import math
import torch
from torch import Tensor
from .optimizer import Optimizer
from typing import List, Optional


class NAdam(Optimizer):
    r"""Implements NAdam algorithm.

    .. math::
       \begin{aligned}
            &\rule{110mm}{0.4pt}                                                                 \\
            &\textbf{input}      : \gamma_t \text{ (lr)}, \: \beta_1,\beta_2 \text{ (betas)},
                \: \theta_0 \text{ (params)}, \: f(\theta) \text{ (objective)}                   \\
            &\hspace{13mm} \: \lambda \text{ (weight decay)}, \:\psi \text{ (momentum decay)}    \\
            &\textbf{initialize} :  m_0 \leftarrow 0 \text{ ( first moment)},
                v_0 \leftarrow 0 \text{ ( second moment)}                                 \\[-1.ex]
            &\rule{110mm}{0.4pt}                                                                 \\
            &\textbf{for} \: t=1 \: \textbf{to} \: \ldots \: \textbf{do}                         \\
            &\hspace{5mm}g_t           \leftarrow   \nabla_{\theta} f_t (\theta_{t-1})           \\
            &\hspace{5mm}if \: \lambda \neq 0                                                    \\
            &\hspace{10mm} g_t \leftarrow g_t + \lambda \theta_{t-1}                             \\
            &\hspace{5mm} \mu_t \leftarrow \beta_1 \big(1 - \frac{1}{2}  0.96^{t \psi} \big)     \\
            &\hspace{5mm} \mu_{t+1} \leftarrow \beta_1 \big(1 - \frac{1}{2} 0.96^{(t+1)\psi}\big)\\
            &\hspace{5mm}m_t           \leftarrow   \beta_1 m_{t-1} + (1 - \beta_1) g_t          \\
            &\hspace{5mm}v_t           \leftarrow   \beta_2 v_{t-1} + (1-\beta_2) g^2_t          \\
            &\hspace{5mm}\widehat{m_t} \leftarrow \mu_{t+1} m_t/(1-\prod_{i=1}^{t+1}\mu_i)\\[-1.ex]
            & \hspace{11mm} + (1-\mu_t) g_t /(1-\prod_{i=1}^{t} \mu_{i})                         \\
            &\hspace{5mm}\widehat{v_t} \leftarrow   v_t/\big(1-\beta_2^t \big)                   \\
            &\hspace{5mm}\theta_t \leftarrow \theta_{t-1} - \gamma \widehat{m_t}/
                \big(\sqrt{\widehat{v_t}} + \epsilon \big)                                       \\
            &\rule{110mm}{0.4pt}                                                          \\[-1.ex]
            &\bf{return} \:  \theta_t                                                     \\[-1.ex]
            &\rule{110mm}{0.4pt}                                                          \\[-1.ex]
       \end{aligned}

    For further details regarding the algorithm we refer to `Incorporating Nesterov Momentum into Adam`_.

    Args:
        params (iterable): iterable of parameters to optimize or dicts defining
            parameter groups
        lr (float, optional): learning rate (default: 2e-3)
        betas (Tuple[float, float], optional): coefficients used for computing
            running averages of gradient and its square (default: (0.9, 0.999))
        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)
        momentum_decay (float, optional): momentum momentum_decay (default: 4e-3)
        foreach (bool, optional): whether foreach implementation of optimizer
            is used (default: None)

    .. _Incorporating Nesterov Momentum into Adam:
        https://openreview.net/forum?id=OM0jvwB8jIp57ZJjtNEZ
    """

    def __init__(self, params, lr=2e-3, betas=(0.9, 0.999), eps=1e-8,
                 weight_decay=0, momentum_decay=4e-3, foreach: Optional[bool] = None):
        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]))
        if not 0.0 <= weight_decay:
            raise ValueError("Invalid weight_decay value: {}".format(weight_decay))
        if not 0.0 <= momentum_decay:
            raise ValueError("Invalid momentum_decay value: {}".format(momentum_decay))
        defaults = dict(lr=lr, betas=betas, eps=eps,
                        weight_decay=weight_decay, momentum_decay=momentum_decay,
                        foreach=foreach)
        super(NAdam, self).__init__(params, defaults)

    def __setstate__(self, state):
        super().__setstate__(state)
        for group in self.param_groups:
            group.setdefault('foreach', None)
        state_values = list(self.state.values())
        step_is_tensor = (len(state_values) != 0) and torch.is_tensor(state_values[0]['step'])
        if not step_is_tensor:
            for s in state_values:
                s['step'] = torch.tensor(float(s['step']))
        mu_product_is_tensor = (len(state_values) != 0) and torch.is_tensor(state_values[0]['mu_product'])
        if not mu_product_is_tensor:
            for s in state_values:
                s['mu_product'] = torch.tensor(s['mu_product'])

    @torch.no_grad()
    def step(self, closure=None):
        """Performs a single optimization step.

        Args:
            closure (callable, optional): A closure that reevaluates the model
                and returns the loss.
        """
        loss = None
        if closure is not None:
            with torch.enable_grad():
                loss = closure()

        for group in self.param_groups:
            params_with_grad = []
            grads = []
            exp_avgs = []
            exp_avg_sqs = []
            mu_products = []
            state_steps = []
            beta1, beta2 = group['betas']

            for p in group['params']:
                if p.grad is not None:
                    params_with_grad.append(p)
                    if p.grad.is_sparse:
                        raise RuntimeError('NAdam does not support sparse gradients')
                    grads.append(p.grad)

                    state = self.state[p]
                    # Lazy state initialization
                    if len(state) == 0:
                        state['step'] = torch.tensor(0.)
                        state['mu_product'] = torch.tensor(1.)
                        # Exponential moving average of gradient values
                        state['exp_avg'] = torch.zeros_like(p, memory_format=torch.preserve_format)
                        # Exponential moving average of squared gradient values
                        state['exp_avg_sq'] = torch.zeros_like(p, memory_format=torch.preserve_format)

                    exp_avgs.append(state['exp_avg'])
                    exp_avg_sqs.append(state['exp_avg_sq'])
                    mu_products.append(state['mu_product'])
                    state_steps.append(state['step'])

            nadam(params_with_grad,
                  grads,
                  exp_avgs,
                  exp_avg_sqs,
                  mu_products,
                  state_steps,
                  beta1=beta1,
                  beta2=beta2,
                  lr=group['lr'],
                  weight_decay=group['weight_decay'],
                  momentum_decay=group['momentum_decay'],
                  eps=group['eps'],
                  foreach=group['foreach'])

        return loss


def nadam(params: List[Tensor],
          grads: List[Tensor],
          exp_avgs: List[Tensor],
          exp_avg_sqs: List[Tensor],
          mu_products: List[Tensor],
          state_steps: List[Tensor],
          # kwonly args with defaults are not supported by functions compiled with torchscript issue #70627
          # setting this as kwarg for now as functional API is compiled by torch/distributed/optim
          foreach: bool = None,
          *,
          beta1: float,
          beta2: float,
          lr: float,
          weight_decay: float,
          momentum_decay: float,
          eps: float):
    r"""Functional API that performs NAdam algorithm computation.

    See :class:`~torch.optim.NAdam` for details.
    """

    if not all([isinstance(t, torch.Tensor) for t in state_steps]):
        raise RuntimeError("API has changed, `state_steps` argument must contain a list of singleton tensors")

    if not all([isinstance(t, torch.Tensor) for t in mu_products]):
        raise RuntimeError("API has changed, `mu_products` argument must contain a list of singleton tensors")

    if foreach is None:
        # Placeholder for more complex foreach logic to be added when value is not set
        foreach = False

    if foreach and torch.jit.is_scripting():
        raise RuntimeError('torch.jit.script not supported with foreach optimizers')

    if foreach and not torch.jit.is_scripting():
        func = _multi_tensor_nadam
    else:
        func = _single_tensor_nadam

    func(params,
         grads,
         exp_avgs,
         exp_avg_sqs,
         mu_products,
         state_steps,
         beta1=beta1,
         beta2=beta2,
         lr=lr,
         weight_decay=weight_decay,
         momentum_decay=momentum_decay,
         eps=eps)


def _single_tensor_nadam(params: List[Tensor],
                         grads: List[Tensor],
                         exp_avgs: List[Tensor],
                         exp_avg_sqs: List[Tensor],
                         mu_products: List[Tensor],
                         state_steps: List[Tensor],
                         *,
                         beta1: float,
                         beta2: float,
                         lr: float,
                         weight_decay: float,
                         momentum_decay: float,
                         eps: float):

    for i, param in enumerate(params):
        grad = grads[i]
        exp_avg = exp_avgs[i]
        exp_avg_sq = exp_avg_sqs[i]
        mu_product = mu_products[i]
        step_t = state_steps[i]
        # update step
        step_t += 1
        step = step_t.item()

        bias_correction2 = 1 - beta2 ** step

        if weight_decay != 0:
            grad = grad.add(param, alpha=weight_decay)

        # calculate the momentum cache \mu^{t} and \mu^{t+1}
        mu = beta1 * (1. - 0.5 * (0.96 ** (step * momentum_decay)))
        mu_next = beta1 * (1. - 0.5 * (0.96 ** ((step + 1) * momentum_decay)))

        # update mu_product
        mu_product *= mu
        mu_product_next = mu_product * mu * mu_next

        # decay the first and second moment running average coefficient
        exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1)
        exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)

        denom = exp_avg_sq.div(bias_correction2).sqrt().add_(eps)
        param.addcdiv_(grad, denom, value=-lr * (1. - mu) / (1. - mu_product.item()))
        param.addcdiv_(exp_avg, denom, value=-lr * mu_next / (1. - mu_product_next.item()))


def _multi_tensor_nadam(params: List[Tensor],
                        grads: List[Tensor],
                        exp_avgs: List[Tensor],
                        exp_avg_sqs: List[Tensor],
                        mu_products: List[Tensor],
                        state_steps: List[Tensor],
                        *,
                        beta1: float,
                        beta2: float,
                        lr: float,
                        weight_decay: float,
                        momentum_decay: float,
                        eps: float):

    if len(params) == 0:
        return

    # update steps
    torch._foreach_add_(state_steps, 1)

    bias_correction1 = [1 - beta1 ** step.item() for step in state_steps]
    bias_correction2 = [1 - beta2 ** step.item() for step in state_steps]
    mus = [beta1 * (1. - 0.5 * (0.96 ** (step.item() * momentum_decay))) for step in state_steps]
    mu_nexts = [beta1 * (1. - 0.5 * (0.96 ** ((step.item() + 1) * momentum_decay)))
                for step in state_steps]

    # update mu_products
    torch._foreach_mul_(mu_products, mus)

    if weight_decay != 0:
        torch._foreach_add_(grads, params, alpha=weight_decay)

    # Decay the first and second moment running average coefficient
    torch._foreach_mul_(exp_avgs, beta1)
    torch._foreach_add_(exp_avgs, grads, alpha=1 - beta1)

    torch._foreach_mul_(exp_avg_sqs, beta2)
    torch._foreach_addcmul_(exp_avg_sqs, grads, grads, 1 - beta2)

    exp_avg_sq_sqrt = torch._foreach_sqrt(exp_avg_sqs)
    bias_correction_sqrt = [math.sqrt(bc) for bc in bias_correction2]
    torch._foreach_div_(exp_avg_sq_sqrt, bias_correction_sqrt)
    denom = torch._foreach_add(exp_avg_sq_sqrt, eps)

    step_size_grads = [(lr * (1. - mu) / (1. - mu_product.item())) * -1
                       for mu_product, mu in zip(mu_products, mus)]
    step_size_expavg = [(lr * mu_next / (1. - mu_product.item() * mu_next)) * -1
                        for mu_product, mu_next in zip(mu_products, mu_nexts)]
    torch._foreach_addcdiv_(params, grads, denom, step_size_grads)
    torch._foreach_addcdiv_(params, exp_avgs, denom, step_size_expavg)