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Phi-beta fit functions

Two solutions of quadratic equation in ARC region

  • POS: y = -B + sqrt(B*B-C)
  • NEG: y = -B - sqrt(B*B-C)

Arc region

pyimgalgos/src/FiberAngles.py

y = funcy_l1_v1(x, phi_deg, bet_deg, DoR=390/913.27, sgnrt=1.)    # or ... sgnrt=-1.)

wide range of x:

narrow range of x:

 

  • For POS root: beta=-13.3 gives minimal y.
  • If two measured peaks are located below this curve then B*B-C < 0, fit returns limit value of beta or not converging.
  • Two solutions for beta -17 and -9 - x and y are the same.
  • NEG-ative root gives wrong curvature

Equatorial region

pyimgalgos/src/FiberAngles.py

y = funcy_l0(x, phi_deg, bet_deg)

Problem with two roots is resolved for EQU region; sign of the root is selected the same as sign of parameter B;

  • For |beta|>~48 solution does not exist for entire range of x

 

 

Fit in the processing script

Example of how to apply fit to data using absolute errors on peak position, get fit parameters with errors, estimate fit quality.

cxif5315/proc-cxif5315-r0169-peaks-from-file-v4.py, v5, v6

essential code
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)

 

Phi-beta fit results and quality

Data: peak list selected by Meng

  • exp=cxif5315:run=169
  • Distribution of parameters for peaks selected by Meng:

EQU region

 

ARC region: 1-st solution for beta (positive root)

ARC region: 2-nd solution for beta (positive root)

 

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.

 

Data: peak list after pfv2r1

EQU region

ARC region

 

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.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

To load this file use helper classes pyimgalgos.TDFileContainer with pyimgalgos.TDPeakRecord

References

 

 


 

 

 

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