# mypy: allow-untyped-defs
r"""Implementation for the RMSprop algorithm."""
from typing import cast, Optional, Union

import torch
from torch import Tensor

from .optimizer import (
    _capturable_doc,
    _default_to_fused_or_foreach,
    _differentiable_doc,
    _disable_dynamo_if_unsupported,
    _foreach_doc,
    _get_capturable_supported_devices,
    _get_scalar_dtype,
    _maximize_doc,
    _params_doc,
    _use_grad_for_differentiable,
    _view_as_real,
    Optimizer,
    ParamsT,
)


__all__ = ["RMSprop", "rmsprop"]


[docs]class RMSprop(Optimizer):  # noqa: D101
    def __init__(
        self,
        params: ParamsT,
        lr: Union[float, Tensor] = 1e-2,
        alpha: float = 0.99,
        eps: float = 1e-8,
        weight_decay: float = 0,
        momentum: float = 0,
        centered: bool = False,
        capturable: bool = False,
        foreach: Optional[bool] = None,
        maximize: bool = False,
        differentiable: bool = False,
    ):  # noqa: D107
        if isinstance(lr, Tensor) and lr.numel() != 1:
            raise ValueError("Tensor lr must be 1-element")
        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,
            capturable=capturable,
            foreach=foreach,
            maximize=maximize,
            differentiable=differentiable,
        )
        super().__init__(params, defaults)

    def __setstate__(self, state):  # noqa: D105
        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)
            group.setdefault("capturable", False)
            for p in group["params"]:
                p_state = self.state.get(p, [])
                if len(p_state) != 0 and not torch.is_tensor(p_state["step"]):
                    step_val = float(p_state["step"])
                    p_state["step"] = (
                        torch.tensor(
                            step_val, dtype=_get_scalar_dtype(), device=p.device
                        )
                        if group["capturable"]
                        else torch.tensor(step_val, dtype=_get_scalar_dtype())
                    )

    def _init_group(
        self,
        group,
        params_with_grad,
        grads,
        square_avgs,
        momentum_buffer_list,
        grad_avgs,
        state_steps,
    ):
        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"] = (
                    torch.zeros((), dtype=_get_scalar_dtype(), device=p.device)
                    if group["capturable"]
                    else torch.zeros((), dtype=_get_scalar_dtype())
                )
                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"])
            state_steps.append(state["step"])

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

        return has_complex

[docs]    @_use_grad_for_differentiable
    def step(self, closure=None):
        """Perform a single optimization step.

        Args:
            closure (Callable, optional): A closure that reevaluates the model
                and returns the loss.
        """
        self._cuda_graph_capture_health_check()

        loss = None
        if closure is not None:
            with torch.enable_grad():
                loss = closure()

        for group in self.param_groups:
            params_with_grad: list[Tensor] = []
            grads: list[Tensor] = []
            square_avgs: list[Tensor] = []
            grad_avgs: list[Tensor] = []
            momentum_buffer_list: list[Tensor] = []
            state_steps: list[Tensor] = []

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

            rmsprop(
                params_with_grad,
                grads,
                square_avgs,
                grad_avgs,
                momentum_buffer_list,
                state_steps,
                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"],
                capturable=group["capturable"],
                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, \: \epsilon \text{ (epsilon)}                                       \\
            &\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.
    """
    + rf"""
    Args:
        {_params_doc}
        lr (float, Tensor, optional): learning rate (default: 1e-2)
        alpha (float, optional): smoothing constant (default: 0.99)
        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 (float, optional): momentum factor (default: 0)
        centered (bool, optional) : if ``True``, compute the centered RMSProp,
            the gradient is normalized by an estimation of its variance
        {_capturable_doc}
        {_foreach_doc}
        {_maximize_doc}
        {_differentiable_doc}

    """
)


def _single_tensor_rmsprop(
    params: list[Tensor],
    grads: list[Tensor],
    square_avgs: list[Tensor],
    grad_avgs: list[Tensor],
    momentum_buffer_list: list[Tensor],
    state_steps: list[Tensor],
    *,
    lr: float,
    alpha: float,
    eps: float,
    weight_decay: float,
    momentum: float,
    centered: bool,
    maximize: bool,
    differentiable: bool,
    capturable: bool,
    has_complex: bool,
):
    for i, param in enumerate(params):
        step = state_steps[i]

        # If compiling, the compiler will handle cudagraph checks, see note [torch.compile x capturable]
        if not torch.compiler.is_compiling() and capturable:
            capturable_supported_devices = _get_capturable_supported_devices()
            assert (
                param.device.type == step.device.type
                and param.device.type in capturable_supported_devices
            ), f"If capturable=True, params and state_steps must be on supported devices: {capturable_supported_devices}."

        grad = grads[i]
        grad = grad if not maximize else -grad
        square_avg = square_avgs[i]

        step += 1

        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],
    state_steps: list[Tensor],
    *,
    lr: float,
    alpha: float,
    eps: float,
    weight_decay: float,
    momentum: float,
    centered: bool,
    maximize: bool,
    differentiable: bool,
    capturable: bool,
    has_complex: bool,
):
    if len(params) == 0:
        return

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

    # If compiling, the compiler will handle cudagraph checks, see note [torch.compile x capturable]
    if not torch.compiler.is_compiling() and capturable:
        capturable_supported_devices = _get_capturable_supported_devices()
        assert all(
            p.device.type == step.device.type
            and p.device.type in capturable_supported_devices
            for p, step in zip(params, state_steps)
        ), f"If capturable=True, params and state_steps must be on supported devices: {capturable_supported_devices}."

    grouped_tensors = Optimizer._group_tensors_by_device_and_dtype(
        [params, grads, square_avgs, grad_avgs, momentum_buffer_list, state_steps]  # type: ignore[list-item]
    )
    for (
        (
            grouped_params_,
            grouped_grads_,
            grouped_square_avgs_,
            grouped_grad_avgs_,
            grouped_momentum_buffer_list_,
            grouped_state_steps_,
        )
    ), _ in grouped_tensors.values():
        grouped_params = cast(list[Tensor], grouped_params_)
        grouped_grads = cast(list[Tensor], grouped_grads_)
        grouped_square_avgs = cast(list[Tensor], grouped_square_avgs_)
        grouped_state_steps = cast(list[Tensor], grouped_state_steps_)

        if has_complex:
            state_and_grads = [grouped_grads, grouped_square_avgs]
            if momentum > 0:
                grouped_momentum_buffer_list = cast(
                    list[Tensor], grouped_momentum_buffer_list_
                )
                state_and_grads.append(grouped_momentum_buffer_list)
            if centered:
                grouped_grad_avgs = cast(list[Tensor], grouped_grad_avgs_)
                state_and_grads.append(grouped_grad_avgs)
            _view_as_real(grouped_params, *state_and_grads)

        if maximize:
            grouped_grads = torch._foreach_neg(grouped_grads)  # type: ignore[assignment]

        # Update steps
        # If steps are on CPU, foreach will fall back to the slow path, which is a for-loop calling t.add(1) over
        # and over. 1 will then be wrapped into a Tensor over and over again, which is slower than if we just
        # wrapped it once now. The alpha is required to assure we go to the right overload.
        if not torch.compiler.is_compiling() and grouped_state_steps[0].is_cpu:
            torch._foreach_add_(
                grouped_state_steps, torch.tensor(1.0, device="cpu"), alpha=1.0
            )
        else:
            torch._foreach_add_(grouped_state_steps, 1)

        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(  # type: ignore[assignment]
                    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:
            grouped_grad_avgs = cast(list[Tensor], 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 = cast(
                list[Tensor], grouped_momentum_buffer_list_
            )
            torch._foreach_mul_(grouped_momentum_buffer_list, momentum)
            torch._foreach_addcdiv_(grouped_momentum_buffer_list, grouped_grads, avg)
            # If LR is a tensor, the else branch will internally call item()
            # which will cause silent incorrectness if we are capturing
            if capturable and isinstance(lr, torch.Tensor):
                momentum_lr = torch._foreach_mul(grouped_momentum_buffer_list, -lr)
                torch._foreach_add_(grouped_params, momentum_lr)
            else:
                torch._foreach_add_(
                    grouped_params, grouped_momentum_buffer_list, alpha=-lr
                )
        else:
            # If LR is a tensor, the else branch will internally call item()
            # which will cause silent incorrectness if we are capturing
            if capturable and isinstance(lr, torch.Tensor):
                torch._foreach_div_(avg, -lr)
                torch._foreach_addcdiv_(grouped_params, grouped_grads, avg)
            else:
                torch._foreach_addcdiv_(grouped_params, grouped_grads, avg, value=-lr)


@_disable_dynamo_if_unsupported(single_tensor_fn=_single_tensor_rmsprop)
def rmsprop(
    params: list[Tensor],
    grads: list[Tensor],
    square_avgs: list[Tensor],
    grad_avgs: list[Tensor],
    momentum_buffer_list: 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: Optional[bool] = None,
    maximize: bool = False,
    differentiable: bool = False,
    capturable: 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.
    """
    # this check is slow during compilation, so we skip it
    # if it's strictly needed we can add this check back in dynamo
    if not torch.compiler.is_compiling() and 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:
        _, 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,
        state_steps,
        lr=lr,
        alpha=alpha,
        eps=eps,
        weight_decay=weight_decay,
        momentum=momentum,
        centered=centered,
        maximize=maximize,
        capturable=capturable,
        differentiable=differentiable,
        has_complex=has_complex,
    )