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-#+HTML_HEAD: -#+HTML_HEAD: -#+HTML_HEAD: -#+HTML_HEAD: -* Quelques explications +* En demandant à la lib maths +Mon ordianteur m'indique que pi vaut /approximativement/ -Ceci est un document org-mode avec quelques exemples de code -R. Une fois ouvert dans emacs, ce document peut aisément être -exporté au format HTML, PDF, et Office. Pour plus de détails sur -org-mode vous pouvez consulter https://orgmode.org/guide/. -Lorsque vous utiliserez le raccourci =C-c C-e h o=, ce document sera -compilé en html. Tout le code contenu sera ré-exécuté, les résultats -récupérés et inclus dans un document final. Si vous ne souhaitez pas -ré-exécuter tout le code à chaque fois, il vous suffit de supprimer -le # et l'espace qui sont devant le ~#+PROPERTY:~ au début de ce -document. -Comme nous vous l'avons montré dans la vidéo, on inclut du code -R de la façon suivante (et on l'exécute en faisant ~C-c C-c~): +#+begin_src python :results output :exports results +print("pi") +#+end_src + +#+RESULTS: +: pi -#+begin_src R :results output :exports both -print("Hello world!") +#+begin_src python :results output :exports results +import numpy as np +print("{:6f}".format(np.pi)) #+end_src #+RESULTS: -: [1] "Hello world!" +: 3.141593 -Voici la même chose, mais avec une session R (c'est le cas le -plus courant, R étant vraiment un langage interactif), donc une -persistance d'un bloc à l'autre (et on l'exécute toujours en faisant -~C-c C-c~). +* En utilisant la méthode des aiguilles de Buffon -#+begin_src R :results output :session *R* :exports both -summary(cars) +Mais calculé avec la *méthode* des + [[https://fr.wikipedia.org/wiki/Aiguille_de_Buffon][aiguilles de Buffon]], on +obtiendrait comme *approximation* : + +#+begin_src python :results output :exports both +from numpy.random import uniform +from numpy import pi, mean, sin, array +N = 100000 +x = array([uniform(0,1) for i in range(N)]) +theta = (pi/2)*x +print(2/(mean(x+sin(theta)>1))) #+end_src #+RESULTS: -: speed dist -: Min. : 4.0 Min. : 2.00 -: 1st Qu.:12.0 1st Qu.: 26.00 -: Median :15.0 Median : 36.00 -: Mean :15.4 Mean : 42.98 -: 3rd Qu.:19.0 3rd Qu.: 56.00 -: Max. :25.0 Max. :120.00 - -Et enfin, voici un exemple de sortie graphique: -#+begin_src R :results output graphics :file "./cars.png" :exports results :width 600 :height 400 :session *R* -plot(cars) +: 3.3638320775026913 + +* Avec un argument "fréquentiel" 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 \sim U(0,1)/ et /Y \sim U(0,1)/ alors /P[X² + Y²\le1]=\pi/4/ (voir [[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_src python :results output :session :exports both +import matplotlib.pyplot as plt +from numpy.random import uniform +from numpy import mean + +N = 1000 +x = [uniform(0,1) for i in range(1000)] +y = [uniform(0,1) for i in range(1000)] +Xb = [] +Yb = [] +Xr = [] +Yr = [] +for i, xx in enumerate(x): + if (xx**2+y[i]**2) <=1: + Xb.append(xx) + Yb.append(y[i]) + else: + Xr.append(xx) + Yr.append(y[i]) + #+end_src #+RESULTS: -[[file:./cars.png]] - -Vous remarquerez le paramètre ~:exports results~ qui indique que le code -ne doit pas apparaître dans la version finale du document. Nous vous -recommandons dans le cadre de ce MOOC de ne pas changer ce paramètre -(indiquer ~both~) car l'objectif est que vos analyses de données soient -parfaitement transparentes pour être reproductibles. - -Attention, la figure ainsi générée n'est pas stockée dans le document -org. C'est un fichier ordinaire, ici nommé ~cars.png~. N'oubliez pas -de le committer si vous voulez que votre analyse soit lisible et -compréhensible sur GitLab. - -Enfin, pour les prochains exercices, nous ne vous fournirons pas -forcément de fichier de départ, ça sera à vous de le créer, par -exemple en repartant de ce document et de le commiter vers -gitlab. N'oubliez pas que nous vous fournissons dans les ressources de -ce MOOC une configuration avec un certain nombre de raccourcis -claviers permettant de créer rapidement les blocs de code R (en -faisant ~ -#+HTML_HEAD: -#+HTML_HEAD: -#+HTML_HEAD: -#+HTML_HEAD: -#+HTML_HEAD: -* Quelques explications +* En demandant à la lib maths +Mon ordianteur m'indique que pi vaut /approximativement/ -Ceci est un document org-mode avec quelques exemples de code -python. Une fois ouvert dans emacs, ce document peut aisément être -exporté au format HTML, PDF, et Office. Pour plus de détails sur -org-mode vous pouvez consulter https://orgmode.org/guide/. -Lorsque vous utiliserez le raccourci =C-c C-e h o=, ce document sera -compilé en html. Tout le code contenu sera ré-exécuté, les résultats -récupérés et inclus dans un document final. Si vous ne souhaitez pas -ré-exécuter tout le code à chaque fois, il vous suffit de supprimer -le # et l'espace qui sont devant le ~#+PROPERTY:~ au début de ce -document. -Comme nous vous l'avons montré dans la vidéo, on inclue du code -python de la façon suivante (et on l'exécute en faisant ~C-c C-c~): +#+begin_src python :results output :exports both +from math import * +pi +#+end_src + +#+RESULTS: + +#+begin_src python :results output :session :exports both +from numpy import pi +print(pi) +#+end_src + +#+RESULTS: +: 3.141592653589793 + +* En utilisant la méthode des aiguilles de Buffon + +Mais calculé avec la *méthode* des + [[https://fr.wikipedia.org/wiki/Aiguille_de_Buffon][aiguilles de Buffon]], on +obtiendrait comme *approximation* : #+begin_src python :results output :exports both -print("Hello world!") +import numpy as np +np.random.seed(seed=42) +N = 10000 +x = np.random.uniform(size=N, low=0, high=1) +theta = np.random.uniform(size=N, low=0, high=pi/2) +2/(sum((x+np.sin(theta))>1)/N) #+end_src #+RESULTS: -: Hello world! -Voici la même chose, mais avec une session python, donc une -persistance d'un bloc à l'autre (et on l'exécute toujours en faisant -~C-c C-c~). -#+begin_src python :results output :session :exports both -import numpy -x=numpy.linspace(-15,15) -print(x) +#+begin_src python :results output :exports both +print(2/(sum((x+np.sin(theta))>1)/N)) #+end_src #+RESULTS: -#+begin_example -[-15. -14.3877551 -13.7755102 -13.16326531 -12.55102041 - -11.93877551 -11.32653061 -10.71428571 -10.10204082 -9.48979592 - -8.87755102 -8.26530612 -7.65306122 -7.04081633 -6.42857143 - -5.81632653 -5.20408163 -4.59183673 -3.97959184 -3.36734694 - -2.75510204 -2.14285714 -1.53061224 -0.91836735 -0.30612245 - 0.30612245 0.91836735 1.53061224 2.14285714 2.75510204 - 3.36734694 3.97959184 4.59183673 5.20408163 5.81632653 - 6.42857143 7.04081633 7.65306122 8.26530612 8.87755102 - 9.48979592 10.10204082 10.71428571 11.32653061 11.93877551 - 12.55102041 13.16326531 13.7755102 14.3877551 15. ] -#+end_example - -Et enfin, voici un exemple de sortie graphique: -#+begin_src python :results output file :session :var matplot_lib_filename="./cosxsx.png" :exports results + +* Avec un argument "fréquentiel" 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 \sim U(0,1)/ et /Y \sim U(0,1)/ alors /P[X² + Y²\le1]=\pi/4/ (voir [[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_src python :results file :session :var matplot_lib_filename=(org-babel-temp-file "figure" ".png") :exports both import matplotlib.pyplot as plt -plt.figure(figsize=(10,5)) -plt.plot(x,numpy.cos(x)/x) -plt.tight_layout() +np.random.seed(seed=42) +N = 1000 +x = np.random.uniform(size=N, low=0, high=1) +y = np.random.uniform(size=N, low=0, high=1) + +accept = (x*x+y*y) <= 1 +reject = np.logical_not(accept) + +fig, ax = plt.subplots(1) +ax.scatter(x[accept], y[accept], c='b', alpha=0.2, edgecolor=None) +ax.scatter(x[reject], y[reject], c='r', alpha=0.2, edgecolor=None) +ax.set_aspect('equal') plt.savefig(matplot_lib_filename) -print(matplot_lib_filename) +matplot_lib_filename +#+end_src + +#+RESULTS: +[[file:/tmp/babel-8KkAW1/figureavCZKO.png]] + + +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_src python :results output :session :exports both +4*np.mean(accept) +print(4*np.mean(accept)) #+end_src #+RESULTS: -[[file:./cosxsx.png]] - -Vous remarquerez le paramètre ~:exports results~ qui indique que le code -ne doit pas apparaître dans la version finale du document. Nous vous -recommandons dans le cadre de ce MOOC de ne pas changer ce paramètre -(indiquer ~both~) car l'objectif est que vos analyses de données soient -parfaitement transparentes pour être reproductibles. - -Attention, la figure ainsi générée n'est pas stockée dans le document -org. C'est un fichier ordinaire, ici nommé ~cosxsx.png~. 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a/monfichier_orgmode.tex +++ /dev/null @@ -1,51 +0,0 @@ -% Created 2022-12-07 mer. 17:11 -% Intended LaTeX compiler: pdflatex -\documentclass[11pt]{article} -\usepackage[utf8]{inputenc} -\usepackage[T1]{fontenc} -\usepackage{graphicx} -\usepackage{grffile} -\usepackage{longtable} -\usepackage{wrapfig} -\usepackage{rotating} -\usepackage[normalem]{ulem} -\usepackage{amsmath} -\usepackage{textcomp} -\usepackage{amssymb} -\usepackage{capt-of} -\usepackage{hyperref} -\author{Hervé PABIOU} -\date{2022-12-07} -\title{Example Org File} -\hypersetup{ - pdfauthor={Hervé PABIOU}, - pdftitle={Example Org File}, - pdfkeywords={}, - pdfsubject={}, - pdfcreator={Emacs 27.1 (Org mode 9.3)}, - pdflang={English}} -\begin{document} - -\maketitle -\tableofcontents - - -\section{Mon fichier Org-Mode} -\label{sec:orgf997746} - -\subsection{Mise en forme de base} -\label{sec:org0c2ba0a} - -\begin{itemize} -\item \texttt{* title} -\item \texttt{** subtitle} -\item \texttt{/italique/} -\item \texttt{*gras*} -\item \texttt{\_underline\_} -\item \texttt{=code=} -\item \texttt{\textasciitilde{}verbatim\textasciitilde{}} -\item \texttt{+strike-through+} -\item \texttt{- list} -\item \texttt{1 enumerate} -\end{itemize} -\end{document} \ No newline at end of file -- 2.18.1