-
Notifications
You must be signed in to change notification settings - Fork 54
/
Copy pathItertools.html
275 lines (247 loc) · 25.6 KB
/
Itertools.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
<!DOCTYPE html>
<html class="writer-html5" lang="en" >
<head>
<meta charset="utf-8" /><meta content="Topic: simple use cases of python itertools, Difficulty: Easy, Category: Tutorial" name="description" />
<meta content="itertools, examples, zip, range, enumerate, chain, combinations" name="keywords" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<title>Python’s “Itertools” — Python Like You Mean It</title>
<link rel="stylesheet" href="../_static/pygments.css" type="text/css" />
<link rel="stylesheet" href="../_static/css/theme.css" type="text/css" />
<link rel="stylesheet" href="../_static/my_theme.css" type="text/css" />
<!--[if lt IE 9]>
<script src="../_static/js/html5shiv.min.js"></script>
<![endif]-->
<script data-url_root="../" id="documentation_options" src="../_static/documentation_options.js"></script>
<script src="../_static/jquery.js"></script>
<script src="../_static/underscore.js"></script>
<script src="../_static/doctools.js"></script>
<script async="async" src="https://www.googletagmanager.com/gtag/js?id=UA-115029372-1"></script>
<script src="../_static/gtag.js"></script>
<script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
<script>window.MathJax = {"tex": {"inlineMath": [["$", "$"], ["\\(", "\\)"]], "processEscapes": true}, "options": {"ignoreHtmlClass": "tex2jax_ignore|mathjax_ignore|document", "processHtmlClass": "tex2jax_process|mathjax_process|math|output_area"}}</script>
<script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<script src="../_static/js/theme.js"></script>
<link rel="index" title="Index" href="../genindex.html" />
<link rel="search" title="Search" href="../search.html" />
<link rel="next" title="Basics of Functions" href="Functions.html" />
<link rel="prev" title="Generators & Comprehension Expressions" href="Generators_and_Comprehensions.html" />
</head>
<body class="wy-body-for-nav">
<div class="wy-grid-for-nav">
<nav data-toggle="wy-nav-shift" class="wy-nav-side">
<div class="wy-side-scroll">
<div class="wy-side-nav-search" >
<a href="../index.html" class="icon icon-home"> Python Like You Mean It
</a>
<div class="version">
1.4
</div>
<div role="search">
<form id="rtd-search-form" class="wy-form" action="../search.html" method="get">
<input type="text" name="q" placeholder="Search docs" />
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</form>
</div>
</div><div class="wy-menu wy-menu-vertical" data-spy="affix" role="navigation" aria-label="Navigation menu">
<p class="caption" role="heading"><span class="caption-text">Table of Contents:</span></p>
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="../intro.html">Python Like You Mean It</a></li>
<li class="toctree-l1"><a class="reference internal" href="../module_1.html">Module 1: Getting Started with Python</a></li>
<li class="toctree-l1 current"><a class="reference internal" href="../module_2.html">Module 2: The Essentials of Python</a><ul class="current">
<li class="toctree-l2"><a class="reference internal" href="Basic_Objects.html">Basic Object Types</a></li>
<li class="toctree-l2"><a class="reference internal" href="SequenceTypes.html">Sequence Types</a></li>
<li class="toctree-l2"><a class="reference internal" href="Variables_and_Assignment.html">Variables & Assignment</a></li>
<li class="toctree-l2"><a class="reference internal" href="Introduction.html">Introducing Control Flow</a></li>
<li class="toctree-l2"><a class="reference internal" href="ConditionalStatements.html">Conditional Statements</a></li>
<li class="toctree-l2"><a class="reference internal" href="ForLoops.html">For-Loops and While-Loops</a></li>
<li class="toctree-l2"><a class="reference internal" href="Iterables.html">Iterables</a></li>
<li class="toctree-l2"><a class="reference internal" href="Generators_and_Comprehensions.html">Generators & Comprehension Expressions</a></li>
<li class="toctree-l2 current"><a class="current reference internal" href="#">Python’s “Itertools”</a><ul>
<li class="toctree-l3"><a class="reference internal" href="#Links-to-Official-Documentation">Links to Official Documentation</a></li>
<li class="toctree-l3"><a class="reference internal" href="#Reading-Comprehension:-Solutions">Reading Comprehension: Solutions</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="Functions.html">Basics of Functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="Scope.html">Scope</a></li>
<li class="toctree-l2"><a class="reference internal" href="DataStructures.html">Data Structures (Part I): Introduction</a></li>
<li class="toctree-l2"><a class="reference internal" href="DataStructures_II_Dictionaries.html">Data Structures (Part II): Dictionaries</a></li>
<li class="toctree-l2"><a class="reference internal" href="DataStructures_III_Sets_and_More.html">Data Structures (Part III): Sets & the Collections Module</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../module_2_problems.html">Module 2: Problems</a></li>
<li class="toctree-l1"><a class="reference internal" href="../module_3.html">Module 3: The Essentials of NumPy</a></li>
<li class="toctree-l1"><a class="reference internal" href="../module_3_problems.html">Module 3: Problems</a></li>
<li class="toctree-l1"><a class="reference internal" href="../module_4.html">Module 4: Object Oriented Programming</a></li>
<li class="toctree-l1"><a class="reference internal" href="../module_5.html">Module 5: Odds and Ends</a></li>
<li class="toctree-l1"><a class="reference internal" href="../changes.html">Changelog</a></li>
</ul>
</div>
</div>
</nav>
<section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" >
<i data-toggle="wy-nav-top" class="fa fa-bars"></i>
<a href="../index.html">Python Like You Mean It</a>
</nav>
<div class="wy-nav-content">
<div class="rst-content">
<div role="navigation" aria-label="Page navigation">
<ul class="wy-breadcrumbs">
<li><a href="../index.html" class="icon icon-home"></a> »</li>
<li><a href="../module_2.html">Module 2: The Essentials of Python</a> »</li>
<li>Python’s “Itertools”</li>
<li class="wy-breadcrumbs-aside">
<a href="../_sources/Module2_EssentialsOfPython/Itertools.md.txt" rel="nofollow"> View page source</a>
</li>
</ul>
<hr/>
</div>
<div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
<div itemprop="articleBody">
<style>
/* CSS overrides for sphinx_rtd_theme */
/* 24px margin */
.nbinput.nblast.container,
.nboutput.nblast.container {
margin-bottom: 19px; /* padding has already 5px */
}
/* ... except between code cells! */
.nblast.container + .nbinput.container {
margin-top: -19px;
}
.admonition > p:before {
margin-right: 4px; /* make room for the exclamation icon */
}
/* Fix math alignment, see https://github.com/rtfd/sphinx_rtd_theme/pull/686 */
.math {
text-align: unset;
}
</style>
<div class="section" id="Python’s-“Itertools”">
<h1>Python’s “Itertools”<a class="headerlink" href="#Python’s-“Itertools”" title="Permalink to this headline"></a></h1>
<p>Python has an <a class="reference external" href="https://docs.python.org/3/library/itertools.html">itertools module</a>, which provides a core set of fast, memory-efficient tools for creating iterators. We will briefly showcase a few itertools here. The majority of these functions create <a class="reference external" href="https://www.pythonlikeyoumeanit.com/Module2_EssentialsOfPython/Generators_and_Comprehensions.html">generators</a>, thus we will have to iterate over them in order to explicitly demonstrate their use. It is hard to overstate the utility of this
module - it is strongly recommended that you take some time to see what it has in store.</p>
<p>There are three built-in functions, <code class="docutils literal notranslate"><span class="pre">range</span></code>, <code class="docutils literal notranslate"><span class="pre">enumerate</span></code>, and <code class="docutils literal notranslate"><span class="pre">zip</span></code>, that belong in itertools, but they are so useful that they are made accessible immediately and do not need to be imported. It is essential that <code class="docutils literal notranslate"><span class="pre">range</span></code>, <code class="docutils literal notranslate"><span class="pre">enumerate</span></code>, and <code class="docutils literal notranslate"><span class="pre">zip</span></code> become tools that you are comfortable using.</p>
<p><strong>range</strong></p>
<p>Generate a sequence of integers in the specified “range”:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># will generate 0.. 1.. 2.. ... 8.. 9</span>
<span class="o">>>></span> <span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
<span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
<span class="o">>>></span> <span class="nb">list</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">))</span>
<span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">]</span>
<span class="c1"># will generate 0.. 3.. 6.. 9</span>
<span class="o">>>></span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="o">>>></span> <span class="nb">list</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
<span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">9</span><span class="p">]</span>
</pre></div>
</div>
<p><strong>enumerate</strong></p>
<p>Enumerates the items in an iterable: yielding a tuple containing the iteration count (starting with 0) and the corresponding item from the the iterable.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># will generate (0, 'apple').. (1, 'banana').. (2, 'cat').. (3, 'dog')]</span>
<span class="o">>>></span> <span class="nb">enumerate</span><span class="p">([</span><span class="s2">"apple"</span><span class="p">,</span> <span class="s2">"banana"</span><span class="p">,</span> <span class="s2">"cat"</span><span class="p">,</span> <span class="s2">"dog"</span><span class="p">])</span>
<span class="o"><</span><span class="nb">enumerate</span> <span class="n">at</span> <span class="mh">0x23e3557b3f0</span><span class="o">></span>
<span class="o">>>></span> <span class="nb">list</span><span class="p">(</span><span class="nb">enumerate</span><span class="p">([</span><span class="s2">"apple"</span><span class="p">,</span> <span class="s2">"banana"</span><span class="p">,</span> <span class="s2">"cat"</span><span class="p">,</span> <span class="s2">"dog"</span><span class="p">]))</span>
<span class="p">[(</span><span class="mi">0</span><span class="p">,</span> <span class="s1">'apple'</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="s1">'banana'</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="s1">'cat'</span><span class="p">),</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="s1">'dog'</span><span class="p">)]</span>
</pre></div>
</div>
<p><strong>zip</strong></p>
<p>Zips together the corresponding elements of several iterables into tuples. This is valuable for “pairing” corresponding items across multiple iterables.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">names</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"Angie"</span><span class="p">,</span> <span class="s2">"Brian"</span><span class="p">,</span> <span class="s2">"Cassie"</span><span class="p">,</span> <span class="s2">"David"</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">exam_1_scores</span> <span class="o">=</span> <span class="p">[</span><span class="mi">90</span><span class="p">,</span> <span class="mi">82</span><span class="p">,</span> <span class="mi">79</span><span class="p">,</span> <span class="mi">87</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">exam_2_scores</span> <span class="o">=</span> <span class="p">[</span><span class="mi">95</span><span class="p">,</span> <span class="mi">84</span><span class="p">,</span> <span class="mi">72</span><span class="p">,</span> <span class="mi">91</span><span class="p">]</span>
<span class="go"># will generate ('Angie', 90, 95).. ('Brian', 82, 84).. ('Cassie', 79, 72).. ('David', 87, 91)]</span>
<span class="gp">>>> </span><span class="nb">zip</span><span class="p">(</span><span class="n">names</span><span class="p">,</span> <span class="n">exam_1_scores</span><span class="p">,</span> <span class="n">exam_2_scores</span><span class="p">)</span>
<span class="go"><zip at 0x20de1082608></span>
<span class="gp">>>> </span><span class="nb">list</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">names</span><span class="p">,</span> <span class="n">exam_1_scores</span><span class="p">,</span> <span class="n">exam_2_scores</span><span class="p">))</span>
<span class="go">[('Angie', 90, 95), ('Brian', 82, 84), ('Cassie', 79, 72), ('David', 87, 91)]</span>
</pre></div>
</div>
<hr class="docutils" />
<p>The following are some of the many useful tools provided by the <code class="docutils literal notranslate"><span class="pre">itertools</span></code> module:</p>
<p><strong>itertools.chain</strong></p>
<p>Chains together multiple iterables, end-to-end, forming a single iterable:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">chain</span>
<span class="gp">>>> </span><span class="n">gen_1</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="c1"># 0.. 2.. 4</span>
<span class="gp">>>> </span><span class="n">gen_2</span> <span class="o">=</span> <span class="p">(</span><span class="n">i</span><span class="o">**</span><span class="mi">2</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">6</span><span class="p">))</span> <span class="c1"># 9.. 16.. 25</span>
<span class="gp">>>> </span><span class="n">iter_3</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"moo"</span><span class="p">,</span> <span class="s2">"cow"</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">iter_4</span> <span class="o">=</span> <span class="s2">"him"</span>
<span class="go"># will generate: 0.. 2.. 4.. 9.. 16.. 25.. 'moo'.. 'cow'.. 'h'.. 'i'.. 'm'</span>
<span class="gp">>>> </span><span class="n">chain</span><span class="p">(</span><span class="n">gen_1</span><span class="p">,</span> <span class="n">gen_2</span><span class="p">,</span> <span class="n">iter_3</span><span class="p">,</span> <span class="n">iter_4</span><span class="p">)</span>
<span class="go"><itertools.chain at 0x20de109ec18></span>
</pre></div>
</div>
<p><strong>itertools.combinations</strong> Generate all length-n tuples storing “combinations” of items from an iterable:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">combinations</span>
<span class="go"># will generate: (0, 1, 2).. (0, 1, 3).. (0, 2, 3).. (1, 2, 3)</span>
<span class="gp">>>> </span><span class="n">combinations</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="mi">3</span><span class="p">)</span> <span class="c1"># generate all length-3 combinations from [0, 1, 2, 3]</span>
<span class="go"><itertools.combinations at 0x20de10a7728></span>
</pre></div>
</div>
<div class="admonition note">
<p class="admonition-title fa fa-exclamation-circle"><strong>Reading Comprehension: Itertools I</strong></p>
<p>Using the <code class="docutils literal notranslate"><span class="pre">itertools.combinations</span></code> function, find the probability that two randomly drawn items from the list <code class="docutils literal notranslate"><span class="pre">["apples",</span> <span class="pre">"bananas",</span> <span class="pre">"pears",</span> <span class="pre">"pears",</span> <span class="pre">"oranges"]</span></code> would yield a combination of “apples” and “pears”.</p>
</div>
<div class="admonition note">
<p class="admonition-title fa fa-exclamation-circle"><strong>Reading Comprehension: Itertools II</strong></p>
<p>Given the list <code class="docutils literal notranslate"><span class="pre">x_vals</span> <span class="pre">=</span> <span class="pre">[0.1,</span> <span class="pre">0.3,</span> <span class="pre">0.6,</span> <span class="pre">0.9]</span></code>, create a generator, <code class="docutils literal notranslate"><span class="pre">y_gen</span></code>, that will generate the y-value <span class="math notranslate nohighlight">\(y = x^2\)</span> for each value of <span class="math notranslate nohighlight">\(x\)</span>. Then, using <code class="docutils literal notranslate"><span class="pre">zip</span></code>, create a list of the <span class="math notranslate nohighlight">\((x, y)\)</span> pairs, each pair stored in a tuple.</p>
</div>
<div class="section" id="Links-to-Official-Documentation">
<h2>Links to Official Documentation<a class="headerlink" href="#Links-to-Official-Documentation" title="Permalink to this headline"></a></h2>
<ul class="simple">
<li><p><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#typesseq-range">range</a></p></li>
<li><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#enumerate">enumerate</a></p></li>
<li><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#zip">zip</a></p></li>
<li><p><a class="reference external" href="https://docs.python.org/3/library/itertools.html">itertools</a></p></li>
</ul>
</div>
<div class="section" id="Reading-Comprehension:-Solutions">
<h2>Reading Comprehension: Solutions<a class="headerlink" href="#Reading-Comprehension:-Solutions" title="Permalink to this headline"></a></h2>
<p><strong>Itertools I: Solution</strong></p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">combinations</span>
<span class="gp">>>> </span><span class="n">ls</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"apples"</span><span class="p">,</span> <span class="s2">"bananas"</span><span class="p">,</span> <span class="s2">"pears"</span><span class="p">,</span> <span class="s2">"pears"</span><span class="p">,</span> <span class="s2">"oranges"</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">comb_ls</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">combinations</span><span class="p">(</span><span class="n">ls</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">comb_ls</span><span class="o">.</span><span class="n">count</span><span class="p">((</span><span class="s2">"apples"</span><span class="p">,</span> <span class="s2">"pears"</span><span class="p">))</span> <span class="o">/</span> <span class="nb">len</span><span class="p">(</span><span class="n">comb_ls</span><span class="p">)</span>
<span class="go">0.2</span>
</pre></div>
</div>
<p><strong>Itertools II: Solution</strong></p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x_vals</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">,</span> <span class="mf">0.6</span><span class="p">,</span> <span class="mf">0.9</span><span class="p">]</span>
<span class="gp">>>> </span><span class="n">y_gen</span> <span class="o">=</span> <span class="p">(</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">x_vals</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">list</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">x_vals</span><span class="p">,</span> <span class="n">y_gen</span><span class="p">))</span>
<span class="go">[(0.1, 0.01), (0.3, 0.09), (0.6, 0.36), (0.9, 0.81)]</span>
</pre></div>
</div>
<p>In this instance, the use of <code class="docutils literal notranslate"><span class="pre">zip</span></code> is a bit contrived. We could have foregone creating <code class="docutils literal notranslate"><span class="pre">y_gen</span></code> by just using the following list-comprehension:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x_vals</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">,</span> <span class="mf">0.6</span><span class="p">,</span> <span class="mf">0.9</span><span class="p">]</span>
<span class="gp">>>> </span><span class="p">[(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">x_vals</span><span class="p">]</span>
<span class="go">[(0.1, 0.01), (0.3, 0.09), (0.6, 0.36), (0.9, 0.81)]</span>
</pre></div>
</div>
</div>
</div>
</div>
</div>
<footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
<a href="Generators_and_Comprehensions.html" class="btn btn-neutral float-left" title="Generators & Comprehension Expressions" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
<a href="Functions.html" class="btn btn-neutral float-right" title="Basics of Functions" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a>
</div>
<hr/>
<div role="contentinfo">
<p>© Copyright 2021, Ryan Soklaski.</p>
</div>
Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
<a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a>
provided by <a href="https://readthedocs.org">Read the Docs</a>.
</footer>
</div>
</div>
</section>
</div>
<script>
jQuery(function () {
SphinxRtdTheme.Navigation.enable(true);
});
</script>
</body>
</html>