add boost on mac

macx64/include/boost/math/tools/bivariate_statistics.hpp

@@ -0,0 +1,97 @@
+//  (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 <iterator>
+#include <tuple>
+#include <boost/assert.hpp>
+#include <boost/multiprecision/detail/number_base.hpp>
+
+
+namespace boost{ namespace math{ namespace tools {
+
+template<class Container>
+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<class Container>
+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<class Container>
+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