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<h2><a href="http://jakevdp.github.io/blog/2012/12/19/sparse-svds-in-python/">Sparse SVDs in Python</a></h2>
<time datetime="" title="2012-12-19T08:21:00-08:00" pubdate>Wed 19 December 2012</time>
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<div class="article_content">
<p>After <a href="http://fseoane.net/blog/2012/singular-value-decomposition-in-scipy/">Fabian's post</a> on the topic, I have recently returned to thinking about the
subject of sparse singular value decompositions (SVDs) in Python.</p>
<p>For those who haven't used it, the SVD is an extremely powerful technique.
It is the core routine of many applications,
from filtering to dimensionality
reduction to graph analysis to supervised classification and much, much more.</p>
<p>I first came across the need for a fast sparse SVD when applying a technique
called Locally Linear Embedding (LLE) to astronomy spectra: it was the first
astronomy paper I published, and you can read it <a href="http://adsabs.harvard.edu/abs/2009AJ....138.1365V">here</a>. In LLE, one visualizes the nonlinear relationship
between high-dimensional observations. The computational cost is extreme: for
<em>N</em> objects, one must compute the null space (intimately related to the SVD)
of a <em>N</em> by <em>N</em> matrix. Using direct methods (e.g. LAPACK), this can scale
as bad as $\mathcal{O}[N^3]$ in both memory and speed!</p>
</div>
<div class="meta">
<div>
<a href="http://jakevdp.github.io/blog/2012/12/19/sparse-svds-in-python/" class="read_more">Read more →</a>
</div>
<div>
<a href="http://jakevdp.github.io/tag/linear-algebra.html" class="tag">linear algebra</a>
<a href="http://jakevdp.github.io/tag/benchmarks.html" class="tag">benchmarks</a>
</div>
</div>
</article>
<div class="separator"></div>
<article>
<header>
<h2><a href="http://jakevdp.github.io/blog/2012/12/06/minesweeper-in-matplotlib/">Minesweeper in Matplotlib</a></h2>
<time datetime="" title="2012-12-06T18:23:00-08:00" pubdate>Thu 06 December 2012</time>
</header>
<div class="article_content">
<p>Lately I've been playing around with interactivity in matplotlib. A couple
weeks ago, I discussed briefly how to use event callbacks to implement
<a href="/blog/2012/11/24/simple-3d-visualization-in-matplotlib/">simple 3D visualization</a>
and later used this as a base for creating a
<a href="/blog/2012/11/26/3d-interactive-rubiks-cube-in-python">working 3D Rubik's cube</a>
entirely in matplotlib.</p>
<p>Today I have a different goal: re-create
<a href="http://en.wikipedia.org/wiki/Minesweeper_%28computer_game%29">minesweeper</a>,
that ubiquitous single-player puzzle game that most of us will admit to
having binged on at least once or twice in their lives. In minesweeper, the
goal is to discover and avoid hidden mines within a gridded minefield, and
the process takes some logic and quick thinking.</p>
<p><img src="/images/minesweeper_2.gif" width="800"></p>
</div>
<div class="meta">
<div>
<a href="http://jakevdp.github.io/blog/2012/12/06/minesweeper-in-matplotlib/" class="read_more">Read more →</a>
</div>
<div>
<a href="http://jakevdp.github.io/tag/matplotlib.html" class="tag">matplotlib</a>
</div>
</div>
</article>
<div class="separator"></div>
<article>
<header>
<h2><a href="http://jakevdp.github.io/blog/2012/12/01/a-primer-on-python-metaclasses/">A Primer on Python Metaclasses</a></h2>
<time datetime="" title="2012-12-01T07:25:00-08:00" pubdate>Sat 01 December 2012</time>
</header>
<div class="article_content">
Most readers are aware that Python is an object-oriented language. By
object-oriented, we mean that Python can define <em>classes</em>, which bundle
<strong>data</strong> and <strong>functionality</strong> into one entity. For example, we may
create a class <code>IntContainer</code> which stores an integer and allows
certain operations to be performed:</p>
<span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">i</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">add_one</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
</pre>
<span class="n">ic</span><span class="o">.</span><span class="n">add_one</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="n">ic</span><span class="o">.</span><span class="n">i</span><span class="p">)</span>
</pre>
<pre>3
</pre>
<p>This is a bit of a silly example, but shows the fundamental nature of
classes: their ability to bundle data and operations into a single
<em>object</em>, which leads to cleaner, more manageable, and more adaptable code.
Additionally, classes can inherit properties from parents and add or
specialize attributes and methods. This <em>object-oriented</em>
approach to programming can be very intuitive and powerful.</p>
<p>What many do not realize, though, is that quite literally
<a href="http://www.diveintopython.net/getting_to_know_python/everything_is_an_object.html"><em>everything</em></a>
in the Python language is an object.</p>
</div>
<div class="meta">
<div>
<a href="http://jakevdp.github.io/blog/2012/12/01/a-primer-on-python-metaclasses/" class="read_more">Read more →</a>
</div>
<div>
<a href="http://jakevdp.github.io/tag/metaclasses.html" class="tag">metaclasses</a>
<a href="http://jakevdp.github.io/tag/tutorial.html" class="tag">tutorial</a>
</div>
</div>
</article>
<div class="separator"></div>
<article>
<header>
<h2><a href="http://jakevdp.github.io/blog/2012/11/26/3d-interactive-rubiks-cube-in-python/">3D Interactive Rubik's Cube in Python</a></h2>
<time datetime="" title="2012-11-26T22:00:00-08:00" pubdate>Mon 26 November 2012</time>
</header>
<div class="article_content">
<p>Over the weekend, I built a interactive 3D Rubik's cube simulator in python
using only <a href="http://matplotlib.org">matplotlib</a> for all the graphics and
interaction. Check out the demonstration here:</p>
<p><span class="videobox">
<video width="680" height="400" preload="none" controls poster="/downloads/videos/MagicCube_frame.jpg"><source src='/downloads/videos/MagicCube.mp4' type='video/mp4; codecs="avc1.42E01E, mp4a.40.2"'></video></span></p>
<p>You can browse the source code at the MagicCube github repository:
<a href="http://github.com/davidwhogg/MagicCube">http://github.com/davidwhogg/MagicCube</a>.</p>
</div>
<div class="meta">
<div>
<a href="http://jakevdp.github.io/blog/2012/11/26/3d-interactive-rubiks-cube-in-python/" class="read_more">Read more →</a>
</div>
<div>
<a href="http://jakevdp.github.io/tag/matplotlib.html" class="tag">matplotlib</a>
</div>
</div>
</article>
<div class="separator"></div>
<article>
<header>
<h2><a href="http://jakevdp.github.io/blog/2012/11/24/simple-3d-visualization-in-matplotlib/">Quaternions and Key Bindings: Simple 3D Visualization in Matplotlib</a></h2>
<time datetime="" title="2012-11-24T11:04:00-08:00" pubdate>Sat 24 November 2012</time>
</header>
<div class="article_content">
<p>Matplotlib is a powerful framework, but its 3D capabilities still have
a lot of room to grow. The <a href="http://matplotlib.org/mpl_toolkits/mplot3d/index.html">mplot3d</a>
toolkit allows for several kinds of 3D plotting, but the ability to create
and rotate solid 3D objects is hindered by the inflexibility of the <code>zorder</code> attribute:
because it is not updated when the view is rotated, things in the "back" will cover
things in the "front", obscuring them and leading to very unnatural-looking results.</p>
<p>I decided to see if I could create a simple script that addresses this. Though it would
be possible to use the built-in <code>mplot3d</code> architecture to take care of rotating and
projecting the points, I decided to do it from scratch for the sake of my own education.</p>
<p>We'll step through it below: by the end of this post we will have created a 3D viewer in
matplotlib which I think is quite nice.</p>
</div>
<div class="meta">
<div>
<a href="http://jakevdp.github.io/blog/2012/11/24/simple-3d-visualization-in-matplotlib/" class="read_more">Read more →</a>
</div>
<div>
<a href="http://jakevdp.github.io/tag/matplotlib.html" class="tag">matplotlib</a>
</div>
</div>
</article>
<div class="separator"></div>
<article>
<header>
<h2><a href="http://jakevdp.github.io/blog/2012/10/14/scipy-sparse-graph-module-word-ladders/">Sparse Graphs in Python: Playing with Word Ladders</a></h2>
<time datetime="" title="2012-10-14T21:23:00-07:00" pubdate>Sun 14 October 2012</time>
</header>
<div class="article_content">
<p>The recent <a href="http://sourceforge.net/projects/scipy/files/">0.11 release</a> of scipy includes several new features,
one of which is the <a href="http://docs.scipy.org/doc/scipy/reference/sparse.csgraph.html">sparse graph submodule</a>
which I contributed, with help from other developers. I'm pretty excited about this: there are some
classic algorithms implemented, and it will open up whole new realms of computational possibilities in Python.</p>
<p>Before we start, I should say: this post is based on a <a href="http://pyvideo.org/video/1346/lightning-talks-wednesday">lightning talk</a> I gave
at Scipy 2012, and some of the material below comes from a <a href="http://docs.scipy.org/doc/scipy/reference/tutorial/csgraph.html">tutorial</a>
I wrote for the scipy documentation.</p>
</div>
<div class="meta">
<div>
<a href="http://jakevdp.github.io/blog/2012/10/14/scipy-sparse-graph-module-word-ladders/" class="read_more">Read more →</a>
</div>
<div>
<a href="http://jakevdp.github.io/tag/scipy.html" class="tag">scipy</a>
<a href="http://jakevdp.github.io/tag/tutorial.html" class="tag">tutorial</a>
</div>
</div>
</article>
<div class="separator"></div>
<article>
<header>
<h2><a href="http://jakevdp.github.io/blog/2012/10/07/xkcd-style-plots-in-matplotlib/">XKCD-style plots in Matplotlib</a></h2>
<time datetime="" title="2012-10-07T13:30:00-07:00" pubdate>Sun 07 October 2012</time>
</header>
<div class="article_content">
<em>Update: the matplotlib pull request has been merged! See</em>
<a href="http://jakevdp.github.io/blog/2013/07/10/XKCD-plots-in-matplotlib/"><em>This post</em></a>
<em>for a description of the XKCD functionality now built-in to matplotlib!</em></p>
<p>One of the problems I've had with typical matplotlib figures is that everything in them is so precise, so perfect. For an example of what I mean, take a look at this figure:</p>
<span class="n">Image</span><span class="p">(</span><span class="s1">'http://jakevdp.github.com/figures/xkcd_version.png'</span><span class="p">)</span>
</pre>
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