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<h2 id="toc-title">Tabla de contenidos</h2>
<ul>
<li><a href="#objetivo" id="toc-objetivo" class="nav-link active"
data-scroll-target="#objetivo">Objetivo</a></li>
<li><a href="#py-numpy-why" id="toc-py-numpy-why" class="nav-link"
data-scroll-target="#py-numpy-why"><span class="header-section-number"> 6.1 </span> Matrices NumPy </a>
<ul class="collapse">
<li><a href="#py-numpy-mem" id="toc-py-numpy-mem" class="nav-link"
data-scroll-target="#py-numpy-mem"><span class="header-section-number"> 6.1.1 </span> Eficiencia en uso de memoria </a></li>
<li><a href="#py-numpy-fast" id="toc-py-numpy-fast" class="nav-link"
data-scroll-target="#py-numpy-fast"><span class="header-section-number"> 6.1.2 </span> Rapidez </a></li>
</ul>
</li>
<li><a href="#py-numpy-atr" id="toc-py-numpy-atr" class="nav-link"
data-scroll-target="#py-numpy-atr"><span class="header-section-number"> 6.2 </span> Atributos básicos de matrices NumPy </a>
</li>
<li><a href="#py-numpy-arit" id="toc-py-numpy-arit" class="nav-link"
data-scroll-target="#py-numpy-arit"><span class="header-section-number"> 6.3 </span> Operaciones aritméticas </a>
</li>
<li><a href="#py-numpy-broad" id="toc-py-numpy-broad" class="nav-link"
data-scroll-target="#py-numpy-broad"><span class="header-section-number"> 6.4 </span> Difusión </a>
</li>
<li><a href="#py-numpy-comp" id="toc-py-numpy-comp" class="nav-link"
data-scroll-target="#py-numpy-comp"><span class="header-section-number"> 6.5 </span> Comparación </a>
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<li><a href="#py-numpy-idx" id="toc-py-numpy-idx" class="nav-link"
data-scroll-target="#py-numpy-idx"><span class="header-section-number"> 6.6 </span> Indexación de arreglos Numpy </a>
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<li><a href="#py-numpy-sub" id="toc-py-numpy-sub" class="nav-link"
data-scroll-target="#py-numpy-sub"><span class="header-section-number"> 6.7 </span> Acceso a subarreglos </a>
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<li><a href="#py-numpy-uni" id="toc-py-numpy-uni" class="nav-link"
data-scroll-target="#py-numpy-uni"><span class="header-section-number"> 6.7.1 </span> Arreglos unidimensionales </a></li>
<li><a href="#py-numpy-mul" id="toc-py-numpy-mul" class="nav-link"
data-scroll-target="#py-numpy-mul"><span class="header-section-number"> 6.7.2 </span> Arreglos multidimensionales </a></li>
<li><a href="#py-numpy-res" id="toc-py-numpy-res" class="nav-link"
data-scroll-target="#py-numpy-res"><span class="header-section-number"> 6.7.3 </span> Reestructuración de arreglos </a></li>
</ul>
</li>
<li><a href="#py-numpy-cd" id="toc-py-numpy-cd" class="nav-link"
data-scroll-target="#py-numpy-cd"><span class="header-section-number"> 6.8 </span> Concatenación y división de matrices </a>
<ul class="collapse">
<li><a href="#py-numpy-con" id="toc-py-numpy-con" class="nav-link"
data-scroll-target="#py-numpy-con"><span class="header-section-number"> 6.8.1 </span> Concatenación </a></li>
<li><a href="#py-numpy-div" id="toc-py-numpy-div" class="nav-link"
data-scroll-target="#py-numpy-div"><span class="header-section-number"> 6.8.2 </span> División </a></li>
</ul>
</li>
<li><a href="#py-numpy-ufun" id="toc-py-numpy-ufun" class="nav-link"
data-scroll-target="#py-numpy-ufun"><span class="header-section-number"> 6.9 </span> Funciones universales </a>
<ul class="collapse">
<li><a href="#py-numpy-fund" id="toc-py-numpy-fund" class="nav-link"
data-scroll-target="#py-numpy-fund"><span class="header-section-number"> 6.9.1 </span> Fundamentos de UFuncs </a></li>
<li><a href="#py-numpy-util" id="toc-py-numpy-util" class="nav-link"
data-scroll-target="#py-numpy-util"><span class="header-section-number"> 6.9.2 </span> UFuncs útiles </a></li>
<li><a href="#py-numpy-agg" id="toc-py-numpy-agg" class="nav-link"
data-scroll-target="#py-numpy-agg"><span class="header-section-number"> 6.9.3 </span> Agregados </a></li>
</ul>
</li>
<li><a href="#practice-exercises" id="toc-practice-exercises" class="nav-link"
data-scroll-target="#practice-exercises"><span class="header-section-number">6.10</span>
Ejercicios prácticos</a></li>
</ul>
</nav>
</div>
<!-- main -->
<main class="content" id="quarto-document-content">
<header id="title-block-header" class="quarto-title-block default">
<div class="quarto-title">
<h1 class="title"><span class="chapter-number">6</span> <span
class="chapter-title">Introducción a NumPy</span></h1>
</div>
<div class="quarto-title-meta"> </div>
</header>
<section id="objetivo" class="level1">
<h1 class="anchored" data-anchor-id="objetivo">Objetivo</h1>
<p>El objetivo de esta clase es introducir a los estudiantes en el uso de Numpy para realizar operaciones matemáticas y estadísticas con arreglos y matrices en Python</p>
</section>
<p><strong>NumPy</strong>, abreviatura de <em>Numerical Python</em>, se utiliza para analizar datos numéricos con Python. Las matrices (<em>arrays</em>) NumPy se utilizan principalmente para crear matrices homogéneas <span class="math inline">\(n-\)</span>dimensionales (<span class="math inline">\(n=1,\dots,n\)</span>). Importemos la biblioteca NumPy para utilizar sus métodos y funciones.</p>
<div id="73b170f7-fadb-4278-a051-4763f048145a" class="cell">
<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="im">import</span> numpy <span class="im">as</span> np</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a>matriz_1 <span class="op">=</span> np.array([[<span class="dv">1</span>,<span class="dv">2</span>],[<span class="dv">3</span>,<span class="dv">4</span>]])</span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a>matriz_1</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="8c7e84ef-0f78-4980-917b-6dfd1351fae7" class="cell">
<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="bu">type</span>(matriz_1)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<!-- 6.1 -->
<section id="py-numpy-why" class="level2" data-number="6.1">
<h2 data-number="6.1" class="anchored" data-anchor-id="py-numpy-why"><span
class="header-section-number">6.1</span> Matrices NumPy </h2>
<p>Las matrices NumPy pueden almacenar datos al igual que otras estructuras de datos, como listas, tuplas y DataFrames (Pandas). Los cálculos realizados con matrices NumPy también se pueden realizar con datos almacenados en otras estructuras de datos. Sin embargo, NumPy es el preferido por su eficiencia, especialmente cuando se trabaja con matrices de datos de gran tamaño.</p>
<section id="py-numpy-mem" class="level3" data-number="6.1.1">
<h3 data-number="6.1.1" class="anchored" data-anchor-id="py-numpy-mem"><span
class="header-section-number">6.1.1 </span> Eficiencia en uso de memoria </h3>
<p>Una matriz NumPy es una colección de tipos de datos <strong>homogéneos</strong> que se almacenan en ubicaciones de memoria <strong>contiguas</strong>. Por otro lado, las estructuras de datos como las listas son una colección de tipos de datos heterogéneos que se almacenan en ubicaciones de memoria no contiguas. Los elementos de datos homogéneos permiten que la matriz NumPy se compacte de forma densa, lo que da como resultado un menor consumo de memoria. Revisemos esto con un ejemplo.</p>
<div id="fc2cc05c-6edd-45b8-84b1-d27fa650ecff" class="cell">
<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a>tuple_ex <span class="op">=</span> <span class="bu">tuple</span>(<span class="bu">range</span>(<span class="dv">1000</span>))</span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a>list_ex <span class="op">=</span> <span class="bu">list</span>(<span class="bu">range</span>(<span class="dv">1000</span>))</span>
<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a>numpy_ex <span class="op">=</span> np.array([<span class="bu">range</span>(<span class="dv">1000</span>)])</span>
<span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a>numpy_ex_2 <span class="op">=</span> np.arange(<span class="dv">1000</span>)</span>
<span id="cb3-5"><a href="#cb3-5" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f"Espacio <tuple> = </span><span class="sc">{</span>tuple_ex<span class="sc">.</span>__sizeof__()<span class="sc">}</span><span class="ss"> bytes"</span>)</span>
<span id="cb3-6"><a href="#cb3-6" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f"Espacio <list> = </span><span class="sc">{</span>list_ex<span class="sc">.</span>__sizeof__()<span class="sc">}</span><span class="ss"> bytes"</span>)</span>
<span id="cb3-7"><a href="#cb3-7" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f"Espacio <NumPy array> = </span><span class="sc">{</span>numpy_ex<span class="sc">.</span>__sizeof__()<span class="sc">}</span><span class="ss"> bytes"</span>)</span>
<span id="cb3-8"><a href="#cb3-8" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f"Espacio <NumPy array> (arange) = </span><span class="sc">{</span>numpy_ex_2<span class="sc">.</span>__sizeof__()<span class="sc">}</span><span class="ss"> bytes"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>Tenga en cuenta que las matrices NumPy son eficientes en el uso de la memoria siempre que sean homogéneas. Perderán la eficiencia de la memoria si se utilizan para almacenar elementos de múltiples tipos de datos.</p>
<p>El siguiente ejemplo compara el tamaño de una matriz NumPy homogénea con el de una matriz NumPy heterogénea similar para ilustrar este punto.</p>
<div id="b74d755a-cc1d-452f-a29f-c3fdf2ee4411" class="cell">
<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>numpy_homogeneo <span class="op">=</span> np.array([[<span class="dv">1</span>,<span class="dv">2</span>],[<span class="dv">3</span>,<span class="dv">3</span>]])</span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f"Espacio <numpy array> homogéneo = </span><span class="sc">{</span>numpy_homogeneo<span class="sc">.</span>__sizeof__()<span class="sc">}</span><span class="ss"> bytes"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="bf51b897-71ec-4e75-8361-ae8eb2c69718" class="cell">
<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>numpy_heterogeneo <span class="op">=</span> np.array([[<span class="dv">1</span>,<span class="st">'2'</span>],[<span class="dv">3</span>,<span class="dv">3</span>]])</span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f"Espacio <numpy array> heterogéneo = </span><span class="sc">{</span>numpy_heterogeneo<span class="sc">.</span>__sizeof__()<span class="sc">}</span><span class="ss"> bytes"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>El tamaño de una matriz NumPy homogénea es mucho menor que el de una matriz con datos heterogéneos. Por lo tanto, las matrices NumPy se utilizan principalmente para almacenar datos homogéneos.</p>
<p>Por otro lado, el tamaño de otras estructuras de datos, como una lista, no depende de si los elementos que contienen son homogéneos o heterogéneos, como se muestra en el siguiente ejemplo.</p>
<div id="06c7278c-6801-4cd8-bd3f-7d1e787e48cf" class="cell">
<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>lista_homogenea <span class="op">=</span> <span class="bu">list</span>([<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">4</span>])</span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f"Espacio <list> homogénea = </span><span class="sc">{</span>lista_homogenea<span class="sc">.</span>__sizeof__()<span class="sc">}</span><span class="ss"> bytes"</span>)</span>
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a>lista_heterogenea <span class="op">=</span> <span class="bu">list</span>([<span class="dv">1</span>,<span class="st">'2'</span>,<span class="dv">3</span>,<span class="dv">4</span>])</span>
<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f"Espacio <list> heterogénea = </span><span class="sc">{</span>lista_heterogenea<span class="sc">.</span>__sizeof__()<span class="sc">}</span><span class="ss"> bytes"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>Tenga en cuenta que la eficiencia de memoria de las matrices NumPy no entra en juego con una cantidad muy pequeña de datos. Por lo tanto, una lista con cuatro elementos (1, 2, 3 y 4) tiene un tamaño menor que una matriz NumPy con los mismos elementos. Sin embargo, con conjuntos de datos más grandes, como el que se mostró anteriormente (secuencia de números enteros de 0 a 999), se puede ver la eficiencia de memoria de las matrices NumPy.</p>
<p>A diferencia de las estructuras de datos como listas, tuplas y diccionarios, todos los elementos de una matriz NumPy deben ser del mismo tipo para aprovechar la eficiencia de memoria de las matrices NumPy.</p>
</section>
<section id="py-numpy-fast" class="level3" data-number="6.1.2">
<h3 data-number="6.1.2" class="anchored" data-anchor-id="py-numpy-fast"><span
class="header-section-number">6.1.2 </span> Rapidez </h3>
<p>Con las matrices NumPy, los cálculos matemáticos se pueden realizar más rápido, en comparación con otras estructuras de datos, debido a las siguientes razones: 1. Como la matriz NumPy está densamente llena de datos homogéneos, también ayuda a recuperar los datos más rápido, lo que hace que los cálculos sean más rápido 2.</p>
<p>Con NumPy, los cálculos vectorizados pueden reemplazar ciclouc<code>for</code> for de Python, que son relativamente más costosos. El paquete NumPy divide los cálculos vectorizados en múltiples fragmentos y luego procesa todos los fragmentos en paralelo. Sin embargo, co ciclo <code>for</code> for, los cálculos se realizarán de a uno por 3. z.</p>
<p>El paquete NumPy integra códigos C y C++ en Python. Estos lenguajes de programación tienen muy poco tiempo de ejecución en comparación con Python.</p>
<p>Veremos la mayor velocidad en los cálculos NumPy en el siguiente nidimensional.</p>
<div id="76a1c8dd-8c08-4d0b-b773-d576fc0ed959" class="cell">
<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="im">import</span> time <span class="im">as</span> tm</span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>start_time <span class="op">=</span> tm.time()</span>
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a>list_ex <span class="op">=</span> <span class="bu">list</span>(<span class="bu">range</span>(<span class="dv">10000000</span>))</span>
<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a>a<span class="op">=</span>(list_ex<span class="op">*</span><span class="dv">2</span>)</span>
<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f"Tiempo para una lista = </span><span class="sc">{</span><span class="dv">1000</span><span class="op">*</span>(tm.time()<span class="op">-</span>start_time)<span class="sc">:0.2f}</span><span class="ss"> ms"</span>)</span>
<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-7"><a href="#cb7-7" aria-hidden="true" tabindex="-1"></a>start_time <span class="op">=</span> tm.time()</span>
<span id="cb7-8"><a href="#cb7-8" aria-hidden="true" tabindex="-1"></a>tuple_ex <span class="op">=</span> <span class="bu">tuple</span>(<span class="bu">range</span>(<span class="dv">10000000</span>))</span>
<span id="cb7-9"><a href="#cb7-9" aria-hidden="true" tabindex="-1"></a>a<span class="op">=</span>(tuple_ex<span class="op">*</span><span class="dv">2</span>)</span>
<span id="cb7-10"><a href="#cb7-10" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f"Tiempo para una tupla = </span><span class="sc">{</span><span class="dv">1000</span><span class="op">*</span>(tm.time()<span class="op">-</span>start_time)<span class="sc">:0.2f}</span><span class="ss"> ms"</span>)</span>
<span id="cb7-11"><a href="#cb7-11" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-12"><a href="#cb7-12" aria-hidden="true" tabindex="-1"></a>start_time <span class="op">=</span> tm.time()</span>
<span id="cb7-13"><a href="#cb7-13" aria-hidden="true" tabindex="-1"></a>numpy_ex <span class="op">=</span> np.arange(<span class="dv">10000000</span>)</span>
<span id="cb7-14"><a href="#cb7-14" aria-hidden="true" tabindex="-1"></a>a<span class="op">=</span>(numpy_ex<span class="op">*</span><span class="dv">2</span>)</span>
<span id="cb7-15"><a href="#cb7-15" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f"Tiempo para una matriz NumPy = </span><span class="sc">{</span><span class="dv">1000</span><span class="op">*</span>(tm.time()<span class="op">-</span>start_time)<span class="sc">:0.2f}</span><span class="ss"> ms"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
</section>
<!-- /6.1 -->
<!-- 6.2 -->
<section id="py-numpy-atr" class="level2" data-number="6.2">
<h2 data-number="6.2" class="anchored" data-anchor-id="py-numpy-atr"><span
class="header-section-number">6.2</span> Atributos básicos de matrices NumPy </h2>
<p>A partir de una matriz Numpy que esté definida</p>
<div id="388de62d-91ba-4e8d-a5ca-494e9ae3975d" class="cell">
<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a>numpy_ej <span class="op">=</span> np.array([[<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">3</span>],[<span class="dv">4</span>,<span class="dv">5</span>,<span class="dv">6</span>]])</span>
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a>numpy_ej</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>podemos acceder a sus atributos digitando el nombre de variable, seguido por un punto (<code>.</code>) y presionando la tecla <kbd>Tab</kbd></p>
<div id="8904d8e7-1525-4cfa-b325-d05c6834ad67" class="cell">
<div class="sourceCode cell-code" id="cb9"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>numpy_ej.</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<h4 ><code>ndim</code></h3>
<p>Muestra el numero de dimensiones (o ejes) de la matriz</p>
<div id="a30cc171-89eb-4368-adfe-1c3df40d0ccf" class="cell">
<div class="sourceCode cell-code" id="cb10"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>numpy_ej.ndim</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<h4 ><code>shape</code></h3>
<p>Se trata de una tupla de números enteros que indica el tamaño de la matriz en cada dimensión. Para una matriz con <span class="math inline">\(n\)</span> filas y <span class="math inline">\(m\)</span> columnas, la forma será <span class="math inline">\((n, m)\)</span>. La longitud de esta tupla de forma es, por tanto, el número de dimensiones (<code>ndim</code>).</p>
<div id="6b4dd5ab-e956-43ce-a0c5-d4b765056834" class="cell">
<div class="sourceCode cell-code" id="cb11"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a>numpy_ej.shape</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<h4 ><code>size</code></h3>
<p>Este es el número total de elementos de la matriz, que es el producto de los elementos de la forma.</p>
<div id="76a534cb-81ec-4639-96ca-efbb5dd929e1" class="cell">
<div class="sourceCode cell-code" id="cb12"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a>numpy_ej.size</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<h4 ><code>dtype</code></h3>
<p>Este es un objeto que describe el tipo de los elementos de la matriz. Se pueden crear o especificar dtypes utilizando tipos estándar de Python. NumPy ofrece muchos, por ejemplo, <code>bool_</code>, <code>character</code>, <code>int_</code>, <code>int8</code>, <code>int16</code>, <code>int32</code>, <code>int64</code>, <code>float_</code>, <code>float8</code>, <code>float16</code>, <code>float32</code>, <code>float64</code>, <code>complex_</code>, <code>complex64</code>, <code>object_</code>.</p>
<div id="4221cf73-81f0-487e-822f-484b0dad3f17" class="cell">
<div class="sourceCode cell-code" id="cb13"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a>numpy_ej.dtype</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<h4 ><code>T</code></h3>
<p>Este atributo se utiliza para transponer la matriz NumPy.</p>
<div id="486a549f-ecd3-4eb8-a33e-8a25bd2ca62c" class="cell">
<div class="sourceCode cell-code" id="cb14"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a>numpy_ej.T</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<!-- /6.2 -->
<!-- 6.3 -->
<section id="py-numpy-arit" class="level2" data-number="6.3">
<h2 data-number="6.3" class="anchored" data-anchor-id="py-numpy-arit"><span
class="header-section-number">6.3</span> Operaciones aritméticas </h2>
<p>Las matrices de Numpy admiten operadores aritméticos como <code>+</code>, <code>-</code>, <code>*</code>, etc. Podemos realizar una operación aritmética en una matriz ya sea con un solo número (también llamado escalar) o con otra matriz de la misma forma. Sin embargo, no podemos realizar una operación aritmética en una matriz con una matriz de una forma diferente.</p>
<p>A continuación, se muestran algunos ejemplos de operaciones aritméticas en matrices.</p>
<div id="885d35d6-835c-492f-8168-a5884ca4628a" class="cell">
<div class="sourceCode cell-code" id="cb15"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a>arr1 <span class="op">=</span> np.array([[<span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">3</span>, <span class="dv">4</span>], </span>
<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a> [<span class="dv">5</span>, <span class="dv">6</span>, <span class="dv">7</span>, <span class="dv">8</span>], </span>
<span id="cb15-3"><a href="#cb15-3" aria-hidden="true" tabindex="-1"></a> [<span class="dv">9</span>, <span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">3</span>]])</span>
<span id="cb15-4"><a href="#cb15-4" aria-hidden="true" tabindex="-1"></a>arr2 <span class="op">=</span> np.array([[<span class="dv">11</span>, <span class="dv">12</span>, <span class="dv">13</span>, <span class="dv">14</span>], </span>
<span id="cb15-5"><a href="#cb15-5" aria-hidden="true" tabindex="-1"></a> [<span class="dv">15</span>, <span class="dv">16</span>, <span class="dv">17</span>, <span class="dv">18</span>], </span>
<span id="cb15-6"><a href="#cb15-6" aria-hidden="true" tabindex="-1"></a> [<span class="dv">19</span>, <span class="dv">11</span>, <span class="dv">12</span>, <span class="dv">13</span>]])</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="20fa345c-7a60-4b14-9902-435e66436790" class="cell">
<div class="sourceCode cell-code" id="cb16"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a>arr1 <span class="op">+</span> arr2</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="a8f1c6ab-0d6b-4838-8ef0-fb52f5ee9d62" class="cell">
<div class="sourceCode cell-code" id="cb17"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a>arr1 <span class="op">-</span> arr2</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="0f8140b9-929f-4d09-b06d-16b903cfefc3" class="cell">
<div class="sourceCode cell-code" id="cb18"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a>arr1 <span class="op">*</span> arr2</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="a35f5aff-cb11-4b0c-b056-fdf522bcf6c4" class="cell">
<div class="sourceCode cell-code" id="cb19"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a>arr1 <span class="op">/</span> arr2</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="53010ff6-1d48-4bdb-a93c-f877964687c2" class="cell">
<div class="sourceCode cell-code" id="cb20"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb20-1"><a href="#cb20-1" aria-hidden="true" tabindex="-1"></a>arr1 <span class="op">%</span> <span class="dv">4</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<!-- /6.3 -->
<!-- 6.4 -->
<section id="py-numpy-broad" class="level2" data-number="6.4">
<h2 data-number="6.4" class="anchored" data-anchor-id="py-numpy-broad"><span
class="header-section-number">6.4</span> Difusión </h2>
<p>La difusión permite realizar operaciones aritméticas entre dos matrices con diferentes cantidades de dimensiones pero formas compatibles.</p>
<p>La <a href="https://numpy.org/doc/stable/user/basics.broadcasting.html">documentación de difusión</a> lo explica sucintamente de la siguiente manera:</p>
<blockquote class="blockquote">
<p>El término difusión describe cómo NumPy trata las matrices con diferentes formas durante las operaciones aritméticas. Sujeto a ciertas restricciones, la matriz más pequeña se difunde a través de la matriz más grande para que tengan formas compatibles. La difusión proporciona un medio para vectorizar las operaciones de matriz de modo que el bucle se produzca en C en lugar de Python. Esto se hace sin hacer copias innecesarias de datos y, por lo general, conduce a implementaciones de algoritmos eficientes.</p>
</blockquote>
<div id="d7a52b49-51f9-4dc9-8463-8fd26b6d956d" class="cell">
<div class="sourceCode cell-code" id="cb21"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb21-1"><a href="#cb21-1" aria-hidden="true" tabindex="-1"></a>arr1 <span class="op">=</span> np.array([[<span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">3</span>, <span class="dv">4</span>], </span>
<span id="cb21-2"><a href="#cb21-2" aria-hidden="true" tabindex="-1"></a> [<span class="dv">5</span>, <span class="dv">6</span>, <span class="dv">7</span>, <span class="dv">8</span>], </span>
<span id="cb21-3"><a href="#cb21-3" aria-hidden="true" tabindex="-1"></a> [<span class="dv">9</span>, <span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">3</span>]])</span>
<span id="cb21-4"><a href="#cb21-4" aria-hidden="true" tabindex="-1"></a>arr2 <span class="op">=</span> np.array([<span class="dv">4</span>, <span class="dv">5</span>, <span class="dv">6</span>, <span class="dv">7</span>])</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="738c1d61-aa60-460c-b9c7-608348c18efd" class="cell">
<div class="sourceCode cell-code" id="cb22"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb22-1"><a href="#cb22-1" aria-hidden="true" tabindex="-1"></a>arr1 <span class="op">+</span> arr2</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>Cuando se evalúa la expresión <code>arr1 + arr2</code>, <code>arr2</code> (que tiene la forma <code>(4,)</code>) se replica tres veces para que coincida con la forma <code>(3, 4)</code> de <code>arr1</code>. Numpy realiza la replicación sin crear realmente tres copias de la matriz de dimensión más pequeña, lo que mejora el rendimiento y utiliza menos memoria.</p>
<p>En la adición de matrices anterior, <code>arr2</code> se difundió a la forma de <code>arr1</code>. Sin embargo, esta difusión solo fue posible porque la dimensión derecha de ambas matrices es 4 y la dimensión izquierda de una de las matrices es 1.</p>
<p>Consulte la documentación de transmisión para comprender las reglas de transmisión:</p>
<blockquote class="blockquote">
<p>Al operar en dos matrices, NumPy compara sus formas elemento por elemento. Comienza con las dimensiones finales (es decir, las más a la derecha) y avanza hacia la izquierda. Dos dimensiones son compatibles cuando:</p>
<ul>
<li>son iguales, o</li>
<li>una de ellas es 1</li>
</ul>
</blockquote>
<p>Si la dimensión más a la derecha de <code>arr2</code> es 3, no se producirá la transmisión, ya que no es igual a la dimensión más a la derecha de <code>arr1</code>:</p>
<div id="f71d9073-20c9-4008-a81b-1b84872b643d" class="cell">
<div class="sourceCode cell-code" id="cb23"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb23-1"><a href="#cb23-1" aria-hidden="true" tabindex="-1"></a>arr2 <span class="op">=</span> np.array([<span class="dv">4</span>, <span class="dv">5</span>, <span class="dv">6</span>])</span>
<span id="cb23-2"><a href="#cb23-2" aria-hidden="true" tabindex="-1"></a>arr1 <span class="op">+</span> arr2</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<!-- /6.4 -->
<!-- 6.5 -->
<section id="py-numpy-comp" class="level2" data-number="6.5">
<h2 data-number="6.5" class="anchored" data-anchor-id="py-numpy-comp"><span
class="header-section-number">6.5</span> Comparación </h2>
<p>Las matrices Numpy admiten operaciones de comparación como <code>==</code>, <code>!=</code>, <code>></code>, etc. El resultado es una matriz de valores booleanos.</p>
<div id="15551ebd-9d1b-4f21-bfb2-0cc79052cb7b" class="cell">
<div class="sourceCode cell-code" id="cb24"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb24-1"><a href="#cb24-1" aria-hidden="true" tabindex="-1"></a>arr1 <span class="op">=</span> np.array([[<span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">3</span>], [<span class="dv">3</span>, <span class="dv">4</span>, <span class="dv">5</span>]])</span>
<span id="cb24-2"><a href="#cb24-2" aria-hidden="true" tabindex="-1"></a>arr2 <span class="op">=</span> np.array([[<span class="dv">2</span>, <span class="dv">2</span>, <span class="dv">3</span>], [<span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">5</span>]])</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="23cdea92-d23b-4327-8526-dfab84e541ad" class="cell">
<div class="sourceCode cell-code" id="cb25"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb25-1"><a href="#cb25-1" aria-hidden="true" tabindex="-1"></a>arr1 <span class="op">==</span> arr2</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="9f9fa301-7edb-4aa5-9b94-06d1eb2f7c5b" class="cell">
<div class="sourceCode cell-code" id="cb26"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb26-1"><a href="#cb26-1" aria-hidden="true" tabindex="-1"></a>arr1 <span class="op">!=</span> arr2</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="23da1ef0-9df6-4125-8095-3c0b1771022f" class="cell">
<div class="sourceCode cell-code" id="cb27"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb27-1"><a href="#cb27-1" aria-hidden="true" tabindex="-1"></a>arr1 <span class="op">>=</span> arr2</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="5e3e2d08-3912-48b8-8b03-dc67a18db7a3" class="cell">
<div class="sourceCode cell-code" id="cb28"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb28-1"><a href="#cb28-1" aria-hidden="true" tabindex="-1"></a>arr1 <span class="op">>=</span> arr2</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>La comparación de matrices se utiliza con frecuencia para contar la cantidad de elementos iguales en dos matrices mediante el método de suma. Recuerde que <code>True</code> se evalúa como 1 y <code>False</code> como 0 cuando se utilizan valores booleanos en operaciones aritméticas.</p>
<div id="24288ac1-dac9-4cea-a5dd-da7f30568410" class="cell">
<div class="sourceCode cell-code" id="cb29"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb29-1"><a href="#cb29-1" aria-hidden="true" tabindex="-1"></a>(arr1 <span class="op">==</span> arr2).<span class="bu">sum</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<!-- /6.5 -->
<!-- 6.6 -->
<section id="py-numpy-idx" class="level2" data-number="6.6">
<h2 data-number="6.6" class="anchored" data-anchor-id="py-numpy-idx"><span
class="header-section-number">6.6</span> Indexación de arreglos Numpy </h2>
<p>Ya estamos familiarizados con la indexación de listas estándar de <code>Python</code>, por lo que la indexación en <code>NumPy</code> nos resultará bastante familiar. En una matriz unidimensional, se puede acceder al <span class="math inline">\(i\)</span>-ésimo valor (contando desde cero) especificando el índice deseado entre corchetes, al igual que con las listas de Python:</p>
<div id="9198ff98-766e-4f84-99ee-7507477b8ffd" class="cell">
<div class="sourceCode cell-code" id="cb30"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb30-1"><a href="#cb30-1" aria-hidden="true" tabindex="-1"></a>np.random.seed(<span class="dv">0</span>)</span>
<span id="cb30-2"><a href="#cb30-2" aria-hidden="true" tabindex="-1"></a>x1 <span class="op">=</span> np.random.randint(<span class="dv">10</span>, size<span class="op">=</span><span class="dv">6</span>)</span>
<span id="cb30-3"><a href="#cb30-3" aria-hidden="true" tabindex="-1"></a>x2 <span class="op">=</span> np.random.randint(<span class="dv">10</span>, size<span class="op">=</span>(<span class="dv">3</span>, <span class="dv">4</span>))</span>
<span id="cb30-4"><a href="#cb30-4" aria-hidden="true" tabindex="-1"></a>x3 <span class="op">=</span> np.random.randint(<span class="dv">10</span>, size<span class="op">=</span>(<span class="dv">3</span>, <span class="dv">4</span>, <span class="dv">5</span>)) </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="8c61cb68-1a49-41a1-b7ed-d8bd8b4fcb4e" class="cell">
<div class="sourceCode cell-code" id="cb31"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb31-1"><a href="#cb31-1" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(x1)</span>
<span id="cb31-2"><a href="#cb31-2" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(x1[<span class="dv">0</span>])</span>
<span id="cb31-3"><a href="#cb31-3" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(x1[<span class="op">-</span><span class="dv">1</span>])</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="aa11cc8c-d15d-4aac-8f6e-fd64b65833e0" class="cell">
<div class="sourceCode cell-code" id="cb32"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb32-1"><a href="#cb32-1" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(x2)</span>
<span id="cb32-2"><a href="#cb32-2" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(x2[<span class="dv">0</span>])</span>
<span id="cb32-3"><a href="#cb32-3" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(x2[<span class="op">-</span><span class="dv">1</span>])</span>
<span id="cb32-4"><a href="#cb32-4" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(x2[<span class="dv">0</span>][<span class="dv">0</span>])</span>
<span id="cb32-5"><a href="#cb32-5" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(x2[<span class="dv">0</span>][<span class="op">-</span><span class="dv">1</span>])</span>
<span id="cb32-6"><a href="#cb32-6" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(x2[<span class="op">-</span><span class="dv">3</span>][<span class="op">-</span><span class="dv">2</span>])</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="702ceb5d-d3fb-4d7c-b8e8-db327f8e80d0" class="cell">
<div class="sourceCode cell-code" id="cb33"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb33-1"><a href="#cb33-1" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(x3)</span>
<span id="cb33-2"><a href="#cb33-2" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(x3[<span class="dv">2</span>])</span>
<span id="cb33-3"><a href="#cb33-3" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(x3[<span class="dv">1</span>][<span class="dv">1</span>][<span class="dv">3</span>])</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>Los valores también se pueden modificar utilizando cualquiera de las notaciones de índice anteriores:</p>
<div id="305f69e5-c037-4fa3-b9ca-4650be41da1d" class="cell">
<div class="sourceCode cell-code" id="cb34"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb34-1"><a href="#cb34-1" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(x2)</span>
<span id="cb34-2"><a href="#cb34-2" aria-hidden="true" tabindex="-1"></a>x2[<span class="dv">0</span>, <span class="dv">0</span>] <span class="op">=</span> <span class="dv">12</span></span>
<span id="cb34-3"><a href="#cb34-3" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(x2)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>Tenga en cuenta que, a diferencia de las listas de <code>Python</code>, las matrices <code>NumPy</code> tienen un tipo fijo. Esto significa, por ejemplo, que si intenta insertar un valor de punto flotante en una matriz de enteros, el valor se truncará silenciosamente. <strong>¡No se deje sorprender por este comportamiento!</strong></p>
<div id="d541f4ce-445e-471d-a53d-4d1731c0133f" class="cell">
<div class="sourceCode cell-code" id="cb35"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb35-1"><a href="#cb35-1" aria-hidden="true" tabindex="-1"></a>x1[<span class="dv">0</span>] <span class="op">=</span> <span class="fl">3.14159</span></span>
<span id="cb35-2"><a href="#cb35-2" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(x1)</span>
<span id="cb35-3"><a href="#cb35-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb35-4"><a href="#cb35-4" aria-hidden="true" tabindex="-1"></a>x4 <span class="op">=</span> np.array([<span class="fl">1.</span>, <span class="dv">3</span>, <span class="dv">4</span>])</span>
<span id="cb35-5"><a href="#cb35-5" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(x4.dtype)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<!-- /6.6 -->
<!-- 6.7 -->
<section id="py-numpy-sub" class="level2" data-number="6.7">
<h2 data-number="6.7" class="anchored" data-anchor-id="py-numpy-sub"><span
class="header-section-number">6.7</span> Acceso a subarreglos </h2>
<p>Así como podemos usar corchetes para acceder a elementos individuales de la matriz, también podemos usarlos para acceder a subarreglos con la notación de división, marcada por el carácter de dos puntos (<code>:</code>). La sintaxis de corte de <code>NumPy</code> sigue la de la lista estándar de Python <code>x[start:stop:step]</code>.</p>
<section id="py-numpy-uni" class="level3" data-number="6.7.1">
<h3 data-number="6.7.1" class="anchored" data-anchor-id="py-numpy-uni"><span
class="header-section-number">6.7.1 </span> Arreglos unidimensionales </h3>
<div id="b32c0235-3bb4-463d-b982-050907f06089" class="cell">
<div class="sourceCode cell-code" id="cb36"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb36-1"><a href="#cb36-1" aria-hidden="true" tabindex="-1"></a>y1 <span class="op">=</span> np.arange(<span class="dv">10</span>)</span>
<span id="cb36-2"><a href="#cb36-2" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'y1 = </span><span class="sc">{</span>y1<span class="sc">}</span><span class="ss">'</span>)</span>
<span id="cb36-3"><a href="#cb36-3" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'y1[:5] = </span><span class="sc">{</span>y1[:<span class="dv">5</span>]<span class="sc">}</span><span class="ss">'</span>)</span>
<span id="cb36-4"><a href="#cb36-4" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'y1[::-1] = </span><span class="sc">{</span>y1[::<span class="op">-</span><span class="dv">1</span>]<span class="sc">}</span><span class="ss">'</span>)</span>
<span id="cb36-5"><a href="#cb36-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb36-6"><a href="#cb36-6" aria-hidden="true" tabindex="-1"></a>y2 <span class="op">=</span> np.arange(<span class="dv">0</span>, <span class="dv">20</span>, <span class="dv">2</span>)</span>
<span id="cb36-7"><a href="#cb36-7" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'</span><span class="ch">\n</span><span class="ss">y2 = </span><span class="sc">{</span>y2<span class="sc">}</span><span class="ss">'</span>)</span>
<span id="cb36-8"><a href="#cb36-8" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'y2[5:] = </span><span class="sc">{</span>y2[<span class="dv">5</span>::<span class="dv">2</span>]<span class="sc">}</span><span class="ss">'</span>)</span>
<span id="cb36-9"><a href="#cb36-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb36-10"><a href="#cb36-10" aria-hidden="true" tabindex="-1"></a>y3 <span class="op">=</span> np.linspace(<span class="dv">0</span>, <span class="dv">1</span>, <span class="dv">9</span>)</span>
<span id="cb36-11"><a href="#cb36-11" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'</span><span class="ch">\n</span><span class="ss">y3 = </span><span class="sc">{</span>y3<span class="sc">}</span><span class="ss">'</span>)</span>
<span id="cb36-12"><a href="#cb36-12" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'y3[2:5] = </span><span class="sc">{</span>y3[<span class="dv">2</span>:<span class="dv">5</span>]<span class="sc">}</span><span class="ss">'</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="py-numpy-mul" class="level3" data-number="6.7.2">
<h3 data-number="6.7.2" class="anchored" data-anchor-id="py-numpy-mul"><span
class="header-section-number">6.7.2 </span> Arreglos multidimensionales </h3>
<p>Los cortes multidimensionales funcionan de la misma manera, con varios cortes separados por comas. Por ejemplo:</p>
<div id="fd917152-1fbb-4630-8378-987086f0ee21" class="cell">
<div class="sourceCode cell-code" id="cb37"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb37-1"><a href="#cb37-1" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'x2 =</span><span class="ch">\n</span><span class="ss"> </span><span class="sc">{</span>x2<span class="sc">}</span><span class="ss">'</span>)</span>
<span id="cb37-2"><a href="#cb37-2" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'</span><span class="ch">\n</span><span class="ss">x2[:2, :3] =</span><span class="ch">\n</span><span class="sc">{</span>x2[:<span class="dv">2</span>, :<span class="dv">3</span>]<span class="sc">}</span><span class="ss">'</span>)</span>
<span id="cb37-3"><a href="#cb37-3" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'</span><span class="ch">\n</span><span class="ss">x2[:3, ::2] =</span><span class="ch">\n</span><span class="ss"> </span><span class="sc">{</span>x2[:<span class="dv">3</span>, ::<span class="dv">2</span>]<span class="sc">}</span><span class="ss">'</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>Una rutina comúnmente necesaria es acceder a filas o columnas individuales de una matriz. Esto se puede hacer combinando la indexación y el corte, utilizando un segmento vacío marcado con dos puntos (<code>:</code>):</p>
<div id="708b34a1-893f-4aea-a39f-394845dde320" class="cell">
<div class="sourceCode cell-code" id="cb38"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb38-1"><a href="#cb38-1" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'x2[:, 0] = </span><span class="ch">\n</span><span class="ss"> </span><span class="sc">{</span>x2[:, <span class="dv">1</span>]<span class="sc">}</span><span class="ss">'</span>) <span class="co"># Primera columna de x2</span></span>
<span id="cb38-2"><a href="#cb38-2" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'x2[0, ;] = </span><span class="ch">\n</span><span class="ss"> </span><span class="sc">{</span>x2[<span class="dv">1</span>, :]<span class="sc">}</span><span class="ss">'</span>) <span class="co"># Primera fila de x2</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div class="alert alert-block alert-warning">
<p>Una cosa importante, y extremadamente útil, que debe saber sobre los segmentos de matriz es que devuelven <b>vistas</b> en lugar de copias de los datos de la matriz.</p>
</div>
<div id="adf2d285-9932-443b-be8e-bdfe70889f9d" class="cell">
<div class="sourceCode cell-code" id="cb39"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb39-1"><a href="#cb39-1" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'x2 = </span><span class="ch">\n</span><span class="ss"> </span><span class="sc">{</span>x2<span class="sc">}</span><span class="ss">'</span>)</span>
<span id="cb39-2"><a href="#cb39-2" aria-hidden="true" tabindex="-1"></a>x2_sub <span class="op">=</span> x2[:<span class="dv">2</span>, :<span class="dv">2</span>]</span>
<span id="cb39-3"><a href="#cb39-3" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'</span><span class="ch">\n</span><span class="ss">x2_sub =</span><span class="ch">\n</span><span class="ss"> </span><span class="sc">{</span>x2_sub<span class="sc">}</span><span class="ss">'</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>Ahora, si modificamos este subarreglo, <strong>¡veremos que el arreglo original ha cambiado!</strong></p>
<div id="a8d938e1-1289-4e2b-a381-e91cde12127e" class="cell">
<div class="sourceCode cell-code" id="cb40"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb40-1"><a href="#cb40-1" aria-hidden="true" tabindex="-1"></a>x2_sub[<span class="dv">0</span>, <span class="dv">0</span>] <span class="op">=</span> <span class="dv">150</span></span>
<span id="cb40-2"><a href="#cb40-2" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'</span><span class="ch">\n</span><span class="ss">x2_sub =</span><span class="ch">\n</span><span class="ss"> </span><span class="sc">{</span>x2_sub<span class="sc">}</span><span class="ss">'</span>)</span>
<span id="cb40-3"><a href="#cb40-3" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'</span><span class="ch">\n</span><span class="ss">x2 = </span><span class="ch">\n</span><span class="ss"> </span><span class="sc">{</span>x2<span class="sc">}</span><span class="ss">'</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>Este comportamiento predeterminado es bastante útil: significa que cuando trabajamos con grandes conjuntos de datos, podemos acceder y procesar partes de estos conjuntos de datos sin necesidad de copiar el búfer de datos subyacente. Pero si queremos crear una copia independiente, podemos usar el método <code>copy()</code> de los arreglos.</p>
<div id="2d78513d-548c-4ea0-bcaf-e9b22a53f702" class="cell">
<div class="sourceCode cell-code" id="cb41"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb41-1"><a href="#cb41-1" aria-hidden="true" tabindex="-1"></a>x2_sub_copy <span class="op">=</span> x2[:<span class="dv">2</span>, :<span class="dv">2</span>].copy()</span>
<span id="cb41-2"><a href="#cb41-2" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'x2_sub_copy =</span><span class="ch">\n</span><span class="ss"> </span><span class="sc">{</span>x2_sub_copy<span class="sc">}</span><span class="ss">'</span>)</span>
<span id="cb41-3"><a href="#cb41-3" aria-hidden="true" tabindex="-1"></a>x2_sub_copy[<span class="dv">0</span>, <span class="dv">0</span>] <span class="op">=</span> <span class="dv">42</span></span>
<span id="cb41-4"><a href="#cb41-4" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'</span><span class="ch">\n</span><span class="ss">x2_sub_copy =</span><span class="ch">\n</span><span class="ss"> </span><span class="sc">{</span>x2_sub_copy<span class="sc">}</span><span class="ss">'</span>)</span>
<span id="cb41-5"><a href="#cb41-5" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'</span><span class="ch">\n</span><span class="ss">x2 = </span><span class="ch">\n</span><span class="ss"> </span><span class="sc">{</span>x2<span class="sc">}</span><span class="ss">'</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="py-numpy-res" class="level3" data-number="6.7.3">
<h3 data-number="6.7.3" class="anchored" data-anchor-id="py-numpy-res"><span
class="header-section-number">6.7.3 </span> Reestructuración de arreglos </h3>
<p>Otro tipo útil de operación es la reestructuración de matrices. Por ejemplo, si desea poner los números del 1 al 9 en una matriz <span class="math inline">\(3 \times 3\)</span>, puede hacer lo siguiente:</p>
<div id="0d9783eb-ecda-4783-b18d-6ea8c4cca366" class="cell">
<div class="sourceCode cell-code" id="cb42"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb42-1"><a href="#cb42-1" aria-hidden="true" tabindex="-1"></a>grid <span class="op">=</span> np.arange(<span class="dv">1</span>, <span class="dv">10</span>).reshape((<span class="dv">3</span>, <span class="dv">3</span>))</span>
<span id="cb42-2"><a href="#cb42-2" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(grid)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>Tenga en cuenta que para que esto funcione, el tamaño de la matriz inicial debe coincidir con el tamaño de la matriz reestructurada. Siempre que sea posible, el método de reestructuración utilizará una vista sin copia de la matriz inicial, pero con búferes de memoria no contiguos, este no es siempre el caso.</p>
<p>Otro patrón de reestructuració común es la conversión de una matriz unidimensional en una matriz bidimensional de filas o columnas. Esto se puede hacer con el método <code>reshape()</code>, o más fácilmente usando la palabra clave <code>newaxis</code> dentro de una operación de división:</p>
<div id="199e5900-33bc-465c-ac9f-df17f96a6616" class="cell">
<div class="sourceCode cell-code" id="cb43"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb43-1"><a href="#cb43-1" aria-hidden="true" tabindex="-1"></a>x <span class="op">=</span> np.array([<span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">3</span>])</span>
<span id="cb43-2"><a href="#cb43-2" aria-hidden="true" tabindex="-1"></a>x</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="0b57b2d8-6fde-4db0-9ae0-b1e301a21467" class="cell">
<div class="sourceCode cell-code" id="cb44"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb44-1"><a href="#cb44-1" aria-hidden="true" tabindex="-1"></a>yy <span class="op">=</span> x.reshape((<span class="dv">3</span>, <span class="dv">1</span>)).copy()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="e104f6cd-c070-4862-8ac1-0121affc86cb" class="cell">
<div class="sourceCode cell-code" id="cb45"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb45-1"><a href="#cb45-1" aria-hidden="true" tabindex="-1"></a>x[:, np.newaxis]</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
</section>
<!-- /6.7 -->
<!-- 6.8 -->
<section id="py-numpy-cd" class="level2" data-number="6.8">
<h2 data-number="6.8" class="anchored" data-anchor-id="py-numpy-cd"><span
class="header-section-number">6.8</span> Concatenación y división de matrices </h2>
<p>Todas las rutinas anteriores funcionaron en matrices individuales. También es posible combinar varios arreglos en uno y, a la inversa, dividir un solo arreglo en varios arreglos. Echaremos un vistazo a esas operaciones aquí.</p>
<section id="py-numpy-con" class="level3" data-number="6.8.1">
<h3 data-number="6.8.1" class="anchored" data-anchor-id="py-numpy-con"><span
class="header-section-number">6.8.1 </span> Concatenación </h3>
<p>La concatenación, o unión de dos matrices en <code>NumPy</code>, se logra principalmente mediante las rutinas <code>np.concatenate</code>, <code>np.vstack</code> y <code>np.hstack</code>. <code>np.concatenate</code> toma una tupla o lista de matrices como primer argumento, como podemos ver aquí:</p>
<div id="410afde0-dc98-4408-b183-936534348685" class="cell">
<div class="sourceCode cell-code" id="cb46"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb46-1"><a href="#cb46-1" aria-hidden="true" tabindex="-1"></a>x <span class="op">=</span> np.array([<span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">3</span>])</span>
<span id="cb46-2"><a href="#cb46-2" aria-hidden="true" tabindex="-1"></a>y <span class="op">=</span> np.array([<span class="dv">3</span>, <span class="dv">2</span>, <span class="dv">1</span>])</span>
<span id="cb46-3"><a href="#cb46-3" aria-hidden="true" tabindex="-1"></a>yy <span class="op">=</span> x.reshape((<span class="dv">3</span>, <span class="dv">1</span>)).copy()</span>
<span id="cb46-4"><a href="#cb46-4" aria-hidden="true" tabindex="-1"></a>np.concatenate([x, y])</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="585723bc-b517-423f-bcde-c9a6eda229f3" class="cell">
<div class="sourceCode cell-code" id="cb47"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb47-1"><a href="#cb47-1" aria-hidden="true" tabindex="-1"></a>np.concatenate([yy,yy])</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>También puede concatenar más de dos matrices a la vez y para matrices bidimensionales:</p>
<div id="d47070dd-0ec0-4cc0-86a3-5cf1433db2ad" class="cell">
<div class="sourceCode cell-code" id="cb48"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb48-1"><a href="#cb48-1" aria-hidden="true" tabindex="-1"></a>z <span class="op">=</span> [<span class="dv">99</span>, <span class="dv">99</span>, <span class="dv">99</span>]</span>
<span id="cb48-2"><a href="#cb48-2" aria-hidden="true" tabindex="-1"></a>np.concatenate([x, y, z])</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="f108661b-e540-4c8c-aa69-9c945aaf221a" class="cell">
<div class="sourceCode cell-code" id="cb49"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb49-1"><a href="#cb49-1" aria-hidden="true" tabindex="-1"></a>grid <span class="op">=</span> np.array([[<span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">3</span>],</span>
<span id="cb49-2"><a href="#cb49-2" aria-hidden="true" tabindex="-1"></a> [<span class="dv">4</span>, <span class="dv">5</span>, <span class="dv">6</span>]])</span>
<span id="cb49-3"><a href="#cb49-3" aria-hidden="true" tabindex="-1"></a>np.concatenate([grid, grid])</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>Para trabajar con arreglos de dimensiones mixtas, puede ser más claro usar las funciones <code>np.vstack</code> (apilado vertical) y <code>np.hstack</code> (apilado horizontal):</p>
<div id="78408bc4-4a34-4756-bf63-49c2c3616c04" class="cell">
<div class="sourceCode cell-code" id="cb50"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb50-1"><a href="#cb50-1" aria-hidden="true" tabindex="-1"></a>x <span class="op">=</span> np.array([<span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">3</span>])</span>
<span id="cb50-2"><a href="#cb50-2" aria-hidden="true" tabindex="-1"></a>grid <span class="op">=</span> np.array([[<span class="dv">9</span>, <span class="dv">8</span>, <span class="dv">7</span>],</span>
<span id="cb50-3"><a href="#cb50-3" aria-hidden="true" tabindex="-1"></a> [<span class="dv">6</span>, <span class="dv">5</span>, <span class="dv">4</span>]])</span>
<span id="cb50-4"><a href="#cb50-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb50-5"><a href="#cb50-5" aria-hidden="true" tabindex="-1"></a>np.vstack([x, grid])</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="d0bcf3fc-f20e-496b-8b93-ac96c289a69d" class="cell">
<div class="sourceCode cell-code" id="cb51"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb51-1"><a href="#cb51-1" aria-hidden="true" tabindex="-1"></a>y <span class="op">=</span> np.array([[<span class="dv">99</span>],</span>
<span id="cb51-2"><a href="#cb51-2" aria-hidden="true" tabindex="-1"></a> [<span class="dv">99</span>]])</span>
<span id="cb51-3"><a href="#cb51-3" aria-hidden="true" tabindex="-1"></a>np.hstack([grid, y])</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>De manera similar, <code>np.dstack</code> apilará matrices a lo largo del tercer eje.</p>
</section>
<section id="py-numpy-div" class="level3" data-number="6.8.2">
<h3 data-number="6.8.2" class="anchored" data-anchor-id="py-numpydiv"><span
class="header-section-number">6.8.2 </span> División </h3>
<p>Lo opuesto a la concatenación es la división, que se implementa mediante las funciones <code>np.split</code>, <code>np.hsplit</code> y <code>np.vsplit</code>. Para cada uno de estos, podemos pasar una lista de índices que dan los puntos de división:</p>
<div id="540697dd-4f61-46c7-aa5f-935ce37e4de2" class="cell">
<div class="sourceCode cell-code" id="cb52"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb52-1"><a href="#cb52-1" aria-hidden="true" tabindex="-1"></a>x <span class="op">=</span> [<span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">3</span>, <span class="dv">99</span>, <span class="dv">99</span>, <span class="dv">3</span>, <span class="dv">2</span>, <span class="dv">1</span>]</span>
<span id="cb52-2"><a href="#cb52-2" aria-hidden="true" tabindex="-1"></a>x1, x2, x3 <span class="op">=</span> np.split(x, [<span class="dv">3</span>, <span class="dv">5</span>])</span>
<span id="cb52-3"><a href="#cb52-3" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(x1, x2, x3)</span>
<span id="cb52-4"><a href="#cb52-4" aria-hidden="true" tabindex="-1"></a>x1[<span class="dv">0</span>] <span class="op">=</span> <span class="dv">15</span></span>
<span id="cb52-5"><a href="#cb52-5" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(x)</span>
<span id="cb52-6"><a href="#cb52-6" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(x1)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>Observe que <span class="math inline">\(N\)</span> puntos de división conducen a <span class="math inline">\(N + 1\)</span> subarreglos. Las funciones relacionadas <code>np.hsplit</code> y <code>np.vsplit</code> son similares:</p>
<div id="8ba2e736-6e2a-498a-9cb4-3024faac4c56" class="cell">
<div class="sourceCode cell-code" id="cb53"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb53-1"><a href="#cb53-1" aria-hidden="true" tabindex="-1"></a>grid <span class="op">=</span> np.arange(<span class="dv">16</span>).reshape((<span class="dv">4</span>, <span class="dv">4</span>))</span>
<span id="cb53-2"><a href="#cb53-2" aria-hidden="true" tabindex="-1"></a>grid</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="5ac530ac-f77b-4a34-990a-2a0f5fa4ca15" class="cell">
<div class="sourceCode cell-code" id="cb54"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb54-1"><a href="#cb54-1" aria-hidden="true" tabindex="-1"></a>upper, lower <span class="op">=</span> np.vsplit(grid, [<span class="dv">2</span>])</span>
<span id="cb54-2"><a href="#cb54-2" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(upper)</span>
<span id="cb54-3"><a href="#cb54-3" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(lower)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="4d397c7a-ccf7-4e4e-9179-ca8e13ddff33" class="cell">
<div class="sourceCode cell-code" id="cb55"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb55-1"><a href="#cb55-1" aria-hidden="true" tabindex="-1"></a>left, right <span class="op">=</span> np.hsplit(grid, [<span class="dv">2</span>])</span>
<span id="cb55-2"><a href="#cb55-2" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(left)</span>
<span id="cb55-3"><a href="#cb55-3" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(right)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>De manera similar, <code>np.dsplit</code> dividirá matrices a lo largo del tercer eje.</p>
</section>
</section>
<!-- /6.8 -->
<!-- 6.9 -->
<section id="py-numpy-ufun" class="level2" data-number="6.9">
<h2 data-number="6.9" class="anchored" data-anchor-id="py-numpy-ufun"><span
class="header-section-number">6.9</span> Funciones universales </h2>
<p>Ya hemos discutido algunos de los aspectos básicos de NumPy. Ahora, profundizaremos en las razones por las que NumPy es tan importante en el mundo de la ciencia de datos de Python. Es decir, proporciona una interfaz fácil y flexible para el cálculo optimizado con matrices de datos.</p>
<p>El cálculo en matrices NumPy puede ser muy rápido o muy lento. La clave para hacerlo rápido es usar operaciones vectorizadas, generalmente implementadas a través de las funciones universales de NumPy (<a href="https://numpy.org/doc/stable/reference/ufuncs.html">UFuncs</a>).</p>
<section id="py-numpy-fund" class="level3" data-number="6.9.1">
<h3 data-number="6.9.1" class="anchored" data-anchor-id="py-nump-fund"><span
class="header-section-number">6.9.1 </span> Fundamentos de UFuncs </h3>
<p>Para muchos tipos de operaciones, NumPy proporciona una interfaz conveniente para este tipo de rutina compilada y tipificada estáticamente. Esto se conoce como operación vectorizada. Esto se puede lograr simplemente realizando una operación en la matriz, que luego se aplicará a cada elemento. Este enfoque vectorizado está diseñado para insertar el bucle en la capa compilada que subyace a NumPy, lo que lleva a una ejecución mucho más rápida.</p>
<div id="2de25792-cafd-42e8-9b28-c84984ae95f2" class="cell">
<div class="sourceCode cell-code" id="cb56"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb56-1"><a href="#cb56-1" aria-hidden="true" tabindex="-1"></a>np.random.seed(<span class="dv">0</span>)</span>
<span id="cb56-2"><a href="#cb56-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb56-3"><a href="#cb56-3" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> compute_reciprocals(values):</span>
<span id="cb56-4"><a href="#cb56-4" aria-hidden="true" tabindex="-1"></a> output <span class="op">=</span> np.empty(<span class="bu">len</span>(values))</span>
<span id="cb56-5"><a href="#cb56-5" aria-hidden="true" tabindex="-1"></a> <span class="cf">for</span> i <span class="kw">in</span> <span class="bu">range</span>(<span class="bu">len</span>(values)):</span>
<span id="cb56-6"><a href="#cb56-6" aria-hidden="true" tabindex="-1"></a> output[i] <span class="op">=</span> <span class="fl">1.0</span> <span class="op">/</span> values[i]</span>
<span id="cb56-7"><a href="#cb56-7" aria-hidden="true" tabindex="-1"></a> <span class="cf">return</span> output</span>
<span id="cb56-8"><a href="#cb56-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb56-9"><a href="#cb56-9" aria-hidden="true" tabindex="-1"></a>big_array <span class="op">=</span> np.random.randint(<span class="dv">1</span>, <span class="dv">100</span>, size<span class="op">=</span><span class="dv">1000000</span>)</span>
<span id="cb56-10"><a href="#cb56-10" aria-hidden="true" tabindex="-1"></a><span class="op">%</span>timeit compute_reciprocals(big_array)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="05a5a571-7c62-4540-a07e-97db14d47e4b" class="cell">
<div class="sourceCode cell-code" id="cb57"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb57-1"><a href="#cb57-1" aria-hidden="true" tabindex="-1"></a><span class="op">%</span>timeit (<span class="fl">1.0</span> <span class="op">/</span> big_array)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>Las operaciones vectorizadas en NumPy se implementan a través de <em>UFuncs</em>, cuyo objetivo principal es ejecutar rápidamente operaciones repetidas en valores en matrices NumPy. Las <em>UFuncs</em> son extremadamente flexibles: antes vimos una operación entre un escalar y una matriz, pero también podemos operar entre dos matrices:</p>
<div id="547dbf3a-cfaf-4d62-a337-0104facd44ea" class="cell">
<div class="sourceCode cell-code" id="cb58"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb58-1"><a href="#cb58-1" aria-hidden="true" tabindex="-1"></a>x <span class="op">=</span> np.arange(<span class="dv">5</span>)</span>
<span id="cb58-2"><a href="#cb58-2" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'x = </span><span class="sc">{</span>x<span class="sc">}</span><span class="ss">'</span>)</span>
<span id="cb58-3"><a href="#cb58-3" aria-hidden="true" tabindex="-1"></a>y <span class="op">=</span> np.arange(<span class="dv">1</span>, <span class="dv">6</span>)</span>
<span id="cb58-4"><a href="#cb58-4" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'y = </span><span class="sc">{</span>y<span class="sc">}</span><span class="ss">'</span>)</span>
<span id="cb58-5"><a href="#cb58-5" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'x/y = </span><span class="sc">{</span>x<span class="op">/</span>y<span class="sc">}</span><span class="ss">'</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="427596df-5b23-4067-a3f7-c8a12e463a10" class="cell">
<div class="sourceCode cell-code" id="cb59"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb59-1"><a href="#cb59-1" aria-hidden="true" tabindex="-1"></a>z <span class="op">=</span> np.arange(<span class="dv">9</span>)</span>
<span id="cb59-2"><a href="#cb59-2" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'z = </span><span class="ch">\n</span><span class="sc">{</span>z<span class="sc">}</span><span class="ss">'</span>)</span>
<span id="cb59-3"><a href="#cb59-3" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f'</span><span class="ch">\n</span><span class="ss"> 2 ** z = </span><span class="ch">\n</span><span class="sc">{</span> <span class="dv">2</span> <span class="op">**</span> z<span class="sc">}</span><span class="ss">'</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>La siguiente tabla enumera los operadores aritméticos implementados en NumPy:</p>
<table class="caption-top table">
<thead>
<tr class="header">
<th style="text-align: center;">Operador</th>
<th style="text-align: left;">UFunc equivalente</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td style="text-align: center;"><code>+</code></td>
<td style="text-align: left;"><code>np.add</code></td>
</tr>
<tr class="even">
<td style="text-align: center;"><code>-</code></td>
<td style="text-align: left;"><code>np.subtract</code></td>
</tr>
<tr class="odd">
<td style="text-align: center;"><code>-</code></td>
<td style="text-align: left;"><code>np.negative</code></td>
</tr>
<tr class="even">
<td style="text-align: center;"><code>*</code></td>
<td style="text-align: left;"><code>np.multiply</code></td>
</tr>
<tr class="odd">
<td style="text-align: center;"><code>/</code></td>
<td style="text-align: left;"><code>np.divide</code></td>
</tr>
<tr class="even">
<td style="text-align: center;"><code>//</code></td>
<td style="text-align: left;"><code>np.floor_divide</code></td>
</tr>
<tr class="odd">
<td style="text-align: center;"><code>**</code></td>
<td style="text-align: left;"><code>np.power</code></td>
</tr>
<tr class="even">
<td style="text-align: center;"><code>%</code></td>
<td style="text-align: left;"><code>np.mod</code></td>
</tr>
</tbody>
</table>
</section>
<section id="py-numpy-util" class="level3" data-number="6.9.2">
<h3 data-number="6.9.2" class="anchored" data-anchor-id="py-numpy-util"><span
class="header-section-number">6.9.2 </span> UFuncs útiles </h3>
<section id="valor-absoluto-signo-y-magnitud" class="level4">
<h4 class="anchored" data-anchor-id="valor-absoluto-signo-y-magnitud">Valor absoluto, signo y magnitud</h4>
<div id="9933fc57-1747-4829-90a7-b9289cb7e75c" class="cell">
<div class="sourceCode cell-code" id="cb60"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb60-1"><a href="#cb60-1" aria-hidden="true" tabindex="-1"></a>x <span class="op">=</span> np.array([<span class="op">-</span><span class="dv">2</span>, <span class="op">-</span><span class="dv">1</span>, <span class="dv">0</span>, <span class="dv">1</span>, <span class="dv">2</span>])</span>
<span id="cb60-2"><a href="#cb60-2" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(np.<span class="bu">abs</span>(x))</span>
<span id="cb60-3"><a href="#cb60-3" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(np.sign(x))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="edd35a48-525a-4291-9968-6ff0b2b3b43f" class="cell">
<div class="sourceCode cell-code" id="cb61"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb61-1"><a href="#cb61-1" aria-hidden="true" tabindex="-1"></a>x <span class="op">=</span> np.array([<span class="dv">3</span> <span class="op">-</span> <span class="ot">4j</span>, <span class="dv">4</span> <span class="op">-</span> <span class="ot">3j</span>, <span class="dv">2</span> <span class="op">+</span> <span class="ot">0j</span>, <span class="dv">0</span> <span class="op">+</span> <span class="ot">1j</span>])</span>
<span id="cb61-2"><a href="#cb61-2" aria-hidden="true" tabindex="-1"></a>np.<span class="bu">abs</span>(x)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="funciones-trigonométricas" class="level4">
<h4 class="anchored" data-anchor-id="funciones-trigonométricas">Funciones trigonométricas</h4>
<div class="alert alert-block alert-info">
<p>Numpy trabaja sobre ángulos en radianes</p>
</div>
<div id="8d9f8b2d-9680-4acf-9fd6-4d602da5216d" class="cell">
<div class="sourceCode cell-code" id="cb62"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb62-1"><a href="#cb62-1" aria-hidden="true" tabindex="-1"></a>theta <span class="op">=</span> np.linspace(<span class="dv">0</span>, np.pi, <span class="dv">3</span>)</span>
<span id="cb62-2"><a href="#cb62-2" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="st">"theta = "</span>, theta)</span>
<span id="cb62-3"><a href="#cb62-3" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="st">"sin(theta) = "</span>, np.sin(theta))</span>
<span id="cb62-4"><a href="#cb62-4" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="st">"cos(theta) = "</span>, np.cos(theta))</span>