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Feb 28th, 2020
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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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