import torch
from torch import Tensor
from .optimizer import Optimizer, required
from typing import List, Optional


class SGD(Optimizer):
    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`__.

    Args:
        params (iterable): iterable of parameters to optimize or dicts defining
            parameter groups
        lr (float): learning rate
        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 (bool, optional): maximize the params based on the objective, instead of
            minimizing (default: False)
        foreach (bool, optional): whether foreach implementation of optimizer
            is used (default: None)

    Example:
        >>> 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.
    """

    def __init__(self, params, lr=required, momentum=0, dampening=0,
                 weight_decay=0, nesterov=False, *, maximize=False, foreach: Optional[bool] = None):
        if lr is not required and lr < 0.0:
            raise ValueError("Invalid learning rate: {}".format(lr))
        if momentum < 0.0:
            raise ValueError("Invalid momentum value: {}".format(momentum))
        if weight_decay < 0.0:
            raise ValueError("Invalid weight_decay value: {}".format(weight_decay))

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

    @torch.no_grad()
    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 = 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'])

            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


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: 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:
        # Placeholder for more complex foreach logic to be added when value is not set
        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 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

        alpha = lr if maximize else -lr
        param.add_(d_p, alpha=alpha)


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

    if has_sparse_grad is None:
        has_sparse_grad = any([grad.is_sparse for grad in grads])

    if weight_decay != 0:
        grads = torch._foreach_add(grads, params, alpha=weight_decay)

    if momentum != 0:
        bufs = []

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

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

                bufs.append(buf)

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

    alpha = lr if maximize else -lr
    if not has_sparse_grad:
        torch._foreach_add_(params, grads, alpha=alpha)
    else:
        # foreach APIs dont support sparse
        for i in range(len(params)):
            params[i].add_(grads[i], alpha=alpha)