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# Source code for torch.optim.rprop

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

    __all__ = ["Rprop", "rprop"]

    class Rprop(Optimizer):
        def __init__(
            self,
            params,
            lr=1e-2,
            etas=(0.5, 1.2),
            step_sizes=(1e-6, 50),
            *,
            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 < etas[0] < 1.0 < etas[1]:
                raise ValueError(f"Invalid eta values: {etas[0]}, {etas[1]}")

            defaults = dict(
                lr=lr,
                etas=etas,
                step_sizes=step_sizes,
                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("foreach", None)
                group.setdefault("maximize", False)
                group.setdefault("differentiable", False)

        def _init_group(self, group, params, grads, prevs, step_sizes):
            for p in group["params"]:
                if p.grad is None:
                    continue
                params.append(p)
                grad = p.grad
                if grad.is_sparse:
                    raise RuntimeError("Rprop does not support sparse gradients")

                grads.append(grad)
                state = self.state[p]

                # State initialization
                if len(state) == 0:
                    state["step"] = 0
                    state["prev"] = torch.zeros_like(
                        p, memory_format=torch.preserve_format
                    )
                    if p.dtype.is_complex:
                        # Complex Number should be as if they are two independent real numbers.
                        # Hence the step_size shouldn't be zero for imaginary part.
                        state["step_size"] = (
                            grad.new()
                            .resize_as_(grad)
                            .fill_(complex(group["lr"], group["lr"]))
                        )
                    else:
                        state["step_size"] = (
                            grad.new().resize_as_(grad).fill_(group["lr"])
                        )

                prevs.append(state["prev"])
                step_sizes.append(state["step_size"])

                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 = []
                grads = []
                prevs = []
                step_sizes = []
                etaminus, etaplus = group["etas"]
                step_size_min, step_size_max = group["step_sizes"]
                foreach = group["foreach"]
                maximize = group["maximize"]

                self._init_group(group, params, grads, prevs, step_sizes)

                rprop(
                    params,
                    grads,
                    prevs,
                    step_sizes,
                    step_size_min=step_size_min,
                    step_size_max=step_size_max,
                    etaminus=etaminus,
                    etaplus=etaplus,
                    foreach=foreach,
                    maximize=maximize,
                    differentiable=group["differentiable"],
                )

            return loss

    Rprop.__doc__ = r"""Implements the resilient backpropagation algorithm.

        .. math::
           \begin{aligned}
                &\rule{110mm}{0.4pt}                                                                 \\
                &\textbf{input}      : \theta_0 \in \mathbf{R}^d \text{ (params)},f(\theta)
                    \text{ (objective)},                                                             \\
                &\hspace{13mm}      \eta_{+/-} \text{ (etaplus, etaminus)}, \Gamma_{max/min}
                    \text{ (step sizes)}                                                             \\
                &\textbf{initialize} :   g^0_{prev} \leftarrow 0,
                    \: \eta_0 \leftarrow \text{lr (learning rate)}                                   \\
                &\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} \textbf{for} \text{  } i = 0, 1, \ldots, d-1 \: \mathbf{do}            \\
                &\hspace{10mm}  \textbf{if} \:   g^i_{prev} g^i_t  > 0                               \\
                &\hspace{15mm}  \eta^i_t \leftarrow \mathrm{min}(\eta^i_{t-1} \eta_{+},
                    \Gamma_{max})                                                                    \\
                &\hspace{10mm}  \textbf{else if}  \:  g^i_{prev} g^i_t < 0                           \\
                &\hspace{15mm}  \eta^i_t \leftarrow \mathrm{max}(\eta^i_{t-1} \eta_{-},
                    \Gamma_{min})                                                                    \\
                &\hspace{15mm}  g^i_t \leftarrow 0                                                   \\
                &\hspace{10mm}  \textbf{else}  \:                                                    \\
                &\hspace{15mm}  \eta^i_t \leftarrow \eta^i_{t-1}                                     \\
                &\hspace{5mm}\theta_t \leftarrow \theta_{t-1}- \eta_t \mathrm{sign}(g_t)             \\
                &\hspace{5mm}g_{prev} \leftarrow  g_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 the paper
        `A Direct Adaptive Method for Faster Backpropagation Learning: The RPROP Algorithm
        <http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.21.1417>`_.
        """ + fr"""
        Args:
            params (iterable): iterable of parameters to optimize or dicts defining
                parameter groups
            lr (float, optional): learning rate (default: 1e-2)
            etas (Tuple[float, float], optional): pair of (etaminus, etaplus), that
                are multiplicative increase and decrease factors
                (default: (0.5, 1.2))
            step_sizes (Tuple[float, float], optional): a pair of minimal and
                maximal allowed step sizes (default: (1e-6, 50))
            {_foreach_doc}
            {_maximize_doc}
            {_differentiable_doc}

        """

    def rprop(
        params: List[Tensor],
        grads: List[Tensor],
        prevs: List[Tensor],
        step_sizes: 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,
        *,
        step_size_min: float,
        step_size_max: float,
        etaminus: float,
        etaplus: float,
    ):
        r"""Functional API that performs rprop algorithm computation.

        See :class:`~torch.optim.Rprop` 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_rprop
        else:
            func = _single_tensor_rprop

        func(
            params,
            grads,
            prevs,
            step_sizes,
            step_size_min=step_size_min,
            step_size_max=step_size_max,
            etaminus=etaminus,
            etaplus=etaplus,
            maximize=maximize,
            differentiable=differentiable,
        )

    def _single_tensor_rprop(
        params: List[Tensor],
        grads: List[Tensor],
        prevs: List[Tensor],
        step_sizes: List[Tensor],
        *,
        step_size_min: float,
        step_size_max: float,
        etaminus: float,
        etaplus: float,
        maximize: bool,
        differentiable: bool,
    ):

        for i, param in enumerate(params):
            grad = grads[i]
            grad = grad if not maximize else -grad
            prev = prevs[i]
            step_size = step_sizes[i]

            if torch.is_complex(param):
                grad = torch.view_as_real(grad)
                prev = torch.view_as_real(prev)
                param = torch.view_as_real(param)
                step_size = torch.view_as_real(step_size)
            if differentiable:
                sign = grad.mul(prev.clone()).sign()
            else:
                sign = grad.mul(prev).sign()
            sign[sign.gt(0)] = etaplus
            sign[sign.lt(0)] = etaminus
            sign[sign.eq(0)] = 1

            # update stepsizes with step size updates
            step_size.mul_(sign).clamp_(step_size_min, step_size_max)

            # for dir<0, dfdx=0
            # for dir>=0 dfdx=dfdx
            grad = grad.clone(memory_format=torch.preserve_format)
            grad[sign.eq(etaminus)] = 0

            # update parameters
            param.addcmul_(grad.sign(), step_size, value=-1)
            prev.copy_(grad)

    def _multi_tensor_rprop(
        params: List[Tensor],
        grads: List[Tensor],
        prevs: List[Tensor],
        step_sizes: List[Tensor],
        *,
        step_size_min: float,
        step_size_max: float,
        etaminus: float,
        etaplus: float,
        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, prevs, step_sizes])
        for ((grouped_params, grouped_grads, grouped_prevs, grouped_step_sizes), _) in grouped_tensors.values():
            # Handle complex params
            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_prevs = _view_complex_as_real(grouped_prevs)
            grouped_params = _view_complex_as_real(grouped_params)
            grouped_step_sizes = _view_complex_as_real(grouped_step_sizes)

            signs = torch._foreach_mul(grouped_grads, grouped_prevs)
            if maximize:
                torch._foreach_neg_(signs)

            # At the end of the step, grouped_prevs will contain the current grads, so we reuse
            # grouped_prevs memory instead of creating a new buffer, but, for clarity, we reassign
            # to keep referring to the buffer as grouped_grads.
            torch._foreach_copy_(grouped_prevs, grouped_grads)
            if maximize:
                torch._foreach_neg_(grouped_prevs)
            grouped_grads = grouped_prevs

            torch._foreach_sign_(signs)
            for sign in signs:
                sign[sign.gt(0)] = etaplus
                sign[sign.lt(0)] = etaminus
                sign[sign.eq(0)] = 1

            # update stepsizes with step size updates
            torch._foreach_mul_(grouped_step_sizes, signs)
            for step_size in grouped_step_sizes:
                step_size.clamp_(step_size_min, step_size_max)

            # for dir<0, dfdx=0
            # for dir>=0 dfdx=dfdx
            grouped_grads = list(grouped_grads)
            for i in range(len(grouped_grads)):
                grouped_grads[i][signs[i].eq(etaminus)] = 0

            # explicitly del signs as it's not used after here to save memory
            del signs

            # update parameters
            grad_signs = [grad.sign() for grad in grouped_grads]
            torch._foreach_addcmul_(grouped_params, grad_signs, grouped_step_sizes, value=-1)

            # Logically, you may expect grouped_prevs to get updated to grouped_grads, but that's
            # basically already happened since we've been using grouped_prevs' memory to store
            # updated grouped_grads!

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