diff --git a/module2/exo1/.gitignore b/module2/exo1/.gitignore new file mode 100644 index 0000000000000000000000000000000000000000..0e2bbd5bf6b56857cfaee1f336f73fdaf3ea49b6 --- /dev/null +++ b/module2/exo1/.gitignore @@ -0,0 +1 @@ +toy_document_fr.html diff --git a/module2/exo1/toy_document_fr.Rmd b/module2/exo1/toy_document_fr.Rmd index b5a81871af5fd73c426bad77cbff97fbeb029734..38b9e8abf5193b0aaa9d0b1e66892941a2ec56c3 100644 --- a/module2/exo1/toy_document_fr.Rmd +++ b/module2/exo1/toy_document_fr.Rmd @@ -1,14 +1,9 @@ ---- -output: - html_document: default - pdf_document: default ---- # À propos du calcul de pi _Arnaud Legrand_ - _25 juin 2018_ + ## En demandant à la lib maths Mon ordinateur m’indique que $\pi$ vaut _approximativement_ diff --git a/module2/exo1/toy_document_fr.html b/module2/exo1/toy_document_fr.html index 51030a55dbedfa267fb47d91b73b0ea1608ce9a9..b8f6a27be8a40914f8bbd908406bbd23d4ed1a2d 100644 --- a/module2/exo1/toy_document_fr.html +++ b/module2/exo1/toy_document_fr.html @@ -166,8 +166,7 @@ pre code {

À propos du calcul de pi

-

Arnaud Legrand

-

25 juin 2018

+

Arnaud Legrand 25 juin 2018

En demandant à la lib maths

Mon ordinateur m’indique que \(\pi\) vaut approximativement

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LaTeX Error: Unicode character π (U+03C0) + not set up for use with LaTeX. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.120 Mon ordinateur m'indique que π + vaut \emph{approximativement} +Here is how much of TeX's memory you used: + 11333 strings out of 475538 + 175182 string characters out of 5775359 + 1926960 words of memory out of 5000000 + 33862 multiletter control sequences out of 15000+600000 + 577316 words of font info for 42 fonts, out of 8000000 for 9000 + 14 hyphenation exceptions out of 8191 + 89i,3n,93p,291b,434s stack positions out of 10000i,1000n,20000p,200000b,200000s + +! ==> Fatal error occurred, no output PDF file produced! diff --git a/module2/exo1/toy_document_fr.tex b/module2/exo1/toy_document_fr.tex new file mode 100644 index 0000000000000000000000000000000000000000..9b19d68bdb1877f658618cb7f35d1c6054b1063b --- /dev/null +++ b/module2/exo1/toy_document_fr.tex @@ -0,0 +1,199 @@ +% Options for packages loaded elsewhere +\PassOptionsToPackage{unicode}{hyperref} +\PassOptionsToPackage{hyphens}{url} +% +\documentclass[ +]{article} +\usepackage{amsmath,amssymb} +\usepackage{lmodern} +\usepackage{iftex} +\ifPDFTeX + \usepackage[T1]{fontenc} + \usepackage[utf8]{inputenc} + \usepackage{textcomp} % provide euro and other symbols +\else % if luatex or xetex + \usepackage{unicode-math} + \defaultfontfeatures{Scale=MatchLowercase} + \defaultfontfeatures[\rmfamily]{Ligatures=TeX,Scale=1} +\fi +% Use upquote if available, for straight quotes in verbatim environments +\IfFileExists{upquote.sty}{\usepackage{upquote}}{} +\IfFileExists{microtype.sty}{% use microtype if available + \usepackage[]{microtype} + \UseMicrotypeSet[protrusion]{basicmath} % disable protrusion for tt fonts +}{} +\makeatletter +\@ifundefined{KOMAClassName}{% if non-KOMA class + \IfFileExists{parskip.sty}{% + \usepackage{parskip} + }{% else + \setlength{\parindent}{0pt} + \setlength{\parskip}{6pt plus 2pt minus 1pt}} +}{% if KOMA class + \KOMAoptions{parskip=half}} +\makeatother +\usepackage{xcolor} +\IfFileExists{xurl.sty}{\usepackage{xurl}}{} % add URL line breaks if available +\IfFileExists{bookmark.sty}{\usepackage{bookmark}}{\usepackage{hyperref}} +\hypersetup{ + hidelinks, + pdfcreator={LaTeX via pandoc}} +\urlstyle{same} % disable monospaced font for URLs +\usepackage[margin=1in]{geometry} +\usepackage{color} +\usepackage{fancyvrb} +\newcommand{\VerbBar}{|} +\newcommand{\VERB}{\Verb[commandchars=\\\{\}]} +\DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}} +% Add ',fontsize=\small' for more characters per line +\usepackage{framed} +\definecolor{shadecolor}{RGB}{248,248,248} +\newenvironment{Shaded}{\begin{snugshade}}{\end{snugshade}} +\newcommand{\AlertTok}[1]{\textcolor[rgb]{0.94,0.16,0.16}{#1}} +\newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} +\newcommand{\AttributeTok}[1]{\textcolor[rgb]{0.77,0.63,0.00}{#1}} 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+\newcommand{\InformationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} +\newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.13,0.29,0.53}{\textbf{#1}}} +\newcommand{\NormalTok}[1]{#1} +\newcommand{\OperatorTok}[1]{\textcolor[rgb]{0.81,0.36,0.00}{\textbf{#1}}} +\newcommand{\OtherTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{#1}} +\newcommand{\PreprocessorTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textit{#1}}} +\newcommand{\RegionMarkerTok}[1]{#1} +\newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}} +\newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} +\newcommand{\StringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} +\newcommand{\VariableTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}} +\newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} +\newcommand{\WarningTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} +\usepackage{graphicx} +\makeatletter +\def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth\else\Gin@nat@width\fi} +\def\maxheight{\ifdim\Gin@nat@height>\textheight\textheight\else\Gin@nat@height\fi} +\makeatother +% Scale images if necessary, so that they will not overflow the page +% margins by default, and it is still possible to overwrite the defaults +% using explicit options in \includegraphics[width, height, ...]{} +\setkeys{Gin}{width=\maxwidth,height=\maxheight,keepaspectratio} +% Set default figure placement to htbp +\makeatletter +\def\fps@figure{htbp} +\makeatother +\setlength{\emergencystretch}{3em} % prevent overfull lines +\providecommand{\tightlist}{% + \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}} +\setcounter{secnumdepth}{-\maxdimen} % remove section numbering +\ifLuaTeX + \usepackage{selnolig} % disable illegal ligatures +\fi + +\author{} +\date{\vspace{-2.5em}} + +\begin{document} + +\hypertarget{uxe0-propos-du-calcul-de-pi}{% +\section{À propos du calcul de pi}\label{uxe0-propos-du-calcul-de-pi}} + +\emph{Arnaud Legrand} + +\emph{25 juin 2018} + +\hypertarget{en-demandant-uxe0-la-lib-maths}{% +\subsection{En demandant à la lib +maths}\label{en-demandant-uxe0-la-lib-maths}} + +Mon ordinateur m'indique que π vaut \emph{approximativement} + +\begin{Shaded} +\begin{Highlighting}[] +\NormalTok{pi} +\end{Highlighting} +\end{Shaded} + +\begin{verbatim} +## [1] 3.141593 +\end{verbatim} + +\hypertarget{en-utilisant-la-muxe9thode-des-aiguilles-de-buffon}{% +\subsection{En utilisant la méthode des aiguilles de +Buffon}\label{en-utilisant-la-muxe9thode-des-aiguilles-de-buffon}} + +Mais calculé avec la \textbf{méthode} des +\href{https://fr.wikipedia.org/wiki/Aiguille_de_Buffon}{aiguilles de +Buffon}, on obtiendrait comme \textbf{approximation} : + +\begin{Shaded} +\begin{Highlighting}[] +\FunctionTok{set.seed}\NormalTok{(}\DecValTok{42}\NormalTok{)} +\NormalTok{N }\OtherTok{=} \DecValTok{100000} +\NormalTok{x }\OtherTok{=} \FunctionTok{runif}\NormalTok{(N)} +\NormalTok{theta }\OtherTok{=}\NormalTok{ pi}\SpecialCharTok{/}\DecValTok{2}\SpecialCharTok{*}\FunctionTok{runif}\NormalTok{(N)} +\DecValTok{2}\SpecialCharTok{/}\NormalTok{(}\FunctionTok{mean}\NormalTok{(x}\SpecialCharTok{+}\FunctionTok{sin}\NormalTok{(theta)}\SpecialCharTok{\textgreater{}}\DecValTok{1}\NormalTok{))} +\end{Highlighting} +\end{Shaded} + +\begin{verbatim} +## [1] 3.14327 +\end{verbatim} + +\hypertarget{avec-un-argument-fruxe9quentiel-de-surface}{% +\subsection{Avec un argument ``fréquentiel'' de +surface}\label{avec-un-argument-fruxe9quentiel-de-surface}} + +Sinon, une méthode plus simple à comprendre et ne faisant pas intervenir +d'appel à la fonction sinus se base sur le fait que si X∼U(0,1) et +Y∼U(0,1) alors P{[}X2+Y2≤1{]}=π/4 (voir +\href{https://fr.wikipedia.org/wiki/M\%C3\%A9thode_de_Monte-Carlo\#D\%C3\%A9termination_de_la_valeur_de_\%CF\%80}{méthode +de Monte Carlo sur Wikipedia}). Le code suivant illustre ce fait: + +\begin{Shaded} +\begin{Highlighting}[] +\FunctionTok{set.seed}\NormalTok{(}\DecValTok{42}\NormalTok{)} +\NormalTok{N }\OtherTok{=} \DecValTok{1000} +\NormalTok{df }\OtherTok{=} \FunctionTok{data.frame}\NormalTok{(}\AttributeTok{X =} \FunctionTok{runif}\NormalTok{(N), }\AttributeTok{Y =} \FunctionTok{runif}\NormalTok{(N))} +\NormalTok{df}\SpecialCharTok{$}\NormalTok{Accept }\OtherTok{=}\NormalTok{ (df}\SpecialCharTok{$}\NormalTok{X}\SpecialCharTok{**}\DecValTok{2} \SpecialCharTok{+}\NormalTok{ df}\SpecialCharTok{$}\NormalTok{Y}\SpecialCharTok{**}\DecValTok{2} \SpecialCharTok{\textless{}=}\DecValTok{1}\NormalTok{)} +\FunctionTok{library}\NormalTok{(ggplot2)} +\end{Highlighting} +\end{Shaded} + +\begin{verbatim} +## Warning: le package 'ggplot2' a été compilé avec la version R 4.3.3 +\end{verbatim} + +\begin{Shaded} +\begin{Highlighting}[] +\FunctionTok{ggplot}\NormalTok{(df, }\FunctionTok{aes}\NormalTok{(}\AttributeTok{x=}\NormalTok{X,}\AttributeTok{y=}\NormalTok{Y,}\AttributeTok{color=}\NormalTok{Accept)) }\SpecialCharTok{+} \FunctionTok{geom\_point}\NormalTok{(}\AttributeTok{alpha=}\NormalTok{.}\DecValTok{2}\NormalTok{) }\SpecialCharTok{+} \FunctionTok{coord\_fixed}\NormalTok{() }\SpecialCharTok{+} \FunctionTok{theme\_bw}\NormalTok{()} +\end{Highlighting} +\end{Shaded} + +\includegraphics{toy_document_fr_files/figure-latex/unnamed-chunk-3-1.pdf} + +Il est alors aisé d'obtenir une approximation (pas terrible) de π en +comptant combien de fois, en moyenne, X2+Y2 est inférieur à 1: + +\begin{Shaded} +\begin{Highlighting}[] +\DecValTok{4}\SpecialCharTok{*}\FunctionTok{mean}\NormalTok{(df}\SpecialCharTok{$}\NormalTok{Accept)} +\end{Highlighting} +\end{Shaded} + +\begin{verbatim} +## [1] 3.156 +\end{verbatim} + +\end{document} diff --git a/mooc-rr.Rproj b/mooc-rr.Rproj new file mode 100644 index 0000000000000000000000000000000000000000..8e3c2ebc99e2e337f7d69948b93529a437590b27 --- /dev/null +++ b/mooc-rr.Rproj @@ -0,0 +1,13 @@ +Version: 1.0 + +RestoreWorkspace: Default +SaveWorkspace: Default +AlwaysSaveHistory: Default + +EnableCodeIndexing: Yes +UseSpacesForTab: Yes +NumSpacesForTab: 2 +Encoding: UTF-8 + +RnwWeave: Sweave +LaTeX: pdfLaTeX