| //===----------------------------------------------------------------------===// |
| // |
| // The LLVM Compiler Infrastructure |
| // |
| // This file is dual licensed under the MIT and the University of Illinois Open |
| // Source Licenses. See LICENSE.TXT for details. |
| // |
| //===----------------------------------------------------------------------===// |
| // |
| // REQUIRES: long_tests |
| |
| // <random> |
| |
| // template<class IntType = int> |
| // class binomial_distribution |
| |
| // template<class _URNG> result_type operator()(_URNG& g); |
| |
| #include <random> |
| #include <numeric> |
| #include <vector> |
| #include <cassert> |
| |
| template <class T> |
| inline |
| T |
| sqr(T x) |
| { |
| return x * x; |
| } |
| |
| void |
| test1() |
| { |
| typedef std::binomial_distribution<> D; |
| typedef std::mt19937_64 G; |
| G g; |
| D d(5, .75); |
| const int N = 1000000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(d.min() <= v && v <= d.max()); |
| u.push_back(v); |
| } |
| double mean = std::accumulate(u.begin(), u.end(), |
| double(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.t() * d.p(); |
| double x_var = x_mean*(1-d.p()); |
| double x_skew = (1-2*d.p()) / std::sqrt(x_var); |
| double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var; |
| 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) < 0.04); |
| } |
| |
| void |
| test2() |
| { |
| typedef std::binomial_distribution<> D; |
| typedef std::mt19937 G; |
| G g; |
| D d(30, .03125); |
| const int N = 100000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(d.min() <= v && v <= d.max()); |
| u.push_back(v); |
| } |
| double mean = std::accumulate(u.begin(), u.end(), |
| double(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.t() * d.p(); |
| double x_var = x_mean*(1-d.p()); |
| double x_skew = (1-2*d.p()) / std::sqrt(x_var); |
| double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var; |
| 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::binomial_distribution<> D; |
| typedef std::mt19937 G; |
| G g; |
| D d(40, .25); |
| const int N = 100000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(d.min() <= v && v <= d.max()); |
| u.push_back(v); |
| } |
| double mean = std::accumulate(u.begin(), u.end(), |
| double(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.t() * d.p(); |
| double x_var = x_mean*(1-d.p()); |
| double x_skew = (1-2*d.p()) / std::sqrt(x_var); |
| double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var; |
| 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) < 0.03); |
| assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.3); |
| } |
| |
| void |
| test4() |
| { |
| typedef std::binomial_distribution<> D; |
| typedef std::mt19937 G; |
| G g; |
| D d(40, 0); |
| const int N = 100000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(d.min() <= v && v <= d.max()); |
| u.push_back(v); |
| } |
| double mean = std::accumulate(u.begin(), u.end(), |
| double(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); |
| // In this case: |
| // skew computes to 0./0. == nan |
| // kurtosis computes to 0./0. == nan |
| // x_skew == inf |
| // x_kurtosis == inf |
| // These tests are commented out because UBSan warns about division by 0 |
| // skew /= u.size() * dev * var; |
| // kurtosis /= u.size() * var * var; |
| // kurtosis -= 3; |
| double x_mean = d.t() * d.p(); |
| double x_var = x_mean*(1-d.p()); |
| // double x_skew = (1-2*d.p()) / std::sqrt(x_var); |
| // double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var; |
| assert(mean == x_mean); |
| assert(var == x_var); |
| // assert(skew == x_skew); |
| // assert(kurtosis == x_kurtosis); |
| } |
| |
| void |
| test5() |
| { |
| typedef std::binomial_distribution<> D; |
| typedef std::mt19937 G; |
| G g; |
| D d(40, 1); |
| const int N = 100000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(d.min() <= v && v <= d.max()); |
| u.push_back(v); |
| } |
| double mean = std::accumulate(u.begin(), u.end(), |
| double(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); |
| // In this case: |
| // skew computes to 0./0. == nan |
| // kurtosis computes to 0./0. == nan |
| // x_skew == -inf |
| // x_kurtosis == inf |
| // These tests are commented out because UBSan warns about division by 0 |
| // skew /= u.size() * dev * var; |
| // kurtosis /= u.size() * var * var; |
| // kurtosis -= 3; |
| double x_mean = d.t() * d.p(); |
| double x_var = x_mean*(1-d.p()); |
| // double x_skew = (1-2*d.p()) / std::sqrt(x_var); |
| // double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var; |
| assert(mean == x_mean); |
| assert(var == x_var); |
| // assert(skew == x_skew); |
| // assert(kurtosis == x_kurtosis); |
| } |
| |
| void |
| test6() |
| { |
| typedef std::binomial_distribution<> D; |
| typedef std::mt19937 G; |
| G g; |
| D d(400, 0.5); |
| const int N = 100000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(d.min() <= v && v <= d.max()); |
| u.push_back(v); |
| } |
| double mean = std::accumulate(u.begin(), u.end(), |
| double(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.t() * d.p(); |
| double x_var = x_mean*(1-d.p()); |
| double x_skew = (1-2*d.p()) / std::sqrt(x_var); |
| double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var; |
| 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) < 0.01); |
| assert(std::abs(kurtosis - x_kurtosis) < 0.01); |
| } |
| |
| void |
| test7() |
| { |
| typedef std::binomial_distribution<> D; |
| typedef std::mt19937 G; |
| G g; |
| D d(1, 0.5); |
| const int N = 100000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(d.min() <= v && v <= d.max()); |
| u.push_back(v); |
| } |
| double mean = std::accumulate(u.begin(), u.end(), |
| double(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.t() * d.p(); |
| double x_var = x_mean*(1-d.p()); |
| double x_skew = (1-2*d.p()) / std::sqrt(x_var); |
| double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var; |
| 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) < 0.01); |
| assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); |
| } |
| |
| void |
| test8() |
| { |
| const int N = 100000; |
| std::mt19937 gen1; |
| std::mt19937 gen2; |
| |
| std::binomial_distribution<> dist1(5, 0.1); |
| std::binomial_distribution<unsigned> dist2(5, 0.1); |
| |
| for(int i = 0; i < N; ++i) { |
| int r1 = dist1(gen1); |
| unsigned r2 = dist2(gen2); |
| assert(r1 >= 0); |
| assert(static_cast<unsigned>(r1) == r2); |
| } |
| } |
| |
| void |
| test9() |
| { |
| typedef std::binomial_distribution<> D; |
| typedef std::mt19937 G; |
| G g; |
| D d(0, 0.005); |
| const int N = 100000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(d.min() <= v && v <= d.max()); |
| u.push_back(v); |
| } |
| double mean = std::accumulate(u.begin(), u.end(), |
| double(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); |
| // In this case: |
| // skew computes to 0./0. == nan |
| // kurtosis computes to 0./0. == nan |
| // x_skew == inf |
| // x_kurtosis == inf |
| // These tests are commented out because UBSan warns about division by 0 |
| // skew /= u.size() * dev * var; |
| // kurtosis /= u.size() * var * var; |
| // kurtosis -= 3; |
| double x_mean = d.t() * d.p(); |
| double x_var = x_mean*(1-d.p()); |
| // double x_skew = (1-2*d.p()) / std::sqrt(x_var); |
| // double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var; |
| assert(mean == x_mean); |
| assert(var == x_var); |
| // assert(skew == x_skew); |
| // assert(kurtosis == x_kurtosis); |
| } |
| |
| void |
| test10() |
| { |
| typedef std::binomial_distribution<> D; |
| typedef std::mt19937 G; |
| G g; |
| D d(0, 0); |
| const int N = 100000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(d.min() <= v && v <= d.max()); |
| u.push_back(v); |
| } |
| double mean = std::accumulate(u.begin(), u.end(), |
| double(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); |
| // In this case: |
| // skew computes to 0./0. == nan |
| // kurtosis computes to 0./0. == nan |
| // x_skew == inf |
| // x_kurtosis == inf |
| // These tests are commented out because UBSan warns about division by 0 |
| // skew /= u.size() * dev * var; |
| // kurtosis /= u.size() * var * var; |
| // kurtosis -= 3; |
| double x_mean = d.t() * d.p(); |
| double x_var = x_mean*(1-d.p()); |
| // double x_skew = (1-2*d.p()) / std::sqrt(x_var); |
| // double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var; |
| assert(mean == x_mean); |
| assert(var == x_var); |
| // assert(skew == x_skew); |
| // assert(kurtosis == x_kurtosis); |
| } |
| |
| void |
| test11() |
| { |
| typedef std::binomial_distribution<> D; |
| typedef std::mt19937 G; |
| G g; |
| D d(0, 1); |
| const int N = 100000; |
| std::vector<D::result_type> u; |
| for (int i = 0; i < N; ++i) |
| { |
| D::result_type v = d(g); |
| assert(d.min() <= v && v <= d.max()); |
| u.push_back(v); |
| } |
| double mean = std::accumulate(u.begin(), u.end(), |
| double(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); |
| // In this case: |
| // skew computes to 0./0. == nan |
| // kurtosis computes to 0./0. == nan |
| // x_skew == -inf |
| // x_kurtosis == inf |
| // These tests are commented out because UBSan warns about division by 0 |
| // skew /= u.size() * dev * var; |
| // kurtosis /= u.size() * var * var; |
| // kurtosis -= 3; |
| double x_mean = d.t() * d.p(); |
| double x_var = x_mean*(1-d.p()); |
| // double x_skew = (1-2*d.p()) / std::sqrt(x_var); |
| // double x_kurtosis = (1-6*d.p()*(1-d.p())) / x_var; |
| assert(mean == x_mean); |
| assert(var == x_var); |
| // assert(skew == x_skew); |
| // assert(kurtosis == x_kurtosis); |
| } |
| |
| int main() |
| { |
| test1(); |
| test2(); |
| test3(); |
| test4(); |
| test5(); |
| test6(); |
| test7(); |
| test8(); |
| test9(); |
| test10(); |
| test11(); |
| } |