# Author: Alex Gezerlis

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

from legendre import legendre

from legroots import legroots

from newtoncotes import f

import numpy as np

def gauleg_params(n):

xs = legroots(n)

cs = 2/((1-xs**2)*legendre(n,xs)[1]**2)

return xs, cs

def gauleg(f,a,b,n):

xs, cs = gauleg_params(n)

coeffp = 0.5*(b+a)

coeffm = 0.5*(b-a)

ts = coeffp + coeffm*xs

contribs = cs*f(ts)

return coeffm*np.sum(contribs)

if __name__ == '__main__':

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

print(ans)

for n in range(2,10):

print(n, gauleg(f,0.,1,n))