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'''

Numerical integration or quadrature for a smooth function f with known values at x_i

This method is the classical approch of suming 'Equally Spaced Abscissas'

method 2:

"Simpson Rule"

'''

from __future__ import print_function

def method_2(boundary, steps):

# "Simpson Rule"

# int(f) = delta_x/2 * (b-a)/3*(f1 + 4f2 + 2f_3 + ... + fn)

h = (boundary[1] - boundary[0]) / steps

a = boundary[0]

b = boundary[1]

x_i = makePoints(a,b,h)

y = 0.0

y += (h/3.0)*f(a)

cnt = 2

for i in x_i:

y += (h/3)*(4-2*(cnt%2))*f(i)

cnt += 1

y += (h/3.0)*f(b)

return y

def makePoints(a,b,h):

x = a + h

while x < (b-h):

yield x

x = x + h

def f(x): #enter your function here

y = (x-0)*(x-0)

return y

def main():

a = 0.0 #Lower bound of integration

b = 1.0 #Upper bound of integration

steps = 10.0 #define number of steps or resolution

boundary = [a, b] #define boundary of integration

y = method_2(boundary, steps)

print('y = {0}'.format(y))

if __name__ == '__main__':

main()

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