import torch
from torch import Tensor
from .optimizer import (Optimizer, _use_grad_for_differentiable, _default_to_fused_or_foreach,
                        _differentiable_doc, _foreach_doc, _maximize_doc)
from typing import List, Optional

__all__ = ['SGD', 'sgd']


class SGD(Optimizer):
    def __init__(self, params, lr=1e-3, momentum=0, dampening=0,
                 weight_decay=0, nesterov=False, *, maximize: bool = False, foreach: Optional[bool] = None,
                 differentiable: bool = False):
        if lr < 0.0:
            raise ValueError(f"Invalid learning rate: {lr}")
        if momentum < 0.0:
            raise ValueError(f"Invalid momentum value: {momentum}")
        if weight_decay < 0.0:
            raise ValueError(f"Invalid weight_decay value: {weight_decay}")

        defaults = dict(lr=lr, momentum=momentum, dampening=dampening,
                        weight_decay=weight_decay, nesterov=nesterov,
                        maximize=maximize, foreach=foreach,
                        differentiable=differentiable)
        if nesterov and (momentum <= 0 or dampening != 0):
            raise ValueError("Nesterov momentum requires a momentum and zero dampening")
        super().__init__(params, defaults)

    def __setstate__(self, state):
        super().__setstate__(state)
        for group in self.param_groups:
            group.setdefault('nesterov', False)
            group.setdefault('maximize', False)
            group.setdefault('foreach', None)
            group.setdefault('differentiable', False)

    def _init_group(self, group, params_with_grad, d_p_list, momentum_buffer_list):
        has_sparse_grad = False

        for p in group['params']:
            if p.grad is not None:
                params_with_grad.append(p)
                d_p_list.append(p.grad)
                if p.grad.is_sparse:
                    has_sparse_grad = True

                state = self.state[p]
                if 'momentum_buffer' not in state:
                    momentum_buffer_list.append(None)
                else:
                    momentum_buffer_list.append(state['momentum_buffer'])

        return has_sparse_grad

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

        Args:
            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:
            params_with_grad = []
            d_p_list = []
            momentum_buffer_list = []

            has_sparse_grad = self._init_group(group, params_with_grad, d_p_list, momentum_buffer_list)

            sgd(params_with_grad,
                d_p_list,
                momentum_buffer_list,
                weight_decay=group['weight_decay'],
                momentum=group['momentum'],
                lr=group['lr'],
                dampening=group['dampening'],
                nesterov=group['nesterov'],
                maximize=group['maximize'],
                has_sparse_grad=has_sparse_grad,
                foreach=group['foreach'])

            # update momentum_buffers in state
            for p, momentum_buffer in zip(params_with_grad, momentum_buffer_list):
                state = self.state[p]
                state['momentum_buffer'] = momentum_buffer

        return loss


SGD.__doc__ = r"""Implements stochastic gradient descent (optionally with momentum).

    .. math::
       \begin{aligned}
            &\rule{110mm}{0.4pt}                                                                 \\
            &\textbf{input}      : \gamma \text{ (lr)}, \: \theta_0 \text{ (params)}, \: f(\theta)
                \text{ (objective)}, \: \lambda \text{ (weight decay)},                          \\
            &\hspace{13mm} \:\mu \text{ (momentum)}, \:\tau \text{ (dampening)},
            \:\textit{ nesterov,}\:\textit{ maximize}                                     \\[-1.ex]
            &\rule{110mm}{0.4pt}                                                                 \\
            &\textbf{for} \: t=1 \: \textbf{to} \: \ldots \: \textbf{do}                         \\
            &\hspace{5mm}g_t           \leftarrow   \nabla_{\theta} f_t (\theta_{t-1})           \\
            &\hspace{5mm}\textbf{if} \: \lambda \neq 0                                           \\
            &\hspace{10mm} g_t \leftarrow g_t + \lambda  \theta_{t-1}                            \\
            &\hspace{5mm}\textbf{if} \: \mu \neq 0                                               \\
            &\hspace{10mm}\textbf{if} \: t > 1                                                   \\
            &\hspace{15mm} \textbf{b}_t \leftarrow \mu \textbf{b}_{t-1} + (1-\tau) g_t           \\
            &\hspace{10mm}\textbf{else}                                                          \\
            &\hspace{15mm} \textbf{b}_t \leftarrow g_t                                           \\
            &\hspace{10mm}\textbf{if} \: \textit{nesterov}                                       \\
            &\hspace{15mm} g_t \leftarrow g_{t} + \mu \textbf{b}_t                             \\
            &\hspace{10mm}\textbf{else}                                                   \\[-1.ex]
            &\hspace{15mm} g_t  \leftarrow  \textbf{b}_t                                         \\
            &\hspace{5mm}\textbf{if} \: \textit{maximize}                                          \\
            &\hspace{10mm}\theta_t \leftarrow \theta_{t-1} + \gamma g_t                   \\[-1.ex]
            &\hspace{5mm}\textbf{else}                                                    \\[-1.ex]
            &\hspace{10mm}\theta_t \leftarrow \theta_{t-1} - \gamma g_t                   \\[-1.ex]
            &\rule{110mm}{0.4pt}                                                          \\[-1.ex]
            &\bf{return} \:  \theta_t                                                     \\[-1.ex]
            &\rule{110mm}{0.4pt}                                                          \\[-1.ex]
       \end{aligned}

    Nesterov momentum is based on the formula from
    `On the importance of initialization and momentum in deep learning`__.
    """ + fr"""
    Args:
        params (iterable): iterable of parameters to optimize or dicts defining
            parameter groups
        lr (float, optional): learning rate (default: 1e-3)
        momentum (float, optional): momentum factor (default: 0)
        weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
        dampening (float, optional): dampening for momentum (default: 0)
        nesterov (bool, optional): enables Nesterov momentum (default: False)
        {_maximize_doc}
        {_foreach_doc}
        {_differentiable_doc}
    """ + r"""

    Example:
        >>> # xdoctest: +SKIP
        >>> optimizer = torch.optim.SGD(model.parameters(), lr=0.1, momentum=0.9)
        >>> optimizer.zero_grad()
        >>> loss_fn(model(input), target).backward()
        >>> optimizer.step()

    __ http://www.cs.toronto.edu/%7Ehinton/absps/momentum.pdf

    .. note::
        The implementation of SGD with Momentum/Nesterov subtly differs from
        Sutskever et. al. and implementations in some other frameworks.

        Considering the specific case of Momentum, the update can be written as

        .. math::
            \begin{aligned}
                v_{t+1} & = \mu * v_{t} + g_{t+1}, \\
                p_{t+1} & = p_{t} - \text{lr} * v_{t+1},
            \end{aligned}

        where :math:`p`, :math:`g`, :math:`v` and :math:`\mu` denote the
        parameters, gradient, velocity, and momentum respectively.

        This is in contrast to Sutskever et. al. and
        other frameworks which employ an update of the form

        .. math::
            \begin{aligned}
                v_{t+1} & = \mu * v_{t} + \text{lr} * g_{t+1}, \\
                p_{t+1} & = p_{t} - v_{t+1}.
            \end{aligned}

        The Nesterov version is analogously modified.

        Moreover, the initial value of the momentum buffer is set to the
        gradient value at the first step. This is in contrast to some other
        frameworks that initialize it to all zeros.

    """


def sgd(params: List[Tensor],
        d_p_list: List[Tensor],
        momentum_buffer_list: List[Optional[Tensor]],
        # kwonly args with defaults are not supported by functions compiled with torchscript issue #70627
        # setting this as kwarg for now as functional API is compiled by torch/distributed/optim
        has_sparse_grad: bool = None,
        foreach: Optional[bool] = None,
        *,
        weight_decay: float,
        momentum: float,
        lr: float,
        dampening: float,
        nesterov: bool,
        maximize: bool):
    r"""Functional API that performs SGD algorithm computation.

    See :class:`~torch.optim.SGD` for details.
    """

    if foreach is None:
        # why must we be explicit about an if statement for torch.jit.is_scripting here?
        # because JIT can't handle Optionals nor fancy conditionals when scripting
        if not torch.jit.is_scripting():
            _, foreach = _default_to_fused_or_foreach(params, differentiable=False, use_fused=False)
        else:
            foreach = False

    if foreach and torch.jit.is_scripting():
        raise RuntimeError('torch.jit.script not supported with foreach optimizers')

    if foreach and not torch.jit.is_scripting():
        func = _multi_tensor_sgd
    else:
        func = _single_tensor_sgd

    func(params,
         d_p_list,
         momentum_buffer_list,
         weight_decay=weight_decay,
         momentum=momentum,
         lr=lr,
         dampening=dampening,
         nesterov=nesterov,
         has_sparse_grad=has_sparse_grad,
         maximize=maximize)

def _single_tensor_sgd(params: List[Tensor],
                       d_p_list: List[Tensor],
                       momentum_buffer_list: List[Optional[Tensor]],
                       *,
                       weight_decay: float,
                       momentum: float,
                       lr: float,
                       dampening: float,
                       nesterov: bool,
                       maximize: bool,
                       has_sparse_grad: bool):

    for i, param in enumerate(params):
        d_p = d_p_list[i] if not maximize else -d_p_list[i]

        if weight_decay != 0:
            d_p = d_p.add(param, alpha=weight_decay)

        if momentum != 0:
            buf = momentum_buffer_list[i]

            if buf is None:
                buf = torch.clone(d_p).detach()
                momentum_buffer_list[i] = buf
            else:
                buf.mul_(momentum).add_(d_p, alpha=1 - dampening)

            if nesterov:
                d_p = d_p.add(buf, alpha=momentum)
            else:
                d_p = buf

        param.add_(d_p, alpha=-lr)


def _multi_tensor_sgd(params: List[Tensor],
                      grads: List[Tensor],
                      momentum_buffer_list: List[Optional[Tensor]],
                      *,
                      weight_decay: float,
                      momentum: float,
                      lr: float,
                      dampening: float,
                      nesterov: bool,
                      maximize: bool,
                      has_sparse_grad: bool):

    if len(params) == 0:
        return

    grouped_tensors = Optimizer._group_tensors_by_device_and_dtype([params, grads, momentum_buffer_list], with_indices=True)
    for ((device_params, device_grads, device_momentum_buffer_list), indices) in grouped_tensors.values():
        device_has_sparse_grad = has_sparse_grad and any(grad.is_sparse for grad in device_grads)

        if maximize:
            device_grads = torch._foreach_neg(device_grads)

        if weight_decay != 0:
            # Re-use the intermediate memory (device_grads) already allocated for maximize
            if maximize:
                torch._foreach_add_(device_grads, device_params, alpha=weight_decay)
            else:
                device_grads = torch._foreach_add(device_grads, device_params, alpha=weight_decay)

        if momentum != 0:
            bufs = []

            all_states_with_momentum_buffer = True
            for i in range(len(device_momentum_buffer_list)):
                if device_momentum_buffer_list[i] is None:
                    all_states_with_momentum_buffer = False
                    break
                else:
                    bufs.append(device_momentum_buffer_list[i])

            if all_states_with_momentum_buffer:
                torch._foreach_mul_(bufs, momentum)
                torch._foreach_add_(bufs, device_grads, alpha=1 - dampening)
            else:
                bufs = []
                for i in range(len(device_momentum_buffer_list)):
                    if device_momentum_buffer_list[i] is None:
                        buf = device_momentum_buffer_list[i] = momentum_buffer_list[indices[i]] = \
                            torch.clone(device_grads[i]).detach()
                    else:
                        buf = device_momentum_buffer_list[i]
                        buf.mul_(momentum).add_(device_grads[i], alpha=1 - dampening)

                    bufs.append(buf)

            if nesterov:
                torch._foreach_add_(device_grads, bufs, alpha=momentum)
            else:
                device_grads = bufs

        if not device_has_sparse_grad:
            torch._foreach_add_(device_params, device_grads, alpha=-lr)
        else:
            # foreach APIs don't support sparse
            for i in range(len(device_params)):
                device_params[i].add_(device_grads[i], alpha=-lr)
