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

xlim = -4,4; fig.gca().set_xlim(xlim)
ylim = -3,3; fig.gca().set_ylim(ylim)
mplwp.mark_axeszero(fig.gca())

def coth(x): return 1.0 / tanh(x)
y1 = np.concatenate((np.linspace(atanh(1./xlim[0]), ylim[0], 3001),
                     [float('NaN')],
                     np.linspace(ylim[1], atanh(1./xlim[1]), 3001)))
x1 = [coth(yy) for yy in y1]
plt.plot(x1, y1, label='arcoth', zorder=4)

def sech(x): return 1.0 / cosh(x)
y2 = np.linspace(ylim[1], 0, 5001)
x2 = [sech(yy) for yy in y2]
plt.plot(x2, y2, label='arsech', zorder=2)
plt.plot(x2[-1], y2[-1], 'o', color=fig.gca().lines[-1].get_color(), zorder=3)

def acsch(x): return asinh(1./x)
x3 = np.concatenate((np.linspace(xlim[0], 1./sinh(ylim[0]), 4001),
                     [float('NaN')],
                     np.linspace(1./sinh(ylim[1]), xlim[1], 4001)))
y3 = [acsch(xx) for xx in x3]
plt.plot(x3, y3, label='arcsch', zorder=1)

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