mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-11 05:40:15 +00:00
ae0fc85401
* Fix ruff errors
Renamed neural_network/input_data.py to neural_network/input_data.py_tf
because it should be left out of the directory for the following
reasons:
1. Its sole purpose is to be used by neural_network/gan.py_tf, which is
itself left out of the directory because of issues with TensorFlow.
2. It was taken directly from TensorFlow's codebase and is actually
already deprecated. If/when neural_network/gan.py_tf is eventually
re-added back to the directory, its implementation should be changed
to not use neural_network/input_data.py anyway.
* updating DIRECTORY.md
* Change input_data.py_tf file extension
Change input_data.py_tf file extension because algorithms-keeper bot is being picky about it
---------
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
61 lines
1.6 KiB
Python
61 lines
1.6 KiB
Python
"""
|
|
Approximates the area under the curve using the trapezoidal rule
|
|
"""
|
|
from __future__ import annotations
|
|
|
|
from collections.abc import Callable
|
|
|
|
|
|
def trapezoidal_area(
|
|
fnc: Callable[[float], float],
|
|
x_start: float,
|
|
x_end: float,
|
|
steps: int = 100,
|
|
) -> float:
|
|
"""
|
|
Treats curve as a collection of linear lines and sums the area of the
|
|
trapezium shape they form
|
|
:param fnc: a function which defines a curve
|
|
:param x_start: left end point to indicate the start of line segment
|
|
:param x_end: right end point to indicate end of line segment
|
|
:param steps: an accuracy gauge; more steps increases the accuracy
|
|
:return: a float representing the length of the curve
|
|
|
|
>>> def f(x):
|
|
... return 5
|
|
>>> f"{trapezoidal_area(f, 12.0, 14.0, 1000):.3f}"
|
|
'10.000'
|
|
>>> def f(x):
|
|
... return 9*x**2
|
|
>>> f"{trapezoidal_area(f, -4.0, 0, 10000):.4f}"
|
|
'192.0000'
|
|
>>> f"{trapezoidal_area(f, -4.0, 4.0, 10000):.4f}"
|
|
'384.0000'
|
|
"""
|
|
x1 = x_start
|
|
fx1 = fnc(x_start)
|
|
area = 0.0
|
|
for _ in range(steps):
|
|
# Approximates small segments of curve as linear and solve
|
|
# for trapezoidal area
|
|
x2 = (x_end - x_start) / steps + x1
|
|
fx2 = fnc(x2)
|
|
area += abs(fx2 + fx1) * (x2 - x1) / 2
|
|
# Increment step
|
|
x1 = x2
|
|
fx1 = fx2
|
|
return area
|
|
|
|
|
|
if __name__ == "__main__":
|
|
|
|
def f(x):
|
|
return x**3 + x**2
|
|
|
|
print("f(x) = x^3 + x^2")
|
|
print("The area between the curve, x = -5, x = 5 and the x axis is:")
|
|
i = 10
|
|
while i <= 100000:
|
|
print(f"with {i} steps: {trapezoidal_area(f, -5, 5, i)}")
|
|
i *= 10
|