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Simulations numériques de marches aléatoires : programmes en Python
Pour une bonne compréhension, ces programmes doivent être étudiés successivement. Il est important d'exécuter le code Python et même de tester des petites modifications.
Génération de nombres aléatoires
<sxh python; title : 01_Random.py> #!/usr/bin/env python #!/usr/bin/python
from random import * # cf. documentation cf http://docs.python.org/library/random.html # random number generation - génération de nombres aléatoires # functions of interest : choice, randint, seed
facepiece=['pile','face'] valeurpiece=[0.01,0.02,0.05,0.1,0.2,0.5,1.,2.]
#for i in range(1):
# choice : random choice of an element from a list #print choice(facepiece), choice(valeurpiece) # randint : return a random integer number between 2 values (including limits) #print randint(0,10) # imprime un nombre aléatoire entre 0 et 10 #print choice(range(0,11,1)) # same function, using choice and range to create the list
# seed(ANY_DATA) : seeding of the random number generator with any (constant) data # in order to generate reproducible random sequences. # seed() - without data - uses internal clock value to “randomly” initiate the generator !
for j in range(3):
#seed('ma chaîne personnielle') # reproducible initialization seed() # to randomly initiate the generator for i in range(10): print randint(1000,9999) print " "
</sxh>
Histogrammes de nombres aléatoires
<sxh python; title : 02_random_histogram.py> #!/usr/bin/env python # -*- coding: utf-8 -*-
from random import * # cf. documentation cf http://docs.python.org/library/random.html import numpy as np import matplotlib.pyplot as plt # http://matplotlib.sourceforge.net/api/pyplot_api.html#module-matplotlib.pyplot import matplotlib.mlab as mlab # http://matplotlib.sourceforge.net/api/mlab_api.html#module-matplotlib.mlab
#seed('ma chaîne personnelle') # reproducible initialization seed()
rval=[] for j in range(10000):
rval.append(randint(0,99)) # append to the list a random (integer) number between 0 and 99
# print rval # uncomment just to see the list of random numbers
# analysis - histogram - see http://matplotlib.sourceforge.net/examples/api/histogram_demo.html # http://fr.wikipedia.org/wiki/Histogramme xh=np.array(rval) # see http://www.scipy.org/Cookbook/BuildingArrays transforme une liste en un tableau numérique de Numpy # print xh
fig = plt.figure() ax = fig.add_subplot(111)
n, bins, patches = ax.hist(xh, 10, facecolor='green', alpha=0.75) print n # les nombres d'occurences par classe print bins # les classes, de largeur identique
# modifier le nombre de nombres générés, les nombres de classes-bins,
plt.show() </sxh>
Représenter le déplacement d'un objet
<sxh python; title : 03_tkinter_simple_move.py> #!/usr/bin/python # -*- coding: utf-8 -*-
from Tkinter import * import time
window = Tk() sizex=400 sizey=100 canvas = Canvas(window, width = sizex, height = sizey) canvas.pack() x = 100 # initial left-most edge of first ball y = 30 # initial top-most edge of first ball r=20 # ball diameter depx=2 # displacement at each move in x direction depy=0 # displacement at each move in y direction
ball=canvas.create_oval(x,y,x+r,y+r,fill=“blue”)
#moves no_moves=10 for j in range(no_moves):
canvas.move(ball, depx, depy) canvas.after(10) # time delay in milliseconds canvas.update()
time.sleep(5) # on attend quelques secondes window.destroy()
</sxh>
Représenter le déplacement de nombreux points
<sxh python; title : 04_tkinter_many_moves.py> #!/usr/bin/python # -*- coding: utf-8 -*-
from Tkinter import * import time
window = Tk() sizex=400 sizey=600 canvas = Canvas(window, width = sizex, height = sizey) canvas.pack() x = 100 # initial left-most edge of first ball y = 30 # initial top-most edge of first ball r=20 # ball diameter depx=2 # displacement at each move in x direction depy=0 # displacement at each move in y direction
# create balls: no_particles= 20 dy = (sizey-2.)/(no_particles+1) # y initial separation between balls print dy ball_list=[] for i in range(no_particles):
ball=canvas.create_oval(x,y,x+r,y+r,fill="blue") y = y+dy ball_list.append(ball)
#moves no_moves=100 for j in range(no_moves):
for ball in ball_list: canvas.move(ball, depx, depy) canvas.after(10) canvas.update()
time.sleep(5) # on attend quelques secondes window.destroy() </sxh>