'''Programma per integrare e^x da 0 a 1'''


import numpy as np
import matplotlib.pyplot as plt

def rettangoli_naif(h,f):
    inte=0.0
    for i in range(f.shape[0]-1):
        inte+=f[i]
    inte*=h
    return inte

def trapezi(h,f):
    inte=f[0]/2.0+f[-1]/2.0
    for i in range(1,f.shape[0]-1):
        inte+=f[i]
    inte*=h
    return inte


def main():

    
    ris=np.exp(1.0)-1.0

    ris_naif=[]
    ris_trap=[]
    mesh=[]

    for n in (10,100,1000,10000):

        h=1.0/n#larghezza intervalli

        x=np.zeros((n+1),dtype=np.float64)
        f=np.zeros((n+1),dtype=np.float64)

        for i in range(n+1):
            x[i]=h*i
            f[i]=np.exp(x[i])

        ris_naif.append(rettangoli_naif(h,f))
        ris_trap.append(trapezi(h,f))
        mesh.append(n)


    for i in range(len(mesh)):
        print(str(ris_naif[i]-ris)+'\t'+str(ris_trap[i]-ris))    

    fig, ax = plt.subplots()

    
    plt.plot(mesh,ris_naif-ris)
    plt.plot(mesh,ris_trap-ris)
    
    plt.show(block=True)
    
    fig, ax = plt.subplots()

    ax.semilogx()
    ax.semilogy()
    plt.plot(mesh,abs(ris_naif-ris))
    plt.plot(mesh,abs(ris_trap-ris))
    
    plt.show(block=True)


if __name__ == "__main__":
    main()