From 74b1d1b23d35929c388d7b21ccd8e2dbcbae3e29 Mon Sep 17 00:00:00 2001 From: "antoine.perederii" Date: Wed, 4 Oct 2023 08:06:26 +0200 Subject: [PATCH] add maths and reseaux --- 2A/Maths/tp/{ => 1_tp}/TP1.pdf | Bin 2A/Maths/tp/{ => 1_tp}/tp1.py | 0 2A/Maths/tp/2_tp/TP2.pdf | Bin 0 -> 259767 bytes 2A/Maths/tp/2_tp/tp2.py | 186 +++++++++++++++++++++++++++++++++ 2A/Reseaux/server.sh | 5 +- 5 files changed, 189 insertions(+), 2 deletions(-) rename 2A/Maths/tp/{ => 1_tp}/TP1.pdf (100%) rename 2A/Maths/tp/{ => 1_tp}/tp1.py (100%) create mode 100644 2A/Maths/tp/2_tp/TP2.pdf create mode 100644 2A/Maths/tp/2_tp/tp2.py diff --git a/2A/Maths/tp/TP1.pdf b/2A/Maths/tp/1_tp/TP1.pdf similarity index 100% rename from 2A/Maths/tp/TP1.pdf rename to 2A/Maths/tp/1_tp/TP1.pdf diff --git a/2A/Maths/tp/tp1.py b/2A/Maths/tp/1_tp/tp1.py similarity index 100% rename from 2A/Maths/tp/tp1.py rename to 2A/Maths/tp/1_tp/tp1.py diff --git a/2A/Maths/tp/2_tp/TP2.pdf b/2A/Maths/tp/2_tp/TP2.pdf new file mode 100644 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100644 index 0000000..2da9f25 --- /dev/null +++ b/2A/Maths/tp/2_tp/tp2.py @@ -0,0 +1,186 @@ +import numpy as np +import matplotlib.pyplot as plt +from scipy.special import factorial,binom + + +rng = np.random.default_rng() + + +print(factorial(5)) +print(binom(7,3)) + + +# k = np.array(range(10)) +# plt.figure("La fonction x^2 sur les entiers de 1 à10") +# plt.plot(k, k**2, 'r') +# plt.show() + + + +# Exercice 1 (Simulation d’une planche). + +#? 1. On considère une bille dans la planche, à un certain étage n donné. Notons k la po- +#? sition actuelle de la bille (k = 0 si elle est complètement à gauche, k = n si elle est +#? complètement à droite). Quelles positions la bille peut-elle atteindre à l’étage suivant ? + +#* la position suivante de la bille sera k - 1 ou k + 1 + +#? 2. On définit la variable aléatoire Y telle que +#? position suivante = position actuelle + Y +#? Quelle loi de probabilité suit la variable Y ? Trouvez comment générer en Python des +#? échantillons de cette loi de probabilité. + +#* loi de bernoulli, n fois + +# Paramètre de la loi de Bernoulli (probabilité de succès) +p = 0.3 + +# Générer un échantillon de la loi de Bernoulli +def bernoulli(p): + if np.random.randint(0,2) <= p : + y = 0 + else : + y = 1 + return y + + + +print(bernoulli(0.5)) + + +#? 3. Déduisez-en un moyen simple de simuler la planche de Galton. Écrivez une fonction +#? qui simule le passage d’une bille à travers une planche de Galton, et renvoie la position +#? d’arrivée de la bille. Cette fonction prend en entrée deux paramètres définissant la nature +#? de la planche (sa hauteur N et son paramètre gauche/droite p), et doit renvoyer un +#? nombre entier aléatoire entre 0 et N (position d’arrivée de la bille). + +def simul_planche(N, p): + position = 0 # La position initiale est 0 (au sommet de la planche) + + for _ in range(N): + position += bernoulli(p) + + # Assurez-vous que la position reste dans les limites de la planche + position = max(0, min(N, position)) + + return position + +# Exemple d'utilisation de la fonction +N = 10 # Hauteur de la planche +p = 0.5 # Probabilité de rebondir à gauche ==> quand équilibré +position_finale = simul_planche(N, p) +print("Position d'arrivée de la bille :", position_finale) + + +#? 4. Simulez un grand nombre de billes (par exemple 10000) passant à travers une planche de +#? Galton de paramètres N = 12 et p = 0.5. Stockez les 10000 positions d’arrivée obtenues. + +# Nombre de billes à simuler +nombre_de_billes = 10000 + +# Liste pour stocker les positions d'arrivée +positions_arrivee = [] + +# Simulation des billes +for _ in range(nombre_de_billes): + positions_arrivee.append(simul_planche(N, p)) #.append, ajoute dans la liste + + +#? Maintenant, positions_arrivee contient les positions d'arrivée de 10 000 billes +#? Vous pouvez les utiliser pour effectuer des analyses ou des calculs statistiques + +positions_arrivee = np.array(positions_arrivee) +moyenne = np.mean(positions_arrivee) +variance = np.var(positions_arrivee) + +print("Moyenne :", moyenne) +print("Variance :", variance) + + +#? 5. Tracez l’histogramme des 10000 positions d’arrivée précédentes. Vous pouvez utiliser la +#? fonction hist de la librairie matplotlib, ou encore la fonction histplot de la +#? librairie seaborn. +#? Question en passant : avec une planche de Galton réelle, et de vraies billes, comment +#? pourrait-on obtenir concrètement cet histogramme ? + +# Tracer l'histogramme +plt.hist(positions_arrivee, bins=range(N+2), align='left', alpha=0.75, rwidth=0.8) +plt.xticks(range(N+1)) +plt.xlabel('Position d\'arrivée') +plt.ylabel('Fréquence') +plt.title(f'Histogramme des positions d\'arrivée pour {nombre_de_billes} billes') +plt.grid(axis='y', alpha=0.75) +plt.show() + + +#? 6. Reproduisez l’expérience avec différentes autres valeurs possibles pour le paramètre p. +#? Quelles sont les conséquences au niveau de l’histogramme ? + +N = 10 # Hauteur de la planche +p = 0.75 # Probabilité de rebondir à gauche ==> quand équilibré +position_finale = simul_planche(N, p) +print("Position d'arrivée de la bille :", position_finale) + +positions_arrivee = [] + +# Simulation des billes +for _ in range(nombre_de_billes): + positions_arrivee.append(simul_planche(N, p)) #.append, ajoute dans la liste + +positions_arrivee = np.array(positions_arrivee) +moyenne = np.mean(positions_arrivee) +variance = np.var(positions_arrivee) + +print("Moyenne :", moyenne) +print("Variance :", variance) + + +# Tracer l'histogramme +plt.hist(positions_arrivee, bins=range(N+2), align='left', alpha=0.75, rwidth=0.8) +plt.xticks(range(N+1)) +plt.xlabel('Position d\'arrivée') +plt.ylabel('Fréquence') +plt.title(f'Histogramme des positions d\'arrivée pour {nombre_de_billes} billes') +plt.grid(axis='y', alpha=0.75) +plt.show() + +# Exercice 2 +from numpy.ma.core import choose +# Exercice 2 +# 1) étant doné que l'expérience est répété plusieur fois c'est une lois binomiale +# 2) P(X =k) = (n|k).p^k.(1-p)^n-k + +galton3=nr.binomial(12, 0.3, 1000) +plt.hist(galton2,bins=12,range=(0,12),density=True) +plt.show() +def loi(N, p): + galton3LOI = [] + for i in range(N+1): + #galton3LOI.append(binom.pmf(i, N, p)) + + galton3LOI.append((binom(N,i))*(p**i)*(1-p)**(N-i)) + + plt.plot(range(N+1), galton3LOI, 'r') + plt.show() + +loi(12,0.5) + + +from scipy.stats import norm + +# Paramètres +N = 1000 +p = 0.5 + +positions = np.random.binomial(N, p, size=10000) + +# Afficher l'histogramme +plt.hist(positions, bins=range(N+2), density=True, alpha=0.6, color='b', label='Histogramme de Galton') + +# Superposer la distribution normale +mu = N * p +sigma = np.sqrt(N * p * (1 - p)) +x = np.arange(0, N+1) +y = norm.pdf(x, mu, sigma) +plt.plot(x, y, 'r', label='Distribution normale') +plt.show() diff --git a/2A/Reseaux/server.sh b/2A/Reseaux/server.sh index b1fabe0..9ab97f9 100755 --- a/2A/Reseaux/server.sh +++ b/2A/Reseaux/server.sh @@ -24,7 +24,7 @@ case $@ in echo -e -n "Connection: close\r\n" echo -e -n "Content-Type: text/plain\r\n" echo -e -n "\r\n" - echo -e -n "403 : Forbiden\n";echo -n "Erreur 403" >&2;exit $? + echo -e -n "403 : Forbiden 2\n";echo -n "Erreur 403" >&2;exit $? fi if [ ! -f $fich ]; then @@ -35,7 +35,8 @@ case $@ in echo -e -n "Content-Type: $mine\r\n" echo -e -n "Connection: close\r\n" echo -e -n "\r\n" - echo -n "404 : Not Found";echo "Erreur 404" >&2 + echo -n "404 : Not Found 2" #ne sert a rien car ne s'affiche pas ! + echo "Erreur 404" >&2 fi mime=$(file -L --brief --mime-type $fich)