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

xlim = -1,6; fig.gca().set_xlim(xlim)
ylim = -4,2; fig.gca().set_ylim(ylim)
mplwp.mark_axeszero(fig.gca())

f = lambda y: exp(y) * y

y1 = np.linspace(-1, ylim[1], 5001)
x1 = [f(yy) for yy in y1]
plt.plot(x1, y1, label='$W_0$')

y2 = np.linspace(ylim[0], -1, 5001)
x2 = [f(yy) for yy in y2]
plt.plot(x2, y2, label='$W_{-1}$')

plt.legend(loc='center right').get_frame().set_alpha(0.9)

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