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+"""Unit tests for layout functions."""
+
+import pytest
+
+import networkx as nx
+
+np = pytest.importorskip("numpy")
+pytest.importorskip("scipy")
+
+
+class TestLayout:
+    @classmethod
+    def setup_class(cls):
+        cls.Gi = nx.grid_2d_graph(5, 5)
+        cls.Gs = nx.Graph()
+        nx.add_path(cls.Gs, "abcdef")
+        cls.bigG = nx.grid_2d_graph(25, 25)  # > 500 nodes for sparse
+
+    def test_spring_fixed_without_pos(self):
+        G = nx.path_graph(4)
+        pytest.raises(ValueError, nx.spring_layout, G, fixed=[0])
+        pos = {0: (1, 1), 2: (0, 0)}
+        pytest.raises(ValueError, nx.spring_layout, G, fixed=[0, 1], pos=pos)
+        nx.spring_layout(G, fixed=[0, 2], pos=pos)  # No ValueError
+
+    def test_spring_init_pos(self):
+        # Tests GH #2448
+        import math
+
+        G = nx.Graph()
+        G.add_edges_from([(0, 1), (1, 2), (2, 0), (2, 3)])
+
+        init_pos = {0: (0.0, 0.0)}
+        fixed_pos = [0]
+        pos = nx.fruchterman_reingold_layout(G, pos=init_pos, fixed=fixed_pos)
+        has_nan = any(math.isnan(c) for coords in pos.values() for c in coords)
+        assert not has_nan, "values should not be nan"
+
+    def test_smoke_empty_graph(self):
+        G = []
+        nx.random_layout(G)
+        nx.circular_layout(G)
+        nx.planar_layout(G)
+        nx.spring_layout(G)
+        nx.fruchterman_reingold_layout(G)
+        nx.spectral_layout(G)
+        nx.shell_layout(G)
+        nx.bipartite_layout(G, G)
+        nx.spiral_layout(G)
+        nx.multipartite_layout(G)
+        nx.kamada_kawai_layout(G)
+
+    def test_smoke_int(self):
+        G = self.Gi
+        nx.random_layout(G)
+        nx.circular_layout(G)
+        nx.planar_layout(G)
+        nx.spring_layout(G)
+        nx.forceatlas2_layout(G)
+        nx.fruchterman_reingold_layout(G)
+        nx.fruchterman_reingold_layout(self.bigG)
+        nx.spectral_layout(G)
+        nx.spectral_layout(G.to_directed())
+        nx.spectral_layout(self.bigG)
+        nx.spectral_layout(self.bigG.to_directed())
+        nx.shell_layout(G)
+        nx.spiral_layout(G)
+        nx.kamada_kawai_layout(G)
+        nx.kamada_kawai_layout(G, dim=1)
+        nx.kamada_kawai_layout(G, dim=3)
+        nx.arf_layout(G)
+
+    def test_smoke_string(self):
+        G = self.Gs
+        nx.random_layout(G)
+        nx.circular_layout(G)
+        nx.planar_layout(G)
+        nx.spring_layout(G)
+        nx.forceatlas2_layout(G)
+        nx.fruchterman_reingold_layout(G)
+        nx.spectral_layout(G)
+        nx.shell_layout(G)
+        nx.spiral_layout(G)
+        nx.kamada_kawai_layout(G)
+        nx.kamada_kawai_layout(G, dim=1)
+        nx.kamada_kawai_layout(G, dim=3)
+        nx.arf_layout(G)
+
+    def check_scale_and_center(self, pos, scale, center):
+        center = np.array(center)
+        low = center - scale
+        hi = center + scale
+        vpos = np.array(list(pos.values()))
+        length = vpos.max(0) - vpos.min(0)
+        assert (length <= 2 * scale).all()
+        assert (vpos >= low).all()
+        assert (vpos <= hi).all()
+
+    def test_scale_and_center_arg(self):
+        sc = self.check_scale_and_center
+        c = (4, 5)
+        G = nx.complete_graph(9)
+        G.add_node(9)
+        sc(nx.random_layout(G, center=c), scale=0.5, center=(4.5, 5.5))
+        # rest can have 2*scale length: [-scale, scale]
+        sc(nx.spring_layout(G, scale=2, center=c), scale=2, center=c)
+        sc(nx.spectral_layout(G, scale=2, center=c), scale=2, center=c)
+        sc(nx.circular_layout(G, scale=2, center=c), scale=2, center=c)
+        sc(nx.shell_layout(G, scale=2, center=c), scale=2, center=c)
+        sc(nx.spiral_layout(G, scale=2, center=c), scale=2, center=c)
+        sc(nx.kamada_kawai_layout(G, scale=2, center=c), scale=2, center=c)
+
+        c = (2, 3, 5)
+        sc(nx.kamada_kawai_layout(G, dim=3, scale=2, center=c), scale=2, center=c)
+
+    def test_planar_layout_non_planar_input(self):
+        G = nx.complete_graph(9)
+        pytest.raises(nx.NetworkXException, nx.planar_layout, G)
+
+    def test_smoke_planar_layout_embedding_input(self):
+        embedding = nx.PlanarEmbedding()
+        embedding.set_data({0: [1, 2], 1: [0, 2], 2: [0, 1]})
+        nx.planar_layout(embedding)
+
+    def test_default_scale_and_center(self):
+        sc = self.check_scale_and_center
+        c = (0, 0)
+        G = nx.complete_graph(9)
+        G.add_node(9)
+        sc(nx.random_layout(G), scale=0.5, center=(0.5, 0.5))
+        sc(nx.spring_layout(G), scale=1, center=c)
+        sc(nx.spectral_layout(G), scale=1, center=c)
+        sc(nx.circular_layout(G), scale=1, center=c)
+        sc(nx.shell_layout(G), scale=1, center=c)
+        sc(nx.spiral_layout(G), scale=1, center=c)
+        sc(nx.kamada_kawai_layout(G), scale=1, center=c)
+
+        c = (0, 0, 0)
+        sc(nx.kamada_kawai_layout(G, dim=3), scale=1, center=c)
+
+    def test_circular_planar_and_shell_dim_error(self):
+        G = nx.path_graph(4)
+        pytest.raises(ValueError, nx.circular_layout, G, dim=1)
+        pytest.raises(ValueError, nx.shell_layout, G, dim=1)
+        pytest.raises(ValueError, nx.shell_layout, G, dim=3)
+        pytest.raises(ValueError, nx.planar_layout, G, dim=1)
+        pytest.raises(ValueError, nx.planar_layout, G, dim=3)
+
+    def test_adjacency_interface_numpy(self):
+        A = nx.to_numpy_array(self.Gs)
+        pos = nx.drawing.layout._fruchterman_reingold(A)
+        assert pos.shape == (6, 2)
+        pos = nx.drawing.layout._fruchterman_reingold(A, dim=3)
+        assert pos.shape == (6, 3)
+        pos = nx.drawing.layout._sparse_fruchterman_reingold(A)
+        assert pos.shape == (6, 2)
+
+    def test_adjacency_interface_scipy(self):
+        A = nx.to_scipy_sparse_array(self.Gs, dtype="d")
+        pos = nx.drawing.layout._sparse_fruchterman_reingold(A)
+        assert pos.shape == (6, 2)
+        pos = nx.drawing.layout._sparse_spectral(A)
+        assert pos.shape == (6, 2)
+        pos = nx.drawing.layout._sparse_fruchterman_reingold(A, dim=3)
+        assert pos.shape == (6, 3)
+
+    def test_single_nodes(self):
+        G = nx.path_graph(1)
+        vpos = nx.shell_layout(G)
+        assert not vpos[0].any()
+        G = nx.path_graph(4)
+        vpos = nx.shell_layout(G, [[0], [1, 2], [3]])
+        assert not vpos[0].any()
+        assert vpos[3].any()  # ensure node 3 not at origin (#3188)
+        assert np.linalg.norm(vpos[3]) <= 1  # ensure node 3 fits (#3753)
+        vpos = nx.shell_layout(G, [[0], [1, 2], [3]], rotate=0)
+        assert np.linalg.norm(vpos[3]) <= 1  # ensure node 3 fits (#3753)
+
+    def test_smoke_initial_pos_forceatlas2(self):
+        pos = nx.circular_layout(self.Gi)
+        npos = nx.forceatlas2_layout(self.Gi, pos=pos)
+
+    def test_smoke_initial_pos_fruchterman_reingold(self):
+        pos = nx.circular_layout(self.Gi)
+        npos = nx.fruchterman_reingold_layout(self.Gi, pos=pos)
+
+    def test_smoke_initial_pos_arf(self):
+        pos = nx.circular_layout(self.Gi)
+        npos = nx.arf_layout(self.Gi, pos=pos)
+
+    def test_fixed_node_fruchterman_reingold(self):
+        # Dense version (numpy based)
+        pos = nx.circular_layout(self.Gi)
+        npos = nx.spring_layout(self.Gi, pos=pos, fixed=[(0, 0)])
+        assert tuple(pos[(0, 0)]) == tuple(npos[(0, 0)])
+        # Sparse version (scipy based)
+        pos = nx.circular_layout(self.bigG)
+        npos = nx.spring_layout(self.bigG, pos=pos, fixed=[(0, 0)])
+        for axis in range(2):
+            assert pos[(0, 0)][axis] == pytest.approx(npos[(0, 0)][axis], abs=1e-7)
+
+    def test_center_parameter(self):
+        G = nx.path_graph(1)
+        nx.random_layout(G, center=(1, 1))
+        vpos = nx.circular_layout(G, center=(1, 1))
+        assert tuple(vpos[0]) == (1, 1)
+        vpos = nx.planar_layout(G, center=(1, 1))
+        assert tuple(vpos[0]) == (1, 1)
+        vpos = nx.spring_layout(G, center=(1, 1))
+        assert tuple(vpos[0]) == (1, 1)
+        vpos = nx.fruchterman_reingold_layout(G, center=(1, 1))
+        assert tuple(vpos[0]) == (1, 1)
+        vpos = nx.spectral_layout(G, center=(1, 1))
+        assert tuple(vpos[0]) == (1, 1)
+        vpos = nx.shell_layout(G, center=(1, 1))
+        assert tuple(vpos[0]) == (1, 1)
+        vpos = nx.spiral_layout(G, center=(1, 1))
+        assert tuple(vpos[0]) == (1, 1)
+
+    def test_center_wrong_dimensions(self):
+        G = nx.path_graph(1)
+        assert id(nx.spring_layout) == id(nx.fruchterman_reingold_layout)
+        pytest.raises(ValueError, nx.random_layout, G, center=(1, 1, 1))
+        pytest.raises(ValueError, nx.circular_layout, G, center=(1, 1, 1))
+        pytest.raises(ValueError, nx.planar_layout, G, center=(1, 1, 1))
+        pytest.raises(ValueError, nx.spring_layout, G, center=(1, 1, 1))
+        pytest.raises(ValueError, nx.spring_layout, G, dim=3, center=(1, 1))
+        pytest.raises(ValueError, nx.spectral_layout, G, center=(1, 1, 1))
+        pytest.raises(ValueError, nx.spectral_layout, G, dim=3, center=(1, 1))
+        pytest.raises(ValueError, nx.shell_layout, G, center=(1, 1, 1))
+        pytest.raises(ValueError, nx.spiral_layout, G, center=(1, 1, 1))
+        pytest.raises(ValueError, nx.kamada_kawai_layout, G, center=(1, 1, 1))
+
+    def test_empty_graph(self):
+        G = nx.empty_graph()
+        vpos = nx.random_layout(G, center=(1, 1))
+        assert vpos == {}
+        vpos = nx.circular_layout(G, center=(1, 1))
+        assert vpos == {}
+        vpos = nx.planar_layout(G, center=(1, 1))
+        assert vpos == {}
+        vpos = nx.bipartite_layout(G, G)
+        assert vpos == {}
+        vpos = nx.spring_layout(G, center=(1, 1))
+        assert vpos == {}
+        vpos = nx.fruchterman_reingold_layout(G, center=(1, 1))
+        assert vpos == {}
+        vpos = nx.spectral_layout(G, center=(1, 1))
+        assert vpos == {}
+        vpos = nx.shell_layout(G, center=(1, 1))
+        assert vpos == {}
+        vpos = nx.spiral_layout(G, center=(1, 1))
+        assert vpos == {}
+        vpos = nx.multipartite_layout(G, center=(1, 1))
+        assert vpos == {}
+        vpos = nx.kamada_kawai_layout(G, center=(1, 1))
+        assert vpos == {}
+        vpos = nx.forceatlas2_layout(G)
+        assert vpos == {}
+        vpos = nx.arf_layout(G)
+        assert vpos == {}
+
+    def test_bipartite_layout(self):
+        G = nx.complete_bipartite_graph(3, 5)
+        top, bottom = nx.bipartite.sets(G)
+
+        vpos = nx.bipartite_layout(G, top)
+        assert len(vpos) == len(G)
+
+        top_x = vpos[list(top)[0]][0]
+        bottom_x = vpos[list(bottom)[0]][0]
+        for node in top:
+            assert vpos[node][0] == top_x
+        for node in bottom:
+            assert vpos[node][0] == bottom_x
+
+        vpos = nx.bipartite_layout(
+            G, top, align="horizontal", center=(2, 2), scale=2, aspect_ratio=1
+        )
+        assert len(vpos) == len(G)
+
+        top_y = vpos[list(top)[0]][1]
+        bottom_y = vpos[list(bottom)[0]][1]
+        for node in top:
+            assert vpos[node][1] == top_y
+        for node in bottom:
+            assert vpos[node][1] == bottom_y
+
+        pytest.raises(ValueError, nx.bipartite_layout, G, top, align="foo")
+
+    def test_multipartite_layout(self):
+        sizes = (0, 5, 7, 2, 8)
+        G = nx.complete_multipartite_graph(*sizes)
+
+        vpos = nx.multipartite_layout(G)
+        assert len(vpos) == len(G)
+
+        start = 0
+        for n in sizes:
+            end = start + n
+            assert all(vpos[start][0] == vpos[i][0] for i in range(start + 1, end))
+            start += n
+
+        vpos = nx.multipartite_layout(G, align="horizontal", scale=2, center=(2, 2))
+        assert len(vpos) == len(G)
+
+        start = 0
+        for n in sizes:
+            end = start + n
+            assert all(vpos[start][1] == vpos[i][1] for i in range(start + 1, end))
+            start += n
+
+        pytest.raises(ValueError, nx.multipartite_layout, G, align="foo")
+
+    def test_kamada_kawai_costfn_1d(self):
+        costfn = nx.drawing.layout._kamada_kawai_costfn
+
+        pos = np.array([4.0, 7.0])
+        invdist = 1 / np.array([[0.1, 2.0], [2.0, 0.3]])
+
+        cost, grad = costfn(pos, np, invdist, meanweight=0, dim=1)
+
+        assert cost == pytest.approx(((3 / 2.0 - 1) ** 2), abs=1e-7)
+        assert grad[0] == pytest.approx((-0.5), abs=1e-7)
+        assert grad[1] == pytest.approx(0.5, abs=1e-7)
+
+    def check_kamada_kawai_costfn(self, pos, invdist, meanwt, dim):
+        costfn = nx.drawing.layout._kamada_kawai_costfn
+
+        cost, grad = costfn(pos.ravel(), np, invdist, meanweight=meanwt, dim=dim)
+
+        expected_cost = 0.5 * meanwt * np.sum(np.sum(pos, axis=0) ** 2)
+        for i in range(pos.shape[0]):
+            for j in range(i + 1, pos.shape[0]):
+                diff = np.linalg.norm(pos[i] - pos[j])
+                expected_cost += (diff * invdist[i][j] - 1.0) ** 2
+
+        assert cost == pytest.approx(expected_cost, abs=1e-7)
+
+        dx = 1e-4
+        for nd in range(pos.shape[0]):
+            for dm in range(pos.shape[1]):
+                idx = nd * pos.shape[1] + dm
+                ps = pos.flatten()
+
+                ps[idx] += dx
+                cplus = costfn(ps, np, invdist, meanweight=meanwt, dim=pos.shape[1])[0]
+
+                ps[idx] -= 2 * dx
+                cminus = costfn(ps, np, invdist, meanweight=meanwt, dim=pos.shape[1])[0]
+
+                assert grad[idx] == pytest.approx((cplus - cminus) / (2 * dx), abs=1e-5)
+
+    def test_kamada_kawai_costfn(self):
+        invdist = 1 / np.array([[0.1, 2.1, 1.7], [2.1, 0.2, 0.6], [1.7, 0.6, 0.3]])
+        meanwt = 0.3
+
+        # 2d
+        pos = np.array([[1.3, -3.2], [2.7, -0.3], [5.1, 2.5]])
+
+        self.check_kamada_kawai_costfn(pos, invdist, meanwt, 2)
+
+        # 3d
+        pos = np.array([[0.9, 8.6, -8.7], [-10, -0.5, -7.1], [9.1, -8.1, 1.6]])
+
+        self.check_kamada_kawai_costfn(pos, invdist, meanwt, 3)
+
+    def test_spiral_layout(self):
+        G = self.Gs
+
+        # a lower value of resolution should result in a more compact layout
+        # intuitively, the total distance from the start and end nodes
+        # via each node in between (transiting through each) will be less,
+        # assuming rescaling does not occur on the computed node positions
+        pos_standard = np.array(list(nx.spiral_layout(G, resolution=0.35).values()))
+        pos_tighter = np.array(list(nx.spiral_layout(G, resolution=0.34).values()))
+        distances = np.linalg.norm(pos_standard[:-1] - pos_standard[1:], axis=1)
+        distances_tighter = np.linalg.norm(pos_tighter[:-1] - pos_tighter[1:], axis=1)
+        assert sum(distances) > sum(distances_tighter)
+
+        # return near-equidistant points after the first value if set to true
+        pos_equidistant = np.array(list(nx.spiral_layout(G, equidistant=True).values()))
+        distances_equidistant = np.linalg.norm(
+            pos_equidistant[:-1] - pos_equidistant[1:], axis=1
+        )
+        assert np.allclose(
+            distances_equidistant[1:], distances_equidistant[-1], atol=0.01
+        )
+
+    def test_spiral_layout_equidistant(self):
+        G = nx.path_graph(10)
+        pos = nx.spiral_layout(G, equidistant=True)
+        # Extract individual node positions as an array
+        p = np.array(list(pos.values()))
+        # Elementwise-distance between node positions
+        dist = np.linalg.norm(p[1:] - p[:-1], axis=1)
+        assert np.allclose(np.diff(dist), 0, atol=1e-3)
+
+    def test_forceatlas2_layout_partial_input_test(self):
+        # check whether partial pos input still returns a full proper position
+        G = self.Gs
+        node = nx.utils.arbitrary_element(G)
+        pos = nx.circular_layout(G)
+        del pos[node]
+        pos = nx.forceatlas2_layout(G, pos=pos)
+        assert len(pos) == len(G)
+
+    def test_rescale_layout_dict(self):
+        G = nx.empty_graph()
+        vpos = nx.random_layout(G, center=(1, 1))
+        assert nx.rescale_layout_dict(vpos) == {}
+
+        G = nx.empty_graph(2)
+        vpos = {0: (0.0, 0.0), 1: (1.0, 1.0)}
+        s_vpos = nx.rescale_layout_dict(vpos)
+        assert np.linalg.norm([sum(x) for x in zip(*s_vpos.values())]) < 1e-6
+
+        G = nx.empty_graph(3)
+        vpos = {0: (0, 0), 1: (1, 1), 2: (0.5, 0.5)}
+        s_vpos = nx.rescale_layout_dict(vpos)
+
+        expectation = {
+            0: np.array((-1, -1)),
+            1: np.array((1, 1)),
+            2: np.array((0, 0)),
+        }
+        for k, v in expectation.items():
+            assert (s_vpos[k] == v).all()
+        s_vpos = nx.rescale_layout_dict(vpos, scale=2)
+        expectation = {
+            0: np.array((-2, -2)),
+            1: np.array((2, 2)),
+            2: np.array((0, 0)),
+        }
+        for k, v in expectation.items():
+            assert (s_vpos[k] == v).all()
+
+    def test_arf_layout_partial_input_test(self):
+        # Checks whether partial pos input still returns a proper position.
+        G = self.Gs
+        node = nx.utils.arbitrary_element(G)
+        pos = nx.circular_layout(G)
+        del pos[node]
+        pos = nx.arf_layout(G, pos=pos)
+        assert len(pos) == len(G)
+
+    def test_arf_layout_negative_a_check(self):
+        """
+        Checks input parameters correctly raises errors. For example,  `a` should be larger than 1
+        """
+        G = self.Gs
+        pytest.raises(ValueError, nx.arf_layout, G=G, a=-1)
+
+    def test_smoke_seed_input(self):
+        G = self.Gs
+        nx.random_layout(G, seed=42)
+        nx.spring_layout(G, seed=42)
+        nx.arf_layout(G, seed=42)
+        nx.forceatlas2_layout(G, seed=42)
+
+
+def test_multipartite_layout_nonnumeric_partition_labels():
+    """See gh-5123."""
+    G = nx.Graph()
+    G.add_node(0, subset="s0")
+    G.add_node(1, subset="s0")
+    G.add_node(2, subset="s1")
+    G.add_node(3, subset="s1")
+    G.add_edges_from([(0, 2), (0, 3), (1, 2)])
+    pos = nx.multipartite_layout(G)
+    assert len(pos) == len(G)
+
+
+def test_multipartite_layout_layer_order():
+    """Return the layers in sorted order if the layers of the multipartite
+    graph are sortable. See gh-5691"""
+    G = nx.Graph()
+    node_group = dict(zip(("a", "b", "c", "d", "e"), (2, 3, 1, 2, 4)))
+    for node, layer in node_group.items():
+        G.add_node(node, subset=layer)
+
+    # Horizontal alignment, therefore y-coord determines layers
+    pos = nx.multipartite_layout(G, align="horizontal")
+
+    layers = nx.utils.groups(node_group)
+    pos_from_layers = nx.multipartite_layout(G, align="horizontal", subset_key=layers)
+    for (n1, p1), (n2, p2) in zip(pos.items(), pos_from_layers.items()):
+        assert n1 == n2 and (p1 == p2).all()
+
+    # Nodes "a" and "d" are in the same layer
+    assert pos["a"][-1] == pos["d"][-1]
+    # positions should be sorted according to layer
+    assert pos["c"][-1] < pos["a"][-1] < pos["b"][-1] < pos["e"][-1]
+
+    # Make sure that multipartite_layout still works when layers are not sortable
+    G.nodes["a"]["subset"] = "layer_0"  # Can't sort mixed strs/ints
+    pos_nosort = nx.multipartite_layout(G)  # smoke test: this should not raise
+    assert pos_nosort.keys() == pos.keys()
+
+
+def _num_nodes_per_bfs_layer(pos):
+    """Helper function to extract the number of nodes in each layer of bfs_layout"""
+    x = np.array(list(pos.values()))[:, 0]  # node positions in layered dimension
+    _, layer_count = np.unique(x, return_counts=True)
+    return layer_count
+
+
+@pytest.mark.parametrize("n", range(2, 7))
+def test_bfs_layout_complete_graph(n):
+    """The complete graph should result in two layers: the starting node and
+    a second layer containing all neighbors."""
+    G = nx.complete_graph(n)
+    pos = nx.bfs_layout(G, start=0)
+    assert np.array_equal(_num_nodes_per_bfs_layer(pos), [1, n - 1])
+
+
+def test_bfs_layout_barbell():
+    G = nx.barbell_graph(5, 3)
+    # Start in one of the "bells"
+    pos = nx.bfs_layout(G, start=0)
+    # start, bell-1, [1] * len(bar)+1, bell-1
+    expected_nodes_per_layer = [1, 4, 1, 1, 1, 1, 4]
+    assert np.array_equal(_num_nodes_per_bfs_layer(pos), expected_nodes_per_layer)
+    # Start in the other "bell" - expect same layer pattern
+    pos = nx.bfs_layout(G, start=12)
+    assert np.array_equal(_num_nodes_per_bfs_layer(pos), expected_nodes_per_layer)
+    # Starting in the center of the bar, expect layers to be symmetric
+    pos = nx.bfs_layout(G, start=6)
+    # Expected layers: {6 (start)}, {5, 7}, {4, 8}, {8 nodes from remainder of bells}
+    expected_nodes_per_layer = [1, 2, 2, 8]
+    assert np.array_equal(_num_nodes_per_bfs_layer(pos), expected_nodes_per_layer)
+
+
+def test_bfs_layout_disconnected():
+    G = nx.complete_graph(5)
+    G.add_edges_from([(10, 11), (11, 12)])
+    with pytest.raises(nx.NetworkXError, match="bfs_layout didn't include all nodes"):
+        nx.bfs_layout(G, start=0)