# # Author: Damian Eads # Date: April 17, 2008 # # Copyright (C) 2008 Damian Eads # # Redistribution and use in source and binary forms, with or without # modification, are permitted provided that the following conditions # are met: # # 1. Redistributions of source code must retain the above copyright # notice, this list of conditions and the following disclaimer. # # 2. Redistributions in binary form must reproduce the above # copyright notice, this list of conditions and the following # disclaimer in the documentation and/or other materials provided # with the distribution. # # 3. The name of the author may not be used to endorse or promote # products derived from this software without specific prior # written permission. # # THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS # OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED # WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE # ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY # DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL # DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE # GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS # INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, # WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING # NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS # SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. import numpy as np from numpy.testing import assert_allclose, assert_equal, assert_, assert_warns import pytest from pytest import raises as assert_raises import scipy.cluster.hierarchy from scipy.cluster.hierarchy import ( ClusterWarning, linkage, from_mlab_linkage, to_mlab_linkage, num_obs_linkage, inconsistent, cophenet, fclusterdata, fcluster, is_isomorphic, single, leaders, correspond, is_monotonic, maxdists, maxinconsts, maxRstat, is_valid_linkage, is_valid_im, to_tree, leaves_list, dendrogram, set_link_color_palette, cut_tree, optimal_leaf_ordering, _order_cluster_tree, _hierarchy, _LINKAGE_METHODS) from scipy.spatial.distance import pdist from scipy.cluster._hierarchy import Heap from scipy.conftest import array_api_compatible from scipy._lib._array_api import xp_assert_close, xp_assert_equal from . import hierarchy_test_data # Matplotlib is not a scipy dependency but is optionally used in dendrogram, so # check if it's available try: import matplotlib # and set the backend to be Agg (no gui) matplotlib.use('Agg') # before importing pyplot import matplotlib.pyplot as plt have_matplotlib = True except Exception: have_matplotlib = False pytestmark = [array_api_compatible, pytest.mark.usefixtures("skip_if_array_api")] skip_if_array_api = pytest.mark.skip_if_array_api class TestLinkage: @skip_if_array_api(cpu_only=True) def test_linkage_non_finite_elements_in_distance_matrix(self, xp): # Tests linkage(Y) where Y contains a non-finite element (e.g. NaN or Inf). # Exception expected. y = xp.zeros((6,)) y[0] = xp.nan assert_raises(ValueError, linkage, y) @skip_if_array_api(cpu_only=True) def test_linkage_empty_distance_matrix(self, xp): # Tests linkage(Y) where Y is a 0x4 linkage matrix. Exception expected. y = xp.zeros((0,)) assert_raises(ValueError, linkage, y) @skip_if_array_api(cpu_only=True) def test_linkage_tdist(self, xp): for method in ['single', 'complete', 'average', 'weighted']: self.check_linkage_tdist(method, xp) def check_linkage_tdist(self, method, xp): # Tests linkage(Y, method) on the tdist data set. Z = linkage(xp.asarray(hierarchy_test_data.ytdist), method) expectedZ = getattr(hierarchy_test_data, 'linkage_ytdist_' + method) xp_assert_close(Z, xp.asarray(expectedZ), atol=1e-10) @skip_if_array_api(cpu_only=True) def test_linkage_X(self, xp): for method in ['centroid', 'median', 'ward']: self.check_linkage_q(method, xp) def check_linkage_q(self, method, xp): # Tests linkage(Y, method) on the Q data set. Z = linkage(xp.asarray(hierarchy_test_data.X), method) expectedZ = getattr(hierarchy_test_data, 'linkage_X_' + method) xp_assert_close(Z, xp.asarray(expectedZ), atol=1e-06) y = scipy.spatial.distance.pdist(hierarchy_test_data.X, metric="euclidean") Z = linkage(xp.asarray(y), method) xp_assert_close(Z, xp.asarray(expectedZ), atol=1e-06) @skip_if_array_api(cpu_only=True) def test_compare_with_trivial(self, xp): rng = np.random.RandomState(0) n = 20 X = rng.rand(n, 2) d = pdist(X) for method, code in _LINKAGE_METHODS.items(): Z_trivial = _hierarchy.linkage(d, n, code) Z = linkage(xp.asarray(d), method) xp_assert_close(Z, xp.asarray(Z_trivial), rtol=1e-14, atol=1e-15) @skip_if_array_api(cpu_only=True) def test_optimal_leaf_ordering(self, xp): Z = linkage(xp.asarray(hierarchy_test_data.ytdist), optimal_ordering=True) expectedZ = getattr(hierarchy_test_data, 'linkage_ytdist_single_olo') xp_assert_close(Z, xp.asarray(expectedZ), atol=1e-10) @skip_if_array_api(cpu_only=True) class TestLinkageTies: _expectations = { 'single': np.array([[0, 1, 1.41421356, 2], [2, 3, 1.41421356, 3]]), 'complete': np.array([[0, 1, 1.41421356, 2], [2, 3, 2.82842712, 3]]), 'average': np.array([[0, 1, 1.41421356, 2], [2, 3, 2.12132034, 3]]), 'weighted': np.array([[0, 1, 1.41421356, 2], [2, 3, 2.12132034, 3]]), 'centroid': np.array([[0, 1, 1.41421356, 2], [2, 3, 2.12132034, 3]]), 'median': np.array([[0, 1, 1.41421356, 2], [2, 3, 2.12132034, 3]]), 'ward': np.array([[0, 1, 1.41421356, 2], [2, 3, 2.44948974, 3]]), } def test_linkage_ties(self, xp): for method in ['single', 'complete', 'average', 'weighted', 'centroid', 'median', 'ward']: self.check_linkage_ties(method, xp) def check_linkage_ties(self, method, xp): X = xp.asarray([[-1, -1], [0, 0], [1, 1]]) Z = linkage(X, method=method) expectedZ = self._expectations[method] xp_assert_close(Z, xp.asarray(expectedZ), atol=1e-06) @skip_if_array_api(cpu_only=True) class TestInconsistent: def test_inconsistent_tdist(self, xp): for depth in hierarchy_test_data.inconsistent_ytdist: self.check_inconsistent_tdist(depth, xp) def check_inconsistent_tdist(self, depth, xp): Z = xp.asarray(hierarchy_test_data.linkage_ytdist_single) xp_assert_close(inconsistent(Z, depth), xp.asarray(hierarchy_test_data.inconsistent_ytdist[depth])) @skip_if_array_api(cpu_only=True) class TestCopheneticDistance: def test_linkage_cophenet_tdist_Z(self, xp): # Tests cophenet(Z) on tdist data set. expectedM = xp.asarray([268, 295, 255, 255, 295, 295, 268, 268, 295, 295, 295, 138, 219, 295, 295]) Z = xp.asarray(hierarchy_test_data.linkage_ytdist_single) M = cophenet(Z) xp_assert_close(M, xp.asarray(expectedM, dtype=xp.float64), atol=1e-10) def test_linkage_cophenet_tdist_Z_Y(self, xp): # Tests cophenet(Z, Y) on tdist data set. Z = xp.asarray(hierarchy_test_data.linkage_ytdist_single) (c, M) = cophenet(Z, xp.asarray(hierarchy_test_data.ytdist)) expectedM = xp.asarray([268, 295, 255, 255, 295, 295, 268, 268, 295, 295, 295, 138, 219, 295, 295], dtype=xp.float64) expectedc = xp.asarray(0.639931296433393415057366837573, dtype=xp.float64)[()] xp_assert_close(c, expectedc, atol=1e-10) xp_assert_close(M, expectedM, atol=1e-10) class TestMLabLinkageConversion: def test_mlab_linkage_conversion_empty(self, xp): # Tests from/to_mlab_linkage on empty linkage array. X = xp.asarray([], dtype=xp.float64) xp_assert_equal(from_mlab_linkage(X), X) xp_assert_equal(to_mlab_linkage(X), X) @skip_if_array_api(cpu_only=True) def test_mlab_linkage_conversion_single_row(self, xp): # Tests from/to_mlab_linkage on linkage array with single row. Z = xp.asarray([[0., 1., 3., 2.]]) Zm = xp.asarray([[1, 2, 3]]) xp_assert_close(from_mlab_linkage(Zm), xp.asarray(Z, dtype=xp.float64), rtol=1e-15) xp_assert_close(to_mlab_linkage(Z), xp.asarray(Zm, dtype=xp.float64), rtol=1e-15) @skip_if_array_api(cpu_only=True) def test_mlab_linkage_conversion_multiple_rows(self, xp): # Tests from/to_mlab_linkage on linkage array with multiple rows. Zm = xp.asarray([[3, 6, 138], [4, 5, 219], [1, 8, 255], [2, 9, 268], [7, 10, 295]]) Z = xp.asarray([[2., 5., 138., 2.], [3., 4., 219., 2.], [0., 7., 255., 3.], [1., 8., 268., 4.], [6., 9., 295., 6.]], dtype=xp.float64) xp_assert_close(from_mlab_linkage(Zm), Z, rtol=1e-15) xp_assert_close(to_mlab_linkage(Z), xp.asarray(Zm, dtype=xp.float64), rtol=1e-15) @skip_if_array_api(cpu_only=True) class TestFcluster: def test_fclusterdata(self, xp): for t in hierarchy_test_data.fcluster_inconsistent: self.check_fclusterdata(t, 'inconsistent', xp) for t in hierarchy_test_data.fcluster_distance: self.check_fclusterdata(t, 'distance', xp) for t in hierarchy_test_data.fcluster_maxclust: self.check_fclusterdata(t, 'maxclust', xp) def check_fclusterdata(self, t, criterion, xp): # Tests fclusterdata(X, criterion=criterion, t=t) on a random 3-cluster data set expectedT = xp.asarray(getattr(hierarchy_test_data, 'fcluster_' + criterion)[t]) X = xp.asarray(hierarchy_test_data.Q_X) T = fclusterdata(X, criterion=criterion, t=t) assert_(is_isomorphic(T, expectedT)) def test_fcluster(self, xp): for t in hierarchy_test_data.fcluster_inconsistent: self.check_fcluster(t, 'inconsistent', xp) for t in hierarchy_test_data.fcluster_distance: self.check_fcluster(t, 'distance', xp) for t in hierarchy_test_data.fcluster_maxclust: self.check_fcluster(t, 'maxclust', xp) def check_fcluster(self, t, criterion, xp): # Tests fcluster(Z, criterion=criterion, t=t) on a random 3-cluster data set. expectedT = xp.asarray(getattr(hierarchy_test_data, 'fcluster_' + criterion)[t]) Z = single(xp.asarray(hierarchy_test_data.Q_X)) T = fcluster(Z, criterion=criterion, t=t) assert_(is_isomorphic(T, expectedT)) def test_fcluster_monocrit(self, xp): for t in hierarchy_test_data.fcluster_distance: self.check_fcluster_monocrit(t, xp) for t in hierarchy_test_data.fcluster_maxclust: self.check_fcluster_maxclust_monocrit(t, xp) def check_fcluster_monocrit(self, t, xp): expectedT = xp.asarray(hierarchy_test_data.fcluster_distance[t]) Z = single(xp.asarray(hierarchy_test_data.Q_X)) T = fcluster(Z, t, criterion='monocrit', monocrit=maxdists(Z)) assert_(is_isomorphic(T, expectedT)) def check_fcluster_maxclust_monocrit(self, t, xp): expectedT = xp.asarray(hierarchy_test_data.fcluster_maxclust[t]) Z = single(xp.asarray(hierarchy_test_data.Q_X)) T = fcluster(Z, t, criterion='maxclust_monocrit', monocrit=maxdists(Z)) assert_(is_isomorphic(T, expectedT)) @skip_if_array_api(cpu_only=True) class TestLeaders: def test_leaders_single(self, xp): # Tests leaders using a flat clustering generated by single linkage. X = hierarchy_test_data.Q_X Y = pdist(X) Y = xp.asarray(Y) Z = linkage(Y) T = fcluster(Z, criterion='maxclust', t=3) Lright = (xp.asarray([53, 55, 56]), xp.asarray([2, 3, 1])) T = xp.asarray(T, dtype=xp.int32) L = leaders(Z, T) assert_allclose(np.concatenate(L), np.concatenate(Lright), rtol=1e-15) @skip_if_array_api(np_only=True, reasons=['`is_isomorphic` only supports NumPy backend']) class TestIsIsomorphic: @skip_if_array_api(np_only=True, reasons=['array-likes only supported for NumPy backend']) def test_array_like(self, xp): assert is_isomorphic([1, 1, 1], [2, 2, 2]) assert is_isomorphic([], []) def test_is_isomorphic_1(self, xp): # Tests is_isomorphic on test case #1 (one flat cluster, different labellings) a = xp.asarray([1, 1, 1]) b = xp.asarray([2, 2, 2]) assert is_isomorphic(a, b) assert is_isomorphic(b, a) def test_is_isomorphic_2(self, xp): # Tests is_isomorphic on test case #2 (two flat clusters, different labelings) a = xp.asarray([1, 7, 1]) b = xp.asarray([2, 3, 2]) assert is_isomorphic(a, b) assert is_isomorphic(b, a) def test_is_isomorphic_3(self, xp): # Tests is_isomorphic on test case #3 (no flat clusters) a = xp.asarray([]) b = xp.asarray([]) assert is_isomorphic(a, b) def test_is_isomorphic_4A(self, xp): # Tests is_isomorphic on test case #4A # (3 flat clusters, different labelings, isomorphic) a = xp.asarray([1, 2, 3]) b = xp.asarray([1, 3, 2]) assert is_isomorphic(a, b) assert is_isomorphic(b, a) def test_is_isomorphic_4B(self, xp): # Tests is_isomorphic on test case #4B # (3 flat clusters, different labelings, nonisomorphic) a = xp.asarray([1, 2, 3, 3]) b = xp.asarray([1, 3, 2, 3]) assert is_isomorphic(a, b) is False assert is_isomorphic(b, a) is False def test_is_isomorphic_4C(self, xp): # Tests is_isomorphic on test case #4C # (3 flat clusters, different labelings, isomorphic) a = xp.asarray([7, 2, 3]) b = xp.asarray([6, 3, 2]) assert is_isomorphic(a, b) assert is_isomorphic(b, a) def test_is_isomorphic_5(self, xp): # Tests is_isomorphic on test case #5 (1000 observations, 2/3/5 random # clusters, random permutation of the labeling). for nc in [2, 3, 5]: self.help_is_isomorphic_randperm(1000, nc, xp=xp) def test_is_isomorphic_6(self, xp): # Tests is_isomorphic on test case #5A (1000 observations, 2/3/5 random # clusters, random permutation of the labeling, slightly # nonisomorphic.) for nc in [2, 3, 5]: self.help_is_isomorphic_randperm(1000, nc, True, 5, xp=xp) def test_is_isomorphic_7(self, xp): # Regression test for gh-6271 a = xp.asarray([1, 2, 3]) b = xp.asarray([1, 1, 1]) assert not is_isomorphic(a, b) def help_is_isomorphic_randperm(self, nobs, nclusters, noniso=False, nerrors=0, *, xp): for k in range(3): a = (np.random.rand(nobs) * nclusters).astype(int) b = np.zeros(a.size, dtype=int) P = np.random.permutation(nclusters) for i in range(0, a.shape[0]): b[i] = P[a[i]] if noniso: Q = np.random.permutation(nobs) b[Q[0:nerrors]] += 1 b[Q[0:nerrors]] %= nclusters a = xp.asarray(a) b = xp.asarray(b) assert is_isomorphic(a, b) == (not noniso) assert is_isomorphic(b, a) == (not noniso) @skip_if_array_api(cpu_only=True) class TestIsValidLinkage: def test_is_valid_linkage_various_size(self, xp): for nrow, ncol, valid in [(2, 5, False), (2, 3, False), (1, 4, True), (2, 4, True)]: self.check_is_valid_linkage_various_size(nrow, ncol, valid, xp) def check_is_valid_linkage_various_size(self, nrow, ncol, valid, xp): # Tests is_valid_linkage(Z) with linkage matrices of various sizes Z = xp.asarray([[0, 1, 3.0, 2, 5], [3, 2, 4.0, 3, 3]], dtype=xp.float64) Z = Z[:nrow, :ncol] assert_(is_valid_linkage(Z) == valid) if not valid: assert_raises(ValueError, is_valid_linkage, Z, throw=True) def test_is_valid_linkage_int_type(self, xp): # Tests is_valid_linkage(Z) with integer type. Z = xp.asarray([[0, 1, 3.0, 2], [3, 2, 4.0, 3]], dtype=xp.int64) assert_(is_valid_linkage(Z) is False) assert_raises(TypeError, is_valid_linkage, Z, throw=True) def test_is_valid_linkage_empty(self, xp): # Tests is_valid_linkage(Z) with empty linkage. Z = xp.zeros((0, 4), dtype=xp.float64) assert_(is_valid_linkage(Z) is False) assert_raises(ValueError, is_valid_linkage, Z, throw=True) def test_is_valid_linkage_4_and_up(self, xp): # Tests is_valid_linkage(Z) on linkage on observation sets between # sizes 4 and 15 (step size 3). for i in range(4, 15, 3): y = np.random.rand(i*(i-1)//2) y = xp.asarray(y) Z = linkage(y) assert_(is_valid_linkage(Z) is True) def test_is_valid_linkage_4_and_up_neg_index_left(self, xp): # Tests is_valid_linkage(Z) on linkage on observation sets between # sizes 4 and 15 (step size 3) with negative indices (left). for i in range(4, 15, 3): y = np.random.rand(i*(i-1)//2) y = xp.asarray(y) Z = linkage(y) Z[i//2,0] = -2 assert_(is_valid_linkage(Z) is False) assert_raises(ValueError, is_valid_linkage, Z, throw=True) def test_is_valid_linkage_4_and_up_neg_index_right(self, xp): # Tests is_valid_linkage(Z) on linkage on observation sets between # sizes 4 and 15 (step size 3) with negative indices (right). for i in range(4, 15, 3): y = np.random.rand(i*(i-1)//2) y = xp.asarray(y) Z = linkage(y) Z[i//2,1] = -2 assert_(is_valid_linkage(Z) is False) assert_raises(ValueError, is_valid_linkage, Z, throw=True) def test_is_valid_linkage_4_and_up_neg_dist(self, xp): # Tests is_valid_linkage(Z) on linkage on observation sets between # sizes 4 and 15 (step size 3) with negative distances. for i in range(4, 15, 3): y = np.random.rand(i*(i-1)//2) y = xp.asarray(y) Z = linkage(y) Z[i//2,2] = -0.5 assert_(is_valid_linkage(Z) is False) assert_raises(ValueError, is_valid_linkage, Z, throw=True) def test_is_valid_linkage_4_and_up_neg_counts(self, xp): # Tests is_valid_linkage(Z) on linkage on observation sets between # sizes 4 and 15 (step size 3) with negative counts. for i in range(4, 15, 3): y = np.random.rand(i*(i-1)//2) y = xp.asarray(y) Z = linkage(y) Z[i//2,3] = -2 assert_(is_valid_linkage(Z) is False) assert_raises(ValueError, is_valid_linkage, Z, throw=True) @skip_if_array_api(cpu_only=True) class TestIsValidInconsistent: def test_is_valid_im_int_type(self, xp): # Tests is_valid_im(R) with integer type. R = xp.asarray([[0, 1, 3.0, 2], [3, 2, 4.0, 3]], dtype=xp.int64) assert_(is_valid_im(R) is False) assert_raises(TypeError, is_valid_im, R, throw=True) def test_is_valid_im_various_size(self, xp): for nrow, ncol, valid in [(2, 5, False), (2, 3, False), (1, 4, True), (2, 4, True)]: self.check_is_valid_im_various_size(nrow, ncol, valid, xp) def check_is_valid_im_various_size(self, nrow, ncol, valid, xp): # Tests is_valid_im(R) with linkage matrices of various sizes R = xp.asarray([[0, 1, 3.0, 2, 5], [3, 2, 4.0, 3, 3]], dtype=xp.float64) R = R[:nrow, :ncol] assert_(is_valid_im(R) == valid) if not valid: assert_raises(ValueError, is_valid_im, R, throw=True) def test_is_valid_im_empty(self, xp): # Tests is_valid_im(R) with empty inconsistency matrix. R = xp.zeros((0, 4), dtype=xp.float64) assert_(is_valid_im(R) is False) assert_raises(ValueError, is_valid_im, R, throw=True) def test_is_valid_im_4_and_up(self, xp): # Tests is_valid_im(R) on im on observation sets between sizes 4 and 15 # (step size 3). for i in range(4, 15, 3): y = np.random.rand(i*(i-1)//2) y = xp.asarray(y) Z = linkage(y) R = inconsistent(Z) assert_(is_valid_im(R) is True) def test_is_valid_im_4_and_up_neg_index_left(self, xp): # Tests is_valid_im(R) on im on observation sets between sizes 4 and 15 # (step size 3) with negative link height means. for i in range(4, 15, 3): y = np.random.rand(i*(i-1)//2) y = xp.asarray(y) Z = linkage(y) R = inconsistent(Z) R[i//2,0] = -2.0 assert_(is_valid_im(R) is False) assert_raises(ValueError, is_valid_im, R, throw=True) def test_is_valid_im_4_and_up_neg_index_right(self, xp): # Tests is_valid_im(R) on im on observation sets between sizes 4 and 15 # (step size 3) with negative link height standard deviations. for i in range(4, 15, 3): y = np.random.rand(i*(i-1)//2) y = xp.asarray(y) Z = linkage(y) R = inconsistent(Z) R[i//2,1] = -2.0 assert_(is_valid_im(R) is False) assert_raises(ValueError, is_valid_im, R, throw=True) def test_is_valid_im_4_and_up_neg_dist(self, xp): # Tests is_valid_im(R) on im on observation sets between sizes 4 and 15 # (step size 3) with negative link counts. for i in range(4, 15, 3): y = np.random.rand(i*(i-1)//2) y = xp.asarray(y) Z = linkage(y) R = inconsistent(Z) R[i//2,2] = -0.5 assert_(is_valid_im(R) is False) assert_raises(ValueError, is_valid_im, R, throw=True) class TestNumObsLinkage: @skip_if_array_api(cpu_only=True) def test_num_obs_linkage_empty(self, xp): # Tests num_obs_linkage(Z) with empty linkage. Z = xp.zeros((0, 4), dtype=xp.float64) assert_raises(ValueError, num_obs_linkage, Z) def test_num_obs_linkage_1x4(self, xp): # Tests num_obs_linkage(Z) on linkage over 2 observations. Z = xp.asarray([[0, 1, 3.0, 2]], dtype=xp.float64) assert_equal(num_obs_linkage(Z), 2) def test_num_obs_linkage_2x4(self, xp): # Tests num_obs_linkage(Z) on linkage over 3 observations. Z = xp.asarray([[0, 1, 3.0, 2], [3, 2, 4.0, 3]], dtype=xp.float64) assert_equal(num_obs_linkage(Z), 3) @skip_if_array_api(cpu_only=True) def test_num_obs_linkage_4_and_up(self, xp): # Tests num_obs_linkage(Z) on linkage on observation sets between sizes # 4 and 15 (step size 3). for i in range(4, 15, 3): y = np.random.rand(i*(i-1)//2) y = xp.asarray(y) Z = linkage(y) assert_equal(num_obs_linkage(Z), i) @skip_if_array_api(cpu_only=True) class TestLeavesList: def test_leaves_list_1x4(self, xp): # Tests leaves_list(Z) on a 1x4 linkage. Z = xp.asarray([[0, 1, 3.0, 2]], dtype=xp.float64) to_tree(Z) assert_allclose(leaves_list(Z), [0, 1], rtol=1e-15) def test_leaves_list_2x4(self, xp): # Tests leaves_list(Z) on a 2x4 linkage. Z = xp.asarray([[0, 1, 3.0, 2], [3, 2, 4.0, 3]], dtype=xp.float64) to_tree(Z) assert_allclose(leaves_list(Z), [0, 1, 2], rtol=1e-15) def test_leaves_list_Q(self, xp): for method in ['single', 'complete', 'average', 'weighted', 'centroid', 'median', 'ward']: self.check_leaves_list_Q(method, xp) def check_leaves_list_Q(self, method, xp): # Tests leaves_list(Z) on the Q data set X = xp.asarray(hierarchy_test_data.Q_X) Z = linkage(X, method) node = to_tree(Z) assert_allclose(node.pre_order(), leaves_list(Z), rtol=1e-15) def test_Q_subtree_pre_order(self, xp): # Tests that pre_order() works when called on sub-trees. X = xp.asarray(hierarchy_test_data.Q_X) Z = linkage(X, 'single') node = to_tree(Z) assert_allclose(node.pre_order(), (node.get_left().pre_order() + node.get_right().pre_order()), rtol=1e-15) @skip_if_array_api(cpu_only=True) class TestCorrespond: def test_correspond_empty(self, xp): # Tests correspond(Z, y) with empty linkage and condensed distance matrix. y = xp.zeros((0,), dtype=xp.float64) Z = xp.zeros((0,4), dtype=xp.float64) assert_raises(ValueError, correspond, Z, y) def test_correspond_2_and_up(self, xp): # Tests correspond(Z, y) on linkage and CDMs over observation sets of # different sizes. for i in range(2, 4): y = np.random.rand(i*(i-1)//2) y = xp.asarray(y) Z = linkage(y) assert_(correspond(Z, y)) for i in range(4, 15, 3): y = np.random.rand(i*(i-1)//2) y = xp.asarray(y) Z = linkage(y) assert_(correspond(Z, y)) def test_correspond_4_and_up(self, xp): # Tests correspond(Z, y) on linkage and CDMs over observation sets of # different sizes. Correspondence should be false. for (i, j) in (list(zip(list(range(2, 4)), list(range(3, 5)))) + list(zip(list(range(3, 5)), list(range(2, 4))))): y = np.random.rand(i*(i-1)//2) y2 = np.random.rand(j*(j-1)//2) y = xp.asarray(y) y2 = xp.asarray(y2) Z = linkage(y) Z2 = linkage(y2) assert not correspond(Z, y2) assert not correspond(Z2, y) def test_correspond_4_and_up_2(self, xp): # Tests correspond(Z, y) on linkage and CDMs over observation sets of # different sizes. Correspondence should be false. for (i, j) in (list(zip(list(range(2, 7)), list(range(16, 21)))) + list(zip(list(range(2, 7)), list(range(16, 21))))): y = np.random.rand(i*(i-1)//2) y2 = np.random.rand(j*(j-1)//2) y = xp.asarray(y) y2 = xp.asarray(y2) Z = linkage(y) Z2 = linkage(y2) assert not correspond(Z, y2) assert not correspond(Z2, y) def test_num_obs_linkage_multi_matrix(self, xp): # Tests num_obs_linkage with observation matrices of multiple sizes. for n in range(2, 10): X = np.random.rand(n, 4) Y = pdist(X) Y = xp.asarray(Y) Z = linkage(Y) assert_equal(num_obs_linkage(Z), n) @skip_if_array_api(cpu_only=True) class TestIsMonotonic: def test_is_monotonic_empty(self, xp): # Tests is_monotonic(Z) on an empty linkage. Z = xp.zeros((0, 4), dtype=xp.float64) assert_raises(ValueError, is_monotonic, Z) def test_is_monotonic_1x4(self, xp): # Tests is_monotonic(Z) on 1x4 linkage. Expecting True. Z = xp.asarray([[0, 1, 0.3, 2]], dtype=xp.float64) assert is_monotonic(Z) def test_is_monotonic_2x4_T(self, xp): # Tests is_monotonic(Z) on 2x4 linkage. Expecting True. Z = xp.asarray([[0, 1, 0.3, 2], [2, 3, 0.4, 3]], dtype=xp.float64) assert is_monotonic(Z) def test_is_monotonic_2x4_F(self, xp): # Tests is_monotonic(Z) on 2x4 linkage. Expecting False. Z = xp.asarray([[0, 1, 0.4, 2], [2, 3, 0.3, 3]], dtype=xp.float64) assert not is_monotonic(Z) def test_is_monotonic_3x4_T(self, xp): # Tests is_monotonic(Z) on 3x4 linkage. Expecting True. Z = xp.asarray([[0, 1, 0.3, 2], [2, 3, 0.4, 2], [4, 5, 0.6, 4]], dtype=xp.float64) assert is_monotonic(Z) def test_is_monotonic_3x4_F1(self, xp): # Tests is_monotonic(Z) on 3x4 linkage (case 1). Expecting False. Z = xp.asarray([[0, 1, 0.3, 2], [2, 3, 0.2, 2], [4, 5, 0.6, 4]], dtype=xp.float64) assert not is_monotonic(Z) def test_is_monotonic_3x4_F2(self, xp): # Tests is_monotonic(Z) on 3x4 linkage (case 2). Expecting False. Z = xp.asarray([[0, 1, 0.8, 2], [2, 3, 0.4, 2], [4, 5, 0.6, 4]], dtype=xp.float64) assert not is_monotonic(Z) def test_is_monotonic_3x4_F3(self, xp): # Tests is_monotonic(Z) on 3x4 linkage (case 3). Expecting False Z = xp.asarray([[0, 1, 0.3, 2], [2, 3, 0.4, 2], [4, 5, 0.2, 4]], dtype=xp.float64) assert not is_monotonic(Z) def test_is_monotonic_tdist_linkage1(self, xp): # Tests is_monotonic(Z) on clustering generated by single linkage on # tdist data set. Expecting True. Z = linkage(xp.asarray(hierarchy_test_data.ytdist), 'single') assert is_monotonic(Z) def test_is_monotonic_tdist_linkage2(self, xp): # Tests is_monotonic(Z) on clustering generated by single linkage on # tdist data set. Perturbing. Expecting False. Z = linkage(xp.asarray(hierarchy_test_data.ytdist), 'single') Z[2,2] = 0.0 assert not is_monotonic(Z) def test_is_monotonic_Q_linkage(self, xp): # Tests is_monotonic(Z) on clustering generated by single linkage on # Q data set. Expecting True. X = xp.asarray(hierarchy_test_data.Q_X) Z = linkage(X, 'single') assert is_monotonic(Z) @skip_if_array_api(cpu_only=True) class TestMaxDists: def test_maxdists_empty_linkage(self, xp): # Tests maxdists(Z) on empty linkage. Expecting exception. Z = xp.zeros((0, 4), dtype=xp.float64) assert_raises(ValueError, maxdists, Z) def test_maxdists_one_cluster_linkage(self, xp): # Tests maxdists(Z) on linkage with one cluster. Z = xp.asarray([[0, 1, 0.3, 4]], dtype=xp.float64) MD = maxdists(Z) expectedMD = calculate_maximum_distances(Z, xp) xp_assert_close(MD, expectedMD, atol=1e-15) def test_maxdists_Q_linkage(self, xp): for method in ['single', 'complete', 'ward', 'centroid', 'median']: self.check_maxdists_Q_linkage(method, xp) def check_maxdists_Q_linkage(self, method, xp): # Tests maxdists(Z) on the Q data set X = xp.asarray(hierarchy_test_data.Q_X) Z = linkage(X, method) MD = maxdists(Z) expectedMD = calculate_maximum_distances(Z, xp) xp_assert_close(MD, expectedMD, atol=1e-15) class TestMaxInconsts: @skip_if_array_api(cpu_only=True) def test_maxinconsts_empty_linkage(self, xp): # Tests maxinconsts(Z, R) on empty linkage. Expecting exception. Z = xp.zeros((0, 4), dtype=xp.float64) R = xp.zeros((0, 4), dtype=xp.float64) assert_raises(ValueError, maxinconsts, Z, R) def test_maxinconsts_difrow_linkage(self, xp): # Tests maxinconsts(Z, R) on linkage and inconsistency matrices with # different numbers of clusters. Expecting exception. Z = xp.asarray([[0, 1, 0.3, 4]], dtype=xp.float64) R = np.random.rand(2, 4) R = xp.asarray(R) assert_raises(ValueError, maxinconsts, Z, R) @skip_if_array_api(cpu_only=True) def test_maxinconsts_one_cluster_linkage(self, xp): # Tests maxinconsts(Z, R) on linkage with one cluster. Z = xp.asarray([[0, 1, 0.3, 4]], dtype=xp.float64) R = xp.asarray([[0, 0, 0, 0.3]], dtype=xp.float64) MD = maxinconsts(Z, R) expectedMD = calculate_maximum_inconsistencies(Z, R, xp=xp) xp_assert_close(MD, expectedMD, atol=1e-15) @skip_if_array_api(cpu_only=True) def test_maxinconsts_Q_linkage(self, xp): for method in ['single', 'complete', 'ward', 'centroid', 'median']: self.check_maxinconsts_Q_linkage(method, xp) def check_maxinconsts_Q_linkage(self, method, xp): # Tests maxinconsts(Z, R) on the Q data set X = xp.asarray(hierarchy_test_data.Q_X) Z = linkage(X, method) R = inconsistent(Z) MD = maxinconsts(Z, R) expectedMD = calculate_maximum_inconsistencies(Z, R, xp=xp) xp_assert_close(MD, expectedMD, atol=1e-15) class TestMaxRStat: def test_maxRstat_invalid_index(self, xp): for i in [3.3, -1, 4]: self.check_maxRstat_invalid_index(i, xp) def check_maxRstat_invalid_index(self, i, xp): # Tests maxRstat(Z, R, i). Expecting exception. Z = xp.asarray([[0, 1, 0.3, 4]], dtype=xp.float64) R = xp.asarray([[0, 0, 0, 0.3]], dtype=xp.float64) if isinstance(i, int): assert_raises(ValueError, maxRstat, Z, R, i) else: assert_raises(TypeError, maxRstat, Z, R, i) @skip_if_array_api(cpu_only=True) def test_maxRstat_empty_linkage(self, xp): for i in range(4): self.check_maxRstat_empty_linkage(i, xp) def check_maxRstat_empty_linkage(self, i, xp): # Tests maxRstat(Z, R, i) on empty linkage. Expecting exception. Z = xp.zeros((0, 4), dtype=xp.float64) R = xp.zeros((0, 4), dtype=xp.float64) assert_raises(ValueError, maxRstat, Z, R, i) def test_maxRstat_difrow_linkage(self, xp): for i in range(4): self.check_maxRstat_difrow_linkage(i, xp) def check_maxRstat_difrow_linkage(self, i, xp): # Tests maxRstat(Z, R, i) on linkage and inconsistency matrices with # different numbers of clusters. Expecting exception. Z = xp.asarray([[0, 1, 0.3, 4]], dtype=xp.float64) R = np.random.rand(2, 4) R = xp.asarray(R) assert_raises(ValueError, maxRstat, Z, R, i) @skip_if_array_api(cpu_only=True) def test_maxRstat_one_cluster_linkage(self, xp): for i in range(4): self.check_maxRstat_one_cluster_linkage(i, xp) def check_maxRstat_one_cluster_linkage(self, i, xp): # Tests maxRstat(Z, R, i) on linkage with one cluster. Z = xp.asarray([[0, 1, 0.3, 4]], dtype=xp.float64) R = xp.asarray([[0, 0, 0, 0.3]], dtype=xp.float64) MD = maxRstat(Z, R, 1) expectedMD = calculate_maximum_inconsistencies(Z, R, 1, xp) xp_assert_close(MD, expectedMD, atol=1e-15) @skip_if_array_api(cpu_only=True) def test_maxRstat_Q_linkage(self, xp): for method in ['single', 'complete', 'ward', 'centroid', 'median']: for i in range(4): self.check_maxRstat_Q_linkage(method, i, xp) def check_maxRstat_Q_linkage(self, method, i, xp): # Tests maxRstat(Z, R, i) on the Q data set X = xp.asarray(hierarchy_test_data.Q_X) Z = linkage(X, method) R = inconsistent(Z) MD = maxRstat(Z, R, 1) expectedMD = calculate_maximum_inconsistencies(Z, R, 1, xp) xp_assert_close(MD, expectedMD, atol=1e-15) @skip_if_array_api(cpu_only=True) class TestDendrogram: def test_dendrogram_single_linkage_tdist(self, xp): # Tests dendrogram calculation on single linkage of the tdist data set. Z = linkage(xp.asarray(hierarchy_test_data.ytdist), 'single') R = dendrogram(Z, no_plot=True) leaves = R["leaves"] assert_equal(leaves, [2, 5, 1, 0, 3, 4]) def test_valid_orientation(self, xp): Z = linkage(xp.asarray(hierarchy_test_data.ytdist), 'single') assert_raises(ValueError, dendrogram, Z, orientation="foo") def test_labels_as_array_or_list(self, xp): # test for gh-12418 Z = linkage(xp.asarray(hierarchy_test_data.ytdist), 'single') labels = xp.asarray([1, 3, 2, 6, 4, 5]) result1 = dendrogram(Z, labels=labels, no_plot=True) result2 = dendrogram(Z, labels=list(labels), no_plot=True) assert result1 == result2 @pytest.mark.skipif(not have_matplotlib, reason="no matplotlib") def test_valid_label_size(self, xp): link = xp.asarray([ [0, 1, 1.0, 4], [2, 3, 1.0, 5], [4, 5, 2.0, 6], ]) plt.figure() with pytest.raises(ValueError) as exc_info: dendrogram(link, labels=list(range(100))) assert "Dimensions of Z and labels must be consistent."\ in str(exc_info.value) with pytest.raises( ValueError, match="Dimensions of Z and labels must be consistent."): dendrogram(link, labels=[]) plt.close() @pytest.mark.skipif(not have_matplotlib, reason="no matplotlib") def test_dendrogram_plot(self, xp): for orientation in ['top', 'bottom', 'left', 'right']: self.check_dendrogram_plot(orientation, xp) def check_dendrogram_plot(self, orientation, xp): # Tests dendrogram plotting. Z = linkage(xp.asarray(hierarchy_test_data.ytdist), 'single') expected = {'color_list': ['C1', 'C0', 'C0', 'C0', 'C0'], 'dcoord': [[0.0, 138.0, 138.0, 0.0], [0.0, 219.0, 219.0, 0.0], [0.0, 255.0, 255.0, 219.0], [0.0, 268.0, 268.0, 255.0], [138.0, 295.0, 295.0, 268.0]], 'icoord': [[5.0, 5.0, 15.0, 15.0], [45.0, 45.0, 55.0, 55.0], [35.0, 35.0, 50.0, 50.0], [25.0, 25.0, 42.5, 42.5], [10.0, 10.0, 33.75, 33.75]], 'ivl': ['2', '5', '1', '0', '3', '4'], 'leaves': [2, 5, 1, 0, 3, 4], 'leaves_color_list': ['C1', 'C1', 'C0', 'C0', 'C0', 'C0'], } fig = plt.figure() ax = fig.add_subplot(221) # test that dendrogram accepts ax keyword R1 = dendrogram(Z, ax=ax, orientation=orientation) R1['dcoord'] = np.asarray(R1['dcoord']) assert_equal(R1, expected) # test that dendrogram accepts and handle the leaf_font_size and # leaf_rotation keywords dendrogram(Z, ax=ax, orientation=orientation, leaf_font_size=20, leaf_rotation=90) testlabel = ( ax.get_xticklabels()[0] if orientation in ['top', 'bottom'] else ax.get_yticklabels()[0] ) assert_equal(testlabel.get_rotation(), 90) assert_equal(testlabel.get_size(), 20) dendrogram(Z, ax=ax, orientation=orientation, leaf_rotation=90) testlabel = ( ax.get_xticklabels()[0] if orientation in ['top', 'bottom'] else ax.get_yticklabels()[0] ) assert_equal(testlabel.get_rotation(), 90) dendrogram(Z, ax=ax, orientation=orientation, leaf_font_size=20) testlabel = ( ax.get_xticklabels()[0] if orientation in ['top', 'bottom'] else ax.get_yticklabels()[0] ) assert_equal(testlabel.get_size(), 20) plt.close() # test plotting to gca (will import pylab) R2 = dendrogram(Z, orientation=orientation) plt.close() R2['dcoord'] = np.asarray(R2['dcoord']) assert_equal(R2, expected) @pytest.mark.skipif(not have_matplotlib, reason="no matplotlib") def test_dendrogram_truncate_mode(self, xp): Z = linkage(xp.asarray(hierarchy_test_data.ytdist), 'single') R = dendrogram(Z, 2, 'lastp', show_contracted=True) plt.close() R['dcoord'] = np.asarray(R['dcoord']) assert_equal(R, {'color_list': ['C0'], 'dcoord': [[0.0, 295.0, 295.0, 0.0]], 'icoord': [[5.0, 5.0, 15.0, 15.0]], 'ivl': ['(2)', '(4)'], 'leaves': [6, 9], 'leaves_color_list': ['C0', 'C0'], }) R = dendrogram(Z, 2, 'mtica', show_contracted=True) plt.close() R['dcoord'] = np.asarray(R['dcoord']) assert_equal(R, {'color_list': ['C1', 'C0', 'C0', 'C0'], 'dcoord': [[0.0, 138.0, 138.0, 0.0], [0.0, 255.0, 255.0, 0.0], [0.0, 268.0, 268.0, 255.0], [138.0, 295.0, 295.0, 268.0]], 'icoord': [[5.0, 5.0, 15.0, 15.0], [35.0, 35.0, 45.0, 45.0], [25.0, 25.0, 40.0, 40.0], [10.0, 10.0, 32.5, 32.5]], 'ivl': ['2', '5', '1', '0', '(2)'], 'leaves': [2, 5, 1, 0, 7], 'leaves_color_list': ['C1', 'C1', 'C0', 'C0', 'C0'], }) def test_dendrogram_colors(self, xp): # Tests dendrogram plots with alternate colors Z = linkage(xp.asarray(hierarchy_test_data.ytdist), 'single') set_link_color_palette(['c', 'm', 'y', 'k']) R = dendrogram(Z, no_plot=True, above_threshold_color='g', color_threshold=250) set_link_color_palette(['g', 'r', 'c', 'm', 'y', 'k']) color_list = R['color_list'] assert_equal(color_list, ['c', 'm', 'g', 'g', 'g']) # reset color palette (global list) set_link_color_palette(None) def test_dendrogram_leaf_colors_zero_dist(self, xp): # tests that the colors of leafs are correct for tree # with two identical points x = xp.asarray([[1, 0, 0], [0, 0, 1], [0, 2, 0], [0, 0, 1], [0, 1, 0], [0, 1, 0]]) z = linkage(x, "single") d = dendrogram(z, no_plot=True) exp_colors = ['C0', 'C1', 'C1', 'C0', 'C2', 'C2'] colors = d["leaves_color_list"] assert_equal(colors, exp_colors) def test_dendrogram_leaf_colors(self, xp): # tests that the colors are correct for a tree # with two near points ((0, 0, 1.1) and (0, 0, 1)) x = xp.asarray([[1, 0, 0], [0, 0, 1.1], [0, 2, 0], [0, 0, 1], [0, 1, 0], [0, 1, 0]]) z = linkage(x, "single") d = dendrogram(z, no_plot=True) exp_colors = ['C0', 'C1', 'C1', 'C0', 'C2', 'C2'] colors = d["leaves_color_list"] assert_equal(colors, exp_colors) def calculate_maximum_distances(Z, xp): # Used for testing correctness of maxdists. n = Z.shape[0] + 1 B = xp.zeros((n-1,), dtype=Z.dtype) q = xp.zeros((3,)) for i in range(0, n - 1): q[:] = 0.0 left = Z[i, 0] right = Z[i, 1] if left >= n: q[0] = B[xp.asarray(left, dtype=xp.int64) - n] if right >= n: q[1] = B[xp.asarray(right, dtype=xp.int64) - n] q[2] = Z[i, 2] B[i] = xp.max(q) return B def calculate_maximum_inconsistencies(Z, R, k=3, xp=np): # Used for testing correctness of maxinconsts. n = Z.shape[0] + 1 dtype = xp.result_type(Z, R) B = xp.zeros((n-1,), dtype=dtype) q = xp.zeros((3,)) for i in range(0, n - 1): q[:] = 0.0 left = Z[i, 0] right = Z[i, 1] if left >= n: q[0] = B[xp.asarray(left, dtype=xp.int64) - n] if right >= n: q[1] = B[xp.asarray(right, dtype=xp.int64) - n] q[2] = R[i, k] B[i] = xp.max(q) return B @skip_if_array_api(cpu_only=True) def test_unsupported_uncondensed_distance_matrix_linkage_warning(xp): assert_warns(ClusterWarning, linkage, xp.asarray([[0, 1], [1, 0]])) def test_euclidean_linkage_value_error(xp): for method in scipy.cluster.hierarchy._EUCLIDEAN_METHODS: assert_raises(ValueError, linkage, xp.asarray([[1, 1], [1, 1]]), method=method, metric='cityblock') @skip_if_array_api(cpu_only=True) def test_2x2_linkage(xp): Z1 = linkage(xp.asarray([1]), method='single', metric='euclidean') Z2 = linkage(xp.asarray([[0, 1], [0, 0]]), method='single', metric='euclidean') xp_assert_close(Z1, Z2, rtol=1e-15) @skip_if_array_api(cpu_only=True) def test_node_compare(xp): np.random.seed(23) nobs = 50 X = np.random.randn(nobs, 4) X = xp.asarray(X) Z = scipy.cluster.hierarchy.ward(X) tree = to_tree(Z) assert_(tree > tree.get_left()) assert_(tree.get_right() > tree.get_left()) assert_(tree.get_right() == tree.get_right()) assert_(tree.get_right() != tree.get_left()) @skip_if_array_api(np_only=True, reasons=['`cut_tree` uses non-standard indexing']) def test_cut_tree(xp): np.random.seed(23) nobs = 50 X = np.random.randn(nobs, 4) X = xp.asarray(X) Z = scipy.cluster.hierarchy.ward(X) cutree = cut_tree(Z) # cutree.dtype varies between int32 and int64 over platforms xp_assert_close(cutree[:, 0], xp.arange(nobs), rtol=1e-15, check_dtype=False) xp_assert_close(cutree[:, -1], xp.zeros(nobs), rtol=1e-15, check_dtype=False) assert_equal(np.asarray(cutree).max(0), np.arange(nobs - 1, -1, -1)) xp_assert_close(cutree[:, [-5]], cut_tree(Z, n_clusters=5), rtol=1e-15) xp_assert_close(cutree[:, [-5, -10]], cut_tree(Z, n_clusters=[5, 10]), rtol=1e-15) xp_assert_close(cutree[:, [-10, -5]], cut_tree(Z, n_clusters=[10, 5]), rtol=1e-15) nodes = _order_cluster_tree(Z) heights = xp.asarray([node.dist for node in nodes]) xp_assert_close(cutree[:, np.searchsorted(heights, [5])], cut_tree(Z, height=5), rtol=1e-15) xp_assert_close(cutree[:, np.searchsorted(heights, [5, 10])], cut_tree(Z, height=[5, 10]), rtol=1e-15) xp_assert_close(cutree[:, np.searchsorted(heights, [10, 5])], cut_tree(Z, height=[10, 5]), rtol=1e-15) @skip_if_array_api(cpu_only=True) def test_optimal_leaf_ordering(xp): # test with the distance vector y Z = optimal_leaf_ordering(linkage(xp.asarray(hierarchy_test_data.ytdist)), xp.asarray(hierarchy_test_data.ytdist)) expectedZ = hierarchy_test_data.linkage_ytdist_single_olo xp_assert_close(Z, xp.asarray(expectedZ), atol=1e-10) # test with the observation matrix X Z = optimal_leaf_ordering(linkage(xp.asarray(hierarchy_test_data.X), 'ward'), xp.asarray(hierarchy_test_data.X)) expectedZ = hierarchy_test_data.linkage_X_ward_olo xp_assert_close(Z, xp.asarray(expectedZ), atol=1e-06) @skip_if_array_api(np_only=True, reasons=['`Heap` only supports NumPy backend']) def test_Heap(xp): values = xp.asarray([2, -1, 0, -1.5, 3]) heap = Heap(values) pair = heap.get_min() assert_equal(pair['key'], 3) assert_equal(pair['value'], -1.5) heap.remove_min() pair = heap.get_min() assert_equal(pair['key'], 1) assert_equal(pair['value'], -1) heap.change_value(1, 2.5) pair = heap.get_min() assert_equal(pair['key'], 2) assert_equal(pair['value'], 0) heap.remove_min() heap.remove_min() heap.change_value(1, 10) pair = heap.get_min() assert_equal(pair['key'], 4) assert_equal(pair['value'], 3) heap.remove_min() pair = heap.get_min() assert_equal(pair['key'], 1) assert_equal(pair['value'], 10)