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import numpy as np
import matplotlib.pyplot as pl
pl.style.use('apw-notebook')
%matplotlib inline
import scipy.optimize as so


    

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focus_fwhm = [
    (2520,3.5,0.2),
    (2515,2.8,0.01),
    (2510,2.4,0.01),
    (2505,3.00,0.01)
]
focus_fwhm = np.array(focus_fwhm, dtype=[('focus',float),('fwhm',float),('fwhm_err',float)])


    

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def model(p,focus):
    return p[0]*(focus-p[3])**2 + p[1]*(focus-p[3]) + p[2]

def errfunc(p,focus,fwhm,fwhm_err):
    return (fwhm - model(p,focus))/fwhm_err


    

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grid = np.linspace(2500,2520,100)
pl.plot(grid, model((1e-2,1e-2,focus_fwhm['fwhm'].min(),np.median(focus_fwhm['focus'])),grid))
pl.plot(focus_fwhm['focus'], focus_fwhm['fwhm'], ls='none', marker='o')


    

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popt,ier = so.leastsq(errfunc, x0=(1E-2,1E-2,2.,2510), 
                      args=(focus_fwhm['focus'], focus_fwhm['fwhm'], focus_fwhm['fwhm_err']))


    

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grid = np.linspace(2500,2520,1024)
pl.plot(grid, model(popt,grid))
pl.plot(focus_fwhm['focus'], focus_fwhm['fwhm'], ls='none', marker='o')


    

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idx = model(popt,grid).argmin()
print("The focus you should use is: {}".format(int(grid[idx])))


    

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