code: """
  Logistic Regression
  """
  
  # Author: Gael Varoquaux <gael.varoquaux@normalesup.org>
  #         Fabian Pedregosa <f@bianp.net>
  #         Alexandre Gramfort <alexandre.gramfort@telecom-paristech.fr>
  #         Manoj Kumar <manojkumarsivaraj334@gmail.com>
  #         Lars Buitinck
  #         Simon Wu <s8wu@uwaterloo.ca>
  #         Arthur Mensch <arthur.mensch@m4x.org
  
  import numbers
  import warnings
  
  import numpy as np
  from scipy import optimize, sparse
  from scipy.special import expit, logsumexp
  from joblib import Parallel, effective_n_jobs
  
  from ._base import LinearClassifierMixin, SparseCoefMixin, BaseEstimator
  from ._sag import sag_solver
  from ..preprocessing import LabelEncoder, LabelBinarizer
  from ..svm._base import _fit_liblinear
  from ..utils import check_array, check_consistent_length, compute_class_weight
  from ..utils import check_random_state
  from ..utils.extmath import log_logistic, safe_sparse_dot, softmax, squared_norm
  from ..utils.extmath import row_norms
  from ..utils.optimize import _newton_cg, _check_optimize_result
  from ..utils.validation import check_is_fitted, _check_sample_weight
  from ..utils.multiclass import check_classification_targets
  from ..utils.fixes import _joblib_parallel_args
  from ..utils.fixes import delayed
  from ..model_selection import check_cv
  from ..metrics import get_scorer
  
  
  _LOGISTIC_SOLVER_CONVERGENCE_MSG = (
      "Please also refer to the documentation for alternative solver options:\n"
      "    https://scikit-learn.org/stable/modules/linear_model.html"
      "#logistic-regression"
  )
  
  
  # .. some helper functions for logistic_regression_path ..
  def _intercept_dot(w, X, y):
      """Computes y * np.dot(X, w).
  
      It takes into consideration if the intercept should be fit or not.
  
      Parameters
      ----------
      w : ndarray of shape (n_features,) or (n_features + 1,)
          Coefficient vector.
  
      X : {array-like, sparse matrix} of shape (n_samples, n_features)
          Training data.
  
      y : ndarray of shape (n_samples,)
          Array of labels.
  
      Returns
      -------
      w : ndarray of shape (n_features,)
          Coefficient vector without the intercept weight (w[-1]) if the
          intercept should be fit. Unchanged otherwise.
  
      c : float
          The intercept.
  
      yz : float
          y * np.dot(X, w).
      """
      c = 0.0
      if w.size == X.shape[1] + 1:
          c = w[-1]
          w = w[:-1]
  
      z = safe_sparse_dot(X, w) + c
      yz = y * z
      return w, c, yz
  
  
  def _logistic_loss_and_grad(w, X, y, alpha, sample_weight=None):
      """Computes the logistic loss and gradient.
  
      Parameters
      ----------
      w : ndarray of shape (n_features,) or (n_features + 1,)
          Coefficient vector.
  
      X : {array-like, sparse matrix} of shape (n_samples, n_features)
          Training data.
  
      y : ndarray of shape (n_samples,)
          Array of labels.
  
      alpha : float
          Regularization parameter. alpha is equal to 1 / C.
  
      sample_weight : array-like of shape (n_samples,), default=None
          Array of weights that are assigned to individual samples.
          If not provided, then each sample is given unit weight.
  
      Returns
      -------
      out : float
          Logistic loss.
  
      grad : ndarray of shape (n_features,) or (n_features + 1,)
          Logistic gradient.
      """
      n_samples, n_features = X.shape
      grad = np.empty_like(w)
  
      w, c, yz = _intercept_dot(w, X, y)
  
      if sample_weight is None:
          sample_weight = np.ones(n_samples)
  
      # Logistic loss is the negative of the log of the logistic function.
      out = -np.sum(sample_weight * log_logistic(yz)) + 0.5 * alpha * np.dot(w, w)
  
      z = expit(yz)
      z0 = sample_weight * (z - 1) * y
  
      grad[:n_features] = safe_sparse_dot(X.T, z0) + alpha * w
  
      # Case where we fit the intercept.
      if grad.shape[0] > n_features:
          grad[-1] = z0.sum()
      return out, grad
  
  
  def _logistic_loss(w, X, y, alpha, sample_weight=None):
      """Computes the logistic loss.
  
      Parameters
      ----------
      w : ndarray of shape (n_features,) or (n_features + 1,)
          Coefficient vector.
  
      X : {array-like, sparse matrix} of shape (n_samples, n_features)
          Training data.
  
      y : ndarray of shape (n_samples,)
          Array of labels.
  
      alpha : float
          Regularization parameter. alpha is equal to 1 / C.
  
      sample_weight : array-like of shape (n_samples,) default=None
          Array of weights that are assigned to individual samples.
          If not provided, then each sample is given unit weight.
  
      Returns
      -------
      out : float
          Logistic loss.
      """
      w, c, yz = _intercept_dot(w, X, y)
  
      if sample_weight is None:
          sample_weight = np.ones(y.shape[0])
  
      # Logistic loss is the negative of the log of the logistic function.
      out = -np.sum(sample_weight * log_logistic(yz)) + 0.5 * alpha * np.dot(w, w)
      return out
  
  
  def _logistic_grad_hess(w, X, y, alpha, sample_weight=None):
      """Computes the gradient and the Hessian, in the case of a logistic loss.
  
      Parameters
      ----------
      w : ndarray of shape (n_features,) or (n_features + 1,)
          Coefficient vector.
  
      X : {array-like, sparse matrix} of shape (n_samples, n_features)
          Training data.
  
      y : ndarray of shape (n_samples,)
          Array of labels.
  
      alpha : float
          Regularization parameter. alpha is equal to 1 / C.
  
      sample_weight : array-like of shape (n_samples,) default=None
          Array of weights that are assigned to individual samples.
          If not provided, then each sample is given unit weight.
  
      Returns
      -------
      grad : ndarray of shape (n_features,) or (n_features + 1,)
          Logistic gradient.
  
      Hs : callable
          Function that takes the gradient as a parameter and returns the
          matrix product of the Hessian and gradient.
      """
      n_samples, n_features = X.shape
      grad = np.empty_like(w)
      fit_intercept = grad.shape[0] > n_features
  
      w, c, yz = _intercept_dot(w, X, y)
  
      if sample_weight is None:
          sample_weight = np.ones(y.shape[0])
  
      z = expit(yz)
      z0 = sample_weight * (z - 1) * y
  
      grad[:n_features] = safe_sparse_dot(X.T, z0) + alpha * w
  
      # Case where we fit the intercept.
      if fit_intercept:
          grad[-1] = z0.sum()
  
      # The mat-vec product of the Hessian
      d = sample_weight * z * (1 - z)
      if sparse.issparse(X):
          dX = safe_sparse_dot(sparse.dia_matrix((d, 0), shape=(n_samples, n_samples)), X)
      else:
          # Precompute as much as possible
          dX = d[:, np.newaxis] * X
  
      if fit_intercept:
          # Calculate the double derivative with respect to intercept
          # In the case of sparse matrices this returns a matrix object.
          dd_intercept = np.squeeze(np.array(dX.sum(axis=0)))
  
      def Hs(s):
          ret = np.empty_like(s)
          if sparse.issparse(X):
              ret[:n_features] = X.T.dot(dX.dot(s[:n_features]))
          else:
              ret[:n_features] = np.linalg.multi_dot([X.T, dX, s[:n_features]])
          ret[:n_features] += alpha * s[:n_features]
  
          # For the fit intercept case.
          if fit_intercept:
              ret[:n_features] += s[-1] * dd_intercept
              ret[-1] = dd_intercept.dot(s[:n_features])
              ret[-1] += d.sum() * s[-1]
          return ret
  
      return grad, Hs
  
  
  def _multinomial_loss(w, X, Y, alpha, sample_weight):
      """Computes multinomial loss and class probabilities.
  
      Parameters
      ----------
      w : ndarray of shape (n_classes * n_features,) or
          (n_classes * (n_features + 1),)
          Coefficient vector.
  
      X : {array-like, sparse matrix} of shape (n_samples, n_features)
          Training data.
  
      Y : ndarray of shape (n_samples, n_classes)
          Transformed labels according to the output of LabelBinarizer.
  
      alpha : float
          Regularization parameter. alpha is equal to 1 / C.
  
      sample_weight : array-like of shape (n_samples,)
          Array of weights that are assigned to individual samples.
  
      Returns
      -------
      loss : float
          Multinomial loss.
  
      p : ndarray of shape (n_samples, n_classes)
          Estimated class probabilities.
  
      w : ndarray of shape (n_classes, n_features)
          Reshaped param vector excluding intercept terms.
  
      Reference
      ---------
      Bishop, C. M. (2006). Pattern recognition and machine learning.
      Springer. (Chapter 4.3.4)
      """
      n_classes = Y.shape[1]
      n_features = X.shape[1]
      fit_intercept = w.size == (n_classes * (n_features + 1))
      w = w.reshape(n_classes, -1)
      sample_weight = sample_weight[:, np.newaxis]
      if fit_intercept:
          intercept = w[:, -1]
          w = w[:, :-1]
      else:
          intercept = 0
      p = safe_sparse_dot(X, w.T)
      p += intercept
      p -= logsumexp(p, axis=1)[:, np.newaxis]
      loss = -(sample_weight * Y * p).sum()
      loss += 0.5 * alpha * squared_norm(w)
      p = np.exp(p, p)
      return loss, p, w
  
  
  def _multinomial_loss_grad(w, X, Y, alpha, sample_weight):
      """Computes the multinomial loss, gradient and class probabilities.
  
      Parameters
      ----------
      w : ndarray of shape (n_classes * n_features,) or
          (n_classes * (n_features + 1),)
          Coefficient vector.
  
      X : {array-like, sparse matrix} of shape (n_samples, n_features)
          Training data.
  
      Y : ndarray of shape (n_samples, n_classes)
          Transformed labels according to the output of LabelBinarizer.
  
      alpha : float
          Regularization parameter. alpha is equal to 1 / C.
  
      sample_weight : array-like of shape (n_samples,)
          Array of weights that are assigned to individual samples.
  
      Returns
      -------
      loss : float
          Multinomial loss.
  
      grad : ndarray of shape (n_classes * n_features,) or \
              (n_classes * (n_features + 1),)
          Ravelled gradient of the multinomial loss.
  
      p : ndarray of shape (n_samples, n_classes)
          Estimated class probabilities
  
      Reference
      ---------
      Bishop, C. M. (2006). Pattern recognition and machine learning.
      Springer. (Chapter 4.3.4)
      """
      n_classes = Y.shape[1]
      n_features = X.shape[1]
      fit_intercept = w.size == n_classes * (n_features + 1)
      grad = np.zeros((n_classes, n_features + bool(fit_intercept)), dtype=X.dtype)
      loss, p, w = _multinomial_loss(w, X, Y, alpha, sample_weight)
      sample_weight = sample_weight[:, np.newaxis]
      diff = sample_weight * (p - Y)
      grad[:, :n_features] = safe_sparse_dot(diff.T, X)
      grad[:, :n_features] += alpha * w
      if fit_intercept:
          grad[:, -1] = diff.sum(axis=0)
      return loss, grad.ravel(), p
  
  
  def _multinomial_grad_hess(w, X, Y, alpha, sample_weight):
      """
      Computes the gradient and the Hessian, in the case of a multinomial loss.
  
      Parameters
      ----------
      w : ndarray of shape (n_classes * n_features,) or
          (n_classes * (n_features + 1),)
          Coefficient vector.
  
      X : {array-like, sparse matrix} of shape (n_samples, n_features)
          Training data.
  
      Y : ndarray of shape (n_samples, n_classes)
          Transformed labels according to the output of LabelBinarizer.
  
      alpha : float
          Regularization parameter. alpha is equal to 1 / C.
  
      sample_weight : array-like of shape (n_samples,)
          Array of weights that are assigned to individual samples.
  
      Returns
      -------
      grad : ndarray of shape (n_classes * n_features,) or \
              (n_classes * (n_features + 1),)
          Ravelled gradient of the multinomial loss.
  
      hessp : callable
          Function that takes in a vector input of shape (n_classes * n_features)
          or (n_classes * (n_features + 1)) and returns matrix-vector product
          with hessian.
  
      References
      ----------
      Barak A. Pearlmutter (1993). Fast Exact Multiplication by the Hessian.
          http://www.bcl.hamilton.ie/~barak/papers/nc-hessian.pdf
      """
      n_features = X.shape[1]
      n_classes = Y.shape[1]
      fit_intercept = w.size == (n_classes * (n_features + 1))
  
      # `loss` is unused. Refactoring to avoid computing it does not
      # significantly speed up the computation and decreases readability
      loss, grad, p = _multinomial_loss_grad(w, X, Y, alpha, sample_weight)
      sample_weight = sample_weight[:, np.newaxis]
  
      # Hessian-vector product derived by applying the R-operator on the gradient
      # of the multinomial loss function.
      def hessp(v):
          v = v.reshape(n_classes, -1)
          if fit_intercept:
              inter_terms = v[:, -1]
              v = v[:, :-1]
          else:
              inter_terms = 0
          # r_yhat holds the result of applying the R-operator on the multinomial
          # estimator.
          r_yhat = safe_sparse_dot(X, v.T)
          r_yhat += inter_terms
          r_yhat += (-p * r_yhat).sum(axis=1)[:, np.newaxis]
          r_yhat *= p
          r_yhat *= sample_weight
          hessProd = np.zeros((n_classes, n_features + bool(fit_intercept)))
          hessProd[:, :n_features] = safe_sparse_dot(r_yhat.T, X)
          hessProd[:, :n_features] += v * alpha
          if fit_intercept:
              hessProd[:, -1] = r_yhat.sum(axis=0)
          return hessProd.ravel()
  
      return grad, hessp
  
  
  def _check_solver(solver, penalty, dual):
      all_solvers = ["liblinear", "newton-cg", "lbfgs", "sag", "saga"]
      if solver not in all_solvers:
          raise ValueError(
              "Logistic Regression supports only solvers in %s, got %s."
              % (all_solvers, solver)
          )
  
      all_penalties = ["l1", "l2", "elasticnet", "none"]
      if penalty not in all_penalties:
          raise ValueError(
              "Logistic Regression supports only penalties in %s, got %s."
              % (all_penalties, penalty)
          )
  
      if solver not in ["liblinear", "saga"] and penalty not in ("l2", "none"):
          raise ValueError(
              "Solver %s supports only 'l2' or 'none' penalties, got %s penalty."
              % (solver, penalty)
          )
      if solver != "liblinear" and dual:
          raise ValueError(
              "Solver %s supports only dual=False, got dual=%s" % (solver, dual)
          )
  
      if penalty == "elasticnet" and solver != "saga":
          raise ValueError(
              "Only 'saga' solver supports elasticnet penalty, got solver={}.".format(
                  solver
              )
          )
  
      if solver == "liblinear" and penalty == "none":
          raise ValueError("penalty='none' is not supported for the liblinear solver")
  
      return solver
  
  
  def _check_multi_class(multi_class, solver, n_classes):
      if multi_class == "auto":
          if solver == "liblinear":
              multi_class = "ovr"
          elif n_classes > 2:
              multi_class = "multinomial"
          else:
              multi_class = "ovr"
      if multi_class not in ("multinomial", "ovr"):
          raise ValueError(
              "multi_class should be 'multinomial', 'ovr' or 'auto'. Got %s."
              % multi_class
          )
      if multi_class == "multinomial" and solver == "liblinear":
          raise ValueError("Solver %s does not support a multinomial backend." % solver)
      return multi_class
  
  
  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,
      class_weight=None,
      dual=False,
      penalty="l2",
      intercept_scaling=1.0,
      multi_class="auto",
      random_state=None,
      check_input=True,
      max_squared_sum=None,
      sample_weight=None,
      l1_ratio=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.
      Note that there will be no speedup with liblinear solver, since it does
      not handle warm-starting.
  
      Read more in the :ref:`User Guide <logistic_regression>`.
  
      Parameters
      ----------
      X : {array-like, sparse matrix} of shape (n_samples, n_features)
          Input data.
  
      y : array-like of shape (n_samples,) or (n_samples, n_targets)
          Input data, target values.
  
      pos_class : int, default=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.
  
      Cs : int or array-like of shape (n_cs,), default=10
          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.
  
      fit_intercept : bool, default=True
          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, default=100
          Maximum number of iterations for the solver.
  
      tol : float, default=1e-4
          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, default=0
          For the liblinear and lbfgs solvers set verbose to any positive
          number for verbosity.
  
      solver : {'lbfgs', 'newton-cg', 'liblinear', 'sag', 'saga'}, \
              default='lbfgs'
          Numerical solver to use.
  
      coef : array-like of shape (n_features,), default=None
          Initialization value for coefficients of logistic regression.
          Useless for liblinear solver.
  
      class_weight : dict or 'balanced', default=None
          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, default=False
          Dual or primal formulation. Dual formulation is only implemented for
          l2 penalty with liblinear solver. Prefer dual=False when
          n_samples > n_features.
  
      penalty : {'l1', 'l2', 'elasticnet'}, default='l2'
          Used to specify the norm used in the penalization. The 'newton-cg',
          'sag' and 'lbfgs' solvers support only l2 penalties. 'elasticnet' is
          only supported by the 'saga' solver.
  
      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 : {'ovr', 'multinomial', 'auto'}, default='auto'
          If the option chosen is 'ovr', then a binary problem is fit for each
          label. For 'multinomial' the loss minimised is the multinomial loss fit
          across the entire probability distribution, *even when the data is
          binary*. 'multinomial' is unavailable when solver='liblinear'.
          'auto' selects 'ovr' if the data is binary, or if solver='liblinear',
          and otherwise selects 'multinomial'.
  
          .. versionadded:: 0.18
             Stochastic Average Gradient descent solver for 'multinomial' case.
          .. versionchanged:: 0.22
              Default changed from 'ovr' to 'auto' in 0.22.
  
      random_state : int, RandomState instance, default=None
          Used when ``solver`` == 'sag', 'saga' or 'liblinear' to shuffle the
          data. See :term:`Glossary <random_state>` for details.
  
      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 of shape(n_samples,), default=None
          Array of weights that are assigned to individual samples.
          If not provided, then each sample is given unit weight.
  
      l1_ratio : float, default=None
          The Elastic-Net mixing parameter, with ``0 <= l1_ratio <= 1``. Only
          used if ``penalty='elasticnet'``. Setting ``l1_ratio=0`` is equivalent
          to using ``penalty='l2'``, while setting ``l1_ratio=1`` is equivalent
          to using ``penalty='l1'``. For ``0 < l1_ratio <1``, the penalty is a
          combination of L1 and L2.
  
      Returns
      -------
      coefs : ndarray of 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. For
          ``multiclass='multinomial'``, the shape is (n_classes, n_cs,
          n_features) or (n_classes, n_cs, n_features + 1).
  
      Cs : ndarray
          Grid of Cs used for cross-validation.
  
      n_iter : array of 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.
  
      .. versionchanged:: 0.19
          The "copy" parameter was removed.
      """
      if isinstance(Cs, numbers.Integral):
          Cs = np.logspace(-4, 4, Cs)
  
      solver = _check_solver(solver, penalty, dual)
  
      # Preprocessing.
      if check_input:
          X = check_array(
              X,
              accept_sparse="csr",
              dtype=np.float64,
              accept_large_sparse=solver not in ["liblinear", "sag", "saga"],
          )
          y = check_array(y, ensure_2d=False, dtype=None)
          check_consistent_length(X, y)
      _, n_features = X.shape
  
      classes = np.unique(y)
      random_state = check_random_state(random_state)
  
      multi_class = _check_multi_class(multi_class, solver, len(classes))
      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
      sample_weight = _check_sample_weight(sample_weight, X, dtype=X.dtype, copy=True)
  
      # 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":
          class_weight_ = compute_class_weight(class_weight, classes=classes, y=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), dtype=X.dtype)
          mask_classes = np.array([-1, 1])
          mask = y == pos_class
          y_bin = np.ones(y.shape, dtype=X.dtype)
          y_bin[~mask] = -1.0
          # for compute_class_weight
  
          if class_weight == "balanced":
              class_weight_ = compute_class_weight(
                  class_weight, classes=mask_classes, y=y_bin
              )
              sample_weight *= class_weight_[le.fit_transform(y_bin)]
  
      else:
          if solver not in ["sag", "saga"]:
              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).astype(X.dtype, copy=False)
  
          w0 = np.zeros(
              (classes.size, n_features + int(fit_intercept)), order="F", dtype=X.dtype
          )
  
      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,
                      )
                  )
  
              if n_classes == 1:
                  w0[0, : coef.shape[1]] = -coef
                  w0[1, : coef.shape[1]] = coef
              else:
                  w0[:, : coef.shape[1]] = coef
  
      if multi_class == "multinomial":
          # scipy.optimize.minimize and newton-cg accepts only
          # ravelled parameters.
          if solver in ["lbfgs", "newton-cg"]:
              w0 = w0.ravel()
          target = Y_multi
          if solver == "lbfgs":
  
              def func(x, *args):
                  return _multinomial_loss_grad(x, *args)[0:2]
  
          elif solver == "newton-cg":
  
              def func(x, *args):
                  return _multinomial_loss(x, *args)[0]
  
              def grad(x, *args):
                  return _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
  
              def grad(x, *args):
                  return _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":
              iprint = [-1, 50, 1, 100, 101][
                  np.searchsorted(np.array([0, 1, 2, 3]), verbose)
              ]
              opt_res = optimize.minimize(
                  func,
                  w0,
                  method="L-BFGS-B",
                  jac=True,
                  args=(X, target, 1.0 / C, sample_weight),
                  options={"iprint": iprint, "gtol": tol, "maxiter": max_iter},
              )
              n_iter_i = _check_optimize_result(
                  solver,
                  opt_res,
                  max_iter,
                  extra_warning_msg=_LOGISTIC_SOLVER_CONVERGENCE_MSG,
              )
              w0, loss = opt_res.x, opt_res.fun
          elif solver == "newton-cg":
              args = (X, target, 1.0 / 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,
                  None,
                  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 in ["sag", "saga"]:
              if multi_class == "multinomial":
                  target = target.astype(X.dtype, copy=False)
                  loss = "multinomial"
              else:
                  loss = "log"
              # alpha is for L2-norm, beta is for L1-norm
              if penalty == "l1":
                  alpha = 0.0
                  beta = 1.0 / C
              elif penalty == "l2":
                  alpha = 1.0 / C
                  beta = 0.0
              else:  # Elastic-Net penalty
                  alpha = (1.0 / C) * (1 - l1_ratio)
                  beta = (1.0 / C) * l1_ratio
  
              w0, n_iter_i, warm_start_sag = sag_solver(
                  X,
                  target,
                  sample_weight,
                  loss,
                  alpha,
                  beta,
                  max_iter,
                  tol,
                  verbose,
                  random_state,
                  False,
                  max_squared_sum,
                  warm_start_sag,
                  is_saga=(solver == "saga"),
              )
  
          else:
              raise ValueError(
                  "solver must be one of {'liblinear', 'lbfgs', "
                  "'newton-cg', 'sag'}, got '%s' instead" % solver
              )
  
          if multi_class == "multinomial":
              n_classes = max(2, classes.size)
              multi_w0 = np.reshape(w0, (n_classes, -1))
              if n_classes == 2:
                  multi_w0 = multi_w0[1][np.newaxis, :]
              coefs.append(multi_w0.copy())
          else:
              coefs.append(w0.copy())
  
          n_iter[i] = n_iter_i
  
      return np.array(coefs), np.array(Cs), n_iter
  
  
  # helper function for LogisticCV
  def _log_reg_scoring_path(
      X,
      y,
      train,
      test,
      pos_class=None,
      Cs=10,
      scoring=None,
      fit_intercept=False,
      max_iter=100,
      tol=1e-4,
      class_weight=None,
      verbose=0,
      solver="lbfgs",
      penalty="l2",
      dual=False,
      intercept_scaling=1.0,
      multi_class="auto",
      random_state=None,
      max_squared_sum=None,
      sample_weight=None,
      l1_ratio=None,
  ):
      """Computes scores across logistic_regression_path
  
      Parameters
      ----------
      X : {array-like, sparse matrix} of shape (n_samples, n_features)
          Training data.
  
      y : array-like of shape (n_samples,) or (n_samples, n_targets)
          Target labels.
  
      train : list of indices
          The indices of the train set.
  
      test : list of indices
          The indices of the test set.
  
      pos_class : int, default=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.
  
      Cs : int or list of floats, default=10
          Each of the values in Cs describes the inverse of
          regularization strength. If Cs is as an int, then a grid of Cs
          values are chosen in a logarithmic scale between 1e-4 and 1e4.
          If not provided, then a fixed set of values for Cs are used.
  
      scoring : callable, default=None
          A string (see model evaluation documentation) or
          a scorer callable object / function with signature
          ``scorer(estimator, X, y)``. For a list of scoring functions
          that can be used, look at :mod:`sklearn.metrics`. The
          default scoring option used is accuracy_score.
  
      fit_intercept : bool, default=False
          If False, then the bias term is set to zero. Else the last
          term of each coef_ gives us the intercept.
  
      max_iter : int, default=100
          Maximum number of iterations for the solver.
  
      tol : float, default=1e-4
          Tolerance for stopping criteria.
  
      class_weight : dict or 'balanced', default=None
          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.
  
      verbose : int, default=0
          For the liblinear and lbfgs solvers set verbose to any positive
          number for verbosity.
  
      solver : {'lbfgs', 'newton-cg', 'liblinear', 'sag', 'saga'}, \
              default='lbfgs'
          Decides which solver to use.
  
      penalty : {'l1', 'l2', 'elasticnet'}, default='l2'
          Used to specify the norm used in the penalization. The 'newton-cg',
          'sag' and 'lbfgs' solvers support only l2 penalties. 'elasticnet' is
          only supported by the 'saga' solver.
  
      dual : bool, default=False
          Dual or primal formulation. Dual formulation is only implemented for
          l2 penalty with liblinear solver. Prefer dual=False when
          n_samples > n_features.
  
      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 equals 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 : {'auto', 'ovr', 'multinomial'}, default='auto'
          If the option chosen is 'ovr', then a binary problem is fit for each
          label. For 'multinomial' the loss minimised is the multinomial loss fit
          across the entire probability distribution, *even when the data is
          binary*. 'multinomial' is unavailable when solver='liblinear'.
  
      random_state : int, RandomState instance, default=None
          Used when ``solver`` == 'sag', 'saga' or 'liblinear' to shuffle the
          data. See :term:`Glossary <random_state>` for details.
  
      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 of shape(n_samples,), default=None
          Array of weights that are assigned to individual samples.
          If not provided, then each sample is given unit weight.
  
      l1_ratio : float, default=None
          The Elastic-Net mixing parameter, with ``0 <= l1_ratio <= 1``. Only
          used if ``penalty='elasticnet'``. Setting ``l1_ratio=0`` is equivalent
          to using ``penalty='l2'``, while setting ``l1_ratio=1`` is equivalent
          to using ``penalty='l1'``. For ``0 < l1_ratio <1``, the penalty is a
          combination of L1 and L2.
  
      Returns
      -------
      coefs : ndarray of 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.
  
      scores : ndarray of shape (n_cs,)
          Scores obtained for each Cs.
  
      n_iter : ndarray of shape(n_cs,)
          Actual number of iteration for each Cs.
      """
      X_train = X[train]
      X_test = X[test]
      y_train = y[train]
      y_test = y[test]
  
      if sample_weight is not None:
          sample_weight = _check_sample_weight(sample_weight, X)
          sample_weight = sample_weight[train]
  
      coefs, Cs, n_iter = _logistic_regression_path(
          X_train,
          y_train,
          Cs=Cs,
          l1_ratio=l1_ratio,
          fit_intercept=fit_intercept,
          solver=solver,
          max_iter=max_iter,
          class_weight=class_weight,
          pos_class=pos_class,
          multi_class=multi_class,
          tol=tol,
          verbose=verbose,
          dual=dual,
          penalty=penalty,
          intercept_scaling=intercept_scaling,
          random_state=random_state,
          check_input=False,
          max_squared_sum=max_squared_sum,
          sample_weight=sample_weight,
      )
  
      log_reg = LogisticRegression(solver=solver, multi_class=multi_class)
  
      # The score method of Logistic Regression has a classes_ attribute.
      if multi_class == "ovr":
          log_reg.classes_ = np.array([-1, 1])
      elif multi_class == "multinomial":
          log_reg.classes_ = np.unique(y_train)
      else:
          raise ValueError(
              "multi_class should be either multinomial or ovr, got %d" % multi_class
          )
  
      if pos_class is not None:
          mask = y_test == pos_class
          y_test = np.ones(y_test.shape, dtype=np.float64)
          y_test[~mask] = -1.0
  
      scores = list()
  
      scoring = get_scorer(scoring)
      for w in coefs:
          if multi_class == "ovr":
              w = w[np.newaxis, :]
          if fit_intercept:
              log_reg.coef_ = w[:, :-1]
              log_reg.intercept_ = w[:, -1]
          else:
              log_reg.coef_ = w
              log_reg.intercept_ = 0.0
  
          if scoring is None:
              scores.append(log_reg.score(X_test, y_test))
          else:
              scores.append(scoring(log_reg, X_test, y_test))
  
      return coefs, Cs, np.array(scores), n_iter
  
  
  class LogisticRegression(LinearClassifierMixin, SparseCoefMixin, BaseEstimator):
      """
      Logistic Regression (aka logit, MaxEnt) classifier.
  
      In the multiclass case, the training algorithm uses the one-vs-rest (OvR)
      scheme if the 'multi_class' option is set to 'ovr', and uses the
      cross-entropy loss if the 'multi_class' option is set to 'multinomial'.
      (Currently the 'multinomial' option is supported only by the 'lbfgs',
      'sag', 'saga' and 'newton-cg' solvers.)
  
      This class implements regularized logistic regression using the
      'liblinear' library, 'newton-cg', 'sag', 'saga' and 'lbfgs' solvers. **Note
      that regularization is applied by default**. It can handle both dense
      and sparse input. Use C-ordered arrays or CSR matrices containing 64-bit
      floats for optimal performance; any other input format will be converted
      (and copied).
  
      The 'newton-cg', 'sag', and 'lbfgs' solvers support only L2 regularization
      with primal formulation, or no regularization. The 'liblinear' solver
      supports both L1 and L2 regularization, with a dual formulation only for
      the L2 penalty. The Elastic-Net regularization is only supported by the
      'saga' solver.
  
      Read more in the :ref:`User Guide <logistic_regression>`.
  
      Parameters
      ----------
      penalty : {'l1', 'l2', 'elasticnet', 'none'}, default='l2'
          Specify the norm of the penalty:
  
          - `'none'`: no penalty is added;
          - `'l2'`: add a L2 penalty term and it is the default choice;
          - `'l1'`: add a L1 penalty term;
          - `'elasticnet'`: both L1 and L2 penalty terms are added.
  
          .. warning::
             Some penalties may not work with some solvers. See the parameter
             `solver` below, to know the compatibility between the penalty and
             solver.
  
          .. versionadded:: 0.19
             l1 penalty with SAGA solver (allowing 'multinomial' + L1)
  
      dual : bool, default=False
          Dual or primal formulation. Dual formulation is only implemented for
          l2 penalty with liblinear solver. Prefer dual=False when
          n_samples > n_features.
  
      tol : float, default=1e-4
          Tolerance for stopping criteria.
  
      C : float, default=1.0
          Inverse of regularization strength; must be a positive float.
          Like in support vector machines, smaller values specify stronger
          regularization.
  
      fit_intercept : bool, default=True
          Specifies if a constant (a.k.a. bias or intercept) should be
          added to the decision function.
  
      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.
  
      class_weight : dict or 'balanced', default=None
          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.
  
          .. versionadded:: 0.17
             *class_weight='balanced'*
  
      random_state : int, RandomState instance, default=None
          Used when ``solver`` == 'sag', 'saga' or 'liblinear' to shuffle the
          data. See :term:`Glossary <random_state>` for details.
  
      solver : {'newton-cg', 'lbfgs', 'liblinear', 'sag', 'saga'}, \
              default='lbfgs'
  
          Algorithm to use in the optimization problem. Default is 'lbfgs'.
          To choose a solver, you might want to consider the following aspects:
  
              - For small datasets, 'liblinear' is a good choice, whereas 'sag'
                and 'saga' are faster for large ones;
              - For multiclass problems, only 'newton-cg', 'sag', 'saga' and
                'lbfgs' handle multinomial loss;
              - 'liblinear' is limited to one-versus-rest schemes.
  
          .. warning::
             The choice of the algorithm depends on the penalty chosen:
             Supported penalties by solver:
  
             - 'newton-cg'   -   ['l2', 'none']
             - 'lbfgs'       -   ['l2', 'none']
             - 'liblinear'   -   ['l1', 'l2']
             - 'sag'         -   ['l2', 'none']
             - 'saga'        -   ['elasticnet', 'l1', 'l2', 'none']
  
          .. note::
             'sag' and 'saga' fast convergence is only guaranteed on
             features with approximately the same scale. You can
             preprocess the data with a scaler from :mod:`sklearn.preprocessing`.
  
          .. seealso::
             Refer to the User Guide for more information regarding
             :class:`LogisticRegression` and more specifically the
             `Table <https://scikit-learn.org/dev/modules/linear_model.html#logistic-regression>`_
             summarazing solver/penalty supports.
             <!--
             # noqa: E501
             -->
  
          .. versionadded:: 0.17
             Stochastic Average Gradient descent solver.
          .. versionadded:: 0.19
             SAGA solver.
          .. versionchanged:: 0.22
              The default solver changed from 'liblinear' to 'lbfgs' in 0.22.
  
      max_iter : int, default=100
          Maximum number of iterations taken for the solvers to converge.
  
      multi_class : {'auto', 'ovr', 'multinomial'}, default='auto'
          If the option chosen is 'ovr', then a binary problem is fit for each
          label. For 'multinomial' the loss minimised is the multinomial loss fit
          across the entire probability distribution, *even when the data is
          binary*. 'multinomial' is unavailable when solver='liblinear'.
          'auto' selects 'ovr' if the data is binary, or if solver='liblinear',
          and otherwise selects 'multinomial'.
  
          .. versionadded:: 0.18
             Stochastic Average Gradient descent solver for 'multinomial' case.
          .. versionchanged:: 0.22
              Default changed from 'ovr' to 'auto' in 0.22.
  
      verbose : int, default=0
          For the liblinear and lbfgs solvers set verbose to any positive
          number for verbosity.
  
      warm_start : bool, default=False
          When set to True, reuse the solution of the previous call to fit as
          initialization, otherwise, just erase the previous solution.
          Useless for liblinear solver. See :term:`the Glossary <warm_start>`.
  
          .. versionadded:: 0.17
             *warm_start* to support *lbfgs*, *newton-cg*, *sag*, *saga* solvers.
  
      n_jobs : int, default=None
          Number of CPU cores used when parallelizing over classes if
          multi_class='ovr'". This parameter is ignored when the ``solver`` is
          set to 'liblinear' regardless of whether 'multi_class' is specified or
          not. ``None`` means 1 unless in a :obj:`joblib.parallel_backend`
          context. ``-1`` means using all processors.
          See :term:`Glossary <n_jobs>` for more details.
  
      l1_ratio : float, default=None
          The Elastic-Net mixing parameter, with ``0 <= l1_ratio <= 1``. Only
          used if ``penalty='elasticnet'``. Setting ``l1_ratio=0`` is equivalent
          to using ``penalty='l2'``, while setting ``l1_ratio=1`` is equivalent
          to using ``penalty='l1'``. For ``0 < l1_ratio <1``, the penalty is a
          combination of L1 and L2.
  
      Attributes
      ----------
  
      classes_ : ndarray of shape (n_classes, )
          A list of class labels known to the classifier.
  
      coef_ : ndarray of shape (1, n_features) or (n_classes, n_features)
          Coefficient of the features in the decision function.
  
          `coef_` is of shape (1, n_features) when the given problem is binary.
          In particular, when `multi_class='multinomial'`, `coef_` corresponds
          to outcome 1 (True) and `-coef_` corresponds to outcome 0 (False).
  
      intercept_ : ndarray of shape (1,) or (n_classes,)
          Intercept (a.k.a. bias) added to the decision function.
  
          If `fit_intercept` is set to False, the intercept is set to zero.
          `intercept_` is of shape (1,) when the given problem is binary.
          In particular, when `multi_class='multinomial'`, `intercept_`
          corresponds to outcome 1 (True) and `-intercept_` corresponds to
          outcome 0 (False).
  
      n_features_in_ : int
          Number of features seen during :term:`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_iter_ : ndarray of shape (n_classes,) or (1, )
          Actual number of iterations for all classes. If binary or multinomial,
          it returns only 1 element. For liblinear solver, only the maximum
          number of iteration across all classes is given.
  
          .. versionchanged:: 0.20
  
              In SciPy <= 1.0.0 the number of lbfgs iterations may exceed
              ``max_iter``. ``n_iter_`` will now report at most ``max_iter``.
  
      See Also
      --------
      SGDClassifier : Incrementally trained logistic regression (when given
          the parameter ``loss="log"``).
      LogisticRegressionCV : Logistic regression with built-in cross validation.
  
      Notes
      -----
      The underlying C implementation uses a random number generator to
      select features when fitting the model. It is thus not uncommon,
      to have slightly different results for the same input data. If
      that happens, try with a smaller tol parameter.
  
      Predict output may not match that of standalone liblinear in certain
      cases. See :ref:`differences from liblinear <liblinear_differences>`
      in the narrative documentation.
  
      References
      ----------
  
      L-BFGS-B -- Software for Large-scale Bound-constrained Optimization
          Ciyou Zhu, Richard Byrd, Jorge Nocedal and Jose Luis Morales.
          http://users.iems.northwestern.edu/~nocedal/lbfgsb.html
  
      LIBLINEAR -- A Library for Large Linear Classification
          https://www.csie.ntu.edu.tw/~cjlin/liblinear/
  
      SAG -- Mark Schmidt, Nicolas Le Roux, and Francis Bach
          Minimizing Finite Sums with the Stochastic Average Gradient
          https://hal.inria.fr/hal-00860051/document
  
      SAGA -- Defazio, A., Bach F. & Lacoste-Julien S. (2014).
              :arxiv:`"SAGA: A Fast Incremental Gradient Method With Support
              for Non-Strongly Convex Composite Objectives" <1407.0202>`
  
      Hsiang-Fu Yu, Fang-Lan Huang, Chih-Jen Lin (2011). Dual coordinate descent
          methods for logistic regression and maximum entropy models.
          Machine Learning 85(1-2):41-75.
          https://www.csie.ntu.edu.tw/~cjlin/papers/maxent_dual.pdf
  
      Examples
      --------
      >>> from sklearn.datasets import load_iris
      >>> from sklearn.linear_model import LogisticRegression
      >>> X, y = load_iris(return_X_y=True)
      >>> clf = LogisticRegression(random_state=0).fit(X, y)
      >>> clf.predict(X[:2, :])
      array([0, 0])
      >>> clf.predict_proba(X[:2, :])
      array([[9.8...e-01, 1.8...e-02, 1.4...e-08],
             [9.7...e-01, 2.8...e-02, ...e-08]])
      >>> clf.score(X, y)
      0.97...
      """
  
      def __init__(
          self,
          penalty="l2",
          *,
          dual=False,
          tol=1e-4,
          C=1.0,
          fit_intercept=True,
          intercept_scaling=1,
          class_weight=None,
          random_state=None,
          solver="lbfgs",
          max_iter=100,
          multi_class="auto",
          verbose=0,
          warm_start=False,
          n_jobs=None,
          l1_ratio=None,
      ):
  
          self.penalty = penalty
          self.dual = dual
          self.tol = tol
          self.C = C
          self.fit_intercept = fit_intercept
          self.intercept_scaling = intercept_scaling
          self.class_weight = class_weight
          self.random_state = random_state
          self.solver = solver
          self.max_iter = max_iter
          self.multi_class = multi_class
          self.verbose = verbose
          self.warm_start = warm_start
          self.n_jobs = n_jobs
          self.l1_ratio = l1_ratio
  
      def fit(self, X, y, sample_weight=None):
          """
          Fit the model according to the given training data.
  
          Parameters
          ----------
          X : {array-like, sparse matrix} of shape (n_samples, n_features)
              Training vector, where `n_samples` is the number of samples and
              `n_features` is the number of features.
  
          y : array-like of shape (n_samples,)
              Target vector relative to X.
  
          sample_weight : array-like of shape (n_samples,) default=None
              Array of weights that are assigned to individual samples.
              If not provided, then each sample is given unit weight.
  
              .. versionadded:: 0.17
                 *sample_weight* support to LogisticRegression.
  
          Returns
          -------
          self
              Fitted estimator.
  
          Notes
          -----
          The SAGA solver supports both float64 and float32 bit arrays.
          """
          solver = _check_solver(self.solver, self.penalty, self.dual)
  
          if not isinstance(self.C, numbers.Number) or self.C < 0:
              raise ValueError("Penalty term must be positive; got (C=%r)" % self.C)
          if self.penalty == "elasticnet":
              if (
                  not isinstance(self.l1_ratio, numbers.Number)
                  or self.l1_ratio < 0
                  or self.l1_ratio > 1
              ):
                  raise ValueError(
                      "l1_ratio must be between 0 and 1; got (l1_ratio=%r)"
                      % self.l1_ratio
                  )
          elif self.l1_ratio is not None:
              warnings.warn(
                  "l1_ratio parameter is only used when penalty is "
                  "'elasticnet'. Got "
                  "(penalty={})".format(self.penalty)
              )
          if self.penalty == "none":
              if self.C != 1.0:  # default values
                  warnings.warn(
                      "Setting penalty='none' will ignore the C and l1_ratio parameters"
                  )
                  # Note that check for l1_ratio is done right above
              C_ = np.inf
              penalty = "l2"
          else:
              C_ = self.C
              penalty = self.penalty
          if not isinstance(self.max_iter, numbers.Number) or self.max_iter < 0:
              raise ValueError(
                  "Maximum number of iteration must be positive; got (max_iter=%r)"
                  % self.max_iter
              )
          if not isinstance(self.tol, numbers.Number) or self.tol < 0:
              raise ValueError(
                  "Tolerance for stopping criteria must be positive; got (tol=%r)"
                  % self.tol
              )
  
          if solver == "lbfgs":
              _dtype = np.float64
          else:
              _dtype = [np.float64, np.float32]
  
          X, y = self._validate_data(
              X,
              y,
              accept_sparse="csr",
              dtype=_dtype,
              order="C",
              accept_large_sparse=solver not in ["liblinear", "sag", "saga"],
          )
          check_classification_targets(y)
          self.classes_ = np.unique(y)
  
          multi_class = _check_multi_class(self.multi_class, solver, len(self.classes_))
  
          if solver == "liblinear":
              if effective_n_jobs(self.n_jobs) != 1:
                  warnings.warn(
                      "'n_jobs' > 1 does not have any effect when"
                      " 'solver' is set to 'liblinear'. Got 'n_jobs'"
                      " = {}.".format(effective_n_jobs(self.n_jobs))
                  )
              self.coef_, self.intercept_, n_iter_ = _fit_liblinear(
                  X,
                  y,
                  self.C,
                  self.fit_intercept,
                  self.intercept_scaling,
                  self.class_weight,
                  self.penalty,
                  self.dual,
                  self.verbose,
                  self.max_iter,
                  self.tol,
                  self.random_state,
                  sample_weight=sample_weight,
              )
              self.n_iter_ = np.array([n_iter_])
              return self
  
          if solver in ["sag", "saga"]:
              max_squared_sum = row_norms(X, squared=True).max()
          else:
              max_squared_sum = None
  
          n_classes = len(self.classes_)
          classes_ = self.classes_
          if n_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]
              )
  
          if len(self.classes_) == 2:
              n_classes = 1
              classes_ = classes_[1:]
  
          if self.warm_start:
              warm_start_coef = getattr(self, "coef_", None)
          else:
              warm_start_coef = None
          if warm_start_coef is not None and self.fit_intercept:
              warm_start_coef = np.append(
                  warm_start_coef, self.intercept_[:, np.newaxis], axis=1
              )
  
          # Hack so that we iterate only once for the multinomial case.
          if multi_class == "multinomial":
              classes_ = [None]
              warm_start_coef = [warm_start_coef]
          if warm_start_coef is None:
              warm_start_coef = [None] * n_classes
  
          path_func = delayed(_logistic_regression_path)
  
          # The SAG solver releases the GIL so it's more efficient to use
          # threads for this solver.
          if solver in ["sag", "saga"]:
              prefer = "threads"
          else:
              prefer = "processes"
          fold_coefs_ = Parallel(
              n_jobs=self.n_jobs,
              verbose=self.verbose,
              **_joblib_parallel_args(prefer=prefer),
          )(
              path_func(
                  X,
                  y,
                  pos_class=class_,
                  Cs=[C_],
                  l1_ratio=self.l1_ratio,
                  fit_intercept=self.fit_intercept,
                  tol=self.tol,
                  verbose=self.verbose,
                  solver=solver,
                  multi_class=multi_class,
                  max_iter=self.max_iter,
                  class_weight=self.class_weight,
                  check_input=False,
                  random_state=self.random_state,
                  coef=warm_start_coef_,
                  penalty=penalty,
                  max_squared_sum=max_squared_sum,
                  sample_weight=sample_weight,
              )
              for class_, warm_start_coef_ in zip(classes_, warm_start_coef)
          )
  
          fold_coefs_, _, n_iter_ = zip(*fold_coefs_)
          self.n_iter_ = np.asarray(n_iter_, dtype=np.int32)[:, 0]
  
          n_features = X.shape[1]
          if multi_class == "multinomial":
              self.coef_ = fold_coefs_[0][0]
          else:
              self.coef_ = np.asarray(fold_coefs_)
              self.coef_ = self.coef_.reshape(
                  n_classes, n_features + int(self.fit_intercept)
              )
  
          if self.fit_intercept:
              self.intercept_ = self.coef_[:, -1]
              self.coef_ = self.coef_[:, :-1]
          else:
              self.intercept_ = np.zeros(n_classes)
  
          return self
  
      def predict_proba(self, X):
          """
          Probability estimates.
  
          The returned estimates for all classes are ordered by the
          label of classes.
  
          For a multi_class problem, if multi_class is set to be "multinomial"
          the softmax function is used to find the predicted probability of
          each class.
          Else use a one-vs-rest approach, i.e calculate the probability
          of each class assuming it to be positive using the logistic function.
          and normalize these values across all the classes.
  
          Parameters
          ----------
          X : array-like of shape (n_samples, n_features)
              Vector to be scored, where `n_samples` is the number of samples and
              `n_features` is the number of features.
  
          Returns
          -------
          T : array-like of shape (n_samples, n_classes)
              Returns the probability of the sample for each class in the model,
              where classes are ordered as they are in ``self.classes_``.
          """
          check_is_fitted(self)
  
          ovr = self.multi_class in ["ovr", "warn"] or (
              self.multi_class == "auto"
              and (self.classes_.size <= 2 or self.solver == "liblinear")
          )
          if ovr:
              return super()._predict_proba_lr(X)
          else:
              decision = self.decision_function(X)
              if decision.ndim == 1:
                  # Workaround for multi_class="multinomial" and binary outcomes
                  # which requires softmax prediction with only a 1D decision.
                  decision_2d = np.c_[-decision, decision]
              else:
                  decision_2d = decision
              return softmax(decision_2d, copy=False)
  
      def predict_log_proba(self, X):
          """
          Predict logarithm of probability estimates.
  
          The returned estimates for all classes are ordered by the
          label of classes.
  
          Parameters
          ----------
          X : array-like of shape (n_samples, n_features)
              Vector to be scored, where `n_samples` is the number of samples and
              `n_features` is the number of features.
  
          Returns
          -------
          T : array-like of shape (n_samples, n_classes)
              Returns the log-probability of the sample for each class in the
              model, where classes are ordered as they are in ``self.classes_``.
          """
          return np.log(self.predict_proba(X))
  
  
  class LogisticRegressionCV(LogisticRegression, LinearClassifierMixin, BaseEstimator):
      """Logistic Regression CV (aka logit, MaxEnt) classifier.
  
      See glossary entry for :term:`cross-validation estimator`.
  
      This class implements logistic regression using liblinear, newton-cg, sag
      of lbfgs optimizer. The newton-cg, sag and lbfgs solvers support only L2
      regularization with primal formulation. The liblinear solver supports both
      L1 and L2 regularization, with a dual formulation only for the L2 penalty.
      Elastic-Net penalty is only supported by the saga solver.
  
      For the grid of `Cs` values and `l1_ratios` values, the best hyperparameter
      is selected by the cross-validator
      :class:`~sklearn.model_selection.StratifiedKFold`, but it can be changed
      using the :term:`cv` parameter. The 'newton-cg', 'sag', 'saga' and 'lbfgs'
      solvers can warm-start the coefficients (see :term:`Glossary<warm_start>`).
  
      Read more in the :ref:`User Guide <logistic_regression>`.
  
      Parameters
      ----------
      Cs : int or list of floats, default=10
          Each of the values in Cs describes the inverse of regularization
          strength. If Cs is as an int, then a grid of Cs values are chosen
          in a logarithmic scale between 1e-4 and 1e4.
          Like in support vector machines, smaller values specify stronger
          regularization.
  
      fit_intercept : bool, default=True
          Specifies if a constant (a.k.a. bias or intercept) should be
          added to the decision function.
  
      cv : int or cross-validation generator, default=None
          The default cross-validation generator used is Stratified K-Folds.
          If an integer is provided, then it is the number of folds used.
          See the module :mod:`sklearn.model_selection` module for the
          list of possible cross-validation objects.
  
          .. versionchanged:: 0.22
              ``cv`` default value if None changed from 3-fold to 5-fold.
  
      dual : bool, default=False
          Dual or primal formulation. Dual formulation is only implemented for
          l2 penalty with liblinear solver. Prefer dual=False when
          n_samples > n_features.
  
      penalty : {'l1', 'l2', 'elasticnet'}, default='l2'
          Specify the norm of the penalty:
  
          - `'l2'`: add a L2 penalty term (used by default);
          - `'l1'`: add a L1 penalty term;
          - `'elasticnet'`: both L1 and L2 penalty terms are added.
  
          .. warning::
             Some penalties may not work with some solvers. See the parameter
             `solver` below, to know the compatibility between the penalty and
             solver.
  
      scoring : str or callable, default=None
          A string (see model evaluation documentation) or
          a scorer callable object / function with signature
          ``scorer(estimator, X, y)``. For a list of scoring functions
          that can be used, look at :mod:`sklearn.metrics`. The
          default scoring option used is 'accuracy'.
  
      solver : {'newton-cg', 'lbfgs', 'liblinear', 'sag', 'saga'}, \
              default='lbfgs'
  
          Algorithm to use in the optimization problem. Default is 'lbfgs'.
          To choose a solver, you might want to consider the following aspects:
  
              - For small datasets, 'liblinear' is a good choice, whereas 'sag'
                and 'saga' are faster for large ones;
              - For multiclass problems, only 'newton-cg', 'sag', 'saga' and
                'lbfgs' handle multinomial loss;
              - 'liblinear' might be slower in :class:`LogisticRegressionCV`
                because it does not handle warm-starting. 'liblinear' is
                limited to one-versus-rest schemes.
  
          .. warning::
             The choice of the algorithm depends on the penalty chosen:
  
             - 'newton-cg'   -   ['l2']
             - 'lbfgs'       -   ['l2']
             - 'liblinear'   -   ['l1', 'l2']
             - 'sag'         -   ['l2']
             - 'saga'        -   ['elasticnet', 'l1', 'l2']
  
          .. note::
             'sag' and 'saga' fast convergence is only guaranteed on features
             with approximately the same scale. You can preprocess the data with
             a scaler from :mod:`sklearn.preprocessing`.
  
          .. versionadded:: 0.17
             Stochastic Average Gradient descent solver.
          .. versionadded:: 0.19
             SAGA solver.
  
      tol : float, default=1e-4
          Tolerance for stopping criteria.
  
      max_iter : int, default=100
          Maximum number of iterations of the optimization algorithm.
  
      class_weight : dict or 'balanced', default=None
          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.
  
          .. versionadded:: 0.17
             class_weight == 'balanced'
  
      n_jobs : int, default=None
          Number of CPU cores used during the cross-validation loop.
          ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
          ``-1`` means using all processors. See :term:`Glossary <n_jobs>`
          for more details.
  
      verbose : int, default=0
          For the 'liblinear', 'sag' and 'lbfgs' solvers set verbose to any
          positive number for verbosity.
  
      refit : bool, default=True
          If set to True, the scores are averaged across all folds, and the
          coefs and the C that corresponds to the best score is taken, and a
          final refit is done using these parameters.
          Otherwise the coefs, intercepts and C that correspond to the
          best scores across folds are averaged.
  
      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 : {'auto, 'ovr', 'multinomial'}, default='auto'
          If the option chosen is 'ovr', then a binary problem is fit for each
          label. For 'multinomial' the loss minimised is the multinomial loss fit
          across the entire probability distribution, *even when the data is
          binary*. 'multinomial' is unavailable when solver='liblinear'.
          'auto' selects 'ovr' if the data is binary, or if solver='liblinear',
          and otherwise selects 'multinomial'.
  
          .. versionadded:: 0.18
             Stochastic Average Gradient descent solver for 'multinomial' case.
          .. versionchanged:: 0.22
              Default changed from 'ovr' to 'auto' in 0.22.
  
      random_state : int, RandomState instance, default=None
          Used when `solver='sag'`, 'saga' or 'liblinear' to shuffle the data.
          Note that this only applies to the solver and not the cross-validation
          generator. See :term:`Glossary <random_state>` for details.
  
      l1_ratios : list of float, default=None
          The list of Elastic-Net mixing parameter, with ``0 <= l1_ratio <= 1``.
          Only used if ``penalty='elasticnet'``. A value of 0 is equivalent to
          using ``penalty='l2'``, while 1 is equivalent to using
          ``penalty='l1'``. For ``0 < l1_ratio <1``, the penalty is a combination
          of L1 and L2.
  
      Attributes
      ----------
      classes_ : ndarray of shape (n_classes, )
          A list of class labels known to the classifier.
  
      coef_ : ndarray of shape (1, n_features) or (n_classes, n_features)
          Coefficient of the features in the decision function.
  
          `coef_` is of shape (1, n_features) when the given problem
          is binary.
  
      intercept_ : ndarray of shape (1,) or (n_classes,)
          Intercept (a.k.a. bias) added to the decision function.
  
          If `fit_intercept` is set to False, the intercept is set to zero.
          `intercept_` is of shape(1,) when the problem is binary.
  
      Cs_ : ndarray of shape (n_cs)
          Array of C i.e. inverse of regularization parameter values used
          for cross-validation.
  
      l1_ratios_ : ndarray of shape (n_l1_ratios)
          Array of l1_ratios used for cross-validation. If no l1_ratio is used
          (i.e. penalty is not 'elasticnet'), this is set to ``[None]``
  
      coefs_paths_ : ndarray of shape (n_folds, n_cs, n_features) or \
                     (n_folds, n_cs, n_features + 1)
          dict with classes as the keys, and the path of coefficients obtained
          during cross-validating across each fold and then across each Cs
          after doing an OvR for the corresponding class as values.
          If the 'multi_class' option is set to 'multinomial', then
          the coefs_paths are the coefficients corresponding to each class.
          Each dict value has shape ``(n_folds, n_cs, n_features)`` or
          ``(n_folds, n_cs, n_features + 1)`` depending on whether the
          intercept is fit or not. If ``penalty='elasticnet'``, the shape is
          ``(n_folds, n_cs, n_l1_ratios_, n_features)`` or
          ``(n_folds, n_cs, n_l1_ratios_, n_features + 1)``.
  
      scores_ : dict
          dict with classes as the keys, and the values as the
          grid of scores obtained during cross-validating each fold, after doing
          an OvR for the corresponding class. If the 'multi_class' option
          given is 'multinomial' then the same scores are repeated across
          all classes, since this is the multinomial class. Each dict value
          has shape ``(n_folds, n_cs`` or ``(n_folds, n_cs, n_l1_ratios)`` if
          ``penalty='elasticnet'``.
  
      C_ : ndarray of shape (n_classes,) or (n_classes - 1,)
          Array of C that maps to the best scores across every class. If refit is
          set to False, then for each class, the best C is the average of the
          C's that correspond to the best scores for each fold.
          `C_` is of shape(n_classes,) when the problem is binary.
  
      l1_ratio_ : ndarray of shape (n_classes,) or (n_classes - 1,)
          Array of l1_ratio that maps to the best scores across every class. If
          refit is set to False, then for each class, the best l1_ratio is the
          average of the l1_ratio's that correspond to the best scores for each
          fold.  `l1_ratio_` is of shape(n_classes,) when the problem is binary.
  
      n_iter_ : ndarray of shape (n_classes, n_folds, n_cs) or (1, n_folds, n_cs)
          Actual number of iterations for all classes, folds and Cs.
          In the binary or multinomial cases, the first dimension is equal to 1.
          If ``penalty='elasticnet'``, the shape is ``(n_classes, n_folds,
          n_cs, n_l1_ratios)`` or ``(1, n_folds, n_cs, n_l1_ratios)``.
  
      n_features_in_ : int
          Number of features seen during :term:`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
  
      See Also
      --------
      LogisticRegression : Logistic regression without tuning the
          hyperparameter `C`.
  
      Examples
      --------
      >>> from sklearn.datasets import load_iris
      >>> from sklearn.linear_model import LogisticRegressionCV
      >>> X, y = load_iris(return_X_y=True)
      >>> clf = LogisticRegressionCV(cv=5, random_state=0).fit(X, y)
      >>> clf.predict(X[:2, :])
      array([0, 0])
      >>> clf.predict_proba(X[:2, :]).shape
      (2, 3)
      >>> clf.score(X, y)
      0.98...
      """
  
      def __init__(
          self,
          *,
          Cs=10,
          fit_intercept=True,
          cv=None,
          dual=False,
          penalty="l2",
          scoring=None,
          solver="lbfgs",
          tol=1e-4,
          max_iter=100,
          class_weight=None,
          n_jobs=None,
          verbose=0,
          refit=True,
          intercept_scaling=1.0,
          multi_class="auto",
          random_state=None,
          l1_ratios=None,
      ):
          self.Cs = Cs
          self.fit_intercept = fit_intercept
          self.cv = cv
          self.dual = dual
          self.penalty = penalty
          self.scoring = scoring
          self.tol = tol
          self.max_iter = max_iter
          self.class_weight = class_weight
          self.n_jobs = n_jobs
          self.verbose = verbose
          self.solver = solver
          self.refit = refit
          self.intercept_scaling = intercept_scaling
          self.multi_class = multi_class
          self.random_state = random_state
          self.l1_ratios = l1_ratios
  
      def fit(self, X, y, sample_weight=None):
          """Fit the model according to the given training data.
  
          Parameters
          ----------
          X : {array-like, sparse matrix} of shape (n_samples, n_features)
              Training vector, where `n_samples` is the number of samples and
              `n_features` is the number of features.
  
          y : array-like of shape (n_samples,)
              Target vector relative to X.
  
          sample_weight : array-like of shape (n_samples,) default=None
              Array of weights that are assigned to individual samples.
              If not provided, then each sample is given unit weight.
  
          Returns
          -------
          self : object
              Fitted LogisticRegressionCV estimator.
          """
          solver = _check_solver(self.solver, self.penalty, self.dual)
  
          if not isinstance(self.max_iter, numbers.Number) or self.max_iter < 0:
              raise ValueError(
                  "Maximum number of iteration must be positive; got (max_iter=%r)"
                  % self.max_iter
              )
          if not isinstance(self.tol, numbers.Number) or self.tol < 0:
              raise ValueError(
                  "Tolerance for stopping criteria must be positive; got (tol=%r)"
                  % self.tol
              )
          if self.penalty == "elasticnet":
              if (
                  self.l1_ratios is None
                  or len(self.l1_ratios) == 0
                  or any(
                      (
                          not isinstance(l1_ratio, numbers.Number)
                          or l1_ratio < 0
                          or l1_ratio > 1
                      )
                      for l1_ratio in self.l1_ratios
                  )
              ):
                  raise ValueError(
                      "l1_ratios must be a list of numbers between "
                      "0 and 1; got (l1_ratios=%r)"
                      % self.l1_ratios
                  )
              l1_ratios_ = self.l1_ratios
          else:
              if self.l1_ratios is not None:
                  warnings.warn(
                      "l1_ratios parameter is only used when penalty "
                      "is 'elasticnet'. Got (penalty={})".format(self.penalty)
                  )
  
              l1_ratios_ = [None]
  
          if self.penalty == "none":
              raise ValueError(
                  "penalty='none' is not useful and not supported by "
                  "LogisticRegressionCV."
              )
  
          X, y = self._validate_data(
              X,
              y,
              accept_sparse="csr",
              dtype=np.float64,
              order="C",
              accept_large_sparse=solver not in ["liblinear", "sag", "saga"],
          )
          check_classification_targets(y)
  
          class_weight = self.class_weight
  
          # Encode for string labels
          label_encoder = LabelEncoder().fit(y)
          y = label_encoder.transform(y)
          if isinstance(class_weight, dict):
              class_weight = {
                  label_encoder.transform([cls])[0]: v for cls, v in class_weight.items()
              }
  
          # The original class labels
          classes = self.classes_ = label_encoder.classes_
          encoded_labels = label_encoder.transform(label_encoder.classes_)
  
          multi_class = _check_multi_class(self.multi_class, solver, len(classes))
  
          if solver in ["sag", "saga"]:
              max_squared_sum = row_norms(X, squared=True).max()
          else:
              max_squared_sum = None
  
          # init cross-validation generator
          cv = check_cv(self.cv, y, classifier=True)
          folds = list(cv.split(X, y))
  
          # Use the label encoded classes
          n_classes = len(encoded_labels)
  
          if n_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]
              )
  
          if n_classes == 2:
              # OvR in case of binary problems is as good as fitting
              # the higher label
              n_classes = 1
              encoded_labels = encoded_labels[1:]
              classes = classes[1:]
  
          # We need this hack to iterate only once over labels, in the case of
          # multi_class = multinomial, without changing the value of the labels.
          if multi_class == "multinomial":
              iter_encoded_labels = iter_classes = [None]
          else:
              iter_encoded_labels = encoded_labels
              iter_classes = classes
  
          # compute the class weights for the entire dataset y
          if class_weight == "balanced":
              class_weight = compute_class_weight(
                  class_weight, classes=np.arange(len(self.classes_)), y=y
              )
              class_weight = dict(enumerate(class_weight))
  
          path_func = delayed(_log_reg_scoring_path)
  
          # The SAG solver releases the GIL so it's more efficient to use
          # threads for this solver.
          if self.solver in ["sag", "saga"]:
              prefer = "threads"
          else:
              prefer = "processes"
  
          fold_coefs_ = Parallel(
              n_jobs=self.n_jobs,
              verbose=self.verbose,
              **_joblib_parallel_args(prefer=prefer),
          )(
              path_func(
                  X,
                  y,
                  train,
                  test,
                  pos_class=label,
                  Cs=self.Cs,
                  fit_intercept=self.fit_intercept,
                  penalty=self.penalty,
                  dual=self.dual,
                  solver=solver,
                  tol=self.tol,
                  max_iter=self.max_iter,
                  verbose=self.verbose,
                  class_weight=class_weight,
                  scoring=self.scoring,
                  multi_class=multi_class,
                  intercept_scaling=self.intercept_scaling,
                  random_state=self.random_state,
                  max_squared_sum=max_squared_sum,
                  sample_weight=sample_weight,
                  l1_ratio=l1_ratio,
              )
              for label in iter_encoded_labels
              for train, test in folds
              for l1_ratio in l1_ratios_
          )
  
          # _log_reg_scoring_path will output different shapes depending on the
          # multi_class param, so we need to reshape the outputs accordingly.
          # Cs is of shape (n_classes . n_folds . n_l1_ratios, n_Cs) and all the
          # rows are equal, so we just take the first one.
          # After reshaping,
          # - scores is of shape (n_classes, n_folds, n_Cs . n_l1_ratios)
          # - coefs_paths is of shape
          #  (n_classes, n_folds, n_Cs . n_l1_ratios, n_features)
          # - n_iter is of shape
          #  (n_classes, n_folds, n_Cs . n_l1_ratios) or
          #  (1, n_folds, n_Cs . n_l1_ratios)
          coefs_paths, Cs, scores, n_iter_ = zip(*fold_coefs_)
          self.Cs_ = Cs[0]
          if multi_class == "multinomial":
              coefs_paths = np.reshape(
                  coefs_paths,
                  (len(folds), len(l1_ratios_) * len(self.Cs_), n_classes, -1),
              )
              # equiv to coefs_paths = np.moveaxis(coefs_paths, (0, 1, 2, 3),
              #                                                 (1, 2, 0, 3))
              coefs_paths = np.swapaxes(coefs_paths, 0, 1)
              coefs_paths = np.swapaxes(coefs_paths, 0, 2)
              self.n_iter_ = np.reshape(
                  n_iter_, (1, len(folds), len(self.Cs_) * len(l1_ratios_))
              )
              # repeat same scores across all classes
              scores = np.tile(scores, (n_classes, 1, 1))
          else:
              coefs_paths = np.reshape(
                  coefs_paths,
                  (n_classes, len(folds), len(self.Cs_) * len(l1_ratios_), -1),
              )
              self.n_iter_ = np.reshape(
                  n_iter_, (n_classes, len(folds), len(self.Cs_) * len(l1_ratios_))
              )
          scores = np.reshape(scores, (n_classes, len(folds), -1))
          self.scores_ = dict(zip(classes, scores))
          self.coefs_paths_ = dict(zip(classes, coefs_paths))
  
          self.C_ = list()
          self.l1_ratio_ = list()
          self.coef_ = np.empty((n_classes, X.shape[1]))
          self.intercept_ = np.zeros(n_classes)
          for index, (cls, encoded_label) in enumerate(
              zip(iter_classes, iter_encoded_labels)
          ):
  
              if multi_class == "ovr":
                  scores = self.scores_[cls]
                  coefs_paths = self.coefs_paths_[cls]
              else:
                  # For multinomial, all scores are the same across classes
                  scores = scores[0]
                  # coefs_paths will keep its original shape because
                  # logistic_regression_path expects it this way
  
              if self.refit:
                  # best_index is between 0 and (n_Cs . n_l1_ratios - 1)
                  # for example, with n_cs=2 and n_l1_ratios=3
                  # the layout of scores is
                  # [c1, c2, c1, c2, c1, c2]
                  #   l1_1 ,  l1_2 ,  l1_3
                  best_index = scores.sum(axis=0).argmax()
  
                  best_index_C = best_index % len(self.Cs_)
                  C_ = self.Cs_[best_index_C]
                  self.C_.append(C_)
  
                  best_index_l1 = best_index // len(self.Cs_)
                  l1_ratio_ = l1_ratios_[best_index_l1]
                  self.l1_ratio_.append(l1_ratio_)
  
                  if multi_class == "multinomial":
                      coef_init = np.mean(coefs_paths[:, :, best_index, :], axis=1)
                  else:
                      coef_init = np.mean(coefs_paths[:, best_index, :], axis=0)
  
                  # Note that y is label encoded and hence pos_class must be
                  # the encoded label / None (for 'multinomial')
                  w, _, _ = _logistic_regression_path(
                      X,
                      y,
                      pos_class=encoded_label,
                      Cs=[C_],
                      solver=solver,
                      fit_intercept=self.fit_intercept,
                      coef=coef_init,
                      max_iter=self.max_iter,
                      tol=self.tol,
                      penalty=self.penalty,
                      class_weight=class_weight,
                      multi_class=multi_class,
                      verbose=max(0, self.verbose - 1),
                      random_state=self.random_state,
                      check_input=False,
                      max_squared_sum=max_squared_sum,
                      sample_weight=sample_weight,
                      l1_ratio=l1_ratio_,
                  )
                  w = w[0]
  
              else:
                  # Take the best scores across every fold and the average of
                  # all coefficients corresponding to the best scores.
                  best_indices = np.argmax(scores, axis=1)
                  if multi_class == "ovr":
                      w = np.mean(
                          [coefs_paths[i, best_indices[i], :] for i in range(len(folds))],
                          axis=0,
                      )
                  else:
                      w = np.mean(
                          [
                              coefs_paths[:, i, best_indices[i], :]
                              for i in range(len(folds))
                          ],
                          axis=0,
                      )
  
                  best_indices_C = best_indices % len(self.Cs_)
                  self.C_.append(np.mean(self.Cs_[best_indices_C]))
  
                  if self.penalty == "elasticnet":
                      best_indices_l1 = best_indices // len(self.Cs_)
                      self.l1_ratio_.append(np.mean(l1_ratios_[best_indices_l1]))
                  else:
                      self.l1_ratio_.append(None)
  
              if multi_class == "multinomial":
                  self.C_ = np.tile(self.C_, n_classes)
                  self.l1_ratio_ = np.tile(self.l1_ratio_, n_classes)
                  self.coef_ = w[:, : X.shape[1]]
                  if self.fit_intercept:
                      self.intercept_ = w[:, -1]
              else:
                  self.coef_[index] = w[: X.shape[1]]
                  if self.fit_intercept:
                      self.intercept_[index] = w[-1]
  
          self.C_ = np.asarray(self.C_)
          self.l1_ratio_ = np.asarray(self.l1_ratio_)
          self.l1_ratios_ = np.asarray(l1_ratios_)
          # if elasticnet was used, add the l1_ratios dimension to some
          # attributes
          if self.l1_ratios is not None:
              # with n_cs=2 and n_l1_ratios=3
              # the layout of scores is
              # [c1, c2, c1, c2, c1, c2]
              #   l1_1 ,  l1_2 ,  l1_3
              # To get a 2d array with the following layout
              #      l1_1, l1_2, l1_3
              # c1 [[ .  ,  .  ,  .  ],
              # c2  [ .  ,  .  ,  .  ]]
              # We need to first reshape and then transpose.
              # The same goes for the other arrays
              for cls, coefs_path in self.coefs_paths_.items():
                  self.coefs_paths_[cls] = coefs_path.reshape(
                      (len(folds), self.l1_ratios_.size, self.Cs_.size, -1)
                  )
                  self.coefs_paths_[cls] = np.transpose(
                      self.coefs_paths_[cls], (0, 2, 1, 3)
                  )
              for cls, score in self.scores_.items():
                  self.scores_[cls] = score.reshape(
                      (len(folds), self.l1_ratios_.size, self.Cs_.size)
                  )
                  self.scores_[cls] = np.transpose(self.scores_[cls], (0, 2, 1))
  
              self.n_iter_ = self.n_iter_.reshape(
                  (-1, len(folds), self.l1_ratios_.size, self.Cs_.size)
              )
              self.n_iter_ = np.transpose(self.n_iter_, (0, 1, 3, 2))
  
          return self
  
      def score(self, X, y, sample_weight=None):
          """Score using the `scoring` option on the given test data and labels.
  
          Parameters
          ----------
          X : array-like of shape (n_samples, n_features)
              Test samples.
  
          y : array-like of shape (n_samples,)
              True labels for X.
  
          sample_weight : array-like of shape (n_samples,), default=None
              Sample weights.
  
          Returns
          -------
          score : float
              Score of self.predict(X) wrt. y.
          """
          scoring = self.scoring or "accuracy"
          scoring = get_scorer(scoring)
  
          return scoring(self, X, y, sample_weight=sample_weight)
  
      def _more_tags(self):
          return {
              "_xfail_checks": {
                  "check_sample_weights_invariance": (
                      "zero sample_weight is not equivalent to removing samples"
                  ),
              }
          }
  
apis: numpy.ones numpy.asarray scipy.sparse.dia_matrix numpy.transpose numpy.append numpy.reshape numpy.empty_like numpy.expand_dims numpy.unique numpy.mean numpy.tile numpy.zeros scipy.optimize.minimize numpy.linalg.multi_dot numpy.argmax numpy.hstack scipy.special.logsumexp numpy.empty scipy.sparse.issparse numpy.swapaxes numpy.exp scipy.special.expit numpy.logspace numpy.array numpy.dot