import numpy as np
import math
import matplotlib.pyplot as plt
import EA

def acos(X):
    Y=np.zeros_like(X)
    for i in range(len(X)):
        Y[i]=math.acos(X[i])
    return Y

def EP1(xi,alpha):
    return alpha*xi - acos((1-alpha*(1-np.cos(xi)))
                           /(1-EA.EA1(xi,alpha)))

def EP2(xi,alpha):
    return alpha*xi - acos((1-(alpha**2)*(1-np.cos(xi)))
                            /(1-EA.EA2(xi,alpha)))

def EP3(xi,alpha):
    theta=xi/2
    return alpha*xi - acos((1-2*alpha*(np.sin(theta)**2)*(1-(1-alpha)*(np.cos(theta)**2)))
                            /(1-EA.EA3(xi,alpha)))

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

#print(EP1(xi,0.5),"\n",EP3(xi,0.5))

for alpha in [0.2,0.5,0.8]:
    fig=plt.figure(1)
    plt.title(r"Erreur de phase en fonction de $\zeta$ pour CFL = "+str(alpha))
    plt.xlabel(r'$\zeta$')
    plt.ylabel(r'$E_\phi$')
    plt.axis([-0.02 , np.pi/8+0.02 , -0.0010, 0.0030])
    plt.plot(xi,abs(EP1(xi,alpha)),'-g',label="Schema 1")
    plt.plot(xi,abs(EP2(xi,alpha)),'-b',label="Schema 2")
    plt.plot(xi,abs(EP3(xi,alpha)),'-r',label="Schema 3")
    plt.legend(loc='upper left')
    plt.grid(True)
    plt.show(block=False)
    #plt.savefig("EP"+"_CFL ="+str(alpha)+".png")
    plt.close('all')