LinearFitErrorsIn2Coord Class Reference

#include <LinearFitErrorsIn2Coord.h>

Public Member Functions
float	intercept (const std::vector< float > &x, const std::vector< float > &y, int ndat, const std::vector< float > &sigx, const std::vector< float > &sigy) const
float	slope (const std::vector< float > &x, const std::vector< float > &y, int ndat, const std::vector< float > &sigx, const std::vector< float > &sigy) const

Private Member Functions
float	variance (const std::vector< float > &x, int ndat) const

Detailed Description

Straight line fit for data with errors on both coordinates source: Numerical Recipes

Definition at line 10 of file LinearFitErrorsIn2Coord.h.

Member Function Documentation

intercept()

float LinearFitErrorsIn2Coord::intercept	(	const std::vector< float > &	x,
		const std::vector< float > &	y,
		int	ndat,
		const std::vector< float > &	sigx,
		const std::vector< float > &	sigy
	)		const

Approached intercept computed with approached slope

Definition at line 31 of file LinearFitErrorsIn2Coord.cc.

References compareTotals::fs, mps_fire::i, slope(), x, and y.

                                                                             {
  float fs = slope(x, y, ndat, sigx, sigy);
  float fi = 0;
  float sumWi = 0;
  for (int i = 0; i != ndat; i++) {
    float wi = 1. / (sigy[i] + fs * fs * sigx[i]);
    fi += wi * (y[i] - fs * x[i]);
    sumWi += wi;
  }

  return fi / sumWi;
}

slope()

float LinearFitErrorsIn2Coord::slope	(	const std::vector< float > &	x,
		const std::vector< float > &	y,
		int	ndat,
		const std::vector< float > &	sigx,
		const std::vector< float > &	sigy
	)		const

Approached slope:

• rescale y and sigy by var(x)/var(y)
• fit a straight line with weights derived from the scaled sum sigx^2 + sigy^2

Definition at line 5 of file LinearFitErrorsIn2Coord.cc.

References LinearFit::fit(), compareTotals::fs, mps_fire::i, l1tEGammaCrystalsEmulatorProducer_cfi::scale, mathSSE::sqrt(), variance(), x, and y.

Referenced by intercept().

                                                                         {
  // scale y and sigy, compute scaled errors
  float scale = sqrt(variance(x, ndat) / variance(y, ndat));
  std::vector<float> yScaled = y;
  std::vector<float> sigyScaled = sigy;
  std::vector<float> sig(ndat);
  for (int i = 0; i != ndat; i++) {
    yScaled[i] *= scale;
    sigyScaled[i] *= scale;
    sig[i] = sqrt(sigx[i] * sigx[i] + sigyScaled[i] * sigyScaled[i]);
  }

  // usual linear fit
  LinearFit lf;
  float fs, fi, covss, covii, covsi;
  lf.fit(x, yScaled, ndat, sig, fs, fi, covss, covii, covsi);

  // unscale result
  fs /= scale;
  return fs;
}

variance()

float LinearFitErrorsIn2Coord::variance ( const std::vector< float > &  x, int  ndat  ) const

private

Definition at line 48 of file LinearFitErrorsIn2Coord.cc.

References nano_mu_digi_cff::float, mps_fire::i, callgraph::m2, and x.

Referenced by slope(), and average.Average::uncertainty().

                                                                                 {
  double m1 = 0., m2 = 0.;
  for (int i = 0; i != ndat; i++) {
    m1 += x[i];
    m2 += x[i] * x[i];
  }
  m1 /= ndat;
  m2 /= ndat;

  return float(m2 - m1 * m1);
}