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PHY 546: Python for Scientific Computing
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#naming-conventions">Naming conventions</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-simple-class">A simple class</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#playing-cards">Playing Cards</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#operators">Operators</a></li>
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<section class="tex2jax_ignore mathjax_ignore" id="classes">
<h1>Classes<a class="headerlink" href="#classes" title="Link to this heading">#</a></h1>
<p>Classes are the fundamental concept for object oriented programming. A class defines a data type with both data and functions that can operate on the data. An object is an instance of a class. Each object will have its own namespace (separate from other instances of the class and other functions, etc. in your program).</p>
<p>We use the dot operator, <code class="docutils literal notranslate"><span class="pre">.</span></code>, to access members of the class (data or functions). We’ve already been doing this a lot, strings, ints, lists, … are all objects in python.</p>
<section id="naming-conventions">
<h2>Naming conventions<a class="headerlink" href="#naming-conventions" title="Link to this heading">#</a></h2>
<p>The python community has some naming convections, defined in PEP-8:</p>
<p><a class="reference external" href="https://www.python.org/dev/peps/pep-0008/">https://www.python.org/dev/peps/pep-0008/</a></p>
<p>The widely adopted ones are:</p>
<ul class="simple">
<li><p>class names start with an uppercase, and use “camelcase” for multiword names, e.g. <code class="docutils literal notranslate"><span class="pre">ShoppingCart</span></code></p></li>
<li><p>variable names (including objects which are instances of a class) are lowercase and use underscores to separate words, e.g., <code class="docutils literal notranslate"><span class="pre">shopping_cart</span></code></p></li>
<li><p>module names should be lowercase with underscores</p></li>
</ul>
</section>
<section id="a-simple-class">
<h2>A simple class<a class="headerlink" href="#a-simple-class" title="Link to this heading">#</a></h2>
<p>Here’s a class that holds some student info</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span><span class="w"> </span><span class="nc">Student</span><span class="p">:</span>
<span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">grade</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">=</span> <span class="n">name</span>
<span class="bp">self</span><span class="o">.</span><span class="n">grade</span> <span class="o">=</span> <span class="n">grade</span>
</pre></div>
</div>
</div>
</div>
<p>This has a function, <code class="docutils literal notranslate"><span class="pre">__init__()</span></code> which is called automatically when we create an instance of the class.</p>
<p>The argument <code class="docutils literal notranslate"><span class="pre">self</span></code> refers to the object that we will create, and points to the memory that they object will use to store the class’s contents.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">Student</span><span class="p">(</span><span class="s2">"Mike"</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">a</span><span class="o">.</span><span class="n">name</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">a</span><span class="o">.</span><span class="n">grade</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Mike
None
</pre></div>
</div>
</div>
</div>
<p>Let’s create a bunch of them, stored in a list</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">students</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">students</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Student</span><span class="p">(</span><span class="s2">"fry"</span><span class="p">,</span> <span class="s2">"F-"</span><span class="p">))</span>
<span class="n">students</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Student</span><span class="p">(</span><span class="s2">"leela"</span><span class="p">,</span> <span class="s2">"A"</span><span class="p">))</span>
<span class="n">students</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Student</span><span class="p">(</span><span class="s2">"zoidberg"</span><span class="p">,</span> <span class="s2">"F"</span><span class="p">))</span>
<span class="n">students</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Student</span><span class="p">(</span><span class="s2">"hubert"</span><span class="p">,</span> <span class="s2">"C+"</span><span class="p">))</span>
<span class="n">students</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Student</span><span class="p">(</span><span class="s2">"bender"</span><span class="p">,</span> <span class="s2">"B"</span><span class="p">))</span>
<span class="n">students</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Student</span><span class="p">(</span><span class="s2">"calculon"</span><span class="p">,</span> <span class="s2">"C"</span><span class="p">))</span>
<span class="n">students</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Student</span><span class="p">(</span><span class="s2">"amy"</span><span class="p">,</span> <span class="s2">"A"</span><span class="p">))</span>
<span class="n">students</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Student</span><span class="p">(</span><span class="s2">"hermes"</span><span class="p">,</span> <span class="s2">"A"</span><span class="p">))</span>
<span class="n">students</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Student</span><span class="p">(</span><span class="s2">"scruffy"</span><span class="p">,</span> <span class="s2">"D"</span><span class="p">))</span>
<span class="n">students</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Student</span><span class="p">(</span><span class="s2">"flexo"</span><span class="p">,</span> <span class="s2">"F"</span><span class="p">))</span>
<span class="n">students</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Student</span><span class="p">(</span><span class="s2">"morbo"</span><span class="p">,</span> <span class="s2">"D"</span><span class="p">))</span>
<span class="n">students</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Student</span><span class="p">(</span><span class="s2">"hypnotoad"</span><span class="p">,</span> <span class="s2">"A+"</span><span class="p">))</span>
<span class="n">students</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Student</span><span class="p">(</span><span class="s2">"zapp"</span><span class="p">,</span> <span class="s2">"Q"</span><span class="p">))</span>
</pre></div>
</div>
</div>
</div>
<div class="admonition-quick-exercise admonition">
<p class="admonition-title">Quick Exercise</p>
<p>Loop over the students in the <code class="docutils literal notranslate"><span class="pre">students</span></code> list and print out the name and grade of each student, one per line.</p>
</div>
<p>We can use list comprehensions with our list of objects. For example, let’s find all the students who have A’s</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">As</span> <span class="o">=</span> <span class="p">[</span><span class="n">q</span><span class="o">.</span><span class="n">name</span> <span class="k">for</span> <span class="n">q</span> <span class="ow">in</span> <span class="n">students</span> <span class="k">if</span> <span class="n">q</span><span class="o">.</span><span class="n">grade</span><span class="o">.</span><span class="n">startswith</span><span class="p">(</span><span class="s2">"A"</span><span class="p">)]</span>
<span class="n">As</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>['leela', 'amy', 'hermes', 'hypnotoad']
</pre></div>
</div>
</div>
</div>
</section>
<section id="playing-cards">
<h2>Playing Cards<a class="headerlink" href="#playing-cards" title="Link to this heading">#</a></h2>
<p>Here’s a more complicated class that represents a playing card. Notice that we are using unicode to represent the suits.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span><span class="w"> </span><span class="nc">Card</span><span class="p">:</span>
<span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">suit</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">):</span>
<span class="k">if</span> <span class="n">suit</span> <span class="o"><</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">suit</span> <span class="o">></span> <span class="mi">4</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"invalid suit, setting to 1"</span><span class="p">)</span>
<span class="n">suit</span> <span class="o">=</span> <span class="mi">1</span>
<span class="bp">self</span><span class="o">.</span><span class="n">suit</span> <span class="o">=</span> <span class="n">suit</span>
<span class="bp">self</span><span class="o">.</span><span class="n">rank</span> <span class="o">=</span> <span class="n">rank</span>
<span class="k">def</span><span class="w"> </span><span class="nf">value</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="w"> </span><span class="sd">""" we want things order primarily by rank then suit """</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">suit</span> <span class="o">+</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">rank</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="mi">14</span>
<span class="c1"># we include this to allow for comparisons with < and > between cards </span>
<span class="k">def</span><span class="w"> </span><span class="fm">__lt__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">value</span><span class="p">()</span> <span class="o"><</span> <span class="n">other</span><span class="o">.</span><span class="n">value</span><span class="p">()</span>
<span class="k">def</span><span class="w"> </span><span class="fm">__eq__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">rank</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">rank</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">suit</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">suit</span>
<span class="k">def</span><span class="w"> </span><span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="fm">__str__</span><span class="p">()</span>
<span class="k">def</span><span class="w"> </span><span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="n">suits</span> <span class="o">=</span> <span class="p">[</span><span class="sa">u</span><span class="s2">"</span><span class="se">\u2660</span><span class="s2">"</span><span class="p">,</span> <span class="c1"># spade</span>
<span class="sa">u</span><span class="s2">"</span><span class="se">\u2665</span><span class="s2">"</span><span class="p">,</span> <span class="c1"># heart</span>
<span class="sa">u</span><span class="s2">"</span><span class="se">\u2666</span><span class="s2">"</span><span class="p">,</span> <span class="c1"># diamond</span>
<span class="sa">u</span><span class="s2">"</span><span class="se">\u2663</span><span class="s2">"</span><span class="p">]</span> <span class="c1"># club</span>
<span class="n">r</span> <span class="o">=</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">rank</span><span class="p">)</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">rank</span> <span class="o">==</span> <span class="mi">11</span><span class="p">:</span>
<span class="n">r</span> <span class="o">=</span> <span class="s2">"J"</span>
<span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">rank</span> <span class="o">==</span> <span class="mi">12</span><span class="p">:</span>
<span class="n">r</span> <span class="o">=</span> <span class="s2">"Q"</span>
<span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">rank</span> <span class="o">==</span> <span class="mi">13</span><span class="p">:</span>
<span class="n">r</span> <span class="o">=</span> <span class="s2">"K"</span>
<span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">rank</span> <span class="o">==</span> <span class="mi">14</span><span class="p">:</span>
<span class="n">r</span> <span class="o">=</span> <span class="s2">"A"</span>
<span class="k">return</span> <span class="n">r</span> <span class="o">+</span><span class="s1">':'</span><span class="o">+</span><span class="n">suits</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">suit</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
</pre></div>
</div>
</div>
</div>
<p>we can create a card easily.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">c1</span> <span class="o">=</span> <span class="n">Card</span><span class="p">()</span>
</pre></div>
</div>
</div>
</div>
<p>We can pass arguments to <code class="docutils literal notranslate"><span class="pre">__init__</span></code> in when we setup the class:</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">c2</span> <span class="o">=</span> <span class="n">Card</span><span class="p">(</span><span class="n">suit</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">rank</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<p>Once we have our object, we can access any of the functions in the class using the <code class="docutils literal notranslate"><span class="pre">dot</span></code> operator</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">c2</span><span class="o">.</span><span class="n">value</span><span class="p">()</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>16
</pre></div>
</div>
</div>
</div>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">c3</span> <span class="o">=</span> <span class="n">Card</span><span class="p">(</span><span class="n">suit</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">rank</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>invalid suit, setting to 1
</pre></div>
</div>
</div>
</div>
<p>The <code class="docutils literal notranslate"><span class="pre">__str__</span></code> method converts the object into a string that can be printed.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="n">c1</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">c2</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>2:♠
2:♥
</pre></div>
</div>
</div>
</div>
<p>the value method assigns a value to the object that can be used in comparisons, and the <code class="docutils literal notranslate"><span class="pre">__lt__</span></code> method is what does the actual comparing</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="n">c1</span> <span class="o">></span> <span class="n">c2</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">c1</span> <span class="o"><</span> <span class="n">c2</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>False
True
</pre></div>
</div>
</div>
</div>
<p>Note that not every operator is defined for our class, so, for instance, we cannot add two cards together:</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">c1</span> <span class="o">+</span> <span class="n">c2</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
<span class="ne">TypeError</span><span class="g g-Whitespace"> </span>Traceback (most recent call last)
<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">12</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
<span class="ne">----> </span><span class="mi">1</span> <span class="n">c1</span> <span class="o">+</span> <span class="n">c2</span>
<span class="ne">TypeError</span>: unsupported operand type(s) for +: 'Card' and 'Card'
</pre></div>
</div>
</div>
</div>
<div class="admonition-quick-exercise admonition">
<p class="admonition-title">Quick Exercise</p>
<ul class="simple">
<li><p>Create a “hand” corresponding to a straight (5 cards of any suite, but in sequence of rank)</p></li>
<li><p>Create another hand corresponding to a flush (5 cards all of the same suit, of any rank)</p></li>
<li><p>Finally create a hand with one of the cards duplicated—this should not be allowed in a standard deck of cards. How would you check for this?</p></li>
</ul>
</div>
</section>
<section id="operators">
<h2>Operators<a class="headerlink" href="#operators" title="Link to this heading">#</a></h2>
<p>We can define operations like <code class="docutils literal notranslate"><span class="pre">+</span></code> and <code class="docutils literal notranslate"><span class="pre">-</span></code> that work on our objects. Here’s a simple example of currency—we keep track of the country and the amount</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span><span class="w"> </span><span class="nc">Currency</span><span class="p">:</span>
<span class="w"> </span><span class="sd">""" a simple class to hold foreign currency """</span>
<span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">amount</span><span class="p">,</span> <span class="n">country</span><span class="o">=</span><span class="s2">"US"</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">amount</span> <span class="o">=</span> <span class="n">amount</span>
<span class="bp">self</span><span class="o">.</span><span class="n">country</span> <span class="o">=</span> <span class="n">country</span>
<span class="k">def</span><span class="w"> </span><span class="fm">__add__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
<span class="k">return</span> <span class="n">Currency</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">amount</span> <span class="o">+</span> <span class="n">other</span><span class="o">.</span><span class="n">amount</span><span class="p">,</span> <span class="n">country</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">country</span><span class="p">)</span>
<span class="k">def</span><span class="w"> </span><span class="fm">__sub__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
<span class="k">return</span> <span class="n">Currency</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">amount</span> <span class="o">-</span> <span class="n">other</span><span class="o">.</span><span class="n">amount</span><span class="p">,</span> <span class="n">country</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">country</span><span class="p">)</span>
<span class="k">def</span><span class="w"> </span><span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">return</span> <span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">amount</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">country</span><span class="si">}</span><span class="s2">"</span>
</pre></div>
</div>
</div>
</div>
<p>We can now create some monetary amounts for different countries</p>
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<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">d1</span> <span class="o">=</span> <span class="n">Currency</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="s2">"US"</span><span class="p">)</span>
<span class="n">d2</span> <span class="o">=</span> <span class="n">Currency</span><span class="p">(</span><span class="mi">15</span><span class="p">,</span> <span class="s2">"US"</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">d2</span> <span class="o">-</span> <span class="n">d1</span><span class="p">)</span>
</pre></div>
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</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>5 US
</pre></div>
</div>
</div>
</div>
<div class="admonition-quick-exercise admonition">
<p class="admonition-title">Quick Exercise</p>
<p>As written, our Currency class has a bug—it does not check whether the amounts are in the same country before adding. Modify the <code class="docutils literal notranslate"><span class="pre">__add__</span></code> method to first check if the countries are the same. If they are, return the new <code class="docutils literal notranslate"><span class="pre">Currency</span></code> object with the sum, otherwise, return <code class="docutils literal notranslate"><span class="pre">None</span></code>.</p>
</div>
</section>
<section id="vectors-example">
<h2><span class="fa fa-star"></span> Vectors Example<a class="headerlink" href="#vectors-example" title="Link to this heading">#</a></h2>
<p>Here we write a class to represent 2-d vectors. Vectors have a direction and a magnitude. We can represent them as a pair of numbers, representing the x and y lengths. We’ll use a tuple internally for this</p>
<p>We want our class to do all the basic operations we do with vectors: add them, multiply by a scalar, cross product, dot product, return the magnitude, etc.</p>
<p>We’ll use the math module to provide some basic functions we might need (like sqrt)</p>
<p>This example will show us how to overload the standard operations in python. Here’s a list of the builtin methods:</p>
<p><a class="reference external" href="https://docs.python.org/3/reference/datamodel.html">https://docs.python.org/3/reference/datamodel.html</a></p>
<p>To make it really clear what’s being called when, I’ve added prints in each of the functions</p>
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<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span><span class="w"> </span><span class="nn">math</span>
</pre></div>
</div>
</div>
</div>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span><span class="w"> </span><span class="nc">Vector</span><span class="p">:</span>
<span class="w"> </span><span class="sd">""" a general two-dimensional vector """</span>
<span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"in __init__"</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">x</span> <span class="o">=</span> <span class="n">x</span>
<span class="bp">self</span><span class="o">.</span><span class="n">y</span> <span class="o">=</span> <span class="n">y</span>
<span class="k">def</span><span class="w"> </span><span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"in __str__"</span><span class="p">)</span>
<span class="k">return</span> <span class="sa">f</span><span class="s2">"(</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="si">}</span><span class="s2"> î + </span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">y</span><span class="si">}</span><span class="s2"> ĵ)"</span>
<span class="k">def</span><span class="w"> </span><span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"in __repr__"</span><span class="p">)</span>
<span class="k">return</span> <span class="sa">f</span><span class="s2">"Vector(</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="si">}</span><span class="s2">, </span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">y</span><span class="si">}</span><span class="s2">)"</span>
<span class="k">def</span><span class="w"> </span><span class="fm">__add__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"in __add__"</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">Vector</span><span class="p">):</span>
<span class="k">return</span> <span class="n">Vector</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span> <span class="o">+</span> <span class="n">other</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">y</span> <span class="o">+</span> <span class="n">other</span><span class="o">.</span><span class="n">y</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># it doesn't make sense to add anything but two vectors</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"we don't know how to add a </span><span class="si">{</span><span class="nb">type</span><span class="p">(</span><span class="n">other</span><span class="p">)</span><span class="si">}</span><span class="s2"> to a Vector"</span><span class="p">)</span>
<span class="k">raise</span> <span class="ne">NotImplementedError</span>
<span class="k">def</span><span class="w"> </span><span class="fm">__sub__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"in __sub__"</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">Vector</span><span class="p">):</span>
<span class="k">return</span> <span class="n">Vector</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span> <span class="o">-</span> <span class="n">other</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">y</span> <span class="o">-</span> <span class="n">other</span><span class="o">.</span><span class="n">y</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># it doesn't make sense to add anything but two vectors</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"we don't know how to add a </span><span class="si">{</span><span class="nb">type</span><span class="p">(</span><span class="n">other</span><span class="p">)</span><span class="si">}</span><span class="s2"> to a Vector"</span><span class="p">)</span>
<span class="k">raise</span> <span class="ne">NotImplementedError</span>
<span class="k">def</span><span class="w"> </span><span class="fm">__mul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"in __mul__"</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="nb">int</span><span class="p">)</span> <span class="ow">or</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="nb">float</span><span class="p">):</span>
<span class="c1"># scalar multiplication changes the magnitude</span>
<span class="k">return</span> <span class="n">Vector</span><span class="p">(</span><span class="n">other</span><span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <span class="n">other</span><span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">y</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"we don't know how to multiply two Vectors"</span><span class="p">)</span>
<span class="k">raise</span> <span class="ne">NotImplementedError</span>
<span class="k">def</span><span class="w"> </span><span class="fm">__matmul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"in __matmul__"</span><span class="p">)</span>
<span class="c1"># a dot product</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">Vector</span><span class="p">):</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="o">*</span><span class="n">other</span><span class="o">.</span><span class="n">x</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">y</span><span class="o">*</span><span class="n">other</span><span class="o">.</span><span class="n">y</span>
<span class="k">else</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"matrix multiplication not defined"</span><span class="p">)</span>
<span class="k">raise</span> <span class="ne">NotImplementedError</span>
<span class="k">def</span><span class="w"> </span><span class="fm">__rmul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"in __rmul__"</span><span class="p">)</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="fm">__mul__</span><span class="p">(</span><span class="n">other</span><span class="p">)</span>
<span class="k">def</span><span class="w"> </span><span class="fm">__truediv__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"in __truediv__"</span><span class="p">)</span>
<span class="c1"># we only know how to multiply by a scalar</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="nb">int</span><span class="p">)</span> <span class="ow">or</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="nb">float</span><span class="p">):</span>
<span class="k">return</span> <span class="n">Vector</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="o">/</span><span class="n">other</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">y</span><span class="o">/</span><span class="n">other</span><span class="p">)</span>
<span class="k">def</span><span class="w"> </span><span class="fm">__abs__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"in __abs__"</span><span class="p">)</span>
<span class="k">return</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="bp">self</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="bp">self</span><span class="o">.</span><span class="n">y</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
<span class="k">def</span><span class="w"> </span><span class="fm">__neg__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"in __neg__"</span><span class="p">)</span>
<span class="k">return</span> <span class="n">Vector</span><span class="p">(</span><span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">y</span><span class="p">)</span>
<span class="k">def</span><span class="w"> </span><span class="nf">cross</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
<span class="c1"># a vector cross product -- we return the magnitude, since it will</span>
<span class="c1"># be in the z-direction, but we are only 2-d </span>
<span class="k">return</span> <span class="nb">abs</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="o">*</span><span class="n">other</span><span class="o">.</span><span class="n">y</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">y</span><span class="o">*</span><span class="n">other</span><span class="o">.</span><span class="n">x</span><span class="p">)</span>
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<p>This is a basic class that provides two methods <code class="docutils literal notranslate"><span class="pre">__str__</span></code> and <code class="docutils literal notranslate"><span class="pre">__repr__</span></code> to show a representation of it. There was some discussion of this on slack. These two functions provide a readable version of our object.</p>
<p>The convection is what <code class="docutils literal notranslate"><span class="pre">__str__</span></code> is human readable while <code class="docutils literal notranslate"><span class="pre">__repr__</span></code> should be a form that can be used to recreate the object (e.g., via <code class="docutils literal notranslate"><span class="pre">eval()</span></code>). See:</p>
<p><a class="reference external" href="http://stackoverflow.com/questions/1436703/difference-between-str-and-repr-in-python">http://stackoverflow.com/questions/1436703/difference-between-str-and-repr-in-python</a></p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">v</span> <span class="o">=</span> <span class="n">Vector</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="n">v</span>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>in __init__
in __repr__
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Vector(1, 2)
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>in __str__
(1 î + 2 ĵ)
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<p>Vectors have a length, and we’ll use the <code class="docutils literal notranslate"><span class="pre">abs()</span></code> builtin to provide the magnitude. For a vector:</p>
<div class="math notranslate nohighlight">
\[\vec{v} = \alpha \hat{i} + \beta \hat{j}\]</div>
<p>we have</p>
<div class="math notranslate nohighlight">
\[|\vec{v}| = \sqrt{\alpha^2 + \beta^2}\]</div>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="nb">abs</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>in __abs__
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>2.23606797749979
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<p>Let’s look at mathematical operations on vectors now. We want to be able to add and subtract two vectors as well as multiply and divide by a scalar.</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">u</span> <span class="o">=</span> <span class="n">Vector</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">5</span><span class="p">)</span>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>in __init__
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">w</span> <span class="o">=</span> <span class="n">u</span> <span class="o">+</span> <span class="n">v</span>
<span class="nb">print</span><span class="p">(</span><span class="n">w</span><span class="p">)</span>