ceph/src/boost/boost/math/statistics/bivariate_statistics.hpp

   1 //  (C) Copyright Nick Thompson 2018.
   2 //  Use, modification and distribution are subject to the
   3 //  Boost Software License, Version 1.0. (See accompanying file
   4 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
   5
   6 #ifndef BOOST_MATH_STATISTICS_BIVARIATE_STATISTICS_HPP
   7 #define BOOST_MATH_STATISTICS_BIVARIATE_STATISTICS_HPP
   8
   9 #include <iterator>
  10 #include <tuple>
  11 #include <boost/assert.hpp>
  12
  13
  14 namespace boost{ namespace math{ namespace statistics {
  15
  16 template<class Container>
  17 auto means_and_covariance(Container const & u, Container const & v)
  18 {
  19     using Real = typename Container::value_type;
  20     using std::size;
  21     BOOST_ASSERT_MSG(size(u) == size(v), "The size of each vector must be the same to compute covariance.");
  22     BOOST_ASSERT_MSG(size(u) > 0, "Computing covariance requires at least one sample.");
  23
  24     // See Equation III.9 of "Numerically Stable, Single-Pass, Parallel Statistics Algorithms", Bennet et al.
  25     Real cov = 0;
  26     Real mu_u = u[0];
  27     Real mu_v = v[0];
  28
  29     for(size_t i = 1; i < size(u); ++i)
  30     {
  31         Real u_tmp = (u[i] - mu_u)/(i+1);
  32         Real v_tmp = v[i] - mu_v;
  33         cov += i*u_tmp*v_tmp;
  34         mu_u = mu_u + u_tmp;
  35         mu_v = mu_v + v_tmp/(i+1);
  36     }
  37
  38     return std::make_tuple(mu_u, mu_v, cov/size(u));
  39 }
  40
  41 template<class Container>
  42 auto covariance(Container const & u, Container const & v)
  43 {
  44     auto [mu_u, mu_v, cov] = boost::math::statistics::means_and_covariance(u, v);
  45     return cov;
  46 }
  47
  48 template<class Container>
  49 auto correlation_coefficient(Container const & u, Container const & v)
  50 {
  51     using Real = typename Container::value_type;
  52     using std::size;
  53     BOOST_ASSERT_MSG(size(u) == size(v), "The size of each vector must be the same to compute covariance.");
  54     BOOST_ASSERT_MSG(size(u) > 0, "Computing covariance requires at least two samples.");
  55
  56     Real cov = 0;
  57     Real mu_u = u[0];
  58     Real mu_v = v[0];
  59     Real Qu = 0;
  60     Real Qv = 0;
  61
  62     for(size_t i = 1; i < size(u); ++i)
  63     {
  64         Real u_tmp = u[i] - mu_u;
  65         Real v_tmp = v[i] - mu_v;
  66         Qu = Qu + (i*u_tmp*u_tmp)/(i+1);
  67         Qv = Qv + (i*v_tmp*v_tmp)/(i+1);
  68         cov += i*u_tmp*v_tmp/(i+1);
  69         mu_u = mu_u + u_tmp/(i+1);
  70         mu_v = mu_v + v_tmp/(i+1);
  71     }
  72
  73     // If both datasets are constant, then they are perfectly correlated.
  74     if (Qu == 0 && Qv == 0)
  75     {
  76         return Real(1);
  77     }
  78     // If one dataset is constant and the other isn't, then they have no correlation:
  79     if (Qu == 0 || Qv == 0)
  80     {
  81         return Real(0);
  82     }
  83
  84     // Make sure rho in [-1, 1], even in the presence of numerical noise.
  85     Real rho = cov/sqrt(Qu*Qv);
  86     if (rho > 1) {
  87         rho = 1;
  88     }
  89     if (rho < -1) {
  90         rho = -1;
  91     }
  92     return rho;
  93 }
  94
  95 }}}
  96 #endif