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Commit 0f90d80d authored by Clément Courageux's avatar Clément Courageux
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module2/exo1/toy_document_orgmode_python_fr.html
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......@@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="fr" xml:lang="fr">
<head>
<!-- 2020-04-01 Wed 10:17 -->
<!-- 2020-04-01 Wed 10:20 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>À propos du calcul de &pi;</title>
......@@ -273,15 +273,15 @@ for the JavaScript code in this tag.
<h2>Table des matières</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org3de6e6c">1. En demandant à la lib maths</a></li>
<li><a href="#org833fcbb">2. En utilisant la méthode des aiguilles de Buffon</a></li>
<li><a href="#org9658f1f">3. Avec un argument "fréquentiel" de surface</a></li>
<li><a href="#orge71b253">1. En demandant à la lib maths</a></li>
<li><a href="#org16efc18">2. En utilisant la méthode des aiguilles de Buffon</a></li>
<li><a href="#org1c65bd9">3. Avec un argument "fréquentiel" de surface</a></li>
</ul>
</div>
</div>
<div id="outline-container-org3de6e6c" class="outline-2">
<h2 id="org3de6e6c"><span class="section-number-2">1</span> En demandant à la lib maths</h2>
<div id="outline-container-orge71b253" class="outline-2">
<h2 id="orge71b253"><span class="section-number-2">1</span> En demandant à la lib maths</h2>
<div class="outline-text-2" id="text-1">
<p>
Mon ordinateur m'indique que &pi; vaut <i>approximativement</i> :
......@@ -299,8 +299,8 @@ pi
</div>
</div>
<div id="outline-container-org833fcbb" class="outline-2">
<h2 id="org833fcbb"><span class="section-number-2">2</span> En utilisant la méthode des aiguilles de Buffon</h2>
<div id="outline-container-org16efc18" class="outline-2">
<h2 id="org16efc18"><span class="section-number-2">2</span> En utilisant la méthode des aiguilles de Buffon</h2>
<div class="outline-text-2" id="text-2">
<p>
Mais calculé avec la <b>méthode</b> des <a href="https://fr.wikipedia.org/wiki/Aiguille_de_Buffon">aiguilles de Buffon</a>, on obtiendrait comme
......@@ -323,8 +323,8 @@ np.random.seed(seed=42)
</div>
</div>
<div id="outline-container-org9658f1f" class="outline-2">
<h2 id="org9658f1f"><span class="section-number-2">3</span> Avec un argument "fréquentiel" de surface</h2>
<div id="outline-container-org1c65bd9" class="outline-2">
<h2 id="org1c65bd9"><span class="section-number-2">3</span> Avec un argument "fréquentiel" de surface</h2>
<div class="outline-text-2" id="text-3">
<p>
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 :
<div id="postamble" class="status">
<p class="date">Date: 01/04/2020</p>
<p class="author">Auteur: Clément</p>
<p class="date">Created: 2020-04-01 Wed 10:17</p>
<p class="date">Created: 2020-04-01 Wed 10:20</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>
......
module2/exo1/toy_document_orgmode_python_fr.html~ 0 → 100644
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<!-- 2020-04-01 Wed 10:17 -->
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<body>
<div id="content">
<h1 class="title">À propos du calcul de &pi;</h1>
<div id="table-of-contents">
<h2>Table des matières</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org3de6e6c">1. En demandant à la lib maths</a></li>
<li><a href="#org833fcbb">2. En utilisant la méthode des aiguilles de Buffon</a></li>
<li><a href="#org9658f1f">3. Avec un argument "fréquentiel" de surface</a></li>
</ul>
</div>
</div>
<div id="outline-container-org3de6e6c" class="outline-2">
<h2 id="org3de6e6c"><span class="section-number-2">1</span> En demandant à la lib maths</h2>
<div class="outline-text-2" id="text-1">
<p>
Mon ordinateur m'indique que &pi; vaut <i>approximativement</i> :
</p>
<div class="org-src-container">
<pre class="src src-python"><span style="color: #0000FF;">from</span> math <span style="color: #0000FF;">import</span> *
pi
</pre>
</div>
<pre class="example">
3.141592653589793
</pre>
</div>
</div>
<div id="outline-container-org833fcbb" class="outline-2">
<h2 id="org833fcbb"><span class="section-number-2">2</span> En utilisant la méthode des aiguilles de Buffon</h2>
<div class="outline-text-2" id="text-2">
<p>
Mais calculé avec la <b>méthode</b> des <a href="https://fr.wikipedia.org/wiki/Aiguille_de_Buffon">aiguilles de Buffon</a>, on obtiendrait comme
<b>approximation</b> :
</p>
<div class="org-src-container">
<pre class="src src-python"><span style="color: #0000FF;">import</span> numpy <span style="color: #0000FF;">as</span> np
np.random.seed(seed=42)
<span style="color: #BA36A5;">N</span> = 10000
<span style="color: #BA36A5;">x</span> = np.random.uniform(size=N, low=0, high=1)
<span style="color: #BA36A5;">theta</span> = np.random.uniform(size=N, low=0, high=pi/2)
2/(<span style="color: #006FE0;">sum</span>((x+np.sin(theta))&gt;1)/N)
</pre>
</div>
<pre class="example">
3.128911138923655
</pre>
</div>
</div>
<div id="outline-container-org9658f1f" class="outline-2">
<h2 id="org9658f1f"><span class="section-number-2">3</span> Avec un argument "fréquentiel" de surface</h2>
<div class="outline-text-2" id="text-3">
<p>
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
<a href="https://fr.wikipedia.org/wiki/M%C3%A9thode_de_Monte-Carlo#D%C3%A9termination_de_la_valeur_de_%CF%80">méthode
yde Monte Carlo</a> sur Wikipedia). Le code suivant illustre ce fait :
</p>
<div class="org-src-container">
<pre class="src src-python"><span style="color: #0000FF;">import</span> matplotlib.pyplot <span style="color: #0000FF;">as</span> plt
np.random.seed(seed=42)
<span style="color: #BA36A5;">N</span> = 1000
<span style="color: #BA36A5;">x</span> = np.random.uniform(size=N, low=0, high=1)
<span style="color: #BA36A5;">y</span> = np.random.uniform(size=N, low=0, high=1)
<span style="color: #BA36A5;">accept</span> = (x*x+y*y) &lt;= 1
<span style="color: #BA36A5;">reject</span> = np.logical_not(accept)
<span style="color: #BA36A5;">fig</span>, <span style="color: #BA36A5;">ax</span> = plt.subplots(1)
ax.scatter(x[accept], y[accept], c=<span style="color: #008000;">'b'</span>, alpha=0.2, edgecolor=<span style="color: #D0372D;">None</span>)
ax.scatter(x[reject], y[reject], c=<span style="color: #008000;">'r'</span>, alpha=0.2, edgecolor=<span style="color: #D0372D;">None</span>)
ax.set_aspect(<span style="color: #008000;">'equal'</span>)
plt.savefig(matplot_lib_filename)
matplot_lib_filename
</pre>
</div>
<p>
<img src="fige.png" alt="fige.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 :
</p>
<div class="org-src-container">
<pre class="src src-python">4*np.mean(accept)
</pre>
</div>
<pre class="example">
3.112
</pre>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="date">Date: 01/04/2020</p>
<p class="author">Auteur: Clément</p>
<p class="date">Created: 2020-04-01 Wed 10:17</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>
</html>
module2/exo2/data.txt 0 → 100644
View file @ 0f90d80d
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
module2/exo2/exercice_python_fr.org
View file @ 0f90d80d
......@@ -11,7 +11,28 @@
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
* 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
......
module2/exo3/exercice_python_fr.org
View file @ 0f90d80d
......@@ -11,7 +11,47 @@
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
* 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
......
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