content: # Authors: Peter Prettenhofer <peter.prettenhofer@gmail.com> (main author)
  #          Mathieu Blondel (partial_fit support)
  #
  # License: BSD 3 clause
  """Classification and regression using Stochastic Gradient Descent (SGD)."""
  
  import numpy as np
  
  from abc import ABCMeta, abstractmethod
  
  from ..externals.joblib import Parallel, delayed
  
  from .base import LinearClassifierMixin, SparseCoefMixin
  from .base import make_dataset
  from ..base import BaseEstimator, RegressorMixin
  from ..utils import check_array, check_random_state, check_X_y
  from ..utils.extmath import safe_sparse_dot
  from ..utils.multiclass import _check_partial_fit_first_call
  from ..utils.validation import check_is_fitted
  from ..externals import six
  
  from .sgd_fast import plain_sgd, average_sgd
  from ..utils.fixes import astype
  from ..utils import compute_class_weight
  from ..utils import deprecated
  from .sgd_fast import Hinge
  from .sgd_fast import SquaredHinge
  from .sgd_fast import Log
  from .sgd_fast import ModifiedHuber
  from .sgd_fast import SquaredLoss
  from .sgd_fast import Huber
  from .sgd_fast import EpsilonInsensitive
  from .sgd_fast import SquaredEpsilonInsensitive
  
  
  LEARNING_RATE_TYPES = {"constant": 1, "optimal": 2, "invscaling": 3,
                         "pa1": 4, "pa2": 5}
  
  PENALTY_TYPES = {"none": 0, "l2": 2, "l1": 1, "elasticnet": 3}
  
  DEFAULT_EPSILON = 0.1
  # Default value of ``epsilon`` parameter.
  
  
  class BaseSGD(six.with_metaclass(ABCMeta, BaseEstimator, SparseCoefMixin)):
      """Base class for SGD classification and regression."""
  
      def __init__(self, loss, penalty='l2', alpha=0.0001, C=1.0,
                   l1_ratio=0.15, fit_intercept=True, n_iter=5, shuffle=True,
                   verbose=0, epsilon=0.1, random_state=None,
                   learning_rate="optimal", eta0=0.0, power_t=0.5,
                   warm_start=False, average=False):
          self.loss = loss
          self.penalty = penalty
          self.learning_rate = learning_rate
          self.epsilon = epsilon
          self.alpha = alpha
          self.C = C
          self.l1_ratio = l1_ratio
          self.fit_intercept = fit_intercept
          self.n_iter = n_iter
          self.shuffle = shuffle
          self.random_state = random_state
          self.verbose = verbose
          self.eta0 = eta0
          self.power_t = power_t
          self.warm_start = warm_start
          self.average = average
  
          self._validate_params()
  
      def set_params(self, *args, **kwargs):
          super(BaseSGD, self).set_params(*args, **kwargs)
          self._validate_params()
          return self
  
      @abstractmethod
      def fit(self, X, y):
          """Fit model."""
  
      def _validate_params(self):
          """Validate input params. """
          if not isinstance(self.shuffle, bool):
              raise ValueError("shuffle must be either True or False")
          if self.n_iter <= 0:
              raise ValueError("n_iter must be > zero")
          if not (0.0 <= self.l1_ratio <= 1.0):
              raise ValueError("l1_ratio must be in [0, 1]")
          if self.alpha < 0.0:
              raise ValueError("alpha must be >= 0")
          if self.learning_rate in ("constant", "invscaling"):
              if self.eta0 <= 0.0:
                  raise ValueError("eta0 must be > 0")
          if self.learning_rate == "optimal" and self.alpha == 0:
              raise ValueError("alpha must be > 0 since "
                               "learning_rate is 'optimal'. alpha is used "
                               "to compute the optimal learning rate.")
  
          # raises ValueError if not registered
          self._get_penalty_type(self.penalty)
          self._get_learning_rate_type(self.learning_rate)
  
          if self.loss not in self.loss_functions:
              raise ValueError("The loss %s is not supported. " % self.loss)
  
      def _get_loss_function(self, loss):
          """Get concrete ``LossFunction`` object for str ``loss``. """
          try:
              loss_ = self.loss_functions[loss]
              loss_class, args = loss_[0], loss_[1:]
              if loss in ('huber', 'epsilon_insensitive',
                          'squared_epsilon_insensitive'):
                  args = (self.epsilon, )
              return loss_class(*args)
          except KeyError:
              raise ValueError("The loss %s is not supported. " % loss)
  
      def _get_learning_rate_type(self, learning_rate):
          try:
              return LEARNING_RATE_TYPES[learning_rate]
          except KeyError:
              raise ValueError("learning rate %s "
                               "is not supported. " % learning_rate)
  
      def _get_penalty_type(self, penalty):
          penalty = str(penalty).lower()
          try:
              return PENALTY_TYPES[penalty]
          except KeyError:
              raise ValueError("Penalty %s is not supported. " % penalty)
  
      def _validate_sample_weight(self, sample_weight, n_samples):
          """Set the sample weight array."""
          if sample_weight is None:
              # uniform sample weights
              sample_weight = np.ones(n_samples, dtype=np.float64, order='C')
          else:
              # user-provided array
              sample_weight = np.asarray(sample_weight, dtype=np.float64,
                                         order="C")
          if sample_weight.shape[0] != n_samples:
              raise ValueError("Shapes of X and sample_weight do not match.")
          return sample_weight
  
      def _allocate_parameter_mem(self, n_classes, n_features, coef_init=None,
                                  intercept_init=None):
          """Allocate mem for parameters; initialize if provided."""
          if n_classes > 2:
              # allocate coef_ for multi-class
              if coef_init is not None:
                  coef_init = np.asarray(coef_init, order="C")
                  if coef_init.shape != (n_classes, n_features):
                      raise ValueError("Provided ``coef_`` does not match "
                                       "dataset. ")
                  self.coef_ = coef_init
              else:
                  self.coef_ = np.zeros((n_classes, n_features),
                                        dtype=np.float64, order="C")
  
              # allocate intercept_ for multi-class
              if intercept_init is not None:
                  intercept_init = np.asarray(intercept_init, order="C")
                  if intercept_init.shape != (n_classes, ):
                      raise ValueError("Provided intercept_init "
                                       "does not match dataset.")
                  self.intercept_ = intercept_init
              else:
                  self.intercept_ = np.zeros(n_classes, dtype=np.float64,
                                             order="C")
          else:
              # allocate coef_ for binary problem
              if coef_init is not None:
                  coef_init = np.asarray(coef_init, dtype=np.float64,
                                         order="C")
                  coef_init = coef_init.ravel()
                  if coef_init.shape != (n_features,):
                      raise ValueError("Provided coef_init does not "
                                       "match dataset.")
                  self.coef_ = coef_init
              else:
                  self.coef_ = np.zeros(n_features,
                                        dtype=np.float64,
                                        order="C")
  
              # allocate intercept_ for binary problem
              if intercept_init is not None:
                  intercept_init = np.asarray(intercept_init, dtype=np.float64)
                  if intercept_init.shape != (1,) and intercept_init.shape != ():
                      raise ValueError("Provided intercept_init "
                                       "does not match dataset.")
                  self.intercept_ = intercept_init.reshape(1,)
              else:
                  self.intercept_ = np.zeros(1, dtype=np.float64, order="C")
  
          # initialize average parameters
          if self.average > 0:
              self.standard_coef_ = self.coef_
              self.standard_intercept_ = self.intercept_
              self.average_coef_ = np.zeros(self.coef_.shape,
                                            dtype=np.float64,
                                            order="C")
              self.average_intercept_ = np.zeros(self.standard_intercept_.shape,
                                                 dtype=np.float64,
                                                 order="C")
  
  
  def _prepare_fit_binary(est, y, i):
      """Initialization for fit_binary.
  
      Returns y, coef, intercept.
      """
      y_i = np.ones(y.shape, dtype=np.float64, order="C")
      y_i[y != est.classes_[i]] = -1.0
      average_intercept = 0
      average_coef = None
  
      if len(est.classes_) == 2:
          if not est.average:
              coef = est.coef_.ravel()
              intercept = est.intercept_[0]
          else:
              coef = est.standard_coef_.ravel()
              intercept = est.standard_intercept_[0]
              average_coef = est.average_coef_.ravel()
              average_intercept = est.average_intercept_[0]
      else:
          if not est.average:
              coef = est.coef_[i]
              intercept = est.intercept_[i]
          else:
              coef = est.standard_coef_[i]
              intercept = est.standard_intercept_[i]
              average_coef = est.average_coef_[i]
              average_intercept = est.average_intercept_[i]
  
      return y_i, coef, intercept, average_coef, average_intercept
  
  
  def fit_binary(est, i, X, y, alpha, C, learning_rate, n_iter,
                 pos_weight, neg_weight, sample_weight):
      """Fit a single binary classifier.
  
      The i'th class is considered the "positive" class.
      """
      # if average is not true, average_coef, and average_intercept will be
      # unused
      y_i, coef, intercept, average_coef, average_intercept = \
          _prepare_fit_binary(est, y, i)
      assert y_i.shape[0] == y.shape[0] == sample_weight.shape[0]
      dataset, intercept_decay = make_dataset(X, y_i, sample_weight)
  
      penalty_type = est._get_penalty_type(est.penalty)
      learning_rate_type = est._get_learning_rate_type(learning_rate)
  
      # XXX should have random_state_!
      random_state = check_random_state(est.random_state)
      # numpy mtrand expects a C long which is a signed 32 bit integer under
      # Windows
      seed = random_state.randint(0, np.iinfo(np.int32).max)
  
      if not est.average:
          return plain_sgd(coef, intercept, est.loss_function_,
                           penalty_type, alpha, C, est.l1_ratio,
                           dataset, n_iter, int(est.fit_intercept),
                           int(est.verbose), int(est.shuffle), seed,
                           pos_weight, neg_weight,
                           learning_rate_type, est.eta0,
                           est.power_t, est.t_, intercept_decay)
  
      else:
          standard_coef, standard_intercept, average_coef, \
              average_intercept = average_sgd(coef, intercept, average_coef,
                                              average_intercept,
                                              est.loss_function_, penalty_type,
                                              alpha, C, est.l1_ratio, dataset,
                                              n_iter, int(est.fit_intercept),
                                              int(est.verbose), int(est.shuffle),
                                              seed, pos_weight, neg_weight,
                                              learning_rate_type, est.eta0,
                                              est.power_t, est.t_,
                                              intercept_decay,
                                              est.average)
  
          if len(est.classes_) == 2:
              est.average_intercept_[0] = average_intercept
          else:
              est.average_intercept_[i] = average_intercept
  
          return standard_coef, standard_intercept
  
  
  class BaseSGDClassifier(six.with_metaclass(ABCMeta, BaseSGD,
                                             LinearClassifierMixin)):
  
      loss_functions = {
          "hinge": (Hinge, 1.0),
          "squared_hinge": (SquaredHinge, 1.0),
          "perceptron": (Hinge, 0.0),
          "log": (Log, ),
          "modified_huber": (ModifiedHuber, ),
          "squared_loss": (SquaredLoss, ),
          "huber": (Huber, DEFAULT_EPSILON),
          "epsilon_insensitive": (EpsilonInsensitive, DEFAULT_EPSILON),
          "squared_epsilon_insensitive": (SquaredEpsilonInsensitive,
                                          DEFAULT_EPSILON),
      }
  
      @abstractmethod
      def __init__(self, loss="hinge", penalty='l2', alpha=0.0001, l1_ratio=0.15,
                   fit_intercept=True, n_iter=5, shuffle=True, verbose=0,
                   epsilon=DEFAULT_EPSILON, n_jobs=1, random_state=None,
                   learning_rate="optimal", eta0=0.0, power_t=0.5,
                   class_weight=None, warm_start=False, average=False):
  
          super(BaseSGDClassifier, self).__init__(loss=loss, penalty=penalty,
                                                  alpha=alpha, l1_ratio=l1_ratio,
                                                  fit_intercept=fit_intercept,
                                                  n_iter=n_iter, shuffle=shuffle,
                                                  verbose=verbose,
                                                  epsilon=epsilon,
                                                  random_state=random_state,
                                                  learning_rate=learning_rate,
                                                  eta0=eta0, power_t=power_t,
                                                  warm_start=warm_start,
                                                  average=average)
          self.class_weight = class_weight
          self.n_jobs = int(n_jobs)
  
      @property
      @deprecated("Attribute loss_function was deprecated in version 0.19 and "
                  "will be removed in 0.21. Use 'loss_function_' instead")
      def loss_function(self):
          return self.loss_function_
  
      def _partial_fit(self, X, y, alpha, C,
                       loss, learning_rate, n_iter,
                       classes, sample_weight,
                       coef_init, intercept_init):
          X, y = check_X_y(X, y, 'csr', dtype=np.float64, order="C")
  
          n_samples, n_features = X.shape
  
          self._validate_params()
          _check_partial_fit_first_call(self, classes)
  
          n_classes = self.classes_.shape[0]
  
          # Allocate datastructures from input arguments
          self._expanded_class_weight = compute_class_weight(self.class_weight,
                                                             self.classes_, y)
          sample_weight = self._validate_sample_weight(sample_weight, n_samples)
  
          if getattr(self, "coef_", None) is None or coef_init is not None:
              self._allocate_parameter_mem(n_classes, n_features,
                                           coef_init, intercept_init)
          elif n_features != self.coef_.shape[-1]:
              raise ValueError("Number of features %d does not match previous "
                               "data %d." % (n_features, self.coef_.shape[-1]))
  
          self.loss_function_ = self._get_loss_function(loss)
          if not hasattr(self, "t_"):
              self.t_ = 1.0
  
          # delegate to concrete training procedure
          if n_classes > 2:
              self._fit_multiclass(X, y, alpha=alpha, C=C,
                                   learning_rate=learning_rate,
                                   sample_weight=sample_weight, n_iter=n_iter)
          elif n_classes == 2:
              self._fit_binary(X, y, alpha=alpha, C=C,
                               learning_rate=learning_rate,
                               sample_weight=sample_weight, n_iter=n_iter)
          else:
              raise ValueError("The number of class labels must be "
                               "greater than one.")
  
          return self
  
      def _fit(self, X, y, alpha, C, loss, learning_rate, coef_init=None,
               intercept_init=None, sample_weight=None):
          if hasattr(self, "classes_"):
              self.classes_ = None
  
          X, y = check_X_y(X, y, 'csr', dtype=np.float64, order="C")
          n_samples, n_features = X.shape
  
          # labels can be encoded as float, int, or string literals
          # np.unique sorts in asc order; largest class id is positive class
          classes = np.unique(y)
  
          if self.warm_start and hasattr(self, "coef_"):
              if coef_init is None:
                  coef_init = self.coef_
              if intercept_init is None:
                  intercept_init = self.intercept_
          else:
              self.coef_ = None
              self.intercept_ = None
  
          if self.average > 0:
              self.standard_coef_ = self.coef_
              self.standard_intercept_ = self.intercept_
              self.average_coef_ = None
              self.average_intercept_ = None
  
          # Clear iteration count for multiple call to fit.
          self.t_ = 1.0
  
          self._partial_fit(X, y, alpha, C, loss, learning_rate, self.n_iter,
                            classes, sample_weight, coef_init, intercept_init)
  
          return self
  
      def _fit_binary(self, X, y, alpha, C, sample_weight,
                      learning_rate, n_iter):
          """Fit a binary classifier on X and y. """
          coef, intercept = fit_binary(self, 1, X, y, alpha, C,
                                       learning_rate, n_iter,
                                       self._expanded_class_weight[1],
                                       self._expanded_class_weight[0],
                                       sample_weight)
  
          self.t_ += n_iter * X.shape[0]
  
          # need to be 2d
          if self.average > 0:
              if self.average <= self.t_ - 1:
                  self.coef_ = self.average_coef_.reshape(1, -1)
                  self.intercept_ = self.average_intercept_
              else:
                  self.coef_ = self.standard_coef_.reshape(1, -1)
                  self.standard_intercept_ = np.atleast_1d(intercept)
                  self.intercept_ = self.standard_intercept_
          else:
              self.coef_ = coef.reshape(1, -1)
              # intercept is a float, need to convert it to an array of length 1
              self.intercept_ = np.atleast_1d(intercept)
  
      def _fit_multiclass(self, X, y, alpha, C, learning_rate,
                          sample_weight, n_iter):
          """Fit a multi-class classifier by combining binary classifiers
  
          Each binary classifier predicts one class versus all others. This
          strategy is called OVA: One Versus All.
          """
          # Use joblib to fit OvA in parallel.
          result = Parallel(n_jobs=self.n_jobs, backend="threading",
                            verbose=self.verbose)(
              delayed(fit_binary)(self, i, X, y, alpha, C, learning_rate,
                                  n_iter, self._expanded_class_weight[i], 1.,
                                  sample_weight)
              for i in range(len(self.classes_)))
  
          for i, (_, intercept) in enumerate(result):
              self.intercept_[i] = intercept
  
          self.t_ += n_iter * X.shape[0]
  
          if self.average > 0:
              if self.average <= self.t_ - 1.0:
                  self.coef_ = self.average_coef_
                  self.intercept_ = self.average_intercept_
              else:
                  self.coef_ = self.standard_coef_
                  self.standard_intercept_ = np.atleast_1d(self.intercept_)
                  self.intercept_ = self.standard_intercept_
  
      def partial_fit(self, X, y, classes=None, sample_weight=None):
          """Fit linear model with Stochastic Gradient Descent.
  
          Parameters
          ----------
          X : {array-like, sparse matrix}, shape (n_samples, n_features)
              Subset of the training data
  
          y : numpy array, shape (n_samples,)
              Subset of the target values
  
          classes : array, shape (n_classes,)
              Classes across all calls to partial_fit.
              Can be obtained by via `np.unique(y_all)`, where y_all is the
              target vector of the entire dataset.
              This argument is required for the first call to partial_fit
              and can be omitted in the subsequent calls.
              Note that y doesn't need to contain all labels in `classes`.
  
          sample_weight : array-like, shape (n_samples,), optional
              Weights applied to individual samples.
              If not provided, uniform weights are assumed.
  
          Returns
          -------
          self : returns an instance of self.
          """
          if self.class_weight in ['balanced']:
              raise ValueError("class_weight '{0}' is not supported for "
                               "partial_fit. In order to use 'balanced' weights,"
                               " use compute_class_weight('{0}', classes, y). "
                               "In place of y you can us a large enough sample "
                               "of the full training set target to properly "
                               "estimate the class frequency distributions. "
                               "Pass the resulting weights as the class_weight "
                               "parameter.".format(self.class_weight))
          return self._partial_fit(X, y, alpha=self.alpha, C=1.0, loss=self.loss,
                                   learning_rate=self.learning_rate, n_iter=1,
                                   classes=classes, sample_weight=sample_weight,
                                   coef_init=None, intercept_init=None)
  
      def fit(self, X, y, coef_init=None, intercept_init=None,
              sample_weight=None):
          """Fit linear model with Stochastic Gradient Descent.
  
          Parameters
          ----------
          X : {array-like, sparse matrix}, shape (n_samples, n_features)
              Training data
  
          y : numpy array, shape (n_samples,)
              Target values
  
          coef_init : array, shape (n_classes, n_features)
              The initial coefficients to warm-start the optimization.
  
          intercept_init : array, shape (n_classes,)
              The initial intercept to warm-start the optimization.
  
          sample_weight : array-like, shape (n_samples,), optional
              Weights applied to individual samples.
              If not provided, uniform weights are assumed. These weights will
              be multiplied with class_weight (passed through the
              constructor) if class_weight is specified
  
          Returns
          -------
          self : returns an instance of self.
          """
          return self._fit(X, y, alpha=self.alpha, C=1.0,
                           loss=self.loss, learning_rate=self.learning_rate,
                           coef_init=coef_init, intercept_init=intercept_init,
                           sample_weight=sample_weight)
  
  
  class SGDClassifier(BaseSGDClassifier):
      """Linear classifiers (SVM, logistic regression, a.o.) with SGD training.
  
      This estimator implements regularized linear models with stochastic
      gradient descent (SGD) learning: the gradient of the loss is estimated
      each sample at a time and the model is updated along the way with a
      decreasing strength schedule (aka learning rate). SGD allows minibatch
      (online/out-of-core) learning, see the partial_fit method.
      For best results using the default learning rate schedule, the data should
      have zero mean and unit variance.
  
      This implementation works with data represented as dense or sparse arrays
      of floating point values for the features. The model it fits can be
      controlled with the loss parameter; by default, it fits a linear support
      vector machine (SVM).
  
      The regularizer is a penalty added to the loss function that shrinks model
      parameters towards the zero vector using either the squared euclidean norm
      L2 or the absolute norm L1 or a combination of both (Elastic Net). If the
      parameter update crosses the 0.0 value because of the regularizer, the
      update is truncated to 0.0 to allow for learning sparse models and achieve
      online feature selection.
  
      Read more in the :ref:`User Guide <sgd>`.
  
      Parameters
      ----------
      loss : str, 'hinge', 'log', 'modified_huber', 'squared_hinge',\
                  'perceptron', or a regression loss: 'squared_loss', 'huber',\
                  'epsilon_insensitive', or 'squared_epsilon_insensitive'
          The loss function to be used. Defaults to 'hinge', which gives a
          linear SVM.
          The 'log' loss gives logistic regression, a probabilistic classifier.
          'modified_huber' is another smooth loss that brings tolerance to
          outliers as well as probability estimates.
          'squared_hinge' is like hinge but is quadratically penalized.
          'perceptron' is the linear loss used by the perceptron algorithm.
          The other losses are designed for regression but can be useful in
          classification as well; see SGDRegressor for a description.
  
      penalty : str, 'none', 'l2', 'l1', or 'elasticnet'
          The penalty (aka regularization term) to be used. Defaults to 'l2'
          which is the standard regularizer for linear SVM models. 'l1' and
          'elasticnet' might bring sparsity to the model (feature selection)
          not achievable with 'l2'.
  
      alpha : float
          Constant that multiplies the regularization term. Defaults to 0.0001
          Also used to compute learning_rate when set to 'optimal'.
  
      l1_ratio : float
          The Elastic Net mixing parameter, with 0 <= l1_ratio <= 1.
          l1_ratio=0 corresponds to L2 penalty, l1_ratio=1 to L1.
          Defaults to 0.15.
  
      fit_intercept : bool
          Whether the intercept should be estimated or not. If False, the
          data is assumed to be already centered. Defaults to True.
  
      n_iter : int, optional
          The number of passes over the training data (aka epochs). The number
          of iterations is set to 1 if using partial_fit.
          Defaults to 5.
  
      shuffle : bool, optional
          Whether or not the training data should be shuffled after each epoch.
          Defaults to True.
  
      random_state : int seed, RandomState instance, or None (default)
          The seed of the pseudo random number generator to use when
          shuffling the data.
  
      verbose : integer, optional
          The verbosity level
  
      epsilon : float
          Epsilon in the epsilon-insensitive loss functions; only if `loss` is
          'huber', 'epsilon_insensitive', or 'squared_epsilon_insensitive'.
          For 'huber', determines the threshold at which it becomes less
          important to get the prediction exactly right.
          For epsilon-insensitive, any differences between the current prediction
          and the correct label are ignored if they are less than this threshold.
  
      n_jobs : integer, optional
          The number of CPUs to use to do the OVA (One Versus All, for
          multi-class problems) computation. -1 means 'all CPUs'. Defaults
          to 1.
  
      learning_rate : string, optional
          The learning rate schedule:
  
          - 'constant': eta = eta0
          - 'optimal': eta = 1.0 / (alpha * (t + t0)) [default]
          - 'invscaling': eta = eta0 / pow(t, power_t)
  
          where t0 is chosen by a heuristic proposed by Leon Bottou.
  
      eta0 : double
          The initial learning rate for the 'constant' or 'invscaling'
          schedules. The default value is 0.0 as eta0 is not used by the
          default schedule 'optimal'.
  
      power_t : double
          The exponent for inverse scaling learning rate [default 0.5].
  
      class_weight : dict, {class_label: weight} or "balanced" or None, optional
          Preset for the class_weight fit parameter.
  
          Weights associated with classes. 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))``
  
      warm_start : bool, optional
          When set to True, reuse the solution of the previous call to fit as
          initialization, otherwise, just erase the previous solution.
  
      average : bool or int, optional
          When set to True, computes the averaged SGD weights and stores the
          result in the ``coef_`` attribute. If set to an int greater than 1,
          averaging will begin once the total number of samples seen reaches
          average. So ``average=10`` will begin averaging after seeing 10
          samples.
  
      Attributes
      ----------
      coef_ : array, shape (1, n_features) if n_classes == 2 else (n_classes,\
              n_features)
          Weights assigned to the features.
  
      intercept_ : array, shape (1,) if n_classes == 2 else (n_classes,)
          Constants in decision function.
  
      loss_function_ : concrete ``LossFunction``
  
      Examples
      --------
      >>> import numpy as np
      >>> from sklearn import linear_model
      >>> X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]])
      >>> Y = np.array([1, 1, 2, 2])
      >>> clf = linear_model.SGDClassifier()
      >>> clf.fit(X, Y)
      ... #doctest: +NORMALIZE_WHITESPACE
      SGDClassifier(alpha=0.0001, average=False, class_weight=None, epsilon=0.1,
              eta0=0.0, fit_intercept=True, l1_ratio=0.15,
              learning_rate='optimal', loss='hinge', n_iter=5, n_jobs=1,
              penalty='l2', power_t=0.5, random_state=None, shuffle=True,
              verbose=0, warm_start=False)
      >>> print(clf.predict([[-0.8, -1]]))
      [1]
  
      See also
      --------
      LinearSVC, LogisticRegression, Perceptron
  
      """
  
      def __init__(self, loss="hinge", penalty='l2', alpha=0.0001, l1_ratio=0.15,
                   fit_intercept=True, n_iter=5, shuffle=True, verbose=0,
                   epsilon=DEFAULT_EPSILON, n_jobs=1, random_state=None,
                   learning_rate="optimal", eta0=0.0, power_t=0.5,
                   class_weight=None, warm_start=False, average=False):
          super(SGDClassifier, self).__init__(
              loss=loss, penalty=penalty, alpha=alpha, l1_ratio=l1_ratio,
              fit_intercept=fit_intercept, n_iter=n_iter, shuffle=shuffle,
              verbose=verbose, epsilon=epsilon, n_jobs=n_jobs,
              random_state=random_state, learning_rate=learning_rate, eta0=eta0,
              power_t=power_t, class_weight=class_weight, warm_start=warm_start,
              average=average)
  
      def _check_proba(self):
          check_is_fitted(self, "t_")
  
          if self.loss not in ("log", "modified_huber"):
              raise AttributeError("probability estimates are not available for"
                                   " loss=%r" % self.loss)
  
      @property
      def predict_proba(self):
          """Probability estimates.
  
          This method is only available for log loss and modified Huber loss.
  
          Multiclass probability estimates are derived from binary (one-vs.-rest)
          estimates by simple normalization, as recommended by Zadrozny and
          Elkan.
  
          Binary probability estimates for loss="modified_huber" are given by
          (clip(decision_function(X), -1, 1) + 1) / 2. For other loss functions
          it is necessary to perform proper probability calibration by wrapping
          the classifier with
          :class:`sklearn.calibration.CalibratedClassifierCV` instead.
  
          Parameters
          ----------
          X : {array-like, sparse matrix}, shape (n_samples, n_features)
  
          Returns
          -------
          array, 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_`.
  
          References
          ----------
          Zadrozny and Elkan, "Transforming classifier scores into multiclass
          probability estimates", SIGKDD'02,
          http://www.research.ibm.com/people/z/zadrozny/kdd2002-Transf.pdf
  
          The justification for the formula in the loss="modified_huber"
          case is in the appendix B in:
          http://jmlr.csail.mit.edu/papers/volume2/zhang02c/zhang02c.pdf
          """
          self._check_proba()
          return self._predict_proba
  
      def _predict_proba(self, X):
          if self.loss == "log":
              return self._predict_proba_lr(X)
  
          elif self.loss == "modified_huber":
              binary = (len(self.classes_) == 2)
              scores = self.decision_function(X)
  
              if binary:
                  prob2 = np.ones((scores.shape[0], 2))
                  prob = prob2[:, 1]
              else:
                  prob = scores
  
              np.clip(scores, -1, 1, prob)
              prob += 1.
              prob /= 2.
  
              if binary:
                  prob2[:, 0] -= prob
                  prob = prob2
              else:
                  # the above might assign zero to all classes, which doesn't
                  # normalize neatly; work around this to produce uniform
                  # probabilities
                  prob_sum = prob.sum(axis=1)
                  all_zero = (prob_sum == 0)
                  if np.any(all_zero):
                      prob[all_zero, :] = 1
                      prob_sum[all_zero] = len(self.classes_)
  
                  # normalize
                  prob /= prob_sum.reshape((prob.shape[0], -1))
  
              return prob
  
          else:
              raise NotImplementedError("predict_(log_)proba only supported when"
                                        " loss='log' or loss='modified_huber' "
                                        "(%r given)" % self.loss)
  
      @property
      def predict_log_proba(self):
          """Log of probability estimates.
  
          This method is only available for log loss and modified Huber loss.
  
          When loss="modified_huber", probability estimates may be hard zeros
          and ones, so taking the logarithm is not possible.
  
          See ``predict_proba`` for details.
  
          Parameters
          ----------
          X : array-like, shape (n_samples, n_features)
  
          Returns
          -------
          T : array-like, 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_`.
          """
          self._check_proba()
          return self._predict_log_proba
  
      def _predict_log_proba(self, X):
          return np.log(self.predict_proba(X))
  
  
  class BaseSGDRegressor(BaseSGD, RegressorMixin):
  
      loss_functions = {
          "squared_loss": (SquaredLoss, ),
          "huber": (Huber, DEFAULT_EPSILON),
          "epsilon_insensitive": (EpsilonInsensitive, DEFAULT_EPSILON),
          "squared_epsilon_insensitive": (SquaredEpsilonInsensitive,
                                          DEFAULT_EPSILON),
      }
  
      @abstractmethod
      def __init__(self, loss="squared_loss", penalty="l2", alpha=0.0001,
                   l1_ratio=0.15, fit_intercept=True, n_iter=5, shuffle=True,
                   verbose=0, epsilon=DEFAULT_EPSILON, random_state=None,
                   learning_rate="invscaling", eta0=0.01, power_t=0.25,
                   warm_start=False, average=False):
          super(BaseSGDRegressor, self).__init__(loss=loss, penalty=penalty,
                                                 alpha=alpha, l1_ratio=l1_ratio,
                                                 fit_intercept=fit_intercept,
                                                 n_iter=n_iter, shuffle=shuffle,
                                                 verbose=verbose,
                                                 epsilon=epsilon,
                                                 random_state=random_state,
                                                 learning_rate=learning_rate,
                                                 eta0=eta0, power_t=power_t,
                                                 warm_start=warm_start,
                                                 average=average)
  
      def _partial_fit(self, X, y, alpha, C, loss, learning_rate,
                       n_iter, sample_weight,
                       coef_init, intercept_init):
          X, y = check_X_y(X, y, "csr", copy=False, order='C', dtype=np.float64)
          y = astype(y, np.float64, copy=False)
  
          n_samples, n_features = X.shape
  
          self._validate_params()
  
          # Allocate datastructures from input arguments
          sample_weight = self._validate_sample_weight(sample_weight, n_samples)
  
          if getattr(self, "coef_", None) is None:
              self._allocate_parameter_mem(1, n_features,
                                           coef_init, intercept_init)
          elif n_features != self.coef_.shape[-1]:
              raise ValueError("Number of features %d does not match previous "
                               "data %d." % (n_features, self.coef_.shape[-1]))
          if self.average > 0 and getattr(self, "average_coef_", None) is None:
              self.average_coef_ = np.zeros(n_features,
                                            dtype=np.float64,
                                            order="C")
              self.average_intercept_ = np.zeros(1,
                                                 dtype=np.float64,
                                                 order="C")
  
          self._fit_regressor(X, y, alpha, C, loss, learning_rate,
                              sample_weight, n_iter)
  
          return self
  
      def partial_fit(self, X, y, sample_weight=None):
          """Fit linear model with Stochastic Gradient Descent.
  
          Parameters
          ----------
          X : {array-like, sparse matrix}, shape (n_samples, n_features)
              Subset of training data
  
          y : numpy array of shape (n_samples,)
              Subset of target values
  
          sample_weight : array-like, shape (n_samples,), optional
              Weights applied to individual samples.
              If not provided, uniform weights are assumed.
  
          Returns
          -------
          self : returns an instance of self.
          """
          return self._partial_fit(X, y, self.alpha, C=1.0,
                                   loss=self.loss,
                                   learning_rate=self.learning_rate, n_iter=1,
                                   sample_weight=sample_weight,
                                   coef_init=None, intercept_init=None)
  
      def _fit(self, X, y, alpha, C, loss, learning_rate, coef_init=None,
               intercept_init=None, sample_weight=None):
          if self.warm_start and getattr(self, "coef_", None) is not None:
              if coef_init is None:
                  coef_init = self.coef_
              if intercept_init is None:
                  intercept_init = self.intercept_
          else:
              self.coef_ = None
              self.intercept_ = None
  
          if self.average > 0:
              self.standard_intercept_ = self.intercept_
              self.standard_coef_ = self.coef_
              self.average_coef_ = None
              self.average_intercept_ = None
  
          # Clear iteration count for multiple call to fit.
          self.t_ = 1.0
  
          return self._partial_fit(X, y, alpha, C, loss, learning_rate,
                                   self.n_iter, sample_weight,
                                   coef_init, intercept_init)
  
      def fit(self, X, y, coef_init=None, intercept_init=None,
              sample_weight=None):
          """Fit linear model with Stochastic Gradient Descent.
  
          Parameters
          ----------
          X : {array-like, sparse matrix}, shape (n_samples, n_features)
              Training data
  
          y : numpy array, shape (n_samples,)
              Target values
  
          coef_init : array, shape (n_features,)
              The initial coefficients to warm-start the optimization.
  
          intercept_init : array, shape (1,)
              The initial intercept to warm-start the optimization.
  
          sample_weight : array-like, shape (n_samples,), optional
              Weights applied to individual samples (1. for unweighted).
  
          Returns
          -------
          self : returns an instance of self.
          """
          return self._fit(X, y, alpha=self.alpha, C=1.0,
                           loss=self.loss, learning_rate=self.learning_rate,
                           coef_init=coef_init,
                           intercept_init=intercept_init,
                           sample_weight=sample_weight)
  
      def _decision_function(self, X):
          """Predict using the linear model
  
          Parameters
          ----------
          X : {array-like, sparse matrix}, shape (n_samples, n_features)
  
          Returns
          -------
          array, shape (n_samples,)
             Predicted target values per element in X.
          """
          check_is_fitted(self, ["t_", "coef_", "intercept_"], all_or_any=all)
  
          X = check_array(X, accept_sparse='csr')
  
          scores = safe_sparse_dot(X, self.coef_.T,
                                   dense_output=True) + self.intercept_
          return scores.ravel()
  
      def predict(self, X):
          """Predict using the linear model
  
          Parameters
          ----------
          X : {array-like, sparse matrix}, shape (n_samples, n_features)
  
          Returns
          -------
          array, shape (n_samples,)
             Predicted target values per element in X.
          """
          return self._decision_function(X)
  
      def _fit_regressor(self, X, y, alpha, C, loss, learning_rate,
                         sample_weight, n_iter):
          dataset, intercept_decay = make_dataset(X, y, sample_weight)
  
          loss_function = self._get_loss_function(loss)
          penalty_type = self._get_penalty_type(self.penalty)
          learning_rate_type = self._get_learning_rate_type(learning_rate)
  
          if not hasattr(self, "t_"):
              self.t_ = 1.0
  
          random_state = check_random_state(self.random_state)
          # numpy mtrand expects a C long which is a signed 32 bit integer under
          # Windows
          seed = random_state.randint(0, np.iinfo(np.int32).max)
  
          if self.average > 0:
              self.standard_coef_, self.standard_intercept_, \
                  self.average_coef_, self.average_intercept_ =\
                  average_sgd(self.standard_coef_,
                              self.standard_intercept_[0],
                              self.average_coef_,
                              self.average_intercept_[0],
                              loss_function,
                              penalty_type,
                              alpha, C,
                              self.l1_ratio,
                              dataset,
                              n_iter,
                              int(self.fit_intercept),
                              int(self.verbose),
                              int(self.shuffle),
                              seed,
                              1.0, 1.0,
                              learning_rate_type,
                              self.eta0, self.power_t, self.t_,
                              intercept_decay, self.average)
  
              self.average_intercept_ = np.atleast_1d(self.average_intercept_)
              self.standard_intercept_ = np.atleast_1d(self.standard_intercept_)
              self.t_ += n_iter * X.shape[0]
  
              if self.average <= self.t_ - 1.0:
                  self.coef_ = self.average_coef_
                  self.intercept_ = self.average_intercept_
              else:
                  self.coef_ = self.standard_coef_
                  self.intercept_ = self.standard_intercept_
  
          else:
              self.coef_, self.intercept_ = \
                  plain_sgd(self.coef_,
                            self.intercept_[0],
                            loss_function,
                            penalty_type,
                            alpha, C,
                            self.l1_ratio,
                            dataset,
                            n_iter,
                            int(self.fit_intercept),
                            int(self.verbose),
                            int(self.shuffle),
                            seed,
                            1.0, 1.0,
                            learning_rate_type,
                            self.eta0, self.power_t, self.t_,
                            intercept_decay)
  
              self.t_ += n_iter * X.shape[0]
              self.intercept_ = np.atleast_1d(self.intercept_)
  
  
  class SGDRegressor(BaseSGDRegressor):
      """Linear model fitted by minimizing a regularized empirical loss with SGD
  
      SGD stands for Stochastic Gradient Descent: the gradient of the loss is
      estimated each sample at a time and the model is updated along the way with
      a decreasing strength schedule (aka learning rate).
  
      The regularizer is a penalty added to the loss function that shrinks model
      parameters towards the zero vector using either the squared euclidean norm
      L2 or the absolute norm L1 or a combination of both (Elastic Net). If the
      parameter update crosses the 0.0 value because of the regularizer, the
      update is truncated to 0.0 to allow for learning sparse models and achieve
      online feature selection.
  
      This implementation works with data represented as dense numpy arrays of
      floating point values for the features.
  
      Read more in the :ref:`User Guide <sgd>`.
  
      Parameters
      ----------
      loss : str, 'squared_loss', 'huber', 'epsilon_insensitive', \
                  or 'squared_epsilon_insensitive'
          The loss function to be used. Defaults to 'squared_loss' which refers
          to the ordinary least squares fit. 'huber' modifies 'squared_loss' to
          focus less on getting outliers correct by switching from squared to
          linear loss past a distance of epsilon. 'epsilon_insensitive' ignores
          errors less than epsilon and is linear past that; this is the loss
          function used in SVR. 'squared_epsilon_insensitive' is the same but
          becomes squared loss past a tolerance of epsilon.
  
      penalty : str, 'none', 'l2', 'l1', or 'elasticnet'
          The penalty (aka regularization term) to be used. Defaults to 'l2'
          which is the standard regularizer for linear SVM models. 'l1' and
          'elasticnet' might bring sparsity to the model (feature selection)
          not achievable with 'l2'.
  
      alpha : float
          Constant that multiplies the regularization term. Defaults to 0.0001
          Also used to compute learning_rate when set to 'optimal'.
  
      l1_ratio : float
          The Elastic Net mixing parameter, with 0 <= l1_ratio <= 1.
          l1_ratio=0 corresponds to L2 penalty, l1_ratio=1 to L1.
          Defaults to 0.15.
  
      fit_intercept : bool
          Whether the intercept should be estimated or not. If False, the
          data is assumed to be already centered. Defaults to True.
  
      n_iter : int, optional
          The number of passes over the training data (aka epochs). The number
          of iterations is set to 1 if using partial_fit.
          Defaults to 5.
  
      shuffle : bool, optional
          Whether or not the training data should be shuffled after each epoch.
          Defaults to True.
  
      random_state : int seed, RandomState instance, or None (default)
          The seed of the pseudo random number generator to use when
          shuffling the data.
  
      verbose : integer, optional
          The verbosity level.
  
      epsilon : float
          Epsilon in the epsilon-insensitive loss functions; only if `loss` is
          'huber', 'epsilon_insensitive', or 'squared_epsilon_insensitive'.
          For 'huber', determines the threshold at which it becomes less
          important to get the prediction exactly right.
          For epsilon-insensitive, any differences between the current prediction
          and the correct label are ignored if they are less than this threshold.
  
      learning_rate : string, optional
          The learning rate schedule:
  
          - 'constant': eta = eta0
          - 'optimal': eta = 1.0 / (alpha * (t + t0)) [default]
          - 'invscaling': eta = eta0 / pow(t, power_t)
  
          where t0 is chosen by a heuristic proposed by Leon Bottou.
  
      eta0 : double, optional
          The initial learning rate [default 0.01].
  
      power_t : double, optional
          The exponent for inverse scaling learning rate [default 0.25].
  
      warm_start : bool, optional
          When set to True, reuse the solution of the previous call to fit as
          initialization, otherwise, just erase the previous solution.
  
      average : bool or int, optional
          When set to True, computes the averaged SGD weights and stores the
          result in the ``coef_`` attribute. If set to an int greater than 1,
          averaging will begin once the total number of samples seen reaches
          average. So ``average=10`` will begin averaging after seeing 10
          samples.
  
      Attributes
      ----------
      coef_ : array, shape (n_features,)
          Weights assigned to the features.
  
      intercept_ : array, shape (1,)
          The intercept term.
  
      average_coef_ : array, shape (n_features,)
          Averaged weights assigned to the features.
  
      average_intercept_ : array, shape (1,)
          The averaged intercept term.
  
      Examples
      --------
      >>> import numpy as np
      >>> from sklearn import linear_model
      >>> n_samples, n_features = 10, 5
      >>> np.random.seed(0)
      >>> y = np.random.randn(n_samples)
      >>> X = np.random.randn(n_samples, n_features)
      >>> clf = linear_model.SGDRegressor()
      >>> clf.fit(X, y)
      ... #doctest: +NORMALIZE_WHITESPACE
      SGDRegressor(alpha=0.0001, average=False, epsilon=0.1, eta0=0.01,
                   fit_intercept=True, l1_ratio=0.15, learning_rate='invscaling',
                   loss='squared_loss', n_iter=5, penalty='l2', power_t=0.25,
                   random_state=None, shuffle=True, verbose=0, warm_start=False)
  
      See also
      --------
      Ridge, ElasticNet, Lasso, SVR
  
      """
      def __init__(self, loss="squared_loss", penalty="l2", alpha=0.0001,
                   l1_ratio=0.15, fit_intercept=True, n_iter=5, shuffle=True,
                   verbose=0, epsilon=DEFAULT_EPSILON, random_state=None,
                   learning_rate="invscaling", eta0=0.01, power_t=0.25,
                   warm_start=False, average=False):
          super(SGDRegressor, self).__init__(loss=loss, penalty=penalty,
                                             alpha=alpha, l1_ratio=l1_ratio,
                                             fit_intercept=fit_intercept,
                                             n_iter=n_iter, shuffle=shuffle,
                                             verbose=verbose,
                                             epsilon=epsilon,
                                             random_state=random_state,
                                             learning_rate=learning_rate,
                                             eta0=eta0, power_t=power_t,
                                             warm_start=warm_start,
                                             average=average)
  