pypose.randn_SO3

class pypose.randn_SO3(*lsize, sigma=1.0, **kwargs)

Returns SO3_type LieTensor filled with the Exponential map of the random so3_type LieTensor.

\[\begin{aligned} \mathrm{data}[*, :] &= \mathrm{Exp}([\delta_x, \delta_y, \delta_z]) \\ &= \mathrm{Exp}([\delta_x', \delta_y', \delta_z'] \cdot \theta), \end{aligned} \]

where \([\delta_x', \delta_y', \delta_z']\) is generated from uniform distribution \(\mathcal{U}_{\mathrm{s}}\) on a standard sphere, \(\mathrm{Exp}()\) is the Exponential map, \(\theta\) is generated from a normal distribution \(\mathcal{N}(0, \sigma)\) where \(\sigma\) (sigma) is the standard deviation.

For detailed explanation, please see pypose.randn_so3() 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, optional) – standard deviation for the angle of the generated rotation. 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 SO3_type LieTensor.

Return type

LieTensor

Example

>>> pp.randn_SO3(sigma=0.1, requires_grad=True)
SO3Type LieTensor:
LieTensor([ 0.0082,  0.0077, -0.0018,  0.9999], requires_grad=True)
>>> pp.randn_SO3(2, sigma=0.1, requires_grad=True, dtype=torch.float64)
SO3Type LieTensor:
tensor([[ 2.6857e-03, -8.3274e-03, -6.0457e-04,  9.9996e-01],
        [ 3.8711e-02, -6.3148e-02, -1.9388e-02,  9.9706e-01]],
        dtype=torch.float64, requires_grad=True)

Visualization of pypose.randn_SO3(). A total of 5000 random rotations are sampled using pypose.randn_SO3() and applied to the basepoint [0, 0, 1] (shown in blue).