From 60d00621ff08fb6961c9abba58d2633256c4da59 Mon Sep 17 00:00:00 2001
From: p-zach <porterdzach@gmail.com>
Date: Wed, 16 Apr 2025 16:28:58 -0400
Subject: [PATCH] Better visualizations

---
 gtsam/inference/doc/BayesTree.ipynb | 350 +++++++++++++++++-----------
 1 file changed, 208 insertions(+), 142 deletions(-)

diff --git a/gtsam/inference/doc/BayesTree.ipynb b/gtsam/inference/doc/BayesTree.ipynb
index 5364adc0a..a9452f4d4 100644
--- a/gtsam/inference/doc/BayesTree.ipynb
+++ b/gtsam/inference/doc/BayesTree.ipynb
@@ -57,7 +57,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 1,
+      "execution_count": 9,
       "metadata": {
         "id": "bayestree_import_code"
       },
@@ -88,7 +88,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 2,
+      "execution_count": 10,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/"
@@ -101,74 +101,165 @@
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "Original Factor Graph:\n",
-            "\n",
-            "size: 7\n",
-            "factor 0: \n",
-            "  A[x0] = [\n",
-            "\t-1\n",
-            "]\n",
-            "  b = [ 0 ]\n",
-            "  Noise model: unit (1) \n",
-            "factor 1: \n",
-            "  A[x0] = [\n",
-            "\t-1\n",
-            "]\n",
-            "  A[x1] = [\n",
-            "\t1\n",
-            "]\n",
-            "  b = [ 0 ]\n",
-            "  Noise model: unit (1) \n",
-            "factor 2: \n",
-            "  A[x1] = [\n",
-            "\t-1\n",
-            "]\n",
-            "  A[x2] = [\n",
-            "\t1\n",
-            "]\n",
-            "  b = [ 0 ]\n",
-            "  Noise model: unit (1) \n",
-            "factor 3: \n",
-            "  A[l1] = [\n",
-            "\t-1\n",
-            "]\n",
-            "  A[x0] = [\n",
-            "\t1\n",
-            "]\n",
-            "  b = [ 0 ]\n",
-            "  Noise model: unit (1) \n",
-            "factor 4: \n",
-            "  A[l1] = [\n",
-            "\t-1\n",
-            "]\n",
-            "  A[x1] = [\n",
-            "\t1\n",
-            "]\n",
-            "  b = [ 0 ]\n",
-            "  Noise model: unit (1) \n",
-            "factor 5: \n",
-            "  A[l2] = [\n",
-            "\t-1\n",
-            "]\n",
-            "  A[x1] = [\n",
-            "\t1\n",
-            "]\n",
-            "  b = [ 0 ]\n",
-            "  Noise model: unit (1) \n",
-            "factor 6: \n",
-            "  A[l2] = [\n",
-            "\t-1\n",
-            "]\n",
-            "  A[x2] = [\n",
-            "\t1\n",
-            "]\n",
-            "  b = [ 0 ]\n",
-            "  Noise model: unit (1) \n"
+            "Original Factor Graph:\n"
           ]
+        },
+        {
+          "data": {
+            "image/svg+xml": [
+              "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
+              "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
+              " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
+              "<!-- Generated by graphviz version 2.50.0 (0)\n",
+              " -->\n",
+              "<!-- Pages: 1 -->\n",
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+              " viewBox=\"0.00 0.00 350.00 83.60\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
+              "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 79.6)\">\n",
+              "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-79.6 346,-79.6 346,4 -4,4\"/>\n",
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+              "<g id=\"node1\" class=\"node\">\n",
+              "<title>var7782220156096217089</title>\n",
+              "<ellipse fill=\"none\" stroke=\"black\" cx=\"99\" cy=\"-57.6\" rx=\"27\" ry=\"18\"/>\n",
+              "<text text-anchor=\"middle\" x=\"99\" y=\"-53.9\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">l1</text>\n",
+              "</g>\n",
+              "<!-- factor3 -->\n",
+              "<g id=\"node9\" class=\"node\">\n",
+              "<title>factor3</title>\n",
+              "<ellipse fill=\"black\" stroke=\"black\" cx=\"75\" cy=\"-1.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
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+              "<path fill=\"none\" stroke=\"black\" d=\"M91.67,-40.17C85.49,-26.32 77.36,-8.1 75.43,-3.76\"/>\n",
+              "</g>\n",
+              "<!-- factor4 -->\n",
+              "<g id=\"node10\" class=\"node\">\n",
+              "<title>factor4</title>\n",
+              "<ellipse fill=\"black\" stroke=\"black\" cx=\"123\" cy=\"-1.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
+              "</g>\n",
+              "<!-- var7782220156096217089&#45;&#45;factor4 -->\n",
+              "<g id=\"edge8\" class=\"edge\">\n",
+              "<title>var7782220156096217089&#45;&#45;factor4</title>\n",
+              "<path fill=\"none\" stroke=\"black\" d=\"M106.33,-40.17C112.51,-26.32 120.64,-8.1 122.57,-3.76\"/>\n",
+              "</g>\n",
+              "<!-- var7782220156096217090 -->\n",
+              "<g id=\"node2\" class=\"node\">\n",
+              "<title>var7782220156096217090</title>\n",
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+              "<text text-anchor=\"middle\" x=\"315\" y=\"-53.9\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">l2</text>\n",
+              "</g>\n",
+              "<!-- factor5 -->\n",
+              "<g id=\"node11\" class=\"node\">\n",
+              "<title>factor5</title>\n",
+              "<ellipse fill=\"black\" stroke=\"black\" cx=\"243\" cy=\"-1.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
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+              "<!-- var7782220156096217090&#45;&#45;factor5 -->\n",
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+              "</g>\n",
+              "<!-- factor6 -->\n",
+              "<g id=\"node12\" class=\"node\">\n",
+              "<title>factor6</title>\n",
+              "<ellipse fill=\"black\" stroke=\"black\" cx=\"279\" cy=\"-1.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
+              "</g>\n",
+              "<!-- var7782220156096217090&#45;&#45;factor6 -->\n",
+              "<g id=\"edge12\" class=\"edge\">\n",
+              "<title>var7782220156096217090&#45;&#45;factor6</title>\n",
+              "<path fill=\"none\" stroke=\"black\" d=\"M304.39,-40.75C295.1,-26.86 282.63,-8.22 279.66,-3.78\"/>\n",
+              "</g>\n",
+              "<!-- var8646911284551352320 -->\n",
+              "<g id=\"node3\" class=\"node\">\n",
+              "<title>var8646911284551352320</title>\n",
+              "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-57.6\" rx=\"27\" ry=\"18\"/>\n",
+              "<text text-anchor=\"middle\" x=\"27\" y=\"-53.9\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">x0</text>\n",
+              "</g>\n",
+              "<!-- factor0 -->\n",
+              "<g id=\"node6\" class=\"node\">\n",
+              "<title>factor0</title>\n",
+              "<ellipse fill=\"black\" stroke=\"black\" cx=\"27\" cy=\"-1.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
+              "</g>\n",
+              "<!-- var8646911284551352320&#45;&#45;factor0 -->\n",
+              "<g id=\"edge1\" class=\"edge\">\n",
+              "<title>var8646911284551352320&#45;&#45;factor0</title>\n",
+              "<path fill=\"none\" stroke=\"black\" d=\"M27,-39.58C27,-25.79 27,-7.97 27,-3.73\"/>\n",
+              "</g>\n",
+              "<!-- factor1 -->\n",
+              "<g id=\"node7\" class=\"node\">\n",
+              "<title>factor1</title>\n",
+              "<ellipse fill=\"black\" stroke=\"black\" cx=\"100\" cy=\"-1.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
+              "</g>\n",
+              "<!-- var8646911284551352320&#45;&#45;factor1 -->\n",
+              "<g id=\"edge2\" class=\"edge\">\n",
+              "<title>var8646911284551352320&#45;&#45;factor1</title>\n",
+              "<path fill=\"none\" stroke=\"black\" d=\"M44.67,-43.58C64.25,-29.15 93.78,-7.38 99.15,-3.43\"/>\n",
+              "</g>\n",
+              "<!-- var8646911284551352320&#45;&#45;factor3 -->\n",
+              "<g id=\"edge7\" class=\"edge\">\n",
+              "<title>var8646911284551352320&#45;&#45;factor3</title>\n",
+              "<path fill=\"none\" stroke=\"black\" d=\"M40.37,-41.61C52.8,-27.68 69.99,-8.41 74.09,-3.81\"/>\n",
+              "</g>\n",
+              "<!-- var8646911284551352321 -->\n",
+              "<g id=\"node4\" class=\"node\">\n",
+              "<title>var8646911284551352321</title>\n",
+              "<ellipse fill=\"none\" stroke=\"black\" cx=\"171\" cy=\"-57.6\" rx=\"27\" ry=\"18\"/>\n",
+              "<text text-anchor=\"middle\" x=\"171\" y=\"-53.9\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">x1</text>\n",
+              "</g>\n",
+              "<!-- var8646911284551352321&#45;&#45;factor1 -->\n",
+              "<g id=\"edge3\" class=\"edge\">\n",
+              "<title>var8646911284551352321&#45;&#45;factor1</title>\n",
+              "<path fill=\"none\" stroke=\"black\" d=\"M153.81,-43.58C134.77,-29.15 106.05,-7.38 100.83,-3.43\"/>\n",
+              "</g>\n",
+              "<!-- factor2 -->\n",
+              "<g id=\"node8\" class=\"node\">\n",
+              "<title>factor2</title>\n",
+              "<ellipse fill=\"black\" stroke=\"black\" cx=\"178\" cy=\"-1.8\" rx=\"1.8\" ry=\"1.8\"/>\n",
+              "</g>\n",
+              "<!-- var8646911284551352321&#45;&#45;factor2 -->\n",
+              "<g id=\"edge4\" class=\"edge\">\n",
+              "<title>var8646911284551352321&#45;&#45;factor2</title>\n",
+              "<path fill=\"none\" stroke=\"black\" d=\"M173.21,-39.58C175.01,-25.79 177.33,-7.97 177.88,-3.73\"/>\n",
+              "</g>\n",
+              "<!-- var8646911284551352321&#45;&#45;factor4 -->\n",
+              "<g id=\"edge9\" class=\"edge\">\n",
+              "<title>var8646911284551352321&#45;&#45;factor4</title>\n",
+              "<path fill=\"none\" stroke=\"black\" d=\"M157.63,-41.61C145.2,-27.68 128.01,-8.41 123.91,-3.81\"/>\n",
+              "</g>\n",
+              "<!-- var8646911284551352321&#45;&#45;factor5 -->\n",
+              "<g id=\"edge11\" class=\"edge\">\n",
+              "<title>var8646911284551352321&#45;&#45;factor5</title>\n",
+              "<path fill=\"none\" stroke=\"black\" d=\"M188.43,-43.58C207.74,-29.15 236.87,-7.38 242.16,-3.43\"/>\n",
+              "</g>\n",
+              "<!-- var8646911284551352322 -->\n",
+              "<g id=\"node5\" class=\"node\">\n",
+              "<title>var8646911284551352322</title>\n",
+              "<ellipse fill=\"none\" stroke=\"black\" cx=\"243\" cy=\"-57.6\" rx=\"27\" ry=\"18\"/>\n",
+              "<text text-anchor=\"middle\" x=\"243\" y=\"-53.9\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">x2</text>\n",
+              "</g>\n",
+              "<!-- var8646911284551352322&#45;&#45;factor2 -->\n",
+              "<g id=\"edge5\" class=\"edge\">\n",
+              "<title>var8646911284551352322&#45;&#45;factor2</title>\n",
+              "<path fill=\"none\" stroke=\"black\" d=\"M226.6,-43.02C209.75,-29.08 185.18,-8.74 179.3,-3.87\"/>\n",
+              "</g>\n",
+              "<!-- var8646911284551352322&#45;&#45;factor6 -->\n",
+              "<g id=\"edge13\" class=\"edge\">\n",
+              "<title>var8646911284551352322&#45;&#45;factor6</title>\n",
+              "<path fill=\"none\" stroke=\"black\" d=\"M253.61,-40.75C262.9,-26.86 275.37,-8.22 278.34,-3.78\"/>\n",
+              "</g>\n",
+              "</g>\n",
+              "</svg>\n"
+            ],
+            "text/plain": [
+              "<graphviz.sources.Source at 0x1d6fb24ec10>"
+            ]
+          },
+          "metadata": {},
+          "output_type": "display_data"
         }
       ],
       "source": [
-        "# Create a simple Gaussian Factor Graph (more complex this time)\n",
+        "# Create a simple Gaussian Factor Graph\n",
         "graph = GaussianFactorGraph()\n",
         "model = gtsam.noiseModel.Isotropic.Sigma(1, 1.0)\n",
         "graph.add(X(0), -np.eye(1), np.zeros(1), model)           # Prior on x0\n",
@@ -180,19 +271,18 @@
         "graph.add(L(2), -np.eye(1), X(2), np.eye(1), np.zeros(1), model) # l2 -> x2 (measurement)\n",
         "\n",
         "print(\"Original Factor Graph:\")\n",
-        "graph.print()"
+        "display(graphviz.Source(graph.dot()))"
       ]
     },
     {
       "cell_type": "code",
-      "execution_count": 5,
+      "execution_count": 12,
       "metadata": {},
       "outputs": [
         {
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "\n",
             "Resulting BayesTree:\n",
             ": cliques: 2, variables: 5\n",
             "- p(x1 l2 x2 )\n",
@@ -213,8 +303,52 @@
             "          [ -0.948683 ]\n",
             "  d = [ 0 0 ]\n",
             "  logNormalizationConstant: -1.03316\n",
-            "  No noise model\n"
+            "  No noise model\n",
+            "\n",
+            "Visualization:\n"
           ]
+        },
+        {
+          "data": {
+            "image/svg+xml": [
+              "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
+              "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
+              " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
+              "<!-- Generated by graphviz version 2.50.0 (0)\n",
+              " -->\n",
+              "<!-- Title: G Pages: 1 -->\n",
+              "<svg width=\"103pt\" height=\"116pt\"\n",
+              " viewBox=\"0.00 0.00 102.89 116.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
+              "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 112)\">\n",
+              "<title>G</title>\n",
+              "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-112 98.89,-112 98.89,4 -4,4\"/>\n",
+              "<!-- 2 -->\n",
+              "<g id=\"node1\" class=\"node\">\n",
+              "<title>2</title>\n",
+              "<ellipse fill=\"none\" stroke=\"black\" cx=\"47.45\" cy=\"-90\" rx=\"44.69\" ry=\"18\"/>\n",
+              "<text text-anchor=\"middle\" x=\"47.45\" y=\"-86.3\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">x1, l2, x2</text>\n",
+              "</g>\n",
+              "<!-- 3 -->\n",
+              "<g id=\"node2\" class=\"node\">\n",
+              "<title>3</title>\n",
+              "<ellipse fill=\"none\" stroke=\"black\" cx=\"47.45\" cy=\"-18\" rx=\"47.39\" ry=\"18\"/>\n",
+              "<text text-anchor=\"middle\" x=\"47.45\" y=\"-14.3\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">l1, x0 : x1</text>\n",
+              "</g>\n",
+              "<!-- 2&#45;&gt;3 -->\n",
+              "<g id=\"edge1\" class=\"edge\">\n",
+              "<title>2&#45;&gt;3</title>\n",
+              "<path fill=\"none\" stroke=\"black\" d=\"M47.45,-71.7C47.45,-63.98 47.45,-54.71 47.45,-46.11\"/>\n",
+              "<polygon fill=\"black\" stroke=\"black\" points=\"50.95,-46.1 47.45,-36.1 43.95,-46.1 50.95,-46.1\"/>\n",
+              "</g>\n",
+              "</g>\n",
+              "</svg>\n"
+            ],
+            "text/plain": [
+              "<graphviz.sources.Source at 0x1d6fb28be10>"
+            ]
+          },
+          "metadata": {},
+          "output_type": "display_data"
         }
       ],
       "source": [
@@ -223,8 +357,10 @@
         "# Note: Multifrontal typically yields multiple roots if graph is disconnected\n",
         "bayes_tree = graph.eliminateMultifrontal(ordering)\n",
         "\n",
-        "print(\"\\nResulting BayesTree:\")\n",
-        "bayes_tree.print()"
+        "print(\"Resulting BayesTree:\")\n",
+        "bayes_tree.print()\n",
+        "print(\"\\nVisualization:\")\n",
+        "display(graphviz.Source(bayes_tree.dot()))"
       ]
     },
     {
@@ -328,76 +464,6 @@
         "print(\"\\nJoint Marginal Factor Graph on (x0, x2):\")\n",
         "joint_x0_x2.print()"
       ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "bayestree_viz_md"
-      },
-      "source": [
-        "## Visualization\n",
-        "\n",
-        "Bayes trees can be visualized using Graphviz."
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": 8,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "bayestree_dot_code",
-        "outputId": "789abcde-f012-3456-789a-bcdef0123456"
-      },
-      "outputs": [
-        {
-          "data": {
-            "image/svg+xml": [
-              "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
-              "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
-              " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
-              "<!-- Generated by graphviz version 2.50.0 (0)\n",
-              " -->\n",
-              "<!-- Title: G Pages: 1 -->\n",
-              "<svg width=\"103pt\" height=\"116pt\"\n",
-              " viewBox=\"0.00 0.00 102.89 116.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
-              "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 112)\">\n",
-              "<title>G</title>\n",
-              "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-112 98.89,-112 98.89,4 -4,4\"/>\n",
-              "<!-- 0 -->\n",
-              "<g id=\"node1\" class=\"node\">\n",
-              "<title>0</title>\n",
-              "<ellipse fill=\"none\" stroke=\"black\" cx=\"47.45\" cy=\"-90\" rx=\"44.69\" ry=\"18\"/>\n",
-              "<text text-anchor=\"middle\" x=\"47.45\" y=\"-86.3\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">x1, l2, x2</text>\n",
-              "</g>\n",
-              "<!-- 1 -->\n",
-              "<g id=\"node2\" class=\"node\">\n",
-              "<title>1</title>\n",
-              "<ellipse fill=\"none\" stroke=\"black\" cx=\"47.45\" cy=\"-18\" rx=\"47.39\" ry=\"18\"/>\n",
-              "<text text-anchor=\"middle\" x=\"47.45\" y=\"-14.3\" font-family=\"Times New Roman,serif\" font-size=\"14.00\">l1, x0 : x1</text>\n",
-              "</g>\n",
-              "<!-- 0&#45;&gt;1 -->\n",
-              "<g id=\"edge1\" class=\"edge\">\n",
-              "<title>0&#45;&gt;1</title>\n",
-              "<path fill=\"none\" stroke=\"black\" d=\"M47.45,-71.7C47.45,-63.98 47.45,-54.71 47.45,-46.11\"/>\n",
-              "<polygon fill=\"black\" stroke=\"black\" points=\"50.95,-46.1 47.45,-36.1 43.95,-46.1 50.95,-46.1\"/>\n",
-              "</g>\n",
-              "</g>\n",
-              "</svg>\n"
-            ],
-            "text/plain": [
-              "<graphviz.sources.Source at 0x1d6fb25a900>"
-            ]
-          },
-          "execution_count": 8,
-          "metadata": {},
-          "output_type": "execute_result"
-        }
-      ],
-      "source": [
-        "graphviz.Source(bayes_tree.dot())"
-      ]
     }
   ],
   "metadata": {