docstr: Performs one symmetric iteration
  
  Performs one iteration of the SyN algorithm:
      1.Compute forward
      2.Compute backward
      3.Update forward
      4.Update backward
      5.Compute inverses
      6.Invert the inverses
  
  Returns
  -------
  der : float
      the derivative of the energy profile, computed by fitting a
      quadratic function to the energy values at the latest T iterations,
      where T = self.energy_window. If the current iteration is less than
      T then np.inf is returned instead.
code: def _iterate(self):
      """Performs one symmetric iteration
  
      Performs one iteration of the SyN algorithm:
          1.Compute forward
          2.Compute backward
          3.Update forward
          4.Update backward
          5.Compute inverses
          6.Invert the inverses
  
      Returns
      -------
      der : float
          the derivative of the energy profile, computed by fitting a
          quadratic function to the energy values at the latest T iterations,
          where T = self.energy_window. If the current iteration is less than
          T then np.inf is returned instead.
      """
      # Acquire current resolution information from scale spaces
      current_moving = self.moving_ss.get_image(self.current_level)
      current_static = self.static_ss.get_image(self.current_level)
  
      current_disp_shape = self.static_ss.get_domain_shape(
          self.current_level
      )
      current_disp_grid2world = self.static_ss.get_affine(
          self.current_level
      )
      current_disp_world2grid = self.static_ss.get_affine_inv(
          self.current_level
      )
      current_disp_spacing = self.static_ss.get_spacing(
          self.current_level
      )
  
      # Warp the input images (smoothed to the current scale) to the common
      # (reference) space at the current resolution
      wstatic = self.static_to_ref.transform_inverse(
          current_static,
          "linear",
          None,
          current_disp_shape,
          current_disp_grid2world,
      )
      wmoving = self.moving_to_ref.transform_inverse(
          current_moving,
          "linear",
          None,
          current_disp_shape,
          current_disp_grid2world,
      )
      # Pass both images to the metric. Now both images are sampled on the
      # reference grid (equal to the static image's grid) and the direction
      # doesn't change across scales
      self.metric.set_moving_image(
          wmoving,
          current_disp_grid2world,
          current_disp_spacing,
          self.static_direction,
      )
      self.metric.use_moving_image_dynamics(
          current_moving, self.moving_to_ref.inverse()
      )
  
      self.metric.set_static_image(
          wstatic,
          current_disp_grid2world,
          current_disp_spacing,
          self.static_direction,
      )
      self.metric.use_static_image_dynamics(
          current_static, self.static_to_ref.inverse()
      )
  
      # Initialize the metric for a new iteration
      self.metric.initialize_iteration()
      if self.callback is not None:
          self.callback(self, RegistrationStages.ITER_START)
  
      # Compute the forward step (to be used to update the forward transform)
      fw_step = np.array(self.metric.compute_forward())
  
      # set zero displacements at the boundary
      fw_step = self.__set_no_boundary_displacement(fw_step)
  
      # Normalize the forward step
      nrm = np.sqrt(
          np.sum((fw_step / current_disp_spacing) ** 2, -1)
      ).max()
      if nrm > 0:
          fw_step /= nrm
  
      # Add to current total field
      self.static_to_ref.forward, md_forward = self.update(
          self.static_to_ref.forward,
          fw_step,
          current_disp_world2grid,
          self.step_length,
      )
      del fw_step
  
      # Keep track of the forward energy
      fw_energy = self.metric.get_energy()
  
      # Compose backward step (to be used to update the backward transform)
      bw_step = np.array(self.metric.compute_backward())
  
      # set zero displacements at the boundary
      bw_step = self.__set_no_boundary_displacement(bw_step)
  
      # Normalize the backward step
      nrm = np.sqrt(
          np.sum((bw_step / current_disp_spacing) ** 2, -1)
      ).max()
      if nrm > 0:
          bw_step /= nrm
  
      # Add to current total field
      self.moving_to_ref.forward, md_backward = self.update(
          self.moving_to_ref.forward,
          bw_step,
          current_disp_world2grid,
          self.step_length,
      )
      del bw_step
  
      # Keep track of the energy
      bw_energy = self.metric.get_energy()
      der = np.inf
      n_iter = len(self.energy_list)
      if len(self.energy_list) >= self.energy_window:
          der = self._get_energy_derivative()
  
      if self.verbosity >= VerbosityLevels.DIAGNOSE:
          ch = "-" if np.isnan(der) else der
          logger.info(
              "%d:\t%0.6f\t%0.6f\t%0.6f\t%s"
              % (
                  n_iter,
                  fw_energy,
                  bw_energy,
                  fw_energy + bw_energy,
                  ch,
              )
          )
  
      self.energy_list.append(fw_energy + bw_energy)
  
      self.__invert_models(
          current_disp_world2grid, current_disp_spacing
      )
  
      # Free resources no longer needed to compute the forward and backward
      # steps
      if self.callback is not None:
          self.callback(self, RegistrationStages.ITER_END)
      self.metric.free_iteration()
  
      return der
  
imports: import logging
  import abc
  import numpy
  import numpy.linalg
  import nibabel
  from nibabel.streamlines import ArraySequence
  from dipy.align import vector_fields
  from dipy.align import floating
  from dipy.align import VerbosityLevels
  from dipy.align import Bunch
  from dipy.align.scalespace import ScaleSpace
label_desc: Use image node_id 7 for calling the SymmetricDiffeomorphicRegistration obj's underlying member method code with example usage: obj._iterate() and returns: der