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numpy_basics.html
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numpy_basics.html
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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<title>numpy_basics</title>
<script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script>
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<div class=" highlight hl-ipython2"><pre><span class="kn">import</span> <span class="nn">numpy</span><span class="o">,</span> <span class="nn">scipy</span><span class="o">,</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span><span class="o">,</span> <span class="nn">pandas</span><span class="o">,</span> <span class="nn">librosa</span>
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<h1 id="NumPy-and-SciPy">NumPy and SciPy<a class="anchor-link" href="#NumPy-and-SciPy">¶</a></h1>
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<p>The quartet of NumPy, SciPy, Matplotlib, and IPython is a popular combination in the Python world. We will use each of these libraries in this workshop.</p>
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<h2 id="Tutorial">Tutorial<a class="anchor-link" href="#Tutorial">¶</a></h2>
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<p><a href="http://www.numpy.org">NumPy</a> is one of the most popular libraries for numerical computing in the world. It is used in several disciplines including image processing, finance, bioinformatics, and more. This entire workshop is based upon NumPy and its derivatives.</p>
<p>If you are new to NumPy, follow this <a href="http://wiki.scipy.org/Tentative_NumPy_Tutorial">NumPy Tutorial</a>.</p>
<p><a href="http://docs.scipy.org/doc/scipy/reference/">SciPy</a> is a Python library for scientific computing which builds on top of NumPy. If NumPy is like the Matlab core, then SciPy is like the Matlab toolboxes. It includes support for linear algebra, sparse matrices, spatial data structions, statistics, and more.</p>
<p>While there is a <a href="http://docs.scipy.org/doc/scipy/reference/tutorial/index.html">SciPy Tutorial</a>, it isn't critical that you follow it for this workshop.</p>
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<h2 id="Special-Arrays">Special Arrays<a class="anchor-link" href="#Special-Arrays">¶</a></h2>
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<div class=" highlight hl-ipython2"><pre><span class="k">print</span> <span class="n">numpy</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
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<pre>[0 1 2 3 4]
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<div class=" highlight hl-ipython2"><pre><span class="k">print</span> <span class="n">numpy</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="n">endpoint</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span>
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<pre>[ 0. 0.5 1. 1.5 2. 2.5 3. 3.5 4. 4.5]
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<div class=" highlight hl-ipython2"><pre><span class="k">print</span> <span class="n">numpy</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
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<pre>[ 0. 0. 0. 0. 0.]
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<div class=" highlight hl-ipython2"><pre><span class="k">print</span> <span class="n">numpy</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
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<pre>[ 1. 1. 1. 1. 1.]
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<div class=" highlight hl-ipython2"><pre><span class="k">print</span> <span class="n">numpy</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="mi">5</span><span class="p">,</span><span class="mi">2</span><span class="p">))</span>
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<pre>[[ 1. 1.]
[ 1. 1.]
[ 1. 1.]
[ 1. 1.]
[ 1. 1.]]
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<div class=" highlight hl-ipython2"><pre><span class="k">print</span> <span class="n">scipy</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span> <span class="c"># random Gaussian, zero-mean unit-variance</span>
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<pre>[ -1.12009510e+00 2.15875646e-03 -7.93208376e-01 -1.02710782e+00
2.37388108e+00]
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<div class=" highlight hl-ipython2"><pre><span class="k">print</span> <span class="n">scipy</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span>
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<pre>[[-0.60527349 -0.82200312]
[-0.67330474 -0.12914043]
[-0.71574719 -0.5962005 ]
[-1.03690426 0.59078457]
[-2.22983691 -1.70858604]]
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<h2 id="Slicing-Arrays">Slicing Arrays<a class="anchor-link" href="#Slicing-Arrays">¶</a></h2>
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<div class=" highlight hl-ipython2"><pre><span class="n">x</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
<span class="k">print</span> <span class="n">x</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">4</span><span class="p">]</span>
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<pre>[2 3]
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<div class=" highlight hl-ipython2"><pre><span class="k">print</span> <span class="n">x</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
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<pre>9
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<p>The optional third parameter indicates the increment value:</p>
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<div class=" highlight hl-ipython2"><pre><span class="k">print</span> <span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">8</span><span class="p">:</span><span class="mi">2</span><span class="p">]</span>
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<pre>[0 2 4 6]
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<div class=" highlight hl-ipython2"><pre><span class="k">print</span> <span class="n">x</span><span class="p">[</span><span class="mi">4</span><span class="p">:</span><span class="mi">2</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
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<pre>[4 3]
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<p>If you omit the start index, the slice implicitly starts from zero:</p>
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<div class=" highlight hl-ipython2"><pre><span class="k">print</span> <span class="n">x</span><span class="p">[:</span><span class="mi">4</span><span class="p">]</span>
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<pre>[0 1 2 3]
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<div class=" highlight hl-ipython2"><pre><span class="k">print</span> <span class="n">x</span><span class="p">[:</span><span class="mi">999</span><span class="p">]</span>
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<pre>[0 1 2 3 4 5 6 7 8 9]
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<div class=" highlight hl-ipython2"><pre><span class="k">print</span> <span class="n">x</span><span class="p">[::</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
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<pre>[9 8 7 6 5 4 3 2 1 0]
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<h2 id="Array-Arithmetic">Array Arithmetic<a class="anchor-link" href="#Array-Arithmetic">¶</a></h2>
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<div class=" highlight hl-ipython2"><pre><span class="n">x</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<span class="k">print</span> <span class="n">x</span><span class="o">+</span><span class="mi">2</span><span class="o">*</span><span class="n">y</span>
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<pre>[ 2. 3. 4. 5. 6.]
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<p><code>dot</code> computes the dot product, or inner product, between arrays or matrices.</p>
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<div class=" highlight hl-ipython2"><pre><span class="n">x</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<span class="k">print</span> <span class="n">numpy</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
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<pre>-4.36027379404
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<div class=" highlight hl-ipython2"><pre><span class="n">x</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span><span class="mi">2</span><span class="p">))</span>
<span class="k">print</span> <span class="n">numpy</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
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<pre>[[ 0.9351335 0.9351335 ]
[-4.22851009 -4.22851009]
[-2.66983557 -2.66983557]
[ 3.18545804 3.18545804]
[ 1.82532797 1.82532797]]
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<h2 id="Boolean-Operations">Boolean Operations<a class="anchor-link" href="#Boolean-Operations">¶</a></h2>
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<div class=" highlight hl-ipython2"><pre><span class="n">x</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
<span class="k">print</span> <span class="n">x</span> <span class="o"><</span> <span class="mi">5</span>
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<pre>[ True True True True True False False False False False]
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<div class=" highlight hl-ipython2"><pre><span class="n">y</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
<span class="k">print</span> <span class="n">x</span> <span class="o"><</span> <span class="n">y</span>
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<pre>[ True False False False False False False False False False]
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<h2 id="Distance-Metrics">Distance Metrics<a class="anchor-link" href="#Distance-Metrics">¶</a></h2>
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<div class=" highlight hl-ipython2"><pre><span class="kn">from</span> <span class="nn">scipy.spatial</span> <span class="kn">import</span> <span class="n">distance</span>
<span class="k">print</span> <span class="n">distance</span><span class="o">.</span><span class="n">euclidean</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">])</span>
<span class="k">print</span> <span class="n">distance</span><span class="o">.</span><span class="n">sqeuclidean</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">])</span>
<span class="k">print</span> <span class="n">distance</span><span class="o">.</span><span class="n">cityblock</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">])</span>
<span class="k">print</span> <span class="n">distance</span><span class="o">.</span><span class="n">chebyshev</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">])</span>
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<pre>5.0
25.0
7
4
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<p>The cosine distance measures the angle between two vectors:</p>
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<div class=" highlight hl-ipython2"><pre><span class="k">print</span> <span class="n">distance</span><span class="o">.</span><span class="n">cosine</span><span class="p">([</span><span class="mi">67</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">89</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="k">print</span> <span class="n">distance</span><span class="o">.</span><span class="n">cosine</span><span class="p">([</span><span class="mi">67</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">89</span><span class="p">])</span>
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<pre>0.0
1.0
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<h2 id="Sorting">Sorting<a class="anchor-link" href="#Sorting">¶</a></h2>
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<p>NumPy arrays have a method, <code>sort</code>, which sorts the array <em>in-place</em>.</p>
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<div class=" highlight hl-ipython2"><pre><span class="n">x</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<span class="k">print</span> <span class="n">x</span>
<span class="n">x</span><span class="o">.</span><span class="n">sort</span><span class="p">()</span>
<span class="k">print</span> <span class="n">x</span>
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<pre>[ 0.70589021 0.14767722 0.06884379 0.37189002 0.43313129]
[ 0.06884379 0.14767722 0.37189002 0.43313129 0.70589021]
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<p><code>numpy.argsort</code> returns an array of indices, <code>ind</code>, such that <code>x[ind]</code> is a sorted version of <code>x</code>.</p>
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<div class=" highlight hl-ipython2"><pre><span class="n">x</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<span class="k">print</span> <span class="n">x</span>
<span class="n">ind</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">argsort</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="k">print</span> <span class="n">ind</span>
<span class="k">print</span> <span class="n">x</span><span class="p">[</span><span class="n">ind</span><span class="p">]</span>