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# Source code for torch.optim.radam

    import math
    import torch
    from torch import Tensor

    from .optimizer import (Optimizer, _use_grad_for_differentiable, _get_value, _dispatch_sqrt, _stack_if_compiling,
                            _default_to_fused_or_foreach, _differentiable_doc, _foreach_doc)
    from typing import List, Optional

    __all__ = ["RAdam", "radam"]

    class RAdam(Optimizer):
        def __init__(
            self,
            params,
            lr=1e-3,
            betas=(0.9, 0.999),
            eps=1e-8,
            weight_decay=0,
            *,
            foreach: Optional[bool] = None,
            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 <= betas[0] < 1.0:
                raise ValueError(f"Invalid beta parameter at index 0: {betas[0]}")
            if not 0.0 <= betas[1] < 1.0:
                raise ValueError(f"Invalid beta parameter at index 1: {betas[1]}")
            if not 0.0 <= weight_decay:
                raise ValueError(f"Invalid weight_decay value: {weight_decay}")
            defaults = dict(
                lr=lr,
                betas=betas,
                eps=eps,
                weight_decay=weight_decay,
                foreach=foreach,
                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("differentiable", 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"]))

        def _init_group(self, group, params_with_grad, grads, exp_avgs, exp_avg_sqs, state_steps):
            for p in group["params"]:
                if p.grad is not None:
                    params_with_grad.append(p)
                    if p.grad.is_sparse:
                        raise RuntimeError("RAdam does not support sparse gradients")
                    grads.append(p.grad)

                    state = self.state[p]
                    # Lazy state initialization
                    if len(state) == 0:
                        state["step"] = torch.tensor(0.0)
                        # Exponential moving average of gradient values
                        state["exp_avg"] = torch.zeros_like(
                            p, memory_format=torch.preserve_format
                        )
                        # Exponential moving average of squared gradient values
                        state["exp_avg_sq"] = torch.zeros_like(
                            p, memory_format=torch.preserve_format
                        )

                    exp_avgs.append(state["exp_avg"])
                    exp_avg_sqs.append(state["exp_avg_sq"])
                    state_steps.append(state["step"])

        @_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 = []
                exp_avgs = []
                exp_avg_sqs = []
                state_steps = []
                beta1, beta2 = group["betas"]

                self._init_group(group, params_with_grad, grads, exp_avgs, exp_avg_sqs, state_steps)

                radam(
                    params_with_grad,
                    grads,
                    exp_avgs,
                    exp_avg_sqs,
                    state_steps,
                    beta1=beta1,
                    beta2=beta2,
                    lr=group["lr"],
                    weight_decay=group["weight_decay"],
                    eps=group["eps"],
                    foreach=group["foreach"],
                    differentiable=group["differentiable"],
                )

            return loss

    RAdam.__doc__ = r"""Implements RAdam algorithm.

        .. 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{ (weightdecay)},                                                   \\
                &\hspace{13mm} \epsilon \text{ (epsilon)}                                            \\
                &\textbf{initialize} :  m_0 \leftarrow 0 \text{ ( first moment)},
                    v_0 \leftarrow 0 \text{ ( second moment)},                                       \\
                &\hspace{18mm} \rho_{\infty} \leftarrow 2/(1-\beta_2) -1                      \\[-1.ex]
                &\rule{110mm}{0.4pt}  \\
                &\textbf{for} \: t=1 \: \textbf{to} \: \ldots \: \textbf{do}                         \\
                &\hspace{6mm}g_t           \leftarrow   \nabla_{\theta} f_t (\theta_{t-1})           \\
                &\hspace{5mm} \textbf{if} \: \lambda \neq 0                                          \\
                &\hspace{10mm} g_t \leftarrow g_t + \lambda \theta_{t-1}                             \\
                &\hspace{6mm}m_t           \leftarrow   \beta_1 m_{t-1} + (1 - \beta_1) g_t          \\
                &\hspace{6mm}v_t           \leftarrow   \beta_2 v_{t-1} + (1-\beta_2) g^2_t          \\
                &\hspace{6mm}\widehat{m_t} \leftarrow   m_t/\big(1-\beta_1^t \big)                   \\
                &\hspace{6mm}\rho_t \leftarrow \rho_{\infty} -
                    2 t \beta^t_2 /\big(1-\beta_2^t \big)                                    \\[0.1.ex]
                &\hspace{6mm}\textbf{if} \: \rho_t > 5                                               \\
                &\hspace{12mm} l_t \leftarrow \frac{\sqrt{ (1-\beta^t_2) }}{ \sqrt{v_t} +\epsilon  } \\
                &\hspace{12mm} r_t \leftarrow
          \sqrt{\frac{(\rho_t-4)(\rho_t-2)\rho_{\infty}}{(\rho_{\infty}-4)(\rho_{\infty}-2) \rho_t}} \\
                &\hspace{12mm}\theta_t \leftarrow \theta_{t-1} - \gamma \widehat{m_t} r_t l_t        \\
                &\hspace{6mm}\textbf{else}                                                           \\
                &\hspace{12mm}\theta_t \leftarrow \theta_{t-1} - \gamma \widehat{m_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 `On the variance of the adaptive learning rate and beyond`_.

        This implementation uses the same weight_decay implementation as Adam (were the weight_decay is applied
        to the gradient) and not the one from AdamW (were weight_decay is applied to the update). This
        is different from the `author's implementation`_.
        """ + fr"""
        Args:
            params (iterable): iterable of parameters to optimize or dicts defining
                parameter groups
            lr (float, optional): learning rate (default: 1e-3)
            betas (Tuple[float, float], optional): coefficients used for computing
                running averages of gradient and its square (default: (0.9, 0.999))
            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_doc}
            {_differentiable_doc}

        .. _On the variance of the adaptive learning rate and beyond:
            https://arxiv.org/abs/1908.03265
        .. _author's implementation:
            https://github.com/LiyuanLucasLiu/RAdam

        """

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

        See :class:`~torch.optim.RAdam` 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:
            _, 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_radam
        else:
            func = _single_tensor_radam

        func(
            params,
            grads,
            exp_avgs,
            exp_avg_sqs,
            state_steps,
            beta1=beta1,
            beta2=beta2,
            lr=lr,
            weight_decay=weight_decay,
            eps=eps,
            differentiable=differentiable,
        )

    def _single_tensor_radam(
        params: List[Tensor],
        grads: List[Tensor],
        exp_avgs: List[Tensor],
        exp_avg_sqs: List[Tensor],
        state_steps: List[Tensor],
        *,
        beta1: float,
        beta2: float,
        lr: float,
        weight_decay: float,
        eps: float,
        differentiable: bool,
    ):

        for i, param in enumerate(params):
            grad = grads[i]
            exp_avg = exp_avgs[i]
            exp_avg_sq = exp_avg_sqs[i]
            step_t = state_steps[i]
            # update step
            step_t += 1
            step = _get_value(step_t)

            bias_correction1 = 1 - beta1 ** step
            bias_correction2 = 1 - beta2 ** step

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

            # Decay the first and second moment running average coefficient
            exp_avg.lerp_(grad, 1 - beta1)
            exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)

            # correcting bias for the first moving moment
            bias_corrected_exp_avg = exp_avg / bias_correction1

            # maximum length of the approximated SMA
            rho_inf = 2 / (1 - beta2) - 1
            # compute the length of the approximated SMA
            rho_t = rho_inf - 2 * step * (beta2 ** step) / bias_correction2

            if rho_t > 5.0:
                # Compute the variance rectification term and update parameters accordingly
                rect = math.sqrt(
                    (rho_t - 4)
                    * (rho_t - 2)
                    * rho_inf
                    / ((rho_inf - 4) * (rho_inf - 2) * rho_t)
                )
                exp_avg_sq_sqrt = exp_avg_sq.sqrt()
                if differentiable:
                    exp_avg_sq_sqrt = exp_avg_sq_sqrt.add(eps)
                else:
                    exp_avg_sq_sqrt = exp_avg_sq_sqrt.add_(eps)
                adaptive_lr = math.sqrt(bias_correction2) / exp_avg_sq_sqrt
                param.add_(bias_corrected_exp_avg * lr * adaptive_lr * rect, alpha=-1.0)
            else:
                param.add_(bias_corrected_exp_avg * lr, alpha=-1.0)

    def _multi_tensor_radam(
        params: List[Tensor],
        grads: List[Tensor],
        exp_avgs: List[Tensor],
        exp_avg_sqs: List[Tensor],
        state_steps: List[Tensor],
        *,
        beta1: float,
        beta2: float,
        lr: float,
        weight_decay: float,
        eps: float,
        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, exp_avgs, exp_avg_sqs, state_steps])
        for ((
            grouped_params,
            grouped_grads,
            grouped_exp_avgs,
            grouped_exp_avg_sqs,
            grouped_state_steps,
        ), _) in grouped_tensors.values():
            # Update steps
            torch._foreach_add_(grouped_state_steps, 1)

            # maximum length of the approximated SMA
            rho_inf = 2 / (1 - beta2) - 1
            # compute the length of the approximated SMA
            rho_t_list = [rho_inf - 2 * _get_value(step) * (beta2 ** _get_value(step)) /
                          (1 - beta2 ** _get_value(step)) for step in grouped_state_steps]

            if weight_decay != 0:
                grouped_grads = torch._foreach_add(grouped_grads, grouped_params, alpha=weight_decay)

            # Decay the first and second moment running average coefficient
            torch._foreach_lerp_(grouped_exp_avgs, grouped_grads, 1 - beta1)

            torch._foreach_mul_(grouped_exp_avg_sqs, beta2)
            torch._foreach_addcmul_(grouped_exp_avg_sqs, grouped_grads, grouped_grads, 1 - beta2)

            # Delete the local intermediate since it won't be used anymore to save on peak memory
            del grouped_grads

            rect = [
                _dispatch_sqrt(
                    (rho_t - 4)
                    * (rho_t - 2)
                    * rho_inf
                    / ((rho_inf - 4) * (rho_inf - 2) * rho_t)
                )
                if rho_t > 5
                else 0
                for rho_t in rho_t_list
            ]
            unrectified = [0 if rect > 0 else 1.0 for rect in rect]

            bias_correction1 = [1 - beta1 ** _get_value(step) for step in grouped_state_steps]
            unrect_step_size = _stack_if_compiling([(lr * rect / bc) * -1 for rect, bc in zip(unrectified, bias_correction1)])
            bias_correction2_sqrt_times_rect_step_size = [
                _dispatch_sqrt(1 - beta2 ** _get_value(step)) * (lr * rect / bc) * -1
                for step, rect, bc in zip(grouped_state_steps, rect, bias_correction1)
            ]

            buffer = torch._foreach_sqrt(grouped_exp_avg_sqs)
            torch._foreach_add_(buffer, eps)
            torch._foreach_div_(buffer, bias_correction2_sqrt_times_rect_step_size)
            torch._foreach_reciprocal_(buffer)
            torch._foreach_add_(buffer, unrect_step_size)

            # Here, buffer = sqrt(1 - beta2^t) * rect_step_size / (sqrt(v) + eps) + unrect_step_size
            torch._foreach_addcmul_(grouped_params, grouped_exp_avgs, buffer)

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