import torch
from torch import Tensor

from .optimizer import Optimizer
from typing import List, Optional


class Adamax(Optimizer):
    r"""Implements Adamax algorithm (a variant of Adam based on infinity norm).

    .. math::
       \begin{aligned}
            &\rule{110mm}{0.4pt}                                                                 \\
            &\textbf{input}      : \gamma \text{ (lr)}, \beta_1, \beta_2
                \text{ (betas)},\theta_0 \text{ (params)},f(\theta) \text{ (objective)},
                \: \lambda \text{ (weight decay)},                                                \\
            &\hspace{13mm}    \epsilon \text{ (epsilon)}                                          \\
            &\textbf{initialize} :  m_0 \leftarrow 0 \text{ ( first moment)},
                u_0 \leftarrow 0 \text{ ( infinity norm)}                                 \\[-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}m_t      \leftarrow   \beta_1 m_{t-1} + (1 - \beta_1) g_t               \\
            &\hspace{5mm}u_t      \leftarrow   \mathrm{max}(\beta_2 u_{t-1}, |g_{t}|+\epsilon)   \\
            &\hspace{5mm}\theta_t \leftarrow \theta_{t-1} - \frac{\gamma m_t}{(1-\beta^t_1) u_t} \\
            &\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 `Adam: A Method for Stochastic Optimization`_.

    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
        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)
        foreach (bool, optional): whether foreach implementation of optimizer is used (default: None)
        maximize (bool, optional): maximize the params based on the objective, instead of
            minimizing (default: False)

    .. _Adam\: A Method for Stochastic Optimization:
        https://arxiv.org/abs/1412.6980
    """

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

        defaults = dict(lr=lr, betas=betas, eps=eps, weight_decay=weight_decay,
                        foreach=foreach, maximize=maximize)
        super(Adamax, self).__init__(params, defaults)

    def __setstate__(self, state):
        super().__setstate__(state)
        for group in self.param_groups:
            group.setdefault('foreach', None)
            group.setdefault('maximize', False)
        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']))

    @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_infs = []
            state_steps = []

            beta1, beta2 = group['betas']
            eps = group['eps']
            lr = group['lr']
            weight_decay = group['weight_decay']
            foreach = group['foreach']
            maximize = group['maximize']

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

                state = self.state[p]

                # State initialization
                if len(state) == 0:
                    state['step'] = torch.tensor(0.)
                    state['exp_avg'] = torch.zeros_like(p, memory_format=torch.preserve_format)
                    state['exp_inf'] = torch.zeros_like(p, memory_format=torch.preserve_format)

                exp_avgs.append(state['exp_avg'])
                exp_infs.append(state['exp_inf'])
                state_steps.append(state['step'])

            adamax(params_with_grad,
                   grads,
                   exp_avgs,
                   exp_infs,
                   state_steps,
                   eps=eps,
                   beta1=beta1,
                   beta2=beta2,
                   lr=lr,
                   weight_decay=weight_decay,
                   foreach=foreach,
                   maximize=maximize)

        return loss


def adamax(params: List[Tensor],
           grads: List[Tensor],
           exp_avgs: List[Tensor],
           exp_infs: 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,
           maximize: bool = False,
           *,
           eps: float,
           beta1: float,
           beta2: float,
           lr: float,
           weight_decay: float):
    r"""Functional API that performs adamax algorithm computation.

    See :class:`~torch.optim.Adamax` 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 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_adamax
    else:
        func = _single_tensor_adamax

    func(params,
         grads,
         exp_avgs,
         exp_infs,
         state_steps,
         eps=eps,
         beta1=beta1,
         beta2=beta2,
         lr=lr,
         weight_decay=weight_decay,
         maximize=maximize)


def _single_tensor_adamax(params: List[Tensor],
                          grads: List[Tensor],
                          exp_avgs: List[Tensor],
                          exp_infs: List[Tensor],
                          state_steps: List[Tensor],
                          *,
                          eps: float,
                          beta1: float,
                          beta2: float,
                          lr: float,
                          weight_decay: float,
                          maximize: bool):

    for i, param in enumerate(params):
        grad = grads[i]
        grad = grad if not maximize else -grad
        exp_avg = exp_avgs[i]
        exp_inf = exp_infs[i]
        step_t = state_steps[i]
        # update step
        step_t += 1
        step = step_t.item()

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

        # Update biased first moment estimate.
        exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1)
        # Update the exponentially weighted infinity norm.
        norm_buf = torch.cat([
            exp_inf.mul_(beta2).unsqueeze(0),
            grad.abs().add_(eps).unsqueeze_(0)
        ], 0)
        torch.amax(norm_buf, 0, keepdim=False, out=exp_inf)

        bias_correction = 1 - beta1 ** step
        clr = lr / bias_correction

        param.addcdiv_(exp_avg, exp_inf, value=-clr)


def _multi_tensor_adamax(params: List[Tensor],
                         grads: List[Tensor],
                         exp_avgs: List[Tensor],
                         exp_infs: List[Tensor],
                         state_steps: List[Tensor],
                         *,
                         beta1: float,
                         beta2: float,
                         lr: float,
                         weight_decay: float,
                         eps: float,
                         maximize: bool):

    if len(params) == 0:
        return

    if maximize:
        grads = torch._foreach_neg(grads)

    # Update steps
    torch._foreach_add_(state_steps, 1)

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

    # Update biased first moment estimate.
    torch._foreach_mul_(exp_avgs, beta1)
    torch._foreach_add_(exp_avgs, grads, alpha=1 - beta1)

    # Update the exponentially weighted infinity norm.
    torch._foreach_mul_(exp_infs, beta2)

    for exp_inf, grad in zip(exp_infs, grads):
        norm_buf = torch.cat([
            exp_inf.unsqueeze(0),
            grad.abs().add_(eps).unsqueeze_(0)
        ], 0)
        torch.max(norm_buf, 0, keepdim=False, out=(exp_inf, exp_inf.new().long()))

    bias_corrections = [1 - beta1 ** step.item() for step in state_steps]
    clr = [-1 * (lr / bias_correction) for bias_correction in bias_corrections]
    torch._foreach_addcdiv_(params, exp_avgs, exp_infs, clr)