feat(maths): add LU decomposition algorithm for matrix factorization#14697
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| def solve_with_lu( | ||
| lower: list[list[float]], upper: list[list[float]], b: list[float] |
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Please provide descriptive name for the parameter: b
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| Matrix = list[list[float]] |
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Variable and function names should follow the snake_case naming convention. Please update the following name accordingly: Matrix
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| def solve_with_lu( | ||
| lower: list[list[float]], upper: list[list[float]], b: list[float] |
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| Reference: https://en.wikipedia.org/wiki/LU_decomposition | ||
| """ | ||
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| Matrix = list[list[float]] |
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Variable and function names should follow the snake_case naming convention. Please update the following name accordingly: Matrix
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| def solve_with_lu( | ||
| lower: list[list[float]], upper: list[list[float]], b: list[float] |
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yes
সোম, ১৮ মে, ২০২৬ তারিখে ৯:৪৩ PM টায় তারিখে algorithms-keeper[bot] <
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- Formatted string literals (f-strings)
<https://docs.python.org/3/tutorial/inputoutput.html#tut-f-strings>
- Type hints <https://docs.python.org/3/library/typing.html>
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------------------------------
In maths/lu_decomposition.py
<#14697?email_source=notifications&email_token=BRHACTQP4FFCTG7ERWEMQQL43MVS3A5CNFSNUABKM5UWIORPF5TWS5BNNB2WEL2QOVWGYUTFOF2WK43UKJSXM2LFO4XTIMZRGE3DGNBRGEZ2M4TFMFZW63VGMF2XI2DPOKSWK5TFNZ2K64DSL5ZGK5TJMV3V6Y3MNFRWW#discussion_r3260196406>
:
> + # Check for zero pivot
+ if upper[k][k] == 0:
+ raise ValueError(
+ "Zero pivot encountered. Matrix may be singular or require partial pivoting."
+ )
+
+ # Compute the k-th column of L
+ for i in range(k + 1, n):
+ sum_val = sum(lower[i][s] * upper[s][k] for s in range(k))
+ lower[i][k] = (matrix[i][k] - sum_val) / upper[k][k]
+
+ return lower, upper
+
+
+def solve_with_lu(
+ lower: list[list[float]], upper: list[list[float]], b: list[float]
Please provide descriptive name for the parameter: b
—
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hey
মঙ্গল, ১৯ মে, ২০২৬ তারিখে ৭:২৩ AM টায় তারিখে algorithms-keeper[bot] <
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… ***@***.***[bot]* commented on this pull request.
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🔗 Relevant Links Repository:
- Contributing guidelines
<https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md>
- Project Euler solution guidelines
<https://github.com/TheAlgorithms/Python/blob/master/project_euler/README.md>
Python:
- Formatted string literals (f-strings)
<https://docs.python.org/3/tutorial/inputoutput.html#tut-f-strings>
- Type hints <https://docs.python.org/3/library/typing.html>
- doctest <https://docs.python.org/3/library/doctest.html>
- unittest <https://docs.python.org/3/library/unittest.html>
- pytest <https://docs.pytest.org/en/stable/>
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------------------------------
In maths/lu_decomposition.py
<#14697?email_source=notifications&email_token=BRHACTXPBRWBD2TS3LSUYOT43OZPPA5CNFSNUABKM5UWIORPF5TWS5BNNB2WEL2QOVWGYUTFOF2WK43UKJSXM2LFO4XTIMZRGUYDKNRXGUYKM4TFMFZW63VGMF2XI2DPOKSWK5TFNZ2K64DSL5ZGK5TJMV3V6Y3MNFRWW#discussion_r3263116960>
:
> +"""
+LU Decomposition
+
+Decomposes a square matrix into a lower triangular matrix (L) and an
+upper triangular matrix (U) such that A = L * U.
+
+This decomposition is useful for:
+- Solving systems of linear equations efficiently
+- Computing matrix determinants
+- Finding matrix inverses
+- Repeated solving with the same coefficient matrix
+
+Reference: https://en.wikipedia.org/wiki/LU_decomposition
+"""
+
+Matrix = list[list[float]]
Variable and function names should follow the snake_case
<https://en.wikipedia.org/wiki/Snake_case> naming convention. Please
update the following name accordingly: Matrix
------------------------------
In maths/lu_decomposition.py
<#14697?email_source=notifications&email_token=BRHACTXPBRWBD2TS3LSUYOT43OZPPA5CNFSNUABKM5UWIORPF5TWS5BNNB2WEL2QOVWGYUTFOF2WK43UKJSXM2LFO4XTIMZRGUYDKNRXGUYKM4TFMFZW63VGMF2XI2DPOKSWK5TFNZ2K64DSL5ZGK5TJMV3V6Y3MNFRWW#discussion_r3263116964>
:
> + # Check for zero pivot
+ if upper[k][k] == 0:
+ raise ValueError(
+ "Zero pivot encountered. Matrix may be singular or require pivoting."
+ )
+
+ # Compute the k-th column of L
+ for i in range(k + 1, n):
+ sum_val = sum(lower[i][s] * upper[s][k] for s in range(k))
+ lower[i][k] = (a[i][k] - sum_val) / upper[k][k]
+
+ return lower, upper
+
+
+def solve_with_lu(
+ lower: list[list[float]], upper: list[list[float]], b: list[float]
Please provide descriptive name for the parameter: b
—
Reply to this email directly, view it on GitHub
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Describe your change:
Checklist:
LU Decomposition Algorithm
Adds LU decomposition (Doolittle algorithm) to the maths module for matrix factorization and solving systems of linear equations.
What This Adds
A new
maths/lu_decomposition.pyfile containing:lu_decomposition(matrix)Performs LU decomposition on a square matrix, returning
(L, U)where:solve_with_lu(lower, upper, b)Solves the system Ax = b using the LU decomposition, via:
Features
__main__blockAlgorithm
Uses the Doolittle algorithm with O(n^3) time complexity for decomposition and O(n^2) for solving. More efficient than Gaussian elimination when solving multiple systems with the same coefficient matrix.
Testing
All 10 doctests pass.