Statistics.cpp 13.4 KB
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// Includes
#include "MantidKernel/Statistics.h"

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#include <algorithm>
#include <functional>
#include <limits>
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#include <cmath>
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#include <numeric>
#include <string>
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#include <stdexcept>
#include <sstream>
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namespace Mantid
{
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  namespace Kernel
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  {

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    using std::string;
    using std::vector;

    /**
     * Generate a Statistics object where all of the values are NaN. This is a good initial default.
     */
    Statistics getNanStatistics()
    {
      double nan = std::numeric_limits<double>::quiet_NaN();

      Statistics stats;
      stats.minimum = nan;
      stats.maximum = nan;
      stats.mean = nan;
      stats.median = nan;
      stats.standard_deviation = nan;

      return stats;
    }

    /**
     * There are enough special cases in determining the median where it useful to
     * put it in a single function.
     */
    template<typename TYPE>
    double getMedian(const vector<TYPE>& data, const size_t num_data, const bool sorted)
    {
      if (num_data == 1)
        return static_cast<double> (*(data.begin()));

      bool is_even = ((num_data % 2) == 0);
      if (is_even)
      {
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        double left = 0.0;
        double right = 0.0;

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        if (sorted)
        {
          // Just get the centre two elements.
          left = static_cast<double> (*(data.begin() + num_data / 2 - 1));
          right = static_cast<double> (*(data.begin() + num_data / 2));
        }
        else
        {
          // If the data is not sorted, make a copy we can mess with
          vector<TYPE> temp(data.begin(), data.end());
          // Get what the centre two elements should be...
          std::nth_element(temp.begin(), temp.begin() + num_data / 2 - 1, temp.end());
          left = static_cast<double> (*(temp.begin() + num_data / 2 - 1));
          std::nth_element(temp.begin(), temp.begin() + num_data / 2, temp.end());
          right = static_cast<double> (*(temp.begin() + num_data / 2));
        }
        // return the average
        return (left + right) / 2.;
      }
      else
      // Odd number
      {
        if (sorted)
        {
          // If sorted and odd, just return the centre value
          return static_cast<double> (*(data.begin() + num_data / 2));
        }
        else
        {
          // If the data is not sorted, make a copy we can mess with
          vector<TYPE> temp(data.begin(), data.end());
          // Make sure the centre value is in the correct position
          std::nth_element(temp.begin(), temp.begin() + num_data / 2, temp.end());
          // Now return the centre value
          return static_cast<double> (*(temp.begin() + num_data / 2));
        }
      }
    }
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    /**
     * There are enough special cases in determining the Z score where it useful to
     * put it in a single function.
     */
    template<typename TYPE>
    std::vector<double> getZscore(const vector<TYPE>& data, const bool sorted)
    {
      if (data.size() < 3)
      {
    	  std::vector<double>Zscore(data.size(),0.);
    	  return Zscore;
      }
      std::vector<double> Zscore;
      double tmp;
      Statistics stats = getStatistics(data, sorted);
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      if(stats.standard_deviation == 0.)
      {
    	  std::vector<double>Zscore(data.size(),0.);
    	  return Zscore;
      }
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      typename vector<TYPE>::const_iterator it = data.begin();
      for (; it != data.end(); ++it)
      {
    	tmp = static_cast<double> (*it);
        Zscore.push_back(fabs((tmp - stats.mean) / stats.standard_deviation));
      }
      return Zscore;
    }
    /**
     * There are enough special cases in determining the modified Z score where it useful to
     * put it in a single function.
     */
    template<typename TYPE>
    std::vector<double> getModifiedZscore(const vector<TYPE>& data, const bool sorted)
    {
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      if (data.size() < 3)
      {
    	  std::vector<double>Zscore(data.size(),0.);
    	  return Zscore;
      }
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      std::vector<double>MADvec;
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      double tmp;
      size_t num_data = data.size(); // cache since it is frequently used
      double median = getMedian(data, num_data, sorted);
      typename vector<TYPE>::const_iterator it = data.begin();
      for (; it != data.end(); ++it)
      {
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        tmp = static_cast<double> (*it);
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        MADvec.push_back(fabs(tmp - median));
      }
      double MAD = getMedian(MADvec, num_data, sorted);
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      if(MAD == 0.)
      {
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        std::vector<double>Zscore(data.size(),0.);
        return Zscore;
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      }
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      MADvec.clear();
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      std::vector<double> Zscore;
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      it = data.begin();
      for (; it != data.end(); ++it)
      {
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        tmp = static_cast<double> (*it);
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        Zscore.push_back(0.6745*fabs((tmp - median) / MAD));
      }
      return Zscore;
    }
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    /**
     * Determine the statistics for a vector of data. If it is sorted then let the
     * function know so it won't make a copy of the data for determining the median.
     */
    template<typename TYPE>
    Statistics getStatistics(const vector<TYPE>& data, const bool sorted)
    {
      Statistics stats = getNanStatistics();
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      size_t num_data = data.size(); // cache since it is frequently used
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      if (num_data == 0)
      { // don't do anything
        return stats;
      }

      // calculate the mean
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      const TYPE sum = std::accumulate(data.begin(), data.end(), static_cast<TYPE>(0), std::plus<TYPE>());
      stats.mean = static_cast<double>(sum)/(static_cast<double>(num_data));
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      // calculate the standard deviation, min, max
      stats.minimum = stats.mean;
      stats.maximum = stats.mean;
      double stddev = 0.;
      double temp;
      typename vector<TYPE>::const_iterator it = data.begin();
      for (; it != data.end(); ++it)
      {
        temp = static_cast<double> (*it);
        stddev += ((temp - stats.mean) * (temp - stats.mean));
        if (temp > stats.maximum)
          stats.maximum = temp;
        if (temp < stats.minimum)
          stats.minimum = temp;
      }
      stats.standard_deviation = sqrt(stddev / (static_cast<double> (num_data)));

      // calculate the median
      stats.median = getMedian(data, num_data, sorted);

      return stats;
    }

    /// Getting statistics of a string array should just give a bunch of NaNs
    template<>
    DLLExport Statistics getStatistics<string> (const vector<string>& data, const bool sorted)
    {
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      UNUSED_ARG(sorted);
      UNUSED_ARG(data);
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      return getNanStatistics();
    }

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    /// Getting statistics of a boolean array should just give a bunch of NaNs
    template<>
    DLLExport Statistics getStatistics<bool> (const vector<bool>& data, const bool sorted)
    {
      UNUSED_ARG(sorted);
      UNUSED_ARG(data);
      return getNanStatistics();
    }
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    /** Return the Rwp of a diffraction pattern data
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      * @param obsI :: array of observed intensity values
      * @param calI :: array of calculated intensity values;
      * @param obsE :: array of error of the observed data;
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      * @return :: RFactor including Rp and Rwp
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      *
      */
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    Rfactor getRFactor(const std::vector<double>& obsI, const std::vector<double>& calI, const std::vector<double>& obsE)
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    {
      // 1. Check
      if (obsI.size() != calI.size() || obsI.size() != obsE.size())
      {
        std::stringstream errss;
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        errss << "GetRFactor() Input Error!  Observed Intensity (" << obsI.size()
              << "), Calculated Intensity (" << calI.size() << ") and Observed Error ("
              << obsE.size() << ") have different number of elements.";
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        throw std::runtime_error(errss.str());
      }
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      if (obsI.size() == 0)
      {
        throw std::runtime_error("getRFactor(): the input arrays are empty.");
      }
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      double sumnom = 0;
      double sumdenom = 0;
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      double sumrpnom = 0;
      double sumrpdenom = 0;
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      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;

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        sumrpnom += fabs(diff);
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        sumrpdenom += fabs(obs_i);
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        sumnom += weight*diff*diff;
        sumdenom += weight*obs_i*obs_i;
      }

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      Rfactor rfactor(0., 0.);
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      rfactor.Rp = (sumrpnom/sumrpdenom);
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      rfactor.Rwp = std::sqrt(sumnom/sumdenom);
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      return rfactor;
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    }

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    /**
     * This will calculate the first n-moments (inclusive) about the origin. For example
     * if maxMoment=2 then this will return 3 values: 0th (total weight), 1st (mean), 2nd (deviation).
     *
     * @param x The independent values
     * @param y The dependent values
     * @param maxMoment The number of moments to calculate
     * @returns The first n-moments.
     */
    template<typename TYPE>
    std::vector<double> getMomentsAboutOrigin(const std::vector<TYPE>& x, const std::vector<TYPE>& y, const int 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(maxMoment+1, 0.);

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      // cache the maximum index
      size_t numPoints = y.size();
      if (isDensity)
        numPoints = x.size()-1;
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      // densities are calculated using Newton's method for numerical integration
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      // as backwards as it sounds, the outer loop should be the points rather than the moments
      for (size_t j = 0; j < numPoints; ++j)
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      {
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        // 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
        double temp = static_cast<double>(y[j]); // correct for histogram
        if (isDensity)
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        {
          const double xDelta = static_cast<double>(x[j+1]-x[j]);
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          temp = .5*(temp + static_cast<double>(y[j+1]))*xDelta;
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        }
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        // accumulate the moments
        result[0] += temp;
        for (size_t i = 1; i < result.size(); ++i)
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        {
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          temp *= xVal;
          result[i] += temp;
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        }
      }

      return result;
    }

    /**
     * This will calculate the first n-moments (inclusive) about the mean (1st moment). For example
     * if maxMoment=2 then this will return 3 values: 0th (total weight), 1st (mean), 2nd (deviation).
     *
     * @param x The independent values
     * @param y The dependent values
     * @param maxMoment The number of moments to calculate
     * @returns The first n-moments.
     */
    template<typename TYPE>
    std::vector<double> getMomentsAboutMean(const std::vector<TYPE>& x, const std::vector<TYPE>& y, const int 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(maxMoment+1, 0.);
      result[0] = momentsAboutOrigin[0];

      // escape early if we need to
      if (maxMoment == 0)
        return result;

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      // 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;
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      // densities are calculated using Newton's method for numerical integration
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      // as backwards as it sounds, the outer loop should be the points rather than the moments
      for (size_t j = 0; j < numPoints; ++j)
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      {
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        // 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)
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        {
          const double xDelta = static_cast<double>(x[j+1]-x[j]);
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          temp = xVal * .5*static_cast<double>(y[j]+y[j+1])*xDelta;
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        }
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        else
        {
          temp = xVal * static_cast<double>(y[j]);
        }

        // accumulate the moment
        result[1] += temp;
        for (size_t i = 2; i < result.size(); ++i)
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        {
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          temp *= xVal;
          result[i] += temp;
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        }
      }

      return result;
    }
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    // -------------------------- Macro to instantiation concrete types --------------------------------
#define INSTANTIATE(TYPE) \
    template MANTID_KERNEL_DLL Statistics getStatistics<TYPE> (const vector<TYPE> &, const bool); \
    template MANTID_KERNEL_DLL std::vector<double> getZscore<TYPE> (const vector<TYPE> &, const bool); \
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    template MANTID_KERNEL_DLL std::vector<double> getModifiedZscore<TYPE> (const vector<TYPE> &, const bool); \
    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);

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    // --------------------------- Concrete instantiations ---------------------------------------------
    INSTANTIATE(float);
    INSTANTIATE(double);
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    INSTANTIATE(int);
    INSTANTIATE(long);
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    INSTANTIATE(long long);
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    INSTANTIATE(unsigned int);
    INSTANTIATE(unsigned long);
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    INSTANTIATE(unsigned long long);
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  } // namespace Kernel
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} // namespace Mantid