Python/maths/line_length.py
Tianyi Zheng ae0fc85401
Fix ruff errors ()
* 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>
2023-08-09 13:25:30 +05:30

66 lines
1.6 KiB
Python

from __future__ import annotations
import math
from collections.abc import Callable
def line_length(
fnc: Callable[[float], float],
x_start: float,
x_end: float,
steps: int = 100,
) -> float:
"""
Approximates the arc length of a line segment by treating the curve as a
sequence of linear lines and summing their lengths
: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 accuracy
:return: a float representing the length of the curve
>>> def f(x):
... return x
>>> f"{line_length(f, 0, 1, 10):.6f}"
'1.414214'
>>> def f(x):
... return 1
>>> f"{line_length(f, -5.5, 4.5):.6f}"
'10.000000'
>>> def f(x):
... return math.sin(5 * x) + math.cos(10 * x) + x * x/10
>>> f"{line_length(f, 0.0, 10.0, 10000):.6f}"
'69.534930'
"""
x1 = x_start
fx1 = fnc(x_start)
length = 0.0
for _ in range(steps):
# Approximates curve as a sequence of linear lines and sums their length
x2 = (x_end - x_start) / steps + x1
fx2 = fnc(x2)
length += math.hypot(x2 - x1, fx2 - fx1)
# Increment step
x1 = x2
fx1 = fx2
return length
if __name__ == "__main__":
def f(x):
return math.sin(10 * x)
print("f(x) = sin(10 * x)")
print("The length of the curve from x = -10 to x = 10 is:")
i = 10
while i <= 100000:
print(f"With {i} steps: {line_length(f, -10, 10, i)}")
i *= 10