pypose.randn_Sim3

class pypose.randn_Sim3(*lsize, sigma=1.0, **kwargs)

Returns Sim3_type LieTensor filled with the Exponential map of the random sim3_type LieTensor generated using randn_sim3().

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

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

For detailed explanation, please see pypose.randn_sim3() 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 (\(\sigma_t\), \(\sigma_r\), and \(\sigma_s\)) for the three 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 Sim_type LieTensor

Return type

LieTensor

Note

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

• a single float – in which all the elements in the Sim3_type share the same sigma, i.e., \(\sigma_{\rm{t}}\) = \(\sigma_{\rm{r}}\) = \(\sigma_{\rm{s}}\) = \(\sigma\).

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

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

Example

For \(\sigma = (\sigma_{\rm{t}}, \sigma_{\rm{r}}, \sigma_{\rm{s}})\)

>>> pp.randn_Sim3(sigma=(1.0, 1.0, 2.0))
Sim3Type LieTensor:
LieTensor([-0.7667, -0.0981,  0.8168,  0.0931,  0.0917,  0.0939,  0.9870, 0.2391])

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

>>> pp.randn_Sim3(2, sigma=(1.0, 1.0, 2.0, 1.0, 2.0))
Sim3Type LieTensor:
tensor([[-0.0117,  0.0708,  1.6853,  0.1089,  0.4186, -0.0877,  0.8973,  0.3969],
        [ 0.2106, -0.0694, -0.0574, -0.2902, -0.4806, -0.0815,  0.8235,  0.0134]])