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/*
* 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
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