Aufgabe rot_3D
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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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"""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],
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[0.0, 0.0, -1.0],
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[0.0, 1.0, 0.0],
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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_y_axis_zero() -> None:
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"""Testet die 3D-Rotation um die y-Achse um 0 Radiant."""
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# Arrange
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angle = 0.0
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axis = "y"
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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_y_axis_pi_half() -> None:
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"""Testet die 3D-Rotation um die y-Achse um pi / 2 Radiant."""
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# Arrange
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angle = math.pi / 2
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axis = "y"
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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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[0.0, 0.0, 1.0],
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[0.0, 1.0, 0.0],
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[-1.0, 0.0, 0.0],
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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_z_axis_zero() -> None:
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"""Testet die 3D-Rotation um die z-Achse um 0 Radiant."""
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# Arrange
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angle = 0.0
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axis = "z"
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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_z_axis_pi_half() -> None:
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"""Testet die 3D-Rotation um die z-Achse um pi / 2 Radiant."""
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# Arrange
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angle = math.pi / 2
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axis = "z"
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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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[0.0, -1.0, 0.0],
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[1.0, 0.0, 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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@pytest.mark.parametrize("invalid_axis", ["w", "123", "", "X", "Y", "Z"])
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def test_rot_3d_invalid_axis(invalid_axis: str) -> None:
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"""Testet, dass ungültige Achsen einen ValueError auslösen."""
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# Arrange
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angle = 1.0
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# Act & Assert
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with pytest.raises(ValueError, match="Ungültige Achse"):
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rot_3d(angle, invalid_axis)
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