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//===----------------------------------------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
//
// REQUIRES: long_tests
// <random>
// template<class RealType = double>
// class extreme_value_distribution
// template<class _URNG> result_type operator()(_URNG& g);
#include <random>
#include <cassert>
#include <vector>
#include <numeric>
template <class T>
inline
T
sqr(T x)
{
return x * x;
}
void
test1()
{
typedef std::extreme_value_distribution<> D;
typedef std::mt19937 G;
G g;
D d(0.5, 2);
const int N = 1000000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (unsigned i = 0; i < u.size(); ++i)
{
double dbl = (u[i] - mean);
double d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
double dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
double x_mean = d.a() + d.b() * 0.577215665;
double x_var = sqr(d.b()) * 1.644934067;
double x_skew = 1.139547;
double x_kurtosis = 12./5;
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
}
void
test2()
{
typedef std::extreme_value_distribution<> D;
typedef std::mt19937 G;
G g;
D d(1, 2);
const int N = 1000000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (unsigned i = 0; i < u.size(); ++i)
{
double dbl = (u[i] - mean);
double d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
double dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
double x_mean = d.a() + d.b() * 0.577215665;
double x_var = sqr(d.b()) * 1.644934067;
double x_skew = 1.139547;
double x_kurtosis = 12./5;
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
}
void
test3()
{
typedef std::extreme_value_distribution<> D;
typedef std::mt19937 G;
G g;
D d(1.5, 3);
const int N = 1000000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (unsigned i = 0; i < u.size(); ++i)
{
double dbl = (u[i] - mean);
double d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
double dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
double x_mean = d.a() + d.b() * 0.577215665;
double x_var = sqr(d.b()) * 1.644934067;
double x_skew = 1.139547;
double x_kurtosis = 12./5;
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
}
void
test4()
{
typedef std::extreme_value_distribution<> D;
typedef std::mt19937 G;
G g;
D d(3, 4);
const int N = 1000000;
std::vector<D::result_type> u;
for (int i = 0; i < N; ++i)
{
D::result_type v = d(g);
u.push_back(v);
}
double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size();
double var = 0;
double skew = 0;
double kurtosis = 0;
for (unsigned i = 0; i < u.size(); ++i)
{
double dbl = (u[i] - mean);
double d2 = sqr(dbl);
var += d2;
skew += dbl * d2;
kurtosis += d2 * d2;
}
var /= u.size();
double dev = std::sqrt(var);
skew /= u.size() * dev * var;
kurtosis /= u.size() * var * var;
kurtosis -= 3;
double x_mean = d.a() + d.b() * 0.577215665;
double x_var = sqr(d.b()) * 1.644934067;
double x_skew = 1.139547;
double x_kurtosis = 12./5;
assert(std::abs((mean - x_mean) / x_mean) < 0.01);
assert(std::abs((var - x_var) / x_var) < 0.01);
assert(std::abs((skew - x_skew) / x_skew) < 0.01);
assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
}
int main()
{
test1();
test2();
test3();
test4();
}
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