""" Nvidia NovoGrad Optimizer.
Original impl by Nvidia from Jasper example:
    - https://github.com/NVIDIA/DeepLearningExamples/blob/master/PyTorch/SpeechRecognition/Jasper
Paper: `Stochastic Gradient Methods with Layer-wise Adaptive Moments for Training of Deep Networks`
    - https://arxiv.org/abs/1905.11286
"""

import torch
from torch.optim.optimizer import Optimizer
import math


class NvNovoGrad(Optimizer):
    """
    Implements Novograd algorithm.

    Args:
        params (iterable): iterable of parameters to optimize or dicts defining
            parameter groups
        lr (float, optional): learning rate (default: 1e-3)
        betas (Tuple[float, float], optional): coefficients used for computing
            running averages of gradient and its square (default: (0.95, 0.98))
        eps (float, optional): term added to the denominator to improve
            numerical stability (default: 1e-8)
        weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
        grad_averaging: gradient averaging
        amsgrad (boolean, optional): whether to use the AMSGrad variant of this
            algorithm from the paper `On the Convergence of Adam and Beyond`_
            (default: False)
    """

    def __init__(
        self,
        params,
        lr=1e-3,
        betas=(0.95, 0.98),
        eps=1e-8,
        weight_decay=0,
        grad_averaging=False,
        amsgrad=False,
    ):
        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,
            grad_averaging=grad_averaging,
            amsgrad=amsgrad,
        )

        super(NvNovoGrad, self).__init__(params, defaults)

    def __setstate__(self, state):
        super(NvNovoGrad, self).__setstate__(state)
        for group in self.param_groups:
            group.setdefault("amsgrad", False)

    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("Sparse gradients are not supported.")
                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