text: """
  Licensed to the Apache Software Foundation (ASF) under one
  or more contributor license agreements.  See the NOTICE file
  distributed with this work for additional information
  regarding copyright ownership.  The ASF licenses this file
  to you under the Apache License, Version 2.0 (the
  "License"); you may not use this file except in compliance
  with the License.  You may obtain a copy of the License at
  
    http://www.apache.org/licenses/LICENSE-2.0
  
  Unless required by applicable law or agreed to in writing,
  software distributed under the License is distributed on an
  "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
  KIND, either express or implied.  See the License for the
  specific language governing permissions and limitations
  under the License.
  @CREDIT: https://github.com/jettify/pytorch-optimizer/tree/master/torch_optimizer
  """
  from typing import Tuple, Union, Iterable, Dict, Any, Optional, Callable
  
  from torch.optim.optimizer import Optimizer
  from torch import Tensor
  
  import torch
  
  __all__ = ('NovoGrad',)
  
  
  class NovoGrad(Optimizer):
      r"""Implements Novograd optimization algorithm.
  
      It has been proposed in `Stochastic Gradient Methods with Layer-wise
      Adaptive Moments for Training of Deep Networks`__.
  
      Arguments:
          params: iterable of parameters to optimize or dicts defining
              parameter groups
          lr: learning rate (default: 1e-3)
          betas: coefficients used for computing
              running averages of gradient and its square (default: (0.95, 0))
          eps: term added to the denominator to improve
              numerical stability (default: 1e-8)
          weight_decay: weight decay (L2 penalty) (default: 0)
          grad_averaging: gradient averaging (default: False)
          amsgrad: whether to use the AMSGrad variant of this
              algorithm from the paper `On the Convergence of Adam and Beyond`
              (default: False)
  
      Example:
          >>> import torch_optimizer as optim
          >>> optimizer = optim.Yogi(model.parameters(), lr=0.1)
          >>> optimizer.zero_grad()
          >>> loss_fn(model(input), target).backward()
          >>> scheduler = StepLR(optimizer, step_size=1, gamma=0.7)
          >>> optimizer.step()
          >>> scheduler.step()
  
      __ https://arxiv.org/abs/1905.11286
  
      Note:
          Reference code: https://github.com/NVIDIA/DeepLearningExamples
      """
  
      def __init__(
          self,
          params: Union[Iterable[Tensor], Iterable[Dict[str, Any]]],
          lr: float = 1e-3,
          betas: Tuple[float, float] = (0.95, 0),
          eps: float = 1e-8,
          weight_decay: float = 0,
          grad_averaging: bool = False,
          amsgrad: bool = False,
      ):
          if lr <= 0.0:
              raise ValueError('Invalid learning rate: {}'.format(lr))
          if eps < 0.0:
              raise ValueError('Invalid epsilon value: {}'.format(eps))
          if not 0.0 <= betas[0] < 1.0:
              raise ValueError(
                  'Invalid beta parameter at index 0: {}'.format(betas[0])
              )
          if not 0.0 <= betas[1] < 1.0:
              raise ValueError(
                  'Invalid beta parameter at index 1: {}'.format(betas[1])
              )
          if weight_decay < 0:
              raise ValueError(
                  'Invalid weight_decay value: {}'.format(weight_decay)
              )
          defaults = dict(
              lr=lr,
              betas=betas,
              eps=eps,
              weight_decay=weight_decay,
              grad_averaging=grad_averaging,
              amsgrad=amsgrad,
          )
  
          super(NovoGrad, self).__init__(params, defaults)
  
      def __setstate__(self, state: dict) -> None:
          super(NovoGrad, self).__setstate__(state)
          for group in self.param_groups:
              group.setdefault('amsgrad', False)
  
      def step(self,
               closure: Optional[Callable[[], float]] = None) -> Optional[float]:
          r"""Performs a single optimization step.
  
          Arguments:
              closure: 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:
              for p in group['params']:
                  if p.grad is None:
                      continue
                  grad = p.grad.data
                  if grad.is_sparse:
                      msg = (
                          'NovoGrad does not support sparse gradients, '
                          'please consider SparseAdam instead'
                      )
                      raise RuntimeError(msg)
                  amsgrad = group['amsgrad']
  
                  state = self.state[p]
  
                  # State initialization
                  if len(state) == 0:
                      state['step'] = 0
                      # Exponential moving average of gradient values
                      state['exp_avg'] = torch.zeros_like(p.data)
                      # Exponential moving average of squared gradient values
                      state['exp_avg_sq'] = torch.zeros([]).to(
                          state['exp_avg'].device
                      )
                      if amsgrad:
                          # Maintains max of all exp. moving avg. of sq.
                          # grad. values
                          state['max_exp_avg_sq'] = torch.zeros([]).to(
                              state['exp_avg'].device
                          )
  
                  exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
                  if amsgrad:
                      max_exp_avg_sq = state['max_exp_avg_sq']
                  beta1, beta2 = group['betas']
  
                  state['step'] += 1
  
                  norm = torch.sum(torch.pow(grad, 2))
  
                  if exp_avg_sq == 0:
                      exp_avg_sq.copy_(norm)
                  else:
                      exp_avg_sq.mul_(beta2).add_(1 - beta2, norm)
  
                  if amsgrad:
                      # Maintains the maximum of all 2nd moment running avg.
                      # till now
                      torch.max(max_exp_avg_sq, exp_avg_sq, out=max_exp_avg_sq)
                      # Use the max. for normalizing running avg. of gradient
                      denom = max_exp_avg_sq.sqrt().add_(group['eps'])
                  else:
                      denom = exp_avg_sq.sqrt().add_(group['eps'])
  
                  grad.div_(denom)
                  if group['weight_decay'] != 0:
                      grad.add_(group['weight_decay'], p.data)
                  if group['grad_averaging']:
                      grad.mul_(1 - beta1)
                  exp_avg.mul_(beta1).add_(grad)
  
                  p.data.add_(-group['lr'], exp_avg)
  
          return loss
  