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kuehnleinma103760 committed 2026-10-22 23:56:08 +02:00
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src/matrixmania/compute.py
+10 -147
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@@ -148,155 +148,18 @@ def project_ortho(
return x * scale, y * scale return x * scale, y * scale
def project_perspective(point: tuple[float, float, float], def project_perspective(
focal_length: float = 1.0, point: tuple[float, float, float],
scale: float = 1.0, focal_length: float = 1.0,
camera_distance: float = 4.0) -> tuple[float, float]: scale: float = 1.0,
camera_distance: float = 4.0,
) -> tuple[float, float]:
"""Projiziert einen 3D-Punkt perspektivisch auf eine 2D-Ebene."""
x, y, z = point x, y, z = point
return (((x * focal_length) / z + camera_distance) * scale, return (
((y * focal_length) / z + camera_distance) * scale) ((x * focal_length) / z + camera_distance) * scale,
((y * focal_length) / z + camera_distance) * scale,
def test_functions() -> None:
"""Testet die mathematischen Hilfsfunktionen für Matrixoperationen."""
a1 = [
[3, 4, -1, 4],
[-2, 2, 5, 1],
]
b1 = [
[1, 3, -2],
[2, 5, 1],
[-1, 4, -4],
[2, 3, 6],
]
expected_c1 = [
[20, 37, 26],
[-1, 27, -8],
]
c1 = matmul(a1, b1)
assert c1 == expected_c1, (
f"Fehler in Beispiel 1: Erwartet {expected_c1}, erhalten {c1}"
) )
print("Test 1 (Skript-Beispiel) erfolgreich bestanden!")
a2 = [
[1, 2],
[3, 4],
]
identity = [
[1, 0],
[0, 1],
]
c2 = matmul(a2, identity)
assert c2 == a2, f"Fehler in Beispiel 2: Erwartet {a2}, erhalten {c2}"
print("Test 2 (Einheitsmatrix) erfolgreich bestanden!")
incompatible_b = [
[1, 2],
[3, 4],
]
try:
matmul(a1, incompatible_b)
raise AssertionError("Fehlerfall wurde nicht abgefangen!")
except ValueError:
print("Test 3 (Fehlerfall inkompatible Dimensionen) erfolgreich abgefangen!")
# Tests für Transpose
example_matrix = [
[1, 2, 3],
[4, 5, 6],
]
expected_transposed = [
[1, 4],
[2, 5],
[3, 6],
]
assert transpose(example_matrix) == expected_transposed, (
f"Erwartet: {expected_transposed}, Erhalten: {transpose(example_matrix)}"
)
print("Test 4 (transpose) erfolgreich bestanden!")
# Test transpose: Leere Matrix
try:
transpose([])
raise AssertionError("Leere Matrix wurde nicht abgefangen!")
except ValueError:
print("Test 5 (transpose leere Matrix) erfolgreich abgefangen!")
# Test transpose: Ungleichmäßige Zeilenlänge
uneven_matrix = [
[1, 2, 3],
[4, 5],
]
try:
transpose(uneven_matrix)
raise AssertionError("Ungleichmäßige Matrix wurde nicht abgefangen!")
except ValueError:
print("Test 6 (transpose ungleichmäßige Matrix) erfolgreich abgefangen!")
# Test 7: Rotation um 0 Radianten (entspricht der Einheitsmatrix)
rot_0 = rot_2d(0.0)
assert math.isclose(rot_0[0][0], 1.0, abs_tol=1e-9)
assert math.isclose(rot_0[0][1], 0.0, abs_tol=1e-9)
assert math.isclose(rot_0[1][0], 0.0, abs_tol=1e-9)
assert math.isclose(rot_0[1][1], 1.0, abs_tol=1e-9)
print("Test rot_2D (0 Radiant) erfolgreich bestanden!")
# Test 8: Rotation um 90 Grad (pi / 2) -> [[0, -1], [1, 0]]
rot_90 = rot_2d(math.pi / 2)
assert math.isclose(rot_90[0][0], 0.0, abs_tol=1e-9)
assert math.isclose(rot_90[0][1], -1.0, abs_tol=1e-9)
assert math.isclose(rot_90[1][0], 1.0, abs_tol=1e-9)
assert math.isclose(rot_90[1][1], 0.0, abs_tol=1e-9)
print("Test rot_2D (pi / 2 Radiant) erfolgreich bestanden!")
# Test 9: Drehung des Vektors (1, 0) um 90 Grad ergibt (0, 1) via matmul
point = [[1.0], [0.0]]
rotated_point = matmul(rot_90, point)
assert math.isclose(rotated_point[0][0], 0.0, abs_tol=1e-9)
assert math.isclose(rotated_point[1][0], 1.0, abs_tol=1e-9)
print("Test rot_2D (Vektordrehung mit matmul) erfolgreich bestanden!")
# Test 10: rot_3d um x-Achse um pi / 2
rot_x_90 = rot_3d(math.pi / 2, "x")
v_y = [[0.0], [1.0], [0.0]]
rotated_v_y = matmul(rot_x_90, v_y)
assert math.isclose(rotated_v_y[0][0], 0.0, abs_tol=1e-9)
assert math.isclose(rotated_v_y[1][0], 0.0, abs_tol=1e-9)
assert math.isclose(rotated_v_y[2][0], 1.0, abs_tol=1e-9)
print("Test rot_3D (x-Achse) erfolgreich bestanden!")
# Test 11: rot_3d um y-Achse um pi / 2
rot_y_90 = rot_3d(math.pi / 2, "y")
v_z = [[0.0], [0.0], [1.0]]
rotated_v_z = matmul(rot_y_90, v_z)
assert math.isclose(rotated_v_z[0][0], 1.0, abs_tol=1e-9)
assert math.isclose(rotated_v_z[1][0], 0.0, abs_tol=1e-9)
assert math.isclose(rotated_v_z[2][0], 0.0, abs_tol=1e-9)
print("Test rot_3D (y-Achse) erfolgreich bestanden!")
# Test 12: rot_3d um z-Achse um pi / 2
rot_z_90 = rot_3d(math.pi / 2, "z")
v_x = [[1.0], [0.0], [0.0]]
rotated_v_x = matmul(rot_z_90, v_x)
assert math.isclose(rotated_v_x[0][0], 0.0, abs_tol=1e-9)
assert math.isclose(rotated_v_x[1][0], 1.0, abs_tol=1e-9)
assert math.isclose(rotated_v_x[2][0], 0.0, abs_tol=1e-9)
print("Test rot_3D (z-Achse) erfolgreich bestanden!")
# Test 13: rot_3d mit ungültiger Achse
try:
rot_3d(math.pi / 2, "invalid")
raise AssertionError("Ungültige Achse wurde nicht abgefangen!")
except ValueError:
print("Test 13 (rot_3d ungültige Achse) erfolgreich abgefangen!")
# Test 14: project_ortho
projected = project_ortho((0.5, -0.5, 10.0), scale=200)
assert projected == (100.0, -100.0), (
f"Fehler in project_ortho: Erwartet (100.0, -100.0), erhalten {projected}"
)
print("Test 14 (project_ortho) erfolgreich bestanden!")
if __name__ == "__main__": if __name__ == "__main__":
test/test_matrixmania/test_compute.py
-154
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@@ -1,154 +0,0 @@
"""Unit-Tests für die mathematischen Matrixfunktionen in compute.py."""
import math
import pytest
from matrixmania.compute import matmul, rot_2d, rot_3d, test_functions, transpose
def test_matmul_valid() -> None:
"""Testet die Matrixmultiplikation mit gültigen Matrizen."""
a = [
[3.0, 4.0, -1.0, 4.0],
[-2.0, 2.0, 5.0, 1.0],
]
b = [
[1.0, 3.0, -2.0],
[2.0, 5.0, 1.0],
[-1.0, 4.0, -4.0],
[2.0, 3.0, 6.0],
]
expected = [
[20.0, 37.0, 26.0],
[-1.0, 27.0, -8.0],
]
assert matmul(a, b) == expected
def test_matmul_invalid_dimensions() -> None:
"""Testet, dass bei inkompatiblen Matrixdimensionen ValueError geworfen wird."""
a = [[1.0, 2.0], [3.0, 4.0]]
b = [[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]
with pytest.raises(ValueError):
matmul(a, b)
def test_matmul_empty_or_uneven() -> None:
"""Testet matmul mit leeren oder ungleichmäßigen Matrizen."""
with pytest.raises(ValueError):
matmul([], [[1.0]])
with pytest.raises(ValueError):
matmul([[1.0, 2.0], [3.0]], [[1.0], [2.0]])
def test_transpose_valid() -> None:
"""Testet das Transponieren einer regulären Matrix."""
matrix = [
[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0],
]
expected = [
[1.0, 4.0],
[2.0, 5.0],
[3.0, 6.0],
]
assert transpose(matrix) == expected
def test_transpose_invalid() -> None:
"""Testet, dass transpose bei leeren oder unregelmäßigen Matrizen Fehler wirft."""
with pytest.raises(ValueError):
transpose([])
with pytest.raises(ValueError):
transpose([[1.0, 2.0], [3.0]])
def test_rot_2d() -> None:
"""Testet die 2D-Rotation für verschiedene Winkel."""
rot_0 = rot_2d(0.0)
assert math.isclose(rot_0[0][0], 1.0, abs_tol=1e-9)
assert math.isclose(rot_0[0][1], 0.0, abs_tol=1e-9)
assert math.isclose(rot_0[1][0], 0.0, abs_tol=1e-9)
assert math.isclose(rot_0[1][1], 1.0, abs_tol=1e-9)
rot_90 = rot_2d(math.pi / 2)
assert math.isclose(rot_90[0][0], 0.0, abs_tol=1e-9)
assert math.isclose(rot_90[0][1], -1.0, abs_tol=1e-9)
assert math.isclose(rot_90[1][0], 1.0, abs_tol=1e-9)
assert math.isclose(rot_90[1][1], 0.0, abs_tol=1e-9)
def test_rot_3d_x_axis() -> None:
"""Testet die 3D-Rotation um die x-Achse."""
matrix_x_0 = rot_3d(0.0, "x")
expected_identity = [
[1.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, 1.0],
]
for r in range(3):
for c in range(3):
assert math.isclose(matrix_x_0[r][c], expected_identity[r][c], abs_tol=1e-9)
matrix_x_90 = rot_3d(math.pi / 2, "x")
v_y = [[0.0], [1.0], [0.0]]
rotated = matmul(matrix_x_90, v_y)
assert math.isclose(rotated[0][0], 0.0, abs_tol=1e-9)
assert math.isclose(rotated[1][0], 0.0, abs_tol=1e-9)
assert math.isclose(rotated[2][0], 1.0, abs_tol=1e-9)
def test_rot_3d_y_axis() -> None:
"""Testet die 3D-Rotation um die y-Achse."""
matrix_y_0 = rot_3d(0.0, "y")
expected_identity = [
[1.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, 1.0],
]
for r in range(3):
for c in range(3):
assert math.isclose(matrix_y_0[r][c], expected_identity[r][c], abs_tol=1e-9)
matrix_y_90 = rot_3d(math.pi / 2, "y")
v_z = [[0.0], [0.0], [1.0]]
rotated = matmul(matrix_y_90, v_z)
assert math.isclose(rotated[0][0], 1.0, abs_tol=1e-9)
assert math.isclose(rotated[1][0], 0.0, abs_tol=1e-9)
assert math.isclose(rotated[2][0], 0.0, abs_tol=1e-9)
def test_rot_3d_z_axis() -> None:
"""Testet die 3D-Rotation um die z-Achse."""
matrix_z_0 = rot_3d(0.0, "z")
expected_identity = [
[1.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, 1.0],
]
for r in range(3):
for c in range(3):
assert math.isclose(matrix_z_0[r][c], expected_identity[r][c], abs_tol=1e-9)
matrix_z_90 = rot_3d(math.pi / 2, "z")
v_x = [[1.0], [0.0], [0.0]]
rotated = matmul(matrix_z_90, v_x)
assert math.isclose(rotated[0][0], 0.0, abs_tol=1e-9)
assert math.isclose(rotated[1][0], 1.0, abs_tol=1e-9)
assert math.isclose(rotated[2][0], 0.0, abs_tol=1e-9)
def test_rot_3d_invalid_axis() -> None:
"""Testet, dass ungültige Achsen einen ValueError auslösen."""
with pytest.raises(ValueError, match="Ungültige Achse"):
rot_3d(1.0, "w")
with pytest.raises(ValueError):
rot_3d(0.5, "123")
with pytest.raises(ValueError):
rot_3d(0.0, "")
def test_test_functions_execution() -> None:
"""Testet die Ausführung der integrierten Testfunktion."""
test_functions()
test/test_matrixmania/test_matmul.py
+85
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@@ -0,0 +1,85 @@
"""Unit-Tests für die mathematischen Matrixfunktionen matmul und transpose."""
import pytest
from matrixmania.compute import matmul, transpose
def test_matmul_valid() -> None:
"""Testet die Matrixmultiplikation mit gültigen Matrizen."""
a = [
[3.0, 4.0, -1.0, 4.0],
[-2.0, 2.0, 5.0, 1.0],
]
b = [
[1.0, 3.0, -2.0],
[2.0, 5.0, 1.0],
[-1.0, 4.0, -4.0],
[2.0, 3.0, 6.0],
]
expected = [
[20.0, 37.0, 26.0],
[-1.0, 27.0, -8.0],
]
assert matmul(a, b) == expected
def test_matmul_identity() -> None:
"""Testet die Matrixmultiplikation mit der Einheitsmatrix."""
a = [
[1.0, 2.0],
[3.0, 4.0],
]
identity = [
[1.0, 0.0],
[0.0, 1.0],
]
assert matmul(a, identity) == a
def test_matmul_invalid_dimensions() -> None:
"""Testet, dass bei inkompatiblen Matrixdimensionen ValueError geworfen wird."""
a = [[1.0, 2.0], [3.0, 4.0]]
b = [[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]
with pytest.raises(ValueError):
matmul(a, b)
def test_matmul_empty_or_uneven() -> None:
"""Testet matmul mit leeren oder ungleichmäßigen Matrizen."""
with pytest.raises(ValueError):
matmul([], [[1.0]])
with pytest.raises(ValueError):
matmul([[1.0]], [])
with pytest.raises(ValueError):
matmul([[]], [[1.0]])
with pytest.raises(ValueError):
matmul([[1.0]], [[]])
with pytest.raises(ValueError):
matmul([[1.0, 2.0], [3.0]], [[1.0], [2.0]])
with pytest.raises(ValueError):
matmul([[1.0, 2.0], [3.0, 4.0]], [[1.0], [2.0, 3.0]])
def test_transpose_valid() -> None:
"""Testet das Transponieren einer regulären Matrix."""
matrix = [
[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0],
]
expected = [
[1.0, 4.0],
[2.0, 5.0],
[3.0, 6.0],
]
assert transpose(matrix) == expected
def test_transpose_invalid() -> None:
"""Testet, dass transpose bei leeren oder unregelmäßigen Matrizen Fehler wirft."""
with pytest.raises(ValueError):
transpose([])
with pytest.raises(ValueError):
transpose([[]])
with pytest.raises(ValueError):
transpose([[1.0, 2.0], [3.0]])