class_docstr: Base class to represent the Se2 group.
  
  The SE(2) is the group of rigid body transformations about the origin of two-dimensional Euclidean
  space :math:`R^2` under the operation of composition.
  See more:
  
  Example:
      >>> so2 = So2.identity(1)
      >>> t = torch.ones((1, 2))
      >>> se2 = Se2(so2, t)
      >>> se2
      rotation: Parameter containing:
      tensor([1.+0.j], requires_grad=True)
      translation: Parameter containing:
      tensor([[1., 1.]], requires_grad=True)
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docstr: Converts elements of lie algebra to elements of lie group.
  
  Args:
      v: vector of shape :math:`(B, 3)`.
  
  Example:
      >>> v = torch.ones((1, 3))
      >>> s = Se2.exp(v)
      >>> s.r
      Parameter containing:
      tensor([0.5403+0.8415j], requires_grad=True)
      >>> s.t
      Parameter containing:
      tensor([[0.3818, 1.3012]], requires_grad=True)
docstr_tok: ["Converts","elements","of","lie","algebra","to","elements","of","lie","group",".","Args",":","v",":","vector","of","shape",":","math",":","`","(","B",",","3",")","`",".","Example",":",">",">",">","v","=","torch.ones","(","(","1",",","3",")",")",">",">",">","s","=","Se2.exp","(","v",")",">",">",">","s.r","Parameter","containing",":","tensor","(","[","0.5403+0.8415j","]",",","requires_grad=True",")",">",">",">","s.t","Parameter","containing",":","tensor","(","[","[","0.3818",",","1.3012","]","]",",","requires_grad=True",")"]
code: def exp(v: Tensor) -> Se2:
      """Converts elements of lie algebra to elements of lie group.
  
      Args:
          v: vector of shape :math:`(B, 3)`.
  
      Example:
          >>> v = torch.ones((1, 3))
          >>> s = Se2.exp(v)
          >>> s.r
          Parameter containing:
          tensor([0.5403+0.8415j], requires_grad=True)
          >>> s.t
          Parameter containing:
          tensor([[0.3818, 1.3012]], requires_grad=True)
      """
      check_v_shape(v)
      theta = v[..., 2]
      so2 = So2.exp(theta)
      z = tensor(0.0, device=v.device, dtype=v.dtype)
      theta_nonzeros = theta != 0.0
      a = where(theta_nonzeros, so2.z.imag / theta, z)
      b = where(theta_nonzeros, (1.0 - so2.z.real) / theta, z)
      x = v[..., 0]
      y = v[..., 1]
      t = stack((a * x - b * y, b * x + a * y), -1)
      return Se2(so2, t)
  
imports: from __future__ import annotations
  from typing import Optional, overload
  from kornia.core import Device, Dtype, Module, Parameter, Tensor, concatenate, pad, rand, stack, tensor, where, zeros_like
  from kornia.core.check import KORNIA_CHECK, KORNIA_CHECK_SAME_DEVICES, KORNIA_CHECK_TYPE
  from kornia.geometry.liegroup._utils import check_se2_omega_shape, check_se2_t_shape, check_v_shape
  from kornia.geometry.liegroup.so2 import So2
  from kornia.geometry.vector import Vector2
label_desc: Use image node_id 13 for calling the Se2 obj's underlying member method code with example usage: obj.exp(v) and returns: Se2