class_docstr: Implements stochastic gradient descent warm (optionally with momentum).
  
  It has been proposed in `Fixing Weight Decay Regularization in Adam <https://arxiv.org/abs/1711.05101>`_.
  
  Nesterov momentum is based on the formula from
  `On the importance of initialization and momentum in deep learning <http://www.cs.toronto.edu/%7Ehinton/absps/momentum.pdf>`_.
  
  :param params (iterable): iterable of parameters to optimize or dicts defining parameter groups
  :param lr: (float): learning rate
  :param momentum: (float, optional): momentum factor (default: 0)
  :param weight_decay: (float, optional): weight decay (L2 penalty) (default: 0)
  :param dampening: (float, optional): dampening for momentum (default: 0)
  :param nesterov: (bool, optional): enables Nesterov momentum (default: False)
  
  Example:
      >>> optimizer = torch.optim.SGD(model.parameters(), lr=0.1, momentum=0.9)
      >>> optimizer.zero_grad()
      >>> loss_fn(model(input_), target).backward()
      >>> optimizer.step()
  
  .. note::
      The implementation of SGD with Momentum/Nesterov subtly differs from
      Sutskever et. al. and implementations in some other frameworks.
  
      Considering the specific case of Momentum, the update can be written as
  
      .. math::
                v = \rho * v + g \\
                p = p - lr * v
  
      where p, g, v and :math:`\rho` denote the parameters, gradient,
      velocity, and momentum respectively.
  
      This is in contrast to Sutskever et. al. and
      other frameworks which employ an update of the form
  
      .. math::
           v = \rho * v + lr * g \\
           p = p - v
  
      The Nesterov version is analogously modified.
docstr: Performs a single optimization step.
  
  :param closure: (callable, optional): A closure that reevaluates the model
      and returns the loss.
docstr_tok: ["Performs","a","single","optimization","step",".",":","param","closure",":","(","callable",",","optional",")",":","A","closure","that","reevaluates","the","model","and","returns","the","loss","."]
code: def step(self, closure=None):
      """Performs a single optimization step.
  
      :param closure: (callable, optional): A closure that reevaluates the model
          and returns the loss.
      """
      loss = None
      if closure is not None:
          loss = closure()
  
      for group in self.param_groups:
          weight_decay = group["weight_decay"]
          momentum = group["momentum"]
          dampening = group["dampening"]
          nesterov = group["nesterov"]
  
          for p in group["params"]:
              if p.grad is None:
                  continue
              d_p = p.grad.data
              if momentum != 0:
                  param_state = self.state[p]
                  if "momentum_buffer" not in param_state:
                      buf = param_state[
                          "momentum_buffer"
                      ] = torch.zeros_like(p.data)
                      buf.mul_(momentum).add_(d_p)
                  else:
                      buf = param_state["momentum_buffer"]
                      buf.mul_(momentum).add_(1 - dampening, d_p)
                  if nesterov:
                      d_p = d_p.add(momentum, buf)
                  else:
                      d_p = buf
              if weight_decay != 0:
                  p.data.add_(-weight_decay, p.data)
  
      return loss
  
imports: import torch
  from torch.optim.optimizer import Optimizer
  from torch.optim import SGD
label_desc: Use image node_id 3 for calling the SGDW obj's underlying member method code with example usage: obj.step(closure) and returns: loss