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<!doctype html>
<html lang="en" class="no-js">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width,initial-scale=1">
<meta name="description" content="Titus 2 is a Portable Format for Analytics (PFA) implementation for Python 3.4+ maintained by Ankit Mahato">
<meta name="author" content="Ankit Mahato">
<link rel="shortcut icon" href="/titus2/images/logo.png">
<meta name="generator" content="mkdocs-1.1.2, mkdocs-material-5.5.12">
<title>Titus 2 : Portable Format for Analytics (PFA) for Python</title>
<link rel="stylesheet" href="/titus2/assets/stylesheets/main.4dd2dd8d.min.css">
<link href="https://fonts.gstatic.com" rel="preconnect" crossorigin>
<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Roboto:300,400,400i,700%7CRoboto+Mono&display=fallback">
<style>body,input{font-family:"Roboto",-apple-system,BlinkMacSystemFont,Helvetica,Arial,sans-serif}code,kbd,pre{font-family:"Roboto Mono",SFMono-Regular,Consolas,Menlo,monospace}</style>
<script>window.ga=window.ga||function(){(ga.q=ga.q||[]).push(arguments)},ga.l=+new Date,ga("create","UA-162081281-1","auto"),ga("set","anonymizeIp",!0),ga("send","pageview"),document.addEventListener("DOMContentLoaded",function(){document.forms.search&&document.forms.search.query.addEventListener("blur",function(){if(this.value){var e=document.location.pathname;ga("send","pageview",e+"?q="+this.value)}})}),document.addEventListener("DOMContentSwitch",function(){ga("send","pageview",document.location.pathname)})</script>
<script async src="https://www.google-analytics.com/analytics.js"></script>
</head>
<body dir="ltr">
<input class="md-toggle" data-md-toggle="drawer" type="checkbox" id="__drawer" autocomplete="off">
<input class="md-toggle" data-md-toggle="search" type="checkbox" id="__search" autocomplete="off">
<label class="md-overlay" for="__drawer"></label>
<div data-md-component="skip">
</div>
<div data-md-component="announce">
</div>
<header class="md-header" data-md-component="header">
<nav class="md-header-nav md-grid" aria-label="Header">
<a href="https://realworldpython.github.io/titus2/" title="Titus 2 : Portable Format for Analytics (PFA) for Python" class="md-header-nav__button md-logo" aria-label="Titus 2 : Portable Format for Analytics (PFA) for Python">
<img src="/titus2/images/logo-white.png" alt="logo">
</a>
<label class="md-header-nav__button md-icon" for="__drawer">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 6h18v2H3V6m0 5h18v2H3v-2m0 5h18v2H3v-2z"/></svg>
</label>
<div class="md-header-nav__title" data-md-component="header-title">
<div class="md-header-nav__ellipsis">
<span class="md-header-nav__topic md-ellipsis">
Titus 2 : Portable Format for Analytics (PFA) for Python
</span>
<span class="md-header-nav__topic md-ellipsis">
</span>
</div>
</div>
<label class="md-header-nav__button md-icon" for="__search">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0116 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 019.5 16 6.5 6.5 0 013 9.5 6.5 6.5 0 019.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5z"/></svg>
</label>
<div class="md-search" data-md-component="search" role="dialog">
<label class="md-search__overlay" for="__search"></label>
<div class="md-search__inner" role="search">
<form class="md-search__form" name="search">
<input type="text" class="md-search__input" name="query" aria-label="Search" placeholder="Search" autocapitalize="off" autocorrect="off" autocomplete="off" spellcheck="false" data-md-component="search-query" data-md-state="active">
<label class="md-search__icon md-icon" for="__search">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0116 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 019.5 16 6.5 6.5 0 013 9.5 6.5 6.5 0 019.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12z"/></svg>
</label>
<button type="reset" class="md-search__icon md-icon" aria-label="Clear" data-md-component="search-reset" tabindex="-1">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 6.41L17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12 19 6.41z"/></svg>
</button>
</form>
<div class="md-search__output">
<div class="md-search__scrollwrap" data-md-scrollfix>
<div class="md-search-result" data-md-component="search-result">
<div class="md-search-result__meta">
Initializing search
</div>
<ol class="md-search-result__list"></ol>
</div>
</div>
</div>
</div>
</div>
<div class="md-header-nav__source">
<a href="https://github.com/animator/titus2" title="Go to repository" class="md-source">
<div class="md-source__icon md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512"><path d="M439.55 236.05L244 40.45a28.87 28.87 0 00-40.81 0l-40.66 40.63 51.52 51.52c27.06-9.14 52.68 16.77 43.39 43.68l49.66 49.66c34.23-11.8 61.18 31 35.47 56.69-26.49 26.49-70.21-2.87-56-37.34L240.22 199v121.85c25.3 12.54 22.26 41.85 9.08 55a34.34 34.34 0 01-48.55 0c-17.57-17.6-11.07-46.91 11.25-56v-123c-20.8-8.51-24.6-30.74-18.64-45L142.57 101 8.45 235.14a28.86 28.86 0 000 40.81l195.61 195.6a28.86 28.86 0 0040.8 0l194.69-194.69a28.86 28.86 0 000-40.81z"/></svg>
</div>
<div class="md-source__repository">
animator/titus2
</div>
</a>
</div>
</nav>
</header>
<div class="md-container" data-md-component="container">
<nav class="md-tabs" aria-label="Tabs" data-md-component="tabs">
<div class="md-tabs__inner md-grid">
<ul class="md-tabs__list">
<li class="md-tabs__item">
<a href="/titus2/." class="md-tabs__link">
titus2
</a>
</li>
<li class="md-tabs__item">
<a href="/titus2/pfa/" class="md-tabs__link">
PFA
</a>
</li>
<li class="md-tabs__item">
<a href="/titus2/status/" class="md-tabs__link">
Status
</a>
</li>
<li class="md-tabs__item">
<a href="/titus2/about/" class="md-tabs__link">
Author
</a>
</li>
<li class="md-tabs__item">
<a href="https://gitter.im/realworldpython/community" target="_blank" class="md-tabs__link">
Discuss
</a>
</li>
<li class="md-tabs__item">
<a href="https://github.com/animator/titus2/issues" target="_blank" class="md-tabs__link">
Report Bug
</a>
</li>
</ul>
</div>
</nav>
<main class="md-main" data-md-component="main">
<div class="md-main__inner md-grid">
<div class="md-sidebar md-sidebar--primary" data-md-component="navigation">
<div class="md-sidebar__scrollwrap">
<div class="md-sidebar__inner">
<nav class="md-nav md-nav--primary" aria-label="Navigation" data-md-level="0">
<label class="md-nav__title" for="__drawer">
<a href="https://realworldpython.github.io/titus2/" title="Titus 2 : Portable Format for Analytics (PFA) for Python" class="md-nav__button md-logo" aria-label="Titus 2 : Portable Format for Analytics (PFA) for Python">
<img src="/titus2/images/logo-white.png" alt="logo">
</a>
Titus 2 : Portable Format for Analytics (PFA) for Python
</label>
<div class="md-nav__source">
<a href="https://github.com/animator/titus2" title="Go to repository" class="md-source">
<div class="md-source__icon md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512"><path d="M439.55 236.05L244 40.45a28.87 28.87 0 00-40.81 0l-40.66 40.63 51.52 51.52c27.06-9.14 52.68 16.77 43.39 43.68l49.66 49.66c34.23-11.8 61.18 31 35.47 56.69-26.49 26.49-70.21-2.87-56-37.34L240.22 199v121.85c25.3 12.54 22.26 41.85 9.08 55a34.34 34.34 0 01-48.55 0c-17.57-17.6-11.07-46.91 11.25-56v-123c-20.8-8.51-24.6-30.74-18.64-45L142.57 101 8.45 235.14a28.86 28.86 0 000 40.81l195.61 195.6a28.86 28.86 0 0040.8 0l194.69-194.69a28.86 28.86 0 000-40.81z"/></svg>
</div>
<div class="md-source__repository">
animator/titus2
</div>
</a>
</div>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle" data-md-toggle="nav-1" type="checkbox" id="nav-1">
<label class="md-nav__link" for="nav-1">
titus2
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" aria-label="titus2" data-md-level="1">
<label class="md-nav__title" for="nav-1">
<span class="md-nav__icon md-icon"></span>
titus2
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="/titus2/." title="Overview" class="md-nav__link">
Overview
</a>
</li>
<li class="md-nav__item">
<a href="/titus2/installation/" title="Installation" class="md-nav__link">
Installation
</a>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle" data-md-toggle="nav-1-3" type="checkbox" id="nav-1-3">
<label class="md-nav__link" for="nav-1-3">
Tutorials
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" aria-label="Tutorials" data-md-level="2">
<label class="md-nav__title" for="nav-1-3">
<span class="md-nav__icon md-icon"></span>
Tutorials
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="/titus2/tutorials/elementary-example/" title="Elementary Example" class="md-nav__link">
Elementary Example
</a>
</li>
<li class="md-nav__item">
<a href="/titus2/tutorials/using-built-in-functions/" title="Using Built-in Functions" class="md-nav__link">
Using Built-in Functions
</a>
</li>
<li class="md-nav__item">
<a href="/titus2/tutorials/pfa-document-structure/" title="PFA Document Structure" class="md-nav__link">
PFA Document Structure
</a>
</li>
<li class="md-nav__item">
<a href="/titus2/tutorials/persistent-storage/" title="Persistent Storage - Cells and Pools" class="md-nav__link">
Persistent Storage - Cells and Pools
</a>
</li>
<li class="md-nav__item">
<a href="/titus2/tutorials/prettypfa-examples/" title="PrettyPFA" class="md-nav__link">
PrettyPFA
</a>
</li>
<li class="md-nav__item">
<a href="/titus2/tutorials/exoplanets/" title="Exoplanets Example" class="md-nav__link">
Exoplanets Example
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item">
<a href="/titus2/contribute/" title="Contribute" class="md-nav__link">
Contribute
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle" data-md-toggle="nav-2" type="checkbox" id="nav-2">
<label class="md-nav__link" for="nav-2">
PFA
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" aria-label="PFA" data-md-level="1">
<label class="md-nav__title" for="nav-2">
<span class="md-nav__icon md-icon"></span>
PFA
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle" data-md-toggle="nav-2-1" type="checkbox" id="nav-2-1">
<label class="md-nav__link" for="nav-2-1">
Portable Format for Analytics (PFA)
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" aria-label="Portable Format for Analytics (PFA)" data-md-level="2">
<label class="md-nav__title" for="nav-2-1">
<span class="md-nav__icon md-icon"></span>
Portable Format for Analytics (PFA)
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="/titus2/pfa/" title="Overview" class="md-nav__link">
Overview
</a>
</li>
<li class="md-nav__item">
<a href="/titus2/pfa/what-is-pfa/" title="What is PFA?" class="md-nav__link">
What is PFA?
</a>
</li>
<li class="md-nav__item">
<a href="/titus2/pfa/why-do-we-need-pfa/" title="Why do we need it?" class="md-nav__link">
Why do we need it?
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle" data-md-toggle="nav-2-2" type="checkbox" id="nav-2-2">
<label class="md-nav__link" for="nav-2-2">
PFA Document Structure
<span class="md-nav__icon md-icon"></span>
</label>
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PFA Document Structure
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<a href="/titus2/pfa/document-structure/" title="Format of a PFA document" class="md-nav__link">
Format of a PFA document
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<a href="/titus2/pfa/locator-marks/" title="Locator marks" class="md-nav__link">
Locator marks
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<a href="/titus2/pfa/names/" title="Names" class="md-nav__link">
Names
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<a href="/titus2/pfa/cell-pool-structure/" title="Cell and pool structure" class="md-nav__link">
Cell and pool structure
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<a href="/titus2/pfa/expressions/" title="Expressions" class="md-nav__link">
Expressions
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Avro Types
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Avro Types
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Inherited Type System
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<a href="/titus2/avro-types/type-specification/" title="Specification of All Types" class="md-nav__link">
Specification of All Types
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<a href="/titus2/avro-types/subtypes-supertypes/" title="Subtypes and Supertypes" class="md-nav__link">
Subtypes and Supertypes
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Function Signatures
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Special Forms
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Special Forms
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Overview
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Forms that call functions
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Special forms that provide function references (not expressions)
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Creating complex objects
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Symbol assignment and reassignment
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<a href="/titus2/special-forms/arrays-maps-records/" title="Extracting from and updating arrays, maps, and records" class="md-nav__link">
Extracting from and updating arrays, maps, and records
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<a href="/titus2/special-forms/cells-pools/" title="Extracting from and updating cells and pools" class="md-nav__link">
Extracting from and updating cells and pools
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<a href="/titus2/special-forms/control-structures/" title="Branching control structures" class="md-nav__link">
Branching control structures
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Loops
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Type-safe casting
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Miscellaneous special forms
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Function Library
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Function Library
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Overview
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<a href="/titus2/function-library/core/" title="Core Library (29)" class="md-nav__link">
Core Library (29)
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Math Library (45)
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Linear Algebra Library (13)
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Metric Library (12)
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Random Number Library (12)
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String Manipulation Library (25)
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<a href="/titus2/function-library/regex/" title="Regular Expressions and Text Pre-processing (15)" class="md-nav__link">
Regular Expressions and Text Pre-processing (15)
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Parsing Library (4)
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Casting Library (13)
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Array Manipulation Library (82)
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Map Manipulation Library (41)
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<a href="/titus2/function-library/bytes/" title="Bytes Manipulation Library (23)" class="md-nav__link">