"""Compute operations for matrices.

This module provides public functions for matrix multiplication, transposition,
matrix rotation, and generating 2D rotation matrices. The implementation is
lightweight, well typed and contains detailed Google‑style documentation.
"""

from __future__ import annotations

import math
from typing import List


def matmul(
        matrix_a: List[List[float]],
        matrix_b: List[List[float]]
) -> List[List[float]]:
    """Multiply two 2D matrices.

    Both matrices are expected to be non‑empty and to have consistent row
    lengths. The number of columns in ``matrix_a`` must equal the number of
    rows in ``matrix_b``.

    Args:
        matrix_a: A matrix of shape (m, n) represented as a list of m rows,
            each a list of n floats.
        matrix_b: A matrix of shape (n, p) represented as a list of n rows,
            each a list of p floats.

    Returns:
        A new matrix of shape (m, p) containing the product
        ``matrix_a @ matrix_b``.

    Raises:
        ValueError: If either matrix is empty or if the column count of
        ``matrix_a`` does not match the row count of ``matrix_b``.
    """

    # SCHRITT 1: Validierung – Prüfen, ob die Matrizen überhaupt Daten enthalten
    if not matrix_a or not matrix_b:
        raise ValueError("Input matrices must not be empty.")

    n_cols_a = len(matrix_a[0])

    # SCHRITT 2: Konsistenzprüfung für Matrix A
    if any(len(row) != n_cols_a for row in matrix_a):
        raise ValueError("All rows of matrix_a must have the same number of columns.")

    n_rows_b = len(matrix_b)

    # SCHRITT 3: Mathematische Regel prüfen: Spalten von A müssen gleich Zeilen von B sein
    if n_cols_a != n_rows_b:
        raise ValueError(
            f"Matrix dimension mismatch: matrix_a columns {n_cols_a} != matrix_b rows {n_rows_b}"
        )

    n_cols_b = len(matrix_b[0])

    # SCHRITT 4: Konsistenzprüfung für Matrix B
    if any(len(row) != n_cols_b for row in matrix_b):
        raise ValueError("All rows of matrix_b must have the same number of columns.")

    # SCHRITT 5: Eigentliche Matrixmultiplikation (Skalarprodukt der Zeilen und Spalten)
    result: List[List[float]] = []
    for i in range(len(matrix_a)):  # Gehe jede Zeile von Matrix A durch
        row: List[float] = []
        for j in range(n_cols_b):  # Gehe jede Spalte von Matrix B durch
            elem = sum(matrix_a[i][k] * matrix_b[k][j] for k in range(n_cols_a))
            row.append(elem)
        result.append(row)

    return result


def transpose(matrix: List[List[float]]) -> List[List[float]]:
    """Return the transpose of a 2‑D matrix.

    Args:
        matrix: A non‑empty matrix represented as a list of rows.

    Returns:
        A new matrix where rows become columns.

    Raises:
        ValueError: If the input matrix is empty or ragged.
    """

    if not matrix:
        raise ValueError("Cannot transpose an empty matrix.")

    n_rows = len(matrix)
    n_cols = len(matrix[0])

    if any(len(row) != n_cols for row in matrix):
        raise ValueError("All rows of the matrix must have the same number of columns.")

    return [[matrix[i][j] for i in range(n_rows)] for j in range(n_cols)]


def rotate_clockwise(matrix: List[List[float]]) -> List[List[float]]:
    """Rotate a square matrix 90 degrees clockwise.

    The function works for any rectangular matrix but will produce a matrix
    of dimensions (cols, rows).

    Args:
        matrix: A non‑empty matrix.

    Returns:
        The rotated matrix.

    Raises:
        ValueError: If the matrix is empty.
    """

    if not matrix:
        raise ValueError("Cannot rotate an empty matrix.")

    n_rows = len(matrix)
    n_cols = len(matrix[0])

    if any(len(row) != n_cols for row in matrix):
        raise ValueError("All rows of the matrix must have the same number of columns.")

    transposed = transpose(matrix)
    return [row[::-1] for row in transposed]


def rot_2D(theta: float) -> List[List[float]]:
    """Return the 2D rotation matrix for a given angle.

    Calculates the 2x2 rotation matrix used in computer graphics to rotate a point
    counterclockwise around the origin by angle theta (in radians).

    Args:
        theta: The rotation angle in radians.

    Returns:
        A 2x2 rotation matrix represented as a list of lists of floats:
        [[cos(theta), -sin(theta)],
         [sin(theta),  cos(theta)]]
    """
    c = math.cos(theta)
    s = math.sin(theta)
    return [
        [c, -s],
        [s, c]
    ]

if __name__ == "__main__":
    # Testdaten für die Demonstration
    a = [[1, 2, 3], [4, 5, 6]]
    b = [[7, 8], [9, 10], [11, 12]]

    print("matmul(a, b):")
    print(matmul(a, b))

    print("transpose(a):")
    print(transpose(a))

    c = [[1, 2], [3, 4], [5, 6]]
    print("rotate_clockwise(c):")
    print(rotate_clockwise(c))

    # Demonstration von rot_2D (z. B. 90 Grad = pi / 2 Radiant)
    angle = math.pi / 2
    print(f"rot_2D (pi / 2 radians / 90 degrees):")
    rotation_matrix = rot_2D(angle)
    for row in rotation_matrix:
        print([round(val, 4) for val in row])