import matplotlib.pyplot as plt
import numpy as np
from scipy.integrate import odeint

        #### Système 2,2 ####



 # On definit ici le systeme differentiel 
 
def syst(y, t, a11, a12, a21, a22) :
	x1, x2 = y 
	dydt = [a11 * x1 + a12 * x2, a21 * x1 + a22 * x2] 
	return dydt 
 
 # Matrice A (choisir les coefficients)
 
a11, a12 = -1,0 
a21, a22 = 0,-3 
 
 # Intervalle de temps sur lequel on trace la solution 
 
t = np.linspace(0, 2, 51) 
 
 # Choix de la condition initiale 
 
y0 = [1,2] 

# On trace x2 en fonction de x1 
 
 # plot en temps positif 
 
sol = odeint(syst, y0, t, args=(a11, a12, a21, a22)) 
plt.plot(sol[:, 0], sol[:, 1], 'b') 
 
 # plot en temps negatif
 
sol = odeint(syst, y0, -t, args=(a11, a12, a21, a22)) 
plt.plot(sol[:, 0], sol[:, 1], 'b') 
 
 # Configuration fenetre graphique  
 
plt.grid() 
plt.xlabel('x1') 
plt.ylabel('x2')       
plt.axis([-1,1,-1,1]) 

 # Representation des tangentes aux trajectoires 
 
g1  = np.linspace(-1,1,15) 
g2  = np.linspace(-1,1,15)
A1, A2 = np.meshgrid(g1,g2) 
V1,V2 = syst((A1,A2),t, a11, a12, a21, a22) 
r1 = np.sqrt(1+V1**2) 
r2 = np.sqrt(1+V2**2) 
plt.quiver(A1, A2, V1/r1, V2/r2) 
plt.show() 



import numpy.linalg as al
A = np.array([[-1, 1 , -1], [-4, -5, 4], [-2, -1, 0]])
L = al.eig(A) 
print(L[0]) 


        #### Système 3,3 ####
        
# Definition du systeme 

def syst(y, t, a11, a12, a13, a21, a22, a23, a31, a32, a33):
	x1, x2, x3 = y 
	dydt = [a11*x1+ a12*x2+ a13*x3, a21*x1+ a22*x2+ a23*x3, a31*x1+ a32*x2+ a33*x3] 
	return dydt 
	
# Definition de la matrice A 
 
a11, a12, a13 = -1, 1 , -1 
a21, a22, a23 = -4, -5, 4 
a31, a32, a33 = -2, -1, 0 
 
# Condition initiale
 
y0 = [0,5,-5] 
 
# Intervalle de temps pour le trace 
 
t = np.linspace(0, 10, 501) 
 
# Creation de la solution X 
 
sol = odeint(syst, y0, t, args=(a11, a12, a13, a21, a22, a23, a31, a32, a33)) 
 
# Configuration du trace 

plt.plot(t, sol[:, 0], 'b-', label='x1(t)') 
plt.plot(t, sol[:, 1], 'g:', label='x2(t)') 
plt.plot(t, sol[:, 2], 'r--', label='x3(t)')
plt.legend(loc='best') 
plt.xlabel('t') 
plt.title(f'[x1(0),x2(0),x3(0)] = [y0[0],y0[1],y0[2]]') 
plt.grid() 
plt.show()