# Author: Alex Gezerlis

# Numerical Methods in Physics with Python (CUP, 2020)

from newtoncotes import f, rectangle, trapezoid, simpson

import numpy as np

def adaptive(f,a,b,integrator,kmax = 20,tol = 1.e-12):

functodenom = {rectangle:1, trapezoid:3, simpson:15}

denom = functodenom[integrator]

n = 2

val = integrator(f,a,b,n)

for k in range(kmax):

nprime = 2*n-1

valprime = integrator(f,a,b,nprime)

err = abs(valprime-val)/denom

err /= abs(valprime)

print(nprime, valprime, err)

if err<tol:

break

n, val = nprime, valprime

else:

valprime = None

return valprime

if __name__ == '__main__':

ans = np.log(1 + np.sqrt(2))

print(ans); print("")

for integrator in (rectangle, trapezoid, simpson):

print(adaptive(f, 0., 1., integrator)); print("")