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

xlim = 0, 1.05; fig.gca().set_xlim(xlim)
ylim = 0, 4.5; fig.gca().set_ylim(ylim)
mplwp.mark_axeszero(fig.gca())

from mpmath import ellipk, ellipe

x = np.linspace(xlim[0], 1, 5001)
y1 = [ellipk(xx**2) for xx in x]
plt.plot(x, y1, label='K(k)', zorder=2)

y2 = [ellipe(xx**2) for xx in x]
plt.plot(x, y2, label='E(k)', zorder=0)
plt.plot(1, ellipe(1), 'o', zorder=1,
         color=fig.gca().lines[-1].get_color())

plt.legend(loc='upper center').get_frame().set_alpha(0.9)
plt.savefig(name)
mplwp.postprocess(name)