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# Source code for torch.optim.adamax

    import torch
    from torch import Tensor

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

    __all__ = ["Adamax", "adamax"]

    class Adamax(Optimizer):
        def __init__(
            self,
            params,
            lr=2e-3,
            betas=(0.9, 0.999),
            eps=1e-8,
            weight_decay=0,
            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 <= 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,
                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)
            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_infs, state_steps):
            for p in group["params"]:
                if p.grad is None:
                    continue
                params_with_grad.append(p)
                if p.grad.is_sparse:
                    raise RuntimeError("Adamax does not support sparse gradients")
                grads.append(p.grad)

                state = self.state[p]

                # State initialization
                if len(state) == 0:
                    state["step"] = torch.tensor(0.0)
                    state["exp_avg"] = torch.zeros_like(
                        p, memory_format=torch.preserve_format
                    )
                    state["exp_inf"] = torch.zeros_like(
                        p, memory_format=torch.preserve_format
                    )

                exp_avgs.append(state["exp_avg"])
                exp_infs.append(state["exp_inf"])
                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_infs = []
                state_steps = []

                beta1, beta2 = group["betas"]
                eps = group["eps"]
                lr = group["lr"]
                weight_decay = group["weight_decay"]
                foreach = group["foreach"]
                maximize = group["maximize"]
                differentiable = group["differentiable"]

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

                adamax(
                    params_with_grad,
                    grads,
                    exp_avgs,
                    exp_infs,
                    state_steps,
                    eps=eps,
                    beta1=beta1,
                    beta2=beta2,
                    lr=lr,
                    weight_decay=weight_decay,
                    foreach=foreach,
                    maximize=maximize,
                    differentiable=differentiable,
                )

            return loss

    Adamax.__doc__ = r"""Implements Adamax algorithm (a variant of Adam based on infinity norm).

        .. 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{ (weight decay)},                                                \\
                &\hspace{13mm}    \epsilon \text{ (epsilon)}                                          \\
                &\textbf{initialize} :  m_0 \leftarrow 0 \text{ ( first moment)},
                    u_0 \leftarrow 0 \text{ ( infinity norm)}                                 \\[-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}m_t      \leftarrow   \beta_1 m_{t-1} + (1 - \beta_1) g_t               \\
                &\hspace{5mm}u_t      \leftarrow   \mathrm{max}(\beta_2 u_{t-1}, |g_{t}|+\epsilon)   \\
                &\hspace{5mm}\theta_t \leftarrow \theta_{t-1} - \frac{\gamma m_t}{(1-\beta^t_1) u_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 `Adam: A Method for Stochastic Optimization`_.
        """ + fr"""
        Args:
            params (iterable): iterable of parameters to optimize or dicts defining
                parameter groups
            lr (float, optional): learning rate (default: 2e-3)
            betas (Tuple[float, float], optional): coefficients used for computing
                running averages of gradient and its square
            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}
            {_maximize_doc}
            {_differentiable_doc}

        .. _Adam\: A Method for Stochastic Optimization:
            https://arxiv.org/abs/1412.6980

        """

    def adamax(
        params: List[Tensor],
        grads: List[Tensor],
        exp_avgs: List[Tensor],
        exp_infs: 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,
        *,
        eps: float,
        beta1: float,
        beta2: float,
        lr: float,
        weight_decay: float,
    ):
        r"""Functional API that performs adamax algorithm computation.

        See :class:`~torch.optim.Adamax` 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_adamax
        else:
            func = _single_tensor_adamax

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

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

        for i, param in enumerate(params):
            grad = grads[i]
            grad = grad if not maximize else -grad
            exp_avg = exp_avgs[i]
            exp_inf = exp_infs[i]
            step_t = state_steps[i]
            # update step
            step_t += 1

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

            if torch.is_complex(param):
                param = torch.view_as_real(param)
                grad = torch.view_as_real(grad)
                exp_avg = torch.view_as_real(exp_avg)
                exp_inf = torch.view_as_real(exp_inf)

            # Update biased first moment estimate.
            exp_avg.lerp_(grad, 1 - beta1)
            # Update the exponentially weighted infinity norm.
            norm_buf = torch.cat(
                [exp_inf.mul_(beta2).unsqueeze(0), grad.abs().add_(eps).unsqueeze_(0)], 0
            )

            if not differentiable:
                torch.amax(norm_buf, 0, keepdim=False, out=exp_inf)
            else:
                exp_inf.copy_(torch.amax(norm_buf, 0, keepdim=False))

            bias_correction = 1 - beta1 ** _get_value(step_t)
            clr = lr / bias_correction

            param.addcdiv_(exp_avg, exp_inf, value=-clr)

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

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

        if len(params) == 0:
            return

        grouped_tensors = Optimizer._group_tensors_by_device_and_dtype([params, grads, exp_avgs, exp_infs, state_steps])
        for ((grouped_params, grouped_grads, grouped_exp_avgs, grouped_exp_infs, grouped_state_steps), _) in grouped_tensors.values():
            if maximize:
                grouped_grads = torch._foreach_neg(grouped_grads)

            grouped_params = [torch.view_as_real(x) if torch.is_complex(x) else x for x in grouped_params]
            grouped_grads = [torch.view_as_real(x) if torch.is_complex(x) else x for x in grouped_grads]
            grouped_exp_avgs = [torch.view_as_real(x) if torch.is_complex(x) else x for x in grouped_exp_avgs]
            grouped_exp_infs = [torch.view_as_real(x) if torch.is_complex(x) else x for x in grouped_exp_infs]

            # Update steps
            torch._foreach_add_(grouped_state_steps, 1)

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

            # Update biased first moment estimate.
            torch._foreach_lerp_(grouped_exp_avgs, grouped_grads, 1 - beta1)

            # Update the exponentially weighted infinity norm.
            torch._foreach_mul_(grouped_exp_infs, beta2)

            for exp_inf, grad in zip(grouped_exp_infs, grouped_grads):
                norm_buf = torch.cat(
                    [exp_inf.unsqueeze(0), grad.abs().add_(eps).unsqueeze_(0)], 0
                )
                torch.max(norm_buf, 0, keepdim=False, out=(exp_inf, exp_inf.new().long()))

            bias_corrections = [1 - beta1 ** _get_value(step) for step in grouped_state_steps]
            clr = _stack_if_compiling([-1 * (lr / bias_correction) for bias_correction in bias_corrections])

            torch._foreach_addcdiv_(grouped_params, grouped_exp_avgs, grouped_exp_infs, clr)

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