Helpers for the 2-D beam-spot description. More...

#include <BeamFit2D.hpp>

Classes
struct	SpotFit
	Result of a beam spot fit: the spot to use, and whether the Gaussian fit (rather than the clipped-moments fallback) made it. More...

Static Public Member Functions
static Bool_t	InEllipseXY (const BeamFit2D &b, Double_t x, Double_t y, Double_t n)
	Whether a point lies inside the fitted ellipse at `n` sigma: the correlation-aware Mahalanobis chi2 below n^2, one level, since a density contour has one.
static void	DrawEllipse (const BeamFit2D &b, Double_t n, Color_t color)
	Draw the `n-sigma` contour of a fitted spot on the current pad.
static Moments2D	ComputeMoments (TH2F *h, Int_t lo_bx, Int_t hi_bx, Int_t lo_by, Int_t hi_by, Double_t thresh, Double_t bw_x, Double_t bw_y)
	Second moments of a histogram region above a threshold.
static Moments2D	ClippedMoments (const std::vector< std::pair< Float_t, Float_t > > &pts, const Moments2D &seed, Double_t clip=3.0)
	Sigma-clipped centroid and covariance of a point sample, the 2-D counterpart of the strip-width clip: each pass keeps the points within `clip` (Mahalanobis) of the current estimate and takes their mean and covariance, scaled up by the variance a 2-D Gaussian loses outside `clip`.
static Moments2D	SeedSpotMoments (TH2F *h, Int_t seed_half_bins)
	Second moments of a coarse spot histogram's seed window: the maximum bin, ± `seed_half_bins` around it, over the bins at or above 0.3 of the peak.
static SpotFit	FitSpotFromPoints (TH2F *h, std::vector< std::pair< Float_t, Float_t > > &pts, const Moments2D &seed)
	A beam spot from a coarse histogram and the same events unbinned: the sample's sigma-clipped moments seeded from `seed`, then a correlated Gaussian on a flat pedestal over a fine histogram re-binned around the clip — the inner 2 sigma fitted, the rest judged.
static BeamFit2D	FitSpot (TH2F h, const Moments2D &seed, Double_t window_nsigma=2.0, Double_t chi2_ndf=nullptr)
	Fit a correlated 2-D Gaussian on a flat pedestal to `h:` ROOT's bigaus written out, Poisson likelihood, Minuit limits from `seed`.
static Bool_t	FitPeak (TH1F h, Double_t seed_mu, Double_t seed_sigma, Double_t window_nsigma, Bool_t fix_mu, Double_t &mu, Double_t &sigma, Double_t chi2_ndf=nullptr)
	The 1-D counterpart: a Gaussian on a flat pedestal, fitted over `window_nsigma` of the seed and judged over the whole of `h`.

Detailed Description

Helpers for the 2-D beam-spot description.

Definition at line 42 of file BeamFit2D.hpp.

Member Function Documentation

◆ ClippedMoments()

Moments2D BeamFitUtils::ClippedMoments	(	const std::vector< std::pair< Float_t, Float_t > > &	pts,
		const Moments2D &	seed,
		Double_t	clip = 3.0 )

static

Sigma-clipped centroid and covariance of a point sample, the 2-D counterpart of the strip-width clip: each pass keeps the points within clip (Mahalanobis) of the current estimate and takes their mean and covariance, scaled up by the variance a 2-D Gaussian loses outside clip.

The widths are then a Gaussian's sigma for a Gaussian spot, and the clipped RMS of anything else; no binning or peak-fraction threshold enters.

Parameters

pts	The (x, y) sample.
seed	Starting estimate, e.g. ComputeMoments over the core. Its widths may be too narrow; the passes grow them.
clip	Mahalanobis radius kept per pass.

Returns: The converged moments; the seed when fewer than 10 points are kept.

Definition at line 94 of file BeamFit2D.cpp.

Referenced by FitSpotFromPoints().

◆ ComputeMoments()

Moments2D BeamFitUtils::ComputeMoments	(	TH2F *	h,
		Int_t	lo_bx,
		Int_t	hi_bx,
		Int_t	lo_by,
		Int_t	hi_by,
		Double_t	thresh,
		Double_t	bw_x,
		Double_t	bw_y )

static

Second moments of a histogram region above a threshold.

Parameters

h	Histogram to measure. Must not be null.
lo_bx	First x bin, inclusive.
hi_bx	Last x bin, inclusive.
lo_by	First y bin, inclusive.
hi_by	Last y bin, inclusive.
thresh	Bin contents at or below this are ignored, which keeps background out of the widths.
bw_x	x bin width, for converting bin indices to physical units.
bw_y	y bin width.

Returns: The moments; weight == 0 when nothing cleared thresh.

Definition at line 42 of file BeamFit2D.cpp.

Referenced by FindBeamGateStrips(), and SeedSpotMoments().

◆ DrawEllipse()

void BeamFitUtils::DrawEllipse	(	const BeamFit2D &	b,
		Double_t	n,
		Color_t	color )

static

Draw the n-sigma contour of a fitted spot on the current pad.

The correlated 2-D Gaussian's TEllipse rotated per the covariance eigen-decomposition, so the drawn contour is the InEllipseXY() gate (chi2 < n^2).

Parameters

b	Fitted spot; ok must be true.
n	Level, in sigma.
color	Line colour of the contour.

Definition at line 24 of file BeamFit2D.cpp.

Referenced by FindBeamGateStrips().

◆ FitPeak()

Bool_t BeamFitUtils::FitPeak	(	TH1F *	h,
		Double_t	seed_mu,
		Double_t	seed_sigma,
		Double_t	window_nsigma,
		Bool_t	fix_mu,
		Double_t &	mu,
		Double_t &	sigma,
		Double_t *	chi2_ndf = nullptr )

static

The 1-D counterpart: a Gaussian on a flat pedestal, fitted over window_nsigma of the seed and judged over the whole of h.

Parameters

h	Histogram to fit, and to judge chi2 over; must not be null, and a couple of bins per seed sigma would do.
seed_mu	Seed centre; sets the fitted window and mu's limits.
seed_sigma	Seed width; positive, and sets the fitted window and sigma's limits at 0.2 to 5 times the seed.
window_nsigma	Half-width fitted, in the seed's sigma.
fix_mu	Hold the centre at `seed_mu`, for a distribution with more than one peak.
mu	Fitted centre, untouched when the fit is rejected.
sigma	Fitted width, untouched when the fit is rejected.
chi2_ndf	Reduced chi2 over the whole of `h`, so what the window excluded is what it notices; -1 if no fit ran.

Returns: kFALSE when the fit failed or ran away; mu and sigma are then untouched.

Definition at line 289 of file BeamFit2D.cpp.

◆ FitSpot()

BeamFit2D BeamFitUtils::FitSpot	(	TH2F *	h,
		const Moments2D &	seed,
		Double_t	window_nsigma = 2.0,
		Double_t *	chi2_ndf = nullptr )

static

Fit a correlated 2-D Gaussian on a flat pedestal to h: ROOT's bigaus written out, Poisson likelihood, Minuit limits from seed.

Parameters

h	Finely binned spot reaching past the fit window; a couple of bins per sigma would fit the binning.
seed	Sets the window and the limits, e.g. ClippedMoments.
window_nsigma	Half-width fitted, in the seed's sigma; narrow keeps a shoulder out of the width (+4 percent at 2, +10 at 4).
chi2_ndf	Reduced chi2 over the whole of `h`, so what the window excluded is what it notices; -1 if no fit ran.

Returns: ok == kFALSE when the fit failed or ran away: keep the seed.

Definition at line 206 of file BeamFit2D.cpp.

Referenced by FitSpotFromPoints().

◆ FitSpotFromPoints()

BeamFitUtils::SpotFit BeamFitUtils::FitSpotFromPoints	(	TH2F *	h,
		std::vector< std::pair< Float_t, Float_t > > &	pts,
		const Moments2D &	seed )

static

A beam spot from a coarse histogram and the same events unbinned: the sample's sigma-clipped moments seeded from seed, then a correlated Gaussian on a flat pedestal over a fine histogram re-binned around the clip — the inner 2 sigma fitted, the rest judged.

Parameters

h	Coarse histogram; names the fine one and supplies the fallback amplitude.
pts	The spot's events unbinned (up to a cap); consumed.
seed	Seed moments, e.g. SeedSpotMoments(); weight must be > 0.

Returns: The spot: the fit when it holds, the clipped moments otherwise.

Definition at line 164 of file BeamFit2D.cpp.

Referenced by FindBeamGateStrips().

◆ InEllipseXY()

Bool_t BeamFitUtils::InEllipseXY	(	const BeamFit2D &	b,
		Double_t	x,
		Double_t	y,
		Double_t	n )

static

Whether a point lies inside the fitted ellipse at n sigma: the correlation-aware Mahalanobis chi2 below n^2, one level, since a density contour has one.

A Gaussian keeps 1 - exp(-n^2/2) inside.

Parameters

b	Fitted spot; ok must be true.
x	Point x coordinate.
y	Point y coordinate.
n	Level, in sigma.

Definition at line 9 of file BeamFit2D.cpp.

Referenced by CollectAnchorSamplesOneSubfile().

◆ SeedSpotMoments()

Moments2D BeamFitUtils::SeedSpotMoments	(	TH2F *	h,
		Int_t	seed_half_bins )

static

Second moments of a coarse spot histogram's seed window: the maximum bin, ± seed_half_bins around it, over the bins at or above 0.3 of the peak.

Parameters

h	Coarse histogram of the spot, already filled.
seed_half_bins	Half-width of the seed window, in bins of `h`.

Returns: The moments; weight <= 0 when no bin clears the threshold.

Definition at line 147 of file BeamFit2D.cpp.

Referenced by FindBeamGateStrips().

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

tooling/include/BeamFit2D.hpp
tooling/src/BeamFit2D.cpp

Classes

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ ClippedMoments()

◆ ComputeMoments()

◆ DrawEllipse()

◆ FitPeak()

◆ FitSpot()

◆ FitSpotFromPoints()

◆ InEllipseXY()

◆ SeedSpotMoments()