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de π @@ -273,15 +273,15 @@ for the JavaScript code in this tag.

Table des matières

-
-

1 En demandant à la lib maths

+
+

1 En demandant à la lib maths

Mon ordinateur m'indique que π vaut approximativement : @@ -299,8 +299,8 @@ pi

-
-

2 En utilisant la méthode des aiguilles de Buffon

+
+

2 En utilisant la méthode des aiguilles de Buffon

Mais calculé avec la méthode des aiguilles de Buffon, on obtiendrait comme @@ -323,8 +323,8 @@ np.random.seed(seed=42)

-
-

3 Avec un argument "fréquentiel" de surface

+
+

3 Avec un argument "fréquentiel" de surface

Sinon, une méthode plus simple à comprendre et ne faisant pas intervenir d'appel @@ -374,7 +374,7 @@ combien de fois, en moyenne, \(X^2+Y^2\) est inférieur à 1 :

Date: 01/04/2020

Auteur: Clément

-

Created: 2020-04-01 Wed 10:17

+

Created: 2020-04-01 Wed 10:20

Validate

diff --git a/module2/exo1/toy_document_orgmode_python_fr.html~ b/module2/exo1/toy_document_orgmode_python_fr.html~ new file mode 100644 index 0000000..b5c7930 --- /dev/null +++ b/module2/exo1/toy_document_orgmode_python_fr.html~ @@ -0,0 +1,381 @@ + + + + + + + +À propos du calcul de π + + + + + + + + + + + + +
+

À propos du calcul de π

+ + +
+

1 En demandant à la lib maths

+
+

+Mon ordinateur m'indique que π vaut approximativement : +

+ +
+
from math import *
+pi
+
+
+ +
+3.141592653589793
+
+
+
+ +
+

2 En utilisant la méthode des aiguilles de Buffon

+
+

+Mais calculé avec la méthode des aiguilles de Buffon, on obtiendrait comme +approximation : +

+ +
+
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)
+
+
+ +
+3.128911138923655
+
+
+
+ +
+

3 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 \(P[X^2+Y^2 \leq1] = \pi/4\) (voir +méthode +yde Monte Carlo sur Wikipedia). Le code suivant illustre ce fait : +

+ +
+
import matplotlib.pyplot as plt
+
+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)
+matplot_lib_filename
+
+
+ +

+fige.png +Il est alors aisé d'obtenir une approximation (pas terrible) de π en comptant +combien de fois, en moyenne, \(X^2+Y^2\) est inférieur à 1 : +

+
+
4*np.mean(accept)
+
+
+ +
+3.112
+
+
+
+
+
+

Date: 01/04/2020

+

Auteur: Clément

+

Created: 2020-04-01 Wed 10:17

+

Validate

+
+ + diff --git a/module2/exo2/data.txt b/module2/exo2/data.txt new file mode 100644 index 0000000..e965fb5 --- /dev/null +++ b/module2/exo2/data.txt @@ -0,0 +1 @@ +14.0, 7.6, 11.2, 12.8, 12.5, 9.9, 14.9, 9.4, 16.9, 10.2, 14.9, 18.1, 7.3, 9.8, 10.9,12.2, 9.9, 2.9, 2.8, 15.4, 15.7, 9.7, 13.1, 13.2, 12.3, 11.7, 16.0, 12.4, 17.9, 12.2, 16.2, 18.7, 8.9, 11.9, 12.1, 14.6, 12.1, 4.7, 3.9, 16.9, 16.8, 11.3, 14.4, 15.7, 14.0, 13.6, 18.0, 13.6, 19.9, 13.7, 17.0, 20.5, 9.9, 12.5, 13.2, 16.1, 13.5, 6.3, 6.4, 17.6, 19.1, 12.8, 15.5, 16.3, 15.2, 14.6, 19.1, 14.4, 21.4, 15.1, 19.6, 21.7, 11.3, 15.0, 14.3, 16.8, 14.0, 6.8, 8.2, 19.9, 20.4, 14.6, 16.4, 18.7, 16.8, 15.8, 20.4, 15.8, 22.4, 16.2, 20.3, 23.4, 12.1, 15.5, 15.4, 18.4, 15.7, 10.2, 8.9, 21.0 diff --git a/module2/exo2/exercice_python_fr.org b/module2/exo2/exercice_python_fr.org index c7157ba..cb38c47 100644 --- a/module2/exo2/exercice_python_fr.org +++ b/module2/exo2/exercice_python_fr.org @@ -11,7 +11,28 @@ #+HTML_HEAD: #+HTML_HEAD: -* Quelques explications + + +#+begin_src python :results output :session :exports both +import numpy as np + +data = [14.0, 7.6, 11.2, 12.8, 12.5, 9.9, 14.9, 9.4, 16.9, 10.2, 14.9, 18.1, 7.3, 9.8, 10.9,12.2, 9.9, 2.9, 2.8, 15.4, 15.7, 9.7, 13.1, 13.2, 12.3, 11.7, 16.0, 12.4, 17.9, 12.2, 16.2, 18.7, 8.9, 11.9, 12.1, 14.6, 12.1, 4.7, 3.9, 16.9, 16.8, 11.3, 14.4, 15.7, 14.0, 13.6, 18.0, 13.6, 19.9, 13.7, 17.0, 20.5, 9.9, 12.5, 13.2, 16.1, 13.5, 6.3, 6.4, 17.6, 19.1, 12.8, 15.5, 16.3, 15.2, 14.6, 19.1, 14.4, 21.4, 15.1, 19.6, 21.7, 11.3, 15.0, 14.3, 16.8, 14.0, 6.8, 8.2, 19.9, 20.4, 14.6, 16.4, 18.7, 16.8, 15.8, 20.4, 15.8, 22.4, 16.2, 20.3, 23.4, 12.1, 15.5, 15.4, 18.4, 15.7, 10.2, 8.9, 21.0] + +print("Average: "+str(np.average(data))) +print("Std: "+str(np.std(data, ddof=1))) +print("Min: "+str(np.min(data))) +print("Max: "+str(np.max(data))) +print("Median: "+str(np.median(data))) +#+end_src + +#+RESULTS: +: Average: 14.113000000000001 +: Std: 4.334094455301447 +: Min: 2.8 +: Max: 23.4 +: Median: 14.5 + +* Quelques explications :noexport: Ceci est un document org-mode avec quelques exemples de code python. Une fois ouvert dans emacs, ce document peut aisément être diff --git a/module2/exo3/exercice_python_fr.org b/module2/exo3/exercice_python_fr.org index c7157ba..6c40189 100644 --- a/module2/exo3/exercice_python_fr.org +++ b/module2/exo3/exercice_python_fr.org @@ -11,7 +11,47 @@ #+HTML_HEAD: #+HTML_HEAD: -* Quelques explications +#+begin_src python :results file :session :var matplot_lib_filename=(org-babel-temp-file "figure1" ".png") :exports both +import matplotlib.pyplot as plt + +import numpy + +data = [14.0, 7.6, 11.2, 12.8, 12.5, 9.9, 14.9, 9.4, 16.9, 10.2, 14.9, 18.1, 7.3, 9.8, 10.9,12.2, 9.9, 2.9, 2.8, 15.4, 15.7, 9.7, 13.1, 13.2, 12.3, 11.7, 16.0, 12.4, 17.9, 12.2, 16.2, 18.7, 8.9, 11.9, 12.1, 14.6, 12.1, 4.7, 3.9, 16.9, 16.8, 11.3, 14.4, 15.7, 14.0, 13.6, 18.0, 13.6, 19.9, 13.7, 17.0, 20.5, 9.9, 12.5, 13.2, 16.1, 13.5, 6.3, 6.4, 17.6, 19.1, 12.8, 15.5, 16.3, 15.2, 14.6, 19.1, 14.4, 21.4, 15.1, 19.6, 21.7, 11.3, 15.0, 14.3, 16.8, 14.0, 6.8, 8.2, 19.9, 20.4, 14.6, 16.4, 18.7, 16.8, 15.8, 20.4, 15.8, 22.4, 16.2, 20.3, 23.4, 12.1, 15.5, 15.4, 18.4, 15.7, 10.2, 8.9, 21.0] + +x=numpy.linspace(-15,15) +plt.figure(figsize=(10,5)) +plt.plot(data) +plt.tight_layout() + +plt.savefig(matplot_lib_filename) +matplot_lib_filename + +#+end_src + +#+RESULTS: +[[file:/tmp/babel-AQqtCi/figureR2yZWS.png]] + +#+begin_src python :results file :session :var matplot_lib_filename=(org-babel-temp-file "figurehist" ".png") :exports both +import matplotlib.pyplot as plt + +import numpy + +x=numpy.linspace(-15,15) +plt.figure(figsize=(10,5)) +plt.hist(data, facecolor='blue',alpha=0.5, edgecolor='black') +plt.grid(b='True', linestyle='--') +plt.tight_layout() + +plt.savefig(matplot_lib_filename) +matplot_lib_filename + +#+end_src + +#+RESULTS: +[[file:/tmp/babel-AQqtCi/figurehist6XxvCK.png]] + + +* Quelques explications :noexport: Ceci est un document org-mode avec quelques exemples de code python. Une fois ouvert dans emacs, ce document peut aisément être -- 2.18.1