# created by Chatgpt

from typing import List
import math
from tabulate import tabulate
Matrix = List[List[float]]

def matmul(Matrix_1: Matrix, Matrix_2: Matrix) -> Matrix:
    """Multipliziert zwei Matrizen."""
    HeightA = len(Matrix_1)
    HeightB = len(Matrix_2)

    if HeightA == 0 or HeightB == 0:
        raise ValueError("Matrizen dürfen nicht leer sein")

    WidthA = len(Matrix_1[0])
    WidthB = len(Matrix_2[0])

    if WidthA != HeightB:
        raise ValueError("Multiplikation der Matrizen nicht zulässig (Spalten A != Zeilen B)")


    Matrix_3 = [[0.0 for _ in range(WidthB)] for _ in range(HeightA)]


    for i in range(HeightA):
        for j in range(WidthB):
            for k in range(WidthA):
                Matrix_3[i][j] += Matrix_1[i][k] * Matrix_2[k][j]

    return Matrix_3


def transpose(matrix: Matrix) -> Matrix:
    """Transponiert eine Matrix."""
    if not matrix:
        raise ValueError("Matrix darf nicht leer sein")

    rows = len(matrix)
    cols = len(matrix[0])

    if not all(len(row) == cols for row in matrix):
        raise ValueError("Matrix hat ungleichmäßige Zeilenlängen")


    transposed_matrix = [[0.0 for _ in range(rows)] for _ in range(cols)]

    for i in range(rows):
        for j in range(cols):
            transposed_matrix[j][i] = matrix[i][j]

    return transposed_matrix


def rot_2D(angle_degrees: float) -> Matrix:
    """Erstellt eine 2D-Rotationsmatrix für den gegebenen Winkel (in Grad)."""
    angle_radians = math.radians(angle_degrees)
    cos_theta = math.cos(angle_radians)
    sin_theta = math.sin(angle_radians)

    rotation_matrix = [
        [cos_theta, -sin_theta],
        [sin_theta, cos_theta]
    ]
    return rotation_matrix



if __name__ == "__main__":
    A = [[1, 2], [3, 4]]
    B = [[2, 0], [1, 2]]

    print("Matrixmultiplikation:")
    print(matmul(A, B))

    print("\nTransponierte Matrix:")
    print(transpose(A))

    print("\nRotationsmatrix (45°):")
    print(rot_2D(45))

matrix= [[1,2,3], [2,3,4]]
print("Matrix A:")
print(tabulate(matrix))