[Add] Kronecker Product

matrix/kronecker_product.py

@@ -0,0 +1,75 @@
+# @Author  : jay2219
+# @File    : kronecker_product.py
+# @Date    : 13/10/2024
+
+"""
+Perform Kronecker product of two matrices.
+https://en.wikipedia.org/wiki/Kronecker_product
+"""
+
+
+def is_2d(matrix: list[list[int]]) -> bool:
+    """
+    >>> is_2d([])
+    True
+    >>> is_2d([1, 2])
+    False
+    >>> is_2d([[1, 2], [3, 4]])
+    True
+    """
+
+    return all(isinstance(matrix, list) and (isinstance(i, list) for i in matrix))
+
+
+def kronecker_product(
+    matrix_a: list[list[int]], matrix_b: list[list[int]]
+) -> list[list[int]]:
+    """
+    :param matrix_a: A 2-D Matrix with dimension m x n
+    :param matrix_b: Another 2-D Matrix with dimension p x q
+    :return: Result of matrix_a ⊗ matrix_b
+    :raises ValueError: If the matrices are not 2-D.
+
+    >>> kronecker_product([[1, 2]], [[5, 6], [7, 8]])
+    [[5, 6, 10, 12], [7, 8, 14, 16]]
+
+    >>> kronecker_product([[1, 2, 3], [4, 5, 6]], [[5, 6], [7, 8]])
+    [[5, 6, 10, 12, 15, 18], [7, 8, 14, 16, 21, 24], [20, 24, 25, 30, 30, 36], [28, 32, 35, 40, 42, 48]]
+
+    >>> kronecker_product([1, 2], [[5, 6], [7, 8]])
+    Traceback (most recent call last):
+        ...
+    ValueError: Input matrices must be 2-D.
+    """
+
+    # Check if the input matrices are valid
+    if not all((is_2d(matrix_a), is_2d(matrix_b))):
+        raise ValueError("Input matrices must be 2-D.")
+
+    if not matrix_a or not matrix_b:
+        return []
+
+    rows_matrix_a, cols_matrix_a = len(matrix_a), len(matrix_a[0])
+    rows_matrix_b, cols_matrix_b = len(matrix_b), len(matrix_b[0])
+
+    # Resultant matrix dimensions
+    result = [
+        [0] * (cols_matrix_a * cols_matrix_b)
+        for _ in range(rows_matrix_a * rows_matrix_b)
+    ]
+
+    for r_index_a in range(rows_matrix_a):
+        for c_index_a in range(cols_matrix_a):
+            for r_index_b in range(rows_matrix_b):
+                for c_index_b in range(cols_matrix_b):
+                    result[r_index_a * rows_matrix_b + r_index_b][
+                        c_index_a * cols_matrix_b + c_index_b
+                    ] = (
+                        matrix_a[r_index_a][c_index_a] * matrix_b[r_index_b][c_index_b]
+                    )
+
+    return result
+
+if __name__ == "__main__":
+    import doctest
+    doctest.testmod()