'''
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()