source: trunk/yat/statistics/utility.cc @ 3745

// $Id: utility.cc 3745 2018-07-27 00:27:02Z peter $

/*
  Copyright (C) 2004 Jari Häkkinen, Peter Johansson
  Copyright (C) 2005 Peter Johansson
  Copyright (C) 2006, 2007, 2008 Jari Häkkinen, Peter Johansson
  Copyright (C) 2009, 2011, 2012 Peter Johansson

  This file is part of the yat library, http://dev.thep.lu.se/yat

  The yat library 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.

  The yat library 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 yat. If not, see <http://www.gnu.org/licenses/>.
*/

#include <config.h>

#include "utility.h"

#include "yat/normalizer/Centralizer.h"
#include "yat/normalizer/ColumnNormalizer.h"

#include <gsl/gsl_cdf.h>
#include <gsl/gsl_randist.h>
#include <gsl/gsl_statistics_double.h>

#include <algorithm>
#include <cassert>
#include <cmath>
#include <limits>

namespace theplu {
namespace yat {
namespace statistics {

  double cdf_hypergeometric_P(unsigned int k, unsigned int n1,
                              unsigned int n2, unsigned int t)
  {
    return gsl_cdf_hypergeometric_P(k, n1, n2, t);
  }


  utility::Matrix correlation(utility::Matrix x)
  {
    using utility::Matrix;
    size_t n = x.columns();
    // centralise
    normalizer::ColumnNormalizer<normalizer::Centralizer<> > normalizer;
    normalizer(x, x);

    Matrix cov(n, n);
    for (size_t i=0; i<n; ++i) {
      for (size_t j=i; j<n; ++j) {
        cov(i, j) = x.column_const_view(i) * x.column_const_view(j);
        cov(j, i) = cov(i, j);
      }
    }

    utility::Vector stddev(n);
    for (size_t i=0; i<n; ++i)
      stddev(i) = std::sqrt(cov(i, i));

    Matrix corr(cov);
    for (size_t i=0; i<n; ++i) {
      corr(i, i) = 1.0;
      for (size_t j=0; j<i; ++j) {
        corr(i, j) = cov(i, j) / (stddev(i) * stddev(j));
        corr(j, i) = corr(i, j);
      }
    }
    return corr;
  }


  double pearson_p_value(double r, unsigned int n)
  {
    assert(n>=2);
    if (n<=2)
      return std::numeric_limits<double>::quiet_NaN();
    if (r>=1.0)
      return 0.0;
    if (r<=-1.0)
      return 1.0;
    return gsl_cdf_tdist_Q(r*std::sqrt((n-2)/(1-r*r)), n-2);
  }


  double kurtosis(const utility::VectorBase& v)
  {
    const gsl_vector* gvp=v.gsl_vector_p();
    return gsl_stats_kurtosis(gvp->data,gvp->stride,gvp->size);
  }


  double skewness(const utility::VectorBase& v)
  {
    const gsl_vector* gvp=v.gsl_vector_p();
    return gsl_stats_skew(gvp->data,gvp->stride,gvp->size);
  }

}}} // of namespace statistics, yat, and theplu