import numpy as np
import matplotlib.pyplot as plt


a = 0
b = 1

nodes = [a,b]

def Adaptiv(f,a,b,tol):
    # beregn T1, T2 og E2:
    T1 = (b-a)*(f(a)+f(b))/2
    T2 = (b-a)*(f(a)+2*f((a+b)/2)+f(b))/4
    E2 = (T2-T1)/3

    if np.abs(E2) <= tol:
        return(T2+E2)
    else:
        c = (a+b)/2
        nodes.append(c)
        Q1 = Adaptiv(f,a,c,tol/2)
        Q2 = Adaptiv(f,c,b,tol/2)
        return(Q1+Q2)

def f(x):
    return(np.sin(x))

def f2(x):
    return(1/(1+25*x**2))


def f3(x):
    return(np.sqrt(x))

tol = 1e-4

res = Adaptiv(f3,a,b,tol)

nodes.sort()

nodes = np.asarray(nodes)

plt.plot(nodes,f3(nodes),'.')
plt.plot(nodes,np.zeros(np.size(nodes)),'r.')
plt.show()