File:Mplwp Voigt-samemax.svg

#!/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-samemax.svg'
fig = mplwp.fig_standard(mpl)

xlim = -5,5; fig.gca().set_xlim(xlim)
ylim = 0, 0.54; fig.gca().set_ylim(ylim)
mplwp.move_axes(fig, 12, 0)
mplwp.mark_axeszero(fig.gca())

from scipy.special import wofz
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)

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

for i, s in enumerate((0, 1/3., 2/3., 1)):
    scalex = voigt(s, 1-s, 0) * sqrt(2 * pi)
    sigma = s * scalex
    gamma = (1-s) * scalex
    print sigma, gamma
    y = voigt(sigma, gamma, x)
    tostr = lambda a: str(int(a)) if a == int(a) else '{:.2f}'.format(a)
    dist = '\,'
    if sigma == round(sigma):
        dist = '\;\ \ \ \ '
    labelstr = r'$\sigma=' + tostr(sigma) + ',' + dist + r'\gamma=' + tostr(gamma) + '$'
    plt.plot(x, y, label=labelstr, zorder=-i)

mpl.rc('legend', borderaxespad=0.7)
plt.legend(loc='upper center', ncol=2).get_frame().set_alpha(0.9)

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