Create kronecker_product.py

maths/kronecker_product.py

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+"""
+Kronecker Product of Two Matrices
+Implementation with type hints, doctests, and detailed Big-O complexity analysis.
+Reference: https://en.wikipedia.org/wiki/Kronecker_product
+"""
+
+from __future__ import annotations
+
+
+def kronecker_product(
+    matrix_a: list[list[float | int]], matrix_b: list[list[float | int]]
+) -> list[list[float | int]]:
+    """
+    Computes the Kronecker product (tensor product) of two matrices A and B.
+
+    If A is an m-by-n matrix and B is a p-by-q matrix, then the Kronecker product
+    A (x) B is the (m*p)-by-(n*q) block matrix.
+
+    Time Complexity: O(m * n * p * q) where A is m x n and B is p x q.
+    Space Complexity: O(m * n * p * q) for the output block matrix.
+
+    >>> kronecker_product([[1, 2], [3, 4]], [[0, 5], [6, 7]])
+    [[0, 5, 0, 10], [6, 7, 12, 14], [0, 15, 0, 20], [18, 21, 24, 28]]
+
+    >>> kronecker_product([[1, -1]], [[2], [3]])
+    [[2, -2], [3, -3]]
+
+    >>> kronecker_product([[1]], [[5, 6], [7, 8]])
+    [[5, 6], [7, 8]]
+
+    >>> kronecker_product([], [[1, 2]])
+    []
+
+    >>> kronecker_product([[1, 2]], [])
+    []
+    """
+    if not matrix_a or not matrix_b:
+        return []
+
+    rows_a = len(matrix_a)
+    cols_a = len(matrix_a[0])
+    rows_b = len(matrix_b)
+    cols_b = len(matrix_b[0])
+
+    if cols_a == 0 or cols_b == 0:
+        return []
+
+    result_rows = rows_a * rows_b
+    result_cols = cols_a * cols_b
+    result: list[list[float | int]] = [
+        [0 for _ in range(result_cols)] for _ in range(result_rows)
+    ]
+
+    for i in range(rows_a):
+        for j in range(cols_a):
+            for k in range(rows_b):
+                for l_idx in range(cols_b):
+                    row_idx = i * rows_b + k
+                    col_idx = j * cols_b + l_idx
+                    result[row_idx][col_idx] = matrix_a[i][j] * matrix_b[k][l_idx]
+
+    return result
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()