Fit

Function and classes for fitting histograms

Base Fit class

This class define generic methods

Fit

 Fit (name='fit', h=None, fit_range=None, npx:int=1000, invert:bool=False,
      par_names=None)

general class for fitting histograms

	Type	Default	Details
name	str	fit	Name of the fitting function
h	NoneType	None	histogram to fit
fit_range	NoneType	None	list or tuple of fit range borders
npx	int	1000	Number of points used to draw the fit function
invert	bool	False
par_names	NoneType	None	List of parameter names of the fitting function

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Fit.init_fit

 Fit.init_fit ()

returns root TF1 fit function

Placeholders

Place holder functions, will be overwritten in the child classes

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Fit.find_fit_range

 Fit.find_fit_range ()

placeholder to be overwritten in child classes, here is simply returns [0, 1000]

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Fit.get_par_names

 Fit.get_par_names ()

placeholder to be overwritten in child classes, here is simply returns []

Setters

functions that set parameter name, limits, start values, as well as clears previous fit functions

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Fit.set_par_names

 Fit.set_par_names ()

Sets fit function parameter names by passing a list of parameter names to the TF1.SetParNames() method

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Fit.set_par_limits

 Fit.set_par_limits ()

placeholder to be overwritten in child classes

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Fit.set_start_values

 Fit.set_start_values ()

placeholder to be overwritten in child classes

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Fit.set_parameters

 Fit.set_parameters (*pars)

Sets fit function parameters by passing a parameter list to the TF1.SetParameters() method

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Fit.clear_old

 Fit.clear_old ()

deletes the previous fit function

Getters

functions that access internal state of the fit class such as parameters and the results of the fit

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Fit.get_parameter

 Fit.get_parameter (i:int)

returns the value and the error of a parameter

	Type	Details
i	int	index of the parameter to get

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Fit.get_parameters

 Fit.get_parameters ()

returns a list of parameter values

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Fit.from_hist

 Fit.from_hist (h)

When Fit (TH1:Fit) is invoked, the fitted function is added to the list of function associated with this histogram. Given an histogram h, one can retrieve an associated function

	Details
h	histogram

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Fit.get_chi2

 Fit.get_chi2 ()

returns chi2 of the fit divided by the number of degrees of freedom

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Fit.formula

 Fit.formula ()

return the formula of the fit function

Info functions

Example:

f = Fit()
f

Fit Fit: fit with 0 parameters

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Fit.print_parameters

 Fit.print_parameters ()

prints parameters names and values

Worker function

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Fit.fit

 Fit.fit (n:int=1, draw=True, minuit=True, fl=0, fh=0)

The method performs the fit and optionally draws fit function overlayed on the histogram

	Type	Default	Details
n	int	1	number of iterations
draw	bool	True	Overlay the fitting function on histogram
minuit	bool	True	Use Minuit2 and Migrad for minimization
fl	int	0	lower fitting range
fh	int	0	upper fitting range

Display function

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Fit.draw

 Fit.draw (*args, **kwargs)

plots the fit functions

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make_fit

 make_fit (h, f, xmin=0, xmax=1, start_values=None, par_names=None,
           name=None, npx=1000)

factory method for making NewFit classes that are inherit from the Fit class

	Type	Default	Details
h			histogram to fit
f			fitting function
xmin	int	0	lower fitting range
xmax	int	1	upper fitting range
start_values	NoneType	None	list initial values
par_names	NoneType	None	list of parameter names
name	NoneType	None	name of the fitting function
npx	int	1000	number of points used to draw the fitting function

Specific fit classes

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PoissonI

 PoissonI (h=None, fit_range=None, npx:int=1000, p0:float=None,
           p1:float=None)

general class for fitting histograms

	Type	Default	Details
h	NoneType	None	histogram to fit
fit_range	NoneType	None	list with the low and high values of the fitting range
npx	int	1000	number of points to use when drawing the fitting function
p0	float	None	initial value for constant parameter
p1	float	None	initial value for lambda parameter

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Expo

 Expo (h=None, xmin=None, xmax=None, npx=100)

general class for fitting histograms

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gauss

 gauss (x, scale, mean_, sigma, off=0)

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Gauss

 Gauss (h=None, fit_range=None, npx=100, fl=3, fh=3, thresh=0.01, **fkw)

general class for fitting histograms

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Landau

 Landau (h=None, fit_range=None, npx=100)

general class for fitting histograms

	Type	Default	Details
h	NoneType	None	histogram to fit
fit_range	NoneType	None
npx	int	100

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Erf

 Erf (h=None, fit_range=None, pars=None, npx=100)

general class for fitting histograms

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crystalball

 crystalball (x, pars, inv=False)

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Crystalball

 Crystalball (h=None, fit_range=None, inv=False, npx=1000)

general class for fitting histograms

# crystal_ball = Crystalball(fit_range=[-10, 10])
# crystal_ball.draw()
# a = get_last_canvas()
# a.draw()

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erfland

 erfland (x, pars)

retruns error function merged with Landau

# from ROOT import TCanvas, TFormula, TF1
# from ROOT import gROOT, gObjectTable
# %jsroot on

# c = TCanvas( 'c', 'Example with Formula', 200, 10, 700, 500 )

# fun1 = TF1( 'fun1', erfland, 0, 10, 8)
# c0, mpv, sigma, c1, xoff, w, yoff = 1, 7, 2, 1, 3, 2, 0
# fun1.SetParameters(c0, mpv, sigma, c1, xoff, w, yoff)
# fun1 = TF1( 'fun1', 'abs(sin(x)/x)', 0, 10 )
# c.SetGridx()
# c.SetGridy()
# fun1.Draw()

# c.Update()

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ErfLand

 ErfLand (h=None, fit_range=None, npx=1000)

general class for fitting histograms

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Langau

 Langau (h=None, nconv:int=100, fit_range=None, npx:int=1000)

general class for fitting histograms

	Type	Default	Details
h	NoneType	None	histogram to fit
nconv	int	100	number of convolutions within the range
fit_range	NoneType	None	fitting range
npx	int	1000	number of points to draw the function

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NLandau

 NLandau (h=None, fit_range=None, npx:int=100, n:int=3)

general class for fitting histograms

	Type	Default	Details
h	NoneType	None	histogram to fit
fit_range	NoneType	None	fitting range
npx	int	100	number of points to draw the fitting function
n	int	3	number of Landaus

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langau

 langau (x:float, pars, nconv:int, nsigma:int=5)

Convoluted Landau and Gaussian Fitting Function (using ROOT’s Landau and Gauss functions)

Fit parameters: par[0]=Width (scale) parameter of Landau density par[1]=Most Probable (MP, location) parameter of Landau density par[2]=Total area (integral -inf to inf, normalization constant) par[3]=Width (sigma) of convoluted Gaussian function

In the Landau distribution (represented by the CERNLIB approximation), the maximum is located at x=-0.22278298 with the location parameter=0. This shift is corrected within this function, so that the actual maximum is identical to the MP parameter.

The code is literally converted to python from the original C at https://root.cern.ch/root/html404/examples/langaus.C.html

	Type	Default	Details
x	float		independent variable
pars			list of langau fit parameters
nconv	int		number of convolutions
nsigma	int	5	number of sigmas, extent of the convolution intergral

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langaupro

 langaupro (params, maxx, FWHM)

Seaches for the location (x value) at the maximum of the Landau-Gaussian convolute and its full width at half-maximum.

The search is probably not very efficient, but it’s a first try.

The code is literally converted to python from the original C at https://root.cern.ch/root/html404/examples/langaus.C.html

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main

 main ()