From b54ad4e3f01c69ce305dcde023c7da73d842d107 Mon Sep 17 00:00:00 2001
From: p-zach <porterdzach@gmail.com>
Date: Mon, 14 Apr 2025 19:07:42 -0400
Subject: [PATCH] BayesTree cleanup

---
 gtsam/inference/doc/BayesTree.ipynb | 49 +++++++++++++++++------------
 1 file changed, 29 insertions(+), 20 deletions(-)

diff --git a/gtsam/inference/doc/BayesTree.ipynb b/gtsam/inference/doc/BayesTree.ipynb
index 50863543f..14100971d 100644
--- a/gtsam/inference/doc/BayesTree.ipynb
+++ b/gtsam/inference/doc/BayesTree.ipynb
@@ -22,11 +22,6 @@
         "$$\n",
         "P(X) = \\prod_k P(F_k | S_k)\n",
         "$$\n",
-        "Alternatively, it can be expressed using clique $P(C_k) = P(F_k, S_k)$ and separator $P(S_k)$ marginals (though GTSAM stores conditionals):\n",
-        "$$\n",
-        "P(X) = \\frac{\\prod_{\\text{cliques } k} P(C_k)}{\\prod_{\\text{separators } S} P(S)^{\\nu(S)-1}}\n",
-        "$$\n",
-        "where $\\nu(S)$ is the number of cliques containing the separator $S$. The first formula $P(X) = \\prod_k P(F_k | S_k)$ is more directly related to the GTSAM `BayesTree` structure.\n",
         "\n",
         "Key properties:\n",
         "*   **Cliques:** Each node (clique) groups variables that are eliminated together.\n",
@@ -167,7 +162,35 @@
             "\t1\n",
             "]\n",
             "  b = [ 0 ]\n",
-            "  Noise model: unit (1) \n",
+            "  Noise model: unit (1) \n"
+          ]
+        }
+      ],
+      "source": [
+        "# Create a simple Gaussian Factor Graph (more complex this time)\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",
+        "graph.add(X(0), -np.eye(1), X(1), np.eye(1), np.zeros(1), model) # x0 -> x1\n",
+        "graph.add(X(1), -np.eye(1), X(2), np.eye(1), np.zeros(1), model) # x1 -> x2\n",
+        "graph.add(L(1), -np.eye(1), X(0), np.eye(1), np.zeros(1), model) # l1 -> x0 (measurement)\n",
+        "graph.add(L(1), -np.eye(1), X(1), np.eye(1), np.zeros(1), model) # l1 -> x1 (measurement)\n",
+        "graph.add(L(2), -np.eye(1), X(1), np.eye(1), np.zeros(1), model) # l2 -> x1 (measurement)\n",
+        "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()"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 4,
+      "metadata": {},
+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
             "\n",
             "Resulting BayesTree:\n",
             ": cliques: 2, variables: 5\n",
@@ -194,20 +217,6 @@
         }
       ],
       "source": [
-        "# Create a simple Gaussian Factor Graph (more complex this time)\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",
-        "graph.add(X(0), -np.eye(1), X(1), np.eye(1), np.zeros(1), model) # x0 -> x1\n",
-        "graph.add(X(1), -np.eye(1), X(2), np.eye(1), np.zeros(1), model) # x1 -> x2\n",
-        "graph.add(L(1), -np.eye(1), X(0), np.eye(1), np.zeros(1), model) # l1 -> x0 (measurement)\n",
-        "graph.add(L(1), -np.eye(1), X(1), np.eye(1), np.zeros(1), model) # l1 -> x1 (measurement)\n",
-        "graph.add(L(2), -np.eye(1), X(1), np.eye(1), np.zeros(1), model) # l2 -> x1 (measurement)\n",
-        "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()\n",
-        "\n",
         "# Eliminate multifrontally using COLAMD ordering\n",
         "ordering = Ordering.Colamd(VariableIndex(graph))\n",
         "# Note: Multifrontal typically yields multiple roots if graph is disconnected\n",