}
    	Number obj_value = 0.; // optimal object (no noise in simulation)
    	ok &= CppAD::NearEqual(check, obj_value, rel_tol, abs_tol);

    	// Use this empty namespace function to avoid warning that it is not used
    	static size_t ode_check_count = 0;
    	ode_check_count++;
    	ok &= count_eval_r() == ode_check_count;

    	return ok;
    }

`

Input File: cppad_ipopt/example/ode_check.cpp