pypose.randn_rxso3

class pypose.randn_rxso3(*lsize, sigma=1.0, **kwargs)

Returns rxso3_type LieTensor filled with random numbers.

\[\mathrm{data}[*, :] = [\delta_x, \delta_y, \delta_z, \log s], \]

where rotation \([\delta_x, \delta_y, \delta_z]\) is generated using pypose.randn_so3() with standard deviation \(\sigma_r\), scale \(\log s\) is generated from a normal distribution \(\mathcal{N}(0, \sigma_s)\). Note that standard deviations \(\sigma_r\) and \(\sigma_s\) are specified by sigma (\(\sigma\)), where \(\sigma = (\sigma_r, \sigma_s)\).

Parameters:

• lsize (int...) – a sequence of integers defining the lshape of the output tensor. Can be a variable number of arguments or a collection like a list or tuple.

• sigma (float or (float...), optional) – standard deviation (\(\sigma_r\), and \(\sigma_s\)) for the two normal distribution. Default: 1.0.

• requires_grad (bool, optional) – If autograd should record operations on the returned tensor. Default: False.

• generator (torch.Generator, optional) – a pseudorandom number generator for sampling

• dtype (torch.dtype, optional) – the desired data type of returned tensor. Default: None. If None, uses a global default (see torch.set_default_tensor_type()).

• layout (torch.layout, optional) – the desired layout of returned Tensor. Default: torch.strided.

• device (torch.device, optional) – the desired device of returned tensor. Default: None. If None, uses the current device for the default tensor type (see torch.set_default_tensor_type()). Device will be the CPU for CPU tensor types and the current CUDA device for CUDA tensor types.

Returns:

a rxso3_type LieTensor

Return type:

LieTensor

Note

The parameter \(\sigma\) can either be:

• a single float – in which all the elements in the rxso3_type share the same sigma, i.e., \(\sigma_{\rm{r}}\) = \(\sigma_{\rm{s}}\) = \(\sigma\).

• a tuple of two floats – in which case, the specific sigmas for the two parts are assigned independently, i.e., \(\sigma\) = (\(\sigma_{\rm{r}}\), \(\sigma_{\rm{s}}\)).

Example

For \(\sigma = (\sigma_r, \sigma_s)\)

>>> pp.randn_rxso3(2, sigma=(1.0, 2.0))
rxso3Type LieTensor:
tensor([[-0.5033, -0.4102, -0.6213, -3.5049],
        [-0.3185,  0.1053, -0.0816, -1.1907]])