#!/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_chebyshevU30.svg'
fig = mplwp.fig_standard(mpl)

xlim = -1.05,1.05; fig.gca().set_xlim(xlim)
ylim = -3,3; fig.gca().set_ylim(ylim)
fig.gca().xaxis.set_major_locator(mpl.ticker.MultipleLocator(0.5))
mplwp.mark_axeszero(fig.gca())

from scipy.special import eval_chebyu

for n in [30]:
    x = np.linspace(xlim[0], xlim[1], 5001)
    y = [eval_chebyu(n, xx) for xx in x]
    plt.plot(x, y, label='U' + mplwp.unicode_sub(n))

x2 = np.linspace(-1, 1, 5001)[1:-1]
y2 = np.array([1. / sqrt(1. - xx**2) for xx in x2])
plt.plot(x2, -y2, '--', color='#CCC', zorder=-1, label='envelope')
plt.plot(x2, y2, '--', color='#CCC', zorder=-1)

mpl.rc('legend', borderaxespad=1.0)
plt.legend(loc='upper center').get_frame().set_alpha(0.9)
plt.savefig(name)
mplwp.postprocess(name)