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diff --git a/module2/exo1/toy_document_orgmode_python_fr.org b/module2/exo1/toy_document_orgmode_python_fr.org index 2a33f58..1a0a07c 100644 --- a/module2/exo1/toy_document_orgmode_python_fr.org +++ b/module2/exo1/toy_document_orgmode_python_fr.org @@ -1,8 +1,10 @@ -#+TITLE: Votre titre -#+AUTHOR: Mathilde -#+DATE: La date du jour +#+TITLE: À propos du calcul de \pi +#+AUTHOR: Konrad Hinsen +#+OPTIONS: toc:1 creator:t +#+DATE: 2019-03-28 Thu 11:06 #+LANGUAGE: fr -# #+PROPERTY: header-args :eval never-export + +#+PROPERTY: header-args :eval never-export #+HTML_HEAD: #+HTML_HEAD: @@ -11,83 +13,70 @@ #+HTML_HEAD: #+HTML_HEAD: -* Quelques explications - -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 -print("Hello world!") -#+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~). +* En demandant à la lib maths +Mon ordinateur m'indique que \pi vaut /approximativement/: #+begin_src python :results output :session :exports both -import numpy -x=numpy.linspace(-15,15) -print(x) +from math import * +print(pi) #+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 +: 3.141592653589793 + +* En utilisant la méthode des aiguilles de Buffon + + Mais calculé avec la *méthode* [[https://fr.wikipedia.org/wiki/Aiguille_de_Buffon][des aiguilles de Buffon]], on obtiendrait + comme *approximation* : + #+begin_src python :results output :session :exports both +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) +print(2/(sum((x+np.sin(theta))>1)/N)) + #+end_src + + #+RESULTS: + : 3.128911138923655 + +* 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 $P[X^2+Y^2 \leq 1]=\pi/4$ (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="exo1.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:exo1.png]] + + +Il est alors aisé d'obtenir une approximation (pas terrible) de \pi en +comptant combien de fois, en moyenne, $X^2+Y^2$ est inférieur à 1 : +#+begin_src python :results output :session :exports both +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~. N'oubliez pas -de le committer si vous voulez que votre analyse soit lisible et -compréhensible sur GitLab. - -Enfin, 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 python (en -faisant ~