from scipy.optimize import curve_fit
  import csv, numpy, glob
  from scipy.special import erf
  import matplotlib.pyplot as plt
  
  '''power function to optimize'''
  def P(x, Po, Pmax, xo, w):
      return Po+0.5*Pmax*(1.-erf(2.**0.5*(x-xo)/w))
  
  
  '''load and fit beam section'''
  files = glob.glob('*.dat')
  files.sort()
  data_waist = []
  plt.close()
  fig, p = plt.subplots(2, 1)
  for f in files:
      with open(f, 'r') as dest_f:
          raw = csv.reader(dest_f, delimiter = '\t', quotechar = '"')
          data = [value for value in raw]
      data = numpy.asarray(data, dtype = float)
      xmes = data[:,0]
      Pmes = data[:,1]
  
      '''optimization with non-linear least squares method'''
      Ppopt, Pcov = curve_fit(P, xmes, Pmes)
      data_waist.append([int(f[-7:-4]), Ppopt[3]])
  
      '''plot'''
      p[0].plot(xmes, Pmes, 'o')
      p[0].plot(numpy.linspace(xmes[0], xmes[-1], 100), P(numpy.linspace(xmes[0], xmes[-1], 100), *Ppopt))
  
  p[0].grid()
  
  '''return waist(z) table'''
  data_waist = numpy.asarray(data_waist, dtype = float)
  print(data_waist)
  
  '''waist function to optimize'''
  def W(z, w0, z0):
      return w0*(1.+((z-z0)*1542e-6/(numpy.pi*w0**2))**2)**0.5
  
  popt, cov = curve_fit(W, data_waist[:,0], data_waist[:,1])
  print(popt[0], popt[1])
  
  p[1].plot(data_waist[:,0], data_waist[:,1], 'bo')
  p[1].plot(data_waist[:,0], -data_waist[:,1], 'bo')
  p[1].plot(numpy.linspace(data_waist[0,0], data_waist[-1,0], 100), W(numpy.linspace(data_waist[0,0], data_waist[-1,0], 100), *popt), 'r')
  p[1].plot(numpy.linspace(data_waist[0,0], data_waist[-1,0], 100), -W(numpy.linspace(data_waist[0,0], data_waist[-1,0], 100), *popt), 'r')
  p[1].grid()
  
  plt.show()