Add matrix_multiplication

matrix/matrix_multiplication_recursion.py

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