libcxx/test/std/numerics/rand/rand.dist/rand.dist.pois/rand.dist.pois.weibull/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 weibull_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::weibull_distribution<> D;
  39         typedef std::mt19937 G;
  40         G g;
  41         D d(0.5, 2);
  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.b() * std::tgamma(1 + 1/d.a());
  68         double x_var = sqr(d.b()) * std::tgamma(1 + 2/d.a()) - sqr(x_mean);
  69         double x_skew = (sqr(d.b())*d.b() * std::tgamma(1 + 3/d.a()) -
  70                         3*x_mean*x_var - sqr(x_mean)*x_mean) /
  71                         (std::sqrt(x_var)*x_var);
  72         double x_kurtosis = (sqr(sqr(d.b())) * std::tgamma(1 + 4/d.a()) -
  73                        4*x_skew*x_var*sqrt(x_var)*x_mean -
  74                        6*sqr(x_mean)*x_var - sqr(sqr(x_mean))) / sqr(x_var) - 3;
  75         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
  76         assert(std::abs((var - x_var) / x_var) < 0.01);
  77         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
  78         assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
  79     }
  80     {
  81         typedef std::weibull_distribution<> D;
  82         typedef std::mt19937 G;
  83         G g;
  84         D d(1, .5);
  85         const int N = 1000000;
  86         std::vector<D::result_type> u;
  87         for (int i = 0; i < N; ++i)
  88         {
  89             D::result_type v = d(g);
  90             assert(d.min() <= v);
  91             u.push_back(v);
  92         }
  93         double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
  94         double var = 0;
  95         double skew = 0;
  96         double kurtosis = 0;
  97         for (std::size_t i = 0; i < u.size(); ++i)
  98         {
  99             double dbl = (u[i] - mean);
 100             double d2 = sqr(dbl);
 101             var += d2;
 102             skew += dbl * d2;
 103             kurtosis += d2 * d2;
 104         }
 105         var /= u.size();
 106         double dev = std::sqrt(var);
 107         skew /= u.size() * dev * var;
 108         kurtosis /= u.size() * var * var;
 109         kurtosis -= 3;
 110         double x_mean = d.b() * std::tgamma(1 + 1/d.a());
 111         double x_var = sqr(d.b()) * std::tgamma(1 + 2/d.a()) - sqr(x_mean);
 112         double x_skew = (sqr(d.b())*d.b() * std::tgamma(1 + 3/d.a()) -
 113                         3*x_mean*x_var - sqr(x_mean)*x_mean) /
 114                         (std::sqrt(x_var)*x_var);
 115         double x_kurtosis = (sqr(sqr(d.b())) * std::tgamma(1 + 4/d.a()) -
 116                        4*x_skew*x_var*sqrt(x_var)*x_mean -
 117                        6*sqr(x_mean)*x_var - sqr(sqr(x_mean))) / sqr(x_var) - 3;
 118         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
 119         assert(std::abs((var - x_var) / x_var) < 0.01);
 120         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
 121         assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
 122     }
 123     {
 124         typedef std::weibull_distribution<> D;
 125         typedef std::mt19937 G;
 126         G g;
 127         D d(2, 3);
 128         const int N = 1000000;
 129         std::vector<D::result_type> u;
 130         for (int i = 0; i < N; ++i)
 131         {
 132             D::result_type v = d(g);
 133             assert(d.min() <= v);
 134             u.push_back(v);
 135         }
 136         double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
 137         double var = 0;
 138         double skew = 0;
 139         double kurtosis = 0;
 140         for (std::size_t i = 0; i < u.size(); ++i)
 141         {
 142             double dbl = (u[i] - mean);
 143             double d2 = sqr(dbl);
 144             var += d2;
 145             skew += dbl * d2;
 146             kurtosis += d2 * d2;
 147         }
 148         var /= u.size();
 149         double dev = std::sqrt(var);
 150         skew /= u.size() * dev * var;
 151         kurtosis /= u.size() * var * var;
 152         kurtosis -= 3;
 153         double x_mean = d.b() * std::tgamma(1 + 1/d.a());
 154         double x_var = sqr(d.b()) * std::tgamma(1 + 2/d.a()) - sqr(x_mean);
 155         double x_skew = (sqr(d.b())*d.b() * std::tgamma(1 + 3/d.a()) -
 156                         3*x_mean*x_var - sqr(x_mean)*x_mean) /
 157                         (std::sqrt(x_var)*x_var);
 158         double x_kurtosis = (sqr(sqr(d.b())) * std::tgamma(1 + 4/d.a()) -
 159                        4*x_skew*x_var*sqrt(x_var)*x_mean -
 160                        6*sqr(x_mean)*x_var - sqr(sqr(x_mean))) / sqr(x_var) - 3;
 161         assert(std::abs((mean - x_mean) / x_mean) < 0.01);
 162         assert(std::abs((var - x_var) / x_var) < 0.01);
 163         assert(std::abs((skew - x_skew) / x_skew) < 0.01);
 164         assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
 165     }
 166
 167   return 0;
 168 }