
"""PyTorch optimization for BERT model."""

import math
import torch
from torch.optim import Optimizer
from torch.optim.optimizer import required   # ? required?
from torch.nn.utils import clip_grad_norm_
import logging

logger = logging.getLogger(__name__)

def warmup_cosine(x, warmup=0.002):
    if x < warmup:
        return x/warmup
    return 0.5 * (1.0 + torch.cos(math.pi * x))

def warmup_constant(x, warmup=0.002):
    """ Linearly increases learning rate over `warmup`*`t_total` (as provided to BertAdam) training steps.
        Learning rate is 1, afterwards. """
    if x < warmup:
        return x/warmup
    return 1.0

def warmup_linear(x, warmup=0.002):
    """ Specifies a triangular learning rate schedule where peak is reached at 
        `warmup`*`t_total`-th (as provided to BertAdam) training step.
        After `t_total`-th training step, learning rate is zero. """
    if x < warmup:
        return x/warmup
    return max((x-1.)/(warmup-1.), 0)

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


class BertAdam(Optimizer):
    """Implements BERT version of Adam algorithm with weight decay fix.
    Params:
        lr: learning rate
        warmup: portion of t_total for the warmup. (Default: -1, no warmup)
        t_total: total number of training steps for the learning rate schedule,
                (Default: -1, constant learning rate)
        schedule: schedule for the warmup. (Default: 'warmup_linear')
        b1: Adams b1.      Default: 0.9
        b2: Adams b2.      Default: 0.999
        e:  Adams epsilon. Default: 1e-6
        weight_decay:      Default: 0.01
        max_grad_norm: Maximum norm for the gradients. Default: 1.0, no clipping.
    """
    def __init__(self, params, lr=required, warmup=-1, t_total=-1, schedule='warmup_linear',
        b1=0.9, b2=0.999, e=1e-6, weight_decay=0.05, max_grad_norm=0.05):
        if lr is not required and lr < 0.0:                   # required?
            raise ValueError("Invalid learning rate: {} - should be >= 0.0".format(lr))
        if schedule not in SCHEDULES:
            raise ValueError("Invalid schedule parameter: {}".format(schedule))
        if not 0.0 <= warmup < 1.0 and not warmup == -1:
            raise ValueError("Invalid warmup: {} - should be in [0.0, 1.0[ or -1".format(warmup))
        if not 0.0 <= b1 < 1.0:
            raise ValueError("Invalid b1 parameter: {} - should be in [0.0, 1.0[".format(b1))
        if not 0.0 <= b2 < 1.0:
            raise ValueError("Invalid b2 parameter: {} - should be in [0.0, 1.0[".format(b2))
        if not e >= 0.0:
            raise ValueError("Invalid epsilon value: {} - should be >= 0.0".format(e))

        defaults = dict(lr=lr, schedule=schedule, warmup=warmup, t_total=t_total,
                        b1=b1, b2=b2, e=e, weight_decay=weight_decay,
                        max_grad_norm=max_grad_norm)
        super(BertAdam, self).__init__(params, defaults)
        self.warned_for_t_total = False

    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]
                if group['t_total'] != -1:
                    schedule_fct = SCHEDULES[group['schedule']]
                    lr_scheduled = group['lr'] * schedule_fct(state['step']/group['t_total'], group['warmup'])
                else:
                    lr_scheduled = group['lr']
                lr.append(lr_scheduled)
        return lr

    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['next_m'] = torch.zeros_like(p.data)
                    # Exponential moving average of squared gradient values
                    state['next_v'] = torch.zeros_like(p.data)

                next_m, next_v = state['next_m'], state['next_v']
                beta1, beta2 = group['b1'], group['b2']

                # Add grad clipping
                if group['max_grad_norm'] > 0:
                    norm = clip_grad_norm_(p, group['max_grad_norm'])
                    
                # Decay the first and second moment running average coefficient
                # In-place operations to update the averages at the same time
                next_m.mul_(beta1).add_(grad, alpha=1 - beta1)
                next_v.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)
                update = next_m / (next_v.sqrt() + group['e'])

                # 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 to 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 group['weight_decay'] > 0.0:
                    update += group['weight_decay'] * p.data

                if group['t_total'] != -1:
                    schedule_fct = SCHEDULES[group['schedule']]
                    progress = state['step']/group['t_total']
                    lr_scheduled = group['lr'] * schedule_fct(progress, group['warmup'])
                    
                    # warning for exceeding t_total (only active with warmup_linear
                    if group['schedule'] == "warmup_linear" and progress > 1. and not self.warned_for_t_total:
                        logger.warning(
                            "Training beyond specified 't_total' steps with schedule '{}'. Learning rate set to {}. "
                            "Please set 't_total' of {} correctly.".format(group['schedule'], lr_scheduled, self.__class__.__name__))
                        self.warned_for_t_total = True
                    # end warning
                else:
                    lr_scheduled = group['lr']

                update_with_lr = lr_scheduled * update
                p.data.add_(-update_with_lr)

                state['step'] += 1

                # step_size = lr_scheduled * math.sqrt(bias_correction2) / bias_correction1
                # No bias correction
                # bias_correction1 = 1 - beta1 ** state['step']
                # bias_correction2 = 1 - beta2 ** state['step']

        return loss
