#!/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 as er:
    print('ImportError:', er)
    print('You need to download mplwp.py from', code_website)
    exit(1)

name = 'mplwp_lorentzcurve1.svg'
fig = mplwp.fig_standard(mpl)

xlim = 0,3; fig.gca().set_xlim(xlim)
ylim = 0,4.5; fig.gca().set_ylim(ylim)
mplwp.set_bordersize(fig, 42.5, 42.5, 18.5, 46.5)

def f(omega, omega0, gamma):
    return 1. / ((omega**2 - omega0**2)**2 + gamma**2 * omega0**2)
omega0 = 1.
gamma = gamma

x = np.linspace(xlim[0], xlim[1], 5001)
y = [f(xx, omega0, 0.5) for xx in x]
plt.plot(x, y, label=r'$\frac{1}{(\omega^2-\omega_0^2)+\gamma^2\omega_0^2}$')
plt.plot([], [], label='${}_{\omega_0 = 1, \gamma=1/2}$', color='none')

plt.legend(loc='upper right', fontsize='x-large')    
plt.xlabel('$\omega$')

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