fix initializer for kamada_kawai_layout (networkx #3658) (#3782)

* fixed high-dimensional initializer for kamada_kawai_layout (networkx #3658)

* added tests for kamada_kawai 3d

* increased test coverage of kamada_kawai_layout

* fixed empty-graph oversight in kamada_kawai_layout

* removed unused variable vpos from smoke tests

Fixes #3658 

2 files changed, 76 insertions, 46 deletions

diff --git a/networkx/drawing/layout.py b/networkx/drawing/layout.py
index 9a41701c..b7779d08 100644
--- a/networkx/drawing/layout.py
+++ b/networkx/drawing/layout.py
@@ -687,6 +687,8 @@ def kamada_kawai_layout(G, dist=None,
 
     G, center = _process_params(G, center, dim)
     nNodes = len(G)
+    if nNodes == 0:
+        return {}
 
     if dist is None:
         dist = dict(nx.shortest_path_length(G, weight=weight))
@@ -701,7 +703,9 @@ def kamada_kawai_layout(G, dist=None,
             dist_mtx[row][col] = rdist[nc]
 
     if pos is None:
-        if dim >= 2:
+        if dim >= 3:
+            pos = random_layout(G, dim=dim)
+        elif dim == 2:
             pos = circular_layout(G, dim=dim)
         else:
             pos = {n: pt for n, pt in zip(G, np.linspace(0, 1, len(G)))}
diff --git a/networkx/drawing/tests/test_layout.py b/networkx/drawing/tests/test_layout.py
index 1a8dc17e..17e06d75 100644
--- a/networkx/drawing/tests/test_layout.py
+++ b/networkx/drawing/tests/test_layout.py
@@ -48,46 +48,48 @@ class TestLayout:
 
     def test_smoke_empty_graph(self):
         G = []
-        vpos = nx.random_layout(G)
-        vpos = nx.circular_layout(G)
-        vpos = nx.planar_layout(G)
-        vpos = nx.spring_layout(G)
-        vpos = nx.fruchterman_reingold_layout(G)
-        vpos = nx.spectral_layout(G)
-        vpos = nx.shell_layout(G)
-        vpos = nx.bipartite_layout(G, G)
-        vpos = nx.spiral_layout(G)
-        # FIXME vpos = nx.kamada_kawai_layout(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.kamada_kawai_layout(G)
 
     def test_smoke_int(self):
         G = self.Gi
-        vpos = nx.random_layout(G)
-        vpos = nx.circular_layout(G)
-        vpos = nx.planar_layout(G)
-        vpos = nx.spring_layout(G)
-        vpos = nx.fruchterman_reingold_layout(G)
-        vpos = nx.fruchterman_reingold_layout(self.bigG)
-        vpos = nx.spectral_layout(G)
-        vpos = nx.spectral_layout(G.to_directed())
-        vpos = nx.spectral_layout(self.bigG)
-        vpos = nx.spectral_layout(self.bigG.to_directed())
-        vpos = nx.shell_layout(G)
-        vpos = nx.spiral_layout(G)
-        vpos = nx.kamada_kawai_layout(G)
-        vpos = nx.kamada_kawai_layout(G, dim=1)
+        nx.random_layout(G)
+        nx.circular_layout(G)
+        nx.planar_layout(G)
+        nx.spring_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)
 
     def test_smoke_string(self):
         G = self.Gs
-        vpos = nx.random_layout(G)
-        vpos = nx.circular_layout(G)
-        vpos = nx.planar_layout(G)
-        vpos = nx.spring_layout(G)
-        vpos = nx.fruchterman_reingold_layout(G)
-        vpos = nx.spectral_layout(G)
-        vpos = nx.shell_layout(G)
-        vpos = nx.spiral_layout(G)
-        vpos = nx.kamada_kawai_layout(G)
-        vpos = nx.kamada_kawai_layout(G, dim=1)
+        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.spiral_layout(G)
+        nx.kamada_kawai_layout(G)
+        nx.kamada_kawai_layout(G, dim=1)
+        nx.kamada_kawai_layout(G, dim=3)
 
     def check_scale_and_center(self, pos, scale, center):
         center = numpy.array(center)
@@ -113,6 +115,10 @@ class TestLayout:
         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)
@@ -135,6 +141,10 @@ class TestLayout:
         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)
@@ -190,7 +200,7 @@ class TestLayout:
 
     def test_center_parameter(self):
         G = nx.path_graph(1)
-        vpos = nx.random_layout(G, center=(1, 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))
@@ -218,6 +228,7 @@ class TestLayout:
         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()
@@ -239,6 +250,8 @@ class TestLayout:
         assert vpos == {}
         vpos = nx.spiral_layout(G, center=(1, 1))
         assert vpos == {}
+        vpos = nx.kamada_kawai_layout(G, center=(1, 1))
+        assert vpos == {}
 
     def test_bipartite_layout(self):
         G = nx.complete_bipartite_graph(3, 5)
@@ -282,19 +295,11 @@ class TestLayout:
         assert almost_equal(grad[0], -0.5)
         assert almost_equal(grad[1], 0.5)
 
-    def test_kamada_kawai_costfn_2d(self):
+    def check_kamada_kawai_costfn(self, pos, invdist, meanwt, dim):
         costfn = nx.drawing.layout._kamada_kawai_costfn
 
-        pos = numpy.array([[1.3, -3.2],
-                           [2.7, -0.3],
-                           [5.1, 2.5]])
-        invdist = 1 / numpy.array([[0.1, 2.1, 1.7],
-                                   [2.1, 0.2, 0.6],
-                                   [1.7, 0.6, 0.3]])
-        meanwt = 0.3
-
         cost, grad = costfn(pos.ravel(), numpy, invdist,
-                            meanweight=meanwt, dim=2)
+                            meanweight=meanwt, dim=dim)
 
         expected_cost = 0.5 * meanwt * numpy.sum(numpy.sum(pos, axis=0) ** 2)
         for i in range(pos.shape[0]):
@@ -321,6 +326,27 @@ class TestLayout:
                 assert almost_equal(grad[idx], (cplus - cminus) / (2 * dx),
                                     places=5)
 
+    def test_kamada_kawai_costfn(self):
+        invdist = 1 / numpy.array([[0.1, 2.1, 1.7],
+                                   [2.1, 0.2, 0.6],
+                                   [1.7, 0.6, 0.3]])
+        meanwt = 0.3
+
+        # 2d
+        pos = numpy.array([[1.3, -3.2],
+                           [2.7, -0.3],
+                           [5.1, 2.5]])
+
+        self.check_kamada_kawai_costfn(pos, invdist, meanwt, 2)
+
+        # 3d
+        pos = numpy.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