"""
From PyTorch:

Copyright (c) 2016-     Facebook, Inc            (<NAME>)
Copyright (c) 2014-     Facebook, Inc            (<NAME>)
Copyright (c) 2011-2014 Idiap Research Institute (<NAME>)
Copyright (c) 2012-2014 Deepmind Technologies    (Koray Kavukcuoglu)
Copyright (c) 2011-2012 NEC Laboratories America (Koray Kavukcuoglu)
Copyright (c) 2011-2013 NYU                      (<NAME>)
Copyright (c) 2006-2010 NEC Laboratories America (<NAME>, <NAME>, <NAME>, <NAME>)
Copyright (c) 2006      Idiap Research Institute (<NAME>)
Copyright (c) 2001-2004 Idiap Research Institute (<NAME>, <NAME>, <NAME>)

From Caffe2:

Copyright (c) 2016-present, Facebook Inc. All rights reserved.

All contributions by Facebook:
Copyright (c) 2016 Facebook Inc.
 
All contributions by Google:
Copyright (c) 2015 Google Inc.
All rights reserved.
 
All contributions by Yangqing Jia:
Copyright (c) 2015 Yangqing Jia
All rights reserved.
 
All contributions from Caffe:
Copyright(c) 2013, 2014, 2015, the respective contributors
All rights reserved.
 
All other contributions:
Copyright(c) 2015, 2016 the respective contributors
All rights reserved.
 
Caffe2 uses a copyright model similar to Caffe: each contributor holds
copyright over their contributions to Caffe2. The project versioning records
all such contribution and copyright details. If a contributor wants to further
mark their specific copyright on a particular contribution, they should
indicate their copyright solely in the commit message of the change when it is
committed.

All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright
   notice, this list of conditions and the following disclaimer.

2. Redistributions in binary form must reproduce the above copyright
   notice, this list of conditions and the following disclaimer in the
   documentation and/or other materials provided with the distribution.

3. Neither the names of Facebook, Deepmind Technologies, NYU, NEC Laboratories America
   and IDIAP Research Institute nor the names of its contributors may be
   used to endorse or promote products derived from this software without
   specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.
"""
import torch

from torch.optim.optimizer import Optimizer


class Adadelta(Optimizer):
    """Implements Adadelta algorithm.

    It has been proposed in `ADADELTA: An Adaptive Learning Rate Method`__.

    Arguments:
        params (iterable): iterable of parameters to optimize or dicts defining
            parameter groups
        rho (float, optional): coefficient used for computing a running average
            of squared gradients (default: 0.9)
        eps (float, optional): term added to the denominator to improve
            numerical stability (default: 1e-6)
        lr (float, optional): coefficient that scale delta before it is applied
            to the parameters (default: 1.0)
        weight_decay (float, optional): weight decay (L2 penalty) (default: 0)

    __ https://arxiv.org/abs/1212.5701
    """

    def __init__(self, params, lr=1.0, rho=0.9, eps=1e-6, weight_decay=0):
        if not 0.0 <= lr:
            raise ValueError("Invalid learning rate: {}".format(lr))
        if not 0.0 <= rho <= 1.0:
            raise ValueError("Invalid rho value: {}".format(rho))
        if not 0.0 <= eps:
            raise ValueError("Invalid epsilon value: {}".format(eps))
        if not 0.0 <= weight_decay:
            raise ValueError("Invalid weight_decay value: {}".format(weight_decay))

        defaults = dict(lr=lr, rho=rho, eps=eps, weight_decay=weight_decay)
        super(Adadelta, self).__init__(params, defaults)

    @torch.no_grad()
    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:
            with torch.enable_grad():
                loss = closure()

        for group in self.param_groups:
            for p in group['params']:
                if p.grad is None:
                    continue
                grad = p.grad
                if grad.is_sparse:
                    raise RuntimeError('Adadelta does not support sparse gradients')
                state = self.state[p]

                # State initialization
                if len(state) == 0:
                    state['step'] = 0
                    state['square_avg'] = torch.zeros_like(p, memory_format=torch.preserve_format)
                    state['acc_delta'] = torch.zeros_like(p, memory_format=torch.preserve_format)

                square_avg, acc_delta = state['square_avg'], state['acc_delta']
                rho, eps = group['rho'], group['eps']

                state['step'] += 1

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

                square_avg.mul_(rho).addcmul_(grad, grad, value=1 - rho)
                std = square_avg.add(eps).sqrt_()
                delta = acc_delta.add(eps).sqrt_().div_(std).mul_(grad)
                p.add_(delta, alpha=-group['lr'])
                acc_delta.mul_(rho).addcmul_(delta, delta, value=1 - rho)

        return loss
