#!/usr/bin/env python
# coding: utf-8

# # Basic usage of tidynamics
# 
# This notebook demonstrates the use of the library [tidynamics](http://lab.pdebuyl.be/tidynamics).
# 
# tidynamics is open-source and developed for research purposes. Consider citing
# the corresponding article if you use it in research or teaching material:
# [![status](http://joss.theoj.org/papers/c4784e48e7514c207d95f440c2a07874/status.svg)](http://joss.theoj.org/papers/c4784e48e7514c207d95f440c2a07874)

# In[ ]:


get_ipython().run_line_magic('matplotlib', 'notebook')
import matplotlib.pyplot as plt
import numpy as np
import tidynamics


# ## Computing the autocorrelation function
# 
# We generate random numbers uniformly in the range -1..1 and compute
# their autocorrelation function using tidynamics's acf routine.
# 
# *Note:* the numerical results for large lags contain fewer samples than
# for short lags and are not accurate. This is intrinsic to the computation
# and not a limitation of the algorithm.

# In[ ]:


data = -1+2*np.random.random(size=1000)

plt.figure()
plt.plot(data)
plt.xlabel('time')
plt.title('data')

plt.figure()
plt.plot(tidynamics.acf(data))
plt.xlabel('lag')
plt.title('autocorrelation function of data')


# ## Computing the mean-square displacement
# 
# We generate a random walk using +1/-1 random steps and compute
# the corresponding mean-square displacement using tidynamics' msd
# routine.
# 
# *Note:* the numerical results for large lags contain fewer samples than
# for short lags and are not accurate. This is intrinsic to the computation
# and not a limitation of the algorithm.

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# Generate random numbers of +1 or -1
steps = -1 + 2*np.random.randint(0, 2, size=1000)
# Add the steps to obtain the position
position = np.cumsum(steps)

plt.figure()
plt.plot(position)
plt.xlabel('time')
plt.title('Position as a function of time for a random walk')

plt.figure()
plt.plot(tidynamics.msd(position))
plt.xlabel('lag')
plt.title('Mean-square displacement for the random walk')


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