mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-21 18:50:15 +00:00
bfcb95b297
* fixup! Format Python code with psf/black push * Create codespell.yml * fixup! Format Python code with psf/black push
51 lines
1.0 KiB
Python
51 lines
1.0 KiB
Python
"""
|
|
Numerical integration or quadrature for a smooth function f with known values at x_i
|
|
|
|
This method is the classical approach of suming 'Equally Spaced Abscissas'
|
|
|
|
method 1:
|
|
"extended trapezoidal rule"
|
|
|
|
"""
|
|
|
|
|
|
def method_1(boundary, steps):
|
|
# "extended trapezoidal rule"
|
|
# int(f) = dx/2 * (f1 + 2f2 + ... + 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 / 2.0) * f(a)
|
|
for i in x_i:
|
|
# print(i)
|
|
y += h * f(i)
|
|
y += (h / 2.0) * 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_1(boundary, steps)
|
|
print(f"y = {y}")
|
|
|
|
|
|
if __name__ == "__main__":
|
|
main()
|