libcxx/test/std/numerics/rand/rand.dist/rand.dist.norm/rand.dist.norm.chisq/eval.pass.cpp

   1 //===----------------------------------------------------------------------===//
   2 //
   3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
   4 // See https://llvm.org/LICENSE.txt for license information.
   5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
   6 //
   7 //===----------------------------------------------------------------------===//
   8 //
   9 // REQUIRES: long_tests
  10
  11 // <random>
  12
  13 // template<class RealType = double>
  14 // class chi_squared_distribution
  15
  16 // template<class _URNG> result_type operator()(_URNG& g);
  17
  18 #include <random>
  19 #include <cassert>
  20 #include <cmath>
  21 #include <cstddef>
  22 #include <numeric>
  23 #include <vector>
  24
  25 #include "test_macros.h"
  26
  27 template <class T>
  28 inline
  29 T
  30 sqr(T x)
  31 {
  32     return x * x;
  33 }
  34
  35 int main(int, char**)
  36 {
  37     {
  38         typedef std::chi_squared_distribution<> D;
  39         typedef std::minstd_rand G;
  40         G g;
  41         D d(0.5);
  42         const int N = 1000000;
  43         std::vector<D::result_type> u;
  44         for (int i = 0; i < N; ++i)
  45         {
  46             D::result_type v = d(g);
  47             assert(d.min() < v);
  48             u.push_back(v);
  49         }
  50         double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
  51         double var = 0;
  52         double skew = 0;
  53         double kurtosis = 0;
  54         for (std::size_t i = 0; i < u.size(); ++i)
  55         {
  56             double dbl = (u[i] - mean);
  57             double d2 = sqr(dbl);
  58             var += d2;
  59             skew += dbl * d2;
  60             kurtosis += d2 * d2;
  61         }
  62         var /= u.size();
  63         double dev = std::sqrt(var);
  64         skew /= u.size() * dev * var;
  65         kurtosis /= u.size() * var * var;
  66         kurtosis -= 3;
  67         double x_mean = d.n();
  68         double x_var = 2 * d.n();
  69         double x_skew = std::sqrt(8 / d.n());
  70         double x_kurtosis = 12 / d.n();
  71         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
  72         assert(std::abs((var - x_var) / x_var) < 0.01);
  73         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
  74         assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.04);
  75     }
  76     {
  77         typedef std::chi_squared_distribution<> D;
  78         typedef std::minstd_rand G;
  79         G g;
  80         D d(1);
  81         const int N = 1000000;
  82         std::vector<D::result_type> u;
  83         for (int i = 0; i < N; ++i)
  84         {
  85             D::result_type v = d(g);
  86             assert(d.min() < v);
  87             u.push_back(v);
  88         }
  89         double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
  90         double var = 0;
  91         double skew = 0;
  92         double kurtosis = 0;
  93         for (std::size_t i = 0; i < u.size(); ++i)
  94         {
  95             double dbl = (u[i] - mean);
  96             double d2 = sqr(dbl);
  97             var += d2;
  98             skew += dbl * d2;
  99             kurtosis += d2 * d2;
 100         }
 101         var /= u.size();
 102         double dev = std::sqrt(var);
 103         skew /= u.size() * dev * var;
 104         kurtosis /= u.size() * var * var;
 105         kurtosis -= 3;
 106         double x_mean = d.n();
 107         double x_var = 2 * d.n();
 108         double x_skew = std::sqrt(8 / d.n());
 109         double x_kurtosis = 12 / d.n();
 110         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
 111         assert(std::abs((var - x_var) / x_var) < 0.01);
 112         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
 113         assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
 114     }
 115     {
 116         typedef std::chi_squared_distribution<> D;
 117         typedef std::mt19937 G;
 118         G g;
 119         D d(2);
 120         const int N = 1000000;
 121         std::vector<D::result_type> u;
 122         for (int i = 0; i < N; ++i)
 123         {
 124             D::result_type v = d(g);
 125             assert(d.min() < v);
 126             u.push_back(v);
 127         }
 128         double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
 129         double var = 0;
 130         double skew = 0;
 131         double kurtosis = 0;
 132         for (std::size_t i = 0; i < u.size(); ++i)
 133         {
 134             double dbl = (u[i] - mean);
 135             double d2 = sqr(dbl);
 136             var += d2;
 137             skew += dbl * d2;
 138             kurtosis += d2 * d2;
 139         }
 140         var /= u.size();
 141         double dev = std::sqrt(var);
 142         skew /= u.size() * dev * var;
 143         kurtosis /= u.size() * var * var;
 144         kurtosis -= 3;
 145         double x_mean = d.n();
 146         double x_var = 2 * d.n();
 147         double x_skew = std::sqrt(8 / d.n());
 148         double x_kurtosis = 12 / d.n();
 149         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
 150         assert(std::abs((var - x_var) / x_var) < 0.01);
 151         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
 152         assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
 153     }
 154
 155   return 0;
 156 }