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

xlim = -3, 1; fig.gca().set_xlim(xlim)
ylim = 0, 5; fig.gca().set_ylim(ylim)
mplwp.mark_axeszero(fig.gca())

from mpmath import ellippi

for k in [0, 0.6, 0.8, 0.9, 0.95]:
    n = np.linspace(xlim[0], xlim[1], 5001)
    y = [ellippi(nn, k**2) for nn in n]
    plt.plot(n, y,
        label=r'$\Pi(n,\ k={:g})$'.format(k).replace('-', u'\u2212'))

plt.xlabel('n')
plt.gca().xaxis.set_label_coords(1.05, 0.06)
plt.legend(loc='upper left').get_frame().set_alpha(0.9)
plt.savefig(name)
mplwp.postprocess(name)