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mian-arham-haroon / repository
A complete SciPy learning repository with lecture notebooks, practice problems, and projects covering numerical analysis, statistics, optimization, and more. Built using Jupyter Notebooks and real datasets, this resource is ideal for anyone exploring scientific computing and applied math in Python.
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Welcome to the SciPy Learning Repository — a collection of my personal lecture notes, practice problems, and real-world projects built while learning scientific computing in Python using SciPy.
This repository is perfect for students, data science learners, and anyone exploring scientific analysis, optimization, and numerical computing with Python.
see on top-level directory
lectures/ - Lecture notes and explanationsprojects/ - Mini and full projects using SciPypractice/ - Practice problems and solutionsgit clone https://github.com/mian-arham-haroon/scipy_learning.git
cd scipy_learning
pip install -r requirements.txt
pip install scipy numpy matplotlib pandas jupyter
jupyter notebook
---
## ✅ 2. `requirements.txt`
```txt
scipy
numpy
matplotlib
pandas
jupyter
Selected from shared topics, language and repository description—not editorial ratings.
ruddra /
A complete docker package for django which is easy to understand and can be deployed anywhere(supports Data Science related libraries like numpy, scipy etc).
79/100 healthsanusanth /
What is Python? Executive Summary Python is an interpreted, object-oriented, high-level programming language with dynamic semantics. Its high-level built in data structures, combined with dynamic typing and dynamic binding, make it very attractive for Rapid Application Development, as well as for use as a scripting or glue language to connect existing components together. Python's simple, easy to learn syntax emphasizes readability and therefore reduces the cost of program maintenance. Python supports modules and packages, which encourages program modularity and code reuse. The Python interpreter and the extensive standard library are available in source or binary form without charge for all major platforms, and can be freely distributed. Often, programmers fall in love with Python because of the increased productivity it provides. Since there is no compilation step, the edit-test-debug cycle is incredibly fast. Debugging Python programs is easy: a bug or bad input will never cause a segmentation fault. Instead, when the interpreter discovers an error, it raises an exception. When the program doesn't catch the exception, the interpreter prints a stack trace. A source level debugger allows inspection of local and global variables, evaluation of arbitrary expressions, setting breakpoints, stepping through the code a line at a time, and so on. The debugger is written in Python itself, testifying to Python's introspective power. On the other hand, often the quickest way to debug a program is to add a few print statements to the source: the fast edit-test-debug cycle makes this simple approach very effective. What is Python? Python is a popular programming language. It was created by Guido van Rossum, and released in 1991. It is used for: web development (server-side), software development, mathematics, system scripting. What can Python do? Python can be used on a server to create web applications. Python can be used alongside software to create workflows. Python can connect to database systems. It can also read and modify files. Python can be used to handle big data and perform complex mathematics. Python can be used for rapid prototyping, or for production-ready software development. Why Python? Python works on different platforms (Windows, Mac, Linux, Raspberry Pi, etc). Python has a simple syntax similar to the English language. Python has syntax that allows developers to write programs with fewer lines than some other programming languages. Python runs on an interpreter system, meaning that code can be executed as soon as it is written. This means that prototyping can be very quick. Python can be treated in a procedural way, an object-oriented way or a functional way. Good to know The most recent major version of Python is Python 3, which we shall be using in this tutorial. However, Python 2, although not being updated with anything other than security updates, is still quite popular. In this tutorial Python will be written in a text editor. It is possible to write Python in an Integrated Development Environment, such as Thonny, Pycharm, Netbeans or Eclipse which are particularly useful when managing larger collections of Python files. Python Syntax compared to other programming languages Python was designed for readability, and has some similarities to the English language with influence from mathematics. Python uses new lines to complete a command, as opposed to other programming languages which often use semicolons or parentheses. Python relies on indentation, using whitespace, to define scope; such as the scope of loops, functions and classes. Other programming languages often use curly-brackets for this purpose. Applications for Python Python is used in many application domains. Here's a sampling. The Python Package Index lists thousands of third party modules for Python. Web and Internet Development Python offers many choices for web development: Frameworks such as Django and Pyramid. Micro-frameworks such as Flask and Bottle. Advanced content management systems such as Plone and django CMS. Python's standard library supports many Internet protocols: HTML and XML JSON E-mail processing. Support for FTP, IMAP, and other Internet protocols. Easy-to-use socket interface. And the Package Index has yet more libraries: Requests, a powerful HTTP client library. Beautiful Soup, an HTML parser that can handle all sorts of oddball HTML. Feedparser for parsing RSS/Atom feeds. Paramiko, implementing the SSH2 protocol. Twisted Python, a framework for asynchronous network programming. Scientific and Numeric Python is widely used in scientific and numeric computing: SciPy is a collection of packages for mathematics, science, and engineering. Pandas is a data analysis and modeling library. IPython is a powerful interactive shell that features easy editing and recording of a work session, and supports visualizations and parallel computing. The Software Carpentry Course teaches basic skills for scientific computing, running bootcamps and providing open-access teaching materials. Education Python is a superb language for teaching programming, both at the introductory level and in more advanced courses. Books such as How to Think Like a Computer Scientist, Python Programming: An Introduction to Computer Science, and Practical Programming. The Education Special Interest Group is a good place to discuss teaching issues. Desktop GUIs The Tk GUI library is included with most binary distributions of Python. Some toolkits that are usable on several platforms are available separately: wxWidgets Kivy, for writing multitouch applications. Qt via pyqt or pyside Platform-specific toolkits are also available: GTK+ Microsoft Foundation Classes through the win32 extensions Software Development Python is often used as a support language for software developers, for build control and management, testing, and in many other ways. SCons for build control. Buildbot and Apache Gump for automated continuous compilation and testing. Roundup or Trac for bug tracking and project management. Business Applications Python is also used to build ERP and e-commerce systems: Odoo is an all-in-one management software that offers a range of business applications that form a complete suite of enterprise management applications. Try ton is a three-tier high-level general purpose application platform.
hiteshsuthar01 /
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w3-button" href="/w3css/default.asp">Learn W3.CSS</a> <a class="w3-bar-item w3-button" href="/colors/default.asp">Learn Colors</a> <a class="w3-bar-item w3-button" href="/icons/default.asp">Learn Icons</a> <a class="w3-bar-item w3-button" href="/graphics/default.asp">Learn Graphics</a> <a class="w3-bar-item w3-button" href="/graphics/svg_intro.asp">Learn SVG</a> <a class="w3-bar-item w3-button" href="/graphics/canvas_intro.asp">Learn Canvas</a> <a class="w3-bar-item w3-button" href="/howto/default.asp">Learn How To</a> <a class="w3-bar-item w3-button" href="/sass/default.php">Learn Sass</a> <div class="w3-hide-large w3-hide-small"> <h3 class="w3-margin-top">Data Analytics</h3> <a class="w3-bar-item w3-button" href="/ai/default.asp">Learn AI</a> <a class="w3-bar-item w3-button" href="/python/python_ml_getting_started.asp">Learn Machine Learning</a> <a class="w3-bar-item w3-button" href="/datascience/default.asp">Learn Data Science</a> <a class="w3-bar-item w3-button" href="/python/numpy/default.asp">Learn NumPy</a> <a class="w3-bar-item w3-button" href="/python/pandas/default.asp">Learn Pandas</a> <a class="w3-bar-item w3-button" href="/python/scipy/index.php">Learn SciPy</a> <a class="w3-bar-item w3-button" href="/python/matplotlib_intro.asp">Learn Matplotlib</a> <a class="w3-bar-item w3-button" href="/statistics/index.php">Learn Statistics</a> <a class="w3-bar-item w3-button" href="/excel/index.php">Learn Excel</a> <h3 class="w3-margin-top">XML Tutorials</h3> <a class="w3-bar-item w3-button" href="/xml/default.asp">Learn XML</a> <a class="w3-bar-item w3-button" href="/xml/ajax_intro.asp">Learn XML AJAX</a> <a class="w3-bar-item w3-button" href="/xml/dom_intro.asp">Learn XML DOM</a> <a class="w3-bar-item w3-button" href="/xml/xml_dtd_intro.asp">Learn XML DTD</a> <a class="w3-bar-item w3-button" href="/xml/schema_intro.asp">Learn XML Schema</a> <a class="w3-bar-item w3-button" href="/xml/xsl_intro.asp">Learn XSLT</a> <a class="w3-bar-item 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href="/java/default.asp">Learn Java</a> <a class="w3-bar-item w3-button" href="/c/index.php">Learn C</a> <a class="w3-bar-item w3-button" href="/cpp/default.asp">Learn C++</a> <a class="w3-bar-item w3-button" href="/cs/index.php">Learn C#</a> <a class="w3-bar-item w3-button" href="/r/default.asp">Learn R</a> <a class="w3-bar-item w3-button" href="/kotlin/index.php">Learn Kotlin</a> <a class="w3-bar-item w3-button" href="/go/index.php">Learn Go</a> <a class="w3-bar-item w3-button" href="/django/index.php">Learn Django</a> <a class="w3-bar-item w3-button" href="/typescript/index.php">Learn TypeScript</a> </div> <div class="w3-col l3 m6"> <h3 class="w3-margin-top">Server Side</h3> <a class="w3-bar-item w3-button" href="/sql/default.asp">Learn SQL</a> <a class="w3-bar-item w3-button" href="/mysql/default.asp">Learn MySQL</a> <a class="w3-bar-item w3-button" href="/php/default.asp">Learn PHP</a> <a class="w3-bar-item w3-button" href="/asp/default.asp">Learn ASP</a> <a class="w3-bar-item w3-button" href="/nodejs/default.asp">Learn Node.js</a> <a class="w3-bar-item w3-button" href="/nodejs/nodejs_raspberrypi.asp">Learn Raspberry Pi</a> <a class="w3-bar-item w3-button" href="/git/default.asp">Learn Git</a> <a class="w3-bar-item w3-button" href="/aws/index.php">Learn AWS Cloud</a> <h3 class="w3-margin-top">Web Building</h3> <a class="w3-bar-item w3-button" href="https://www.w3schools.com/spaces" target="_blank" onclick="ga('send', 'event', 'spacesFromTutorialsAcc', 'click');" title="Get Your Own Website With W3schools Spaces">Create a Website <span class="ribbon-topnav ws-yellow">NEW</span></a> <a class="w3-bar-item w3-button" href="/where_to_start.asp">Where To Start</a> <a class="w3-bar-item w3-button" href="/w3css/w3css_templates.asp">Web Templates</a> <a class="w3-bar-item w3-button" href="/browsers/default.asp">Web Statistics</a> <a class="w3-bar-item w3-button" href="/cert/default.asp">Web Certificates</a> <a class="w3-bar-item w3-button" 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Pandas</a> <a class="w3-bar-item w3-button" href="/python/scipy/index.php">Learn SciPy</a> <a class="w3-bar-item w3-button" href="/python/matplotlib_intro.asp">Learn Matplotlib</a> <a class="w3-bar-item w3-button" href="/statistics/index.php">Learn Statistics</a> <a class="w3-bar-item w3-button" href="/excel/index.php">Learn Excel</a> <a class="w3-bar-item w3-button" href="/googlesheets/index.php">Learn Google Sheets</a> <h3 class="w3-margin-top">XML Tutorials</h3> <a class="w3-bar-item w3-button" href="/xml/default.asp">Learn XML</a> <a class="w3-bar-item w3-button" href="/xml/ajax_intro.asp">Learn XML AJAX</a> <a class="w3-bar-item w3-button" href="/xml/dom_intro.asp">Learn XML DOM</a> <a class="w3-bar-item w3-button" href="/xml/xml_dtd_intro.asp">Learn XML DTD</a> <a class="w3-bar-item w3-button" href="/xml/schema_intro.asp">Learn XML Schema</a> <a class="w3-bar-item w3-button" href="/xml/xsl_intro.asp">Learn XSLT</a> <a class="w3-bar-item w3-button" href="/xml/xpath_intro.asp">Learn XPath</a> <a class="w3-bar-item w3-button" href="/xml/xquery_intro.asp">Learn XQuery</a> </div> </div> </div> <br class="hidesm"> </nav> <nav id="nav_references" class="w3-hide-small" style="position: absolute; padding-bottom: 60px; display: none;"> <div class="w3-content" style="max-width:1100px;font-size:18px"> <span onclick="w3_close_nav('references')" class="w3-button w3-xxxlarge w3-display-topright w3-hover-white sectionxsclosenavspan" style="padding-right:30px;padding-left:30px;">×</span><br> <div class="w3-row-padding w3-bar-block"> <div class="w3-container" style="padding-left:13px"> <h2 style="color:#FFF4A3;"><b>References</b></h2> </div> <div class="w3-col l3 m6"> <h3 class="w3-margin-top">HTML</h3> <a class="w3-bar-item w3-button" href="/tags/default.asp">HTML Tag Reference</a> <a class="w3-bar-item w3-button" href="/tags/ref_html_browsersupport.asp">HTML Browser Support</a> <a class="w3-bar-item w3-button" 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href="/bootstrap4/bootstrap_ref_all_classes.asp">Bootstrap 4 Reference</a> <a class="w3-bar-item w3-button" href="/w3css/w3css_references.asp">W3.CSS Reference</a> <a class="w3-bar-item w3-button" href="/icons/icons_reference.asp">Icon Reference</a> <a class="w3-bar-item w3-button" href="/sass/sass_functions_string.php">Sass Reference</a> </div> <div class="w3-col l3 m6"> <h3 class="w3-margin-top">JavaScript</h3> <a class="w3-bar-item w3-button" href="/jsref/default.asp">JavaScript Reference</a> <a class="w3-bar-item w3-button" href="/jsref/default.asp">HTML DOM Reference</a> <a class="w3-bar-item w3-button" href="/jquery/jquery_ref_overview.asp">jQuery Reference</a> <a class="w3-bar-item w3-button" href="/angular/angular_ref_directives.asp">AngularJS Reference</a> <a class="w3-bar-item w3-button" href="/appml/appml_reference.asp">AppML Reference</a> <a class="w3-bar-item w3-button" href="/w3js/w3js_references.asp">W3.JS Reference</a> <h3 class="w3-margin-top">Programming</h3> <a class="w3-bar-item w3-button" href="/python/python_reference.asp">Python Reference</a> <a class="w3-bar-item w3-button" href="/java/java_ref_keywords.asp">Java Reference</a> </div> <div class="w3-col l3 m6"> <h3 class="w3-margin-top">Server Side</h3> <a class="w3-bar-item w3-button" href="/sql/sql_ref_keywords.asp">SQL Reference</a> <a class="w3-bar-item w3-button" href="/mysql/mysql_ref_functions.asp">MySQL Reference</a> <a class="w3-bar-item w3-button" href="/php/php_ref_overview.asp">PHP Reference</a> <a class="w3-bar-item w3-button" href="/asp/asp_ref_response.asp">ASP Reference</a> <h3 class="w3-margin-top">XML</h3> <a class="w3-bar-item w3-button" href="/xml/dom_nodetype.asp">XML DOM Reference</a> <a class="w3-bar-item w3-button" href="/xml/dom_http.asp">XML Http Reference</a> <a class="w3-bar-item w3-button" href="/xml/xsl_elementref.asp">XSLT Reference</a> <a class="w3-bar-item w3-button" href="/xml/schema_elements_ref.asp">XML Schema Reference</a> </div> <div class="w3-col l3 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Previous</span></a> <a class="w3-btn" href="default.asp"><span class="w3-hide-small">Complete HTML </span>Reference</a> <a class="w3-right w3-btn" href="tag_param.asp"><span class="w3-hide-small">Next </span>❯</a> </div> <br> <div class="w3-example"> <h3>Example</h3> <p>A paragraph is marked up as follows:</p> <div class="w3-code notranslate htmlHigh"> <span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue"><</span>p<span class="tagcolor" style="color:mediumblue">></span></span>This is some text in a paragraph.<span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue"><</span>/p<span class="tagcolor" style="color:mediumblue">></span></span> </div> <a target="_blank" href="tryit.asp?filename=tryhtml_paragraphs1" class="w3-btn w3-margin-bottom">Try it Yourself »</a> </div> <p>More "Try it Yourself" examples below.</p> <hr> <h2>Definition and Usage</h2> <p>The <code class="w3-codespan"><p></code> tag defines a paragraph.</p> <p>Browsers automatically add a single blank line before and after each <code class="w3-codespan"><p></code> element.</p> <p><strong>Tip:</strong> Use CSS to <a href="/html/html_css.asp">style paragraphs</a>.</p> <hr> <h2>Browser Support</h2> <table class="browserref notranslate"> <tbody><tr> <th style="width:20%;font-size:16px;text-align:left;">Element</th> <th style="width:16%;" class="bsChrome" title="Chrome"></th> <th style="width:16%;" class="bsEdge" title="Internet Explorer / Edge"></th> <th style="width:16%;" class="bsFirefox" title="Firefox"></th> <th style="width:16%;" class="bsSafari" title="Safari"></th> <th style="width:16%;" class="bsOpera" title="Opera"></th> </tr><tr> <td style="text-align:left;"><p></td> <td>Yes</td> <td>Yes</td> <td>Yes</td> <td>Yes</td> <td>Yes</td> </tr> </tbody></table> <hr> <h2>Global Attributes</h2> <p>The <code class="w3-codespan"><p></code> tag also supports the <a href="ref_standardattributes.asp">Global Attributes in HTML</a>.</p> <hr> <h2>Event Attributes</h2> <p>The <code class="w3-codespan"><p></code> tag also supports the <a href="ref_eventattributes.asp">Event Attributes in HTML</a>.</p> <hr> <div id="midcontentadcontainer" style="overflow:auto;text-align:center"> <!-- MidContent --> <!-- <p class="adtext">Advertisement</p> --> <div id="adngin-mid_content-0" data-google-query-id="CKfs_8ueqvcCFXiOSwUd2fYBLg"><div id="sn_ad_label_adngin-mid_content-0" class="sn_ad_label" style="color:#000000;font-size:12px;margin:0;text-align:center;">ADVERTISEMENT</div><div id="google_ads_iframe_/22152718,16833175/sws-hb//w3schools.com//mid_content_1__container__" style="border: 0pt none; display: inline-block; width: 300px; height: 250px;"><iframe frameborder="0" src="https://56d0da6c34aaa471db22bb4266aac656.safeframe.googlesyndication.com/safeframe/1-0-38/html/container.html" id="google_ads_iframe_/22152718,16833175/sws-hb//w3schools.com//mid_content_1" title="3rd party ad content" name="" scrolling="no" marginwidth="0" marginheight="0" width="300" height="250" data-is-safeframe="true" sandbox="allow-forms allow-popups allow-popups-to-escape-sandbox allow-same-origin allow-scripts allow-top-navigation-by-user-activation" role="region" aria-label="Advertisement" tabindex="0" data-google-container-id="8" style="border: 0px; vertical-align: bottom;" data-load-complete="true"></iframe></div></div> </div> <hr> <h2>More Examples</h2> <div class="w3-example"> <h3>Example</h3> <p>Align text in a paragraph (with CSS):</p> <div class="w3-code notranslate htmlHigh"> <span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue"><</span>p<span class="attributecolor" style="color:red"> style<span class="attributevaluecolor" style="color:mediumblue">="text-align:right"</span></span><span class="tagcolor" style="color:mediumblue">></span></span>This is some text in a paragraph.<span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue"><</span>/p<span class="tagcolor" style="color:mediumblue">></span></span> </div> <a target="_blank" href="tryit.asp?filename=tryhtml_p_align_css" class="w3-btn w3-margin-bottom">Try it Yourself »</a> </div> <div class="w3-example"> <h3>Example</h3> <p>Style paragraphs with CSS:</p> <div class="w3-code notranslate htmlHigh"> <span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue"><</span>html<span class="tagcolor" style="color:mediumblue">></span></span><br><span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue"><</span>head<span class="tagcolor" style="color:mediumblue">></span></span><br><span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue"><</span>style<span class="tagcolor" style="color:mediumblue">></span></span><span class="cssselectorcolor" style="color:brown"><br>p <span class="cssdelimitercolor" style="color:black">{</span><span class="csspropertycolor" style="color:red"><br> color<span class="csspropertyvaluecolor" style="color:mediumblue"><span class="cssdelimitercolor" style="color:black">:</span> navy<span class="cssdelimitercolor" style="color:black">;</span></span><br> text-indent<span class="csspropertyvaluecolor" style="color:mediumblue"><span class="cssdelimitercolor" style="color:black">:</span> 30px<span class="cssdelimitercolor" style="color:black">;</span></span><br> text-transform<span class="csspropertyvaluecolor" style="color:mediumblue"><span class="cssdelimitercolor" style="color:black">:</span> uppercase<span class="cssdelimitercolor" style="color:black">;</span></span><br></span><span class="cssdelimitercolor" style="color:black">}</span><br></span><span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue"><</span>/style<span class="tagcolor" style="color:mediumblue">></span></span><br> <span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue"><</span>/head<span class="tagcolor" style="color:mediumblue">></span></span><br><span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue"><</span>body<span class="tagcolor" style="color:mediumblue">></span></span><br><br><span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue"><</span>p<span class="tagcolor" style="color:mediumblue">></span></span>Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.<span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue"><</span>/p<span class="tagcolor" style="color:mediumblue">></span></span><br><br><span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue"><</span>/body<span class="tagcolor" style="color:mediumblue">></span></span><br><span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue"><</span>/html<span class="tagcolor" style="color:mediumblue">></span></span> </div> <a target="_blank" href="tryit.asp?filename=tryhtml_p_style_css" class="w3-btn w3-margin-bottom">Try it Yourself »</a> </div> <div class="w3-example"> <h3>Example</h3> <p> More on paragraphs:</p> <div class="w3-code notranslate htmlHigh"> <span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue"><</span>p<span class="tagcolor" style="color:mediumblue">></span></span><br>This paragraph<br>contains a lot of lines<br>in the source code,<br> but the browser <br>ignores it.<br><span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue"><</span>/p<span class="tagcolor" style="color:mediumblue">></span></span> </div> <a target="_blank" href="tryit.asp?filename=tryhtml_paragraphs2" class="w3-btn w3-margin-bottom">Try it Yourself »</a> </div> <div class="w3-example"> <h3>Example</h3> <p>Poem problems in HTML:</p> <div class="w3-code notranslate htmlHigh"> <span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue"><</span>p<span class="tagcolor" style="color:mediumblue">></span></span><br>My Bonnie lies over the ocean.<br>My Bonnie lies over the sea.<br>My Bonnie lies over the ocean.<br>Oh, bring back my Bonnie to me.<br><span class="tagnamecolor" style="color:brown"><span class="tagcolor" style="color:mediumblue"><</span>/p<span class="tagcolor" style="color:mediumblue">></span></span> </div> <a target="_blank" href="tryit.asp?filename=tryhtml_poem" class="w3-btn w3-margin-bottom">Try it Yourself »</a> </div> <hr> <h2>Related Pages</h2> <p>HTML tutorial: <a href="/html/html_paragraphs.asp">HTML Paragraphs</a></p> <p>HTML DOM reference: <a href="/jsref/dom_obj_paragraph.asp">Paragraph Object</a></p> <hr> <h2>Default CSS Settings</h2> <p>Most browsers will display the <code class="w3-codespan"><p></code> element with the following default values:</p> <div class="w3-example"> <h3>Example</h3> <div class="w3-code notranslate cssHigh"><span class="cssselectorcolor" style="color:brown"> p <span class="cssdelimitercolor" style="color:black">{</span><span class="csspropertycolor" style="color:red"><br> display<span class="csspropertyvaluecolor" style="color:mediumblue"><span class="cssdelimitercolor" style="color:black">:</span> block<span class="cssdelimitercolor" style="color:black">;</span></span><br> margin-top<span class="csspropertyvaluecolor" style="color:mediumblue"><span class="cssdelimitercolor" style="color:black">:</span> 1em<span class="cssdelimitercolor" style="color:black">;</span></span><br> margin-bottom<span class="csspropertyvaluecolor" style="color:mediumblue"><span class="cssdelimitercolor" style="color:black">:</span> 1em<span class="cssdelimitercolor" style="color:black">;</span></span><br> margin-left<span class="csspropertyvaluecolor" style="color:mediumblue"><span class="cssdelimitercolor" style="color:black">:</span> 0<span class="cssdelimitercolor" style="color:black">;</span></span><br> margin-right<span class="csspropertyvaluecolor" style="color:mediumblue"><span class="cssdelimitercolor" style="color:black">:</span> 0<span class="cssdelimitercolor" style="color:black">;</span></span><br></span><span class="cssdelimitercolor" style="color:black">}</span> </span></div> <a target="_blank" href="tryit.asp?filename=tryhtml_p_default_css" class="w3-btn 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Quickstart tutorial Prerequisites Before reading this tutorial you should know a bit of Python. If you would like to refresh your memory, take a look at the Python tutorial. If you wish to work the examples in this tutorial, you must also have some software installed on your computer. Please see https://scipy.org/install.html for instructions. Learner profile This tutorial is intended as a quick overview of algebra and arrays in NumPy and want to understand how n-dimensional (n>=2) arrays are represented and can be manipulated. In particular, if you don’t know how to apply common functions to n-dimensional arrays (without using for-loops), or if you want to understand axis and shape properties for n-dimensional arrays, this tutorial might be of help. Learning Objectives After this tutorial, you should be able to: Understand the difference between one-, two- and n-dimensional arrays in NumPy; Understand how to apply some linear algebra operations to n-dimensional arrays without using for-loops; Understand axis and shape properties for n-dimensional arrays. The Basics NumPy’s main object is the homogeneous multidimensional array. It is a table of elements (usually numbers), all of the same type, indexed by a tuple of non-negative integers. In NumPy dimensions are called axes. For example, the coordinates of a point in 3D space [1, 2, 1] has one axis. That axis has 3 elements in it, so we say it has a length of 3. In the example pictured below, the array has 2 axes. The first axis has a length of 2, the second axis has a length of 3. [[ 1., 0., 0.], [ 0., 1., 2.]] NumPy’s array class is called ndarray. It is also known by the alias array. Note that numpy.array is not the same as the Standard Python Library class array.array, which only handles one-dimensional arrays and offers less functionality. The more important attributes of an ndarray object are: ndarray.ndim the number of axes (dimensions) of the array. ndarray.shape the dimensions of the array. This is a tuple of integers indicating the size of the array in each dimension. For a matrix with n rows and m columns, shape will be (n,m). The length of the shape tuple is therefore the number of axes, ndim. ndarray.size the total number of elements of the array. This is equal to the product of the elements of shape. ndarray.dtype an object describing the type of the elements in the array. One can create or specify dtype’s using standard Python types. Additionally NumPy provides types of its own. numpy.int32, numpy.int16, and numpy.float64 are some examples. ndarray.itemsize the size in bytes of each element of the array. For example, an array of elements of type float64 has itemsize 8 (=64/8), while one of type complex32 has itemsize 4 (=32/8). It is equivalent to ndarray.dtype.itemsize. ndarray.data the buffer containing the actual elements of the array. Normally, we won’t need to use this attribute because we will access the elements in an array using indexing facilities. An example >>> import numpy as np a = np.arange(15).reshape(3, 5) a array([[ 0, 1, 2, 3, 4], [ 5, 6, 7, 8, 9], [10, 11, 12, 13, 14]]) a.shape (3, 5) a.ndim 2 a.dtype.name 'int64' a.itemsize 8 a.size 15 type(a) <class 'numpy.ndarray'> b = np.array([6, 7, 8]) b array([6, 7, 8]) type(b) <class 'numpy.ndarray'> Array Creation There are several ways to create arrays. For example, you can create an array from a regular Python list or tuple using the array function. The type of the resulting array is deduced from the type of the elements in the sequences. >>> >>> import numpy as np >>> a = np.array([2,3,4]) >>> a array([2, 3, 4]) >>> a.dtype dtype('int64') >>> b = np.array([1.2, 3.5, 5.1]) >>> b.dtype dtype('float64') A frequent error consists in calling array with multiple arguments, rather than providing a single sequence as an argument. >>> >>> a = np.array(1,2,3,4) # WRONG Traceback (most recent call last): ... TypeError: array() takes from 1 to 2 positional arguments but 4 were given >>> a = np.array([1,2,3,4]) # RIGHT array transforms sequences of sequences into two-dimensional arrays, sequences of sequences of sequences into three-dimensional arrays, and so on. >>> >>> b = np.array([(1.5,2,3), (4,5,6)]) >>> b array([[1.5, 2. , 3. ], [4. , 5. , 6. ]]) The type of the array can also be explicitly specified at creation time: >>> >>> c = np.array( [ [1,2], [3,4] ], dtype=complex ) >>> c array([[1.+0.j, 2.+0.j], [3.+0.j, 4.+0.j]]) Often, the elements of an array are originally unknown, but its size is known. Hence, NumPy offers several functions to create arrays with initial placeholder content. These minimize the necessity of growing arrays, an expensive operation. The function zeros creates an array full of zeros, the function ones creates an array full of ones, and the function empty creates an array whose initial content is random and depends on the state of the memory. By default, the dtype of the created array is float64. >>> >>> np.zeros((3, 4)) array([[0., 0., 0., 0.], [0., 0., 0., 0.], [0., 0., 0., 0.]]) >>> np.ones( (2,3,4), dtype=np.int16 ) # dtype can also be specified array([[[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]], [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]], dtype=int16) >>> np.empty( (2,3) ) # uninitialized array([[ 3.73603959e-262, 6.02658058e-154, 6.55490914e-260], # may vary [ 5.30498948e-313, 3.14673309e-307, 1.00000000e+000]]) To create sequences of numbers, NumPy provides the arange function which is analogous to the Python built-in range, but returns an array. >>> >>> np.arange( 10, 30, 5 ) array([10, 15, 20, 25]) >>> np.arange( 0, 2, 0.3 ) # it accepts float arguments array([0. , 0.3, 0.6, 0.9, 1.2, 1.5, 1.8]) When arange is used with floating point arguments, it is generally not possible to predict the number of elements obtained, due to the finite floating point precision. For this reason, it is usually better to use the function linspace that receives as an argument the number of elements that we want, instead of the step: >>> >>> from numpy import pi >>> np.linspace( 0, 2, 9 ) # 9 numbers from 0 to 2 array([0. , 0.25, 0.5 , 0.75, 1. , 1.25, 1.5 , 1.75, 2. ]) >>> x = np.linspace( 0, 2*pi, 100 ) # useful to evaluate function at lots of points >>> f = np.sin(x) See also array, zeros, zeros_like, ones, ones_like, empty, empty_like, arange, linspace, numpy.random.Generator.rand, numpy.random.Generator.randn, fromfunction, fromfile Printing Arrays When you print an array, NumPy displays it in a similar way to nested lists, but with the following layout: the last axis is printed from left to right, the second-to-last is printed from top to bottom, the rest are also printed from top to bottom, with each slice separated from the next by an empty line. One-dimensional arrays are then printed as rows, bidimensionals as matrices and tridimensionals as lists of matrices. >>> >>> a = np.arange(6) # 1d array >>> print(a) [0 1 2 3 4 5] >>> >>> b = np.arange(12).reshape(4,3) # 2d array >>> print(b) [[ 0 1 2] [ 3 4 5] [ 6 7 8] [ 9 10 11]] >>> >>> c = np.arange(24).reshape(2,3,4) # 3d array >>> print(c) [[[ 0 1 2 3] [ 4 5 6 7] [ 8 9 10 11]] [[12 13 14 15] [16 17 18 19] [20 21 22 23]]] See below to get more details on reshape. If an array is too large to be printed, NumPy automatically skips the central part of the array and only prints the corners: >>> >>> print(np.arange(10000)) [ 0 1 2 ... 9997 9998 9999] >>> >>> print(np.arange(10000).reshape(100,100)) [[ 0 1 2 ... 97 98 99] [ 100 101 102 ... 197 198 199] [ 200 201 202 ... 297 298 299] ... [9700 9701 9702 ... 9797 9798 9799] [9800 9801 9802 ... 9897 9898 9899] [9900 9901 9902 ... 9997 9998 9999]] To disable this behaviour and force NumPy to print the entire array, you can change the printing options using set_printoptions. >>> >>> np.set_printoptions(threshold=sys.maxsize) # sys module should be imported Basic Operations Arithmetic operators on arrays apply elementwise. A new array is created and filled with the result. >>> >>> a = np.array( [20,30,40,50] ) >>> b = np.arange( 4 ) >>> b array([0, 1, 2, 3]) >>> c = a-b >>> c array([20, 29, 38, 47]) >>> b**2 array([0, 1, 4, 9]) >>> 10*np.sin(a) array([ 9.12945251, -9.88031624, 7.4511316 , -2.62374854]) >>> a<35 array([ True, True, False, False]) Unlike in many matrix languages, the product operator * operates elementwise in NumPy arrays. The matrix product can be performed using the @ operator (in python >=3.5) or the dot function or method: >>> >>> A = np.array( [[1,1], ... [0,1]] ) >>> B = np.array( [[2,0], ... [3,4]] ) >>> A * B # elementwise product array([[2, 0], [0, 4]]) >>> A @ B # matrix product array([[5, 4], [3, 4]]) >>> A.dot(B) # another matrix product array([[5, 4], [3, 4]]) Some operations, such as += and *=, act in place to modify an existing array rather than create a new one. >>> >>> rg = np.random.default_rng(1) # create instance of default random number generator >>> a = np.ones((2,3), dtype=int) >>> b = rg.random((2,3)) >>> a *= 3 >>> a array([[3, 3, 3], [3, 3, 3]]) >>> b += a >>> b array([[3.51182162, 3.9504637 , 3.14415961], [3.94864945, 3.31183145, 3.42332645]]) >>> a += b # b is not automatically converted to integer type Traceback (most recent call last): ... numpy.core._exceptions.UFuncTypeError: Cannot cast ufunc 'add' output from dtype('float64') to dtype('int64') with casting rule 'same_kind' When operating with arrays of different types, the type of the resulting array corresponds to the more general or precise one (a behavior known as upcasting). >>> >>> a = np.ones(3, dtype=np.int32) >>> b = np.linspace(0,pi,3) >>> b.dtype.name 'float64' >>> c = a+b >>> c array([1. , 2.57079633, 4.14159265]) >>> c.dtype.name 'float64' >>> d = np.exp(c*1j) >>> d array([ 0.54030231+0.84147098j, -0.84147098+0.54030231j, -0.54030231-0.84147098j]) >>> d.dtype.name 'complex128' Many unary operations, such as computing the sum of all the elements in the array, are implemented as methods of the ndarray class. >>> >>> a = rg.random((2,3)) >>> a array([[0.82770259, 0.40919914, 0.54959369], [0.02755911, 0.75351311, 0.53814331]]) >>> a.sum() 3.1057109529998157 >>> a.min() 0.027559113243068367 >>> a.max() 0.8277025938204418 By default, these operations apply to the array as though it were a list of numbers, regardless of its shape. However, by specifying the axis parameter you can apply an operation along the specified axis of an array: >>> >>> b = np.arange(12).reshape(3,4) >>> b array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> >>> b.sum(axis=0) # sum of each column array([12, 15, 18, 21]) >>> >>> b.min(axis=1) # min of each row array([0, 4, 8]) >>> >>> b.cumsum(axis=1) # cumulative sum along each row array([[ 0, 1, 3, 6], [ 4, 9, 15, 22], [ 8, 17, 27, 38]]) Universal Functions NumPy provides familiar mathematical functions such as sin, cos, and exp. In NumPy, these are called “universal functions”(ufunc). Within NumPy, these functions operate elementwise on an array, producing an array as output. >>> >>> B = np.arange(3) >>> B array([0, 1, 2]) >>> np.exp(B) array([1. , 2.71828183, 7.3890561 ]) >>> np.sqrt(B) array([0. , 1. , 1.41421356]) >>> C = np.array([2., -1., 4.]) >>> np.add(B, C) array([2., 0., 6.]) See also all, any, apply_along_axis, argmax, argmin, argsort, average, bincount, ceil, clip, conj, corrcoef, cov, cross, cumprod, cumsum, diff, dot, floor, inner, invert, lexsort, max, maximum, mean, median, min, minimum, nonzero, outer, prod, re, round, sort, std, sum, trace, transpose, var, vdot, vectorize, where Indexing, Slicing and Iterating One-dimensional arrays can be indexed, sliced and iterated over, much like lists and other Python sequences. >>> >>> a = np.arange(10)**3 >>> a array([ 0, 1, 8, 27, 64, 125, 216, 343, 512, 729]) >>> a[2] 8 >>> a[2:5] array([ 8, 27, 64]) # equivalent to a[0:6:2] = 1000; # from start to position 6, exclusive, set every 2nd element to 1000 >>> a[:6:2] = 1000 >>> a array([1000, 1, 1000, 27, 1000, 125, 216, 343, 512, 729]) >>> a[ : :-1] # reversed a array([ 729, 512, 343, 216, 125, 1000, 27, 1000, 1, 1000]) >>> for i in a: ... print(i**(1/3.)) ... 9.999999999999998 1.0 9.999999999999998 3.0 9.999999999999998 4.999999999999999 5.999999999999999 6.999999999999999 7.999999999999999 8.999999999999998 Multidimensional arrays can have one index per axis. These indices are given in a tuple separated by commas: >>> >>> def f(x,y): ... return 10*x+y ... >>> b = np.fromfunction(f,(5,4),dtype=int) >>> b array([[ 0, 1, 2, 3], [10, 11, 12, 13], [20, 21, 22, 23], [30, 31, 32, 33], [40, 41, 42, 43]]) >>> b[2,3] 23 >>> b[0:5, 1] # each row in the second column of b array([ 1, 11, 21, 31, 41]) >>> b[ : ,1] # equivalent to the previous example array([ 1, 11, 21, 31, 41]) >>> b[1:3, : ] # each column in the second and third row of b array([[10, 11, 12, 13], [20, 21, 22, 23]]) When fewer indices are provided than the number of axes, the missing indices are considered complete slices: >>> >>> b[-1] # the last row. Equivalent to b[-1,:] array([40, 41, 42, 43]) The expression within brackets in b[i] is treated as an i followed by as many instances of : as needed to represent the remaining axes. NumPy also allows you to write this using dots as b[i,...]. The dots (...) represent as many colons as needed to produce a complete indexing tuple. For example, if x is an array with 5 axes, then x[1,2,...] is equivalent to x[1,2,:,:,:], x[...,3] to x[:,:,:,:,3] and x[4,...,5,:] to x[4,:,:,5,:]. >>> >>> c = np.array( [[[ 0, 1, 2], # a 3D array (two stacked 2D arrays) ... [ 10, 12, 13]], ... [[100,101,102], ... [110,112,113]]]) >>> c.shape (2, 2, 3) >>> c[1,...] # same as c[1,:,:] or c[1] array([[100, 101, 102], [110, 112, 113]]) >>> c[...,2] # same as c[:,:,2] array([[ 2, 13], [102, 113]]) Iterating over multidimensional arrays is done with respect to the first axis: >>> >>> for row in b: ... print(row) ... [0 1 2 3] [10 11 12 13] [20 21 22 23] [30 31 32 33] [40 41 42 43] However, if one wants to perform an operation on each element in the array, one can use the flat attribute which is an iterator over all the elements of the array: >>> >>> for element in b.flat: ... print(element) ... 0 1 2 3 10 11 12 13 20 21 22 23 30 31 32 33 40 41 42 43 See also Indexing, Indexing (reference), newaxis, ndenumerate, indices Shape Manipulation Changing the shape of an array An array has a shape given by the number of elements along each axis: >>> >>> a = np.floor(10*rg.random((3,4))) >>> a array([[3., 7., 3., 4.], [1., 4., 2., 2.], [7., 2., 4., 9.]]) >>> a.shape (3, 4) The shape of an array can be changed with various commands. Note that the following three commands all return a modified array, but do not change the original array: >>> >>> a.ravel() # returns the array, flattened array([3., 7., 3., 4., 1., 4., 2., 2., 7., 2., 4., 9.]) >>> a.reshape(6,2) # returns the array with a modified shape array([[3., 7.], [3., 4.], [1., 4.], [2., 2.], [7., 2.], [4., 9.]]) >>> a.T # returns the array, transposed array([[3., 1., 7.], [7., 4., 2.], [3., 2., 4.], [4., 2., 9.]]) >>> a.T.shape (4, 3) >>> a.shape (3, 4) The order of the elements in the array resulting from ravel() is normally “C-style”, that is, the rightmost index “changes the fastest”, so the element after a[0,0] is a[0,1]. If the array is reshaped to some other shape, again the array is treated as “C-style”. NumPy normally creates arrays stored in this order, so ravel() will usually not need to copy its argument, but if the array was made by taking slices of another array or created with unusual options, it may need to be copied. The functions ravel() and reshape() can also be instructed, using an optional argument, to use FORTRAN-style arrays, in which the leftmost index changes the fastest. The reshape function returns its argument with a modified shape, whereas the ndarray.resize method modifies the array itself: >>> >>> a array([[3., 7., 3., 4.], [1., 4., 2., 2.], [7., 2., 4., 9.]]) >>> a.resize((2,6)) >>> a array([[3., 7., 3., 4., 1., 4.], [2., 2., 7., 2., 4., 9.]]) If a dimension is given as -1 in a reshaping operation, the other dimensions are automatically calculated: >>> >>> a.reshape(3,-1) array([[3., 7., 3., 4.], [1., 4., 2., 2.], [7., 2., 4., 9.]]) See also ndarray.shape, reshape, resize, ravel Stacking together different arrays Several arrays can be stacked together along different axes: >>> >>> a = np.floor(10*rg.random((2,2))) >>> a array([[9., 7.], [5., 2.]]) >>> b = np.floor(10*rg.random((2,2))) >>> b array([[1., 9.], [5., 1.]]) >>> np.vstack((a,b)) array([[9., 7.], [5., 2.], [1., 9.], [5., 1.]]) >>> np.hstack((a,b)) array([[9., 7., 1., 9.], [5., 2., 5., 1.]]) The function column_stack stacks 1D arrays as columns into a 2D array. It is equivalent to hstack only for 2D arrays: >>> >>> from numpy import newaxis >>> np.column_stack((a,b)) # with 2D arrays array([[9., 7., 1., 9.], [5., 2., 5., 1.]]) >>> a = np.array([4.,2.]) >>> b = np.array([3.,8.]) >>> np.column_stack((a,b)) # returns a 2D array array([[4., 3.], [2., 8.]]) >>> np.hstack((a,b)) # the result is different array([4., 2., 3., 8.]) >>> a[:,newaxis] # view `a` as a 2D column vector array([[4.], [2.]]) >>> np.column_stack((a[:,newaxis],b[:,newaxis])) array([[4., 3.], [2., 8.]]) >>> np.hstack((a[:,newaxis],b[:,newaxis])) # the result is the same array([[4., 3.], [2., 8.]]) On the other hand, the function row_stack is equivalent to vstack for any input arrays. In fact, row_stack is an alias for vstack: >>> >>> np.column_stack is np.hstack False >>> np.row_stack is np.vstack True In general, for arrays with more than two dimensions, hstack stacks along their second axes, vstack stacks along their first axes, and concatenate allows for an optional arguments giving the number of the axis along which the concatenation should happen. Note In complex cases, r_ and c_ are useful for creating arrays by stacking numbers along one axis. They allow the use of range literals (“:”) >>> >>> np.r_[1:4,0,4] array([1, 2, 3, 0, 4]) When used with arrays as arguments, r_ and c_ are similar to vstack and hstack in their default behavior, but allow for an optional argument giving the number of the axis along which to concatenate. See also hstack, vstack, column_stack, concatenate, c_, r_ Splitting one array into several smaller ones Using hsplit, you can split an array along its horizontal axis, either by specifying the number of equally shaped arrays to return, or by specifying the columns after which the division should occur: >>> >>> a = np.floor(10*rg.random((2,12))) >>> a array([[6., 7., 6., 9., 0., 5., 4., 0., 6., 8., 5., 2.], [8., 5., 5., 7., 1., 8., 6., 7., 1., 8., 1., 0.]]) # Split a into 3 >>> np.hsplit(a,3) [array([[6., 7., 6., 9.], [8., 5., 5., 7.]]), array([[0., 5., 4., 0.], [1., 8., 6., 7.]]), array([[6., 8., 5., 2.], [1., 8., 1., 0.]])] # Split a after the third and the fourth column >>> np.hsplit(a,(3,4)) [array([[6., 7., 6.], [8., 5., 5.]]), array([[9.], [7.]]), array([[0., 5., 4., 0., 6., 8., 5., 2.], [1., 8., 6., 7., 1., 8., 1., 0.]])] vsplit splits along the vertical axis, and array_split allows one to specify along which axis to split. Copies and Views When operating and manipulating arrays, their data is sometimes copied into a new array and sometimes not. This is often a source of confusion for beginners. There are three cases: No Copy at All Simple assignments make no copy of objects or their data. >>> >>> a = np.array([[ 0, 1, 2, 3], ... [ 4, 5, 6, 7], ... [ 8, 9, 10, 11]]) >>> b = a # no new object is created >>> b is a # a and b are two names for the same ndarray object True Python passes mutable objects as references, so function calls make no copy. >>> >>> def f(x): ... print(id(x)) ... >>> id(a) # id is a unique identifier of an object 148293216 # may vary >>> f(a) 148293216 # may vary View or Shallow Copy Different array objects can share the same data. The view method creates a new array object that looks at the same data. >>> >>> c = a.view() >>> c is a False >>> c.base is a # c is a view of the data owned by a True >>> c.flags.owndata False >>> >>> c = c.reshape((2, 6)) # a's shape doesn't change >>> a.shape (3, 4) >>> c[0, 4] = 1234 # a's data changes >>> a array([[ 0, 1, 2, 3], [1234, 5, 6, 7], [ 8, 9, 10, 11]]) Slicing an array returns a view of it: >>> >>> s = a[ : , 1:3] # spaces added for clarity; could also be written "s = a[:, 1:3]" >>> s[:] = 10 # s[:] is a view of s. Note the difference between s = 10 and s[:] = 10 >>> a array([[ 0, 10, 10, 3], [1234, 10, 10, 7], [ 8, 10, 10, 11]]) Deep Copy The copy method makes a complete copy of the array and its data. >>> >>> d = a.copy() # a new array object with new data is created >>> d is a False >>> d.base is a # d doesn't share anything with a False >>> d[0,0] = 9999 >>> a array([[ 0, 10, 10, 3], [1234, 10, 10, 7], [ 8, 10, 10, 11]]) Sometimes copy should be called after slicing if the original array is not required anymore. For example, suppose a is a huge intermediate result and the final result b only contains a small fraction of a, a deep copy should be made when constructing b with slicing: >>> >>> a = np.arange(int(1e8)) >>> b = a[:100].copy() >>> del a # the memory of ``a`` can be released. If b = a[:100] is used instead, a is referenced by b and will persist in memory even if del a is executed. Functions and Methods Overview Here is a list of some useful NumPy functions and methods names ordered in categories. See Routines for the full list. Array Creation arange, array, copy, empty, empty_like, eye, fromfile, fromfunction, identity, linspace, logspace, mgrid, ogrid, ones, ones_like, r_, zeros, zeros_like Conversions ndarray.astype, atleast_1d, atleast_2d, atleast_3d, mat Manipulations array_split, column_stack, concatenate, diagonal, dsplit, dstack, hsplit, hstack, ndarray.item, newaxis, ravel, repeat, reshape, resize, squeeze, swapaxes, take, transpose, vsplit, vstack Questions all, any, nonzero, where Ordering argmax, argmin, argsort, max, min, ptp, searchsorted, sort Operations choose, compress, cumprod, cumsum, inner, ndarray.fill, imag, prod, put, putmask, real, sum Basic Statistics cov, mean, std, var Basic Linear Algebra cross, dot, outer, linalg.svd, vdot Less Basic Broadcasting rules Broadcasting allows universal functions to deal in a meaningful way with inputs that do not have exactly the same shape. The first rule of broadcasting is that if all input arrays do not have the same number of dimensions, a “1” will be repeatedly prepended to the shapes of the smaller arrays until all the arrays have the same number of dimensions. The second rule of broadcasting ensures that arrays with a size of 1 along a particular dimension act as if they had the size of the array with the largest shape along that dimension. The value of the array element is assumed to be the same along that dimension for the “broadcast” array. After application of the broadcasting rules, the sizes of all arrays must match. More details can be found in Broadcasting. Advanced indexing and index tricks NumPy offers more indexing facilities than regular Python sequences. In addition to indexing by integers and slices, as we saw before, arrays can be indexed by arrays of integers and arrays of booleans. Indexing with Arrays of Indices >>> >>> a = np.arange(12)**2 # the first 12 square numbers >>> i = np.array([1, 1, 3, 8, 5]) # an array of indices >>> a[i] # the elements of a at the positions i array([ 1, 1, 9, 64, 25]) >>> >>> j = np.array([[3, 4], [9, 7]]) # a bidimensional array of indices >>> a[j] # the same shape as j array([[ 9, 16], [81, 49]]) When the indexed array a is multidimensional, a single array of indices refers to the first dimension of a. The following example shows this behavior by converting an image of labels into a color image using a palette. >>> >>> palette = np.array([[0, 0, 0], # black ... [255, 0, 0], # red ... [0, 255, 0], # green ... [0, 0, 255], # blue ... [255, 255, 255]]) # white >>> image = np.array([[0, 1, 2, 0], # each value corresponds to a color in the palette ... [0, 3, 4, 0]]) >>> palette[image] # the (2, 4, 3) color image array([[[ 0, 0, 0], [255, 0, 0], [ 0, 255, 0], [ 0, 0, 0]], [[ 0, 0, 0], [ 0, 0, 255], [255, 255, 255], [ 0, 0, 0]]]) We can also give indexes for more than one dimension. The arrays of indices for each dimension must have the same shape. >>> >>> a = np.arange(12).reshape(3,4) >>> a array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> i = np.array([[0, 1], # indices for the first dim of a ... [1, 2]]) >>> j = np.array([[2, 1], # indices for the second dim ... [3, 3]]) >>> >>> a[i, j] # i and j must have equal shape array([[ 2, 5], [ 7, 11]]) >>> >>> a[i, 2] array([[ 2, 6], [ 6, 10]]) >>> >>> a[:, j] # i.e., a[ : , j] array([[[ 2, 1], [ 3, 3]], [[ 6, 5], [ 7, 7]], [[10, 9], [11, 11]]]) In Python, arr[i, j] is exactly the same as arr[(i, j)]—so we can put i and j in a tuple and then do the indexing with that. >>> >>> l = (i, j) # equivalent to a[i, j] >>> a[l] array([[ 2, 5], [ 7, 11]]) However, we can not do this by putting i and j into an array, because this array will be interpreted as indexing the first dimension of a. >>> >>> s = np.array([i, j]) # not what we want >>> a[s] Traceback (most recent call last): File "<stdin>", line 1, in <module> IndexError: index 3 is out of bounds for axis 0 with size 3 # same as a[i, j] >>> a[tuple(s)] array([[ 2, 5], [ 7, 11]]) Another common use of indexing with arrays is the search of the maximum value of time-dependent series: >>> >>> time = np.linspace(20, 145, 5) # time scale >>> data = np.sin(np.arange(20)).reshape(5,4) # 4 time-dependent series >>> time array([ 20. , 51.25, 82.5 , 113.75, 145. ]) >>> data array([[ 0. , 0.84147098, 0.90929743, 0.14112001], [-0.7568025 , -0.95892427, -0.2794155 , 0.6569866 ], [ 0.98935825, 0.41211849, -0.54402111, -0.99999021], [-0.53657292, 0.42016704, 0.99060736, 0.65028784], [-0.28790332, -0.96139749, -0.75098725, 0.14987721]]) # index of the maxima for each series >>> ind = data.argmax(axis=0) >>> ind array([2, 0, 3, 1]) # times corresponding to the maxima >>> time_max = time[ind] >>> >>> data_max = data[ind, range(data.shape[1])] # => data[ind[0],0], data[ind[1],1]... >>> time_max array([ 82.5 , 20. , 113.75, 51.25]) >>> data_max array([0.98935825, 0.84147098, 0.99060736, 0.6569866 ]) >>> np.all(data_max == data.max(axis=0)) True You can also use indexing with arrays as a target to assign to: >>> >>> a = np.arange(5) >>> a array([0, 1, 2, 3, 4]) >>> a[[1,3,4]] = 0 >>> a array([0, 0, 2, 0, 0]) However, when the list of indices contains repetitions, the assignment is done several times, leaving behind the last value: >>> >>> a = np.arange(5) >>> a[[0,0,2]]=[1,2,3] >>> a array([2, 1, 3, 3, 4]) This is reasonable enough, but watch out if you want to use Python’s += construct, as it may not do what you expect: >>> >>> a = np.arange(5) >>> a[[0,0,2]]+=1 >>> a array([1, 1, 3, 3, 4]) Even though 0 occurs twice in the list of indices, the 0th element is only incremented once. This is because Python requires “a+=1” to be equivalent to “a = a + 1”. Indexing with Boolean Arrays When we index arrays with arrays of (integer) indices we are providing the list of indices to pick. With boolean indices the approach is different; we explicitly choose which items in the array we want and which ones we don’t. The most natural way one can think of for boolean indexing is to use boolean arrays that have the same shape as the original array: >>> >>> a = np.arange(12).reshape(3,4) >>> b = a > 4 >>> b # b is a boolean with a's shape array([[False, False, False, False], [False, True, True, True], [ True, True, True, True]]) >>> a[b] # 1d array with the selected elements array([ 5, 6, 7, 8, 9, 10, 11]) This property can be very useful in assignments: >>> >>> a[b] = 0 # All elements of 'a' higher than 4 become 0 >>> a array([[0, 1, 2, 3], [4, 0, 0, 0], [0, 0, 0, 0]]) You can look at the following example to see how to use boolean indexing to generate an image of the Mandelbrot set: >>> import numpy as np import matplotlib.pyplot as plt def mandelbrot( h,w, maxit=20 ): """Returns an image of the Mandelbrot fractal of size (h,w).""" y,x = np.ogrid[ -1.4:1.4:h*1j, -2:0.8:w*1j ] c = x+y*1j z = c divtime = maxit + np.zeros(z.shape, dtype=int) for i in range(maxit): z = z**2 + c diverge = z*np.conj(z) > 2**2 # who is diverging div_now = diverge & (divtime==maxit) # who is diverging now divtime[div_now] = i # note when z[diverge] = 2 # avoid diverging too much return divtime plt.imshow(mandelbrot(400,400)) ../_images/quickstart-1.png The second way of indexing with booleans is more similar to integer indexing; for each dimension of the array we give a 1D boolean array selecting the slices we want: >>> >>> a = np.arange(12).reshape(3,4) >>> b1 = np.array([False,True,True]) # first dim selection >>> b2 = np.array([True,False,True,False]) # second dim selection >>> >>> a[b1,:] # selecting rows array([[ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> >>> a[b1] # same thing array([[ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> >>> a[:,b2] # selecting columns array([[ 0, 2], [ 4, 6], [ 8, 10]]) >>> >>> a[b1,b2] # a weird thing to do array([ 4, 10]) Note that the length of the 1D boolean array must coincide with the length of the dimension (or axis) you want to slice. In the previous example, b1 has length 3 (the number of rows in a), and b2 (of length 4) is suitable to index the 2nd axis (columns) of a. The ix_() function The ix_ function can be used to combine different vectors so as to obtain the result for each n-uplet. For example, if you want to compute all the a+b*c for all the triplets taken from each of the vectors a, b and c: >>> >>> a = np.array([2,3,4,5]) >>> b = np.array([8,5,4]) >>> c = np.array([5,4,6,8,3]) >>> ax,bx,cx = np.ix_(a,b,c) >>> ax array([[[2]], [[3]], [[4]], [[5]]]) >>> bx array([[[8], [5], [4]]]) >>> cx array([[[5, 4, 6, 8, 3]]]) >>> ax.shape, bx.shape, cx.shape ((4, 1, 1), (1, 3, 1), (1, 1, 5)) >>> result = ax+bx*cx >>> result array([[[42, 34, 50, 66, 26], [27, 22, 32, 42, 17], [22, 18, 26, 34, 14]], [[43, 35, 51, 67, 27], [28, 23, 33, 43, 18], [23, 19, 27, 35, 15]], [[44, 36, 52, 68, 28], [29, 24, 34, 44, 19], [24, 20, 28, 36, 16]], [[45, 37, 53, 69, 29], [30, 25, 35, 45, 20], [25, 21, 29, 37, 17]]]) >>> result[3,2,4] 17 >>> a[3]+b[2]*c[4] 17 You could also implement the reduce as follows: >>> >>> def ufunc_reduce(ufct, *vectors): ... vs = np.ix_(*vectors) ... r = ufct.identity ... for v in vs: ... r = ufct(r,v) ... return r and then use it as: >>> >>> ufunc_reduce(np.add,a,b,c) array([[[15, 14, 16, 18, 13], [12, 11, 13, 15, 10], [11, 10, 12, 14, 9]], [[16, 15, 17, 19, 14], [13, 12, 14, 16, 11], [12, 11, 13, 15, 10]], [[17, 16, 18, 20, 15], [14, 13, 15, 17, 12], [13, 12, 14, 16, 11]], [[18, 17, 19, 21, 16], [15, 14, 16, 18, 13], [14, 13, 15, 17, 12]]]) The advantage of this version of reduce compared to the normal ufunc.reduce is that it makes use of the Broadcasting Rules in order to avoid creating an argument array the size of the output times the number of vectors. Indexing with strings See Structured arrays. Linear Algebra Work in progress. Basic linear algebra to be included here. Simple Array Operations See linalg.py in numpy folder for more. >>> >>> import numpy as np >>> a = np.array([[1.0, 2.0], [3.0, 4.0]]) >>> print(a) [[1. 2.] [3. 4.]] >>> a.transpose() array([[1., 3.], [2., 4.]]) >>> np.linalg.inv(a) array([[-2. , 1. ], [ 1.5, -0.5]]) >>> u = np.eye(2) # unit 2x2 matrix; "eye" represents "I" >>> u array([[1., 0.], [0., 1.]]) >>> j = np.array([[0.0, -1.0], [1.0, 0.0]]) >>> j @ j # matrix product array([[-1., 0.], [ 0., -1.]]) >>> np.trace(u) # trace 2.0 >>> y = np.array([[5.], [7.]]) >>> np.linalg.solve(a, y) array([[-3.], [ 4.]]) >>> np.linalg.eig(j) (array([0.+1.j, 0.-1.j]), array([[0.70710678+0.j , 0.70710678-0.j ], [0. -0.70710678j, 0. +0.70710678j]])) Parameters: square matrix Returns The eigenvalues, each repeated according to its multiplicity. The normalized (unit "length") eigenvectors, such that the column ``v[:,i]`` is the eigenvector corresponding to the eigenvalue ``w[i]`` . Tricks and Tips Here we give a list of short and useful tips. “Automatic” Reshaping To change the dimensions of an array, you can omit one of the sizes which will then be deduced automatically: >>> >>> a = np.arange(30) >>> b = a.reshape((2, -1, 3)) # -1 means "whatever is needed" >>> b.shape (2, 5, 3) >>> b array([[[ 0, 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]]]) Vector Stacking How do we construct a 2D array from a list of equally-sized row vectors? In MATLAB this is quite easy: if x and y are two vectors of the same length you only need do m=[x;y]. In NumPy this works via the functions column_stack, dstack, hstack and vstack, depending on the dimension in which the stacking is to be done. For example: >>> >>> x = np.arange(0,10,2) >>> y = np.arange(5) >>> m = np.vstack([x,y]) >>> m array([[0, 2, 4, 6, 8], [0, 1, 2, 3, 4]]) >>> xy = np.hstack([x,y]) >>> xy array([0, 2, 4, 6, 8, 0, 1, 2, 3, 4]) The logic behind those functions in more than two dimensions can be strange. See also NumPy for Matlab users Histograms The NumPy histogram function applied to an array returns a pair of vectors: the histogram of the array and a vector of the bin edges. Beware: matplotlib also has a function to build histograms (called hist, as in Matlab) that differs from the one in NumPy. The main difference is that pylab.hist plots the histogram automatically, while numpy.histogram only generates the data. >>> import numpy as np rg = np.random.default_rng(1) import matplotlib.pyplot as plt # Build a vector of 10000 normal deviates with variance 0.5^2 and mean 2 mu, sigma = 2, 0.5 v = rg.normal(mu,sigma,10000) # Plot a normalized histogram with 50 bins plt.hist(v, bins=50, density=1) # matplotlib version (plot) # Compute the histogram with numpy and then plot it (n, bins) = np.histogram(v, bins=50, density=True) # NumPy version (no plot) plt.plot(.5*(bins[1:]+bins[:-1]), n) ../_images/quickstart-2.png Further reading The Python tutorial NumPy Reference SciPy Tutorial SciPy Lecture Notes A matlab, R, IDL, NumPy/SciPy dictionary © Copyright 2008-2020, The SciPy community. Last updated on Jun 29, 2020. Created using Sphinx 2.4.4.
54/100 healthRabbani218 /
This commit aggregates all four required projects for the freeCodeCamp Data Analysis with Python Developer Certification).\n\nProjects completed:\n- NumPy Mean, Variance, Standard Deviation Calculator\n- Pandas Demographic Data Analyzer\n- Matplotlib/Seaborn Medical Data Visualizer\n- SciPy Sea Level Predictor
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This repository showcases Python projects completed for a Data Analysis with Python certification, demonstrating skills in data manipulation, visualization, and statistical analysis using libraries like NumPy, Pandas, Matplotlib, Seaborn, and SciPy.
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