import math
from typing import List, Optional

import torch
from torch import Tensor

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

__all__ = ["RAdam", "radam"]


class RAdam(Optimizer):
    def __init__(
        self,
        params,
        lr=1e-3,
        betas=(0.9, 0.999),
        eps=1e-8,
        weight_decay=0,
        decoupled_weight_decay: bool = False,
        *,
        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,
            decoupled_weight_decay=decoupled_weight_decay,
            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)
            group.setdefault("decoupled_weight_decay", 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"],
                decoupled_weight_decay=group["decoupled_weight_decay"],
            )

        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)}, \textit{decoupled\_weight\_decay}         \\
            &\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{6mm} \theta_t \leftarrow \theta_{t-1}                                       \\
            &\hspace{6mm} \textbf{if} \: \lambda \neq 0                                          \\
            &\hspace{12mm}\textbf{if} \: \textit{decoupled\_weight\_decay}                       \\
            &\hspace{18mm} \theta_t \leftarrow \theta_{t} - \gamma \lambda \theta_{t}            \\
            &\hspace{12mm}\textbf{else}                                                          \\
            &\hspace{18mm} g_t \leftarrow g_t + \lambda \theta_{t}                               \\
            &\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 - \gamma \widehat{m_t} r_t l_t        \\
            &\hspace{6mm}\textbf{else}                                                           \\
            &\hspace{12mm}\theta_t \leftarrow \theta_t - \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 provides an option to use either the original weight_decay implementation as in Adam
    (where the weight_decay is applied to the gradient) or the one from AdamW (where weight_decay is applied
    to the weight) through the decoupled_weight_decay option. When decoupled_weight_decay is set to False
    (default), it uses the original Adam style weight decay, otherwise, it uses the AdamW style which
    corresponds more closely to the `author's implementation`_ in the RAdam paper. Further information
    about decoupled weight decay can be found in `Decoupled Weight Decay Regularization`_.

    """ + 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)
        decoupled_weight_decay (bool, optional): whether to use decoupled weight
            decay as in AdamW to obtain RAdamW (default: False)
        {_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
    .. _Decoupled Weight Decay Regularization:
        https://arxiv.org/abs/1711.05101

    """


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
    decoupled_weight_decay: bool = False,
    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,
        decoupled_weight_decay=decoupled_weight_decay,
        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,
    decoupled_weight_decay: 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:
            if decoupled_weight_decay:
                param.mul_(1 - lr * weight_decay)
            else:
                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,
    decoupled_weight_decay: 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, 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:
            if decoupled_weight_decay:
                torch._foreach_mul_(grouped_params, 1 - lr * weight_decay)
            else:
                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)