Implement Strassen's matrix multiplication algorithm #13755
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This file implements Strassen's matrix multiplication algorithm, which is faster than the standard O(n^3) method for large matrices. It includes helper functions for matrix operations and benchmarks the performance of Strassen's algorithm against standard multiplication.
Implement Strassen's matrix multiplication algorithm
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| # type Matrix = list[list[int]] # psf/black currently fails on this line | ||
| Matrix = list[list[int]] |
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Variable and function names should follow the snake_case naming convention. Please update the following name accordingly: Matrix
| return result | ||
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| def pad_matrix(matrix: Matrix, target_size: int) -> Matrix: |
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As there is no test file in this pull request nor any test function or class in the file matrix/strassen.py, please provide doctest for the function pad_matrix
| return padded_matrix | ||
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| def unpad_matrix(matrix: Matrix, original_size: int) -> Matrix: |
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As there is no test file in this pull request nor any test function or class in the file matrix/strassen.py, please provide doctest for the function unpad_matrix
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Pull request overview
Adds a new matrix multiplication implementation using Strassen’s divide-and-conquer algorithm (with padding to power-of-two sizes), including helper utilities, doctests, and an optional benchmark.
Changes:
- Introduces
strassen()with recursive Strassen multiplication and automatic zero-padding/unpadding for non-power-of-two sizes. - Adds supporting helpers (add/subtract, split/combine, pad/unpad) plus sample matrices for doctests.
- Provides a
__main__doctest runner and a small benchmark comparing against iterative multiplication.
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| if not matrix_a or not matrix_b: | ||
| return [] | ||
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| if not ( | ||
| len(matrix_a) == len(matrix_b) and is_square(matrix_a) and is_square(matrix_b) | ||
| ): | ||
| raise ValueError("Matrices must be square and of the same dimensions") |
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strassen() returns [] whenever either input is empty (if not matrix_a or not matrix_b). This means calls like strassen([], [[1]]) silently return an empty result even though the matrices are not the same dimensions and cannot be multiplied. Either tighten the condition to only treat the ( [], [] ) case as a valid empty multiply (and raise ValueError otherwise), or explicitly document/test that any empty input returns [] despite dimension mismatch.
| def split_matrix(matrix: Matrix) -> tuple[Matrix, Matrix, Matrix, Matrix]: | ||
| """ | ||
| Splits a given matrix into four equal quadrants. | ||
| >>> a, b, c, d = split_matrix(matrix_count_up) | ||
| >>> a | ||
| [[1, 2], [5, 6]] | ||
| >>> b | ||
| [[3, 4], [7, 8]] | ||
| >>> c | ||
| [[9, 10], [13, 14]] | ||
| >>> d | ||
| [[11, 12], [15, 16]] | ||
| """ | ||
| n = len(matrix) // 2 | ||
| a11 = [row[:n] for row in matrix[:n]] | ||
| a12 = [row[n:] for row in matrix[:n]] | ||
| a21 = [row[:n] for row in matrix[n:]] | ||
| a22 = [row[n:] for row in matrix[n:]] | ||
| return a11, a12, a21, a22 |
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split_matrix() claims it splits into four equal quadrants, but for odd-sized matrices it will produce uneven quadrant sizes (because it uses n = len(matrix) // 2 without validation). Since this is a public helper in the module, either validate that the input dimension is even (or power-of-two) and raise a clear error, or update the docstring to state the precondition explicitly.
| next_power_of_2 = 1 << n.bit_length() | ||
| a = pad_matrix(matrix_a, next_power_of_2) | ||
| b = pad_matrix(matrix_b, next_power_of_2) | ||
| n = next_power_of_2 |
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Variable n is not used.
| n = next_power_of_2 |
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