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<h1>Numpy</h1>
<!-- Table of contents -->
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<h2> Contents </h2>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#creating-numpy-arrays">Creating Numpy Arrays</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#math-with-numpy-arrays">Math with Numpy Arrays</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#arrays-of-different-shapes">Arrays of different shapes</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#accessing-subsets-of-numpy-arrays-slicing">Accessing subsets of Numpy Arrays - “Slicing”</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#slicing-with-lists-and-strings">Slicing with lists and strings</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#masks">Masks</a></li>
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<section class="tex2jax_ignore mathjax_ignore" id="numpy">
<h1>Numpy<a class="headerlink" href="#numpy" title="Link to this heading">#</a></h1>
<p>The original goals for the development of Python were to make it easy to read and write and flexible for many different tasks. This is reflected
in the easy to use, but powerful, dynamically typed data types like lists, dictionaries. Unfortunately that same flexibility is limiting in terms
of raw computational performance. For this Python relies on dedicated libraries such as <a class="reference external" href="https://numpy.org">Numpy</a> which provide array-based programming
idioms for fast execution of numerical calculations on data.</p>
<p>There are many excellent tutorials out there on Numpy. For example, a succinct beginners guide is available from the Numpy website:</p>
<ul class="simple">
<li><p><a class="reference external" href="https://numpy.org/doc/stable/user/absolute_beginners.html">Numpy - Absolute Basics for Beginners</a></p></li>
</ul>
<p>Other useful user documentation and tutorials can be found here:</p>
<ul class="simple">
<li><p><a class="reference external" href="https://numpy.org/doc/stable/user/index.html">Numpy User Guide (web version)</a> - <a class="reference external" href="https://docs.python.org/3/tutorial/">Numpy User Guide (pdf version)</a></p></li>
<li><p><a class="reference external" href="https://numpy.org/numpy-tutorials/">Numpy Tutorials</a></p></li>
</ul>
<p>Here we are just going to quickly review some basic and useful aspects of numpy which will help bootstrap people for the exercises. The links above are
then a useful path to do more sophisticated things. For simplicity in this quick introduction/review we will focus mostly on the 1 dimensional case, but note that the package is much more powerful than that and supports multi-dimenstional arrays.</p>
<section id="creating-numpy-arrays">
<h2>Creating Numpy Arrays<a class="headerlink" href="#creating-numpy-arrays" title="Link to this heading">#</a></h2>
<p>Numpy array can be initialized directly and explicitly as arrays:</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="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="n">a1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</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="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="nb">print</span><span class="p">(</span><span class="n">a1</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>[1 2 3 4 5 6]
</pre></div>
</div>
</div>
</div>
<p>Dedicated functions are available to create arrays of various types:</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">a2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="c1"># all ones, the function argument is the array length</span>
<span class="nb">print</span><span class="p">(</span><span class="n">a2</span><span class="p">)</span>
<span class="n">a3</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="mi">10</span><span class="p">)</span> <span class="c1"># all zeroes, the function argument is the array length</span>
<span class="nb">print</span><span class="p">(</span><span class="n">a3</span><span class="p">)</span>
<span class="n">a4</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">full</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span><span class="mf">7.0</span><span class="p">)</span> <span class="c1"># all a specified value (here 7.0, the 2nd argument), the first argument is the array length</span>
<span class="nb">print</span><span class="p">(</span><span class="n">a4</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>[1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
[7. 7. 7. 7. 7. 7. 7. 7. 7. 7.]
</pre></div>
</div>
</div>
</div>
<p>One can also create an array by specifying a first number, last number and a step size.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">start</span><span class="p">,</span><span class="n">stop</span><span class="p">,</span><span class="n">step</span><span class="p">)</span>
</pre></div>
</div>
<p>Note that the rule here is “up to, but not including, the ‘stop’ value”)</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">a5</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">10</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">a5</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>[0 2 4 6 8]
</pre></div>
</div>
</div>
</div>
<p>If one wants N values linearly spaced between an initial and a final value:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">first</span><span class="p">,</span><span class="n">last</span><span class="p">,</span><span class="n">number</span><span class="p">)</span>
</pre></div>
</div>
<p>Note that in this case (unlike arange) the “last” value will be the final element.</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">a6</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mf">0.</span><span class="p">,</span><span class="mi">10</span><span class="p">,</span><span class="mi">20</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">a6</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>[ 0. 0.52631579 1.05263158 1.57894737 2.10526316 2.63157895
3.15789474 3.68421053 4.21052632 4.73684211 5.26315789 5.78947368
6.31578947 6.84210526 7.36842105 7.89473684 8.42105263 8.94736842
9.47368421 10. ]
</pre></div>
</div>
</div>
</div>
</section>
<section id="math-with-numpy-arrays">
<h2>Math with Numpy Arrays<a class="headerlink" href="#math-with-numpy-arrays" title="Link to this heading">#</a></h2>
<p>The powerful aspect of numpy is that one can do math with these arrays. Both via scalar operations:</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">b1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">11</span><span class="p">,</span><span class="mi">12</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">b1</span><span class="p">)</span>
<span class="n">b2</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">b1</span>
<span class="nb">print</span><span class="p">(</span><span class="n">b2</span><span class="p">)</span>
<span class="n">b3</span> <span class="o">=</span> <span class="n">b2</span> <span class="o">+</span> <span class="mi">2</span>
<span class="nb">print</span><span class="p">(</span><span class="n">b3</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>[ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.]
[ 0. 2. 4. 6. 8. 10. 12. 14. 16. 18. 20. 22.]
[ 2. 4. 6. 8. 10. 12. 14. 16. 18. 20. 22. 24.]
</pre></div>
</div>
</div>
</div>
<p>And via operations with different arrays (e.g. here element-wise addition):</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">b4</span> <span class="o">=</span> <span class="n">b1</span> <span class="o">+</span> <span class="n">b2</span>
<span class="nb">print</span><span class="p">(</span><span class="n">b4</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>[ 0. 3. 6. 9. 12. 15. 18. 21. 24. 27. 30. 33.]
</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">b5</span> <span class="o">=</span> <span class="n">b4</span> <span class="o">/</span> <span class="mi">3</span>
<span class="nb">print</span><span class="p">(</span><span class="n">b5</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>[ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.]
</pre></div>
</div>
</div>
</div>
<p>As we will see this can be useful for plotting functions, for example:</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">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">20</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">y</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>[0. 0.26315789 0.52631579 0.78947368 1.05263158 1.31578947
1.57894737 1.84210526 2.10526316 2.36842105 2.63157895 2.89473684
3.15789474 3.42105263 3.68421053 3.94736842 4.21052632 4.47368421
4.73684211 5. ]
[ 0. 0.06925208 0.27700831 0.6232687 1.10803324 1.73130194
2.49307479 3.3933518 4.43213296 5.60941828 6.92520776 8.37950139
9.97229917 11.70360111 13.5734072 15.58171745 17.72853186 20.01385042
22.43767313 25. ]
</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="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</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>[<matplotlib.lines.Line2D at 0x10d334f50>]
</pre></div>
</div>
<img alt="_images/37f815744aedcfdaccec790b585cdaf673ec6c623c27d27a7cfb74faa0f2522e.png" src="_images/37f815744aedcfdaccec790b585cdaf673ec6c623c27d27a7cfb74faa0f2522e.png" />
</div>
</div>
</section>
<section id="arrays-of-different-shapes">
<h2>Arrays of different shapes<a class="headerlink" href="#arrays-of-different-shapes" title="Link to this heading">#</a></h2>
<p>The example arrays we show here are primarily one dimensional, but Numpy is a generalized package supporting multi-dimensional arrays.</p>
<p>(There are rules related to math with arrays of different sizes and shapes. We don’t cover that aspect here, but see the documentation links above.)</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">np</span><span class="o">.</span><span class="n">array</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><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="nb">print</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">'The number of axes/dimensions of the array = </span><span class="si">{</span><span class="n">a</span><span class="o">.</span><span class="n">ndim</span><span class="si">}</span><span class="s1">'</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">'The shape of the array = </span><span class="si">{</span><span class="n">a</span><span class="o">.</span><span class="n">shape</span><span class="si">}</span><span class="s1">'</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">'The size of the array = </span><span class="si">{</span><span class="n">a</span><span class="o">.</span><span class="n">size</span><span class="si">}</span><span class="s1">'</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>[[0 1 2]
[3 4 5]]
The number of axes/dimensions of the array = 2
The shape of the array = (2, 3)
The size of the array = 6
</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">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</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><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">6</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="nb">print</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">'The number of axes/dimensions of the array = </span><span class="si">{</span><span class="n">a</span><span class="o">.</span><span class="n">ndim</span><span class="si">}</span><span class="s1">'</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">'The shape of the array = </span><span class="si">{</span><span class="n">a</span><span class="o">.</span><span class="n">shape</span><span class="si">}</span><span class="s1">'</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">'The size of the array = </span><span class="si">{</span><span class="n">a</span><span class="o">.</span><span class="n">size</span><span class="si">}</span><span class="s1">'</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>[[0 1 2]
[3 4 5]
[6 7 8]]
The number of axes/dimensions of the array = 2
The shape of the array = (3, 3)
The size of the array = 9
</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">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</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><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">6</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="nb">print</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">'The number of axes/dimensions of the array = </span><span class="si">{</span><span class="n">a</span><span class="o">.</span><span class="n">ndim</span><span class="si">}</span><span class="s1">'</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">'The shape of the array = </span><span class="si">{</span><span class="n">a</span><span class="o">.</span><span class="n">shape</span><span class="si">}</span><span class="s1">'</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">'The size of the array = </span><span class="si">{</span><span class="n">a</span><span class="o">.</span><span class="n">size</span><span class="si">}</span><span class="s1">'</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>[[0 1 2]
[3 4 5]
[6 7 8]]
The number of axes/dimensions of the array = 2
The shape of the array = (3, 3)
The size of the array = 9
</pre></div>
</div>
</div>
</div>
<p>It is also possible to use the arange(), linspace() and other functions to create 1-dimensional arrays and then reshape them to other shapes.</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">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">9</span><span class="p">)</span>
<span class="nb">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">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">9</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span>
<span class="nb">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">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="mi">9</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">c</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>[0 1 2 3 4 5 6 7 8]
[[0 1 2]
[3 4 5]
[6 7 8]]
[[0. 0. 0.]
[0. 0. 0.]
[0. 0. 0.]]
</pre></div>
</div>
</div>
</div>
</section>
<section id="accessing-subsets-of-numpy-arrays-slicing">
<h2>Accessing subsets of Numpy Arrays - “Slicing”<a class="headerlink" href="#accessing-subsets-of-numpy-arrays-slicing" title="Link to this heading">#</a></h2>
<p>An important and useful aspect of Numpy arrays is the ability to access subsets of the arrays (referred to as “slicing”) in various ways:</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">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</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="nb">print</span><span class="p">(</span><span class="n">c1</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>[0. 1. 2. 3. 4. 5.]
</pre></div>
</div>
</div>
</div>
<p>The syntax for accessing a subset (slice) involves specifying a start index, a stop index and a step:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span> <span class="n">c1</span><span class="p">[</span><span class="n">start</span><span class="p">:</span><span class="n">stop</span><span class="p">:</span><span class="n">step</span><span class="p">]</span>
</pre></div>
</div>
<p>The following rules apply:</p>
<ul class="simple">
<li><p>The index numbering assigns “0” to the first element (as in C/C++, not as in FORTRAN/Julia!)</p></li>
<li><p>The step index is optional and assumed to be one if omitted.</p></li>
<li><p>If stop is specified, the elements selected will be <strong>“up to, but not including, the element at the stop index”</strong></p></li>
<li><p>If the start element is not specified, elements will be included from the first element onwards.</p></li>
<li><p>If the stop element is not specified, elements will be included up to and including the last element</p></li>
</ul>
<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="mi">0</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">c1</span><span class="p">[:</span><span class="mi">2</span><span class="p">])</span> <span class="c1"># will start from first element</span>
<span class="nb">print</span><span class="p">(</span><span class="n">c1</span><span class="p">[</span><span class="mi">0</span><span class="p">:])</span> <span class="c1"># will go up to -and- include the last element</span>
<span class="nb">print</span><span class="p">(</span><span class="n">c1</span><span class="p">[</span><span class="mi">3</span><span class="p">:])</span> <span class="c1"># start with the element index 3 and go up to -and- include the last element</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>[0. 1.]
[0. 1.]
[0. 1. 2. 3. 4. 5.]
[3. 4. 5.]
</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="nb">print</span><span class="p">(</span><span class="n">c1</span><span class="p">[</span><span class="mi">0</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="c1"># step by 3</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>[0. 2. 4.]
</pre></div>
</div>
</div>
</div>
<p>Negative indices can also be used, with “-1” being the last last element, “-2” the penultimate one, etc.</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="mi">3</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> <span class="c1"># start with the element index 3 and go up to but not including the -1th (last) element</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>[3. 4.]
</pre></div>
</div>
</div>
</div>
<p>A negative step can be used to reverse the array:</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="o">-</span><span class="mi">1</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>[5. 4. 3. 2. 1. 0.]
</pre></div>
</div>
</div>
</div>
</section>
<section id="slicing-with-lists-and-strings">
<h2>Slicing with lists and strings<a class="headerlink" href="#slicing-with-lists-and-strings" title="Link to this heading">#</a></h2>
<p>Note that the slicing syntax can be applied also to other ordered data types such as lists and strings</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">l1</span> <span class="o">=</span> <span class="p">[</span><span class="s1">'apple'</span><span class="p">,</span> <span class="s1">'orange'</span><span class="p">,</span> <span class="s1">'mango'</span><span class="p">,</span> <span class="s1">'banana'</span><span class="p">]</span>
<span class="nb">print</span><span class="p">(</span><span class="n">l1</span><span class="p">[</span><span class="mi">0</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">l1</span><span class="p">[::</span><span class="o">-</span><span class="mi">1</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>['apple', 'orange']
['banana', 'mango', 'orange', 'apple']
</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">s1</span> <span class="o">=</span> <span class="s1">'Abracadabra'</span>
<span class="nb">print</span><span class="p">(</span><span class="n">s1</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="nb">print</span><span class="p">(</span><span class="n">s1</span><span class="p">[::</span><span class="o">-</span><span class="mi">1</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>Abra
arbadacarbA
</pre></div>
</div>
</div>
</div>
</section>
<section id="masks">
<h2>Masks<a class="headerlink" href="#masks" title="Link to this heading">#</a></h2>
<p>Once you have a numpy array, it is also possible to select elements according to some boolean condition.</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">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">11</span><span class="p">)</span>
<span class="n">a</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>array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
</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">b</span> <span class="o">=</span> <span class="n">a</span><span class="p">[</span><span class="n">a</span><span class="o">></span><span class="mi">5</span><span class="p">]</span> <span class="c1"># Select only elments whose value is greater than 5</span>
<span class="n">b</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>array([ 6, 7, 8, 9, 10])
</pre></div>
</div>
</div>
</div>
<p>The use of conditionals with Numpy arrays actually returns an array of boolean values whose indices correspond to the original array. A useful trick is to save this in a variable:</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">mask</span> <span class="o">=</span> <span class="n">a</span> <span class="o">></span> <span class="mi">5</span>
<span class="n">mask</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>array([False, False, False, False, False, False, True, True, True,
True, True])
</pre></div>
</div>
</div>
</div>
<p>This mask can be use as the original condition was used (though as a variable it is more flexible):</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">c</span> <span class="o">=</span> <span class="n">a</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
<span class="n">c</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>array([ 6, 7, 8, 9, 10])
</pre></div>
</div>
</div>
</div>
<p>You can also use the mask to choose some elements of the array for assignment. A very useful feature is that the syntax <code class="docutils literal notranslate"><span class="pre">~mask</span></code> can also be used to chose the logical <code class="docutils literal notranslate"><span class="pre">not</span></code> of the mask. So here for example one can use the <code class="docutils literal notranslate"><span class="pre">mask</span></code> to set elements greater than 5 to 5 and the <code class="docutils literal notranslate"><span class="pre">~mask</span></code> to set the other elements to 0.</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="p">[</span><span class="o">~</span><span class="n">mask</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">a</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span> <span class="o">=</span> <span class="mi">5</span>
<span class="n">a</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>array([0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5])
</pre></div>
</div>
</div>
</div>
</section>
</section>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#creating-numpy-arrays">Creating Numpy Arrays</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#math-with-numpy-arrays">Math with Numpy Arrays</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#arrays-of-different-shapes">Arrays of different shapes</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#accessing-subsets-of-numpy-arrays-slicing">Accessing subsets of Numpy Arrays - “Slicing”</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#slicing-with-lists-and-strings">Slicing with lists and strings</a></li>
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