def remove_low_information_features(feature_matrix, features=None):
    """Select features that have at least 2 unique values and that are not all null

        Args:
            feature_matrix (:class:`pd.DataFrame`): DataFrame whose columns are feature names and rows are instances
            features (list[:class:`featuretools.FeatureBase`] or list[str], optional): List of features to select

        Returns:
            (feature_matrix, features)

    """
    keep = [c for c in feature_matrix
            if (feature_matrix[c].nunique(dropna=False) > 1 and
                feature_matrix[c].dropna().shape[0] > 0)]
    feature_matrix = feature_matrix[keep]
    if features is not None:
        features = [f for f in features
                    if f.get_name() in feature_matrix.columns]
        return feature_matrix, features
    return feature_matrix