Added thirdparty: boost library

thirdparty/include/boost/histogram/accumulators/weighted_mean.hpp

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+// Copyright 2018 Hans Dembinski
+//
+// 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)
+
+#ifndef BOOST_HISTOGRAM_ACCUMULATORS_WEIGHTED_MEAN_HPP
+#define BOOST_HISTOGRAM_ACCUMULATORS_WEIGHTED_MEAN_HPP
+
+#include <boost/core/nvp.hpp>
+#include <boost/histogram/detail/square.hpp>
+#include <boost/histogram/fwd.hpp> // for weighted_mean<>
+#include <boost/histogram/weight.hpp>
+#include <cassert>
+#include <type_traits>
+
+namespace boost {
+namespace histogram {
+namespace accumulators {
+
+/**
+  Calculates mean and variance of weighted sample.
+
+  Uses West's incremental algorithm to improve numerical stability
+  of mean and variance computation.
+*/
+template <class ValueType>
+class weighted_mean {
+public:
+  using value_type = ValueType;
+  using const_reference = const value_type&;
+
+  weighted_mean() = default;
+
+  /// Allow implicit conversion from other weighted_means.
+  template <class T>
+  weighted_mean(const weighted_mean<T>& o)
+      : sum_of_weights_{o.sum_of_weights_}
+      , sum_of_weights_squared_{o.sum_of_weights_squared_}
+      , weighted_mean_{o.weighted_mean_}
+      , sum_of_weighted_deltas_squared_{o.sum_of_weighted_deltas_squared_} {}
+
+  /// Initialize to external sum of weights, sum of weights squared, mean, and variance.
+  weighted_mean(const_reference wsum, const_reference wsum2, const_reference mean,
+                const_reference variance)
+      : sum_of_weights_(wsum)
+      , sum_of_weights_squared_(wsum2)
+      , weighted_mean_(mean)
+      , sum_of_weighted_deltas_squared_(
+            variance * (sum_of_weights_ - sum_of_weights_squared_ / sum_of_weights_)) {}
+
+  /// Insert sample x.
+  void operator()(const_reference x) { operator()(weight(1), x); }
+
+  /// Insert sample x with weight w.
+  void operator()(const weight_type<value_type>& w, const_reference x) {
+    sum_of_weights_ += w.value;
+    sum_of_weights_squared_ += w.value * w.value;
+    const auto delta = x - weighted_mean_;
+    weighted_mean_ += w.value * delta / sum_of_weights_;
+    sum_of_weighted_deltas_squared_ += w.value * delta * (x - weighted_mean_);
+  }
+
+  /// Add another weighted_mean.
+  weighted_mean& operator+=(const weighted_mean& rhs) {
+    if (rhs.sum_of_weights_ == 0) return *this;
+
+    // see mean.hpp for derivation of correct formula
+
+    const auto n1 = sum_of_weights_;
+    const auto mu1 = weighted_mean_;
+    const auto n2 = rhs.sum_of_weights_;
+    const auto mu2 = rhs.weighted_mean_;
+
+    sum_of_weights_ += rhs.sum_of_weights_;
+    sum_of_weights_squared_ += rhs.sum_of_weights_squared_;
+    weighted_mean_ = (n1 * mu1 + n2 * mu2) / sum_of_weights_;
+
+    sum_of_weighted_deltas_squared_ += rhs.sum_of_weighted_deltas_squared_;
+    sum_of_weighted_deltas_squared_ += n1 * detail::square(weighted_mean_ - mu1);
+    sum_of_weighted_deltas_squared_ += n2 * detail::square(weighted_mean_ - mu2);
+
+    return *this;
+  }
+
+  /** Scale by value.
+
+   This acts as if all samples were scaled by the value.
+  */
+  weighted_mean& operator*=(const_reference s) noexcept {
+    weighted_mean_ *= s;
+    sum_of_weighted_deltas_squared_ *= s * s;
+    return *this;
+  }
+
+  bool operator==(const weighted_mean& rhs) const noexcept {
+    return sum_of_weights_ == rhs.sum_of_weights_ &&
+           sum_of_weights_squared_ == rhs.sum_of_weights_squared_ &&
+           weighted_mean_ == rhs.weighted_mean_ &&
+           sum_of_weighted_deltas_squared_ == rhs.sum_of_weighted_deltas_squared_;
+  }
+
+  bool operator!=(const weighted_mean& rhs) const noexcept { return !operator==(rhs); }
+
+  /// Return sum of weights.
+  const_reference sum_of_weights() const noexcept { return sum_of_weights_; }
+
+  /// Return sum of weights squared (variance of weight distribution).
+  const_reference sum_of_weights_squared() const noexcept {
+    return sum_of_weights_squared_;
+  }
+
+  /** Return effective counts.
+
+    This corresponds to the equivalent number of unweighted samples that would
+    have the same variance as this sample. count() should be used to check whether
+    value() and variance() are defined, see documentation of value() and variance().
+    count() can be used to compute the variance of the mean by dividing variance()
+    by count().
+  */
+  value_type count() const noexcept {
+    // see https://en.wikipedia.org/wiki/Effective_sample_size#weighted_samples
+    return detail::square(sum_of_weights_) / sum_of_weights_squared_;
+  }
+
+  /** Return mean value of accumulated weighted samples.
+
+    The result is undefined, if count() == 0.
+  */
+  const_reference value() const noexcept { return weighted_mean_; }
+
+  /** Return variance of accumulated weighted samples.
+
+    The result is undefined, if count() == 0 or count() == 1.
+  */
+  value_type variance() const {
+    // see https://en.wikipedia.org/wiki/Weighted_arithmetic_mean#Reliability_weights
+    return sum_of_weighted_deltas_squared_ /
+           (sum_of_weights_ - sum_of_weights_squared_ / sum_of_weights_);
+  }
+
+  template <class Archive>
+  void serialize(Archive& ar, unsigned /* version */) {
+    ar& make_nvp("sum_of_weights", sum_of_weights_);
+    ar& make_nvp("sum_of_weights_squared", sum_of_weights_squared_);
+    ar& make_nvp("weighted_mean", weighted_mean_);
+    ar& make_nvp("sum_of_weighted_deltas_squared", sum_of_weighted_deltas_squared_);
+  }
+
+private:
+  value_type sum_of_weights_{};
+  value_type sum_of_weights_squared_{};
+  value_type weighted_mean_{};
+  value_type sum_of_weighted_deltas_squared_{};
+};
+
+} // namespace accumulators
+} // namespace histogram
+} // namespace boost
+
+#ifndef BOOST_HISTOGRAM_DOXYGEN_INVOKED
+namespace std {
+template <class T, class U>
+/// Specialization for boost::histogram::accumulators::weighted_mean.
+struct common_type<boost::histogram::accumulators::weighted_mean<T>,
+                   boost::histogram::accumulators::weighted_mean<U>> {
+  using type = boost::histogram::accumulators::weighted_mean<common_type_t<T, U>>;
+};
+} // namespace std
+#endif
+
+#endif