Statistics.cpp

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// Mantid Repository : https://github.com/mantidproject/mantid
//
// Copyright © 2018 ISIS Rutherford Appleton Laboratory UKRI,
//   NScD Oak Ridge National Laboratory, European Spallation Source,
//   Institut Laue - Langevin & CSNS, Institute of High Energy Physics, CAS
// SPDX - License - Identifier: GPL - 3.0 +
// Includes
#include "MantidKernel/Statistics.h"
#include "MantidKernel/Logger.h"
 
#include <boost/accumulators/accumulators.hpp>
#include <boost/accumulators/statistics/max.hpp>
#include <boost/accumulators/statistics/min.hpp>
#include <boost/accumulators/statistics/stats.hpp>
#include <boost/accumulators/statistics/variance.hpp>
 
#include <algorithm>
#include <cfloat>
#include <cmath>
#include <limits>
#include <sstream>
 
namespace Mantid::Kernel {
namespace {
Logger logger("Statistics");
 
void assertMomentIsValid(const int maxMoment) {
  if (maxMoment < 0) {
    std::stringstream msg;
    msg << "moment = " << maxMoment << " is statistically meaningless";
    throw std::runtime_error(msg.str());
  }
}
} // namespace
 
using std::string;
using std::vector;
 
template <typename Range> Statistics getStatisticsImpl(Range const &data, const unsigned int flags);
template <typename Range> std::vector<double> getZscoreImpl(Range const &data);
 
Statistics::Statistics() {
  constexpr double nan = std::numeric_limits<double>::quiet_NaN();
  minimum = nan;
  maximum = nan;
  mean = nan;
  median = nan;
  standard_deviation = nan;
}
 
template <typename Range> double getMedian(Range const &data) {
  using value_type = std::decay_t<decltype(data[0])>;
  const size_t size = data.size();
  if (size == 1)
    return static_cast<double>(data[0]);
 
  const bool isSorted = std::is_sorted(data.begin(), data.end());
  const bool is_even = (size % 2 == 0);
  if (isSorted) {
    if (is_even)
      return (static_cast<double>(data[size / 2 - 1]) + static_cast<double>(data[size / 2])) / 2;
    else
      return static_cast<double>(data[size / 2]);
  } else {
    std::vector<value_type> tmpSortedData(data.begin(), data.end());
    std::sort(tmpSortedData.begin(), tmpSortedData.end());
    if (is_even)
      return (static_cast<double>(tmpSortedData[size / 2 - 1]) + static_cast<double>(tmpSortedData[size / 2])) / 2;
    else
      return static_cast<double>(tmpSortedData[size / 2]);
  }
}
 
template <typename Range> std::vector<double> getZscoreImpl(Range const &data) {
  std::vector<double> Zscore;
  if (data.size() < 3) {
    Zscore.resize(data.size(), 0.);
    return Zscore;
  }
  Statistics stats = getStatisticsImpl(data, StatOptions::AllStats);
  if (stats.standard_deviation == 0.) {
    Zscore.resize(data.size(), 0.);
    return Zscore;
  }
  for (auto it = data.begin(); it != data.end(); ++it) {
    auto tmp = static_cast<double>(*it);
    // unclear why Zscore is non-negative, was first implemented in #5316
    Zscore.emplace_back(fabs((stats.mean - tmp) / stats.standard_deviation));
  }
  return Zscore;
}
 
template <typename TYPE> std::vector<double> getZscore(const vector<TYPE> &data) { return getZscoreImpl(data); }
 
std::vector<double> getZscore(std::span<double const> data) { return getZscoreImpl(data); }
template <typename TYPE> std::vector<double> getWeightedZscore(const vector<TYPE> &data, const vector<TYPE> &weights) {
  std::vector<double> Zscore;
  if (data.size() < 3) {
    Zscore.resize(data.size(), 0.);
    return Zscore;
  }
  Statistics stats = getStatistics(data);
  if (stats.standard_deviation == 0.) {
    Zscore.resize(data.size(), 0.);
    return Zscore;
  }
  double sumWeights = 0.0;
  double sumWeightedData = 0.0;
  double weightedVariance = 0.0;
  for (size_t it = 0; it != data.size(); ++it) {
    sumWeights += static_cast<double>(weights[it]);
    sumWeightedData += static_cast<double>(weights[it] * data[it]);
  }
  double weightedMean = sumWeightedData / sumWeights;
  for (size_t it = 0; it != data.size(); ++it) {
    weightedVariance += std::pow(static_cast<double>(data[it]) - weightedMean, 2) *
                        std::pow(static_cast<double>(weights[it]) / sumWeights, 2);
  }
  for (auto it = data.cbegin(); it != data.cend(); ++it) {
    Zscore.emplace_back(fabs((static_cast<double>(*it) - weightedMean) / std::sqrt(weightedVariance)));
  }
  return Zscore;
}
template <typename TYPE> std::vector<double> getModifiedZscore(const vector<TYPE> &data) {
  if (data.size() < 3) {
    std::vector<double> Zscore(data.size(), 0.);
    return Zscore;
  }
  std::vector<double> MADvec;
  double tmp;
  double median = getMedian(data);
  for (auto it = data.cbegin(); it != data.cend(); ++it) {
    tmp = static_cast<double>(*it);
    MADvec.emplace_back(fabs(tmp - median));
  }
  double MAD = getMedian(MADvec);
  if (MAD == 0.) {
    std::vector<double> Zscore(data.size(), 0.);
    return Zscore;
  }
  MADvec.clear();
  std::vector<double> Zscore;
  for (auto it = data.begin(); it != data.end(); ++it) {
    tmp = static_cast<double>(*it);
    Zscore.emplace_back(0.6745 * fabs((tmp - median) / MAD));
  }
  return Zscore;
}
 
template <typename Range> Statistics getStatisticsImpl(Range const &data, const unsigned int flags) {
  Statistics statistics;
  if (data.empty()) { // don't do anything
    return statistics;
  }
  // calculate the mean if this or the stddev is requested
  const bool stddev = ((flags & StatOptions::UncorrectedStdDev) || (flags & StatOptions::CorrectedStdDev));
  if (stddev) {
    using namespace boost::accumulators;
    accumulator_set<double, stats<tag::min, tag::max, tag::variance>> acc;
    for (auto &value : data) {
      acc(static_cast<double>(value));
    }
    statistics.minimum = min(acc);
    statistics.maximum = max(acc);
    statistics.mean = mean(acc);
    double var = variance(acc);
 
    if (flags & StatOptions::CorrectedStdDev) {
      auto ndofs = static_cast<double>(data.size());
      var *= ndofs / (ndofs - 1.0);
    }
    statistics.standard_deviation = std::sqrt(var);
 
  } else if (flags & StatOptions::Mean) {
    using namespace boost::accumulators;
    accumulator_set<double, stats<tag::mean>> acc;
    for (auto &value : data) {
      acc(static_cast<double>(value));
    }
    statistics.mean = mean(acc);
  }
 
  // calculate the median if requested
  if (flags & StatOptions::Median) {
    statistics.median = getMedian(data);
  }
 
  return statistics;
}
 
template <typename TYPE> Statistics getStatistics(const vector<TYPE> &data, const unsigned int flags) {
  return getStatisticsImpl(data, flags);
}
 
Statistics getStatistics(std::span<double const> data, const unsigned int flags) {
  return getStatisticsImpl(data, flags);
}
 
template <> DLLExport Statistics getStatistics<string>(const vector<string> &data, const unsigned int flags) {
  UNUSED_ARG(flags);
  UNUSED_ARG(data);
  return Statistics(); // default is all nan
}
 
template <> DLLExport Statistics getStatistics<bool>(const vector<bool> &data, const unsigned int flags) {
  UNUSED_ARG(flags);
  UNUSED_ARG(data);
  return Statistics(); // default is all nan
}
 
Rfactor getRFactor(std::span<double const> obsI, std::span<double const> calI, std::span<double const> obsE) {
  // 1. Check
  if (obsI.size() != calI.size() || obsI.size() != obsE.size()) {
    std::stringstream errss;
    errss << "GetRFactor() Input Error!  Observed Intensity (" << obsI.size() << "), Calculated Intensity ("
          << calI.size() << ") and Observed Error (" << obsE.size() << ") have different number of elements.";
    throw std::runtime_error(errss.str());
  }
  if (obsI.empty()) {
    throw std::runtime_error("getRFactor(): the input arrays are empty.");
  }
 
  double sumnom = 0;
  double sumdenom = 0;
  double sumrpnom = 0;
  double sumrpdenom = 0;
 
  size_t numpts = obsI.size();
  for (size_t i = 0; i < numpts; ++i) {
    double cal_i = calI[i];
    double obs_i = obsI[i];
    double sigma = obsE[i];
    double weight = 1.0 / (sigma * sigma);
    double diff = obs_i - cal_i;
 
    if (weight == weight && weight <= DBL_MAX) {
      // If weight is not NaN.
      sumrpnom += fabs(diff);
      sumrpdenom += fabs(obs_i);
 
      double tempnom = weight * diff * diff;
      double tempden = weight * obs_i * obs_i;
 
      sumnom += tempnom;
      sumdenom += tempden;
 
      if (tempnom != tempnom || tempden != tempden) {
        logger.error() << "***** Error! ****** Data indexed " << i << " is NaN. "
                       << "i = " << i << ": cal = " << calI[i] << ", obs = " << obs_i << ", weight = " << weight
                       << ". \n";
      }
    }
  }
 
  Rfactor rfactor(0., 0.);
  rfactor.Rp = (sumrpnom / sumrpdenom);
  rfactor.Rwp = std::sqrt(sumnom / sumdenom);
 
  if (rfactor.Rwp != rfactor.Rwp)
    logger.debug() << "Rwp is NaN.  Denominator = " << sumnom << "; Nominator = " << sumdenom << ". \n";
 
  return rfactor;
}
 
template <typename TYPE>
std::vector<double> getMomentsAboutOrigin(const std::vector<TYPE> &x, const std::vector<TYPE> &y, const int maxMoment) {
  assertMomentIsValid(maxMoment);
 
  // densities have the same number of x and y
  bool isDensity(x.size() == y.size());
 
  // if it isn't a density then check for histogram
  if ((!isDensity) && (x.size() != y.size() + 1)) {
    std::stringstream msg;
    msg << "length of x (" << x.size() << ") and y (" << y.size() << ")do not match";
    throw std::out_of_range(msg.str());
  }
 
  // initialize a result vector with all zeros
  std::vector<double> result(std::size_t(maxMoment + 1), 0.);
 
  // cache the maximum index
  size_t numPoints = y.size();
  if (isDensity)
    numPoints = x.size() - 1;
 
  // densities are calculated using Newton's method for numerical integration
  // as backwards as it sounds, the outer loop should be the points rather
  // than
  // the moments
  for (size_t j = 0; j < numPoints; ++j) {
    // reduce item lookup - and central x for histogram
    const double xVal = .5 * static_cast<double>(x[j] + x[j + 1]);
    // this variable will be (x^n)*y
    auto temp = static_cast<double>(y[j]); // correct for histogram
    if (isDensity) {
      const auto xDelta = static_cast<double>(x[j + 1] - x[j]);
      temp = .5 * (temp + static_cast<double>(y[j + 1])) * xDelta;
    }
 
    // accumulate the moments
    result[0] += temp;
    for (size_t i = 1; i < result.size(); ++i) {
      temp *= xVal;
      result[i] += temp;
    }
  }
 
  return result;
}
 
template <typename TYPE>
std::vector<double> getMomentsAboutMean(const std::vector<TYPE> &x, const std::vector<TYPE> &y, const int maxMoment) {
  assertMomentIsValid(maxMoment);
 
  // get the zeroth (integrated value) and first moment (mean)
  std::vector<double> momentsAboutOrigin = getMomentsAboutOrigin(x, y, 1);
  const double mean = momentsAboutOrigin[1];
 
  // initialize a result vector with all zeros
  std::vector<double> result(std::size_t(maxMoment + 1), 0.);
  result[0] = momentsAboutOrigin[0];
 
  // escape early if we need to
  if (maxMoment == 0)
    return result;
 
  // densities have the same number of x and y
  bool isDensity(x.size() == y.size());
 
  // cache the maximum index
  size_t numPoints = y.size();
  if (isDensity)
    numPoints = x.size() - 1;
 
  // densities are calculated using Newton's method for numerical integration
  // as backwards as it sounds, the outer loop should be the points rather
  // than
  // the moments
  for (size_t j = 0; j < numPoints; ++j) {
    // central x in histogram with a change of variables - and just change for
    // density
    const double xVal = .5 * static_cast<double>(x[j] + x[j + 1]) - mean; // change of variables
 
    // this variable will be (x^n)*y
    double temp;
    if (isDensity) {
      const auto xDelta = static_cast<double>(x[j + 1] - x[j]);
      temp = xVal * .5 * static_cast<double>(y[j] + y[j + 1]) * xDelta;
    } else {
      temp = xVal * static_cast<double>(y[j]);
    }
 
    // accumulate the moment
    result[1] += temp;
    for (size_t i = 2; i < result.size(); ++i) {
      temp *= xVal;
      result[i] += temp;
    }
  }
 
  return result;
}
 
// -------------------------- Macro to instantiation concrete types
// --------------------------------
#define INSTANTIATE(TYPE)                                                                                              \
  template MANTID_KERNEL_DLL Statistics getStatistics<TYPE>(const vector<TYPE> &, const unsigned int);                 \
  template MANTID_KERNEL_DLL std::vector<double> getZscore<TYPE>(const vector<TYPE> &);                                \
  template MANTID_KERNEL_DLL std::vector<double> getWeightedZscore<TYPE>(const vector<TYPE> &, const vector<TYPE> &);  \
  template MANTID_KERNEL_DLL std::vector<double> getModifiedZscore<TYPE>(const vector<TYPE> &);                        \
  template MANTID_KERNEL_DLL std::vector<double> getMomentsAboutOrigin<TYPE>(                                          \
      const std::vector<TYPE> &x, const std::vector<TYPE> &y, const int maxMoment);                                    \
  template MANTID_KERNEL_DLL std::vector<double> getMomentsAboutMean<TYPE>(                                            \
      const std::vector<TYPE> &x, const std::vector<TYPE> &y, const int maxMoment);
 
// --------------------------- Concrete instantiations
// ---------------------------------------------
INSTANTIATE(float)
INSTANTIATE(double)
INSTANTIATE(int)
INSTANTIATE(long)
INSTANTIATE(long long)
INSTANTIATE(unsigned int)
INSTANTIATE(unsigned long)
INSTANTIATE(unsigned long long)
 
} // namespace Mantid::Kernel