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// Copyright 2023 Google LLC // SPDX-License-Identifier: Apache-2.0 // // Licensed under the Apache License, Version 2.0 (the "License"); // you may not use this file except in compliance with the License. // You may obtain a copy of the License at // // http://www.apache.org/licenses/LICENSE-2.0 // // Unless required by applicable law or agreed to in writing, software // distributed under the License is distributed on an "AS IS" BASIS, // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. // See the License for the specific language governing permissions and // limitations under the License. #ifndef HIGHWAY_HWY_ROBUST_STATISTICS_H_ #define HIGHWAY_HWY_ROBUST_STATISTICS_H_ #include // std::sort, std::find_if #include #include // std::pair #include #include "hwy/base.h" namespace hwy { namespace robust_statistics { // Sorts integral values in ascending order (e.g. for Mode). About 3x faster // than std::sort for input distributions with very few unique values. template void CountingSort(T* values, size_t num_values) { // Unique values and their frequency (similar to flat_map). using Unique = std::pair; std::vector unique; for (size_t i = 0; i < num_values; ++i) { const T value = values[i]; const auto pos = std::find_if(unique.begin(), unique.end(), [value](const Unique u) { return u.first == value; }); if (pos == unique.end()) { unique.push_back(std::make_pair(value, 1)); } else { ++pos->second; } } // Sort in ascending order of value (pair.first). std::sort(unique.begin(), unique.end()); // Write that many copies of each unique value to the array. T* HWY_RESTRICT p = values; for (const auto& value_count : unique) { std::fill(p, p + value_count.second, value_count.first); p += value_count.second; } HWY_ASSERT(p == values + num_values); } // @return i in [idx_begin, idx_begin + half_count) that minimizes // sorted[i + half_count] - sorted[i]. template size_t MinRange(const T* const HWY_RESTRICT sorted, const size_t idx_begin, const size_t half_count) { T min_range = std::numeric_limits::max(); size_t min_idx = 0; for (size_t idx = idx_begin; idx < idx_begin + half_count; ++idx) { HWY_ASSERT(sorted[idx] <= sorted[idx + half_count]); const T range = sorted[idx + half_count] - sorted[idx]; if (range < min_range) { min_range = range; min_idx = idx; } } return min_idx; } // Returns an estimate of the mode by calling MinRange on successively // halved intervals. "sorted" must be in ascending order. This is the // Half Sample Mode estimator proposed by Bickel in "On a fast, robust // estimator of the mode", with complexity O(N log N). The mode is less // affected by outliers in highly-skewed distributions than the median. // The averaging operation below assumes "T" is an unsigned integer type. template T ModeOfSorted(const T* const HWY_RESTRICT sorted, const size_t num_values) { size_t idx_begin = 0; size_t half_count = num_values / 2; while (half_count > 1) { idx_begin = MinRange(sorted, idx_begin, half_count); half_count >>= 1; } const T x = sorted[idx_begin + 0]; if (half_count == 0) { return x; } HWY_ASSERT(half_count == 1); const T average = (x + sorted[idx_begin + 1] + 1) / 2; return average; } // Returns the mode. Side effect: sorts "values". template T Mode(T* values, const size_t num_values) { CountingSort(values, num_values); return ModeOfSorted(values, num_values); } template T Mode(T (&values)[N]) { return Mode(&values[0], N); } // Returns the median value. Side effect: sorts "values". template T Median(T* values, const size_t num_values) { HWY_ASSERT(num_values != 0); std::sort(values, values + num_values); const size_t half = num_values / 2; // Odd count: return middle if (num_values % 2) { return values[half]; } // Even count: return average of middle two. return (values[half] + values[half - 1] + 1) / 2; } // Returns a robust measure of variability. template T MedianAbsoluteDeviation(const T* values, const size_t num_values, const T median) { HWY_ASSERT(num_values != 0); std::vector abs_deviations; abs_deviations.reserve(num_values); for (size_t i = 0; i < num_values; ++i) { const int64_t abs = ScalarAbs(static_cast(values[i]) - static_cast(median)); abs_deviations.push_back(static_cast(abs)); } return Median(abs_deviations.data(), num_values); } } // namespace robust_statistics } // namespace hwy #endif // HIGHWAY_HWY_ROBUST_STATISTICS_H_