is_real

Quaternion.is_real() → bool

Returns a bool value, where True if quaternion is real.

A real quaternion has all elements of its vector part equal to zero: \(\mathbf{q} = w + 0i + 0j + 0k = \begin{pmatrix} q_w & \mathbf{0}\end{pmatrix}\)

\[\begin{split}\left\{ \begin{array}{ll} \mathrm{True} & \: \mathbf{q}_v = \begin{bmatrix} 0 & 0 & 0 \end{bmatrix} \\ \mathrm{False} & \: \mathrm{otherwise} \end{array} \right.\end{split}\]

Returns:

out – Boolean equal to True if \(q_v = 0\).

Return type:

bool

Examples

>>> q = Quaternion()
>>> q
Quaternion([1., 0., 0., 0.])
>>> q.is_real()
True
>>> q = Quaternion([0., 1., 2., 3.])
>>> q
Quaternion([0.        , 0.26726124, 0.53452248, 0.80178373])
>>> q.is_real()
False
>>> q = Quaternion([1., 2., 3., 4.])
>>> q
Quaternion([0.18257419, 0.36514837, 0.54772256, 0.73029674])
>>> q.is_real()
False
>>> q = Quaternion([5., 0., 0., 0.])    # All quaternions are normalized, by default
>>> q
Quaternion([1., 0., 0., 0.])
>>> q.is_real()
True