#!/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.
# 

# # 4.6. Using stride tricks with NumPy

# Every array has a number of dimensions, a shape, a data type, and strides. Strides are integer numbers describing, for each dimension, the byte step in the contiguous block of memory. The address of an item in the array is a linear combination of its indices: the coefficients are the strides.

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import numpy as np


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id = lambda x: x.__array_interface__['data'][0]


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x = np.zeros(10); x.strides


# This vector contains float64 (8 bytes) items: one needs to go 8 bytes forward to go from one item to the next.

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y = np.zeros((10, 10)); y.strides


# In the first dimension (vertical), one needs to go 80 bytes (10 float64 items) forward to go from one item to the next, because the items are internally stored in row-major order. In the second dimension (horizontal), one needs to go 8 bytes forward to go from one item to the next.

# ### Broadcasting revisited

# We create a new array pointing to the same memory block as `a`, but with a different shape. The strides are such that this array looks like it is a vertically tiled version of `a`. NumPy is *tricked*: it thinks `b` is a 2D `n * n` array with `n^2` elements, whereas the data buffer really contains only `n` elements.

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n = 1000; a = np.arange(n)


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b = np.lib.stride_tricks.as_strided(a, (n, n), (0, 4))


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b


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b.size, b.shape, b.nbytes


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get_ipython().run_line_magic('timeit', 'b * b.T')


# This first version does not involve any copy, as `b` and `b.T` are arrays pointing to the same data buffer in memory, but with different strides.

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get_ipython().run_line_magic('timeit', 'np.tile(a, (n, 1)) * np.tile(a[:, np.newaxis], (1, n))')


# > 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).