NAG Library Manual, Mark 28.4
```/* nag::ad::d02pq Passive Example Program.
*/

#include <dco.hpp>
#include <iostream>

// Function which calls NAG AD routines.
// Solves the equation y''=-y, y0(=y(0))=0, y0'(=y'(0))=1 by solving the ODE
// system:
//    y1'=r1*y2,  y2'=-r2*y1
// over the range [0,2*pi] with initial conditions y1=0, y2=1.
template <typename T> void func(std::vector<T> &r, std::vector<T> &y);

int main()
{
std::cout << "nag::ad::d02pq Passive Example Program Results\n\n";

// Set problem parameters
std::vector<double> r{1.0, 1.0};
// Solution y
std::vector<double> y{0.0, 1.0};

// Call driver
func(r, y);

// Print outputs
std::cout.setf(std::ios::scientific, std::ios::floatfield);
std::cout.precision(6);
std::cout << " Solution computed with required tolerance " << 1e-4
<< std::endl;
for (std::size_t i = 0; i < y.size(); i++)
{
std::cout << " y" << i + 1 << " = " << y[i] << std::endl;
}
std::cout << std::endl;

return 0;
}

// function which calls NAG AD Library routines
template <typename T> void func(std::vector<T> &r, std::vector<T> &y)
{
// Active variables
const Integer n      = y.size();
const Integer liwsav = 130, lrwsav = 350 + 32 * n;

std::vector<T>       thresh(n, 1e-8), ypnow(n), rwsav(lrwsav);
std::vector<Integer> iwsav(liwsav);

// Set parameters for the integrator.
Integer method = 2;
T       tol = 1e-4, hstart = 0.0, tend = 2.0 * nag_math_pi, tstart = 0.0;
// Create AD configuration data object
Integer           ifail = 0;

// Initialize Runge-Kutta method for integrating ODE
ifail = 0;
method, hstart, iwsav.data(), rwsav.data(), ifail);

T tnow = tstart;

const T &          t,
const Integer &    n,
const T            y[],
T                  yp[])
{
yp[0] = r[0] * y[1];
yp[1] = -r[1] * y[0];
};
do
{
ifail = 0;
// Solve an initial value problem for a 1st order system of ODEs