def logistic_regression_path(X, y, pos_class=None, Cs=10, fit_intercept=True,
                             max_iter=100, tol=1e-4, verbose=0,
                             solver='lbfgs', coef=None, copy=False,
                             class_weight=None, dual=False, penalty='l2',
                             intercept_scaling=1., multi_class='ovr',
                             random_state=None, check_input=True,
                             max_squared_sum=None, sample_weight=None):
    """Compute a Logistic Regression model for a list of regularization
    parameters.

    This is an implementation that uses the result of the previous model
    to speed up computations along the set of solutions, making it faster
    than sequentially calling LogisticRegression for the different parameters.

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

    Parameters
    ----------
    X : array-like or sparse matrix, shape (n_samples, n_features)
        Input data.

    y : array-like, shape (n_samples,)
        Input data, target values.

    Cs : int | array-like, shape (n_cs,)
        List of values for the regularization parameter or integer specifying
        the number of regularization parameters that should be used. In this
        case, the parameters will be chosen in a logarithmic scale between
        1e-4 and 1e4.

    pos_class : int, None
        The class with respect to which we perform a one-vs-all fit.
        If None, then it is assumed that the given problem is binary.

    fit_intercept : bool
        Whether to fit an intercept for the model. In this case the shape of
        the returned array is (n_cs, n_features + 1).

    max_iter : int
        Maximum number of iterations for the solver.

    tol : float
        Stopping criterion. For the newton-cg and lbfgs solvers, the iteration
        will stop when ``max{|g_i | i = 1, ..., n} <= tol``
        where ``g_i`` is the i-th component of the gradient.

    verbose : int
        For the liblinear and lbfgs solvers set verbose to any positive
        number for verbosity.

    solver : {'lbfgs', 'newton-cg', 'liblinear', 'sag'}
        Numerical solver to use.

    coef : array-like, shape (n_features,), default None
        Initialization value for coefficients of logistic regression.
        Useless for liblinear solver.

    copy : bool, default False
        Whether or not to produce a copy of the data. A copy is not required
        anymore. This parameter is deprecated and will be removed in 0.19.

    class_weight : dict or 'balanced', optional
        Weights associated with classes in the form ``{class_label: weight}``.
        If not given, all classes are supposed to have weight one.

        The "balanced" mode uses the values of y to automatically adjust
        weights inversely proportional to class frequencies in the input data
        as ``n_samples / (n_classes * np.bincount(y))``.

        Note that these weights will be multiplied with sample_weight (passed
        through the fit method) if sample_weight is specified.

    dual : bool
        Dual or primal formulation. Dual formulation is only implemented for
        l2 penalty with liblinear solver. Prefer dual=False when
        n_samples > n_features.

    penalty : str, 'l1' or 'l2'
        Used to specify the norm used in the penalization. The 'newton-cg',
        'sag' and 'lbfgs' solvers support only l2 penalties.

    intercept_scaling : float, default 1.
        Useful only when the solver 'liblinear' is used
        and self.fit_intercept is set to True. In this case, x becomes
        [x, self.intercept_scaling],
        i.e. a "synthetic" feature with constant value equal to
        intercept_scaling is appended to the instance vector.
        The intercept becomes ``intercept_scaling * synthetic_feature_weight``.

        Note! the synthetic feature weight is subject to l1/l2 regularization
        as all other features.
        To lessen the effect of regularization on synthetic feature weight
        (and therefore on the intercept) intercept_scaling has to be increased.

    multi_class : str, {'ovr', 'multinomial'}
        Multiclass option can be either 'ovr' or 'multinomial'. If the option
        chosen is 'ovr', then a binary problem is fit for each label. Else
        the loss minimised is the multinomial loss fit across
        the entire probability distribution. Works only for the 'lbfgs' and
        'newton-cg' solvers.

    random_state : int seed, RandomState instance, or None (default)
        The seed of the pseudo random number generator to use when
        shuffling the data. Used only in solvers 'sag' and 'liblinear'.

    check_input : bool, default True
        If False, the input arrays X and y will not be checked.

    max_squared_sum : float, default None
        Maximum squared sum of X over samples. Used only in SAG solver.
        If None, it will be computed, going through all the samples.
        The value should be precomputed to speed up cross validation.

    sample_weight : array-like, shape(n_samples,) optional
        Array of weights that are assigned to individual samples.
        If not provided, then each sample is given unit weight.

    Returns
    -------
    coefs : ndarray, shape (n_cs, n_features) or (n_cs, n_features + 1)
        List of coefficients for the Logistic Regression model. If
        fit_intercept is set to True then the second dimension will be
        n_features + 1, where the last item represents the intercept.

    Cs : ndarray
        Grid of Cs used for cross-validation.

    n_iter : array, shape (n_cs,)
        Actual number of iteration for each Cs.

    Notes
    -----
    You might get slightly different results with the solver liblinear than
    with the others since this uses LIBLINEAR which penalizes the intercept.
    """
    if copy:
        warnings.warn("A copy is not required anymore. The 'copy' parameter "
                      "is deprecated and will be removed in 0.19.",
                      DeprecationWarning)

    if isinstance(Cs, numbers.Integral):
        Cs = np.logspace(-4, 4, Cs)

    _check_solver_option(solver, multi_class, penalty, dual)

    # Preprocessing.
    if check_input or copy:
        X = check_array(X, accept_sparse='csr', dtype=np.float64)
        y = check_array(y, ensure_2d=False, copy=copy, dtype=None)
        check_consistent_length(X, y)
    _, n_features = X.shape
    classes = np.unique(y)
    random_state = check_random_state(random_state)

    if pos_class is None and multi_class != 'multinomial':
        if (classes.size > 2):
            raise ValueError('To fit OvR, use the pos_class argument')
        # np.unique(y) gives labels in sorted order.
        pos_class = classes[1]

    # If sample weights exist, convert them to array (support for lists)
    # and check length
    # Otherwise set them to 1 for all examples
    if sample_weight is not None:
        sample_weight = np.array(sample_weight, dtype=np.float64, order='C')
        check_consistent_length(y, sample_weight)
    else:
        sample_weight = np.ones(X.shape[0])

    # If class_weights is a dict (provided by the user), the weights
    # are assigned to the original labels. If it is "balanced", then
    # the class_weights are assigned after masking the labels with a OvR.
    le = LabelEncoder()

    if isinstance(class_weight, dict) or multi_class == 'multinomial':
        if solver == "liblinear":
            if classes.size == 2:
                # Reconstruct the weights with keys 1 and -1
                temp = {1: class_weight[pos_class],
                        -1: class_weight[classes[0]]}
                class_weight = temp.copy()
            else:
                raise ValueError("In LogisticRegressionCV the liblinear "
                                 "solver cannot handle multiclass with "
                                 "class_weight of type dict. Use the lbfgs, "
                                 "newton-cg or sag solvers or set "
                                 "class_weight='balanced'")
        else:
            class_weight_ = compute_class_weight(class_weight, classes, y)
            sample_weight *= class_weight_[le.fit_transform(y)]

    # For doing a ovr, we need to mask the labels first. for the
    # multinomial case this is not necessary.
    if multi_class == 'ovr':
        w0 = np.zeros(n_features + int(fit_intercept))
        mask_classes = np.array([-1, 1])
        mask = (y == pos_class)
        y_bin = np.ones(y.shape, dtype=np.float64)
        y_bin[~mask] = -1.
        # for compute_class_weight

        # 'auto' is deprecated and will be removed in 0.19
        if class_weight in ("auto", "balanced"):
            class_weight_ = compute_class_weight(class_weight, mask_classes,
                                                 y_bin)
            sample_weight *= class_weight_[le.fit_transform(y_bin)]

    else:
        if solver != 'sag':
            lbin = LabelBinarizer()
            Y_multi = lbin.fit_transform(y)
            if Y_multi.shape[1] == 1:
                Y_multi = np.hstack([1 - Y_multi, Y_multi])
        else:
            # SAG multinomial solver needs LabelEncoder, not LabelBinarizer
            le = LabelEncoder()
            Y_multi = le.fit_transform(y)

        w0 = np.zeros((classes.size, n_features + int(fit_intercept)),
                      order='F')

    if coef is not None:
        # it must work both giving the bias term and not
        if multi_class == 'ovr':
            if coef.size not in (n_features, w0.size):
                raise ValueError(
                    'Initialization coef is of shape %d, expected shape '
                    '%d or %d' % (coef.size, n_features, w0.size))
            w0[:coef.size] = coef
        else:
            # For binary problems coef.shape[0] should be 1, otherwise it
            # should be classes.size.
            n_classes = classes.size
            if n_classes == 2:
                n_classes = 1

            if (coef.shape[0] != n_classes or
                    coef.shape[1] not in (n_features, n_features + 1)):
                raise ValueError(
                    'Initialization coef is of shape (%d, %d), expected '
                    'shape (%d, %d) or (%d, %d)' % (
                        coef.shape[0], coef.shape[1], classes.size,
                        n_features, classes.size, n_features + 1))
            w0[:, :coef.shape[1]] = coef

    if multi_class == 'multinomial':
        # fmin_l_bfgs_b and newton-cg accepts only ravelled parameters.
        if solver in ['lbfgs', 'newton-cg']:
            w0 = w0.ravel()
        target = Y_multi
        if solver == 'lbfgs':
            func = lambda x, *args: _multinomial_loss_grad(x, *args)[0:2]
        elif solver == 'newton-cg':
            func = lambda x, *args: _multinomial_loss(x, *args)[0]
            grad = lambda x, *args: _multinomial_loss_grad(x, *args)[1]
            hess = _multinomial_grad_hess
        warm_start_sag = {'coef': w0.T}
    else:
        target = y_bin
        if solver == 'lbfgs':
            func = _logistic_loss_and_grad
        elif solver == 'newton-cg':
            func = _logistic_loss
            grad = lambda x, *args: _logistic_loss_and_grad(x, *args)[1]
            hess = _logistic_grad_hess
        warm_start_sag = {'coef': np.expand_dims(w0, axis=1)}

    coefs = list()
    n_iter = np.zeros(len(Cs), dtype=np.int32)
    for i, C in enumerate(Cs):
        if solver == 'lbfgs':
            try:
                w0, loss, info = optimize.fmin_l_bfgs_b(
                    func, w0, fprime=None,
                    args=(X, target, 1. / C, sample_weight),
                    iprint=(verbose > 0) - 1, pgtol=tol, maxiter=max_iter)
            except __HOLE__:
                # old scipy doesn't have maxiter
                w0, loss, info = optimize.fmin_l_bfgs_b(
                    func, w0, fprime=None,
                    args=(X, target, 1. / C, sample_weight),
                    iprint=(verbose > 0) - 1, pgtol=tol)
            if info["warnflag"] == 1 and verbose > 0:
                warnings.warn("lbfgs failed to converge. Increase the number "
                              "of iterations.")
            try:
                n_iter_i = info['nit'] - 1
            except:
                n_iter_i = info['funcalls'] - 1
        elif solver == 'newton-cg':
            args = (X, target, 1. / C, sample_weight)
            w0, n_iter_i = newton_cg(hess, func, grad, w0, args=args,
                                     maxiter=max_iter, tol=tol)
        elif solver == 'liblinear':
            coef_, intercept_, n_iter_i, = _fit_liblinear(
                X, target, C, fit_intercept, intercept_scaling, class_weight,
                penalty, dual, verbose, max_iter, tol, random_state,
                sample_weight=sample_weight)
            if fit_intercept:
                w0 = np.concatenate([coef_.ravel(), intercept_])
            else:
                w0 = coef_.ravel()

        elif solver == 'sag':
            if multi_class == 'multinomial':
                target = target.astype(np.float64)
                loss = 'multinomial'
            else:
                loss = 'log'

            w0, n_iter_i, warm_start_sag = sag_solver(
                X, target, sample_weight, loss, 1. / C, max_iter, tol,
                verbose, random_state, False, max_squared_sum, warm_start_sag)

        else:
            raise ValueError("solver must be one of {'liblinear', 'lbfgs', "
                             "'newton-cg', 'sag'}, got '%s' instead" % solver)

        if multi_class == 'multinomial':
            multi_w0 = np.reshape(w0, (classes.size, -1))
            if classes.size == 2:
                multi_w0 = multi_w0[1][np.newaxis, :]
            coefs.append(multi_w0)
        else:
            coefs.append(w0.copy())

        n_iter[i] = n_iter_i

    return coefs, np.array(Cs), n_iter


# helper function for LogisticCV
dataset/ETHPy150Open scikit-learn/scikit-learn/sklearn/linear_model/logistic.py/logistic_regression_path