741 lines
23 KiB
C++
741 lines
23 KiB
C++
//===----------------------------------------------------------------------===//
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//
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// The LLVM Compiler Infrastructure
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//
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// This file is dual licensed under the MIT and the University of Illinois Open
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// Source Licenses. See LICENSE.TXT for details.
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//
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//===----------------------------------------------------------------------===//
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//
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// REQUIRES: long_tests
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// <random>
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// template<class RealType = double>
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// class piecewise_constant_distribution
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// template<class _URNG> result_type operator()(_URNG& g);
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#include <random>
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#include <vector>
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#include <iterator>
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#include <numeric>
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#include <algorithm> // for sort
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#include <cassert>
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template <class T>
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inline
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T
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sqr(T x)
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{
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return x*x;
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}
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void
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test1()
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{
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typedef std::piecewise_constant_distribution<> D;
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typedef std::mt19937_64 G;
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G g;
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double b[] = {10, 14, 16, 17};
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double p[] = {25, 62.5, 12.5};
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const size_t Np = sizeof(p) / sizeof(p[0]);
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D d(b, b+Np+1, p);
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const int N = 1000000;
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std::vector<D::result_type> u;
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for (int i = 0; i < N; ++i)
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{
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D::result_type v = d(g);
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assert(d.min() <= v && v < d.max());
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u.push_back(v);
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}
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std::vector<double> prob(std::begin(p), std::end(p));
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double s = std::accumulate(prob.begin(), prob.end(), 0.0);
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for (int i = 0; i < prob.size(); ++i)
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prob[i] /= s;
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std::sort(u.begin(), u.end());
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for (int i = 0; i < Np; ++i)
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{
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typedef std::vector<D::result_type>::iterator I;
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I lb = std::lower_bound(u.begin(), u.end(), b[i]);
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I ub = std::lower_bound(u.begin(), u.end(), b[i+1]);
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const size_t Ni = ub - lb;
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if (prob[i] == 0)
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assert(Ni == 0);
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else
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{
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assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01);
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double mean = std::accumulate(lb, ub, 0.0) / Ni;
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double var = 0;
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double skew = 0;
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double kurtosis = 0;
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for (I j = lb; j != ub; ++j)
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{
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double dbl = (*j - mean);
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double d2 = sqr(dbl);
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var += d2;
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skew += dbl * d2;
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kurtosis += d2 * d2;
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}
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var /= Ni;
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double dev = std::sqrt(var);
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skew /= Ni * dev * var;
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kurtosis /= Ni * var * var;
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kurtosis -= 3;
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double x_mean = (b[i+1] + b[i]) / 2;
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double x_var = sqr(b[i+1] - b[i]) / 12;
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double x_skew = 0;
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double x_kurtosis = -6./5;
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assert(std::abs((mean - x_mean) / x_mean) < 0.01);
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assert(std::abs((var - x_var) / x_var) < 0.01);
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assert(std::abs(skew - x_skew) < 0.01);
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assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
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}
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}
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}
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void
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test2()
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{
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typedef std::piecewise_constant_distribution<> D;
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typedef std::mt19937_64 G;
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G g;
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double b[] = {10, 14, 16, 17};
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double p[] = {0, 62.5, 12.5};
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const size_t Np = sizeof(p) / sizeof(p[0]);
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D d(b, b+Np+1, p);
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const int N = 1000000;
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std::vector<D::result_type> u;
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for (int i = 0; i < N; ++i)
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{
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D::result_type v = d(g);
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assert(d.min() <= v && v < d.max());
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u.push_back(v);
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}
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std::vector<double> prob(std::begin(p), std::end(p));
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double s = std::accumulate(prob.begin(), prob.end(), 0.0);
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for (int i = 0; i < prob.size(); ++i)
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prob[i] /= s;
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std::sort(u.begin(), u.end());
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for (int i = 0; i < Np; ++i)
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{
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typedef std::vector<D::result_type>::iterator I;
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I lb = std::lower_bound(u.begin(), u.end(), b[i]);
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I ub = std::lower_bound(u.begin(), u.end(), b[i+1]);
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const size_t Ni = ub - lb;
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if (prob[i] == 0)
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assert(Ni == 0);
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else
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{
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assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01);
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double mean = std::accumulate(lb, ub, 0.0) / Ni;
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double var = 0;
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double skew = 0;
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double kurtosis = 0;
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for (I j = lb; j != ub; ++j)
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{
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double dbl = (*j - mean);
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double d2 = sqr(dbl);
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var += d2;
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skew += dbl * d2;
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kurtosis += d2 * d2;
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}
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var /= Ni;
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double dev = std::sqrt(var);
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skew /= Ni * dev * var;
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kurtosis /= Ni * var * var;
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kurtosis -= 3;
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double x_mean = (b[i+1] + b[i]) / 2;
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double x_var = sqr(b[i+1] - b[i]) / 12;
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double x_skew = 0;
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double x_kurtosis = -6./5;
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assert(std::abs((mean - x_mean) / x_mean) < 0.01);
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assert(std::abs((var - x_var) / x_var) < 0.01);
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assert(std::abs(skew - x_skew) < 0.01);
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assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
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}
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}
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}
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void
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test3()
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{
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typedef std::piecewise_constant_distribution<> D;
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typedef std::mt19937_64 G;
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G g;
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double b[] = {10, 14, 16, 17};
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double p[] = {25, 0, 12.5};
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const size_t Np = sizeof(p) / sizeof(p[0]);
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D d(b, b+Np+1, p);
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const int N = 1000000;
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std::vector<D::result_type> u;
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for (int i = 0; i < N; ++i)
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{
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D::result_type v = d(g);
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assert(d.min() <= v && v < d.max());
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u.push_back(v);
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}
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std::vector<double> prob(std::begin(p), std::end(p));
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double s = std::accumulate(prob.begin(), prob.end(), 0.0);
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for (int i = 0; i < prob.size(); ++i)
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prob[i] /= s;
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std::sort(u.begin(), u.end());
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for (int i = 0; i < Np; ++i)
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{
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typedef std::vector<D::result_type>::iterator I;
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I lb = std::lower_bound(u.begin(), u.end(), b[i]);
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I ub = std::lower_bound(u.begin(), u.end(), b[i+1]);
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const size_t Ni = ub - lb;
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if (prob[i] == 0)
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assert(Ni == 0);
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else
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{
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assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01);
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double mean = std::accumulate(lb, ub, 0.0) / Ni;
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double var = 0;
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double skew = 0;
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double kurtosis = 0;
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for (I j = lb; j != ub; ++j)
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{
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double dbl = (*j - mean);
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double d2 = sqr(dbl);
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var += d2;
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skew += dbl * d2;
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kurtosis += d2 * d2;
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}
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var /= Ni;
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double dev = std::sqrt(var);
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skew /= Ni * dev * var;
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kurtosis /= Ni * var * var;
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kurtosis -= 3;
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double x_mean = (b[i+1] + b[i]) / 2;
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double x_var = sqr(b[i+1] - b[i]) / 12;
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double x_skew = 0;
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double x_kurtosis = -6./5;
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assert(std::abs((mean - x_mean) / x_mean) < 0.01);
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assert(std::abs((var - x_var) / x_var) < 0.01);
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assert(std::abs(skew - x_skew) < 0.01);
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assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
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}
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}
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}
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void
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test4()
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{
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typedef std::piecewise_constant_distribution<> D;
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typedef std::mt19937_64 G;
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G g;
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double b[] = {10, 14, 16, 17};
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double p[] = {25, 62.5, 0};
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const size_t Np = sizeof(p) / sizeof(p[0]);
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D d(b, b+Np+1, p);
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const int N = 1000000;
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std::vector<D::result_type> u;
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for (int i = 0; i < N; ++i)
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{
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D::result_type v = d(g);
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assert(d.min() <= v && v < d.max());
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u.push_back(v);
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}
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std::vector<double> prob(std::begin(p), std::end(p));
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double s = std::accumulate(prob.begin(), prob.end(), 0.0);
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for (int i = 0; i < prob.size(); ++i)
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prob[i] /= s;
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std::sort(u.begin(), u.end());
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for (int i = 0; i < Np; ++i)
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{
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typedef std::vector<D::result_type>::iterator I;
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I lb = std::lower_bound(u.begin(), u.end(), b[i]);
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I ub = std::lower_bound(u.begin(), u.end(), b[i+1]);
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const size_t Ni = ub - lb;
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if (prob[i] == 0)
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assert(Ni == 0);
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else
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{
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assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01);
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double mean = std::accumulate(lb, ub, 0.0) / Ni;
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double var = 0;
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double skew = 0;
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double kurtosis = 0;
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for (I j = lb; j != ub; ++j)
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{
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double dbl = (*j - mean);
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double d2 = sqr(dbl);
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var += d2;
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skew += dbl * d2;
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kurtosis += d2 * d2;
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}
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var /= Ni;
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double dev = std::sqrt(var);
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skew /= Ni * dev * var;
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kurtosis /= Ni * var * var;
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kurtosis -= 3;
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double x_mean = (b[i+1] + b[i]) / 2;
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double x_var = sqr(b[i+1] - b[i]) / 12;
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double x_skew = 0;
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double x_kurtosis = -6./5;
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assert(std::abs((mean - x_mean) / x_mean) < 0.01);
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assert(std::abs((var - x_var) / x_var) < 0.01);
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assert(std::abs(skew - x_skew) < 0.01);
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assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
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}
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}
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}
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void
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test5()
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{
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typedef std::piecewise_constant_distribution<> D;
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typedef std::mt19937_64 G;
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G g;
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double b[] = {10, 14, 16, 17};
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double p[] = {25, 0, 0};
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const size_t Np = sizeof(p) / sizeof(p[0]);
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D d(b, b+Np+1, p);
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const int N = 100000;
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std::vector<D::result_type> u;
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for (int i = 0; i < N; ++i)
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{
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D::result_type v = d(g);
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assert(d.min() <= v && v < d.max());
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u.push_back(v);
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}
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std::vector<double> prob(std::begin(p), std::end(p));
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double s = std::accumulate(prob.begin(), prob.end(), 0.0);
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for (int i = 0; i < prob.size(); ++i)
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prob[i] /= s;
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std::sort(u.begin(), u.end());
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for (int i = 0; i < Np; ++i)
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{
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typedef std::vector<D::result_type>::iterator I;
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I lb = std::lower_bound(u.begin(), u.end(), b[i]);
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I ub = std::lower_bound(u.begin(), u.end(), b[i+1]);
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const size_t Ni = ub - lb;
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if (prob[i] == 0)
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assert(Ni == 0);
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else
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{
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assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01);
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double mean = std::accumulate(lb, ub, 0.0) / Ni;
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double var = 0;
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double skew = 0;
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double kurtosis = 0;
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for (I j = lb; j != ub; ++j)
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{
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double dbl = (*j - mean);
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double d2 = sqr(dbl);
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var += d2;
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skew += dbl * d2;
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kurtosis += d2 * d2;
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}
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var /= Ni;
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double dev = std::sqrt(var);
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skew /= Ni * dev * var;
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kurtosis /= Ni * var * var;
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kurtosis -= 3;
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double x_mean = (b[i+1] + b[i]) / 2;
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double x_var = sqr(b[i+1] - b[i]) / 12;
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double x_skew = 0;
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double x_kurtosis = -6./5;
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assert(std::abs((mean - x_mean) / x_mean) < 0.01);
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assert(std::abs((var - x_var) / x_var) < 0.01);
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assert(std::abs(skew - x_skew) < 0.01);
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assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
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}
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}
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}
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void
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test6()
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{
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typedef std::piecewise_constant_distribution<> D;
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typedef std::mt19937_64 G;
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G g;
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double b[] = {10, 14, 16, 17};
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double p[] = {0, 25, 0};
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const size_t Np = sizeof(p) / sizeof(p[0]);
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D d(b, b+Np+1, p);
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const int N = 100000;
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std::vector<D::result_type> u;
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for (int i = 0; i < N; ++i)
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{
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D::result_type v = d(g);
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assert(d.min() <= v && v < d.max());
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u.push_back(v);
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}
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std::vector<double> prob(std::begin(p), std::end(p));
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double s = std::accumulate(prob.begin(), prob.end(), 0.0);
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for (int i = 0; i < prob.size(); ++i)
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prob[i] /= s;
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std::sort(u.begin(), u.end());
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for (int i = 0; i < Np; ++i)
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{
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typedef std::vector<D::result_type>::iterator I;
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I lb = std::lower_bound(u.begin(), u.end(), b[i]);
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I ub = std::lower_bound(u.begin(), u.end(), b[i+1]);
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const size_t Ni = ub - lb;
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if (prob[i] == 0)
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assert(Ni == 0);
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else
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{
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assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01);
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double mean = std::accumulate(lb, ub, 0.0) / Ni;
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double var = 0;
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double skew = 0;
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double kurtosis = 0;
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for (I j = lb; j != ub; ++j)
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{
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double dbl = (*j - mean);
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double d2 = sqr(dbl);
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var += d2;
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skew += dbl * d2;
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kurtosis += d2 * d2;
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}
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var /= Ni;
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double dev = std::sqrt(var);
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skew /= Ni * dev * var;
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kurtosis /= Ni * var * var;
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kurtosis -= 3;
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double x_mean = (b[i+1] + b[i]) / 2;
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double x_var = sqr(b[i+1] - b[i]) / 12;
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double x_skew = 0;
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double x_kurtosis = -6./5;
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assert(std::abs((mean - x_mean) / x_mean) < 0.01);
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assert(std::abs((var - x_var) / x_var) < 0.01);
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assert(std::abs(skew - x_skew) < 0.01);
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assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
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}
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}
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}
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void
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test7()
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{
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typedef std::piecewise_constant_distribution<> D;
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typedef std::mt19937_64 G;
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G g;
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double b[] = {10, 14, 16, 17};
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double p[] = {0, 0, 1};
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const size_t Np = sizeof(p) / sizeof(p[0]);
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D d(b, b+Np+1, p);
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const int N = 100000;
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std::vector<D::result_type> u;
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for (int i = 0; i < N; ++i)
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{
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D::result_type v = d(g);
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assert(d.min() <= v && v < d.max());
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u.push_back(v);
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}
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std::vector<double> prob(std::begin(p), std::end(p));
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double s = std::accumulate(prob.begin(), prob.end(), 0.0);
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for (int i = 0; i < prob.size(); ++i)
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prob[i] /= s;
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std::sort(u.begin(), u.end());
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for (int i = 0; i < Np; ++i)
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{
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typedef std::vector<D::result_type>::iterator I;
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I lb = std::lower_bound(u.begin(), u.end(), b[i]);
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I ub = std::lower_bound(u.begin(), u.end(), b[i+1]);
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const size_t Ni = ub - lb;
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if (prob[i] == 0)
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assert(Ni == 0);
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else
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{
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assert(std::abs((double)Ni/N - prob[i]) / prob[i] < .01);
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double mean = std::accumulate(lb, ub, 0.0) / Ni;
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double var = 0;
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double skew = 0;
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double kurtosis = 0;
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for (I j = lb; j != ub; ++j)
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{
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double dbl = (*j - mean);
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double d2 = sqr(dbl);
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var += d2;
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skew += dbl * d2;
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kurtosis += d2 * d2;
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}
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var /= Ni;
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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 (int i = 0; i < prob.size(); ++i)
|
|
prob[i] /= s;
|
|
std::sort(u.begin(), u.end());
|
|
for (int 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 (int i = 0; i < prob.size(); ++i)
|
|
prob[i] /= s;
|
|
std::sort(u.begin(), u.end());
|
|
for (int 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 (int i = 0; i < prob.size(); ++i)
|
|
prob[i] /= s;
|
|
std::sort(u.begin(), u.end());
|
|
for (int 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 (int i = 0; i < prob.size(); ++i)
|
|
prob[i] /= s;
|
|
std::sort(u.begin(), u.end());
|
|
for (int 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();
|
|
}
|