"""
Several basic tests for hierarchical clustering procedures

"""
# Authors: Vincent Michel, 2010, Gael Varoquaux 2012,
#          Matteo Visconti di Oleggio Castello 2014
# License: BSD 3 clause
from tempfile import mkdtemp
import shutil
import pytest
from functools import partial

import numpy as np
from scipy import sparse
from scipy.cluster import hierarchy

from sklearn.metrics.cluster import adjusted_rand_score
from sklearn.utils._testing import assert_almost_equal
from sklearn.utils._testing import assert_array_almost_equal
from sklearn.utils._testing import assert_raise_message
from sklearn.utils._testing import ignore_warnings

from sklearn.cluster import ward_tree
from sklearn.cluster import AgglomerativeClustering, FeatureAgglomeration
from sklearn.cluster._agglomerative import (_hc_cut, _TREE_BUILDERS,
                                            linkage_tree,
                                            _fix_connectivity)
from sklearn.feature_extraction.image import grid_to_graph
from sklearn.metrics.pairwise import PAIRED_DISTANCES, cosine_distances,\
    manhattan_distances, pairwise_distances
from sklearn.metrics.cluster import normalized_mutual_info_score
from sklearn.neighbors import kneighbors_graph
from sklearn.cluster._hierarchical_fast import average_merge, max_merge
from sklearn.utils._fast_dict import IntFloatDict
from sklearn.utils._testing import assert_array_equal
from sklearn.utils._testing import assert_warns
from sklearn.datasets import make_moons, make_circles


def test_linkage_misc():
    # Misc tests on linkage
    rng = np.random.RandomState(42)
    X = rng.normal(size=(5, 5))
    with pytest.raises(ValueError):
        AgglomerativeClustering(linkage='foo').fit(X)

    with pytest.raises(ValueError):
        linkage_tree(X, linkage='foo')

    with pytest.raises(ValueError):
        linkage_tree(X, connectivity=np.ones((4, 4)))

    # Smoke test FeatureAgglomeration
    FeatureAgglomeration().fit(X)

    # test hierarchical clustering on a precomputed distances matrix
    dis = cosine_distances(X)

    res = linkage_tree(dis, affinity="precomputed")
    assert_array_equal(res[0], linkage_tree(X, affinity="cosine")[0])

    # test hierarchical clustering on a precomputed distances matrix
    res = linkage_tree(X, affinity=manhattan_distances)
    assert_array_equal(res[0], linkage_tree(X, affinity="manhattan")[0])


def test_structured_linkage_tree():
    # Check that we obtain the correct solution for structured linkage trees.
    rng = np.random.RandomState(0)
    mask = np.ones([10, 10], dtype=np.bool)
    # Avoiding a mask with only 'True' entries
    mask[4:7, 4:7] = 0
    X = rng.randn(50, 100)
    connectivity = grid_to_graph(*mask.shape)
    for tree_builder in _TREE_BUILDERS.values():
        children, n_components, n_leaves, parent = \
            tree_builder(X.T, connectivity=connectivity)
        n_nodes = 2 * X.shape[1] - 1
        assert len(children) + n_leaves == n_nodes
        # Check that ward_tree raises a ValueError with a connectivity matrix
        # of the wrong shape
        with pytest.raises(ValueError):
            tree_builder(X.T, connectivity=np.ones((4, 4)))
        # Check that fitting with no samples raises an error
        with pytest.raises(ValueError):
            tree_builder(X.T[:0], connectivity=connectivity)


def test_unstructured_linkage_tree():
    # Check that we obtain the correct solution for unstructured linkage trees.
    rng = np.random.RandomState(0)
    X = rng.randn(50, 100)
    for this_X in (X, X[0]):
        # With specified a number of clusters just for the sake of
        # raising a warning and testing the warning code
        with ignore_warnings():
            children, n_nodes, n_leaves, parent = assert_warns(
                UserWarning, ward_tree, this_X.T, n_clusters=10)
        n_nodes = 2 * X.shape[1] - 1
        assert len(children) + n_leaves == n_nodes

    for tree_builder in _TREE_BUILDERS.values():
        for this_X in (X, X[0]):
            with ignore_warnings():
                children, n_nodes, n_leaves, parent = assert_warns(
                    UserWarning, tree_builder, this_X.T, n_clusters=10)

            n_nodes = 2 * X.shape[1] - 1
            assert len(children) + n_leaves == n_nodes


def test_height_linkage_tree():
    # Check that the height of the results of linkage tree is sorted.
    rng = np.random.RandomState(0)
    mask = np.ones([10, 10], dtype=np.bool)
    X = rng.randn(50, 100)
    connectivity = grid_to_graph(*mask.shape)
    for linkage_func in _TREE_BUILDERS.values():
        children, n_nodes, n_leaves, parent = linkage_func(
            X.T, connectivity=connectivity)
        n_nodes = 2 * X.shape[1] - 1
        assert len(children) + n_leaves == n_nodes


def test_agglomerative_clustering_wrong_arg_memory():
    # Test either if an error is raised when memory is not
    # either a str or a joblib.Memory instance
    rng = np.random.RandomState(0)
    n_samples = 100
    X = rng.randn(n_samples, 50)
    memory = 5
    clustering = AgglomerativeClustering(memory=memory)
    with pytest.raises(ValueError):
        clustering.fit(X)


def test_zero_cosine_linkage_tree():
    # Check that zero vectors in X produce an error when
    # 'cosine' affinity is used
    X = np.array([[0, 1],
                  [0, 0]])
    msg = 'Cosine affinity cannot be used when X contains zero vectors'
    assert_raise_message(ValueError, msg, linkage_tree, X, affinity='cosine')


def test_agglomerative_clustering():
    # Check that we obtain the correct number of clusters with
    # agglomerative clustering.
    rng = np.random.RandomState(0)
    mask = np.ones([10, 10], dtype=np.bool)
    n_samples = 100
    X = rng.randn(n_samples, 50)
    connectivity = grid_to_graph(*mask.shape)
    for linkage in ("ward", "complete", "average", "single"):
        clustering = AgglomerativeClustering(n_clusters=10,
                                             connectivity=connectivity,
                                             linkage=linkage)
        clustering.fit(X)
        # test caching
        try:
            tempdir = mkdtemp()
            clustering = AgglomerativeClustering(
                n_clusters=10, connectivity=connectivity,
                memory=tempdir,
                linkage=linkage)
            clustering.fit(X)
            labels = clustering.labels_
            assert np.size(np.unique(labels)) == 10
        finally:
            shutil.rmtree(tempdir)
        # Turn caching off now
        clustering = AgglomerativeClustering(
            n_clusters=10, connectivity=connectivity, linkage=linkage)
        # Check that we obtain the same solution with early-stopping of the
        # tree building
        clustering.compute_full_tree = False
        clustering.fit(X)
        assert_almost_equal(normalized_mutual_info_score(clustering.labels_,
                                                         labels), 1)
        clustering.connectivity = None
        clustering.fit(X)
        assert np.size(np.unique(clustering.labels_)) == 10
        # Check that we raise a TypeError on dense matrices
        clustering = AgglomerativeClustering(
            n_clusters=10,
            connectivity=sparse.lil_matrix(
                connectivity.toarray()[:10, :10]),
            linkage=linkage)
        with pytest.raises(ValueError):
            clustering.fit(X)

    # Test that using ward with another metric than euclidean raises an
    # exception
    clustering = AgglomerativeClustering(
        n_clusters=10,
        connectivity=connectivity.toarray(),
        affinity="manhattan",
        linkage="ward")
    with pytest.raises(ValueError):
        clustering.fit(X)

    # Test using another metric than euclidean works with linkage complete
    for affinity in PAIRED_DISTANCES.keys():
        # Compare our (structured) implementation to scipy
        clustering = AgglomerativeClustering(
            n_clusters=10,
            connectivity=np.ones((n_samples, n_samples)),
            affinity=affinity,
            linkage="complete")
        clustering.fit(X)
        clustering2 = AgglomerativeClustering(
            n_clusters=10,
            connectivity=None,
            affinity=affinity,
            linkage="complete")
        clustering2.fit(X)
        assert_almost_equal(normalized_mutual_info_score(clustering2.labels_,
                                                         clustering.labels_),
                            1)

    # Test that using a distance matrix (affinity = 'precomputed') has same
    # results (with connectivity constraints)
    clustering = AgglomerativeClustering(n_clusters=10,
                                         connectivity=connectivity,
                                         linkage="complete")
    clustering.fit(X)
    X_dist = pairwise_distances(X)
    clustering2 = AgglomerativeClustering(n_clusters=10,
                                          connectivity=connectivity,
                                          affinity='precomputed',
                                          linkage="complete")
    clustering2.fit(X_dist)
    assert_array_equal(clustering.labels_, clustering2.labels_)


def test_ward_agglomeration():
    # Check that we obtain the correct solution in a simplistic case
    rng = np.random.RandomState(0)
    mask = np.ones([10, 10], dtype=np.bool)
    X = rng.randn(50, 100)
    connectivity = grid_to_graph(*mask.shape)
    agglo = FeatureAgglomeration(n_clusters=5, connectivity=connectivity)
    agglo.fit(X)
    assert np.size(np.unique(agglo.labels_)) == 5

    X_red = agglo.transform(X)
    assert X_red.shape[1] == 5
    X_full = agglo.inverse_transform(X_red)
    assert np.unique(X_full[0]).size == 5
    assert_array_almost_equal(agglo.transform(X_full), X_red)

    # Check that fitting with no samples raises a ValueError
    with pytest.raises(ValueError):
        agglo.fit(X[:0])


def test_single_linkage_clustering():
    # Check that we get the correct result in two emblematic cases
    moons, moon_labels = make_moons(noise=0.05, random_state=42)
    clustering = AgglomerativeClustering(n_clusters=2, linkage='single')
    clustering.fit(moons)
    assert_almost_equal(normalized_mutual_info_score(clustering.labels_,
                                                     moon_labels), 1)

    circles, circle_labels = make_circles(factor=0.5, noise=0.025,
                                          random_state=42)
    clustering = AgglomerativeClustering(n_clusters=2, linkage='single')
    clustering.fit(circles)
    assert_almost_equal(normalized_mutual_info_score(clustering.labels_,
                                                     circle_labels), 1)


def assess_same_labelling(cut1, cut2):
    """Util for comparison with scipy"""
    co_clust = []
    for cut in [cut1, cut2]:
        n = len(cut)
        k = cut.max() + 1
        ecut = np.zeros((n, k))
        ecut[np.arange(n), cut] = 1
        co_clust.append(np.dot(ecut, ecut.T))
    assert (co_clust[0] == co_clust[1]).all()


def test_sparse_scikit_vs_scipy():
    # Test scikit linkage with full connectivity (i.e. unstructured) vs scipy
    n, p, k = 10, 5, 3
    rng = np.random.RandomState(0)

    # Not using a lil_matrix here, just to check that non sparse
    # matrices are well handled
    connectivity = np.ones((n, n))
    for linkage in _TREE_BUILDERS.keys():
        for i in range(5):
            X = .1 * rng.normal(size=(n, p))
            X -= 4. * np.arange(n)[:, np.newaxis]
            X -= X.mean(axis=1)[:, np.newaxis]

            out = hierarchy.linkage(X, method=linkage)

            children_ = out[:, :2].astype(np.int, copy=False)
            children, _, n_leaves, _ = _TREE_BUILDERS[linkage](
                X, connectivity=connectivity)

            # Sort the order of child nodes per row for consistency
            children.sort(axis=1)
            assert_array_equal(children, children_, 'linkage tree differs'
                                                    ' from scipy impl for'
                                                    ' linkage: ' + linkage)

            cut = _hc_cut(k, children, n_leaves)
            cut_ = _hc_cut(k, children_, n_leaves)
            assess_same_labelling(cut, cut_)

    # Test error management in _hc_cut
    with pytest.raises(ValueError):
        _hc_cut(n_leaves + 1, children, n_leaves)


# Make sure our custom mst_linkage_core gives
# the same results as scipy's builtin
@pytest.mark.parametrize('seed', range(5))
def test_vector_scikit_single_vs_scipy_single(seed):
    n_samples, n_features, n_clusters = 10, 5, 3
    rng = np.random.RandomState(seed)
    X = .1 * rng.normal(size=(n_samples, n_features))
    X -= 4. * np.arange(n_samples)[:, np.newaxis]
    X -= X.mean(axis=1)[:, np.newaxis]

    out = hierarchy.linkage(X, method='single')
    children_scipy = out[:, :2].astype(np.int)

    children, _, n_leaves, _ = _TREE_BUILDERS['single'](X)

    # Sort the order of child nodes per row for consistency
    children.sort(axis=1)
    assert_array_equal(children, children_scipy,
                       'linkage tree differs'
                       ' from scipy impl for'
                       ' single linkage.')

    cut = _hc_cut(n_clusters, children, n_leaves)
    cut_scipy = _hc_cut(n_clusters, children_scipy, n_leaves)
    assess_same_labelling(cut, cut_scipy)


def test_identical_points():
    # Ensure identical points are handled correctly when using mst with
    # a sparse connectivity matrix
    X = np.array([[0, 0, 0], [0, 0, 0],
                  [1, 1, 1], [1, 1, 1],
                  [2, 2, 2], [2, 2, 2]])
    true_labels = np.array([0, 0, 1, 1, 2, 2])
    connectivity = kneighbors_graph(X, n_neighbors=3, include_self=False)
    connectivity = 0.5 * (connectivity + connectivity.T)
    connectivity, n_components = _fix_connectivity(X,
                                                   connectivity,
                                                   'euclidean')

    for linkage in ('single', 'average', 'average', 'ward'):
        clustering = AgglomerativeClustering(n_clusters=3,
                                             linkage=linkage,
                                             connectivity=connectivity)
        clustering.fit(X)

        assert_almost_equal(normalized_mutual_info_score(clustering.labels_,
                                                         true_labels), 1)


def test_connectivity_propagation():
    # Check that connectivity in the ward tree is propagated correctly during
    # merging.
    X = np.array([(.014, .120), (.014, .099), (.014, .097),
                  (.017, .153), (.017, .153), (.018, .153),
                  (.018, .153), (.018, .153), (.018, .153),
                  (.018, .153), (.018, .153), (.018, .153),
                  (.018, .152), (.018, .149), (.018, .144)])
    connectivity = kneighbors_graph(X, 10, include_self=False)
    ward = AgglomerativeClustering(
        n_clusters=4, connectivity=connectivity, linkage='ward')
    # If changes are not propagated correctly, fit crashes with an
    # IndexError
    ward.fit(X)


def test_ward_tree_children_order():
    # Check that children are ordered in the same way for both structured and
    # unstructured versions of ward_tree.

    # test on five random datasets
    n, p = 10, 5
    rng = np.random.RandomState(0)

    connectivity = np.ones((n, n))
    for i in range(5):
        X = .1 * rng.normal(size=(n, p))
        X -= 4. * np.arange(n)[:, np.newaxis]
        X -= X.mean(axis=1)[:, np.newaxis]

        out_unstructured = ward_tree(X)
        out_structured = ward_tree(X, connectivity=connectivity)

        assert_array_equal(out_unstructured[0], out_structured[0])


def test_ward_linkage_tree_return_distance():
    # Test return_distance option on linkage and ward trees

    # test that return_distance when set true, gives same
    # output on both structured and unstructured clustering.
    n, p = 10, 5
    rng = np.random.RandomState(0)

    connectivity = np.ones((n, n))
    for i in range(5):
        X = .1 * rng.normal(size=(n, p))
        X -= 4. * np.arange(n)[:, np.newaxis]
        X -= X.mean(axis=1)[:, np.newaxis]

        out_unstructured = ward_tree(X, return_distance=True)
        out_structured = ward_tree(X, connectivity=connectivity,
                                   return_distance=True)

        # get children
        children_unstructured = out_unstructured[0]
        children_structured = out_structured[0]

        # check if we got the same clusters
        assert_array_equal(children_unstructured, children_structured)

        # check if the distances are the same
        dist_unstructured = out_unstructured[-1]
        dist_structured = out_structured[-1]

        assert_array_almost_equal(dist_unstructured, dist_structured)

        for linkage in ['average', 'complete', 'single']:
            structured_items = linkage_tree(
                X, connectivity=connectivity, linkage=linkage,
                return_distance=True)[-1]
            unstructured_items = linkage_tree(
                X, linkage=linkage, return_distance=True)[-1]
            structured_dist = structured_items[-1]
            unstructured_dist = unstructured_items[-1]
            structured_children = structured_items[0]
            unstructured_children = unstructured_items[0]
            assert_array_almost_equal(structured_dist, unstructured_dist)
            assert_array_almost_equal(
                structured_children, unstructured_children)

    # test on the following dataset where we know the truth
    # taken from scipy/cluster/tests/hierarchy_test_data.py
    X = np.array([[1.43054825, -7.5693489],
                  [6.95887839, 6.82293382],
                  [2.87137846, -9.68248579],
                  [7.87974764, -6.05485803],
                  [8.24018364, -6.09495602],
                  [7.39020262, 8.54004355]])
    # truth
    linkage_X_ward = np.array([[3., 4., 0.36265956, 2.],
                               [1., 5., 1.77045373, 2.],
                               [0., 2., 2.55760419, 2.],
                               [6., 8., 9.10208346, 4.],
                               [7., 9., 24.7784379, 6.]])

    linkage_X_complete = np.array(
        [[3., 4., 0.36265956, 2.],
         [1., 5., 1.77045373, 2.],
         [0., 2., 2.55760419, 2.],
         [6., 8., 6.96742194, 4.],
         [7., 9., 18.77445997, 6.]])

    linkage_X_average = np.array(
        [[3., 4., 0.36265956, 2.],
         [1., 5., 1.77045373, 2.],
         [0., 2., 2.55760419, 2.],
         [6., 8., 6.55832839, 4.],
         [7., 9., 15.44089605, 6.]])

    n_samples, n_features = np.shape(X)
    connectivity_X = np.ones((n_samples, n_samples))

    out_X_unstructured = ward_tree(X, return_distance=True)
    out_X_structured = ward_tree(X, connectivity=connectivity_X,
                                 return_distance=True)

    # check that the labels are the same
    assert_array_equal(linkage_X_ward[:, :2], out_X_unstructured[0])
    assert_array_equal(linkage_X_ward[:, :2], out_X_structured[0])

    # check that the distances are correct
    assert_array_almost_equal(linkage_X_ward[:, 2], out_X_unstructured[4])
    assert_array_almost_equal(linkage_X_ward[:, 2], out_X_structured[4])

    linkage_options = ['complete', 'average', 'single']
    X_linkage_truth = [linkage_X_complete, linkage_X_average]
    for (linkage, X_truth) in zip(linkage_options, X_linkage_truth):
        out_X_unstructured = linkage_tree(
            X, return_distance=True, linkage=linkage)
        out_X_structured = linkage_tree(
            X, connectivity=connectivity_X, linkage=linkage,
            return_distance=True)

        # check that the labels are the same
        assert_array_equal(X_truth[:, :2], out_X_unstructured[0])
        assert_array_equal(X_truth[:, :2], out_X_structured[0])

        # check that the distances are correct
        assert_array_almost_equal(X_truth[:, 2], out_X_unstructured[4])
        assert_array_almost_equal(X_truth[:, 2], out_X_structured[4])


def test_connectivity_fixing_non_lil():
    # Check non regression of a bug if a non item assignable connectivity is
    # provided with more than one component.
    # create dummy data
    x = np.array([[0, 0], [1, 1]])
    # create a mask with several components to force connectivity fixing
    m = np.array([[True, False], [False, True]])
    c = grid_to_graph(n_x=2, n_y=2, mask=m)
    w = AgglomerativeClustering(connectivity=c, linkage='ward')
    assert_warns(UserWarning, w.fit, x)


def test_int_float_dict():
    rng = np.random.RandomState(0)
    keys = np.unique(rng.randint(100, size=10).astype(np.intp, copy=False))
    values = rng.rand(len(keys))

    d = IntFloatDict(keys, values)
    for key, value in zip(keys, values):
        assert d[key] == value

    other_keys = np.arange(50, dtype=np.intp)[::2]
    other_values = np.full(50, 0.5)[::2]
    other = IntFloatDict(other_keys, other_values)
    # Complete smoke test
    max_merge(d, other, mask=np.ones(100, dtype=np.intp), n_a=1, n_b=1)
    average_merge(d, other, mask=np.ones(100, dtype=np.intp), n_a=1, n_b=1)


def test_connectivity_callable():
    rng = np.random.RandomState(0)
    X = rng.rand(20, 5)
    connectivity = kneighbors_graph(X, 3, include_self=False)
    aglc1 = AgglomerativeClustering(connectivity=connectivity)
    aglc2 = AgglomerativeClustering(
        connectivity=partial(kneighbors_graph, n_neighbors=3,
                             include_self=False))
    aglc1.fit(X)
    aglc2.fit(X)
    assert_array_equal(aglc1.labels_, aglc2.labels_)


def test_connectivity_ignores_diagonal():
    rng = np.random.RandomState(0)
    X = rng.rand(20, 5)
    connectivity = kneighbors_graph(X, 3, include_self=False)
    connectivity_include_self = kneighbors_graph(X, 3, include_self=True)
    aglc1 = AgglomerativeClustering(connectivity=connectivity)
    aglc2 = AgglomerativeClustering(connectivity=connectivity_include_self)
    aglc1.fit(X)
    aglc2.fit(X)
    assert_array_equal(aglc1.labels_, aglc2.labels_)


def test_compute_full_tree():
    # Test that the full tree is computed if n_clusters is small
    rng = np.random.RandomState(0)
    X = rng.randn(10, 2)
    connectivity = kneighbors_graph(X, 5, include_self=False)

    # When n_clusters is less, the full tree should be built
    # that is the number of merges should be n_samples - 1
    agc = AgglomerativeClustering(n_clusters=2, connectivity=connectivity)
    agc.fit(X)
    n_samples = X.shape[0]
    n_nodes = agc.children_.shape[0]
    assert n_nodes == n_samples - 1

    # When n_clusters is large, greater than max of 100 and 0.02 * n_samples.
    # we should stop when there are n_clusters.
    n_clusters = 101
    X = rng.randn(200, 2)
    connectivity = kneighbors_graph(X, 10, include_self=False)
    agc = AgglomerativeClustering(n_clusters=n_clusters,
                                  connectivity=connectivity)
    agc.fit(X)
    n_samples = X.shape[0]
    n_nodes = agc.children_.shape[0]
    assert n_nodes == n_samples - n_clusters


def test_n_components():
    # Test n_components returned by linkage, average and ward tree
    rng = np.random.RandomState(0)
    X = rng.rand(5, 5)

    # Connectivity matrix having five components.
    connectivity = np.eye(5)

    for linkage_func in _TREE_BUILDERS.values():
        assert ignore_warnings(linkage_func)(X, connectivity)[1] == 5


def test_agg_n_clusters():
    # Test that an error is raised when n_clusters <= 0

    rng = np.random.RandomState(0)
    X = rng.rand(20, 10)
    for n_clus in [-1, 0]:
        agc = AgglomerativeClustering(n_clusters=n_clus)
        msg = ("n_clusters should be an integer greater than 0."
               " %s was provided." % str(agc.n_clusters))
        assert_raise_message(ValueError, msg, agc.fit, X)


def test_affinity_passed_to_fix_connectivity():
    # Test that the affinity parameter is actually passed to the pairwise
    # function

    size = 2
    rng = np.random.RandomState(0)
    X = rng.randn(size, size)
    mask = np.array([True, False, False, True])

    connectivity = grid_to_graph(n_x=size, n_y=size,
                                 mask=mask, return_as=np.ndarray)

    class FakeAffinity:
        def __init__(self):
            self.counter = 0

        def increment(self, *args, **kwargs):
            self.counter += 1
            return self.counter

    fa = FakeAffinity()

    linkage_tree(X, connectivity=connectivity, affinity=fa.increment)

    assert fa.counter == 3


@pytest.mark.parametrize('linkage', ['ward', 'complete', 'average'])
def test_agglomerative_clustering_with_distance_threshold(linkage):
    # Check that we obtain the correct number of clusters with
    # agglomerative clustering with distance_threshold.
    rng = np.random.RandomState(0)
    mask = np.ones([10, 10], dtype=np.bool)
    n_samples = 100
    X = rng.randn(n_samples, 50)
    connectivity = grid_to_graph(*mask.shape)
    # test when distance threshold is set to 10
    distance_threshold = 10
    for conn in [None, connectivity]:
        clustering = AgglomerativeClustering(
            n_clusters=None,
            distance_threshold=distance_threshold,
            connectivity=conn, linkage=linkage)
        clustering.fit(X)
        clusters_produced = clustering.labels_
        num_clusters_produced = len(np.unique(clustering.labels_))
        # test if the clusters produced match the point in the linkage tree
        # where the distance exceeds the threshold
        tree_builder = _TREE_BUILDERS[linkage]
        children, n_components, n_leaves, parent, distances = \
            tree_builder(X, connectivity=conn, n_clusters=None,
                         return_distance=True)
        num_clusters_at_threshold = np.count_nonzero(
            distances >= distance_threshold) + 1
        # test number of clusters produced
        assert num_clusters_at_threshold == num_clusters_produced
        # test clusters produced
        clusters_at_threshold = _hc_cut(n_clusters=num_clusters_produced,
                                        children=children,
                                        n_leaves=n_leaves)
        assert np.array_equiv(clusters_produced,
                              clusters_at_threshold)


def test_small_distance_threshold():
    rng = np.random.RandomState(0)
    n_samples = 10
    X = rng.randint(-300, 300, size=(n_samples, 3))
    # this should result in all data in their own clusters, given that
    # their pairwise distances are bigger than .1 (which may not be the case
    # with a different random seed).
    clustering = AgglomerativeClustering(
        n_clusters=None,
        distance_threshold=1.,
        linkage="single").fit(X)
    # check that the pairwise distances are indeed all larger than .1
    all_distances = pairwise_distances(X, metric='minkowski', p=2)
    np.fill_diagonal(all_distances, np.inf)
    assert np.all(all_distances > .1)
    assert clustering.n_clusters_ == n_samples


def test_cluster_distances_with_distance_threshold():
    rng = np.random.RandomState(0)
    n_samples = 100
    X = rng.randint(-10, 10, size=(n_samples, 3))
    # check the distances within the clusters and with other clusters
    distance_threshold = 4
    clustering = AgglomerativeClustering(
        n_clusters=None,
        distance_threshold=distance_threshold,
        linkage="single").fit(X)
    labels = clustering.labels_
    D = pairwise_distances(X, metric="minkowski", p=2)
    # to avoid taking the 0 diagonal in min()
    np.fill_diagonal(D, np.inf)
    for label in np.unique(labels):
        in_cluster_mask = labels == label
        max_in_cluster_distance = (D[in_cluster_mask][:, in_cluster_mask]
                                   .min(axis=0).max())
        min_out_cluster_distance = (D[in_cluster_mask][:, ~in_cluster_mask]
                                    .min(axis=0).min())
        # single data point clusters only have that inf diagonal here
        if in_cluster_mask.sum() > 1:
            assert max_in_cluster_distance < distance_threshold
        assert min_out_cluster_distance >= distance_threshold


@pytest.mark.parametrize('linkage', ['ward', 'complete', 'average'])
@pytest.mark.parametrize(('threshold', 'y_true'),
                         [(0.5, [1, 0]), (1.0, [1, 0]), (1.5, [0, 0])])
def test_agglomerative_clustering_with_distance_threshold_edge_case(
        linkage, threshold, y_true):
    # test boundary case of distance_threshold matching the distance
    X = [[0], [1]]
    clusterer = AgglomerativeClustering(
        n_clusters=None,
        distance_threshold=threshold,
        linkage=linkage)
    y_pred = clusterer.fit_predict(X)
    assert adjusted_rand_score(y_true, y_pred) == 1


def test_dist_threshold_invalid_parameters():
    X = [[0], [1]]
    with pytest.raises(ValueError, match="Exactly one of "):
        AgglomerativeClustering(n_clusters=None,
                                distance_threshold=None).fit(X)

    with pytest.raises(ValueError, match="Exactly one of "):
        AgglomerativeClustering(n_clusters=2,
                                distance_threshold=1).fit(X)

    X = [[0], [1]]
    with pytest.raises(ValueError, match="compute_full_tree must be True if"):
        AgglomerativeClustering(n_clusters=None,
                                distance_threshold=1,
                                compute_full_tree=False).fit(X)


def test_invalid_shape_precomputed_dist_matrix():
    # Check that an error is raised when affinity='precomputed'
    # and a non square matrix is passed (PR #16257).
    rng = np.random.RandomState(0)
    X = rng.rand(5, 3)
    with pytest.raises(ValueError, match="Distance matrix should be square, "):
        AgglomerativeClustering(affinity='precomputed',
                                linkage='complete').fit(X)