def test_reference_vwu_projection():
    """When a non-orthogonal vector is provided, the setter should project out
    any component along reference_uvw so the stored vector is orthogonal.
    """
    pa = stats.PolarAzimuthal()  # default reference_uvw == (0, 0, 1)

    # Provide a vector that is not orthogonal to (0,0,1)
    pa.reference_vwu = (2.0, 0.5, 0.3)

    reference_v = np.asarray(pa.reference_vwu)
    reference_u = np.asarray(pa.reference_uvw)

    # reference_v should be orthogonal to reference_u
    assert abs(np.dot(reference_v, reference_u)) < 1e-6


def test_reference_vwu_normalization():
    """When a non-normalized vector is provided, the setter should normalize
    the projected vector to unit length.
    """
    pa = stats.PolarAzimuthal()  # default reference_uvw == (0, 0, 1)

    # Provide a vector that is neither orthogonal to (0,0,1) nor unit-length
    pa.reference_vwu = (2.0, 0.5, 0.3)

    reference_v = np.asarray(pa.reference_vwu)

    # reference_v should be unit length
    assert np.isclose(np.linalg.norm(reference_v), 1.0, atol=1e-12)