text: /*
   *  (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)
   */
  
  #include <iostream>
  #include <iomanip>
  #include <vector>
  #include <array>
  #include <forward_list>
  #include <algorithm>
  #include <random>
  #include <boost/core/lightweight_test.hpp>
  #include <boost/numeric/ublas/vector.hpp>
  #include <boost/math/constants/constants.hpp>
  #include <boost/math/statistics/univariate_statistics.hpp>
  #include <boost/math/statistics/bivariate_statistics.hpp>
  #include <boost/multiprecision/cpp_bin_float.hpp>
  #include <boost/multiprecision/cpp_complex.hpp>
  
  using boost::multiprecision::cpp_bin_float_50;
  using boost::multiprecision::cpp_complex_50;
  
  /*
   * Test checklist:
   * 1) Does it work with multiprecision?
   * 2) Does it work with .cbegin()/.cend() if the data is not altered?
   * 3) Does it work with ublas and std::array? (Checking Eigen and Armadillo will make the CI system really unhappy.)
   * 4) Does it work with std::forward_list if a forward iterator is all that is required?
   * 5) Does it work with complex data if complex data is sensible?
   */
  
  using  boost::math::statistics::means_and_covariance;
  using  boost::math::statistics::covariance;
  
  template<class Real>
  void test_covariance()
  {
      std::cout << std::setprecision(std::numeric_limits<Real>::digits10+1);
      Real tol = std::numeric_limits<Real>::epsilon();
      using std::abs;
  
      // Covariance of a single thing is zero:
      std::array<Real, 1> u1{8};
      std::array<Real, 1> v1{17};
      auto [mu_u1, mu_v1, cov1] = means_and_covariance(u1, v1);
  
      BOOST_TEST(abs(cov1) < tol);
      BOOST_TEST(abs(mu_u1 - 8) < tol);
      BOOST_TEST(abs(mu_v1 - 17) < tol);
  
  
      std::array<Real, 2> u2{8, 4};
      std::array<Real, 2> v2{3, 7};
      auto [mu_u2, mu_v2, cov2] = means_and_covariance(u2, v2);
  
      BOOST_TEST(abs(cov2+4) < tol);
      BOOST_TEST(abs(mu_u2 - 6) < tol);
      BOOST_TEST(abs(mu_v2 - 5) < tol);
  
      std::vector<Real> u3{1,2,3};
      std::vector<Real> v3{1,1,1};
  
      auto [mu_u3, mu_v3, cov3] = means_and_covariance(u3, v3);
  
      // Since v is constant, covariance(u,v) = 0 against everything any u:
      BOOST_TEST(abs(cov3) < tol);
      BOOST_TEST(abs(mu_u3 - 2) < tol);
      BOOST_TEST(abs(mu_v3 - 1) < tol);
      // Make sure we pull the correct symbol out of means_and_covariance:
      cov3 = covariance(u3, v3);
      BOOST_TEST(abs(cov3) < tol);
  
      cov3 = covariance(v3, u3);
      // Covariance is symmetric: cov(u,v) = cov(v,u)
      BOOST_TEST(abs(cov3) < tol);
  
      // cov(u,u) = sigma(u)^2:
      cov3 = covariance(u3, u3);
      Real expected = Real(2)/Real(3);
  
      BOOST_TEST(abs(cov3 - expected) < tol);
  
      std::mt19937 gen(15);
      // Can't template standard library on multiprecision, so use double and cast back:
      std::uniform_real_distribution<double> dis(-1.0, 1.0);
      std::vector<Real> u(500);
      std::vector<Real> v(500);
      for(size_t i = 0; i < u.size(); ++i)
      {
          u[i] = (Real) dis(gen);
          v[i] = (Real) dis(gen);
      }
  
      Real mu_u = boost::math::statistics::mean(u);
      Real mu_v = boost::math::statistics::mean(v);
      Real sigma_u_sq = boost::math::statistics::variance(u);
      Real sigma_v_sq = boost::math::statistics::variance(v);
  
      auto [mu_u_, mu_v_, cov_uv] = means_and_covariance(u, v);
      BOOST_TEST(abs(mu_u - mu_u_) < tol);
      BOOST_TEST(abs(mu_v - mu_v_) < tol);
  
      // Cauchy-Schwartz inequality:
      BOOST_TEST(cov_uv*cov_uv <= sigma_u_sq*sigma_v_sq);
      // cov(X, X) = sigma(X)^2:
      Real cov_uu = covariance(u, u);
      BOOST_TEST(abs(cov_uu - sigma_u_sq) < tol);
      Real cov_vv = covariance(v, v);
      BOOST_TEST(abs(cov_vv - sigma_v_sq) < tol);
  
  }
  
  template<class Real>
  void test_correlation_coefficient()
  {
      using boost::math::statistics::correlation_coefficient;
  
      Real tol = std::numeric_limits<Real>::epsilon();
      std::vector<Real> u{1};
      std::vector<Real> v{1};
      Real rho_uv = correlation_coefficient(u, v);
      BOOST_TEST(abs(rho_uv - 1) < tol);
  
      u = {1,1};
      v = {1,1};
      rho_uv = correlation_coefficient(u, v);
      BOOST_TEST(abs(rho_uv - 1) < tol);
  
      u = {1, 2, 3};
      v = {1, 2, 3};
      rho_uv = correlation_coefficient(u, v);
      BOOST_TEST(abs(rho_uv - 1) < tol);
  
      u = {1, 2, 3};
      v = {-1, -2, -3};
      rho_uv = correlation_coefficient(u, v);
      BOOST_TEST(abs(rho_uv + 1) < tol);
  
      rho_uv = correlation_coefficient(v, u);
      BOOST_TEST(abs(rho_uv + 1) < tol);
  
      u = {1, 2, 3};
      v = {0, 0, 0};
      rho_uv = correlation_coefficient(v, u);
      BOOST_TEST(abs(rho_uv) < tol);
  
      u = {1, 2, 3};
      v = {0, 0, 3};
      rho_uv = correlation_coefficient(v, u);
      // mu_u = 2, sigma_u^2 = 2/3, mu_v = 1, sigma_v^2 = 2, cov(u,v) = 1.
      BOOST_TEST(abs(rho_uv - sqrt(Real(3))/Real(2)) < tol);
  }
  
  int main()
  {
      test_covariance<float>();
      test_covariance<double>();
      test_covariance<long double>();
      test_covariance<cpp_bin_float_50>();
  
      test_correlation_coefficient<float>();
      test_correlation_coefficient<double>();
      test_correlation_coefficient<long double>();
      test_correlation_coefficient<cpp_bin_float_50>();
  
      return boost::report_errors();
  }
  