/* * Created by Joachim on 16/04/2019. * Adapted from donated nonius code. * * Distributed under the Boost Software License, Version 1.0. (See accompanying * file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) */ // Statistical analysis tools #ifndef TWOBLUECUBES_CATCH_DETAIL_ANALYSIS_HPP_INCLUDED #define TWOBLUECUBES_CATCH_DETAIL_ANALYSIS_HPP_INCLUDED #include "../catch_clock.hpp" #include "../catch_estimate.hpp" #include "../catch_outlier_classification.hpp" #include <algorithm> #include <functional> #include <vector> #include <iterator> #include <numeric> #include <tuple> #include <cmath> #include <utility> #include <cstddef> #include <random> namespace Catch { namespace Benchmark { namespace Detail { using sample = std::vector<double>; double weighted_average_quantile(int k, int q, std::vector<double>::iterator first, std::vector<double>::iterator last); template <typename Iterator> OutlierClassification classify_outliers(Iterator first, Iterator last) { std::vector<double> copy(first, last); auto q1 = weighted_average_quantile(1, 4, copy.begin(), copy.end()); auto q3 = weighted_average_quantile(3, 4, copy.begin(), copy.end()); auto iqr = q3 - q1; auto los = q1 - (iqr * 3.); auto lom = q1 - (iqr * 1.5); auto him = q3 + (iqr * 1.5); auto his = q3 + (iqr * 3.); OutlierClassification o; for (; first != last; ++first) { auto&& t = *first; if (t < los) ++o.low_severe; else if (t < lom) ++o.low_mild; else if (t > his) ++o.high_severe; else if (t > him) ++o.high_mild; ++o.samples_seen; } return o; } template <typename Iterator> double mean(Iterator first, Iterator last) { auto count = last - first; double sum = std::accumulate(first, last, 0.); return sum / count; } template <typename URng, typename Iterator, typename Estimator> sample resample(URng& rng, int resamples, Iterator first, Iterator last, Estimator& estimator) { auto n = last - first; std::uniform_int_distribution<decltype(n)> dist(0, n - 1); sample out; out.reserve(resamples); std::generate_n(std::back_inserter(out), resamples, [n, first, &estimator, &dist, &rng] { std::vector<double> resampled; resampled.reserve(n); std::generate_n(std::back_inserter(resampled), n, [first, &dist, &rng] { return first[dist(rng)]; }); return estimator(resampled.begin(), resampled.end()); }); std::sort(out.begin(), out.end()); return out; } template <typename Estimator, typename Iterator> sample jackknife(Estimator&& estimator, Iterator first, Iterator last) { auto n = last - first; auto second = std::next(first); sample results; results.reserve(n); for (auto it = first; it != last; ++it) { std::iter_swap(it, first); results.push_back(estimator(second, last)); } return results; } inline double normal_cdf(double x) { return std::erfc(-x / std::sqrt(2.0)) / 2.0; } double erfc_inv(double x); double normal_quantile(double p); template <typename Iterator, typename Estimator> Estimate<double> bootstrap(double confidence_level, Iterator first, Iterator last, sample const& resample, Estimator&& estimator) { auto n_samples = last - first; double point = estimator(first, last); // Degenerate case with a single sample if (n_samples == 1) return { point, point, point, confidence_level }; sample jack = jackknife(estimator, first, last); double jack_mean = mean(jack.begin(), jack.end()); double sum_squares, sum_cubes; 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> { auto d = jack_mean - x; auto d2 = d * d; auto d3 = d2 * d; return { sqcb.first + d2, sqcb.second + d3 }; }); double accel = sum_cubes / (6 * std::pow(sum_squares, 1.5)); int n = static_cast<int>(resample.size()); double prob_n = std::count_if(resample.begin(), resample.end(), [point](double x) { return x < point; }) / (double)n; // degenerate case with uniform samples if (prob_n == 0) return { point, point, point, confidence_level }; double bias = normal_quantile(prob_n); double z1 = normal_quantile((1. - confidence_level) / 2.); auto cumn = [n](double x) -> int { return std::lround(normal_cdf(x) * n); }; auto a = [bias, accel](double b) { return bias + b / (1. - accel * b); }; double b1 = bias + z1; double b2 = bias - z1; double a1 = a(b1); double a2 = a(b2); auto lo = std::max(cumn(a1), 0); auto hi = std::min(cumn(a2), n - 1); return { point, resample[lo], resample[hi], confidence_level }; } double outlier_variance(Estimate<double> mean, Estimate<double> stddev, int n); struct bootstrap_analysis { Estimate<double> mean; Estimate<double> standard_deviation; double outlier_variance; }; bootstrap_analysis analyse_samples(double confidence_level, int n_resamples, std::vector<double>::iterator first, std::vector<double>::iterator last); } // namespace Detail } // namespace Benchmark } // namespace Catch #endif // TWOBLUECUBES_CATCH_DETAIL_ANALYSIS_HPP_INCLUDED