#!/usr/bin/python
# -*- coding: utf8 -*-

import matplotlib.pyplot as plt
import matplotlib as mpl
import numpy as np
from math import *

code_website = 'http://commons.wikimedia.org/wiki/User:Geek3/mplwp'
try:
    import mplwp
except ImportError, er:
    print 'ImportError:', er
    print 'You need to download mplwp.py from', code_website
    exit(1)

name = 'mplwp_Voigt-HWHM1.svg'
fig = mplwp.fig_standard(mpl)

xlim = -5,5; fig.gca().set_xlim(xlim)
ylim = 0, 0.65; fig.gca().set_ylim(ylim)
mplwp.move_axes(fig, 12, 0)
mplwp.mark_axeszero(fig.gca())

from scipy.special import wofz
from scipy.optimize import brentq
def voigt(sigma, gamma, x):
    if sigma == 0.:
        return gamma / (pi * (x**2 + gamma**2))
    else:
        return wofz((x + 1j * gamma) / (sqrt(2)*sigma)).real / (sqrt(2*pi)*sigma)

def sigma_gamma_FWHM(FWHM, sigma_fraction):
    s0, g0 = sigma_fraction, 1-sigma_fraction
    max_y = voigt(s0, g0, 0)
    hwhm =  brentq(lambda x, s, g: voigt(s, g, x) - 0.5 * max_y,
                0, 2, args=(s0, g0), disp=False)
    return s0 * FWHM/2. / hwhm, g0 * FWHM/2. / hwhm

x = np.linspace(xlim[0], xlim[1], 5001)

for i, sigma_fraction in enumerate((0, 1/3., 2/3., 1)):
    s, g = sigma_gamma_FWHM(2., sigma_fraction)
    y = voigt(s, g, x)
    plt.plot(x, y, label=r'$\sigma={:.2f},\,\gamma={:.2f}$'.format(s, g), zorder=-i)

mpl.rc('legend', borderaxespad=0.6)
plt.legend(loc='upper center', ncol=2).get_frame().set_alpha(0.9)

plt.savefig(name)
mplwp.postprocess(name)