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                    PHY 546: Python for Scientific Computing
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  <section class="tex2jax_ignore mathjax_ignore" id="functions">
<h1>Functions<a class="headerlink" href="#functions" title="Link to this heading">#</a></h1>
<p>Functions are used to organize program flow, especially to allow us to easily do commonly needed tasks over and over again.  We’ve already used a lot of functions, such as those that work on lists (<code class="docutils literal notranslate"><span class="pre">append()</span></code> and <code class="docutils literal notranslate"><span class="pre">pop()</span></code>) or strings (like <code class="docutils literal notranslate"><span class="pre">replace()</span></code>).  Here we see how to write our own functions</p>
<p>A function takes arguments, listed in the <code class="docutils literal notranslate"><span class="pre">()</span></code> and returns a value.  Even if you don’t explicitly give a return value, one will be return (e.g., <code class="docutils literal notranslate"><span class="pre">None</span></code>).</p>
<p>Here’s a simple example of a function that takes a single argument, <code class="docutils literal notranslate"><span class="pre">i</span></code></p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">my_fun</span><span class="p">(</span><span class="n">i</span><span class="p">):</span>
    <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;in the function, i = </span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
</pre></div>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">my_fun</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
<span class="n">my_fun</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
</pre></div>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>in the function, i = 10
in the function, i = 5
</pre></div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Functions are one place where <em>scope</em> comes into play.  A function has its own <em>namespace</em>.  If a variable is not defined in that function, then it will look to the namespace from where it was called to see if that variable exists there.</p>
<p>However, you should avoid this as much as possible (variables that persist across namespaces are called global variables).</p>
<p>Functions always return a value—if one is not explicitly given, then they return <code class="docutils literal notranslate"><span class="pre">None</span></code>, otherwise, they can return values (even multiple values) of any type</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">my_fun</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
<span class="n">a</span>
</pre></div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>in the function, i = 10
</pre></div>
<p>Here’s a simple function that takes two numbers and returns their product.</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">multiply</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
    <span class="k">return</span> <span class="n">a</span><span class="o">*</span><span class="n">b</span>
<span class="n">c</span> <span class="o">=</span> <span class="n">multiply</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">c</span>
</pre></div>
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>12
</pre></div>
<div class="admonition-quick-exercise admonition">
<p class="admonition-title">Quick Exercise</p>
<p>Write a simple function that takes a sentence (as a string) and returns an integer equal to the length of the longest word in the sentence.  The <code class="docutils literal notranslate"><span class="pre">len()</span></code> function and the <code class="docutils literal notranslate"><span class="pre">.split()</span></code> methods will be useful here.</p>
<p><code class="docutils literal notranslate"><span class="pre">None</span></code> is a special quantity in python (analogous to <code class="docutils literal notranslate"><span class="pre">null</span></code> in some other languages).  We can test on <code class="docutils literal notranslate"><span class="pre">None</span></code>—the preferred manner is to use <code class="docutils literal notranslate"><span class="pre">is</span></code>:</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">do_nothing</span><span class="p">():</span>
    <span class="k">pass</span>
</pre></div>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">do_nothing</span><span class="p">()</span>
<span class="k">if</span> <span class="n">a</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
    <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;we didn&#39;t do anything&quot;</span><span class="p">)</span>
</pre></div>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>we didn&#39;t do anything
</pre></div>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="ow">is</span> <span class="kc">None</span>
</pre></div>
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>True
</pre></div>
<section id="keyword-arguments">
<h2>Keyword arguments<a class="headerlink" href="#keyword-arguments" title="Link to this heading">#</a></h2>
<p>You can have optional arguments which provide defaults.  Here’s a simple function that computes <span class="math notranslate nohighlight">\(\sin(\theta)\)</span> where <span class="math notranslate nohighlight">\(\theta\)</span> can optionally be in degrees.</p>
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<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>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">my_sin</span><span class="p">(</span><span class="n">theta</span><span class="p">,</span> <span class="n">in_degrees</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
    <span class="k">if</span> <span class="n">in_degrees</span><span class="p">:</span>
        <span class="k">return</span> <span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">radians</span><span class="p">(</span><span class="n">theta</span><span class="p">))</span>
    <span class="k">return</span> <span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
</pre></div>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">my_sin</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">4</span><span class="p">),</span> <span class="n">my_sin</span><span class="p">(</span><span class="mi">45</span><span class="p">,</span> <span class="n">in_degrees</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>                    
</pre></div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>(0.7071067811865475, 0.7071067811865475)
</pre></div>
<div class="admonition important">
<p class="admonition-title">Important</p>
<p>It is important to note that python evaluates the optional arguments once—when the function is defined.  This means that if you make the default an empty object, for instance, it will persist across all call.</p>
<p><strong>This leads to one of the most common errors for beginners</strong></p>
<p>Here’s an example of trying to initialize to an empty list:</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">f</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">L</span><span class="o">=</span><span class="p">[]):</span>
    <span class="n">L</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">L</span>
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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">f</span><span class="p">(</span><span class="mi">1</span><span class="p">))</span>
<span class="nb">print</span><span class="p">(</span><span class="n">f</span><span class="p">(</span><span class="mi">2</span><span class="p">))</span>
<span class="nb">print</span><span class="p">(</span><span class="n">f</span><span class="p">(</span><span class="mi">3</span><span class="p">))</span>
</pre></div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[1]
</pre></div>
<p>Notice that each call does not create its own separate list.  Instead a single empty list was created when the function was first processed, and this list persists in memory as the default value for the optional argument <code class="docutils literal notranslate"><span class="pre">L</span></code>.</p>
<p>If we want a unique list created each time (e.g., a separate place in memory), we instead initialize the argument’s value to <code class="docutils literal notranslate"><span class="pre">None</span></code> and then check its actual value and create an empty list in the function body itself if the default value was unchanged.</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">fnew</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">L</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
    <span class="k">if</span> <span class="n">L</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
        <span class="n">L</span> <span class="o">=</span> <span class="p">[]</span>
    <span class="n">L</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">L</span>
</pre></div>
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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">fnew</span><span class="p">(</span><span class="mi">1</span><span class="p">))</span>
<span class="nb">print</span><span class="p">(</span><span class="n">fnew</span><span class="p">(</span><span class="mi">2</span><span class="p">))</span>
<span class="nb">print</span><span class="p">(</span><span class="n">fnew</span><span class="p">(</span><span class="mi">3</span><span class="p">))</span>
</pre></div>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[1]
</pre></div>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">L</span> <span class="o">=</span> <span class="n">fnew</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">fnew</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="n">L</span><span class="o">=</span><span class="n">L</span><span class="p">))</span>
</pre></div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[1, 2]
</pre></div>
<p>Notice that the same <code class="docutils literal notranslate"><span class="pre">None</span></code> that we saw previously comes into play here.</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">L</span>
</pre></div>
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[1, 2]
</pre></div>
<section id="lambdas">
<h2>Lambdas<a class="headerlink" href="#lambdas" title="Link to this heading">#</a></h2>
<p>Lambdas are “disposible” functions.  These are small, nameless functions that are often used as arguments in other functions.</p>
<p>Ex, from the official tutorial: we have a list of tuples.  We want to sort the list based on the second item in the tuple.  The <code class="docutils literal notranslate"><span class="pre">sort</span></code> method can take a <code class="docutils literal notranslate"><span class="pre">key</span></code> optional argument that tells us how to interpret the list item for sorting</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">pairs</span> <span class="o">=</span> <span class="p">[(</span><span class="mi">1</span><span class="p">,</span> <span class="s1">&#39;one&#39;</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="s1">&#39;two&#39;</span><span class="p">),</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="s1">&#39;three&#39;</span><span class="p">),</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="s1">&#39;four&#39;</span><span class="p">)]</span>
<span class="n">pairs</span><span class="o">.</span><span class="n">sort</span><span class="p">(</span><span class="n">key</span><span class="o">=</span><span class="k">lambda</span> <span class="n">p</span><span class="p">:</span> <span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
</pre></div>
<div class="cell docutils container">
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">pairs</span>
</pre></div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[(4, &#39;four&#39;), (1, &#39;one&#39;), (3, &#39;three&#39;), (2, &#39;two&#39;)]
</pre></div>
<p>Here we use a lambda in an extract from a list (with the filter function)</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">squares</span> <span class="o">=</span> <span class="p">[</span><span class="n">x</span><span class="o">**</span><span class="mi">2</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="mi">100</span><span class="p">)]</span>
<span class="n">sq</span> <span class="o">=</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="k">2</span> == 0 and x%3 == 0, squares))
<span class="n">sq</span>
</pre></div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[0,
</pre></div>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">help</span><span class="p">(</span><span class="nb">filter</span><span class="p">)</span>
</pre></div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Help on class filter in module builtins:
class filter(object)
 |  filter(function, iterable, /)
 |  Return an iterator yielding those items of iterable for which function(item)
 |  is true. If function is None, return the items that are true.
 |  Methods defined here:
 |  __iter__(self, /)
 |      Implement iter(self).
 |  __next__(self, /)
 |      Implement next(self).
 |  __reduce__(self, /)
 |      Return state information for pickling.
 |  ----------------------------------------------------------------------
 |  Static methods defined here:
 |  __new__(*args, **kwargs)
 |      Create and return a new object.  See help(type) for accurate signature.
</pre></div>
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