NAG Library Manual, Mark 27.3
Interfaces:  FL   CL   CPP   AD
```/* nag_interp_dim5_scat_shep_eval (e01tnc) Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
*
* Mark 27.3, 2021.
*/

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

#ifdef __cplusplus
extern "C" {
#endif
static double NAG_CALL funct(double x[]);
#ifdef __cplusplus
}
#endif

#define X(I, J) x[I * 5 + J]
#define XE(I, J) xe[I * 5 + J]

int main(void) {
/* Scalars */
Integer exit_status, i, m, n, nq, nw, liq, lrq, lstate, subid;
Integer lseed = 1;
double fun;
Nag_BaseRNG genid;
NagError fail;
/* Arrays */
double *f = 0, *q = 0, *qx = 0, *rq = 0, *xe = 0, *x = 0;
Integer *iq = 0, *state = 0;
Integer seed[1], seed2[1];

exit_status = 0;

INIT_FAIL(fail);

printf("nag_interp_dim5_scat_shep_eval (e01tnc) Example Program Results\n");

/* Skip heading in data file */
scanf("%*[^\n] ");

/* Input the seeds. */
scanf("%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &seed[0], &seed2[0]);

/* Choose the base generator */
genid = Nag_Basic;
subid = 0;

/* Get the length of the state array */
lstate = -1;
nag_rand_init_repeat(genid, subid, seed, lseed, state, &lstate, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_rand_init_repeat (g05kfc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Input the number of nodes. */
scanf("%" NAG_IFMT "%*[^\n] ", &m);

/* Allocate memory */
lrq = 21 * m + 11;
liq = 2 * m + 1;
if (!(f = NAG_ALLOC(m, double)) || !(x = NAG_ALLOC(m * 5, double)) ||
!(rq = NAG_ALLOC(lrq, double)) || !(iq = NAG_ALLOC(liq, Integer)) ||
!(state = NAG_ALLOC(lstate, Integer))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Initialize the generator to a repeatable sequence */
nag_rand_init_repeat(genid, subid, seed, lseed, state, &lstate, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_rand_init_repeat (g05kfc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Generate the data points X */
nag_rand_dist_uniform01(m * 5, state, x, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_rand_dist_uniform01 (g05sac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Evaluate F */
for (i = 0; i < m; ++i) {
f[i] = funct(&X(i, 0));
}

/* Generate the interpolant. */
nq = 0;
nw = 0;

/* nag_interp_dim5_scat_shep (e01tmc).
* Interpolating functions, modified Shepard's method, five
* variables
*/
nag_interp_dim5_scat_shep(m, x, f, nw, nq, iq, rq, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_interp_dim5_scat_shep (e01tmc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

/* Input the number of evaluation points. */
scanf("%" NAG_IFMT "%*[^\n] ", &n);

/* Allocate memory for nag_interp_dim5_scat_shep_eval (e01tnc) */
if (!(q = NAG_ALLOC(n, double)) || !(qx = NAG_ALLOC(n * 5, double)) ||
!(xe = NAG_ALLOC(n * 5, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Generate repeatable evaluation points. */
nag_rand_init_repeat(genid, subid, seed2, lseed, state, &lstate, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_rand_init_repeat (g05kfc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
nag_rand_dist_uniform01(n * 5, state, xe, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_rand_dist_uniform01 (g05sac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_interp_dim5_scat_shep_eval (e01tnc).
* Evaluate interpolant and first derivatives computed by
* nag_interp_dim5_scat_shep (e01tmc).
*/
fail.print = Nag_TRUE;
nag_interp_dim5_scat_shep_eval(m, x, f, iq, rq, n, xe, q, qx, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_interp_dim5_scat_shep_eval (e01tnc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

printf("\n     i     f(x)      q(x)   |f(x)-Q(x)|\n");
for (i = 0; i < n; ++i) {
fun = funct(&XE(i, 0));
printf("%6" NAG_IFMT "%10.4f%10.4f%10.4f\n", i, fun, q[i],
fabs(fun - q[i]));
}

END:
NAG_FREE(f);
NAG_FREE(q);
NAG_FREE(qx);
NAG_FREE(rq);
NAG_FREE(xe);
NAG_FREE(x);
NAG_FREE(iq);
NAG_FREE(state);

return exit_status;
}

static double NAG_CALL funct(double x[]) {
/* Scalars */
double ret_val;

ret_val = ((1.25 + cos(5.4 * x[4])) * cos(6.0 * x[0]) * cos(6.0 * x[1]) *
cos(6.0 * x[2])) /
(6.0 + 6.0 * pow((3.0 * x[3] - 1.0), 2.0));
return ret_val;
}
```