def test_is_classifier():
svc = SVC()
assert is_classifier(svc)
assert is_classifier(GridSearchCV(svc, {'C': [0.1, 1]}))
assert is_classifier(Pipeline([('svc', svc)]))
assert is_classifier(
Pipeline([('svc_cv', GridSearchCV(svc, {'C': [0.1, 1]}))]))
def test_ovo_gridsearch():
ovo = OneVsOneClassifier(LinearSVC(random_state=0))
Cs = [0.1, 0.5, 0.8]
cv = GridSearchCV(ovo, {'estimator__C': Cs})
cv.fit(iris.data, iris.target)
best_C = cv.best_estimator_.estimators_[0].C
assert best_C in Cs
def test_multi_output_predict_proba():
sgd_linear_clf = SGDClassifier(random_state=1, max_iter=5)
param = {'loss': ('hinge', 'log', 'modified_huber')}
# inner function for custom scoring
def custom_scorer(estimator, X, y):
if hasattr(estimator, "predict_proba"):
return 1.0
else:
return 0.0
grid_clf = GridSearchCV(sgd_linear_clf,
param_grid=param,
scoring=custom_scorer,
cv=3)
multi_target_linear = MultiOutputClassifier(grid_clf)
multi_target_linear.fit(X, y)
multi_target_linear.predict_proba(X)
# SGDClassifier defaults to loss='hinge' which is not a probabilistic
# loss function; therefore it does not expose a predict_proba method
sgd_linear_clf = SGDClassifier(random_state=1, max_iter=5)
multi_target_linear = MultiOutputClassifier(sgd_linear_clf)
multi_target_linear.fit(X, y)
err_msg = "The base estimator should implement predict_proba method"
with pytest.raises(ValueError, match=err_msg):
multi_target_linear.predict_proba(X)
def test_ecoc_gridsearch():
ecoc = OutputCodeClassifier(LinearSVC(random_state=0), random_state=0)
Cs = [0.1, 0.5, 0.8]
cv = GridSearchCV(ecoc, {'estimator__C': Cs})
cv.fit(iris.data, iris.target)
best_C = cv.best_estimator_.estimators_[0].C
assert best_C in Cs
def _test_ridge_cv_normalize(filter_):
ridge_cv = RidgeCV(normalize=True, cv=3)
ridge_cv.fit(filter_(10. * X_diabetes), y_diabetes)
gs = GridSearchCV(Ridge(normalize=True, solver='sparse_cg'),
cv=3,
param_grid={'alpha': ridge_cv.alphas})
gs.fit(filter_(10. * X_diabetes), y_diabetes)
assert gs.best_estimator_.alpha == ridge_cv.alpha_
def test_gridsearch():
# Check that base trees can be grid-searched.
# AdaBoost classification
boost = AdaBoostClassifier(base_estimator=DecisionTreeClassifier())
parameters = {
'n_estimators': (1, 2),
'base_estimator__max_depth': (1, 2),
'algorithm': ('SAMME', 'SAMME.R')
}
clf = GridSearchCV(boost, parameters)
clf.fit(iris.data, iris.target)
# AdaBoost regression
boost = AdaBoostRegressor(base_estimator=DecisionTreeRegressor(),
random_state=0)
parameters = {'n_estimators': (1, 2), 'base_estimator__max_depth': (1, 2)}
clf = GridSearchCV(boost, parameters)
clf.fit(boston.data, boston.target)
def test_kde_pipeline_gridsearch():
# test that kde plays nice in pipelines and grid-searches
X, _ = make_blobs(cluster_std=.1,
random_state=1,
centers=[[0, 1], [1, 0], [0, 0]])
pipe1 = make_pipeline(StandardScaler(with_mean=False, with_std=False),
KernelDensity(kernel="gaussian"))
params = dict(kerneldensity__bandwidth=[0.001, 0.01, 0.1, 1, 10])
search = GridSearchCV(pipe1, param_grid=params)
search.fit(X)
assert search.best_params_['kerneldensity__bandwidth'] == .1
def test_gridsearch_pipeline():
# Test if we can do a grid-search to find parameters to separate
# circles with a perceptron model.
X, y = make_circles(n_samples=400, factor=.3, noise=.05, random_state=0)
kpca = KernelPCA(kernel="rbf", n_components=2)
pipeline = Pipeline([("kernel_pca", kpca),
("Perceptron", Perceptron(max_iter=5))])
param_grid = dict(kernel_pca__gamma=2.**np.arange(-2, 2))
grid_search = GridSearchCV(pipeline, cv=3, param_grid=param_grid)
grid_search.fit(X, y)
assert grid_search.best_score_ == 1
def test_imputation_pipeline_grid_search():
# Test imputation within a pipeline + gridsearch.
X = sparse_random_matrix(100, 100, density=0.10)
missing_values = X.data[0]
pipeline = Pipeline([('imputer',
SimpleImputer(missing_values=missing_values)),
('tree', tree.DecisionTreeRegressor(random_state=0))])
parameters = {'imputer__strategy': ["mean", "median", "most_frequent"]}
Y = sparse_random_matrix(100, 1, density=0.10).toarray()
gs = GridSearchCV(pipeline, parameters)
gs.fit(X, Y)
def test_gridsearch():
"""Check GridSearch support."""
clf1 = LogisticRegression(random_state=1)
clf2 = RandomForestClassifier(random_state=1)
clf3 = GaussianNB()
eclf = VotingClassifier(estimators=[
('lr', clf1), ('rf', clf2), ('gnb', clf3)],
voting='soft')
params = {'lr__C': [1.0, 100.0],
'voting': ['soft', 'hard'],
'weights': [[0.5, 0.5, 0.5], [1.0, 0.5, 0.5]]}
grid = GridSearchCV(estimator=eclf, param_grid=params)
grid.fit(iris.data, iris.target)
def test_raises_on_score_list():
# Test that when a list of scores is returned, we raise proper errors.
X, y = make_blobs(random_state=0)
f1_scorer_no_average = make_scorer(f1_score, average=None)
clf = DecisionTreeClassifier()
assert_raises(ValueError,
cross_val_score,
clf,
X,
y,
scoring=f1_scorer_no_average)
grid_search = GridSearchCV(clf,
scoring=f1_scorer_no_average,
param_grid={'max_depth': [1, 2]})
assert_raises(ValueError, grid_search.fit, X, y)
def test_set_params_passes_all_parameters():
# Make sure all parameters are passed together to set_params
# of nested estimator. Regression test for #9944
class TestDecisionTree(DecisionTreeClassifier):
def set_params(self, **kwargs):
super().set_params(**kwargs)
# expected_kwargs is in test scope
assert kwargs == expected_kwargs
return self
expected_kwargs = {'max_depth': 5, 'min_samples_leaf': 2}
for est in [
Pipeline([('estimator', TestDecisionTree())]),
GridSearchCV(TestDecisionTree(), {})
]:
est.set_params(estimator__max_depth=5, estimator__min_samples_leaf=2)
def test_check_scoring_gridsearchcv():
# test that check_scoring works on GridSearchCV and pipeline.
# slightly redundant non-regression test.
grid = GridSearchCV(LinearSVC(), param_grid={'C': [.1, 1]}, cv=3)
scorer = check_scoring(grid, "f1")
assert isinstance(scorer, _PredictScorer)
pipe = make_pipeline(LinearSVC())
scorer = check_scoring(pipe, "f1")
assert isinstance(scorer, _PredictScorer)
# check that cross_val_score definitely calls the scorer
# and doesn't make any assumptions about the estimator apart from having a
# fit.
scores = cross_val_score(EstimatorWithFit(), [[1], [2], [3]], [1, 0, 1],
scoring=DummyScorer(),
cv=3)
assert_array_equal(scores, 1)
def test_ovr_multilabel_predict_proba():
base_clf = MultinomialNB(alpha=1)
for au in (False, True):
X, Y = datasets.make_multilabel_classification(n_samples=100,
n_features=20,
n_classes=5,
n_labels=3,
length=50,
allow_unlabeled=au,
random_state=0)
X_train, Y_train = X[:80], Y[:80]
X_test = X[80:]
clf = OneVsRestClassifier(base_clf).fit(X_train, Y_train)
# Decision function only estimator.
decision_only = OneVsRestClassifier(svm.SVR()).fit(X_train, Y_train)
assert not hasattr(decision_only, 'predict_proba')
# Estimator with predict_proba disabled, depending on parameters.
decision_only = OneVsRestClassifier(svm.SVC(probability=False))
assert not hasattr(decision_only, 'predict_proba')
decision_only.fit(X_train, Y_train)
assert not hasattr(decision_only, 'predict_proba')
assert hasattr(decision_only, 'decision_function')
# Estimator which can get predict_proba enabled after fitting
gs = GridSearchCV(svm.SVC(probability=False),
param_grid={'probability': [True]})
proba_after_fit = OneVsRestClassifier(gs)
assert not hasattr(proba_after_fit, 'predict_proba')
proba_after_fit.fit(X_train, Y_train)
assert hasattr(proba_after_fit, 'predict_proba')
Y_pred = clf.predict(X_test)
Y_proba = clf.predict_proba(X_test)
# predict assigns a label if the probability that the
# sample has the label is greater than 0.5.
pred = Y_proba > .5
assert_array_equal(pred, Y_pred)
def test_ridgecv_sample_weight():
rng = np.random.RandomState(0)
alphas = (0.1, 1.0, 10.0)
# There are different algorithms for n_samples > n_features
# and the opposite, so test them both.
for n_samples, n_features in ((6, 5), (5, 10)):
y = rng.randn(n_samples)
X = rng.randn(n_samples, n_features)
sample_weight = 1.0 + rng.rand(n_samples)
cv = KFold(5)
ridgecv = RidgeCV(alphas=alphas, cv=cv)
ridgecv.fit(X, y, sample_weight=sample_weight)
# Check using GridSearchCV directly
parameters = {'alpha': alphas}
gs = GridSearchCV(Ridge(), parameters, cv=cv)
gs.fit(X, y, sample_weight=sample_weight)
assert ridgecv.alpha_ == gs.best_estimator_.alpha
assert_array_almost_equal(ridgecv.coef_, gs.best_estimator_.coef_)
from mrex.datasets import load_digits
from mrex.neighbors import KernelDensity
from mrex.decomposition import PCA
from mrex.model_selection import GridSearchCV
# load the data
digits = load_digits()
# project the 64-dimensional data to a lower dimension
pca = PCA(n_components=15, whiten=False)
data = pca.fit_transform(digits.data)
# use grid search cross-validation to optimize the bandwidth
params = {'bandwidth': np.logspace(-1, 1, 20)}
grid = GridSearchCV(KernelDensity(), params)
grid.fit(data)
print("best bandwidth: {0}".format(grid.best_estimator_.bandwidth))
# use the best estimator to compute the kernel density estimate
kde = grid.best_estimator_
# sample 44 new points from the data
new_data = kde.sample(44, random_state=0)
new_data = pca.inverse_transform(new_data)
# turn data into a 4x11 grid
new_data = new_data.reshape((4, 11, -1))
real_data = digits.data[:44].reshape((4, 11, -1))
def check_gridsearch(name):
forest = FOREST_CLASSIFIERS[name]()
clf = GridSearchCV(forest, {'n_estimators': (1, 2), 'max_depth': (1, 2)})
clf.fit(iris.data, iris.target)
def __init__(self,
name,
construct,
skip_methods=(),
fit_args=make_classification()):
self.name = name
self.construct = construct
self.fit_args = fit_args
self.skip_methods = skip_methods
DELEGATING_METAESTIMATORS = [
DelegatorData('Pipeline', lambda est: Pipeline([('est', est)])),
DelegatorData(
'GridSearchCV',
lambda est: GridSearchCV(est, param_grid={'param': [5]}, cv=2),
skip_methods=['score']),
DelegatorData('RandomizedSearchCV',
lambda est: RandomizedSearchCV(
est, param_distributions={'param': [5]}, cv=2, n_iter=1),
skip_methods=['score']),
DelegatorData('RFE', RFE, skip_methods=['transform', 'inverse_transform']),
DelegatorData('RFECV',
RFECV,
skip_methods=['transform', 'inverse_transform']),
DelegatorData('BaggingClassifier',
BaggingClassifier,
skip_methods=[
'transform', 'inverse_transform', 'score',
'predict_proba', 'predict_log_proba', 'predict'
])
C_OPTIONS = [1, 10, 100, 1000]
param_grid = [
{
'reduce_dim': [PCA(iterated_power=7), NMF()],
'reduce_dim__n_components': N_FEATURES_OPTIONS,
'classify__C': C_OPTIONS
},
{
'reduce_dim': [SelectKBest(chi2)],
'reduce_dim__k': N_FEATURES_OPTIONS,
'classify__C': C_OPTIONS
},
]
reducer_labels = ['PCA', 'NMF', 'KBest(chi2)']
grid = GridSearchCV(pipe, n_jobs=1, param_grid=param_grid)
X, y = load_digits(return_X_y=True)
grid.fit(X, y)
mean_scores = np.array(grid.cv_results_['mean_test_score'])
# scores are in the order of param_grid iteration, which is alphabetical
mean_scores = mean_scores.reshape(len(C_OPTIONS), -1, len(N_FEATURES_OPTIONS))
# select score for best C
mean_scores = mean_scores.max(axis=0)
bar_offsets = (np.arange(len(N_FEATURES_OPTIONS)) * (len(reducer_labels) + 1) +
.5)
plt.figure()
COLORS = 'bgrcmyk'
for i, (label, reducer_scores) in enumerate(zip(reducer_labels, mean_scores)):
plt.bar(bar_offsets + i, reducer_scores, label=label, color=COLORS[i])
'vect__ngram_range': ((1, 1), (1, 2)), # unigrams or bigrams
# 'tfidf__use_idf': (True, False),
# 'tfidf__norm': ('l1', 'l2'),
'clf__max_iter': (20, ),
'clf__alpha': (0.00001, 0.000001),
'clf__penalty': ('l2', 'elasticnet'),
# 'clf__max_iter': (10, 50, 80),
}
if __name__ == "__main__":
# multiprocessing requires the fork to happen in a __main__ protected
# block
# find the best parameters for both the feature extraction and the
# classifier
grid_search = GridSearchCV(pipeline, parameters, n_jobs=-1, verbose=1)
print("Performing grid search...")
print("pipeline:", [name for name, _ in pipeline.steps])
print("parameters:")
pprint(parameters)
t0 = time()
grid_search.fit(data.data, data.target)
print("done in %0.3fs" % (time() - t0))
print()
print("Best score: %0.3f" % grid_search.best_score_)
print("Best parameters set:")
best_parameters = grid_search.best_estimator_.get_params()
for param_name in sorted(parameters.keys()):
print("\t%s: %r" % (param_name, best_parameters[param_name]))
X_train, X_test, y_train, y_test = train_test_split(
X, y, test_size=0.5, random_state=0)
# Set the parameters by cross-validation
tuned_parameters = [{'kernel': ['rbf'], 'gamma': [1e-3, 1e-4],
'C': [1, 10, 100, 1000]},
{'kernel': ['linear'], 'C': [1, 10, 100, 1000]}]
scores = ['precision', 'recall']
for score in scores:
print("# Tuning hyper-parameters for %s" % score)
print()
clf = GridSearchCV(
SVC(), tuned_parameters, scoring='%s_macro' % score
)
clf.fit(X_train, y_train)
print("Best parameters set found on development set:")
print()
print(clf.best_params_)
print()
print("Grid scores on development set:")
print()
means = clf.cv_results_['mean_test_score']
stds = clf.cv_results_['std_test_score']
for mean, std, params in zip(means, stds, clf.cv_results_['params']):
print("%0.3f (+/-%0.03f) for %r"
% (mean, std * 2, params))
print()
X, y = iris.data, iris.target
# This dataset is way too high-dimensional. Better do PCA:
pca = PCA(n_components=2)
# Maybe some original features where good, too?
selection = SelectKBest(k=1)
# Build estimator from PCA and Univariate selection:
combined_features = FeatureUnion([("pca", pca), ("univ_select", selection)])
# Use combined features to transform dataset:
X_features = combined_features.fit(X, y).transform(X)
print("Combined space has", X_features.shape[1], "features")
svm = SVC(kernel="linear")
# Do grid search over k, n_components and C:
pipeline = Pipeline([("features", combined_features), ("svm", svm)])
param_grid = dict(features__pca__n_components=[1, 2, 3],
features__univ_select__k=[1, 2],
svm__C=[0.1, 1, 10])
grid_search = GridSearchCV(pipeline, param_grid=param_grid, verbose=10)
grid_search.fit(X, y)
print(grid_search.best_estimator_)
"min_samples_split": sp_randint(2, 11),
"bootstrap": [True, False],
"criterion": ["gini", "entropy"]}
# run randomized search
n_iter_search = 20
random_search = RandomizedSearchCV(clf, param_distributions=param_dist,
n_iter=n_iter_search)
start = time()
random_search.fit(X, y)
print("RandomizedSearchCV took %.2f seconds for %d candidates"
" parameter settings." % ((time() - start), n_iter_search))
report(random_search.cv_results_)
# use a full grid over all parameters
param_grid = {"max_depth": [3, None],
"max_features": [1, 3, 10],
"min_samples_split": [2, 3, 10],
"bootstrap": [True, False],
"criterion": ["gini", "entropy"]}
# run grid search
grid_search = GridSearchCV(clf, param_grid=param_grid)
start = time()
grid_search.fit(X, y)
print("GridSearchCV took %.2f seconds for %d candidate parameter settings."
% (time() - start, len(grid_search.cv_results_['params'])))
report(grid_search.cv_results_)
# Append classifier to preprocessing pipeline.
# Now we have a full prediction pipeline.
clf = Pipeline(steps=[('preprocessor',
preprocessor), ('classifier', LogisticRegression())])
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)
clf.fit(X_train, y_train)
print("model score: %.3f" % clf.score(X_test, y_test))
###############################################################################
# Using the prediction pipeline in a grid search
###############################################################################
# Grid search can also be performed on the different preprocessing steps
# defined in the ``ColumnTransformer`` object, together with the classifier's
# hyperparameters as part of the ``Pipeline``.
# We will search for both the imputer strategy of the numeric preprocessing
# and the regularization parameter of the logistic regression using
# :class:`mrex.model_selection.GridSearchCV`.
param_grid = {
'preprocessor__num__imputer__strategy': ['mean', 'median'],
'classifier__C': [0.1, 1.0, 10, 100],
}
grid_search = GridSearchCV(clf, param_grid, cv=10)
grid_search.fit(X_train, y_train)
print(("best logistic regression from grid search: %.3f" %
grid_search.score(X_test, y_test)))
def test_set_params_updates_valid_params():
# Check that set_params tries to set SVC().C, not
# DecisionTreeClassifier().C
gscv = GridSearchCV(DecisionTreeClassifier(), {})
gscv.set_params(estimator=SVC(), estimator__C=42.0)
assert gscv.estimator.C == 42.0
# #############################################################################
# Compute the coefs of a Bayesian Ridge with GridSearch
cv = KFold(2) # cross-validation generator for model selection
ridge = BayesianRidge()
cachedir = tempfile.mkdtemp()
mem = Memory(location=cachedir, verbose=1)
# Ward agglomeration followed by BayesianRidge
connectivity = grid_to_graph(n_x=size, n_y=size)
ward = FeatureAgglomeration(n_clusters=10,
connectivity=connectivity,
memory=mem)
clf = Pipeline([('ward', ward), ('ridge', ridge)])
# Select the optimal number of parcels with grid search
clf = GridSearchCV(clf, {'ward__n_clusters': [10, 20, 30]}, n_jobs=1, cv=cv)
clf.fit(X, y) # set the best parameters
coef_ = clf.best_estimator_.steps[-1][1].coef_
coef_ = clf.best_estimator_.steps[0][1].inverse_transform(coef_)
coef_agglomeration_ = coef_.reshape(size, size)
# Anova univariate feature selection followed by BayesianRidge
f_regression = mem.cache(feature_selection.f_regression) # caching function
anova = feature_selection.SelectPercentile(f_regression)
clf = Pipeline([('anova', anova), ('ridge', ridge)])
# Select the optimal percentage of features with grid search
clf = GridSearchCV(clf, {'anova__percentile': [5, 10, 20]}, cv=cv)
clf.fit(X, y) # set the best parameters
coef_ = clf.best_estimator_.steps[-1][1].coef_
coef_ = clf.best_estimator_.steps[0][1].inverse_transform(coef_.reshape(1, -1))
coef_selection_ = coef_.reshape(size, size)
colors = ['navy', 'cyan', 'darkorange']
lw = 2
for clf, cs, X, y in clf_sets:
# set up the plot for each regressor
fig, axes = plt.subplots(nrows=2, sharey=True, figsize=(9, 10))
for k, train_size in enumerate(np.linspace(0.3, 0.7, 3)[::-1]):
param_grid = dict(C=cs)
# To get nice curve, we need a large number of iterations to
# reduce the variance
grid = GridSearchCV(clf,
refit=False,
param_grid=param_grid,
cv=ShuffleSplit(train_size=train_size,
test_size=.3,
n_splits=250,
random_state=1))
grid.fit(X, y)
scores = grid.cv_results_['mean_test_score']
scales = [
(1, 'No scaling'),
((n_samples * train_size), '1/n_samples'),
]
for ax, (scaler, name) in zip(axes, scales):
ax.set_xlabel('C')
ax.set_ylabel('CV Score')
grid_cs = cs * float(scaler) # scale the C's
from mrex.linear_model import LassoCV
from mrex.linear_model import Lasso
from mrex.model_selection import KFold
from mrex.model_selection import GridSearchCV
X, y = datasets.load_diabetes(return_X_y=True)
X = X[:150]
y = y[:150]
lasso = Lasso(random_state=0, max_iter=10000)
alphas = np.logspace(-4, -0.5, 30)
tuned_parameters = [{'alpha': alphas}]
n_folds = 5
clf = GridSearchCV(lasso, tuned_parameters, cv=n_folds, refit=False)
clf.fit(X, y)
scores = clf.cv_results_['mean_test_score']
scores_std = clf.cv_results_['std_test_score']
plt.figure().set_size_inches(8, 6)
plt.semilogx(alphas, scores)
# plot error lines showing +/- std. errors of the scores
std_error = scores_std / np.sqrt(n_folds)
plt.semilogx(alphas, scores + std_error, 'b--')
plt.semilogx(alphas, scores - std_error, 'b--')
# alpha=0.2 controls the translucency of the fill color
plt.fill_between(alphas, scores + std_error, scores - std_error, alpha=0.2)
# #############################################################################
# Generate sample data
X = 5 * rng.rand(10000, 1)
y = np.sin(X).ravel()
# Add noise to targets
y[::5] += 3 * (0.5 - rng.rand(X.shape[0] // 5))
X_plot = np.linspace(0, 5, 100000)[:, None]
# #############################################################################
# Fit regression model
train_size = 100
svr = GridSearchCV(SVR(kernel='rbf', gamma=0.1),
param_grid={
"C": [1e0, 1e1, 1e2, 1e3],
"gamma": np.logspace(-2, 2, 5)
})
kr = GridSearchCV(KernelRidge(kernel='rbf', gamma=0.1),
param_grid={
"alpha": [1e0, 0.1, 1e-2, 1e-3],
"gamma": np.logspace(-2, 2, 5)
})
t0 = time.time()
svr.fit(X[:train_size], y[:train_size])
svr_fit = time.time() - t0
print("SVR complexity and bandwidth selected and model fitted in %.3f s" %
svr_fit)
ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright,
edgecolors='k')
# and testing points
ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright, alpha=0.6,
edgecolors='k')
ax.set_xlim(xx.min(), xx.max())
ax.set_ylim(yy.min(), yy.max())
ax.set_xticks(())
ax.set_yticks(())
# iterate over classifiers
for est_idx, (name, (estimator, param_grid)) in \
enumerate(zip(names, classifiers)):
ax = axes[ds_cnt, est_idx + 1]
clf = GridSearchCV(estimator=estimator, param_grid=param_grid)
with ignore_warnings(category=ConvergenceWarning):
clf.fit(X_train, y_train)
score = clf.score(X_test, y_test)
print('%s: %.2f' % (name, score))
# plot the decision boundary. For that, we will assign a color to each
# point in the mesh [x_min, x_max]*[y_min, y_max].
if hasattr(clf, "decision_function"):
Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])
else:
Z = clf.predict_proba(np.c_[xx.ravel(), yy.ravel()])[:, 1]
# put the result into a color plot
Z = Z.reshape(xx.shape)
ax.contourf(xx, yy, Z, cmap=cm, alpha=.8)