import math
import torch
from .optimizer import Optimizer


class ASGD(Optimizer):
    """Implements Averaged Stochastic Gradient Descent.

    It has been proposed in `Acceleration of stochastic approximation by
    averaging`_.

    Arguments:
        params (iterable): iterable of parameters to optimize or dicts defining
            parameter groups
        lr (float, optional): learning rate (default: 1e-2)
        lambd (float, optional): decay term (default: 1e-4)
        alpha (float, optional): power for eta update (default: 0.75)
        t0 (float, optional): point at which to start averaging (default: 1e6)
        weight_decay (float, optional): weight decay (L2 penalty) (default: 0)

    .. _Acceleration of stochastic approximation by averaging:
        http://dl.acm.org/citation.cfm?id=131098
    """

    def __init__(self, params, lr=1e-2, lambd=1e-4, alpha=0.75, t0=1e6, weight_decay=0):
        if not 0.0 <= lr:
            raise ValueError("Invalid learning rate: {}".format(lr))
        if not 0.0 <= weight_decay:
            raise ValueError("Invalid weight_decay value: {}".format(weight_decay))

        defaults = dict(lr=lr, lambd=lambd, alpha=alpha, t0=t0,
                        weight_decay=weight_decay)
        super(ASGD, self).__init__(params, defaults)

    def step(self, closure=None):
        """Performs a single optimization step.

        Arguments:
            closure (callable, optional): 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:
            for p in group['params']:
                if p.grad is None:
                    continue
                grad = p.grad.data
                if grad.is_sparse:
                    raise RuntimeError('ASGD does not support sparse gradients')
                state = self.state[p]

                # State initialization
                if len(state) == 0:
                    state['step'] = 0
                    state['eta'] = group['lr']
                    state['mu'] = 1
                    state['ax'] = torch.zeros_like(p.data)

                state['step'] += 1

                if group['weight_decay'] != 0:
                    grad = grad.add(group['weight_decay'], p.data)

                # decay term
                p.data.mul_(1 - group['lambd'] * state['eta'])

                # update parameter
                p.data.add_(-state['eta'], grad)

                # averaging
                if state['mu'] != 1:
                    state['ax'].add_(p.data.sub(state['ax']).mul(state['mu']))
                else:
                    state['ax'].copy_(p.data)

                # update eta and mu
                state['eta'] = (group['lr'] /
                                math.pow((1 + group['lambd'] * group['lr'] * state['step']), group['alpha']))
                state['mu'] = 1 / max(1, state['step'] - group['t0'])

        return loss