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Here we discuss how to apply fit to data using absolute errors on peak position, get fit parameters with errors, estimate fit quality.

Data

exp=cxif5315:run=169

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Fit in the processing script

cxif5315/proc-cxif5315-r0169-peaks-from-file-v4.py

from scipy.optimize import curve_fit
from scipy.stats import chi2

        xn = np.array([pk.x/L for pk in sp.lst_equ_evt_peaks], dtype=np.double)
        yn = np.array([pk.y/L for pk in sp.lst_equ_evt_peaks], dtype=np.double)
        en = np.array([pk.csigma*sp.PIXEL_SIZE/L for pk in sp.lst_equ_evt_peaks], dtype=np.double)
        #en = np.array([max(pk.rsigma,pk.csigma)*sp.PIXEL_SIZE/L for pk in sp.lst_equ_evt_peaks], dtype=np.double)

        p0 = [-3.2,-16.0] # phi, beta angle central values

            popt, pcov = curve_fit(funcy, xn, yn, p0, en, absolute_sigma=True)
 
            sp.fib_chi2 = np.sum(((funcy(xn, *popt) - yn) / en)**2)
            sp.fib_ndof = len(xn) - 1
            sp.fib_prob = chi2.sf(sp.fib_chi2, sp.fib_ndof, loc=0, scale=1)

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Plots

Distribution of parameters for peaks found by peak_finder_v2:

 Image ModifiedImage Modified

 Image Modified

Image Modified

For 2-peak events fit does not have any freedom - curve can exactly be fitted to 3 points (including origin); chi2=0 and probability is always 1.

For >2-peak events chi2 and probability show some distribution.

Peak list with phi-beta fit results

After phi-beta fit peaks are saved in the file with name like

result/peak-fit-cxif5315-r0169-2016-04-04T16:16:38.

References

txt

Comparing to regular peak parameters this file has extended data for each peak by

...  fit-phi fit-beta  phi-err  beta-err  fit-chi2  ndof  fit-prob
...     1.30  -42.98  3.800454 10.236941  0.000000     1  1.000000
...    -4.75  -23.85  0.265462  1.212093  1.734365     3  0.629321

References

• scipy.optimize.curve_fit
• scipy.stats.chi2

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