/* nag_sum_fft_realherm_1d (c06pac) Example Program.
 *
 * Copyright 2023 Numerical Algorithms Group.
 *
 * Mark 29.2, 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;
}