mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-10-06 13:49:30 +00:00
897f1d0fb4
* Improved Formatting and Style
I improved formatting and style to make PyLama happier.
Linters used:
- mccabe
- pep257
- pydocstyle
- pep8
- pycodestyle
- pyflakes
- pylint
- isort
* Create volume.py
This script calculates the volumes of various shapes.
* Delete lucasSeries.py
* Revert "Delete lucasSeries.py"
This reverts commit 64c19f7a6c.
* Update lucasSeries.py
50 lines
1.1 KiB
Python
50 lines
1.1 KiB
Python
|
|
"""
|
|
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 = make_points(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 make_points(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()
|