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

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

xlim = 0,4; fig.gca().set_xlim(xlim)
ylim = -0.05, 1.05; fig.gca().set_ylim(ylim)
mplwp.mark_axeszero(fig.gca())

def P(t, delta):
    Omega = sqrt(1.0 + delta**2) # take Omega0=1 here
    return (1.0 - cos(Omega * t)) / (2.0 * Omega**2)

for delta in [0., 1., 2.]:
    x = np.linspace(xlim[0], xlim[1], 5001)
    y = [P(xx*pi, delta) for xx in x]
    if delta==0: u = '0'
    elif delta==1: u = '\Omega_0'
    else: u = '{:g}\Omega_0'.format(delta)
    plt.plot(x, y, label='$P_2(\Omega_0t),\;\Delta={}$'.format(u))

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