#!/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_legendreQ2a.svg'
fig = mplwp.fig_standard(mpl)

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

from scipy.special import lqmn

l = 2
for m in range(-l, l   1):
    if m >= 0:
        f = lambda x: lqmn(m, l, x)[0][m, l]
    else:
        f = lambda x: ((-1)**m * factorial(l m) / float(factorial(l-m))
            * lqmn(-m, l, x)[0][m, l])
    x = np.linspace(xlim[0], xlim[1], 5001)
    y = [f(xx) for xx in x]
    plt.plot(x, y, label='Q'
          mplwp.unicode_sub(l)   mplwp.unicode_super('('   str(m)   ')'))

plt.legend(loc='lower center', ncol=3).get_frame().set_alpha(0.9)

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