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# Source code for torch.optim.rmsprop

    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)
    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):
            for p in group["params"]:
                if p.grad is None:
                    continue
                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

        @_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 = []

                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"],
                )

            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,
        *,
        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,
        )

    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,
    ):

        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,
    ):

        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 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)

            def _view_complex_as_real(tensor_list):
                return [
                    torch.view_as_real(t) if torch.is_complex(t) else t for t in tensor_list
                ]

            grouped_grads = _view_complex_as_real(grouped_grads)
            grouped_params = _view_complex_as_real(grouped_params)
            grouped_square_avgs = _view_complex_as_real(grouped_square_avgs)

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

            if centered:
                grouped_grad_avgs = _view_complex_as_real(grouped_grad_avgs)
                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:
                grouped_momentum_buffer_list = _view_complex_as_real(grouped_momentum_buffer_list)
                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)

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