| //===----------------------------------------------------------------------===// |
| // |
| // 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 RealType = double> |
| // class piecewise_constant_distribution |
| |
| // template<class _URNG> result_type operator()(_URNG& g); |
| |
| #include <random> |
| #include <vector> |
| #include <iterator> |
| #include <numeric> |
| #include <algorithm> // for sort |
| #include <cassert> |
| |
| template <class T> |
| inline |
| T |
| sqr(T x) |
| { |
| return x*x; |
| } |
| |
| void |
| test1() |
| { |
| typedef std::piecewise_constant_distribution<> D; |
| typedef std::mt19937_64 G; |
| G g; |
| double b[] = {10, 14, 16, 17}; |
| double p[] = {25, 62.5, 12.5}; |
| const size_t Np = sizeof(p) / sizeof(p[0]); |
| D d(b, b+Np+1, p); |
| 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); |
| } |
| std::vector<double> prob(std::begin(p), std::end(p)); |
| double s = std::accumulate(prob.begin(), prob.end(), 0.0); |
| for (std::size_t i = 0; i < prob.size(); ++i) |
| prob[i] /= s; |
| std::sort(u.begin(), u.end()); |
| for (std::size_t i = 0; i < Np; ++i) |
| { |
| typedef std::vector<D::result_type>::iterator I; |
| I lb = std::lower_bound(u.begin(), u.end(), b[i]); |
| I ub = std::lower_bound(u.begin(), u.end(), b[i+1]); |
| const size_t Ni = ub - lb; |
| if (prob[i] == 0) |
| assert(Ni == 0); |
| else |
| { |
| assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01); |
| double mean = std::accumulate(lb, ub, 0.0) / Ni; |
| double var = 0; |
| double skew = 0; |
| double kurtosis = 0; |
| for (I j = lb; j != ub; ++j) |
| { |
| double dbl = (*j - mean); |
| double d2 = sqr(dbl); |
| var += d2; |
| skew += dbl * d2; |
| kurtosis += d2 * d2; |
| } |
| var /= Ni; |
| double dev = std::sqrt(var); |
| skew /= Ni * dev * var; |
| kurtosis /= Ni * var * var; |
| kurtosis -= 3; |
| double x_mean = (b[i+1] + b[i]) / 2; |
| double x_var = sqr(b[i+1] - b[i]) / 12; |
| double x_skew = 0; |
| double x_kurtosis = -6./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) < 0.01); |
| assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); |
| } |
| } |
| } |
| |
| void |
| test2() |
| { |
| typedef std::piecewise_constant_distribution<> D; |
| typedef std::mt19937_64 G; |
| G g; |
| double b[] = {10, 14, 16, 17}; |
| double p[] = {0, 62.5, 12.5}; |
| const size_t Np = sizeof(p) / sizeof(p[0]); |
| D d(b, b+Np+1, p); |
| 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); |
| } |
| std::vector<double> prob(std::begin(p), std::end(p)); |
| double s = std::accumulate(prob.begin(), prob.end(), 0.0); |
| for (std::size_t i = 0; i < prob.size(); ++i) |
| prob[i] /= s; |
| std::sort(u.begin(), u.end()); |
| for (std::size_t i = 0; i < Np; ++i) |
| { |
| typedef std::vector<D::result_type>::iterator I; |
| I lb = std::lower_bound(u.begin(), u.end(), b[i]); |
| I ub = std::lower_bound(u.begin(), u.end(), b[i+1]); |
| const size_t Ni = ub - lb; |
| if (prob[i] == 0) |
| assert(Ni == 0); |
| else |
| { |
| assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01); |
| double mean = std::accumulate(lb, ub, 0.0) / Ni; |
| double var = 0; |
| double skew = 0; |
| double kurtosis = 0; |
| for (I j = lb; j != ub; ++j) |
| { |
| double dbl = (*j - mean); |
| double d2 = sqr(dbl); |
| var += d2; |
| skew += dbl * d2; |
| kurtosis += d2 * d2; |
| } |
| var /= Ni; |
| double dev = std::sqrt(var); |
| skew /= Ni * dev * var; |
| kurtosis /= Ni * var * var; |
| kurtosis -= 3; |
| double x_mean = (b[i+1] + b[i]) / 2; |
| double x_var = sqr(b[i+1] - b[i]) / 12; |
| double x_skew = 0; |
| double x_kurtosis = -6./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) < 0.01); |
| assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); |
| } |
| } |
| } |
| |
| void |
| test3() |
| { |
| typedef std::piecewise_constant_distribution<> D; |
| typedef std::mt19937_64 G; |
| G g; |
| double b[] = {10, 14, 16, 17}; |
| double p[] = {25, 0, 12.5}; |
| const size_t Np = sizeof(p) / sizeof(p[0]); |
| D d(b, b+Np+1, p); |
| 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); |
| } |
| std::vector<double> prob(std::begin(p), std::end(p)); |
| double s = std::accumulate(prob.begin(), prob.end(), 0.0); |
| for (std::size_t i = 0; i < prob.size(); ++i) |
| prob[i] /= s; |
| std::sort(u.begin(), u.end()); |
| for (std::size_t i = 0; i < Np; ++i) |
| { |
| typedef std::vector<D::result_type>::iterator I; |
| I lb = std::lower_bound(u.begin(), u.end(), b[i]); |
| I ub = std::lower_bound(u.begin(), u.end(), b[i+1]); |
| const size_t Ni = ub - lb; |
| if (prob[i] == 0) |
| assert(Ni == 0); |
| else |
| { |
| assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01); |
| double mean = std::accumulate(lb, ub, 0.0) / Ni; |
| double var = 0; |
| double skew = 0; |
| double kurtosis = 0; |
| for (I j = lb; j != ub; ++j) |
| { |
| double dbl = (*j - mean); |
| double d2 = sqr(dbl); |
| var += d2; |
| skew += dbl * d2; |
| kurtosis += d2 * d2; |
| } |
| var /= Ni; |
| double dev = std::sqrt(var); |
| skew /= Ni * dev * var; |
| kurtosis /= Ni * var * var; |
| kurtosis -= 3; |
| double x_mean = (b[i+1] + b[i]) / 2; |
| double x_var = sqr(b[i+1] - b[i]) / 12; |
| double x_skew = 0; |
| double x_kurtosis = -6./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) < 0.01); |
| assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); |
| } |
| } |
| } |
| |
| void |
| test4() |
| { |
| typedef std::piecewise_constant_distribution<> D; |
| typedef std::mt19937_64 G; |
| G g; |
| double b[] = {10, 14, 16, 17}; |
| double p[] = {25, 62.5, 0}; |
| const size_t Np = sizeof(p) / sizeof(p[0]); |
| D d(b, b+Np+1, p); |
| 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); |
| } |
| std::vector<double> prob(std::begin(p), std::end(p)); |
| double s = std::accumulate(prob.begin(), prob.end(), 0.0); |
| for (std::size_t i = 0; i < prob.size(); ++i) |
| prob[i] /= s; |
| std::sort(u.begin(), u.end()); |
| for (std::size_t i = 0; i < Np; ++i) |
| { |
| typedef std::vector<D::result_type>::iterator I; |
| I lb = std::lower_bound(u.begin(), u.end(), b[i]); |
| I ub = std::lower_bound(u.begin(), u.end(), b[i+1]); |
| const size_t Ni = ub - lb; |
| if (prob[i] == 0) |
| assert(Ni == 0); |
| else |
| { |
| assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01); |
| double mean = std::accumulate(lb, ub, 0.0) / Ni; |
| double var = 0; |
| double skew = 0; |
| double kurtosis = 0; |
| for (I j = lb; j != ub; ++j) |
| { |
| double dbl = (*j - mean); |
| double d2 = sqr(dbl); |
| var += d2; |
| skew += dbl * d2; |
| kurtosis += d2 * d2; |
| } |
| var /= Ni; |
| double dev = std::sqrt(var); |
| skew /= Ni * dev * var; |
| kurtosis /= Ni * var * var; |
| kurtosis -= 3; |
| double x_mean = (b[i+1] + b[i]) / 2; |
| double x_var = sqr(b[i+1] - b[i]) / 12; |
| double x_skew = 0; |
| double x_kurtosis = -6./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) < 0.01); |
| assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); |
| } |
| } |
| } |
| |
| void |
| test5() |
| { |
| typedef std::piecewise_constant_distribution<> D; |
| typedef std::mt19937_64 G; |
| G g; |
| double b[] = {10, 14, 16, 17}; |
| double p[] = {25, 0, 0}; |
| const size_t Np = sizeof(p) / sizeof(p[0]); |
| D d(b, b+Np+1, p); |
| 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); |
| } |
| std::vector<double> prob(std::begin(p), std::end(p)); |
| double s = std::accumulate(prob.begin(), prob.end(), 0.0); |
| for (std::size_t i = 0; i < prob.size(); ++i) |
| prob[i] /= s; |
| std::sort(u.begin(), u.end()); |
| for (std::size_t i = 0; i < Np; ++i) |
| { |
| typedef std::vector<D::result_type>::iterator I; |
| I lb = std::lower_bound(u.begin(), u.end(), b[i]); |
| I ub = std::lower_bound(u.begin(), u.end(), b[i+1]); |
| const size_t Ni = ub - lb; |
| if (prob[i] == 0) |
| assert(Ni == 0); |
| else |
| { |
| assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01); |
| double mean = std::accumulate(lb, ub, 0.0) / Ni; |
| double var = 0; |
| double skew = 0; |
| double kurtosis = 0; |
| for (I j = lb; j != ub; ++j) |
| { |
| double dbl = (*j - mean); |
| double d2 = sqr(dbl); |
| var += d2; |
| skew += dbl * d2; |
| kurtosis += d2 * d2; |
| } |
| var /= Ni; |
| double dev = std::sqrt(var); |
| skew /= Ni * dev * var; |
| kurtosis /= Ni * var * var; |
| kurtosis -= 3; |
| double x_mean = (b[i+1] + b[i]) / 2; |
| double x_var = sqr(b[i+1] - b[i]) / 12; |
| double x_skew = 0; |
| double x_kurtosis = -6./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) < 0.01); |
| assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); |
| } |
| } |
| } |
| |
| void |
| test6() |
| { |
| typedef std::piecewise_constant_distribution<> D; |
| typedef std::mt19937_64 G; |
| G g; |
| double b[] = {10, 14, 16, 17}; |
| double p[] = {0, 25, 0}; |
| const size_t Np = sizeof(p) / sizeof(p[0]); |
| D d(b, b+Np+1, p); |
| 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); |
| } |
| std::vector<double> prob(std::begin(p), std::end(p)); |
| double s = std::accumulate(prob.begin(), prob.end(), 0.0); |
| for (std::size_t i = 0; i < prob.size(); ++i) |
| prob[i] /= s; |
| std::sort(u.begin(), u.end()); |
| for (std::size_t i = 0; i < Np; ++i) |
| { |
| typedef std::vector<D::result_type>::iterator I; |
| I lb = std::lower_bound(u.begin(), u.end(), b[i]); |
| I ub = std::lower_bound(u.begin(), u.end(), b[i+1]); |
| const size_t Ni = ub - lb; |
| if (prob[i] == 0) |
| assert(Ni == 0); |
| else |
| { |
| assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01); |
| double mean = std::accumulate(lb, ub, 0.0) / Ni; |
| double var = 0; |
| double skew = 0; |
| double kurtosis = 0; |
| for (I j = lb; j != ub; ++j) |
| { |
| double dbl = (*j - mean); |
| double d2 = sqr(dbl); |
| var += d2; |
| skew += dbl * d2; |
| kurtosis += d2 * d2; |
| } |
| var /= Ni; |
| double dev = std::sqrt(var); |
| skew /= Ni * dev * var; |
| kurtosis /= Ni * var * var; |
| kurtosis -= 3; |
| double x_mean = (b[i+1] + b[i]) / 2; |
| double x_var = sqr(b[i+1] - b[i]) / 12; |
| double x_skew = 0; |
| double x_kurtosis = -6./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) < 0.01); |
| assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); |
| } |
| } |
| } |
| |
| void |
| test7() |
| { |
| typedef std::piecewise_constant_distribution<> D; |
| typedef std::mt19937_64 G; |
| G g; |
| double b[] = {10, 14, 16, 17}; |
| double p[] = {0, 0, 1}; |
| const size_t Np = sizeof(p) / sizeof(p[0]); |
| D d(b, b+Np+1, p); |
| 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); |
| } |
| std::vector<double> prob(std::begin(p), std::end(p)); |
| double s = std::accumulate(prob.begin(), prob.end(), 0.0); |
| for (std::size_t i = 0; i < prob.size(); ++i) |
| prob[i] /= s; |
| std::sort(u.begin(), u.end()); |
| for (std::size_t i = 0; i < Np; ++i) |
| { |
| typedef std::vector<D::result_type>::iterator I; |
| I lb = std::lower_bound(u.begin(), u.end(), b[i]); |
| I ub = std::lower_bound(u.begin(), u.end(), b[i+1]); |
| const size_t Ni = ub - lb; |
| if (prob[i] == 0) |
| assert(Ni == 0); |
| else |
| { |
| assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01); |
| double mean = std::accumulate(lb, ub, 0.0) / Ni; |
| double var = 0; |
| double skew = 0; |
| double kurtosis = 0; |
| for (I j = lb; j != ub; ++j) |
| { |
| double dbl = (*j - mean); |
| double d2 = sqr(dbl); |
| var += d2; |
| skew += dbl * d2; |
| kurtosis += d2 * d2; |
| } |
| var /= Ni; |
| double dev = std::sqrt(var); |
| skew /= Ni * dev * var; |
| kurtosis /= Ni * var * var; |
| kurtosis -= 3; |
| double x_mean = (b[i+1] + b[i]) / 2; |
| double x_var = sqr(b[i+1] - b[i]) / 12; |
| double x_skew = 0; |
| double x_kurtosis = -6./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) < 0.01); |
| assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); |
| } |
| } |
| } |
| |
| void |
| test8() |
| { |
| typedef std::piecewise_constant_distribution<> D; |
| typedef std::mt19937_64 G; |
| G g; |
| double b[] = {10, 14, 16}; |
| double p[] = {75, 25}; |
| const size_t Np = sizeof(p) / sizeof(p[0]); |
| D d(b, b+Np+1, p); |
| 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); |
| } |
| std::vector<double> prob(std::begin(p), std::end(p)); |
| double s = std::accumulate(prob.begin(), prob.end(), 0.0); |
| for (std::size_t i = 0; i < prob.size(); ++i) |
| prob[i] /= s; |
| std::sort(u.begin(), u.end()); |
| for (std::size_t i = 0; i < Np; ++i) |
| { |
| typedef std::vector<D::result_type>::iterator I; |
| I lb = std::lower_bound(u.begin(), u.end(), b[i]); |
| I ub = std::lower_bound(u.begin(), u.end(), b[i+1]); |
| const size_t Ni = ub - lb; |
| if (prob[i] == 0) |
| assert(Ni == 0); |
| else |
| { |
| assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01); |
| double mean = std::accumulate(lb, ub, 0.0) / Ni; |
| double var = 0; |
| double skew = 0; |
| double kurtosis = 0; |
| for (I j = lb; j != ub; ++j) |
| { |
| double dbl = (*j - mean); |
| double d2 = sqr(dbl); |
| var += d2; |
| skew += dbl * d2; |
| kurtosis += d2 * d2; |
| } |
| var /= Ni; |
| double dev = std::sqrt(var); |
| skew /= Ni * dev * var; |
| kurtosis /= Ni * var * var; |
| kurtosis -= 3; |
| double x_mean = (b[i+1] + b[i]) / 2; |
| double x_var = sqr(b[i+1] - b[i]) / 12; |
| double x_skew = 0; |
| double x_kurtosis = -6./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) < 0.01); |
| assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); |
| } |
| } |
| } |
| |
| void |
| test9() |
| { |
| typedef std::piecewise_constant_distribution<> D; |
| typedef std::mt19937_64 G; |
| G g; |
| double b[] = {10, 14, 16}; |
| double p[] = {0, 25}; |
| const size_t Np = sizeof(p) / sizeof(p[0]); |
| D d(b, b+Np+1, p); |
| 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); |
| } |
| std::vector<double> prob(std::begin(p), std::end(p)); |
| double s = std::accumulate(prob.begin(), prob.end(), 0.0); |
| for (std::size_t i = 0; i < prob.size(); ++i) |
| prob[i] /= s; |
| std::sort(u.begin(), u.end()); |
| for (std::size_t i = 0; i < Np; ++i) |
| { |
| typedef std::vector<D::result_type>::iterator I; |
| I lb = std::lower_bound(u.begin(), u.end(), b[i]); |
| I ub = std::lower_bound(u.begin(), u.end(), b[i+1]); |
| const size_t Ni = ub - lb; |
| if (prob[i] == 0) |
| assert(Ni == 0); |
| else |
| { |
| assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01); |
| double mean = std::accumulate(lb, ub, 0.0) / Ni; |
| double var = 0; |
| double skew = 0; |
| double kurtosis = 0; |
| for (I j = lb; j != ub; ++j) |
| { |
| double dbl = (*j - mean); |
| double d2 = sqr(dbl); |
| var += d2; |
| skew += dbl * d2; |
| kurtosis += d2 * d2; |
| } |
| var /= Ni; |
| double dev = std::sqrt(var); |
| skew /= Ni * dev * var; |
| kurtosis /= Ni * var * var; |
| kurtosis -= 3; |
| double x_mean = (b[i+1] + b[i]) / 2; |
| double x_var = sqr(b[i+1] - b[i]) / 12; |
| double x_skew = 0; |
| double x_kurtosis = -6./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) < 0.01); |
| assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); |
| } |
| } |
| } |
| |
| void |
| test10() |
| { |
| typedef std::piecewise_constant_distribution<> D; |
| typedef std::mt19937_64 G; |
| G g; |
| double b[] = {10, 14, 16}; |
| double p[] = {1, 0}; |
| const size_t Np = sizeof(p) / sizeof(p[0]); |
| D d(b, b+Np+1, p); |
| 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); |
| } |
| std::vector<double> prob(std::begin(p), std::end(p)); |
| double s = std::accumulate(prob.begin(), prob.end(), 0.0); |
| for (std::size_t i = 0; i < prob.size(); ++i) |
| prob[i] /= s; |
| std::sort(u.begin(), u.end()); |
| for (std::size_t i = 0; i < Np; ++i) |
| { |
| typedef std::vector<D::result_type>::iterator I; |
| I lb = std::lower_bound(u.begin(), u.end(), b[i]); |
| I ub = std::lower_bound(u.begin(), u.end(), b[i+1]); |
| const size_t Ni = ub - lb; |
| if (prob[i] == 0) |
| assert(Ni == 0); |
| else |
| { |
| assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01); |
| double mean = std::accumulate(lb, ub, 0.0) / Ni; |
| double var = 0; |
| double skew = 0; |
| double kurtosis = 0; |
| for (I j = lb; j != ub; ++j) |
| { |
| double dbl = (*j - mean); |
| double d2 = sqr(dbl); |
| var += d2; |
| skew += dbl * d2; |
| kurtosis += d2 * d2; |
| } |
| var /= Ni; |
| double dev = std::sqrt(var); |
| skew /= Ni * dev * var; |
| kurtosis /= Ni * var * var; |
| kurtosis -= 3; |
| double x_mean = (b[i+1] + b[i]) / 2; |
| double x_var = sqr(b[i+1] - b[i]) / 12; |
| double x_skew = 0; |
| double x_kurtosis = -6./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) < 0.01); |
| assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); |
| } |
| } |
| } |
| |
| void |
| test11() |
| { |
| typedef std::piecewise_constant_distribution<> D; |
| typedef std::mt19937_64 G; |
| G g; |
| double b[] = {10, 14}; |
| double p[] = {1}; |
| const size_t Np = sizeof(p) / sizeof(p[0]); |
| D d(b, b+Np+1, p); |
| 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); |
| } |
| std::vector<double> prob(std::begin(p), std::end(p)); |
| double s = std::accumulate(prob.begin(), prob.end(), 0.0); |
| for (std::size_t i = 0; i < prob.size(); ++i) |
| prob[i] /= s; |
| std::sort(u.begin(), u.end()); |
| for (std::size_t i = 0; i < Np; ++i) |
| { |
| typedef std::vector<D::result_type>::iterator I; |
| I lb = std::lower_bound(u.begin(), u.end(), b[i]); |
| I ub = std::lower_bound(u.begin(), u.end(), b[i+1]); |
| const size_t Ni = ub - lb; |
| if (prob[i] == 0) |
| assert(Ni == 0); |
| else |
| { |
| assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01); |
| double mean = std::accumulate(lb, ub, 0.0) / Ni; |
| double var = 0; |
| double skew = 0; |
| double kurtosis = 0; |
| for (I j = lb; j != ub; ++j) |
| { |
| double dbl = (*j - mean); |
| double d2 = sqr(dbl); |
| var += d2; |
| skew += dbl * d2; |
| kurtosis += d2 * d2; |
| } |
| var /= Ni; |
| double dev = std::sqrt(var); |
| skew /= Ni * dev * var; |
| kurtosis /= Ni * var * var; |
| kurtosis -= 3; |
| double x_mean = (b[i+1] + b[i]) / 2; |
| double x_var = sqr(b[i+1] - b[i]) / 12; |
| double x_skew = 0; |
| double x_kurtosis = -6./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) < 0.01); |
| assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01); |
| } |
| } |
| } |
| |
| int main() |
| { |
| test1(); |
| test2(); |
| test3(); |
| test4(); |
| test5(); |
| test6(); |
| test7(); |
| test8(); |
| test9(); |
| test10(); |
| test11(); |
| } |