class_docstr: Base class to represent the Se3 group.
  
  The SE(3) is the group of rigid body transformations about the origin of three-dimensional Euclidean
  space :math:`R^3` under the operation of composition.
  See more: https://ingmec.ual.es/~jlblanco/papers/jlblanco2010geometry3D_techrep.pdf
  
  Example:
      >>> q = Quaternion.identity()
      >>> s = Se3(q, torch.ones(3))
      >>> s.r
      Parameter containing:
      tensor([1., 0., 0., 0.], requires_grad=True)
      >>> s.t
      Parameter containing:
      tensor([1., 1., 1.], requires_grad=True)
docstr: Converts elements from vector space to lie algebra.
  
  Args:
      v: vector of shape :math:`(B, 6)`.
  
  Returns:
      matrix of shape :math:`(B, 4, 4)`.
  
  Example:
      >>> v = torch.ones((1, 6))
      >>> m = Se3.hat(v)
      >>> m
      tensor([[[ 0., -1.,  1.,  1.],
               [ 1.,  0., -1.,  1.],
               [-1.,  1.,  0.,  1.],
               [ 0.,  0.,  0.,  0.]]])
code: def hat(v: Tensor) -> Tensor:
      """Converts elements from vector space to lie algebra.
  
      Args:
          v: vector of shape :math:`(B, 6)`.
  
      Returns:
          matrix of shape :math:`(B, 4, 4)`.
  
      Example:
          >>> v = torch.ones((1, 6))
          >>> m = Se3.hat(v)
          >>> m
          tensor([[[ 0., -1.,  1.,  1.],
                   [ 1.,  0., -1.,  1.],
                   [-1.,  1.,  0.,  1.],
                   [ 0.,  0.,  0.,  0.]]])
      """
      # KORNIA_CHECK_SHAPE(v, ["B", "6"])  # FIXME: resolve shape bugs. @edgarriba
      upsilon, omega = v[..., :3], v[..., 3:]
      rt = concatenate((So3.hat(omega), upsilon[..., None]), -1)
      return pad(rt, (0, 0, 0, 1))
  
imports: from __future__ import annotations
  from typing import Optional
  from kornia.core import Device, Dtype, Module, Parameter, Tensor, concatenate, eye, pad, stack, tensor, where, zeros_like
  from kornia.core.check import KORNIA_CHECK, KORNIA_CHECK_SAME_DEVICES
  from kornia.geometry.liegroup.so3 import So3
  from kornia.geometry.linalg import batched_dot_product
  from kornia.geometry.quaternion import Quaternion
  from kornia.geometry.vector import Vector3
label_desc: Use image node_id 14 for calling the Se3 obj's underlying member method code with example usage: obj.hat(v) and returns: pad