code: def step(self, closure=None):
      loss = None
      if closure is not None:
          with torch.enable_grad():
              loss = closure()
  
      for group in self.param_groups:
          for p in group["params"]:
              if p.grad is None:
                  continue
              grad = p.grad.float()
              if grad.is_sparse:
                  raise RuntimeError(
                      "RAdam does not support sparse gradients"
                  )
  
              p_fp32 = p.float()
  
              state = self.state[p]
  
              if len(state) == 0:
                  state["step"] = 0
                  state["exp_avg"] = torch.zeros_like(p_fp32)
                  state["exp_avg_sq"] = torch.zeros_like(p_fp32)
              else:
                  state["exp_avg"] = state["exp_avg"].type_as(p_fp32)
                  state["exp_avg_sq"] = state["exp_avg_sq"].type_as(
                      p_fp32
                  )
  
              exp_avg, exp_avg_sq = (
                  state["exp_avg"],
                  state["exp_avg_sq"],
              )
              beta1, beta2 = group["betas"]
  
              exp_avg_sq.mul_(beta2).addcmul_(
                  grad, grad, value=1 - beta2
              )
              exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1)
  
              state["step"] += 1
              buffered = group["buffer"][int(state["step"] % 10)]
              if state["step"] == buffered[0]:
                  num_sma, step_size = buffered[1], buffered[2]
              else:
                  buffered[0] = state["step"]
                  beta2_t = beta2 ** state["step"]
                  num_sma_max = 2 / (1 - beta2) - 1
                  num_sma = num_sma_max - 2 * state[
                      "step"
                  ] * beta2_t / (1 - beta2_t)
                  buffered[1] = num_sma
  
                  # more conservative since it's an approximated value
                  if num_sma >= 5:
                      step_size = (
                          group["lr"]
                          * math.sqrt(
                              (1 - beta2_t)
                              * (num_sma - 4)
                              / (num_sma_max - 4)
                              * (num_sma - 2)
                              / num_sma
                              * num_sma_max
                              / (num_sma_max - 2)
                          )
                          / (1 - beta1 ** state["step"])
                      )
                  else:
                      step_size = group["lr"] / (
                          1 - beta1 ** state["step"]
                      )
                  buffered[2] = step_size
  
              if group["weight_decay"] != 0:
                  p_fp32.add_(
                      p_fp32, alpha=-group["weight_decay"] * group["lr"]
                  )
  
              # more conservative since it's an approximated value
              if num_sma >= 5:
                  denom = exp_avg_sq.sqrt().add_(group["eps"])
                  p_fp32.addcdiv_(exp_avg, denom, value=-step_size)
              else:
                  p_fp32.add_(exp_avg, alpha=-step_size)
  
              p.copy_(p_fp32)
  
      return loss
  
file_path: pytorch-image-models/timm/optim/radam.py
imports: import math
  import torch
  from torch.optim.optimizer import Optimizer
label_desc: Use image node_id 3 for calling the RAdam obj's underlying member method code with example usage: obj.step(closure) and returns: loss