import  math
import numpy as np
def A(x):
    return ((2019*x**5)-(2018*x**4)+(2017*x**3))
def B(x):
    return (1/(1+25*x**2))
def C(x):
    return (math.sin((9*x)+1)/x)

def Romberg(f,a,b,n):
    sum=0
    h = b - a
    R = np.zeros((n+1 , n+1 ))
    R[0][0] = 0.5 * h * (f(a) + f(b))

    for i in range(1,n+1):
        h *= 0.5
        sum = 0
        for k in range(1,2**i,2):
            sum += f(a + k * h)

        R[i][0] = 0.5 * R[i-1][0] + sum * h


        for j in range(1,i+1):
            R[i][j] = R[i][j-1] + (R[i][j-1] - R[i-1][j-1]) / ((4**j)-1)


    return R

def prettyprint(R):
    float_formatter = lambda x: "%.6f" % x
    np.set_printoptions(formatter={'float_kind':float_formatter})
    for i, row in enumerate(R):
        print("%3d" % (i + 1), row[:i + 1])
    print("Wynik to %.18f\n" % R[-1][-1])

n = 15

prettyprint(Romberg(A, -1.0, 2.0, 15))


prettyprint(Romberg(B, -1.0, 1.0, 15))


prettyprint(Romberg(C, 1, 2 * math.pi, 15))