def test_Pullback_GivenRotatedBasis_ReturnRotatedVectors(self):
transformation = OrthogonalTransformation(x=(0, 1, 0),
y=(-1, 0, 0),
z=(0, 0, 1))
vectors = [(0, 1, 0), (-1, 1, 0), (-1, 1, 1)]
expected_vectors = [(1, 0, 0), (1, 1, 0), (1, 1, 1)]
assert_allclose(transformation.pullback(vectors), expected_vectors)
def test_PullBack_ComplexExample_ReturnCorrectVectors(self):
transformation = OrthogonalTransformation(x=(-2, 0, 2),
y=(-1, 2, -1),
z=(-1, -1, -1))
vectors = ((+0, +0, +0), (-2, +0, +2), (-2, -2, +4), (+0, -6, +6),
(+2, -8, +6), (+4, -8, +4), (+4, -6, +2), (+2, -2, +0))
expected_vectors = ((+0, +0, +0), (+2 * sqrt(2), +0, +0),
(+3 * sqrt(2), -1 * sqrt(6),
+0), (+3 * sqrt(2), -3 * sqrt(6),
+0), (+2 * sqrt(2), -4 * sqrt(6),
+0), (+0, -4 * sqrt(6), +0),
(-1 * sqrt(2), -3 * sqrt(6),
+0), (-1 * sqrt(2), -1 * sqrt(6), +0))
assert_allclose(transformation.pullback(vectors),
expected_vectors,
atol=1e-8)
def test_PullBack_ComplexExample_ReturnCorrectVectors(self):
transformation = OrthogonalTransformation(x=(-2, 0, 2), y=(-1, 2, -1), z=(-1, -1, -1))
vectors = (
(+0, +0, +0),
(-2, +0, +2),
(-2, -2, +4),
(+0, -6, +6),
(+2, -8, +6),
(+4, -8, +4),
(+4, -6, +2),
(+2, -2, +0),
)
expected_vectors = (
(+0, +0, +0),
(+2 * sqrt(2), +0, +0),
(+3 * sqrt(2), -1 * sqrt(6), +0),
(+3 * sqrt(2), -3 * sqrt(6), +0),
(+2 * sqrt(2), -4 * sqrt(6), +0),
(+0, -4 * sqrt(6), +0),
(-1 * sqrt(2), -3 * sqrt(6), +0),
(-1 * sqrt(2), -1 * sqrt(6), +0),
)
assert_allclose(transformation.pullback(vectors), expected_vectors, atol=1e-8)
def test_Pullback_GivenRotatedBasis_ReturnRotatedVectors(self):
transformation = OrthogonalTransformation(x=(0, 1, 0), y=(-1, 0, 0), z=(0, 0, 1))
vectors = [(0, 1, 0), (-1, 1, 0), (-1, 1, 1)]
expected_vectors = [(1, 0, 0), (1, 1, 0), (1, 1, 1)]
assert_allclose(transformation.pullback(vectors), expected_vectors)
def test_Pullback_GivenUnitBasis_ReturnOriginalVectors(self):
transformation = OrthogonalTransformation(x=(1, 0, 0), y=(0, 1, 0), z=(0, 0, 1))
vectors = [(1, 0, 0), (1, 1, 0), (1, 1, 1)]
assert_allclose(transformation.pullback(vectors), vectors)
def test_Pullback_GivenUnitBasis_ReturnOriginalVectors(self):
transformation = OrthogonalTransformation(x=(1, 0, 0),
y=(0, 1, 0),
z=(0, 0, 1))
vectors = [(1, 0, 0), (1, 1, 0), (1, 1, 1)]
assert_allclose(transformation.pullback(vectors), vectors)