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

# > This is one of the 100 recipes of the [IPython Cookbook](http://ipython-books.github.io/), the definitive guide to high-performance scientific computing and data science in Python.
# 

# # 4.2. Profiling your code easily with cProfile and IPython

# Standard imports.

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import numpy as np
import matplotlib.pyplot as plt


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get_ipython().run_line_magic('matplotlib', 'inline')


# This function generates an array with random, uniformly distributed +1 and -1.

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def step(*shape):
    # Create a random n-vector with +1 or -1 values.
    return 2 * (np.random.random_sample(shape) < .5) - 1


# We simulate $n$ random walks, and look at the histogram of the walks over time.

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get_ipython().run_cell_magic('prun', '-s cumulative -q -l 10 -T prun0', '# We profile the cell, sort the report by "cumulative time",\n# limit it to 10 lines, and save it to a file "prun0".\nn = 10000\niterations = 50\nx = np.cumsum(step(iterations, n), axis=0)\nbins = np.arange(-30, 30, 1)\ny = np.vstack([np.histogram(x[i,:], bins)[0] for i in range(iterations)])\n')


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print(open('prun0', 'r').read())


# The most expensive functions are respectively `histogram` (37 ms), `rand` (19 ms), and `cumsum` (5 ms).

# We plot the array `y`, representing the distribution of the particles over time.

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plt.figure(figsize=(6,6));
plt.imshow(y, cmap='hot');


# We now run the same code with 10 times more iterations.

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get_ipython().run_cell_magic('prun', '-s cumulative -q -l 10 -T prun1', 'n = 10000\niterations = 500\nx = np.cumsum(step(iterations, n), axis=0)\nbins = np.arange(-30, 30, 1)\ny = np.vstack([np.histogram(x[i,:], bins)[0] for i in range(iterations)])\n')


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print(open('prun1', 'r').read())


# The most expensive functions are this time respectively `histogram` (566 ms), `cumsum` (388 ms) and `rand` (241 ms). `cumsum`'s execution time was negligible in the first case, whereas it is not in this case (due to the higher number of iterations).

# > You'll find all the explanations, figures, references, and much more in the book (to be released later this summer).
# 
# > [IPython Cookbook](http://ipython-books.github.io/), by [Cyrille Rossant](http://cyrille.rossant.net), Packt Publishing, 2014 (500 pages).