# -*- coding: utf-8 -*-
"""
Éditeur de Spyder

Ceci est un script temporaire.
"""

from numpy import *
from matplotlib.pyplot import *
from random import random

from mpl_toolkits.mplot3d import Axes3D

#1
def trace_graphe(f,a,b,pas):
    plot([a+k*pas for k in range(int((b-a)/pas))],[f(a+k*pas) for k in range(int((b-a)/pas))],"+")
    show()
    return

#2
def petit_nuage():
    for i in range(50):
        plot([random()*10],[random()*10],"+")
    show()
    return

#3
def euler(F,a,b,y0,n):
    listeTemps = [a]
    listeY = [y0]
    h = (b-a)/(n-1)
    for i in range(1,n):
        listeY.append(listeY[-1]+F(listeTemps[-1], listeY[-1] * h))
        listeTemps.append(listeTemps[-1]+h)
    return listeTemps,listeY

#4
m = asarray

def euler_vectorielle(F,a,b,y0,n):
    listeTemps = [a]
    listeY = [y0]
    h = (b-a)/(n-1)
    for i in range(1,n):
        deltaY = m(F(listeTemps[-1], listeY[-1])) * h
        listeY.append(m(listeY[-1]) + m(deltaY))
        listeTemps.append(listeTemps[-1]+h)
    return listeTemps, listeY

#F = lambda t, u:[-u[0], u[0]-u[1], u[1]]
#x, y = euler_vectorielle(F, 0, 10, [1,0,0], 100)
#plot(x,y)
#show()

#5
def trajectoire(F,a,b,y0,n):
    couples = euler_vectorielle(F,a,b,y0,n)[1]
    listeX = [couples[k][0] for k in range(len(couples))]
    listeY = [couples[k][1] for k in range(len(couples))]
    plot(listeX, listeY, "--")
#   show()
    return()

#F = lambda t,u: [u[0]+3*u[1], -3*u[0]+ u[1]]
#trajectoire(F, 0, 10, [1,1], 1000)

#6
def conditions(F,a,b,y0,n,[])