NAG Library Manual, Mark 27.2
Interfaces:  FL   CL   CPP   AD
```/* D02PU_P0W_F C++ Header Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
*
* Mark 27.2, 2021.
*/

#include <iostream>
#include <math.h>
#include <nag.h>
#include <stdio.h>
using namespace std;

#ifdef __cplusplus
extern "C"
{
#endif
static void NAG_CALL f(void *&        ad_handle,
const double & t,
const Integer &n,
const double   y[],
double         yp[],
Integer        iuser[],
double         ruser[]);
#ifdef __cplusplus
}
#endif

int main(void)
{
const Integer n      = 4;
const Integer liwsav = 130;
const Integer lrwsav = 350 + 32 * n;

Integer exit_status = 0;

double * rwsav = 0, *thresh = 0, *ygot = 0, *ymax = 0;
double * ypgot = 0, *y = 0, ruser[1];
Integer *iwsav  = 0, iuser[1];
double * rmserr = 0;

cout << "D02PU_P0W_F C++ Header Example Program Results\n\n";

thresh = new double[n];
ygot   = new double[n];
y      = new double[n];
ypgot  = new double[n];
ymax   = new double[n];
iwsav  = new Integer[liwsav];
rwsav  = new double[lrwsav];
rmserr = new double[n];

// Set initial conditions for ODE and parameters for the integrator.
Integer method = 3;
double  tol, hstart, tend, tstart, eps;
eps    = 0.7;
tstart = 0.0;
tol    = 1.0e-6;
tend   = 3.0 * nag_math_pi;
hstart = 0.0;
for (int i = 0; i < n; ++i)
{
thresh[i] = 1.0e-10;
}

cout << "\n  Calculation with tol = " << tol << endl;

cout.setf(ios::fixed);
cout.setf(ios::right);
cout.precision(3);
cout << "\n    t         y1         y2         y3         y4" << endl;
cout.width(6);
cout << tstart;

y[0] = 1.0 - eps;
y[1] = 0.0;
y[2] = 0.0;
y[3] = sqrt((1.0 + eps) / (1.0 - eps));
for (int k = 0; k < n; k++)
{
cout.width(11);
cout << y[k];
}
cout << endl;

// Initialize Runge-Kutta method for integrating ODE
Integer ifail     = 0;
void *  ad_handle = 0;
nag::ad::d02pq(ad_handle, n, tstart, tend, y, tol, thresh, method, hstart,
iwsav, rwsav, ifail);

double tgot, twant;
twant = tend;

ifail = 2;
while (ifail > 1 && ifail < 5)
{
ifail = -1;
nag::ad::d02pe(ad_handle, f, n, twant, tgot, ygot, ypgot, ymax, -1, iuser,
-1, ruser, iwsav, rwsav, ifail);
}

if (ifail == 0)
{
cout.width(6);
cout << tgot;
for (int k = 0; k < n; ++k)
{
cout.width(11);
cout << ygot[k];
}
cout << endl;

// Get Error estimates
double errmax, terrmx;
ifail = 0;
nag::ad::d02pu(ad_handle, n, rmserr, errmax, terrmx, iwsav, rwsav, ifail);

cout.setf(ios::scientific, ios::floatfield);
cout.precision(2);
cout << "\n Componentwise error assessment\n        ";
for (int k = 0; k < n; ++k)
{
cout.width(11);
cout << rmserr[k];
}
cout << endl;
cout.precision(3);
cout << "\n Worst global error observed was ";
cout.width(9);
cout << errmax << endl;
cout << "              it occurred at T = ";
cout.width(8);
cout << terrmx << endl;

double  hnext, waste;
Integer fevals, stepcost, stepsok;
ifail = 0;
nag::ad::d02pt(ad_handle, fevals, stepcost, waste, stepsok, hnext, iwsav,
rwsav, ifail);
cout << "\n Cost of the integration in evaluations of f is " << fevals;
cout << endl;
}
delete[] thresh;
delete[] ygot;
delete[] y;
delete[] ypgot;
delete[] ymax;
delete[] iwsav;
delete[] rwsav;
delete[] rmserr;
return exit_status;
}

static void NAG_CALL f(void *&        ad_handle,
const double & t,
const Integer &n,
const double   y[],
double         yp[],
Integer        iuser[],
double         ruser[])
{
double r;
r     = 1.0 / sqrt(y[0] * y[0] + y[1] * y[1]);
r     = r * r * r;
yp[0] = y[2];
yp[1] = y[3];
yp[2] = -y[0] * r;
yp[3] = -y[1] * r;
}
```