{"id":4249,"date":"2022-08-08T09:57:49","date_gmt":"2022-08-08T09:57:49","guid":{"rendered":"https:\/\/www.pythontutorial.net\/?page_id=4249"},"modified":"2022-08-16T03:36:00","modified_gmt":"2022-08-16T03:36:00","slug":"numpy-array-indexing","status":"publish","type":"page","link":"https:\/\/www.pythontutorial.net\/python-numpy\/numpy-array-indexing\/","title":{"rendered":"NumPy Array Indexing"},"content":{"rendered":"\n<p><strong>Summary<\/strong>: in this tutorial, you&#8217;ll learn how to access elements of a numpy array using indices.<\/p>\n\n\n\n<p>Like a <a href=\"https:\/\/www.pythontutorial.net\/python-basics\/python-list\/\">list<\/a>, you can use the square bracket notation (<code>[]<\/code>) to access elements of a <a href=\"https:\/\/www.pythontutorial.net\/python-numpy\/create-numpy-array\/\">numpy array<\/a>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id='numpy-array-indexing-on-1-d-arrays'>NumPy array indexing on 1-D arrays <a href=\"#numpy-array-indexing-on-1-d-arrays\" class=\"anchor\" id=\"numpy-array-indexing-on-1-d-arrays\" title=\"Anchor for NumPy array indexing on 1-D arrays\">#<\/a><\/h2>\n\n\n\n<p>Along a single axis, you can select elements using indices. The first element starts with index 0, the second element starts with index 1, and so on.<\/p>\n\n\n\n<p>Besides the non-negative indices, you can use negative indices to locate elements. For example, the last element has an index -1, the second last element has an index -2, and so on.<\/p>\n\n\n\n<p>The following example shows how to access elements of a one-dimensional array:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/www.pythontutorial.net\/wp-content\/uploads\/2022\/08\/numpy-array-indexing-1-d-array.svg\" alt=\"numpy array indexing - 1-d array\" class=\"wp-image-4269\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-1\" data-shcb-language-name=\"Python\" data-shcb-language-slug=\"python\"><span><code class=\"hljs language-python\"><span class=\"hljs-keyword\">import<\/span> numpy <span class=\"hljs-keyword\">as<\/span> np\n\na = np.arange(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">5<\/span>)\nprint(a)\n\nprint(a&#91;<span class=\"hljs-number\">0<\/span>])\nprint(a&#91;<span class=\"hljs-number\">1<\/span>])\nprint(a&#91;<span class=\"hljs-number\">-1<\/span>])<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-1\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">Python<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">python<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>Output:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-2\" data-shcb-language-name=\"Python\" data-shcb-language-slug=\"python\"><span><code class=\"hljs language-python\">&#91;<span class=\"hljs-number\">0<\/span> <span class=\"hljs-number\">1<\/span> <span class=\"hljs-number\">2<\/span> <span class=\"hljs-number\">3<\/span> <span class=\"hljs-number\">4<\/span>]\n<span class=\"hljs-number\">0<\/span>\n<span class=\"hljs-number\">1<\/span>\n<span class=\"hljs-number\">4<\/span>\n<span class=\"hljs-number\">3<\/span><\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-2\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">Python<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">python<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>In this example:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>The a[0] returns the first element (0)<\/li><li>The a[1] returns the second element (1)<\/li><li>The a[-1] returns the last element (4)<\/li><li>The a[-2] returns the second last element (3)<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id='numpy-array-indexing-on-2-d-arrays'>NumPy array indexing on 2-D arrays <a href=\"#numpy-array-indexing-on-2-d-arrays\" class=\"anchor\" id=\"numpy-array-indexing-on-2-d-arrays\" title=\"Anchor for NumPy array indexing on 2-D arrays\">#<\/a><\/h2>\n\n\n\n<p>With 2-D and multidimensional arrays, you can select elements as you do with 1-D arrays but for each dimension (or axis). For example:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/www.pythontutorial.net\/wp-content\/uploads\/2022\/08\/numpy-array-indexing-2d-array.svg\" alt=\"NumPy Array Indexing - 2D array\" class=\"wp-image-4263\"\/><\/figure>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-3\" data-shcb-language-name=\"Python\" data-shcb-language-slug=\"python\"><span><code class=\"hljs language-python\"><span class=\"hljs-keyword\">import<\/span> numpy <span class=\"hljs-keyword\">as<\/span> np\n\na = np.array(&#91;\n    &#91;<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">3<\/span>],\n    &#91;<span class=\"hljs-number\">4<\/span>, <span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">6<\/span>]\n])\n\nprint(a.shape)\n\nprint(a&#91;<span class=\"hljs-number\">0<\/span>])  <span class=\"hljs-comment\"># &#91;1 2 3]<\/span>\nprint(a&#91;<span class=\"hljs-number\">1<\/span>])  <span class=\"hljs-comment\"># &#91;4 5 6]<\/span>\n\nprint(a&#91;<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0<\/span>])  <span class=\"hljs-comment\"># 1<\/span>\nprint(a&#91;<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">0<\/span>])  <span class=\"hljs-comment\"># 4<\/span>\nprint(a&#91;<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">2<\/span>])  <span class=\"hljs-comment\"># 3<\/span>\nprint(a&#91;<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">2<\/span>])  <span class=\"hljs-comment\"># 6<\/span>\nprint(a&#91;<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">-1<\/span>])  <span class=\"hljs-comment\"># 3<\/span>\nprint(a&#91;<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">-1<\/span>])  <span class=\"hljs-comment\"># 6<\/span><\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-3\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">Python<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">python<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>Output:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-4\" data-shcb-language-name=\"Python\" data-shcb-language-slug=\"python\"><span><code class=\"hljs language-python\">(<span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">3<\/span>)\n&#91;<span class=\"hljs-number\">1<\/span> <span class=\"hljs-number\">2<\/span> <span class=\"hljs-number\">3<\/span>]\n&#91;<span class=\"hljs-number\">4<\/span> <span class=\"hljs-number\">5<\/span> <span class=\"hljs-number\">6<\/span>]\n<span class=\"hljs-number\">1<\/span>\n<span class=\"hljs-number\">4<\/span>\n<span class=\"hljs-number\">3<\/span>\n<span class=\"hljs-number\">6<\/span>\n<span class=\"hljs-number\">3<\/span>\n<span class=\"hljs-number\">6<\/span><\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-4\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">Python<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">python<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>In this example, the numpy array a has the shape (2,3) therefore it has two axes: <\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>The first axis has 2 elements (2 lists)<\/li><li>The second axis has three elements (3 numbers)<\/li><\/ul>\n\n\n\n<p>The following explains how the array indexing works:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>The a[0] returns the first element of the first axis, which is [1 2 3].<\/li><li>The a[1] returns the second element of the first axis, which is [4 5 6]<\/li><li>The a[0, 0] = 1: 0 selects the first element of the first axis ([1 2 3]) and the first element of the second axis.<\/li><li>The a[1, 0] = 4: 1 selects the second element of the first axis ([4 5 6]) and 0 selects the first element of the second axis.<\/li><li>The a[0, 2]) = 3: 0 selects the first element of the first axis ([1 2 3]) axis and 2 selects the third element of the second axis.<\/li><li>The a[1, 2] = 6: 1 selects the second element of the first axis ([4 5 6]) and 2 selects the third element of the second axis.<\/li><li>The a[0, -1] = 3: 0 selects the first element of the first axis ([1 2 3]) and -1 selects the last element of the second axis.<\/li><li>The a[1, -1] = 6: 1 selects the second element of the first axis ([1 2 3]) and -1 selects the last element of the second axis.<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id='numpy-array-indexing-on-3-d-arrays'>NumPy array indexing on 3-D arrays <a href=\"#numpy-array-indexing-on-3-d-arrays\" class=\"anchor\" id=\"numpy-array-indexing-on-3-d-arrays\" title=\"Anchor for NumPy array indexing on 3-D arrays\">#<\/a><\/h2>\n\n\n\n<p>The following example creates a 3-D numpy array:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/www.pythontutorial.net\/wp-content\/uploads\/2022\/08\/numpy-array-indexing-3d-array.svg\" alt=\"NumPy Array Indexing - 3D array\" class=\"wp-image-4265\"\/><\/figure>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-5\" data-shcb-language-name=\"Python\" data-shcb-language-slug=\"python\"><span><code class=\"hljs language-python\"><span class=\"hljs-keyword\">import<\/span> numpy <span class=\"hljs-keyword\">as<\/span> np\n\na = np.array(&#91;\n    &#91;&#91;<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">2<\/span>], &#91;<span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">4<\/span>], &#91;<span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">6<\/span>]],\n    &#91;&#91;<span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">6<\/span>], &#91;<span class=\"hljs-number\">7<\/span>, <span class=\"hljs-number\">8<\/span>], &#91;<span class=\"hljs-number\">9<\/span>, <span class=\"hljs-number\">10<\/span>]],\n])\n\nprint(a.shape)<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-5\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">Python<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">python<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>Output:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-6\" data-shcb-language-name=\"Python\" data-shcb-language-slug=\"python\"><span><code class=\"hljs language-python\">(<span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">2<\/span>)<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-6\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">Python<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">python<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>The array has three axes. <\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>The first axis has 2 elements (2 lists of lists of numbers)<\/li><li>The second axis has 3 elements  (3 lists of numbers)<\/li><li>The third axis has 2 elements (2 numbers)<\/li><\/ul>\n\n\n\n<p>For example:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-7\" data-shcb-language-name=\"Python\" data-shcb-language-slug=\"python\"><span><code class=\"hljs language-python\"><span class=\"hljs-keyword\">import<\/span> numpy <span class=\"hljs-keyword\">as<\/span> np\n\na = np.array(&#91;\n    &#91;&#91;<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">2<\/span>], &#91;<span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">4<\/span>], &#91;<span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">6<\/span>]],\n    &#91;&#91;<span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">6<\/span>], &#91;<span class=\"hljs-number\">7<\/span>, <span class=\"hljs-number\">8<\/span>], &#91;<span class=\"hljs-number\">9<\/span>, <span class=\"hljs-number\">10<\/span>]],\n])\n\nprint(a&#91;<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">1<\/span>])  <span class=\"hljs-comment\"># 2<\/span><\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-7\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">Python<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">python<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>The following expression returns 2:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-8\" data-shcb-language-name=\"Python\" data-shcb-language-slug=\"python\"><span><code class=\"hljs language-python\">a&#91;<span class=\"hljs-number\">0<\/span>,<span class=\"hljs-number\">0<\/span>,<span class=\"hljs-number\">1<\/span>]<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-8\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">Python<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">python<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>The first number 0 selects the first element of the first axis so it returns:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-9\" data-shcb-language-name=\"Python\" data-shcb-language-slug=\"python\"><span><code class=\"hljs language-python\">&#91;&#91;<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">2<\/span>], &#91;<span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">4<\/span>], &#91;<span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">6<\/span>]]<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-9\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">Python<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">python<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>The second number 0 selects the first element of the second axis so it returns:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-10\" data-shcb-language-name=\"Python\" data-shcb-language-slug=\"python\"><span><code class=\"hljs language-python\">&#91;<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">2<\/span>]<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-10\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">Python<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">python<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>The third number (1) selects the second element of the third axis which returns 2.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id='summary'>Summary <a href=\"#summary\" class=\"anchor\" id=\"summary\" title=\"Anchor for Summary\">#<\/a><\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li>Use square bracket notation [] with an index to access elements of a numpy array.<\/li><li>Use zero and positive indexes to start selecting from the beginning of the array.<\/li><li>Use negative indexes to start selecting from the end of the array.<\/li><\/ul>\n<div class=\"helpful-block-content\" data-title=\"\">\n\t<header>\n\t\t<div class=\"wth-question\">Was this tutorial helpful ?<\/div>\n\t\t<div 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