text: import math
  import torch
  import torch.nn as nn
  import torch.nn.init as init
  import torch.nn.functional as F
  import torch.optim as optim
  from torch.optim import Optimizer
  
  class LaProp(Optimizer):
      def __init__(self, params, lr=4e-4, betas=(0.9, 0.999), eps=1e-15,
                   weight_decay=0, amsgrad=False, centered=False):
  
          self.steps_before_using_centered = 10
  
          if not 0.0 <= lr:
              raise ValueError("Invalid learning rate: {}".format(lr))
          if not 0.0 <= eps:
              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]))
          defaults = dict(lr=lr, betas=betas, eps=eps,
                          weight_decay=weight_decay, amsgrad=amsgrad, centered=centered)
          super(LaProp, self).__init__(params, defaults)
  
      def step(self, closure=None):
          """Performs a single optimization step.
          Arguments:
              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:
              for p in group['params']:
                  if p.grad is None:
                      continue
                  grad = p.grad.data
                  if grad.is_sparse:
                      raise RuntimeError('Adam does not support sparse gradients, please consider SparseAdam instead')
                  amsgrad = group['amsgrad']
                  centered = group['centered']
  
                  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 learning rates
                      state['exp_avg_lr_1'] = 0.; state['exp_avg_lr_2'] = 0.
                      # Exponential moving average of squared gradient values
                      state['exp_avg_sq'] = torch.zeros_like(p.data)
                      if centered:
                      # Exponential moving average of gradient values as calculated by beta2
                          state['exp_mean_avg_beta2'] = torch.zeros_like(p.data)
                      if amsgrad:
                          # Maintains max of all exp. moving avg. of sq. grad. values
                          state['max_exp_avg_sq'] = torch.zeros_like(p.data)
  
                  exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
                  if centered:
                      exp_mean_avg_beta2 = state['exp_mean_avg_beta2']
                  if amsgrad:
                      max_exp_avg_sq = state['max_exp_avg_sq']
                  beta1, beta2 = group['betas']
  
                  state['step'] += 1
  
                  # Decay the first and second moment running average coefficient
                  exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)
  
                  state['exp_avg_lr_1'] = state['exp_avg_lr_1'] * beta1 + (1 - beta1) * group['lr']
                  state['exp_avg_lr_2'] = state['exp_avg_lr_2'] * beta2 + (1 - beta2)
  
                  bias_correction1 = state['exp_avg_lr_1'] / group['lr'] if group['lr']!=0. else 1. #1 - beta1 ** state['step']
                  step_size = 1 / bias_correction1
  
                  bias_correction2 = state['exp_avg_lr_2']
                  
                  denom = exp_avg_sq
                  if centered:
                      exp_mean_avg_beta2.mul_(beta2).add_(1 - beta2, grad)
                      if state['step'] > self.steps_before_using_centered:
                          mean = exp_mean_avg_beta2 ** 2
                          denom = denom - mean
  
                  if amsgrad:
                      if not (centered and state['step'] <= self.steps_before_using_centered): 
                          # Maintains the maximum of all (centered) 2nd moment running avg. till now
                          torch.max(max_exp_avg_sq, denom, out=max_exp_avg_sq)
                          # Use the max. for normalizing running avg. of gradient
                          denom = max_exp_avg_sq
  
                  denom = denom.div(bias_correction2).sqrt_().add_(group['eps'])
                  step_of_this_grad = grad / denom
                  exp_avg.mul_(beta1).add_( (1 - beta1) * group['lr'], step_of_this_grad)
                  
                  p.data.add_(-step_size, exp_avg )
                  if group['weight_decay'] != 0:
                      p.data.add_( - group['weight_decay'], p.data)
  
          return loss