Différences

Ci-dessous, les différences entre deux révisions de la page.

--- teaching:exos:simulations_random_walks_codes [2013/11/13 16:35] – créée villersd
+++ teaching:exos:simulations_random_walks_codes [2018/11/05 12:09] (Version actuelle) – [Avec analyse de la distribution :] villersd
@@ Ligne 1: / Ligne 1: @@
 ====== Simulations numériques de marches aléatoires : programmes en Python ======
-<sxh python; title : 01_Random.py>
+<note tip>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.
-#!/usr/bin/env python
+</note>
+===== Génération de nombres aléatoires =====
+<code python 01_random.py>
 #!/usr/bin/python
+# -*- coding: utf-8 -*-
+"""
+cf. documentation cf http://docs.python.org/library/random.html
+random number generation - génération de nombres aléatoires
+functions of interest : choice, randint, seed
+"""
 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']
+facepiece = ['pile','face']
-valeurpiece=[0.01,0.02,0.05,0.1,0.2,0.5,1.,2.]
+valeurpiece = [0.01,0.02,0.05,0.1,0.2,0.5,1.,2.]
-#for i in range(1):
+for i in range(1):
     # choice : random choice of an element from a list
-    #print choice(facepiece), choice(valeurpiece)
+    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(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
+    print(choice(range(0,11,1)))  # same function, using choice and range to create the list
@@ Ligne 29: / Ligne 35: @@
     seed()   # to randomly initiate the generator
     for i in range(10):
-        print randint(1000,9999)
+        print(randint(1000,9999))
-    print " "
+    print(" ")
-</sxh>
+</code>
+===== Histogrammes de nombres aléatoires  =====
+<code python 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(100000):
+    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, 50, 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()
+</code>
+===== Représenter le déplacement d'un objet  =====
+<code python 03_tkinter_simple_move.py>
+#!/usr/bin/python
+# -*- coding: utf-8 -*-
+from tkinter import *
+import time
+window = Tk()
+sizex = 400
+sizey = 200
+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 = 1            # displacement at each move in y direction
+ball=canvas.create_oval(x,y,x+r,y+r,fill="blue")
+#moves
+no_moves = 140
+for j in range(no_moves):
+    canvas.move(ball, depx, depy)
+    canvas.after(20)         # time delay in milliseconds
+    canvas.update()
+time.sleep(5) # on attend quelques secondes
+window.destroy()
+</code>
+===== Représenter le déplacement de nombreux points =====
+<code python 04_tkinter_many_moves.py>
+#!/usr/bin/python
+# -*- coding: utf-8 -*-
+from tkinter import *
+import time
+from random import *
+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 = 16                  # 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.*y)/(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, choice([-2, 2]) )
+#        canvas.move(ball, depx, depy)
+    canvas.after(10)
+    canvas.update()
+time.sleep(5) # on attend quelques secondes
+window.destroy()
+</code>
+===== Marche aléatoire d'un petit nombre de pas =====
+<code python 05_tkinter_random_walk_few_steps_1D.py>
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+from tkinter import *
+from random import choice     # 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
+window = Tk()
+sizex = 200
+sizey = 600
+canvas = Canvas(window, width = sizex, height = sizey)
+canvas.pack()
+x = 100		# initial left-most edge of first ball
+y = 1		# initial top-most edge of first ball
+r = 4                  # ball diameter
+depx = 10            # displacement at each move in x direction
+depy = 0
+# create balls:
+no_particles = 6400
+dy = (sizey-2.*y)/(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="red")
+    y = y+dy
+    ball_list.append(ball)
+#moves
+no_moves = 6  # number of moves
+for j in range(no_moves):
+    for ball in ball_list:
+        canvas.move(ball, choice([-1,1])*depx, depy)
+    canvas.after(1)
+    canvas.update()
+#analysis - histogram
+# see http://matplotlib.sourceforge.net/examples/api/histogram_demo.html
+xpos=[]
+for ball in ball_list:
+    posi = canvas.coords(ball)
+    xpos.append(((no_moves+1.)/no_moves)*(posi[0]-x)/depx)
+    # le facteur (no_moves+1.)/no_moves) permet de gérer la largeur des barres de l'histogramme
+xh = np.array(xpos)  # see http://www.scipy.org/Cookbook/BuildingArrays
+#print(xh)
+fig = plt.figure()
+ax = fig.add_subplot(111)
+n, bins, patches = ax.hist(xh, (no_moves)+1, facecolor='green', alpha=0.75)
+print(n,bins, patches)
+plt.show()
+#window.mainloop()
+</code>
+===== Marche aléatoire d'un grand nombre de pas =====
+<code python 06_tkinter_random_walk_many_steps_1D.py>
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+from tkinter import *
+from random import choice     # 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
+window = Tk()
+sizex = 400
+sizey = 400
+canvas = Canvas(window, width = sizex, height = sizey)
+canvas.pack()
+x = 200		# initial left-most edge of first ball
+y = 1		# initial top-most edge of first ball
+r = 4                  # ball diameter
+depx = 1            # displacement at each move in x direction
+depy = 0
+# create balls:
+no_particles = 1600
+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 = 200
+for j in range(no_moves):
+    for ball in ball_list:
+        canvas.move(ball, choice([-1,1])*depx, depy)
+    canvas.after(1)
+    canvas.update()
+#analysis - histogram
+# see http://matplotlib.sourceforge.net/examples/api/histogram_demo.html
+xpos = []
+for ball in ball_list:
+    posi = canvas.coords(ball)
+    xpos.append((posi[0]-x)/depx)
+xh = np.array(xpos)  # see http://www.scipy.org/Cookbook/BuildingArrays
+#  compute the mean mu and sigma  from xh (and/or theoretical value from random walk result)
+mu = np.mean(xh)
+sigma = np.std(xh)
+fig = plt.figure()
+ax = fig.add_subplot(111)
+# print xh
+n, bins, patches = ax.hist(xh, 10, facecolor='green', alpha=0.75)
+print(n,bins, patches)
+# hist uses np.histogram to create 'n' and 'bins'. cf. http://docs.scipy.org/doc/numpy/reference/generated/numpy.histogram.html
+ax.set_xlabel('X positions')
+ax.set_ylabel('Occurences')
+ax.grid(True)
+plt.show()
+#window.mainloop()
+</code>
+==== Avec analyse de la distribution : ====
+<code python 07_tkinter_random_walk_many_steps_1D-analysis.py>
+# -*- coding: utf-8 -*-
+from tkinter import *
+from random import choice     # 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
+window = Tk()
+sizex = 400
+sizey = 400
+canvas = Canvas(window, width = sizex, height = sizey)
+canvas.pack()
+x = 200		# initial left-most edge of first ball
+y = 1		# initial top-most edge of first ball
+r = 4                  # ball diameter
+depx = 1            # displacement at each move in x direction
+depy = 0
+# create balls:
+no_particles = 1000
+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 = 400
+for j in range(no_moves):
+    for ball in ball_list:
+        canvas.move(ball, choice([-1,-1,-1,-1,1,1,1,1,1,1])*depx, depy) #drift
+    canvas.after(1)
+    canvas.update()
+#analysis - histogram
+# see http://matplotlib.sourceforge.net/examples/api/histogram_demo.html
+xpos = []
+for ball in ball_list:
+    posi = canvas.coords(ball)
+    xpos.append(posi[0]-x)
+xh = np.array(xpos)  # see http://www.scipy.org/Cookbook/BuildingArrays
+#  compute the mean mu and sigma  from xh (and/or theoretical value from random walk result)
+mu = np.mean(xh)
+sigma = np.std(xh)
+fig = plt.figure()
+ax = fig.add_subplot(111)
+# print xh
+n, bins, patches = ax.hist(xh, 20, facecolor='green', alpha=0.75)
+print(mu, sigma)
+print(n,bins, patches)
+# hist uses np.histogram to create 'n' and 'bins'.
+# np.histogram returns the bin edges, so there will be ii probability
+# density values in n, ii+1 bin edges in bins and ii patches.  To get
+# everything lined up, we'll compute the bin centers
+bincenters = 0.5*(bins[1:]+bins[:-1])
+# add a 'best fit' line for the normal PDF
+yh = (bins[1]-bins[0])*no_particles*mlab.normpdf( bincenters, mu, sigma)  # http://matplotlib.sourceforge.net/api/mlab_api.html#matplotlib.mlab.normpdf
+l = ax.plot(bincenters, yh, 'r--', linewidth=1)
+#print n
+ax.set_xlabel('X positions')
+ax.set_ylabel('Occurences')
+ax.grid(True)
+plt.show()
+#window.mainloop()
+</code>