base.py

from __future__ import print_function

import numpy as np
import scipy.sparse as sp
import warnings
from abc import ABCMeta, abstractmethod

from . import libsvm, liblinear
from . import libsvm_sparse
from ..base import BaseEstimator, ClassifierMixin
from ..preprocessing import LabelEncoder
from ..utils import check_array, check_random_state, column_or_1d
from ..utils import ConvergenceWarning, compute_class_weight, deprecated
from ..utils.extmath import safe_sparse_dot
from ..utils.validation import check_is_fitted
from ..externals import six

LIBSVM_IMPL = ['c_svc', 'nu_svc', 'one_class', 'epsilon_svr', 'nu_svr']


def _one_vs_one_coef(dual_coef, n_support, support_vectors):
    """Generate primal coefficients from dual coefficients
    for the one-vs-one multi class LibSVM in the case
    of a linear kernel."""

    # get 1vs1 weights for all n*(n-1) classifiers.
    # this is somewhat messy.
    # shape of dual_coef_ is nSV * (n_classes -1)
    # see docs for details
    n_class = dual_coef.shape[0] + 1

    # XXX we could do preallocation of coef but
    # would have to take care in the sparse case
    coef = []
    sv_locs = np.cumsum(np.hstack([[0], n_support]))
    for class1 in range(n_class):
        # SVs for class1:
        sv1 = support_vectors[sv_locs[class1]:sv_locs[class1 + 1], :]
        for class2 in range(class1 + 1, n_class):
            # SVs for class1:
            sv2 = support_vectors[sv_locs[class2]:sv_locs[class2 + 1], :]

            # dual coef for class1 SVs:
            alpha1 = dual_coef[class2 - 1, sv_locs[class1]:sv_locs[class1 + 1]]
            # dual coef for class2 SVs:
            alpha2 = dual_coef[class1, sv_locs[class2]:sv_locs[class2 + 1]]
            # build weight for class1 vs class2

            coef.append(safe_sparse_dot(alpha1, sv1)
                        + safe_sparse_dot(alpha2, sv2))
    return coef


class BaseLibSVM(six.with_metaclass(ABCMeta, BaseEstimator)):
    """Base class for estimators that use libsvm as backing library

    This implements support vector machine classification and regression.

    Parameter documentation is in the derived `SVC` class.
    """

    # The order of these must match the integer values in LibSVM.
    # XXX These are actually the same in the dense case. Need to factor
    # this out.
    _sparse_kernels = ["linear", "poly", "rbf", "sigmoid", "precomputed"]

    @abstractmethod
    def __init__(self, impl, kernel, degree, gamma, coef0,
                 tol, C, nu, epsilon, shrinking, probability, cache_size,
                 class_weight, verbose, max_iter, random_state):

        if impl not in LIBSVM_IMPL:  # pragma: no cover
            raise ValueError("impl should be one of %s, %s was given" % (
                LIBSVM_IMPL, impl))

        self._impl = impl
        self.kernel = kernel
        self.degree = degree
        self.gamma = gamma
        self.coef0 = coef0
        self.tol = tol
        self.C = C
        self.nu = nu
        self.epsilon = epsilon
        self.shrinking = shrinking
        self.probability = probability
        self.cache_size = cache_size
        self.class_weight = class_weight
        self.verbose = verbose
        self.max_iter = max_iter
        self.random_state = random_state

    @property
    def _pairwise(self):
        # Used by cross_val_score.
        kernel = self.kernel
        return kernel == "precomputed" or callable(kernel)

    def fit(self, X, y, sample_weight=None):
        """Fit the SVM model according to the given training data.

        Parameters
        ----------
        X : {array-like, sparse matrix}, shape (n_samples, n_features)
            Training vectors, where n_samples is the number of samples
            and n_features is the number of features.
            For kernel="precomputed", the expected shape of X is
            (n_samples, n_samples).

        y : array-like, shape (n_samples,)
            Target values (class labels in classification, real numbers in
            regression)

        sample_weight : array-like, shape (n_samples,)
            Per-sample weights. Rescale C per sample. Higher weights
            force the classifier to put more emphasis on these points.

        Returns
        -------
        self : object
            Returns self.

        Notes
        ------
        If X and y are not C-ordered and contiguous arrays of np.float64 and
        X is not a scipy.sparse.csr_matrix, X and/or y may be copied.

        If X is a dense array, then the other methods will not support sparse
        matrices as input.
        """

        rnd = check_random_state(self.random_state)

        sparse = sp.isspmatrix(X)
        if sparse and self.kernel == "precomputed":
            raise TypeError("Sparse precomputed kernels are not supported.")
        self._sparse = sparse and not callable(self.kernel)

        X = check_array(X, accept_sparse='csr', dtype=np.float64, order='C')
        y = self._validate_targets(y)

        sample_weight = np.asarray([]
                                   if sample_weight is None
                                   else sample_weight, dtype=np.float64)
        solver_type = LIBSVM_IMPL.index(self._impl)

        # input validation
        if solver_type != 2 and X.shape[0] != y.shape[0]:
            raise ValueError("X and y have incompatible shapes.\n" +
                             "X has %s samples, but y has %s." %
                             (X.shape[0], y.shape[0]))

        if self.kernel == "precomputed" and X.shape[0] != X.shape[1]:
            raise ValueError("X.shape[0] should be equal to X.shape[1]")

        if sample_weight.shape[0] > 0 and sample_weight.shape[0] != X.shape[0]:
            raise ValueError("sample_weight and X have incompatible shapes: "
                             "%r vs %r\n"
                             "Note: Sparse matrices cannot be indexed w/"
                             "boolean masks (use `indices=True` in CV)."
                             % (sample_weight.shape, X.shape))

        if (self.kernel in ['poly', 'rbf']) and (self.gamma == 0):
            # if custom gamma is not provided ...
            self._gamma = 1.0 / X.shape[1]
        else:
            self._gamma = self.gamma

        kernel = self.kernel
        if callable(kernel):
            kernel = 'precomputed'

        fit = self._sparse_fit if self._sparse else self._dense_fit
        if self.verbose:  # pragma: no cover
            print('[LibSVM]', end='')

        seed = rnd.randint(np.iinfo('i').max)
        fit(X, y, sample_weight, solver_type, kernel, random_seed=seed)
        # see comment on the other call to np.iinfo in this file

        self.shape_fit_ = X.shape

        # In binary case, we need to flip the sign of coef, intercept and
        # decision function. Use self._intercept_ and self._dual_coef_ internally.
        self._intercept_ = self.intercept_.copy()
        self._dual_coef_ = self.dual_coef_
        if self._impl in ['c_svc', 'nu_svc'] and len(self.classes_) == 2:
            self.intercept_ *= -1
            self.dual_coef_ = -self.dual_coef_

        return self

    def _validate_targets(self, y):
        """Validation of y and class_weight.

        Default implementation for SVR and one-class; overridden in BaseSVC.
        """
        # XXX this is ugly.
        # Regression models should not have a class_weight_ attribute.
        self.class_weight_ = np.empty(0)
        return np.asarray(y, dtype=np.float64, order='C')

    def _warn_from_fit_status(self):
        assert self.fit_status_ in (0, 1)
        if self.fit_status_ == 1:
            warnings.warn('Solver terminated early (max_iter=%i).'
                          '  Consider pre-processing your data with'
                          ' StandardScaler or MinMaxScaler.'
                          % self.max_iter, ConvergenceWarning)

    def _dense_fit(self, X, y, sample_weight, solver_type, kernel,
                   random_seed):
        if callable(self.kernel):
            # you must store a reference to X to compute the kernel in predict
            # TODO: add keyword copy to copy on demand
            self.__Xfit = X
            X = self._compute_kernel(X)

            if X.shape[0] != X.shape[1]:
                raise ValueError("X.shape[0] should be equal to X.shape[1]")

        libsvm.set_verbosity_wrap(self.verbose)

        # we don't pass **self.get_params() to allow subclasses to
        # add other parameters to __init__
        self.support_, self.support_vectors_, self.n_support_, \
            self.dual_coef_, self.intercept_, self.probA_, \
            self.probB_, self.fit_status_ = libsvm.fit(
                X, y,
                svm_type=solver_type, sample_weight=sample_weight,
                class_weight=self.class_weight_, kernel=kernel, C=self.C,
                nu=self.nu, probability=self.probability, degree=self.degree,
                shrinking=self.shrinking, tol=self.tol,
                cache_size=self.cache_size, coef0=self.coef0,
                gamma=self._gamma, epsilon=self.epsilon,
                max_iter=self.max_iter, random_seed=random_seed)

        self._warn_from_fit_status()

    def _sparse_fit(self, X, y, sample_weight, solver_type, kernel,
                    random_seed):
        X.data = np.asarray(X.data, dtype=np.float64, order='C')
        X.sort_indices()

        kernel_type = self._sparse_kernels.index(kernel)

        libsvm_sparse.set_verbosity_wrap(self.verbose)

        self.support_, self.support_vectors_, dual_coef_data, \
            self.intercept_, self.n_support_, \
            self.probA_, self.probB_, self.fit_status_ = \
            libsvm_sparse.libsvm_sparse_train(
                X.shape[1], X.data, X.indices, X.indptr, y, solver_type,
                kernel_type, self.degree, self._gamma, self.coef0, self.tol,
                self.C, self.class_weight_,
                sample_weight, self.nu, self.cache_size, self.epsilon,
                int(self.shrinking), int(self.probability), self.max_iter,
                random_seed)

        self._warn_from_fit_status()

        if hasattr(self, "classes_"):
            n_class = len(self.classes_) - 1
        else:   # regression
            n_class = 1
        n_SV = self.support_vectors_.shape[0]

        dual_coef_indices = np.tile(np.arange(n_SV), n_class)
        dual_coef_indptr = np.arange(0, dual_coef_indices.size + 1,
                                     dual_coef_indices.size / n_class)
        self.dual_coef_ = sp.csr_matrix(
            (dual_coef_data, dual_coef_indices, dual_coef_indptr),
            (n_class, n_SV))

    def predict(self, X):
        """Perform regression on samples in X.

        For an one-class model, +1 or -1 is returned.

        Parameters
        ----------
        X : {array-like, sparse matrix}, shape (n_samples, n_features)
            For kernel="precomputed", the expected shape of X is
            (n_samples_test, n_samples_train).

        Returns
        -------
        y_pred : array, shape (n_samples,)
        """
        X = self._validate_for_predict(X)
        predict = self._sparse_predict if self._sparse else self._dense_predict
        return predict(X)

    def _dense_predict(self, X):
        n_samples, n_features = X.shape
        X = self._compute_kernel(X)
        if X.ndim == 1:
            X = check_array(X, order='C')

        kernel = self.kernel
        if callable(self.kernel):
            kernel = 'precomputed'
            if X.shape[1] != self.shape_fit_[0]:
                raise ValueError("X.shape[1] = %d should be equal to %d, "
                                 "the number of samples at training time" %
                                 (X.shape[1], self.shape_fit_[0]))

        svm_type = LIBSVM_IMPL.index(self._impl)

        return libsvm.predict(
            X, self.support_, self.support_vectors_, self.n_support_,
            self._dual_coef_, self._intercept_,
            self.probA_, self.probB_, svm_type=svm_type, kernel=kernel,
            degree=self.degree, coef0=self.coef0, gamma=self._gamma,
            cache_size=self.cache_size)

    def _sparse_predict(self, X):
        # Precondition: X is a csr_matrix of dtype np.float64.
        kernel = self.kernel
        if callable(kernel):
            kernel = 'precomputed'

        kernel_type = self._sparse_kernels.index(kernel)

        C = 0.0  # C is not useful here

        return libsvm_sparse.libsvm_sparse_predict(
            X.data, X.indices, X.indptr,
            self.support_vectors_.data,
            self.support_vectors_.indices,
            self.support_vectors_.indptr,
            self._dual_coef_.data, self._intercept_,
            LIBSVM_IMPL.index(self._impl), kernel_type,
            self.degree, self._gamma, self.coef0, self.tol,
            C, self.class_weight_,
            self.nu, self.epsilon, self.shrinking,
            self.probability, self.n_support_,
            self.probA_, self.probB_)

    def _compute_kernel(self, X):
        """Return the data transformed by a callable kernel"""
        if callable(self.kernel):
            # in the case of precomputed kernel given as a function, we
            # have to compute explicitly the kernel matrix
            kernel = self.kernel(X, self.__Xfit)
            if sp.issparse(kernel):
                kernel = kernel.toarray()
            X = np.asarray(kernel, dtype=np.float64, order='C')
        return X

    @deprecated(" and will be removed in 0.19")
    def decision_function(self, X):
        """Distance of the samples X to the separating hyperplane.

        Parameters
        ----------
        X : array-like, shape (n_samples, n_features)
            For kernel="precomputed", the expected shape of X is
            [n_samples_test, n_samples_train].

        Returns
        -------
        X : array-like, shape (n_samples, n_class * (n_class-1) / 2)
            Returns the decision function of the sample for each class
            in the model.
        """
        return self._decision_function(X)

    def _decision_function(self, X):
        """Distance of the samples X to the separating hyperplane.

        Parameters
        ----------
        X : array-like, shape (n_samples, n_features)

        Returns
        -------
        X : array-like, shape (n_samples, n_class * (n_class-1) / 2)
            Returns the decision function of the sample for each class
            in the model.
        """
        # NOTE: _validate_for_predict contains check for is_fitted
        # hence must be placed before any other attributes are used.
        X = self._validate_for_predict(X)
        X = self._compute_kernel(X)

        if self._sparse:
            dec_func = self._sparse_decision_function(X)
        else:
            dec_func = self._dense_decision_function(X)

        # In binary case, we need to flip the sign of coef, intercept and
        # decision function.
        if self._impl in ['c_svc', 'nu_svc'] and len(self.classes_) == 2:
            return -dec_func.ravel()

        return dec_func

    def _dense_decision_function(self, X):
        X = check_array(X, dtype=np.float64, order="C")

        kernel = self.kernel
        if callable(kernel):
            kernel = 'precomputed'

        return libsvm.decision_function(
            X, self.support_, self.support_vectors_, self.n_support_,
            self._dual_coef_, self._intercept_,
            self.probA_, self.probB_,
            svm_type=LIBSVM_IMPL.index(self._impl),
            kernel=kernel, degree=self.degree, cache_size=self.cache_size,
            coef0=self.coef0, gamma=self._gamma)

    def _sparse_decision_function(self, X):
        X.data = np.asarray(X.data, dtype=np.float64, order='C')

        kernel = self.kernel
        if hasattr(kernel, '__call__'):
            kernel = 'precomputed'

        kernel_type = self._sparse_kernels.index(kernel)

        return libsvm_sparse.libsvm_sparse_decision_function(
            X.data, X.indices, X.indptr,
            self.support_vectors_.data,
            self.support_vectors_.indices,
            self.support_vectors_.indptr,
            self._dual_coef_.data, self._intercept_,
            LIBSVM_IMPL.index(self._impl), kernel_type,
            self.degree, self._gamma, self.coef0, self.tol,
            self.C, self.class_weight_,
            self.nu, self.epsilon, self.shrinking,
            self.probability, self.n_support_,
            self.probA_, self.probB_)

    def _validate_for_predict(self, X):
        check_is_fitted(self, 'support_')

        X = check_array(X, accept_sparse='csr', dtype=np.float64, order="C")
        if self._sparse and not sp.isspmatrix(X):
            X = sp.csr_matrix(X)
        if self._sparse:
            X.sort_indices()

        if sp.issparse(X) and not self._sparse and not callable(self.kernel):
            raise ValueError(
                "cannot use sparse input in %r trained on dense data"
                % type(self).__name__)
        n_samples, n_features = X.shape

        if self.kernel == "precomputed":
            if X.shape[1] != self.shape_fit_[0]:
                raise ValueError("X.shape[1] = %d should be equal to %d, "
                                 "the number of samples at training time" %
                                 (X.shape[1], self.shape_fit_[0]))
        elif n_features != self.shape_fit_[1]:
            raise ValueError("X.shape[1] = %d should be equal to %d, "
                             "the number of features at training time" %
                             (n_features, self.shape_fit_[1]))
        return X

    @property
    def coef_(self):
        if self.kernel != 'linear':
            raise ValueError('coef_ is only available when using a '
                             'linear kernel')

        coef = self._get_coef()

        # coef_ being a read-only property, it's better to mark the value as
        # immutable to avoid hiding potential bugs for the unsuspecting user.
        if sp.issparse(coef):
            # sparse matrix do not have global flags
            coef.data.flags.writeable = False
        else:
            # regular dense array
            coef.flags.writeable = False
        return coef

    def _get_coef(self):
        return safe_sparse_dot(self._dual_coef_, self.support_vectors_)


class BaseSVC(BaseLibSVM, ClassifierMixin):
    """ABC for LibSVM-based classifiers."""

    def _validate_targets(self, y):
        y_ = column_or_1d(y, warn=True)
        cls, y = np.unique(y_, return_inverse=True)
        self.class_weight_ = compute_class_weight(self.class_weight, cls, y_)
        if len(cls) < 2:
            raise ValueError(
                "The number of classes has to be greater than one; got %d"
                % len(cls))

        self.classes_ = cls

        return np.asarray(y, dtype=np.float64, order='C')

    def decision_function(self, X):
        """Distance of the samples X to the separating hyperplane.

        Parameters
        ----------
        X : array-like, shape (n_samples, n_features)

        Returns
        -------
        X : array-like, shape (n_samples, n_class * (n_class-1) / 2)
            Returns the decision function of the sample for each class
            in the model.
        """
        return self._decision_function(X)

    def predict(self, X):
        """Perform classification on samples in X.

        For an one-class model, +1 or -1 is returned.

        Parameters
        ----------
        X : {array-like, sparse matrix}, shape (n_samples, n_features)
            For kernel="precomputed", the expected shape of X is
            [n_samples_test, n_samples_train]

        Returns
        -------
        y_pred : array, shape (n_samples,)
            Class labels for samples in X.
        """
        y = super(BaseSVC, self).predict(X)
        return self.classes_.take(np.asarray(y, dtype=np.intp))

    # Hacky way of getting predict_proba to raise an AttributeError when
    # probability=False using properties. Do not use this in new code; when
    # probabilities are not available depending on a setting, introduce two
    # estimators.
    def _check_proba(self):
        if not self.probability:
            raise AttributeError("predict_proba is not available when"
                                 " probability=%r" % self.probability)
        if self._impl not in ('c_svc', 'nu_svc'):
            raise AttributeError("predict_proba only implemented for SVC"
                                 " and NuSVC")

    @property
    def predict_proba(self):
        """Compute probabilities of possible outcomes for samples in X.

        The model need to have probability information computed at training
        time: fit with attribute `probability` set to True.

        Parameters
        ----------
        X : array-like, shape (n_samples, n_features)
            For kernel="precomputed", the expected shape of X is
            [n_samples_test, n_samples_train]

        Returns
        -------
        T : array-like, shape (n_samples, n_classes)
            Returns the probability of the sample for each class in
            the model. The columns correspond to the classes in sorted
            order, as they appear in the attribute `classes_`.

        Notes
        -----
        The probability model is created using cross validation, so
        the results can be slightly different than those obtained by
        predict. Also, it will produce meaningless results on very small
        datasets.
        """
        self._check_proba()
        return self._predict_proba

    def _predict_proba(self, X):
        X = self._validate_for_predict(X)
        pred_proba = (self._sparse_predict_proba
                      if self._sparse else self._dense_predict_proba)
        return pred_proba(X)

    @property
    def predict_log_proba(self):
        """Compute log probabilities of possible outcomes for samples in X.

        The model need to have probability information computed at training
        time: fit with attribute `probability` set to True.

        Parameters
        ----------
        X : array-like, shape (n_samples, n_features)
            For kernel="precomputed", the expected shape of X is
            [n_samples_test, n_samples_train]

        Returns
        -------
        T : array-like, shape (n_samples, n_classes)
            Returns the log-probabilities of the sample for each class in
            the model. The columns correspond to the classes in sorted
            order, as they appear in the attribute `classes_`.

        Notes
        -----
        The probability model is created using cross validation, so
        the results can be slightly different than those obtained by
        predict. Also, it will produce meaningless results on very small
        datasets.
        """
        self._check_proba()
        return self._predict_log_proba

    def _predict_log_proba(self, X):
        return np.log(self.predict_proba(X))

    def _dense_predict_proba(self, X):
        X = self._compute_kernel(X)

        kernel = self.kernel
        if callable(kernel):
            kernel = 'precomputed'

        svm_type = LIBSVM_IMPL.index(self._impl)
        pprob = libsvm.predict_proba(
            X, self.support_, self.support_vectors_, self.n_support_,
            self._dual_coef_, self._intercept_,
            self.probA_, self.probB_,
            svm_type=svm_type, kernel=kernel, degree=self.degree,
            cache_size=self.cache_size, coef0=self.coef0, gamma=self._gamma)

        return pprob

    def _sparse_predict_proba(self, X):
        X.data = np.asarray(X.data, dtype=np.float64, order='C')

        kernel = self.kernel
        if callable(kernel):
            kernel = 'precomputed'

        kernel_type = self._sparse_kernels.index(kernel)

        return libsvm_sparse.libsvm_sparse_predict_proba(
            X.data, X.indices, X.indptr,
            self.support_vectors_.data,
            self.support_vectors_.indices,
            self.support_vectors_.indptr,
            self._dual_coef_.data, self._intercept_,
            LIBSVM_IMPL.index(self._impl), kernel_type,
            self.degree, self._gamma, self.coef0, self.tol,
            self.C, self.class_weight_,
            self.nu, self.epsilon, self.shrinking,
            self.probability, self.n_support_,
            self.probA_, self.probB_)

    def _get_coef(self):
        if self.dual_coef_.shape[0] == 1:
            # binary classifier
            coef = safe_sparse_dot(self.dual_coef_, self.support_vectors_)
        else:
            # 1vs1 classifier
            coef = _one_vs_one_coef(self.dual_coef_, self.n_support_,
                                    self.support_vectors_)
            if sp.issparse(coef[0]):
                coef = sp.vstack(coef).tocsr()
            else:
                coef = np.vstack(coef)

        return coef


def _get_liblinear_solver_type(multi_class, penalty, loss, dual):
    """Find the liblinear magic number for the solver.

    This number depends on the values of the following attributes:
      - multi_class
      - penalty
      - loss
      - dual

    The same number is also internally used by LibLinear to determine
    which solver to use.
    """
    # nested dicts containing level 1: available loss functions,
    # level2: available penalties for the given loss functin,
    # level3: wether the dual solver is available for the specified
    # combination of loss function and penalty
    _solver_type_dict = {
        'logistic_regression': {
            'l1': {False: 6},
            'l2': {False: 0, True: 7}},
        'hinge': {
            'l2': {True: 3}},
        'squared_hinge': {
            'l1': {False: 5},
            'l2': {False: 2, True: 1}},
        'epsilon_insensitive': {
            'l2': {True: 13}},
        'squared_epsilon_insensitive': {
            'l2': {False: 11, True: 12}},
        'crammer_singer': 4
    }

    if multi_class == 'crammer_singer':
        return _solver_type_dict[multi_class]
    elif multi_class != 'ovr':
        raise ValueError("`multi_class` must be one of `ovr`, "
                         "`crammer_singer`, got %r" % multi_class)

    # FIXME loss.lower() --> loss in 0.18
    _solver_pen = _solver_type_dict.get(loss.lower(), None)
    if _solver_pen is None:
        error_string = ("loss='%s' is not supported" % loss)
    else:
        # FIME penalty.lower() --> penalty in 0.18
        _solver_dual = _solver_pen.get(penalty.lower(), None)
        if _solver_dual is None:
            error_string = ("The combination of penalty='%s'"
                            "and loss='%s' is not supported"
                            % (penalty, loss))
        else:
            solver_num = _solver_dual.get(dual, None)
            if solver_num is None:
                error_string = ("loss='%s' and penalty='%s'"
                                "are not supported when dual=%s"
                                % (penalty, loss, dual))
            else:
                return solver_num
    raise ValueError('Unsupported set of arguments: %s, '
                     'Parameters: penalty=%r, loss=%r, dual=%r'
                     % (error_string, penalty, loss, dual))


def _fit_liblinear(X, y, C, fit_intercept, intercept_scaling, class_weight,
                   penalty, dual, verbose, max_iter, tol,
                   random_state=None, multi_class='ovr',
                   loss='logistic_regression', epsilon=0.1):
    """Used by Logistic Regression (and CV) and LinearSVC.

    Preprocessing is done in this function before supplying it to liblinear.

    Parameters
    ----------
    X : {array-like, sparse matrix}, shape (n_samples, n_features)
        Training vector, where n_samples in the number of samples and
        n_features is the number of features.

    y : array-like, shape (n_samples,)
        Target vector relative to X

    C : float
        Inverse of cross-validation parameter. Lower the C, the more
        the penalization.

    fit_intercept : bool
        Whether or not to fit the intercept, that is to add a intercept
        term to the decision function.

    intercept_scaling : float
        LibLinear internally penalizes the intercept and this term is subject
        to regularization just like the other terms of the feature vector.
        In order to avoid this, one should increase the intercept_scaling.
        such that the feature vector becomes [x, intercept_scaling].

    class_weight : {dict, 'auto'}, optional
        Weight assigned to each class. If class_weight provided is 'auto',
        then the weights provided are inverses of the frequency in the
        target vector.

    penalty : str, {'l1', 'l2'}
        The norm of the penalty used in regularization.

    dual : bool
        Dual or primal formulation,

    verbose : int
        Set verbose to any positive number for verbosity.

    max_iter : int
        Number of iterations.

    tol : float
        Stopping condition.

    random_state : int seed, RandomState instance, or None (default)
        The seed of the pseudo random number generator to use when
        shuffling the data.

    multi_class : str, {'ovr', 'crammer_singer'}
        `ovr` trains n_classes one-vs-rest classifiers, while `crammer_singer`
        optimizes a joint objective over all classes.
        While `crammer_singer` is interesting from an theoretical perspective
        as it is consistent it is seldom used in practice and rarely leads to
        better accuracy and is more expensive to compute.
        If `crammer_singer` is chosen, the options loss, penalty and dual will
        be ignored.

    loss : str, {'logistic_regression', 'hinge', 'squared_hinge',
                 'epsilon_insensitive', 'squared_epsilon_insensitive}
        The loss function used to fit the model.

    epsilon : float, optional (default=0.1)
        Epsilon parameter in the epsilon-insensitive loss function. Note
        that the value of this parameter depends on the scale of the target
        variable y. If unsure, set epsilon=0.


    Returns
    -------
    coef_ : ndarray, shape (n_features, n_features + 1)
        The coefficent vector got by minimizing the objective function.

    intercept_ : float
        The intercept term added to the vector.

    n_iter_ : int
        Maximum number of iterations run across all classes.
    """
    # FIXME Remove case insensitivity in 0.18 ---------------------
    loss_l, penalty_l = loss.lower(), penalty.lower()

    msg = ("loss='%s' has been deprecated in favor of "
           "loss='%s' as of 0.16. Backward compatibility"
           " for the uppercase notation will be removed in %s")
    if (not loss.islower()) and loss_l not in ('l1', 'l2'):
        warnings.warn(msg % (loss, loss_l, "0.18"),
                      DeprecationWarning)
    if not penalty.islower():
        warnings.warn(msg.replace("loss", "penalty")
                      % (penalty, penalty_l, "0.18"),
                      DeprecationWarning)
    # -------------------------------------------------------------

    # FIXME loss_l --> loss in 0.18
    if loss_l not in ['epsilon_insensitive', 'squared_epsilon_insensitive']:
        enc = LabelEncoder()
        y_ind = enc.fit_transform(y)
        classes_ = enc.classes_
        if len(classes_) < 2:
            raise ValueError("This solver needs samples of at least 2 classes"
                             " in the data, but the data contains only one"
                             " class: %r" % classes_[0])

        class_weight_ = compute_class_weight(class_weight, classes_, y)
    else:
        class_weight_ = np.empty(0, dtype=np.float)
        y_ind = y
    liblinear.set_verbosity_wrap(verbose)
    rnd = check_random_state(random_state)
    if verbose:
        print('[LibLinear]', end='')

    # LinearSVC breaks when intercept_scaling is <= 0
    bias = -1.0
    if fit_intercept:
        if intercept_scaling <= 0:
            raise ValueError("Intercept scaling is %r but needs to be greater than 0."
                             " To disable fitting an intercept,"
                             " set fit_intercept=False." % intercept_scaling)
        else:
            bias = intercept_scaling

    libsvm.set_verbosity_wrap(verbose)
    libsvm_sparse.set_verbosity_wrap(verbose)
    liblinear.set_verbosity_wrap(verbose)

    # LibLinear wants targets as doubles, even for classification
    y_ind = np.asarray(y_ind, dtype=np.float64).ravel()
    solver_type = _get_liblinear_solver_type(multi_class, penalty, loss, dual)
    raw_coef_, n_iter_ = liblinear.train_wrap(
        X, y_ind, sp.isspmatrix(X), solver_type, tol, bias, C,
        class_weight_, max_iter, rnd.randint(np.iinfo('i').max),
        epsilon)
    # Regarding rnd.randint(..) in the above signature:
    # seed for srand in range [0..INT_MAX); due to limitations in Numpy
    # on 32-bit platforms, we can't get to the UINT_MAX limit that
    # srand supports
    n_iter_ = max(n_iter_)
    if n_iter_ >= max_iter and verbose > 0:
        warnings.warn("Liblinear failed to converge, increase "
                      "the number of iterations.", ConvergenceWarning)

    if fit_intercept:
        coef_ = raw_coef_[:, :-1]
        intercept_ = intercept_scaling * raw_coef_[:, -1]
    else:
        coef_ = raw_coef_
        intercept_ = 0.

    return coef_, intercept_, n_iter_