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* pre-commit: Upgrade psf/black for stable style 2023 Updating https://github.com/psf/black ... updating 22.12.0 -> 23.1.0 for their `2023 stable style`. * https://github.com/psf/black/blob/main/CHANGES.md#2310 > This is the first [psf/black] release of 2023, and following our stability policy, it comes with a number of improvements to our stable style… Also, add https://github.com/tox-dev/pyproject-fmt and https://github.com/abravalheri/validate-pyproject to pre-commit. I only modified `.pre-commit-config.yaml` and all other files were modified by pre-commit.ci and psf/black. * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
66 lines
1.6 KiB
Python
66 lines
1.6 KiB
Python
from __future__ import annotations
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import math
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from collections.abc import Callable
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def line_length(
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fnc: Callable[[int | float], int | float],
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x_start: int | float,
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x_end: int | float,
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steps: int = 100,
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) -> float:
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"""
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Approximates the arc length of a line segment by treating the curve as a
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sequence of linear lines and summing their lengths
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:param fnc: a function which defines a curve
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:param x_start: left end point to indicate the start of line segment
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:param x_end: right end point to indicate end of line segment
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:param steps: an accuracy gauge; more steps increases accuracy
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:return: a float representing the length of the curve
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>>> def f(x):
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... return x
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>>> f"{line_length(f, 0, 1, 10):.6f}"
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'1.414214'
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>>> def f(x):
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... return 1
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>>> f"{line_length(f, -5.5, 4.5):.6f}"
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'10.000000'
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>>> def f(x):
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... return math.sin(5 * x) + math.cos(10 * x) + x * x/10
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>>> f"{line_length(f, 0.0, 10.0, 10000):.6f}"
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'69.534930'
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"""
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x1 = x_start
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fx1 = fnc(x_start)
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length = 0.0
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for _ in range(steps):
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# Approximates curve as a sequence of linear lines and sums their length
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x2 = (x_end - x_start) / steps + x1
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fx2 = fnc(x2)
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length += math.hypot(x2 - x1, fx2 - fx1)
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# Increment step
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x1 = x2
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fx1 = fx2
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return length
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if __name__ == "__main__":
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def f(x):
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return math.sin(10 * x)
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print("f(x) = sin(10 * x)")
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print("The length of the curve from x = -10 to x = 10 is:")
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i = 10
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while i <= 100000:
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print(f"With {i} steps: {line_length(f, -10, 10, i)}")
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i *= 10
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