/* nag_quad_md_sphere (d01fdc) Example Program.
 *
 * Copyright 2023 Numerical Algorithms Group.
 *
 * Mark 29.3, 2023.
 */
#include <math.h>
#include <nag.h>
#include <stdio.h>

#ifdef __cplusplus
extern "C" {
#endif
static double NAG_CALL f(Integer ndim, const double x[], Nag_Comm *comm);
static void NAG_CALL region(Integer ndim, const double x[], Integer j,
                            double *c, double *d, Nag_Comm *comm);
#ifdef __cplusplus
}
#endif

int main(void) {
  static double ruser[2] = {-1.0, -1.0};
  Integer exit_status = 0;
  double r0, result, sigma, u;
  Integer i, limit, ncalls, ndim;
  Nag_Comm comm;
  NagError fail;

  INIT_FAIL(fail);

  printf("nag_quad_md_sphere (d01fdc) Example Program Results\n");

  /* For communication with user-supplied functions: */
  comm.user = ruser;

  /* Skip heading in data file */
  scanf("%*[^\n] ");
  scanf("%" NAG_IFMT "", &ndim);
  scanf("%" NAG_IFMT "", &limit);
  scanf("%lf %*[^\n] ", &u);

  for (i = 1; i <= 2; i++) {
    /* nag_quad_md_sphere (d01fdc).
     * Multidimensional quadrature, Sag-Szekeres method,
     * general product region or n-sphere.
     */
    switch (i) {
    case 1:
      printf("\nSphere-to-sphere transformation\n");
      sigma = 1.5;
      r0 = 0.9;
      nag_quad_md_sphere(ndim, f, sigma, NULLFN, limit, r0, u, &result, &ncalls,
                         &comm, &fail);
      break;
    case 2:
      printf("\nProduct region transformation\n");
      sigma = -1.0;
      r0 = 0.8;
      nag_quad_md_sphere(ndim, f, sigma, region, limit, r0, u, &result, &ncalls,
                         &comm, &fail);
      break;
    }
    if (fail.code != NE_NOERROR) {
      printf("Error from nag_quad_md_sphere (d01fdc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

    printf("\nEstimated value of the integral = %9.3f"
           "\nNumber of integrand evaluations = %4" NAG_IFMT "\n",
           result, ncalls);
  }

END:
  return exit_status;
}

static double NAG_CALL f(Integer ndim, const double x[], Nag_Comm *comm) {
  Integer i;
  double x_sq = 0.0;

  if (comm->user[0] == -1.0) {
    printf("(User-supplied callback f, first invocation.)\n");
    comm->user[0] = 0.0;
  }

  for (i = 0; i < ndim; i++)
    x_sq += pow(x[i], 2.0);

  return 1.0 / sqrt(fabs(pow(1.5, 2) - x_sq));
}

static void NAG_CALL region(Integer ndim, const double x[], Integer j,
                            double *c, double *d, Nag_Comm *comm) {
  Integer i;
  double x_sq = 0.0;

  if (comm->user[1] == -1.0) {
    printf("(User-supplied callback region, first invocation.)\n");
    comm->user[1] = 0.0;
  }
  if (j > 1) {
    for (i = 0; i < (j - 1); i++)
      x_sq += pow(x[i], 2.0);
    *d = sqrt(fabs(pow(1.5, 2) - x_sq));
    *c = -*d;
  } else {
    *c = -1.5;
    *d = 1.5;
  }
}