Source code for numerical.fit

#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""Function and approximation.

.. module:: fit
  :platform: *nix, Windows
  :synopsis: Function and approximation.

.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de>
"""
from __future__ import print_function
from pylab import array, argmax, gradient, exp, sqrt, log, linspace
from scipy.optimize import curve_fit

def gauss(x, *p):
  """Gauss distribution function.

  .. math::
    f(x)=ae^{-(x-b)^{2}/(2c^{2})}

  :param x: positions where the gauss function will be calculated
  :type x: int or float or list or numpy.ndarray
  :param p: gauss parameters [a, b, c, d]:

    * a -- amplitude (:math:`\int y \\,\\mathrm{d}x=1 \Leftrightarrow a=1/(c\\sqrt{2\\pi})` )
    * b -- expected value :math:`\\mu` (position of maximum, default = 0)
    * c -- standard deviation :math:`\\sigma` (variance :math:`\\sigma^2=c^2`)
    * d -- vertical offset (default = 0)
  :type p: list

  :returns: gauss values at given positions x
  :rtype: numpy.ndarray
  """
  x = array(x)  # cast e. g. list to numpy array
  a, b, c, d = p
  return a*exp(-(x - b)**2./(2. * c**2.)) + d

def gauss_fit(x, y, e=None, x_fit=None, verbose=False):
  """Fit Gauss distribution function to data.

  :param x: positions
  :type x: int or float or list or numpy.ndarray
  :param y: values
  :type y: int or float or list or numpy.ndarray
  :param e: error values (default = None)
  :type e: int or float or list or numpy.ndarray
  :param x_fit: positions of fitted function (default = None, if None then x
    is used)
  :type x_fit: int or float or list or numpy.ndarray
  :param verbose: verbose information (default = False)
  :type verbose: bool

  :returns:
    * numpy.ndarray -- fitted values (y_fit)
    * numpy.ndarray -- parameters of gauss distribution function (popt:
      amplitude a, expected value :math:`\\mu`, standard deviation
      :math:`\\sigma`, vertical offset d)
    * numpy.float64 -- full width at half maximum (FWHM)
  :rtype: tuple

  .. seealso::
    :meth:`gauss`
  """
  x = array(x)  # cast e. g. list to numpy array
  y = array(y)  # cast e. g. list to numpy array
  y_max = max(y)
  y_max_pos = argmax(y)
  x_y_max = x[y_max_pos]

  # starting parameter
  p0 = [y_max, x_y_max, .1, y[0]]
  if verbose:
    print('p0:', end=' ')
    print(p0)
  if e is not None:
    popt, pcov = curve_fit(gauss, x, y, p0=p0, sigma=e)
  else:
    popt, pcov = curve_fit(gauss, x, y, p0=p0)
  if verbose:
    print('popt:', end=' ')
    print(popt)
    #print(pcov)

  FWHM = 2*sqrt(2*log(2))*popt[2]
  if verbose:
    print('FWHM', FWHM)

  if x_fit is None:
    x_fit = x
  y_fit = gauss(x_fit, *popt)

  return y_fit, popt, FWHM

if __name__ == "__main__":
  True