pypose.RxSO3

pypose.RxSO3 = functools.partial(<class 'pypose.lietensor.lietensor.LieTensor'>, ltype=<pypose.lietensor.lietensor.RxSO3Type object>)

Alias of RxSO3 type LieTensor.

Parameters:

data (Tensor, or list, or ‘int…’) –

A Tensor object, or constructing a Tensor object from list, which defines tensor data (see below), or from ‘int…’, which defines tensor shape.

The shape of Tensor object must be (*, 5), where * is empty, one, or more batched dimensions (the lshape of this LieTensor), otherwise error will be raised.

Internally, RxSO3 LieTensors are stored by concatenating the unit quaternion representing the rotation with a scaling factor:

\[\mathrm{data}[*, :] = [q_x, q_y, q_z, q_w, s], \]

where \(\begin{pmatrix} q_x & q_y & q_z & q_w \end{pmatrix}^T\) is the unit quaternion as in pypose.SO3 and \(s \in \mathbb{R}\) is the scaling factor.

Examples

>>> pp.RxSO3(torch.randn(2, 5))
RxSO3Type LieTensor:
tensor([[-0.3693,  2.5155, -0.5384, -0.8119, -0.4798],
        [-0.4058, -0.5909, -0.4918, -0.2994,  0.5440]])
>>> pp.RxSO3([0, 0, 0, 1, 1])
RxSO3Type LieTensor:
tensor([0., 0., 0., 1., 1.])

If data is tensor-like, the last dimension should correspond to the 5 elements of the above embedding.

Note

It is not advised to construct RxSO3 Tensors by specifying storage sizes with ‘int…’, which does not initialize data.

Consider using pypose.randn_RxSO3 or pypose.identity_RxSO3 instead.

See pypose.Log, pypose.Inv, pypose.Act, pypose.Retr, pypose.Adj, pypose.AdjT, pypose.Jinvp for implementations of relevant operations.