rnn.py

import math
import torch
import warnings
import itertools
import numbers

from .module import Module
from ..parameter import Parameter
from ..utils.rnn import PackedSequence, get_packed_sequence
from .. import init
from .. import _VF
from ..._jit_internal import weak_module, weak_script_method, weak_script, \
    _parameter_list

_rnn_impls = {
    'GRU': _VF.gru,
    'RNN_TANH': _VF.rnn_tanh,
    'RNN_RELU': _VF.rnn_relu,
}


@weak_script
def apply_permutation(tensor, permutation, dim=1):
    # type: (Tensor, Tensor, int) -> Tensor
    return tensor.index_select(dim, permutation)


class RNNBase(Module):
    __constants__ = ['mode', 'input_size', 'hidden_size', 'num_layers', 'bias',
                     'batch_first', 'dropout', 'bidirectional', '_flat_parameters']

    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.bidirectional = bidirectional
        num_directions = 2 if bidirectional else 1

        if not isinstance(dropout, numbers.Number) or not 0 <= dropout <= 1 or \
                isinstance(dropout, bool):
            raise ValueError("dropout should be a number in range [0, 1] "
                             "representing the probability of an element being "
                             "zeroed")
        if dropout > 0 and num_layers == 1:
            warnings.warn("dropout option adds dropout after all but last "
                          "recurrent layer, so non-zero dropout expects "
                          "num_layers greater than 1, but got dropout={} and "
                          "num_layers={}".format(dropout, num_layers))

        if mode == 'LSTM':
            gate_size = 4 * hidden_size
        elif mode == 'GRU':
            gate_size = 3 * hidden_size
        elif mode == 'RNN_TANH':
            gate_size = hidden_size
        elif mode == 'RNN_RELU':
            gate_size = hidden_size
        else:
            raise ValueError("Unrecognized RNN mode: " + mode)

        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))
                # Second bias vector included for CuDNN compatibility. Only one
                # bias vector is needed in standard definition.
                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):
            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().
        all_weights = self._flat_weights
        unique_data_ptrs = set(p.data_ptr() for p in all_weights)
        if len(unique_data_ptrs) != len(all_weights):
            return

        with torch.cuda.device_of(any_param):
            import torch.backends.cudnn.rnn as rnn

            # NB: This is a temporary hack while we still don't have Tensor
            # bindings for ATen functions
            with torch.no_grad():
                # NB: this is an INPLACE function on all_weights, that's why the
                # no_grad() is necessary.
                torch._cudnn_rnn_flatten_weight(
                    all_weights, (4 if self.bias else 2),
                    self.input_size, rnn.get_cudnn_mode(self.mode), self.hidden_size, self.num_layers,
                    self.batch_first, bool(self.bidirectional))

    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():
            init.uniform_(weight, -stdv, stdv)

    @_parameter_list
    def get_flat_weights(self):
        return self._flat_weights

    @weak_script_method
    def check_input(self, input, batch_sizes):
        # type: (Tensor, Optional[Tensor]) -> None
        expected_input_dim = 2 if batch_sizes is not None else 3
        if input.dim() != expected_input_dim:
            raise RuntimeError(
                'input must have {} dimensions, got {}'.format(
                    expected_input_dim, input.dim()))
        if self.input_size != input.size(-1):
            raise RuntimeError(
                'input.size(-1) must be equal to input_size. Expected {}, got {}'.format(
                    self.input_size, input.size(-1)))

    @weak_script_method
    def get_expected_hidden_size(self, input, batch_sizes):
        # type: (Tensor, Optional[Tensor]) -> Tuple[int, int, int]
        if batch_sizes is not None:
            mini_batch = batch_sizes[0]
            mini_batch = int(mini_batch)
        else:
            mini_batch = input.size(0) if self.batch_first else input.size(1)
        num_directions = 2 if self.bidirectional else 1
        expected_hidden_size = (self.num_layers * num_directions,
                                mini_batch, self.hidden_size)
        return expected_hidden_size

    @weak_script_method
    def check_hidden_size(self, hx, expected_hidden_size, msg='Expected hidden size {}, got {}'):
        # type: (Tensor, Tuple[int, int, int], str) -> None
        if hx.size() != expected_hidden_size:
            raise RuntimeError(msg.format(expected_hidden_size, tuple(hx.size())))

    def check_forward_args(self, input, hidden, batch_sizes):
        self.check_input(input, batch_sizes)
        expected_hidden_size = self.get_expected_hidden_size(input, batch_sizes)

        self.check_hidden_size(hidden, expected_hidden_size)

    def permute_hidden(self, hx, permutation):
        if permutation is None:
            return hx
        return apply_permutation(hx, permutation)

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

        if hx is None:
            num_directions = 2 if self.bidirectional else 1
            hx = torch.zeros(self.num_layers * num_directions,
                             max_batch_size, self.hidden_size,
                             dtype=input.dtype, device=input.device)
        else:
            # Each batch of the hidden state should match the input sequence that
            # the user believes he/she is passing in.
            hx = self.permute_hidden(hx, sorted_indices)

        self.check_forward_args(input, hx, batch_sizes)
        _impl = _rnn_impls[self.mode]
        if batch_sizes is None:
            result = _impl(input, hx, self.get_flat_weights(), self.bias, self.num_layers,
                           self.dropout, self.training, self.bidirectional, self.batch_first)
        else:
            result = _impl(input, batch_sizes, hx, self.get_flat_weights(), self.bias,
                           self.num_layers, self.dropout, self.training, self.bidirectional)
        output = result[0]
        hidden = result[1]

        if is_packed:
            output = PackedSequence(output, batch_sizes, sorted_indices, unsorted_indices)
        return output, self.permute_hidden(hidden, unsorted_indices)

    def extra_repr(self):
        s = '{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}'
        return s.format(**self.__dict__)

    def __setstate__(self, d):
        super(RNNBase, self).__setstate__(d)
        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 _flat_weights(self):
        return [p for layerparams in self.all_weights for p in layerparams]

    @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 :math:`tanh` or :math:`ReLU` non-linearity to an
    input sequence.


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

    .. math::
        h_t = \text{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`, :math:`x_t` is
    the input at time `t`, and :math:`h_{(t-1)}` is the hidden state of the
    previous layer at time `t-1` or the initial hidden state at time `0`.
    If :attr:`nonlinearity` is ``'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. E.g., setting ``num_layers=2``
            would mean stacking two RNNs together to form a `stacked RNN`,
            with the second RNN taking in outputs of the first RNN and
            computing the final results. Default: 1
        nonlinearity: The non-linearity to use. Can be either ``'tanh'`` or ``'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)`. Default: ``False``
        dropout: If non-zero, introduces a `Dropout` layer on the outputs of each
            RNN layer except the last layer, with dropout probability equal to
            :attr:`dropout`. Default: 0
        bidirectional: If ``True``, becomes a bidirectional RNN. Default: ``False``

    Inputs: input, h_0
        - **input** of shape `(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`
          or :func:`torch.nn.utils.rnn.pack_sequence`
          for details.
        - **h_0** of shape `(num_layers * num_directions, batch, hidden_size)`: tensor
          containing the initial hidden state for each element in the batch.
          Defaults to zero if not provided. If the RNN is bidirectional,
          num_directions should be 2, else it should be 1.

    Outputs: output, h_n
        - **output** of shape `(seq_len, batch, num_directions * hidden_size)`: 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.

          For the unpacked case, the directions can be separated
          using ``output.view(seq_len, batch, num_directions, hidden_size)``,
          with forward and backward being direction `0` and `1` respectively.
          Similarly, the directions can be separated in the packed case.
        - **h_n** of shape `(num_layers * num_directions, batch, hidden_size)`: tensor
          containing the hidden state for `t = seq_len`.

          Like *output*, the layers can be separated using
          ``h_n.view(num_layers, num_directions, batch, hidden_size)``.

    Shape:
        - Input1: :math:`(L, N, H_{in})` tensor containing input features where
          :math:`H_{in}=\text{input\_size}` and `L` represents a sequence length.
        - Input2: :math:`(S, N, H_{out})` tensor
          containing the initial hidden state for each element in the batch.
          :math:`H_{out}=\text{hidden\_size}`
          Defaults to zero if not provided. where :math:`S=\text{num\_layers} * \text{num\_directions}`
          If the RNN is bidirectional, num_directions should be 2, else it should be 1.
        - Output1: :math:`(L, N, H_{all})` where :math:`H_all=\text{num\_directions} * \text{hidden\_size}`
        - Output2: :math:`(S, N, H_{out})` tensor containing the next hidden state
          for each element in the batch

    Attributes:
        weight_ih_l[k]: the learnable input-hidden weights of the k-th layer,
            of shape `(hidden_size, input_size)` for `k = 0`. Otherwise, the shape is
            `(hidden_size, num_directions * hidden_size)`
        weight_hh_l[k]: the learnable hidden-hidden weights of the k-th layer,
            of shape `(hidden_size, 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)`

    .. note::
        All the weights and biases are initialized from :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})`
        where :math:`k = \frac{1}{\text{hidden\_size}}`

    .. include:: cudnn_persistent_rnn.rst

    Examples::

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


@weak_module
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_{hg} 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 input at time `t`, :math:`h_{(t-1)}`
    is the hidden state of the layer at time `t-1` or the initial hidden
    state at time `0`, and :math:`i_t`, :math:`f_t`, :math:`g_t`,
    :math:`o_t` are the input, forget, cell, and output gates, respectively.
    :math:`\sigma` is the sigmoid function, and :math:`*` is the Hadamard product.

    In a multilayer LSTM, the input :math:`x^{(l)}_t` of the :math:`l` -th layer
    (:math:`l >= 2`) is the hidden state :math:`h^{(l-1)}_t` of the previous layer multiplied by
    dropout :math:`\delta^{(l-1)}_t` where each :math:`\delta^{(l-1)}_t` is a Bernoulli random
    variable which is :math:`0` with probability :attr:`dropout`.

    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. E.g., setting ``num_layers=2``
            would mean stacking two LSTMs together to form a `stacked LSTM`,
            with the second LSTM taking in outputs of the first LSTM and
            computing the final results. Default: 1
        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). Default: ``False``
        dropout: If non-zero, introduces a `Dropout` layer on the outputs of each
            LSTM layer except the last layer, with dropout probability equal to
            :attr:`dropout`. Default: 0
        bidirectional: If ``True``, becomes a bidirectional LSTM. Default: ``False``

    Inputs: input, (h_0, c_0)
        - **input** of shape `(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` or
          :func:`torch.nn.utils.rnn.pack_sequence` for details.
        - **h_0** of shape `(num_layers * num_directions, batch, hidden_size)`: tensor
          containing the initial hidden state for each element in the batch.
          If the LSTM is bidirectional, num_directions should be 2, else it should be 1.
        - **c_0** of shape `(num_layers * num_directions, batch, hidden_size)`: tensor
          containing the initial cell state for each element in the batch.

          If `(h_0, c_0)` is not provided, both **h_0** and **c_0** default to zero.


    Outputs: output, (h_n, c_n)
        - **output** of shape `(seq_len, batch, num_directions * hidden_size)`: tensor
          containing the output features `(h_t)` from the last layer of the LSTM,
          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.

          For the unpacked case, the directions can be separated
          using ``output.view(seq_len, batch, num_directions, hidden_size)``,
          with forward and backward being direction `0` and `1` respectively.
          Similarly, the directions can be separated in the packed case.
        - **h_n** of shape `(num_layers * num_directions, batch, hidden_size)`: tensor
          containing the hidden state for `t = seq_len`.

          Like *output*, the layers can be separated using
          ``h_n.view(num_layers, num_directions, batch, hidden_size)`` and similarly for *c_n*.
        - **c_n** of shape `(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 :math:`\text{k}^{th}` layer
            `(W_ii|W_if|W_ig|W_io)`, of shape `(4*hidden_size, input_size)` for `k = 0`.
            Otherwise, the shape is `(4*hidden_size, num_directions * hidden_size)`
        weight_hh_l[k] : the learnable hidden-hidden weights of the :math:`\text{k}^{th}` layer
            `(W_hi|W_hf|W_hg|W_ho)`, of shape `(4*hidden_size, hidden_size)`
        bias_ih_l[k] : the learnable input-hidden bias of the :math:`\text{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 :math:`\text{k}^{th}` layer
            `(b_hi|b_hf|b_hg|b_ho)`, of shape `(4*hidden_size)`

    .. note::
        All the weights and biases are initialized from :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})`
        where :math:`k = \frac{1}{\text{hidden\_size}}`

    .. include:: cudnn_persistent_rnn.rst

    Examples::

        >>> rnn = nn.LSTM(10, 20, 2)
        >>> input = torch.randn(5, 3, 10)
        >>> h0 = torch.randn(2, 3, 20)
        >>> c0 = torch.randn(2, 3, 20)
        >>> output, (hn, cn) = rnn(input, (h0, c0))
    """
    __overloads__ = {'forward': ['forward_packed', 'forward_tensor']}

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

    @weak_script_method
    def check_forward_args(self, input, hidden, batch_sizes):
        # type: (Tensor, Tuple[Tensor, Tensor], Optional[Tensor]) -> None
        self.check_input(input, batch_sizes)
        expected_hidden_size = self.get_expected_hidden_size(input, batch_sizes)

        self.check_hidden_size(hidden[0], expected_hidden_size,
                               'Expected hidden[0] size {}, got {}')
        self.check_hidden_size(hidden[1], expected_hidden_size,
                               'Expected hidden[1] size {}, got {}')

    @weak_script_method
    def permute_hidden(self, hx, permutation):
        # type: (Tuple[Tensor, Tensor], Optional[Tensor]) -> Tuple[Tensor, Tensor]
        if permutation is None:
            return hx
        return apply_permutation(hx[0], permutation), apply_permutation(hx[1], permutation)

    @weak_script_method
    def forward_impl(self, input, hx, batch_sizes, max_batch_size, sorted_indices):
        # type: (Tensor, Optional[Tuple[Tensor, Tensor]], Optional[Tensor], int, Optional[Tensor]) -> Tuple[Tensor, Tuple[Tensor, Tensor]]  # noqa
        if hx is None:
            num_directions = 2 if self.bidirectional else 1
            zeros = torch.zeros(self.num_layers * num_directions,
                                max_batch_size, self.hidden_size,
                                dtype=input.dtype, device=input.device)
            hx = (zeros, zeros)
        else:
            # Each batch of the hidden state should match the input sequence that
            # the user believes he/she is passing in.
            hx = self.permute_hidden(hx, sorted_indices)

        self.check_forward_args(input, hx, batch_sizes)
        if batch_sizes is None:
            result = _VF.lstm(input, hx, self.get_flat_weights(), self.bias, self.num_layers,
                              self.dropout, self.training, self.bidirectional, self.batch_first)
        else:
            result = _VF.lstm(input, batch_sizes, hx, self.get_flat_weights(), self.bias,
                              self.num_layers, self.dropout, self.training, self.bidirectional)
        output = result[0]
        hidden = result[1:]

        return output, hidden

    @weak_script_method
    def forward_tensor(self, input, hx=None):
        # type: (Tensor, Optional[Tuple[Tensor, Tensor]]) -> Tuple[Tensor, Tuple[Tensor, Tensor]]
        batch_sizes = None
        max_batch_size = input.size(0) if self.batch_first else input.size(1)
        sorted_indices = None
        unsorted_indices = None

        output, hidden = self.forward_impl(input, hx, batch_sizes, max_batch_size, sorted_indices)

        return output, self.permute_hidden(hidden, unsorted_indices)

    @weak_script_method
    def forward_packed(self, input, hx=None):
        # type: (Tuple[Tensor, Tensor, Optional[Tensor], Optional[Tensor]], Optional[Tuple[Tensor, Tensor]]) -> Tuple[Tuple[Tensor, Tensor, Optional[Tensor], Optional[Tensor]], Tuple[Tensor, Tensor]]  # noqa
        input, batch_sizes, sorted_indices, unsorted_indices = input
        max_batch_size = batch_sizes[0]
        max_batch_size = int(max_batch_size)

        output, hidden = self.forward_impl(input, hx, batch_sizes, max_batch_size, sorted_indices)

        output = get_packed_sequence(output, batch_sizes, sorted_indices, unsorted_indices)
        return output, self.permute_hidden(hidden, unsorted_indices)

    def forward(self, input, hx=None):
        if isinstance(input, PackedSequence):
            return self.forward_packed(input, hx)
        else:
            return self.forward_tensor(input, hx)


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 input
    at time `t`, :math:`h_{(t-1)}` is the hidden state of the layer
    at time `t-1` or the initial hidden state at time `0`, and :math:`r_t`,
    :math:`z_t`, :math:`n_t` are the reset, update, and new gates, respectively.
    :math:`\sigma` is the sigmoid function, and :math:`*` is the Hadamard product.

    In a multilayer GRU, the input :math:`x^{(l)}_t` of the :math:`l` -th layer
    (:math:`l >= 2`) is the hidden state :math:`h^{(l-1)}_t` of the previous layer multiplied by
    dropout :math:`\delta^{(l-1)}_t` where each :math:`\delta^{(l-1)}_t` is a Bernoulli random
    variable which is :math:`0` with probability :attr:`dropout`.

    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. E.g., setting ``num_layers=2``
            would mean stacking two GRUs together to form a `stacked GRU`,
            with the second GRU taking in outputs of the first GRU and
            computing the final results. Default: 1
        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). Default: ``False``
        dropout: If non-zero, introduces a `Dropout` layer on the outputs of each
            GRU layer except the last layer, with dropout probability equal to
            :attr:`dropout`. Default: 0
        bidirectional: If ``True``, becomes a bidirectional GRU. Default: ``False``

    Inputs: input, h_0
        - **input** of shape `(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** of shape `(num_layers * num_directions, batch, hidden_size)`: tensor
          containing the initial hidden state for each element in the batch.
          Defaults to zero if not provided. If the RNN is bidirectional,
          num_directions should be 2, else it should be 1.

    Outputs: output, h_n
        - **output** of shape `(seq_len, batch, num_directions * hidden_size)`: tensor
          containing the output features h_t from the last layer of the GRU,
          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.
          For the unpacked case, the directions can be separated
          using ``output.view(seq_len, batch, num_directions, hidden_size)``,
          with forward and backward being direction `0` and `1` respectively.

          Similarly, the directions can be separated in the packed case.
        - **h_n** of shape `(num_layers * num_directions, batch, hidden_size)`: tensor
          containing the hidden state for `t = seq_len`

          Like *output*, the layers can be separated using
          ``h_n.view(num_layers, num_directions, batch, hidden_size)``.

    Shape:
        - Input1: :math:`(L, N, H_{in})` tensor containing input features where
          :math:`H_{in}=\text{input\_size}` and `L` represents a sequence length.
        - Input2: :math:`(S, N, H_{out})` tensor
          containing the initial hidden state for each element in the batch.
          :math:`H_{out}=\text{hidden\_size}`
          Defaults to zero if not provided. where :math:`S=\text{num\_layers} * \text{num\_directions}`
          If the RNN is bidirectional, num_directions should be 2, else it should be 1.
        - Output1: :math:`(L, N, H_{all})` where :math:`H_all=\text{num\_directions} * \text{hidden\_size}`
        - Output2: :math:`(S, N, H_{out})` tensor containing the next hidden state
          for each element in the batch

    Attributes:
        weight_ih_l[k] : the learnable input-hidden weights of the :math:`\text{k}^{th}` layer
            (W_ir|W_iz|W_in), of shape `(3*hidden_size, input_size)` for `k = 0`.
            Otherwise, the shape is `(3*hidden_size, num_directions * hidden_size)`
        weight_hh_l[k] : the learnable hidden-hidden weights of the :math:`\text{k}^{th}` layer
            (W_hr|W_hz|W_hn), of shape `(3*hidden_size, hidden_size)`
        bias_ih_l[k] : the learnable input-hidden bias of the :math:`\text{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 :math:`\text{k}^{th}` layer
            (b_hr|b_hz|b_hn), of shape `(3*hidden_size)`

    .. note::
        All the weights and biases are initialized from :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})`
        where :math:`k = \frac{1}{\text{hidden\_size}}`

    .. include:: cudnn_persistent_rnn.rst

    Examples::

        >>> rnn = nn.GRU(10, 20, 2)
        >>> input = torch.randn(5, 3, 10)
        >>> h0 = 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):
    __constants__ = ['input_size', 'hidden_size', 'bias']

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

    def extra_repr(self):
        s = '{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}'
        return s.format(**self.__dict__)

    @weak_script_method
    def check_forward_input(self, input):
        if input.size(1) != self.input_size:
            raise RuntimeError(
                "input has inconsistent input_size: got {}, expected {}".format(
                    input.size(1), self.input_size))

    @weak_script_method
    def check_forward_hidden(self, input, hx, hidden_label=''):
        # type: (Tensor, Tensor, str) -> None
        if input.size(0) != hx.size(0):
            raise RuntimeError(
                "Input batch size {} doesn't match hidden{} batch size {}".format(
                    input.size(0), hidden_label, hx.size(0)))

        if hx.size(1) != self.hidden_size:
            raise RuntimeError(
                "hidden{} has inconsistent hidden_size: got {}, expected {}".format(
                    hidden_label, hx.size(1), self.hidden_size))

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


@weak_module
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 :attr:`nonlinearity` is `'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. Can be either ``'tanh'`` or ``'relu'``. Default: ``'tanh'``

    Inputs: input, hidden
        - **input** of shape `(batch, input_size)`: tensor containing input features
        - **hidden** of shape `(batch, hidden_size)`: tensor containing the initial hidden
          state for each element in the batch.
          Defaults to zero if not provided.

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

    Shape:
        - Input1: :math:`(N, H_{in})` tensor containing input features where
          :math:`H_{in}` = `input_size`
        - Input2: :math:`(N, H_{out})` tensor containing the initial hidden
          state for each element in the batch where :math:`H_{out}` = `hidden_size`
          Defaults to zero if not provided.
        - Output: :math:`(N, H_{out})` tensor containing the next hidden state
          for each element in the batch

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

    .. note::
        All the weights and biases are initialized from :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})`
        where :math:`k = \frac{1}{\text{hidden\_size}}`

    Examples::

        >>> rnn = nn.RNNCell(10, 20)
        >>> input = torch.randn(6, 3, 10)
        >>> hx = torch.randn(3, 20)
        >>> output = []
        >>> for i in range(6):
                hx = rnn(input[i], hx)
                output.append(hx)
    """
    __constants__ = ['input_size', 'hidden_size', 'bias', 'nonlinearity']

    def __init__(self, input_size, hidden_size, bias=True, nonlinearity="tanh"):
        super(RNNCell, self).__init__(input_size, hidden_size, bias, num_chunks=1)
        self.nonlinearity = nonlinearity

    @weak_script_method
    def forward(self, input, hx=None):
        # type: (Tensor, Optional[Tensor]) -> Tensor
        self.check_forward_input(input)
        if hx is None:
            hx = torch.zeros(input.size(0), self.hidden_size, dtype=input.dtype, device=input.device)
        self.check_forward_hidden(input, hx, '')
        if self.nonlinearity == "tanh":
            ret = _VF.rnn_tanh_cell(
                input, hx,
                self.weight_ih, self.weight_hh,
                self.bias_ih, self.bias_hh,
            )
        elif self.nonlinearity == "relu":
            ret = _VF.rnn_relu_cell(
                input, hx,
                self.weight_ih, self.weight_hh,
                self.bias_ih, self.bias_hh,
            )
        else:
            ret = input  # TODO: remove when jit supports exception flow
            raise RuntimeError(
                "Unknown nonlinearity: {}".format(self.nonlinearity))
        return ret


@weak_module
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_{hg} 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, and :math:`*` is the Hadamard product.

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

          If `(h_0, c_0)` is not provided, both **h_0** and **c_0** default to zero.

    Outputs: (h_1, c_1)
        - **h_1** of shape `(batch, hidden_size)`: tensor containing the next hidden state
          for each element in the batch
        - **c_1** of shape `(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, input_size)`
        weight_hh: the learnable hidden-hidden weights, of shape
            `(4*hidden_size, 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)`

    .. note::
        All the weights and biases are initialized from :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})`
        where :math:`k = \frac{1}{\text{hidden\_size}}`

    Examples::

        >>> rnn = nn.LSTMCell(10, 20)
        >>> input = torch.randn(6, 3, 10)
        >>> hx = torch.randn(3, 20)
        >>> cx = 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__(input_size, hidden_size, bias, num_chunks=4)

    @weak_script_method
    def forward(self, input, hx=None):
        # type: (Tensor, Optional[Tuple[Tensor, Tensor]]) -> Tuple[Tensor, Tensor]
        self.check_forward_input(input)
        if hx is None:
            zeros = torch.zeros(input.size(0), self.hidden_size, dtype=input.dtype, device=input.device)
            hx = (zeros, zeros)
        self.check_forward_hidden(input, hx[0], '[0]')
        self.check_forward_hidden(input, hx[1], '[1]')
        return _VF.lstm_cell(
            input, hx,
            self.weight_ih, self.weight_hh,
            self.bias_ih, self.bias_hh,
        )


@weak_module
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, and :math:`*` is the Hadamard product.

    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** of shape `(batch, input_size)`: tensor containing input features
        - **hidden** of shape `(batch, hidden_size)`: tensor containing the initial hidden
          state for each element in the batch.
          Defaults to zero if not provided.

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

    Shape:
        - Input1: :math:`(N, H_{in})` tensor containing input features where
          :math:`H_{in}` = `input_size`
        - Input2: :math:`(N, H_{out})` tensor containing the initial hidden
          state for each element in the batch where :math:`H_{out}` = `hidden_size`
          Defaults to zero if not provided.
        - Output: :math:`(N, H_{out})` 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, input_size)`
        weight_hh: the learnable hidden-hidden weights, of shape
            `(3*hidden_size, 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)`

    .. note::
        All the weights and biases are initialized from :math:`\mathcal{U}(-\sqrt{k}, \sqrt{k})`
        where :math:`k = \frac{1}{\text{hidden\_size}}`

    Examples::

        >>> rnn = nn.GRUCell(10, 20)
        >>> input = torch.randn(6, 3, 10)
        >>> hx = 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__(input_size, hidden_size, bias, num_chunks=3)

    @weak_script_method
    def forward(self, input, hx=None):
        # type: (Tensor, Optional[Tensor]) -> Tensor
        self.check_forward_input(input)
        if hx is None:
            hx = torch.zeros(input.size(0), self.hidden_size, dtype=input.dtype, device=input.device)
        self.check_forward_hidden(input, hx, '')
        return _VF.gru_cell(
            input, hx,
            self.weight_ih, self.weight_hh,
            self.bias_ih, self.bias_hh,
        )