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<title>
Additional Exercises – Programming with Python
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<div class="container">
<h1 class="maintitle">Analyzing Patient Data - Exercises</h1>
<article>
<blockquote class="challenge">
<h2 id="slicing-strings">Slicing Strings</h2>
<p>A section of an array is called a <a href="../reference.html#slice">slice</a>.
We can take slices of character strings as well:</p>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="n">element</span> <span class="o">=</span> <span class="s">'oxygen'</span>
<span class="k">print</span><span class="p">(</span><span class="s">'first three characters:'</span><span class="p">,</span> <span class="n">element</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">3</span><span class="p">])</span>
<span class="k">print</span><span class="p">(</span><span class="s">'last three characters:'</span><span class="p">,</span> <span class="n">element</span><span class="p">[</span><span class="mi">3</span><span class="p">:</span><span class="mi">6</span><span class="p">])</span>
</code></pre></div> </div>
<div class="language-plaintext output highlighter-rouge"><div class="highlight"><pre class="highlight"><code>first three characters: oxy
last three characters: gen
</code></pre></div> </div>
<p>What is the value of <code class="language-plaintext highlighter-rouge">element[:4]</code>?
What about <code class="language-plaintext highlighter-rouge">element[4:]</code>?
Or <code class="language-plaintext highlighter-rouge">element[:]</code>?</p>
<blockquote class="solution">
<h2 id="solution">Solution</h2>
<div class="language-plaintext output highlighter-rouge"><div class="highlight"><pre class="highlight"><code>oxyg
en
oxygen
</code></pre></div> </div>
</blockquote>
<p>What is <code class="language-plaintext highlighter-rouge">element[-1]</code>?
What is <code class="language-plaintext highlighter-rouge">element[-2]</code>?</p>
<blockquote class="solution">
<h2 id="solution-1">Solution</h2>
<div class="language-plaintext output highlighter-rouge"><div class="highlight"><pre class="highlight"><code>n
e
</code></pre></div> </div>
</blockquote>
<p>Given those answers,
explain what <code class="language-plaintext highlighter-rouge">element[1:-1]</code> does.</p>
<blockquote class="solution">
<h2 id="solution-2">Solution</h2>
<p>Creates a substring from index 1 up to (not including) the final index,
effectively removing the first and last letters from ‘oxygen’</p>
</blockquote>
<p>How can we rewrite the slice for getting the last three characters of <code class="language-plaintext highlighter-rouge">element</code>,
so that it works even if we assign a different string to <code class="language-plaintext highlighter-rouge">element</code>?
Test your solution with the following strings: <code class="language-plaintext highlighter-rouge">carpentry</code>, <code class="language-plaintext highlighter-rouge">clone</code>, <code class="language-plaintext highlighter-rouge">hi</code>.</p>
<blockquote class="solution">
<h2 id="solution-3">Solution</h2>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="n">element</span> <span class="o">=</span> <span class="s">'oxygen'</span>
<span class="k">print</span><span class="p">(</span><span class="s">'last three characters:'</span><span class="p">,</span> <span class="n">element</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">:])</span>
<span class="n">element</span> <span class="o">=</span> <span class="s">'carpentry'</span>
<span class="k">print</span><span class="p">(</span><span class="s">'last three characters:'</span><span class="p">,</span> <span class="n">element</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">:])</span>
<span class="n">element</span> <span class="o">=</span> <span class="s">'clone'</span>
<span class="k">print</span><span class="p">(</span><span class="s">'last three characters:'</span><span class="p">,</span> <span class="n">element</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">:])</span>
<span class="n">element</span> <span class="o">=</span> <span class="s">'hi'</span>
<span class="k">print</span><span class="p">(</span><span class="s">'last three characters:'</span><span class="p">,</span> <span class="n">element</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">:])</span>
</code></pre></div> </div>
<div class="language-plaintext output highlighter-rouge"><div class="highlight"><pre class="highlight"><code>last three characters: gen
last three characters: try
last three characters: one
last three characters: hi
</code></pre></div> </div>
</blockquote>
</blockquote>
<blockquote class="challenge">
<h2 id="thin-slices">Thin Slices</h2>
<p>The expression <code class="language-plaintext highlighter-rouge">element[3:3]</code> produces an <a href="../reference.html#empty-string">empty string</a>,
i.e., a string that contains no characters.
If <code class="language-plaintext highlighter-rouge">data</code> holds our array of patient data,
what does <code class="language-plaintext highlighter-rouge">data[3:3, 4:4]</code> produce?
What about <code class="language-plaintext highlighter-rouge">data[3:3, :]</code>?</p>
<blockquote class="solution">
<h2 id="solution-4">Solution</h2>
<div class="language-plaintext output highlighter-rouge"><div class="highlight"><pre class="highlight"><code>array([], shape=(0, 0), dtype=float64)
array([], shape=(0, 40), dtype=float64)
</code></pre></div> </div>
</blockquote>
</blockquote>
<blockquote class="challenge">
<h2 id="stacking-arrays">Stacking Arrays</h2>
<p>Arrays can be concatenated and stacked on top of one another,
using NumPy’s <code class="language-plaintext highlighter-rouge">vstack</code> and <code class="language-plaintext highlighter-rouge">hstack</code> functions for vertical and horizontal stacking, respectively.</p>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kn">import</span> <span class="nn">numpy</span>
<span class="n">A</span> <span class="o">=</span> <span class="n">numpy</span><span class="p">.</span><span class="n">array</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="p">[</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">6</span><span class="p">],</span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">]])</span>
<span class="k">print</span><span class="p">(</span><span class="s">'A = '</span><span class="p">)</span>
<span class="k">print</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
<span class="n">B</span> <span class="o">=</span> <span class="n">numpy</span><span class="p">.</span><span class="n">hstack</span><span class="p">([</span><span class="n">A</span><span class="p">,</span> <span class="n">A</span><span class="p">])</span>
<span class="k">print</span><span class="p">(</span><span class="s">'B = '</span><span class="p">)</span>
<span class="k">print</span><span class="p">(</span><span class="n">B</span><span class="p">)</span>
<span class="n">C</span> <span class="o">=</span> <span class="n">numpy</span><span class="p">.</span><span class="n">vstack</span><span class="p">([</span><span class="n">A</span><span class="p">,</span> <span class="n">A</span><span class="p">])</span>
<span class="k">print</span><span class="p">(</span><span class="s">'C = '</span><span class="p">)</span>
<span class="k">print</span><span class="p">(</span><span class="n">C</span><span class="p">)</span>
</code></pre></div> </div>
<div class="language-plaintext output highlighter-rouge"><div class="highlight"><pre class="highlight"><code>A =
[[1 2 3]
[4 5 6]
[7 8 9]]
B =
[[1 2 3 1 2 3]
[4 5 6 4 5 6]
[7 8 9 7 8 9]]
C =
[[1 2 3]
[4 5 6]
[7 8 9]
[1 2 3]
[4 5 6]
[7 8 9]]
</code></pre></div> </div>
<p>Write some additional code that slices the first and last columns of <code class="language-plaintext highlighter-rouge">A</code>,
and stacks them into a 3x2 array.
Make sure to <code class="language-plaintext highlighter-rouge">print</code> the results to verify your solution.</p>
<blockquote class="solution">
<h2 id="solution-5">Solution</h2>
<p>A ‘gotcha’ with array indexing is that singleton dimensions
are dropped by default. That means <code class="language-plaintext highlighter-rouge">A[:, 0]</code> is a one dimensional
array, which won’t stack as desired. To preserve singleton dimensions,
the index itself can be a slice or array. For example, <code class="language-plaintext highlighter-rouge">A[:, :1]</code> returns
a two dimensional array with one singleton dimension (i.e. a column
vector).</p>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="n">D</span> <span class="o">=</span> <span class="n">numpy</span><span class="p">.</span><span class="n">hstack</span><span class="p">((</span><span class="n">A</span><span class="p">[:,</span> <span class="p">:</span><span class="mi">1</span><span class="p">],</span> <span class="n">A</span><span class="p">[:,</span> <span class="o">-</span><span class="mi">1</span><span class="p">:]))</span>
<span class="k">print</span><span class="p">(</span><span class="s">'D = '</span><span class="p">)</span>
<span class="k">print</span><span class="p">(</span><span class="n">D</span><span class="p">)</span>
</code></pre></div> </div>
<div class="language-plaintext output highlighter-rouge"><div class="highlight"><pre class="highlight"><code>D =
[[1 3]
[4 6]
[7 9]]
</code></pre></div> </div>
</blockquote>
<blockquote class="solution">
<h2 id="solution-6">Solution</h2>
<p>An alternative way to achieve the same result is to use Numpy’s
delete function to remove the second column of A.</p>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="n">D</span> <span class="o">=</span> <span class="n">numpy</span><span class="p">.</span><span class="n">delete</span><span class="p">(</span><span class="n">A</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="k">print</span><span class="p">(</span><span class="s">'D = '</span><span class="p">)</span>
<span class="k">print</span><span class="p">(</span><span class="n">D</span><span class="p">)</span>
</code></pre></div> </div>
<div class="language-plaintext output highlighter-rouge"><div class="highlight"><pre class="highlight"><code>D =
[[1 3]
[4 6]
[7 9]]
</code></pre></div> </div>
</blockquote>
</blockquote>
<blockquote class="challenge">
<h2 id="change-in-inflammation">Change In Inflammation</h2>
<p>The patient data is <em>longitudinal</em> in the sense that each row represents a
series of observations relating to one individual. This means that
the change in inflammation over time is a meaningful concept.
Let’s find out how to calculate changes in the data contained in an array
with NumPy.</p>
<p>The <code class="language-plaintext highlighter-rouge">numpy.diff()</code> function takes an array and returns the differences
between two successive values. Let’s use it to examine the changes
each day across the first week of patient 3 from our inflammation dataset.</p>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="n">patient3_week1</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="p">:</span><span class="mi">7</span><span class="p">]</span>
<span class="k">print</span><span class="p">(</span><span class="n">patient3_week1</span><span class="p">)</span>
</code></pre></div> </div>
<div class="language-plaintext output highlighter-rouge"><div class="highlight"><pre class="highlight"><code> [0. 0. 2. 0. 4. 2. 2.]
</code></pre></div> </div>
<p>Calling <code class="language-plaintext highlighter-rouge">numpy.diff(patient3_week1)</code> would do the following calculations</p>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="p">[</span> <span class="mi">0</span> <span class="o">-</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span> <span class="o">-</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span> <span class="o">-</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">4</span> <span class="o">-</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span> <span class="o">-</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">2</span> <span class="o">-</span> <span class="mi">2</span> <span class="p">]</span>
</code></pre></div> </div>
<p>and return the 6 difference values in a new array.</p>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="n">numpy</span><span class="p">.</span><span class="n">diff</span><span class="p">(</span><span class="n">patient3_week1</span><span class="p">)</span>
</code></pre></div> </div>
<div class="language-plaintext output highlighter-rouge"><div class="highlight"><pre class="highlight"><code>array([ 0., 2., -2., 4., -2., 0.])
</code></pre></div> </div>
<p>Note that the array of differences is shorter by one element (length 6).</p>
<p>When calling <code class="language-plaintext highlighter-rouge">numpy.diff</code> with a multi-dimensional array, an <code class="language-plaintext highlighter-rouge">axis</code> argument may
be passed to the function to specify which axis to process. When applying
<code class="language-plaintext highlighter-rouge">numpy.diff</code> to our 2D inflammation array <code class="language-plaintext highlighter-rouge">data</code>, which axis would we specify?</p>
<blockquote class="solution">
<h2 id="solution-7">Solution</h2>
<p>Since the row axis (0) is patients, it does not make sense to get the
difference between two arbitrary patients. The column axis (1) is in
days, so the difference is the change in inflammation – a meaningful
concept.</p>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="n">numpy</span><span class="p">.</span><span class="n">diff</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
</code></pre></div> </div>
</blockquote>
<p>If the shape of an individual data file is <code class="language-plaintext highlighter-rouge">(60, 40)</code> (60 rows and 40
columns), what would the shape of the array be after you run the <code class="language-plaintext highlighter-rouge">diff()</code>
function and why?</p>
<blockquote class="solution">
<h2 id="solution-8">Solution</h2>
<p>The shape will be <code class="language-plaintext highlighter-rouge">(60, 39)</code> because there is one fewer difference between
columns than there are columns in the data.</p>
</blockquote>
<p>How would you find the largest change in inflammation for each patient? Does
it matter if the change in inflammation is an increase or a decrease?</p>
<blockquote class="solution">
<h2 id="solution-9">Solution</h2>
<p>By using the <code class="language-plaintext highlighter-rouge">numpy.max()</code> function after you apply the <code class="language-plaintext highlighter-rouge">numpy.diff()</code>
function, you will get the largest difference between days.</p>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="n">numpy</span><span class="p">.</span><span class="nb">max</span><span class="p">(</span><span class="n">numpy</span><span class="p">.</span><span class="n">diff</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">),</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
</code></pre></div> </div>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="n">array</span><span class="p">([</span> <span class="mf">7.</span><span class="p">,</span> <span class="mf">12.</span><span class="p">,</span> <span class="mf">11.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">11.</span><span class="p">,</span> <span class="mf">13.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">8.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">7.</span><span class="p">,</span>
<span class="mf">7.</span><span class="p">,</span> <span class="mf">13.</span><span class="p">,</span> <span class="mf">7.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">8.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">9.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">13.</span><span class="p">,</span> <span class="mf">7.</span><span class="p">,</span>
<span class="mf">12.</span><span class="p">,</span> <span class="mf">9.</span><span class="p">,</span> <span class="mf">12.</span><span class="p">,</span> <span class="mf">11.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">7.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">11.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">8.</span><span class="p">,</span>
<span class="mf">11.</span><span class="p">,</span> <span class="mf">12.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">9.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">13.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">7.</span><span class="p">,</span> <span class="mf">7.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">13.</span><span class="p">,</span>
<span class="mf">12.</span><span class="p">,</span> <span class="mf">8.</span><span class="p">,</span> <span class="mf">8.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">9.</span><span class="p">,</span> <span class="mf">8.</span><span class="p">,</span> <span class="mf">13.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">7.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span>
<span class="mf">8.</span><span class="p">,</span> <span class="mf">12.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">7.</span><span class="p">,</span> <span class="mf">12.</span><span class="p">])</span>
</code></pre></div> </div>
<p>If inflammation values <em>decrease</em> along an axis, then the difference from
one element to the next will be negative. If
you are interested in the <strong>magnitude</strong> of the change and not the
direction, the <code class="language-plaintext highlighter-rouge">numpy.absolute()</code> function will provide that.</p>
<p>Notice the difference if you get the largest <em>absolute</em> difference
between readings.</p>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="n">numpy</span><span class="p">.</span><span class="nb">max</span><span class="p">(</span><span class="n">numpy</span><span class="p">.</span><span class="n">absolute</span><span class="p">(</span><span class="n">numpy</span><span class="p">.</span><span class="n">diff</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)),</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
</code></pre></div> </div>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="n">array</span><span class="p">([</span> <span class="mf">12.</span><span class="p">,</span> <span class="mf">14.</span><span class="p">,</span> <span class="mf">11.</span><span class="p">,</span> <span class="mf">13.</span><span class="p">,</span> <span class="mf">11.</span><span class="p">,</span> <span class="mf">13.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">12.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span>
<span class="mf">12.</span><span class="p">,</span> <span class="mf">13.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">11.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">12.</span><span class="p">,</span> <span class="mf">13.</span><span class="p">,</span> <span class="mf">9.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">13.</span><span class="p">,</span> <span class="mf">9.</span><span class="p">,</span>
<span class="mf">12.</span><span class="p">,</span> <span class="mf">9.</span><span class="p">,</span> <span class="mf">12.</span><span class="p">,</span> <span class="mf">11.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">13.</span><span class="p">,</span> <span class="mf">9.</span><span class="p">,</span> <span class="mf">13.</span><span class="p">,</span> <span class="mf">11.</span><span class="p">,</span> <span class="mf">11.</span><span class="p">,</span> <span class="mf">8.</span><span class="p">,</span>
<span class="mf">11.</span><span class="p">,</span> <span class="mf">12.</span><span class="p">,</span> <span class="mf">13.</span><span class="p">,</span> <span class="mf">9.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">13.</span><span class="p">,</span> <span class="mf">11.</span><span class="p">,</span> <span class="mf">11.</span><span class="p">,</span> <span class="mf">13.</span><span class="p">,</span> <span class="mf">11.</span><span class="p">,</span> <span class="mf">13.</span><span class="p">,</span>
<span class="mf">13.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">9.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">9.</span><span class="p">,</span> <span class="mf">9.</span><span class="p">,</span> <span class="mf">13.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">9.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span>
<span class="mf">11.</span><span class="p">,</span> <span class="mf">13.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">,</span> <span class="mf">12.</span><span class="p">])</span>
</code></pre></div> </div>
</blockquote>
</blockquote>
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