# Copyright The Lightning team.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from collections.abc import Sequence
from typing import Any, List, Optional, Union

from torch import Tensor

from torchmetrics.functional.clustering.davies_bouldin_score import davies_bouldin_score
from torchmetrics.metric import Metric
from torchmetrics.utilities.data import dim_zero_cat
from torchmetrics.utilities.imports import _MATPLOTLIB_AVAILABLE
from torchmetrics.utilities.plot import _AX_TYPE, _PLOT_OUT_TYPE

if not _MATPLOTLIB_AVAILABLE:
    __doctest_skip__ = ["DaviesBouldinScore.plot"]


class DaviesBouldinScore(Metric):
    r"""Compute `Davies-Bouldin Score`_ for clustering algorithms.

    Given the following quantities:

    .. math::
        S_i = \left( \frac{1}{T_i} \sum_{j=1}^{T_i} ||X_j - A_i||^2_2 \right)^{1/2}

    where :math:`T_i` is the number of samples in cluster :math:`i`, :math:`X_j` is the :math:`j`-th sample in cluster
    :math:`i`, and :math:`A_i` is the centroid of cluster :math:`i`. This quantity is the average distance between all
    the samples in cluster :math:`i` and its centroid. Let

    .. math::
        M_{i,j} = ||A_i - A_j||_2

    e.g. the distance between the centroids of cluster :math:`i` and cluster :math:`j`. Then the Davies-Bouldin score
    is defined as:

    .. math::
        DB = \frac{1}{n_{clusters}} \sum_{i=1}^{n_{clusters}} \max_{j \neq i} \left( \frac{S_i + S_j}{M_{i,j}} \right)

    This clustering metric is an intrinsic measure, because it does not rely on ground truth labels for the evaluation.
    Instead it examines how well the clusters are separated from each other. The score is higher when clusters are dense
    and well separated, which relates to a standard concept of a cluster.

    As input to ``forward`` and ``update`` the metric accepts the following input:

    - ``data`` (:class:`~torch.Tensor`): float tensor with shape ``(N,d)`` with the embedded data. ``d`` is the
      dimensionality of the embedding space.
    - ``labels`` (:class:`~torch.Tensor`): single integer tensor with shape ``(N,)`` with cluster labels

    As output of ``forward`` and ``compute`` the metric returns the following output:

    - ``chs`` (:class:`~torch.Tensor`): A tensor with the Calinski Harabasz Score

    Args:
        kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.

    Example::
        >>> from torch import randn, randint
        >>> from torchmetrics.clustering import DaviesBouldinScore
        >>> data = randn(10, 3)
        >>> labels = randint(3, (10,))
        >>> metric = DaviesBouldinScore()
        >>> metric(data, labels)
        tensor(1.2540)

    """

    is_differentiable: bool = True
    higher_is_better: bool = True
    full_state_update: bool = False
    plot_lower_bound: float = 0.0
    data: List[Tensor]
    labels: List[Tensor]

    def __init__(self, **kwargs: Any) -> None:
        super().__init__(**kwargs)

        self.add_state("data", default=[], dist_reduce_fx="cat")
        self.add_state("labels", default=[], dist_reduce_fx="cat")

    def update(self, data: Tensor, labels: Tensor) -> None:
        """Update metric state with new data and labels."""
        self.data.append(data)
        self.labels.append(labels)

    def compute(self) -> Tensor:
        """Compute the Davies Bouldin Score over all data and labels."""
        return davies_bouldin_score(dim_zero_cat(self.data), dim_zero_cat(self.labels))

    def plot(self, val: Union[Tensor, Sequence[Tensor], None] = None, ax: Optional[_AX_TYPE] = None) -> _PLOT_OUT_TYPE:
        """Plot a single or multiple values from the metric.

        Args:
            val: Either a single result from calling `metric.forward` or `metric.compute` or a list of these results.
                If no value is provided, will automatically call `metric.compute` and plot that result.
            ax: An matplotlib axis object. If provided will add plot to that axis

        Returns:
            Figure and Axes object

        Raises:
            ModuleNotFoundError:
                If `matplotlib` is not installed

        .. plot::
            :scale: 75

            >>> # Example plotting a single value
            >>> import torch
            >>> from torchmetrics.clustering import DaviesBouldinScore
            >>> metric = DaviesBouldinScore()
            >>> metric.update(torch.randn(20, 3), torch.randint(0, 2, (20,)))
            >>> fig_, ax_ = metric.plot(metric.compute())

        .. plot::
            :scale: 75

            >>> # Example plotting multiple values
            >>> import torch
            >>> from torchmetrics.clustering import DaviesBouldinScore
            >>> metric = DaviesBouldinScore()
            >>> values = []
            >>> for _ in range(10):
            ...     values.append(metric(torch.randn(20, 3), torch.randint(0, 2, (20,))))
            >>> fig_, ax_ = metric.plot(values)

        """
        return self._plot(val, ax)