import math

def matmul(matrix_a:list[list[float]], matrix_b: list[list[float]]) -> list[list[float]]:
    """
    Add two numbers together.
    :param matrix_a: The first Matrix
    :type matrix_a: list[list[float]]
    :param matrix_b: The second Matrix
    :type matrix_b: list[list[float]]
    :return: The Matrix Multiplication of matrix_a and matrix_b
    :rtype: list[list[float]]
    """
    try:
        if len(matrix_a[0]) != len(matrix_b):
            raise ValueError("Differing Matrix Size")
        target_height = len(matrix_a)
        target_width = len(matrix_b[0])

        end_matrix : list[list[float]]= []


        for height in range(target_height):
            end_matrix.append([])
            for width in range(target_width):
                row = matrix_a[height]
                column_ = []
                for b in matrix_b:
                    column_.append(b[width])
                result_quarter = 0
                for i in range(len(row)):
                    result_quarter += row[i] * column_[i]
                end_matrix[height].append(float(result_quarter))

        return end_matrix
    except ValueError:
        print("An Error has occurred")
    except IndexError:
        print("Tried to call non-existing Index")
    except TypeError:
        print("Tried to insert not a Number")



def transpose(matrix:list[list[float]]) -> list[list[float]]:
    """
    Transposes a matrix.
    :param matrix: The Matrix, that will be transposed
    :type matrix: list[list[float]]
    :return: The transposed matrix
    :rtype: list[list[float]]
    """

    transposed_matrix = []
    for x in range(len(matrix[0])):
        column = []
        for b in matrix:
            column.append(b[x])
        transposed_matrix.append(column)

    return transposed_matrix

def rot_2d(angle:float) -> list[list[float]]:
    """
    Creates a Rotation Matrix out of the given angle
    :param angle: The rotation in radians
    :type angle: float
    :return: The Rotation Matrix
    :rtype: list[list[float]]
    """
    sin = round(math.sin(angle), 4)
    cos = round(math.cos(angle), 4)
    return [[cos, -sin],
            [sin, cos]]




def print_matrix(matrix:list[list[float]]) -> None:
    for row in matrix:
        print(row)

if __name__ == "__main__":
    matrix_bsp_a = [[1, 2, 3], [4, 5, 6]]
    matrix_bsp_b = [[1, 2], [3, 4], [5, 6]]
    matrix_bsp_c = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
    matrix_bsp_d = [[1, 4, 7], [2, 5, 8], [3, 6, 9]]

    if False:
        matrix_bsp_result = matmul(matrix_bsp_c, matrix_bsp_d)
        print_matrix(matrix_bsp_result)

    if False:
        matrix_bsp_result = transpose(matrix_bsp_d)
        #print_matrix(matrix_bsp_c)
        print_matrix(matrix_bsp_result)

    if True:
        print_matrix(rot_2d(math.pi*.25))


    # Test Kommenter

    print("Done")