feat: add numerical laplace transform by Tushar-R-Tyagi · Pull Request #14602 · TheAlgorithms/Python

Tushar-R-Tyagi · 2026-04-28T18:34:56Z

Describe your change:

I have added a numerical implementation of the Laplace transform in the maths/ directory.

Add an algorithm?
Fix a bug or typo in an existing algorithm?
Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
Documentation change?

Checklist:

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Tushar-R-Tyagi · 2026-04-28T18:38:32Z

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Pull request overview

Adds a numerical (sampled-data) Laplace transform implementation to the maths/ algorithms collection.

Changes:

Introduces laplace_transform() that applies an exponential kernel and integrates via the trapezoidal rule.
Adds doctest examples for two basic reference functions.

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Copilot · 2026-04-28T18:39:13Z

+    if s_value < 0:
+        raise ValueError("s_value must be non-negative for convergence.")


The convergence check if s_value < 0: raise ... is not generally correct for the Laplace transform (e.g., for f(t)=e^{-t}, the transform converges for Re(s) > -1). Also, since this implementation integrates over a finite sampled window, negative s_value won't inherently diverge. Consider removing this restriction, or (if you keep it) documenting it as a deliberate limitation rather than a convergence requirement.

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

jgohel9902 · 2026-05-01T14:19:07Z

+    >>> abs(res - 0.5) < 1e-3
+    True
+    """
+    if delta_t <= 0:


Good input validation — catching non-positive delta_t early prevents
silent numerical errors. Consider also validating that s_value is
non-negative since the docstring on line 18 states this implementation
only supports non-negative s values, but there is no guard for it:

if s_value < 0:
raise ValueError("s_value must be non-negative for this implementation.")

Added validation for s_value < 0 with a ValueError. Thanks for this catch.

jgohel9902 · 2026-05-01T14:19:17Z

+        raise ValueError("function_values array cannot be empty.")
+
+    # Time vector corresponding to the function values
+    time_vector = np.arange(len(function_values)) * delta_t


Using np.arange(len(function_values)) * delta_t works correctly but
np.linspace would be more semantically clear and consistent with the
doctests which already use np.linspace:

time_vector = np.linspace(0, (len(function_values) - 1) * delta_t,
len(function_values))

This makes the time vector construction more readable and explicit.

I agree, Linspace is much clearer. I have replaced arange with linspace to make the time vector construction more readable.

jgohel9902 · 2026-05-01T14:19:29Z

@@ -0,0 +1,66 @@
+"""
+This module provides a numerical implementation of the Laplace Transform.


The module docstring is minimal — just one line and a Wikipedia link.
Consider expanding it to match the quality of the function docstring:

"""
Laplace Transform — Numerical Implementation.

Computes the numerical Laplace Transform using the trapezoidal
integration rule. Supports real-valued, non-negative Laplace
parameters only.

Reference: https://en.wikipedia.org/wiki/Laplace_transform
"""

Thanks for this suggestion. I have updated the module just like you recommended.

psyduck1203 · 2026-05-04T15:52:16Z

Hi @Tushar-R-Tyagi, nice fix!

I noticed the issue (#14606) mentions enforcing validation of non-negative s_value. Also checked the code reviews from @jgohel9902. It would make sense to also handle edge cases like:

non-numeric inputs (e.g., strings)
complex numbers (since only real-valued parameters are supported)

Happy to extend any help if needed.

Updated module docstring, added validation for non-negative s_value, and replaced arrange with linspace for clarity.

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Removed extra blank lines and cleaned up docstring.

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Tushar-R-Tyagi · 2026-05-04T18:04:02Z

ruff check .

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algorithms-keeper · 2026-05-04T18:13:01Z

@@ -0,0 +1,74 @@
+"""


An error occurred while parsing the file: maths/laplace_transformation.py

Traceback (most recent call last): File "/opt/render/project/src/algorithms_keeper/parser/python_parser.py", line 146, in parse reports = lint_file( ^^^^^^^^^^ libcst._exceptions.ParserSyntaxError: Syntax Error @ 1:1. tokenizer error: no matching outer block for dedent """ ^

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feat: add numerical laplace transform

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Tushar-R-Tyagi and others added 3 commits April 28, 2026 20:41

Update maths/laplace_transformation.py

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Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

refactor: add input validation and fix doctest precision

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Merge branch 'master' of https://github.com/Tushar-R-Tyagi/Python

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Tushar-R-Tyagi and others added 2 commits May 4, 2026 19:51

fix: address PR review comments

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Updated module docstring, added validation for non-negative s_value, and replaced arrange with linspace for clarity.

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algorithms-keeper Bot added the tests are failing Do not merge until tests pass label May 4, 2026

Tushar-R-Tyagi and others added 2 commits May 4, 2026 20:02

Refactor docstring and remove unnecessary blank lines

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Removed extra blank lines and cleaned up docstring.

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Refactor error handling for s_value check

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Tushar-R-Tyagi and others added 2 commits May 4, 2026 20:14

Fix indentation for s_value validation

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algorithms-keeper Bot removed the tests are failing Do not merge until tests pass label May 4, 2026

		if s_value < 0:
		raise ValueError("s_value must be non-negative for convergence.")

		@@ -0,0 +1,66 @@
		"""
		This module provides a numerical implementation of the Laplace Transform.

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Tushar-R-Tyagi commented Apr 28, 2026

Describe your change:

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