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Add matrix_multiplication (#10045)
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ojas wani
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matrix/matrix_multiplication_recursion.py
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180
matrix/matrix_multiplication_recursion.py
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# @Author : ojas-wani
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# @File : matrix_multiplication_recursion.py
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# @Date : 10/06/2023
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"""
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Perform matrix multiplication using a recursive algorithm.
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https://en.wikipedia.org/wiki/Matrix_multiplication
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"""
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# type Matrix = list[list[int]] # psf/black currenttly fails on this line
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Matrix = list[list[int]]
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matrix_1_to_4 = [
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[1, 2],
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[3, 4],
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]
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matrix_5_to_8 = [
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[5, 6],
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[7, 8],
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]
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matrix_5_to_9_high = [
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[5, 6],
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[7, 8],
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[9],
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]
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matrix_5_to_9_wide = [
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[5, 6],
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[7, 8, 9],
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]
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matrix_count_up = [
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[1, 2, 3, 4],
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[5, 6, 7, 8],
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[9, 10, 11, 12],
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[13, 14, 15, 16],
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]
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matrix_unordered = [
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[5, 8, 1, 2],
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[6, 7, 3, 0],
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[4, 5, 9, 1],
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[2, 6, 10, 14],
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]
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matrices = (
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matrix_1_to_4,
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matrix_5_to_8,
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matrix_5_to_9_high,
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matrix_5_to_9_wide,
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matrix_count_up,
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matrix_unordered,
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)
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def is_square(matrix: Matrix) -> bool:
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"""
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>>> is_square([])
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True
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>>> is_square(matrix_1_to_4)
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True
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>>> is_square(matrix_5_to_9_high)
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False
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"""
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len_matrix = len(matrix)
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return all(len(row) == len_matrix for row in matrix)
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def matrix_multiply(matrix_a: Matrix, matrix_b: Matrix) -> Matrix:
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"""
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>>> matrix_multiply(matrix_1_to_4, matrix_5_to_8)
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[[19, 22], [43, 50]]
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"""
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return [
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[sum(a * b for a, b in zip(row, col)) for col in zip(*matrix_b)]
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for row in matrix_a
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]
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def matrix_multiply_recursive(matrix_a: Matrix, matrix_b: Matrix) -> Matrix:
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"""
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:param matrix_a: A square Matrix.
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:param matrix_b: Another square Matrix with the same dimensions as matrix_a.
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:return: Result of matrix_a * matrix_b.
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:raises ValueError: If the matrices cannot be multiplied.
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>>> matrix_multiply_recursive([], [])
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[]
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>>> matrix_multiply_recursive(matrix_1_to_4, matrix_5_to_8)
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[[19, 22], [43, 50]]
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>>> matrix_multiply_recursive(matrix_count_up, matrix_unordered)
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[[37, 61, 74, 61], [105, 165, 166, 129], [173, 269, 258, 197], [241, 373, 350, 265]]
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>>> matrix_multiply_recursive(matrix_1_to_4, matrix_5_to_9_wide)
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Traceback (most recent call last):
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...
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ValueError: Invalid matrix dimensions
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>>> matrix_multiply_recursive(matrix_1_to_4, matrix_5_to_9_high)
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Traceback (most recent call last):
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...
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ValueError: Invalid matrix dimensions
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>>> matrix_multiply_recursive(matrix_1_to_4, matrix_count_up)
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Traceback (most recent call last):
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...
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ValueError: Invalid matrix dimensions
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"""
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if not matrix_a or not matrix_b:
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return []
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if not all(
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(len(matrix_a) == len(matrix_b), is_square(matrix_a), is_square(matrix_b))
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):
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raise ValueError("Invalid matrix dimensions")
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# Initialize the result matrix with zeros
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result = [[0] * len(matrix_b[0]) for _ in range(len(matrix_a))]
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# Recursive multiplication of matrices
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def multiply(
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i_loop: int,
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j_loop: int,
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k_loop: int,
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matrix_a: Matrix,
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matrix_b: Matrix,
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result: Matrix,
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) -> None:
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"""
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:param matrix_a: A square Matrix.
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:param matrix_b: Another square Matrix with the same dimensions as matrix_a.
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:param result: Result matrix
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:param i: Index used for iteration during multiplication.
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:param j: Index used for iteration during multiplication.
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:param k: Index used for iteration during multiplication.
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>>> 0 > 1 # Doctests in inner functions are never run
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True
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"""
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if i_loop >= len(matrix_a):
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return
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if j_loop >= len(matrix_b[0]):
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return multiply(i_loop + 1, 0, 0, matrix_a, matrix_b, result)
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if k_loop >= len(matrix_b):
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return multiply(i_loop, j_loop + 1, 0, matrix_a, matrix_b, result)
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result[i_loop][j_loop] += matrix_a[i_loop][k_loop] * matrix_b[k_loop][j_loop]
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return multiply(i_loop, j_loop, k_loop + 1, matrix_a, matrix_b, result)
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# Perform the recursive matrix multiplication
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multiply(0, 0, 0, matrix_a, matrix_b, result)
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return result
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if __name__ == "__main__":
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from doctest import testmod
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failure_count, test_count = testmod()
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if not failure_count:
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matrix_a = matrices[0]
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for matrix_b in matrices[1:]:
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print("Multiplying:")
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for row in matrix_a:
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print(row)
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print("By:")
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for row in matrix_b:
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print(row)
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print("Result:")
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try:
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result = matrix_multiply_recursive(matrix_a, matrix_b)
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for row in result:
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print(row)
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assert result == matrix_multiply(matrix_a, matrix_b)
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except ValueError as e:
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print(f"{e!r}")
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print()
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matrix_a = matrix_b
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print("Benchmark:")
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from functools import partial
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from timeit import timeit
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mytimeit = partial(timeit, globals=globals(), number=100_000)
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for func in ("matrix_multiply", "matrix_multiply_recursive"):
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print(f"{func:>25}(): {mytimeit(f'{func}(matrix_count_up, matrix_unordered)')}")
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