class_docstr: Class for modeling a linear 1D localization problem.
  
  The state is made of a scalar position and scalar speed, thus a 2D vector.
  A sensor provides acceleration inputs, while another one provides sparse
  measurements of the position.
docstr: Compute the Jacobian associated to the affine propagation..
  
  The Jacobian is given by :math:`\begin{bmatrix} 1 & dt \\ & 1
  \end{bmatrix}`.
  
  Parameters
  ----------
  state : unused
  sensor_input : array-like, shape=[2]
      Vector representing the information from the accelerometer.
  
  Returns
  -------
  jacobian : array-like, shape=[dim, dim]
      Jacobian of the propagation.
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code: def propagation_jacobian(self, state, sensor_input):
      r"""Compute the Jacobian associated to the affine propagation..
  
      The Jacobian is given by :math:`\begin{bmatrix} 1 & dt \\ & 1
      \end{bmatrix}`.
  
      Parameters
      ----------
      state : unused
      sensor_input : array-like, shape=[2]
          Vector representing the information from the accelerometer.
  
      Returns
      -------
      jacobian : array-like, shape=[dim, dim]
          Jacobian of the propagation.
      """
      dt, _ = sensor_input
      dim = self.group.dim
      position_line = gs.hstack(
          (gs.eye(dim // 2), dt * gs.eye(dim // 2))
      )
      speed_line = gs.hstack(
          (gs.zeros((dim // 2, dim // 2)), gs.eye(dim // 2))
      )
      jac = gs.vstack((position_line, speed_line))
      return jac
  
imports: import geomstats.backend
  from geomstats.geometry.euclidean import Euclidean
  from geomstats.geometry.matrices import Matrices
  from geomstats.geometry.special_euclidean import SpecialEuclidean
label_desc: Use image node_id 3 for calling the LocalizationLinear obj's underlying member method code with example usage: obj.propagation_jacobian(state, sensor_input) and returns: jac