import math

import torch
from torch.nn import Parameter
from overrides import overrides

from allennlp.nn import util
from allennlp.nn.activations import Activation
from allennlp.modules.matrix_attention.matrix_attention import MatrixAttention


@MatrixAttention.register("linear")
class LinearMatrixAttention(MatrixAttention):
    """
    This ``MatrixAttention`` takes two matrices as input and returns a matrix of attentions
    by performing a dot product between a vector of weights and some
    combination of the two input matrices, followed by an (optional) activation function.  The
    combination used is configurable.

    If the two vectors are ``x`` and ``y``, we allow the following kinds of combinations: ``x``,
    ``y``, ``x*y``, ``x+y``, ``x-y``, ``x/y``, where each of those binary operations is performed
    elementwise.  You can list as many combinations as you want, comma separated.  For example, you
    might give ``x,y,x*y`` as the ``combination`` parameter to this class.  The computed similarity
    function would then be ``w^T [x; y; x*y] + b``, where ``w`` is a vector of weights, ``b`` is a
    bias parameter, and ``[;]`` is vector concatenation.

    Note that if you want a bilinear similarity function with a diagonal weight matrix W, where the
    similarity function is computed as `x * w * y + b` (with `w` the diagonal of `W`), you can
    accomplish that with this class by using "x*y" for `combination`.

    Parameters
    ----------
    tensor_1_dim : ``int``
        The dimension of the first tensor, ``x``, described above.  This is ``x.size()[-1]`` - the
        length of the vector that will go into the similarity computation.  We need this so we can
        build weight vectors correctly.
    tensor_2_dim : ``int``
        The dimension of the second tensor, ``y``, described above.  This is ``y.size()[-1]`` - the
        length of the vector that will go into the similarity computation.  We need this so we can
        build weight vectors correctly.
    combination : ``str``, optional (default="x,y")
        Described above.
    activation : ``Activation``, optional (default=linear (i.e. no activation))
        An activation function applied after the ``w^T * [x;y] + b`` calculation.  Default is no
        activation.
    """

    def __init__(self,
                 tensor_1_dim: int,
                 tensor_2_dim: int,
                 combination: str = 'x,y',
                 activation: Activation = None) -> None:
        super().__init__()
        self._combination = combination
        combined_dim = util.get_combined_dim(combination, [tensor_1_dim, tensor_2_dim])
        self._weight_vector = Parameter(torch.Tensor(combined_dim))
        self._bias = Parameter(torch.Tensor(1))
        self._activation = activation or Activation.by_name('linear')()
        self.reset_parameters()

    def reset_parameters(self):
        std = math.sqrt(6 / (self._weight_vector.size(0) + 1))
        self._weight_vector.data.uniform_(-std, std)
        self._bias.data.fill_(0)

    @overrides
    def forward(self,  # pylint: disable=arguments-differ
                matrix_1: torch.Tensor,
                matrix_2: torch.Tensor) -> torch.Tensor:
        combined_tensors = util.combine_tensors_and_multiply(self._combination,
                                                             [matrix_1.unsqueeze(2), matrix_2.unsqueeze(1)],
                                                             self._weight_vector)
        return self._activation(combined_tensors + self._bias)
