The class holds arrays of bins and bin centers, and a wave generator object containing information on the waveform function. More...

#include <NNWaveFitTool.h>

Public Member Functions
	NNWaveFitTool (const nnFitterBins &bins, const nnFitterBinData &binCenters, const WaveGenerator &wave)
	Constructor takes arrays of signals and bin probabilities.

const nnFitterBins &	getBins () const
	Get edges of time shift bins.

const nnFitterBinData &	getBinCenters () const
	Get mean bin time shifts.

void	shiftInTime (nnFitterBinData &p, double timeShift)
	Shift the probability array in time.

void	multiply (nnFitterBinData &p, const nnFitterBinData &p1)
	Multiply probabilities.

std::shared_ptr< nnFitterBinData >	pFromInterval (double left, double right)
	Convert a uniform distribution to time-shift-like pdf.

std::tuple< double, double >	getTimeShift (const nnFitterBinData &p)
	Return std::tuple containing time shift and its error.

std::tuple< double, double, double >	getAmplitudeChi2 (const apvSamples &samples, double timeShift, double tau)
	Return std::tuple with signal amplitude, its error, and chi2 of the fit.

double	pLessThan (nnFitterBinData p1, nnFitterBinData p2)
	Return the probability X < Y, where X and Y are random variables with binned pdfs p1 and p2.

Protected Member Functions
void	normalize (nnFitterBinData &p)
	Normalize the probability distribution.

Private Attributes
const nnFitterBins &	m_bins
	Edges of bins.

const nnFitterBinData &	m_binCenters
	Centers of bins.

nnFitterBinData	m_altBinData
	Bin data array for re-use.

apvSamples	m_altSamples
	Array of 6 apv samples for re-use.

WaveGenerator	m_waveGenerator
	APV signal generator.

Detailed Description

The class holds arrays of bins and bin centers, and a wave generator object containing information on the waveform function.

It can compute probability distribution updates in clustering, or the parameters of waveform fit, such as the time shift, amplitude and their errors, and it can do compatibility tests.

Definition at line 91 of file NNWaveFitTool.h.

Constructor & Destructor Documentation

◆ NNWaveFitTool()

NNWaveFitTool	(	const nnFitterBins &	bins,
		const nnFitterBinData &	binCenters,
		const WaveGenerator &	wave
	)

inline

Constructor takes arrays of signals and bin probabilities.

Parameters

bins	Pointer to array of time bin edges
binCenters	Pointer to array of mean bin times
wave	Wave generator to generate waveform samples.

Definition at line 98 of file NNWaveFitTool.h.

                                              :
        m_bins(bins), m_binCenters(binCenters), m_waveGenerator(wave)
      {
        m_altBinData.resize(m_binCenters.size());
      }

Member Function Documentation

◆ getAmplitudeChi2()

tuple< double, double, double > getAmplitudeChi2	(	const apvSamples &	samples,
		double	timeShift,
		double	tau
	)

Return std::tuple with signal amplitude, its error, and chi2 of the fit.

The amplitude is calculated using linear regression through origin, its error as the error of the regression coefficient.

Parameters

samples	array of 6 samples to fit
timeShift	fitted time shift
tau	width of the waveform

Returns: std::tuple of amplitude, its error, and chi2

Definition at line 27 of file NNWaveFitTool.cc.

{
  // Amplitude
  auto tw = m_waveGenerator(timeShift, tau);
  double waveNorm = inner_product(
                      tw.begin(), tw.end(), tw.begin(), 0.0);
  double amplitude = 0.0;
  double amplitudeError = 100.0;
  if (waveNorm > 0.0) {
    amplitude = inner_product(samples.begin(), samples.end(),
                              tw.begin(), 0.0) / waveNorm;
    amplitudeError = 1.0 / sqrt(waveNorm);
  }
  // Chi2
  transform(samples.begin(), samples.end(), tw.begin(), m_altSamples.begin(),
            [amplitude](double s, double w)->double { return s - w* amplitude;});
  size_t ndf = accumulate(samples.begin(), samples.end(), size_t(0),
                          [](size_t sum, double x)->size_t { return ((x > 3) ? sum + 1 : sum); }
                         ) - 2;
  double chi2 = sqrt(1.0 / ndf * inner_product(m_altSamples.begin(), m_altSamples.end(),
                                               m_altSamples.begin(), 0.0));
  return make_tuple(amplitude, amplitudeError, chi2);
}

◆ getBinCenters()

const nnFitterBinData & getBinCenters ( ) const

inline

Get mean bin time shifts.

Returns: pointer to array of bin time shifts

Definition at line 115 of file NNWaveFitTool.h.

115{ return m_binCenters; }

◆ getBins()

const nnFitterBins & getBins ( ) const

inline

Get edges of time shift bins.

Returns: pointer to array of bin edges

Definition at line 110 of file NNWaveFitTool.h.

110{ return m_bins; }

◆ getTimeShift()

tuple< double, double > getTimeShift ( const nnFitterBinData & p )

Return std::tuple containing time shift and its error.

Parameters

p	array of bin probabilities

Returns: std::tuple of timeShift, timeShiftError

Definition at line 16 of file NNWaveFitTool.cc.

{
  // calculate time estimate and error
  double timeShift = inner_product(p.begin(), p.end(), m_binCenters.begin(), 0.0);
  // use altBinData storage to sum squared residuals
  transform(m_binCenters.begin(), m_binCenters.end(), m_altBinData.begin(),
            [timeShift](double t)->double { return (t - timeShift) * (t - timeShift);});
  double timeShiftError = sqrt(inner_product(p.begin(), p.end(), m_altBinData.begin(), 0.0));
  return make_tuple(timeShift, timeShiftError);
}

◆ multiply()

void multiply	(	nnFitterBinData &	p,
		const nnFitterBinData &	p1
	)

inline

Multiply probabilities.

Modify first probability distribution by multiplying it with the second.

Definition at line 129 of file NNWaveFitTool.h.

      {
        std::transform(p.begin(), p.end(),
                       p1.begin(), p.begin(), std::multiplies<double>());
        normalize(p);
      }

◆ normalize()

void normalize ( nnFitterBinData & p )

inlineprotected

Normalize the probability distribution.

After shifting, multiplications or other ooperations on probabilities, we need to restore the normalization and re-build the list used for calculation of EmpiricalDistributionFunction. If probabilities vanish over all bins, return uniform distribution.

Definition at line 178 of file NNWaveFitTool.h.

      {
        double pnorm = std::accumulate(p.begin(), p.end(), 0.0);
        // If the norm is too small, return default distribution.
        if (pnorm < 1.0e-10) {
          double uniformP = 1.0 / std::distance(p.begin(), p.end());
          std::fill(p.begin(), p.end(), uniformP);
        } else {
          // Normalize if the norm makes sense.
          std::transform(p.begin(), p.end(), p.begin(),
                         std::bind(std::divides<double>(), std::placeholders::_1, pnorm));
        }
      }

◆ pFromInterval()

shared_ptr< nnFitterBinData > pFromInterval	(	double	left,
		double	right
	)

Convert a uniform distribution to time-shift-like pdf.

Parameters

left	Left edge of the interval
right	Right edge of the interval

Returns: pointer to binned pdf representing the uniform distribution between left and right.

Definition at line 66 of file NNWaveFitTool.cc.

{
  auto uniCdf = [left, right](double x)->double {
    if (x < left) return 0.0;
    if (x > right) return 1.0;
    return (x - left) / (right - left);
  };
  auto result = shared_ptr<nnFitterBinData>(new nnFitterBinData(m_binCenters.size()));
  for (size_t i = 1; i < m_bins.size(); ++i)(*result)[i - 1] = uniCdf(m_bins[i] - m_bins[i - 1]);
  return result;
}

◆ pLessThan()

double pLessThan	(	nnFitterBinData	p1,
		nnFitterBinData	p2
	)

Return the probability X < Y, where X and Y are random variables with binned pdfs p1 and p2.

Parameters

p1	binned pdf for X
p2	binned pdf for Y

Definition at line 78 of file NNWaveFitTool.cc.

{
  // The formula is integral(P1(x)F2(x)dx.
  // We do sum(F1[i]P[i]
  EmpiricalDistributionFunction edf1(p1, m_bins);
  double result = 0;
  for (size_t i2 = 1; i2 < m_binCenters.size(); ++i2)
    result += edf1(m_binCenters[i2 - 1]) * p2[i2];
  return result;
}

◆ shiftInTime()

void shiftInTime	(	nnFitterBinData &	p,
		double	timeShift
	)

Shift the probability array in time.

The method works by linearly interpolating the EmpiricalDistributionFunction to calculate values for a shifted set of bins.

Parameters

p	the probability array to be modified.
timeShift	the size of the shift.

Definition at line 52 of file NNWaveFitTool.cc.

{
  // Calculate  at bin boundaries shifted by timeShift, new p's are differences.
  EmpiricalDistributionFunction edf(p, m_bins);
  auto ibin = m_bins.begin();
  double lowEdf = edf(-timeShift + *ibin++);
  for (auto& prob : p) {
    double highEdf = edf(-timeShift + *ibin++);
    prob = highEdf - lowEdf;
    lowEdf = highEdf;
  }
  normalize(p);
}

Member Data Documentation

◆ m_altBinData

nnFitterBinData m_altBinData

private

Bin data array for re-use.

Definition at line 195 of file NNWaveFitTool.h.

◆ m_altSamples

apvSamples m_altSamples

private

Array of 6 apv samples for re-use.

Definition at line 196 of file NNWaveFitTool.h.

◆ m_binCenters

const nnFitterBinData& m_binCenters

private

Centers of bins.

Definition at line 194 of file NNWaveFitTool.h.

◆ m_bins

const nnFitterBins& m_bins

private

Edges of bins.

Definition at line 193 of file NNWaveFitTool.h.

◆ m_waveGenerator

WaveGenerator m_waveGenerator

private

APV signal generator.

Definition at line 197 of file NNWaveFitTool.h.

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

svd/reconstruction/include/NNWaveFitTool.h
svd/reconstruction/src/NNWaveFitTool.cc

Public Member Functions

Protected Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ NNWaveFitTool()

Member Function Documentation

◆ getAmplitudeChi2()

◆ getBinCenters()

◆ getBins()

◆ getTimeShift()

◆ multiply()

◆ normalize()

◆ pFromInterval()

◆ pLessThan()

◆ shiftInTime()

Member Data Documentation

◆ m_altBinData

◆ m_altSamples

◆ m_binCenters

◆ m_bins

◆ m_waveGenerator