/* nag_quad_md_sphere (d01fdc) Example Program.
 *
 * Copyright 2011, Numerical Algorithms Group.
 *
 * Mark 23, 2011.
 */
#include <stdio.h>
#include <math.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagd01.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)
{
  Integer exit_status = 0;
  double  r0, result, sigma, u;
  Integer i, limit, ncalls, ndim;
  NagError fail;

  INIT_FAIL(fail);

  printf("nag_quad_md_sphere (d01fdc) Example Program Results\n");
  /* Skip heading in data file */
  scanf("%*[^\n] ");
  scanf("%ld", &ndim);
  scanf("%ld", &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, NAGCOMM_NULL, &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, NAGCOMM_NULL, &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 = %4ld\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;

  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 (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;
    }
}