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


class Rprop(Optimizer):
    r"""Implements the resilient backpropagation algorithm.

    .. math::
       \begin{aligned}
            &\rule{110mm}{0.4pt}                                                                 \\
            &\textbf{input}      : \theta_0 \in \mathbf{R}^d \text{ (params)},f(\theta)
                \text{ (objective)},                                                             \\
            &\hspace{13mm}      \eta_{+/-} \text{ (etaplus, etaminus)}, \Gamma_{max/min}
                \text{ (step sizes)}                                                             \\
            &\textbf{initialize} :   g^0_{prev} \leftarrow 0,
                \: \eta_0 \leftarrow \text{lr (learning rate)}                                   \\
            &\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{for} \text{  } i = 0, 1, \ldots, d-1 \: \mathbf{do}            \\
            &\hspace{10mm}  \textbf{if} \:   g^i_{prev} g^i_t  > 0                               \\
            &\hspace{15mm}  \eta^i_t \leftarrow \mathrm{min}(\eta^i_{t-1} \eta_{+},
                \Gamma_{max})                                                                    \\
            &\hspace{10mm}  \textbf{else if}  \:  g^i_{prev} g^i_t < 0                           \\
            &\hspace{15mm}  \eta^i_t \leftarrow \mathrm{max}(\eta^i_{t-1} \eta_{-},
                \Gamma_{min})                                                                    \\
            &\hspace{10mm}  \textbf{else}  \:                                                    \\
            &\hspace{15mm}  \eta^i_t \leftarrow \eta^i_{t-1}                                     \\
            &\hspace{5mm}\theta_t \leftarrow \theta_{t-1}- \eta_t \mathrm{sign}(g_t)             \\
            &\hspace{5mm}g_{prev} \leftarrow  g_t                                                \\
            &\rule{110mm}{0.4pt}                                                          \\[-1.ex]
            &\bf{return} \:  \theta_t                                                     \\[-1.ex]
            &\rule{110mm}{0.4pt}                                                          \\[-1.ex]
       \end{aligned}

    For further details regarding the algorithm we refer to the paper
    `A Direct Adaptive Method for Faster Backpropagation Learning: The RPROP Algorithm
    <http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.21.1417>`_.

    Args:
        params (iterable): iterable of parameters to optimize or dicts defining
            parameter groups
        lr (float, optional): learning rate (default: 1e-2)
        etas (Tuple[float, float], optional): pair of (etaminus, etaplis), that
            are multiplicative increase and decrease factors
            (default: (0.5, 1.2))
        step_sizes (Tuple[float, float], optional): a pair of minimal and
            maximal allowed step sizes (default: (1e-6, 50))
        foreach (bool, optional): whether foreach implementation of optimizer
            is used (default: None)
    """

    def __init__(self, params, lr=1e-2, etas=(0.5, 1.2), step_sizes=(1e-6, 50),
                 foreach: Optional[bool] = None):
        if not 0.0 <= lr:
            raise ValueError("Invalid learning rate: {}".format(lr))
        if not 0.0 < etas[0] < 1.0 < etas[1]:
            raise ValueError("Invalid eta values: {}, {}".format(etas[0], etas[1]))

        defaults = dict(lr=lr, etas=etas, step_sizes=step_sizes, foreach=foreach)
        super(Rprop, self).__init__(params, defaults)

    def __setstate__(self, state):
        super().__setstate__(state)
        for group in self.param_groups:
            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 = []
            grads = []
            prevs = []
            step_sizes = []
            etaminus, etaplus = group['etas']
            step_size_min, step_size_max = group['step_sizes']
            foreach = group['foreach']

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

                grads.append(grad)
                state = self.state[p]

                # State initialization
                if len(state) == 0:
                    state['step'] = 0
                    state['prev'] = torch.zeros_like(p, memory_format=torch.preserve_format)
                    state['step_size'] = grad.new().resize_as_(grad).fill_(group['lr'])

                prevs.append(state['prev'])
                step_sizes.append(state['step_size'])

                state['step'] += 1

            rprop(params,
                  grads,
                  prevs,
                  step_sizes,
                  step_size_min=step_size_min,
                  step_size_max=step_size_max,
                  etaminus=etaminus,
                  etaplus=etaplus,
                  foreach=foreach)

        return loss


def rprop(params: List[Tensor],
          grads: List[Tensor],
          prevs: List[Tensor],
          step_sizes: List[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
          foreach: bool = None,
          *,
          step_size_min: float,
          step_size_max: float,
          etaminus: float,
          etaplus: float):
    r"""Functional API that performs rprop algorithm computation.

    See :class:`~torch.optim.Rprop` 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_rprop
    else:
        func = _single_tensor_rprop

    func(params,
         grads,
         prevs,
         step_sizes,
         step_size_min=step_size_min,
         step_size_max=step_size_max,
         etaminus=etaminus,
         etaplus=etaplus)


def _single_tensor_rprop(params: List[Tensor],
                         grads: List[Tensor],
                         prevs: List[Tensor],
                         step_sizes: List[Tensor],
                         *,
                         step_size_min: float,
                         step_size_max: float,
                         etaminus: float,
                         etaplus: float):

    for i, param in enumerate(params):
        grad = grads[i]
        prev = prevs[i]
        step_size = step_sizes[i]

        sign = grad.mul(prev).sign()
        sign[sign.gt(0)] = etaplus
        sign[sign.lt(0)] = etaminus
        sign[sign.eq(0)] = 1

        # update stepsizes with step size updates
        step_size.mul_(sign).clamp_(step_size_min, step_size_max)

        # for dir<0, dfdx=0
        # for dir>=0 dfdx=dfdx
        grad = grad.clone(memory_format=torch.preserve_format)
        grad[sign.eq(etaminus)] = 0

        # update parameters
        param.addcmul_(grad.sign(), step_size, value=-1)

        prev.copy_(grad)


def _multi_tensor_rprop(params: List[Tensor],
                        grads: List[Tensor],
                        prevs: List[Tensor],
                        step_sizes: List[Tensor],
                        *,
                        step_size_min: float,
                        step_size_max: float,
                        etaminus: float,
                        etaplus: float):

    if len(params) == 0:
        return

    signs = torch._foreach_mul(grads, prevs)
    signs = [s.sign() for s in signs]
    for sign in signs:
        sign[sign.gt(0)] = etaplus
        sign[sign.lt(0)] = etaminus
        sign[sign.eq(0)] = 1

    # update stepsizes with step size updates
    torch._foreach_mul_(step_sizes, signs)
    for step_size in step_sizes:
        step_size.clamp_(step_size_min, step_size_max)

    # for dir<0, dfdx=0
    # for dir>=0 dfdx=dfdx
    for i in range(len(grads)):
        grads[i] = grads[i].clone(memory_format=torch.preserve_format)
        grads[i][signs[i].eq(etaminus)] = 0

    # update parameters
    grad_signs = [grad.sign() for grad in grads]
    torch._foreach_addcmul_(params, grad_signs, step_sizes, value=-1)

    for i in range(len(prevs)):
        prevs[i].copy_(grads[i])