import math

import torch
from torch.optim.optimizer import Optimizer

from .types import OptFloat, OptLossClosure, Params

__all__ = ('SGDP',)


class SGDP(Optimizer):
    r"""Implements SGDP algorithm.

    It has been proposed in `Slowing Down the Weight Norm Increase in
    Momentum-based Optimizers`__

    Arguments:
        params: iterable of parameters to optimize or dicts defining
            parameter groups
        lr: learning rate (default: 1e-3)
        momentum: momentum factor (default: 0)
        dampening: dampening for momentum (default: 0)
        eps: term added to the denominator to improve
            numerical stability (default: 1e-8)
        weight_decay: weight decay (L2 penalty) (default: 0)
        delta: threhold that determines whether a set of parameters is scale
            invariant or not (default: 0.1)
        wd_ratio: relative weight decay applied on scale-invariant parameters
            compared to that applied on scale-variant parameters (default: 0.1)
        nesterov: enables Nesterov momentum (default: False)


    Example:
        >>> import torch_optimizer as optim
        >>> optimizer = optim.SGDP(model.parameters(), lr=0.1)
        >>> optimizer.zero_grad()
        >>> loss_fn(model(input), target).backward()
        >>> optimizer.step()

     __ https://arxiv.org/abs/2006.08217

    Note:
        Reference code: https://github.com/clovaai/AdamP
    """

    def __init__(
        self,
        params: Params,
        lr: float = 1e-3,
        momentum: float = 0,
        dampening: float = 0,
        eps: float = 1e-8,
        weight_decay: float = 0,
        delta: float = 0.1,
        wd_ratio: float = 0.1,
        nesterov: bool = False,
    ) -> None:
        if lr <= 0.0:
            raise ValueError('Invalid learning rate: {}'.format(lr))
        if eps < 0.0:
            raise ValueError('Invalid epsilon value: {}'.format(eps))
        if momentum < 0.0:
            raise ValueError('Invalid momentum value: {}'.format(momentum))
        if dampening < 0.0:
            raise ValueError('Invalid dampening value: {}'.format(dampening))
        if weight_decay < 0:
            raise ValueError(
                'Invalid weight_decay value: {}'.format(weight_decay)
            )
        if delta < 0:
            raise ValueError('Invalid delta value: {}'.format(delta))
        if wd_ratio < 0:
            raise ValueError('Invalid wd_ratio value: {}'.format(wd_ratio))

        defaults = dict(
            lr=lr,
            momentum=momentum,
            dampening=dampening,
            eps=eps,
            weight_decay=weight_decay,
            delta=delta,
            wd_ratio=wd_ratio,
            nesterov=nesterov,
        )
        super(SGDP, self).__init__(params, defaults)

    @staticmethod
    def _channel_view(x):
        return x.view(x.size(0), -1)

    @staticmethod
    def _layer_view(x):
        return x.view(1, -1)

    @staticmethod
    def _cosine_similarity(x, y, eps, view_func):
        x = view_func(x)
        y = view_func(y)

        x_norm = x.norm(dim=1).add_(eps)
        y_norm = y.norm(dim=1).add_(eps)
        dot = (x * y).sum(dim=1)

        return dot.abs() / x_norm / y_norm

    def _projection(self, p, grad, perturb, delta, wd_ratio, eps):
        wd = 1
        expand_size = [-1] + [1] * (len(p.shape) - 1)
        for view_func in [self._channel_view, self._layer_view]:

            cosine_sim = self._cosine_similarity(grad, p.data, eps, view_func)

            if cosine_sim.max() < delta / math.sqrt(view_func(p.data).size(1)):
                p_n = p.data / view_func(p.data).norm(dim=1).view(
                    expand_size
                ).add_(eps)
                perturb -= p_n * view_func(p_n * perturb).sum(dim=1).view(
                    expand_size
                )
                wd = wd_ratio

                return perturb, wd

        return perturb, wd

    def step(self, closure: OptLossClosure = None) -> OptFloat:
        r"""Performs a single optimization step.

        Arguments:
            closure: A closure that reevaluates the model and returns the loss.
        """
        loss = None
        if closure is not None:
            loss = closure()

        for group in self.param_groups:
            weight_decay = group['weight_decay']
            momentum = group['momentum']
            dampening = group['dampening']
            nesterov = group['nesterov']

            for p in group['params']:
                if p.grad is None:
                    continue

                grad = p.grad.data
                state = self.state[p]

                # State initialization
                if len(state) == 0:
                    state['momentum'] = torch.zeros_like(p.data)

                # SGD
                buf = state['momentum']
                buf.mul_(momentum).add_(grad, alpha=1 - dampening)
                if nesterov:
                    d_p = grad + momentum * buf
                else:
                    d_p = buf

                # Projection
                wd_ratio = 1
                if len(p.shape) > 1:
                    d_p, wd_ratio = self._projection(
                        p,
                        grad,
                        d_p,
                        group['delta'],
                        group['wd_ratio'],
                        group['eps'],
                    )

                # Weight decay
                if weight_decay != 0:
                    p.data.mul_(
                        1
                        - group['lr']
                        * group['weight_decay']
                        * wd_ratio
                        / (1 - momentum)
                    )

                # Step
                p.data.add_(d_p, alpha=-group['lr'])

        return loss