1 //===----------------------------------------------------------------------===// 2 // 3 // The LLVM Compiler Infrastructure 4 // 5 // This file is dual licensed under the MIT and the University of Illinois Open 6 // Source Licenses. See LICENSE.TXT for details. 7 // 8 //===----------------------------------------------------------------------===// 9 // 10 // REQUIRES: long_tests 11 12 // <random> 13 14 // template<class RealType = double> 15 // class lognormal_distribution 16 17 // template<class _URNG> result_type operator()(_URNG& g); 18 19 #include <random> 20 #include <cassert> 21 #include <vector> 22 #include <numeric> 23 24 template <class T> 25 inline 26 T 27 sqr(T x) 28 { 29 return x * x; 30 } 31 32 void 33 test1() 34 { 35 typedef std::lognormal_distribution<> D; 36 typedef std::mt19937 G; 37 G g; 38 D d(-1./8192, 0.015625); 39 const int N = 1000000; 40 std::vector<D::result_type> u; 41 for (int i = 0; i < N; ++i) 42 { 43 D::result_type v = d(g); 44 assert(v > 0); 45 u.push_back(v); 46 } 47 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 48 double var = 0; 49 double skew = 0; 50 double kurtosis = 0; 51 for (unsigned i = 0; i < u.size(); ++i) 52 { 53 double dbl = (u[i] - mean); 54 double d2 = sqr(dbl); 55 var += d2; 56 skew += dbl * d2; 57 kurtosis += d2 * d2; 58 } 59 var /= u.size(); 60 double dev = std::sqrt(var); 61 skew /= u.size() * dev * var; 62 kurtosis /= u.size() * var * var; 63 kurtosis -= 3; 64 double x_mean = std::exp(d.m() + sqr(d.s())/2); 65 double x_var = (std::exp(sqr(d.s())) - 1) * std::exp(2*d.m() + sqr(d.s())); 66 double x_skew = (std::exp(sqr(d.s())) + 2) * 67 std::sqrt((std::exp(sqr(d.s())) - 1)); 68 double x_kurtosis = std::exp(4*sqr(d.s())) + 2*std::exp(3*sqr(d.s())) + 69 3*std::exp(2*sqr(d.s())) - 6; 70 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 71 assert(std::abs((var - x_var) / x_var) < 0.01); 72 assert(std::abs((skew - x_skew) / x_skew) < 0.05); 73 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.25); 74 } 75 76 void 77 test2() 78 { 79 typedef std::lognormal_distribution<> D; 80 typedef std::mt19937 G; 81 G g; 82 D d(-1./32, 0.25); 83 const int N = 1000000; 84 std::vector<D::result_type> u; 85 for (int i = 0; i < N; ++i) 86 { 87 D::result_type v = d(g); 88 assert(v > 0); 89 u.push_back(v); 90 } 91 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 92 double var = 0; 93 double skew = 0; 94 double kurtosis = 0; 95 for (unsigned i = 0; i < u.size(); ++i) 96 { 97 double dbl = (u[i] - mean); 98 double d2 = sqr(dbl); 99 var += d2; 100 skew += dbl * d2; 101 kurtosis += d2 * d2; 102 } 103 var /= u.size(); 104 double dev = std::sqrt(var); 105 skew /= u.size() * dev * var; 106 kurtosis /= u.size() * var * var; 107 kurtosis -= 3; 108 double x_mean = std::exp(d.m() + sqr(d.s())/2); 109 double x_var = (std::exp(sqr(d.s())) - 1) * std::exp(2*d.m() + sqr(d.s())); 110 double x_skew = (std::exp(sqr(d.s())) + 2) * 111 std::sqrt((std::exp(sqr(d.s())) - 1)); 112 double x_kurtosis = std::exp(4*sqr(d.s())) + 2*std::exp(3*sqr(d.s())) + 113 3*std::exp(2*sqr(d.s())) - 6; 114 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 115 assert(std::abs((var - x_var) / x_var) < 0.01); 116 assert(std::abs((skew - x_skew) / x_skew) < 0.01); 117 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03); 118 } 119 120 void 121 test3() 122 { 123 typedef std::lognormal_distribution<> D; 124 typedef std::mt19937 G; 125 G g; 126 D d(-1./8, 0.5); 127 const int N = 1000000; 128 std::vector<D::result_type> u; 129 for (int i = 0; i < N; ++i) 130 { 131 D::result_type v = d(g); 132 assert(v > 0); 133 u.push_back(v); 134 } 135 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 136 double var = 0; 137 double skew = 0; 138 double kurtosis = 0; 139 for (unsigned i = 0; i < u.size(); ++i) 140 { 141 double dbl = (u[i] - mean); 142 double d2 = sqr(dbl); 143 var += d2; 144 skew += dbl * d2; 145 kurtosis += d2 * d2; 146 } 147 var /= u.size(); 148 double dev = std::sqrt(var); 149 skew /= u.size() * dev * var; 150 kurtosis /= u.size() * var * var; 151 kurtosis -= 3; 152 double x_mean = std::exp(d.m() + sqr(d.s())/2); 153 double x_var = (std::exp(sqr(d.s())) - 1) * std::exp(2*d.m() + sqr(d.s())); 154 double x_skew = (std::exp(sqr(d.s())) + 2) * 155 std::sqrt((std::exp(sqr(d.s())) - 1)); 156 double x_kurtosis = std::exp(4*sqr(d.s())) + 2*std::exp(3*sqr(d.s())) + 157 3*std::exp(2*sqr(d.s())) - 6; 158 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 159 assert(std::abs((var - x_var) / x_var) < 0.01); 160 assert(std::abs((skew - x_skew) / x_skew) < 0.02); 161 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.05); 162 } 163 164 void 165 test4() 166 { 167 typedef std::lognormal_distribution<> D; 168 typedef std::mt19937 G; 169 G g; 170 D d; 171 const int N = 1000000; 172 std::vector<D::result_type> u; 173 for (int i = 0; i < N; ++i) 174 { 175 D::result_type v = d(g); 176 assert(v > 0); 177 u.push_back(v); 178 } 179 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 180 double var = 0; 181 double skew = 0; 182 double kurtosis = 0; 183 for (unsigned i = 0; i < u.size(); ++i) 184 { 185 double dbl = (u[i] - mean); 186 double d2 = sqr(dbl); 187 var += d2; 188 skew += dbl * d2; 189 kurtosis += d2 * d2; 190 } 191 var /= u.size(); 192 double dev = std::sqrt(var); 193 skew /= u.size() * dev * var; 194 kurtosis /= u.size() * var * var; 195 kurtosis -= 3; 196 double x_mean = std::exp(d.m() + sqr(d.s())/2); 197 double x_var = (std::exp(sqr(d.s())) - 1) * std::exp(2*d.m() + sqr(d.s())); 198 double x_skew = (std::exp(sqr(d.s())) + 2) * 199 std::sqrt((std::exp(sqr(d.s())) - 1)); 200 double x_kurtosis = std::exp(4*sqr(d.s())) + 2*std::exp(3*sqr(d.s())) + 201 3*std::exp(2*sqr(d.s())) - 6; 202 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 203 assert(std::abs((var - x_var) / x_var) < 0.02); 204 assert(std::abs((skew - x_skew) / x_skew) < 0.08); 205 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.4); 206 } 207 208 void 209 test5() 210 { 211 typedef std::lognormal_distribution<> D; 212 typedef std::mt19937 G; 213 G g; 214 D d(-0.78125, 1.25); 215 const int N = 1000000; 216 std::vector<D::result_type> u; 217 for (int i = 0; i < N; ++i) 218 { 219 D::result_type v = d(g); 220 assert(v > 0); 221 u.push_back(v); 222 } 223 double mean = std::accumulate(u.begin(), u.end(), 0.0) / u.size(); 224 double var = 0; 225 double skew = 0; 226 double kurtosis = 0; 227 for (unsigned i = 0; i < u.size(); ++i) 228 { 229 double dbl = (u[i] - mean); 230 double d2 = sqr(dbl); 231 var += d2; 232 skew += dbl * d2; 233 kurtosis += d2 * d2; 234 } 235 var /= u.size(); 236 double dev = std::sqrt(var); 237 skew /= u.size() * dev * var; 238 kurtosis /= u.size() * var * var; 239 kurtosis -= 3; 240 double x_mean = std::exp(d.m() + sqr(d.s())/2); 241 double x_var = (std::exp(sqr(d.s())) - 1) * std::exp(2*d.m() + sqr(d.s())); 242 double x_skew = (std::exp(sqr(d.s())) + 2) * 243 std::sqrt((std::exp(sqr(d.s())) - 1)); 244 double x_kurtosis = std::exp(4*sqr(d.s())) + 2*std::exp(3*sqr(d.s())) + 245 3*std::exp(2*sqr(d.s())) - 6; 246 assert(std::abs((mean - x_mean) / x_mean) < 0.01); 247 assert(std::abs((var - x_var) / x_var) < 0.04); 248 assert(std::abs((skew - x_skew) / x_skew) < 0.2); 249 assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.7); 250 } 251 252 int main() 253 { 254 test1(); 255 test2(); 256 test3(); 257 test4(); 258 test5(); 259 } 260
