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

# add pi to xaxis labels
def flabel(x, i):
    return u'{}\u03C0'.format(x).replace('-', u'\u2212')
fig.gca().yaxis.set_major_formatter(mpl.ticker.FuncFormatter(flabel))

# make space for labels
mplwp.move_axes(fig, 21, 0)
fig.gca().yaxis.set_major_locator(mpl.ticker.MultipleLocator(0.25))

xlim = -4,4; fig.gca().set_xlim(xlim)
ylim = -0.625, 1.125; fig.gca().set_ylim(ylim)
mplwp.mark_axeszero(fig.gca())

y1 = np.linspace(-0.5, 0.5, 5001)
x1 = [sin(pi*yy) for yy in y1]
plt.plot(x1, y1, label='arcsin')
plt.plot([-1,1], [-0.5,0.5], '.', color=fig.gca().lines[-1].get_color())

y2 = np.linspace(0, 1, 5001)
x2 = [cos(pi*yy) for yy in y2]
plt.plot(x2, y2, label='arccos')
plt.plot([1,-1], [0,1], '.', color=fig.gca().lines[-1].get_color())

x3 = np.linspace(xlim[0], xlim[1], 5001)
y3 = [atan(xx)/pi for xx in x3]
plt.plot(x3, y3, label='arctan')

x4 = np.linspace(xlim[0], xlim[1], 5001)
y4 = [0.5 - atan(xx)/pi for xx in x4]
plt.plot(x4, y4, label='arccot')

def sec(y):
    a = cos(pi*y)
    if fabs(a) < 0.1: return float('NaN')
    return 1.0 / a
y5 = np.linspace(0, 1, 5001)
x5 = [sec(yy) for yy in y5]
plt.plot(x5, y5, label='arcsec')
plt.plot([1,-1], [0,1], '.', color=fig.gca().lines[-1].get_color())

def csc(y):
    a = sin(pi*y)
    if fabs(a) < 0.1: return float('NaN')
    return 1.0 / a
y6 = np.linspace(-0.5, 0.5, 5001)
x6 = [csc(yy) for yy in y6]
plt.plot(x6, y6, label='arccsc')
plt.plot([-1,1], [-0.5,0.5], '.', color=fig.gca().lines[-1].get_color())

mpl.rc('legend', borderaxespad=0.8)
plt.legend(loc='upper right', ncol=2, columnspacing=1.2,
    handletextpad=0.4).get_frame().set_alpha(0.9)
    
plt.savefig(name)
mplwp.postprocess(name)