import math
import torch
import warnings

from .module import Module
from ..parameter import Parameter
from ..utils.rnn import PackedSequence


class RNNBase(Module):

    def __init__(self, mode, input_size, hidden_size,
                 num_layers=1, bias=True, batch_first=False,
                 dropout=0, bidirectional=False):
        super(RNNBase, self).__init__()
        self.mode = mode
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.num_layers = num_layers
        self.bias = bias
        self.batch_first = batch_first
        self.dropout = dropout
        self.dropout_state = {}
        self.bidirectional = bidirectional
        num_directions = 2 if bidirectional else 1

        if mode == 'LSTM':
            gate_size = 4 * hidden_size
        elif mode == 'GRU':
            gate_size = 3 * hidden_size
        else:
            gate_size = hidden_size

        self._all_weights = []
        for layer in range(num_layers):
            for direction in range(num_directions):
                layer_input_size = input_size if layer == 0 else hidden_size * num_directions

                w_ih = Parameter(torch.Tensor(gate_size, layer_input_size))
                w_hh = Parameter(torch.Tensor(gate_size, hidden_size))
                b_ih = Parameter(torch.Tensor(gate_size))
                b_hh = Parameter(torch.Tensor(gate_size))
                layer_params = (w_ih, w_hh, b_ih, b_hh)

                suffix = '_reverse' if direction == 1 else ''
                param_names = ['weight_ih_l{}{}', 'weight_hh_l{}{}']
                if bias:
                    param_names += ['bias_ih_l{}{}', 'bias_hh_l{}{}']
                param_names = [x.format(layer, suffix) for x in param_names]

                for name, param in zip(param_names, layer_params):
                    setattr(self, name, param)
                self._all_weights.append(param_names)

        self.flatten_parameters()
        self.reset_parameters()

    def flatten_parameters(self):
        """Resets parameter data pointer so that they can use faster code paths.

        Right now, this works only if the module is on the GPU and cuDNN is enabled.
        Otherwise, it's a no-op.
        """
        any_param = next(self.parameters()).data
        if not any_param.is_cuda or not torch.backends.cudnn.is_acceptable(any_param):
            self._data_ptrs = []
            return

        # If any parameters alias, we fall back to the slower, copying code path. This is
        # a sufficient check, because overlapping parameter buffers that don't completely
        # alias would break the assumptions of the uniqueness check in
        # Module.named_parameters().
        unique_data_ptrs = set(p.data_ptr() for l in self.all_weights for p in l)
        if len(unique_data_ptrs) != sum(len(l) for l in self.all_weights):
            self._data_ptrs = []
            return

        with torch.cuda.device_of(any_param):
            # This is quite ugly, but it allows us to reuse the cuDNN code without larger
            # modifications. It's really a low-level API that doesn't belong in here, but
            # let's make this exception.
            from torch.backends.cudnn import rnn
            from torch.backends import cudnn
            from torch.nn._functions.rnn import CudnnRNN
            handle = cudnn.get_handle()
            with warnings.catch_warnings(record=True):
                fn = CudnnRNN(
                    self.mode,
                    self.input_size,
                    self.hidden_size,
                    num_layers=self.num_layers,
                    batch_first=self.batch_first,
                    dropout=self.dropout,
                    train=self.training,
                    bidirectional=self.bidirectional,
                    dropout_state=self.dropout_state,
                )

            # Initialize descriptors
            fn.datatype = cudnn._typemap[any_param.type()]
            fn.x_descs = cudnn.descriptor(any_param.new(1, self.input_size), 1)
            fn.rnn_desc = rnn.init_rnn_descriptor(fn, handle)

            # Allocate buffer to hold the weights
            self._param_buf_size = rnn.get_num_weights(handle, fn.rnn_desc, fn.x_descs[0], fn.datatype)
            fn.weight_buf = any_param.new(self._param_buf_size).zero_()
            fn.w_desc = rnn.init_weight_descriptor(fn, fn.weight_buf)

            # Slice off views into weight_buf
            all_weights = [[p.data for p in l] for l in self.all_weights]
            params = rnn.get_parameters(fn, handle, fn.weight_buf)

            # Copy weights and update their storage
            rnn._copyParams(all_weights, params)
            for orig_layer_param, new_layer_param in zip(all_weights, params):
                for orig_param, new_param in zip(orig_layer_param, new_layer_param):
                    orig_param.set_(new_param.view_as(orig_param))

            self._data_ptrs = list(p.data.data_ptr() for p in self.parameters())

    def _apply(self, fn):
        ret = super(RNNBase, self)._apply(fn)
        self.flatten_parameters()
        return ret

    def reset_parameters(self):
        stdv = 1.0 / math.sqrt(self.hidden_size)
        for weight in self.parameters():
            weight.data.uniform_(-stdv, stdv)

    def forward(self, input, hx=None):
        is_packed = isinstance(input, PackedSequence)
        if is_packed:
            input, batch_sizes = input
            max_batch_size = batch_sizes[0]
        else:
            batch_sizes = None
            max_batch_size = input.size(0) if self.batch_first else input.size(1)

        if hx is None:
            num_directions = 2 if self.bidirectional else 1
            hx = torch.autograd.Variable(input.data.new(self.num_layers *
                                                        num_directions,
                                                        max_batch_size,
                                                        self.hidden_size).zero_(), requires_grad=False)
            if self.mode == 'LSTM':
                hx = (hx, hx)

        has_flat_weights = list(p.data.data_ptr() for p in self.parameters()) == self._data_ptrs
        if has_flat_weights:
            first_data = next(self.parameters()).data
            assert first_data.storage().size() == self._param_buf_size
            flat_weight = first_data.new().set_(first_data.storage(), 0, torch.Size([self._param_buf_size]))
        else:
            flat_weight = None
        func = self._backend.RNN(
            self.mode,
            self.input_size,
            self.hidden_size,
            num_layers=self.num_layers,
            batch_first=self.batch_first,
            dropout=self.dropout,
            train=self.training,
            bidirectional=self.bidirectional,
            batch_sizes=batch_sizes,
            dropout_state=self.dropout_state,
            flat_weight=flat_weight
        )
        output, hidden = func(input, self.all_weights, hx)
        if is_packed:
            output = PackedSequence(output, batch_sizes)
        return output, hidden

    def __repr__(self):
        s = '{name}({input_size}, {hidden_size}'
        if self.num_layers != 1:
            s += ', num_layers={num_layers}'
        if self.bias is not True:
            s += ', bias={bias}'
        if self.batch_first is not False:
            s += ', batch_first={batch_first}'
        if self.dropout != 0:
            s += ', dropout={dropout}'
        if self.bidirectional is not False:
            s += ', bidirectional={bidirectional}'
        s += ')'
        return s.format(name=self.__class__.__name__, **self.__dict__)

    def __setstate__(self, d):
        super(RNNBase, self).__setstate__(d)
        self.__dict__.setdefault('_data_ptrs', [])
        if 'all_weights' in d:
            self._all_weights = d['all_weights']
        if isinstance(self._all_weights[0][0], str):
            return
        num_layers = self.num_layers
        num_directions = 2 if self.bidirectional else 1
        self._all_weights = []
        for layer in range(num_layers):
            for direction in range(num_directions):
                suffix = '_reverse' if direction == 1 else ''
                weights = ['weight_ih_l{}{}', 'weight_hh_l{}{}', 'bias_ih_l{}{}', 'bias_hh_l{}{}']
                weights = [x.format(layer, suffix) for x in weights]
                if self.bias:
                    self._all_weights += [weights]
                else:
                    self._all_weights += [weights[:2]]

    @property
    def all_weights(self):
        return [[getattr(self, weight) for weight in weights] for weights in self._all_weights]


class RNN(RNNBase):
    r"""Applies a multi-layer Elman RNN with tanh or ReLU non-linearity to an
    input sequence.


    For each element in the input sequence, each layer computes the following
    function:

    .. math::

        h_t = \tanh(w_{ih} * x_t + b_{ih}  +  w_{hh} * h_{(t-1)} + b_{hh})

    where :math:`h_t` is the hidden state at time `t`, and :math:`x_t` is
    the hidden state of the previous layer at time `t` or :math:`input_t`
    for the first layer. If nonlinearity='relu', then `ReLU` is used instead
    of `tanh`.

    Args:
        input_size: The number of expected features in the input x
        hidden_size: The number of features in the hidden state h
        num_layers: Number of recurrent layers.
        nonlinearity: The non-linearity to use ['tanh'|'relu']. Default: 'tanh'
        bias: If ``False``, then the layer does not use bias weights b_ih and b_hh.
            Default: ``True``
        batch_first: If ``True``, then the input and output tensors are provided
            as (batch, seq, feature)
        dropout: If non-zero, introduces a dropout layer on the outputs of each
            RNN layer except the last layer
        bidirectional: If ``True``, becomes a bidirectional RNN. Default: ``False``

    Inputs: input, h_0
        - **input** (seq_len, batch, input_size): tensor containing the features
          of the input sequence. The input can also be a packed variable length
          sequence. See :func:`torch.nn.utils.rnn.pack_padded_sequence`
          for details.
        - **h_0** (num_layers * num_directions, batch, hidden_size): tensor
          containing the initial hidden state for each element in the batch.

    Outputs: output, h_n
        - **output** (seq_len, batch, hidden_size * num_directions): tensor
          containing the output features (h_k) from the last layer of the RNN,
          for each k.  If a :class:`torch.nn.utils.rnn.PackedSequence` has
          been given as the input, the output will also be a packed sequence.
        - **h_n** (num_layers * num_directions, batch, hidden_size): tensor
          containing the hidden state for k=seq_len.

    Attributes:
        weight_ih_l[k]: the learnable input-hidden weights of the k-th layer,
            of shape `(input_size x hidden_size)`
        weight_hh_l[k]: the learnable hidden-hidden weights of the k-th layer,
            of shape `(hidden_size x hidden_size)`
        bias_ih_l[k]: the learnable input-hidden bias of the k-th layer,
            of shape `(hidden_size)`
        bias_hh_l[k]: the learnable hidden-hidden bias of the k-th layer,
            of shape `(hidden_size)`

    Examples::

        >>> rnn = nn.RNN(10, 20, 2)
        >>> input = Variable(torch.randn(5, 3, 10))
        >>> h0 = Variable(torch.randn(2, 3, 20))
        >>> output, hn = rnn(input, h0)
    """

    def __init__(self, *args, **kwargs):
        if 'nonlinearity' in kwargs:
            if kwargs['nonlinearity'] == 'tanh':
                mode = 'RNN_TANH'
            elif kwargs['nonlinearity'] == 'relu':
                mode = 'RNN_RELU'
            else:
                raise ValueError("Unknown nonlinearity '{}'".format(
                    kwargs['nonlinearity']))
            del kwargs['nonlinearity']
        else:
            mode = 'RNN_TANH'

        super(RNN, self).__init__(mode, *args, **kwargs)


class LSTM(RNNBase):
    r"""Applies a multi-layer long short-term memory (LSTM) RNN to an input
    sequence.


    For each element in the input sequence, each layer computes the following
    function:

    .. math::

            \begin{array}{ll}
            i_t = \sigma(W_{ii} x_t + b_{ii} + W_{hi} h_{(t-1)} + b_{hi}) \\
            f_t = \sigma(W_{if} x_t + b_{if} + W_{hf} h_{(t-1)} + b_{hf}) \\
            g_t = \tanh(W_{ig} x_t + b_{ig} + W_{hc} h_{(t-1)} + b_{hg}) \\
            o_t = \sigma(W_{io} x_t + b_{io} + W_{ho} h_{(t-1)} + b_{ho}) \\
            c_t = f_t * c_{(t-1)} + i_t * g_t \\
            h_t = o_t * \tanh(c_t)
            \end{array}

    where :math:`h_t` is the hidden state at time `t`, :math:`c_t` is the cell
    state at time `t`, :math:`x_t` is the hidden state of the previous layer at
    time `t` or :math:`input_t` for the first layer, and :math:`i_t`,
    :math:`f_t`, :math:`g_t`, :math:`o_t` are the input, forget, cell,
    and out gates, respectively. :math:`\sigma` is the sigmoid function.

    Args:
        input_size: The number of expected features in the input x
        hidden_size: The number of features in the hidden state h
        num_layers: Number of recurrent layers.
        bias: If ``False``, then the layer does not use bias weights b_ih and b_hh.
            Default: ``True``
        batch_first: If ``True``, then the input and output tensors are provided
            as (batch, seq, feature)
        dropout: If non-zero, introduces a dropout layer on the outputs of each
            RNN layer except the last layer
        bidirectional: If ``True``, becomes a bidirectional RNN. Default: ``False``

    Inputs: input, (h_0, c_0)
        - **input** (seq_len, batch, input_size): tensor containing the features
          of the input sequence.
          The input can also be a packed variable length sequence.
          See :func:`torch.nn.utils.rnn.pack_padded_sequence` for details.
        - **h_0** (num_layers \* num_directions, batch, hidden_size): tensor
          containing the initial hidden state for each element in the batch.
        - **c_0** (num_layers \* num_directions, batch, hidden_size): tensor
          containing the initial cell state for each element in the batch.


    Outputs: output, (h_n, c_n)
        - **output** (seq_len, batch, hidden_size * num_directions): tensor
          containing the output features `(h_t)` from the last layer of the RNN,
          for each t. If a :class:`torch.nn.utils.rnn.PackedSequence` has been
          given as the input, the output will also be a packed sequence.
        - **h_n** (num_layers * num_directions, batch, hidden_size): tensor
          containing the hidden state for t=seq_len
        - **c_n** (num_layers * num_directions, batch, hidden_size): tensor
          containing the cell state for t=seq_len

    Attributes:
        weight_ih_l[k] : the learnable input-hidden weights of the k-th layer
            `(W_ii|W_if|W_ig|W_io)`, of shape `(4*hidden_size x input_size)`
        weight_hh_l[k] : the learnable hidden-hidden weights of the k-th layer
            `(W_hi|W_hf|W_hg|W_ho)`, of shape `(4*hidden_size x hidden_size)`
        bias_ih_l[k] : the learnable input-hidden bias of the k-th layer
            `(b_ii|b_if|b_ig|b_io)`, of shape `(4*hidden_size)`
        bias_hh_l[k] : the learnable hidden-hidden bias of the k-th layer
            `(b_hi|b_hf|b_hg|b_ho)`, of shape `(4*hidden_size)`

    Examples::

        >>> rnn = nn.LSTM(10, 20, 2)
        >>> input = Variable(torch.randn(5, 3, 10))
        >>> h0 = Variable(torch.randn(2, 3, 20))
        >>> c0 = Variable(torch.randn(2, 3, 20))
        >>> output, hn = rnn(input, (h0, c0))
    """

    def __init__(self, *args, **kwargs):
        super(LSTM, self).__init__('LSTM', *args, **kwargs)


class GRU(RNNBase):
    r"""Applies a multi-layer gated recurrent unit (GRU) RNN to an input sequence.


    For each element in the input sequence, each layer computes the following
    function:

    .. math::

            \begin{array}{ll}
            r_t = \sigma(W_{ir} x_t + b_{ir} + W_{hr} h_{(t-1)} + b_{hr}) \\
            z_t = \sigma(W_{iz} x_t + b_{iz} + W_{hz} h_{(t-1)} + b_{hz}) \\
            n_t = \tanh(W_{in} x_t + b_{in} + r_t * (W_{hn} h_{(t-1)}+ b_{hn})) \\
            h_t = (1 - z_t) * n_t + z_t * h_{(t-1)} \\
            \end{array}

    where :math:`h_t` is the hidden state at time `t`, :math:`x_t` is the hidden
    state of the previous layer at time `t` or :math:`input_t` for the first
    layer, and :math:`r_t`, :math:`z_t`, :math:`n_t` are the reset, input,
    and new gates, respectively. :math:`\sigma` is the sigmoid function.

    Args:
        input_size: The number of expected features in the input x
        hidden_size: The number of features in the hidden state h
        num_layers: Number of recurrent layers.
        bias: If ``False``, then the layer does not use bias weights b_ih and b_hh.
            Default: ``True``
        batch_first: If ``True``, then the input and output tensors are provided
            as (batch, seq, feature)
        dropout: If non-zero, introduces a dropout layer on the outputs of each
            RNN layer except the last layer
        bidirectional: If ``True``, becomes a bidirectional RNN. Default: ``False``

    Inputs: input, h_0
        - **input** (seq_len, batch, input_size): tensor containing the features
          of the input sequence. The input can also be a packed variable length
          sequence. See :func:`torch.nn.utils.rnn.pack_padded_sequence`
          for details.
        - **h_0** (num_layers * num_directions, batch, hidden_size): tensor
          containing the initial hidden state for each element in the batch.

    Outputs: output, h_n
        - **output** (seq_len, batch, hidden_size * num_directions): tensor
          containing the output features h_t from the last layer of the RNN,
          for each t. If a :class:`torch.nn.utils.rnn.PackedSequence` has been
          given as the input, the output will also be a packed sequence.
        - **h_n** (num_layers * num_directions, batch, hidden_size): tensor
          containing the hidden state for t=seq_len

    Attributes:
        weight_ih_l[k] : the learnable input-hidden weights of the k-th layer
            (W_ir|W_iz|W_in), of shape `(3*hidden_size x input_size)`
        weight_hh_l[k] : the learnable hidden-hidden weights of the k-th layer
            (W_hr|W_hz|W_hn), of shape `(3*hidden_size x hidden_size)`
        bias_ih_l[k] : the learnable input-hidden bias of the k-th layer
            (b_ir|b_iz|b_in), of shape `(3*hidden_size)`
        bias_hh_l[k] : the learnable hidden-hidden bias of the k-th layer
            (b_hr|b_hz|b_hn), of shape `(3*hidden_size)`
    Examples::

        >>> rnn = nn.GRU(10, 20, 2)
        >>> input = Variable(torch.randn(5, 3, 10))
        >>> h0 = Variable(torch.randn(2, 3, 20))
        >>> output, hn = rnn(input, h0)
    """

    def __init__(self, *args, **kwargs):
        super(GRU, self).__init__('GRU', *args, **kwargs)


class RNNCellBase(Module):

    def __repr__(self):
        s = '{name}({input_size}, {hidden_size}'
        if 'bias' in self.__dict__ and self.bias is not True:
            s += ', bias={bias}'
        if 'nonlinearity' in self.__dict__ and self.nonlinearity != "tanh":
            s += ', nonlinearity={nonlinearity}'
        s += ')'
        return s.format(name=self.__class__.__name__, **self.__dict__)


class RNNCell(RNNCellBase):
    r"""An Elman RNN cell with tanh or ReLU non-linearity.

    .. math::

        h' = \tanh(w_{ih} * x + b_{ih}  +  w_{hh} * h + b_{hh})

    If nonlinearity='relu', then ReLU is used in place of tanh.

    Args:
        input_size: The number of expected features in the input x
        hidden_size: The number of features in the hidden state h
        bias: If ``False``, then the layer does not use bias weights b_ih and b_hh.
            Default: ``True``
        nonlinearity: The non-linearity to use ['tanh'|'relu']. Default: 'tanh'

    Inputs: input, hidden
        - **input** (batch, input_size): tensor containing input features
        - **hidden** (batch, hidden_size): tensor containing the initial hidden
          state for each element in the batch.

    Outputs: h'
        - **h'** (batch, hidden_size): tensor containing the next hidden state
          for each element in the batch

    Attributes:
        weight_ih: the learnable input-hidden weights, of shape
            `(input_size x hidden_size)`
        weight_hh: the learnable hidden-hidden weights, of shape
            `(hidden_size x hidden_size)`
        bias_ih: the learnable input-hidden bias, of shape `(hidden_size)`
        bias_hh: the learnable hidden-hidden bias, of shape `(hidden_size)`

    Examples::

        >>> rnn = nn.RNNCell(10, 20)
        >>> input = Variable(torch.randn(6, 3, 10))
        >>> hx = Variable(torch.randn(3, 20))
        >>> output = []
        >>> for i in range(6):
        ...     hx = rnn(input[i], hx)
        ...     output.append(hx)
    """

    def __init__(self, input_size, hidden_size, bias=True, nonlinearity="tanh"):
        super(RNNCell, self).__init__()
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.bias = bias
        self.nonlinearity = nonlinearity
        self.weight_ih = Parameter(torch.Tensor(hidden_size, input_size))
        self.weight_hh = Parameter(torch.Tensor(hidden_size, hidden_size))
        if bias:
            self.bias_ih = Parameter(torch.Tensor(hidden_size))
            self.bias_hh = Parameter(torch.Tensor(hidden_size))
        else:
            self.register_parameter('bias_ih', None)
            self.register_parameter('bias_hh', None)
        self.reset_parameters()

    def reset_parameters(self):
        stdv = 1.0 / math.sqrt(self.hidden_size)
        for weight in self.parameters():
            weight.data.uniform_(-stdv, stdv)

    def forward(self, input, hx):
        if self.nonlinearity == "tanh":
            func = self._backend.RNNTanhCell
        elif self.nonlinearity == "relu":
            func = self._backend.RNNReLUCell
        else:
            raise RuntimeError(
                "Unknown nonlinearity: {}".format(self.nonlinearity))

        return func(
            input, hx,
            self.weight_ih, self.weight_hh,
            self.bias_ih, self.bias_hh,
        )


class LSTMCell(RNNCellBase):
    r"""A long short-term memory (LSTM) cell.

    .. math::

        \begin{array}{ll}
        i = \sigma(W_{ii} x + b_{ii} + W_{hi} h + b_{hi}) \\
        f = \sigma(W_{if} x + b_{if} + W_{hf} h + b_{hf}) \\
        g = \tanh(W_{ig} x + b_{ig} + W_{hc} h + b_{hg}) \\
        o = \sigma(W_{io} x + b_{io} + W_{ho} h + b_{ho}) \\
        c' = f * c + i * g \\
        h' = o * \tanh(c') \\
        \end{array}

    where :math:`\sigma` is the sigmoid function.

    Args:
        input_size: The number of expected features in the input x
        hidden_size: The number of features in the hidden state h
        bias: If `False`, then the layer does not use bias weights `b_ih` and
            `b_hh`. Default: ``True``

    Inputs: input, (h_0, c_0)
        - **input** (batch, input_size): tensor containing input features
        - **h_0** (batch, hidden_size): tensor containing the initial hidden
          state for each element in the batch.
        - **c_0** (batch. hidden_size): tensor containing the initial cell state
          for each element in the batch.

    Outputs: h_1, c_1
        - **h_1** (batch, hidden_size): tensor containing the next hidden state
          for each element in the batch
        - **c_1** (batch, hidden_size): tensor containing the next cell state
          for each element in the batch

    Attributes:
        weight_ih: the learnable input-hidden weights, of shape
            `(4*hidden_size x input_size)`
        weight_hh: the learnable hidden-hidden weights, of shape
            `(4*hidden_size x hidden_size)`
        bias_ih: the learnable input-hidden bias, of shape `(4*hidden_size)`
        bias_hh: the learnable hidden-hidden bias, of shape `(4*hidden_size)`

    Examples::

        >>> rnn = nn.LSTMCell(10, 20)
        >>> input = Variable(torch.randn(6, 3, 10))
        >>> hx = Variable(torch.randn(3, 20))
        >>> cx = Variable(torch.randn(3, 20))
        >>> output = []
        >>> for i in range(6):
        ...     hx, cx = rnn(input[i], (hx, cx))
        ...     output.append(hx)
    """

    def __init__(self, input_size, hidden_size, bias=True):
        super(LSTMCell, self).__init__()
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.bias = bias
        self.weight_ih = Parameter(torch.Tensor(4 * hidden_size, input_size))
        self.weight_hh = Parameter(torch.Tensor(4 * hidden_size, hidden_size))
        if bias:
            self.bias_ih = Parameter(torch.Tensor(4 * hidden_size))
            self.bias_hh = Parameter(torch.Tensor(4 * hidden_size))
        else:
            self.register_parameter('bias_ih', None)
            self.register_parameter('bias_hh', None)
        self.reset_parameters()

    def reset_parameters(self):
        stdv = 1.0 / math.sqrt(self.hidden_size)
        for weight in self.parameters():
            weight.data.uniform_(-stdv, stdv)

    def forward(self, input, hx):
        return self._backend.LSTMCell(
            input, hx,
            self.weight_ih, self.weight_hh,
            self.bias_ih, self.bias_hh,
        )


class GRUCell(RNNCellBase):
    r"""A gated recurrent unit (GRU) cell

    .. math::

        \begin{array}{ll}
        r = \sigma(W_{ir} x + b_{ir} + W_{hr} h + b_{hr}) \\
        z = \sigma(W_{iz} x + b_{iz} + W_{hz} h + b_{hz}) \\
        n = \tanh(W_{in} x + b_{in} + r * (W_{hn} h + b_{hn})) \\
        h' = (1 - z) * n + z * h
        \end{array}

    where :math:`\sigma` is the sigmoid function.

    Args:
        input_size: The number of expected features in the input x
        hidden_size: The number of features in the hidden state h
        bias: If `False`, then the layer does not use bias weights `b_ih` and
            `b_hh`. Default: `True`

    Inputs: input, hidden
        - **input** (batch, input_size): tensor containing input features
        - **hidden** (batch, hidden_size): tensor containing the initial hidden
          state for each element in the batch.

    Outputs: h'
        - **h'**: (batch, hidden_size): tensor containing the next hidden state
          for each element in the batch

    Attributes:
        weight_ih: the learnable input-hidden weights, of shape
            `(3*hidden_size x input_size)`
        weight_hh: the learnable hidden-hidden weights, of shape
            `(3*hidden_size x hidden_size)`
        bias_ih: the learnable input-hidden bias, of shape `(3*hidden_size)`
        bias_hh: the learnable hidden-hidden bias, of shape `(3*hidden_size)`

    Examples::

        >>> rnn = nn.GRUCell(10, 20)
        >>> input = Variable(torch.randn(6, 3, 10))
        >>> hx = Variable(torch.randn(3, 20))
        >>> output = []
        >>> for i in range(6):
        ...     hx = rnn(input[i], hx)
        ...     output.append(hx)
    """

    def __init__(self, input_size, hidden_size, bias=True):
        super(GRUCell, self).__init__()
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.bias = bias
        self.weight_ih = Parameter(torch.Tensor(3 * hidden_size, input_size))
        self.weight_hh = Parameter(torch.Tensor(3 * hidden_size, hidden_size))
        if bias:
            self.bias_ih = Parameter(torch.Tensor(3 * hidden_size))
            self.bias_hh = Parameter(torch.Tensor(3 * hidden_size))
        else:
            self.register_parameter('bias_ih', None)
            self.register_parameter('bias_hh', None)
        self.reset_parameters()

    def reset_parameters(self):
        stdv = 1.0 / math.sqrt(self.hidden_size)
        for weight in self.parameters():
            weight.data.uniform_(-stdv, stdv)

    def forward(self, input, hx):
        return self._backend.GRUCell(
            input, hx,
            self.weight_ih, self.weight_hh,
            self.bias_ih, self.bias_hh,
        )
