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<div class="section" id="functions">
<h1>Functions<a class="headerlink" href="#functions" title="Permalink to this headline">¶</a></h1>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="o">%</span><span class="n">matplotlib</span> <span class="n">inline</span>
</pre></div>
</div>
<div class="section" id="what-s-wrong-with-this-code">
<h2>What’s wrong with this code?<a class="headerlink" href="#what-s-wrong-with-this-code" title="Permalink to this headline">¶</a></h2>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="n">max_iter</span> <span class="o">=</span> <span class="mi">100</span>
<span class="n">h</span><span class="p">,</span> <span class="n">w</span> <span class="o">=</span> <span class="mi">400</span><span class="p">,</span> <span class="mi">400</span>
<span class="n">img</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">h</span><span class="p">,</span> <span class="n">w</span><span class="p">))</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="s1">'int'</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">real</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mf">1.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="n">w</span><span class="p">)):</span>
<span class="k">for</span> <span class="n">j</span><span class="p">,</span> <span class="n">imag</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">h</span><span class="p">)):</span>
<span class="n">c</span> <span class="o">=</span> <span class="nb">complex</span><span class="p">(</span><span class="n">real</span><span class="p">,</span> <span class="n">imag</span><span class="p">)</span>
<span class="n">z</span> <span class="o">=</span> <span class="mi">0</span> <span class="o">+</span> <span class="mi">0</span><span class="n">j</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">max_iter</span><span class="p">):</span>
<span class="n">z</span> <span class="o">=</span> <span class="n">z</span><span class="o">*</span><span class="n">z</span> <span class="o">+</span> <span class="n">c</span>
<span class="k">if</span> <span class="nb">abs</span><span class="p">(</span><span class="n">z</span><span class="p">)</span> <span class="o">></span> <span class="mi">2</span><span class="p">:</span>
<span class="k">break</span>
<span class="n">img</span><span class="p">[</span><span class="n">j</span><span class="p">,</span> <span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">k</span>
<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">img</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">jet</span><span class="p">)</span>
<span class="k">pass</span>
</pre></div>
</div>
<img alt="_images/02_Functions_3_0.png" src="_images/02_Functions_3_0.png" />
<ul class="simple">
<li>hard to understand</li>
<li>uses global variables</li>
<li>not re-usable except by copy and paste</li>
</ul>
</div>
<div class="section" id="refactoring-to-use-functions">
<h2>Refactoring to use functions<a class="headerlink" href="#refactoring-to-use-functions" title="Permalink to this headline">¶</a></h2>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">mandel</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">z</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_iter</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">max_iter</span><span class="p">):</span>
<span class="n">z</span> <span class="o">=</span> <span class="n">z</span><span class="o">*</span><span class="n">z</span> <span class="o">+</span> <span class="n">c</span>
<span class="k">if</span> <span class="nb">abs</span><span class="p">(</span><span class="n">z</span><span class="p">)</span> <span class="o">></span> <span class="mi">2</span><span class="p">:</span>
<span class="k">return</span> <span class="n">k</span>
<span class="k">return</span> <span class="n">k</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">mandelbrot</span><span class="p">(</span><span class="n">w</span><span class="p">,</span> <span class="n">h</span><span class="p">,</span> <span class="n">xl</span><span class="o">=-</span><span class="mf">1.5</span><span class="p">,</span> <span class="n">xu</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">yl</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span> <span class="n">yu</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
<span class="n">img</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">h</span><span class="p">,</span> <span class="n">w</span><span class="p">))</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="s1">'int'</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">real</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">xl</span><span class="p">,</span> <span class="n">xu</span><span class="p">,</span> <span class="n">w</span><span class="p">)):</span>
<span class="k">for</span> <span class="n">j</span><span class="p">,</span> <span class="n">imag</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">yl</span><span class="p">,</span> <span class="n">yu</span><span class="p">,</span> <span class="n">h</span><span class="p">)):</span>
<span class="n">c</span> <span class="o">=</span> <span class="nb">complex</span><span class="p">(</span><span class="n">real</span><span class="p">,</span> <span class="n">imag</span><span class="p">)</span>
<span class="n">img</span><span class="p">[</span><span class="n">j</span><span class="p">,</span> <span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">mandel</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
<span class="k">return</span> <span class="n">img</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="n">img</span> <span class="o">=</span> <span class="n">mandelbrot</span><span class="p">(</span><span class="n">w</span><span class="o">=</span><span class="mi">400</span><span class="p">,</span> <span class="n">h</span><span class="o">=</span><span class="mi">400</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">img</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">jet</span><span class="p">)</span>
<span class="k">pass</span>
</pre></div>
</div>
<img alt="_images/02_Functions_8_0.png" src="_images/02_Functions_8_0.png" />
</div>
<div class="section" id="function-is-re-usable">
<h2>Function is re-usable<a class="headerlink" href="#function-is-re-usable" title="Permalink to this headline">¶</a></h2>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="n">img</span> <span class="o">=</span> <span class="n">mandelbrot</span><span class="p">(</span><span class="n">w</span><span class="o">=</span><span class="mi">400</span><span class="p">,</span> <span class="n">h</span><span class="o">=</span><span class="mi">400</span><span class="p">,</span> <span class="n">xl</span><span class="o">=-</span><span class="mf">0.75</span><span class="p">,</span> <span class="n">xu</span><span class="o">=-</span><span class="mf">0.73</span><span class="p">,</span> <span class="n">yl</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">yu</span><span class="o">=</span><span class="mf">0.12</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">img</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">jet</span><span class="p">)</span>
<span class="k">pass</span>
</pre></div>
</div>
<img alt="_images/02_Functions_10_0.png" src="_images/02_Functions_10_0.png" />
<div class="section" id="anonymous-functions-lambdas">
<h3>Anonymous functions (lambdas)<a class="headerlink" href="#anonymous-functions-lambdas" title="Permalink to this headline">¶</a></h3>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">square</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="k">return</span> <span class="n">x</span><span class="o">*</span><span class="n">x</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="n">square</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="mi">9</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="n">square2</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">x</span><span class="o">*</span><span class="n">x</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="n">square2</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="mi">9</span>
</pre></div>
</div>
</div>
<div class="section" id="first-class-functions">
<h3>First class functions<a class="headerlink" href="#first-class-functions" title="Permalink to this headline">¶</a></h3>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="c1"># functions can be treated the same way as (say) an integer</span>
</pre></div>
</div>
</div>
</div>
<div class="section" id="functions-can-be-passed-in-as-arguments">
<h2>Functions can be passed in as arguments<a class="headerlink" href="#functions-can-be-passed-in-as-arguments" title="Permalink to this headline">¶</a></h2>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">grad</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">h</span><span class="o">=</span><span class="mf">0.01</span><span class="p">):</span>
<span class="k">return</span> <span class="p">(</span><span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="o">+</span><span class="n">h</span><span class="p">)</span> <span class="o">-</span> <span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="o">-</span><span class="n">h</span><span class="p">))</span><span class="o">/</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">h</span><span class="p">)</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">f</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="k">return</span> <span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">5</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="mi">3</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="n">grad</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">f</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="mf">5.000000000000004</span>
</pre></div>
</div>
</div>
<div class="section" id="functions-can-also-be-returned-by-functions">
<h2>Functions can also be returned by functions<a class="headerlink" href="#functions-can-also-be-returned-by-functions" title="Permalink to this headline">¶</a></h2>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">time</span>
<span class="k">def</span> <span class="nf">timer</span><span class="p">(</span><span class="n">f</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">g</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
<span class="n">start</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">f</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="n">elapsed</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">start</span>
<span class="k">return</span> <span class="n">result</span><span class="p">,</span> <span class="n">elapsed</span>
<span class="k">return</span> <span class="n">g</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">f</span><span class="p">(</span><span class="n">n</span><span class="o">=</span><span class="mi">1000000</span><span class="p">):</span>
<span class="n">s</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">([</span><span class="n">x</span><span class="o">*</span><span class="n">x</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">)])</span>
<span class="k">return</span> <span class="n">s</span>
<span class="n">timed_func</span> <span class="o">=</span> <span class="n">timer</span><span class="p">(</span><span class="n">f</span><span class="p">)</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="n">timed_func</span><span class="p">()</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="p">(</span><span class="mi">333332833333500000</span><span class="p">,</span> <span class="mf">0.18930506706237793</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="section" id="decorators">
<h2>Decorators<a class="headerlink" href="#decorators" title="Permalink to this headline">¶</a></h2>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="nd">@timer</span>
<span class="k">def</span> <span class="nf">g</span><span class="p">(</span><span class="n">n</span><span class="o">=</span><span class="mi">1000000</span><span class="p">):</span>
<span class="n">s</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">([</span><span class="n">x</span><span class="o">*</span><span class="n">x</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">)])</span>
<span class="k">return</span> <span class="n">s</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="n">g</span><span class="p">()</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="p">(</span><span class="mi">333332833333500000</span><span class="p">,</span> <span class="mf">0.192213773727417</span><span class="p">)</span>
</pre></div>
</div>
<div class="section" id="map-filter-reduce">
<h3>Map, filter, reduce<a class="headerlink" href="#map-filter-reduce" title="Permalink to this headline">¶</a></h3>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="nb">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">x</span><span class="o">*</span><span class="n">x</span><span class="p">,</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">])</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="o"><</span><span class="nb">map</span> <span class="n">at</span> <span class="mh">0x10996d5c0</span><span class="o">></span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="nb">list</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">x</span><span class="o">*</span><span class="n">x</span><span class="p">,</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">]))</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="mi">16</span><span class="p">]</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="nb">list</span><span class="p">(</span><span class="nb">filter</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">x</span><span class="o">%</span><span class="mi">2</span><span class="o">==</span><span class="mi">0</span><span class="p">,</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">]))</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">]</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">functools</span> <span class="k">import</span> <span class="n">reduce</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="n">reduce</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">:</span> <span class="n">x</span><span class="o">*</span><span class="n">y</span><span class="p">,</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">],</span> <span class="mi">10</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="mi">240</span>
</pre></div>
</div>
</div>
<div class="section" id="list-comprehension">
<h3>List comprehension<a class="headerlink" href="#list-comprehension" title="Permalink to this headline">¶</a></h3>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">x</span><span class="o">*</span><span class="n">x</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">]]</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="mi">16</span><span class="p">]</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">x</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">]</span> <span class="k">if</span> <span class="n">x</span><span class="o">%</span><span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span><span class="p">]</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">]</span>
</pre></div>
</div>
</div>
<div class="section" id="set-and-dictionary-comprehension">
<h3>Set and dictionary comprehension<a class="headerlink" href="#set-and-dictionary-comprehension" title="Permalink to this headline">¶</a></h3>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">i</span><span class="o">%</span><span class="mi">3</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">)}</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="p">{</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">}</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="o">%</span><span class="mi">3</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">)}</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="p">{</span><span class="mi">0</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">4</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">6</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">7</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">8</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">9</span><span class="p">:</span> <span class="mi">0</span><span class="p">}</span>
</pre></div>
</div>
</div>
<div class="section" id="generator-expressions">
<h3>Generator expressions<a class="headerlink" href="#generator-expressions" title="Permalink to this headline">¶</a></h3>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">i</span><span class="o">**</span><span class="mi">2</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span><span class="mi">15</span><span class="p">))</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="o"><</span><span class="n">generator</span> <span class="nb">object</span> <span class="o"><</span><span class="n">genexpr</span><span class="o">></span> <span class="n">at</span> <span class="mh">0x109e5ca40</span><span class="o">></span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="p">(</span><span class="n">i</span><span class="o">**</span><span class="mi">2</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span><span class="mi">15</span><span class="p">)):</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="mi">100</span>
<span class="mi">121</span>
<span class="mi">144</span>
<span class="mi">169</span>
<span class="mi">196</span>
</pre></div>
</div>
<div class="section" id="id1">
<h4>Generator expressions<a class="headerlink" href="#id1" title="Permalink to this headline">¶</a></h4>
<p>Generator expressions return a potentially infinite stream, but one at a
time thus sparing memory. They are ubiquitous in Python 3, allowing us
to handle arbitrarily large data sets.</p>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="c1"># Note that count can generate an infinite stream</span>
<span class="k">def</span> <span class="nf">count</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
<span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
<span class="k">yield</span> <span class="n">i</span>
<span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="n">c</span> <span class="o">=</span> <span class="n">count</span><span class="p">()</span>
<span class="nb">next</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="mi">0</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="nb">next</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="mi">1</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="nb">next</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="mi">2</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="nb">list</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="s1">'abcde'</span><span class="p">,</span> <span class="n">count</span><span class="p">(</span><span class="mi">10</span><span class="p">)))</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="p">[(</span><span class="s1">'a'</span><span class="p">,</span> <span class="mi">10</span><span class="p">),</span> <span class="p">(</span><span class="s1">'b'</span><span class="p">,</span> <span class="mi">11</span><span class="p">),</span> <span class="p">(</span><span class="s1">'c'</span><span class="p">,</span> <span class="mi">12</span><span class="p">),</span> <span class="p">(</span><span class="s1">'d'</span><span class="p">,</span> <span class="mi">13</span><span class="p">),</span> <span class="p">(</span><span class="s1">'e'</span><span class="p">,</span> <span class="mi">14</span><span class="p">)]</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">count</span><span class="p">():</span>
<span class="nb">print</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<span class="k">if</span> <span class="n">i</span> <span class="o">>=</span> <span class="mi">10</span><span class="p">:</span>
<span class="k">break</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="mi">0</span>
<span class="mi">1</span>
<span class="mi">2</span>
<span class="mi">3</span>
<span class="mi">4</span>
<span class="mi">5</span>
<span class="mi">6</span>
<span class="mi">7</span>
<span class="mi">8</span>
<span class="mi">9</span>
<span class="mi">10</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">palindrome_numbers</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="k">yield from</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<span class="k">yield from</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="nb">list</span><span class="p">(</span><span class="n">palindrome_numbers</span><span class="p">(</span><span class="mi">5</span><span class="p">))</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
</pre></div>
</div>
</div>
</div>
<div class="section" id="itertools">
<h3>Itertools<a class="headerlink" href="#itertools" title="Permalink to this headline">¶</a></h3>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">itertools</span> <span class="k">as</span> <span class="nn">it</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">it</span><span class="o">.</span><span class="n">islice</span><span class="p">(</span><span class="n">count</span><span class="p">(),</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">10</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="mi">5</span>
<span class="mi">6</span>
<span class="mi">7</span>
<span class="mi">8</span>
<span class="mi">9</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">it</span><span class="o">.</span><span class="n">takewhile</span><span class="p">(</span><span class="k">lambda</span> <span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="o"><</span> <span class="mi">5</span><span class="p">,</span> <span class="n">count</span><span class="p">()):</span>
<span class="nb">print</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="mi">0</span>
<span class="mi">1</span>
<span class="mi">2</span>
<span class="mi">3</span>
<span class="mi">4</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">operator</span> <span class="k">as</span> <span class="nn">op</span>
<span class="p">[</span><span class="n">i</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">it</span><span class="o">.</span><span class="n">starmap</span><span class="p">(</span><span class="n">op</span><span class="o">.</span><span class="n">add</span><span class="p">,</span> <span class="p">[(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">)])]</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">7</span><span class="p">]</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="n">fruits</span> <span class="o">=</span> <span class="p">[</span><span class="s1">'appple'</span><span class="p">,</span> <span class="s1">'banana'</span><span class="p">,</span> <span class="s1">'cherry'</span><span class="p">,</span> <span class="s1">'durain'</span><span class="p">,</span> <span class="s1">'eggplant'</span><span class="p">,</span> <span class="s1">'fig'</span><span class="p">]</span>
<span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">group</span> <span class="ow">in</span> <span class="n">it</span><span class="o">.</span><span class="n">groupby</span><span class="p">(</span><span class="nb">sorted</span><span class="p">(</span><span class="n">fruits</span><span class="p">,</span> <span class="n">key</span><span class="o">=</span><span class="nb">len</span><span class="p">),</span> <span class="nb">len</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="nb">list</span><span class="p">(</span><span class="n">group</span><span class="p">))</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="mi">3</span> <span class="p">[</span><span class="s1">'fig'</span><span class="p">]</span>
<span class="mi">6</span> <span class="p">[</span><span class="s1">'appple'</span><span class="p">,</span> <span class="s1">'banana'</span><span class="p">,</span> <span class="s1">'cherry'</span><span class="p">,</span> <span class="s1">'durain'</span><span class="p">]</span>
<span class="mi">8</span> <span class="p">[</span><span class="s1">'eggplant'</span><span class="p">]</span>
</pre></div>
</div>
</div>
</div>
<div class="section" id="functools">
<h2>Functools<a class="headerlink" href="#functools" title="Permalink to this headline">¶</a></h2>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">functools</span> <span class="k">as</span> <span class="nn">fn</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="n">rng1</span> <span class="o">=</span> <span class="n">fn</span><span class="o">.</span><span class="n">partial</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="o">.</span><span class="mi">3</span><span class="p">)</span>
<span class="n">rng2</span> <span class="o">=</span> <span class="n">fn</span><span class="o">.</span><span class="n">partial</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="n">rng1</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">array</span><span class="p">([</span> <span class="mf">2.13849718</span><span class="p">,</span> <span class="mf">1.5807533</span> <span class="p">,</span> <span class="mf">1.92939089</span><span class="p">,</span> <span class="mf">2.32091577</span><span class="p">,</span> <span class="mf">1.75429334</span><span class="p">,</span>
<span class="mf">2.39892103</span><span class="p">,</span> <span class="mf">2.13631947</span><span class="p">,</span> <span class="mf">1.90810476</span><span class="p">,</span> <span class="mf">1.54398362</span><span class="p">,</span> <span class="mf">2.22273936</span><span class="p">])</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="n">rng2</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">array</span><span class="p">([</span> <span class="mf">9.46427924</span><span class="p">,</span> <span class="mf">10.75766948</span><span class="p">,</span> <span class="mf">9.79962611</span><span class="p">,</span> <span class="mf">10.46099347</span><span class="p">,</span>
<span class="mf">10.44005324</span><span class="p">,</span> <span class="mf">9.69270764</span><span class="p">,</span> <span class="mf">8.788236</span> <span class="p">,</span> <span class="mf">10.32903729</span><span class="p">,</span>
<span class="mf">8.98723117</span><span class="p">,</span> <span class="mf">9.97326292</span><span class="p">])</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="n">fn</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">op</span><span class="o">.</span><span class="n">add</span><span class="p">,</span> <span class="n">rng2</span><span class="p">(</span><span class="mi">10</span><span class="p">))</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="mf">95.284222396568097</span>
</pre></div>
</div>
<div class="section" id="modules">
<h3>Modules<a class="headerlink" href="#modules" title="Permalink to this headline">¶</a></h3>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pandas</span> <span class="k">import</span> <span class="n">DataFrame</span><span class="p">,</span> <span class="n">Series</span>
<span class="kn">import</span> <span class="nn">scipy.stats</span> <span class="k">as</span> <span class="nn">ss</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="n">DataFrame</span><span class="p">(</span><span class="n">ss</span><span class="o">.</span><span class="n">beta</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">5</span><span class="p">)</span><span class="o">.</span><span class="n">rvs</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">)),</span> <span class="n">columns</span><span class="o">=</span><span class="p">[</span><span class="s1">'a'</span><span class="p">,</span> <span class="s1">'b'</span><span class="p">,</span> <span class="s1">'c'</span><span class="p">,</span> <span class="s1">'d'</span><span class="p">])</span>
</pre></div>
</div>
<div>
<table border="1" class="dataframe">
<thead>
<tr style="text-align: right;">
<th></th>
<th>a</th>
<th>b</th>
<th>c</th>
<th>d</th>
</tr>
</thead>
<tbody>
<tr>
<th>0</th>
<td>0.128479</td>
<td>0.285557</td>
<td>0.380817</td>
<td>0.223367</td>
</tr>
<tr>
<th>1</th>
<td>0.391506</td>
<td>0.282001</td>
<td>0.231474</td>
<td>0.196180</td>
</tr>
<tr>
<th>2</th>
<td>0.567670</td>
<td>0.122379</td>
<td>0.278288</td>
<td>0.151692</td>
</tr>
</tbody>
</table>
</div></div>
</div>
<div class="section" id="where-does-python-search-for-modules">
<h2>Where does Python search for modules?<a class="headerlink" href="#where-does-python-search-for-modules" title="Permalink to this headline">¶</a></h2>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">sys</span>
<span class="n">sys</span><span class="o">.</span><span class="n">path</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">''</span><span class="p">,</span>
<span class="s1">'/Users/cliburn/anaconda2/envs/p3/lib/python3.5/site-packages/StreamLib-1.0.1-py3.5.egg'</span><span class="p">,</span>
<span class="s1">'/Users/cliburn/anaconda2/envs/p3/lib/python3.5/site-packages/julia-0.1.1-py3.5.egg'</span><span class="p">,</span>
<span class="s1">'/Users/cliburn/anaconda2/envs/p3/lib/python3.5/site-packages/pybind11-1.9.dev0-py3.5.egg'</span><span class="p">,</span>
<span class="s1">'/Users/cliburn/anaconda2/envs/p3/lib/python3.5/site-packages/scikits.odes-2.3.0.dev0-py3.5-macosx-10.6-x86_64.egg'</span><span class="p">,</span>
<span class="s1">'/Users/cliburn/anaconda2/envs/p3/lib/python3.5/site-packages/ReFlowRESTClient-0.4-py3.5.egg'</span><span class="p">,</span>
<span class="s1">'/Users/cliburn/spark/python'</span><span class="p">,</span>
<span class="s1">'/Users/cliburn/git-teach/sta-663-2017-public/notebook'</span><span class="p">,</span>
<span class="s1">'/Users/cliburn/anaconda2/envs/p3/lib/python35.zip'</span><span class="p">,</span>
<span class="s1">'/Users/cliburn/anaconda2/envs/p3/lib/python3.5'</span><span class="p">,</span>
<span class="s1">'/Users/cliburn/anaconda2/envs/p3/lib/python3.5/plat-darwin'</span><span class="p">,</span>
<span class="s1">'/Users/cliburn/anaconda2/envs/p3/lib/python3.5/lib-dynload'</span><span class="p">,</span>
<span class="s1">'/Users/cliburn/.local/lib/python3.5/site-packages'</span><span class="p">,</span>
<span class="s1">'/Users/cliburn/anaconda2/envs/p3/lib/python3.5/site-packages'</span><span class="p">,</span>
<span class="s1">'/Users/cliburn/anaconda2/envs/p3/lib/python3.5/site-packages/Sphinx-1.4.1-py3.5.egg'</span><span class="p">,</span>
<span class="s1">'/Users/cliburn/anaconda2/envs/p3/lib/python3.5/site-packages/aeosa'</span><span class="p">,</span>
<span class="s1">'/Users/cliburn/anaconda2/envs/p3/lib/python3.5/site-packages/IPython/extensions'</span><span class="p">,</span>
<span class="s1">'/Users/cliburn/.ipython'</span><span class="p">]</span>
</pre></div>
</div>
</div>
<div class="section" id="creating-your-own-module">
<h2>Creating your own module<a class="headerlink" href="#creating-your-own-module" title="Permalink to this headline">¶</a></h2>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="o">%%</span><span class="n">file</span> <span class="n">my_module</span><span class="o">.</span><span class="n">py</span>
<span class="n">PI</span> <span class="o">=</span> <span class="mf">3.14</span>
<span class="k">def</span> <span class="nf">my_f</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="k">return</span> <span class="n">PI</span><span class="o">*</span><span class="n">x</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">Overwriting</span> <span class="n">my_module</span><span class="o">.</span><span class="n">py</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">my_module</span> <span class="k">as</span> <span class="nn">mm</span>
<span class="n">mm</span><span class="o">.</span><span class="n">PI</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="mf">3.14</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="n">mm</span><span class="o">.</span><span class="n">my_f</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="mf">6.28</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">my_module</span> <span class="k">import</span> <span class="n">PI</span>
</pre></div>
</div>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="n">PI</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="mi">2</span>
</pre></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="mf">12.56</span>
</pre></div>
</div>
<p><strong>Note</strong>: Modules can also be nested within each other - e.g.
<code class="docutils literal"><span class="pre">numpy.random</span></code> to creaate a <em>package</em>. We will explore how to create
packages in a later session.</p>
</div>
</div>
</div>
</div>
</div>
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<h3><a href="index-2.html">Table Of Contents</a></h3>
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="00_Jupyter.html">Notes on using Jupyter</a></li>
<li class="toctree-l1"><a class="reference internal" href="01_Introduction_To_Python.html">Introduction to Python</a></li>
<li class="toctree-l1 current"><a class="current reference internal" href="#">Functions</a><ul>
<li class="toctree-l2"><a class="reference internal" href="#what-s-wrong-with-this-code">What’s wrong with this code?</a></li>
<li class="toctree-l2"><a class="reference internal" href="#refactoring-to-use-functions">Refactoring to use functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="#function-is-re-usable">Function is re-usable</a></li>
<li class="toctree-l2"><a class="reference internal" href="#functions-can-be-passed-in-as-arguments">Functions can be passed in as arguments</a></li>
<li class="toctree-l2"><a class="reference internal" href="#functions-can-also-be-returned-by-functions">Functions can also be returned by functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="#decorators">Decorators</a></li>
<li class="toctree-l2"><a class="reference internal" href="#functools">Functools</a></li>
<li class="toctree-l2"><a class="reference internal" href="#where-does-python-search-for-modules">Where does Python search for modules?</a></li>
<li class="toctree-l2"><a class="reference internal" href="#creating-your-own-module">Creating your own module</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="03_Classes.html">Classes</a></li>
<li class="toctree-l1"><a class="reference internal" href="04_Strings.html">Strings</a></li>
<li class="toctree-l1"><a class="reference internal" href="05_Numbers.html">Using <code class="docutils literal"><span class="pre">numpy</span></code></a></li>
<li class="toctree-l1"><a class="reference internal" href="06_Graphics.html">Graphics in Python</a></li>
<li class="toctree-l1"><a class="reference internal" href="07_Data.html">Data</a></li>
<li class="toctree-l1"><a class="reference internal" href="08_SQL.html">SQL</a></li>
<li class="toctree-l1"><a class="reference internal" href="09_Machine_Learning.html">Machine Learning with <code class="docutils literal"><span class="pre">sklearn</span></code></a></li>
<li class="toctree-l1"><a class="reference internal" href="10A_CodeOptimization.html">Code Optimization</a></li>
<li class="toctree-l1"><a class="reference internal" href="10B_Numba.html">Just-in-time compilation (JIT)</a></li>
<li class="toctree-l1"><a class="reference internal" href="10C_Cython.html">Cython</a></li>
<li class="toctree-l1"><a class="reference internal" href="11A_Parallel_Programming.html">Parallel Programming</a></li>
<li class="toctree-l1"><a class="reference internal" href="11B_Threads_Processses_Concurrency.html">Multi-Core Parallelism</a></li>
<li class="toctree-l1"><a class="reference internal" href="11C_IPyParallel.html">Using <code class="docutils literal"><span class="pre">ipyparallel</span></code></a></li>
<li class="toctree-l1"><a class="reference internal" href="12A_C%2b%2b.html">Using C++</a></li>
<li class="toctree-l1"><a class="reference internal" href="12B_C%2b%2b_Python_pybind11.html">Using <code class="docutils literal"><span class="pre">pybind11</span></code></a></li>
<li class="toctree-l1"><a class="reference internal" href="13A_LinearAlgebra1.html">Linear Algebra Review</a></li>
<li class="toctree-l1"><a class="reference internal" href="13A_LinearAlgebra1.html#linear-algebra-and-linear-systems">Linear Algebra and Linear Systems</a></li>
<li class="toctree-l1"><a class="reference internal" href="13B_LinearAlgebra2.html">Matrix Decompositions</a></li>
<li class="toctree-l1"><a class="reference internal" href="13C_LinearAlgebraExamples.html">Linear Algebra Examples</a></li>
<li class="toctree-l1"><a class="reference internal" href="13D_PCA.html">Applications of Linear Alebra: PCA</a></li>
<li class="toctree-l1"><a class="reference internal" href="13E_SparseMatrices.html">Sparse Matrices</a></li>
<li class="toctree-l1"><a class="reference internal" href="14A_Optimization_One_Dimension.html">Optimization and Root Finding</a></li>
<li class="toctree-l1"><a class="reference internal" href="14B_Multivariate_Optimization.html">Algorithms for Optimization and Root Finding for Multivariate Problems</a></li>
<li class="toctree-l1"><a class="reference internal" href="14C_Optimization_In_Python.html">Using optimization routines from <code class="docutils literal"><span class="pre">scipy</span></code> and <code class="docutils literal"><span class="pre">statsmodels</span></code></a></li>
<li class="toctree-l1"><a class="reference internal" href="15A_Random_Numbers.html">Random numbers and probability models</a></li>
<li class="toctree-l1"><a class="reference internal" href="15B_ResamplingAndSimulation.html">Resampling and Monte Carlo Simulations</a></li>
<li class="toctree-l1"><a class="reference internal" href="15C_MonteCarloIntegration.html">Numerical Evaluation of Integrals</a></li>
<li class="toctree-l1"><a class="reference internal" href="16_PGM.html">Probabilistic Graphical Models with <code class="docutils literal"><span class="pre">pgmpy</span></code></a></li>
<li class="toctree-l1"><a class="reference internal" href="17_Functional_Programming.html">Working with large data sets</a></li>
<li class="toctree-l1"><a class="reference internal" href="17A_Intermediate_Sized_Data.html">Biggish Data</a></li>
<li class="toctree-l1"><a class="reference internal" href="17B_Big_Data_Structures.html">Efficient storage of data in memory</a></li>
<li class="toctree-l1"><a class="reference internal" href="18A_Dask.html">Working with large data sets</a></li>
<li class="toctree-l1"><a class="reference internal" href="10B_Numba.html">Just-in-time compilation (JIT)</a></li>
<li class="toctree-l1"><a class="reference internal" href="18B_Spark.html">Using Spark</a></li>
<li class="toctree-l1"><a class="reference internal" href="18C_Efficiency_In_Spark.html">Using Spark Efficiently</a></li>
<li class="toctree-l1"><a class="reference internal" href="18D_Spark_MLib.html">Spark MLLib</a></li>
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