FilesExpand file tree

 all-subsequences

/

simpson_rule.py

Copy path

Blame

More file actions

Blame

More file actions

Latest commit

 

History

History

History

49 lines (39 loc) · 1003 Bytes

 all-subsequences

/

simpson_rule.py

Top

File metadata and controls

• Code
• Blame

49 lines (39 loc) · 1003 Bytes

Raw

Copy raw file

Download raw file

Open symbols panel

Edit and raw actions

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

'''

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()