"""
Sequential feature selection
"""
from numbers import Integral, Real

import numpy as np

from ..base import BaseEstimator, MetaEstimatorMixin, _fit_context, clone, is_classifier
from ..metrics import get_scorer_names
from ..model_selection import check_cv, cross_val_score
from ..utils._param_validation import HasMethods, Interval, RealNotInt, StrOptions
from ..utils._tags import _safe_tags
from ..utils.validation import check_is_fitted
from ._base import SelectorMixin


class SequentialFeatureSelector(SelectorMixin, MetaEstimatorMixin, BaseEstimator):
    """Transformer that performs Sequential Feature Selection.

    This Sequential Feature Selector adds (forward selection) or
    removes (backward selection) features to form a feature subset in a
    greedy fashion. At each stage, this estimator chooses the best feature to
    add or remove based on the cross-validation score of an estimator. In
    the case of unsupervised learning, this Sequential Feature Selector
    looks only at the features (X), not the desired outputs (y).

    Read more in the :ref:`User Guide <sequential_feature_selection>`.

    .. versionadded:: 0.24

    Parameters
    ----------
    estimator : estimator instance
        An unfitted estimator.

    n_features_to_select : "auto", int or float, default="auto"
        If `"auto"`, the behaviour depends on the `tol` parameter:

        - if `tol` is not `None`, then features are selected while the score
          change does not exceed `tol`.
        - otherwise, half of the features are selected.

        If integer, the parameter is the absolute number of features to select.
        If float between 0 and 1, it is the fraction of features to select.

        .. versionadded:: 1.1
           The option `"auto"` was added in version 1.1.

        .. versionchanged:: 1.3
           The default changed from `"warn"` to `"auto"` in 1.3.

    tol : float, default=None
        If the score is not incremented by at least `tol` between two
        consecutive feature additions or removals, stop adding or removing.

        `tol` can be negative when removing features using `direction="backward"`.
        It can be useful to reduce the number of features at the cost of a small
        decrease in the score.

        `tol` is enabled only when `n_features_to_select` is `"auto"`.

        .. versionadded:: 1.1

    direction : {'forward', 'backward'}, default='forward'
        Whether to perform forward selection or backward selection.

    scoring : str or callable, default=None
        A single str (see :ref:`scoring_parameter`) or a callable
        (see :ref:`scoring`) to evaluate the predictions on the test set.

        NOTE that when using a custom scorer, it should return a single
        value.

        If None, the estimator's score method is used.

    cv : int, cross-validation generator or an iterable, default=None
        Determines the cross-validation splitting strategy.
        Possible inputs for cv are:

        - None, to use the default 5-fold cross validation,
        - integer, to specify the number of folds in a `(Stratified)KFold`,
        - :term:`CV splitter`,
        - An iterable yielding (train, test) splits as arrays of indices.

        For integer/None inputs, if the estimator is a classifier and ``y`` is
        either binary or multiclass, :class:`StratifiedKFold` is used. In all
        other cases, :class:`KFold` is used. These splitters are instantiated
        with `shuffle=False` so the splits will be the same across calls.

        Refer :ref:`User Guide <cross_validation>` for the various
        cross-validation strategies that can be used here.

    n_jobs : int, default=None
        Number of jobs to run in parallel. When evaluating a new feature to
        add or remove, the cross-validation procedure is parallel over the
        folds.
        ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
        ``-1`` means using all processors. See :term:`Glossary <n_jobs>`
        for more details.

    Attributes
    ----------
    n_features_in_ : int
        Number of features seen during :term:`fit`. Only defined if the
        underlying estimator exposes such an attribute when fit.

        .. versionadded:: 0.24

    feature_names_in_ : ndarray of shape (`n_features_in_`,)
        Names of features seen during :term:`fit`. Defined only when `X`
        has feature names that are all strings.

        .. versionadded:: 1.0

    n_features_to_select_ : int
        The number of features that were selected.

    support_ : ndarray of shape (n_features,), dtype=bool
        The mask of selected features.

    See Also
    --------
    GenericUnivariateSelect : Univariate feature selector with configurable
        strategy.
    RFE : Recursive feature elimination based on importance weights.
    RFECV : Recursive feature elimination based on importance weights, with
        automatic selection of the number of features.
    SelectFromModel : Feature selection based on thresholds of importance
        weights.

    Examples
    --------
    >>> from sklearn.feature_selection import SequentialFeatureSelector
    >>> from sklearn.neighbors import KNeighborsClassifier
    >>> from sklearn.datasets import load_iris
    >>> X, y = load_iris(return_X_y=True)
    >>> knn = KNeighborsClassifier(n_neighbors=3)
    >>> sfs = SequentialFeatureSelector(knn, n_features_to_select=3)
    >>> sfs.fit(X, y)
    SequentialFeatureSelector(estimator=KNeighborsClassifier(n_neighbors=3),
                              n_features_to_select=3)
    >>> sfs.get_support()
    array([ True, False,  True,  True])
    >>> sfs.transform(X).shape
    (150, 3)
    """

    _parameter_constraints: dict = {
        "estimator": [HasMethods(["fit"])],
        "n_features_to_select": [
            StrOptions({"auto"}),
            Interval(RealNotInt, 0, 1, closed="right"),
            Interval(Integral, 0, None, closed="neither"),
        ],
        "tol": [None, Interval(Real, None, None, closed="neither")],
        "direction": [StrOptions({"forward", "backward"})],
        "scoring": [None, StrOptions(set(get_scorer_names())), callable],
        "cv": ["cv_object"],
        "n_jobs": [None, Integral],
    }

    def __init__(
        self,
        estimator,
        *,
        n_features_to_select="auto",
        tol=None,
        direction="forward",
        scoring=None,
        cv=5,
        n_jobs=None,
    ):
        self.estimator = estimator
        self.n_features_to_select = n_features_to_select
        self.tol = tol
        self.direction = direction
        self.scoring = scoring
        self.cv = cv
        self.n_jobs = n_jobs

    @_fit_context(
        # SequentialFeatureSelector.estimator is not validated yet
        prefer_skip_nested_validation=False
    )
    def fit(self, X, y=None):
        """Learn the features to select from X.

        Parameters
        ----------
        X : array-like of shape (n_samples, n_features)
            Training vectors, where `n_samples` is the number of samples and
            `n_features` is the number of predictors.

        y : array-like of shape (n_samples,), default=None
            Target values. This parameter may be ignored for
            unsupervised learning.

        Returns
        -------
        self : object
            Returns the instance itself.
        """
        tags = self._get_tags()
        X = self._validate_data(
            X,
            accept_sparse="csc",
            ensure_min_features=2,
            force_all_finite=not tags.get("allow_nan", True),
        )
        n_features = X.shape[1]

        if self.n_features_to_select == "auto":
            if self.tol is not None:
                # With auto feature selection, `n_features_to_select_` will be updated
                # to `support_.sum()` after features are selected.
                self.n_features_to_select_ = n_features - 1
            else:
                self.n_features_to_select_ = n_features // 2
        elif isinstance(self.n_features_to_select, Integral):
            if self.n_features_to_select >= n_features:
                raise ValueError("n_features_to_select must be < n_features.")
            self.n_features_to_select_ = self.n_features_to_select
        elif isinstance(self.n_features_to_select, Real):
            self.n_features_to_select_ = int(n_features * self.n_features_to_select)

        if self.tol is not None and self.tol < 0 and self.direction == "forward":
            raise ValueError("tol must be positive when doing forward selection")

        cv = check_cv(self.cv, y, classifier=is_classifier(self.estimator))

        cloned_estimator = clone(self.estimator)

        # the current mask corresponds to the set of features:
        # - that we have already *selected* if we do forward selection
        # - that we have already *excluded* if we do backward selection
        current_mask = np.zeros(shape=n_features, dtype=bool)
        n_iterations = (
            self.n_features_to_select_
            if self.n_features_to_select == "auto" or self.direction == "forward"
            else n_features - self.n_features_to_select_
        )

        old_score = -np.inf
        is_auto_select = self.tol is not None and self.n_features_to_select == "auto"
        for _ in range(n_iterations):
            new_feature_idx, new_score = self._get_best_new_feature_score(
                cloned_estimator, X, y, cv, current_mask
            )
            if is_auto_select and ((new_score - old_score) < self.tol):
                break

            old_score = new_score
            current_mask[new_feature_idx] = True

        if self.direction == "backward":
            current_mask = ~current_mask

        self.support_ = current_mask
        self.n_features_to_select_ = self.support_.sum()

        return self

    def _get_best_new_feature_score(self, estimator, X, y, cv, current_mask):
        # Return the best new feature and its score to add to the current_mask,
        # i.e. return the best new feature and its score to add (resp. remove)
        # when doing forward selection (resp. backward selection).
        # Feature will be added if the current score and past score are greater
        # than tol when n_feature is auto,
        candidate_feature_indices = np.flatnonzero(~current_mask)
        scores = {}
        for feature_idx in candidate_feature_indices:
            candidate_mask = current_mask.copy()
            candidate_mask[feature_idx] = True
            if self.direction == "backward":
                candidate_mask = ~candidate_mask
            X_new = X[:, candidate_mask]
            scores[feature_idx] = cross_val_score(
                estimator,
                X_new,
                y,
                cv=cv,
                scoring=self.scoring,
                n_jobs=self.n_jobs,
            ).mean()
        new_feature_idx = max(scores, key=lambda feature_idx: scores[feature_idx])
        return new_feature_idx, scores[new_feature_idx]

    def _get_support_mask(self):
        check_is_fitted(self)
        return self.support_

    def _more_tags(self):
        return {
            "allow_nan": _safe_tags(self.estimator, key="allow_nan"),
        }
