er 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 \odot c_{t-1} + i_t \odot g_t \\
            h_t = o_t \odot \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:`\odot` is the Hadamard product.

    In a multilayer LSTM, the input :math:`x^{(l)}_t` of the :math:`l` -th layer
    (:math:`l \ge 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`.

    If ``proj_size > 0`` is specified, LSTM with projections will be used. This changes
    the LSTM cell in the following way. First, the dimension of :math:`h_t` will be changed from
    ``hidden_size`` to ``proj_size`` (dimensions of :math:`W_{hi}` will be changed accordingly).
    Second, the output hidden state of each layer will be multiplied by a learnable projection
    matrix: :math:`h_t = W_{hr}h_t`. Note that as a consequence of this, the output
    of LSTM network will be of different shape as well. See Inputs/Outputs sections below for exact
    dimensions of all variables. You can find more details in https://arxiv.org/abs/1402.1128.

    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)` instead of `(seq, batch, feature)`.
            Note that this does not apply to hidden or cell states. See the
            Inputs/Outputs sections below for details.  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``
        proj_size: If ``> 0``, will use LSTM with projections of corresponding size. Default: 0

    Inputs: input, (h_0, c_0)
        * **input**: tensor of shape :math:`(L, H_{in})` for unbatched input,
          :math:`(L, N, H_{in})` when ``batch_first=False`` or
          :math:`(N, L, H_{in})` when ``batch_first=True`` 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**: tensor of shape :math:`(D * \text{num\_layers}, H_{out})` for unbatched input or
          :math:`(D * \text{num\_layers}, N, H_{out})` containing the
          initial hidden state for each element in the input sequence.
          Defaults to zeros if (h_0, c_0) is not provided.
        * **c_0**: tensor of shape :math:`(D * \text{num\_layers}, H_{cell})` for unbatched input or
          :math:`(D * \text{num\_layers}, N, H_{cell})` containing the
          initial cell state for each element in the input sequence.
          Defaults to zeros if (h_0, c_0) is not provided.

        where:

        .. math::
            \begin{aligned}
                N ={} & \text{batch size} \\
                L ={} & \text{sequence length} \\
                D ={} & 2 \text{ if bidirectional=True otherwise } 1 \\
                H_{in} ={} & \text{input\_size} \\
                H_{cell} ={} & \text{hidden\_size} \\
                H_{out} ={} & \text{proj\_size if } \text{proj\_size}>0 \text{ otherwise hidden\_size} \\
            \end{aligned}

    Outputs: output, (h_n, c_n)
        * **output**: tensor of shape :math:`(L, D * H_{out})` for unbatched input,
          :math:`(L, N, D * H_{out})` when ``batch_first=False`` or
          :math:`(N, L, D * H_{out})` when ``batch_first=True`` 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. When ``bidirectional=True``, `output` will contain
          a concatenation of the forward and reverse hidden states at each time step in the sequence.
        * **h_n**: tensor of shape :math:`(D * \text{num\_layers}, H_{out})` for unbatched input or
          :math:`(D * \text{num\_layers}, N, H_{out})` containing the
          final hidden state for each element in the sequence. When ``bidirectional=True``,
          `h_n` will contain a concatenation of the final forward and reverse hidden states, respectively.
        * **c_n**: tensor of shape :math:`(D * \text{num\_layers}, H_{cell})` for unbatched input or
          :math:`(D * \text{num\_layers}, N, H_{cell})` containing the
          final cell state for each element in the sequence. When ``bidirectional=True``,
          `c_n` will contain a concatenation of the final forward and reverse cell states, respectively.

    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)`. If
            ``proj_size > 0`` was specified, the shape will be
            `(4*hidden_size, num_directions * proj_size)` for `k > 0`
        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)`. If ``proj_size > 0``
            was specified, the shape will be `(4*hidden_size, proj_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)`
        weight_hr_l[k] : the learnable projection weights of the :math:`\text{k}^{th}` layer
            of shape `(proj_size, hidden_size)`. Only present when ``proj_size > 0`` was
            specified.
        weight_ih_l[k]_reverse: Analogous to `weight_ih_l[k]` for the reverse direction.
            Only present when ``bidirectional=True``.
        weight_hh_l[k]_reverse:  Analogous to `weight_hh_l[k]` for the reverse direction.
            Only present when ``bidirectional=True``.
        bias_ih_l[k]_reverse:  Analogous to `bias_ih_l[k]` for the reverse direction.
            Only present when ``bidirectional=True``.
        bias_hh_l[k]_reverse:  Analogous to `bias_hh_l[k]` for the reverse direction.
            Only present when ``bidirectional=True``.
        weight_hr_l[k]_reverse:  Analogous to `weight_hr_l[k]` for the reverse direction.
            Only present when ``bidirectional=True`` and ``proj_size > 0`` was specified.

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

    .. note::
        For bidirectional LSTMs, forward and backward are directions 0 and 1 respectively.
        Example of splitting the output layers when ``batch_first=False``:
        ``output.view(seq_len, batch, num_directions, hidden_size)``.

    .. note::
        For bidirectional LSTMs, `h_n` is not equivalent to the last element of `output`; the
        former contains the final forward and reverse hidden states, while the latter contains the
        final forward hidden state and the initial reverse hidden state.

    .. note::
        ``batch_first`` argument is ignored for unbatched inputs.

    .. note::
        ``proj_size`` should be smaller than ``hidden_size``.

    .. include:: ../cudnn_rnn_determinism.rst

    .. 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))
    r