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

xlim = -2*pi, 2*pi; fig.gca().set_xlim(xlim)
ylim = -1.1, 1.1; fig.gca().set_ylim(ylim)
xticks = np.linspace(-2*pi, 2*pi, 5)
fig.gca().set_xticks(xticks)
def pilabel(x):
    if x == 0: return '0'
    return u'{}\u03C0'.format(int(x/pi)).replace('-', u'\u2212')
fig.gca().set_xticklabels([pilabel(x) for x in xticks])
mplwp.mark_axeszero(fig.gca())

import mpmath
def Cl(phi, n=2):
    if n % 2 == 0:
        return float(mpmath.polylog(n, e**(1j*phi)).imag)
    elif n % 2 == 1:
        return float(mpmath.polylog(n, e**(1j*phi)).real)

x = np.linspace(xlim[0], xlim[1], 5001)
y = [Cl(xx, 2) for xx in x]
plt.plot(x, y, label=ur'$Cl_2$')

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