import math
import torch
from torch.optim import Optimizer
from torch.nn.utils import clip_grad_norm_

def warmup_cosine(x, warmup=0.002):
    s = 1 if x <= warmup else 0
    return s*(x/warmup) + (1-s)*(0.5 * (1 + torch.cos(math.pi * x)))

def warmup_constant(x, warmup=0.002):
    s = 1 if x <= warmup else 0
    return s*(x/warmup) + (1-s)*1

def warmup_linear(x, warmup=0.002):
    s = 1 if x <= warmup else 0
    return (s*(x/warmup) + (1-s))*(1-x)

SCHEDULES = {
    'warmup_cosine':warmup_cosine,
    'warmup_constant':warmup_constant,
    'warmup_linear':warmup_linear,
}


class BERTAdam(Optimizer):
    """Implements Open AI version of Adam algorithm with weight decay fix.
    """
    def __init__(self, params, lr, schedule, warmup, t_total,
                 b1=0.9, b2=0.999, e=1e-6, l2=0,
                 vector_l2=False, max_grad_norm=-1, **kwargs):
        if not 0.0 <= lr:
            raise ValueError("Invalid learning rate: {}".format(lr))
        if schedule not in SCHEDULES:
            raise ValueError("Invalid schedule parameter: {}".format(schedule))
        if not 0 <= warmup:
            raise ValueError("Invalid warmup: {}".format(warmup))
        if not 0.0 <= b1 < 1.0:
            raise ValueError("Invalid b1 parameter: {}".format(b1))
        if not 0.0 <= b2 < 1.0:
            raise ValueError("Invalid b2 parameter: {}".format(b2))
        if not 0.0 <= e:
            raise ValueError("Invalid epsilon value: {}".format(e))
        defaults = dict(lr=lr, schedule=schedule, warmup=warmup, t_total=t_total,
                        b1=b1, b2=b2, e=e, l2=l2, vector_l2=vector_l2,
                        max_grad_norm=max_grad_norm)
        super(BERTAdam, self).__init__(params, defaults)

    def get_lr(self):
        lr = []
        for group in self.param_groups:
            for p in group['params']:
                state = self.state[p]
                if len(state) == 0:
                    return [0]
                schedule_fct = SCHEDULES[group['schedule']]
                lr_scheduled = group['lr'] * schedule_fct(state['step']/group['t_total'], group['warmup'])
                lr.append(lr_scheduled)
        return lr

    def to(self, device):
        """ Move the optimizer state to a specified device"""
        for state in self.state.values():
            state['exp_avg'].to(device)
            state['exp_avg_sq'].to(device)

    def initialize_step(self, initial_step):
        """Initialize state with a defined step (but we don't have stored averaged).
        Arguments:
            initial_step (int): Initial step number.
        """
        for group in self.param_groups:
            for p in group['params']:
                state = self.state[p]
                # State initialization
                state['step'] = initial_step
                # Exponential moving average of gradient values
                state['exp_avg'] = torch.zeros_like(p.data)
                # Exponential moving average of squared gradient values
                state['exp_avg_sq'] = torch.zeros_like(p.data)

    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('Adam does not support sparse gradients, please consider SparseAdam instead')

                state = self.state[p]

                # State initialization
                if len(state) == 0:
                    state['step'] = 0
                    # Exponential moving average of gradient values
                    state['exp_avg'] = torch.zeros_like(p.data)
                    # Exponential moving average of squared gradient values
                    state['exp_avg_sq'] = torch.zeros_like(p.data)

                exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
                beta1, beta2 = group['b1'], group['b2']

                state['step'] += 1

                # Add grad clipping
                if group['max_grad_norm'] > 0:
                    clip_grad_norm_(p, group['max_grad_norm'])

                # Decay the first and second moment running average coefficient
                exp_avg.mul_(beta1).add_(1 - beta1, grad)
                exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)
                denom = exp_avg_sq.sqrt().add_(group['e'])

                bias_correction1 = 1 - beta1 ** state['step']
                bias_correction2 = 1 - beta2 ** state['step']

                schedule_fct = SCHEDULES[group['schedule']]
                lr_scheduled = group['lr'] * schedule_fct(state['step']/group['t_total'], group['warmup'])
                step_size = lr_scheduled * math.sqrt(bias_correction2) / bias_correction1

                p.data.addcdiv_(-step_size, exp_avg, denom)

                # Just adding the square of the weights to the loss function is *not*
                # the correct way of using L2 regularization/weight decay with Adam,
                # since that will interact with the m and v parameters in strange ways.
                #
                # Instead we want ot decay the weights in a manner that doesn't interact
                # with the m/v parameters. This is equivalent to adding the square
                # of the weights to the loss with plain (non-momentum) SGD.
                if (len(p.size()) > 1 or group['vector_l2']) and group['l2'] > 0:
                    p.data.add_(-lr_scheduled * group['l2'], p.data)

        return loss