Added link to Julia version

This commit is contained in:
Nicolas Rougier 2014-06-22 17:01:01 +02:00
parent 46c152c1ca
commit 3a04802449
3 changed files with 154 additions and 64 deletions

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@ -32,6 +32,9 @@ is:</p>
<p class="last">The level names came from an old-game (Dungeon Master)</p>
</div>
<p>Repository is at: <a class="reference external" href="https://github.com/rougier/numpy-100">https://github.com/rougier/numpy-100</a></p>
<p>The corresponding <a class="reference external" href="https://github.com/rougier/numpy-100/blob/master/README.ipynb">IPython notebook</a> is available
from the github repo, thanks to the <a class="reference external" href="https://github.com/esc/rst2ipynb">rst2ipynb</a> conversion tool by <a class="reference external" href="http://haenel.co">Valentin Haenel</a></p>
<p>Thanks to Michiaki Ariga, there is now a <a class="reference external" href="https://github.com/chezou/julia-100-exercises">Julia version</a>.</p>
<div class="section" id="neophyte">
<h1>Neophyte</h1>
<ol class="arabic">
@ -49,42 +52,50 @@ is:</p>
<li><p class="first">Create a null vector of size 10</p>
<pre class="code python literal-block">
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">zeros</span><span class="punctuation">(</span><span class="literal number integer">10</span><span class="punctuation">)</span>
<span class="keyword">print</span> <span class="name">Z</span>
</pre>
</li>
<li><p class="first">Create a null vector of size 10 but the fifth value which is 1</p>
<pre class="code python literal-block">
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">zeros</span><span class="punctuation">(</span><span class="literal number integer">10</span><span class="punctuation">)</span>
<span class="name">Z</span><span class="punctuation">[</span><span class="literal number integer">4</span><span class="punctuation">]</span> <span class="operator">=</span> <span class="literal number integer">1</span>
<span class="keyword">print</span> <span class="name">Z</span>
</pre>
</li>
<li><p class="first">Create a vector with values ranging from 10 to 99</p>
<li><p class="first">Create a vector with values ranging from 10 to 49</p>
<pre class="code python literal-block">
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">arange</span><span class="punctuation">(</span><span class="literal number integer">10</span><span class="punctuation">,</span><span class="literal number integer">100</span><span class="punctuation">)</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">arange</span><span class="punctuation">(</span><span class="literal number integer">10</span><span class="punctuation">,</span><span class="literal number integer">50</span><span class="punctuation">)</span>
<span class="keyword">print</span> <span class="name">Z</span>
</pre>
</li>
<li><p class="first">Create a 3x3 matrix with values ranging from 0 to 8</p>
<pre class="code python literal-block">
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">arange</span><span class="punctuation">(</span><span class="literal number integer">9</span><span class="punctuation">)</span><span class="operator">.</span><span class="name">reshape</span><span class="punctuation">(</span><span class="literal number integer">3</span><span class="punctuation">,</span><span class="literal number integer">3</span><span class="punctuation">)</span>
<span class="keyword">print</span> <span class="name">Z</span>
</pre>
</li>
<li><p class="first">Find indices of non-zero elements from [1,2,0,0,4,0]</p>
<pre class="code python literal-block">
<span class="name">nz</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">nonzero</span><span class="punctuation">([</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">2</span><span class="punctuation">,</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">4</span><span class="punctuation">,</span><span class="literal number integer">0</span><span class="punctuation">])</span>
<span class="keyword">print</span> <span class="name">nz</span>
</pre>
</li>
<li><p class="first">Create a 3x3 identity matrix</p>
<pre class="code python literal-block">
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">eye</span><span class="punctuation">(</span><span class="literal number integer">3</span><span class="punctuation">)</span>
<span class="keyword">print</span> <span class="name">Z</span>
</pre>
</li>
<li><p class="first">Create a 5x5 matrix with values 1,2,3,4 just below the diagonal</p>
<pre class="code python literal-block">
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">diag</span><span class="punctuation">(</span><span class="literal number integer">1</span><span class="operator">+</span><span class="name">np</span><span class="operator">.</span><span class="name">arange</span><span class="punctuation">(</span><span class="literal number integer">4</span><span class="punctuation">),</span><span class="name">k</span><span class="operator">=-</span><span class="literal number integer">1</span><span class="punctuation">)</span>
<span class="keyword">print</span> <span class="name">Z</span>
</pre>
</li>
<li><p class="first">Create a 10x10x10 array with random values</p>
<li><p class="first">Create a 3x3x3 array with random values</p>
<pre class="code python literal-block">
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">random</span><span class="punctuation">((</span><span class="literal number integer">10</span><span class="punctuation">,</span><span class="literal number integer">10</span><span class="punctuation">,</span><span class="literal number integer">10</span><span class="punctuation">))</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">random</span><span class="punctuation">((</span><span class="literal number integer">3</span><span class="punctuation">,</span><span class="literal number integer">3</span><span class="punctuation">,</span><span class="literal number integer">3</span><span class="punctuation">))</span>
<span class="keyword">print</span> <span class="name">Z</span>
</pre>
</li>
</ol>
@ -94,20 +105,23 @@ is:</p>
<ol class="arabic">
<li><p class="first">Create a 8x8 matrix and fill it with a checkerboard pattern</p>
<pre class="code python literal-block">
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">zeros</span><span class="punctuation">((</span><span class="literal number integer">8</span><span class="punctuation">,</span><span class="literal number integer">8</span><span class="punctuation">))</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">zeros</span><span class="punctuation">((</span><span class="literal number integer">8</span><span class="punctuation">,</span><span class="literal number integer">8</span><span class="punctuation">),</span><span class="name">dtype</span><span class="operator">=</span><span class="name builtin">int</span><span class="punctuation">)</span>
<span class="name">Z</span><span class="punctuation">[</span><span class="literal number integer">1</span><span class="punctuation">::</span><span class="literal number integer">2</span><span class="punctuation">,::</span><span class="literal number integer">2</span><span class="punctuation">]</span> <span class="operator">=</span> <span class="literal number integer">1</span>
<span class="name">Z</span><span class="punctuation">[::</span><span class="literal number integer">2</span><span class="punctuation">,</span><span class="literal number integer">1</span><span class="punctuation">::</span><span class="literal number integer">2</span><span class="punctuation">]</span> <span class="operator">=</span> <span class="literal number integer">1</span>
<span class="keyword">print</span> <span class="name">Z</span>
</pre>
</li>
<li><p class="first">Create a 10x10 array with random values and find the minimum and maximum values</p>
<pre class="code python literal-block">
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">random</span><span class="punctuation">((</span><span class="literal number integer">10</span><span class="punctuation">,</span><span class="literal number integer">10</span><span class="punctuation">))</span>
<span class="name">Zmin</span><span class="punctuation">,</span> <span class="name">Zmax</span> <span class="operator">=</span> <span class="name">Z</span><span class="operator">.</span><span class="name">min</span><span class="punctuation">(),</span> <span class="name">Z</span><span class="operator">.</span><span class="name">max</span><span class="punctuation">()</span>
<span class="keyword">print</span> <span class="name">Zmin</span><span class="punctuation">,</span> <span class="name">Zmax</span>
</pre>
</li>
<li><p class="first">Create a checkerboard 8x8 matrix using the tile function</p>
<pre class="code python literal-block">
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">tile</span><span class="punctuation">(</span> <span class="name">np</span><span class="operator">.</span><span class="name">array</span><span class="punctuation">([[</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">1</span><span class="punctuation">],[</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">0</span><span class="punctuation">]]),</span> <span class="punctuation">(</span><span class="literal number integer">4</span><span class="punctuation">,</span><span class="literal number integer">4</span><span class="punctuation">))</span>
<span class="keyword">print</span> <span class="name">Z</span>
</pre>
</li>
<li><p class="first">Normalize a 5x5 random matrix (between 0 and 1)</p>
@ -115,41 +129,48 @@ is:</p>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">random</span><span class="punctuation">((</span><span class="literal number integer">5</span><span class="punctuation">,</span><span class="literal number integer">5</span><span class="punctuation">))</span>
<span class="name">Zmax</span><span class="punctuation">,</span><span class="name">Zmin</span> <span class="operator">=</span> <span class="name">Z</span><span class="operator">.</span><span class="name">max</span><span class="punctuation">(),</span> <span class="name">Z</span><span class="operator">.</span><span class="name">min</span><span class="punctuation">()</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="punctuation">(</span><span class="name">Z</span> <span class="operator">-</span> <span class="name">Zmin</span><span class="punctuation">)</span><span class="operator">/</span><span class="punctuation">(</span><span class="name">Zmax</span> <span class="operator">-</span> <span class="name">Zmin</span><span class="punctuation">)</span>
<span class="keyword">print</span> <span class="name">Z</span>
</pre>
</li>
<li><p class="first">Multiply a 5x3 matrix by a 3x2 matrix (real matrix product)</p>
<pre class="code python literal-block">
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">dot</span><span class="punctuation">(</span><span class="name">np</span><span class="operator">.</span><span class="name">ones</span><span class="punctuation">((</span><span class="literal number integer">5</span><span class="punctuation">,</span><span class="literal number integer">3</span><span class="punctuation">)),</span> <span class="name">np</span><span class="operator">.</span><span class="name">ones</span><span class="punctuation">((</span><span class="literal number integer">3</span><span class="punctuation">,</span><span class="literal number integer">2</span><span class="punctuation">)))</span>
<span class="keyword">print</span> <span class="name">Z</span>
</pre>
</li>
<li><p class="first">Create a 10x10 matrix with row values ranging from 0 to 9</p>
<li><p class="first">Create a 5x5 matrix with row values ranging from 0 to 4</p>
<pre class="code python literal-block">
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">zeros</span><span class="punctuation">((</span><span class="literal number integer">10</span><span class="punctuation">,</span><span class="literal number integer">10</span><span class="punctuation">))</span>
<span class="name">Z</span> <span class="operator">+=</span> <span class="name">np</span><span class="operator">.</span><span class="name">arange</span><span class="punctuation">(</span><span class="literal number integer">10</span><span class="punctuation">)</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">zeros</span><span class="punctuation">((</span><span class="literal number integer">5</span><span class="punctuation">,</span><span class="literal number integer">5</span><span class="punctuation">))</span>
<span class="name">Z</span> <span class="operator">+=</span> <span class="name">np</span><span class="operator">.</span><span class="name">arange</span><span class="punctuation">(</span><span class="literal number integer">5</span><span class="punctuation">)</span>
<span class="keyword">print</span> <span class="name">Z</span>
</pre>
</li>
<li><p class="first">Create a vector of size 1000 with values ranging from 0 to 1, both excluded</p>
<li><p class="first">Create a vector of size 10 with values ranging from 0 to 1, both excluded</p>
<pre class="code python literal-block">
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">linspace</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">1002</span><span class="punctuation">,</span><span class="name">endpoint</span><span class="operator">=</span><span class="name builtin pseudo">True</span><span class="punctuation">)[</span><span class="literal number integer">1</span><span class="punctuation">:</span><span class="operator">-</span><span class="literal number integer">1</span><span class="punctuation">]</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">linspace</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">12</span><span class="punctuation">,</span><span class="name">endpoint</span><span class="operator">=</span><span class="name builtin pseudo">True</span><span class="punctuation">)[</span><span class="literal number integer">1</span><span class="punctuation">:</span><span class="operator">-</span><span class="literal number integer">1</span><span class="punctuation">]</span>
<span class="keyword">print</span> <span class="name">Z</span>
</pre>
</li>
<li><p class="first">Create a random vector of size 100 and sort it</p>
<li><p class="first">Create a random vector of size 10 and sort it</p>
<pre class="code python literal-block">
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">random</span><span class="punctuation">(</span><span class="literal number integer">100</span><span class="punctuation">)</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">random</span><span class="punctuation">(</span><span class="literal number integer">10</span><span class="punctuation">)</span>
<span class="name">Z</span><span class="operator">.</span><span class="name">sort</span><span class="punctuation">()</span>
<span class="keyword">print</span> <span class="name">Z</span>
</pre>
</li>
<li><p class="first">Consider two random matrices A anb B, check if they are equal.</p>
<li><p class="first">Consider two random array A anb B, check if they are equal.</p>
<pre class="code python literal-block">
<span class="name">A</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">randint</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">2</span><span class="punctuation">,(</span><span class="literal number integer">2</span><span class="punctuation">,</span><span class="literal number integer">2</span><span class="punctuation">))</span>
<span class="name">B</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">randint</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">2</span><span class="punctuation">,(</span><span class="literal number integer">2</span><span class="punctuation">,</span><span class="literal number integer">2</span><span class="punctuation">))</span>
<span class="name">A</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">randint</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">2</span><span class="punctuation">,</span><span class="literal number integer">5</span><span class="punctuation">)</span>
<span class="name">B</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">randint</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">2</span><span class="punctuation">,</span><span class="literal number integer">5</span><span class="punctuation">)</span>
<span class="name">equal</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">allclose</span><span class="punctuation">(</span><span class="name">A</span><span class="punctuation">,</span><span class="name">B</span><span class="punctuation">)</span>
<span class="keyword">print</span> <span class="name">equal</span>
</pre>
</li>
<li><p class="first">Create a random vector of size 1000 and find the mean value</p>
<li><p class="first">Create a random vector of size 30 and find the mean value</p>
<pre class="code python literal-block">
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">random</span><span class="punctuation">(</span><span class="literal number integer">1000</span><span class="punctuation">)</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">random</span><span class="punctuation">(</span><span class="literal number integer">30</span><span class="punctuation">)</span>
<span class="name">m</span> <span class="operator">=</span> <span class="name">Z</span><span class="operator">.</span><span class="name">mean</span><span class="punctuation">()</span>
<span class="keyword">print</span> <span class="name">m</span>
</pre>
</li>
</ol>
@ -161,21 +182,25 @@ is:</p>
<pre class="code python literal-block">
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">zeros</span><span class="punctuation">(</span><span class="literal number integer">10</span><span class="punctuation">)</span>
<span class="name">Z</span><span class="operator">.</span><span class="name">flags</span><span class="operator">.</span><span class="name">writeable</span> <span class="operator">=</span> <span class="name builtin pseudo">False</span>
<span class="name">Z</span><span class="punctuation">[</span><span class="literal number integer">0</span><span class="punctuation">]</span> <span class="operator">=</span> <span class="literal number integer">1</span>
</pre>
</li>
<li><p class="first">Consider a random 100x2 matrix representing cartesian coordinates, convert
<li><p class="first">Consider a random 10x2 matrix representing cartesian coordinates, convert
them to polar coordinates</p>
<pre class="code python literal-block">
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">random</span><span class="punctuation">((</span><span class="literal number integer">100</span><span class="punctuation">,</span><span class="literal number integer">2</span><span class="punctuation">))</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">random</span><span class="punctuation">((</span><span class="literal number integer">10</span><span class="punctuation">,</span><span class="literal number integer">2</span><span class="punctuation">))</span>
<span class="name">X</span><span class="punctuation">,</span><span class="name">Y</span> <span class="operator">=</span> <span class="name">Z</span><span class="punctuation">[:,</span><span class="literal number integer">0</span><span class="punctuation">],</span> <span class="name">Z</span><span class="punctuation">[:,</span><span class="literal number integer">1</span><span class="punctuation">]</span>
<span class="name">R</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">sqrt</span><span class="punctuation">(</span><span class="name">X</span><span class="operator">**</span><span class="literal number integer">2</span><span class="operator">+</span><span class="name">Y</span><span class="operator">**</span><span class="literal number integer">2</span><span class="punctuation">)</span>
<span class="name">T</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">arctan2</span><span class="punctuation">(</span><span class="name">Y</span><span class="punctuation">,</span><span class="name">X</span><span class="punctuation">)</span>
<span class="keyword">print</span> <span class="name">R</span>
<span class="keyword">print</span> <span class="name">T</span>
</pre>
</li>
<li><p class="first">Create random vector of size 100 and replace the maximum value by 0</p>
<li><p class="first">Create random vector of size 10 and replace the maximum value by 0</p>
<pre class="code python literal-block">
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">random</span><span class="punctuation">(</span><span class="literal number integer">100</span><span class="punctuation">)</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">random</span><span class="punctuation">(</span><span class="literal number integer">10</span><span class="punctuation">)</span>
<span class="name">Z</span><span class="punctuation">[</span><span class="name">Z</span><span class="operator">.</span><span class="name">argmax</span><span class="punctuation">()]</span> <span class="operator">=</span> <span class="literal number integer">0</span>
<span class="keyword">print</span> <span class="name">Z</span>
</pre>
</li>
<li><p class="first">Create a structured array with <tt class="docutils literal">x</tt> and <tt class="docutils literal">y</tt> coordinates covering the
@ -184,6 +209,7 @@ them to polar coordinates</p>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">zeros</span><span class="punctuation">((</span><span class="literal number integer">10</span><span class="punctuation">,</span><span class="literal number integer">10</span><span class="punctuation">),</span> <span class="punctuation">[(</span><span class="literal string">'x'</span><span class="punctuation">,</span><span class="name builtin">float</span><span class="punctuation">),(</span><span class="literal string">'y'</span><span class="punctuation">,</span><span class="name builtin">float</span><span class="punctuation">)])</span>
<span class="name">Z</span><span class="punctuation">[</span><span class="literal string">'x'</span><span class="punctuation">],</span> <span class="name">Z</span><span class="punctuation">[</span><span class="literal string">'y'</span><span class="punctuation">]</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">meshgrid</span><span class="punctuation">(</span><span class="name">np</span><span class="operator">.</span><span class="name">linspace</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">10</span><span class="punctuation">),</span>
<span class="name">np</span><span class="operator">.</span><span class="name">linspace</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">10</span><span class="punctuation">))</span>
<span class="keyword">print</span> <span class="name">Z</span>
</pre>
</li>
<li><p class="first">Print the minimum and maximum representable value for each numpy scalar type</p>
@ -199,11 +225,12 @@ them to polar coordinates</p>
</li>
<li><p class="first">Create a structured array representing a position (x,y) and a color (r,g,b)</p>
<pre class="code python literal-block">
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">zeros</span><span class="punctuation">(</span><span class="literal number integer">10</span><span class="punctuation">,</span> <span class="punctuation">[</span> <span class="punctuation">(</span><span class="literal string">'position'</span><span class="punctuation">,</span> <span class="punctuation">[</span> <span class="punctuation">(</span><span class="literal string">'x'</span><span class="punctuation">,</span> <span class="name builtin">float</span><span class="punctuation">,</span> <span class="literal number integer">1</span><span class="punctuation">),</span>
<span class="punctuation">(</span><span class="literal string">'y'</span><span class="punctuation">,</span> <span class="name builtin">float</span><span class="punctuation">,</span> <span class="literal number integer">1</span><span class="punctuation">)]),</span>
<span class="punctuation">(</span><span class="literal string">'color'</span><span class="punctuation">,</span> <span class="punctuation">[</span> <span class="punctuation">(</span><span class="literal string">'r'</span><span class="punctuation">,</span> <span class="name builtin">float</span><span class="punctuation">,</span> <span class="literal number integer">1</span><span class="punctuation">),</span>
<span class="punctuation">(</span><span class="literal string">'g'</span><span class="punctuation">,</span> <span class="name builtin">float</span><span class="punctuation">,</span> <span class="literal number integer">1</span><span class="punctuation">),</span>
<span class="punctuation">(</span><span class="literal string">'b'</span><span class="punctuation">,</span> <span class="name builtin">float</span><span class="punctuation">,</span> <span class="literal number integer">1</span><span class="punctuation">)])])</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">zeros</span><span class="punctuation">(</span><span class="literal number integer">10</span><span class="punctuation">,</span> <span class="punctuation">[</span> <span class="punctuation">(</span><span class="literal string">'position'</span><span class="punctuation">,</span> <span class="punctuation">[</span> <span class="punctuation">(</span><span class="literal string">'x'</span><span class="punctuation">,</span> <span class="name builtin">float</span><span class="punctuation">,</span> <span class="literal number integer">1</span><span class="punctuation">),</span>
<span class="punctuation">(</span><span class="literal string">'y'</span><span class="punctuation">,</span> <span class="name builtin">float</span><span class="punctuation">,</span> <span class="literal number integer">1</span><span class="punctuation">)]),</span>
<span class="punctuation">(</span><span class="literal string">'color'</span><span class="punctuation">,</span> <span class="punctuation">[</span> <span class="punctuation">(</span><span class="literal string">'r'</span><span class="punctuation">,</span> <span class="name builtin">float</span><span class="punctuation">,</span> <span class="literal number integer">1</span><span class="punctuation">),</span>
<span class="punctuation">(</span><span class="literal string">'g'</span><span class="punctuation">,</span> <span class="name builtin">float</span><span class="punctuation">,</span> <span class="literal number integer">1</span><span class="punctuation">),</span>
<span class="punctuation">(</span><span class="literal string">'b'</span><span class="punctuation">,</span> <span class="name builtin">float</span><span class="punctuation">,</span> <span class="literal number integer">1</span><span class="punctuation">)])])</span>
<span class="keyword">print</span> <span class="name">Z</span>
</pre>
</li>
<li><p class="first">Consider a random vector with shape (100,2) representing coordinates, find
@ -212,18 +239,22 @@ point by point distances</p>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">random</span><span class="punctuation">((</span><span class="literal number integer">10</span><span class="punctuation">,</span><span class="literal number integer">2</span><span class="punctuation">))</span>
<span class="name">X</span><span class="punctuation">,</span><span class="name">Y</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">atleast_2d</span><span class="punctuation">(</span><span class="name">Z</span><span class="punctuation">[:,</span><span class="literal number integer">0</span><span class="punctuation">]),</span> <span class="name">np</span><span class="operator">.</span><span class="name">atleast_2d</span><span class="punctuation">(</span><span class="name">Z</span><span class="punctuation">[:,</span><span class="literal number integer">1</span><span class="punctuation">])</span>
<span class="name">D</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">sqrt</span><span class="punctuation">(</span> <span class="punctuation">(</span><span class="name">X</span><span class="operator">-</span><span class="name">X</span><span class="operator">.</span><span class="name">T</span><span class="punctuation">)</span><span class="operator">**</span><span class="literal number integer">2</span> <span class="operator">+</span> <span class="punctuation">(</span><span class="name">Y</span><span class="operator">-</span><span class="name">Y</span><span class="operator">.</span><span class="name">T</span><span class="punctuation">)</span><span class="operator">**</span><span class="literal number integer">2</span><span class="punctuation">)</span>
<span class="keyword">print</span> <span class="name">D</span>
<span class="comment"># Much faster with scipy</span>
<span class="keyword namespace">import</span> <span class="name namespace">scipy</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">random</span><span class="punctuation">((</span><span class="literal number integer">10</span><span class="punctuation">,</span><span class="literal number integer">2</span><span class="punctuation">))</span>
<span class="name">D</span> <span class="operator">=</span> <span class="name">scipy</span><span class="operator">.</span><span class="name">spatial</span><span class="operator">.</span><span class="name">distance</span><span class="operator">.</span><span class="name">cdist</span><span class="punctuation">(</span><span class="name">Z</span><span class="punctuation">,</span><span class="name">Z</span><span class="punctuation">)</span>
<span class="keyword">print</span> <span class="name">D</span>
</pre>
</li>
<li><p class="first">Generate a generic 2D Gaussian-like array</p>
<pre class="code python literal-block">
<span class="name">X</span><span class="punctuation">,</span> <span class="name">Y</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">meshgrid</span><span class="punctuation">(</span><span class="name">np</span><span class="operator">.</span><span class="name">linspace</span><span class="punctuation">(</span><span class="operator">-</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">100</span><span class="punctuation">),</span> <span class="name">np</span><span class="operator">.</span><span class="name">linspace</span><span class="punctuation">(</span><span class="operator">-</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">100</span><span class="punctuation">))</span>
<span class="name">X</span><span class="punctuation">,</span> <span class="name">Y</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">meshgrid</span><span class="punctuation">(</span><span class="name">np</span><span class="operator">.</span><span class="name">linspace</span><span class="punctuation">(</span><span class="operator">-</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">10</span><span class="punctuation">),</span> <span class="name">np</span><span class="operator">.</span><span class="name">linspace</span><span class="punctuation">(</span><span class="operator">-</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">10</span><span class="punctuation">))</span>
<span class="name">D</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">sqrt</span><span class="punctuation">(</span><span class="name">X</span><span class="operator">*</span><span class="name">X</span><span class="operator">+</span><span class="name">Y</span><span class="operator">*</span><span class="name">Y</span><span class="punctuation">)</span>
<span class="name">sigma</span><span class="punctuation">,</span> <span class="name">mu</span> <span class="operator">=</span> <span class="literal number float">1.0</span><span class="punctuation">,</span> <span class="literal number float">0.0</span>
<span class="name">G</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">exp</span><span class="punctuation">(</span><span class="operator">-</span><span class="punctuation">(</span> <span class="punctuation">(</span><span class="name">D</span><span class="operator">-</span><span class="name">mu</span><span class="punctuation">)</span><span class="operator">**</span><span class="literal number integer">2</span> <span class="operator">/</span> <span class="punctuation">(</span> <span class="literal number float">2.0</span> <span class="operator">*</span> <span class="name">sigma</span><span class="operator">**</span><span class="literal number integer">2</span> <span class="punctuation">)</span> <span class="punctuation">)</span> <span class="punctuation">)</span>
<span class="keyword">print</span> <span class="name">G</span>
</pre>
</li>
<li><p class="first">Consider the vector [1, 2, 3, 4, 5], how to build a new vector with 3
@ -235,11 +266,15 @@ consecutive zeros interleaved between each value ?</p>
<span class="name">nz</span> <span class="operator">=</span> <span class="literal number integer">3</span>
<span class="name">Z0</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">zeros</span><span class="punctuation">(</span><span class="name builtin">len</span><span class="punctuation">(</span><span class="name">Z</span><span class="punctuation">)</span> <span class="operator">+</span> <span class="punctuation">(</span><span class="name builtin">len</span><span class="punctuation">(</span><span class="name">Z</span><span class="punctuation">)</span><span class="operator">-</span><span class="literal number integer">1</span><span class="punctuation">)</span><span class="operator">*</span><span class="punctuation">(</span><span class="name">nz</span><span class="punctuation">))</span>
<span class="name">Z0</span><span class="punctuation">[::</span><span class="name">nz</span><span class="operator">+</span><span class="literal number integer">1</span><span class="punctuation">]</span> <span class="operator">=</span> <span class="name">Z</span>
<span class="keyword">print</span> <span class="name">Z0</span>
</pre>
</li>
<li><p class="first">Find the nearest value from a given value in an array</p>
<pre class="code python literal-block">
<span class="name">Z</span><span class="operator">.</span><span class="name">flat</span><span class="punctuation">[</span><span class="name">np</span><span class="operator">.</span><span class="name">abs</span><span class="punctuation">(</span><span class="name">Z</span> <span class="operator">-</span> <span class="name">z</span><span class="punctuation">)</span><span class="operator">.</span><span class="name">argmin</span><span class="punctuation">()]</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">uniform</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">10</span><span class="punctuation">)</span>
<span class="name">z</span> <span class="operator">=</span> <span class="literal number float">0.5</span>
<span class="name">m</span> <span class="operator">=</span> <span class="name">Z</span><span class="operator">.</span><span class="name">flat</span><span class="punctuation">[</span><span class="name">np</span><span class="operator">.</span><span class="name">abs</span><span class="punctuation">(</span><span class="name">Z</span> <span class="operator">-</span> <span class="name">z</span><span class="punctuation">)</span><span class="operator">.</span><span class="name">argmin</span><span class="punctuation">()]</span>
<span class="keyword">print</span> <span class="name">m</span>
</pre>
</li>
</ol>
@ -255,7 +290,7 @@ consecutive zeros interleaved between each value ?</p>
</pre>
<p>How to read it ?</p>
<pre class="code python literal-block">
<span class="name">Z</span> <span class="operator">=</span> <span class="name">genfromtxt</span><span class="punctuation">(</span><span class="literal string">&quot;missing.dat&quot;</span><span class="punctuation">,</span> <span class="name">delimiter</span><span class="operator">=</span><span class="literal string">&quot;,&quot;</span><span class="punctuation">)</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">genfromtxt</span><span class="punctuation">(</span><span class="literal string">&quot;missing.dat&quot;</span><span class="punctuation">,</span> <span class="name">delimiter</span><span class="operator">=</span><span class="literal string">&quot;,&quot;</span><span class="punctuation">)</span>
</pre>
</li>
<li><p class="first">Consider a generator function that generates 10 integers and use it to build an
@ -265,6 +300,7 @@ array</p>
<span class="keyword">for</span> <span class="name">x</span> <span class="operator word">in</span> <span class="name builtin">xrange</span><span class="punctuation">(</span><span class="literal number integer">10</span><span class="punctuation">):</span>
<span class="keyword">yield</span> <span class="name">x</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">fromiter</span><span class="punctuation">(</span><span class="name">generate</span><span class="punctuation">(),</span><span class="name">dtype</span><span class="operator">=</span><span class="name builtin">float</span><span class="punctuation">,</span><span class="name">count</span><span class="operator">=-</span><span class="literal number integer">1</span><span class="punctuation">)</span>
<span class="keyword">print</span> <span class="name">Z</span>
</pre>
</li>
<li><p class="first">Consider a given vector, how to add 1 to each element indexed by a second
@ -275,6 +311,7 @@ vector (be careful with repeated indices) ?</p>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">ones</span><span class="punctuation">(</span><span class="literal number integer">10</span><span class="punctuation">)</span>
<span class="name">I</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">randint</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="name builtin">len</span><span class="punctuation">(</span><span class="name">Z</span><span class="punctuation">),</span><span class="literal number integer">20</span><span class="punctuation">)</span>
<span class="name">Z</span> <span class="operator">+=</span> <span class="name">np</span><span class="operator">.</span><span class="name">bincount</span><span class="punctuation">(</span><span class="name">I</span><span class="punctuation">,</span> <span class="name">minlength</span><span class="operator">=</span><span class="name builtin">len</span><span class="punctuation">(</span><span class="name">Z</span><span class="punctuation">))</span>
<span class="keyword">print</span> <span class="name">Z</span>
</pre>
</li>
<li><p class="first">How to accumulate elements of a vector (X) to an array (F) based on an index
@ -285,6 +322,7 @@ list (I) ?</p>
<span class="name">X</span> <span class="operator">=</span> <span class="punctuation">[</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">2</span><span class="punctuation">,</span><span class="literal number integer">3</span><span class="punctuation">,</span><span class="literal number integer">4</span><span class="punctuation">,</span><span class="literal number integer">5</span><span class="punctuation">,</span><span class="literal number integer">6</span><span class="punctuation">]</span>
<span class="name">I</span> <span class="operator">=</span> <span class="punctuation">[</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">3</span><span class="punctuation">,</span><span class="literal number integer">9</span><span class="punctuation">,</span><span class="literal number integer">3</span><span class="punctuation">,</span><span class="literal number integer">4</span><span class="punctuation">,</span><span class="literal number integer">1</span><span class="punctuation">]</span>
<span class="name">F</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">bincount</span><span class="punctuation">(</span><span class="name">I</span><span class="punctuation">,</span><span class="name">X</span><span class="punctuation">)</span>
<span class="keyword">print</span> <span class="name">F</span>
</pre>
</li>
<li><p class="first">Considering a (w,h,3) image of (dtype=ubyte), compute the number of unique
@ -296,26 +334,27 @@ colors</p>
<span class="name">I</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">randint</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">2</span><span class="punctuation">,(</span><span class="name">h</span><span class="punctuation">,</span><span class="name">w</span><span class="punctuation">,</span><span class="literal number integer">3</span><span class="punctuation">))</span><span class="operator">.</span><span class="name">astype</span><span class="punctuation">(</span><span class="name">np</span><span class="operator">.</span><span class="name">ubyte</span><span class="punctuation">)</span>
<span class="name">F</span> <span class="operator">=</span> <span class="name">I</span><span class="punctuation">[</span><span class="operator">...</span><span class="punctuation">,</span><span class="literal number integer">0</span><span class="punctuation">]</span><span class="operator">*</span><span class="literal number integer">256</span><span class="operator">*</span><span class="literal number integer">256</span> <span class="operator">+</span> <span class="name">I</span><span class="punctuation">[</span><span class="operator">...</span><span class="punctuation">,</span><span class="literal number integer">1</span><span class="punctuation">]</span><span class="operator">*</span><span class="literal number integer">256</span> <span class="operator">+</span><span class="name">I</span><span class="punctuation">[</span><span class="operator">...</span><span class="punctuation">,</span><span class="literal number integer">2</span><span class="punctuation">]</span>
<span class="name">n</span> <span class="operator">=</span> <span class="name builtin">len</span><span class="punctuation">(</span><span class="name">np</span><span class="operator">.</span><span class="name">unique</span><span class="punctuation">(</span><span class="name">F</span><span class="punctuation">))</span>
<span class="name">np</span><span class="operator">.</span><span class="name">unique</span><span class="punctuation">(</span><span class="name">I</span><span class="punctuation">)</span>
<span class="keyword">print</span> <span class="name">np</span><span class="operator">.</span><span class="name">unique</span><span class="punctuation">(</span><span class="name">I</span><span class="punctuation">)</span>
</pre>
</li>
<li><p class="first">Considering a four dimensions array, how to get sum over the last two axis at once ?</p>
<pre class="code python literal-block">
<span class="name">A</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">randint</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">10</span><span class="punctuation">,(</span><span class="literal number integer">3</span><span class="punctuation">,</span><span class="literal number integer">4</span><span class="punctuation">,</span><span class="literal number integer">3</span><span class="punctuation">,</span><span class="literal number integer">4</span><span class="punctuation">))</span>
<span class="name builtin">sum</span> <span class="operator">=</span> <span class="name">A</span><span class="operator">.</span><span class="name">reshape</span><span class="punctuation">(</span><span class="name">A</span><span class="operator">.</span><span class="name">shape</span><span class="punctuation">[:</span><span class="operator">-</span><span class="literal number integer">2</span><span class="punctuation">]</span> <span class="operator">+</span> <span class="punctuation">(</span><span class="operator">-</span><span class="literal number integer">1</span><span class="punctuation">,))</span><span class="operator">.</span><span class="name">sum</span><span class="punctuation">(</span><span class="name">axis</span><span class="operator">=-</span><span class="literal number integer">1</span><span class="punctuation">)</span>
<span class="keyword">print</span>
</pre>
</li>
<li><p class="first">Considering a one-dimensional vector D, how to compute means of subsets of D
using a vector S of same size describing subset indices ?</p>
<pre class="code python literal-block">
<span class="comment"># Jaime Fernández del Río</span>
<span class="comment"># Author: Jaime Fernández del Río</span>
<span class="name">D</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">uniform</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">100</span><span class="punctuation">)</span>
<span class="name">S</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">randint</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">10</span><span class="punctuation">,</span><span class="literal number integer">100</span><span class="punctuation">)</span>
<span class="name">D_sums</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">bincount</span><span class="punctuation">(</span><span class="name">S</span><span class="punctuation">,</span> <span class="name">weights</span><span class="operator">=</span><span class="name">D</span><span class="punctuation">)</span>
<span class="name">D_counts</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">bincount</span><span class="punctuation">(</span><span class="name">S</span><span class="punctuation">)</span>
<span class="name">D_means</span> <span class="operator">=</span> <span class="name">D_sums</span> <span class="operator">/</span> <span class="name">D_counts</span>
<span class="keyword">print</span> <span class="name">D_means</span>
</pre>
</li>
</ol>
@ -328,36 +367,50 @@ first row is (Z[0],Z[1],Z[2]) and each subsequent row is shifted by 1 (last
row should be (Z[-3],Z[-2],Z[-1])</p>
<pre class="code python literal-block">
<span class="comment"># Author: Joe Kington / Erik Rigtorp</span>
<span class="keyword namespace">from</span> <span class="name namespace">numpy.lib</span> <span class="keyword namespace">import</span> <span class="name">stride_tricks</span>
<span class="keyword">def</span> <span class="name function">rolling</span><span class="punctuation">(</span><span class="name">a</span><span class="punctuation">,</span> <span class="name">window</span><span class="punctuation">):</span>
<span class="name">shape</span> <span class="operator">=</span> <span class="punctuation">(</span><span class="name">a</span><span class="operator">.</span><span class="name">size</span> <span class="operator">-</span> <span class="name">window</span> <span class="operator">+</span> <span class="literal number integer">1</span><span class="punctuation">,</span> <span class="name">window</span><span class="punctuation">)</span>
<span class="name">strides</span> <span class="operator">=</span> <span class="punctuation">(</span><span class="name">a</span><span class="operator">.</span><span class="name">itemsize</span><span class="punctuation">,</span> <span class="name">a</span><span class="operator">.</span><span class="name">itemsize</span><span class="punctuation">)</span>
<span class="keyword">return</span> <span class="name">np</span><span class="operator">.</span><span class="name">lib</span><span class="operator">.</span><span class="name">stride_tricks</span><span class="operator">.</span><span class="name">as_strided</span><span class="punctuation">(</span><span class="name">a</span><span class="punctuation">,</span> <span class="name">shape</span><span class="operator">=</span><span class="name">shape</span><span class="punctuation">,</span> <span class="name">strides</span><span class="operator">=</span><span class="name">strides</span><span class="punctuation">)</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">rolling</span><span class="punctuation">(</span><span class="name">np</span><span class="operator">.</span><span class="name">arange</span><span class="punctuation">(</span><span class="literal number integer">100</span><span class="punctuation">),</span> <span class="literal number integer">3</span><span class="punctuation">)</span>
<span class="keyword">return</span> <span class="name">stride_tricks</span><span class="operator">.</span><span class="name">as_strided</span><span class="punctuation">(</span><span class="name">a</span><span class="punctuation">,</span> <span class="name">shape</span><span class="operator">=</span><span class="name">shape</span><span class="punctuation">,</span> <span class="name">strides</span><span class="operator">=</span><span class="name">strides</span><span class="punctuation">)</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">rolling</span><span class="punctuation">(</span><span class="name">np</span><span class="operator">.</span><span class="name">arange</span><span class="punctuation">(</span><span class="literal number integer">10</span><span class="punctuation">),</span> <span class="literal number integer">3</span><span class="punctuation">)</span>
<span class="keyword">print</span> <span class="name">Z</span>
</pre>
</li>
<li><p class="first">Consider a set of 100 triplets describing 100 triangles (with shared
<li><p class="first">Consider a set of 10 triplets describing 10 triangles (with shared
vertices), find the set of unique line segments composing all the triangles.</p>
<pre class="code python literal-block">
<span class="comment"># Author: Nicolas Rougier</span>
<span class="name">faces</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">randint</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">100</span><span class="punctuation">,(</span><span class="literal number integer">100</span><span class="punctuation">,</span><span class="literal number integer">3</span><span class="punctuation">))</span>
<span class="comment"># Author: Nicolas P. Rougier</span>
<span class="name">faces</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">randint</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">100</span><span class="punctuation">,(</span><span class="literal number integer">10</span><span class="punctuation">,</span><span class="literal number integer">3</span><span class="punctuation">))</span>
<span class="name">F</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">roll</span><span class="punctuation">(</span><span class="name">faces</span><span class="operator">.</span><span class="name">repeat</span><span class="punctuation">(</span><span class="literal number integer">2</span><span class="punctuation">,</span><span class="name">axis</span><span class="operator">=</span><span class="literal number integer">1</span><span class="punctuation">),</span><span class="operator">-</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="name">axis</span><span class="operator">=</span><span class="literal number integer">1</span><span class="punctuation">)</span>
<span class="name">F</span> <span class="operator">=</span> <span class="name">F</span><span class="operator">.</span><span class="name">reshape</span><span class="punctuation">(</span><span class="name builtin">len</span><span class="punctuation">(</span><span class="name">F</span><span class="punctuation">)</span><span class="operator">*</span><span class="literal number integer">3</span><span class="punctuation">,</span><span class="literal number integer">2</span><span class="punctuation">)</span>
<span class="name">F</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">sort</span><span class="punctuation">(</span><span class="name">F</span><span class="punctuation">,</span><span class="name">axis</span><span class="operator">=</span><span class="literal number integer">1</span><span class="punctuation">)</span>
<span class="name">G</span> <span class="operator">=</span> <span class="name">F</span><span class="operator">.</span><span class="name">view</span><span class="punctuation">(</span> <span class="name">dtype</span><span class="operator">=</span><span class="punctuation">[(</span><span class="literal string">'p0'</span><span class="punctuation">,</span><span class="name">F</span><span class="operator">.</span><span class="name">dtype</span><span class="punctuation">),(</span><span class="literal string">'p1'</span><span class="punctuation">,</span><span class="name">F</span><span class="operator">.</span><span class="name">dtype</span><span class="punctuation">)]</span> <span class="punctuation">)</span>
<span class="name">G</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">unique</span><span class="punctuation">(</span><span class="name">G</span><span class="punctuation">)</span>
<span class="keyword">print</span> <span class="name">G</span>
</pre>
</li>
<li><p class="first">Given an array C that is a bincount, how to produce an array A such that
np.bincount(A) == C ?</p>
<pre class="code python literal-block">
<span class="comment"># Jaime Fernández del Río</span>
<span class="comment"># Author: Jaime Fernández del Río</span>
<span class="name">C</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">bincount</span><span class="punctuation">([</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">2</span><span class="punctuation">,</span><span class="literal number integer">3</span><span class="punctuation">,</span><span class="literal number integer">4</span><span class="punctuation">,</span><span class="literal number integer">4</span><span class="punctuation">,</span><span class="literal number integer">6</span><span class="punctuation">])</span>
<span class="name">A</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">repeat</span><span class="punctuation">(</span><span class="name">np</span><span class="operator">.</span><span class="name">arange</span><span class="punctuation">(</span><span class="name builtin">len</span><span class="punctuation">(</span><span class="name">C</span><span class="punctuation">)),</span> <span class="name">C</span><span class="punctuation">)</span>
<span class="keyword">print</span> <span class="name">A</span>
</pre>
</li>
<li><p class="first">How to compute averages using a sliding window over an array ?</p>
<pre class="code python literal-block">
<span class="comment"># Author: Jaime Fernández del Río</span>
<span class="keyword">def</span> <span class="name function">moving_average</span><span class="punctuation">(</span><span class="name">a</span><span class="punctuation">,</span> <span class="name">n</span><span class="operator">=</span><span class="literal number integer">3</span><span class="punctuation">)</span> <span class="punctuation">:</span>
<span class="name">ret</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">cumsum</span><span class="punctuation">(</span><span class="name">a</span><span class="punctuation">,</span> <span class="name">dtype</span><span class="operator">=</span><span class="name builtin">float</span><span class="punctuation">)</span>
<span class="name">ret</span><span class="punctuation">[</span><span class="name">n</span><span class="punctuation">:]</span> <span class="operator">=</span> <span class="name">ret</span><span class="punctuation">[</span><span class="name">n</span><span class="punctuation">:]</span> <span class="operator">-</span> <span class="name">ret</span><span class="punctuation">[:</span><span class="operator">-</span><span class="name">n</span><span class="punctuation">]</span>
<span class="keyword">return</span> <span class="name">ret</span><span class="punctuation">[</span><span class="name">n</span> <span class="operator">-</span> <span class="literal number integer">1</span><span class="punctuation">:]</span> <span class="operator">/</span> <span class="name">n</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">arange</span><span class="punctuation">(</span><span class="literal number integer">20</span><span class="punctuation">)</span>
<span class="keyword">print</span> <span class="name">moving_average</span><span class="punctuation">(</span><span class="name">Z</span><span class="punctuation">,</span> <span class="name">n</span><span class="operator">=</span><span class="literal number integer">3</span><span class="punctuation">)</span>
</pre>
</li>
</ol>
@ -365,13 +418,15 @@ np.bincount(A) == C ?</p>
<div class="section" id="artisan">
<h1>Artisan</h1>
<ol class="arabic">
<li><p class="first">Considering a 100x3 matrix, extract rows with unequal values (e.g. [2,2,3])</p>
<li><p class="first">Considering a 10x3 matrix, extract rows with unequal values (e.g. [2,2,3])</p>
<pre class="code python literal-block">
<span class="comment"># Author: Robert Kern</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">randint</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">5</span><span class="punctuation">,(</span><span class="literal number integer">100</span><span class="punctuation">,</span><span class="literal number integer">3</span><span class="punctuation">))</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">randint</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">5</span><span class="punctuation">,(</span><span class="literal number integer">10</span><span class="punctuation">,</span><span class="literal number integer">3</span><span class="punctuation">))</span>
<span class="name">E</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">logical_and</span><span class="operator">.</span><span class="name">reduce</span><span class="punctuation">(</span><span class="name">Z</span><span class="punctuation">[:,</span><span class="literal number integer">1</span><span class="punctuation">:]</span> <span class="operator">==</span> <span class="name">Z</span><span class="punctuation">[:,:</span><span class="operator">-</span><span class="literal number integer">1</span><span class="punctuation">],</span> <span class="name">axis</span><span class="operator">=</span><span class="literal number integer">1</span><span class="punctuation">)</span>
<span class="name">U</span> <span class="operator">=</span> <span class="name">Z</span><span class="punctuation">[</span><span class="operator">~</span><span class="name">E</span><span class="punctuation">]</span>
<span class="keyword">print</span> <span class="name">Z</span>
<span class="keyword">print</span> <span class="name">U</span>
</pre>
</li>
<li><p class="first">Convert a vector of ints into a matrix binary representation.</p>
@ -380,12 +435,12 @@ np.bincount(A) == C ?</p>
<span class="name">I</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">array</span><span class="punctuation">([</span><span class="literal number integer">0</span><span class="punctuation">,</span> <span class="literal number integer">1</span><span class="punctuation">,</span> <span class="literal number integer">2</span><span class="punctuation">,</span> <span class="literal number integer">3</span><span class="punctuation">,</span> <span class="literal number integer">15</span><span class="punctuation">,</span> <span class="literal number integer">16</span><span class="punctuation">,</span> <span class="literal number integer">32</span><span class="punctuation">,</span> <span class="literal number integer">64</span><span class="punctuation">,</span> <span class="literal number integer">128</span><span class="punctuation">])</span>
<span class="name">B</span> <span class="operator">=</span> <span class="punctuation">((</span><span class="name">I</span><span class="operator">.</span><span class="name">reshape</span><span class="punctuation">(</span><span class="operator">-</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">1</span><span class="punctuation">)</span> <span class="operator">&amp;</span> <span class="punctuation">(</span><span class="literal number integer">2</span><span class="operator">**</span><span class="name">np</span><span class="operator">.</span><span class="name">arange</span><span class="punctuation">(</span><span class="literal number integer">8</span><span class="punctuation">)))</span> <span class="operator">!=</span> <span class="literal number integer">0</span><span class="punctuation">)</span><span class="operator">.</span><span class="name">astype</span><span class="punctuation">(</span><span class="name builtin">int</span><span class="punctuation">)</span>
<span class="name">B</span> <span class="operator">=</span> <span class="name">B</span><span class="punctuation">[:,::</span><span class="operator">-</span><span class="literal number integer">1</span><span class="punctuation">]</span>
<span class="keyword">print</span> <span class="name">B</span><span class="punctuation">[:,::</span><span class="operator">-</span><span class="literal number integer">1</span><span class="punctuation">]</span>
<span class="comment"># Author: Daniel T. McDonald</span>
<span class="name">I</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">array</span><span class="punctuation">([</span><span class="literal number integer">0</span><span class="punctuation">,</span> <span class="literal number integer">1</span><span class="punctuation">,</span> <span class="literal number integer">2</span><span class="punctuation">,</span> <span class="literal number integer">3</span><span class="punctuation">,</span> <span class="literal number integer">15</span><span class="punctuation">,</span> <span class="literal number integer">16</span><span class="punctuation">,</span> <span class="literal number integer">32</span><span class="punctuation">,</span> <span class="literal number integer">64</span><span class="punctuation">,</span> <span class="literal number integer">128</span><span class="punctuation">],</span> <span class="name">dtype</span><span class="operator">=</span><span class="name">np</span><span class="operator">.</span><span class="name">uint8</span><span class="punctuation">)</span>
<span class="name">np</span><span class="operator">.</span><span class="name">unpackbits</span><span class="punctuation">(</span><span class="name">I</span><span class="punctuation">[:,</span> <span class="name">np</span><span class="operator">.</span><span class="name">newaxis</span><span class="punctuation">],</span> <span class="name">axis</span><span class="operator">=</span><span class="literal number integer">1</span><span class="punctuation">)</span>
<span class="keyword">print</span> <span class="name">np</span><span class="operator">.</span><span class="name">unpackbits</span><span class="punctuation">(</span><span class="name">I</span><span class="punctuation">[:,</span> <span class="name">np</span><span class="operator">.</span><span class="name">newaxis</span><span class="punctuation">],</span> <span class="name">axis</span><span class="operator">=</span><span class="literal number integer">1</span><span class="punctuation">)</span>
</pre>
</li>
</ol>
@ -399,10 +454,10 @@ necessary)</p>
<pre class="code python literal-block">
<span class="comment"># Author: Nicolas Rougier</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">random</span><span class="punctuation">((</span><span class="literal number integer">25</span><span class="punctuation">,</span><span class="literal number integer">25</span><span class="punctuation">))</span>
<span class="name">shape</span> <span class="operator">=</span> <span class="punctuation">(</span><span class="literal number integer">3</span><span class="punctuation">,</span><span class="literal number integer">3</span><span class="punctuation">)</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">randint</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">10</span><span class="punctuation">,(</span><span class="literal number integer">10</span><span class="punctuation">,</span><span class="literal number integer">10</span><span class="punctuation">))</span>
<span class="name">shape</span> <span class="operator">=</span> <span class="punctuation">(</span><span class="literal number integer">5</span><span class="punctuation">,</span><span class="literal number integer">5</span><span class="punctuation">)</span>
<span class="name">fill</span> <span class="operator">=</span> <span class="literal number integer">0</span>
<span class="name">position</span> <span class="operator">=</span> <span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">0</span><span class="punctuation">)</span>
<span class="name">position</span> <span class="operator">=</span> <span class="punctuation">(</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">1</span><span class="punctuation">)</span>
<span class="name">R</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">ones</span><span class="punctuation">(</span><span class="name">shape</span><span class="punctuation">,</span> <span class="name">dtype</span><span class="operator">=</span><span class="name">Z</span><span class="operator">.</span><span class="name">dtype</span><span class="punctuation">)</span><span class="operator">*</span><span class="name">fill</span>
<span class="name">P</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">array</span><span class="punctuation">(</span><span class="name builtin">list</span><span class="punctuation">(</span><span class="name">position</span><span class="punctuation">))</span><span class="operator">.</span><span class="name">astype</span><span class="punctuation">(</span><span class="name builtin">int</span><span class="punctuation">)</span>
@ -422,15 +477,18 @@ necessary)</p>
<span class="name">r</span> <span class="operator">=</span> <span class="punctuation">[</span><span class="name builtin">slice</span><span class="punctuation">(</span><span class="name">start</span><span class="punctuation">,</span><span class="name">stop</span><span class="punctuation">)</span> <span class="keyword">for</span> <span class="name">start</span><span class="punctuation">,</span><span class="name">stop</span> <span class="operator word">in</span> <span class="name builtin">zip</span><span class="punctuation">(</span><span class="name">R_start</span><span class="punctuation">,</span><span class="name">R_stop</span><span class="punctuation">)]</span>
<span class="name">z</span> <span class="operator">=</span> <span class="punctuation">[</span><span class="name builtin">slice</span><span class="punctuation">(</span><span class="name">start</span><span class="punctuation">,</span><span class="name">stop</span><span class="punctuation">)</span> <span class="keyword">for</span> <span class="name">start</span><span class="punctuation">,</span><span class="name">stop</span> <span class="operator word">in</span> <span class="name builtin">zip</span><span class="punctuation">(</span><span class="name">Z_start</span><span class="punctuation">,</span><span class="name">Z_stop</span><span class="punctuation">)]</span>
<span class="name">R</span><span class="punctuation">[</span><span class="name">r</span><span class="punctuation">]</span> <span class="operator">=</span> <span class="name">Z</span><span class="punctuation">[</span><span class="name">z</span><span class="punctuation">]</span>
<span class="keyword">print</span> <span class="name">Z</span>
<span class="keyword">print</span> <span class="name">R</span>
</pre>
</li>
<li><p class="first">Consider an array Z = [1,2,3,4,5,6,7,8,9,10,11,12,13,14], how to generate an
array R = [[1,2,3,4], [2,3,4,5], [3,4,5,6], ..., [11,12,13,14]] ?</p>
<pre class="code python literal-block">
<span class="comment"># Stéfan van der Walt</span>
<span class="comment"># Author: Stéfan van der Walt</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">arange</span><span class="punctuation">(</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">15</span><span class="punctuation">)</span>
<span class="name">R</span> <span class="operator">=</span> <span class="name">as_strided</span><span class="punctuation">(</span><span class="name">Z</span><span class="punctuation">,(</span><span class="literal number integer">11</span><span class="punctuation">,</span><span class="literal number integer">4</span><span class="punctuation">),(</span><span class="literal number integer">4</span><span class="punctuation">,</span><span class="literal number integer">4</span><span class="punctuation">))</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">arange</span><span class="punctuation">(</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">15</span><span class="punctuation">,</span><span class="name">dtype</span><span class="operator">=</span><span class="name">uint32</span><span class="punctuation">)</span>
<span class="name">R</span> <span class="operator">=</span> <span class="name">stride_tricks</span><span class="operator">.</span><span class="name">as_strided</span><span class="punctuation">(</span><span class="name">Z</span><span class="punctuation">,(</span><span class="literal number integer">11</span><span class="punctuation">,</span><span class="literal number integer">4</span><span class="punctuation">),(</span><span class="literal number integer">4</span><span class="punctuation">,</span><span class="literal number integer">4</span><span class="punctuation">))</span>
<span class="keyword">print</span> <span class="name">R</span>
</pre>
</li>
</ol>
@ -449,22 +507,24 @@ in B ?</p>
<span class="name">C</span> <span class="operator">=</span> <span class="punctuation">(</span><span class="name">A</span><span class="punctuation">[</span><span class="operator">...</span><span class="punctuation">,</span> <span class="name">np</span><span class="operator">.</span><span class="name">newaxis</span><span class="punctuation">,</span> <span class="name">np</span><span class="operator">.</span><span class="name">newaxis</span><span class="punctuation">]</span> <span class="operator">==</span> <span class="name">B</span><span class="punctuation">)</span>
<span class="name">rows</span> <span class="operator">=</span> <span class="punctuation">(</span><span class="name">C</span><span class="operator">.</span><span class="name">sum</span><span class="punctuation">(</span><span class="name">axis</span><span class="operator">=</span><span class="punctuation">(</span><span class="literal number integer">1</span><span class="punctuation">,</span><span class="literal number integer">2</span><span class="punctuation">,</span><span class="literal number integer">3</span><span class="punctuation">))</span> <span class="operator">&gt;=</span> <span class="name">B</span><span class="operator">.</span><span class="name">shape</span><span class="punctuation">[</span><span class="literal number integer">1</span><span class="punctuation">])</span><span class="operator">.</span><span class="name">nonzero</span><span class="punctuation">()[</span><span class="literal number integer">0</span><span class="punctuation">]</span>
<span class="keyword">print</span> <span class="name">rows</span>
</pre>
</li>
<li><p class="first">Extract all the contiguous 3x3 blocks from a random 10x10 matrix.</p>
<pre class="code python literal-block">
<span class="comment"># Chris Barker</span>
<span class="comment"># Author: Chris Barker</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">randint</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">5</span><span class="punctuation">,(</span><span class="literal number integer">10</span><span class="punctuation">,</span><span class="literal number integer">10</span><span class="punctuation">))</span>
<span class="name">n</span> <span class="operator">=</span> <span class="literal number integer">3</span>
<span class="name">i</span> <span class="operator">=</span> <span class="literal number integer">1</span> <span class="operator">+</span> <span class="punctuation">(</span><span class="name">Z</span><span class="operator">.</span><span class="name">shape</span><span class="punctuation">[</span><span class="literal number integer">0</span><span class="punctuation">]</span><span class="operator">-</span><span class="literal number integer">3</span><span class="punctuation">)</span>
<span class="name">j</span> <span class="operator">=</span> <span class="literal number integer">1</span> <span class="operator">+</span> <span class="punctuation">(</span><span class="name">Z</span><span class="operator">.</span><span class="name">shape</span><span class="punctuation">[</span><span class="literal number integer">1</span><span class="punctuation">]</span><span class="operator">-</span><span class="literal number integer">3</span><span class="punctuation">)</span>
<span class="name">C</span> <span class="operator">=</span> <span class="name">stride_tricks</span><span class="operator">.</span><span class="name">as_strided</span><span class="punctuation">(</span><span class="name">Z</span><span class="punctuation">,</span> <span class="name">shape</span><span class="operator">=</span><span class="punctuation">(</span><span class="name">i</span><span class="punctuation">,</span> <span class="name">j</span><span class="punctuation">,</span> <span class="name">n</span><span class="punctuation">,</span> <span class="name">n</span><span class="punctuation">),</span> <span class="name">strides</span><span class="operator">=</span><span class="name">Z</span><span class="operator">.</span><span class="name">strides</span> <span class="operator">+</span> <span class="name">Z</span><span class="operator">.</span><span class="name">strides</span><span class="punctuation">)</span>
<span class="keyword">print</span> <span class="name">C</span>
</pre>
</li>
<li><p class="first">Create a 2D array subclass such that Z[i,j] == Z[j,i]</p>
<pre class="code python literal-block">
<span class="comment"># Eric O. Lebigot</span>
<span class="comment"># Author: Eric O. Lebigot</span>
<span class="comment"># Note: only works for 2d array and value setting using indices</span>
<span class="keyword">class</span> <span class="name class">Symetric</span><span class="punctuation">(</span><span class="name">np</span><span class="operator">.</span><span class="name">ndarray</span><span class="punctuation">):</span>
@ -475,11 +535,29 @@ in B ?</p>
<span class="keyword">def</span> <span class="name function">symetric</span><span class="punctuation">(</span><span class="name">Z</span><span class="punctuation">):</span>
<span class="keyword">return</span> <span class="name">np</span><span class="operator">.</span><span class="name">asarray</span><span class="punctuation">(</span><span class="name">Z</span> <span class="operator">+</span> <span class="name">Z</span><span class="operator">.</span><span class="name">T</span> <span class="operator">-</span> <span class="name">np</span><span class="operator">.</span><span class="name">diag</span><span class="punctuation">(</span><span class="name">Z</span><span class="operator">.</span><span class="name">diagonal</span><span class="punctuation">()))</span><span class="operator">.</span><span class="name">view</span><span class="punctuation">(</span><span class="name">Symetric</span><span class="punctuation">)</span>
<span class="name">S</span> <span class="operator">=</span> <span class="name">symetric</span><span class="punctuation">(</span><span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">randint</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">10</span><span class="punctuation">,(</span><span class="literal number integer">5</span><span class="punctuation">,</span><span class="literal number integer">5</span><span class="punctuation">))</span>
<span class="name">S</span> <span class="operator">=</span> <span class="name">symetric</span><span class="punctuation">(</span><span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">randint</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">10</span><span class="punctuation">,(</span><span class="literal number integer">5</span><span class="punctuation">,</span><span class="literal number integer">5</span><span class="punctuation">)))</span>
<span class="name">S</span><span class="punctuation">[</span><span class="literal number integer">2</span><span class="punctuation">,</span><span class="literal number integer">3</span><span class="punctuation">]</span> <span class="operator">=</span> <span class="literal number integer">42</span>
<span class="keyword">print</span> <span class="name">S</span>
</pre>
</li>
<li><p class="first">Consider a set of p matrices wich shape (n,n) and a set of p vectors with shape (n,1).
How to compute the sum of of the p matrix products at once ? (result has shape (n,1))</p>
<pre class="code python literal-block">
<span class="comment"># Author: Stéfan van der Walt</span>
<span class="name">p</span><span class="punctuation">,</span> <span class="name">n</span> <span class="operator">=</span> <span class="literal number integer">10</span><span class="punctuation">,</span> <span class="literal number integer">20</span>
<span class="name">M</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">ones</span><span class="punctuation">((</span><span class="name">p</span><span class="punctuation">,</span><span class="name">n</span><span class="punctuation">,</span><span class="name">n</span><span class="punctuation">))</span>
<span class="name">V</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">ones</span><span class="punctuation">((</span><span class="name">p</span><span class="punctuation">,</span><span class="name">n</span><span class="punctuation">,</span><span class="literal number integer">1</span><span class="punctuation">))</span>
<span class="name">S</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">tensordot</span><span class="punctuation">(</span><span class="name">M</span><span class="punctuation">,</span> <span class="name">V</span><span class="punctuation">,</span> <span class="name">axes</span><span class="operator">=</span><span class="punctuation">[[</span><span class="literal number integer">0</span><span class="punctuation">,</span> <span class="literal number integer">2</span><span class="punctuation">],</span> <span class="punctuation">[</span><span class="literal number integer">0</span><span class="punctuation">,</span> <span class="literal number integer">1</span><span class="punctuation">]])</span>
<span class="keyword">print</span> <span class="name">S</span>
<span class="comment"># It works, because:</span>
<span class="comment"># M is (p,n,n)</span>
<span class="comment"># V is (p,n,1)</span>
<span class="comment"># Thus, summing over the paired axes 0 and 0 (of M and V independently),</span>
<span class="comment"># and 2 and 1, to remain with a (n,1) vector.</span>
</pre>
</li>
</ol>
</div>
<div class="section" id="master">
@ -491,12 +569,13 @@ in B ?</p>
<p class="last">See <a class="reference external" href="http://stackoverflow.com/questions/16970982/find-unique-rows-in-numpy-array/">stackoverflow</a> for explanations.</p>
</div>
<pre class="code python literal-block">
<span class="comment"># Jaime Fernández del Río</span>
<span class="comment"># Author: Jaime Fernández del Río</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">randint</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">2</span><span class="punctuation">,(</span><span class="literal number integer">6</span><span class="punctuation">,</span><span class="literal number integer">6</span><span class="punctuation">))</span>
<span class="name">Z</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">randint</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">2</span><span class="punctuation">,(</span><span class="literal number integer">6</span><span class="punctuation">,</span><span class="literal number integer">3</span><span class="punctuation">))</span>
<span class="name">T</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">ascontiguousarray</span><span class="punctuation">(</span><span class="name">Z</span><span class="punctuation">)</span><span class="operator">.</span><span class="name">view</span><span class="punctuation">(</span><span class="name">np</span><span class="operator">.</span><span class="name">dtype</span><span class="punctuation">((</span><span class="name">np</span><span class="operator">.</span><span class="name">void</span><span class="punctuation">,</span> <span class="name">Z</span><span class="operator">.</span><span class="name">dtype</span><span class="operator">.</span><span class="name">itemsize</span> <span class="operator">*</span> <span class="name">Z</span><span class="operator">.</span><span class="name">shape</span><span class="punctuation">[</span><span class="literal number integer">1</span><span class="punctuation">])))</span>
<span class="name">_</span><span class="punctuation">,</span> <span class="name">idx</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">unique</span><span class="punctuation">(</span><span class="name">T</span><span class="punctuation">,</span> <span class="name">return_index</span><span class="operator">=</span><span class="name builtin pseudo">True</span><span class="punctuation">)</span>
<span class="name">uZ</span> <span class="operator">=</span> <span class="name">Z</span><span class="punctuation">[</span><span class="name">idx</span><span class="punctuation">]</span>
<span class="keyword">print</span> <span class="name">uZ</span>
</pre>
</li>
</ol>

View File

@ -77,6 +77,14 @@
"[Valentin Haenel](http://haenel.co)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Thanks to Michiaki Ariga, there is now a [Julia\n",
"version](https://github.com/chezou/julia-100-exercises).\n"
]
},
{
"cell_type": "heading",
"level": 2,
@ -859,7 +867,7 @@
"cell_type": "code",
"collapsed": false,
"input": [
"# Jaime Fern\u00e1ndez del R\u00edo\n",
"# Author: Jaime Fern\u00e1ndez del R\u00edo\n",
"\n",
"D = np.random.uniform(0,1,100)\n",
"S = np.random.randint(0,10,100)\n",
@ -920,7 +928,7 @@
"cell_type": "code",
"collapsed": false,
"input": [
"# Author: Nicolas Rougier\n",
"# Author: Nicolas P. Rougier\n",
"\n",
"faces = np.random.randint(0,100,(10,3))\n",
"F = np.roll(faces.repeat(2,axis=1),-1,axis=1)\n",
@ -946,7 +954,7 @@
"cell_type": "code",
"collapsed": false,
"input": [
"# Jaime Fern\u00e1ndez del R\u00edo\n",
"# Author: Jaime Fern\u00e1ndez del R\u00edo\n",
"\n",
"C = np.bincount([1,1,2,3,4,4,6])\n",
"A = np.repeat(np.arange(len(C)), C)\n",
@ -1180,7 +1188,7 @@
"cell_type": "code",
"collapsed": false,
"input": [
"# Eric O. Lebigot\n",
"# Author: Eric O. Lebigot\n",
"# Note: only works for 2d array and value setting using indices\n",
"\n",
"class Symetric(np.ndarray):\n",
@ -1212,7 +1220,7 @@
"cell_type": "code",
"collapsed": false,
"input": [
"# St\u00e9fan van der Walt\n",
"# Author: St\u00e9fan van der Walt\n",
"\n",
"p, n = 10, 20\n",
"M = np.ones((p,n,n))\n",
@ -1221,10 +1229,10 @@
"print S\n",
"\n",
"# It works, because:\n",
"# M is (P, N, N)\n",
"# V is (P, N, 1)\n",
"# M is (p,n,n)\n",
"# V is (p,n,1)\n",
"# Thus, summing over the paired axes 0 and 0 (of M and V independently),\n",
"# and 2 and 1, to remain with a Mx1 vector."
"# and 2 and 1, to remain with a (n,1) vector."
],
"language": "python",
"metadata": {},
@ -1266,7 +1274,7 @@
"cell_type": "code",
"collapsed": false,
"input": [
"# Jaime Fern\u00e1ndez del R\u00edo\n",
"# Author: Jaime Fern\u00e1ndez del R\u00edo\n",
"\n",
"Z = np.random.randint(0,2,(6,3))\n",
"T = np.ascontiguousarray(Z).view(np.dtype((np.void, Z.dtype.itemsize * Z.shape[1])))\n",

View File

@ -34,6 +34,9 @@ from the github repo, thanks to the `rst2ipynb
<https://github.com/esc/rst2ipynb>`_ conversion tool by `Valentin Haenel
<http://haenel.co>`_
Thanks to Michiaki Ariga, there is now a `Julia version <https://github.com/chezou/julia-100-exercises>`_.
.. **Contents**
.. .. contents::
.. :local: