```/* nag_ode_ivp_adams_roots (d02qfc) Example Program.
*
* Copyright 2019 Numerical Algorithms Group.
*
* Mark 27.0, 2019.
*
*/

#include <nag.h>
#include <stdio.h>

#ifdef __cplusplus
extern "C"
{
#endif
static void NAG_CALL ftry02(Integer neqf, double x, const double y[],
double yp[], Nag_User *comm);
static double NAG_CALL gtry02(Integer neqf, double x, const double y[],
const double yp[], Integer k, Nag_User *comm);
#ifdef __cplusplus
}
#endif

#define NEQF 2
#define NEQG 2
int main(void)
{
static Integer use_comm[2] = { 1, 1 };
Nag_Boolean alter_g, crit, one_step, sophist, vectol;
Integer exit_status = 0, i, max_step, neqf, neqg;
NagError fail;
Nag_Start state;
Nag_User comm;
double *atol = 0, *rtol = 0, t, tcrit, tout, *y = 0;

INIT_FAIL(fail);

/* For communication with user-supplied functions: */
comm.p = (Pointer) &use_comm;

neqf = NEQF;
neqg = NEQG;
if (neqf < 1) {
exit_status = 1;
return exit_status;
}
else {
if (!(y = NAG_ALLOC(neqf, double)) ||
!(atol = NAG_ALLOC(neqf, double)) ||
!(rtol = NAG_ALLOC(neqf, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
}
tcrit = 10.0;
state = Nag_NewStart;
vectol = Nag_TRUE;
one_step = Nag_FALSE;
crit = Nag_TRUE;
max_step = 0;
sophist = Nag_TRUE;
for (i = 0; i <= 1; ++i) {
rtol[i] = 0.0001;
atol[i] = 1e-06;
}

* Setup function for nag_ode_ivp_adams_roots (d02qfc)
*/
nag_ode_ivp_adams_setup(&state, neqf, vectol, atol, rtol, one_step, crit,
tcrit, 0.0, max_step, neqg, &alter_g, sophist, &opt,
&fail);
if (fail.code != NE_NOERROR) {
fail.message);
exit_status = 1;
goto END;
}

t = 0.0;
tout = tcrit;
y[0] = 0.0;
y[1] = 1.0;

do {
* Ordinary differential equation solver using Adams method
* (sophisticated use)
*/
nag_ode_ivp_adams_roots(neqf, ftry02, &t, y, tout, gtry02,
&comm, &opt, &fail);
if (fail.code != NE_NOERROR) {
fail.message);
exit_status = 1;
goto END;
}

if (opt.root) {
printf("\nRoot at %14.5e\n", t);
printf("for event equation %1" NAG_IFMT "", opt.index);
printf(" with type %1" NAG_IFMT "", opt.type);
printf(" and residual %14.5e\n", opt.resids[opt.index - 1]);

printf(" Y(1) = %14.5e   Y'(1) = %14.5e\n", y[0], opt.yp[0]);

for (i = 1; i <= neqg; ++i) {
if (i != opt.index && opt.events[i - 1] != 0) {
printf("and also for event equation %1" NAG_IFMT "", i);
printf(" with type %1" NAG_IFMT "", opt.events[i - 1]);
printf(" and residual %14.5e\n", opt.resids[i - 1]);
}
}
}
} while (opt.tcurr < tout && opt.root);

/* Free the memory which was allocated by
* nag_ode_ivp_adams_setup (d02qwc) to the pointers inside opt.
*/
* Freeing function for use with nag_ode_ivp_adams_roots (d02qfc)
*/
END:
NAG_FREE(y);
NAG_FREE(atol);
NAG_FREE(rtol);
return exit_status;
}

static void NAG_CALL ftry02(Integer neqf, double x, const double y[], double
yp[], Nag_User *comm)
{
Integer *use_comm = (Integer *) comm->p;

if (use_comm[0]) {
printf("(User-supplied callback ftry02, first invocation.)\n");
use_comm[0] = 0;
}

yp[0] = y[1];
yp[1] = -y[0];
} /* ftry02 */

static double NAG_CALL gtry02(Integer neqf, double x, const double y[], double
const yp[], Integer k, Nag_User *comm)
{
Integer *use_comm = (Integer *) comm->p;

if (use_comm[1]) {
printf("(User-supplied callback gtry02, first invocation.)\n");
use_comm[1] = 0;
}

if (k == 1)
return yp[0];
else
return y[0];
} /* gtry02 */
```