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LaTeX is a document preparation system used for the communication and publication of scientific documents. LaTeX is free software and is distributed under the LaTeX Project Public License New to LaTeX? Start with our Learn L a T e X in 30 minutes guide. For more specific introductions, have a look at: Create your first document in L a T e X; Paragraphs and new lines; Bold, italics and underlining; Lists; Mathematics; Bibliographies and references; Images; Tables; Overleaf guides. Create your first Overleaf document; Uploading a project to Overleaf; Copying a projec

LaTeX-Dokumente haben eine genau festgelegte Struktur und bestehen im wesentlichen aus zwei Teilen: Der Präambel und dem eigentlichen Dokumentkörper. In der Präambel werden alle für das gesamte Dokument gültigen Einstellungen getroffen sowie zusätzlich benötigte Makropakete geladen. Im Dokumentkörper steht dann der zu setzende Text, angereichert mit den notwendigen Formatbefehlen, die im Durchschnitt etwa 3% der einzugebenden Textmenge ausmachen. Wer schon einmal eine HTML-Datei. Documentation supplied as part of the L a T e X distribution. latex-doc-ptr. A direction-finder for L a T e X resources available online. latex-essential. Essential information for writing L a T e X documents. latex-hlp. A VMS help file for L a T e X 2.09. latex-info. Unofficial reference manual for L a T e X. lkort . A short introduction to L a T e X, in Dutch. ltnews. The latest L a T e X.

Standard Document Classes for LATEX version 2e Copyright (C) 1992 by Leslie Lamport Copyright (C) 1994-2020 by Frank Mittelbach Johannes Braams LATEX3 Project Team 2020/04/10 This le is maintained by the LATEX Project team. Bug reports can be opened (category latex) at https://latex-project.org/bugs.html. Contents 1 The docstrip modules3 2 Initial Code LaTeX Error: \rubbish undefined.^^J^^JSee the LaTeX manual or LaTeX= Companion for explanation.^^JType H <return> for immediate help.....3 \renewcommand{\rubbish} {} However if you put \def\@TeXversion{3.14}in texsys.cfgthe following format will beused: LaTeX Error: \rubbish undefined. ee the LaTeX manual or LaTeX Companion for explanation

LaTeX Documentatio

• LaTeX - A document preparation system. LaTeX is a high-quality typesetting system; it includes features designed for the production of technical and scientific documentation. LaTeX is the de facto standard for the communication and publication of scientific documents. LaTeX is available as free software. You don't have to pay for using LaTeX, i.e., there are no license fees, etc
• scrguide.pdf - Dokumentation zum KOMA-Script. symbols.pdf - Eine umfangreiche Symbolreferenz. latexreferenz.pdf - eine Referenz der LaTeX Umgebungen, Makros, Längen und Zähler. einfuehrung.pdf - Manuela Jürgens' LaTeX - Einführung und ein bißchen mehr
• Creating a document in LaTeX L a T e X is a great tool to create documents. It's based on the 'WYSIWYM' (what you see is what you mean) idea, meaning you only have to focus on the contents of your document and the computer will take care of the formatting
• A beamer presentation is created like any other LATEX document: It has a preamble and a body, the body contains\sectionsand\subsections,thedifferentslides(called frames inbeamer)areputinenvironments, theyarestructuredusingitemize andenumerate environments,andsoon
• LaTeX uses document classes, to influence the overall layout of your document. For instance, there's one class to layout articles, one class to layout books (called book) and many more, which we probably don't need. In my tutorials, I will always use the class article

Documentation - Overleaf, Online LaTeX Edito

e. X macros, and a working knowledge of LaT. e. X should be sufficient to design new bibliography and citation styles. Bib LaT. e. X uses its own data backend program called biber to read and process the bibliographic data. With biber , Bib LaT. e In fact, LaTeX' documentation system is far more complete than JavaDoc or similar systems. Package writers are strongly encouraged to practice literal programming, i.e. they don't comment/document their code. Rather, they write a documentation which contains the code (not the other way round, as in the case of JavaDoc). This usually means that package documentation is very comprehensive.

LaTeX-Kompendium: Schnellkurs: Das erste Dokument

In this article, we will start the documentation to LaTeX and help you in understanding the LaTeX syntax. As we are already aware, LaTeX is a great tool to create documents, and it is based on the idea 'WYSIWYM'(what you see is what you mean) idea. The concept is pretty straightforward; all you need to do is focus on writing the content of the document, and the LaTeX engine will take care of formatting. In our previous article, we have shown you the power of LaTeX with a simple. LaTeX Templates { The best source of free quality LaTeX templates } Academic Journals; Articles; Assignments; Books; Calendars; Conference Posters; Cover Letters; Curricula Vitae/Résumés; Essays; Formal Letters; Laboratory Books; Laboratory Reports; Miscellaneous; Newsletters; Presentations; Theses; Title Pages; Template Categories . Academic Journals (10) Articles (4) Assignments (4) Books. Tables are common elements in most scientific documents, L a T e X provides a large set of tools to customize tables, change the size, combine cells, change the colour of cells and so on. This article explains how

CTAN: LaTeX documentatio

1. Biblatex is a modern program to process bibliography information, provides an easier and more flexible interface and a better language localization than the other two options. This article explains how to use biblatex to manage and format the bibliography in a LaTeX document
2. Suggestions. Maybe you are interested in the following packages as well. forms16be: Initialize form properties using big-endian encoding; rmannot: Create rich media annotations in a PDF fil
3. LATEX (pronounced lay-tek) is a document preparation system for producing professional-looking documents, it is not a word processor. It is particularly suited to producing long, structured documents, and is very good at type-setting equations. It is available as free software for most operating systems
4. Du kannst folgende HTML-Tags benutzen:   <acronym title=>
      <q.
5. LaTeX-Kompendium LaTeX-Wörterbuch InDeX Beschreibung [ Bearbeiten ] Durch die Angabe der Dokumentklasse kann die Grundstruktur des Dokumentes festgelegt werden
6. L a T e X documents are plain documents with a .tex extension (see the Creating a document in LaTeX article for examples), this plain text file has some markup commands that are meant to format the document but, how do you actually generate the final output?. It depends on the type of document you want to generate
• There are four standard document letting. book ; report ; article ; letter (normally American format) Each document use exactly one document class. so \documentclass{article} or \documentclass{report} Not \documentclass{article, report
• Advantages of LaTeX Documents. LaTeX documents obviously have advantages for mathematicians and anyone else who uses equations in their writing. The systems is commonly used for documents in physics, statistics, computer science, engineering, and other fields that need to write down a lot of equations. But it's also used by linguists, economists, philosophers, children's book authors.
• consistency of document and font type and font size, direct use of TEX math mode in axis descriptions, consistency of data and gures (no third party tool necessary), interdocument consistency using preamble con gurations and styles. Although not necessary, separate .pdf or .eps graphics can be generated using the external library devel- oped as part of TikZ. pgfplots is build completely on.

The package builds upon the graphics package, providing a key-value interface for optional arguments to the \includegraphics command. This interface provides facilities that go far beyond what the graphics package offers on its own. For extended documentation, see epslatex. The package is part of the latex-graphics bundle, which is one of the collections in the L a T e X 'required' set of. ThebiblatexPackage ProgrammableBibliographiesandCitations PhilipKime,MoritzWemheuer, PhilippLehman Version3.16 December31,2020 Contents ListofTables For details, refer to the hyperref LaTeX docs. Default: 5. New in version 4.0.0. hmargin, vmargin. The dimensions of the horizontal (resp. vertical) margins, passed as hmargin (resp. vmargin) option to the geometry package. Example: 'sphinxsetup': 'hmargin={2in,1.5in}, vmargin={1.5in,2in}, marginpar=1in', Japanese documents currently accept only the one-dimension format for these parameters. \begin{document} \title{LaTeX Typesetting By Example} \author{Phil Farrell\\ Stanford University School of Earth Sciences} \renewcommand{\today}{November 2, 1994} \maketitle This article demonstrates a basic set of LaTeX formatting commands. Compare the typeset output side-by-side with the input document. \section {Plain Text} Type your text in free-format; lines can be as long or as short as.

LaTeX - A document preparation syste

Ein minimales LaTeX-Dokument besteht aus dem Befehl \begin{document} dem eigentlichen Text also sowie dem Befehl \end{document} mit einer vorangestellten Präambel, LINK die mindestens die Dokumentenklasse LINK erläutert. Sonst weiß LaTeX ja nicht, dass und was es kompilieren soll. \documentclass [ngerman] {scrartcl} %lädt die Dokumentklasse %Artikel von Koma-Skript, als Option. TeX/LaTeX Information. This page is no longer maintained! The information is (mostly) still correct as far as it goes, but there are new versions and new editions of everything, and most importantly, there is no discussion here of XeTeX and other new developments and macros that are important for linguists.. This document tries to provide some information useful to linguists using LaTeX at the.

Document Class nach LaTeX. A Document Preparation System. Leslie Lamport, 2. Auflage, 1994. Abgerufen von. LaTeX table/figure FAQ: How do I reference a table or figure in a LaTeX document? Being able to automatically reference a figure within a LaTeX document is a very cool thing. This referencing capability lets you easily give readers the exact number of a figure, or tell them what page number a figure is located on with the use of a few simple commands ( \label , \ref , and \pageref )

KOMA-Script existiert seit 1994 und existierte davor als LaTeX 2.09-Paket. Es ist eine Menge Arbeit, die Implementierung und Dokumentation von KOMA-Script weiter zu verbessern - beinahe zu viel für einen allein. Daher wurde dieses Projekt ins Leben gerufen, dessen Ziel es war, eine neue Dokumentation zu erstellen und zu pflegen LaTeX symbols have either names (denoted by backslash) or special characters. They are organized into seven classes based on their role in a mathematical expression. This is not a comprehensive list. Refer to the external references at the end of this article for more information. 1 Class 0 (Ord) symbols: Simple / ordinary (noun) 1.1 Latin letters and Arabic numerals 1.2 Greek letters 1.3. Typesetting the documentation requires a number of packages in addition to those needed to use the package. This is mainly because of the number of demonstration items included in the text. To compile the documentation without error, you will need the packages: • amsmath The CTAN archiv

Dokumentationen [LaTeX@TU Graz

LaTeX-Wörterbuch: documentclass. Aus Wikibooks. Zur Navigation springen Zur Suche springen. LaTeX-Kompendium LaTeX-Wörterbuch InDeX. Beschreibung . Durch die Angabe der Dokumentklasse kann die Grundstruktur des Dokumentes festgelegt werden. Weiterhin ist es jedoch nützlich, zusätzliche Schriftbildinformationen mit anzugeben, um das Dokument vollständig festzulegen. Einige dieser. LaTeX Tutorial provides step-by-step lessons to learn how to use LaTeX in no time. It allows you to start creating beautiful documents for your reports, books and papers through easy and simple tutorials. Skip to content. MENU. LaTeX-Tutorial.com. Search. Search for: Blog; Installation; Quick Start ; Tutorials Submenu Toggle 01 First Document; 02 Sections; 03 Packages; 04 Math; 05 Figures; 06.

LaTeX-Kompendium. ACHTUNG: Dieses Buch oder Kapitel bedarf dringend einer Überarbeitung oder Erweiterung. Wenn du Lust hast, beteilige dich an der Verbesserung! Eine gute Möglichkeit, Zitate einzufügen und zu formatieren, ist BibTeX (. B I B T E X {\displaystyle {\mathrm {B {\scriptstyle {IB}}\!T\!_ {\displaystyle E}\!X} }} ) A Basic Document Writing LaTeX Code Special Characters Another type of command Don't de ne any formatting or structure Print non-standard characters or characters which usually mean something else Ex. nLaTeX, ntextbackslash, n% Note: % is a special character reserved for comments (after a %, the rest of a line is ignored by the compiler) Introduction to LATEX A Basic Document Writing LaTeX.

Creating a document in LaTeX - Overleaf, Online LaTeX Edito

1. Documentation for AMS-LaTeX . To view documentation for a package in an installation based on TeX Live, the easiest way is to type this at a command-line prompt: texdoc -l package name The desired item can be selected from the offered list
2. To set up a TeX/LaTeX system on macOS, download and open this disk image. Then drag the MiKTeX icon onto the Applications folder. Then drag the MiKTeX icon onto the Applications folder. Please read the tutorial , if you want step-by-step guidance
3. imal effort. The purpose.
4. \begin{document} Am Ende des Dokuments sollte der Befehl \end{document} gesetzt werden. Alles was nach diesem Befehl steht, wird vom Compiler nicht mehr be-achtet. Standardm aˇig hat eine Titelseite folgenden Aufbau: \begin{titlepage} \title{Die Leiden des jungen Werthers} \date{1774} 3 \author{Johann Wolfgang von Goethe} \maketitle \end{titlepage} Der Befehl maketitle gibt das Titelblatt an.
5. Zwischen \begin{document} und \end{document} schreiben Sie Ihren LaTeX-Code. Speichern Sie die Datei nun unter einem beliebigen Namen als tex-Datei ab. Wechseln Sie in der Werkzeugleiste im zweiten Dropdown-Feld von rechts auf den Punkt PDFLaTeX und klicken Sie auf den Pfeil links daneben. In dem Ordner, indem auch Ihre tex-Datei gespeichert ist, finden Sie nun die erstellte PDF-Datei. PDF.
6. Umfangreicher LaTeX-Editor mit integrierten Tools und Funktionen wie Syntax-Highlighting, 370 mathematischen Symbolen und Ausdrücken, Suchen und Ersetzen . Lizenz: Open Source

Your first LaTeX document - LaTeX-Tutorial

Multiple images / subfigures in LaTeX. Sometimes when writing a document, adding single images is not optimal, especially when the reader is supposed to compare several results or graphs. In such situations, it might be necessary to use a different environment, called subfigure. The subfigure environment allows you to place multiple images at a certain location next to each other and the usage. LATEX-Einführungskurs Präsentationen mit Beamer Paul Fink Eva Endres Institut für Statistik, LMU München 14. Oktober 2016 1/3 This makes a Latex document a real living working space, the out put of which is the final polished pdf document. Yes it's a pain to learn! But for me it was worth the effort and my thesis is. The next two steps merge the reference section with our LaTeX document and then assign successive numbers in the last step. Autogenerate footnotes in $$\LaTeX$$ using BibLaTeX. The abilities of BibTeX are limited to basic styles as depicted in the examples shown above. Sometimes it is necessary to cite all literature in footnotes and maintaining all of them by hand can be a frustrating task.

MathJax Documentation. MathJax is an open-source JavaScript display engine for LaTeX, MathML, and AsciiMath notation that works in all modern browsers, with built-in support for assistive technology like screen readers. Version 3.0 of MathJax is a complete rewrite of MathJax from the ground up, and its usage and configuration is significantly. Each LaTeX document that uses the s ngs package should contain a line like the following near the top of the document: \usepackage[<options>]{songs} Supported <options> include the following: lyric chorded slides rawtext: Output Type. The s ngs package can produce four kinds of books: lyric books, chord books, books of overhead slides, and raw text output. You can specify which kind of book is. LaTeX documentclass options illustrated. 13. February 2013 by tom 21 Comments. The three most commonly used standard document-classes in LaTeX include: article, report and book. A number of global options allows customization of certain elements of the document by the author. Different document-classes might have different default settings How do I insert code into a LaTeX document? Is there something like: \begin{code}## Heading ## \end{code} The only thing that I really need is indentation and a fixed width font. Syntax highlighting could be nice although it is definitely not required. latex. Share. Improve this question . Follow edited Jan 9 '19 at 4:06. Peter Mortensen. 28.2k 21 21 gold badges 94 94 silver badges 123 123.

CTAN: Package BibLaTe

• LaTeX ( [ˈlaːtɛç]), in Eigenschreibweise , ist ein Softwarepaket, das die Benutzung des Textsatzsystems TeX mit Hilfe von Makros vereinfacht. LaTeX wurde Anfang der 1980er Jahre von Leslie Lamport entwickelt. Der Name bedeutet so viel wie Lamport TeX.Die Entwicklung wurde seit den 1990er Jahren von einer Anzahl Entwicklern weitergeführt
• This is my \emph{first} document prepared in \LaTeX. \end{document} Be especially careful with the \ character (called the backslash) and note that this is different from the more familiar / (the slash) in and/or and save the ﬁle onto the hard disk as myfile.tex. (Instead of myfile you can use any name you wish, but be sure to have.tex at the end as the extension.) The process of compiling.
• us character issue (thanks!!). Renamed internal variables in order to prevent conflicts with other packages
• Links to additional information and documentation for some of the basic components of the TeX system: web2c - tds - pdftex - kpathsea - dvips. TeX Live also includes all the documentation that the individual package and program authors have provided, mostly in the texmf*/doc subdirectories. The top-level doc.html file in the distribution has a comprehensive listing, including the manuals above.

1.Run latex acmart.ins. ‚is will produce the •le acmart.cls 2.Put the •les acmart.clsand ACM-Reference-Format.bstin places where LATEX can •nd them (see [1] or the documentation for your TEX system). 3.Update the database of •le names. Again, see [1] or the documentation for your TEX system for the system-speci•c details LaTeX Extra > LaTeX Pakete > Acronym Die Seite als PDF Acronym Paket. acronym - Abkürzungsverzeichnis mit L A T E X Eine Möglichkeit mit L A T E X ein Abkürzungsverzeichnis zu erstellen stellt die Verwendung des Paketes acronym dar. Daneben existieren aber auch noch weitere Pakete, die auch für die Erstellung eines solchen Verzeichnisses genutzt werden können, wie zum Beispiel das acro.

class sphinx.builders.latex. LaTeXBuilder [source] ¶. This builder produces a bunch of LaTeX files in the output directory. You have to specify which documents are to be included in which LaTeX files via the latex_documents configuration value. There are a few configuration values that customize the output of this builder, see the chapter Options for LaTeX output for details Du kannst aber beispielsweise die Option english beim Laden von babel in struture.tex in ngerman ändern. Nicht wundern, wenn dann beim ersten LaTeX-Lauf nach der Änderung ein Fehler in der aux-, der toc-, der lof- oder sonstigen Hilfsdateien gemeldet wird. Das ist normal und lässt sich einfach aussitzen LaTeX Extra > LaTeX Pakete > Inputenc Die Seite als PDF Inputenc Paket. 1 Umlaute ohne Pakete Da es sich bei L A T E X um ein Programm handelt, das ursprünglich in den USA entwickelt worden ist, sind deutsche Umlaute (ebenso wenig wie die Sonderzeichen andere Sprachen) nicht vorgesehen. Der Grund hierfür liegt daran, dass Latex primär nicht für das im Deutschen verwendete erweiterte. An UPDATED version of this video is available here: https://youtu.be/0ivLZh9xK1QLaTeX tutorial using Texmaker. Topics include: creating and building a docume.. HTML. The following raw HTML features are potentially dangerous for untrusted inputs, so they are disabled by default, and attempting to use them produces the command names in red (which you can configure via the errorColor option).To fully trust your LaTeX input, you need to pass an option of trust: true; you can also enable just some of the commands or for just some URLs via the trust option

biber. Biber is a sophisticated bibliography processing backend for the LaTeX biblatex package. It supports a unsurpassed feature set for automated conformance to complex bibliography style requirements such as labelling, sorting and name handling. It has comprehensive Unicode support LaTeX is a document preparation system. ⇒ The LaTeX project home page . It's on DICE machines, with custom document classes for the School of Informatics. ⇒ LaTeX on DICE. ⇒ Informatics document classes for LaTeX . Or you can use Overleaf, a collaborative online LaTeX service. Overleaf has lots of help for beginners LaTeX Workshop is an extension for Visual Studio Code, aiming to provide core features for LaTeX typesetting with Visual Studio Code. This project won't be successful without contributions from the community, especially from the current and past key contributors: Jerome Lelong @jlelong. Takashi Tamura @tamuratak. Tecosaur @tecosaur

tex core - LaTeX, package documentation look-up - TeX

• See Converting a LaTeX document to a PDF document. When Doxygen is finished processing, in the latex directory there's a file called 'refman.tex'. Using Doxygen 1.8.4+ (on Windows), there is also a make.bat script so you don't even need to open the command line. Configure Doxygen for LaTeX output. GENERATE_LATEX = YES LATEX_OUTPUT = latex.
• Latex is a stable dispersion of polymer microparticles in water. Latexes are found in nature, but synthetic latexes are common as well.. Latex as found in nature is a milky fluid found in 10% of all flowering plants (angiosperms). It is a complex emulsion consisting of proteins, alkaloids, starches, sugars, oils, tannins, resins, and gums that coagulate on exposure to air
• Changes to your LaTeX workflow: The first step in efficiently managing a Git+LaTeX workflow is to make a few changes to your LaTeX habits. For starters, write each sentence on a separate line. Git was written to version control source code, where each line is distinct and has a specific purpose. When you write documents in LaTeX, you often.
• Our goal is to make writing LaTeX documents as easy and comfortable as possible. Some of the outstanding features of TeXstudio are an integrated pdf viewer with (almost) word-level synchronization, live inline preview, advanced syntax-highlighting, live checking of references, citations, latex commands, spelling and grammar

LaTeX (pronounced lay-tech) is a method of creating documents using plain text, stylized using markup tags, similar to HTML/CSS or Markdown.LaTeX is most commonly used to create documents for academia, such as academic journals. In LaTeX, the author doesn't stylize the document directly, like in a word processor such as Microsoft Word, LibreOffice Writer, or Apple Pages; instead they write. A LaTeX document consists of two main pieces, the preamble and the body, the bibliography can be considered a third piece depending on how you structure it, but that will be discussed in the BibTex tab of this guide. It is recommended that the user creates a new folder on their computer for each LaTeX document they are working on. When LaTeX compiles a .tex file it generates several files in. Latex Dokumentation. Auf den Rechnern der Fakultät ist die Latexdistributuion TexLive installiert. Zusätzlich gibt es einige weitere Klassen, die im Folgenden beschrieben werden. Vorlagen für Briefe und Aushänge im Corporate Design 2019. Um Briefe mit neuem Fakultätsbriefkopf zu erstellen, gibt es die Klasse math-brief-2019. Ein Beispielbrief mit Erläuterungen liegt auf jedem Linux. Tutorial für Einsteiger. Im Zuge des Tutorials werden wir schrittweise ein erstes Dokument mit LaTeX erstellen. Wir empfehlen, die angegebenen Befehle und Texte selbst einzutippen, anstatt sie mit Copy&Paste zu übertragen. Der Lerneffekt ist dabei größer. Wir verweisen auf die Einsteiger-Dokumentation LATEX 2ε-Kurzbeschreibung (l2kurz)

LaTeX Dokumentation - IT-Service der Fakultät für Physik - LMU München. Links und Funktionen. www.lmu.de. LMU Portal. Fakultät für Physik. Webmail Preface LATEX [1] is a typesetting system that is very suitable for producing scien- tific and mathematical documents of high typographical quality. It is also suitable for producing all sorts of other documents, from simple letters t

LaTex Command Syntax And LaTex Documentation MyWindowsHu

LaTeX forum ⇒ Document Classes ⇒ moderncv | Class Documentation for its Commands. Information and discussion about specific document classes and how to create your own document classes. 6 posts • Page 1 of 1. _samir Posts: 5 Joined: Sun Sep 30, 2012 6:24 pm. moderncv | Class Documentation for its Commands . Post by _samir » Sun Sep 30, 2012 7:08 pm . Hi guys. I'm new to LaTeX and this. For documentation describing the tree-dvips macros, just type latex tree-manual and then print tree-manual.dvi. \section*{Notes for My Paper} This says to make a section heading consisting of what is between the curly brackets, and the * says not to number it The le exam.cls provides the exam document class, which attempts to make it easy for even a LATEX novice to prepare exams. Speci cally, exam.cls sets the page layout so that there are one inch margins all around (no matter what size paper you're using) and provides commands that make it easy to format questions, create exible headers and footers, change the margins, and create grading tables. document summary, included in LaTeX, ConTeXt, AsciiDoc, and docx documents keywords list of keywords to be included in HTML, PDF, ODT, pptx, docx and AsciiDoc metadata; repeat as for author, above subject document subject, included in ODT, PDF, docx and pptx metadata description document description, included in ODT, docx and pptx metadata. Some applications show this as Comments metadata. Using Latex, one only has to focus on the contents of an article, and the formatting part would be taken care of by the latex tool itself. \end {landscape} \end {document} LaTex is a tool mainly used for typesetting. One should not get confused with Latex, a polymer mainly used in the world of Chemistry

Sample LaTeX documents. If you have TeX installed and just want to get started, you can peruse and process this introductory LaTeX document (small2e). When you've mastered that, move on to this more complex example (sample2e). The basic procedure is to create plain text files in any editor or GUI front end (TeXworks, TeXShop, GNU Emacs, etc.), and then run pdflatex myfile.tex from a command. A simple guide to LaTeX - Step by Step. Learn about LaTeX in short lessons with full code examples. A comprehensive guide to basic and advanced features. These tutorials, provide a hands-on introduction to LaTeX. You will see, the usage is very simple. Even if you have only used word processors (e.g. Word) before, you can learn LaTeX in no time

LATEX Command Summary This listing contains short descriptions of the control sequences that are likely to be handy for users of LAT EX v2.09 layered on T X v2.0.Some of these commands are LATEX macros, while oth- ers belong to plain TEX; no attempt to di eren LaTeX editor for macOS, macOS, iOS, iPad, iPhone and iPod Touch, with syntax highlighting, multi-file support and integrated PDF . Documentation. Support. Help . Docs. Support. Create an account Log in . Mac iOS Windows Connect. Research is hard, writing should be easy. Available for macOS, iOS and soon on Windows. Texpad macOS. Try out the fastest and most pleasurable way to write LaTeX. 10. Vim with LaTeX-Suite. Vim is an open-source and very powerful editor. Vim-LaTeX is an extension for Vim that lets you edit and compile LaTex documents. It brings a minimalist and powerful approach to text editing. Use Vim-LaTeX to bring the best of both the worlds into your document editing processes Overleaf verfügt über eine komplette, vorbereitete LaTeX-Umgebung, die auf unseren Servern läuft. Mit Overleaf bekommst du die gleiche LaTeX-Umgebung, wo auch immer du bist. Wenn du mit deinen Kollegen und Schülern auf Overleaf arbeitest, kannst du davon ausgehen, dass es keine Versionsinkonsistenzen oder Paketkonflikte gibt

LaTeX Template

While preparing a document in LaTeX, you may want to use colors for different purposes. Those purposes might be to color text or highlight text by changing its background color. You may even want to do both, highlight colored text. In this tutorial, we're going to discuss how to color and highlight text, and how to define our own colors. Coloring text. To color text in a document, you first. Los geht's: LaTeX vs. Word! Bring it on! Ansage: Microsoft Word ist ein Standard. Nun, unter Umständen ist das gar kein Märchen. Jedenfalls für ein genügend breit dehnbares Verständnis zum Begriff Standard. Viele Organisationen verwenden Microsoft Office. Es hat sich als Quasi-Standard etabliert - ohne je standardisiert worden zu sein. Das Dateiformat (doc, docx) hat allerdings. NASA-LaTeX-Docs. Please refer to the official documentation: NASA-LaTeX-Docs Documentation. Usage: With this LaTeX package, the formatting is all handled internally so that report developers only need to create their own content following a provided template (or even create their own). If not using a template (example: AIAA or IEEE submission.

Tables - Overleaf, Online LaTeX Edito

Insert PDF file in LaTeX document. Ask Question Asked 8 years, 1 month ago. Active 1 year, 11 months ago. Viewed 530k times 121. 46. I have a problem when I insert a PDF file in LaTeX: \usepackage[final]{pdfpages} \includepdf[pages=-]{file.pdf} The problem is that the PDF page is not centered: I've tried to place tags center, but nothing works. Thank you for your response. I still have the. LaTeX-Kompendium: Chemie. Aus Wikibooks. Zur Navigation springen Zur Suche springen. LaTeX-Kompendium. Der Artikel befindet sich in Überarbeitung, Status: Inhaltsverzeichnis. 1 Einleitendes; 2 Strukturformeln und Reaktionsgleichungen. 2.1 mhchem; 2.2 chemformula; 3 Referenzen; Einleitendes . Für den Satz chemischer Dokumente gibt es seit einigen Jahren eine ganze Reihe von Paketen, die dem. Eine einfache Tabellenumgebung wird mit tabular wie folgt erstellt: \begin {tabular} [Platzierung] {Format} Inhalt der Tabelle. \end {tabular} Die Spalten werden in LaTeX einzeln formatiert. Dabei. As another example, if you use TextMate on Mac OS X to edit your Latex documents, you can use its spell-checking features. Seems to work fairly well. - Jukka Suomela Jul 26 '10 at 20:25. 4. Personally use the new set :spell in Vim 7, and Automatic Spell Checking available in all system languages in Kile. - EricR Aug 4 '10 at 15:52. I'd point out that every dedicated TeX editor I know of.

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text:
# Performance Tips¶

In the following sections, we briefly go through a few techniques that can help make your Julia code run as fast as possible.

## Avoid global variables¶

A global variable might have its value, and therefore its type, change at any point. This makes it difficult for the compiler to optimize code using global variables. Variables should be local, or passed as arguments to functions, whenever possible.

Any code that is performance critical or being benchmarked should be inside a function.

We find that global names are frequently constants, and declaring them as such greatly improves performance:

const DEFAULT_VAL = 0

Uses of non-constant globals can be optimized by annotating their types at the point of use:

global x
y = f(x::Int + 1)

Writing functions is better style. It leads to more reusable code and clarifies what steps are being done, and what their inputs and outputs are.

NOTE: All code in the REPL is evaluated in global scope, so a variable defined and assigned at toplevel will be a global variable.

In the following REPL session:

julia> x = 1.0

is equivalent to:

julia> global x = 1.0

so all the performance issues discussed previously apply.

## Measure performance with @time and pay attention to memory allocation¶

The most useful tool for measuring performance is the @time macro. The following example illustrates good working style:

julia> function f(n)
s = 0
for i = 1:n
s += i/2
end
s
end
f (generic function with 1 method)

julia> @time f(1)
elapsed time: 0.004710563 seconds (93504 bytes allocated)
0.5

julia> @time f(10^6)
elapsed time: 0.04123202 seconds (32002136 bytes allocated)
2.5000025e11

On the first call (@time f(1)), f gets compiled. (If you’ve not yet used @time in this session, it will also compile functions needed for timing.) You should not take the results of this run seriously. For the second run, note that in addition to reporting the time, it also indicated that a large amount of memory was allocated. This is the single biggest advantage of @time vs. functions like tic() and toc(), which only report time.

Unexpected memory allocation is almost always a sign of some problem with your code, usually a problem with type-stability. Consequently, in addition to the allocation itself, it’s very likely that the code generated for your function is far from optimal. Take such indications seriously and follow the advice below.

As a teaser, note that an improved version of this function allocates no memory (except to pass back the result back to the REPL) and has an order of magnitude faster execution after the first call:

julia> @time f_improved(1)   # first call
elapsed time: 0.003702172 seconds (78944 bytes allocated)
0.5

julia> @time f_improved(10^6)
elapsed time: 0.004313644 seconds (112 bytes allocated)
2.5000025e11

Below you’ll learn how to spot the problem with f and how to fix it.

In some situations, your function may need to allocate memory as part of its operation, and this can complicate the simple picture above. In such cases, consider using one of the tools below to diagnose problems, or write a version of your function that separates allocation from its algorithmic aspects (see Pre-allocating outputs).

## Tools¶

Julia and its package ecosystem includes tools that may help you diagnose problems and improve the performance of your code:

• Profiling allows you to measure the performance of your running code and identify lines that serve as bottlenecks. For complex projects, the ProfileView package can help you visualize your profiling results.
• Unexpectedly-large memory allocations—as reported by @time, @allocated, or the profiler (through calls to the garbage-collection routines)—hint that there might be issues with your code. If you don’t see another reason for the allocations, suspect a type problem. You can also start Julia with the --track-allocation=user option and examine the resulting *.mem files to see information about where those allocations occur. See Memory allocation analysis.
• @code_warntype generates a representation of your code that can be helpful in finding expressions that result in type uncertainty. See @code_warntype below.
• The Lint and TypeCheck packages can also warn you of certain types of programming errors.

## Avoid containers with abstract type parameters¶

When working with parameterized types, including arrays, it is best to avoid parameterizing with abstract types where possible.

Consider the following:

a = Real[]    # typeof(a) = Array{Real,1}
if (f = rand()) < .8
push!(a, f)
end

Because a is a an array of abstract type Real, it must be able to hold any Real value. Since Real objects can be of arbitrary size and structure, a must be represented as an array of pointers to individually allocated Real objects. Because f will always be a Float64, we should instead, use:

a = Float64[] # typeof(a) = Array{Float64,1}

which will create a contiguous block of 64-bit floating-point values that can be manipulated efficiently.

## Type declarations¶

In many languages with optional type declarations, adding declarations is the principal way to make code run faster. This is not the case in Julia. In Julia, the compiler generally knows the types of all function arguments, local variables, and expressions. However, there are a few specific instances where declarations are helpful.

### Avoid fields with abstract type¶

Types can be declared without specifying the types of their fields:

julia> type MyAmbiguousType
a
end

This allows a to be of any type. This can often be useful, but it does have a downside: for objects of type MyAmbiguousType, the compiler will not be able to generate high-performance code. The reason is that the compiler uses the types of objects, not their values, to determine how to build code. Unfortunately, very little can be inferred about an object of type MyAmbiguousType:

julia> b = MyAmbiguousType("Hello")
MyAmbiguousType("Hello")

julia> c = MyAmbiguousType(17)
MyAmbiguousType(17)

julia> typeof(b)
MyAmbiguousType

julia> typeof(c)
MyAmbiguousType

b and c have the same type, yet their underlying representation of data in memory is very different. Even if you stored just numeric values in field a, the fact that the memory representation of a UInt8 differs from a Float64 also means that the CPU needs to handle them using two different kinds of instructions. Since the required information is not available in the type, such decisions have to be made at run-time. This slows performance.

You can do better by declaring the type of a. Here, we are focused on the case where a might be any one of several types, in which case the natural solution is to use parameters. For example:

julia> type MyType{T<:AbstractFloat}
a::T
end

This is a better choice than

julia> type MyStillAmbiguousType
a::AbstractFloat
end

because the first version specifies the type of a from the type of the wrapper object. For example:

julia> m = MyType(3.2)
MyType{Float64}(3.2)

julia> t = MyStillAmbiguousType(3.2)
MyStillAmbiguousType(3.2)

julia> typeof(m)
MyType{Float64}

julia> typeof(t)
MyStillAmbiguousType

The type of field a can be readily determined from the type of m, but not from the type of t. Indeed, in t it’s possible to change the type of field a:

julia> typeof(t.a)
Float64

julia> t.a = 4.5f0
4.5f0

julia> typeof(t.a)
Float32

In contrast, once m is constructed, the type of m.a cannot change:

julia> m.a = 4.5f0
4.5f0

julia> typeof(m.a)
Float64

The fact that the type of m.a is known from m‘s type—coupled with the fact that its type cannot change mid-function—allows the compiler to generate highly-optimized code for objects like m but not for objects like t.

Of course, all of this is true only if we construct m with a concrete type. We can break this by explicitly constructing it with an abstract type:

julia> m = MyType{AbstractFloat}(3.2)
MyType{AbstractFloat}(3.2)

julia> typeof(m.a)
Float64

julia> m.a = 4.5f0
4.5f0

julia> typeof(m.a)
Float32

For all practical purposes, such objects behave identically to those of MyStillAmbiguousType.

It’s quite instructive to compare the sheer amount code generated for a simple function

func(m::MyType) = m.a+1

using

code_llvm(func,(MyType{Float64},))
code_llvm(func,(MyType{AbstractFloat},))
code_llvm(func,(MyType,))

For reasons of length the results are not shown here, but you may wish to try this yourself. Because the type is fully-specified in the first case, the compiler doesn’t need to generate any code to resolve the type at run-time. This results in shorter and faster code.

### Avoid fields with abstract containers¶

The same best practices also work for container types:

julia> type MySimpleContainer{A<:AbstractVector}
a::A
end

julia> type MyAmbiguousContainer{T}
a::AbstractVector{T}
end

For example:

julia> c = MySimpleContainer(1:3);

julia> typeof(c)
MySimpleContainer{UnitRange{Int64}}

julia> c = MySimpleContainer([1:3;]);

julia> typeof(c)
MySimpleContainer{Array{Int64,1}}

julia> b = MyAmbiguousContainer(1:3);

julia> typeof(b)
MyAmbiguousContainer{Int64}

julia> b = MyAmbiguousContainer([1:3;]);

julia> typeof(b)
MyAmbiguousContainer{Int64}

For MySimpleContainer, the object is fully-specified by its type and parameters, so the compiler can generate optimized functions. In most instances, this will probably suffice.

While the compiler can now do its job perfectly well, there are cases where you might wish that your code could do different things depending on the element type of a. Usually the best way to achieve this is to wrap your specific operation (here, foo) in a separate function:

function sumfoo(c::MySimpleContainer)
s = 0
for x in c.a
s += foo(x)
end
s
end

foo(x::Integer) = x
foo(x::AbstractFloat) = round(x)

This keeps things simple, while allowing the compiler to generate optimized code in all cases.

However, there are cases where you may need to declare different versions of the outer function for different element types of a. You could do it like this:

function myfun{T<:AbstractFloat}(c::MySimpleContainer{Vector{T}})
...
end
function myfun{T<:Integer}(c::MySimpleContainer{Vector{T}})
...
end

This works fine for Vector{T}, but we’d also have to write explicit versions for UnitRange{T} or other abstract types. To prevent such tedium, you can use two parameters in the declaration of MyContainer:

type MyContainer{T, A<:AbstractVector}
a::A
end
MyContainer(v::AbstractVector) = MyContainer{eltype(v), typeof(v)}(v)

julia> b = MyContainer(1.3:5);

julia> typeof(b)
MyContainer{Float64,UnitRange{Float64}}

Note the somewhat surprising fact that T doesn’t appear in the declaration of field a, a point that we’ll return to in a moment. With this approach, one can write functions such as:

function myfunc{T<:Integer, A<:AbstractArray}(c::MyContainer{T,A})
return c.a[1]+1
end
# Note: because we can only define MyContainer for
# A<:AbstractArray, and any unspecified parameters are arbitrary,
# the previous could have been written more succinctly as
#     function myfunc{T<:Integer}(c::MyContainer{T})

function myfunc{T<:AbstractFloat}(c::MyContainer{T})
return c.a[1]+2
end

function myfunc{T<:Integer}(c::MyContainer{T,Vector{T}})
return c.a[1]+3
end

julia> myfunc(MyContainer(1:3))
2

julia> myfunc(MyContainer(1.0:3))
3.0

julia> myfunc(MyContainer([1:3]))
4

As you can see, with this approach it’s possible to specialize on both the element type T and the array type A.

However, there’s one remaining hole: we haven’t enforced that A has element type T, so it’s perfectly possible to construct an object like this:

julia> b = MyContainer{Int64, UnitRange{Float64}}(1.3:5);

julia> typeof(b)
MyContainer{Int64,UnitRange{Float64}}

To prevent this, we can add an inner constructor:

type MyBetterContainer{T<:Real, A<:AbstractVector}
a::A

MyBetterContainer(v::AbstractVector{T}) = new(v)
end
MyBetterContainer(v::AbstractVector) = MyBetterContainer{eltype(v),typeof(v)}(v)

julia> b = MyBetterContainer(1.3:5);

julia> typeof(b)
MyBetterContainer{Float64,UnitRange{Float64}}

julia> b = MyBetterContainer{Int64, UnitRange{Float64}}(1.3:5);
ERROR: no method MyBetterContainer(UnitRange{Float64},)

The inner constructor requires that the element type of A be T.

### Annotate values taken from untyped locations¶

It is often convenient to work with data structures that may contain values of any type (arrays of type Array{Any}). But, if you’re using one of these structures and happen to know the type of an element, it helps to share this knowledge with the compiler:

function foo(a::Array{Any,1})
x = a[1]::Int32
b = x+1
...
end

Here, we happened to know that the first element of a would be an Int32. Making an annotation like this has the added benefit that it will raise a run-time error if the value is not of the expected type, potentially catching certain bugs earlier.

### Declare types of keyword arguments¶

Keyword arguments can have declared types:

function with_keyword(x; name::Int = 1)
...
end

Functions are specialized on the types of keyword arguments, so these declarations will not affect performance of code inside the function. However, they will reduce the overhead of calls to the function that include keyword arguments.

Functions with keyword arguments have near-zero overhead for call sites that pass only positional arguments.

Passing dynamic lists of keyword arguments, as in f(x; keywords...), can be slow and should be avoided in performance-sensitive code.

## Break functions into multiple definitions¶

Writing a function as many small definitions allows the compiler to directly call the most applicable code, or even inline it.

Here is an example of a “compound function” that should really be written as multiple definitions:

function norm(A)
if isa(A, Vector)
return sqrt(real(dot(A,A)))
elseif isa(A, Matrix)
return max(svd(A)[2])
else
error("norm: invalid argument")
end
end

This can be written more concisely and efficiently as:

norm(x::Vector) = sqrt(real(dot(x,x)))
norm(A::Matrix) = max(svd(A)[2])

## Write “type-stable” functions¶

When possible, it helps to ensure that a function always returns a value of the same type. Consider the following definition:

pos(x) = x < 0 ? 0 : x

Although this seems innocent enough, the problem is that 0 is an integer (of type Int) and x might be of any type. Thus, depending on the value of x, this function might return a value of either of two types. This behavior is allowed, and may be desirable in some cases. But it can easily be fixed as follows:

pos(x) = x < 0 ? zero(x) : x

There is also a one() function, and a more general oftype(x,y) function, which returns y converted to the type of x.

## Avoid changing the type of a variable¶

An analogous “type-stability” problem exists for variables used repeatedly within a function:

function foo()
x = 1
for i = 1:10
x = x/bar()
end
return x
end

Local variable x starts as an integer, and after one loop iteration becomes a floating-point number (the result of / operator). This makes it more difficult for the compiler to optimize the body of the loop. There are several possible fixes:

• Initialize x with x = 1.0
• Declare the type of x: x::Float64 = 1
• Use an explicit conversion: x = one(T)

## Separate kernel functions (aka, function barriers)¶

Many functions follow a pattern of performing some set-up work, and then running many iterations to perform a core computation. Where possible, it is a good idea to put these core computations in separate functions. For example, the following contrived function returns an array of a randomly-chosen type:

function strange_twos(n)
a = Array(rand(Bool) ? Int64 : Float64, n)
for i = 1:n
a[i] = 2
end
return a
end

This should be written as:

function fill_twos!(a)
for i=1:length(a)
a[i] = 2
end
end

function strange_twos(n)
a = Array(rand(Bool) ? Int64 : Float64, n)
fill_twos!(a)
return a
end

Julia’s compiler specializes code for argument types at function boundaries, so in the original implementation it does not know the type of a during the loop (since it is chosen randomly). Therefore the second version is generally faster since the inner loop can be recompiled as part of fill_twos! for different types of a.

The second form is also often better style and can lead to more code reuse.

This pattern is used in several places in the standard library. For example, see hvcat_fill in abstractarray.jl, or the fill! function, which we could have used instead of writing our own fill_twos!.

Functions like strange_twos occur when dealing with data of uncertain type, for example data loaded from an input file that might contain either integers, floats, strings, or something else.

## Types with values-as-parameters¶

Let’s say you want to create an N-dimensional array that has size 3 along each axis. Such arrays can be created like this:

A = fill(5.0, (3, 3))

This approach works very well: the compiler can figure out that A is an Array{Float64,2} because it knows the type of the fill value (5.0::Float64) and the dimensionality ((3, 3)::NTuple{2,Int}). This implies that the compiler can generate very efficient code for any future usage of A in the same function.

But now let’s say you want to write a function that creates a 3×3×... array in arbitrary dimensions; you might be tempted to write a function

function array3(fillval, N)
fill(fillval, ntuple(d->3, N))
end

This works, but (as you can verify for yourself using @code_warntype array3(5.0, 2)) the problem is that the output type cannot be inferred: the argument N is a value of type Int, and type-inference does not (and cannot) predict its value in advance. This means that code using the output of this function has to be conservative, checking the type on each access of A; such code will be very slow.

Now, one very good way to solve such problems is by using the function-barrier technique. However, in some cases you might want to eliminate the type-instability altogether. In such cases, one approach is to pass the dimensionality as a parameter, for example through Val{T} (see “Value types”):

function array3{N}(fillval, ::Type{Val{N}})
fill(fillval, ntuple(d->3, Val{N}))
end

Julia has a specialized version of ntuple that accepts a Val{::Int} as the second parameter; by passing N as a type-parameter, you make its “value” known to the compiler. Consequently, this version of array3 allows the compiler to predict the return type.

However, making use of such techniques can be surprisingly subtle. For example, it would be of no help if you called array3 from a function like this:

function call_array3(fillval, n)
A = array3(fillval, Val{n})
end

Here, you’ve created the same problem all over again: the compiler can’t guess the type of n, so it doesn’t know the type of Val{n}. Attempting to use Val, but doing so incorrectly, can easily make performance worse in many situations. (Only in situations where you’re effectively combining Val with the function-barrier trick, to make the kernel function more efficient, should code like the above be used.)

An example of correct usage of Val would be:

function filter3{T,N}(A::AbstractArray{T,N})
kernel = array3(1, Val{N})
filter(A, kernel)
end

In this example, N is passed as a parameter, so its “value” is known to the compiler. Essentially, Val{T} works only when T is either hard-coded (Val{3}) or already specified in the type-domain.

## The dangers of abusing multiple dispatch (aka, more on types with values-as-parameters)¶

Once one learns to appreciate multiple dispatch, there’s an understandable tendency to go crazy and try to use it for everything. For example, you might imagine using it to store information, e.g.

immutable Car{Make,Model}
year::Int
...more fields...
end

and then dispatch on objects like Car{:Honda,:Accord}(year, args...).

This might be worthwhile when the following are true:

• You require CPU-intensive processing on each Car, and it becomes vastly more efficient if you know the Make and Model at compile time.
• You have homogenous lists of the same type of Car to process, so that you can store them all in an Array{Car{:Honda,:Accord},N}.

When the latter holds, a function processing such a homogenous array can be productively specialized: Julia knows the type of each element in advance (all objects in the container have the same concrete type), so Julia can “look up” the correct method calls when the function is being compiled (obviating the need to check at run-time) and thereby emit efficient code for processing the whole list.

When these do not hold, then it’s likely that you’ll get no benefit; worse, the resulting “combinatorial explosion of types” will be counterproductive. If items[i+1] has a different type than item[i], Julia has to look up the type at run-time, search for the appropriate method in method tables, decide (via type intersection) which one matches, determine whether it has been JIT-compiled yet (and do so if not), and then make the call. In essence, you’re asking the full type- system and JIT-compilation machinery to basically execute the equivalent of a switch statement or dictionary lookup in your own code.

Some run-time benchmarks comparing (1) type dispatch, (2) dictionary lookup, and (3) a “switch” statement can be found on the mailing list.

Perhaps even worse than the run-time impact is the compile-time impact: Julia will compile specialized functions for each different Car{Make, Model}; if you have hundreds or thousands of such types, then every function that accepts such an object as a parameter (from a custom get_year function you might write yourself, to the generic push! function in the standard library) will have hundreds or thousands of variants compiled for it. Each of these increases the size of the cache of compiled code, the length of internal lists of methods, etc. Excess enthusiasm for values-as-parameters can easily waste enormous resources.

## Access arrays in memory order, along columns¶

Multidimensional arrays in Julia are stored in column-major order. This means that arrays are stacked one column at a time. This can be verified using the vec function or the syntax [:] as shown below (notice that the array is ordered [1 3 2 4], not [1 2 3 4]):

julia> x = [1 2; 3 4]
2×2 Array{Int64,2}:
1  2
3  4

julia> x[:]
4-element Array{Int64,1}:
1
3
2
4

This convention for ordering arrays is common in many languages like Fortran, Matlab, and R (to name a few). The alternative to column-major ordering is row-major ordering, which is the convention adopted by C and Python (numpy) among other languages. Remembering the ordering of arrays can have significant performance effects when looping over arrays. A rule of thumb to keep in mind is that with column-major arrays, the first index changes most rapidly. Essentially this means that looping will be faster if the inner-most loop index is the first to appear in a slice expression.

Consider the following contrived example. Imagine we wanted to write a function that accepts a Vector and returns a square Matrix with either the rows or the columns filled with copies of the input vector. Assume that it is not important whether rows or columns are filled with these copies (perhaps the rest of the code can be easily adapted accordingly). We could conceivably do this in at least four ways (in addition to the recommended call to the built-in repmat()):

function copy_cols{T}(x::Vector{T})
n = size(x, 1)
out = Array{T}(n, n)
for i=1:n
out[:, i] = x
end
out
end

function copy_rows{T}(x::Vector{T})
n = size(x, 1)
out = Array{T}(n, n)
for i=1:n
out[i, :] = x
end
out
end

function copy_col_row{T}(x::Vector{T})
n = size(x, 1)
out = Array{T}(n, n)
for col=1:n, row=1:n
out[row, col] = x[row]
end
out
end

function copy_row_col{T}(x::Vector{T})
n = size(x, 1)
out = Array{T}(n, n)
for row=1:n, col=1:n
out[row, col] = x[col]
end
out
end

Now we will time each of these functions using the same random 10000 by 1 input vector:

julia> x = randn(10000);

julia> fmt(f) = println(rpad(string(f)*": ", 14, ' '), @elapsed f(x))

julia> map(fmt, Any[copy_cols, copy_rows, copy_col_row, copy_row_col]);
copy_cols:    0.331706323
copy_rows:    1.799009911
copy_col_row: 0.415630047
copy_row_col: 1.721531501

Notice that copy_cols is much faster than copy_rows. This is expected because copy_cols respects the column-based memory layout of the Matrix and fills it one column at a time. Additionally, copy_col_row is much faster than copy_row_col because it follows our rule of thumb that the first element to appear in a slice expression should be coupled with the inner-most loop.

## Pre-allocating outputs¶

If your function returns an Array or some other complex type, it may have to allocate memory. Unfortunately, oftentimes allocation and its converse, garbage collection, are substantial bottlenecks.

Sometimes you can circumvent the need to allocate memory on each function call by preallocating the output. As a trivial example, compare

function xinc(x)
return [x, x+1, x+2]
end

function loopinc()
y = 0
for i = 1:10^7
ret = xinc(i)
y += ret[2]
end
y
end

with

function xinc!{T}(ret::AbstractVector{T}, x::T)
ret[1] = x
ret[2] = x+1
ret[3] = x+2
nothing
end

function loopinc_prealloc()
ret = Array{Int}(3)
y = 0
for i = 1:10^7
xinc!(ret, i)
y += ret[2]
end
y
end

Timing results:

julia> @time loopinc()
elapsed time: 1.955026528 seconds (1279975584 bytes allocated)
50000015000000

julia> @time loopinc_prealloc()
elapsed time: 0.078639163 seconds (144 bytes allocated)
50000015000000

Preallocation has other advantages, for example by allowing the caller to control the “output” type from an algorithm. In the example above, we could have passed a SubArray rather than an Array, had we so desired.

Taken to its extreme, pre-allocation can make your code uglier, so performance measurements and some judgment may be required. However, for “vectorized” (element-wise) functions, the convenient syntax x .= f.(y) can be used for in-place operations with fused loops and no temporary arrays (Dot Syntax for Vectorizing Functions).

## Avoid string interpolation for I/O¶

When writing data to a file (or other I/O device), forming extra intermediate strings is a source of overhead. Instead of:

println(file, "$a$b")

use:

println(file, a, " ", b)

The first version of the code forms a string, then writes it to the file, while the second version writes values directly to the file. Also notice that in some cases string interpolation can be harder to read. Consider:

println(file, "$(f(a))$(f(b))")

versus:

println(file, f(a), f(b))

## Optimize network I/O during parallel execution¶

When executing a remote function in parallel:

responses = Vector{Any}(nworkers())
@sync begin
for (idx, pid) in enumerate(workers())
@async responses[idx] = remotecall_fetch(pid, foo, args...)
end
end

is faster than:

refs = Vector{Any}(nworkers())
for (idx, pid) in enumerate(workers())
refs[idx] = @spawnat pid foo(args...)
end
responses = [fetch(r) for r in refs]

The former results in a single network round-trip to every worker, while the latter results in two network calls - first by the @spawnat and the second due to the fetch (or even a wait). The fetch/wait is also being executed serially resulting in an overall poorer performance.

## Fix deprecation warnings¶

A deprecated function internally performs a lookup in order to print a relevant warning only once. This extra lookup can cause a significant slowdown, so all uses of deprecated functions should be modified as suggested by the warnings.

## Tweaks¶

These are some minor points that might help in tight inner loops.

## Performance Annotations¶

Sometimes you can enable better optimization by promising certain program properties.

• Use @inbounds to eliminate array bounds checking within expressions. Be certain before doing this. If the subscripts are ever out of bounds, you may suffer crashes or silent corruption.
• Use @fastmath to allow floating point optimizations that are correct for real numbers, but lead to differences for IEEE numbers. Be careful when doing this, as this may change numerical results. This corresponds to the -ffast-math option of clang.
• Write @simd in front of for loops that are amenable to vectorization. This feature is experimental and could change or disappear in future versions of Julia.

Note: While @simd needs to be placed directly in front of a loop, both @inbounds and @fastmath can be applied to several statements at once, e.g. using begin ... end, or even to a whole function.

Here is an example with both @inbounds and @simd markup:

function inner( x, y )
s = zero(eltype(x))
for i=1:length(x)
@inbounds s += x[i]*y[i]
end
s
end

function innersimd( x, y )
s = zero(eltype(x))
@simd for i=1:length(x)
@inbounds s += x[i]*y[i]
end
s
end

function timeit( n, reps )
x = rand(Float32,n)
y = rand(Float32,n)
s = zero(Float64)
time = @elapsed for j in 1:reps
s+=inner(x,y)
end
println("GFlop/sec        = ",2.0*n*reps/time*1E-9)
time = @elapsed for j in 1:reps
s+=innersimd(x,y)
end
println("GFlop/sec (SIMD) = ",2.0*n*reps/time*1E-9)
end

timeit(1000,1000)

On a computer with a 2.4GHz Intel Core i5 processor, this produces:

GFlop/sec        = 1.9467069505224963
GFlop/sec (SIMD) = 17.578554163920018

(GFlop/sec measures the performance, and larger numbers are better.) The range for a @simd for loop should be a one-dimensional range. A variable used for accumulating, such as s in the example, is called a reduction variable. By using @simd, you are asserting several properties of the loop:

• It is safe to execute iterations in arbitrary or overlapping order, with special consideration for reduction variables.
• Floating-point operations on reduction variables can be reordered, possibly causing different results than without @simd.
• No iteration ever waits on another iteration to make forward progress.

A loop containing break, continue, or @goto will cause a compile-time error.

Using @simd merely gives the compiler license to vectorize. Whether it actually does so depends on the compiler. To actually benefit from the current implementation, your loop should have the following additional properties:

• The loop must be an innermost loop.
• The loop body must be straight-line code. This is why @inbounds is currently needed for all array accesses. The compiler can sometimes turn short &&, ||, and ?: expressions into straight-line code, if it is safe to evaluate all operands unconditionally. Consider using ifelse() instead of ?: in the loop if it is safe to do so.
• Accesses must have a stride pattern and cannot be “gathers” (random-index reads) or “scatters” (random-index writes).
• The stride should be unit stride.
• In some simple cases, for example with 2-3 arrays accessed in a loop, the LLVM auto-vectorization may kick in automatically, leading to no further speedup with @simd.

Here is an example with all three kinds of markup. This program first calculates the finite difference of a one-dimensional array, and then evaluates the L2-norm of the result:

function init!(u)
n = length(u)
dx = 1.0 / (n-1)
@fastmath @inbounds @simd for i in 1:n
u[i] = sin(2pi*dx*i)
end
end

function deriv!(u, du)
n = length(u)
dx = 1.0 / (n-1)
@fastmath @inbounds du[1] = (u[2] - u[1]) / dx
@fastmath @inbounds @simd for i in 2:n-1
du[i] = (u[i+1] - u[i-1]) / (2*dx)
end
@fastmath @inbounds du[n] = (u[n] - u[n-1]) / dx
end

function norm(u)
n = length(u)
T = eltype(u)
s = zero(T)
@fastmath @inbounds @simd for i in 1:n
s += u[i]^2
end
@fastmath @inbounds return sqrt(s/n)
end

function main()
n = 2000
u = Array{Float64}(n)
init!(u)
du = similar(u)

deriv!(u, du)
nu = norm(du)

@time for i in 1:10^6
deriv!(u, du)
nu = norm(du)
end

println(nu)
end

main()

On a computer with a 2.7 GHz Intel Core i7 processor, this produces:

$julia wave.jl; elapsed time: 1.207814709 seconds (0 bytes allocated)$ julia --math-mode=ieee wave.jl;
elapsed time: 4.487083643 seconds (0 bytes allocated)

Here, the option --math-mode=ieee disables the @fastmath macro, so that we can compare results.

In this case, the speedup due to @fastmath is a factor of about 3.7. This is unusually large – in general, the speedup will be smaller. (In this particular example, the working set of the benchmark is small enough to fit into the L1 cache of the processor, so that memory access latency does not play a role, and computing time is dominated by CPU usage. In many real world programs this is not the case.) Also, in this case this optimization does not change the result – in general, the result will be slightly different. In some cases, especially for numerically unstable algorithms, the result can be very different.

The annotation @fastmath re-arranges floating point expressions, e.g. changing the order of evaluation, or assuming that certain special cases (inf, nan) cannot occur. In this case (and on this particular computer), the main difference is that the expression 1 / (2*dx) in the function deriv is hoisted out of the loop (i.e. calculated outside the loop), as if one had written idx = 1 / (2*dx). In the loop, the expression ... / (2*dx) then becomes ... * idx, which is much faster to evaluate. Of course, both the actual optimization that is applied by the compiler as well as the resulting speedup depend very much on the hardware. You can examine the change in generated code by using Julia’s code_native() function.

## Treat Subnormal Numbers as Zeros¶

Subnormal numbers, formerly called denormal numbers, are useful in many contexts, but incur a performance penalty on some hardware. A call set_zero_subnormals(true) grants permission for floating-point operations to treat subnormal inputs or outputs as zeros, which may improve performance on some hardware. A call set_zero_subnormals(false) enforces strict IEEE behavior for subnormal numbers.

Below is an example where subnormals noticeably impact performance on some hardware:

function timestep{T}( b::Vector{T}, a::Vector{T}, Δt::T )
@assert length(a)==length(b)
n = length(b)
b[1] = 1                            # Boundary condition
for i=2:n-1
b[i] = a[i] + (a[i-1] - T(2)*a[i] + a[i+1]) * Δt
end
b[n] = 0                            # Boundary condition
end

function heatflow{T}( a::Vector{T}, nstep::Integer )
b = similar(a)
for t=1:div(nstep,2)                # Assume nstep is even
timestep(b,a,T(0.1))
timestep(a,b,T(0.1))
end
end

heatflow(zeros(Float32,10),2)           # Force compilation
for trial=1:6
a = zeros(Float32,1000)
set_zero_subnormals(iseven(trial))  # Odd trials use strict IEEE arithmetic
@time heatflow(a,1000)
end

This example generates many subnormal numbers because the values in a become an exponentially decreasing curve, which slowly flattens out over time.

Treating subnormals as zeros should be used with caution, because doing so breaks some identities, such as x-y==0 implies x==y:

julia> x=3f-38; y=2f-38;

julia> set_zero_subnormals(false); (x-y,x==y)
(1.0000001f-38,false)

julia> set_zero_subnormals(true); (x-y,x==y)
(0.0f0,false)

In some applications, an alternative to zeroing subnormal numbers is to inject a tiny bit of noise. For example, instead of initializing a with zeros, initialize it with:

a = rand(Float32,1000) * 1.f-9

## @code_warntype¶

The macro @code_warntype (or its function variant code_warntype()) can sometimes be helpful in diagnosing type-related problems. Here’s an example:

pos(x) = x < 0 ? 0 : x

function f(x)
y = pos(x)
sin(y*x+1)
end

julia> @code_warntype f(3.2)
Variables:
x::Float64
y::UNION(INT64,FLOAT64)
_var0::Float64
_var3::Tuple{Int64}
_var4::UNION(INT64,FLOAT64)
_var1::Float64
_var2::Float64

Body:
begin  # none, line 2:
_var0 = (top(box))(Float64,(top(sitofp))(Float64,0))
unless (top(box))(Bool,(top(or_int))((top(lt_float))(x::Float64,_var0::Float64)::Bool,(top(box))(Bool,(top(and_int))((top(box))(Bool,(top(and_int))((top(eq_float))(x::Float64,_var0::Float64)::Bool,(top(lt_float))(_var0::Float64,9.223372036854776e18)::Bool)),(top(slt_int))((top(box))(Int64,(top(fptosi))(Int64,_var0::Float64)),0)::Bool)))) goto 1
_var4 = 0
goto 2
1:
_var4 = x::Float64
2:
y = _var4::UNION(INT64,FLOAT64) # line 3:
_var1 = y::UNION(INT64,FLOAT64) * x::Float64::Float64
return (GlobalRef(Base.Math,:nan_dom_err))((top(ccall))($(Expr(:call1, :(top(tuple)), "sin", GlobalRef(Base.Math,:libm))),Float64,$(Expr(:call1, :(top(tuple)), :Float64)),_var2::Float64,0)::Float64,_var2::Float64)::Float64
end::Float64

Interpreting the output of @code_warntype, like that of its cousins @code_lowered, @code_typed, @code_llvm, and @code_native, takes a little practice. Your code is being presented in form that has been partially digested on its way to generating compiled machine code. Most of the expressions are annotated by a type, indicated by the ::T (where T might be Float64, for example). The most important characteristic of @code_warntype is that non-concrete types are displayed in red; in the above example, such output is shown in all-caps.

The top part of the output summarizes the type information for the different variables internal to the function. You can see that y, one of the variables you created, is a Union{Int64,Float64}, due to the type-instability of pos. There is another variable, _var4, which you can see also has the same type.

The next lines represent the body of f. The lines starting with a number followed by a colon (1:, 2:) are labels, and represent targets for jumps (via goto) in your code. Looking at the body, you can see that pos has been inlined into f—everything before 2: comes from code defined in pos.

Starting at 2:, the variable y is defined, and again annotated as a Union type. Next, we see that the compiler created the temporary variable _var1 to hold the result of y*x. Because a Float64 times either an Int64 or Float64 yields a Float64, all type-instability ends here. The net result is that f(x::Float64) will not be type-unstable in its output, even if some of the intermediate computations are type-unstable.

How you use this information is up to you. Obviously, it would be far and away best to fix pos to be type-stable: if you did so, all of the variables in f would be concrete, and its performance would be optimal. However, there are circumstances where this kind of ephemeral type instability might not matter too much: for example, if pos is never used in isolation, the fact that f‘s output is type-stable (for Float64 inputs) will shield later code from the propagating effects of type instability. This is particularly relevant in cases where fixing the type instability is difficult or impossible: for example, currently it’s not possible to infer the return type of an anonymous function. In such cases, the tips above (e.g., adding type annotations and/or breaking up functions) are your best tools to contain the “damage” from type instability.

The following examples may help you interpret expressions marked as containing non-leaf types:

• Function body ending in end::Union{T1,T2})
• Interpretation: function with unstable return type
• Suggestion: make the return value type-stable, even if you have to annotate it
• f(x::T)::Union{T1,T2}
• Interpretation: call to a type-unstable function
• Suggestion: fix the function, or if necessary annotate the return value
• (top(arrayref))(A::Array{Any,1},1)::Any
• Interpretation: accessing elements of poorly-typed arrays
• Suggestion: use arrays with better-defined types, or if necessary annotate the type of individual element accesses
• (top(getfield))(A::ArrayContainer{Float64},:data)::Array{Float64,N}
• Interpretation: getting a field that is of non-leaf type. In this case, ArrayContainer had a field data::Array{T}. But Array needs the dimension N, too, to be a concrete type.
• Suggestion: use concrete types like Array{T,3} or Array{T,N}, where N is now a parameter of ArrayContainer

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