Aufgabe rot_3D
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@@ -1 +1,5 @@
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from .compute import matmul, transpose, rot_2d
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"""MatrixMania - Paket für Matrixoperationen."""
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from .compute import matmul, rot_2d, rot_3d, transpose
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__all__ = ["matmul", "rot_2d", "rot_3d", "transpose"]
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@@ -5,7 +5,9 @@ import math
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from tabulate import tabulate
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def matmul(matrix_a: list[list[float]], matrix_b: list[list[float]]) -> list[list[float]]:
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def matmul(
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matrix_a: list[list[float]], matrix_b: list[list[float]]
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) -> list[list[float]]:
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"""Berechnet das Matrixprodukt zweier Matrizen (matrix_a @ matrix_b).
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:param matrix_a: Die linke Matrix.
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@@ -21,11 +23,15 @@ def matmul(matrix_a: list[list[float]], matrix_b: list[list[float]]) -> list[lis
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rows_a, cols_a = len(matrix_a), len(matrix_a[0])
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rows_b, cols_b = len(matrix_b), len(matrix_b[0])
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if any(len(row) != cols_a for row in matrix_a) or any(len(row) != cols_b for row in matrix_b):
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if any(len(row) != cols_a for row in matrix_a) or any(
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len(row) != cols_b for row in matrix_b
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):
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raise ValueError("Alle Zeilen einer Matrix müssen dieselbe Länge besitzen.")
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if cols_a != rows_b:
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raise ValueError("Matrixdimensionen stimmen für die Multiplikation nicht überein.")
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raise ValueError(
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"Matrixdimensionen stimmen für die Multiplikation nicht überein."
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)
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result: list[list[float]] = []
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for i in range(rows_a):
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@@ -78,10 +84,56 @@ def rot_2d(angle: float) -> list[list[float]]:
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def rot_3d(angle: float, axis: str) -> list[list[float]]:
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pass
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"""Berechnet die 3D-Rotationsmatrix für einen Drehwinkel um eine Achse.
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Die Rotationsmatrizen lauten:
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- Für die x-Achse R_x(theta):
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[[1, 0, 0],
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[0, cos(theta), -sin(theta)],
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[0, sin(theta), cos(theta)]]
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- Für die y-Achse R_y(theta):
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[[cos(theta), 0, sin(theta)],
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[0, 1, 0],
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[-sin(theta), 0, cos(theta)]]
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- Für die z-Achse R_z(theta):
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[[cos(theta), -sin(theta), 0],
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[sin(theta), cos(theta), 0],
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[0, 0, 1]]
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:param angle: Der Rotationswinkel im Bogenmaß (Radiant).
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:param axis: Die Rotationsachse ('x', 'y' oder 'z').
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:return: Die 3x3-Rotationsmatrix als verschachtelte Liste.
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:raises ValueError: Wenn die Achse nicht 'x', 'y' oder 'z' ist.
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"""
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if axis not in ("x", "y", "z"):
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raise ValueError(
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f"Ungültige Achse '{axis}'. Erlaubte Werte sind 'x', 'y' oder 'z'."
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)
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cos_theta = math.cos(angle)
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sin_theta = math.sin(angle)
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if axis == "x":
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return [
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[1.0, 0.0, 0.0],
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[0.0, cos_theta, -sin_theta],
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[0.0, sin_theta, cos_theta],
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]
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if axis == "y":
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return [
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[cos_theta, 0.0, sin_theta],
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[0.0, 1.0, 0.0],
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[-sin_theta, 0.0, cos_theta],
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]
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return [
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[cos_theta, -sin_theta, 0.0],
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[sin_theta, cos_theta, 0.0],
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[0.0, 0.0, 1.0],
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]
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def test_functions():
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def test_functions() -> None:
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"""Testet die mathematischen Hilfsfunktionen für Matrixoperationen."""
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a1 = [
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[3, 4, -1, 4],
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[-2, 2, 5, 1],
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@@ -97,7 +149,9 @@ def test_functions():
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[-1, 27, -8],
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]
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c1 = matmul(a1, b1)
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assert c1 == expected_c1, f"Fehler in Beispiel 1: Erwartet {expected_c1}, erhalten {c1}"
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assert c1 == expected_c1, (
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f"Fehler in Beispiel 1: Erwartet {expected_c1}, erhalten {c1}"
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)
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print("Test 1 (Skript-Beispiel) erfolgreich bestanden!")
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a2 = [
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@@ -178,5 +232,40 @@ def test_functions():
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assert math.isclose(rotated_point[1][0], 1.0, abs_tol=1e-9)
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print("Test rot_2D (Vektordrehung mit matmul) erfolgreich bestanden!")
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# Test 10: rot_3d um x-Achse um pi / 2
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rot_x_90 = rot_3d(math.pi / 2, "x")
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v_y = [[0.0], [1.0], [0.0]]
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rotated_v_y = matmul(rot_x_90, v_y)
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assert math.isclose(rotated_v_y[0][0], 0.0, abs_tol=1e-9)
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assert math.isclose(rotated_v_y[1][0], 0.0, abs_tol=1e-9)
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assert math.isclose(rotated_v_y[2][0], 1.0, abs_tol=1e-9)
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print("Test rot_3D (x-Achse) erfolgreich bestanden!")
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# Test 11: rot_3d um y-Achse um pi / 2
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rot_y_90 = rot_3d(math.pi / 2, "y")
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v_z = [[0.0], [0.0], [1.0]]
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rotated_v_z = matmul(rot_y_90, v_z)
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assert math.isclose(rotated_v_z[0][0], 1.0, abs_tol=1e-9)
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assert math.isclose(rotated_v_z[1][0], 0.0, abs_tol=1e-9)
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assert math.isclose(rotated_v_z[2][0], 0.0, abs_tol=1e-9)
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print("Test rot_3D (y-Achse) erfolgreich bestanden!")
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# Test 12: rot_3d um z-Achse um pi / 2
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rot_z_90 = rot_3d(math.pi / 2, "z")
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v_x = [[1.0], [0.0], [0.0]]
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rotated_v_x = matmul(rot_z_90, v_x)
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assert math.isclose(rotated_v_x[0][0], 0.0, abs_tol=1e-9)
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assert math.isclose(rotated_v_x[1][0], 1.0, abs_tol=1e-9)
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assert math.isclose(rotated_v_x[2][0], 0.0, abs_tol=1e-9)
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print("Test rot_3D (z-Achse) erfolgreich bestanden!")
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# Test 13: rot_3d mit ungültiger Achse
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try:
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rot_3d(math.pi / 2, "invalid")
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raise AssertionError("Ungültige Achse wurde nicht abgefangen!")
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except ValueError:
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print("Test 13 (rot_3d ungültige Achse) erfolgreich abgefangen!")
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if __name__ == "__main__":
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print(tabulate(rot_2d(1.0)))
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print(tabulate(rot_2d(1.0)))
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@@ -0,0 +1,154 @@
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"""Unit-Tests für die mathematischen Matrixfunktionen in compute.py."""
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import math
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import pytest
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from matrixmania.compute import matmul, rot_2d, rot_3d, test_functions, transpose
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def test_matmul_valid() -> None:
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"""Testet die Matrixmultiplikation mit gültigen Matrizen."""
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a = [
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[3.0, 4.0, -1.0, 4.0],
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[-2.0, 2.0, 5.0, 1.0],
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]
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b = [
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[1.0, 3.0, -2.0],
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[2.0, 5.0, 1.0],
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[-1.0, 4.0, -4.0],
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[2.0, 3.0, 6.0],
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]
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expected = [
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[20.0, 37.0, 26.0],
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[-1.0, 27.0, -8.0],
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]
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assert matmul(a, b) == expected
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def test_matmul_invalid_dimensions() -> None:
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"""Testet, dass bei inkompatiblen Matrixdimensionen ValueError geworfen wird."""
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a = [[1.0, 2.0], [3.0, 4.0]]
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b = [[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]
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with pytest.raises(ValueError):
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matmul(a, b)
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def test_matmul_empty_or_uneven() -> None:
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"""Testet matmul mit leeren oder ungleichmäßigen Matrizen."""
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with pytest.raises(ValueError):
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matmul([], [[1.0]])
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with pytest.raises(ValueError):
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matmul([[1.0, 2.0], [3.0]], [[1.0], [2.0]])
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def test_transpose_valid() -> None:
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"""Testet das Transponieren einer regulären Matrix."""
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matrix = [
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[1.0, 2.0, 3.0],
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[4.0, 5.0, 6.0],
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]
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expected = [
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[1.0, 4.0],
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[2.0, 5.0],
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[3.0, 6.0],
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]
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assert transpose(matrix) == expected
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def test_transpose_invalid() -> None:
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"""Testet, dass transpose bei leeren oder unregelmäßigen Matrizen Fehler wirft."""
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with pytest.raises(ValueError):
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transpose([])
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with pytest.raises(ValueError):
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transpose([[1.0, 2.0], [3.0]])
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def test_rot_2d() -> None:
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"""Testet die 2D-Rotation für verschiedene Winkel."""
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rot_0 = rot_2d(0.0)
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assert math.isclose(rot_0[0][0], 1.0, abs_tol=1e-9)
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assert math.isclose(rot_0[0][1], 0.0, abs_tol=1e-9)
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assert math.isclose(rot_0[1][0], 0.0, abs_tol=1e-9)
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assert math.isclose(rot_0[1][1], 1.0, abs_tol=1e-9)
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rot_90 = rot_2d(math.pi / 2)
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assert math.isclose(rot_90[0][0], 0.0, abs_tol=1e-9)
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assert math.isclose(rot_90[0][1], -1.0, abs_tol=1e-9)
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assert math.isclose(rot_90[1][0], 1.0, abs_tol=1e-9)
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assert math.isclose(rot_90[1][1], 0.0, abs_tol=1e-9)
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def test_rot_3d_x_axis() -> None:
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"""Testet die 3D-Rotation um die x-Achse."""
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matrix_x_0 = rot_3d(0.0, "x")
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expected_identity = [
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[1.0, 0.0, 0.0],
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[0.0, 1.0, 0.0],
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[0.0, 0.0, 1.0],
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]
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for r in range(3):
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for c in range(3):
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assert math.isclose(matrix_x_0[r][c], expected_identity[r][c], abs_tol=1e-9)
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matrix_x_90 = rot_3d(math.pi / 2, "x")
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v_y = [[0.0], [1.0], [0.0]]
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rotated = matmul(matrix_x_90, v_y)
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assert math.isclose(rotated[0][0], 0.0, abs_tol=1e-9)
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assert math.isclose(rotated[1][0], 0.0, abs_tol=1e-9)
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assert math.isclose(rotated[2][0], 1.0, abs_tol=1e-9)
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def test_rot_3d_y_axis() -> None:
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"""Testet die 3D-Rotation um die y-Achse."""
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matrix_y_0 = rot_3d(0.0, "y")
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expected_identity = [
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[1.0, 0.0, 0.0],
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[0.0, 1.0, 0.0],
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[0.0, 0.0, 1.0],
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]
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for r in range(3):
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for c in range(3):
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assert math.isclose(matrix_y_0[r][c], expected_identity[r][c], abs_tol=1e-9)
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matrix_y_90 = rot_3d(math.pi / 2, "y")
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v_z = [[0.0], [0.0], [1.0]]
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rotated = matmul(matrix_y_90, v_z)
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assert math.isclose(rotated[0][0], 1.0, abs_tol=1e-9)
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assert math.isclose(rotated[1][0], 0.0, abs_tol=1e-9)
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assert math.isclose(rotated[2][0], 0.0, abs_tol=1e-9)
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def test_rot_3d_z_axis() -> None:
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"""Testet die 3D-Rotation um die z-Achse."""
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matrix_z_0 = rot_3d(0.0, "z")
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expected_identity = [
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[1.0, 0.0, 0.0],
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[0.0, 1.0, 0.0],
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[0.0, 0.0, 1.0],
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]
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for r in range(3):
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for c in range(3):
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assert math.isclose(matrix_z_0[r][c], expected_identity[r][c], abs_tol=1e-9)
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matrix_z_90 = rot_3d(math.pi / 2, "z")
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v_x = [[1.0], [0.0], [0.0]]
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rotated = matmul(matrix_z_90, v_x)
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assert math.isclose(rotated[0][0], 0.0, abs_tol=1e-9)
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assert math.isclose(rotated[1][0], 1.0, abs_tol=1e-9)
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assert math.isclose(rotated[2][0], 0.0, abs_tol=1e-9)
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def test_rot_3d_invalid_axis() -> None:
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"""Testet, dass ungültige Achsen einen ValueError auslösen."""
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with pytest.raises(ValueError, match="Ungültige Achse"):
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rot_3d(1.0, "w")
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with pytest.raises(ValueError):
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rot_3d(0.5, "123")
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with pytest.raises(ValueError):
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rot_3d(0.0, "")
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def test_test_functions_execution() -> None:
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"""Testet die Ausführung der integrierten Testfunktion."""
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test_functions()
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@@ -0,0 +1,198 @@
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"""Unit-Tests für die Rotationsfunktionen in compute.py."""
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import math
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import pytest
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from matrixmania import rot_2d, rot_3d
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def test_rot_2d_zero_angle() -> None:
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"""Testet die 2D-Rotation um 0 Radiant (Einheitsmatrix)."""
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# Arrange
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angle = 0.0
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# Act
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result = rot_2d(angle)
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# Assert
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assert math.isclose(result[0][0], 1.0, abs_tol=1e-9)
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assert math.isclose(result[0][1], 0.0, abs_tol=1e-9)
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assert math.isclose(result[1][0], 0.0, abs_tol=1e-9)
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assert math.isclose(result[1][1], 1.0, abs_tol=1e-9)
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def test_rot_2d_pi_half() -> None:
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"""Testet die 2D-Rotation um pi / 2 Radiant (90 Grad)."""
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# Arrange
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angle = math.pi / 2
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# Act
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result = rot_2d(angle)
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# Assert
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assert math.isclose(result[0][0], 0.0, abs_tol=1e-9)
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assert math.isclose(result[0][1], -1.0, abs_tol=1e-9)
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assert math.isclose(result[1][0], 1.0, abs_tol=1e-9)
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assert math.isclose(result[1][1], 0.0, abs_tol=1e-9)
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def test_rot_2d_pi() -> None:
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"""Testet die 2D-Rotation um pi Radiant (180 Grad)."""
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# Arrange
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angle = math.pi
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# Act
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result = rot_2d(angle)
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# Assert
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assert math.isclose(result[0][0], -1.0, abs_tol=1e-9)
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assert math.isclose(result[0][1], 0.0, abs_tol=1e-9)
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assert math.isclose(result[1][0], 0.0, abs_tol=1e-9)
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assert math.isclose(result[1][1], -1.0, abs_tol=1e-9)
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def test_rot_2d_negative_angle() -> None:
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"""Testet die 2D-Rotation mit einem negativen Winkel (-pi / 2)."""
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# Arrange
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angle = -math.pi / 2
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# Act
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result = rot_2d(angle)
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# Assert
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assert math.isclose(result[0][0], 0.0, abs_tol=1e-9)
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assert math.isclose(result[0][1], 1.0, abs_tol=1e-9)
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assert math.isclose(result[1][0], -1.0, abs_tol=1e-9)
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assert math.isclose(result[1][1], 0.0, abs_tol=1e-9)
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def test_rot_3d_x_axis_zero() -> None:
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"""Testet die 3D-Rotation um die x-Achse um 0 Radiant."""
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# Arrange
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angle = 0.0
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axis = "x"
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# Act
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result = rot_3d(angle, axis)
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# Assert
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expected = [
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[1.0, 0.0, 0.0],
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[0.0, 1.0, 0.0],
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[0.0, 0.0, 1.0],
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]
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for row in range(3):
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for col in range(3):
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assert math.isclose(result[row][col], expected[row][col], abs_tol=1e-9)
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def test_rot_3d_x_axis_pi_half() -> None:
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"""Testet die 3D-Rotation um die x-Achse um pi / 2 Radiant."""
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# Arrange
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angle = math.pi / 2
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axis = "x"
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# Act
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result = rot_3d(angle, axis)
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# Assert
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expected = [
|
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[1.0, 0.0, 0.0],
|
||||
[0.0, 0.0, -1.0],
|
||||
[0.0, 1.0, 0.0],
|
||||
]
|
||||
for row in range(3):
|
||||
for col in range(3):
|
||||
assert math.isclose(result[row][col], expected[row][col], abs_tol=1e-9)
|
||||
|
||||
|
||||
def test_rot_3d_y_axis_zero() -> None:
|
||||
"""Testet die 3D-Rotation um die y-Achse um 0 Radiant."""
|
||||
# Arrange
|
||||
angle = 0.0
|
||||
axis = "y"
|
||||
|
||||
# Act
|
||||
result = rot_3d(angle, axis)
|
||||
|
||||
# Assert
|
||||
expected = [
|
||||
[1.0, 0.0, 0.0],
|
||||
[0.0, 1.0, 0.0],
|
||||
[0.0, 0.0, 1.0],
|
||||
]
|
||||
for row in range(3):
|
||||
for col in range(3):
|
||||
assert math.isclose(result[row][col], expected[row][col], abs_tol=1e-9)
|
||||
|
||||
|
||||
def test_rot_3d_y_axis_pi_half() -> None:
|
||||
"""Testet die 3D-Rotation um die y-Achse um pi / 2 Radiant."""
|
||||
# Arrange
|
||||
angle = math.pi / 2
|
||||
axis = "y"
|
||||
|
||||
# Act
|
||||
result = rot_3d(angle, axis)
|
||||
|
||||
# Assert
|
||||
expected = [
|
||||
[0.0, 0.0, 1.0],
|
||||
[0.0, 1.0, 0.0],
|
||||
[-1.0, 0.0, 0.0],
|
||||
]
|
||||
for row in range(3):
|
||||
for col in range(3):
|
||||
assert math.isclose(result[row][col], expected[row][col], abs_tol=1e-9)
|
||||
|
||||
|
||||
def test_rot_3d_z_axis_zero() -> None:
|
||||
"""Testet die 3D-Rotation um die z-Achse um 0 Radiant."""
|
||||
# Arrange
|
||||
angle = 0.0
|
||||
axis = "z"
|
||||
|
||||
# Act
|
||||
result = rot_3d(angle, axis)
|
||||
|
||||
# Assert
|
||||
expected = [
|
||||
[1.0, 0.0, 0.0],
|
||||
[0.0, 1.0, 0.0],
|
||||
[0.0, 0.0, 1.0],
|
||||
]
|
||||
for row in range(3):
|
||||
for col in range(3):
|
||||
assert math.isclose(result[row][col], expected[row][col], abs_tol=1e-9)
|
||||
|
||||
|
||||
def test_rot_3d_z_axis_pi_half() -> None:
|
||||
"""Testet die 3D-Rotation um die z-Achse um pi / 2 Radiant."""
|
||||
# Arrange
|
||||
angle = math.pi / 2
|
||||
axis = "z"
|
||||
|
||||
# Act
|
||||
result = rot_3d(angle, axis)
|
||||
|
||||
# Assert
|
||||
expected = [
|
||||
[0.0, -1.0, 0.0],
|
||||
[1.0, 0.0, 0.0],
|
||||
[0.0, 0.0, 1.0],
|
||||
]
|
||||
for row in range(3):
|
||||
for col in range(3):
|
||||
assert math.isclose(result[row][col], expected[row][col], abs_tol=1e-9)
|
||||
|
||||
|
||||
@pytest.mark.parametrize("invalid_axis", ["w", "123", "", "X", "Y", "Z"])
|
||||
def test_rot_3d_invalid_axis(invalid_axis: str) -> None:
|
||||
"""Testet, dass ungültige Achsen einen ValueError auslösen."""
|
||||
# Arrange
|
||||
angle = 1.0
|
||||
|
||||
# Act & Assert
|
||||
with pytest.raises(ValueError, match="Ungültige Achse"):
|
||||
rot_3d(angle, invalid_axis)
|
||||
Reference in new issue
Block a user