import numpy as np
import sympy
import matplotlib.pyplot as plt

def EA1(xi,alpha):
    return 1-np.sqrt(1-2*alpha*(1-alpha)*(1-np.cos(xi)))

def EA2(xi,alpha):
    return 1-np.sqrt(1-(alpha**2)*(1-alpha**2)*((1-np.cos(xi))**2))

def EA3(xi,alpha):
    theta=xi/2
    return 1-np.sqrt((1-2*alpha*(np.sin(theta)**2)*(1-(1-alpha)*(np.cos(theta)**2)))**2
        +(2*alpha*np.cos(theta)*np.sin(theta)*(1+(1-alpha)*(np.sin(theta)**2)))**2)

xi = np.linspace(0,np.pi/8,1000)

for alpha in [0.2,0.5,0.8]:
    fig=plt.figure(1)
    plt.title(r"Erreur d'amplitude en fonction de $\zeta$ pour CFL = "+str(alpha))
    plt.xlabel(r'$\zeta$')
    plt.ylabel(r'$E_A$')
    plt.axis([-0.02 , np.pi/8+0.02 , 1e-15, 1e-1])
    plt.semilogy(xi,EA1(xi,alpha),'-g',label="Schema 1")
    plt.semilogy(xi,EA2(xi,alpha),'-b',label="Schema 2")
    plt.semilogy(xi,EA3(xi,alpha),'-r',label="Schema 3")
    plt.legend()
    plt.grid(True)
    plt.show(block=False)
    #plt.savefig("EA"+"_CFL ="+str(alpha)+".png")
    plt.close('all')