# Author: Alex Gezerlis

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

from math import exp, sqrt

def f(x):

return exp(x - sqrt(x)) - x

def bisection(f,x0,x1,kmax=200,tol=1.e-8):

f0 = f(x0)

for k in range(1,kmax):

x2 = (x0+x1)/2

f2 = f(x2)

if f0*f2 < 0:

x1 = x2

else:

x0, f0 = x2, f2

x2new = (x0+x1)/2

xdiff = abs(x2new-x2)

rowf = "{0:2d} {1:1.16f} {2:1.16f} {3:1.16f}"

print(rowf.format(k,x2new,xdiff,abs(f(x2new))))

if abs(xdiff/x2new) < tol:

break

else:

x2new = None

return x2new

if __name__ == '__main__':

root = bisection(f,0.,1.5)

print(root); print("")

root = bisection(f,1.5,3.)

print(root)