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module2/exo1/toy_document_orgmode_python_fr.html
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<head> <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 http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" /> <meta name="viewport" content="width=device-width, initial-scale=1" />
<title>À propos du calcul de &pi;</title> <title>À propos du calcul de &pi;</title>
...@@ -273,15 +273,15 @@ for the JavaScript code in this tag. ...@@ -273,15 +273,15 @@ for the JavaScript code in this tag.
<h2>Table des matières</h2> <h2>Table des matières</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org3de6e6c">1. En demandant à la lib maths</a></li> <li><a href="#orge71b253">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="#org16efc18">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="#org1c65bd9">3. Avec un argument "fréquentiel" de surface</a></li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-org3de6e6c" class="outline-2"> <div id="outline-container-orge71b253" class="outline-2">
<h2 id="org3de6e6c"><span class="section-number-2">1</span> En demandant à la lib maths</h2> <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"> <div class="outline-text-2" id="text-1">
<p> <p>
Mon ordinateur m'indique que &pi; vaut <i>approximativement</i> : Mon ordinateur m'indique que &pi; vaut <i>approximativement</i> :
...@@ -299,8 +299,8 @@ pi ...@@ -299,8 +299,8 @@ pi
</div> </div>
</div> </div>
<div id="outline-container-org833fcbb" class="outline-2"> <div id="outline-container-org16efc18" class="outline-2">
<h2 id="org833fcbb"><span class="section-number-2">2</span> En utilisant la méthode des aiguilles de Buffon</h2> <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"> <div class="outline-text-2" id="text-2">
<p> <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 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) ...@@ -323,8 +323,8 @@ np.random.seed(seed=42)
</div> </div>
</div> </div>
<div id="outline-container-org9658f1f" class="outline-2"> <div id="outline-container-org1c65bd9" class="outline-2">
<h2 id="org9658f1f"><span class="section-number-2">3</span> Avec un argument "fréquentiel" de surface</h2> <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"> <div class="outline-text-2" id="text-3">
<p> <p>
Sinon, une méthode plus simple à comprendre et ne faisant pas intervenir d'appel 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 : ...@@ -374,7 +374,7 @@ combien de fois, en moyenne, \(X^2+Y^2\) est inférieur à 1 :
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="date">Date: 01/04/2020</p> <p class="date">Date: 01/04/2020</p>
<p class="author">Auteur: Clément</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> <p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>
</body> </body>
......
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<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
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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
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...@@ -11,7 +11,28 @@ ...@@ -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/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.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 Ceci est un document org-mode avec quelques exemples de code
python. Une fois ouvert dans emacs, ce document peut aisément être python. Une fois ouvert dans emacs, ce document peut aisément être
......
module2/exo3/exercice_python_fr.org
View file @ 0f90d80d
...@@ -11,7 +11,47 @@ ...@@ -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/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.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 Ceci est un document org-mode avec quelques exemples de code
python. Une fois ouvert dans emacs, ce document peut aisément être python. Une fois ouvert dans emacs, ce document peut aisément être
......
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