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  1. # -*- coding: utf-8 -*-
  2. """
  3. Éditeur de Spyder
  4.  
  5. Ceci est un script temporaire.
  6. """
  7.  
  8. from numpy import *
  9. from matplotlib.pyplot import *
  10. from random import random
  11.  
  12. from mpl_toolkits.mplot3d import Axes3D
  13.  
  14. #1
  15. def trace_graphe(f,a,b,pas):
  16.     plot([a+k*pas for k in range(int((b-a)/pas))],[f(a+k*pas) for k in range(int((b-a)/pas))],"+")
  17.     show()
  18.     return
  19.    
  20. #2
  21. def petit_nuage():
  22.     for i in range(50):
  23.         plot([random()*10],[random()*10],"+")
  24.     show()
  25.     return
  26.    
  27. #3
  28. def euler(F,a,b,y0,n):
  29.     listeTemps = [a]
  30.     listeY = [y0]
  31.     h = (b-a)/(n-1)
  32.     for i in range(1,n):
  33.         listeY.append(listeY[-1]+F(listeTemps[-1], listeY[-1] * h))
  34.         listeTemps.append(listeTemps[-1]+h)
  35.     return listeTemps,listeY
  36.  
  37. #4
  38. m = asarray
  39.  
  40. def euler_vectorielle(F,a,b,y0,n):
  41.     listeTemps = [a]
  42.     listeY = [y0]
  43.     h = (b-a)/(n-1)
  44.     for i in range(1,n):
  45.         deltaY = m(F(listeTemps[-1], listeY[-1])) * h
  46.         listeY.append(m(listeY[-1]) + m(deltaY))
  47.         listeTemps.append(listeTemps[-1]+h)
  48.     return listeTemps, listeY
  49.    
  50. #F = lambda t, u:[-u[0], u[0]-u[1], u[1]]
  51. #x, y = euler_vectorielle(F, 0, 10, [1,0,0], 100)
  52. #plot(x,y)
  53. #show()
  54.  
  55. #5
  56. def trajectoire(F,a,b,y0,n):
  57.     couples = euler_vectorielle(F,a,b,y0,n)[1]
  58.     listeX = [couples[k][0] for k in range(len(couples))]
  59.     listeY = [couples[k][1] for k in range(len(couples))]
  60.     plot(listeX, listeY, "--")
  61. #   show()
  62.     return()
  63.    
  64. #F = lambda t,u: [u[0]+3*u[1], -3*u[0]+ u[1]]
  65. #trajectoire(F, 0, 10, [1,1], 1000)
  66.    
  67. #6
  68. def conditions(F,a,b,y0,n,[])
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