Check the significance of all features (columns) of feature matrix X and return a possibly reduced feature matrix
    only containing relevant features.

    The feature matrix must be a pandas.DataFrame in the format:

        +-------+-----------+-----------+-----+-----------+
        | index | feature_1 | feature_2 | ... | feature_N |
        +=======+===========+===========+=====+===========+
        | A     | ...       | ...       | ... | ...       |
        +-------+-----------+-----------+-----+-----------+
        | B     | ...       | ...       | ... | ...       |
        +-------+-----------+-----------+-----+-----------+
        | ...   | ...       | ...       | ... | ...       |
        +-------+-----------+-----------+-----+-----------+
        | ...   | ...       | ...       | ... | ...       |
        +-------+-----------+-----------+-----+-----------+
        | ...   | ...       | ...       | ... | ...       |
        +-------+-----------+-----------+-----+-----------+


    Each column will be handled as a feature and tested for its significance to the target.

    The target vector must be a pandas.Series or numpy.array in the form

        +-------+--------+
        | index | target |
        +=======+========+
        | A     | ...    |
        +-------+--------+
        | B     | ...    |
        +-------+--------+
        | .     | ...    |
        +-------+--------+
        | .     | ...    |
        +-------+--------+

    and must contain all id's that are in the feature matrix. If y is a numpy.array without index, it is assumed
    that y has the same order and length than X and the rows correspond to each other.

    Examples
    ========

    >>> from tsfresh.examples import load_robot_execution_failures
    >>> from tsfresh import extract_features, select_features
    >>> df, y = load_robot_execution_failures()
    >>> X_extracted = extract_features(df, column_id='id', column_sort='time')
    >>> X_selected = select_features(X_extracted, y)

    :param X: Feature matrix in the format mentioned before which will be reduced to only the relevant features.
              It can contain both binary or real-valued features at the same time.
    :type X: pandas.DataFrame

    :param y: Target vector which is needed to test which features are relevant. Can be binary or real-valued.
    :type y: pandas.Series or numpy.ndarray

    :param test_for_binary_target_binary_feature: Which test to be used for binary target, binary feature (currently unused)
    :type test_for_binary_target_binary_feature: str

    :param test_for_binary_target_real_feature: Which test to be used for binary target, real feature
    :type test_for_binary_target_real_feature: str

    :param test_for_real_target_binary_feature: Which test to be used for real target, binary feature (currently unused)
    :type test_for_real_target_binary_feature: str

    :param test_for_real_target_real_feature: Which test to be used for real target, real feature (currently unused)
    :type test_for_real_target_real_feature: str

    :param fdr_level: The FDR level that should be respected, this is the theoretical expected percentage of irrelevant
                      features among all created features.
    :type fdr_level: float

    :param hypotheses_independent: Can the significance of the features be assumed to be independent?
                                   Normally, this should be set to False as the features are never
                                   independent (e.g. mean and median)
    :type hypotheses_independent: bool

    :param n_jobs: Number of processes to use during the p-value calculation
    :type n_jobs: int

    :param chunksize: The size of one chunk that is submitted to the worker
        process for the parallelisation.  Where one chunk is defined as a
        singular time series for one id and one kind. If you set the chunksize
        to 10, then it means that one task is to calculate all features for 10
        time series.  If it is set it to None, depending on distributor,
        heuristics are used to find the optimal chunksize. If you get out of
        memory exceptions, you can try it with the dask distributor and a
        smaller chunksize.
    :type chunksize: None or int

    :param ml_task: The intended machine learning task. Either `'classification'`, `'regression'` or `'auto'`.
                    Defaults to `'auto'`, meaning the intended task is inferred from `y`.
                    If `y` has a boolean, integer or object dtype, the task is assumend to be classification,
                    else regression.
    :type ml_task: str

    :return: The same DataFrame as X, but possibly with reduced number of columns ( = features).
    :rtype: pandas.DataFrame

    :raises: ``ValueError`` when the target vector does not fit to the feature matrix
             or `ml_task` is not one of `'auto'`, `'classification'` or `'regression'`.

def select_features(X, y, test_for_binary_target_binary_feature=defaults.TEST_FOR_BINARY_TARGET_BINARY_FEATURE,
                    test_for_binary_target_real_feature=defaults.TEST_FOR_BINARY_TARGET_REAL_FEATURE,
                    test_for_real_target_binary_feature=defaults.TEST_FOR_REAL_TARGET_BINARY_FEATURE,
                    test_for_real_target_real_feature=defaults.TEST_FOR_REAL_TARGET_REAL_FEATURE,
                    fdr_level=defaults.FDR_LEVEL, hypotheses_independent=defaults.HYPOTHESES_INDEPENDENT,
                    n_jobs=defaults.N_PROCESSES, chunksize=defaults.CHUNKSIZE,
                    ml_task='auto'):
    """
    Check the significance of all features (columns) of feature matrix X and return a possibly reduced feature matrix
    only containing relevant features.

    The feature matrix must be a pandas.DataFrame in the format:

        +-------+-----------+-----------+-----+-----------+
        | index | feature_1 | feature_2 | ... | feature_N |
        +=======+===========+===========+=====+===========+
        | A     | ...       | ...       | ... | ...       |
        +-------+-----------+-----------+-----+-----------+
        | B     | ...       | ...       | ... | ...       |
        +-------+-----------+-----------+-----+-----------+
        | ...   | ...       | ...       | ... | ...       |
        +-------+-----------+-----------+-----+-----------+
        | ...   | ...       | ...       | ... | ...       |
        +-------+-----------+-----------+-----+-----------+
        | ...   | ...       | ...       | ... | ...       |
        +-------+-----------+-----------+-----+-----------+


    Each column will be handled as a feature and tested for its significance to the target.

    The target vector must be a pandas.Series or numpy.array in the form

        +-------+--------+
        | index | target |
        +=======+========+
        | A     | ...    |
        +-------+--------+
        | B     | ...    |
        +-------+--------+
        | .     | ...    |
        +-------+--------+
        | .     | ...    |
        +-------+--------+

    and must contain all id's that are in the feature matrix. If y is a numpy.array without index, it is assumed
    that y has the same order and length than X and the rows correspond to each other.

    Examples
    ========

    >>> from tsfresh.examples import load_robot_execution_failures
    >>> from tsfresh import extract_features, select_features
    >>> df, y = load_robot_execution_failures()
    >>> X_extracted = extract_features(df, column_id='id', column_sort='time')
    >>> X_selected = select_features(X_extracted, y)

    :param X: Feature matrix in the format mentioned before which will be reduced to only the relevant features.
              It can contain both binary or real-valued features at the same time.
    :type X: pandas.DataFrame

    :param y: Target vector which is needed to test which features are relevant. Can be binary or real-valued.
    :type y: pandas.Series or numpy.ndarray

    :param test_for_binary_target_binary_feature: Which test to be used for binary target, binary feature (currently unused)
    :type test_for_binary_target_binary_feature: str

    :param test_for_binary_target_real_feature: Which test to be used for binary target, real feature
    :type test_for_binary_target_real_feature: str

    :param test_for_real_target_binary_feature: Which test to be used for real target, binary feature (currently unused)
    :type test_for_real_target_binary_feature: str

    :param test_for_real_target_real_feature: Which test to be used for real target, real feature (currently unused)
    :type test_for_real_target_real_feature: str

    :param fdr_level: The FDR level that should be respected, this is the theoretical expected percentage of irrelevant
                      features among all created features.
    :type fdr_level: float

    :param hypotheses_independent: Can the significance of the features be assumed to be independent?
                                   Normally, this should be set to False as the features are never
                                   independent (e.g. mean and median)
    :type hypotheses_independent: bool

    :param n_jobs: Number of processes to use during the p-value calculation
    :type n_jobs: int

    :param chunksize: The size of one chunk that is submitted to the worker
        process for the parallelisation.  Where one chunk is defined as a
        singular time series for one id and one kind. If you set the chunksize
        to 10, then it means that one task is to calculate all features for 10
        time series.  If it is set it to None, depending on distributor,
        heuristics are used to find the optimal chunksize. If you get out of
        memory exceptions, you can try it with the dask distributor and a
        smaller chunksize.
    :type chunksize: None or int

    :param ml_task: The intended machine learning task. Either `'classification'`, `'regression'` or `'auto'`.
                    Defaults to `'auto'`, meaning the intended task is inferred from `y`.
                    If `y` has a boolean, integer or object dtype, the task is assumend to be classification,
                    else regression.
    :type ml_task: str

    :return: The same DataFrame as X, but possibly with reduced number of columns ( = features).
    :rtype: pandas.DataFrame

    :raises: ``ValueError`` when the target vector does not fit to the feature matrix
             or `ml_task` is not one of `'auto'`, `'classification'` or `'regression'`.
    """
    assert isinstance(X, pd.DataFrame), "Please pass features in X as pandas.DataFrame."
    check_for_nans_in_columns(X)
    assert isinstance(y, (pd.Series, np.ndarray)), "The type of target vector y must be one of: " \
                                                   "pandas.Series, numpy.ndarray"
    assert len(y) > 1, "y must contain at least two samples."
    assert len(X) == len(y), "X and y must contain the same number of samples."
    assert len(set(y)) > 1, "Feature selection is only possible if more than 1 label/class is provided"

    if isinstance(y, pd.Series) and set(X.index) != set(y.index):
        raise ValueError("Index of X and y must be identical if provided")

    if isinstance(y, np.ndarray):
        y = pd.Series(y, index=X.index)

    relevance_table = calculate_relevance_table(
        X, y, ml_task=ml_task, n_jobs=n_jobs, chunksize=chunksize,
        test_for_binary_target_real_feature=test_for_binary_target_real_feature,
        fdr_level=fdr_level, hypotheses_independent=hypotheses_independent,
    )

    relevant_features = relevance_table[relevance_table.relevant].feature

    return X.loc[:, relevant_features]