from typing import Optional, Sequence
import torch
import torch.nn as nn


__all__ = ['MultipleKernelMaximumMeanDiscrepancy']


class MultipleKernelMaximumMeanDiscrepancy(nn.Module):
    r"""The Multiple Kernel Maximum Mean Discrepancy (MK-MMD) used in
    `Learning Transferable Features with Deep Adaptation Networks (ICML 2015) <https://arxiv.org/pdf/1502.02791>`_

    Given source domain :math:`\mathcal{D}_s` of :math:`n_s` labeled points and target domain :math:`\mathcal{D}_t`
    of :math:`n_t` unlabeled points drawn i.i.d. from P and Q respectively, the deep networks will generate
    activations as :math:`\{z_i^s\}_{i=1}^{n_s}` and :math:`\{z_i^t\}_{i=1}^{n_t}`.
    The MK-MMD :math:`D_k (P, Q)` between probability distributions P and Q is defined as

    .. math::
        D_k(P, Q) \triangleq \| E_p [\phi(z^s)] - E_q [\phi(z^t)] \|^2_{\mathcal{H}_k},

    :math:`k` is a kernel function in the function space

    .. math::
        \mathcal{K} \triangleq \{ k=\sum_{u=1}^{m}\beta_{u} k_{u} \}

    where :math:`k_{u}` is a single kernel.

    Using kernel trick, MK-MMD can be computed as

    .. math::
        \hat{D}_k(P, Q) &=
        \dfrac{1}{n_s^2} \sum_{i=1}^{n_s}\sum_{j=1}^{n_s} k(z_i^{s}, z_j^{s})\\
        &+ \dfrac{1}{n_t^2} \sum_{i=1}^{n_t}\sum_{j=1}^{n_t} k(z_i^{t}, z_j^{t})\\
        &- \dfrac{2}{n_s n_t} \sum_{i=1}^{n_s}\sum_{j=1}^{n_t} k(z_i^{s}, z_j^{t}).\\

    Args:
        kernels (tuple(torch.nn.Module)): kernel functions.
        linear (bool): whether use the linear version of DAN. Default: False

    Inputs:
        - z_s (tensor): activations from the source domain, :math:`z^s`
        - z_t (tensor): activations from the target domain, :math:`z^t`

    Shape:
        - Inputs: :math:`(minibatch, *)`  where * means any dimension
        - Outputs: scalar

    .. note::
        Activations :math:`z^{s}` and :math:`z^{t}` must have the same shape.

    .. note::
        The kernel values will add up when there are multiple kernels.

    Examples::

        >>> from dalib.modules.kernels import GaussianKernel
        >>> feature_dim = 1024
        >>> batch_size = 10
        >>> kernels = (GaussianKernel(alpha=0.5), GaussianKernel(alpha=1.), GaussianKernel(alpha=2.))
        >>> loss = MultipleKernelMaximumMeanDiscrepancy(kernels)
        >>> # features from source domain and target domain
        >>> z_s, z_t = torch.randn(batch_size, feature_dim), torch.randn(batch_size, feature_dim)
        >>> output = loss(z_s, z_t)
    """

    def __init__(self, kernels: Sequence[nn.Module], linear: Optional[bool] = False):
        super(MultipleKernelMaximumMeanDiscrepancy, self).__init__()
        self.kernels = kernels
        self.index_matrix = None
        self.linear = linear

    def forward(self, z_s: torch.Tensor, z_t: torch.Tensor) -> torch.Tensor:
        features = torch.cat([z_s, z_t], dim=0)
        batch_size = int(z_s.size(0))
        self.index_matrix = _update_index_matrix(batch_size, self.index_matrix, self.linear).to(z_s.device)


        kernel_matrix = sum([kernel(features) for kernel in self.kernels])  # Add up the matrix of each kernel
        # Add 2 / (n-1) to make up for the value on the diagonal
        # to ensure loss is positive in the non-linear version
        loss = (kernel_matrix * self.index_matrix).sum() + 2. / float(batch_size - 1)

        return loss


def _update_index_matrix(batch_size: int, index_matrix: Optional[torch.Tensor] = None,
                         linear: Optional[bool] = True) -> torch.Tensor:
    r"""
    Update the `index_matrix` which convert `kernel_matrix` to loss.
    If `index_matrix` is a tensor with shape (2 x batch_size, 2 x batch_size), then return `index_matrix`.
    Else return a new tensor with shape (2 x batch_size, 2 x batch_size).
    """
    if index_matrix is None or index_matrix.size(0) != batch_size * 2:
        index_matrix = torch.zeros(2 * batch_size, 2 * batch_size)
        if linear:
            for i in range(batch_size):
                s1, s2 = i, (i + 1) % batch_size
                t1, t2 = s1 + batch_size, s2 + batch_size
                index_matrix[s1, s2] = 1. / float(batch_size)
                index_matrix[t1, t2] = 1. / float(batch_size)
                index_matrix[s1, t2] = -1. / float(batch_size)
                index_matrix[s2, t1] = -1. / float(batch_size)
        else:
            for i in range(batch_size):
                for j in range(batch_size):
                    if i != j:
                        index_matrix[i][j] = 1. / float(batch_size * (batch_size - 1))
                        index_matrix[i + batch_size][j + batch_size] = 1. / float(batch_size * (batch_size - 1))
            for i in range(batch_size):
                for j in range(batch_size):
                    index_matrix[i][j + batch_size] = -1. / float(batch_size * batch_size)
                    index_matrix[i + batch_size][j] = -1. / float(batch_size * batch_size)
    return index_matrix
