Binning Class Reference

Binning of a data distribution Provides PDF and CDF values of the distribution per bin. More...

#include <Binning.h>

Collaboration diagram for Binning:

Public Member Functions
	Binning (unsigned int nBins=0)
	Creates an empty binning with nBins.
unsigned int	getBin (float datapoint) const
	Gets the bin corresponding to the given datapoint.
void	normalizePDFs ()
	Normalizes the PDF values, so their sum is 1.
void	calculateCDFsFromPDFs ()
	Calculates the CDF values from the pdf values, which are assumed to be normalized.

Static Public Member Functions
static Binning	CreateEqualFrequency (const std::vector< float > &data, const std::vector< float > &weights, const std::vector< bool > &isSignal, unsigned int nBins)
	Create an equal frequency (aka equal-statistics) binning.
static Binning	CreateEquidistant (const std::vector< float > &data, const std::vector< float > &weights, const std::vector< bool > &isSignal, unsigned int nBins)
	Create an equidistant binning.

Public Attributes
double	m_signal_yield
	Signal yield in data distribution.
double	m_bckgrd_yield
	Background yield in data distribution.
std::vector< float >	m_signal_pdf
	Signal pdf of data distribution per bin.
std::vector< float >	m_signal_cdf
	Signal cdf of data distribution per bin.
std::vector< float >	m_bckgrd_pdf
	Background pdf of data distribution per bin.
std::vector< float >	m_bckgrd_cdf
	Background cdf of data distribution per bin.
std::vector< float >	m_boundaries
	Boundaries of data distribution, including minimum and maximum value as first and last boundary.

Detailed Description

Binning of a data distribution Provides PDF and CDF values of the distribution per bin.

Definition at line 27 of file Binning.h.

Constructor & Destructor Documentation

Binning()

Binning ( unsigned int  nBins = 0 )

explicit

Creates an empty binning with nBins.

Parameters

nBins

number of bins

Definition at line 21 of file Binning.cc.

    {
 
      m_signal_pdf.resize(nBins, 0.0);
      m_signal_cdf.resize(nBins, 0.0);
      m_bckgrd_pdf.resize(nBins, 0.0);
      m_bckgrd_cdf.resize(nBins, 0.0);
      m_boundaries.resize(nBins + 1, 0.0);
 
      m_signal_yield = 0;
      m_bckgrd_yield = 0;
    }

Member Function Documentation

calculateCDFsFromPDFs()

void calculateCDFsFromPDFs

(

)

Calculates the CDF values from the pdf values, which are assumed to be normalized.

Definition at line 73 of file Binning.cc.

    {
 
      unsigned int nBins = m_signal_pdf.size();
 
      m_signal_cdf = m_signal_pdf;
      m_bckgrd_cdf = m_bckgrd_pdf;
 
      for (unsigned int iBin = 0; iBin < nBins; ++iBin) {
        m_signal_cdf[iBin] *= (m_boundaries[iBin + 1] - m_boundaries[iBin]) / (m_boundaries[nBins] - m_boundaries[0]);
        m_bckgrd_cdf[iBin] *= (m_boundaries[iBin + 1] - m_boundaries[iBin]) / (m_boundaries[nBins] - m_boundaries[0]);
      }
 
      for (unsigned int iBin = 1; iBin < nBins; ++iBin) {
        m_signal_cdf[iBin] += m_signal_cdf[iBin - 1];
        m_bckgrd_cdf[iBin] += m_bckgrd_cdf[iBin - 1];
      }
 
    }

CreateEqualFrequency()

Binning CreateEqualFrequency ( const std::vector< float > &  data, const std::vector< float > &  weights, const std::vector< bool > &  isSignal, unsigned int  nBins  )

static

Create an equal frequency (aka equal-statistics) binning.

Parameters

data	data-points sampled from the distribution
weights	weights for each data-point
isSignal	per data point
nBins	number of bins

Definition at line 93 of file Binning.cc.

    {
 
      Binning binning(nBins);
 
      unsigned int nEvents = data.size();
 
      std::vector<unsigned int> indices(nEvents);
      std::iota(indices.begin(), indices.end(), 0);
      std::sort(indices.begin(), indices.end(), [&](unsigned int i, unsigned int j) {return data[i] < data[j]; });
 
      double sum_weights = 0;
      for (auto& w : weights)
        sum_weights += w;
      double weight_per_bin = sum_weights / nBins;
 
      unsigned int bin = 1;
      double current_weight = 0;
      binning.m_boundaries[0] = data[indices[0]];
      binning.m_boundaries[nBins] = data[indices[nEvents - 1]];
 
      for (unsigned int iEvent = 0; iEvent < nEvents; ++iEvent) {
        unsigned int index = indices[iEvent];
        current_weight += weights[index];
        if (current_weight >= weight_per_bin and bin < nBins and binning.m_boundaries[bin - 1] < data[index]) {
          auto number_of_bins = static_cast<unsigned int>(current_weight / weight_per_bin);
          current_weight -= weight_per_bin * number_of_bins;
          for (unsigned int i = 0; i < number_of_bins; ++i) {
            binning.m_boundaries[bin] = data[index];
            bin++;
          }
        }
        if (isSignal[index]) {
          binning.m_signal_pdf[bin - 1] += weights[index];
        } else {
          binning.m_bckgrd_pdf[bin - 1] += weights[index];
        }
      }
 
      binning.normalizePDFs();
      binning.calculateCDFsFromPDFs();
 
      return binning;
    }

CreateEquidistant()

Binning CreateEquidistant ( const std::vector< float > &  data, const std::vector< float > &  weights, const std::vector< bool > &  isSignal, unsigned int  nBins  )

static

Create an equidistant binning.

Parameters

data	data-points sampled from the distribution
weights	weights for each data-point
isSignal	per data point
nBins	number of bins

Definition at line 139 of file Binning.cc.

    {
 
      Binning binning(nBins);
 
      auto minmax = std::minmax_element(data.begin(), data.end());
      float min = *(minmax.first);
      float max = *(minmax.second);
      float step = (max - min) / nBins;
 
      for (unsigned int iBin = 0; iBin <= nBins; ++iBin) {
        binning.m_boundaries[iBin] = min + step * iBin;
      }
 
      for (unsigned int iEvent = 0; iEvent < data.size(); ++iEvent) {
        unsigned int bin = binning.getBin(data[iEvent]);
 
        if (isSignal[iEvent])
          binning.m_signal_pdf[bin] += weights[iEvent];
        else
          binning.m_bckgrd_pdf[bin] += weights[iEvent];
 
      }
 
      binning.normalizePDFs();
      binning.calculateCDFsFromPDFs();
 
      return binning;
 
    }

getBin()

unsigned int getBin

(

float

datapoint

)

const

Gets the bin corresponding to the given datapoint.

There are no overflow/underflow bins, so data points outside the original range are mapped to the first and last bin.

Parameters

datapoint

for which the bin is returned

Definition at line 34 of file Binning.cc.

    {
 
      auto it = std::upper_bound(m_boundaries.begin(), m_boundaries.end(), datapoint);
      unsigned int bin = std::distance(m_boundaries.begin(), it);
      if (bin == 0)
        bin = 1;
      if (bin == m_boundaries.size())
        bin = m_boundaries.size() - 1;
      return bin - 1;
 
    }

normalizePDFs()

void normalizePDFs

(

)

Normalizes the PDF values, so their sum is 1.

Definition at line 47 of file Binning.cc.

    {
 
      unsigned int nBins = m_signal_pdf.size();
 
      m_signal_yield = 0;
      m_bckgrd_yield = 0;
 
      // Total number of events
      for (unsigned int iBin = 0; iBin < nBins; ++iBin) {
        m_signal_yield += m_signal_pdf[iBin];
        m_bckgrd_yield += m_bckgrd_pdf[iBin];
      }
 
      // Each bin is normed to its width
      double last_valid_bound = m_boundaries[0];
      for (unsigned int iBin = 0; iBin < nBins; ++iBin) {
        m_signal_pdf[iBin] /= m_signal_yield * (m_boundaries[iBin + 1] - last_valid_bound) / (m_boundaries[nBins] - m_boundaries[0]);
        m_bckgrd_pdf[iBin] /= m_bckgrd_yield * (m_boundaries[iBin + 1] - last_valid_bound) / (m_boundaries[nBins] - m_boundaries[0]);
        if (iBin + 1 < nBins and m_boundaries[iBin + 2] > m_boundaries[iBin + 1]) {
          last_valid_bound = m_boundaries[iBin + 1];
        }
      }
 
    }

Member Data Documentation

m_bckgrd_cdf

std::vector<float> m_bckgrd_cdf

Background cdf of data distribution per bin.

Definition at line 59 of file Binning.h.

m_bckgrd_pdf

std::vector<float> m_bckgrd_pdf

Background pdf of data distribution per bin.

Definition at line 58 of file Binning.h.

m_bckgrd_yield

double m_bckgrd_yield

Background yield in data distribution.

Definition at line 54 of file Binning.h.

m_boundaries

std::vector<float> m_boundaries

Boundaries of data distribution, including minimum and maximum value as first and last boundary.

Definition at line 61 of file Binning.h.

m_signal_cdf

std::vector<float> m_signal_cdf

Signal cdf of data distribution per bin.

Definition at line 57 of file Binning.h.

m_signal_pdf

std::vector<float> m_signal_pdf

Signal pdf of data distribution per bin.

Definition at line 56 of file Binning.h.

m_signal_yield

double m_signal_yield

Signal yield in data distribution.

Definition at line 53 of file Binning.h.

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The documentation for this class was generated from the following files:

• mva/utility/include/Binning.h
• mva/utility/src/Binning.cc