Vehicle-Anti-Theft-Face-Recognition-System/venv/Lib/site-packages/sklearn/linear_model/tests/test_sgd.py

import pickle
import pytest

import numpy as np
import scipy.sparse as sp
import joblib

from sklearn.utils._testing import assert_array_equal
from sklearn.utils._testing import assert_almost_equal
from sklearn.utils._testing import assert_array_almost_equal
from sklearn.utils._testing import assert_raises
from sklearn.utils._testing import assert_raises_regexp
from sklearn.utils._testing import assert_warns
from sklearn.utils._testing import ignore_warnings
from sklearn.utils.fixes import parse_version

from sklearn import linear_model, datasets, metrics
from sklearn.base import clone, is_classifier
from sklearn.preprocessing import LabelEncoder, scale, MinMaxScaler
from sklearn.preprocessing import StandardScaler
from sklearn.exceptions import ConvergenceWarning
from sklearn.model_selection import StratifiedShuffleSplit, ShuffleSplit
from sklearn.linear_model import _sgd_fast as sgd_fast
from sklearn.model_selection import RandomizedSearchCV


def _update_kwargs(kwargs):
    if "random_state" not in kwargs:
        kwargs["random_state"] = 42

    if "tol" not in kwargs:
        kwargs["tol"] = None
    if "max_iter" not in kwargs:
        kwargs["max_iter"] = 5


class _SparseSGDClassifier(linear_model.SGDClassifier):
    def fit(self, X, y, *args, **kw):
        X = sp.csr_matrix(X)
        return super().fit(X, y, *args, **kw)

    def partial_fit(self, X, y, *args, **kw):
        X = sp.csr_matrix(X)
        return super().partial_fit(X, y, *args, **kw)

    def decision_function(self, X):
        X = sp.csr_matrix(X)
        return super().decision_function(X)

    def predict_proba(self, X):
        X = sp.csr_matrix(X)
        return super().predict_proba(X)


class _SparseSGDRegressor(linear_model.SGDRegressor):
    def fit(self, X, y, *args, **kw):
        X = sp.csr_matrix(X)
        return linear_model.SGDRegressor.fit(self, X, y, *args, **kw)

    def partial_fit(self, X, y, *args, **kw):
        X = sp.csr_matrix(X)
        return linear_model.SGDRegressor.partial_fit(self, X, y, *args, **kw)

    def decision_function(self, X, *args, **kw):
        # XXX untested as of v0.22
        X = sp.csr_matrix(X)
        return linear_model.SGDRegressor.decision_function(self, X, *args,
                                                           **kw)


def SGDClassifier(**kwargs):
    _update_kwargs(kwargs)
    return linear_model.SGDClassifier(**kwargs)


def SGDRegressor(**kwargs):
    _update_kwargs(kwargs)
    return linear_model.SGDRegressor(**kwargs)


def SparseSGDClassifier(**kwargs):
    _update_kwargs(kwargs)
    return _SparseSGDClassifier(**kwargs)


def SparseSGDRegressor(**kwargs):
    _update_kwargs(kwargs)
    return _SparseSGDRegressor(**kwargs)


# Test Data

# test sample 1
X = np.array([[-2, -1], [-1, -1], [-1, -2], [1, 1], [1, 2], [2, 1]])
Y = [1, 1, 1, 2, 2, 2]
T = np.array([[-1, -1], [2, 2], [3, 2]])
true_result = [1, 2, 2]

# test sample 2; string class labels
X2 = np.array([[-1, 1], [-0.75, 0.5], [-1.5, 1.5],
               [1, 1], [0.75, 0.5], [1.5, 1.5],
               [-1, -1], [0, -0.5], [1, -1]])
Y2 = ["one"] * 3 + ["two"] * 3 + ["three"] * 3
T2 = np.array([[-1.5, 0.5], [1, 2], [0, -2]])
true_result2 = ["one", "two", "three"]

# test sample 3
X3 = np.array([[1, 1, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0],
               [0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0],
               [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1],
               [0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0]])
Y3 = np.array([1, 1, 1, 1, 2, 2, 2, 2])

# test sample 4 - two more or less redundant feature groups
X4 = np.array([[1, 0.9, 0.8, 0, 0, 0], [1, .84, .98, 0, 0, 0],
               [1, .96, .88, 0, 0, 0], [1, .91, .99, 0, 0, 0],
               [0, 0, 0, .89, .91, 1], [0, 0, 0, .79, .84, 1],
               [0, 0, 0, .91, .95, 1], [0, 0, 0, .93, 1, 1]])
Y4 = np.array([1, 1, 1, 1, 2, 2, 2, 2])

iris = datasets.load_iris()

# test sample 5 - test sample 1 as binary classification problem
X5 = np.array([[-2, -1], [-1, -1], [-1, -2], [1, 1], [1, 2], [2, 1]])
Y5 = [1, 1, 1, 2, 2, 2]
true_result5 = [0, 1, 1]


###############################################################################
# Common Test Case to classification and regression

# a simple implementation of ASGD to use for testing
# uses squared loss to find the gradient
def asgd(klass, X, y, eta, alpha, weight_init=None, intercept_init=0.0):
    if weight_init is None:
        weights = np.zeros(X.shape[1])
    else:
        weights = weight_init

    average_weights = np.zeros(X.shape[1])
    intercept = intercept_init
    average_intercept = 0.0
    decay = 1.0

    # sparse data has a fixed decay of .01
    if klass in (SparseSGDClassifier, SparseSGDRegressor):
        decay = .01

    for i, entry in enumerate(X):
        p = np.dot(entry, weights)
        p += intercept
        gradient = p - y[i]
        weights *= 1.0 - (eta * alpha)
        weights += -(eta * gradient * entry)
        intercept += -(eta * gradient) * decay

        average_weights *= i
        average_weights += weights
        average_weights /= i + 1.0

        average_intercept *= i
        average_intercept += intercept
        average_intercept /= i + 1.0

    return average_weights, average_intercept


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier,
                                   SGDRegressor, SparseSGDRegressor])
def test_sgd_bad_alpha(klass):
    # Check whether expected ValueError on bad alpha
    assert_raises(ValueError, klass, alpha=-.1)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier,
                                   SGDRegressor, SparseSGDRegressor])
def test_sgd_bad_penalty(klass):
    # Check whether expected ValueError on bad penalty
    assert_raises(ValueError, klass, penalty='foobar',
                  l1_ratio=0.85)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier,
                                   SGDRegressor, SparseSGDRegressor])
def test_sgd_bad_loss(klass):
    # Check whether expected ValueError on bad loss
    assert_raises(ValueError, klass, loss="foobar")


def _test_warm_start(klass, X, Y, lr):
    # Test that explicit warm restart...
    clf = klass(alpha=0.01, eta0=0.01, shuffle=False,
                learning_rate=lr)
    clf.fit(X, Y)

    clf2 = klass(alpha=0.001, eta0=0.01, shuffle=False,
                 learning_rate=lr)
    clf2.fit(X, Y,
             coef_init=clf.coef_.copy(),
             intercept_init=clf.intercept_.copy())

    # ... and implicit warm restart are equivalent.
    clf3 = klass(alpha=0.01, eta0=0.01, shuffle=False,
                 warm_start=True, learning_rate=lr)
    clf3.fit(X, Y)

    assert clf3.t_ == clf.t_
    assert_array_almost_equal(clf3.coef_, clf.coef_)

    clf3.set_params(alpha=0.001)
    clf3.fit(X, Y)

    assert clf3.t_ == clf2.t_
    assert_array_almost_equal(clf3.coef_, clf2.coef_)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier,
                                   SGDRegressor, SparseSGDRegressor])
@pytest.mark.parametrize('lr',
                         ["constant", "optimal", "invscaling", "adaptive"])
def test_warm_start(klass, lr):
    _test_warm_start(klass, X, Y, lr)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier,
                                   SGDRegressor, SparseSGDRegressor])
def test_input_format(klass):
    # Input format tests.
    clf = klass(alpha=0.01, shuffle=False)
    clf.fit(X, Y)
    Y_ = np.array(Y)[:, np.newaxis]

    Y_ = np.c_[Y_, Y_]
    assert_raises(ValueError, clf.fit, X, Y_)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier,
                                   SGDRegressor, SparseSGDRegressor])
def test_clone(klass):
    # Test whether clone works ok.
    clf = klass(alpha=0.01, penalty='l1')
    clf = clone(clf)
    clf.set_params(penalty='l2')
    clf.fit(X, Y)

    clf2 = klass(alpha=0.01, penalty='l2')
    clf2.fit(X, Y)

    assert_array_equal(clf.coef_, clf2.coef_)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier,
                                   SGDRegressor, SparseSGDRegressor])
def test_plain_has_no_average_attr(klass):
    clf = klass(average=True, eta0=.01)
    clf.fit(X, Y)

    assert hasattr(clf, '_average_coef')
    assert hasattr(clf, '_average_intercept')
    assert hasattr(clf, '_standard_intercept')
    assert hasattr(clf, '_standard_coef')

    clf = klass()
    clf.fit(X, Y)

    assert not hasattr(clf, '_average_coef')
    assert not hasattr(clf, '_average_intercept')
    assert not hasattr(clf, '_standard_intercept')
    assert not hasattr(clf, '_standard_coef')


# TODO: remove in 0.25
@pytest.mark.parametrize('klass', [SGDClassifier, SGDRegressor])
def test_sgd_deprecated_attr(klass):
    est = klass(average=True, eta0=.01)
    est.fit(X, Y)

    msg = "Attribute {} was deprecated"
    for att in ['average_coef_', 'average_intercept_',
                'standard_coef_', 'standard_intercept_']:
        with pytest.warns(FutureWarning, match=msg.format(att)):
            getattr(est, att)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier,
                                   SGDRegressor, SparseSGDRegressor])
def test_late_onset_averaging_not_reached(klass):
    clf1 = klass(average=600)
    clf2 = klass()
    for _ in range(100):
        if is_classifier(clf1):
            clf1.partial_fit(X, Y, classes=np.unique(Y))
            clf2.partial_fit(X, Y, classes=np.unique(Y))
        else:
            clf1.partial_fit(X, Y)
            clf2.partial_fit(X, Y)

    assert_array_almost_equal(clf1.coef_, clf2.coef_, decimal=16)
    assert_almost_equal(clf1.intercept_, clf2.intercept_, decimal=16)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier,
                                   SGDRegressor, SparseSGDRegressor])
def test_late_onset_averaging_reached(klass):
    eta0 = .001
    alpha = .0001
    Y_encode = np.array(Y)
    Y_encode[Y_encode == 1] = -1.0
    Y_encode[Y_encode == 2] = 1.0

    clf1 = klass(average=7, learning_rate="constant",
                 loss='squared_loss', eta0=eta0,
                 alpha=alpha, max_iter=2, shuffle=False)
    clf2 = klass(average=0, learning_rate="constant",
                 loss='squared_loss', eta0=eta0,
                 alpha=alpha, max_iter=1, shuffle=False)

    clf1.fit(X, Y_encode)
    clf2.fit(X, Y_encode)

    average_weights, average_intercept = \
        asgd(klass, X, Y_encode, eta0, alpha,
             weight_init=clf2.coef_.ravel(),
             intercept_init=clf2.intercept_)

    assert_array_almost_equal(clf1.coef_.ravel(),
                              average_weights.ravel(),
                              decimal=16)
    assert_almost_equal(clf1.intercept_, average_intercept, decimal=16)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier,
                                   SGDRegressor, SparseSGDRegressor])
def test_sgd_bad_alpha_for_optimal_learning_rate(klass):
    # Check whether expected ValueError on bad alpha, i.e. 0
    # since alpha is used to compute the optimal learning rate
    assert_raises(ValueError, klass,
                  alpha=0, learning_rate="optimal")


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier,
                                   SGDRegressor, SparseSGDRegressor])
def test_early_stopping(klass):
    X = iris.data[iris.target > 0]
    Y = iris.target[iris.target > 0]
    for early_stopping in [True, False]:
        max_iter = 1000
        clf = klass(early_stopping=early_stopping, tol=1e-3,
                    max_iter=max_iter).fit(X, Y)
        assert clf.n_iter_ < max_iter


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier,
                                   SGDRegressor, SparseSGDRegressor])
def test_adaptive_longer_than_constant(klass):
    clf1 = klass(learning_rate="adaptive", eta0=0.01, tol=1e-3,
                 max_iter=100)
    clf1.fit(iris.data, iris.target)
    clf2 = klass(learning_rate="constant", eta0=0.01, tol=1e-3,
                 max_iter=100)
    clf2.fit(iris.data, iris.target)
    assert clf1.n_iter_ > clf2.n_iter_


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier,
                                   SGDRegressor, SparseSGDRegressor])
def test_validation_set_not_used_for_training(klass):
    X, Y = iris.data, iris.target
    validation_fraction = 0.4
    seed = 42
    shuffle = False
    max_iter = 10
    clf1 = klass(early_stopping=True,
                 random_state=np.random.RandomState(seed),
                 validation_fraction=validation_fraction,
                 learning_rate='constant', eta0=0.01,
                 tol=None, max_iter=max_iter, shuffle=shuffle)
    clf1.fit(X, Y)
    assert clf1.n_iter_ == max_iter

    clf2 = klass(early_stopping=False,
                 random_state=np.random.RandomState(seed),
                 learning_rate='constant', eta0=0.01,
                 tol=None, max_iter=max_iter, shuffle=shuffle)

    if is_classifier(clf2):
        cv = StratifiedShuffleSplit(test_size=validation_fraction,
                                    random_state=seed)
    else:
        cv = ShuffleSplit(test_size=validation_fraction,
                          random_state=seed)
    idx_train, idx_val = next(cv.split(X, Y))
    idx_train = np.sort(idx_train)  # remove shuffling
    clf2.fit(X[idx_train], Y[idx_train])
    assert clf2.n_iter_ == max_iter

    assert_array_equal(clf1.coef_, clf2.coef_)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier,
                                   SGDRegressor, SparseSGDRegressor])
def test_n_iter_no_change(klass):
    X, Y = iris.data, iris.target
    # test that n_iter_ increases monotonically with n_iter_no_change
    for early_stopping in [True, False]:
        n_iter_list = [klass(early_stopping=early_stopping,
                             n_iter_no_change=n_iter_no_change,
                             tol=1e-4, max_iter=1000
                             ).fit(X, Y).n_iter_
                       for n_iter_no_change in [2, 3, 10]]
        assert_array_equal(n_iter_list, sorted(n_iter_list))


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier,
                                   SGDRegressor, SparseSGDRegressor])
def test_not_enough_sample_for_early_stopping(klass):
    # test an error is raised if the training or validation set is empty
    clf = klass(early_stopping=True, validation_fraction=0.99)
    with pytest.raises(ValueError):
        clf.fit(X3, Y3)


###############################################################################
# Classification Test Case

@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_sgd_clf(klass):
    # Check that SGD gives any results :-)

    for loss in ("hinge", "squared_hinge", "log", "modified_huber"):
        clf = klass(penalty='l2', alpha=0.01, fit_intercept=True,
                    loss=loss, max_iter=10, shuffle=True)
        clf.fit(X, Y)
        # assert_almost_equal(clf.coef_[0], clf.coef_[1], decimal=7)
        assert_array_equal(clf.predict(T), true_result)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_sgd_bad_l1_ratio(klass):
    # Check whether expected ValueError on bad l1_ratio
    assert_raises(ValueError, klass, l1_ratio=1.1)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_sgd_bad_learning_rate_schedule(klass):
    # Check whether expected ValueError on bad learning_rate
    assert_raises(ValueError, klass, learning_rate="<unknown>")


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_sgd_bad_eta0(klass):
    # Check whether expected ValueError on bad eta0
    assert_raises(ValueError, klass, eta0=0,
                  learning_rate="constant")


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_sgd_max_iter_param(klass):
    # Test parameter validity check
    assert_raises(ValueError, klass, max_iter=-10000)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_sgd_shuffle_param(klass):
    # Test parameter validity check
    assert_raises(ValueError, klass, shuffle="false")


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_sgd_early_stopping_param(klass):
    # Test parameter validity check
    assert_raises(ValueError, klass, early_stopping="false")


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_sgd_validation_fraction(klass):
    # Test parameter validity check
    assert_raises(ValueError, klass, validation_fraction=-.1)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_sgd_n_iter_no_change(klass):
    # Test parameter validity check
    assert_raises(ValueError, klass, n_iter_no_change=0)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_argument_coef(klass):
    # Checks coef_init not allowed as model argument (only fit)
    # Provided coef_ does not match dataset
    assert_raises(TypeError, klass, coef_init=np.zeros((3,)))


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_provide_coef(klass):
    # Checks coef_init shape for the warm starts
    # Provided coef_ does not match dataset.
    assert_raises(ValueError, klass().fit,
                  X, Y, coef_init=np.zeros((3,)))


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_set_intercept(klass):
    # Checks intercept_ shape for the warm starts
    # Provided intercept_ does not match dataset.
    assert_raises(ValueError, klass().fit,
                  X, Y, intercept_init=np.zeros((3,)))


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_sgd_early_stopping_with_partial_fit(klass):
    # Test parameter validity check
    assert_raises(ValueError,
                  klass(early_stopping=True).partial_fit, X, Y)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_set_intercept_binary(klass):
    # Checks intercept_ shape for the warm starts in binary case
    klass().fit(X5, Y5, intercept_init=0)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_average_binary_computed_correctly(klass):
    # Checks the SGDClassifier correctly computes the average weights
    eta = .1
    alpha = 2.
    n_samples = 20
    n_features = 10
    rng = np.random.RandomState(0)
    X = rng.normal(size=(n_samples, n_features))
    w = rng.normal(size=n_features)

    clf = klass(loss='squared_loss',
                learning_rate='constant',
                eta0=eta, alpha=alpha,
                fit_intercept=True,
                max_iter=1, average=True, shuffle=False)

    # simple linear function without noise
    y = np.dot(X, w)
    y = np.sign(y)

    clf.fit(X, y)

    average_weights, average_intercept = asgd(klass, X, y, eta, alpha)
    average_weights = average_weights.reshape(1, -1)
    assert_array_almost_equal(clf.coef_,
                              average_weights,
                              decimal=14)
    assert_almost_equal(clf.intercept_, average_intercept, decimal=14)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_set_intercept_to_intercept(klass):
    # Checks intercept_ shape consistency for the warm starts
    # Inconsistent intercept_ shape.
    clf = klass().fit(X5, Y5)
    klass().fit(X5, Y5, intercept_init=clf.intercept_)
    clf = klass().fit(X, Y)
    klass().fit(X, Y, intercept_init=clf.intercept_)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_sgd_at_least_two_labels(klass):
    # Target must have at least two labels
    clf = klass(alpha=0.01, max_iter=20)
    assert_raises(ValueError, clf.fit, X2, np.ones(9))


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_partial_fit_weight_class_balanced(klass):
    # partial_fit with class_weight='balanced' not supported"""
    regex = (r"class_weight 'balanced' is not supported for "
             r"partial_fit\. In order to use 'balanced' weights, "
             r"use compute_class_weight\('balanced', classes=classes, y=y\). "
             r"In place of y you can us a large enough sample "
             r"of the full training set target to properly "
             r"estimate the class frequency distributions\. "
             r"Pass the resulting weights as the class_weight "
             r"parameter\.")
    assert_raises_regexp(ValueError,
                         regex,
                         klass(class_weight='balanced').partial_fit,
                         X, Y, classes=np.unique(Y))


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_sgd_multiclass(klass):
    # Multi-class test case
    clf = klass(alpha=0.01, max_iter=20).fit(X2, Y2)
    assert clf.coef_.shape == (3, 2)
    assert clf.intercept_.shape == (3,)
    assert clf.decision_function([[0, 0]]).shape == (1, 3)
    pred = clf.predict(T2)
    assert_array_equal(pred, true_result2)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_sgd_multiclass_average(klass):
    eta = .001
    alpha = .01
    # Multi-class average test case
    clf = klass(loss='squared_loss',
                learning_rate='constant',
                eta0=eta, alpha=alpha,
                fit_intercept=True,
                max_iter=1, average=True, shuffle=False)

    np_Y2 = np.array(Y2)
    clf.fit(X2, np_Y2)
    classes = np.unique(np_Y2)

    for i, cl in enumerate(classes):
        y_i = np.ones(np_Y2.shape[0])
        y_i[np_Y2 != cl] = -1
        average_coef, average_intercept = asgd(klass, X2, y_i, eta, alpha)
        assert_array_almost_equal(average_coef, clf.coef_[i], decimal=16)
        assert_almost_equal(average_intercept,
                            clf.intercept_[i],
                            decimal=16)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_sgd_multiclass_with_init_coef(klass):
    # Multi-class test case
    clf = klass(alpha=0.01, max_iter=20)
    clf.fit(X2, Y2, coef_init=np.zeros((3, 2)),
            intercept_init=np.zeros(3))
    assert clf.coef_.shape == (3, 2)
    assert clf.intercept_.shape, (3,)
    pred = clf.predict(T2)
    assert_array_equal(pred, true_result2)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_sgd_multiclass_njobs(klass):
    # Multi-class test case with multi-core support
    clf = klass(alpha=0.01, max_iter=20, n_jobs=2).fit(X2, Y2)
    assert clf.coef_.shape == (3, 2)
    assert clf.intercept_.shape == (3,)
    assert clf.decision_function([[0, 0]]).shape == (1, 3)
    pred = clf.predict(T2)
    assert_array_equal(pred, true_result2)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_set_coef_multiclass(klass):
    # Checks coef_init and intercept_init shape for multi-class
    # problems
    # Provided coef_ does not match dataset
    clf = klass()
    assert_raises(ValueError, clf.fit, X2, Y2, coef_init=np.zeros((2, 2)))

    # Provided coef_ does match dataset
    clf = klass().fit(X2, Y2, coef_init=np.zeros((3, 2)))

    # Provided intercept_ does not match dataset
    clf = klass()
    assert_raises(ValueError, clf.fit, X2, Y2,
                  intercept_init=np.zeros((1,)))

    # Provided intercept_ does match dataset.
    clf = klass().fit(X2, Y2, intercept_init=np.zeros((3,)))


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_sgd_predict_proba_method_access(klass):
    # Checks that SGDClassifier predict_proba and predict_log_proba methods
    # can either be accessed or raise an appropriate error message
    # otherwise. See
    # https://github.com/scikit-learn/scikit-learn/issues/10938 for more
    # details.
    for loss in linear_model.SGDClassifier.loss_functions:
        clf = SGDClassifier(loss=loss)
        if loss in ('log', 'modified_huber'):
            assert hasattr(clf, 'predict_proba')
            assert hasattr(clf, 'predict_log_proba')
        else:
            message = ("probability estimates are not "
                       "available for loss={!r}".format(loss))
            assert not hasattr(clf, 'predict_proba')
            assert not hasattr(clf, 'predict_log_proba')
            with pytest.raises(AttributeError,
                               match=message):
                clf.predict_proba
            with pytest.raises(AttributeError,
                               match=message):
                clf.predict_log_proba


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_sgd_proba(klass):
    # Check SGD.predict_proba

    # Hinge loss does not allow for conditional prob estimate.
    # We cannot use the factory here, because it defines predict_proba
    # anyway.
    clf = SGDClassifier(loss="hinge", alpha=0.01,
                        max_iter=10, tol=None).fit(X, Y)
    assert not hasattr(clf, "predict_proba")
    assert not hasattr(clf, "predict_log_proba")

    # log and modified_huber losses can output probability estimates
    # binary case
    for loss in ["log", "modified_huber"]:
        clf = klass(loss=loss, alpha=0.01, max_iter=10)
        clf.fit(X, Y)
        p = clf.predict_proba([[3, 2]])
        assert p[0, 1] > 0.5
        p = clf.predict_proba([[-1, -1]])
        assert p[0, 1] < 0.5

        p = clf.predict_log_proba([[3, 2]])
        assert p[0, 1] > p[0, 0]
        p = clf.predict_log_proba([[-1, -1]])
        assert p[0, 1] < p[0, 0]

    # log loss multiclass probability estimates
    clf = klass(loss="log", alpha=0.01, max_iter=10).fit(X2, Y2)

    d = clf.decision_function([[.1, -.1], [.3, .2]])
    p = clf.predict_proba([[.1, -.1], [.3, .2]])
    assert_array_equal(np.argmax(p, axis=1), np.argmax(d, axis=1))
    assert_almost_equal(p[0].sum(), 1)
    assert np.all(p[0] >= 0)

    p = clf.predict_proba([[-1, -1]])
    d = clf.decision_function([[-1, -1]])
    assert_array_equal(np.argsort(p[0]), np.argsort(d[0]))

    lp = clf.predict_log_proba([[3, 2]])
    p = clf.predict_proba([[3, 2]])
    assert_array_almost_equal(np.log(p), lp)

    lp = clf.predict_log_proba([[-1, -1]])
    p = clf.predict_proba([[-1, -1]])
    assert_array_almost_equal(np.log(p), lp)

    # Modified Huber multiclass probability estimates; requires a separate
    # test because the hard zero/one probabilities may destroy the
    # ordering present in decision_function output.
    clf = klass(loss="modified_huber", alpha=0.01, max_iter=10)
    clf.fit(X2, Y2)
    d = clf.decision_function([[3, 2]])
    p = clf.predict_proba([[3, 2]])
    if klass != SparseSGDClassifier:
        assert np.argmax(d, axis=1) == np.argmax(p, axis=1)
    else:   # XXX the sparse test gets a different X2 (?)
        assert np.argmin(d, axis=1) == np.argmin(p, axis=1)

    # the following sample produces decision_function values < -1,
    # which would cause naive normalization to fail (see comment
    # in SGDClassifier.predict_proba)
    x = X.mean(axis=0)
    d = clf.decision_function([x])
    if np.all(d < -1):  # XXX not true in sparse test case (why?)
        p = clf.predict_proba([x])
        assert_array_almost_equal(p[0], [1 / 3.] * 3)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_sgd_l1(klass):
    # Test L1 regularization
    n = len(X4)
    rng = np.random.RandomState(13)
    idx = np.arange(n)
    rng.shuffle(idx)

    X = X4[idx, :]
    Y = Y4[idx]

    clf = klass(penalty='l1', alpha=.2, fit_intercept=False,
                max_iter=2000, tol=None, shuffle=False)
    clf.fit(X, Y)
    assert_array_equal(clf.coef_[0, 1:-1], np.zeros((4,)))
    pred = clf.predict(X)
    assert_array_equal(pred, Y)

    # test sparsify with dense inputs
    clf.sparsify()
    assert sp.issparse(clf.coef_)
    pred = clf.predict(X)
    assert_array_equal(pred, Y)

    # pickle and unpickle with sparse coef_
    clf = pickle.loads(pickle.dumps(clf))
    assert sp.issparse(clf.coef_)
    pred = clf.predict(X)
    assert_array_equal(pred, Y)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_class_weights(klass):
    # Test class weights.
    X = np.array([[-1.0, -1.0], [-1.0, 0], [-.8, -1.0],
                  [1.0, 1.0], [1.0, 0.0]])
    y = [1, 1, 1, -1, -1]

    clf = klass(alpha=0.1, max_iter=1000, fit_intercept=False,
                class_weight=None)
    clf.fit(X, y)
    assert_array_equal(clf.predict([[0.2, -1.0]]), np.array([1]))

    # we give a small weights to class 1
    clf = klass(alpha=0.1, max_iter=1000, fit_intercept=False,
                class_weight={1: 0.001})
    clf.fit(X, y)

    # now the hyperplane should rotate clock-wise and
    # the prediction on this point should shift
    assert_array_equal(clf.predict([[0.2, -1.0]]), np.array([-1]))


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_equal_class_weight(klass):
    # Test if equal class weights approx. equals no class weights.
    X = [[1, 0], [1, 0], [0, 1], [0, 1]]
    y = [0, 0, 1, 1]
    clf = klass(alpha=0.1, max_iter=1000, class_weight=None)
    clf.fit(X, y)

    X = [[1, 0], [0, 1]]
    y = [0, 1]
    clf_weighted = klass(alpha=0.1, max_iter=1000,
                         class_weight={0: 0.5, 1: 0.5})
    clf_weighted.fit(X, y)

    # should be similar up to some epsilon due to learning rate schedule
    assert_almost_equal(clf.coef_, clf_weighted.coef_, decimal=2)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_wrong_class_weight_label(klass):
    # ValueError due to not existing class label.
    clf = klass(alpha=0.1, max_iter=1000, class_weight={0: 0.5})
    assert_raises(ValueError, clf.fit, X, Y)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_wrong_class_weight_format(klass):
    # ValueError due to wrong class_weight argument type.
    clf = klass(alpha=0.1, max_iter=1000, class_weight=[0.5])
    assert_raises(ValueError, clf.fit, X, Y)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_weights_multiplied(klass):
    # Tests that class_weight and sample_weight are multiplicative
    class_weights = {1: .6, 2: .3}
    rng = np.random.RandomState(0)
    sample_weights = rng.random_sample(Y4.shape[0])
    multiplied_together = np.copy(sample_weights)
    multiplied_together[Y4 == 1] *= class_weights[1]
    multiplied_together[Y4 == 2] *= class_weights[2]

    clf1 = klass(alpha=0.1, max_iter=20, class_weight=class_weights)
    clf2 = klass(alpha=0.1, max_iter=20)

    clf1.fit(X4, Y4, sample_weight=sample_weights)
    clf2.fit(X4, Y4, sample_weight=multiplied_together)

    assert_almost_equal(clf1.coef_, clf2.coef_)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_balanced_weight(klass):
    # Test class weights for imbalanced data"""
    # compute reference metrics on iris dataset that is quite balanced by
    # default
    X, y = iris.data, iris.target
    X = scale(X)
    idx = np.arange(X.shape[0])
    rng = np.random.RandomState(6)
    rng.shuffle(idx)
    X = X[idx]
    y = y[idx]
    clf = klass(alpha=0.0001, max_iter=1000,
                class_weight=None, shuffle=False).fit(X, y)
    f1 = metrics.f1_score(y, clf.predict(X), average='weighted')
    assert_almost_equal(f1, 0.96, decimal=1)

    # make the same prediction using balanced class_weight
    clf_balanced = klass(alpha=0.0001, max_iter=1000,
                         class_weight="balanced",
                         shuffle=False).fit(X, y)
    f1 = metrics.f1_score(y, clf_balanced.predict(X), average='weighted')
    assert_almost_equal(f1, 0.96, decimal=1)

    # Make sure that in the balanced case it does not change anything
    # to use "balanced"
    assert_array_almost_equal(clf.coef_, clf_balanced.coef_, 6)

    # build an very very imbalanced dataset out of iris data
    X_0 = X[y == 0, :]
    y_0 = y[y == 0]

    X_imbalanced = np.vstack([X] + [X_0] * 10)
    y_imbalanced = np.concatenate([y] + [y_0] * 10)

    # fit a model on the imbalanced data without class weight info
    clf = klass(max_iter=1000, class_weight=None, shuffle=False)
    clf.fit(X_imbalanced, y_imbalanced)
    y_pred = clf.predict(X)
    assert metrics.f1_score(y, y_pred, average='weighted') < 0.96

    # fit a model with balanced class_weight enabled
    clf = klass(max_iter=1000, class_weight="balanced",
                shuffle=False)
    clf.fit(X_imbalanced, y_imbalanced)
    y_pred = clf.predict(X)
    assert metrics.f1_score(y, y_pred, average='weighted') > 0.96


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_sample_weights(klass):
    # Test weights on individual samples
    X = np.array([[-1.0, -1.0], [-1.0, 0], [-.8, -1.0],
                  [1.0, 1.0], [1.0, 0.0]])
    y = [1, 1, 1, -1, -1]

    clf = klass(alpha=0.1, max_iter=1000, fit_intercept=False)
    clf.fit(X, y)
    assert_array_equal(clf.predict([[0.2, -1.0]]), np.array([1]))

    # we give a small weights to class 1
    clf.fit(X, y, sample_weight=[0.001] * 3 + [1] * 2)

    # now the hyperplane should rotate clock-wise and
    # the prediction on this point should shift
    assert_array_equal(clf.predict([[0.2, -1.0]]), np.array([-1]))


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_wrong_sample_weights(klass):
    # Test if ValueError is raised if sample_weight has wrong shape
    clf = klass(alpha=0.1, max_iter=1000, fit_intercept=False)
    # provided sample_weight too long
    assert_raises(ValueError, clf.fit, X, Y, sample_weight=np.arange(7))


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_partial_fit_exception(klass):
    clf = klass(alpha=0.01)
    # classes was not specified
    assert_raises(ValueError, clf.partial_fit, X3, Y3)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_partial_fit_binary(klass):
    third = X.shape[0] // 3
    clf = klass(alpha=0.01)
    classes = np.unique(Y)

    clf.partial_fit(X[:third], Y[:third], classes=classes)
    assert clf.coef_.shape == (1, X.shape[1])
    assert clf.intercept_.shape == (1,)
    assert clf.decision_function([[0, 0]]).shape == (1, )
    id1 = id(clf.coef_.data)

    clf.partial_fit(X[third:], Y[third:])
    id2 = id(clf.coef_.data)
    # check that coef_ haven't been re-allocated
    assert id1, id2

    y_pred = clf.predict(T)
    assert_array_equal(y_pred, true_result)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_partial_fit_multiclass(klass):
    third = X2.shape[0] // 3
    clf = klass(alpha=0.01)
    classes = np.unique(Y2)

    clf.partial_fit(X2[:third], Y2[:third], classes=classes)
    assert clf.coef_.shape == (3, X2.shape[1])
    assert clf.intercept_.shape == (3,)
    assert clf.decision_function([[0, 0]]).shape == (1, 3)
    id1 = id(clf.coef_.data)

    clf.partial_fit(X2[third:], Y2[third:])
    id2 = id(clf.coef_.data)
    # check that coef_ haven't been re-allocated
    assert id1, id2


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_partial_fit_multiclass_average(klass):
    third = X2.shape[0] // 3
    clf = klass(alpha=0.01, average=X2.shape[0])
    classes = np.unique(Y2)

    clf.partial_fit(X2[:third], Y2[:third], classes=classes)
    assert clf.coef_.shape == (3, X2.shape[1])
    assert clf.intercept_.shape == (3,)

    clf.partial_fit(X2[third:], Y2[third:])
    assert clf.coef_.shape == (3, X2.shape[1])
    assert clf.intercept_.shape == (3,)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_fit_then_partial_fit(klass):
    # Partial_fit should work after initial fit in the multiclass case.
    # Non-regression test for #2496; fit would previously produce a
    # Fortran-ordered coef_ that subsequent partial_fit couldn't handle.
    clf = klass()
    clf.fit(X2, Y2)
    clf.partial_fit(X2, Y2)     # no exception here


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
@pytest.mark.parametrize('lr',
                         ["constant", "optimal", "invscaling", "adaptive"])
def test_partial_fit_equal_fit_classif(klass, lr):
    for X_, Y_, T_ in ((X, Y, T), (X2, Y2, T2)):
        clf = klass(alpha=0.01, eta0=0.01, max_iter=2,
                    learning_rate=lr, shuffle=False)
        clf.fit(X_, Y_)
        y_pred = clf.decision_function(T_)
        t = clf.t_

        classes = np.unique(Y_)
        clf = klass(alpha=0.01, eta0=0.01, learning_rate=lr,
                    shuffle=False)
        for i in range(2):
            clf.partial_fit(X_, Y_, classes=classes)
        y_pred2 = clf.decision_function(T_)

        assert clf.t_ == t
        assert_array_almost_equal(y_pred, y_pred2, decimal=2)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_regression_losses(klass):
    random_state = np.random.RandomState(1)
    clf = klass(alpha=0.01, learning_rate="constant",
                eta0=0.1, loss="epsilon_insensitive",
                random_state=random_state)
    clf.fit(X, Y)
    assert 1.0 == np.mean(clf.predict(X) == Y)

    clf = klass(alpha=0.01, learning_rate="constant",
                eta0=0.1, loss="squared_epsilon_insensitive",
                random_state=random_state)
    clf.fit(X, Y)
    assert 1.0 == np.mean(clf.predict(X) == Y)

    clf = klass(alpha=0.01, loss="huber", random_state=random_state)
    clf.fit(X, Y)
    assert 1.0 == np.mean(clf.predict(X) == Y)

    clf = klass(alpha=0.01, learning_rate="constant", eta0=0.01,
                loss="squared_loss", random_state=random_state)
    clf.fit(X, Y)
    assert 1.0 == np.mean(clf.predict(X) == Y)


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_warm_start_multiclass(klass):
    _test_warm_start(klass, X2, Y2, "optimal")


@pytest.mark.parametrize('klass', [SGDClassifier, SparseSGDClassifier])
def test_multiple_fit(klass):
    # Test multiple calls of fit w/ different shaped inputs.
    clf = klass(alpha=0.01, shuffle=False)
    clf.fit(X, Y)
    assert hasattr(clf, "coef_")

    # Non-regression test: try fitting with a different label set.
    y = [["ham", "spam"][i] for i in LabelEncoder().fit_transform(Y)]
    clf.fit(X[:, :-1], y)


###############################################################################
# Regression Test Case

@pytest.mark.parametrize('klass', [SGDRegressor, SparseSGDRegressor])
def test_sgd_reg(klass):
    # Check that SGD gives any results.
    clf = klass(alpha=0.1, max_iter=2, fit_intercept=False)
    clf.fit([[0, 0], [1, 1], [2, 2]], [0, 1, 2])
    assert clf.coef_[0] == clf.coef_[1]


@pytest.mark.parametrize('klass', [SGDRegressor, SparseSGDRegressor])
def test_sgd_averaged_computed_correctly(klass):
    # Tests the average regressor matches the naive implementation

    eta = .001
    alpha = .01
    n_samples = 20
    n_features = 10
    rng = np.random.RandomState(0)
    X = rng.normal(size=(n_samples, n_features))
    w = rng.normal(size=n_features)

    # simple linear function without noise
    y = np.dot(X, w)

    clf = klass(loss='squared_loss',
                learning_rate='constant',
                eta0=eta, alpha=alpha,
                fit_intercept=True,
                max_iter=1, average=True, shuffle=False)

    clf.fit(X, y)
    average_weights, average_intercept = asgd(klass, X, y, eta, alpha)

    assert_array_almost_equal(clf.coef_,
                              average_weights,
                              decimal=16)
    assert_almost_equal(clf.intercept_, average_intercept, decimal=16)


@pytest.mark.parametrize('klass', [SGDRegressor, SparseSGDRegressor])
def test_sgd_averaged_partial_fit(klass):
    # Tests whether the partial fit yields the same average as the fit
    eta = .001
    alpha = .01
    n_samples = 20
    n_features = 10
    rng = np.random.RandomState(0)
    X = rng.normal(size=(n_samples, n_features))
    w = rng.normal(size=n_features)

    # simple linear function without noise
    y = np.dot(X, w)

    clf = klass(loss='squared_loss',
                learning_rate='constant',
                eta0=eta, alpha=alpha,
                fit_intercept=True,
                max_iter=1, average=True, shuffle=False)

    clf.partial_fit(X[:int(n_samples / 2)][:], y[:int(n_samples / 2)])
    clf.partial_fit(X[int(n_samples / 2):][:], y[int(n_samples / 2):])
    average_weights, average_intercept = asgd(klass, X, y, eta, alpha)

    assert_array_almost_equal(clf.coef_,
                              average_weights,
                              decimal=16)
    assert_almost_equal(clf.intercept_[0], average_intercept, decimal=16)


@pytest.mark.parametrize('klass', [SGDRegressor, SparseSGDRegressor])
def test_average_sparse(klass):
    # Checks the average weights on data with 0s

    eta = .001
    alpha = .01
    clf = klass(loss='squared_loss',
                learning_rate='constant',
                eta0=eta, alpha=alpha,
                fit_intercept=True,
                max_iter=1, average=True, shuffle=False)

    n_samples = Y3.shape[0]

    clf.partial_fit(X3[:int(n_samples / 2)][:], Y3[:int(n_samples / 2)])
    clf.partial_fit(X3[int(n_samples / 2):][:], Y3[int(n_samples / 2):])
    average_weights, average_intercept = asgd(klass, X3, Y3, eta, alpha)

    assert_array_almost_equal(clf.coef_,
                              average_weights,
                              decimal=16)
    assert_almost_equal(clf.intercept_, average_intercept, decimal=16)


@pytest.mark.parametrize('klass', [SGDRegressor, SparseSGDRegressor])
def test_sgd_least_squares_fit(klass):
    xmin, xmax = -5, 5
    n_samples = 100
    rng = np.random.RandomState(0)
    X = np.linspace(xmin, xmax, n_samples).reshape(n_samples, 1)

    # simple linear function without noise
    y = 0.5 * X.ravel()

    clf = klass(loss='squared_loss', alpha=0.1, max_iter=20,
                fit_intercept=False)
    clf.fit(X, y)
    score = clf.score(X, y)
    assert score > 0.99

    # simple linear function with noise
    y = 0.5 * X.ravel() + rng.randn(n_samples, 1).ravel()

    clf = klass(loss='squared_loss', alpha=0.1, max_iter=20,
                fit_intercept=False)
    clf.fit(X, y)
    score = clf.score(X, y)
    assert score > 0.5


@pytest.mark.parametrize('klass', [SGDRegressor, SparseSGDRegressor])
def test_sgd_epsilon_insensitive(klass):
    xmin, xmax = -5, 5
    n_samples = 100
    rng = np.random.RandomState(0)
    X = np.linspace(xmin, xmax, n_samples).reshape(n_samples, 1)

    # simple linear function without noise
    y = 0.5 * X.ravel()

    clf = klass(loss='epsilon_insensitive', epsilon=0.01,
                alpha=0.1, max_iter=20,
                fit_intercept=False)
    clf.fit(X, y)
    score = clf.score(X, y)
    assert score > 0.99

    # simple linear function with noise
    y = 0.5 * X.ravel() + rng.randn(n_samples, 1).ravel()

    clf = klass(loss='epsilon_insensitive', epsilon=0.01,
                alpha=0.1, max_iter=20,
                fit_intercept=False)
    clf.fit(X, y)
    score = clf.score(X, y)
    assert score > 0.5


@pytest.mark.parametrize('klass', [SGDRegressor, SparseSGDRegressor])
def test_sgd_huber_fit(klass):
    xmin, xmax = -5, 5
    n_samples = 100
    rng = np.random.RandomState(0)
    X = np.linspace(xmin, xmax, n_samples).reshape(n_samples, 1)

    # simple linear function without noise
    y = 0.5 * X.ravel()

    clf = klass(loss="huber", epsilon=0.1, alpha=0.1, max_iter=20,
                fit_intercept=False)
    clf.fit(X, y)
    score = clf.score(X, y)
    assert score > 0.99

    # simple linear function with noise
    y = 0.5 * X.ravel() + rng.randn(n_samples, 1).ravel()

    clf = klass(loss="huber", epsilon=0.1, alpha=0.1, max_iter=20,
                fit_intercept=False)
    clf.fit(X, y)
    score = clf.score(X, y)
    assert score > 0.5


@pytest.mark.parametrize('klass', [SGDRegressor, SparseSGDRegressor])
def test_elasticnet_convergence(klass):
    # Check that the SGD output is consistent with coordinate descent

    n_samples, n_features = 1000, 5
    rng = np.random.RandomState(0)
    X = rng.randn(n_samples, n_features)
    # ground_truth linear model that generate y from X and to which the
    # models should converge if the regularizer would be set to 0.0
    ground_truth_coef = rng.randn(n_features)
    y = np.dot(X, ground_truth_coef)

    # XXX: alpha = 0.1 seems to cause convergence problems
    for alpha in [0.01, 0.001]:
        for l1_ratio in [0.5, 0.8, 1.0]:
            cd = linear_model.ElasticNet(alpha=alpha, l1_ratio=l1_ratio,
                                         fit_intercept=False)
            cd.fit(X, y)
            sgd = klass(penalty='elasticnet', max_iter=50,
                        alpha=alpha, l1_ratio=l1_ratio,
                        fit_intercept=False)
            sgd.fit(X, y)
            err_msg = ("cd and sgd did not converge to comparable "
                       "results for alpha=%f and l1_ratio=%f"
                       % (alpha, l1_ratio))
            assert_almost_equal(cd.coef_, sgd.coef_, decimal=2,
                                err_msg=err_msg)


@ignore_warnings
@pytest.mark.parametrize('klass', [SGDRegressor, SparseSGDRegressor])
def test_partial_fit(klass):
    third = X.shape[0] // 3
    clf = klass(alpha=0.01)

    clf.partial_fit(X[:third], Y[:third])
    assert clf.coef_.shape == (X.shape[1], )
    assert clf.intercept_.shape == (1,)
    assert clf.predict([[0, 0]]).shape == (1, )
    id1 = id(clf.coef_.data)

    clf.partial_fit(X[third:], Y[third:])
    id2 = id(clf.coef_.data)
    # check that coef_ haven't been re-allocated
    assert id1, id2


@pytest.mark.parametrize('klass', [SGDRegressor, SparseSGDRegressor])
@pytest.mark.parametrize('lr',
                         ["constant", "optimal", "invscaling", "adaptive"])
def test_partial_fit_equal_fit(klass, lr):
    clf = klass(alpha=0.01, max_iter=2, eta0=0.01,
                learning_rate=lr, shuffle=False)
    clf.fit(X, Y)
    y_pred = clf.predict(T)
    t = clf.t_

    clf = klass(alpha=0.01, eta0=0.01,
                learning_rate=lr, shuffle=False)
    for i in range(2):
        clf.partial_fit(X, Y)
    y_pred2 = clf.predict(T)

    assert clf.t_ == t
    assert_array_almost_equal(y_pred, y_pred2, decimal=2)


@pytest.mark.parametrize('klass', [SGDRegressor, SparseSGDRegressor])
def test_loss_function_epsilon(klass):
    clf = klass(epsilon=0.9)
    clf.set_params(epsilon=0.1)
    assert clf.loss_functions['huber'][1] == 0.1


def test_l1_ratio():
    # Test if l1 ratio extremes match L1 and L2 penalty settings.
    X, y = datasets.make_classification(n_samples=1000,
                                        n_features=100, n_informative=20,
                                        random_state=1234)

    # test if elasticnet with l1_ratio near 1 gives same result as pure l1
    est_en = SGDClassifier(alpha=0.001, penalty='elasticnet', tol=None,
                           max_iter=6, l1_ratio=0.9999999999,
                           random_state=42).fit(X, y)
    est_l1 = SGDClassifier(alpha=0.001, penalty='l1', max_iter=6,
                           random_state=42, tol=None).fit(X, y)
    assert_array_almost_equal(est_en.coef_, est_l1.coef_)

    # test if elasticnet with l1_ratio near 0 gives same result as pure l2
    est_en = SGDClassifier(alpha=0.001, penalty='elasticnet', tol=None,
                           max_iter=6, l1_ratio=0.0000000001,
                           random_state=42).fit(X, y)
    est_l2 = SGDClassifier(alpha=0.001, penalty='l2', max_iter=6,
                           random_state=42, tol=None).fit(X, y)
    assert_array_almost_equal(est_en.coef_, est_l2.coef_)


def test_underflow_or_overlow():
    with np.errstate(all='raise'):
        # Generate some weird data with hugely unscaled features
        rng = np.random.RandomState(0)
        n_samples = 100
        n_features = 10

        X = rng.normal(size=(n_samples, n_features))
        X[:, :2] *= 1e300
        assert np.isfinite(X).all()

        # Use MinMaxScaler to scale the data without introducing a numerical
        # instability (computing the standard deviation naively is not possible
        # on this data)
        X_scaled = MinMaxScaler().fit_transform(X)
        assert np.isfinite(X_scaled).all()

        # Define a ground truth on the scaled data
        ground_truth = rng.normal(size=n_features)
        y = (np.dot(X_scaled, ground_truth) > 0.).astype(np.int32)
        assert_array_equal(np.unique(y), [0, 1])

        model = SGDClassifier(alpha=0.1, loss='squared_hinge', max_iter=500)

        # smoke test: model is stable on scaled data
        model.fit(X_scaled, y)
        assert np.isfinite(model.coef_).all()

        # model is numerically unstable on unscaled data
        msg_regxp = (r"Floating-point under-/overflow occurred at epoch #.*"
                     " Scaling input data with StandardScaler or MinMaxScaler"
                     " might help.")
        assert_raises_regexp(ValueError, msg_regxp, model.fit, X, y)


def test_numerical_stability_large_gradient():
    # Non regression test case for numerical stability on scaled problems
    # where the gradient can still explode with some losses
    model = SGDClassifier(loss='squared_hinge', max_iter=10, shuffle=True,
                          penalty='elasticnet', l1_ratio=0.3, alpha=0.01,
                          eta0=0.001, random_state=0, tol=None)
    with np.errstate(all='raise'):
        model.fit(iris.data, iris.target)
    assert np.isfinite(model.coef_).all()


@pytest.mark.parametrize('penalty', ['l2', 'l1', 'elasticnet'])
def test_large_regularization(penalty):
    # Non regression tests for numerical stability issues caused by large
    # regularization parameters
    model = SGDClassifier(alpha=1e5, learning_rate='constant', eta0=0.1,
                          penalty=penalty, shuffle=False,
                          tol=None, max_iter=6)
    with np.errstate(all='raise'):
        model.fit(iris.data, iris.target)
    assert_array_almost_equal(model.coef_, np.zeros_like(model.coef_))


def test_tol_parameter():
    # Test that the tol parameter behaves as expected
    X = StandardScaler().fit_transform(iris.data)
    y = iris.target == 1

    # With tol is None, the number of iteration should be equal to max_iter
    max_iter = 42
    model_0 = SGDClassifier(tol=None, random_state=0, max_iter=max_iter)
    model_0.fit(X, y)
    assert max_iter == model_0.n_iter_

    # If tol is not None, the number of iteration should be less than max_iter
    max_iter = 2000
    model_1 = SGDClassifier(tol=0, random_state=0, max_iter=max_iter)
    model_1.fit(X, y)
    assert max_iter > model_1.n_iter_
    assert model_1.n_iter_ > 5

    # A larger tol should yield a smaller number of iteration
    model_2 = SGDClassifier(tol=0.1, random_state=0, max_iter=max_iter)
    model_2.fit(X, y)
    assert model_1.n_iter_ > model_2.n_iter_
    assert model_2.n_iter_ > 3

    # Strict tolerance and small max_iter should trigger a warning
    model_3 = SGDClassifier(max_iter=3, tol=1e-3, random_state=0)
    model_3 = assert_warns(ConvergenceWarning, model_3.fit, X, y)
    assert model_3.n_iter_ == 3


def _test_gradient_common(loss_function, cases):
    # Test gradient of different loss functions
    # cases is a list of (p, y, expected)
    for p, y, expected in cases:
        assert_almost_equal(loss_function.dloss(p, y), expected)


def test_gradient_hinge():
    # Test Hinge (hinge / perceptron)
    # hinge
    loss = sgd_fast.Hinge(1.0)
    cases = [
        # (p, y, expected)
        (1.1, 1.0, 0.0), (-2.0, -1.0, 0.0),
        (1.0, 1.0, -1.0), (-1.0, -1.0, 1.0), (0.5, 1.0, -1.0),
        (2.0, -1.0, 1.0), (-0.5, -1.0, 1.0), (0.0, 1.0, -1.0)
    ]
    _test_gradient_common(loss, cases)

    # perceptron
    loss = sgd_fast.Hinge(0.0)
    cases = [
        # (p, y, expected)
        (1.0, 1.0, 0.0), (-0.1, -1.0, 0.0),
        (0.0, 1.0, -1.0), (0.0, -1.0, 1.0), (0.5, -1.0, 1.0),
        (2.0, -1.0, 1.0), (-0.5, 1.0, -1.0), (-1.0, 1.0, -1.0),
    ]
    _test_gradient_common(loss, cases)


def test_gradient_squared_hinge():
    # Test SquaredHinge
    loss = sgd_fast.SquaredHinge(1.0)
    cases = [
        # (p, y, expected)
        (1.0, 1.0, 0.0), (-2.0, -1.0, 0.0), (1.0, -1.0, 4.0),
        (-1.0, 1.0, -4.0), (0.5, 1.0, -1.0), (0.5, -1.0, 3.0)
    ]
    _test_gradient_common(loss, cases)


def test_gradient_log():
    # Test Log (logistic loss)
    loss = sgd_fast.Log()
    cases = [
        # (p, y, expected)
        (1.0, 1.0, -1.0 / (np.exp(1.0) + 1.0)),
        (1.0, -1.0, 1.0 / (np.exp(-1.0) + 1.0)),
        (-1.0, -1.0, 1.0 / (np.exp(1.0) + 1.0)),
        (-1.0, 1.0, -1.0 / (np.exp(-1.0) + 1.0)),
        (0.0, 1.0, -0.5), (0.0, -1.0, 0.5),
        (17.9, -1.0, 1.0), (-17.9, 1.0, -1.0),
    ]
    _test_gradient_common(loss, cases)
    assert_almost_equal(loss.dloss(18.1, 1.0), np.exp(-18.1) * -1.0, 16)
    assert_almost_equal(loss.dloss(-18.1, -1.0), np.exp(-18.1) * 1.0, 16)


def test_gradient_squared_loss():
    # Test SquaredLoss
    loss = sgd_fast.SquaredLoss()
    cases = [
        # (p, y, expected)
        (0.0, 0.0, 0.0), (1.0, 1.0, 0.0), (1.0, 0.0, 1.0),
        (0.5, -1.0, 1.5), (-2.5, 2.0, -4.5)
    ]
    _test_gradient_common(loss, cases)


def test_gradient_huber():
    # Test Huber
    loss = sgd_fast.Huber(0.1)
    cases = [
        # (p, y, expected)
        (0.0, 0.0, 0.0), (0.1, 0.0, 0.1), (0.0, 0.1, -0.1),
        (3.95, 4.0, -0.05), (5.0, 2.0, 0.1), (-1.0, 5.0, -0.1)
    ]
    _test_gradient_common(loss, cases)


def test_gradient_modified_huber():
    # Test ModifiedHuber
    loss = sgd_fast.ModifiedHuber()
    cases = [
        # (p, y, expected)
        (1.0, 1.0, 0.0), (-1.0, -1.0, 0.0), (2.0, 1.0, 0.0),
        (0.0, 1.0, -2.0), (-1.0, 1.0, -4.0), (0.5, -1.0, 3.0),
        (0.5, -1.0, 3.0), (-2.0, 1.0, -4.0), (-3.0, 1.0, -4.0)
    ]
    _test_gradient_common(loss, cases)


def test_gradient_epsilon_insensitive():
    # Test EpsilonInsensitive
    loss = sgd_fast.EpsilonInsensitive(0.1)
    cases = [
        (0.0, 0.0, 0.0), (0.1, 0.0, 0.0), (-2.05, -2.0, 0.0),
        (3.05, 3.0, 0.0), (2.2, 2.0, 1.0), (2.0, -1.0, 1.0),
        (2.0, 2.2, -1.0), (-2.0, 1.0, -1.0)
    ]
    _test_gradient_common(loss, cases)


def test_gradient_squared_epsilon_insensitive():
    # Test SquaredEpsilonInsensitive
    loss = sgd_fast.SquaredEpsilonInsensitive(0.1)
    cases = [
        (0.0, 0.0, 0.0), (0.1, 0.0, 0.0), (-2.05, -2.0, 0.0),
        (3.05, 3.0, 0.0), (2.2, 2.0, 0.2), (2.0, -1.0, 5.8),
        (2.0, 2.2, -0.2), (-2.0, 1.0, -5.8)
    ]
    _test_gradient_common(loss, cases)


def test_multi_thread_multi_class_and_early_stopping():
    # This is a non-regression test for a bad interaction between
    # early stopping internal attribute and thread-based parallelism.
    clf = SGDClassifier(alpha=1e-3, tol=1e-3, max_iter=1000,
                        early_stopping=True, n_iter_no_change=100,
                        random_state=0, n_jobs=2)
    clf.fit(iris.data, iris.target)
    assert clf.n_iter_ > clf.n_iter_no_change
    assert clf.n_iter_ < clf.n_iter_no_change + 20
    assert clf.score(iris.data, iris.target) > 0.8


def test_multi_core_gridsearch_and_early_stopping():
    # This is a non-regression test for a bad interaction between
    # early stopping internal attribute and process-based multi-core
    # parallelism.
    param_grid = {
        'alpha': np.logspace(-4, 4, 9),
        'n_iter_no_change': [5, 10, 50],
    }

    clf = SGDClassifier(tol=1e-2, max_iter=1000, early_stopping=True,
                        random_state=0)
    search = RandomizedSearchCV(clf, param_grid, n_iter=3, n_jobs=2,
                                random_state=0)
    search.fit(iris.data, iris.target)
    assert search.best_score_ > 0.8


@pytest.mark.parametrize("backend",
                         ["loky", "multiprocessing", "threading"])
def test_SGDClassifier_fit_for_all_backends(backend):
    # This is a non-regression smoke test. In the multi-class case,
    # SGDClassifier.fit fits each class in a one-versus-all fashion using
    # joblib.Parallel.  However, each OvA step updates the coef_ attribute of
    # the estimator in-place. Internally, SGDClassifier calls Parallel using
    # require='sharedmem'. This test makes sure SGDClassifier.fit works
    # consistently even when the user asks for a backend that does not provide
    # sharedmem semantics.

    # We further test a case where memmapping would have been used if
    # SGDClassifier.fit was called from a loky or multiprocessing backend. In
    # this specific case, in-place modification of clf.coef_ would have caused
    # a segmentation fault when trying to write in a readonly memory mapped
    # buffer.

    if (parse_version(joblib.__version__) < parse_version('0.12')
            and backend == 'loky'):
        pytest.skip('loky backend does not exist in joblib <0.12')

    random_state = np.random.RandomState(42)

    # Create a classification problem with 50000 features and 20 classes. Using
    # loky or multiprocessing this make the clf.coef_ exceed the threshold
    # above which memmaping is used in joblib and loky (1MB as of 2018/11/1).
    X = sp.random(500, 2000, density=0.02, format='csr',
                  random_state=random_state)
    y = random_state.choice(20, 500)

    # Begin by fitting a SGD classifier sequentially
    clf_sequential = SGDClassifier(max_iter=1000, n_jobs=1,
                                   random_state=42)
    clf_sequential.fit(X, y)

    # Fit a SGDClassifier using the specified backend, and make sure the
    # coefficients are equal to those obtained using a sequential fit
    clf_parallel = SGDClassifier(max_iter=1000, n_jobs=4,
                                 random_state=42)
    with joblib.parallel_backend(backend=backend):
        clf_parallel.fit(X, y)
    assert_array_almost_equal(clf_sequential.coef_, clf_parallel.coef_)