# -*- coding: utf-8 -*-
"""
Created on Mon Mar 28 08:44:09 2016

@author: nemenman
"""

import numpy as np
import numpy.random as nprnd
import matplotlib.pyplot as plt

# random increments
x = 2*(nprnd.random(100) > 0.5) - 1
y = 2*(nprnd.random(100) > 0.5) - 1

# corresponding current coordinates
cumX = np.cumsum(x)
cumY = np.cumsum(y)

plt.plot(cumX, cumY, 'b-o')
plt.show()


# comparing different ways of generating random walks
# random increments
x = 2*(nprnd.random(10000) > 0.5) - 1
y = 2*(nprnd.random(10000) > 0.5) - 1
xr = 2*(2*nprnd.random(10000) - 1)
yr = 2*(2*nprnd.random(10000) - 1)

# corresponding current coordinates
cumX = np.cumsum(x)
cumY = np.cumsum(y)
cumXr = np.cumsum(xr)
cumYr = np.cumsum(yr)


plt.plot(cumX, cumY, 'b-')
plt.plot(cumXr, cumYr, 'r-')
plt.show()

# showing the mean square proportional to time law
# note how we "vectorize" all computations, and avoid loops
n_trials = 10000
trial_length = 10000
xx = 2*(nprnd.random((trial_length, n_trials)) > 0.5) - 1
yy = 2*(nprnd.random((trial_length, n_trials)) > 0.5) - 1
cumXX = np.cumsum(xx, 0)
cumYY = np.cumsum(yy, 0)

meanX = np.mean(cumXX, 1)
meanY = np.mean(cumYY, 1)
meanR2 = np.mean(cumXX**2 + cumYY**2, 1)

plt.plot(meanX, 'b')
plt.plot(meanY, 'r')
plt.xlabel('time')
plt.ylabel('displacement')
plt.show()

plt.plot(meanR2, 'g')
plt.xlabel('time')
plt.ylabel('distance squared')
plt.show()

plt.hist(cumXX[-1,:],30)