# Author: Alex Gezerlis

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

import numpy as np

def f(x):

return 1/(1 + 25*x**2)

def generatedata(n,f,nodes="cheb"):

if nodes=="cheb":

dataxs = -np.cos(np.linspace(0,np.pi,n))

else:

dataxs = np.linspace(-1,1,n)

datays = f(dataxs)

return dataxs, datays

def weights(dataxs):

n = dataxs.size

ws = np.ones(n)

for k in range(n):

for j in range(n):

if j == k:

continue

ws[k] *= (dataxs[k]-dataxs[j])

return 1/ws

def bary(dataxs,datays,ws,x):

k = np.where(x == dataxs)[0]

if k.size == 0:

nume = np.sum(ws*datays/(x-dataxs))

denom = np.sum(ws/(x-dataxs))

val = nume/denom

else:

val = datays[k[0]]

return val

if __name__ == '__main__':

dataxs, datays = generatedata(15, f)

ws = weights(dataxs)

x = 0.3; pofx = bary(dataxs, datays, ws, x)

print(x, pofx, f(x))