#!/usr/bin/python
# -*- coding: utf8 -*-

import matplotlib.pyplot as plt
import matplotlib as mpl
import numpy as np
from math import *

code_website = 'https://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_incomplete_ellipticFm.svg'
fig = mplwp.fig_standard(mpl)

xlim = 0, 90; fig.gca().set_xlim(xlim)
ylim = 0, 3; fig.gca().set_ylim(ylim)
fig.gca().xaxis.set_major_locator(mpl.ticker.MultipleLocator(15))
# add degrees to xaxis labels
def deglabel(x, i):
    return u'{}\u00B0'.format(int(x))
fig.gca().xaxis.set_major_formatter(mpl.ticker.FuncFormatter(deglabel))
mplwp.mark_axeszero(fig.gca())

from scipy.special import ellipkinc

x = np.linspace(xlim[0], xlim[1], 5001)
for m in np.linspace(0, 1, 6):
    y = [ellipkinc(radians(xx), m) for xx in x]
    plt.plot(x, y, label=r'$F(\varphi, m\!=\!{:.1f})$'.format(m),
             zorder=-2-m)

plt.xlabel(r'$\varphi$')
fig.gca().xaxis.set_label_coords(1.06, 0.02)
plt.legend(loc='upper left', borderaxespad=1)
plt.savefig(name)
mplwp.postprocess(name)