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<!DOCTYPE html>
<html lang="en-us">
<head>
<meta charset="UTF-8">
<title>Scientific python cheat sheet by IPGP</title>
<meta name="viewport" content="width=device-width, initial-scale=1.5">
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<body>
<section class="main-content">
<h1>
<a id="scientific-python-cheatsheet" class="anchor" href="#scientific-python-cheatsheet" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Scientific Python Cheatsheet</h1>
<p><strong>Table of Contents</strong></p>
<ul>
<li style="font-size: 0.8rem;">
<a href="#scientific-python-cheatsheet">Scientific Python Cheatsheet</a>
<ul>
<li>
<a href="#pure-python">Pure Python</a>
<ul>
<li><a href="#types">Types</a></li>
<li><a href="#lists">Lists</a></li>
<li><a href="#dictionaries">Dictionaries</a></li>
<li><a href="#strings">Strings</a></li>
<li><a href="#operators">Operators</a></li>
<li>
<a href="#control-flow">Control Flow</a>
<ul>
<li><a href="#ifelifelse">if/elif/else</a></li>
<li><a href="#for">for</a></li>
<li><a href="#while">while</a></li>
<li><a href="#break">break</a></li>
<li><a href="#continue">continue</a></li>
</ul>
</li>
<li>
<a href="#functions-classes-generators-decorators">Functions, Classes, Generators, Decorators</a>
<ul>
<li><a href="#function">Function</a></li>
<li><a href="#class">Class</a></li>
<li><a href="#generators">Generators</a></li>
<li><a href="#decorators">Decorators</a></li>
</ul>
</li>
</ul>
</li>
<li>
<a href="#numpy">NumPy</a>
<ul>
<li><a href="#array-initialization">array initialization</a></li>
<li><a href="#reading-writing-files">reading/ writing files</a></li>
<li><a href="#array-properties-and-operations">array properties and operations</a></li>
<li><a href="#indexing">indexing</a></li>
<li><a href="#boolean-arrays">boolean arrays</a></li>
<li><a href="#elementwise-operations-and-math-functions">elementwise operations and math functions</a></li>
<li><a href="#inner--outer-products">inner / outer products</a></li>
<li><a href="#interpolation-integration">interpolation, integration</a></li>
<li><a href="#fft">fft</a></li>
<li><a href="#rounding">rounding</a></li>
<li><a href="#random-variables">random variables</a></li>
</ul>
</li>
<li>
<a href="#matplotlib">Matplotlib</a>
<ul>
<li><a href="#figures-and-axes">figures and axes</a></li>
<li><a href="#figures-and-axes-properties">figures and axes properties</a></li>
<li><a href="#plotting-routines">plotting routines</a></li>
</ul>
</li>
</ul>
</li>
</ul>
<div class="group">
<h2>
<a id="pure-python" class="anchor" href="#pure-python" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Pure Python</h2>
<h3>
<a id="types" class="anchor" href="#types" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Types</h3>
<div class="highlight highlight-source-python"><pre>a <span class="pl-k">=</span> <span class="pl-c1">2</span> <span class="pl-c"># integer</span>
b <span class="pl-k">=</span> <span class="pl-c1">5.0</span> <span class="pl-c"># float</span>
c <span class="pl-k">=</span> <span class="pl-c1">8.3e5</span> <span class="pl-c"># exponential</span>
d <span class="pl-k">=</span> <span class="pl-c1">1.5</span> <span class="pl-k">+</span> <span class="pl-c1">0.5<span class="pl-k">j</span></span> <span class="pl-c"># complex</span>
e <span class="pl-k">=</span> <span class="pl-c1">3</span> <span class="pl-k">></span> <span class="pl-c1">4</span> <span class="pl-c"># boolean</span>
f <span class="pl-k">=</span> <span class="pl-s"><span class="pl-pds">'</span>word<span class="pl-pds">'</span></span> <span class="pl-c"># string</span></pre></div>
<h3>
<a id="lists" class="anchor" href="#lists" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Lists</h3>
<div class="highlight highlight-source-python"><pre>a <span class="pl-k">=</span> [<span class="pl-s"><span class="pl-pds">'</span>red<span class="pl-pds">'</span></span>, <span class="pl-s"><span class="pl-pds">'</span>blue<span class="pl-pds">'</span></span>, <span class="pl-s"><span class="pl-pds">'</span>green<span class="pl-pds">'</span></span>] <span class="pl-c"># manually initialization</span>
b <span class="pl-k">=</span> <span class="pl-c1">range</span>(<span class="pl-c1">5</span>) <span class="pl-c"># initialization through a function</span>
c <span class="pl-k">=</span> [nu<span class="pl-k">**</span><span class="pl-c1">2</span> <span class="pl-k">for</span> nu <span class="pl-k">in</span> b] <span class="pl-c"># initialize through list comprehension</span>
d <span class="pl-k">=</span> [nu<span class="pl-k">**</span><span class="pl-c1">2</span> <span class="pl-k">for</span> nu <span class="pl-k">in</span> b <span class="pl-k">if</span> b <span class="pl-k"><</span> <span class="pl-c1">3</span>] <span class="pl-c"># list comprehension withcondition</span>
e <span class="pl-k">=</span> c[<span class="pl-c1">0</span>] <span class="pl-c"># access element</span>
f <span class="pl-k">=</span> e[<span class="pl-c1">1</span>: <span class="pl-c1">2</span>] <span class="pl-c"># access a slice of the list</span>
g <span class="pl-k">=</span> [<span class="pl-s"><span class="pl-pds">'</span>re<span class="pl-pds">'</span></span>, <span class="pl-s"><span class="pl-pds">'</span>bl<span class="pl-pds">'</span></span>] <span class="pl-k">+</span> [<span class="pl-s"><span class="pl-pds">'</span>gr<span class="pl-pds">'</span></span>] <span class="pl-c"># list concatenation</span>
h <span class="pl-k">=</span> [<span class="pl-s"><span class="pl-pds">'</span>re<span class="pl-pds">'</span></span>] <span class="pl-k">*</span> <span class="pl-c1">5</span> <span class="pl-c"># repeat a list</span>
[<span class="pl-s"><span class="pl-pds">'</span>re<span class="pl-pds">'</span></span>, <span class="pl-s"><span class="pl-pds">'</span>bl<span class="pl-pds">'</span></span>].index(<span class="pl-s"><span class="pl-pds">'</span>re<span class="pl-pds">'</span></span>) <span class="pl-c"># returns index of 're'</span>
<span class="pl-s"><span class="pl-pds">'</span>re<span class="pl-pds">'</span></span> <span class="pl-k">in</span> [<span class="pl-s"><span class="pl-pds">'</span>re<span class="pl-pds">'</span></span>, <span class="pl-s"><span class="pl-pds">'</span>bl<span class="pl-pds">'</span></span>] <span class="pl-c"># true if 're' in list</span>
<span class="pl-c1">sorted</span>([<span class="pl-c1">3</span>, <span class="pl-c1">2</span>, <span class="pl-c1">1</span>]) <span class="pl-c"># returns sorted list</span>
z <span class="pl-k">=</span> [<span class="pl-s"><span class="pl-pds">'</span>red<span class="pl-pds">'</span></span>] <span class="pl-k">+</span> [<span class="pl-s"><span class="pl-pds">'</span>green<span class="pl-pds">'</span></span>, <span class="pl-s"><span class="pl-pds">'</span>blue<span class="pl-pds">'</span></span>] <span class="pl-c"># list concatenation</span></pre></div>
<h3>
<a id="dictionaries" class="anchor" href="#dictionaries" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Dictionaries</h3>
<div class="highlight highlight-source-python"><pre>a <span class="pl-k">=</span> {<span class="pl-s"><span class="pl-pds">'</span>red<span class="pl-pds">'</span></span>: <span class="pl-s"><span class="pl-pds">'</span>rouge<span class="pl-pds">'</span></span>, <span class="pl-s"><span class="pl-pds">'</span>blue<span class="pl-pds">'</span></span>: <span class="pl-s"><span class="pl-pds">'</span>bleu<span class="pl-pds">'</span></span>, <span class="pl-s"><span class="pl-pds">'</span>green<span class="pl-pds">'</span></span>: <span class="pl-s"><span class="pl-pds">'</span>vert<span class="pl-pds">'</span></span>} <span class="pl-c"># dictionary</span>
b <span class="pl-k">=</span> a[<span class="pl-s"><span class="pl-pds">'</span>red<span class="pl-pds">'</span></span>] <span class="pl-c"># translate item</span>
c <span class="pl-k">=</span> [value <span class="pl-k">for</span> key, value <span class="pl-k">in</span> b.items()] <span class="pl-c"># loop through contents</span>
d <span class="pl-k">=</span> a.get(<span class="pl-s"><span class="pl-pds">'</span>yellow<span class="pl-pds">'</span></span>, <span class="pl-s"><span class="pl-pds">'</span>no translation found<span class="pl-pds">'</span></span>) <span class="pl-c"># return default</span></pre></div>
<h3>
<a id="strings" class="anchor" href="#strings" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Strings</h3>
<div class="highlight highlight-source-python"><pre>a <span class="pl-k">=</span> <span class="pl-s"><span class="pl-pds">'</span>red<span class="pl-pds">'</span></span> <span class="pl-c"># assignment</span>
char <span class="pl-k">=</span> a[<span class="pl-c1">2</span>] <span class="pl-c"># access individual characters</span>
<span class="pl-s"><span class="pl-pds">'</span>red <span class="pl-pds">'</span></span> <span class="pl-k">+</span> <span class="pl-s"><span class="pl-pds">'</span>blue<span class="pl-pds">'</span></span> <span class="pl-c"># string concatenation</span>
<span class="pl-s"><span class="pl-pds">'</span>1, 2, three<span class="pl-pds">'</span></span>.split(<span class="pl-s"><span class="pl-pds">'</span>,<span class="pl-pds">'</span></span>) <span class="pl-c"># split string into list</span>
<span class="pl-s"><span class="pl-pds">'</span>.<span class="pl-pds">'</span></span>.join([<span class="pl-s"><span class="pl-pds">'</span>1<span class="pl-pds">'</span></span>, <span class="pl-s"><span class="pl-pds">'</span>2<span class="pl-pds">'</span></span>, <span class="pl-s"><span class="pl-pds">'</span>three<span class="pl-pds">'</span></span>]) <span class="pl-c"># concatenate list into string</span></pre></div>
<h3>
<a id="operators" class="anchor" href="#operators" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Operators</h3>
<div class="highlight highlight-source-python"><pre>a <span class="pl-k">=</span> <span class="pl-c1">2</span> <span class="pl-c"># assignment</span>
a <span class="pl-k">+=</span> <span class="pl-c1">1</span> (<span class="pl-k">*</span>=, <span class="pl-k">/</span>=) <span class="pl-c"># change and assign</span>
<span class="pl-c1">3</span> <span class="pl-k">+</span> <span class="pl-c1">2</span> <span class="pl-c"># addition</span>
<span class="pl-c1">3</span> <span class="pl-k">/</span> <span class="pl-c1">2</span> <span class="pl-c"># integer division (python2) or float division (python3)</span>
<span class="pl-c1">3</span> <span class="pl-k">//</span> <span class="pl-c1">2</span> <span class="pl-c"># integer division</span>
<span class="pl-c1">3</span> <span class="pl-k">*</span> <span class="pl-c1">2</span> <span class="pl-c"># multiplication</span>
<span class="pl-c1">3</span> <span class="pl-k">**</span> <span class="pl-c1">2</span> <span class="pl-c"># exponent</span>
<span class="pl-c1">3</span> <span class="pl-k">%</span> <span class="pl-c1">2</span> <span class="pl-c"># remainder</span>
<span class="pl-c1">abs</span>() <span class="pl-c"># absolute value</span>
<span class="pl-c1">1</span> <span class="pl-k">==</span> <span class="pl-c1">1</span> <span class="pl-c"># equal</span>
<span class="pl-c1">2</span> <span class="pl-k">></span> <span class="pl-c1">1</span> <span class="pl-c"># larger</span>
<span class="pl-c1">2</span> <span class="pl-k"><</span> <span class="pl-c1">1</span> <span class="pl-c"># smaller</span>
<span class="pl-c1">1</span> <span class="pl-k">!=</span> <span class="pl-c1">2</span> <span class="pl-c"># not equal</span>
<span class="pl-c1">1</span> <span class="pl-k">!=</span> <span class="pl-c1">2</span> <span class="pl-k">and</span> <span class="pl-c1">2</span> <span class="pl-k"><</span> <span class="pl-c1">3</span> <span class="pl-c"># logical AND</span>
<span class="pl-c1">1</span> <span class="pl-k">!=</span> <span class="pl-c1">2</span> <span class="pl-k">or</span> <span class="pl-c1">2</span> <span class="pl-k"><</span> <span class="pl-c1">3</span> <span class="pl-c"># logical OR</span>
<span class="pl-k">not</span> <span class="pl-c1">1</span> <span class="pl-k">==</span> <span class="pl-c1">2</span> <span class="pl-c"># logical NOT</span>
a <span class="pl-k">in</span> b <span class="pl-c"># test if a is in b</span>
a <span class="pl-k">is</span> b <span class="pl-c"># test if objects point to the same memory (id)</span></pre></div>
<h3>
<a id="control-flow" class="anchor" href="#control-flow" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Control Flow</h3>
<h4>
<a id="ifelifelse" class="anchor" href="#ifelifelse" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>if/elif/else</h4>
<div class="highlight highlight-source-python"><pre>a, b <span class="pl-k">=</span> <span class="pl-c1">1</span>, <span class="pl-c1">2</span>
<span class="pl-k">if</span> a <span class="pl-k">+</span> b <span class="pl-k">==</span> <span class="pl-c1">3</span>:
<span class="pl-c1">print</span> <span class="pl-s"><span class="pl-pds">'</span>True<span class="pl-pds">'</span></span>
<span class="pl-k">elif</span> a <span class="pl-k">+</span> b <span class="pl-k">==</span> <span class="pl-c1">1</span>:
<span class="pl-c1">print</span> <span class="pl-s"><span class="pl-pds">'</span>False<span class="pl-pds">'</span></span>
<span class="pl-k">else</span>:
<span class="pl-c1">print</span> <span class="pl-s"><span class="pl-pds">'</span>?<span class="pl-pds">'</span></span></pre></div>
<h4>
<a id="for" class="anchor" href="#for" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>for</h4>
<div class="highlight highlight-source-python"><pre>a <span class="pl-k">=</span> [<span class="pl-s"><span class="pl-pds">'</span>red<span class="pl-pds">'</span></span>, <span class="pl-s"><span class="pl-pds">'</span>blue<span class="pl-pds">'</span></span>,
<span class="pl-s"><span class="pl-pds">'</span>green<span class="pl-pds">'</span></span>]
<span class="pl-k">for</span> color <span class="pl-k">in</span> a:
<span class="pl-c1">print</span> color</pre></div>
<h4>
<a id="while" class="anchor" href="#while" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>while</h4>
<div class="highlight highlight-source-python"><pre>number <span class="pl-k">=</span> <span class="pl-c1">1</span>
<span class="pl-k">while</span> number <span class="pl-k"><</span> <span class="pl-c1">10</span>:
<span class="pl-c1">print</span> number
number <span class="pl-k">+=</span> <span class="pl-c1">1</span></pre></div>
<h4>
<a id="break" class="anchor" href="#break" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>break</h4>
<div class="highlight highlight-source-python"><pre>number <span class="pl-k">=</span> <span class="pl-c1">1</span>
<span class="pl-k">while</span> <span class="pl-c1">True</span>:
<span class="pl-c1">print</span> number
number <span class="pl-k">+=</span> <span class="pl-c1">1</span>
<span class="pl-k">if</span> number <span class="pl-k">></span> <span class="pl-c1">10</span>:
<span class="pl-k">break</span></pre></div>
<h4>
<a id="continue" class="anchor" href="#continue" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>continue</h4>
<div class="highlight highlight-source-python"><pre><span class="pl-k">for</span> i <span class="pl-k">in</span> <span class="pl-c1">range</span>(<span class="pl-c1">20</span>):
<span class="pl-k">if</span> i <span class="pl-k">%</span> <span class="pl-c1">2</span> <span class="pl-k">==</span> <span class="pl-c1">0</span>:
<span class="pl-k">continue</span>
<span class="pl-c1">print</span> i</pre></div>
<h3>
<a id="functions-classes-generators-decorators" class="anchor" href="#functions-classes-generators-decorators" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Functions, Classes, Generators, Decorators</h3>
<h4>
<a id="function" class="anchor" href="#function" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Function</h4>
<div class="highlight highlight-source-python"><pre><span class="pl-k">def</span> <span class="pl-en">myfunc</span>(<span class="pl-smi">a1</span>, <span class="pl-smi">a2</span>):
<span class="pl-k">return</span> x
x <span class="pl-k">=</span> my_function(a1,a2)</pre></div>
<h4>
<a id="class" class="anchor" href="#class" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Class</h4>
<div class="highlight highlight-source-python"><pre><span class="pl-k">class</span> <span class="pl-en">Point</span>(<span class="pl-c1">object</span>):
<span class="pl-k">def</span> <span class="pl-c1">__init__</span>(<span class="pl-smi"><span class="pl-smi">self</span></span>, <span class="pl-smi">x</span>):
<span class="pl-v">self</span>.x <span class="pl-k">=</span> x
<span class="pl-k">def</span> <span class="pl-c1">__call__</span>(<span class="pl-smi"><span class="pl-smi">self</span></span>):
<span class="pl-c1">print</span> <span class="pl-v">self</span>.x
x <span class="pl-k">=</span> Point(<span class="pl-c1">3</span>)</pre></div>
<h4>
<a id="generators" class="anchor" href="#generators" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Generators</h4>
<div class="highlight highlight-source-python"><pre><span class="pl-k">def</span> <span class="pl-en">firstn</span>(<span class="pl-smi">n</span>):
num <span class="pl-k">=</span> <span class="pl-c1">0</span>
<span class="pl-k">while</span> num <span class="pl-k"><</span> n:
<span class="pl-k">yield</span> num
num <span class="pl-k">+=</span> <span class="pl-c1">1</span>
x <span class="pl-k">=</span> [<span class="pl-k">for</span> i <span class="pl-k">in</span> firstn(<span class="pl-c1">10</span>)]</pre></div>
<h4>
<a id="decorators" class="anchor" href="#decorators" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Decorators</h4>
<div class="highlight highlight-source-python"><pre><span class="pl-k">class</span> <span class="pl-en">myDecorator</span>(<span class="pl-c1">object</span>):
<span class="pl-k">def</span> <span class="pl-c1">__init__</span>(<span class="pl-smi"><span class="pl-smi">self</span></span>, <span class="pl-smi">f</span>):
<span class="pl-v">self</span>.f <span class="pl-k">=</span> f
<span class="pl-k">def</span> <span class="pl-c1">__call__</span>(<span class="pl-smi"><span class="pl-smi">self</span></span>):
<span class="pl-c1">print</span> <span class="pl-s"><span class="pl-pds">"</span>call<span class="pl-pds">"</span></span>
<span class="pl-v">self</span>.f()
<span class="pl-en">@myDecorator</span>
<span class="pl-k">def</span> <span class="pl-en">my_funct</span>():
<span class="pl-c1">print</span> <span class="pl-s"><span class="pl-pds">'</span>func<span class="pl-pds">'</span></span>
my_func()</pre></div>
</div>
<div class="group">
<h2>
<a id="numpy" class="anchor" href="#numpy" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>NumPy</h2>
<h3>
<a id="array-initialization" class="anchor" href="#array-initialization" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>array initialization</h3>
<div class="highlight highlight-source-python"><pre>np.array([<span class="pl-c1">2</span>, <span class="pl-c1">3</span>, <span class="pl-c1">4</span>]) <span class="pl-c"># direct initialization</span>
np.empty(<span class="pl-c1">20</span>, <span class="pl-v">dtype</span><span class="pl-k">=</span>np.float32) <span class="pl-c"># single precision array with 20 entries</span>
np.zeros(<span class="pl-c1">200</span>) <span class="pl-c"># initialize 200 zeros</span>
np.ones((<span class="pl-c1">3</span>,<span class="pl-c1">3</span>), <span class="pl-v">dtype</span><span class="pl-k">=</span>np.int32) <span class="pl-c"># 3 x 3 integer matrix with ones</span>
np.eye(<span class="pl-c1">200</span>) <span class="pl-c"># ones on the diagonal</span>
np.zeros_like(a) <span class="pl-c"># returns array with zeros and the shape of a</span>
np.linspace(<span class="pl-c1">0</span>., <span class="pl-c1">10</span>., <span class="pl-c1">100</span>) <span class="pl-c"># 100 points from 0 to 10</span>
np.arange(<span class="pl-c1">0</span>, <span class="pl-c1">100</span>, <span class="pl-c1">2</span>) <span class="pl-c"># points from 0 to <100 with step width 2</span>
np.logspace(<span class="pl-k">-</span><span class="pl-c1">5</span>, <span class="pl-c1">2</span>, <span class="pl-c1">100</span>) <span class="pl-c"># 100 log-spaced points between 1e-5 and 1e2</span>
np.copy(a) <span class="pl-c"># copy array to new memory</span></pre></div>
<h3>
<a id="reading-writing-files" class="anchor" href="#reading-writing-files" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>reading/ writing files</h3>
<div class="highlight highlight-source-python"><pre>np.fromfile(fname<span class="pl-k">/</span><span class="pl-c1">object</span>, <span class="pl-v">dtype</span><span class="pl-k">=</span>np.float32, <span class="pl-v">count</span><span class="pl-k">=</span><span class="pl-c1">5</span>) <span class="pl-c"># read binary data from file</span>
np.loadtxt(fname<span class="pl-k">/</span><span class="pl-c1">object</span>, <span class="pl-v">skiprows</span><span class="pl-k">=</span><span class="pl-c1">2</span>, <span class="pl-v">delimiter</span><span class="pl-k">=</span><span class="pl-s"><span class="pl-pds">'</span>,<span class="pl-pds">'</span></span>) <span class="pl-c"># read ascii data from file</span></pre></div>
<h3>
<a id="array-properties-and-operations" class="anchor" href="#array-properties-and-operations" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>array properties and operations</h3>
<div class="highlight highlight-source-python"><pre>a.shape <span class="pl-c"># a tuple with the lengths of each axis</span>
<span class="pl-c1">len</span>(a) <span class="pl-c"># length of axis 0</span>
a.ndim <span class="pl-c"># number of dimensions (axes)</span>
a.sort(<span class="pl-v">axis</span><span class="pl-k">=</span><span class="pl-c1">1</span>) <span class="pl-c"># sort array along axis</span>
a.flatten() <span class="pl-c"># collapse array to one dimension</span>
a.conj() <span class="pl-c"># return complex conjugate</span>
a.astype(np.int16) <span class="pl-c"># cast to integer</span>
np.argmax(a, <span class="pl-v">axis</span><span class="pl-k">=</span><span class="pl-c1">2</span>) <span class="pl-c"># return index of maximum along a given axis</span>
np.cumsum(a) <span class="pl-c"># return cumulative sum</span>
np.any(a) <span class="pl-c"># True if any element is True</span>
np.all(a) <span class="pl-c"># True if all elements are True</span>
np.argsort(a, <span class="pl-v">axis</span><span class="pl-k">=</span><span class="pl-c1">1</span>) <span class="pl-c"># return sorted index array along axis</span></pre></div>
<h3>
<a id="indexing" class="anchor" href="#indexing" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>indexing</h3>
<div class="highlight highlight-source-python"><pre>a <span class="pl-k">=</span> np.arange(<span class="pl-c1">100</span>) <span class="pl-c"># initialization with 0 - 99</span>
a[: <span class="pl-c1">3</span>] <span class="pl-k">=</span> <span class="pl-c1">0</span> <span class="pl-c"># set the first three indices to zero</span>
a[<span class="pl-c1">1</span>: <span class="pl-c1">5</span>] <span class="pl-k">=</span> <span class="pl-c1">1</span> <span class="pl-c"># set indices 1-4 to 1</span>
a[start:stop:step] <span class="pl-c"># general form of indexing/slicing</span>
a[<span class="pl-c1">None</span>, :] <span class="pl-c"># transform to column vector</span>
a[[<span class="pl-c1">1</span>, <span class="pl-c1">1</span>, <span class="pl-c1">3</span>, <span class="pl-c1">8</span>]] <span class="pl-c"># return array with values of the indices</span>
a <span class="pl-k">=</span> a.reshape(<span class="pl-c1">10</span>, <span class="pl-c1">10</span>) <span class="pl-c"># transform to 10 x 10 matrix</span>
a.<span class="pl-c1">T</span> <span class="pl-c"># return transposed view</span>
np.transpose(a, (<span class="pl-c1">2</span>, <span class="pl-c1">1</span>, <span class="pl-c1">0</span>)) <span class="pl-c"># transpose array to new axis order</span>
a[a <span class="pl-k"><</span> <span class="pl-c1">2</span>] <span class="pl-c"># returns array that fulfills elementwise condition</span></pre></div>
<h3>
<a id="boolean-arrays" class="anchor" href="#boolean-arrays" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>boolean arrays</h3>
<div class="highlight highlight-source-python"><pre>a <span class="pl-k"><</span> <span class="pl-c1">2</span> <span class="pl-c"># returns array with boolean values</span>
np.logical_and(a <span class="pl-k"><</span> <span class="pl-c1">2</span>, b <span class="pl-k">></span> <span class="pl-c1">10</span>) <span class="pl-c"># elementwise logical and</span>
np.logical_or(a <span class="pl-k"><</span> <span class="pl-c1">2</span>, b <span class="pl-k">></span> <span class="pl-c1">10</span>) <span class="pl-c"># elementwise logical or</span>
<span class="pl-k">~</span>a <span class="pl-c"># invert boolean array</span>
np.invert(a) <span class="pl-c"># invert boolean array</span></pre></div>
<h3>
<a id="elementwise-operations-and-math-functions" class="anchor" href="#elementwise-operations-and-math-functions" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>elementwise operations and math functions</h3>
<div class="highlight highlight-source-python"><pre>a <span class="pl-k">*</span> <span class="pl-c1">5</span> <span class="pl-c"># multiplication with scalar</span>
a <span class="pl-k">+</span> <span class="pl-c1">5</span> <span class="pl-c"># addition with scalar</span>
a <span class="pl-k">+</span> b <span class="pl-c"># addition with array b</span>
a <span class="pl-k">/</span> b <span class="pl-c"># division with b (np.NaN for division by zero)</span>
np.exp(a) <span class="pl-c"># exponential (complex and real)</span>
np.sin(a) <span class="pl-c"># sine</span>
np.cos(a) <span class="pl-c"># cosine</span>
np.arctan2(y,x) <span class="pl-c"># arctan(y/x)</span>
np.arcsin(x) <span class="pl-c"># arcsin</span>
np.radians(a) <span class="pl-c"># degrees to radians</span>
np.degrees(a) <span class="pl-c"># radians to degrees</span>
np.var(a) <span class="pl-c"># variance of array</span>
np.std(a, <span class="pl-v">axis</span><span class="pl-k">=</span><span class="pl-c1">1</span>) <span class="pl-c"># standard deviation</span></pre></div>
<h3>
<a id="inner--outer-products" class="anchor" href="#inner--outer-products" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>inner / outer products</h3>
<div class="highlight highlight-source-python"><pre>np.dot(a, b) <span class="pl-c"># inner matrix product: a_mi b_in</span>
np.einsum(<span class="pl-s"><span class="pl-pds">'</span>ijkl,klmn->ijmn<span class="pl-pds">'</span></span>, a, b) <span class="pl-c"># einstein summation convention</span>
np.sum(a, <span class="pl-v">axis</span><span class="pl-k">=</span><span class="pl-c1">1</span>) <span class="pl-c"># sum over axis 1</span>
np.abs(a) <span class="pl-c"># return array with absolute values</span>
a[<span class="pl-c1">None</span>, :] <span class="pl-k">+</span> b[:, <span class="pl-c1">None</span>] <span class="pl-c"># outer sum</span>
a[<span class="pl-c1">None</span>, :] <span class="pl-k">*</span> b[<span class="pl-c1">None</span>, :] <span class="pl-c"># outer product</span>
np.outer(a, b) <span class="pl-c"># outer product</span>
np.sum(a <span class="pl-k">*</span> a.<span class="pl-c1">T</span>) <span class="pl-c"># matrix norm</span></pre></div>
<h3>
<a id="interpolation-integration" class="anchor" href="#interpolation-integration" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>interpolation, integration</h3>
<div class="highlight highlight-source-python"><pre>np.trapz(y, <span class="pl-v">x</span><span class="pl-k">=</span>x, <span class="pl-v">axis</span><span class="pl-k">=</span><span class="pl-c1">1</span>) <span class="pl-c"># integrate along axis 1</span>
np.interp(x, xp, yp) <span class="pl-c"># interpolate function xp, yp at points x</span></pre></div>
<h3>
<a id="fft" class="anchor" href="#fft" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>fft</h3>
<div class="highlight highlight-source-python"><pre>np.fft.fft(y) <span class="pl-c"># complex fourier transform of y</span>
np.fft.fftfreqs(<span class="pl-c1">len</span>(y)) <span class="pl-c"># fft frequencies for a given length</span>
np.fft.fftshift(freqs) <span class="pl-c"># shifts zero frequency to the middle</span>
np.fft.rfft(y) <span class="pl-c"># real fourier transform of y</span>
np.fft.rfftfreqs(<span class="pl-c1">len</span>(y)) <span class="pl-c"># real fft frequencies for a given length</span></pre></div>
<h3>
<a id="rounding" class="anchor" href="#rounding" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>rounding</h3>
<div class="highlight highlight-source-python"><pre>np.ceil(a) <span class="pl-c"># rounds to nearest upper int</span>
np.floor(a) <span class="pl-c"># rounds to nearest lower int</span>
np.round(a) <span class="pl-c"># rounds to neares int</span></pre></div>
<h3>
<a id="random-variables" class="anchor" href="#random-variables" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>random variables</h3>
<div class="highlight highlight-source-python"><pre>np.random.normal(<span class="pl-v">loc</span><span class="pl-k">=</span><span class="pl-c1">0</span>, <span class="pl-v">scale</span><span class="pl-k">=</span><span class="pl-c1">2</span>, <span class="pl-v">size</span><span class="pl-k">=</span><span class="pl-c1">100</span>) <span class="pl-c"># 100 normal distributed random numbers</span>
np.random.seed(<span class="pl-c1">23032</span>) <span class="pl-c"># resets the seed value</span>
np.random.rand(<span class="pl-c1">200</span>) <span class="pl-c"># 200 random numbers in [0, 1)</span>
np.random.uniform(<span class="pl-c1">1</span>, <span class="pl-c1">30</span>, <span class="pl-c1">200</span>) <span class="pl-c"># 200 random numbers in [1, 30)</span>
np.random.random_integers(<span class="pl-c1">1</span>, <span class="pl-c1">15</span>, <span class="pl-c1">300</span>) <span class="pl-c"># 300 random integers between [1, 15]</span></pre></div>
</div>
<div class="group">
<h2>
<a id="matplotlib" class="anchor" href="#matplotlib" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Matplotlib</h2>
<h3>
<a id="figures-and-axes" class="anchor" href="#figures-and-axes" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>figures and axes</h3>
<div class="highlight highlight-source-python"><pre>fig <span class="pl-k">=</span> plt.figure(<span class="pl-v">figsize</span><span class="pl-k">=</span>(<span class="pl-c1">5</span>, <span class="pl-c1">2</span>), <span class="pl-v">facecolor</span><span class="pl-k">=</span><span class="pl-s"><span class="pl-pds">'</span>black<span class="pl-pds">'</span></span>) <span class="pl-c"># initialize figure</span>
ax <span class="pl-k">=</span> fig.add_subplot(<span class="pl-c1">3</span>, <span class="pl-c1">2</span>, <span class="pl-c1">2</span>) <span class="pl-c"># add second subplot in a 3 x 2 grid</span>
fig, axes <span class="pl-k">=</span> plt.subplots(<span class="pl-c1">5</span>, <span class="pl-c1">2</span>, <span class="pl-v">figsize</span><span class="pl-k">=</span>(<span class="pl-c1">5</span>, <span class="pl-c1">5</span>)) <span class="pl-c"># return fig and array of axes in a 5 x 2 grid</span>
ax <span class="pl-k">=</span> fig.add_axes([left, bottom, width, height]) <span class="pl-c"># manually add axes at a certain position</span></pre></div>
<h3>
<a id="figures-and-axes-properties" class="anchor" href="#figures-and-axes-properties" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>figures and axes properties</h3>
<div class="highlight highlight-source-python"><pre>fig.suptitle(<span class="pl-s"><span class="pl-pds">'</span>title<span class="pl-pds">'</span></span>) <span class="pl-c"># big figure title</span>
fig.subplots_adjust(<span class="pl-v">bottom</span><span class="pl-k">=</span><span class="pl-c1">0.1</span>, <span class="pl-v">right</span><span class="pl-k">=</span><span class="pl-c1">0.8</span>, <span class="pl-v">top</span><span class="pl-k">=</span><span class="pl-c1">0.9</span>, <span class="pl-v">wspace</span><span class="pl-k">=</span><span class="pl-c1">0.2</span>,
<span class="pl-v">hspace</span><span class="pl-k">=</span><span class="pl-c1">0.5</span>) <span class="pl-c"># adjust subplot positions</span>
fig.tight_layout(<span class="pl-v">pad</span><span class="pl-k">=</span><span class="pl-c1">0.1</span>,<span class="pl-v">h_pad</span><span class="pl-k">=</span><span class="pl-c1">0.5</span>, <span class="pl-v">w_pad</span><span class="pl-k">=</span><span class="pl-c1">0.5</span>, <span class="pl-v">rect</span><span class="pl-k">=</span><span class="pl-c1">None</span>) <span class="pl-c"># adjust</span>
subplots to fit perfectly into fig
ax.set_xlabel() <span class="pl-c"># set xlabel</span>
ax.set_ylabel() <span class="pl-c"># set ylabel</span>
ax.set_xlim(<span class="pl-c1">1</span>, <span class="pl-c1">2</span>) <span class="pl-c"># sets x limits</span>
ax.set_ylim(<span class="pl-c1">3</span>, <span class="pl-c1">4</span>) <span class="pl-c"># sets y limits</span>
ax.set_title(<span class="pl-s"><span class="pl-pds">'</span>blabla<span class="pl-pds">'</span></span>) <span class="pl-c"># sets the axis title</span>
ax.set(<span class="pl-v">xlabel</span><span class="pl-k">=</span><span class="pl-s"><span class="pl-pds">'</span>bla<span class="pl-pds">'</span></span>) <span class="pl-c"># set multiple parameters at once</span>
ax.legend(<span class="pl-v">loc</span><span class="pl-k">=</span><span class="pl-s"><span class="pl-pds">'</span>upper center<span class="pl-pds">'</span></span>) <span class="pl-c"># activate legend</span>
ax.grid(<span class="pl-c1">True</span>, <span class="pl-v">which</span><span class="pl-k">=</span><span class="pl-s"><span class="pl-pds">'</span>both<span class="pl-pds">'</span></span>) <span class="pl-c"># activate grid</span>
bbox <span class="pl-k">=</span> ax.get_position() <span class="pl-c"># returns the axes bounding box</span>
bbox.x0 <span class="pl-k">+</span> bbox.width <span class="pl-c"># bounding box parameters</span></pre></div>
<h3>
<a id="plotting-routines" class="anchor" href="#plotting-routines" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>plotting routines</h3>
<div class="highlight highlight-source-python"><pre>ax.plot(x,y, <span class="pl-s"><span class="pl-pds">'</span>-o<span class="pl-pds">'</span></span>, <span class="pl-v">c</span><span class="pl-k">=</span><span class="pl-s"><span class="pl-pds">'</span>red<span class="pl-pds">'</span></span>, <span class="pl-v">lw</span><span class="pl-k">=</span><span class="pl-c1">2</span>, <span class="pl-v">label</span><span class="pl-k">=</span><span class="pl-s"><span class="pl-pds">'</span>bla<span class="pl-pds">'</span></span>) <span class="pl-c"># plots a line</span>
ax.scatter(x,y, <span class="pl-v">s</span><span class="pl-k">=</span><span class="pl-c1">20</span>, <span class="pl-v">c</span><span class="pl-k">=</span>color) <span class="pl-c"># scatter plot</span>
ax.pcolormesh(xx,yy,zz, <span class="pl-v">shading</span><span class="pl-k">=</span><span class="pl-s"><span class="pl-pds">'</span>gouraud<span class="pl-pds">'</span></span>) <span class="pl-c"># fast colormesh function</span>
ax.colormesh(xx,yy,zz, <span class="pl-v">norm</span><span class="pl-k">=</span>norm) <span class="pl-c"># slower colormesh function</span>
ax.contour(xx,yy,zz, <span class="pl-v">cmap</span><span class="pl-k">=</span><span class="pl-s"><span class="pl-pds">'</span>jet<span class="pl-pds">'</span></span>) <span class="pl-c"># contour line plot</span>
ax.contourf(xx,yy,zz, <span class="pl-v">vmin</span><span class="pl-k">=</span><span class="pl-c1">2</span>, <span class="pl-v">vmax</span><span class="pl-k">=</span><span class="pl-c1">4</span>) <span class="pl-c"># filled contours plot</span>
n, bins, patch <span class="pl-k">=</span> ax.hist(x, <span class="pl-c1">50</span>) <span class="pl-c"># histogram</span>
ax.imshow(matrix, <span class="pl-v">origin</span><span class="pl-k">=</span><span class="pl-s"><span class="pl-pds">'</span>lower<span class="pl-pds">'</span></span>, <span class="pl-v">extent</span><span class="pl-k">=</span>(x1, x2, y1, y2)) <span class="pl-c"># show image</span>
ax.specgram(y, <span class="pl-v">FS</span><span class="pl-k">=</span><span class="pl-c1">0.1</span>, <span class="pl-v">noverlap</span><span class="pl-k">=</span><span class="pl-c1">128</span>, <span class="pl-v">scale</span><span class="pl-k">=</span><span class="pl-s"><span class="pl-pds">'</span>linear<span class="pl-pds">'</span></span>) <span class="pl-c"># plot a spectrogram</span></pre></div>
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