BipolarFit Class Reference

#include <BipolarFit.h>

Collaboration diagram for BipolarFit:

Public Member Functions
	BipolarFit ()
	~BipolarFit ()
int	Fit (double *x, const double ex, const double pedestal, const double predefinedwidth, double *result, double *errors, double *chi2)

Private Member Functions
void	InvertMatrix (double matrix[][3], const int dim, int *)
void	InvertSymmetric4x4 (double W[][4])
double	FindInitValues (double *x, double *initValues, int *maxsample)
int	TheFitter (double *x, const double ex, double *initValues, int imeas, int *meas, int ipar, int *par, double *chi2, double *result)
void	Derivative (double A[][3], double fp[][1], double p0[][1], int imeas, int *meas)
double	bipolar (double *, double *)
double	FindPow (double z)

Private Attributes
double	m_n
double	m_powcachez
double	m_powcachezn
double	m_zmax
double	m_bipolarNormalization
double	m_tsampling

Detailed Description

Definition at line 23 of file BipolarFit.h.

Constructor & Destructor Documentation

BipolarFit()

BipolarFit::BipolarFit

(

)

Definition at line 24 of file BipolarFit.cxx.

{
  m_n=12.;
  m_powcachez = -9999.;
  m_powcachezn= -9999.;
  m_zmax= m_n+1 - std::sqrt(m_n+1.0);
  m_bipolarNormalization = FindPow(m_zmax)*(1-m_zmax/(m_n+1))*std::exp(-m_zmax);
  m_tsampling = 25.;
 
}

~BipolarFit()

BipolarFit::~BipolarFit

(

)

Definition at line 35 of file BipolarFit.cxx.

{}

Member Function Documentation

bipolar()

double BipolarFit::bipolar ( double *  x, double *  parm  )

private

Definition at line 100 of file BipolarFit.cxx.

{
  // the bipolar pulse function is
  //
  // z = (x-parm[0])*m_tsampling/parm[3]
  // m_zmax = m_n+1 - sqrt(m_n+1)
  // aa = exp(m_n*log(m_zmax))*(1-m_zmax/(m_n+1))*exp(-m_zmax)
  // parm[0]*exp(m_n*log(z))*(1-z/(m_n+1))*exp(-z)/aa
  //
  // for timing reasons instead of x (ie # of sample) 
  // the z is given
  double z = x[0];
 
 
  //const double m_tsampling = 25.;// nsec
  //z=(x[0]-parm[1])*m_tsampling/(parm[2]);
  if(z<0.)
    return 0.;
 
  return parm[0]*FindPow(z)*(1-z/(m_n+1))*std::exp(-z)/m_bipolarNormalization;
}

Derivative()

void BipolarFit::Derivative ( double  A[][3], double  fp[][1], double  p0[][1], int  imeas, int *  meas  )

private

Definition at line 123 of file BipolarFit.cxx.

{
  //calculate the derivatives and the 0th order approximation 
  //around the ADC samplings
  double norm = p0[0][0];
  //double parm[3]={1.,p0[1][0],p0[2][0]};
  for(int i=0;i<imeas;i++)
  {
    int ii = meas[i];
    double z = (ii-p0[1][0])*m_tsampling/p0[2][0];
    double repquant = 0.;
    double dFdzNormalized = 0.;
    if(z>0.)
    {
      repquant = FindPow(z)*std::exp(-z)/m_bipolarNormalization;
      dFdzNormalized= repquant*(m_n/z+z/13.-2.);
    }
 
    A[ii][0] = repquant*(1.-z/13.);
    //A[ii][0] = bipolar(&z,parm);
    fp[ii][0] = norm * A[ii][0];
 
    //double normOverZmax = norm/m_bipolarNormalization;
    double commonpart = norm* dFdzNormalized;//(z,parm);
    A[ii][1] = commonpart * (-m_tsampling/p0[2][0]);
    A[ii][2] = commonpart * (-z/p0[2][0]);
  }
  // end of derivative/zeroth order calculations
}

FindInitValues()

double BipolarFit::FindInitValues ( double *  x, double *  initValues, int *  maxsample  )

private

Definition at line 54 of file BipolarFit.cxx.

{
  // find maximum sample imax:
  double peakingTime=-99.;        // interpolated peaking time in samples
  double amplitude=-99.;      // interpolated amplitude
  double amin, amax;    
  int imax = 0;
  const int numSample=4;
  amax = x[0];
  amin = x[0];
  for(int j=1; j<numSample; j++)
  {
    if(amax<x[j])
    {
      amax = x[j];
      imax = j;
    }
    if(amin>x[j]) 
      amin = x[j];
  }
 
  // calculate peak and amplitude:
  (*maxsample)=imax;
  if((imax==0) || (imax==numSample-1))  // no interpolation possible
  {
    peakingTime = imax;
    amplitude = amax;
  } 
  else  // do parabolic interpolation
  {      
    double a, b, c; // coeffients of parabola y=a*x*x+b*x+c
    a = 0.5*(x[imax+1]+x[imax-1]-2.0*x[imax]);
    b = 0.5*(x[imax+1]-x[imax-1]);
    c = x[imax];
 
    peakingTime = -0.5*b/a;
    amplitude = a*peakingTime*peakingTime + b*peakingTime + c;
    peakingTime += imax; // it was relative to imax
  }
 
  initValues[0] = amplitude;
  initValues[1] = peakingTime - m_zmax*initValues[2]/m_tsampling;
  return x[imax];
}

FindPow()

double BipolarFit::FindPow ( double  z )

private

Definition at line 39 of file BipolarFit.cxx.

{
  if(std::abs(m_powcachez-z)<1.e-4)
    return m_powcachezn;
 
  double zpower = z*z*z;
  zpower *= zpower;
  zpower *= zpower; 
 
  m_powcachez = z;
  m_powcachezn= zpower;
  return zpower;
}

Fit()

int BipolarFit::Fit	(	double *	x,
		const double	ex,
		const double	pedestal,
		const double	predefinedwidth,
		double *	result,
		double *	errors,
		double *	chi2
	)

Input : x -> the ADC measurements in the 4 samplings ex -> the electronic noise in ADC counts Output: result -> the result of the fit errors -> the errors of the fit parameters chi2 -> the chi2 of the fit Returns: status of the fit

The function return an integer representing different exit status. — Bipolar fit tried — 0 --> Bipolar fit converged OK 1 --> The fit converged but its chi2 is bad 2 --> The fit converged but estimated shaping time very different from expected 3 --> Maximum number of iterations reached OK 4 --> Diverging fit. Return parabola interpolation OK 5 --> One sample saturated. Bipolar fit tried nevertheless 6 --> Late pulse the. The constant shaping time fit converged but the full fit didn't. Return fix shaping time fit results. OK — Bipolar fit not tried — 6 --> More samples saturated. Return estimate based on parabola interpolation 7 --> Parabola interpolation indicates amplitude <5sigmaNoise. Return parabola estimated parameters. OK 8 --> Distorted pulse shape. Fit likely to fail if attempted.parabola interpolation returned 9 --> Too late pulse. Bipolar fit not attempted, return rough estimate OK 10 --> It seems that a reasonable pulse exist, but the fit gave substantially lower value than the parabola. return the parabola (which is kind of lower bound for normal pulses).

Parameters

errors

errors

Definition at line 203 of file BipolarFit.cxx.

{
  // initial parameter estimates using parabola interpolation
  double initValues[3]={0.};
  int imax = -1;
  initValues[2]=predefinedwidth;
  double samplemax = FindInitValues(x,initValues,&imax);
  result[0] = initValues[0];
  result[1] = initValues[1];
  result[2] = initValues[2];
 
  // do not fit noise
  if(samplemax < 5.*ex)
    return 7;
 
  bool onesaturated = false;
  if(imax==0)
  {
    if(x[imax+1]<0. && x[imax+2]<0.)
      return 8;
  }
  else if(imax==3)
  {
    // don't fit too late pulses
    if(initValues[1]+m_zmax*initValues[2]/m_tsampling>2.75)
      return 9; 
  }
  else
  {
    if(x[imax-1]<0. && (x[imax+1]<2. || -x[imax-1]-x[imax]>0.))
      return 8;
    if(x[imax]+pedestal>4000.)
    {
      if(x[imax-1]+pedestal>4000. || x[imax+1]+pedestal>4000.)
        return 6;
      else
      {
        onesaturated=true;
      }
    }  
  }
  //always fix width and fit two parameters
  bool fitpar[3] = {true,true,false};
  bool usemeas[4] = {true,true,true,true};
  if(initValues[1]+m_zmax*initValues[2]/m_tsampling<2.0)
  {
    fitpar[2] = false;
    usemeas[3]= false;
  }
  //if(initValues[1]>0.)
  //{
  //  usemeas[0]= false;
  //  fitpar[2] = false;
  //}
 
  if(onesaturated)
  {
    usemeas[imax]= false;
    fitpar[2] = false; 
  }
  int imeas =0;
  int meas[4] = {0};
  for(int i=0;i<4;i++)
    if(usemeas[i])
    {
      meas[imeas]=i;
      imeas++;
    }
  int ipar =0;
  int par[3] = {0};
  for(int i=0;i<3;i++)
    if(fitpar[i])
    {
      par[ipar]=i;
      ipar++;
    }  
 
  int FitStatus = TheFitter(x,ex,initValues,imeas,meas,ipar,par,chi2,result);
  // the parabola interpolated estimate is most of the time a lower bound (for high pulses)!
  if(result[0]> 10.*ex && result[0]<0.90*initValues[0])
  {
    result[0] = initValues[0];
    return 10;
  }
 
  if(onesaturated)
    return 5;
 
 
  return FitStatus;
}

InvertMatrix()

void BipolarFit::InvertMatrix ( double  matrix[][3], const int  dim, int *  correspdim  )

private

Definition at line 154 of file BipolarFit.cxx.

{
  // invert 2x2 or 3x3 symmetric matrix
  if(dim==2)
  {
    int ii=correspdim[0];
    int jj=correspdim[1];
    double determinant= -matrix[jj][ii]*matrix[ii][jj] +matrix[ii][ii]*matrix[jj][jj];
    double i00 = matrix[ii][ii];
    matrix[ii][ii] = matrix[jj][jj]/determinant;
    matrix[jj][jj] = i00/determinant;
    matrix[ii][jj] = -matrix[ii][jj]/determinant;
    matrix[jj][ii] = matrix[ii][jj];
 
  }
  else if(dim==3)
  {
    double sm12 = matrix[0][1]*matrix[0][1];
    double sm13 = matrix[0][2]*matrix[0][2];
    double sm23 = matrix[1][2]*matrix[1][2];
    double determinant = matrix[0][0]*matrix[1][1]*matrix[2][2]
      -matrix[0][0]*sm23-sm12*matrix[2][2]
      +2.*matrix[0][1]*matrix[0][2]*matrix[1][2]
      -matrix[1][1]*sm13;
 
    double i00 = matrix[1][1]*matrix[2][2]-sm23;
    double i11 = matrix[0][0]*matrix[2][2]-sm13;
    double i22 = matrix[0][0]*matrix[1][1]-sm12;
 
    matrix[1][0] = (matrix[0][2]*matrix[1][2]-matrix[2][2]*matrix[0][1])/determinant;
    matrix[2][0] = (matrix[0][1]*matrix[1][2]-matrix[0][2]*matrix[1][1])/determinant;
    matrix[2][1] = (matrix[0][1]*matrix[0][2]-matrix[0][0]*matrix[1][2])/determinant;
    matrix[0][1] = matrix[1][0];
    matrix[0][2] = matrix[2][0];
    matrix[1][2] = matrix[2][1];
    matrix[0][0] = i00/determinant;
    matrix[1][1] = i11/determinant;
    matrix[2][2] = i22/determinant;
 
  }
  else
  {
    //int ierr;
    //matrix.invert(ierr);
    printf("this is not a 2x2 or 3x3 matrix\n");
  }
}

InvertSymmetric4x4()

void BipolarFit::InvertSymmetric4x4 ( double  W[][4] )

private

Definition at line 326 of file BipolarFit.cxx.

{
  double Determinant = W[0][3]*W[0][3]*W[1][2]*W[1][2] - 2.*W[0][2]*W[0][3]*W[1][2]*W[1][3]
    +W[0][2]*W[0][2]*W[1][3]*W[1][3]-W[0][3]*W[0][3]*W[1][1]*W[2][2] + 2.*W[0][1]*W[0][3]*W[1][3]*W[2][2] - W[0][0]*W[1][3]*W[1][3]*W[2][2]+2.*W[0][2]*W[0][3]*W[1][1]*W[2][3]
    - 2.*W[0][1]*W[0][3]*W[1][2]*W[2][3] - 2.*W[0][1]*W[0][2]*W[1][3]*W[2][3]+2.*W[0][0]*W[1][2]*W[1][3]*W[2][3]+W[0][1]*W[0][1]*W[2][3]*W[2][3]-W[0][0]*W[1][1]*W[2][3]*W[2][3]-W[0][2]*W[0][2]*W[1][1]*W[3][3]+2.*W[0][1]*W[0][2]*W[1][2]*W[3][3]-W[0][0]*W[1][2]*W[1][2]*W[3][3]-W[0][1]*W[0][1]*W[2][2]*W[3][3]+W[0][0]*W[1][1]*W[2][2]*W[3][3];
 
  W[0][1] = W[3][0]*W[3][1]*W[2][2]-W[3][0]*W[2][1]*W[3][2] - W[2][0]*W[3][1]*W[3][2]+W[1][0]*W[3][2]*W[3][2]+W[2][0]*W[2][1]*W[3][3]-W[1][0]*W[2][2]*W[3][3];
  W[0][2] = -W[3][0]*W[2][1]*W[3][1]+W[2][0]*W[3][1]*W[3][1]+W[3][0]*W[1][1]*W[3][2]-W[1][0]*W[3][1]*W[3][2]-W[2][0]*W[1][1]*W[3][3]+W[1][0]*W[2][1]*W[3][3];
  W[0][3] = W[3][0]*W[2][1]*W[2][1]-W[2][0]*W[2][1]*W[3][1]-W[3][0]*W[1][1]*W[2][2]+W[1][0]*W[3][1]*W[2][2]+W[2][0]*W[1][1]*W[3][2]-W[1][0]*W[2][1]*W[3][2];
  W[1][2] = W[3][0]*W[3][0]*W[2][1]-W[2][0]*W[3][0]*W[3][1]-W[1][0]*W[3][0]*W[3][2]+W[0][0]*W[3][1]*W[3][2]+W[1][0]*W[2][0]*W[3][3]-W[0][0]*W[2][1]*W[3][3];
 
  W[1][3] = -W[2][0]*W[3][0]*W[2][1]+W[2][0]*W[2][0]*W[3][1]+W[1][0]*W[3][0]*W[2][2]-W[0][0]*W[3][1]*W[2][2]-W[1][0]*W[2][0]*W[3][2]+W[0][0]*W[2][1]*W[3][2];
  W[2][3] = W[2][0]*W[3][0]*W[1][1]-W[1][0]*W[3][0]*W[2][1]-W[1][0]*W[2][0]*W[3][1]+W[0][0]*W[2][1]*W[3][1]+W[1][0]*W[1][0]*W[3][2]-W[0][0]*W[1][1]*W[3][2];
 
  double W00 = -W[3][1]*W[3][1]*W[2][2]+2.*W[2][1]*W[3][1]*W[3][2]-W[1][1]*W[3][2]*W[3][2]-W[2][1]*W[2][1]*W[3][3]+W[1][1]*W[2][2]*W[3][3];
  double W11 = -W[3][0]*W[3][0]*W[2][2]+2.*W[2][0]*W[3][0]*W[3][2]-W[0][0]*W[3][2]*W[3][2]-W[2][0]*W[2][0]*W[3][3]+W[0][0]*W[2][2]*W[3][3];
  double W22 = -W[3][0]*W[3][0]*W[1][1]+2.*W[1][0]*W[3][0]*W[3][1]-W[0][0]*W[3][1]*W[3][1]-W[1][0]*W[1][0]*W[3][3]+W[0][0]*W[1][1]*W[3][3];
  double W33 = -W[2][0]*W[2][0]*W[1][1]+2.*W[1][0]*W[2][0]*W[2][1]-W[0][0]*W[2][1]*W[2][1]-W[1][0]*W[1][0]*W[2][2]+W[0][0]*W[1][1]*W[2][2];
 
  for(int i=0;i<3;i++)
  {
    for(int j=1;j<4;j++)
    {
      if(i>=j)
        continue;
      W[i][j] = W[i][j]/Determinant;
      W[j][i] = W[i][j];
    }
  }
  W[0][0] = W00/Determinant;
  W[1][1] = W11/Determinant;
  W[2][2] = W22/Determinant;
  W[3][3] = W33/Determinant;
}

TheFitter()

int BipolarFit::TheFitter ( double *  x, const double  ex, double *  initValues, int  imeas, int *  meas, int  ipar, int *  par, double *  chi2, double *  result  )

private

Definition at line 362 of file BipolarFit.cxx.

{
  // maximum iterations
  const int maxIter = 7;
  // tolerances
  double fitTolerance0 = 0.10;
  double fitTolerance1 = 0.01;
  //HepMatrix p0(3,1,0); // the matrix of the initial fit parameters 
  double p0[3][1]={{0.}};
  for(int j=0;j<3;j++)
    p0[j][0] = initValues[j];
 
  //HepMatrix m(4,1,0); // the matrix of ADC measurements (samples: 0,1,2,3)
  double m[4][1]={{0.}};
  //HepMatrix W(4,4,0); // the error matrix of the ADC measurements 
  double W[4][4]={{0.}};
  for(int i=0;i<4;i++)
  {
    m[i][0] = x[i];
    W[i][i] = ex*ex;
  }
  // covariances 
  W[0][1] =  0.03*ex*ex;
  W[0][2] = -0.411*ex*ex;
  W[0][3] = -0.188*ex*ex;
  W[1][2] =  0.0275*ex*ex;
  W[1][3] = -0.4303*ex*ex;
  W[2][3] =  0.*ex*ex;
  W[1][0] = W[0][1];
  W[2][0] = W[0][2];
  W[3][0] = W[0][3];
  W[2][1] = W[1][2];
  W[3][1] = W[1][3];
  W[3][2] = W[2][3]; 
 
  //WW.invert(ierr);
  InvertSymmetric4x4(W);
 
  // Taylor expansion of the bipolar pulse model around the
  // samplings : F(x) = F(p0) + A *(p-p0) + higher.order
  //HepMatrix fp(4,1,0); // the matrix of 0th order approximation 
  double fp[4][1]={{0.}};
  //HepMatrix A(4,3,0);  // the matrix of derivatives 
  double A[4][3]={{0.}};
  // remarks : 
  // if the pulse peaks in the last sampling fit with a constant shaping time
  // if the pulse peaks in the first sampling fit without using the last sampling 
  // (too large contribution to the chi2
  int counter=0;
  bool converged=false;
  double amplitudeChangeOld = 0.;
  bool diverganceCandidate = false;
  //HepMatrix weight(3,3,1); // weight matrix allocated once
  // the non-fitted parts are taken care appropriately
  // at least if the fitting parameters or measurements
  // don't change during the fitting procedure
  double weight[3][3]={{0.}};
  weight[0][0]=1.;
  weight[1][1]=1.;
  weight[2][2]=1.;
 
  //HepMatrix residFactor(3,4,0); // residFactor allocated once
  double residFactor[3][4]={{0.}};
  while(!converged && counter<maxIter) // fit loop
  {
    Derivative(A,fp,p0,imeas,meas);// calculate the matrix of derivatives and 0th order approximation
    // matrix multiplication
    // the weight matrix is symmetric
    // weight= A.T()*W*A;//.assign(A.T()*W*A);
 
    double helpmatrix[4][3]={{0.}};
    for(int i=0;i<imeas;i++)
    {
      int ii=meas[i];
      for(int j=0;j<ipar;j++)
      {
        int jj=par[j];
        for(int k=0;k<imeas;k++)
        {
          int kk=meas[k];
          helpmatrix[ii][jj] += W[ii][kk]*A[kk][jj];
        }
      }
    }
    for(int i=0;i<ipar;i++)
    {   
      int ii=par[i];
      for(int j=i;j<ipar;j++)
      {
        int jj=par[j];
        weight[ii][jj] = 0.; 
        for(int k=0;k<imeas;k++)
        {
          int kk=meas[k];
          weight[ii][jj] += A[kk][ii]*helpmatrix[kk][jj];//A[kk][ii]*A[kk][jj];
        }
        //weight[ii][jj]*=W[0][0];
        weight[jj][ii] =weight[ii][jj];
      }
    }
    //weight.invert(ierr); // inversion of weight matrix
    // hand-made inversion of 2x2 or 3x3 symmetric matrix
    InvertMatrix(weight,ipar,par);
 
    //calculate W*(A.T()*W)
    //residFactor = weight*(A.T()*W);
    double helpmatrix2[3][4]={{0.}};
    for(int i=0;i<ipar;i++)
    {
      int ii=par[i];
      for(int j=0;j<imeas;j++)
      {
        int jj=meas[j];
        for(int k=0;k<imeas;k++)
        {
          int kk=meas[k];
          helpmatrix2[ii][jj] += A[kk][ii] * W[kk][jj];
        }
      }
    }
 
    for(int i=0;i<ipar;i++)
    {   
      int ii = par[i];
      for(int j=0;j<imeas;j++)
      {
        int jj=meas[j];
        residFactor[ii][jj]=0.;
        for(int k=0;k<ipar;k++)
        {
          int kk=par[k];
          residFactor[ii][jj] += weight[ii][kk]*helpmatrix2[kk][jj];
        }
        //residFactor[ii][jj]*=W[0][0];
      }
    }
 
    double paramDiff[3] = {0.};
    for(int i=0;i<ipar;i++)
    {
      int ii=par[i];
      //estimation of new parameters
      //paramDiff[i][0] += (weight*(A.T()*W)*(m-fp))[i][0];
      for(int j=0;j<imeas;j++)
      {
        int jj = meas[j];
        paramDiff[ii] += residFactor[ii][jj]*(m[jj][0]-fp[jj][0]);
      }
      p0[ii][0] += paramDiff[ii];
    }
    // if the parameters are going nuts keep them sensible
    if(p0[1][0]>1. || p0[1][0]<-3.)
      p0[1][0] = initValues[1];
 
    double amplitudeChangeNew = std::abs(paramDiff[0]);
    if(std::abs(paramDiff[0])<fitTolerance0 && std::abs(paramDiff[1])<fitTolerance1)
    {
      converged = true;
      // calculate chi2
      double residual[4]= {0.};
      for(int i=0;i<imeas;i++)
      {
        int ii=meas[i];
        residual[i] = m[ii][0]-fp[ii][0];
      }
 
      double tmpChi2 = 0.;
      double helpmatrixchi2[4][1]={{0.}};
      for(int i=0;i<imeas;i++)
      {
        int ii=meas[i];
        for(int k=0;k<imeas;k++)
        {
          int kk=meas[k];
          helpmatrixchi2[ii][0] += W[ii][kk]*residual[kk];
        }
      }
      for(int k=0;k<imeas;k++)
      {
        int kk=meas[k];
        tmpChi2 += residual[kk]*helpmatrixchi2[kk][0];
      }
      (*chi2) = tmpChi2;
    }
    else if(counter>4 && (amplitudeChangeNew>4.*amplitudeChangeOld))
    {
      if(diverganceCandidate)
      {
        //diverging fit
        //return parabola interpolation
        printf("Diverging fit\n");
        return 4;
      }
      else
        diverganceCandidate = true;
    }
    if(p0[0][0]<0.)
    {
      //negative amplitude
      //fit diverged
      // return parabola
      return 4;
    }
    //if after a couple of iterations the amplitude is low
    // reduce the tolerances (or the maximum iterations) 
    // low amplitude pulses tend to oscillate and exhaust all iterations
    if(p0[0][0]<20.)
    {
      fitTolerance0 = 0.1;
      fitTolerance1 = 0.05;
    }
    amplitudeChangeOld = amplitudeChangeNew;
    counter++;
  }
  result[0]=p0[0][0];
  result[1]=m_zmax*p0[2][0]/m_tsampling+p0[1][0];
  result[2]=p0[2][0];
 
  if(counter==maxIter)
    return 3;
  return 0;
}

Member Data Documentation

m_bipolarNormalization

double BipolarFit::m_bipolarNormalization

private

Definition at line 45 of file BipolarFit.h.

m_n

double BipolarFit::m_n

private

Definition at line 41 of file BipolarFit.h.

m_powcachez

double BipolarFit::m_powcachez

private

Definition at line 42 of file BipolarFit.h.

m_powcachezn

double BipolarFit::m_powcachezn

private

Definition at line 43 of file BipolarFit.h.

m_tsampling

double BipolarFit::m_tsampling

private

Definition at line 46 of file BipolarFit.h.

m_zmax

double BipolarFit::m_zmax

private

Definition at line 44 of file BipolarFit.h.

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

• BipolarFit.h
• BipolarFit.cxx