import torch
from torch import Tensor
from .optimizer import (Optimizer, _default_to_fused_or_foreach, _use_grad_for_differentiable,
                        _differentiable_doc, _foreach_doc, _maximize_doc, _view_as_real)
from typing import List, Optional

__all__ = ["RMSprop", "rmsprop"]


class RMSprop(Optimizer):
    def __init__(
        self,
        params,
        lr=1e-2,
        alpha=0.99,
        eps=1e-8,
        weight_decay=0,
        momentum=0,
        centered=False,
        foreach: Optional[bool] = None,
        maximize: bool = False,
        differentiable: bool = False,
    ):
        if not 0.0 <= lr:
            raise ValueError(f"Invalid learning rate: {lr}")
        if not 0.0 <= eps:
            raise ValueError(f"Invalid epsilon value: {eps}")
        if not 0.0 <= momentum:
            raise ValueError(f"Invalid momentum value: {momentum}")
        if not 0.0 <= weight_decay:
            raise ValueError(f"Invalid weight_decay value: {weight_decay}")
        if not 0.0 <= alpha:
            raise ValueError(f"Invalid alpha value: {alpha}")

        defaults = dict(
            lr=lr,
            momentum=momentum,
            alpha=alpha,
            eps=eps,
            centered=centered,
            weight_decay=weight_decay,
            foreach=foreach,
            maximize=maximize,
            differentiable=differentiable,
        )
        super().__init__(params, defaults)

    def __setstate__(self, state):
        super().__setstate__(state)
        for group in self.param_groups:
            group.setdefault("momentum", 0)
            group.setdefault("centered", False)
            group.setdefault("foreach", None)
            group.setdefault("maximize", False)
            group.setdefault("differentiable", False)

    def _init_group(self, group, params_with_grad, grads, square_avgs, momentum_buffer_list, grad_avgs):
        has_complex = False
        for p in group["params"]:
            if p.grad is None:
                continue
            has_complex |= torch.is_complex(p)
            params_with_grad.append(p)

            if p.grad.is_sparse:
                raise RuntimeError("RMSprop does not support sparse gradients")
            grads.append(p.grad)

            state = self.state[p]

            # State initialization
            if len(state) == 0:
                state["step"] = 0
                state["square_avg"] = torch.zeros_like(
                    p, memory_format=torch.preserve_format
                )
                if group["momentum"] > 0:
                    state["momentum_buffer"] = torch.zeros_like(
                        p, memory_format=torch.preserve_format
                    )
                if group["centered"]:
                    state["grad_avg"] = torch.zeros_like(
                        p, memory_format=torch.preserve_format
                    )
            square_avgs.append(state["square_avg"])

            if group["momentum"] > 0:
                momentum_buffer_list.append(state["momentum_buffer"])
            if group["centered"]:
                grad_avgs.append(state["grad_avg"])

            if group["differentiable"] and isinstance(state["step"], Tensor):
                raise RuntimeError("`step` can't be a tensor")

            state["step"] += 1
        return has_complex

    @_use_grad_for_differentiable
    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 = []
            square_avgs = []
            grad_avgs = []
            momentum_buffer_list = []

            has_complex = self._init_group(group, params_with_grad, grads, square_avgs, momentum_buffer_list, grad_avgs)

            rmsprop(
                params_with_grad,
                grads,
                square_avgs,
                grad_avgs,
                momentum_buffer_list,
                lr=group["lr"],
                alpha=group["alpha"],
                eps=group["eps"],
                weight_decay=group["weight_decay"],
                momentum=group["momentum"],
                centered=group["centered"],
                foreach=group["foreach"],
                maximize=group["maximize"],
                differentiable=group["differentiable"],
                has_complex=has_complex,
            )

        return loss


RMSprop.__doc__ = r"""Implements RMSprop algorithm.

    .. math::
       \begin{aligned}
            &\rule{110mm}{0.4pt}                                                                 \\
            &\textbf{input}      : \alpha \text{ (alpha)},\: \gamma \text{ (lr)},
                \: \theta_0 \text{ (params)}, \: f(\theta) \text{ (objective)}                   \\
            &\hspace{13mm}   \lambda \text{ (weight decay)},\: \mu \text{ (momentum)},\: centered\\
            &\textbf{initialize} : v_0 \leftarrow 0 \text{ (square average)}, \:
                \textbf{b}_0 \leftarrow 0 \text{ (buffer)}, \: g^{ave}_0 \leftarrow 0     \\[-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}v_t           \leftarrow   \alpha v_{t-1} + (1 - \alpha) g^2_t
                \hspace{8mm}                                                                     \\
            &\hspace{5mm} \tilde{v_t} \leftarrow v_t                                             \\
            &\hspace{5mm}if \: centered                                                          \\
            &\hspace{10mm} g^{ave}_t \leftarrow g^{ave}_{t-1} \alpha + (1-\alpha) g_t            \\
            &\hspace{10mm} \tilde{v_t} \leftarrow \tilde{v_t} -  \big(g^{ave}_{t} \big)^2        \\
            &\hspace{5mm}if \: \mu > 0                                                           \\
            &\hspace{10mm} \textbf{b}_t\leftarrow \mu \textbf{b}_{t-1} +
                g_t/ \big(\sqrt{\tilde{v_t}} +  \epsilon \big)                                   \\
            &\hspace{10mm} \theta_t \leftarrow \theta_{t-1} - \gamma \textbf{b}_t                \\
            &\hspace{5mm} else                                                                   \\
            &\hspace{10mm}\theta_t      \leftarrow   \theta_{t-1} -
                \gamma  g_t/ \big(\sqrt{\tilde{v_t}} + \epsilon \big)  \hspace{3mm}              \\
            &\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
    `lecture notes <https://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf>`_ by G. Hinton.
    and centered version `Generating Sequences
    With Recurrent Neural Networks <https://arxiv.org/pdf/1308.0850v5.pdf>`_.
    The implementation here takes the square root of the gradient average before
    adding epsilon (note that TensorFlow interchanges these two operations). The effective
    learning rate is thus :math:`\gamma/(\sqrt{v} + \epsilon)` where :math:`\gamma`
    is the scheduled learning rate and :math:`v` is the weighted moving average
    of the squared gradient.
    """ + fr"""
    Args:
        params (iterable): iterable of parameters to optimize or dicts defining
            parameter groups
        lr (float, optional): learning rate (default: 1e-2)
        momentum (float, optional): momentum factor (default: 0)
        alpha (float, optional): smoothing constant (default: 0.99)
        eps (float, optional): term added to the denominator to improve
            numerical stability (default: 1e-8)
        centered (bool, optional) : if ``True``, compute the centered RMSProp,
            the gradient is normalized by an estimation of its variance
        weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
        {_foreach_doc}
        {_maximize_doc}
        {_differentiable_doc}

    """


def rmsprop(
    params: List[Tensor],
    grads: List[Tensor],
    square_avgs: List[Tensor],
    grad_avgs: List[Tensor],
    momentum_buffer_list: 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: Optional[bool] = None,
    maximize: bool = False,
    differentiable: bool = False,
    has_complex: bool = False,
    *,
    lr: float,
    alpha: float,
    eps: float,
    weight_decay: float,
    momentum: float,
    centered: bool,
):
    r"""Functional API that performs rmsprop algorithm computation.
    See :class:`~torch.optim.RMSProp` for details.
    """

    if foreach is None:
        _, foreach = _default_to_fused_or_foreach(params, differentiable, use_fused=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_rmsprop
    else:
        func = _single_tensor_rmsprop

    func(
        params,
        grads,
        square_avgs,
        grad_avgs,
        momentum_buffer_list,
        lr=lr,
        alpha=alpha,
        eps=eps,
        weight_decay=weight_decay,
        momentum=momentum,
        centered=centered,
        maximize=maximize,
        differentiable=differentiable,
        has_complex=has_complex,
    )


def _single_tensor_rmsprop(
    params: List[Tensor],
    grads: List[Tensor],
    square_avgs: List[Tensor],
    grad_avgs: List[Tensor],
    momentum_buffer_list: List[Tensor],
    *,
    lr: float,
    alpha: float,
    eps: float,
    weight_decay: float,
    momentum: float,
    centered: bool,
    maximize: bool,
    differentiable: bool,
    has_complex: bool,
):

    for i, param in enumerate(params):
        grad = grads[i]
        grad = grad if not maximize else -grad
        square_avg = square_avgs[i]

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

        is_complex_param = torch.is_complex(param)
        if is_complex_param:
            param = torch.view_as_real(param)
            grad = torch.view_as_real(grad)
            square_avg = torch.view_as_real(square_avg)

        square_avg.mul_(alpha).addcmul_(grad, grad, value=1 - alpha)

        if centered:
            grad_avg = grad_avgs[i]
            if is_complex_param:
                grad_avg = torch.view_as_real(grad_avg)
            grad_avg.lerp_(grad, 1 - alpha)
            avg = square_avg.addcmul(grad_avg, grad_avg, value=-1).sqrt_()
        else:
            avg = square_avg.sqrt()

        if differentiable:
            avg = avg.add(eps)
        else:
            avg = avg.add_(eps)

        if momentum > 0:
            buf = momentum_buffer_list[i]
            if is_complex_param:
                buf = torch.view_as_real(buf)
            buf.mul_(momentum).addcdiv_(grad, avg)
            param.add_(buf, alpha=-lr)
        else:
            param.addcdiv_(grad, avg, value=-lr)


def _multi_tensor_rmsprop(
    params: List[Tensor],
    grads: List[Tensor],
    square_avgs: List[Tensor],
    grad_avgs: List[Tensor],
    momentum_buffer_list: List[Tensor],
    *,
    lr: float,
    alpha: float,
    eps: float,
    weight_decay: float,
    momentum: float,
    centered: bool,
    maximize: bool,
    differentiable: bool,
    has_complex: bool,
):

    if len(params) == 0:
        return

    assert not differentiable, "_foreach ops don't support autograd"

    grouped_tensors = Optimizer._group_tensors_by_device_and_dtype([params, grads, square_avgs, grad_avgs, momentum_buffer_list])
    for (((grouped_params, grouped_grads, grouped_square_avgs, grouped_grad_avgs,
         grouped_momentum_buffer_list)), _) in grouped_tensors.values():
        if has_complex:
            state_and_grads = [grouped_grads, grouped_square_avgs]
            if momentum > 0:
                state_and_grads.append(grouped_momentum_buffer_list)
            if centered:
                state_and_grads.append(grouped_grad_avgs)
            _view_as_real(grouped_params, *state_and_grads)

        if maximize:
            grouped_grads = torch._foreach_neg(grouped_grads)

        if weight_decay != 0:
            # Re-use the intermediate memory (grouped_grads) already allocated for maximize
            if maximize:
                torch._foreach_add_(grouped_grads, grouped_params, alpha=weight_decay)
            else:
                grouped_grads = torch._foreach_add(grouped_grads, grouped_params, alpha=weight_decay)

        torch._foreach_mul_(grouped_square_avgs, alpha)
        torch._foreach_addcmul_(grouped_square_avgs, grouped_grads, grouped_grads, value=1 - alpha)

        if centered:
            torch._foreach_lerp_(grouped_grad_avgs, grouped_grads, 1 - alpha)
            avg = torch._foreach_addcmul(grouped_square_avgs, grouped_grad_avgs, grouped_grad_avgs, value=-1)
            torch._foreach_sqrt_(avg)
            torch._foreach_add_(avg, eps)
        else:
            avg = torch._foreach_sqrt(grouped_square_avgs)
            torch._foreach_add_(avg, eps)

        if momentum > 0:
            torch._foreach_mul_(grouped_momentum_buffer_list, momentum)
            torch._foreach_addcdiv_(grouped_momentum_buffer_list, grouped_grads, avg)
            torch._foreach_add_(grouped_params, grouped_momentum_buffer_list, alpha=-lr)
        else:
            torch._foreach_addcdiv_(grouped_params, grouped_grads, avg, value=-lr)