Erster Stand: compute.py
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# Regeln für dieses Projekt
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- Code nach PEP 8, Zeilenlänge maximal 88 Zeichen.
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- Jede Funktion und Methode hat einen Docstring und Type Hints.
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- Vor jedem Commit: `ruff check` und `ruff format`.
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"""
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Mathematical matrix multiplication, transposition, and rotation without external libraries.
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The ``matmul`` function implements a straightforward algorithm that
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multiplies two 2‑D matrices where each element is a ``float``.
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The functions perform validity checks on the dimensions:
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- Matrices must be non-empty lists of lists and rectangular.
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"""
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from __future__ import annotations
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import math
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def matmul(a: list[list[float]], b: list[list[float]]) -> list[list[float]]:
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"""Multiply two 2‑D matrices."""
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if not a or not a[0]:
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raise ValueError("Matrix 'a' must not be empty")
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if not b or not b[0]:
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raise ValueError("Matrix 'b' must not be empty")
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a_rows = len(a)
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a_cols = len(a[0])
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for row in a:
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if len(row) != a_cols:
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raise ValueError("Matrix 'a' rows must all have the same length")
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b_rows = len(b)
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b_cols = len(b[0])
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for row in b:
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if len(row) != b_cols:
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raise ValueError("Matrix 'b' rows must all have the same length")
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if a_cols != b_rows:
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raise ValueError(
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f"Cannot multiply: number of columns in 'a' ({a_cols}) "
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f"does not equal number of rows in 'b' ({b_rows})"
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)
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result: list[list[float]] = []
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for i in range(a_rows):
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result_row: list[float] = []
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for j in range(b_cols):
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element = 0.0
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for k in range(a_cols):
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element += a[i][k] * b[k][j]
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result_row.append(element)
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result.append(result_row)
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return result
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def transpose(a: list[list[float]]) -> list[list[float]]:
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"""Transposes a 2‑D matrix."""
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if not a or not a[0]:
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raise ValueError("Matrix must not be empty")
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a_rows = len(a)
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a_cols = len(a[0])
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for row in a:
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if len(row) != a_cols:
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raise ValueError("Matrix rows must all have the same length")
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result: list[list[float]] = []
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for j in range(a_cols):
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result_row: list[float] = []
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for i in range(a_rows):
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result_row.append(a[i][j])
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result.append(result_row)
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return result
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def rot_2D(theta: float) -> list[list[float]]:
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"""Erzeugt eine 2D-Rotationsmatrix für den Winkel theta (im Bogenmaß)."""
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cos_t = math.cos(theta)
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sin_t = math.sin(theta)
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return [
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[cos_t, -sin_t],
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[sin_t, cos_t]
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]
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if __name__ == "__main__":
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# Valid example: multiplication
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matrix_a = [[1, 2, 3], [4, 5, 6]]
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matrix_b = [[7, 8], [9, 10], [11, 12]]
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print("Valid multiplication result:")
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print(matmul(matrix_a, matrix_b))
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# Valid example: transposition
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print("\nTransposed matrix_a result:")
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print(transpose(matrix_a))
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# Valid example: rotation (2D)
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print("\nRotated 2D matrix (theta = 0.5) result:")
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print(rot_2D(0.5))
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# Example that raises ValueError
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try:
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invalid_b = [[1, 2], [3, 4]]
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print("\nThis should raise an error:")
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print(matmul(matrix_a, invalid_b))
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except ValueError as e:
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print("Caught ValueError as expected:", e)
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"""Basisklasse ``Game`` für einfache pygame-Anwendungen."""
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import pygame
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class Game:
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"""Basisklasse für pygame-Spiele.
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Unterklassen passen das Verhalten durch Überschreiben von
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:meth:`handle_event`, :meth:`update_game` und :meth:`draw_game` an.
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"""
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def __init__(
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self,
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title: str,
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fps: int = 60,
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size: tuple[int, int] = (640, 400),
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) -> None:
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"""Legt Fenstertitel, Bildrate und Fenstergröße fest.
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Args:
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title: Titel des Fensters.
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fps: Maximale Bilder pro Sekunde.
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size: Fenstergröße als (Breite, Höhe) in Pixeln.
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"""
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self.title: str = title
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self.fps: int = fps
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self.size: tuple[int, int] = size
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self.clock: pygame.time.Clock = pygame.time.Clock()
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self.dt: float = 0
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self.screen: pygame.Surface | None = None
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def init_game(self) -> None:
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"""Initialisiert pygame und erzeugt das Fenster."""
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pygame.init()
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pygame.display.set_caption(self.title)
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self.screen = pygame.display.set_mode(self.size)
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def game_loop(self) -> None:
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"""Führt die Hauptschleife aus, bis Events oder Update ``False`` liefern."""
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while True:
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# Berechnung der Zeitdifferenz seit dem letzten Frame
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self.dt = self.clock.tick(self.fps) / 1000
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if self.event_handling() == False:
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break
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if self.update_game() == False:
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break
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self.draw_game()
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def exit_game(self) -> None:
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"""Beendet pygame."""
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pygame.quit()
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def event_handling(self) -> bool:
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"""Verteilt alle anstehenden Events an :meth:`handle_event`.
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Bleibt in der Unterklasse unverändert.
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Returns:
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``False``, sobald ein Event das Spiel beenden soll, sonst ``True``.
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"""
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for event in pygame.event.get():
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if not self.handle_event(event):
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return False
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return True
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def handle_event(self, event: pygame.event.Event) -> bool:
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"""Verarbeitet ein einzelnes Event.
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Wird in der Unterklasse überschrieben.
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Args:
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event: Das zu verarbeitende pygame-Event.
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Returns:
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``False`` bei ``pygame.QUIT``, sonst ``True``.
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"""
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if event.type == pygame.QUIT:
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return False
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return True
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def update_game(self) -> bool:
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"""Aktualisiert den Spielzustand um einen Frame.
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Returns:
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``False``, wenn das Spiel beendet werden soll, sonst ``True``.
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"""
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return True
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def draw_game(self) -> None:
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"""Zeichnet den aktuellen Frame und bringt ihn zur Anzeige."""
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pygame.display.flip()
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def run(self) -> None:
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"""Startet das Spiel: Initialisierung, Hauptschleife, Beenden."""
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self.init_game()
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self.game_loop()
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self.exit_game()
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import pygame
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from compute import matmul, rot_2D, transpose
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from game import Game
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EARTH_RADIUS = 30
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MOON_RADIUS = 10
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BLACK = (0, 0, 0)
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WHITE = (255, 255, 255)
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BLUE = (0, 0, 255)
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class Moon(Game):
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"""Der Mond kreist um die Erde."""
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def __init__(
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self,
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title: str = "Moon",
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fps: int = 60,
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size: tuple[int, int] = (640, 400),
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) -> None:
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"""Legt Startposition, Drehwinkel und Rotationsmatrix fest."""
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super().__init__(title, fps, size)
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# Startposition des Mondes relativ zum Mittelpunkt (z. B. 120 Pixel nach rechts)
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self.position_moon = (120.0, 0.0)
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# Kleiner Drehwinkel im Bogenmaß und Erstellung der Rotationsmatrix
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theta = 0.01
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self.rot_moon = rot_2D(theta)
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def update_game(self) -> bool:
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"""Dreht den Mond ein Stück weiter."""
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# Mondposition mit der Rotationsmatrix weiterdrehen
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point = transpose([list(self.position_moon)]) # [x, y] wird zur Spalte [[x], [y]]
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result = matmul(self.rot_moon, point) # Ergebnis: [[x'], [y']]
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self.position_moon = (result[0][0], result[1][0])
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return True
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def draw_game(self) -> None:
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"""Zeichnet Erde und Mond."""
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# Bildschirm löschen
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self.screen.fill(BLACK)
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# Mittelpunkt des Fensters ermitteln
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center_x = self.screen.get_width() // 2
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center_y = self.screen.get_height() // 2
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# Erde als blauen Kreis in der Mitte zeichnen
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pygame.draw.circle(self.screen, BLUE, (center_x, center_y), EARTH_RADIUS)
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# Mond als weißen Kreis auf der Kreisbahn zeichnen
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moon_x = int(center_x + self.position_moon[0])
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moon_y = int(center_y + self.position_moon[1])
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pygame.draw.circle(self.screen, WHITE, (moon_x, moon_y), MOON_RADIUS)
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# Bild anzeigen
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pygame.display.flip()
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if __name__ == "__main__":
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# Moon-Objekt erzeugen und starten
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game = Moon()
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game.run()
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[project]
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name = "matrixmania"
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version = "0.1.0"
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