code: def step(self, closure=None):
      loss = None
      if closure is not None:
          loss = closure()
  
      for group in self.param_groups:
          for p in group["params"]:
              if p.grad is None:
                  continue
              grad = p.grad.data.float()
              if grad.is_sparse:
                  raise RuntimeError(
                      "Ralamb does not support sparse gradients"
                  )
  
              p_data_fp32 = p.data.float()
  
              state = self.state[p]
  
              if len(state) == 0:
                  state["step"] = 0
                  state["exp_avg"] = torch.zeros_like(p_data_fp32)
                  state["exp_avg_sq"] = torch.zeros_like(p_data_fp32)
              else:
                  state["exp_avg"] = state["exp_avg"].type_as(
                      p_data_fp32
                  )
                  state["exp_avg_sq"] = state["exp_avg_sq"].type_as(
                      p_data_fp32
                  )
  
              exp_avg, exp_avg_sq = (
                  state["exp_avg"],
                  state["exp_avg_sq"],
              )
              beta1, beta2 = group["betas"]
  
              # Decay the first and second moment running average coefficient
              # m_t
              exp_avg.mul_(beta1).add_(1 - beta1, grad)
              # v_t
              exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)
  
              state["step"] += 1
              buffered = self.buffer[int(state["step"] % 10)]
  
              if state["step"] == buffered[0]:
                  N_sma, radam_step_size = buffered[1], buffered[2]
              else:
                  buffered[0] = state["step"]
                  beta2_t = beta2 ** state["step"]
                  N_sma_max = 2 / (1 - beta2) - 1
                  N_sma = N_sma_max - 2 * state["step"] * beta2_t / (
                      1 - beta2_t
                  )
                  buffered[1] = N_sma
  
                  # more conservative since it's an approximated value
                  if N_sma >= 5:
                      radam_step_size = (
                          group["lr"]
                          * math.sqrt(
                              (1 - beta2_t)
                              * (N_sma - 4)
                              / (N_sma_max - 4)
                              * (N_sma - 2)
                              / N_sma
                              * N_sma_max
                              / (N_sma_max - 2)
                          )
                          / (1 - beta1 ** state["step"])
                      )
                  else:
                      radam_step_size = group["lr"] / (
                          1 - beta1 ** state["step"]
                      )
                  buffered[2] = radam_step_size
  
              if group["weight_decay"] != 0:
                  p_data_fp32.add_(
                      -group["weight_decay"] * group["lr"], p_data_fp32
                  )
  
              # more conservative since it's an approximated value
              radam_step = p_data_fp32.clone()
              if N_sma >= 5:
                  denom = exp_avg_sq.sqrt().add_(group["eps"])
                  radam_step.addcdiv_(-radam_step_size, exp_avg, denom)
              else:
                  radam_step.add_(-radam_step_size, exp_avg)
  
              radam_norm = radam_step.pow(2).sum().sqrt()
              weight_norm = p.data.pow(2).sum().sqrt().clamp(0, 10)
              if 0 in (weight_norm, radam_norm):
                  trust_ratio = 1
              else:
                  trust_ratio = weight_norm / radam_norm
  
              state["weight_norm"] = weight_norm
              state["adam_norm"] = radam_norm
              state["trust_ratio"] = trust_ratio
  
              if N_sma >= 5:
                  p_data_fp32.addcdiv_(
                      -radam_step_size * trust_ratio, exp_avg, denom
                  )
              else:
                  p_data_fp32.add_(
                      -radam_step_size * trust_ratio, exp_avg
                  )
  
              p.data.copy_(p_data_fp32)
  
      return loss
  
imports: from torch.optim.optimizer import Optimizer
  import torch
  import math
label_desc: Use image node_id 2 for calling the Ralamb obj's underlying member method code with example usage: obj.step(closure) and returns: loss