mirror of https://github.com/catchorg/Catch2.git
343 lines
14 KiB
C++
343 lines
14 KiB
C++
/*
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* Created by Joachim on 16/04/2019.
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* Adapted from donated nonius code.
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*
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* Distributed under the Boost Software License, Version 1.0. (See accompanying
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* file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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*/
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// Statistical analysis tools
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#ifndef TWOBLUECUBES_CATCH_DETAIL_ANALYSIS_HPP_INCLUDED
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#define TWOBLUECUBES_CATCH_DETAIL_ANALYSIS_HPP_INCLUDED
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#include "../catch_clock.hpp"
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#include "../catch_estimate.hpp"
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#include "../catch_outlier_classification.hpp"
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#include <algorithm>
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#include <cassert>
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#include <functional>
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#include <iterator>
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#include <vector>
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#include <array>
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#include <random>
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#include <numeric>
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#include <tuple>
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#include <cmath>
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#include <utility>
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#include <cstddef>
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#ifdef CATCH_USE_ASYNC
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#include <future>
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#endif
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namespace Catch {
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namespace Benchmark {
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namespace Detail {
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using sample = std::vector<double>;
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template <typename Iterator>
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double weighted_average_quantile(int k, int q, Iterator first, Iterator last) {
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auto count = last - first;
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double idx = (count - 1) * k / static_cast<double>(q);
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int j = static_cast<int>(idx);
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double g = idx - j;
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std::nth_element(first, first + j, last);
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auto xj = first[j];
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if (g == 0) return xj;
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auto xj1 = *std::min_element(first + (j + 1), last);
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return xj + g * (xj1 - xj);
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}
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template <typename Iterator>
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OutlierClassification classify_outliers(Iterator first, Iterator last) {
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std::vector<double> copy(first, last);
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auto q1 = weighted_average_quantile(1, 4, copy.begin(), copy.end());
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auto q3 = weighted_average_quantile(3, 4, copy.begin(), copy.end());
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auto iqr = q3 - q1;
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auto los = q1 - (iqr * 3.);
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auto lom = q1 - (iqr * 1.5);
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auto him = q3 + (iqr * 1.5);
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auto his = q3 + (iqr * 3.);
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OutlierClassification o;
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for (; first != last; ++first) {
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auto&& t = *first;
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if (t < los) ++o.low_severe;
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else if (t < lom) ++o.low_mild;
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else if (t > his) ++o.high_severe;
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else if (t > him) ++o.high_mild;
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++o.samples_seen;
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}
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return o;
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}
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template <typename Iterator>
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double mean(Iterator first, Iterator last) {
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auto count = last - first;
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double sum = std::accumulate(first, last, 0.);
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return sum / count;
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}
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template <typename Iterator>
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double standard_deviation(Iterator first, Iterator last) {
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auto m = mean(first, last);
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double variance = std::accumulate(first, last, 0., [m](double a, double b) {
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double diff = b - m;
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return a + diff * diff;
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}) / (last - first);
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return std::sqrt(variance);
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}
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template <typename URng, typename Iterator, typename Estimator>
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sample resample(URng& rng, int resamples, Iterator first, Iterator last, Estimator& estimator) {
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auto n = last - first;
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std::uniform_int_distribution<decltype(n)> dist(0, n - 1);
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sample out;
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out.reserve(resamples);
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std::generate_n(std::back_inserter(out), resamples, [n, first, &estimator, &dist, &rng] {
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std::vector<double> resampled;
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resampled.reserve(n);
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std::generate_n(std::back_inserter(resampled), n, [first, &dist, &rng] { return first[dist(rng)]; });
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return estimator(resampled.begin(), resampled.end());
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});
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std::sort(out.begin(), out.end());
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return out;
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}
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template <typename Estimator, typename Iterator>
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sample jackknife(Estimator&& estimator, Iterator first, Iterator last) {
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auto n = last - first;
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auto second = std::next(first);
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sample results;
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results.reserve(n);
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for (auto it = first; it != last; ++it) {
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std::iter_swap(it, first);
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results.push_back(estimator(second, last));
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}
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return results;
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}
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inline double normal_cdf(double x) {
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return std::erfc(-x / std::sqrt(2.0)) / 2.0;
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}
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inline double erf_inv(double x) {
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// Code accompanying the article "Approximating the erfinv function" in GPU Computing Gems, Volume 2
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double w, p;
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w = -log((1.0 - x)*(1.0 + x));
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if (w < 6.250000) {
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w = w - 3.125000;
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p = -3.6444120640178196996e-21;
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p = -1.685059138182016589e-19 + p * w;
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p = 1.2858480715256400167e-18 + p * w;
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p = 1.115787767802518096e-17 + p * w;
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p = -1.333171662854620906e-16 + p * w;
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p = 2.0972767875968561637e-17 + p * w;
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p = 6.6376381343583238325e-15 + p * w;
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p = -4.0545662729752068639e-14 + p * w;
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p = -8.1519341976054721522e-14 + p * w;
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p = 2.6335093153082322977e-12 + p * w;
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p = -1.2975133253453532498e-11 + p * w;
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p = -5.4154120542946279317e-11 + p * w;
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p = 1.051212273321532285e-09 + p * w;
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p = -4.1126339803469836976e-09 + p * w;
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p = -2.9070369957882005086e-08 + p * w;
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p = 4.2347877827932403518e-07 + p * w;
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p = -1.3654692000834678645e-06 + p * w;
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p = -1.3882523362786468719e-05 + p * w;
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p = 0.0001867342080340571352 + p * w;
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p = -0.00074070253416626697512 + p * w;
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p = -0.0060336708714301490533 + p * w;
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p = 0.24015818242558961693 + p * w;
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p = 1.6536545626831027356 + p * w;
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} else if (w < 16.000000) {
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w = sqrt(w) - 3.250000;
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p = 2.2137376921775787049e-09;
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p = 9.0756561938885390979e-08 + p * w;
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p = -2.7517406297064545428e-07 + p * w;
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p = 1.8239629214389227755e-08 + p * w;
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p = 1.5027403968909827627e-06 + p * w;
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p = -4.013867526981545969e-06 + p * w;
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p = 2.9234449089955446044e-06 + p * w;
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p = 1.2475304481671778723e-05 + p * w;
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p = -4.7318229009055733981e-05 + p * w;
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p = 6.8284851459573175448e-05 + p * w;
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p = 2.4031110387097893999e-05 + p * w;
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p = -0.0003550375203628474796 + p * w;
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p = 0.00095328937973738049703 + p * w;
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p = -0.0016882755560235047313 + p * w;
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p = 0.0024914420961078508066 + p * w;
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p = -0.0037512085075692412107 + p * w;
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p = 0.005370914553590063617 + p * w;
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p = 1.0052589676941592334 + p * w;
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p = 3.0838856104922207635 + p * w;
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} else {
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w = sqrt(w) - 5.000000;
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p = -2.7109920616438573243e-11;
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p = -2.5556418169965252055e-10 + p * w;
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p = 1.5076572693500548083e-09 + p * w;
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p = -3.7894654401267369937e-09 + p * w;
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p = 7.6157012080783393804e-09 + p * w;
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p = -1.4960026627149240478e-08 + p * w;
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p = 2.9147953450901080826e-08 + p * w;
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p = -6.7711997758452339498e-08 + p * w;
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p = 2.2900482228026654717e-07 + p * w;
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p = -9.9298272942317002539e-07 + p * w;
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p = 4.5260625972231537039e-06 + p * w;
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p = -1.9681778105531670567e-05 + p * w;
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p = 7.5995277030017761139e-05 + p * w;
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p = -0.00021503011930044477347 + p * w;
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p = -0.00013871931833623122026 + p * w;
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p = 1.0103004648645343977 + p * w;
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p = 4.8499064014085844221 + p * w;
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}
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return p * x;
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}
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inline double erfc_inv(double x) {
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return erf_inv(1.0 - x);
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}
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inline double normal_quantile(double p) {
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static const double ROOT_TWO = std::sqrt(2.0);
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double result = 0.0;
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assert(p >= 0 && p <= 1);
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if (p < 0 || p > 1) {
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return result;
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}
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result = -erfc_inv(2.0 * p);
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// result *= normal distribution standard deviation (1.0) * sqrt(2)
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result *= /*sd * */ ROOT_TWO;
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// result += normal disttribution mean (0)
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return result;
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}
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template <typename Iterator, typename Estimator>
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Estimate<double> bootstrap(double confidence_level, Iterator first, Iterator last, sample const& resample, Estimator&& estimator) {
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auto n_samples = last - first;
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double point = estimator(first, last);
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// Degenerate case with a single sample
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if (n_samples == 1) return { point, point, point, confidence_level };
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sample jack = jackknife(estimator, first, last);
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double jack_mean = mean(jack.begin(), jack.end());
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double sum_squares, sum_cubes;
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std::tie(sum_squares, sum_cubes) = std::accumulate(jack.begin(), jack.end(), std::make_pair(0., 0.), [jack_mean](std::pair<double, double> sqcb, double x) -> std::pair<double, double> {
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auto d = jack_mean - x;
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auto d2 = d * d;
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auto d3 = d2 * d;
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return { sqcb.first + d2, sqcb.second + d3 };
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});
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double accel = sum_cubes / (6 * std::pow(sum_squares, 1.5));
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int n = static_cast<int>(resample.size());
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double prob_n = std::count_if(resample.begin(), resample.end(), [point](double x) { return x < point; }) / (double)n;
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// degenerate case with uniform samples
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if (prob_n == 0) return { point, point, point, confidence_level };
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double bias = normal_quantile(prob_n);
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double z1 = normal_quantile((1. - confidence_level) / 2.);
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auto cumn = [n](double x) -> int {
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return std::lround(normal_cdf(x) * n); };
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auto a = [bias, accel](double b) { return bias + b / (1. - accel * b); };
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double b1 = bias + z1;
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double b2 = bias - z1;
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double a1 = a(b1);
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double a2 = a(b2);
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auto lo = std::max(cumn(a1), 0);
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auto hi = std::min(cumn(a2), n - 1);
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return { point, resample[lo], resample[hi], confidence_level };
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}
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inline double outlier_variance(Estimate<double> mean, Estimate<double> stddev, int n) {
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double sb = stddev.point;
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double mn = mean.point / n;
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double mg_min = mn / 2.;
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double sg = std::min(mg_min / 4., sb / std::sqrt(n));
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double sg2 = sg * sg;
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double sb2 = sb * sb;
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auto c_max = [n, mn, sb2, sg2](double x) -> double {
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double k = mn - x;
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double d = k * k;
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double nd = n * d;
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double k0 = -n * nd;
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double k1 = sb2 - n * sg2 + nd;
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double det = k1 * k1 - 4 * sg2 * k0;
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return (int)(-2. * k0 / (k1 + std::sqrt(det)));
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};
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auto var_out = [n, sb2, sg2](double c) {
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double nc = n - c;
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return (nc / n) * (sb2 - nc * sg2);
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};
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return std::min(var_out(1), var_out(std::min(c_max(0.), c_max(mg_min)))) / sb2;
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}
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struct bootstrap_analysis {
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Estimate<double> mean;
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Estimate<double> standard_deviation;
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double outlier_variance;
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};
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template <typename Iterator>
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bootstrap_analysis analyse_samples(double confidence_level, int n_resamples, Iterator first, Iterator last) {
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static std::random_device entropy;
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auto n = static_cast<int>(last - first); // seriously, one can't use integral types without hell in C++
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auto mean = &Detail::mean<Iterator>;
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auto stddev = &Detail::standard_deviation<Iterator>;
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#ifdef CATCH_USE_ASYNC
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auto Estimate = [=](double(*f)(Iterator, Iterator)) {
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auto seed = entropy();
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return std::async(std::launch::async, [=] {
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std::mt19937 rng(seed);
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auto resampled = resample(rng, n_resamples, first, last, f);
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return bootstrap(confidence_level, first, last, resampled, f);
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});
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};
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auto mean_future = Estimate(mean);
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auto stddev_future = Estimate(stddev);
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auto mean_estimate = mean_future.get();
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auto stddev_estimate = stddev_future.get();
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#else
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auto Estimate = [=](double(*f)(Iterator, Iterator)) {
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auto seed = entropy();
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std::mt19937 rng(seed);
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auto resampled = resample(rng, n_resamples, first, last, f);
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return bootstrap(confidence_level, first, last, resampled, f);
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};
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auto mean_estimate = Estimate(mean);
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auto stddev_estimate = Estimate(stddev);
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#endif // CATCH_USE_ASYNC
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double outlier_variance = Detail::outlier_variance(mean_estimate, stddev_estimate, n);
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return { mean_estimate, stddev_estimate, outlier_variance };
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}
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} // namespace Detail
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} // namespace Benchmark
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} // namespace Catch
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#endif // TWOBLUECUBES_CATCH_DETAIL_ANALYSIS_HPP_INCLUDED
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