FittingFunctions Namespace Reference

Raw model functions in TF1 form: f(Double_t *x, Double_t *par). More...

Functions
Double_t	Gaussian (Double_t *x, Double_t *par)
	Gaussian peak.
Double_t	LinearBackground (Double_t *x, Double_t *par)
	Straight-line background.
Double_t	Step (Double_t *x, Double_t *par)
	Resolution-smeared step shelf below the peak.
Double_t	LowTail (Double_t *x, Double_t *par)
	Combined exponential and linear tail below the peak.
Double_t	HighTail (Double_t *x, Double_t *par)
	Exponential tail above the peak, from pileup.
Double_t	PeakFunction (Double_t *x, Double_t *par)
	One peak with every optional component, plus a linear background.
Double_t	DoublePeakFunction (Double_t *x, Double_t *par)
	Two peaks sharing one linear background.
Double_t	TriplePeakFunction (Double_t *x, Double_t *par)
	Three peaks sharing one linear background.

Detailed Description

Raw model functions in TF1 form: f(Double_t *x, Double_t *par).

Exposed so a caller can build a custom TF1 from the same components the class uses. Every function is un-normalised — amplitudes are peak heights in counts, not yields.

In the composite functions the step and tail amplitudes are expressed as ratios of the Gaussian amplitude rather than absolute heights, which is what keeps a constrained fit meaningful when the peak height changes. Tail ratio parameters are decay constants in units of sigma, so tau = ratio * sigma.

Function Documentation

DoublePeakFunction()

Double_t FittingFunctions::DoublePeakFunction	(	Double_t *	x,
		Double_t *	par )

Two peaks sharing one linear background.

Each peak occupies a ten-parameter block laid out as parameters 0 to 9 of PeakFunction(): peak one at [0..9], peak two at [10..19], with the background constant and slope appended at [20] and [21].

Parameters

x	Observable; only x[0] is used.
par	The 22 parameters above.

Returns

The summed model value.

Definition at line 186 of file FittingUtils.cpp.

Referenced by FittingUtils::FitDoublePeak(), and FittingUtils::FitDoublePeak().

Gaussian()

Double_t FittingFunctions::Gaussian	(	Double_t *	x,
		Double_t *	par )

Gaussian peak.

Parameters

x	Observable; only x[0] is used.
par	[0] centroid, [1] sigma, [2] peak height.

Returns

The un-normalised Gaussian value.

Definition at line 73 of file FittingUtils.cpp.

Referenced by DoublePeakFunction(), PeakFunction(), FittingUtils::PlotFitSinglePeak(), and TriplePeakFunction().

HighTail()

Double_t FittingFunctions::HighTail	(	Double_t *	x,
		Double_t *	par )

Exponential tail above the peak, from pileup.

Parameters

x	Observable; only x[0] is used.
par	[0] centroid, [1] sigma, [2] amplitude, [3] decay constant in units of sigma.

Returns

The tail value; zero when sigma <= 0, the amplitude is zero, or the decay constant is non-positive.

Definition at line 115 of file FittingUtils.cpp.

Referenced by DoublePeakFunction(), PeakFunction(), FittingUtils::PlotFitSinglePeak(), and TriplePeakFunction().

LinearBackground()

Double_t FittingFunctions::LinearBackground	(	Double_t *	x,
		Double_t *	par )

Straight-line background.

Parameters

x	Observable; only x[0] is used.
par	[0] constant, [1] slope.

Returns

slope * x + constant.

Definition at line 81 of file FittingUtils.cpp.

Referenced by DoublePeakFunction(), FittingUtils::FitSinglePeak(), PeakFunction(), FittingUtils::PlotFitDoublePeak(), FittingUtils::PlotFitSinglePeak(), FittingUtils::PlotFitTriplePeak(), and TriplePeakFunction().

LowTail()

Double_t FittingFunctions::LowTail	(	Double_t *	x,
		Double_t *	par )

Combined exponential and linear tail below the peak.

Parameters

x	Observable; only x[0] is used.
par	[0] centroid, [1] sigma, [2] exponential amplitude, [3] exponential decay in units of sigma, [4] linear amplitude, [5] linear slope.

Returns

The summed tail, cut off above the centroid by a complementary error function. Zero when sigma <= 0 or both amplitudes are zero.

Definition at line 87 of file FittingUtils.cpp.

Referenced by DoublePeakFunction(), PeakFunction(), FittingUtils::PlotFitSinglePeak(), and TriplePeakFunction().

PeakFunction()

Double_t FittingFunctions::PeakFunction	(	Double_t *	x,
		Double_t *	par )

One peak with every optional component, plus a linear background.

Twelve parameters: [0] centroid, [1] sigma, [2] Gaussian height, [3] step amplitude, [4] low exponential tail amplitude, [5] its decay in units of sigma, [6] low linear tail amplitude, [7] its slope, [8] high exponential tail amplitude, [9] its decay in units of sigma, [10] background constant, [11] background slope.

Parameters

x	Observable; only x[0] is used.
par	The twelve parameters above.

Returns

The summed model value.

Note

Parameters 3, 4, 6 and 8 are ratios of the Gaussian amplitude, not absolute heights. Setting a ratio to zero disables that component.

Definition at line 154 of file FittingUtils.cpp.

Referenced by FittingUtils::FittingUtils().

Step()

Double_t FittingFunctions::Step	(	Double_t *	x,
		Double_t *	par )

Resolution-smeared step shelf below the peak.

Parameters

x	Observable; only x[0] is used.
par	[0] centroid, [1] sigma, [2] step amplitude.

Returns

The shelf value; zero when sigma <= 0 or the denominator underflows.

Definition at line 138 of file FittingUtils.cpp.

Referenced by DoublePeakFunction(), PeakFunction(), FittingUtils::PlotFitSinglePeak(), and TriplePeakFunction().

TriplePeakFunction()

Double_t FittingFunctions::TriplePeakFunction	(	Double_t *	x,
		Double_t *	par )

Three peaks sharing one linear background.

As DoublePeakFunction(), with a third ten-parameter block at [20..29] and the background appended at [30] and [31].

Parameters

x	Observable; only x[0] is used.
par	The 32 parameters above.

Returns

The summed model value.

Definition at line 246 of file FittingUtils.cpp.

Referenced by FittingUtils::FitTriplePeak().