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 #
 # Licensed to the Apache Software Foundation (ASF) under one or more
 # contributor license agreements.  See the NOTICE file distributed with
 # this work for additional information regarding copyright ownership.
 # The ASF licenses this file to You under the Apache License, Version 2.0
 # (the "License"); you may not use this file except in compliance with
 # the License.  You may obtain a copy of the License at
 #
 #    http://www.apache.org/licenses/LICENSE-2.0
 #
 # Unless required by applicable law or agreed to in writing, software
 # distributed under the License is distributed on an "AS IS" BASIS,
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
 #
 
 import sys
 import warnings
 
 import numpy as np
 
 from pyspark import RDD, since
 from pyspark.streaming.dstream import DStream
 from pyspark.mllib.common import callMLlibFunc, _py2java, _java2py, inherit_doc
 from pyspark.mllib.linalg import SparseVector, _convert_to_vector
 from pyspark.mllib.util import Saveable, Loader
 
 __all__ = ['LabeledPoint', 'LinearModel',
            'LinearRegressionModel', 'LinearRegressionWithSGD',
            'RidgeRegressionModel', 'RidgeRegressionWithSGD',
            'LassoModel', 'LassoWithSGD', 'IsotonicRegressionModel',
            'IsotonicRegression', 'StreamingLinearAlgorithm',
            'StreamingLinearRegressionWithSGD']
 
 
 class LabeledPoint(object):
 
     """
     Class that represents the features and labels of a data point.
 
     :param label:
       Label for this data point.
     :param features:
       Vector of features for this point (NumPy array, list,
       pyspark.mllib.linalg.SparseVector, or scipy.sparse column matrix).
 
     .. note:: 'label' and 'features' are accessible as class attributes.
 
     .. versionadded:: 1.0.0
     """
 
     def __init__(self, label, features):
         self.label = float(label)
         self.features = _convert_to_vector(features)
 
     def __reduce__(self):
         return (LabeledPoint, (self.label, self.features))
 
     def __str__(self):
         return "(" + ",".join((str(self.label), str(self.features))) + ")"
 
     def __repr__(self):
         return "LabeledPoint(%s, %s)" % (self.label, self.features)
 
 
 class LinearModel(object):
 
     """
     A linear model that has a vector of coefficients and an intercept.
 
     :param weights:
       Weights computed for every feature.
     :param intercept:
       Intercept computed for this model.
 
     .. versionadded:: 0.9.0
     """
 
     def __init__(self, weights, intercept):
         self._coeff = _convert_to_vector(weights)
         self._intercept = float(intercept)
 
     @property
     @since("1.0.0")
     def weights(self):
         """Weights computed for every feature."""
         return self._coeff
 
     @property
     @since("1.0.0")
     def intercept(self):
         """Intercept computed for this model."""
         return self._intercept
 
     def __repr__(self):
         return "(weights=%s, intercept=%r)" % (self._coeff, self._intercept)
 
 
 @inherit_doc
 class LinearRegressionModelBase(LinearModel):
 
     """A linear regression model.
 
     >>> lrmb = LinearRegressionModelBase(np.array([1.0, 2.0]), 0.1)
     >>> abs(lrmb.predict(np.array([-1.03, 7.777])) - 14.624) < 1e-6
     True
     >>> abs(lrmb.predict(SparseVector(2, {0: -1.03, 1: 7.777})) - 14.624) < 1e-6
     True
 
     .. versionadded:: 0.9.0
     """
 
     @since("0.9.0")
     def predict(self, x):
         """
         Predict the value of the dependent variable given a vector or
         an RDD of vectors containing values for the independent variables.
         """
         if isinstance(x, RDD):
             return x.map(self.predict)
         x = _convert_to_vector(x)
         return self.weights.dot(x) + self.intercept
 
 
 @inherit_doc
 class LinearRegressionModel(LinearRegressionModelBase):
 
     """A linear regression model derived from a least-squares fit.
 
     >>> from pyspark.mllib.regression import LabeledPoint
     >>> data = [
     ...     LabeledPoint(0.0, [0.0]),
     ...     LabeledPoint(1.0, [1.0]),
     ...     LabeledPoint(3.0, [2.0]),
     ...     LabeledPoint(2.0, [3.0])
     ... ]
     >>> lrm = LinearRegressionWithSGD.train(sc.parallelize(data), iterations=10,
     ...     initialWeights=np.array([1.0]))
     >>> abs(lrm.predict(np.array([0.0])) - 0) < 0.5
     True
     >>> abs(lrm.predict(np.array([1.0])) - 1) < 0.5
     True
     >>> abs(lrm.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
     True
     >>> abs(lrm.predict(sc.parallelize([[1.0]])).collect()[0] - 1) < 0.5
     True
     >>> import os, tempfile
     >>> path = tempfile.mkdtemp()
     >>> lrm.save(sc, path)
     >>> sameModel = LinearRegressionModel.load(sc, path)
     >>> abs(sameModel.predict(np.array([0.0])) - 0) < 0.5
     True
     >>> abs(sameModel.predict(np.array([1.0])) - 1) < 0.5
     True
     >>> abs(sameModel.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
     True
     >>> from shutil import rmtree
     >>> try:
     ...     rmtree(path)
     ... except:
     ...     pass
     >>> data = [
     ...     LabeledPoint(0.0, SparseVector(1, {0: 0.0})),
     ...     LabeledPoint(1.0, SparseVector(1, {0: 1.0})),
     ...     LabeledPoint(3.0, SparseVector(1, {0: 2.0})),
     ...     LabeledPoint(2.0, SparseVector(1, {0: 3.0}))
     ... ]
     >>> lrm = LinearRegressionWithSGD.train(sc.parallelize(data), iterations=10,
     ...     initialWeights=np.array([1.0]))
     >>> abs(lrm.predict(np.array([0.0])) - 0) < 0.5
     True
     >>> abs(lrm.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
     True
     >>> lrm = LinearRegressionWithSGD.train(sc.parallelize(data), iterations=10, step=1.0,
     ...    miniBatchFraction=1.0, initialWeights=np.array([1.0]), regParam=0.1, regType="l2",
     ...    intercept=True, validateData=True)
     >>> abs(lrm.predict(np.array([0.0])) - 0) < 0.5
     True
     >>> abs(lrm.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
     True
 
     .. versionadded:: 0.9.0
     """
     @since("1.4.0")
     def save(self, sc, path):
         """Save a LinearRegressionModel."""
         java_model = sc._jvm.org.apache.spark.mllib.regression.LinearRegressionModel(
             _py2java(sc, self._coeff), self.intercept)
         java_model.save(sc._jsc.sc(), path)
 
     @classmethod
     @since("1.4.0")
     def load(cls, sc, path):
         """Load a LinearRegressionModel."""
         java_model = sc._jvm.org.apache.spark.mllib.regression.LinearRegressionModel.load(
             sc._jsc.sc(), path)
         weights = _java2py(sc, java_model.weights())
         intercept = java_model.intercept()
         model = LinearRegressionModel(weights, intercept)
         return model
 
 
 # train_func should take two parameters, namely data and initial_weights, and
 # return the result of a call to the appropriate JVM stub.
 # _regression_train_wrapper is responsible for setup and error checking.
 def _regression_train_wrapper(train_func, modelClass, data, initial_weights):
     from pyspark.mllib.classification import LogisticRegressionModel
     first = data.first()
     if not isinstance(first, LabeledPoint):
         raise TypeError("data should be an RDD of LabeledPoint, but got %s" % type(first))
     if initial_weights is None:
         initial_weights = [0.0] * len(data.first().features)
     if (modelClass == LogisticRegressionModel):
         weights, intercept, numFeatures, numClasses = train_func(
             data, _convert_to_vector(initial_weights))
         return modelClass(weights, intercept, numFeatures, numClasses)
     else:
         weights, intercept = train_func(data, _convert_to_vector(initial_weights))
         return modelClass(weights, intercept)
 
 
 class LinearRegressionWithSGD(object):
     """
     .. versionadded:: 0.9.0
     .. note:: Deprecated in 2.0.0. Use ml.regression.LinearRegression.
     """
     @classmethod
     @since("0.9.0")
     def train(cls, data, iterations=100, step=1.0, miniBatchFraction=1.0,
               initialWeights=None, regParam=0.0, regType=None, intercept=False,
               validateData=True, convergenceTol=0.001):
         """
         Train a linear regression model using Stochastic Gradient
         Descent (SGD). This solves the least squares regression
         formulation
 
             f(weights) = 1/(2n) ||A weights - y||^2
 
         which is the mean squared error. Here the data matrix has n rows,
         and the input RDD holds the set of rows of A, each with its
         corresponding right hand side label y.
         See also the documentation for the precise formulation.
 
         :param data:
           The training data, an RDD of LabeledPoint.
         :param iterations:
           The number of iterations.
           (default: 100)
         :param step:
           The step parameter used in SGD.
           (default: 1.0)
         :param miniBatchFraction:
           Fraction of data to be used for each SGD iteration.
           (default: 1.0)
         :param initialWeights:
           The initial weights.
           (default: None)
         :param regParam:
           The regularizer parameter.
           (default: 0.0)
         :param regType:
           The type of regularizer used for training our model.
           Supported values:
 
             - "l1" for using L1 regularization
             - "l2" for using L2 regularization
             - None for no regularization (default)
         :param intercept:
           Boolean parameter which indicates the use or not of the
           augmented representation for training data (i.e., whether bias
           features are activated or not).
           (default: False)
         :param validateData:
           Boolean parameter which indicates if the algorithm should
           validate data before training.
           (default: True)
         :param convergenceTol:
           A condition which decides iteration termination.
           (default: 0.001)
         """
         warnings.warn(
             "Deprecated in 2.0.0. Use ml.regression.LinearRegression.", DeprecationWarning)
 
         def train(rdd, i):
             return callMLlibFunc("trainLinearRegressionModelWithSGD", rdd, int(iterations),
                                  float(step), float(miniBatchFraction), i, float(regParam),
                                  regType, bool(intercept), bool(validateData),
                                  float(convergenceTol))
 
         return _regression_train_wrapper(train, LinearRegressionModel, data, initialWeights)
 
 
 @inherit_doc
 class LassoModel(LinearRegressionModelBase):
 
     """A linear regression model derived from a least-squares fit with
     an l_1 penalty term.
 
     >>> from pyspark.mllib.regression import LabeledPoint
     >>> data = [
     ...     LabeledPoint(0.0, [0.0]),
     ...     LabeledPoint(1.0, [1.0]),
     ...     LabeledPoint(3.0, [2.0]),
     ...     LabeledPoint(2.0, [3.0])
     ... ]
     >>> lrm = LassoWithSGD.train(
     ...     sc.parallelize(data), iterations=10, initialWeights=np.array([1.0]))
     >>> abs(lrm.predict(np.array([0.0])) - 0) < 0.5
     True
     >>> abs(lrm.predict(np.array([1.0])) - 1) < 0.5
     True
     >>> abs(lrm.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
     True
     >>> abs(lrm.predict(sc.parallelize([[1.0]])).collect()[0] - 1) < 0.5
     True
     >>> import os, tempfile
     >>> path = tempfile.mkdtemp()
     >>> lrm.save(sc, path)
     >>> sameModel = LassoModel.load(sc, path)
     >>> abs(sameModel.predict(np.array([0.0])) - 0) < 0.5
     True
     >>> abs(sameModel.predict(np.array([1.0])) - 1) < 0.5
     True
     >>> abs(sameModel.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
     True
     >>> from shutil import rmtree
     >>> try:
     ...    rmtree(path)
     ... except:
     ...    pass
     >>> data = [
     ...     LabeledPoint(0.0, SparseVector(1, {0: 0.0})),
     ...     LabeledPoint(1.0, SparseVector(1, {0: 1.0})),
     ...     LabeledPoint(3.0, SparseVector(1, {0: 2.0})),
     ...     LabeledPoint(2.0, SparseVector(1, {0: 3.0}))
     ... ]
     >>> lrm = LinearRegressionWithSGD.train(sc.parallelize(data), iterations=10,
     ...     initialWeights=np.array([1.0]))
     >>> abs(lrm.predict(np.array([0.0])) - 0) < 0.5
     True
     >>> abs(lrm.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
     True
     >>> lrm = LassoWithSGD.train(sc.parallelize(data), iterations=10, step=1.0,
     ...     regParam=0.01, miniBatchFraction=1.0, initialWeights=np.array([1.0]), intercept=True,
     ...     validateData=True)
     >>> abs(lrm.predict(np.array([0.0])) - 0) < 0.5
     True
     >>> abs(lrm.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
     True
 
     .. versionadded:: 0.9.0
     """
     @since("1.4.0")
     def save(self, sc, path):
         """Save a LassoModel."""
         java_model = sc._jvm.org.apache.spark.mllib.regression.LassoModel(
             _py2java(sc, self._coeff), self.intercept)
         java_model.save(sc._jsc.sc(), path)
 
     @classmethod
     @since("1.4.0")
     def load(cls, sc, path):
         """Load a LassoModel."""
         java_model = sc._jvm.org.apache.spark.mllib.regression.LassoModel.load(
             sc._jsc.sc(), path)
         weights = _java2py(sc, java_model.weights())
         intercept = java_model.intercept()
         model = LassoModel(weights, intercept)
         return model
 
 
 class LassoWithSGD(object):
     """
     .. versionadded:: 0.9.0
     .. note:: Deprecated in 2.0.0. Use ml.regression.LinearRegression with elasticNetParam = 1.0.
             Note the default regParam is 0.01 for LassoWithSGD, but is 0.0 for LinearRegression.
     """
     @classmethod
     @since("0.9.0")
     def train(cls, data, iterations=100, step=1.0, regParam=0.01,
               miniBatchFraction=1.0, initialWeights=None, intercept=False,
               validateData=True, convergenceTol=0.001):
         """
         Train a regression model with L1-regularization using Stochastic
         Gradient Descent. This solves the l1-regularized least squares
         regression formulation
 
             f(weights) = 1/(2n) ||A weights - y||^2  + regParam ||weights||_1
 
         Here the data matrix has n rows, and the input RDD holds the set
         of rows of A, each with its corresponding right hand side label y.
         See also the documentation for the precise formulation.
 
         :param data:
           The training data, an RDD of LabeledPoint.
         :param iterations:
           The number of iterations.
           (default: 100)
         :param step:
           The step parameter used in SGD.
           (default: 1.0)
         :param regParam:
           The regularizer parameter.
           (default: 0.01)
         :param miniBatchFraction:
           Fraction of data to be used for each SGD iteration.
           (default: 1.0)
         :param initialWeights:
           The initial weights.
           (default: None)
         :param intercept:
           Boolean parameter which indicates the use or not of the
           augmented representation for training data (i.e. whether bias
           features are activated or not).
           (default: False)
         :param validateData:
           Boolean parameter which indicates if the algorithm should
           validate data before training.
           (default: True)
         :param convergenceTol:
           A condition which decides iteration termination.
           (default: 0.001)
         """
         warnings.warn(
             "Deprecated in 2.0.0. Use ml.regression.LinearRegression with elasticNetParam = 1.0. "
             "Note the default regParam is 0.01 for LassoWithSGD, but is 0.0 for LinearRegression.",
             DeprecationWarning)
 
         def train(rdd, i):
             return callMLlibFunc("trainLassoModelWithSGD", rdd, int(iterations), float(step),
                                  float(regParam), float(miniBatchFraction), i, bool(intercept),
                                  bool(validateData), float(convergenceTol))
 
         return _regression_train_wrapper(train, LassoModel, data, initialWeights)
 
 
 @inherit_doc
 class RidgeRegressionModel(LinearRegressionModelBase):
 
     """A linear regression model derived from a least-squares fit with
     an l_2 penalty term.
 
     >>> from pyspark.mllib.regression import LabeledPoint
     >>> data = [
     ...     LabeledPoint(0.0, [0.0]),
     ...     LabeledPoint(1.0, [1.0]),
     ...     LabeledPoint(3.0, [2.0]),
     ...     LabeledPoint(2.0, [3.0])
     ... ]
     >>> lrm = RidgeRegressionWithSGD.train(sc.parallelize(data), iterations=10,
     ...     initialWeights=np.array([1.0]))
     >>> abs(lrm.predict(np.array([0.0])) - 0) < 0.5
     True
     >>> abs(lrm.predict(np.array([1.0])) - 1) < 0.5
     True
     >>> abs(lrm.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
     True
     >>> abs(lrm.predict(sc.parallelize([[1.0]])).collect()[0] - 1) < 0.5
     True
     >>> import os, tempfile
     >>> path = tempfile.mkdtemp()
     >>> lrm.save(sc, path)
     >>> sameModel = RidgeRegressionModel.load(sc, path)
     >>> abs(sameModel.predict(np.array([0.0])) - 0) < 0.5
     True
     >>> abs(sameModel.predict(np.array([1.0])) - 1) < 0.5
     True
     >>> abs(sameModel.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
     True
     >>> from shutil import rmtree
     >>> try:
     ...    rmtree(path)
     ... except:
     ...    pass
     >>> data = [
     ...     LabeledPoint(0.0, SparseVector(1, {0: 0.0})),
     ...     LabeledPoint(1.0, SparseVector(1, {0: 1.0})),
     ...     LabeledPoint(3.0, SparseVector(1, {0: 2.0})),
     ...     LabeledPoint(2.0, SparseVector(1, {0: 3.0}))
     ... ]
     >>> lrm = LinearRegressionWithSGD.train(sc.parallelize(data), iterations=10,
     ...     initialWeights=np.array([1.0]))
     >>> abs(lrm.predict(np.array([0.0])) - 0) < 0.5
     True
     >>> abs(lrm.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
     True
     >>> lrm = RidgeRegressionWithSGD.train(sc.parallelize(data), iterations=10, step=1.0,
     ...     regParam=0.01, miniBatchFraction=1.0, initialWeights=np.array([1.0]), intercept=True,
     ...     validateData=True)
     >>> abs(lrm.predict(np.array([0.0])) - 0) < 0.5
     True
     >>> abs(lrm.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
     True
 
     .. versionadded:: 0.9.0
     """
     @since("1.4.0")
     def save(self, sc, path):
         """Save a RidgeRegressionMode."""
         java_model = sc._jvm.org.apache.spark.mllib.regression.RidgeRegressionModel(
             _py2java(sc, self._coeff), self.intercept)
         java_model.save(sc._jsc.sc(), path)
 
     @classmethod
     @since("1.4.0")
     def load(cls, sc, path):
         """Load a RidgeRegressionMode."""
         java_model = sc._jvm.org.apache.spark.mllib.regression.RidgeRegressionModel.load(
             sc._jsc.sc(), path)
         weights = _java2py(sc, java_model.weights())
         intercept = java_model.intercept()
         model = RidgeRegressionModel(weights, intercept)
         return model
 
 
 class RidgeRegressionWithSGD(object):
     """
     .. versionadded:: 0.9.0
     .. note:: Deprecated in 2.0.0. Use ml.regression.LinearRegression with elasticNetParam = 0.0.
             Note the default regParam is 0.01 for RidgeRegressionWithSGD, but is 0.0 for
             LinearRegression.
     """
     @classmethod
     @since("0.9.0")
     def train(cls, data, iterations=100, step=1.0, regParam=0.01,
               miniBatchFraction=1.0, initialWeights=None, intercept=False,
               validateData=True, convergenceTol=0.001):
         """
         Train a regression model with L2-regularization using Stochastic
         Gradient Descent. This solves the l2-regularized least squares
         regression formulation
 
             f(weights) = 1/(2n) ||A weights - y||^2 + regParam/2 ||weights||^2
 
         Here the data matrix has n rows, and the input RDD holds the set
         of rows of A, each with its corresponding right hand side label y.
         See also the documentation for the precise formulation.
 
         :param data:
           The training data, an RDD of LabeledPoint.
         :param iterations:
           The number of iterations.
           (default: 100)
         :param step:
           The step parameter used in SGD.
           (default: 1.0)
         :param regParam:
           The regularizer parameter.
           (default: 0.01)
         :param miniBatchFraction:
           Fraction of data to be used for each SGD iteration.
           (default: 1.0)
         :param initialWeights:
           The initial weights.
           (default: None)
         :param intercept:
           Boolean parameter which indicates the use or not of the
           augmented representation for training data (i.e. whether bias
           features are activated or not).
           (default: False)
         :param validateData:
           Boolean parameter which indicates if the algorithm should
           validate data before training.
           (default: True)
         :param convergenceTol:
           A condition which decides iteration termination.
           (default: 0.001)
         """
         warnings.warn(
             "Deprecated in 2.0.0. Use ml.regression.LinearRegression with elasticNetParam = 0.0. "
             "Note the default regParam is 0.01 for RidgeRegressionWithSGD, but is 0.0 for "
             "LinearRegression.", DeprecationWarning)
 
         def train(rdd, i):
             return callMLlibFunc("trainRidgeModelWithSGD", rdd, int(iterations), float(step),
                                  float(regParam), float(miniBatchFraction), i, bool(intercept),
                                  bool(validateData), float(convergenceTol))
 
         return _regression_train_wrapper(train, RidgeRegressionModel, data, initialWeights)
 
 
 class IsotonicRegressionModel(Saveable, Loader):
 
     """
     Regression model for isotonic regression.
 
     :param boundaries:
       Array of boundaries for which predictions are known. Boundaries
       must be sorted in increasing order.
     :param predictions:
       Array of predictions associated to the boundaries at the same
       index. Results of isotonic regression and therefore monotone.
     :param isotonic:
       Indicates whether this is isotonic or antitonic.
 
     >>> data = [(1, 0, 1), (2, 1, 1), (3, 2, 1), (1, 3, 1), (6, 4, 1), (17, 5, 1), (16, 6, 1)]
     >>> irm = IsotonicRegression.train(sc.parallelize(data))
     >>> irm.predict(3)
     2.0
     >>> irm.predict(5)
     16.5
     >>> irm.predict(sc.parallelize([3, 5])).collect()
     [2.0, 16.5]
     >>> import os, tempfile
     >>> path = tempfile.mkdtemp()
     >>> irm.save(sc, path)
     >>> sameModel = IsotonicRegressionModel.load(sc, path)
     >>> sameModel.predict(3)
     2.0
     >>> sameModel.predict(5)
     16.5
     >>> from shutil import rmtree
     >>> try:
     ...     rmtree(path)
     ... except OSError:
     ...     pass
 
     .. versionadded:: 1.4.0
     """
 
     def __init__(self, boundaries, predictions, isotonic):
         self.boundaries = boundaries
         self.predictions = predictions
         self.isotonic = isotonic
 
     @since("1.4.0")
     def predict(self, x):
         """
         Predict labels for provided features.
         Using a piecewise linear function.
         1) If x exactly matches a boundary then associated prediction
         is returned. In case there are multiple predictions with the
         same boundary then one of them is returned. Which one is
         undefined (same as java.util.Arrays.binarySearch).
         2) If x is lower or higher than all boundaries then first or
         last prediction is returned respectively. In case there are
         multiple predictions with the same boundary then the lowest
         or highest is returned respectively.
         3) If x falls between two values in boundary array then
         prediction is treated as piecewise linear function and
         interpolated value is returned. In case there are multiple
         values with the same boundary then the same rules as in 2)
         are used.
 
         :param x:
           Feature or RDD of Features to be labeled.
         """
         if isinstance(x, RDD):
             return x.map(lambda v: self.predict(v))
         return np.interp(x, self.boundaries, self.predictions)
 
     @since("1.4.0")
     def save(self, sc, path):
         """Save an IsotonicRegressionModel."""
         java_boundaries = _py2java(sc, self.boundaries.tolist())
         java_predictions = _py2java(sc, self.predictions.tolist())
         java_model = sc._jvm.org.apache.spark.mllib.regression.IsotonicRegressionModel(
             java_boundaries, java_predictions, self.isotonic)
         java_model.save(sc._jsc.sc(), path)
 
     @classmethod
     @since("1.4.0")
     def load(cls, sc, path):
         """Load an IsotonicRegressionModel."""
         java_model = sc._jvm.org.apache.spark.mllib.regression.IsotonicRegressionModel.load(
             sc._jsc.sc(), path)
         py_boundaries = _java2py(sc, java_model.boundaryVector()).toArray()
         py_predictions = _java2py(sc, java_model.predictionVector()).toArray()
         return IsotonicRegressionModel(py_boundaries, py_predictions, java_model.isotonic)
 
 
 class IsotonicRegression(object):
     """
     Isotonic regression.
     Currently implemented using parallelized pool adjacent violators
     algorithm. Only univariate (single feature) algorithm supported.
 
     Sequential PAV implementation based on:
 
       Tibshirani, Ryan J., Holger Hoefling, and Robert Tibshirani.
       "Nearly-isotonic regression." Technometrics 53.1 (2011): 54-61.
       Available from http://www.stat.cmu.edu/~ryantibs/papers/neariso.pdf
 
     Sequential PAV parallelization based on:
 
         Kearsley, Anthony J., Richard A. Tapia, and Michael W. Trosset.
         "An approach to parallelizing isotonic regression."
         Applied Mathematics and Parallel Computing. Physica-Verlag HD, 1996. 141-147.
         Available from http://softlib.rice.edu/pub/CRPC-TRs/reports/CRPC-TR96640.pdf
 
     See `Isotonic regression (Wikipedia) <http://en.wikipedia.org/wiki/Isotonic_regression>`_.
 
     .. versionadded:: 1.4.0
     """
 
     @classmethod
     @since("1.4.0")
     def train(cls, data, isotonic=True):
         """
         Train an isotonic regression model on the given data.
 
         :param data:
           RDD of (label, feature, weight) tuples.
         :param isotonic:
           Whether this is isotonic (which is default) or antitonic.
           (default: True)
         """
         boundaries, predictions = callMLlibFunc("trainIsotonicRegressionModel",
                                                 data.map(_convert_to_vector), bool(isotonic))
         return IsotonicRegressionModel(boundaries.toArray(), predictions.toArray(), isotonic)
 
 
 class StreamingLinearAlgorithm(object):
     """
     Base class that has to be inherited by any StreamingLinearAlgorithm.
 
     Prevents reimplementation of methods predictOn and predictOnValues.
 
     .. versionadded:: 1.5.0
     """
     def __init__(self, model):
         self._model = model
 
     @since("1.5.0")
     def latestModel(self):
         """
         Returns the latest model.
         """
         return self._model
 
     def _validate(self, dstream):
         if not isinstance(dstream, DStream):
             raise TypeError(
                 "dstream should be a DStream object, got %s" % type(dstream))
         if not self._model:
             raise ValueError(
                 "Model must be intialized using setInitialWeights")
 
     @since("1.5.0")
     def predictOn(self, dstream):
         """
         Use the model to make predictions on batches of data from a
         DStream.
 
         :return:
           DStream containing predictions.
         """
         self._validate(dstream)
         return dstream.map(lambda x: self._model.predict(x))
 
     @since("1.5.0")
     def predictOnValues(self, dstream):
         """
         Use the model to make predictions on the values of a DStream and
         carry over its keys.
 
         :return:
           DStream containing the input keys and the predictions as values.
         """
         self._validate(dstream)
         return dstream.mapValues(lambda x: self._model.predict(x))
 
 
 @inherit_doc
 class StreamingLinearRegressionWithSGD(StreamingLinearAlgorithm):
     """
     Train or predict a linear regression model on streaming data.
     Training uses Stochastic Gradient Descent to update the model
     based on each new batch of incoming data from a DStream
     (see `LinearRegressionWithSGD` for model equation).
 
     Each batch of data is assumed to be an RDD of LabeledPoints.
     The number of data points per batch can vary, but the number
     of features must be constant. An initial weight vector must
     be provided.
 
     :param stepSize:
       Step size for each iteration of gradient descent.
       (default: 0.1)
     :param numIterations:
       Number of iterations run for each batch of data.
       (default: 50)
     :param miniBatchFraction:
       Fraction of each batch of data to use for updates.
       (default: 1.0)
     :param convergenceTol:
       Value used to determine when to terminate iterations.
       (default: 0.001)
 
     .. versionadded:: 1.5.0
     """
     def __init__(self, stepSize=0.1, numIterations=50, miniBatchFraction=1.0, convergenceTol=0.001):
         self.stepSize = stepSize
         self.numIterations = numIterations
         self.miniBatchFraction = miniBatchFraction
         self.convergenceTol = convergenceTol
         self._model = None
         super(StreamingLinearRegressionWithSGD, self).__init__(
             model=self._model)
 
     @since("1.5.0")
     def setInitialWeights(self, initialWeights):
         """
         Set the initial value of weights.
 
         This must be set before running trainOn and predictOn
         """
         initialWeights = _convert_to_vector(initialWeights)
         self._model = LinearRegressionModel(initialWeights, 0)
         return self
 
     @since("1.5.0")
     def trainOn(self, dstream):
         """Train the model on the incoming dstream."""
         self._validate(dstream)
 
         def update(rdd):
             # LinearRegressionWithSGD.train raises an error for an empty RDD.
             if not rdd.isEmpty():
                 self._model = LinearRegressionWithSGD.train(
                     rdd, self.numIterations, self.stepSize,
                     self.miniBatchFraction, self._model.weights,
                     intercept=self._model.intercept, convergenceTol=self.convergenceTol)
 
         dstream.foreachRDD(update)
 
 
 def _test():
     import doctest
     from pyspark.sql import SparkSession
     import pyspark.mllib.regression
     globs = pyspark.mllib.regression.__dict__.copy()
     spark = SparkSession.builder\
         .master("local[2]")\
         .appName("mllib.regression tests")\
         .getOrCreate()
     globs['sc'] = spark.sparkContext
     (failure_count, test_count) = doctest.testmod(globs=globs, optionflags=doctest.ELLIPSIS)
     spark.stop()
     if failure_count:
         sys.exit(-1)
 
 if __name__ == "__main__":
     _test()

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