pypose.randn_SE3

class pypose.randn_SE3(*lsize, sigma=1.0, **kwargs)

Returns SE3_type LieTensor filled with the Exponential map of the random se3_type LieTensor generated using pypose.randn_se3().

\[\mathrm{data}[*, :] = \mathrm{Exp}([\tau_x, \tau_y, \tau_z, \delta_x, \delta_y, \delta_z]), \]

where \([\tau_x, \tau_y, \tau_z]\) is generated from a normal distribution \(\mathcal{N}(0, \sigma_t)\), \([\delta_x, \delta_y, \delta_z]\) is generated using pypose.randn_so3() with with standard deviation \(\sigma_r\), and \(\mathrm{Exp}()\) is the Exponential map. Note that standard deviations \(\sigma_t\) and \(\sigma_r\) are specified by sigma (\(\sigma\)), where \(\sigma = (\sigma_t, \sigma_r)\).

For detailed explanation, please see pypose.randn_se3() and pypose.Exp().

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 (\(\sigma_t\) and \(\sigma_r\)) 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 SE3_type LieTensor

Return type

LieTensor

Note

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

• a single float – in which all the elements in the SE3_type share the same sigma, i.e., \(\sigma_{\rm{t}}\) = \(\sigma_{\rm{r}}\) = \(\sigma\).

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

• a tuple of four floats – in which case, the specific sigmas for each translation data are assigned independently, i.e., \(\sigma\) = (\(\sigma_{\rm{tx}}\), \(\sigma_{\rm{ty}}\), \(\sigma_{\rm{tz}}\), \(\sigma_{\rm{r}}\)).

Example

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

>>> pp.randn_SE3(2, sigma=(1.0, 2.0))
SE3Type LieTensor:
tensor([[ 0.2947, -1.6990, -0.5535,  0.4439,  0.2777,  0.0518,  0.8504],
        [ 0.6825,  0.2963,  0.3410,  0.3375, -0.2355,  0.7389, -0.5335]])

For \(\sigma = (\sigma_{tx}, \sigma_{ty}, \sigma_{tz}, \sigma_{r})\)

>>> pp.randn_SE3(2, sigma=(1.0, 1.5, 2.0, 2.0))
SE3Type LieTensor:
tensor([[-1.5689, -0.6772,  0.3580, -0.2509,  0.8257, -0.4950,  0.1018],
        [ 0.2613, -2.7613,  0.2151, -0.8802,  0.2619,  0.3044,  0.2531]])