class_docstr: Class that performs the main optimization.
  Keeps track of the current x and iterates through data to learn x given the penalty and order.
class_docstr_tok: ["Class","that","performs","the","main","optimization",".","Keeps","track","of","the","current","x","and","iterates","through","data","to","learn","x","given","the","penalty","and","order","."]
docstr: Completes the forward operation and computes gradients for learnability and penalty.
docstr_tok: ["Completes","the","forward","operation","and","computes","gradients","for","learnability","and","penalty","."]
code: def forward_and_backward(self, s, xsub, ysub, retain_graph=False):
      """
      Completes the forward operation and computes gradients for learnability and penalty.
      """
      f_train = self.f_train(s, xsub, ysub)
      pen = self.penalty(s).unsqueeze(0).unsqueeze(0)
      # pylint: disable=E1102
      grad_outputs = torch.tensor(
          [[1]], dtype=torch.get_default_dtype(), device=self.device
      )
      (g1,) = torch.autograd.grad(
          [f_train], [self.x], grad_outputs, retain_graph=True
      )
      # pylint: disable=E1102
      grad_outputs = torch.tensor(
          [[1]], dtype=torch.get_default_dtype(), device=self.device
      )
      (g2,) = torch.autograd.grad(
          [pen], [self.x], grad_outputs, retain_graph=retain_graph
      )
      return f_train, pen, g1, g2
  
imports: import time
  import numpy
  import scipy.special
  import torch
  import torch.nn
  from .None import constants
  from .None import syssettings
  from .fginitialize import ChunkDataLoader
label_desc: Use image node_id 3 for calling the Solver obj's underlying member method code with example usage: obj.forward_and_backward(s, xsub, ysub, retain_graph) and returns: f_train,  pen,  g1,  g2