|
| 1 | +# @Author : ojas-wani |
| 2 | +# @File : matrix_multiplication_recursion.py |
| 3 | +# @Date : 10/06/2023 |
| 4 | + |
| 5 | + |
| 6 | +""" |
| 7 | +Perform matrix multiplication using a recursive algorithm. |
| 8 | +https://en.wikipedia.org/wiki/Matrix_multiplication |
| 9 | +""" |
| 10 | +# type Matrix = list[list[int]] # psf/black currenttly fails on this line |
| 11 | +Matrix = list[list[int]] |
| 12 | + |
| 13 | +matrix_1_to_4 = [ |
| 14 | + [1, 2], |
| 15 | + [3, 4], |
| 16 | +] |
| 17 | + |
| 18 | +matrix_5_to_8 = [ |
| 19 | + [5, 6], |
| 20 | + [7, 8], |
| 21 | +] |
| 22 | + |
| 23 | +matrix_5_to_9_high = [ |
| 24 | + [5, 6], |
| 25 | + [7, 8], |
| 26 | + [9], |
| 27 | +] |
| 28 | + |
| 29 | +matrix_5_to_9_wide = [ |
| 30 | + [5, 6], |
| 31 | + [7, 8, 9], |
| 32 | +] |
| 33 | + |
| 34 | +matrix_count_up = [ |
| 35 | + [1, 2, 3, 4], |
| 36 | + [5, 6, 7, 8], |
| 37 | + [9, 10, 11, 12], |
| 38 | + [13, 14, 15, 16], |
| 39 | +] |
| 40 | + |
| 41 | +matrix_unordered = [ |
| 42 | + [5, 8, 1, 2], |
| 43 | + [6, 7, 3, 0], |
| 44 | + [4, 5, 9, 1], |
| 45 | + [2, 6, 10, 14], |
| 46 | +] |
| 47 | +matrices = ( |
| 48 | + matrix_1_to_4, |
| 49 | + matrix_5_to_8, |
| 50 | + matrix_5_to_9_high, |
| 51 | + matrix_5_to_9_wide, |
| 52 | + matrix_count_up, |
| 53 | + matrix_unordered, |
| 54 | +) |
| 55 | + |
| 56 | + |
| 57 | +def is_square(matrix: Matrix) -> bool: |
| 58 | + """ |
| 59 | + >>> is_square([]) |
| 60 | + True |
| 61 | + >>> is_square(matrix_1_to_4) |
| 62 | + True |
| 63 | + >>> is_square(matrix_5_to_9_high) |
| 64 | + False |
| 65 | + """ |
| 66 | + len_matrix = len(matrix) |
| 67 | + return all(len(row) == len_matrix for row in matrix) |
| 68 | + |
| 69 | + |
| 70 | +def matrix_multiply(matrix_a: Matrix, matrix_b: Matrix) -> Matrix: |
| 71 | + """ |
| 72 | + >>> matrix_multiply(matrix_1_to_4, matrix_5_to_8) |
| 73 | + [[19, 22], [43, 50]] |
| 74 | + """ |
| 75 | + return [ |
| 76 | + [sum(a * b for a, b in zip(row, col)) for col in zip(*matrix_b)] |
| 77 | + for row in matrix_a |
| 78 | + ] |
| 79 | + |
| 80 | + |
| 81 | +def matrix_multiply_recursive(matrix_a: Matrix, matrix_b: Matrix) -> Matrix: |
| 82 | + """ |
| 83 | + :param matrix_a: A square Matrix. |
| 84 | + :param matrix_b: Another square Matrix with the same dimensions as matrix_a. |
| 85 | + :return: Result of matrix_a * matrix_b. |
| 86 | + :raises ValueError: If the matrices cannot be multiplied. |
| 87 | +
|
| 88 | + >>> matrix_multiply_recursive([], []) |
| 89 | + [] |
| 90 | + >>> matrix_multiply_recursive(matrix_1_to_4, matrix_5_to_8) |
| 91 | + [[19, 22], [43, 50]] |
| 92 | + >>> matrix_multiply_recursive(matrix_count_up, matrix_unordered) |
| 93 | + [[37, 61, 74, 61], [105, 165, 166, 129], [173, 269, 258, 197], [241, 373, 350, 265]] |
| 94 | + >>> matrix_multiply_recursive(matrix_1_to_4, matrix_5_to_9_wide) |
| 95 | + Traceback (most recent call last): |
| 96 | + ... |
| 97 | + ValueError: Invalid matrix dimensions |
| 98 | + >>> matrix_multiply_recursive(matrix_1_to_4, matrix_5_to_9_high) |
| 99 | + Traceback (most recent call last): |
| 100 | + ... |
| 101 | + ValueError: Invalid matrix dimensions |
| 102 | + >>> matrix_multiply_recursive(matrix_1_to_4, matrix_count_up) |
| 103 | + Traceback (most recent call last): |
| 104 | + ... |
| 105 | + ValueError: Invalid matrix dimensions |
| 106 | + """ |
| 107 | + if not matrix_a or not matrix_b: |
| 108 | + return [] |
| 109 | + if not all( |
| 110 | + (len(matrix_a) == len(matrix_b), is_square(matrix_a), is_square(matrix_b)) |
| 111 | + ): |
| 112 | + raise ValueError("Invalid matrix dimensions") |
| 113 | + |
| 114 | + # Initialize the result matrix with zeros |
| 115 | + result = [[0] * len(matrix_b[0]) for _ in range(len(matrix_a))] |
| 116 | + |
| 117 | + # Recursive multiplication of matrices |
| 118 | + def multiply( |
| 119 | + i_loop: int, |
| 120 | + j_loop: int, |
| 121 | + k_loop: int, |
| 122 | + matrix_a: Matrix, |
| 123 | + matrix_b: Matrix, |
| 124 | + result: Matrix, |
| 125 | + ) -> None: |
| 126 | + """ |
| 127 | + :param matrix_a: A square Matrix. |
| 128 | + :param matrix_b: Another square Matrix with the same dimensions as matrix_a. |
| 129 | + :param result: Result matrix |
| 130 | + :param i: Index used for iteration during multiplication. |
| 131 | + :param j: Index used for iteration during multiplication. |
| 132 | + :param k: Index used for iteration during multiplication. |
| 133 | + >>> 0 > 1 # Doctests in inner functions are never run |
| 134 | + True |
| 135 | + """ |
| 136 | + if i_loop >= len(matrix_a): |
| 137 | + return |
| 138 | + if j_loop >= len(matrix_b[0]): |
| 139 | + return multiply(i_loop + 1, 0, 0, matrix_a, matrix_b, result) |
| 140 | + if k_loop >= len(matrix_b): |
| 141 | + return multiply(i_loop, j_loop + 1, 0, matrix_a, matrix_b, result) |
| 142 | + result[i_loop][j_loop] += matrix_a[i_loop][k_loop] * matrix_b[k_loop][j_loop] |
| 143 | + return multiply(i_loop, j_loop, k_loop + 1, matrix_a, matrix_b, result) |
| 144 | + |
| 145 | + # Perform the recursive matrix multiplication |
| 146 | + multiply(0, 0, 0, matrix_a, matrix_b, result) |
| 147 | + return result |
| 148 | + |
| 149 | + |
| 150 | +if __name__ == "__main__": |
| 151 | + from doctest import testmod |
| 152 | + |
| 153 | + failure_count, test_count = testmod() |
| 154 | + if not failure_count: |
| 155 | + matrix_a = matrices[0] |
| 156 | + for matrix_b in matrices[1:]: |
| 157 | + print("Multiplying:") |
| 158 | + for row in matrix_a: |
| 159 | + print(row) |
| 160 | + print("By:") |
| 161 | + for row in matrix_b: |
| 162 | + print(row) |
| 163 | + print("Result:") |
| 164 | + try: |
| 165 | + result = matrix_multiply_recursive(matrix_a, matrix_b) |
| 166 | + for row in result: |
| 167 | + print(row) |
| 168 | + assert result == matrix_multiply(matrix_a, matrix_b) |
| 169 | + except ValueError as e: |
| 170 | + print(f"{e!r}") |
| 171 | + print() |
| 172 | + matrix_a = matrix_b |
| 173 | + |
| 174 | + print("Benchmark:") |
| 175 | + from functools import partial |
| 176 | + from timeit import timeit |
| 177 | + |
| 178 | + mytimeit = partial(timeit, globals=globals(), number=100_000) |
| 179 | + for func in ("matrix_multiply", "matrix_multiply_recursive"): |
| 180 | + print(f"{func:>25}(): {mytimeit(f'{func}(matrix_count_up, matrix_unordered)')}") |
![pre-commit-ci[bot]](https://avatars.githubusercontent.com/in/68672?v=4&size=40){kind=avatar}
0 commit comments