// 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 mean value of accumulated weighted samples.

    The result is undefined, if `sum_of_weights() == 0`.
  */
  const_reference value() const noexcept { return weighted_mean_; }

  /** Return variance of accumulated weighted samples.

    The result is undefined, if `sum_of_weights() == 0` or
    `sum_of_weights() == sum_of_weights_squared()`.
  */
  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