NAG Library Manual, Mark 29.3
Interfaces:  FL   CL   CPP   AD
```/* nag_sum_fft_realherm_1d (c06pac) Example Program.
*
* Copyright 2023 Numerical Algorithms Group.
*
* Mark 29.3, 2023.
*/

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

int main(void) {
/* Scalars */
Integer exit_status = 0, i, n;
/* Arrays */
double *x = 0, *x_orig, *x_back;
/* Nag Types */
NagError fail;

INIT_FAIL(fail);

printf("nag_sum_fft_realherm_1d (c06pac) Example Program Results\n");

/* Read dimensions of array and array values from data file. */
scanf("%*[^\n]%" NAG_IFMT "%*[^\n]", &n);
if (!(x = NAG_ALLOC(n + 2, double)) || !(x_orig = NAG_ALLOC(n, double)) ||
!(x_back = NAG_ALLOC(n + 2, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
for (i = 0; i < n; i++) {
scanf("%lf", &x_orig[i]);
x[i] = x_orig[i];
}

/* Compute discrete Fourier transform of real array x using
* nag_sum_fft_realherm_1d (c06pac).
*/
nag_sum_fft_realherm_1d(Nag_ForwardTransform, x, n, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sum_fft_realherm_1d (c06pac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

for (i = 0; i < n + 2; i++)
x_back[i] = x[i];

/* Compute inverse discrete Fourier transform of Hermitian array x using
* nag_sum_fft_realherm_1d (c06pac).
*/
nag_sum_fft_realherm_1d(Nag_BackwardTransform, x_back, n, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sum_fft_realherm_1d (c06pac).\n%s\n", fail.message);
exit_status = 2;
goto END;
}

printf("\n%2s%7s%22s%17s\n", "i", "x", "z = FFT(x)", "InvFFT(z)");
for (i = 0; i < n; i++) {
if (i <= n / 2) {
printf("%2" NAG_IFMT "  %8.5f   (%8.5f, %8.5f )   %8.5f\n", i, x_orig[i],
x[2 * i], x[2 * i + 1], x_back[i]);
} else {
printf("%2" NAG_IFMT "  %8.5f   (%8.5f, %8.5f )   %8.5f\n", i, x_orig[i],
x[2 * (n - i)], -x[2 * (n - i) + 1], x_back[i]);
}
}
END:
NAG_FREE(x);
NAG_FREE(x_orig);
NAG_FREE(x_back);

return exit_status;
}
```