/usr/include/boost/math/tools
Edit: /usr/include/boost/math/tools/bivariate_statistics.hpp (2858B)
// (C) Copyright Nick Thompson 2018.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_MATH_TOOLS_BIVARIATE_STATISTICS_HPP
#define BOOST_MATH_TOOLS_BIVARIATE_STATISTICS_HPP
#include
#include
#include
#include
BOOST_HEADER_DEPRECATED("");
namespace boost{ namespace math{ namespace tools {
template
auto means_and_covariance(Container const & u, Container const & v)
{
using Real = typename Container::value_type;
using std::size;
BOOST_ASSERT_MSG(size(u) == size(v), "The size of each vector must be the same to compute covariance.");
BOOST_ASSERT_MSG(size(u) > 0, "Computing covariance requires at least one sample.");
// See Equation III.9 of "Numerically Stable, Single-Pass, Parallel Statistics Algorithms", Bennet et al.
Real cov = 0;
Real mu_u = u[0];
Real mu_v = v[0];
for(size_t i = 1; i < size(u); ++i)
{
Real u_tmp = (u[i] - mu_u)/(i+1);
Real v_tmp = v[i] - mu_v;
cov += i*u_tmp*v_tmp;
mu_u = mu_u + u_tmp;
mu_v = mu_v + v_tmp/(i+1);
}
return std::make_tuple(mu_u, mu_v, cov/size(u));
}
template
auto covariance(Container const & u, Container const & v)
{
auto [mu_u, mu_v, cov] = boost::math::tools::means_and_covariance(u, v);
return cov;
}
template
auto correlation_coefficient(Container const & u, Container const & v)
{
using Real = typename Container::value_type;
using std::size;
BOOST_ASSERT_MSG(size(u) == size(v), "The size of each vector must be the same to compute covariance.");
BOOST_ASSERT_MSG(size(u) > 0, "Computing covariance requires at least two samples.");
Real cov = 0;
Real mu_u = u[0];
Real mu_v = v[0];
Real Qu = 0;
Real Qv = 0;
for(size_t i = 1; i < size(u); ++i)
{
Real u_tmp = u[i] - mu_u;
Real v_tmp = v[i] - mu_v;
Qu = Qu + (i*u_tmp*u_tmp)/(i+1);
Qv = Qv + (i*v_tmp*v_tmp)/(i+1);
cov += i*u_tmp*v_tmp/(i+1);
mu_u = mu_u + u_tmp/(i+1);
mu_v = mu_v + v_tmp/(i+1);
}
// If both datasets are constant, then they are perfectly correlated.
if (Qu == 0 && Qv == 0)
{
return Real(1);
}
// If one dataset is constant and the other isn't, then they have no correlation:
if (Qu == 0 || Qv == 0)
{
return Real(0);
}
// Make sure rho in [-1, 1], even in the presence of numerical noise.
Real rho = cov/sqrt(Qu*Qv);
if (rho > 1) {
rho = 1;
}
if (rho < -1) {
rho = -1;
}
return rho;
}
}}}
#endif