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zr4|YD5w9b(PMPI)6>50;bSD@NWu-^~>F~tF#A{YTEWBT5Jqvu7?HTu9N)bMN`VNSt z^su*;_m9cN(fg%0^X~*ZpFhDM-V?h#9&PbwG>CuNRO_KVI0=5x$1KRlxe9vd-gMW= zgh!W@kpujpnF+Z#Efj;27<0%e;%3j)NdG^-FM&vah4G{G*`Va9P?7+N(bvk$60$>>RemHvEqGRqh$nY<=Z;=X=-4#&a8?i}--GU>m&u z>sF=BcxDdKTT*eQlZluUVq)nP74ls#j(xq7QvdYRr%xZjxc3hXZ^0Z_)7L_P#eiSn!9kB+GmVDGT^^GOUNB8{sLu?HjWl4O z{NU9rkoA-R6Be4GpRRZHs #+HTML_HEAD: -* Quelques explications +* En demandant à la lib maths -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/. +Mon ordinateur m'indique que \pi vaut approximativement: -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. +#+begin_src python :results output :session :exports both +from math import * +pi +#+end_src -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 +* En utilisant la méthode des aiguilles de Buffon -#+RESULTS: -: Hello world! +Mais calculé avec la *méthode* des aiguilles de [[https://fr.wikipedia.org/wiki/Aiguille_de_Buffon][Buffon]], on obtiendrait comme *approximation* : -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) +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: -#+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 ∼ U(0,1) et Y ∼ U(0,1) alors P[X^2+Y^2 ≤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 output file :session :var matplot_lib_filename="./random_uniform_pi.png" :exports results 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) #+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 ~