# ----------------------------------------------------------------------------
# Copyright (c) 2013--, scikit-bio development team.
#
# Distributed under the terms of the Modified BSD License.
#
# The full license is in the file LICENSE.txt, distributed with this software.
# ----------------------------------------------------------------------------

import numpy as np

from skbio.diversity._util import (
    _validate_counts_vector,
    _validate_taxa_and_tree,
    vectorize_counts_and_tree,
    _check_taxa_alias,
)


def _setup_pd(counts, taxa, tree, validate, rooted, single_sample):
    if validate:
        if single_sample:
            # only validate count if operating in single sample mode, they
            # will have already been validated otherwise
            counts = _validate_counts_vector(counts)
            _validate_taxa_and_tree(counts, taxa, tree, rooted)
        else:
            _validate_taxa_and_tree(counts[0], taxa, tree, rooted)

    counts_by_node, _, branch_lengths = vectorize_counts_and_tree(counts, taxa, tree)

    return counts_by_node, branch_lengths


def _faith_pd(counts_by_node, branch_lengths):
    """Calculate Faith's phylogenetic diversity (Faith's PD) metric.

    Parameters
    ----------
    counts_by_node : ndarray of shape (n_samples, n_nodes)
        Total counts/abundances of taxa descending from individual nodes of the tree.
    branch_lengths : ndarray of shape (n_nodes,)
        Branch lengths of corresponding nodes of the tree.

    Returns
    -------
    float
        Faith's phylogenetic diversity (PD).

    """
    return (branch_lengths * (counts_by_node > 0)).sum()


def faith_pd(counts, taxa=None, tree=None, validate=True, otu_ids=None):
    r"""Calculate Faith's phylogenetic diversity (Faith's PD) metric.

    The Faith's PD metric is defined as:

    .. math::

       PD = \sum_{b \in T \sqcup R} l(b)

    where :math:`T` is a minimum set of branches (:math:`b`) in a rooted tree that
    connect all taxa in a community. :math:`R` is a set of branches from the lowest
    common ancestor (LCA) of the taxa to the root of the tree. :math:`PD` is the sum of
    lengths (:math:`l`) of branches in both sets.

    Parameters
    ----------
    counts : 1-D array_like, int
        Vectors of counts/abundances of taxa for one sample.
    taxa : list, np.array
        Vector of taxon IDs corresponding to tip names in ``tree``. Must be the same
        length as ``counts``. Required.
    tree : skbio.TreeNode
        Tree relating taxa. The set of tip names in the tree can be a superset of
        ``taxa``, but not a subset. Required.
    validate : bool, optional
        Whether validate the input data (default: True). This step can be slow, so if
        validation is run elsewhere it can be disabled here. However, invalid input
        data can lead to invalid results or error messages that are hard to interpret,
        so this step should not be bypassed if you're not certain that your input data
        are valid. See :mod:`skbio.diversity` for the description of what validation
        entails so you can determine if you can safely disable validation.
    otu_ids : list, np.array
        Alias of ``taxa`` for backward compatibility. Deprecated and to be removed in a
        future release.

    Returns
    -------
    float
        Faith's phylogenetic diversity (PD).

    Raises
    ------
    ValueError, MissingNodeError, DuplicateNodeError
        If validation fails. Exact error will depend on what was invalid.

    See Also
    --------
    phydiv
    skbio.diversity
    skbio.diversity.alpha_diversity

    Notes
    -----
    Faith's phylogenetic diversity, often referred to as PD, was originally described
    in [1]_. It is the total phylogenetic branch length spanning all taxa of a
    community.

    It was clarified that the calculation should extend to the root of the tree [2]_,
    such that a single-taxon community will not have PD = 0. The root should be
    ancestral to all taxa being considered in the study, but does not need to be the
    origin of life. One should choose the root according to the scope of the study.

    Unrooted and abundance-weighted variants of PD are implemented in :func:`phydiv`.

    Several other metrics, such as evolutionary history (EH) [3]_ and functional
    diversity (FD) [4]_, are equivalent to PD in calculation.

    If computing Faith's PD for multiple samples, using
    :func:`skbio.diversity.alpha_diversity` will be much faster than calling this
    function individually on each sample.

    This implementation of Faith's PD is based on the array-based implementation of
    UniFrac described in [5]_.

    .. note::

        This implementation differs from that in PyCogent (and therefore QIIME versions
        less than 2.0.0) by imposing a few additional restrictions on the inputs.
        First, the input tree must be rooted. In PyCogent, if an unrooted tree was
        provided that had a single trifurcating node (a newick convention for unrooted
        trees) that node was considered the root of the tree. Next, all taxa must be
        tips in the tree. PyCogent would silently ignore taxa that were not present the
        tree. To reproduce Faith PD results from PyCogent with scikit-bio, ensure that
        your PyCogent Faith PD calculations are performed on a rooted tree and that all
        taxa are present in the tree.

    References
    ----------
    .. [1] Faith, D. P. Conservation evaluation and phylogenetic diversity. Biol.
       Conserv. (1992).

    .. [2] Faith, D. P., & Baker, A. M. (2006). Phylogenetic diversity (PD) and
       biodiversity conservation: some bioinformatics challenges. Evolutionary
       bioinformatics, 2, 117693430600200007.

    .. [3] Nee, S., & May, R. M. (1997). Extinction and the loss of evolutionary
       history. Science, 278(5338), 692-694.

    .. [4] Petchey OL, Gaston KJ. Functional diversity (FD), species richness and
       community composition. Ecology letters. 2002 May;5(3):402-11.

    .. [5] Hamady M, Lozupone C, Knight R. Fast UniFrac: facilitating high-throughput
       phylogenetic analyses of microbial communities including analysis of
       pyrosequencing and PhyloChip data. ISME J. 4(1):17-27 (2010).

    Examples
    --------
    Assume we have the following abundance data for a sample ``u``, represented as a
    counts vector. These counts represent the number of times specific taxa were
    observed in the sample.

    >>> u_counts = [1, 0, 0, 4, 1, 2, 3, 0]

    Because Faith PD is a phylogenetic diversity metric, we need to know which taxon
    each count corresponds to, which we'll provide as ``taxa``.

    >>> taxa = ['U1', 'U2', 'U3', 'U4', 'U5', 'U6', 'U7', 'U8']

    We also need a phylogenetic tree that relates the taxa to one another.

    >>> from skbio import TreeNode
    >>> tree = TreeNode.read(['(((((U1:0.5,U2:0.5):0.5,U3:1.0):1.0):0.0,'
    ...                       '(U4:0.75,(U5:0.5,((U6:0.33,U7:0.62):0.5'
    ...                       ',U8:0.5):0.5):0.5):1.25):0.0)root;'])

    We can then compute the Faith PD of the sample.

    >>> from skbio.diversity.alpha import faith_pd
    >>> pd = faith_pd(u_counts, taxa, tree)
    >>> print(round(pd, 2))
    6.95

    """
    # TODO: Remove `otu_ids` and make `taxa` and `tree` required in a future version.

    taxa = _check_taxa_alias(taxa, tree, otu_ids)

    counts_by_node, branch_lengths = _setup_pd(
        counts, taxa, tree, validate, rooted=True, single_sample=True
    )

    return _faith_pd(counts_by_node, branch_lengths)


def _phydiv(counts_by_node, branch_lengths, rooted, weight):
    """Calculate generalized phylogenetic diversity (PD) metrics.

    Parameters
    ----------
    counts_by_node : ndarray of shape (n_samples, n_nodes)
        Total counts/abundances of taxa descending from individual nodes of the tree.
    branch_lengths : ndarray of shape (n_nodes,)
        Branch lengths of corresponding nodes of the tree.
    rooted : bool
        Whether the metric is calculated considering the root of the tree.
    weight : bool or float
        Whether and to what degree branch lengths should be weighted by the relative
        abundance of taxa descending from the branch.

    Returns
    -------
    float
        Phylogenetic diversity (PD).

    """
    # select branches connecting taxa
    included = counts_by_node > 0

    # get total counts
    counts_sum = counts_by_node.max()
    if counts_sum == 0.0:
        return 0.0

    # in unrooted mode, remove branches to root
    if rooted is False:
        included &= counts_by_node < counts_sum

    # in unweighted mode, simply sum branch lengths
    if not weight:
        return (branch_lengths * included).sum()

    # get relative abundances
    fracs_by_node = counts_by_node / counts_sum

    # calculate balances in unrooted mode
    if rooted is False:
        fracs_by_node = 2 * np.minimum(fracs_by_node, 1 - fracs_by_node)

    # raise relative abundances to the power of theta
    if isinstance(weight, float) and weight < 1.0:
        fracs_by_node **= weight

    return (branch_lengths * fracs_by_node).sum()


def phydiv(
    counts, taxa=None, tree=None, rooted=None, weight=False, validate=True, otu_ids=None
):
    r"""Calculate generalized phylogenetic diversity (PD) metrics.

    Parameters
    ----------
    counts : 1-D array_like, int
        Vectors of counts/abundances of taxa for one sample.
    taxa : list, np.array
        Vector of taxon IDs corresponding to tip names in ``tree``. Must be the same
        length as ``counts``. Required.
    tree : skbio.TreeNode
        Tree relating taxa. The set of tip names in the tree can be a superset of
        ``taxa``, but not a subset. Required.
    rooted : bool, optional
        Whether the metric is calculated considering the root of the tree. By default,
        this will be determined based on whether the input tree is rooted. However, one
        can override it by explicitly specifying True (rooted) or False (unrooted).
    weight : bool or float, optional
        Whether branch lengths should be weighted by the relative abundance of taxa
        descending from the branch (default: False). A float within [0, 1] indicates
        the degree of partial-weighting (0: unweighted, 1: fully-weighted).
    validate : bool, optional
        Whether validate the input data. See :func:`faith_pd` for details.
    otu_ids : list, np.array
        Alias of ``taxa`` for backward compatibility. Deprecated and to be removed in a
        future release.

    Returns
    -------
    float
        Phylogenetic diversity (PD).

    Raises
    ------
    ValueError, MissingNodeError, DuplicateNodeError
        If validation fails. Exact error will depend on what was invalid.

    See Also
    --------
    faith_pd
    skbio.diversity
    skbio.diversity.alpha_diversity

    Notes
    -----
    Phylogenetic diversity (PD) metrics measure the diversity of a community with
    consideration of the phylogenetic relationships among taxa. In general, PD is the
    sum of branch lengths spanning across taxa, optionally weighted by their relative
    abundances in the community.

    The most widely-adopted PD metric, Faith's PD [1]_, is defined as:

    .. math::

       PD = \sum_{b \in T \sqcup R} l(b)

    where :math:`T` is a minimum set of branches (:math:`b`) in a rooted tree that
    connect all taxa in a community. :math:`R` is a set of branches from the lowest
    common ancestor (LCA) of the taxa to the root of the tree. :math:`PD` is the sum of
    lengths (:math:`l`) of branches in both sets.

    It is equivalent to ``phydiv(..., rooted=True, weight=False)``.

    ---

    A variant of PD, which does not include the root in the calculation, was referred
    to by some authors as unrooted phylogenetic diversity (uPD) [2]_, as in contrast to
    rooted phylogenetic diversity (rPD, i.e., Faith's PD). uPD is defined as:

    .. math::

       PD = \sum_{b \in T} l(b)

    It is equivalent to ``phydiv(..., rooted=False, weight=False)``.

    See :func:`faith_pd` for a discussion of the root.

    ---

    PD (rooted or unrooted) considers only the presence of taxa. Therefore, it can be
    considered as the phylogenetic generalization of species richness. However, there
    are advantages of incorporating abundance information in the measurement [3]_. A
    generalized framework of abundance-weighted PD is provided in [4]_.

    Abundance-weighted rooted PD (equivalent to :math:`RBWPD_{1}` described in [4]_) is
    analogous to the :math:`PD_{aw}` metric originally described in [5]_ with a
    multiplier. It is defined as:

    .. math::

       PD = \sum_{b \in T \sqcup R} l(b) p(b)

    where :math:`p` is the sum of relative (proportional) abundances of taxa descending
    from branch (:math:`b`).

    It is equivalent to ``phydiv(..., rooted=True, weight=True)``.

    ---

    Abundance-weighted unrooted PD (equivalent to :math:`BWPD_{1}` described in [4]_)
    is analogous to the :math:`\delta nPD` metric originally described in [6]_ with a
    multiplier. It is defined as:

    .. math::

       PD = 2 \sum_{b \in T} l(b) \min(p(b),1-p(b))

    In which the term :math:`2\min(p(b),1-p(b))` is the lesser of the relative
    abundance of descending taxa on either side of a branch, multiplied by two. It is
    referred to as the "balance" of taxon abundance in [4]_.

    It is equivalent to ``phydiv(..., rooted=False, weight=True)``.

    ---

    The contribution of taxon abundance to the metric can be adjusted using the
    ``weight`` parameter when it is a float within [0, 1]. This factor was referred to
    as :math:`\theta` in [4]_. The metric, :math:`BWPD_{\theta}`, referred to as the
    balance-weighted phylogenetic diversity in [4]_, is defined as:

    .. math::

       PD = \sum_{b \in T} l(b) (2\min(p(b),1-p(b)))^\theta

    It is equivalent to ``phydiv(..., rooted=False, weight=theta)``.

    This metric falls back to unweighted PD when :math:`\theta=0` or fully-weighted PD
    when :math:`\theta=1`. The original publication tested :math:`\theta=0.25` or
    :math:`0.5` [4]_.

    The parameter :math:`\theta` is analogous to the parameter :math:`\alpha` in the
    generalized UniFrac metric [7]_.

    ---

    Likewise, the rooted version of balance-weighted phylogenetic diversity,
    :math:`RBWPD_{\theta}` [4]_ (although "balance" is not involved), is defined as:

    .. math::

        PD = \sum_{b \in T \sqcup R} l(b) p(b)^\theta

    It is equivalent to ``phydiv(..., rooted=True, weight=theta)``.

    ---

    It is important to report which metric is used. For practical perspective, we
    recommend the following denotions:

    - :math:`rPD`: rooted, unweighted PD (Faith's PD [1]_).
    - :math:`uPD`: unrooted, unweighted PD (uPD [2]_).
    - :math:`rPD_{w}`: rooted, weighted PD (analogous to :math:`PD_{aw}` [3]_).
    - :math:`uPD_{w}`: unrooted, weighted PD (analogous to :math:`\delta nPD` [4]_).
    - :math:`rPD_{w\theta}`: rooted, weighted PD with parameter :math:`\theta`
      (:math:`RBWPD_{\theta}` [5]_).
    - :math:`uPD_{w\theta}`: unrooted, weighted PD with parameter :math:`\theta`
      (:math:`BWPD_{\theta}` [5]_).

    References
    ----------
    .. [1] Faith, D. P. Conservation evaluation and phylogenetic diversity. Biol.
       Conserv. (1992).

    .. [2] Pardi, F., & Goldman, N. (2007). Resource-aware taxon selection for
       maximizing phylogenetic diversity. Systematic biology, 56(3), 431-444.

    .. [3] Chao, A., Chiu, C. H., & Jost, L. (2016). Phylogenetic diversity measures
       and their decomposition: a framework based on Hill numbers. Biodiversity
       Conservation and Phylogenetic Systematics, 14, 141-72.

    .. [4] McCoy, C. O., & Matsen IV, F. A. (2013). Abundance-weighted phylogenetic
       diversity measures distinguish microbial community states and are robust to
       sampling depth. PeerJ, 1, e157.

    .. [5] Vellend, M., Cornwell, W. K., Magnuson-Ford, K., & Mooers, A. Ø. (2011).
       Measuring phylogenetic biodiversity. Biological diversity: frontiers in
       measurement and assessment, 194-207.

    .. [6] Barker, G. M. (2002). Phylogenetic diversity: a quantitative framework for
       measurement of priority and achievement in biodiversity conservation. Biological
       Journal of the Linnean Society, 76(2), 165-194.

    .. [7] Chen, J., Bittinger, K., Charlson, E. S., Hoffmann, C., Lewis, J., Wu, G.
       D., ... & Li, H. (2012). Associating microbiome composition with environmental
       covariates using generalized UniFrac distances. Bioinformatics, 28(16),
       2106-2113.

    """
    taxa = _check_taxa_alias(taxa, tree, otu_ids)

    # whether tree is rooted should not affect whether metric can be calculated
    # ; it is common unrooted PD is calculated on a rooted tree
    counts_by_node, branch_lengths = _setup_pd(
        counts, taxa, tree, validate, rooted=False, single_sample=True
    )

    # if not specified, determine whether metric should be calculated in rooted
    # mode according to the tree
    if rooted is None:
        rooted = len(tree.root().children) == 2

    # validate weight parameter
    if (
        not isinstance(weight, (bool, int, float))
        or (w_ := float(weight)) < 0.0
        or w_ > 1.0
    ):
        raise ValueError("Weight parameter must be Boolean or within [0, 1].")

    return _phydiv(counts_by_node, branch_lengths, rooted, weight)
