#include <complex.h>
#include <math.h>
#include <omp.h>
#include <string.h>

#include <gsl/gsl_sf.h>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_poly.h>
#include <gsl/gsl_randist.h>

#include "extent-sampling.h"
#include "utils.h"

#define DIMENSION_START 5
#define DIMENSION_STEP 5
#define DIMENSION_STOP 100

#define RTOLS 3
#define RTOL1 0.2
#define RTOL2 0.1
#define RTOL3 0.05

#define MAX_EXTENT 1.0

#define POLYNOMIAL_DEGREE 3
double poly_coeffs[POLYNOMIAL_DEGREE + 1] = {-0.09375, 0.6875, -1.5, 1};

typedef double (*true_integral_t) (unsigned int);
gsl_rng* r;

double uniform_oracle (const gsl_vector* x) {
  return gsl_ran_flat(r, 0, MAX_EXTENT);
}

double polynomial_integrand  (double r, const gsl_vector* x) {
  return gsl_poly_eval(poly_coeffs, POLYNOMIAL_DEGREE + 1, r);
}

double polynomial_true_integral (unsigned int n) {
  double integrand[POLYNOMIAL_DEGREE + 1];
  for (int k=0; k<=POLYNOMIAL_DEGREE; k++)
    integrand[k] = poly_coeffs[k]/(n + k)/(n + k + 1);
  return surface_area_of_ball(n)
    / MAX_EXTENT
    * gsl_pow_uint(MAX_EXTENT, n + 1)
    * gsl_poly_eval(integrand, POLYNOMIAL_DEGREE+1, MAX_EXTENT);
}

double gaussian_integrand  (double r, const gsl_vector* x) {
  return exp(-gsl_pow_2(r)/2);
}

double gaussian_true_integral (unsigned int n) {
  return pow(2, 0.5*n - 1)
    * surface_area_of_ball(n)
    / MAX_EXTENT
    * (MAX_EXTENT*lower_incomplete_gamma(0.5*n, 0.5*gsl_pow_2(MAX_EXTENT))
       - sqrt(2) * lower_incomplete_gamma(0.5*(n + 1), 0.5*gsl_pow_2(MAX_EXTENT)));
}

double x_coordinate_integrand (double r, const gsl_vector* x) {
  return fabs(r*gsl_vector_get(x, 0));
}

double x_coordinate_true_integral (unsigned int n) {
  return surface_area_of_ball(n+3) / 2 / (n+2) / gsl_pow_2(M_PI)
    * gsl_pow_uint(MAX_EXTENT, n+1)
    / MAX_EXTENT;
}

void run_experiment (integrand_t integrand, extent_oracle_t oracle, true_integral_t true_integral, const char* filename_prefix)
{
  gsl_rstat_workspace* stats = gsl_rstat_alloc();
  printf("dimension\trtol=%g\trtol=%g\trtol=%g\n", RTOL1, RTOL2, RTOL3);
  double rtol[RTOLS] = {RTOL1, RTOL2, RTOL3};
  FILE *fp[RTOLS];
  for (int i=0; i<RTOLS; i++) {
    char *filename;
    asprintf(&filename, "%s-%g.dat", filename_prefix, rtol[i]);
    fp[i] = fopen(filename, "w");
    fprintf(fp[i], "dimension\tsamples\n");
    free(filename);
  }
  for (int dim=DIMENSION_START; dim<=DIMENSION_STOP; dim+=DIMENSION_STEP) {
    printf("%d\t", dim);
    for (int i=0; i<RTOLS; i++) {
      integral(integrand, oracle, true_integral(dim), r, dim, rtol[i], stats);
      fprintf(fp[i], "%d\t%zd\n", dim, gsl_rstat_n(stats));
      printf("%zd\t", gsl_rstat_n(stats));
    }
    printf("\n");
    gsl_rstat_reset(stats);
  }
  for (int i=0; i<RTOLS; i++) fclose(fp[i]);
  gsl_rstat_free(stats);
}

int main (int argc, char** argv)
{
  gsl_rng_env_setup();
  r = gsl_rng_alloc(gsl_rng_default);

  printf("# polynomial\n");
  run_experiment(polynomial_integrand, uniform_oracle, polynomial_true_integral, "integral-polynomial");
  printf("# gaussian\n");
  run_experiment(gaussian_integrand, uniform_oracle, gaussian_true_integral, "integral-gaussian");
  printf("# x-coordinate\n");
  run_experiment(x_coordinate_integrand, uniform_oracle, x_coordinate_true_integral, "integral-x-coordinate");

  gsl_rng_free(r);
  return 0;
}