def test_unit(array):
vector = Vector(array)
vector_unit = vector.unit()
assert math.isclose(vector_unit.norm(), 1)
assert (vector.norm() * vector_unit).is_close(array)
assert vector_unit.is_parallel(vector)
angle = vector.angle_between(vector_unit)
assert math.isclose(angle, 0, abs_tol=ATOL)
def test_two_vectors(arrays):
array_a, array_b = arrays
vector_a = Vector(array_a)
is_perpendicular = vector_a.is_perpendicular(array_b)
is_parallel = vector_a.is_parallel(array_b)
# Two non-zero vectors cannot be both perpendicular and parallel.
assert not (is_perpendicular and is_parallel)
angle = vector_a.angle_between(array_b)
if is_perpendicular:
assert math.isclose(angle, np.pi / 2)
if is_parallel:
assert math.isclose(angle, 0, abs_tol=ATOL) or math.isclose(
angle, np.pi, rel_tol=1e-6)
# The zero vector is perpendicular and parallel to any other vector.
vector_zero = np.zeros(vector_a.size)
assert vector_a.is_perpendicular(vector_zero)
assert vector_a.is_parallel(vector_zero)
# The angle with the zero vector is undefined.
message_expected = "The vectors must have non-zero magnitudes."
with pytest.raises(ValueError, match=message_expected):
vector_a.angle_between(vector_zero)
# The projection of vector B onto A is parallel to A.
vector_b_projected = vector_a.project_vector(array_b)
assert vector_a.is_parallel(vector_b_projected)
# The projection is zero if vectors A and B are perpendicular.
if is_perpendicular:
assert vector_b_projected.is_zero(abs_tol=ATOL)