#!/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_Glaisher-Clausen.svg'
fig = mplwp.fig_standard(mpl)

xlim = 0, 2*pi; fig.gca().set_xlim(xlim)
ylim = -1.7, 1.7; fig.gca().set_ylim(ylim)
xticks = np.linspace(0, 2*pi, 5)
fig.gca().set_xticks(xticks)
def pilabel(x):
    if x == 0: return '0'
    return u'{:g}\u03C0'.format(x/pi).replace('-', u'\u2212')
fig.gca().set_xticklabels([pilabel(x) for x in xticks])
mplwp.mark_axeszero(fig.gca())

import mpmath
def Sl(phi, n=2):
    if n == 1 and phi % (2*pi) == 0: return 0.0
    if n % 2 == 0:
        return float(mpmath.polylog(n, e**(1j*phi)).real)
    elif n % 2 == 1:
        return float(mpmath.polylog(n, e**(1j*phi)).imag)

x = np.linspace(xlim[0], xlim[1], 10001)
for i in range(1, 4+1):
    y = [Sl(xx, i) for xx in x]
    plt.plot(x, y, label=ur'$Sl_{}$'.format(i), zorder=-i)

mpl.rc('legend', borderaxespad=0.8)
plt.legend(loc='upper center', ncol=2).get_frame().set_alpha(0.9)
plt.savefig(name)
mplwp.postprocess(name)