/* randist/test.c
 *
 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007, 2010 James Theiler, Brian Gough
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 3 of the License, or (at
 * your option) any later version.
 *
 * This program is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
 */

#include <config.h>
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_randist.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_test.h>
#include <gsl/gsl_ieee_utils.h>
#include <gsl/gsl_integration.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_cdf.h>

#define N 100000

/* Convient test dimension for multivariant distributions */
#define MULTI_DIM 10

void testMoments (double (*f) (void), const char *name,
                  double a, double b, double p);
void testPDF (double (*f) (void), double (*pdf) (double), const char *name);
void testDiscretePDF (double (*f) (void), double (*pdf) (unsigned int),
                      const char *name);

void test_shuffle (void);
void test_choose (void);
double test_beta (void);
double test_beta_pdf (double x);
double test_bernoulli (void);
double test_bernoulli_pdf (unsigned int n);

double test_binomial (void);
double test_binomial_pdf (unsigned int n);
double test_binomial_large (void);
double test_binomial_large_pdf (unsigned int n);
double test_binomial_huge (void);
double test_binomial_huge_pdf (unsigned int n);
double test_binomial_max (void);
double test_binomial_max_pdf (unsigned int n);
double test_binomial0 (void);
double test_binomial0_pdf (unsigned int n);
double test_binomial1 (void);
double test_binomial1_pdf (unsigned int n);

double test_binomial_knuth (void);
double test_binomial_knuth_pdf (unsigned int n);
double test_binomial_large_knuth (void);
double test_binomial_large_knuth_pdf (unsigned int n);
double test_binomial_huge_knuth (void);
double test_binomial_huge_knuth_pdf (unsigned int n);

double test_cauchy (void);
double test_cauchy_pdf (double x);
double test_chisq (void);
double test_chisq_pdf (double x);
double test_chisqnu2 (void);
double test_chisqnu2_pdf (double x);
double test_dirichlet (void);
double test_dirichlet_pdf (double x);
double test_dirichlet_small (void);
double test_dirichlet_small_pdf (double x);
void test_dirichlet_moments (void);
double test_discrete1 (void);
double test_discrete1_pdf (unsigned int n);
double test_discrete2 (void);
double test_discrete2_pdf (unsigned int n);
double test_discrete3 (void);
double test_discrete3_pdf (unsigned int n);
double test_erlang (void);
double test_erlang_pdf (double x);
double test_exponential (void);
double test_exponential_pdf (double x);
double test_exppow0 (void);
double test_exppow0_pdf (double x);
double test_exppow1 (void);
double test_exppow1_pdf (double x);
double test_exppow1a (void);
double test_exppow1a_pdf (double x);
double test_exppow2 (void);
double test_exppow2_pdf (double x);
double test_exppow2a (void);
double test_exppow2a_pdf (double x);
double test_exppow2b (void);
double test_exppow2b_pdf (double x);
double test_fdist (void);
double test_fdist_pdf (double x);
double test_fdist_large (void);
double test_fdist_large_pdf (double x);
double test_flat (void);
double test_flat_pdf (double x);
double test_gamma (void);
double test_gamma_pdf (double x);
double test_gamma1 (void);
double test_gamma1_pdf (double x);
double test_gamma_int (void);
double test_gamma_int_pdf (double x);
double test_gamma_large (void);
double test_gamma_large_pdf (double x);
double test_gamma_vlarge (void);
double test_gamma_vlarge_pdf (double x);
double test_gamma_small (void);
double test_gamma_small_pdf (double x);
double test_gamma_mt (void);
double test_gamma_mt_pdf (double x);
double test_gamma_mt1 (void);
double test_gamma_mt1_pdf (double x);
double test_gamma_mt_int (void);
double test_gamma_mt_int_pdf (double x);
double test_gamma_mt_large (void);
double test_gamma_mt_large_pdf (double x);
double test_gamma_mt_small (void);
double test_gamma_mt_small_pdf (double x);
double test_gamma_knuth_vlarge (void);
double test_gamma_knuth_vlarge_pdf (double x);
double test_gaussian (void);
double test_gaussian_pdf (double x);
double test_gaussian_ratio_method (void);
double test_gaussian_ratio_method_pdf (double x);
double test_gaussian_ziggurat (void);
double test_gaussian_ziggurat_pdf (double x);
double test_gaussian_tail (void);
double test_gaussian_tail_pdf (double x);
double test_gaussian_tail1 (void);
double test_gaussian_tail1_pdf (double x);
double test_gaussian_tail2 (void);
double test_gaussian_tail2_pdf (double x);
double test_ugaussian (void);
double test_ugaussian_pdf (double x);
double test_ugaussian_ratio_method (void);
double test_ugaussian_ratio_method_pdf (double x);
double test_ugaussian_tail (void);
double test_ugaussian_tail_pdf (double x);
double test_bivariate_gaussian1 (void);
double test_bivariate_gaussian1_pdf (double x);
double test_bivariate_gaussian2 (void);
double test_bivariate_gaussian2_pdf (double x);
double test_bivariate_gaussian3 (void);
double test_bivariate_gaussian3_pdf (double x);
double test_bivariate_gaussian4 (void);
double test_bivariate_gaussian4_pdf (double x);
void test_multivariate_gaussian_log_pdf (void);
void test_multivariate_gaussian_pdf (void);
void test_multivariate_gaussian (void);
double test_gumbel1 (void);
double test_gumbel1_pdf (double x);
double test_gumbel2 (void);
double test_gumbel2_pdf (double x);
double test_geometric (void);
double test_geometric_pdf (unsigned int x);
double test_geometric1 (void);
double test_geometric1_pdf (unsigned int x);
double test_hypergeometric1 (void);
double test_hypergeometric1_pdf (unsigned int x);
double test_hypergeometric2 (void);
double test_hypergeometric2_pdf (unsigned int x);
double test_hypergeometric3 (void);
double test_hypergeometric3_pdf (unsigned int x);
double test_hypergeometric4 (void);
double test_hypergeometric4_pdf (unsigned int x);
double test_hypergeometric5 (void);
double test_hypergeometric5_pdf (unsigned int x);
double test_hypergeometric6 (void);
double test_hypergeometric6_pdf (unsigned int x);
double test_landau (void);
double test_landau_pdf (double x);
double test_levy1 (void);
double test_levy1_pdf (double x);
double test_levy2 (void);
double test_levy2_pdf (double x);
double test_levy1a (void);
double test_levy1a_pdf (double x);
double test_levy2a (void);
double test_levy2a_pdf (double x);
double test_levy_skew1 (void);
double test_levy_skew1_pdf (double x);
double test_levy_skew2 (void);
double test_levy_skew2_pdf (double x);
double test_levy_skew1a (void);
double test_levy_skew1a_pdf (double x);
double test_levy_skew2a (void);
double test_levy_skew2a_pdf (double x);
double test_levy_skew1b (void);
double test_levy_skew1b_pdf (double x);
double test_levy_skew2b (void);
double test_levy_skew2b_pdf (double x);
double test_logistic (void);
double test_logistic_pdf (double x);
double test_lognormal (void);
double test_lognormal_pdf (double x);
double test_logarithmic (void);
double test_logarithmic_pdf (unsigned int n);
double test_multinomial (void);
double test_multinomial_pdf (unsigned int n);
double test_multinomial_large (void);
double test_multinomial_large_pdf (unsigned int n);
void test_multinomial_moments (void);
double test_negative_binomial (void);
double test_negative_binomial_pdf (unsigned int n);
double test_pascal (void);
double test_pascal_pdf (unsigned int n);
double test_pareto (void);
double test_pareto_pdf (double x);
double test_poisson (void);
double test_poisson_pdf (unsigned int x);
double test_poisson_large (void);
double test_poisson_large_pdf (unsigned int x);
double test_dir2d (void);
double test_dir2d_pdf (double x);
double test_dir2d_trig_method (void);
double test_dir2d_trig_method_pdf (double x);
double test_dir3dxy (void);
double test_dir3dxy_pdf (double x);
double test_dir3dyz (void);
double test_dir3dyz_pdf (double x);
double test_dir3dzx (void);
double test_dir3dzx_pdf (double x);
double test_rayleigh (void);
double test_rayleigh_pdf (double x);
double test_rayleigh_tail (void);
double test_rayleigh_tail_pdf (double x);
double test_tdist1 (void);
double test_tdist1_pdf (double x);
double test_tdist2 (void);
double test_tdist2_pdf (double x);
double test_laplace (void);
double test_laplace_pdf (double x);
double test_weibull (void);
double test_weibull_pdf (double x);
double test_weibull1 (void);
double test_weibull1_pdf (double x);

gsl_rng *r_global;

static gsl_ran_discrete_t *g1 = NULL;
static gsl_ran_discrete_t *g2 = NULL;
static gsl_ran_discrete_t *g3 = NULL;

int
main (void)
{
  gsl_ieee_env_setup ();

  gsl_rng_env_setup ();
  r_global = gsl_rng_alloc (gsl_rng_default);

#define FUNC(x)  test_ ## x,                     "test gsl_ran_" #x
#define FUNC2(x) test_ ## x, test_ ## x ## _pdf, "test gsl_ran_" #x

  test_shuffle ();
  test_choose ();

  testMoments (FUNC (ugaussian), 0.0, 100.0, 0.5);
  testMoments (FUNC (ugaussian), -1.0, 1.0, 0.6826895);
  testMoments (FUNC (ugaussian), 3.0, 3.5, 0.0011172689);
  testMoments (FUNC (ugaussian_tail), 3.0, 3.5, 0.0011172689 / 0.0013498981);
  testMoments (FUNC (exponential), 0.0, 1.0, 1 - exp (-0.5));
  testMoments (FUNC (cauchy), 0.0, 10000.0, 0.5);

  testMoments (FUNC (discrete1), -0.5, 0.5, 0.59);
  testMoments (FUNC (discrete1), 0.5, 1.5, 0.40);
  testMoments (FUNC (discrete1), 1.5, 3.5, 0.01);

  testMoments (FUNC (discrete2), -0.5,  0.5, 1.0/45.0 );
  testMoments (FUNC (discrete2),  8.5,  9.5, 0 );

  testMoments (FUNC (discrete3), -0.5, 0.5, 0.05 );
  testMoments (FUNC (discrete3),  0.5, 1.5, 0.05 );
  testMoments (FUNC (discrete3), -0.5, 9.5, 0.5 );

  test_dirichlet_moments ();
  test_multinomial_moments ();

  testPDF (FUNC2 (beta));
  testPDF (FUNC2 (cauchy));
  testPDF (FUNC2 (chisq));
  testPDF (FUNC2 (chisqnu2));
  testPDF (FUNC2 (dirichlet));
  testPDF (FUNC2 (dirichlet_small));
  testPDF (FUNC2 (erlang));
  testPDF (FUNC2 (exponential));

  testPDF (FUNC2 (exppow0));
  testPDF (FUNC2 (exppow1));
  testPDF (FUNC2 (exppow1a));
  testPDF (FUNC2 (exppow2));
  testPDF (FUNC2 (exppow2a));
  testPDF (FUNC2 (exppow2b));

  testPDF (FUNC2 (fdist));
  testPDF (FUNC2 (fdist_large));
  testPDF (FUNC2 (flat));
  testPDF (FUNC2 (gamma));
  testPDF (FUNC2 (gamma1));
  testPDF (FUNC2 (gamma_int));
  testPDF (FUNC2 (gamma_large));
  testPDF (FUNC2 (gamma_vlarge));
  testPDF (FUNC2 (gamma_knuth_vlarge));
  testPDF (FUNC2 (gamma_small));
  testPDF (FUNC2 (gamma_mt));
  testPDF (FUNC2 (gamma_mt1));
  testPDF (FUNC2 (gamma_mt_int));
  testPDF (FUNC2 (gamma_mt_large));
  testPDF (FUNC2 (gamma_mt_small));
  testPDF (FUNC2 (gaussian));
  testPDF (FUNC2 (gaussian_ratio_method));
  testPDF (FUNC2 (gaussian_ziggurat));
  testPDF (FUNC2 (ugaussian));
  testPDF (FUNC2 (ugaussian_ratio_method));
  testPDF (FUNC2 (gaussian_tail));
  testPDF (FUNC2 (gaussian_tail1));
  testPDF (FUNC2 (gaussian_tail2));
  testPDF (FUNC2 (ugaussian_tail));

  testPDF (FUNC2 (bivariate_gaussian1));
  testPDF (FUNC2 (bivariate_gaussian2));
  testPDF (FUNC2 (bivariate_gaussian3));
  testPDF (FUNC2 (bivariate_gaussian4));

  test_multivariate_gaussian_log_pdf ();
  test_multivariate_gaussian_pdf ();
  test_multivariate_gaussian ();

  testPDF (FUNC2 (gumbel1));
  testPDF (FUNC2 (gumbel2));
  testPDF (FUNC2 (landau));
  testPDF (FUNC2 (levy1));
  testPDF (FUNC2 (levy2));
  testPDF (FUNC2 (levy1a));
  testPDF (FUNC2 (levy2a));
  testPDF (FUNC2 (levy_skew1));
  testPDF (FUNC2 (levy_skew2));
  testPDF (FUNC2 (levy_skew1a));
  testPDF (FUNC2 (levy_skew2a));
  testPDF (FUNC2 (levy_skew1b));
  testPDF (FUNC2 (levy_skew2b));
  testPDF (FUNC2 (logistic));
  testPDF (FUNC2 (lognormal));
  testPDF (FUNC2 (pareto));
  testPDF (FUNC2 (rayleigh));
  testPDF (FUNC2 (rayleigh_tail));
  testPDF (FUNC2 (tdist1));
  testPDF (FUNC2 (tdist2));
  testPDF (FUNC2 (laplace));
  testPDF (FUNC2 (weibull));
  testPDF (FUNC2 (weibull1));

  testPDF (FUNC2 (dir2d));
  testPDF (FUNC2 (dir2d_trig_method));
  testPDF (FUNC2 (dir3dxy));
  testPDF (FUNC2 (dir3dyz));
  testPDF (FUNC2 (dir3dzx));

  testDiscretePDF (FUNC2 (discrete1));
  testDiscretePDF (FUNC2 (discrete2));
  testDiscretePDF (FUNC2 (discrete3));
  testDiscretePDF (FUNC2 (poisson));
  testDiscretePDF (FUNC2 (poisson_large));
  testDiscretePDF (FUNC2 (bernoulli));
  testDiscretePDF (FUNC2 (binomial));
  testDiscretePDF (FUNC2 (binomial0));
  testDiscretePDF (FUNC2 (binomial1));
  testDiscretePDF (FUNC2 (binomial_knuth));
  testDiscretePDF (FUNC2 (binomial_large));
  testDiscretePDF (FUNC2 (binomial_large_knuth));
  testDiscretePDF (FUNC2 (binomial_huge));
  testDiscretePDF (FUNC2 (binomial_huge_knuth));
  testDiscretePDF (FUNC2 (binomial_max));
  testDiscretePDF (FUNC2 (geometric));
  testDiscretePDF (FUNC2 (geometric1));
  testDiscretePDF (FUNC2 (hypergeometric1));
  testDiscretePDF (FUNC2 (hypergeometric2));
  testDiscretePDF (FUNC2 (hypergeometric3));
  testDiscretePDF (FUNC2 (hypergeometric4));
  testDiscretePDF (FUNC2 (hypergeometric5));
  testDiscretePDF (FUNC2 (hypergeometric6));
  testDiscretePDF (FUNC2 (logarithmic));
  testDiscretePDF (FUNC2 (multinomial));
  testDiscretePDF (FUNC2 (multinomial_large));
  testDiscretePDF (FUNC2 (negative_binomial));
  testDiscretePDF (FUNC2 (pascal));

  gsl_rng_free (r_global);
  gsl_ran_discrete_free (g1);
  gsl_ran_discrete_free (g2);
  gsl_ran_discrete_free (g3);

  exit (gsl_test_summary ());
}

void
test_shuffle (void)
{
  double count[10][10];
  int x[10] = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 };
  int i, j, status = 0;

  for (i = 0; i < 10; i++)
    {
      for (j = 0; j < 10; j++)
        {
          count[i][j] = 0;
        }
    }

  for (i = 0; i < N; i++)
    {
      for (j = 0; j < 10; j++)
        x[j] = j;

      gsl_ran_shuffle (r_global, x, 10, sizeof (int));

      for (j = 0; j < 10; j++)
        count[x[j]][j]++;
    }

  for (i = 0; i < 10; i++)
    {
      for (j = 0; j < 10; j++)
        {
          double expected = N / 10.0;
          double d = fabs (count[i][j] - expected);
          double sigma = d / sqrt (expected);
          if (sigma > 5 && d > 1)
            {
              status = 1;
              gsl_test (status,
                        "gsl_ran_shuffle %d,%d (%g observed vs %g expected)",
                        i, j, count[i][j] / N, 0.1);
            }
        }
    }

  gsl_test (status, "gsl_ran_shuffle on {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}");

}

void
test_choose (void)
{
  double count[10];
  int x[10] = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 };
  int y[3] = { 0, 1, 2 };
  int i, j, status = 0;

  for (i = 0; i < 10; i++)
    {
      count[i] = 0;
    }

  for (i = 0; i < N; i++)
    {
      for (j = 0; j < 10; j++)
        x[j] = j;

      gsl_ran_choose (r_global, y, 3, x, 10, sizeof (int));

      for (j = 0; j < 3; j++)
        count[y[j]]++;
    }

  for (i = 0; i < 10; i++)
    {
      double expected = 3.0 * N / 10.0;
      double d = fabs (count[i] - expected);
      double sigma = d / sqrt (expected);
      if (sigma > 5 && d > 1)
        {
          status = 1;
          gsl_test (status,
                    "gsl_ran_choose %d (%g observed vs %g expected)",
                    i, count[i] / N, 0.1);
        }
    }

  gsl_test (status, "gsl_ran_choose (3) on {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}");

}

void
testMoments (double (*f) (void), const char *name,
             double a, double b, double p)
{
  int i;
  double count = 0, expected, sigma;
  int status;

  for (i = 0; i < N; i++)
    {
      double r = f ();
      if (r < b && r > a)
        count++;
    }

  expected = p * N;
  sigma = (expected > 0) ? fabs (count - expected) / sqrt (expected) : fabs(count - expected);

  status = (sigma > 3);

  gsl_test (status, "%s [%g,%g] (%g observed vs %g expected)",
            name, a, b, count / N, p);
}

#define BINS 100

typedef double pdf_func(double);

/* Keep track of invalid values during integration */
static int pdf_errors = 0;
static double pdf_errval = 0.0;

double
wrapper_function (double x, void *params)
{
  pdf_func * pdf = (pdf_func *)params;
  double P = pdf(x);
  if (!gsl_finite(P)) {
    pdf_errors++;
    pdf_errval = P;
    P = 0; /* skip invalid value now, but return pdf_errval at the end */
  }
  return P;
}

double
integrate (pdf_func * pdf, double a, double b)
{
  double result, abserr;
  size_t n = 1000;
  gsl_function f;
  gsl_integration_workspace * w = gsl_integration_workspace_alloc (n);
  f.function = &wrapper_function;
  f.params = (void *)pdf;
  pdf_errors = 0;
  gsl_integration_qags (&f, a, b, 1e-16, 1e-4, n, w, &result, &abserr);
  gsl_integration_workspace_free (w);
  if (pdf_errors) return pdf_errval;
  return result;
}

void
testPDF (double (*f) (void), double (*pdf) (double), const char *name)
{
  double count[BINS], edge[BINS], p[BINS];
  double a = -5.0, b = +5.0;
  double dx = (b - a) / BINS;
  double bin;
  double total = 0, mean;
  int i, j, status = 0, status_i = 0, attempts = 0;
  long int n0 = 0, n = N;

  for (i = 0; i < BINS; i++)
    {
      /* Compute the integral of p(x) from x to x+dx */

      double x = a + i * dx;

      if (fabs (x) < 1e-10)     /* hit the origin exactly */
        x = 0.0;

      p[i]  = integrate (pdf, x, x+dx);
    }

  for (i = 0; i < BINS; i++)
    {
      count[i] = 0;
      edge[i] = 0;
    }

 trial:
  attempts++;

  for (i = n0; i < n; i++)
    {
      double r = f ();
      total += r;

      if (r < b && r > a)
        {
          double u = (r - a) / dx;
          double f = modf(u, &bin);
          j = (int)bin;

          if (f == 0)
            edge[j]++;
          else
            count[j]++;
        }
    }

  /* Sort out where the hits on the edges should go */

  for (i = 0; i < BINS; i++)
    {
      /* If the bin above is empty, its lower edge hits belong in the
         lower bin */

      if (i + 1 < BINS && count[i+1] == 0) {
        count[i] += edge[i+1];
        edge[i+1] = 0;
      }

      count[i] += edge[i];
      edge[i] = 0;
    }

  mean = (total / n);

  status = !gsl_finite(mean);
  if (status) {
    gsl_test (status, "%s, finite mean, observed %g", name, mean);
    return;
  }

  for (i = 0; i < BINS; i++)
    {
      double x = a + i * dx;
      double d = fabs (count[i] - n * p[i]);
      if (!gsl_finite(p[i]))
        {
          status_i = 1;
        }
      else if (p[i] != 0)
        {
          double s = d / sqrt (n * p[i]);
          status_i = (s > 5) && (d > 2);
        }
      else
        {
          status_i = (count[i] != 0);
        }

      /* Extend the sample if there is an outlier on the first attempt
         to avoid spurious failures when running large numbers of tests. */
      if (status_i && attempts < 50)
        {
          n0 = n;
          n = 2.0*n;
          goto trial;
        }

      status |= status_i;
      if (status_i)
        gsl_test (status_i, "%s [%g,%g) (%g/%d=%g observed vs %g expected)",
                  name, x, x + dx, count[i], n, count[i] / n, p[i]);
    }

  if (status == 0)
    gsl_test (status, "%s, sampling against pdf over range [%g,%g) ",
              name, a, b);
}

void
testDiscretePDF (double (*f) (void), double (*pdf) (unsigned int),
                 const char *name)
{
  double count[BINS], p[BINS];
  unsigned int i;
  int status = 0, status_i = 0;

  for (i = 0; i < BINS; i++)
    count[i] = 0;

  for (i = 0; i < N; i++)
    {
      int r = (int) (f ());
      if (r >= 0 && r < BINS)
        count[r]++;
    }

  for (i = 0; i < BINS; i++)
    p[i] = pdf (i);

  for (i = 0; i < BINS; i++)
    {
      double d = fabs (count[i] - N * p[i]);
      if (p[i] != 0)
        {
          double s = d / sqrt (N * p[i]);
          status_i = (s > 5) && (d > 1);
        }
      else
        {
          status_i = (count[i] != 0);
        }
      status |= status_i;
      if (status_i)
        gsl_test (status_i, "%s i=%d (%g observed vs %g expected)",
                  name, i, count[i] / N, p[i]);
    }

  if (status == 0)
    gsl_test (status, "%s, sampling against pdf over range [%d,%d) ",
              name, 0, BINS);
}

double
test_beta (void)
{
  return gsl_ran_beta (r_global, 2.0, 3.0);
}

double
test_beta_pdf (double x)
{
  return gsl_ran_beta_pdf (x, 2.0, 3.0);
}

double
test_bernoulli (void)
{
  return gsl_ran_bernoulli (r_global, 0.3);
}

double
test_bernoulli_pdf (unsigned int n)
{
  return gsl_ran_bernoulli_pdf (n, 0.3);
}

double
test_binomial (void)
{
  return gsl_ran_binomial (r_global, 0.3, 5);
}

double
test_binomial_pdf (unsigned int n)
{
  return gsl_ran_binomial_pdf (n, 0.3, 5);
}

double
test_binomial0 (void)
{
  return gsl_ran_binomial (r_global, 0, 8);
}

double
test_binomial0_pdf (unsigned int n)
{
  return gsl_ran_binomial_pdf (n, 0, 8);
}

double
test_binomial1 (void)
{
  return gsl_ran_binomial (r_global, 1, 8);
}

double
test_binomial1_pdf (unsigned int n)
{
  return gsl_ran_binomial_pdf (n, 1, 8);
}

double
test_binomial_knuth (void)
{
  return gsl_ran_binomial_knuth (r_global, 0.3, 5);
}

double
test_binomial_knuth_pdf (unsigned int n)
{
  return gsl_ran_binomial_pdf (n, 0.3, 5);
}

double
test_binomial_large (void)
{
  return gsl_ran_binomial (r_global, 0.3, 55);
}

double
test_binomial_large_pdf (unsigned int n)
{
  return gsl_ran_binomial_pdf (n, 0.3, 55);
}

double
test_binomial_large_knuth (void)
{
  return gsl_ran_binomial_knuth (r_global, 0.3, 55);
}

double
test_binomial_large_knuth_pdf (unsigned int n)
{
  return gsl_ran_binomial_pdf (n, 0.3, 55);
}

double
test_binomial_huge (void)
{
  return gsl_ran_binomial (r_global, 0.3, 5500);
}

double
test_binomial_huge_pdf (unsigned int n)
{
  return gsl_ran_binomial_pdf (n, 0.3, 5500);
}

double
test_binomial_huge_knuth (void)
{
  return gsl_ran_binomial_knuth (r_global, 0.3, 5500);
}

double
test_binomial_huge_knuth_pdf (unsigned int n)
{
  return gsl_ran_binomial_pdf (n, 0.3, 5500);
}

double
test_binomial_max (void)
{
  return gsl_ran_binomial (r_global, 1e-8, 1<<31);
}

double
test_binomial_max_pdf (unsigned int n)
{
  return gsl_ran_binomial_pdf (n, 1e-8, 1<<31);
}

double
test_cauchy (void)
{
  return gsl_ran_cauchy (r_global, 2.0);
}

double
test_cauchy_pdf (double x)
{
  return gsl_ran_cauchy_pdf (x, 2.0);
}

double
test_chisq (void)
{
  return gsl_ran_chisq (r_global, 13.0);
}

double
test_chisq_pdf (double x)
{
  return gsl_ran_chisq_pdf (x, 13.0);
}

double
test_chisqnu2 (void)
{
  return gsl_ran_chisq (r_global, 2.0);
}

double
test_chisqnu2_pdf (double x)
{
  return gsl_ran_chisq_pdf (x, 2.0);
}

double
test_dir2d (void)
{
  double x = 0, y = 0, theta;
  gsl_ran_dir_2d (r_global, &x, &y);
  theta = atan2 (x, y);
  return theta;
}

double
test_dir2d_pdf (double x)
{
  if (x > -M_PI && x <= M_PI)
    {
      return 1 / (2 * M_PI);
    }
  else
    {
      return 0;
    }
}

double
test_dir2d_trig_method (void)
{
  double x = 0, y = 0, theta;
  gsl_ran_dir_2d_trig_method (r_global, &x, &y);
  theta = atan2 (x, y);
  return theta;
}

double
test_dir2d_trig_method_pdf (double x)
{
  if (x > -M_PI && x <= M_PI)
    {
      return 1 / (2 * M_PI);
    }
  else
    {
      return 0;
    }
}

double
test_dir3dxy (void)
{
  double x = 0, y = 0, z = 0, theta;
  gsl_ran_dir_3d (r_global, &x, &y, &z);
  theta = atan2 (x, y);
  return theta;
}

double
test_dir3dxy_pdf (double x)
{
  if (x > -M_PI && x <= M_PI)
    {
      return 1 / (2 * M_PI);
    }
  else
    {
      return 0;
    }
}

double
test_dir3dyz (void)
{
  double x = 0, y = 0, z = 0, theta;
  gsl_ran_dir_3d (r_global, &x, &y, &z);
  theta = atan2 (y, z);
  return theta;
}

double
test_dir3dyz_pdf (double x)
{
  if (x > -M_PI && x <= M_PI)
    {
      return 1 / (2 * M_PI);
    }
  else
    {
      return 0;
    }
}

double
test_dir3dzx (void)
{
  double x = 0, y = 0, z = 0, theta;
  gsl_ran_dir_3d (r_global, &x, &y, &z);
  theta = atan2 (z, x);
  return theta;
}

double
test_dir3dzx_pdf (double x)
{
  if (x > -M_PI && x <= M_PI)
    {
      return 1 / (2 * M_PI);
    }
  else
    {
      return 0;
    }
}

double
test_dirichlet (void)
{
  /* This is a bit of a lame test, since when K=2, the Dirichlet distribution
     becomes a beta distribution */
  size_t K = 2;
  double alpha[2] = { 2.5, 5.0 };
  double theta[2] = { 0.0, 0.0 };

  gsl_ran_dirichlet (r_global, K, alpha, theta);

  return theta[0];
}

double
test_dirichlet_pdf (double x)
{
  size_t K = 2;
  double alpha[2] = { 2.5, 5.0 };
  double theta[2];

  if (x <= 0.0 || x >= 1.0)
    return 0.0;                 /* Out of range */

  theta[0] = x;
  theta[1] = 1.0 - x;

  return gsl_ran_dirichlet_pdf (K, alpha, theta);
}

double
test_dirichlet_small (void)
{
  size_t K = 2;
  double alpha[2] = { 2.5e-3, 5.0e-3};
  double theta[2] = { 0.0, 0.0 };

  gsl_ran_dirichlet (r_global, K, alpha, theta);

  return theta[0];
}

double
test_dirichlet_small_pdf (double x)
{
  size_t K = 2;
  double alpha[2] = { 2.5e-3, 5.0e-3 };
  double theta[2];

  if (x <= 0.0 || x >= 1.0)
    return 0.0;                 /* Out of range */

  theta[0] = x;
  theta[1] = 1.0 - x;

  return gsl_ran_dirichlet_pdf (K, alpha, theta);
}

/* Check that the observed means of the Dirichlet variables are
   within reasonable statistical errors of their correct values. */

#define DIRICHLET_K 10

void
test_dirichlet_moments (void)
{
  double alpha[DIRICHLET_K];
  double theta[DIRICHLET_K];
  double theta_sum[DIRICHLET_K];

  double alpha_sum = 0.0;
  double mean, obs_mean, sd, sigma;
  int status, k, n;

  for (k = 0; k < DIRICHLET_K; k++)
    {
      alpha[k] = gsl_ran_exponential (r_global, 0.1);
      alpha_sum += alpha[k];
      theta_sum[k] = 0.0;
    }

  for (n = 0; n < N; n++)
    {
      gsl_ran_dirichlet (r_global, DIRICHLET_K, alpha, theta);
      for (k = 0; k < DIRICHLET_K; k++)
        theta_sum[k] += theta[k];
    }

  for (k = 0; k < DIRICHLET_K; k++)
    {
      mean = alpha[k] / alpha_sum;
      sd =
        sqrt ((alpha[k] * (1. - alpha[k] / alpha_sum)) /
              (alpha_sum * (alpha_sum + 1.)));
      obs_mean = theta_sum[k] / N;
      sigma = sqrt ((double) N) * fabs (mean - obs_mean) / sd;

      status = (sigma > 3.0);

      gsl_test (status,
                "test gsl_ran_dirichlet: mean (%g observed vs %g expected)",
                obs_mean, mean);
    }
}

/* Check that the observed means of the multinomial variables are
   within reasonable statistical errors of their correct values. */

void
test_multinomial_moments (void)
{
  const unsigned int sum_n = 100;

  const double p[MULTI_DIM] ={ 0.2, 0.20, 0.17, 0.14, 0.12,
                               0.07, 0.05, 0.02, 0.02, 0.01 };

  unsigned int  x[MULTI_DIM];
  double x_sum[MULTI_DIM];

  double mean, obs_mean, sd, sigma;
  int status, k, n;

  for (k = 0; k < MULTI_DIM; k++)
    x_sum[k] =0.0;

  for (n = 0; n < N; n++)
    {
      gsl_ran_multinomial (r_global, MULTI_DIM, sum_n, p, x);
      for (k = 0; k < MULTI_DIM; k++)
        x_sum[k] += x[k];
    }

  for (k = 0; k < MULTI_DIM; k++)
    {
      mean = p[k] * sum_n;
      sd = p[k] * (1.-p[k]) * sum_n;

      obs_mean = x_sum[k] / N;
      sigma = sqrt ((double) N) * fabs (mean - obs_mean) / sd;

      status = (sigma > 3.0);

      gsl_test (status,
                "test gsl_ran_multinomial: mean (%g observed vs %g expected)",
                obs_mean, mean);
    }
}

double
test_discrete1 (void)
{
  static double P[3] = { 0.59, 0.4, 0.01 };
  if (g1 == NULL)
    {
      g1 = gsl_ran_discrete_preproc (3, P);
    }
  return gsl_ran_discrete (r_global, g1);
}

double
test_discrete1_pdf (unsigned int n)
{
  return gsl_ran_discrete_pdf ((size_t) n, g1);
}

double
test_discrete2 (void)
{
  static double P[10] = { 1, 9, 3, 4, 5, 8, 6, 7, 2, 0 };
  if (g2 == NULL)
    {
      g2 = gsl_ran_discrete_preproc (10, P);
    }
  return gsl_ran_discrete (r_global, g2);
}

double
test_discrete2_pdf (unsigned int n)
{
  return gsl_ran_discrete_pdf ((size_t) n, g2);
}
double
test_discrete3 (void)
{
  static double P[20];
  if (g3 == NULL)
    { int i;
      for (i=0; i<20; ++i) P[i]=1.0/20;
      g3 = gsl_ran_discrete_preproc (20, P);
    }
  return gsl_ran_discrete (r_global, g3);
}

double
test_discrete3_pdf (unsigned int n)
{
  return gsl_ran_discrete_pdf ((size_t) n, g3);
}

double
test_erlang (void)
{
  return gsl_ran_erlang (r_global, 3.0, 4.0);
}

double
test_erlang_pdf (double x)
{
  return gsl_ran_erlang_pdf (x, 3.0, 4.0);
}

double
test_exponential (void)
{
  return gsl_ran_exponential (r_global, 2.0);
}

double
test_exponential_pdf (double x)
{
  return gsl_ran_exponential_pdf (x, 2.0);
}

double
test_exppow0 (void)
{
  return gsl_ran_exppow (r_global, 3.7, 0.3);
}

double
test_exppow0_pdf (double x)
{
  return gsl_ran_exppow_pdf (x, 3.7, 0.3);
}

double
test_exppow1 (void)
{
  return gsl_ran_exppow (r_global, 3.7, 1.0);
}

double
test_exppow1_pdf (double x)
{
  return gsl_ran_exppow_pdf (x, 3.7, 1.0);
}

double
test_exppow1a (void)
{
  return gsl_ran_exppow (r_global, 3.7, 1.9);
}

double
test_exppow1a_pdf (double x)
{
  return gsl_ran_exppow_pdf (x, 3.7, 1.9);
}

double
test_exppow2 (void)
{
  return gsl_ran_exppow (r_global, 3.7, 2.0);
}

double
test_exppow2_pdf (double x)
{
  return gsl_ran_exppow_pdf (x, 3.7, 2.0);
}

double
test_exppow2a (void)
{
  return gsl_ran_exppow (r_global, 3.7, 3.5);
}

double
test_exppow2a_pdf (double x)
{
  return gsl_ran_exppow_pdf (x, 3.7, 3.5);
}

double
test_exppow2b (void)
{
  return gsl_ran_exppow (r_global, 3.7, 7.5);
}

double
test_exppow2b_pdf (double x)
{
  return gsl_ran_exppow_pdf (x, 3.7, 7.5);
}

double
test_fdist (void)
{
  return gsl_ran_fdist (r_global, 3.0, 4.0);
}

double
test_fdist_pdf (double x)
{
  return gsl_ran_fdist_pdf (x, 3.0, 4.0);
}

/* Test case for bug #28500: overflow in gsl_ran_fdist_pdf */

double
test_fdist_large (void)
{
  return gsl_ran_fdist (r_global, 8.0, 249.0);
}

double
test_fdist_large_pdf (double x)
{
  return gsl_ran_fdist_pdf (x, 8.0, 249.0);
}

double
test_flat (void)
{
  return gsl_ran_flat (r_global, 3.0, 4.0);
}

double
test_flat_pdf (double x)
{
  return gsl_ran_flat_pdf (x, 3.0, 4.0);
}

double
test_gamma (void)
{
  return gsl_ran_gamma (r_global, 2.5, 2.17);
}

double
test_gamma_pdf (double x)
{
  return gsl_ran_gamma_pdf (x, 2.5, 2.17);
}

double
test_gamma1 (void)
{
  return gsl_ran_gamma (r_global, 1.0, 2.17);
}

double
test_gamma1_pdf (double x)
{
  return gsl_ran_gamma_pdf (x, 1.0, 2.17);
}

double
test_gamma_int (void)
{
  return gsl_ran_gamma (r_global, 10.0, 2.17);
}

double
test_gamma_int_pdf (double x)
{
  return gsl_ran_gamma_pdf (x, 10.0, 2.17);
}

double
test_gamma_large (void)
{
  return gsl_ran_gamma (r_global, 20.0, 2.17);
}

double
test_gamma_large_pdf (double x)
{
  return gsl_ran_gamma_pdf (x, 20.0, 2.17);
}

double
test_gamma_small (void)
{
  return gsl_ran_gamma (r_global, 0.92, 2.17);
}

double
test_gamma_small_pdf (double x)
{
  return gsl_ran_gamma_pdf (x, 0.92, 2.17);
}

double
test_gamma_vlarge (void)
{
  /* Scale the distribution to get it into the range [-5,5] */
  double c = 2.71828181565;
  double b = 6.32899304917e-10;
  double d = 1e4;
  return (gsl_ran_gamma (r_global, 4294967296.0, b) - c) * d;
}

double
test_gamma_vlarge_pdf (double x)
{
  double c = 2.71828181565;
  double b = 6.32899304917e-10;
  double d = 1e4;
  return gsl_ran_gamma_pdf ((x / d) + c, 4294967296.0, b) / d;
}

double
test_gamma_mt (void)
{
  return gsl_ran_gamma_mt (r_global, 2.5, 2.17);
}

double
test_gamma_mt_pdf (double x)
{
  return gsl_ran_gamma_pdf (x, 2.5, 2.17);
}

double
test_gamma_mt1 (void)
{
  return gsl_ran_gamma_mt (r_global, 1.0, 2.17);
}

double
test_gamma_mt1_pdf (double x)
{
  return gsl_ran_gamma_pdf (x, 1.0, 2.17);
}

double
test_gamma_mt_int (void)
{
  return gsl_ran_gamma_mt (r_global, 10.0, 2.17);
}

double
test_gamma_mt_int_pdf (double x)
{
  return gsl_ran_gamma_pdf (x, 10.0, 2.17);
}

double
test_gamma_mt_large (void)
{
  return gsl_ran_gamma_mt (r_global, 20.0, 2.17);
}

double
test_gamma_mt_large_pdf (double x)
{
  return gsl_ran_gamma_pdf (x, 20.0, 2.17);
}

double
test_gamma_mt_small (void)
{
  return gsl_ran_gamma_mt (r_global, 0.92, 2.17);
}

double
test_gamma_mt_small_pdf (double x)
{
  return gsl_ran_gamma_pdf (x, 0.92, 2.17);
}

double
test_gamma_knuth_vlarge (void)
{
  /* Scale the distribution to get it into the range [-5,5] */
  double c = 2.71828181565;
  double b = 6.32899304917e-10;
  double d = 1e4;
  return (gsl_ran_gamma_knuth (r_global, 4294967296.0, b) - c) * d;
}

double
test_gamma_knuth_vlarge_pdf (double x)
{
  double c = 2.71828181565;
  double b = 6.32899304917e-10;
  double d = 1e4;
  return gsl_ran_gamma_pdf ((x / d) + c, 4294967296.0, b) / d;
}

double
test_gaussian (void)
{
  return gsl_ran_gaussian (r_global, 3.0);
}

double
test_gaussian_pdf (double x)
{
  return gsl_ran_gaussian_pdf (x, 3.0);
}

double
test_gaussian_ratio_method (void)
{
  return gsl_ran_gaussian_ratio_method (r_global, 3.0);
}

double
test_gaussian_ratio_method_pdf (double x)
{
  return gsl_ran_gaussian_pdf (x, 3.0);
}

double
test_gaussian_ziggurat (void)
{
  return gsl_ran_gaussian_ziggurat (r_global, 3.12);
}

double
test_gaussian_ziggurat_pdf (double x)
{
  return gsl_ran_gaussian_pdf (x, 3.12);
}

double
test_gaussian_tail (void)
{
  return gsl_ran_gaussian_tail (r_global, 1.7, 0.25);
}

double
test_gaussian_tail_pdf (double x)
{
  return gsl_ran_gaussian_tail_pdf (x, 1.7, 0.25);
}

double
test_gaussian_tail1 (void)
{
  return gsl_ran_gaussian_tail (r_global, -1.7, 5.0);
}

double
test_gaussian_tail1_pdf (double x)
{
  return gsl_ran_gaussian_tail_pdf (x, -1.7, 5.0);
}

double
test_gaussian_tail2 (void)
{
  return gsl_ran_gaussian_tail (r_global, 0.1, 2.0);
}

double
test_gaussian_tail2_pdf (double x)
{
  return gsl_ran_gaussian_tail_pdf (x, 0.1, 2.0);
}

double
test_ugaussian (void)
{
  return gsl_ran_ugaussian (r_global);
}

double
test_ugaussian_pdf (double x)
{
  return gsl_ran_ugaussian_pdf (x);
}

double
test_ugaussian_ratio_method (void)
{
  return gsl_ran_ugaussian_ratio_method (r_global);
}

double
test_ugaussian_ratio_method_pdf (double x)
{
  return gsl_ran_ugaussian_pdf (x);
}

double
test_ugaussian_tail (void)
{
  return gsl_ran_ugaussian_tail (r_global, 3.0);
}

double
test_ugaussian_tail_pdf (double x)
{
  return gsl_ran_ugaussian_tail_pdf (x, 3.0);
}

double
test_bivariate_gaussian1 (void)
{
  double x = 0, y = 0;
  gsl_ran_bivariate_gaussian (r_global, 3.0, 2.0, 0.3, &x, &y);
  return x;
}

double
test_bivariate_gaussian1_pdf (double x)
{
  return gsl_ran_gaussian_pdf (x, 3.0);
}

double
test_bivariate_gaussian2 (void)
{
  double x = 0, y = 0;
  gsl_ran_bivariate_gaussian (r_global, 3.0, 2.0, 0.3, &x, &y);
  return y;
}

double
test_bivariate_gaussian2_pdf (double y)
{
  int i, n = 10;
  double sum = 0;
  double a = -10, b = 10, dx = (b - a) / n;
  for (i = 0; i < n; i++)
    {
      double x = a + i * dx;
      sum += gsl_ran_bivariate_gaussian_pdf (x, y, 3.0, 2.0, 0.3) * dx;
    }
  return sum;
}

double
test_bivariate_gaussian3 (void)
{
  double x = 0, y = 0;
  gsl_ran_bivariate_gaussian (r_global, 3.0, 2.0, 0.3, &x, &y);
  return x + y;
}

double
test_bivariate_gaussian3_pdf (double x)
{
  double sx = 3.0, sy = 2.0, r = 0.3;
  double su = (sx + r * sy);
  double sv = sy * sqrt (1 - r * r);
  double sigma = sqrt (su * su + sv * sv);

  return gsl_ran_gaussian_pdf (x, sigma);
}

double
test_bivariate_gaussian4 (void)
{
  double x = 0, y = 0;
  gsl_ran_bivariate_gaussian (r_global, 3.0, 2.0, -0.5, &x, &y);
  return x + y;
}

double
test_bivariate_gaussian4_pdf (double x)
{
  double sx = 3.0, sy = 2.0, r = -0.5;
  double su = (sx + r * sy);
  double sv = sy * sqrt (1 - r * r);
  double sigma = sqrt (su * su + sv * sv);

  return gsl_ran_gaussian_pdf (x, sigma);
}

/* Examples from R (GPL): http://www.r-project.org/
 * library(mvtnorm); packageVersion("mvtnorm") # 1.0.5
 * mu <- c(1, 2)
 * Sigma <- matrix(c(4,2, 2,3), ncol=2)
 * x <- c(0, 0)
 * sprintf("%.15f", dmvnorm(x=x, mean=mu, sigma=Sigma, log=TRUE)) # -3.565097837249263
 */
void
test_multivariate_gaussian_log_pdf (void)
{
  size_t d = 2;
  const double exp_res = -3.565097837249263;
  double obs_res;
  gsl_vector * mu = gsl_vector_calloc(d);
  gsl_matrix * Sigma = gsl_matrix_calloc(d, d);
  gsl_matrix * L = gsl_matrix_calloc(d, d);
  gsl_vector * x = gsl_vector_calloc(d);
  gsl_vector * work = gsl_vector_calloc(d);

  gsl_vector_set(mu, 0, 1);
  gsl_vector_set(mu, 1, 2);

  gsl_matrix_set(Sigma, 0, 0, 4);
  gsl_matrix_set(Sigma, 1, 1, 3);
  gsl_matrix_set(Sigma, 0, 1, 2);
  gsl_matrix_set(Sigma, 1, 0, 2);

  gsl_matrix_memcpy(L, Sigma);
  gsl_linalg_cholesky_decomp1(L);

  gsl_ran_multivariate_gaussian_log_pdf(x, mu, L, &obs_res, work);
  gsl_test_rel(obs_res, exp_res, 1.0e-10, "gsl_ran_multivariate_gaussian_log_pdf");

  gsl_vector_free(mu);
  gsl_matrix_free(Sigma);
  gsl_matrix_free(L);
  gsl_vector_free(x);
  gsl_vector_free(work);
}

/* Examples from R (GPL): http://www.r-project.org/
 * library(mvtnorm); packageVersion("mvtnorm") # 1.0.5
 * mu <- c(1, 2)
 * Sigma <- matrix(c(4,2, 2,3), ncol=2)
 * x <- c(0, 0)
 * sprintf("%.15f", dmvnorm(x=x, mean=mu, sigma=Sigma, log=FALSE)) # 0.028294217120391
 */
void
test_multivariate_gaussian_pdf (void)
{
  size_t d = 2;
  const double exp_res = 0.028294217120391;
  double obs_res = 0;
  gsl_vector * mu = gsl_vector_calloc(d);
  gsl_matrix * Sigma = gsl_matrix_calloc(d, d);
  gsl_matrix * L = gsl_matrix_calloc(d, d);
  gsl_vector * x = gsl_vector_calloc(d);
  gsl_vector * work = gsl_vector_calloc(d);

  gsl_vector_set(mu, 0, 1);
  gsl_vector_set(mu, 1, 2);

  gsl_matrix_set(Sigma, 0, 0, 4);
  gsl_matrix_set(Sigma, 1, 1, 3);
  gsl_matrix_set(Sigma, 0, 1, 2);
  gsl_matrix_set(Sigma, 1, 0, 2);

  gsl_matrix_memcpy(L, Sigma);
  gsl_linalg_cholesky_decomp1(L);

  gsl_ran_multivariate_gaussian_pdf(x, mu, L, &obs_res, work);
  gsl_test_rel(obs_res, exp_res, 1.0e-10, "gsl_ran_multivariate_gaussian_pdf");

  gsl_vector_free(mu);
  gsl_matrix_free(Sigma);
  gsl_matrix_free(L);
  gsl_vector_free(x);
  gsl_vector_free(work);
}

/* Draw N random vectors according to a given MVN(mu,Sigma). Then, check that
 * one can't reject the null hypothesis that the sample mean is equal to
 * the true mean, using Hotelling's test statistic at 95% confidence level.
 * Details in "Applied Multivariate Statistical Analysis" by  Johnson & Wichern
 * (2001), section 5, page 212.
 */
void
test_multivariate_gaussian (void)
{
  size_t d = 2, i = 0;
  int status = 0;
  double T2 = 0, threshold = 0, alpha = 0.05, pvalue = 0;
  gsl_vector * mu = gsl_vector_calloc(d);
  gsl_matrix * Sigma = gsl_matrix_calloc(d, d);
  gsl_matrix * L = gsl_matrix_calloc(d, d);
  gsl_vector * sample = gsl_vector_calloc(d);
  gsl_matrix * samples = gsl_matrix_calloc(N, d);
  gsl_vector * mu_hat = gsl_vector_calloc(d);
  gsl_matrix * Sigma_hat = gsl_matrix_calloc(d, d);
  gsl_vector * mu_hat_ctr = gsl_vector_calloc(d);
  gsl_matrix * Sigma_hat_inv = gsl_matrix_calloc(d, d);
  gsl_vector * tmp = gsl_vector_calloc(d);

  /* set the true values of parameters mu and Sigma */
  gsl_vector_set(mu, 0, 1);
  gsl_vector_set(mu, 1, 2);
  gsl_matrix_set(Sigma, 0, 0, 4);
  gsl_matrix_set(Sigma, 1, 1, 3);
  gsl_matrix_set(Sigma, 0, 1, 2);
  gsl_matrix_set(Sigma, 1, 0, 2);

  /* draw N random vectors */
  gsl_matrix_memcpy(L, Sigma);
  gsl_linalg_cholesky_decomp1(L);
  for (i = 0; i < N; ++i) {
    gsl_ran_multivariate_gaussian(r_global, mu, L, sample);
    gsl_matrix_set_row(samples, i, sample);
  }

  /* compute the maximum-likelihood estimates */
  gsl_ran_multivariate_gaussian_mean (samples, mu_hat);
  gsl_ran_multivariate_gaussian_vcov (samples, Sigma_hat);

  /* compute Hotelling's test statistic:
     T^2 = n (hat{mu} - mu)' hat{Sigma}^-1 (hat{mu} - mu) */
  gsl_vector_memcpy(mu_hat_ctr, mu_hat);
  gsl_vector_sub(mu_hat_ctr, mu);
  gsl_matrix_memcpy(Sigma_hat_inv, Sigma_hat);
  gsl_linalg_cholesky_decomp1(Sigma_hat_inv);
  gsl_linalg_cholesky_invert(Sigma_hat_inv);
  gsl_blas_dgemv(CblasNoTrans, 1, Sigma_hat_inv, mu_hat_ctr, 0, tmp);
  gsl_blas_ddot(mu_hat_ctr, tmp, &T2);
  T2 *= N;

  /* test if the null hypothesis (hat{mu} = mu) can be rejected
   at the alpha level*/
  threshold = (N-1) * d / (double)(N-d) * gsl_cdf_fdist_Pinv(1-alpha, d, N-d);
  status = (T2 > threshold);
  gsl_test(status,
           "test gsl_ran_multivariate_gaussian: T2 %f < %f",
           T2, threshold);
  pvalue = gsl_cdf_fdist_Q(T2, d, N-d);
  status = (pvalue < alpha);
  gsl_test(status,
           "test gsl_ran_multivariate_gaussian: p value %f > %f",
           pvalue, alpha);

  gsl_vector_free(mu);
  gsl_matrix_free(Sigma);
  gsl_matrix_free(L);
  gsl_vector_free(sample);
  gsl_matrix_free(samples);
  gsl_vector_free(mu_hat);
  gsl_matrix_free(Sigma_hat);
  gsl_vector_free(mu_hat_ctr);
  gsl_matrix_free(Sigma_hat_inv);
  gsl_vector_free(tmp);
}

double
test_geometric (void)
{
  return gsl_ran_geometric (r_global, 0.5);
}

double
test_geometric_pdf (unsigned int n)
{
  return gsl_ran_geometric_pdf (n, 0.5);
}

double
test_geometric1 (void)
{
  return gsl_ran_geometric (r_global, 1.0);
}

double
test_geometric1_pdf (unsigned int n)
{
  return gsl_ran_geometric_pdf (n, 1.0);
}

double
test_hypergeometric1 (void)
{
  return gsl_ran_hypergeometric (r_global, 5, 7, 4);
}

double
test_hypergeometric1_pdf (unsigned int n)
{
  return gsl_ran_hypergeometric_pdf (n, 5, 7, 4);
}

double
test_hypergeometric2 (void)
{
  return gsl_ran_hypergeometric (r_global, 5, 7, 11);
}

double
test_hypergeometric2_pdf (unsigned int n)
{
  return gsl_ran_hypergeometric_pdf (n, 5, 7, 11);
}

double
test_hypergeometric3 (void)
{
  return gsl_ran_hypergeometric (r_global, 5, 7, 1);
}

double
test_hypergeometric3_pdf (unsigned int n)
{
  return gsl_ran_hypergeometric_pdf (n, 5, 7, 1);
}

double
test_hypergeometric4 (void)
{
  return gsl_ran_hypergeometric (r_global, 5, 7, 20);
}

double
test_hypergeometric4_pdf (unsigned int n)
{
  return gsl_ran_hypergeometric_pdf (n, 5, 7, 20);
}

double
test_hypergeometric5 (void)
{
  return gsl_ran_hypergeometric (r_global, 2, 7, 5);
}

double
test_hypergeometric5_pdf (unsigned int n)
{
  return gsl_ran_hypergeometric_pdf (n, 2, 7, 5);
}

double
test_hypergeometric6 (void)
{
  return gsl_ran_hypergeometric (r_global, 2, 10, 3);
}

double
test_hypergeometric6_pdf (unsigned int n)
{
  return gsl_ran_hypergeometric_pdf (n, 2, 10, 3);
}

double
test_gumbel1 (void)
{
  return gsl_ran_gumbel1 (r_global, 3.12, 4.56);
}

double
test_gumbel1_pdf (double x)
{
  return gsl_ran_gumbel1_pdf (x, 3.12, 4.56);
}

double
test_gumbel2 (void)
{
  return gsl_ran_gumbel2 (r_global, 3.12, 4.56);
}

double
test_gumbel2_pdf (double x)
{
  return gsl_ran_gumbel2_pdf (x, 3.12, 4.56);
}

double
test_landau (void)
{
  return gsl_ran_landau (r_global);
}

double
test_landau_pdf (double x)
{
  return gsl_ran_landau_pdf (x);
}

double
test_levy1 (void)
{
  return gsl_ran_levy (r_global, 5.0, 1.0);
}

double
test_levy1_pdf (double x)
{
  return gsl_ran_cauchy_pdf (x, 5.0);
}

double
test_levy2 (void)
{
  return gsl_ran_levy (r_global, 5.0, 2.0);
}

double
test_levy2_pdf (double x)
{
  return gsl_ran_gaussian_pdf (x, sqrt (2.0) * 5.0);
}

double
test_levy1a (void)
{
  return gsl_ran_levy (r_global, 5.0, 1.01);
}

double
test_levy1a_pdf (double x)
{
  return gsl_ran_cauchy_pdf (x, 5.0);
}

double
test_levy2a (void)
{
  return gsl_ran_levy (r_global, 5.0, 1.99);
}

double
test_levy2a_pdf (double x)
{
  return gsl_ran_gaussian_pdf (x, sqrt (2.0) * 5.0);
}

double
test_levy_skew1 (void)
{
  return gsl_ran_levy_skew (r_global, 5.0, 1.0, 0.0);
}

double
test_levy_skew1_pdf (double x)
{
  return gsl_ran_cauchy_pdf (x, 5.0);
}

double
test_levy_skew2 (void)
{
  return gsl_ran_levy_skew (r_global, 5.0, 2.0, 0.0);
}

double
test_levy_skew2_pdf (double x)
{
  return gsl_ran_gaussian_pdf (x, sqrt (2.0) * 5.0);
}

double
test_levy_skew1a (void)
{
  return gsl_ran_levy_skew (r_global, 5.0, 1.01, 0.0);
}

double
test_levy_skew1a_pdf (double x)
{
  return gsl_ran_cauchy_pdf (x, 5.0);
}

double
test_levy_skew2a (void)
{
  return gsl_ran_levy_skew (r_global, 5.0, 1.99, 0.0);
}

double
test_levy_skew2a_pdf (double x)
{
  return gsl_ran_gaussian_pdf (x, sqrt (2.0) * 5.0);
}

double
test_levy_skew1b (void)
{
  return gsl_ran_levy_skew (r_global, 5.0, 1.01, 0.001);
}

double
test_levy_skew1b_pdf (double x)
{
  return gsl_ran_cauchy_pdf (x, 5.0);
}

double
test_levy_skew2b (void)
{
  return gsl_ran_levy_skew (r_global, 5.0, 1.99, 0.001);
}

double
test_levy_skew2b_pdf (double x)
{
  return gsl_ran_gaussian_pdf (x, sqrt (2.0) * 5.0);
}

double
test_logistic (void)
{
  return gsl_ran_logistic (r_global, 3.1);
}

double
test_logistic_pdf (double x)
{
  return gsl_ran_logistic_pdf (x, 3.1);
}

double
test_logarithmic (void)
{
  return gsl_ran_logarithmic (r_global, 0.4);
}

double
test_logarithmic_pdf (unsigned int n)
{
  return gsl_ran_logarithmic_pdf (n, 0.4);
}

double
test_lognormal (void)
{
  return gsl_ran_lognormal (r_global, 2.7, 1.3);
}

double
test_lognormal_pdf (double x)
{
  return gsl_ran_lognormal_pdf (x, 2.7, 1.3);
}

double
test_multinomial (void)
{
  const size_t K = 3;
  const unsigned int sum_n = BINS;
  unsigned int n[3];
  /* Test use of weights instead of probabilities. */
  const double p[] = { 2., 7., 1.};

  gsl_ran_multinomial ( r_global, K, sum_n, p, n);

  return n[0];
}

double
test_multinomial_pdf (unsigned int n_0)
{
  /* The margional distribution of just 1 variate  is binomial. */
  size_t K = 2;
  /* Test use of weights instead of probabilities */
  double p[] = { 0.4, 1.6};
  const unsigned int sum_n = BINS;
  unsigned int n[2];

  n[0] = n_0;
  n[1] =sum_n - n_0;

  return gsl_ran_multinomial_pdf (K, p, n);
}

double
test_multinomial_large (void)
{
  const unsigned int sum_n = BINS;
  unsigned int n[MULTI_DIM];
  const double p[MULTI_DIM] = { 0.2, 0.20, 0.17, 0.14, 0.12,
                                0.07, 0.05, 0.04, 0.01, 0.00  };

  gsl_ran_multinomial ( r_global, MULTI_DIM, sum_n, p, n);

  return n[0];
}

double
test_multinomial_large_pdf (unsigned int n_0)
{
  return test_multinomial_pdf(n_0);
}

double
test_negative_binomial (void)
{
  return gsl_ran_negative_binomial (r_global, 0.3, 20.0);
}

double
test_negative_binomial_pdf (unsigned int n)
{
  return gsl_ran_negative_binomial_pdf (n, 0.3, 20.0);
}

double
test_pascal (void)
{
  return gsl_ran_pascal (r_global, 0.8, 3);
}

double
test_pascal_pdf (unsigned int n)
{
  return gsl_ran_pascal_pdf (n, 0.8, 3);
}

double
test_pareto (void)
{
  return gsl_ran_pareto (r_global, 1.9, 2.75);
}

double
test_pareto_pdf (double x)
{
  return gsl_ran_pareto_pdf (x, 1.9, 2.75);
}

double
test_rayleigh (void)
{
  return gsl_ran_rayleigh (r_global, 1.9);
}

double
test_rayleigh_pdf (double x)
{
  return gsl_ran_rayleigh_pdf (x, 1.9);
}

double
test_rayleigh_tail (void)
{
  return gsl_ran_rayleigh_tail (r_global, 2.7, 1.9);
}

double
test_rayleigh_tail_pdf (double x)
{
  return gsl_ran_rayleigh_tail_pdf (x, 2.7, 1.9);
}

double
test_poisson (void)
{
  return gsl_ran_poisson (r_global, 5.0);
}

double
test_poisson_pdf (unsigned int n)
{
  return gsl_ran_poisson_pdf (n, 5.0);
}

double
test_poisson_large (void)
{
  return gsl_ran_poisson (r_global, 30.0);
}

double
test_poisson_large_pdf (unsigned int n)
{
  return gsl_ran_poisson_pdf (n, 30.0);
}

double
test_tdist1 (void)
{
  return gsl_ran_tdist (r_global, 1.75);
}

double
test_tdist1_pdf (double x)
{
  return gsl_ran_tdist_pdf (x, 1.75);
}

double
test_tdist2 (void)
{
  return gsl_ran_tdist (r_global, 12.75);
}

double
test_tdist2_pdf (double x)
{
  return gsl_ran_tdist_pdf (x, 12.75);
}

double
test_laplace (void)
{
  return gsl_ran_laplace (r_global, 2.75);
}

double
test_laplace_pdf (double x)
{
  return gsl_ran_laplace_pdf (x, 2.75);
}

double
test_weibull (void)
{
  return gsl_ran_weibull (r_global, 3.14, 2.75);
}

double
test_weibull_pdf (double x)
{
  return gsl_ran_weibull_pdf (x, 3.14, 2.75);
}

double
test_weibull1 (void)
{
  return gsl_ran_weibull (r_global, 2.97, 1.0);
}

double
test_weibull1_pdf (double x)
{
  return gsl_ran_weibull_pdf (x, 2.97, 1.0);
}


/*****************
 * @file leastsq.h
 * @date 4/1/08
 * @author Douglas Applegate
 *
 * @brief Provides a wrapper around the GSL libraries for fitting functions
 *****************/

//CVSID $Id: leastsq.h,v 1.1 2008-04-04 01:43:12 mallen Exp $

////////////////////////////////////////////////////

#ifndef LEASTSQ_H
#define LEASTSQ_H

#include <gsl/gsl_vector.h>
#include <gsl/gsl_matrix.h>

/**
 * Function prototype for fitting function and its derivative
 * @param double x position at which to evaluate function
 * @param const double* parameter values to use in evaluation
 */
typedef double (*FitFunction_t)(double, const double*);

/**
 * Provides non-linear fitting functionality
 */
class Leastsq {

 public:

  /**
   * Initializes object with basic fit information
   * @param fitFunc function to fit to data
   * @param dfitFunc array of fit function derivatives, one for each param
   * @param nparams number of parameters that fitFunc and dfitFunc accept
   */
  Leastsq(FitFunction_t fitFunc,
	  FitFunction_t* dfitFunc,
	  int nparams);

  /**
   * Default constructor
   */
  virtual ~Leastsq();

  /**
   * Fits function to the given data, starting at initial guess
   * @param x x values of data
   * @param y y values of data
   * @param ndata number of data points
   * @param guess initial parameter values for fit
   *
   * @returns status status code for fit. 1 == fit ran fine
   */
  int doFit(const double* x, const double* y, int ndata, double* guess);

  /////GETTERS

  double numParams() const {return _nparams;};

  const double** covarMatrix() const {
    return const_cast<const double**>(_covar);
  };

  double chisq() const {return _chisq;};

  const double* parameters() const {
    return const_cast<const double*>(_parameters);
  };

 protected:

  /////INSTANCE METHODS

  int gslFitFunction(const gsl_vector* x,
		     void* params,
		     gsl_vector* result);

  int gslDFitFunction(const gsl_vector* x,
		      void* params,
		      gsl_matrix* J);

  /////Instance Variables

  FitFunction_t _fitFunc; ///< Function to fit to data
  FitFunction_t* _dfitFunc; ///< Analytical derivative of fitFunc
  int _nparams; ///< Number of parameters in fitFunc and dfitFunc
  double** _covar; ///< Covariance Matrix
  double _chisq; ///< Chisq or residual from fit
  double* _parameters; ///< Best fit parameters
  const double* _x; ///< x values of data
  const double* _y; ///< y values of data
  int _ndata; ///< number of data
};

#endif


/* interpolation/gsl_spline2d.h
 *
 * Copyright 2012 David Zaslavsky
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 3 of the License, or (at
 * your option) any later version.
 *
 * This program is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
 */

#ifndef __GSL_SPLINE2D_H__
#define __GSL_SPLINE2D_H__

#include <gsl/gsl_interp.h>
#include <gsl/gsl_interp2d.h>

#undef __BEGIN_DECLS
#undef __END_DECLS
#ifdef __cplusplus
# define __BEGIN_DECLS extern "C" {
# define __END_DECLS }
#else
# define __BEGIN_DECLS /* empty */
# define __END_DECLS /* empty */
#endif

__BEGIN_DECLS

/*
 * A 2D interpolation object which stores the arrays defining the function.
 * In all other respects, this is just like a gsl_interp2d object.
 */
typedef struct
{
  gsl_interp2d interp_object; /* low-level interpolation object */
  double * xarr;              /* x data array */
  double * yarr;              /* y data array */
  double * zarr;              /* z data array */
} gsl_spline2d;

gsl_spline2d * gsl_spline2d_alloc(const gsl_interp2d_type * T, size_t xsize, size_t ysize);

int gsl_spline2d_init(gsl_spline2d * interp, const double xa[],
                      const double ya[], const double za[],
                      size_t xsize, size_t ysize);

void gsl_spline2d_free(gsl_spline2d * interp);

double gsl_spline2d_eval(const gsl_spline2d * interp, const double x,
                         const double y, gsl_interp_accel* xa, gsl_interp_accel* ya);

int gsl_spline2d_eval_e(const gsl_spline2d * interp, const double x,
                        const double y, gsl_interp_accel* xa, gsl_interp_accel* ya,
                        double * z);

double gsl_spline2d_eval_deriv_x(const gsl_spline2d * interp, const double x,
                                 const double y, gsl_interp_accel* xa, gsl_interp_accel* ya);

int gsl_spline2d_eval_deriv_x_e(const gsl_spline2d * interp, const double x,
                                const double y, gsl_interp_accel* xa,
                                gsl_interp_accel* ya, double * z);

double gsl_spline2d_eval_deriv_y(const gsl_spline2d * interp, const double x,
                                 const double y, gsl_interp_accel* xa,
                                 gsl_interp_accel* ya);

int gsl_spline2d_eval_deriv_y_e(const gsl_spline2d * interp, const double x,
                                const double y, gsl_interp_accel* xa,
                                gsl_interp_accel* ya, double * z);

double gsl_spline2d_eval_deriv_xx(const gsl_spline2d * interp, const double x,
                                  const double y, gsl_interp_accel* xa, gsl_interp_accel* ya);

int gsl_spline2d_eval_deriv_xx_e(const gsl_spline2d * interp, const double x,
                                 const double y, gsl_interp_accel* xa,
                                 gsl_interp_accel* ya, double * z);

double gsl_spline2d_eval_deriv_yy(const gsl_spline2d * interp, const double x,
                                  const double y, gsl_interp_accel* xa, gsl_interp_accel* ya);

int gsl_spline2d_eval_deriv_yy_e(const gsl_spline2d * interp, const double x,
                                 const double y, gsl_interp_accel* xa,
                                 gsl_interp_accel* ya, double * z);

double gsl_spline2d_eval_deriv_xy(const gsl_spline2d * interp, const double x,
                                  const double y, gsl_interp_accel* xa, gsl_interp_accel* ya);

int gsl_spline2d_eval_deriv_xy_e(const gsl_spline2d * interp, const double x,
                                 const double y, gsl_interp_accel* xa,
                                 gsl_interp_accel* ya, double * z);

size_t gsl_spline2d_min_size(const gsl_spline2d * interp);

const char * gsl_spline2d_name(const gsl_spline2d * interp);

int gsl_spline2d_set(const gsl_spline2d * interp, double zarr[],
                     const size_t i, const size_t j, const double z);
double gsl_spline2d_get(const gsl_spline2d * interp, const double zarr[],
                        const size_t i, const size_t j);

__END_DECLS

#endif /* __GSL_SPLINE2D_H__ */


#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <sys/time.h>
#include <math.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>
#include <gsl/gsl_blas.h>

#include <omp.h>

#include "util.h"

int main(int argc, char *argv[]) {
    char* input_fileName1 = argv[1];
    char* input_fileName2 = argv[2];
    int N_doc_bg = atoi(argv[3]);
    int N_kw = atoi(argv[4]);
    int N_obs = atoi(argv[5]);
    int N_iter = atoi(argv[6]);
    char* output_fileName = argv[7];
    int N_doc = 480000 / 2;

    int* matrix = (int*) malloc(sizeof(int) * N_obs * N_obs);
    int* matrix_bg = (int*) malloc(sizeof(int) * N_kw * N_kw);
    int* matrix_padded = (int*) malloc(sizeof(int) * N_obs * N_obs);
    int* true_index = (int*) malloc(sizeof(int) * N_kw);
    int* permutation = (int*) malloc(sizeof(int) * N_obs);
    gsl_matrix* matrix_obs;

    for (int round = 0; round < 10; round++)
    {
        char input_fileName1_extend[40];
        char input_fileName2_extend[40];
        sprintf(input_fileName1_extend, "%s%d", input_fileName1, round);
        sprintf(input_fileName2_extend, "%s%d", input_fileName2, round);

        // Setup
        struct timeval tv1,tv2;
        gettimeofday(&tv1, NULL);
        read_matrix(&true_index, &matrix_bg, 1.0*N_doc/N_doc_bg, N_kw, input_fileName2_extend);
        read_matrix(&true_index, &matrix, 1.0, N_obs, input_fileName1_extend);
        gettimeofday(&tv2, NULL);
        printf("Reading done: %f.\n", (double) (tv2.tv_usec - tv1.tv_usec) / 1000000 + (double) (tv2.tv_sec - tv1.tv_sec));
        fflush(stdout);

        // compute the maximum frequency of a keyword
        int freq_max = 0;
        for (int ii = 0; ii < N_kw; ii++)
            if (matrix_bg[ii*N_kw+ii] > freq_max)
                freq_max = matrix_bg[ii*N_kw+ii];
        for (int ii = 0; ii < N_obs; ii++)
            if (matrix[ii*N_obs+ii] > freq_max)
                freq_max = matrix[ii*N_obs+ii];
        printf("Max frequency: %d\n", freq_max);

        for (int iter = 0; iter < 10; iter++)
        {
            printf("Run %d\n", iter);
            matrix_obs = gsl_matrix_alloc(N_obs, N_obs);

            gettimeofday(&tv1, NULL);
            pad_matrix(&matrix_padded, &matrix, N_obs, N_doc, freq_max);
            gettimeofday(&tv2, NULL);
            printf("Padding done: %f.\n", (double) (tv2.tv_usec - tv1.tv_usec) / 1000000 + (double) (tv2.tv_sec - tv1.tv_sec));
            fflush(stdout);

            gettimeofday(&tv1, NULL);
            observe_matrix(matrix_obs, &matrix_padded, N_obs);
            gettimeofday(&tv2, NULL);
            printf("Observed matrix generated: %f.\n", (double) (tv2.tv_usec - tv1.tv_usec) / 1000000 + (double) (tv2.tv_sec - tv1.tv_sec));
            fflush(stdout);

            // Permute observed matrix randomly and attack
            gettimeofday(&tv1, NULL);
            attack(matrix_obs, &matrix_bg, &permutation, N_kw, N_obs, N_doc, freq_max, N_iter);
            gettimeofday(&tv2, NULL);
            printf("Main attack done: %d.\n", (tv2.tv_sec - tv1.tv_sec));
            fflush(stdout);

            char output_fileName_full[40];
            sprintf(output_fileName_full, "%s%d-%d", output_fileName, round, iter);
            print_result(output_fileName_full, &permutation, &true_index, N_obs);
            //sprintf(output_fileName_full, "%s%d-%d-full", output_fileName, round, iter);
            //print_full_result(output_fileName_full, &permutation, &true_index, N_obs);
        }
    }

    free(matrix);
    free(matrix_padded);
    gsl_matrix_free(matrix_obs);
    return(0);
}

double log_score(int idx1, int idx2, gsl_matrix* matrix_obs, int** matrix, int** permutation, int N_kw, int N_doc, int freq_max)
{
    if (idx1 == idx2)
        return(0.0);

    int idx1_m = (*permutation)[idx1];
    int idx2_m = (*permutation)[idx2];

    int n1 = 2*freq_max - (*matrix)[idx1_m*N_kw + idx1_m];
    int n2 = 2*freq_max - (*matrix)[idx2_m*N_kw + idx2_m];

    /*
    int N_upper = 3 * sqrt((*matrix)[idx1_m*N_kw + idx2_m] * (N_doc - (*matrix)[idx1_m*N_kw + idx2_m]) / (double) N_doc);
    int N_lower = (*matrix)[idx1_m*N_kw + idx2_m] - N_upper;
    N_upper = (*matrix)[idx1_m*N_kw + idx2_m] + N_upper;
    int count_total = (int) gsl_matrix_get(matrix_obs, idx1, idx2);

    double score = 0;
    double prob = (*matrix)[idx1_m*N_kw + idx2_m] / (double) N_doc;
    for (int kk = N_lower; kk < N_upper+1; kk+=20)
        score +=  gsl_ran_binomial_pdf(kk, prob, N_doc) * gsl_ran_hypergeometric_pdf(count_total - kk, n1, 2*N_doc - n1, n2);
    */

    double mean = 1.0 * freq_max / N_doc * (n1 + n2);
    double var = 1.0 * (*matrix)[idx1_m*N_kw + idx2_m] / N_doc * (N_doc - (*matrix)[idx1_m*N_kw + idx2_m]);
    var += 1.0 * n1 / N_doc * freq_max * (2 * N_doc - 2*freq_max) / N_doc;
    var += 1.0 * n2 / N_doc * freq_max * (2 * N_doc - 2*freq_max) / N_doc;
    int count_total = (int) gsl_matrix_get(matrix_obs, idx1, idx2);

    int N_upper = 3 * sqrt((*matrix)[idx1_m*N_kw + idx2_m] * (N_doc - (*matrix)[idx1_m*N_kw + idx2_m]) / (double) N_doc);
    int N_lower = (*matrix)[idx1_m*N_kw + idx2_m] - N_upper;
    N_upper = (*matrix)[idx1_m*N_kw + idx2_m] + N_upper;

    mean += (*matrix)[idx1_m*N_kw + idx2_m];
    var += (*matrix)[idx1_m*N_kw + idx2_m] / N_doc * (N_doc - (*matrix)[idx1_m*N_kw + idx2_m]);

    double score = gsl_ran_gaussian_pdf(count_total - mean, sqrt(var));

    if (score == 0)
        return(-500.0);
    return(log(score));
}

void attack(gsl_matrix* matrix_obs, int** matrix, int** permutation, int N_kw, int N_obs, int N_doc, int freq_max, int N_iter)
{
    // Initialise data structures
    double* score_matrix = (double*) malloc(sizeof(double) * N_obs * N_obs);
    double* score_row1 = (double*) malloc(sizeof(double) * N_obs);
    double* score_row2 = (double*) malloc(sizeof(double) * N_obs);

    int* permutation_tmp = (int*) malloc(sizeof(int) * N_obs);
    int* permutation_inv = (int*) malloc(sizeof(int) * N_kw);

    // Initialise permutations
    for (int ii = 0; ii < N_obs; ii++)
        (*permutation)[ii] = ii;
    for (int ii = 0; ii < N_obs; ii++)
        permutation_tmp[ii] = ii;
    for (int ii = 0; ii < N_kw; ii++)
        permutation_inv[ii] = -1;
    for (int ii = 0; ii < N_obs; ii++)
        permutation_inv[permutation_tmp[ii]] = ii;

    // Initialising RNG
    const gsl_rng_type * T;
    gsl_rng * r;
    gsl_rng_env_setup();
    T = gsl_rng_default;
    r = gsl_rng_alloc (T);

    struct timeval tv1,tv2;
    gettimeofday(&tv1, NULL);

    // Compute initial score
    #pragma omp parallel for shared(score_matrix, matrix_obs, matrix)
    for (int ii = 0; ii < N_obs * N_obs; ii++)
        score_matrix[ii] = log_score((int) (ii / N_obs), ii % N_obs, matrix_obs, matrix, permutation, N_kw, N_doc, freq_max);
    gettimeofday(&tv2, NULL);
    printf("Initial score computed: %f.\n", (double) (tv2.tv_usec - tv1.tv_usec) / 1000000 + (double) (tv2.tv_sec - tv1.tv_sec));

    // Iterations of simulated annealing
    double temp = (double) N_kw;
    int N_stuck = 0;
    for (int iter = 0; iter < N_iter; iter++)
    {
        /* Status code */
        if (iter % (N_iter / 10) == 0)
        {
            gettimeofday(&tv1, NULL);
            printf("Iteration: %d, %d, %d.\n", iter, N_stuck, (int) (tv1.tv_sec - tv2.tv_sec));
            fflush(stdout);
            gettimeofday(&tv2, NULL);
        }

	    // used to be 20k
        if (N_stuck >= 80000)
            iter = N_iter;

        /* Main code */
        int idx1, idx2;
        permutation_generation(&idx1, &idx2, &permutation_tmp, permutation, &permutation_inv, N_kw, N_obs);

        int ii = 0;
        #pragma omp parallel for shared(score_row1)
        for (ii = 0; ii < N_obs; ii++)
            score_row1[ii] = log_score(idx1, ii, matrix_obs, matrix, &permutation_tmp, N_kw, N_doc, freq_max);

        if (idx2 >= 0)
            #pragma omp parallel for shared(score_row2)
            for (ii = 0; ii < N_obs; ii++)
                score_row2[ii] = log_score(idx2, ii, matrix_obs, matrix, &permutation_tmp, N_kw, N_doc, freq_max);

        double score_diff = 0;
        for (int ii = 0; ii < N_obs; ii++)
            score_diff += score_row1[ii];
        for (int ii = 0; ii < N_obs; ii++)
            score_diff -= score_matrix[idx1*N_obs + ii];
        if (idx2 >= 0)
        {
            for (int ii = 0; ii < N_obs; ii++)
                score_diff += score_row2[ii];
            for (int ii = 0; ii < N_obs; ii++)
                score_diff -= score_matrix[idx2*N_obs + ii];
        }

        // compute difference in score, with exponentiation
        score_diff = score_diff / temp;

        if (score_diff < -40)
            score_diff = 0;
        else if (score_diff > 0)
            score_diff = 1.01;
        else
            score_diff = exp(score_diff);

        if (gsl_ran_flat(r, 0, 1) < score_diff)
        {
            // Update the scores
            for (int ii = 0; ii < N_obs; ii++)
                score_matrix[idx1*N_obs + ii] = score_row1[ii];
            for (int ii = 0; ii < N_obs; ii++)
                score_matrix[ii*N_obs + idx1] = score_row1[ii];
            if (idx2 >= 0)
            {
                for (int ii = 0; ii < N_obs; ii++)
                    score_matrix[idx2*N_obs + ii] = score_row2[ii];
                for (int ii = 0; ii < N_obs; ii++)
                    score_matrix[ii*N_obs + idx2] = score_row2[ii];
            }

            // Update the permutation
            permutation_inv[(*permutation)[idx1]] = -1;
            (*permutation)[idx1] = permutation_tmp[idx1];
            permutation_inv[permutation_tmp[idx1]] = idx1;
            if (idx2 >= 0)
            {
                (*permutation)[idx2] = permutation_tmp[idx2];
                permutation_inv[permutation_tmp[idx2]] = idx2;
            }
            N_stuck = 0;
        }
        else
        {
            // Update the permutation
            permutation_tmp[idx1] = (*permutation)[idx1];
            if (idx2 >= 0)
                permutation_tmp[idx2] = (*permutation)[idx2];
            N_stuck += 1;
        }

        temp *= 0.995;
    }

    free(score_matrix);
    free(score_row1);
    free(score_row2);
    gsl_rng_free(r);
}

void print_result(char* output_fileName, int** permutation, int** true_index, int N_obs)
{
    FILE* fp = fopen(output_fileName, "w");
    int count = 0;
    for (int ii = 0; ii < N_obs; ii++)
        if ((*permutation)[ii] == (*true_index)[ii])
            count++;

    fprintf(fp, "%d\n", count);
    fclose(fp);
    printf("Success: %d/%d.\n", count, N_obs);
}

void print_full_result(char* output_fileName, int** permutation, int** true_index, int N_obs)
{
    FILE* fp = fopen(output_fileName, "w");
    int count = 0;
    for (int ii = 0; ii < N_obs; ii++)
        if ((*permutation)[ii] == (*true_index)[ii])
            count++;

    printf("Success: %d/%d.\n", count, N_obs);
    fprintf(fp, "%d\n", count);
    for (int ii = 0; ii < N_obs; ii++)
        fprintf(fp, "%d,%d\n", (*permutation)[ii], (*true_index)[ii]);

    fclose(fp);
}


/**
 * @file square_root.h
 * @brief Updating complex Cholesky factorizations.
 * @author John McDonough and Kenichi Kumatani
 */

#ifndef SQUARE_ROOT_H
#define SQUARE_ROOT_H

#include <stdio.h>
#include <assert.h>

#include <gsl/gsl_block.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_complex.h>
#include <gsl/gsl_complex_math.h>
#include "common/jexception.h"

void cholesky_backsub(const gsl_matrix* A, gsl_vector* x);

void vector_matrix_product(const gsl_vector_complex* vec,
			 const gsl_matrix_complex* mat, gsl_matrix* D);

void make_conjugate_symmetric(gsl_matrix_complex* mat);

void cholesky_forwardsub(const gsl_matrix* A, gsl_vector* x);

void cholesky_forwardsub_complex(const gsl_matrix_complex* lt,
			       const gsl_vector_complex* rhs,
			       gsl_vector_complex* lhs,
			       bool conjugate = false);

void cholesky_backsub_complex(const gsl_matrix_complex* lt,
                              const gsl_vector_complex* rhs,
                              gsl_vector_complex* lhs,
                              bool conjugate = false);

void rank_one_update_cholesky_factor(gsl_matrix_complex* A11,
                                     const double alpha_m,
                                     const gsl_vector_complex* c_m);

void propagate_covar_square_root_real(gsl_matrix* A11,
                                      gsl_matrix* A12,
                                      gsl_matrix* A21,
                                      gsl_matrix* A22, bool flag = false);

void sweep_lower_triangular(gsl_matrix* A, gsl_matrix* B);

void propagate_covar_square_root_step1(gsl_matrix_complex* A12,
                                       gsl_matrix_complex* A22);

void propagate_covar_square_root_step2a(gsl_matrix_complex* A11,
                                        gsl_matrix_complex* A12,
                                        gsl_matrix_complex* A21,
                                        gsl_matrix_complex* A22);

void propagate_covar_square_root_step2b(gsl_matrix_complex* A22);

void propagate_covar_square_root(gsl_matrix_complex* A11,
                                 gsl_matrix_complex* A12,
                                 gsl_matrix_complex* A21,
                                 gsl_matrix_complex* A22);

void propagate_info_square_root(gsl_matrix_complex* sqrt_Pm_inv,
                                gsl_matrix_complex* A12,
                                gsl_vector_complex* a_21,
                                gsl_vector_complex* a_22, bool rankOneA12 = true);

void propagate_info_square_root_step2_rls(gsl_matrix_complex* sqrt_Pm_inv,
                                          gsl_vector_complex* a_12,
                                          gsl_vector_complex* a_21,
                                          gsl_complex a_22);

void propagate_info_square_root_rls(gsl_matrix_complex* sqrt_Pm_inv,
                                    gsl_vector_complex* a_12,
                                    gsl_vector_complex* a_21,
                                    gsl_complex a_22);

void add_diagonal_loading(gsl_matrix_complex* sqrt_Pm_inv, int dim, double wght);

gsl_vector* cholesky_diagonal(gsl_vector* v, const gsl_matrix* m);
gsl_vector* square_diagonal(gsl_vector* v, const gsl_matrix* m);

#endif


#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <glib.h>
#include <omp.h>

// libgsl0-dev
#include <gsl/gsl_math.h>
#include <gsl/gsl_rng.h>
#include <sys/time.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_sort_double.h>

double pi(int n, int batch) {
    const gsl_rng_type * T;
    gsl_rng * r;
    gsl_rng_env_setup();

    T = gsl_rng_default;
    r = gsl_rng_alloc (T);

    int end = (n / batch);
    double sum = 0;

    int i, j;
    // GRand * grand = g_rand_new ();
    //g_rand_double(grand);
    #pragma omp parallel for default(shared)  firstprivate(r) private(j)  reduction (+:sum)
    for (i = 0; i < end; i++) {
        for (j=0; j<batch; j++) {
            double a = gsl_rng_uniform_pos (r);
            double b = gsl_rng_uniform_pos (r);
            double c = (a * a) + (b * b);

            if (c <= 1) {
                sum += c;
            }
        }
    }
    return 8 * sum / n;
}

int main () {
    printf("%0.15f\n", pi(100000000, 1000));
}


#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <math.h>
//#include<ctype.h>
#include<string.h>
#include <gsl/gsl_fit.h>

#include "system_evol.h"
#include "initial_conditions.h"
#include "solver.h"
#include "chaotic_variables.h"

#define Distance(x, y) (sqrt((x) * (x) + (y) * (y)))
#define M 1 //masa de la particula
#define R sqrt(9) // define una region efectiva del potencial de radio R.
#define T 0
#define X 1
#define Y 2
#define VX 3
#define VY 4
#define En 5

extern double dt, t, phi; //declaradas en system_evol.c


/* eigen/gsl_eigen.h
 *
 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2006, 2007 Gerard Jungman, Brian Gough, Patrick Alken
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 3 of the License, or (at
 * your option) any later version.
 *
 * This program is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
 */

#ifndef __GSL_EIGEN_H__
#define __GSL_EIGEN_H__

#include <gsl/gsl_vector.h>
#include <gsl/gsl_matrix.h>

#undef __BEGIN_DECLS
#undef __END_DECLS
#ifdef __cplusplus
# define __BEGIN_DECLS extern "C" {
# define __END_DECLS }
#else
# define __BEGIN_DECLS /* empty */
# define __END_DECLS /* empty */
#endif

__BEGIN_DECLS

typedef struct {
  size_t size;
  double * d;
  double * sd;
} gsl_eigen_symm_workspace;

gsl_eigen_symm_workspace * gsl_eigen_symm_alloc (const size_t n);
void gsl_eigen_symm_free (gsl_eigen_symm_workspace * w);
int gsl_eigen_symm (gsl_matrix * A, gsl_vector * eval, gsl_eigen_symm_workspace * w);

typedef struct {
  size_t size;
  double * d;
  double * sd;
  double * gc;
  double * gs;
} gsl_eigen_symmv_workspace;

gsl_eigen_symmv_workspace * gsl_eigen_symmv_alloc (const size_t n);
void gsl_eigen_symmv_free (gsl_eigen_symmv_workspace * w);
int gsl_eigen_symmv (gsl_matrix * A, gsl_vector * eval, gsl_matrix * evec, gsl_eigen_symmv_workspace * w);

typedef struct {
  size_t size;
  double * d;
  double * sd;
  double * tau;
} gsl_eigen_herm_workspace;

gsl_eigen_herm_workspace * gsl_eigen_herm_alloc (const size_t n);
void gsl_eigen_herm_free (gsl_eigen_herm_workspace * w);
int gsl_eigen_herm (gsl_matrix_complex * A, gsl_vector * eval,
                         gsl_eigen_herm_workspace * w);

typedef struct {
  size_t size;
  double * d;
  double * sd;
  double * tau;
  double * gc;
  double * gs;
} gsl_eigen_hermv_workspace;

gsl_eigen_hermv_workspace * gsl_eigen_hermv_alloc (const size_t n);
void gsl_eigen_hermv_free (gsl_eigen_hermv_workspace * w);
int gsl_eigen_hermv (gsl_matrix_complex * A, gsl_vector * eval,
                           gsl_matrix_complex * evec,
                           gsl_eigen_hermv_workspace * w);

typedef struct {
  size_t size;           /* matrix size */
  size_t max_iterations; /* max iterations since last eigenvalue found */
  size_t n_iter;         /* number of iterations since last eigenvalue found */
  size_t n_evals;        /* number of eigenvalues found so far */

  int compute_t;         /* compute Schur form T = Z^t A Z */

  gsl_matrix *H;         /* pointer to Hessenberg matrix */
  gsl_matrix *Z;         /* pointer to Schur vector matrix */
} gsl_eigen_francis_workspace;

gsl_eigen_francis_workspace * gsl_eigen_francis_alloc (void);
void gsl_eigen_francis_free (gsl_eigen_francis_workspace * w);
void gsl_eigen_francis_T (const int compute_t,
                          gsl_eigen_francis_workspace * w);
int gsl_eigen_francis (gsl_matrix * H, gsl_vector_complex * eval,
                       gsl_eigen_francis_workspace * w);
int gsl_eigen_francis_Z (gsl_matrix * H, gsl_vector_complex * eval,
                         gsl_matrix * Z,
                         gsl_eigen_francis_workspace * w);

typedef struct {
  size_t size;                 /* size of matrices */
  gsl_vector *diag;            /* diagonal matrix elements from balancing */
  gsl_vector *tau;             /* Householder coefficients */
  gsl_matrix *Z;               /* pointer to Z matrix */
  int do_balance;              /* perform balancing transformation? */
  size_t n_evals;              /* number of eigenvalues found */

  gsl_eigen_francis_workspace *francis_workspace_p;
} gsl_eigen_nonsymm_workspace;

gsl_eigen_nonsymm_workspace * gsl_eigen_nonsymm_alloc (const size_t n);
void gsl_eigen_nonsymm_free (gsl_eigen_nonsymm_workspace * w);
void gsl_eigen_nonsymm_params (const int compute_t, const int balance,
                               gsl_eigen_nonsymm_workspace *w);
int gsl_eigen_nonsymm (gsl_matrix * A, gsl_vector_complex * eval,
                       gsl_eigen_nonsymm_workspace * w);
int gsl_eigen_nonsymm_Z (gsl_matrix * A, gsl_vector_complex * eval,
                         gsl_matrix * Z, gsl_eigen_nonsymm_workspace * w);

typedef struct {
  size_t size;                 /* size of matrices */
  gsl_vector *work;            /* scratch workspace */
  gsl_vector *work2;           /* scratch workspace */
  gsl_vector *work3;           /* scratch workspace */

  gsl_matrix *Z;               /* pointer to Schur vectors */

  gsl_eigen_nonsymm_workspace *nonsymm_workspace_p;
} gsl_eigen_nonsymmv_workspace;

gsl_eigen_nonsymmv_workspace * gsl_eigen_nonsymmv_alloc (const size_t n);
void gsl_eigen_nonsymmv_free (gsl_eigen_nonsymmv_workspace * w);
void gsl_eigen_nonsymmv_params (const int balance,
                                gsl_eigen_nonsymmv_workspace *w);
int gsl_eigen_nonsymmv (gsl_matrix * A, gsl_vector_complex * eval,
                        gsl_matrix_complex * evec,
                        gsl_eigen_nonsymmv_workspace * w);
int gsl_eigen_nonsymmv_Z (gsl_matrix * A, gsl_vector_complex * eval,
                          gsl_matrix_complex * evec, gsl_matrix * Z,
                          gsl_eigen_nonsymmv_workspace * w);

typedef struct {
  size_t size;            /* size of matrices */
  gsl_eigen_symm_workspace *symm_workspace_p;
} gsl_eigen_gensymm_workspace;

gsl_eigen_gensymm_workspace * gsl_eigen_gensymm_alloc (const size_t n);
void gsl_eigen_gensymm_free (gsl_eigen_gensymm_workspace * w);
int gsl_eigen_gensymm (gsl_matrix * A, gsl_matrix * B,
                       gsl_vector * eval, gsl_eigen_gensymm_workspace * w);
int gsl_eigen_gensymm_standardize (gsl_matrix * A, const gsl_matrix * B);

typedef struct {
  size_t size;            /* size of matrices */
  gsl_eigen_symmv_workspace *symmv_workspace_p;
} gsl_eigen_gensymmv_workspace;

gsl_eigen_gensymmv_workspace * gsl_eigen_gensymmv_alloc (const size_t n);
void gsl_eigen_gensymmv_free (gsl_eigen_gensymmv_workspace * w);
int gsl_eigen_gensymmv (gsl_matrix * A, gsl_matrix * B,
                        gsl_vector * eval, gsl_matrix * evec,
                        gsl_eigen_gensymmv_workspace * w);

typedef struct {
  size_t size;            /* size of matrices */
  gsl_eigen_herm_workspace *herm_workspace_p;
} gsl_eigen_genherm_workspace;

gsl_eigen_genherm_workspace * gsl_eigen_genherm_alloc (const size_t n);
void gsl_eigen_genherm_free (gsl_eigen_genherm_workspace * w);
int gsl_eigen_genherm (gsl_matrix_complex * A, gsl_matrix_complex * B,
                       gsl_vector * eval, gsl_eigen_genherm_workspace * w);
int gsl_eigen_genherm_standardize (gsl_matrix_complex * A,
                                   const gsl_matrix_complex * B);

typedef struct {
  size_t size;            /* size of matrices */
  gsl_eigen_hermv_workspace *hermv_workspace_p;
} gsl_eigen_genhermv_workspace;

gsl_eigen_genhermv_workspace * gsl_eigen_genhermv_alloc (const size_t n);
void gsl_eigen_genhermv_free (gsl_eigen_genhermv_workspace * w);
int gsl_eigen_genhermv (gsl_matrix_complex * A, gsl_matrix_complex * B,
                        gsl_vector * eval, gsl_matrix_complex * evec,
                        gsl_eigen_genhermv_workspace * w);

typedef struct {
  size_t size;            /* size of matrices */
  gsl_vector *work;       /* scratch workspace */

  size_t n_evals;         /* number of eigenvalues found */
  size_t max_iterations;  /* maximum QZ iterations allowed */
  size_t n_iter;          /* number of iterations since last eigenvalue found */
  double eshift;          /* exceptional shift counter */

  int needtop;            /* need to compute top index? */

  double atol;            /* tolerance for splitting A matrix */
  double btol;            /* tolerance for splitting B matrix */

  double ascale;          /* scaling factor for shifts */
  double bscale;          /* scaling factor for shifts */

  gsl_matrix *H;          /* pointer to hessenberg matrix */
  gsl_matrix *R;          /* pointer to upper triangular matrix */

  int compute_s;          /* compute generalized Schur form S */
  int compute_t;          /* compute generalized Schur form T */

  gsl_matrix *Q;          /* pointer to left Schur vectors */
  gsl_matrix *Z;          /* pointer to right Schur vectors */
} gsl_eigen_gen_workspace;

gsl_eigen_gen_workspace * gsl_eigen_gen_alloc (const size_t n);
void gsl_eigen_gen_free (gsl_eigen_gen_workspace * w);
void gsl_eigen_gen_params (const int compute_s, const int compute_t,
                           const int balance, gsl_eigen_gen_workspace * w);
int gsl_eigen_gen (gsl_matrix * A, gsl_matrix * B,
                   gsl_vector_complex * alpha, gsl_vector * beta,
                   gsl_eigen_gen_workspace * w);
int gsl_eigen_gen_QZ (gsl_matrix * A, gsl_matrix * B,
                      gsl_vector_complex * alpha, gsl_vector * beta,
                      gsl_matrix * Q, gsl_matrix * Z,
                      gsl_eigen_gen_workspace * w);

typedef struct {
  size_t size;            /* size of matrices */

  gsl_vector *work1;      /* 1-norm of columns of A */
  gsl_vector *work2;      /* 1-norm of columns of B */
  gsl_vector *work3;      /* real part of eigenvector */
  gsl_vector *work4;      /* imag part of eigenvector */
  gsl_vector *work5;      /* real part of back-transformed eigenvector */
  gsl_vector *work6;      /* imag part of back-transformed eigenvector */

  gsl_matrix *Q;          /* pointer to left Schur vectors */
  gsl_matrix *Z;          /* pointer to right Schur vectors */

  gsl_eigen_gen_workspace *gen_workspace_p;
} gsl_eigen_genv_workspace;

gsl_eigen_genv_workspace * gsl_eigen_genv_alloc (const size_t n);
void gsl_eigen_genv_free (gsl_eigen_genv_workspace * w);
int gsl_eigen_genv (gsl_matrix * A, gsl_matrix * B,
                    gsl_vector_complex * alpha, gsl_vector * beta,
                    gsl_matrix_complex * evec,
                    gsl_eigen_genv_workspace * w);
int gsl_eigen_genv_QZ (gsl_matrix * A, gsl_matrix * B,
                       gsl_vector_complex * alpha, gsl_vector * beta,
                       gsl_matrix_complex * evec,
                       gsl_matrix * Q, gsl_matrix * Z,
                       gsl_eigen_genv_workspace * w);

typedef enum {
  GSL_EIGEN_SORT_VAL_ASC,
  GSL_EIGEN_SORT_VAL_DESC,
  GSL_EIGEN_SORT_ABS_ASC,
  GSL_EIGEN_SORT_ABS_DESC
}
gsl_eigen_sort_t;

/* Sort eigensystem results based on eigenvalues.
 * Sorts in order of increasing value or increasing
 * absolute value.
 *
 * exceptions: GSL_EBADLEN
 */

int gsl_eigen_symmv_sort(gsl_vector * eval, gsl_matrix * evec,
                         gsl_eigen_sort_t sort_type);

int gsl_eigen_hermv_sort(gsl_vector * eval, gsl_matrix_complex * evec,
                         gsl_eigen_sort_t sort_type);

int gsl_eigen_nonsymmv_sort(gsl_vector_complex * eval,
                            gsl_matrix_complex * evec,
                            gsl_eigen_sort_t sort_type);

int gsl_eigen_gensymmv_sort (gsl_vector * eval, gsl_matrix * evec,
                             gsl_eigen_sort_t sort_type);

int gsl_eigen_genhermv_sort (gsl_vector * eval, gsl_matrix_complex * evec,
                             gsl_eigen_sort_t sort_type);

int gsl_eigen_genv_sort (gsl_vector_complex * alpha, gsl_vector * beta,
                         gsl_matrix_complex * evec,
                         gsl_eigen_sort_t sort_type);

/* Prototypes for the schur module */

int gsl_schur_gen_eigvals(const gsl_matrix *A, const gsl_matrix *B,
                          double *wr1, double *wr2, double *wi,
                          double *scale1, double *scale2);

int gsl_schur_solve_equation(double ca, const gsl_matrix *A, double z,
                             double d1, double d2, const gsl_vector *b,
                             gsl_vector *x, double *s, double *xnorm,
                             double smin);

int gsl_schur_solve_equation_z(double ca, const gsl_matrix *A,
                               gsl_complex *z, double d1, double d2,
                               const gsl_vector_complex *b,
                               gsl_vector_complex *x, double *s,
                               double *xnorm, double smin);

/* The following functions are obsolete: */

/* Eigensolve by Jacobi Method
 *
 * The data in the matrix input is destroyed.
 *
 * exceptions:
 */
int
gsl_eigen_jacobi(gsl_matrix * matrix,
                      gsl_vector * eval,
                      gsl_matrix * evec,
                      unsigned int max_rot,
                      unsigned int * nrot);

/* Invert by Jacobi Method
 *
 * exceptions:
 */
int
gsl_eigen_invert_jacobi(const gsl_matrix * matrix,
                             gsl_matrix * ainv,
                             unsigned int max_rot);

__END_DECLS

#endif /* __GSL_EIGEN_H__ */


#include "example_z.h"
#include <stdlib.h>
#include <lapacke.h>

void random_zvec(int len, BBLAS_Complex64_t *vec)
{
//	BBLAS_Complex64_t *work =
//		(BBLAS_Complex64_t*) malloc(sizeof(BBLAS_Complex64_t)*len);
//	int info = 0;
	double scalar = 1.0;
	int seed = 2;
	int zero = 0;
	int one = 1;
	int lenm1 = len-1;
	int colmaj = BblasColMajor;
	LAPACKE_zlagge(colmaj, len, one, lenm1, zero, &scalar, vec, len, &seed);
}

void random_mat(int m, int n, BBLAS_Complex64_t *mat)
{
//	BBLAS_Complex64_t *work = malloc(sizeof(BBLAS_Complex64_t)*m*n);
//	int info = 0;
	double scalar = 1.0;
	int seed = 2;
	int mm1 = m-1;
	int nn1 = n-1;
	int colmaj = BblasColMajor;
	LAPACKE_zlagge(colmaj, m, n, mm1, nn1, &scalar, mat, m, &seed);
}

BBLAS_Complex64_t randz()
{
	BBLAS_Complex64_t val;
	random_mat(1, 1, &val);
	return val;
}

void set_params_fixed_zgemv(struct zgemv_batchf_example *zgemv_example)
{
	int batch_count = rand() % 50;
	zgemv_example->batch_count = batch_count;
	zgemv_example->trans = rand() % 3+111;
	int m = rand() % 200;
	zgemv_example->m = m;
	int n = rand() % 200;
	zgemv_example->n = n;
	zgemv_example->alpha = randz();
	/* arrayA */
	BBLAS_Complex64_t **arrayA =
		(BBLAS_Complex64_t**) malloc(sizeof(BBLAS_Complex64_t*)*batch_count);
	for (int i = 0; i < batch_count; i++)
	{
		arrayA[i] = (BBLAS_Complex64_t*) malloc(sizeof(BBLAS_Complex64_t)*m*n);
		random_mat(m, n, arrayA[i]);
	}
	zgemv_example->arrayA = arrayA;
	zgemv_example->lda = zgemv_example->m;
	/* arrayx */
	BBLAS_Complex64_t **arrayx =
		(BBLAS_Complex64_t**) malloc(sizeof(BBLAS_Complex64_t*)*batch_count);
	int curdim;
	if (zgemv_example->trans == BblasNoTrans)
	{
		curdim = n;
	}
	else
	{
		curdim = m;
	}
	for (int i = 0; i < batch_count; i++)
	{
		arrayx[i] =
			(BBLAS_Complex64_t*) malloc(sizeof(BBLAS_Complex64_t)*curdim);
		random_zvec(curdim, arrayx[i]);
	}
	zgemv_example->arrayx = arrayx;
	zgemv_example->incx = 1;
	zgemv_example->beta = randz();
	/* arrayy */
	BBLAS_Complex64_t **arrayy =
		(BBLAS_Complex64_t**) malloc(sizeof(BBLAS_Complex64_t*)*batch_count);
	if (zgemv_example->trans == BblasNoTrans)
	{
		curdim = m;
	}
	else
	{
		curdim = n;
	}
	for (int i = 0; i < batch_count; i++)
	{
		arrayy[i] =
			(BBLAS_Complex64_t*) malloc(sizeof(BBLAS_Complex64_t)*curdim);
		random_zvec(curdim, arrayy[i]);
	}
	zgemv_example->arrayy = arrayy;
	zgemv_example->incy = 1;
}

void set_params_variable_zgemv(struct zgemv_batchv_example *zgemv_example)
{
	int batch_count = rand() % 50;
	zgemv_example->batch_count = batch_count;
	int *trans = (int*) malloc(sizeof(int)*batch_count);
	for(int i = 0; i < batch_count; i++)
	{
		trans[i] = rand() % 3 + 111;
	}
	zgemv_example->trans = (enum BBLAS_TRANS*) trans;
	int *m = (int*) malloc(sizeof(int)*batch_count);
	for (int i = 0; i < batch_count; i++)
	{
		m[i] = rand() % 200;
	}
	zgemv_example->m = m;
	int *n = (int*) malloc(sizeof(int)*batch_count);
	for (int i = 0; i < batch_count; i++)
	{
		n[i] = rand() % 200;
	}
	zgemv_example->n = n;
	BBLAS_Complex64_t *alpha = malloc(sizeof(BBLAS_Complex64_t)*batch_count);
	for (int i = 0; i < batch_count; i++)
	{
		alpha[i] = randz();
	}
	zgemv_example->alpha = alpha;
	/* arrayA */
	BBLAS_Complex64_t **arrayA =
		(BBLAS_Complex64_t**) malloc(sizeof(BBLAS_Complex64_t*)*batch_count);
	for (int i = 0; i < batch_count; i++)
	{
		arrayA[i] = (BBLAS_Complex64_t*) malloc(sizeof(BBLAS_Complex64_t)*m[i]*n[i]);
		random_mat(m[i], n[i], arrayA[i]);
	}
	zgemv_example->arrayA = arrayA;
	int *lda = (int*) malloc(sizeof(int)*batch_count);
	for (int i = 0; i < batch_count; i++)
	{
		lda[i] = m[i];
	}
	zgemv_example->lda = lda;
	/* arrayx */
	BBLAS_Complex64_t **arrayx =
		(BBLAS_Complex64_t**) malloc(sizeof(BBLAS_Complex64_t*)*batch_count);
	int curdim;
	for (int i = 0; i < batch_count; i++)
	{
		if (trans[i] == BblasNoTrans)
		{
			curdim = n[i];
		}
		else
		{
			curdim = m[i];
		}
		arrayx[i] =
			(BBLAS_Complex64_t*) malloc(sizeof(BBLAS_Complex64_t)*curdim);
		random_zvec(curdim, arrayx[i]);
	}
	zgemv_example->arrayx = arrayx;
	int *incx = (int*) malloc(sizeof(int)*batch_count);
	for (int i = 0; i < batch_count; i++)
	{
		incx[i] = 1;
	}
	zgemv_example->incx = incx;
	BBLAS_Complex64_t *beta = malloc(sizeof(BBLAS_Complex64_t)*batch_count);
	for (int i = 0; i < batch_count; i++)
	{
		beta[i] = randz();
	}
	zgemv_example->beta = beta;
	/* arrayy */
	BBLAS_Complex64_t **arrayy =
		(BBLAS_Complex64_t**) malloc(sizeof(BBLAS_Complex64_t*)*batch_count);
	for (int i = 0; i < batch_count; i++)
	{
		if (trans[i] == BblasNoTrans)
		{
			curdim = m[i];
		}
		else
		{
			curdim = n[i];
		}
		arrayy[i] =
			(BBLAS_Complex64_t*) malloc(sizeof(BBLAS_Complex64_t)*curdim);
		random_zvec(curdim, arrayy[i]);
	}
	zgemv_example->arrayy = arrayy;
	int *incy = (int*) malloc(sizeof(int)*batch_count);
	for (int i = 0; i < batch_count; i++)
	{
		incy[i] = 1;
	}
	zgemv_example->incy = incy;
}

void set_params_fixed_zgemm(struct zgemm_batchf_example *zgemm_example)
{
    int i;
    int batch_count;
    int m;
    int n;
    int k;
    int lda;
    int ldb;

	batch_count = rand() % 5;
	zgemm_example->batch_count = batch_count;
	zgemm_example->transA = rand() % 3+111;
	zgemm_example->transB = rand() % 3+111;
	m = rand() % 20;
	zgemm_example->m = m;
	n = rand() % 20;
	zgemm_example->n = n;
	k = rand() % 20;
	zgemm_example->k = k;
	zgemm_example->alpha = randz();
	zgemm_example->beta = randz();

    /* arrayA */
	BBLAS_Complex64_t **arrayA =
		(BBLAS_Complex64_t**) malloc(sizeof(BBLAS_Complex64_t*)*batch_count);
	for (i = 0; i < batch_count; i++)
	{
		arrayA[i] = (BBLAS_Complex64_t*) malloc(sizeof(BBLAS_Complex64_t)*m*k);
		random_mat(m, k, arrayA[i]);
	}
	zgemm_example->arrayA = arrayA;
	if (zgemm_example->transA == BblasNoTrans)
	{
		lda = m;
	}
	else
	{
		lda = k;
	}
	zgemm_example->lda = lda;

    /* arrayB */
	BBLAS_Complex64_t **arrayB =
		(BBLAS_Complex64_t**) malloc(sizeof(BBLAS_Complex64_t*)*batch_count);
	for (i = 0; i < batch_count; i++)
	{
		arrayB[i] = (BBLAS_Complex64_t*) malloc(sizeof(BBLAS_Complex64_t)*k*n);
		random_mat(k, n, arrayB[i]);
	}
	zgemm_example->arrayB = arrayB;
	if (zgemm_example->transB == BblasNoTrans)
	{
		ldb = k;
	}
	else
	{
		ldb = n;
	}
	zgemm_example->ldb = ldb;

    /* arrayC */
	BBLAS_Complex64_t **arrayC =
		(BBLAS_Complex64_t**) malloc(sizeof(BBLAS_Complex64_t*)*batch_count);
	for (i = 0; i < batch_count; i++)
	{
		arrayC[i] = (BBLAS_Complex64_t*) malloc(sizeof(BBLAS_Complex64_t)*m*n);
		random_mat(m, n, arrayC[i]);
	}
	zgemm_example->arrayC = arrayC;
	zgemm_example->ldc = m;
}

// One pointer (op) approach

void set_params_fixed_zgemm_stride(struct zgemm_batchf_example_stride *zgemm_example)
{
    int i;
    int batch_count;
    int m;
    int n;
    int k;
    int lda;
    int ldb;
    enum BBLAS_TRANS transA;
    enum BBLAS_TRANS transB;

	batch_count = rand() % 5;
	zgemm_example->batch_count = batch_count;
    transA = BblasNoTrans;
    zgemm_example->transA = transA;
	transB = BblasNoTrans;
    zgemm_example->transB = transB;
	m = rand() % 20;
	zgemm_example->m = m;
	n = rand() % 20;
	zgemm_example->n = n;
	k = rand() % 20;
	zgemm_example->k = k;
	zgemm_example->alpha = randz();
	zgemm_example->beta = randz();

    /* arrayA */
	BBLAS_Complex64_t *arrayA =
		(BBLAS_Complex64_t*) malloc(sizeof(BBLAS_Complex64_t)*batch_count*m*k);
	for (i = 0; i < batch_count; i++)
	{
		random_mat(m, k, &arrayA[i*m*k]);
	}
	zgemm_example->arrayA = arrayA;
	if (zgemm_example->transA == BblasNoTrans)
	{
		lda = m;
	}
	else
	{
		lda = k;
	}
	zgemm_example->lda = lda;
	zgemm_example->strideA = m*k;

    /* arrayB */
	BBLAS_Complex64_t *arrayB =
		(BBLAS_Complex64_t*) malloc(sizeof(BBLAS_Complex64_t*)*batch_count*k*n);
	for (i = 0; i < batch_count; i++)
	{
		random_mat(k, n, &arrayB[i*k*n]);
	}
	zgemm_example->arrayB = arrayB;
	if (zgemm_example->transB == BblasNoTrans)
	{
		ldb = k;
	}
	else
	{
		ldb = n;
	}
	zgemm_example->ldb = ldb;
	zgemm_example->strideB = k*n;

    /* arrayC */
	BBLAS_Complex64_t *arrayC =
		(BBLAS_Complex64_t*) malloc(sizeof(BBLAS_Complex64_t*)*batch_count*m*n);
	for (i = 0; i < batch_count; i++)
	{
		random_mat(m, n, &arrayC[i*m*n]);
	}
	zgemm_example->arrayC = arrayC;
	zgemm_example->ldc = m;
	zgemm_example->strideC = m*n;
}

void set_params_variable_zgemm(struct zgemm_batchv_example *zgemm_example)
{
    int i;
    int batch_count;
    int lda;
    int ldb;

    batch_count = rand() % 5;
    zgemm_example->batch_count = batch_count;
	for (i = 0; i < batch_count; i++)
	{
	    zgemm_example->transA[i] = rand() % 3+111;
	    zgemm_example->transB[i] = rand() % 3+111;
	    zgemm_example->m[i] = rand() % 20;
	    zgemm_example->n[i] = rand() % 20;
	    zgemm_example->k[i] = rand() % 20;
	    zgemm_example->alpha[i] = randz();
	    zgemm_example->beta[i] = randz();
    }

    /* arrayA */
	BBLAS_Complex64_t **arrayA =
		(BBLAS_Complex64_t**) malloc(sizeof(BBLAS_Complex64_t*)*batch_count);
	for (i = 0; i < batch_count; i++)
	{
		arrayA[i] = (BBLAS_Complex64_t*) malloc(sizeof(BBLAS_Complex64_t)*
                zgemm_example->m[i]*zgemm_example->k[i]);
		random_mat(zgemm_example->m[i], zgemm_example->k[i], arrayA[i]);
	    if (zgemm_example->transA[i] == BblasNoTrans)
	    {
		    lda = zgemm_example->m[i];
	    }
	    else
	    {
		    lda = zgemm_example->k[i];
	    }
	    zgemm_example->lda[i] = lda;
	}
	zgemm_example->arrayA = arrayA;

    /* arrayB */
	BBLAS_Complex64_t **arrayB =
		(BBLAS_Complex64_t**) malloc(sizeof(BBLAS_Complex64_t*)*batch_count);
	for (i = 0; i < batch_count; i++)
	{
		arrayB[i] = (BBLAS_Complex64_t*) malloc(sizeof(BBLAS_Complex64_t)*
                zgemm_example->k[i]*zgemm_example->n[i]);
		random_mat(zgemm_example->k[i], zgemm_example->n[i], arrayB[i]);
        if (zgemm_example->transB[i] == BblasNoTrans)
	    {
		    ldb = zgemm_example->k[i];
	    }
	    else
	    {
		    ldb = zgemm_example->n[i];
	    }
	    zgemm_example->ldb[i] = ldb;
	}
	zgemm_example->arrayB = arrayB;

    /* arrayC */
	BBLAS_Complex64_t **arrayC =
		(BBLAS_Complex64_t**) malloc(sizeof(BBLAS_Complex64_t*)*batch_count);
	for (i = 0; i < batch_count; i++)
	{
		arrayC[i] = (BBLAS_Complex64_t*) malloc(sizeof(BBLAS_Complex64_t)*
                zgemm_example->m[i]*zgemm_example->n[i]);
		random_mat(zgemm_example->m[i], zgemm_example->n[i], arrayC[i]);
	    zgemm_example->ldc[i] = zgemm_example->m[i];
	}
	zgemm_example->arrayC = arrayC;

}