{ "cells": [ { "cell_type": "markdown", "id": "b4dd7036", "metadata": {}, "source": [ "# Tutorial: Branch Decomposition of a Reeb Graph" ] }, { "cell_type": "markdown", "id": "8696deda", "metadata": {}, "source": [ "A **branch decomposition** breaks a Reeb graph into a collection of non-overlapping upward paths called *branches*. Each branch travels strictly upward in function value, starting at either a local minimum or a saddle point and ending at either a local maximum or another saddle point.\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Each branch stores:\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "- The function values at its two endpoints (`f_low`, `f_high`)\n", "\n", "\n", "\n", "- Attachment information: which earlier branch each endpoint belongs to (pointing to itself if it is a local min/max)\n", "\n", "\n", "\n", "This tutorial follows the branch decomposition viewpoint developed in Samira Jabry's thesis, [*Unsmoothing of Reeb Graphs*](https://www.proquest.com/dissertations-theses/unsmoothing-reeb-graphs/docview/3231769569/se-2), Saint Louis University, 2025:\n", "\n", "\n", "\n", "For the API and class reference, see the [branch decomposition documentation page](../modules/reeb/branchdecomp.html).\n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "462d6378", "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "\n", "from cereeberus import ReebGraph\n", "import cereeberus.data.ex_reebgraphs as ex_rg\n", "from cereeberus.reeb.branchdecomp import BranchDecomp" ] }, { "cell_type": "markdown", "id": "6783161d", "metadata": {}, "source": [ "## A simple example: the dancing man\n", "\n", "We'll start with the `dancing_man` example graph, which is a connected Reeb graph with several saddle points." ] }, { "cell_type": "code", "execution_count": 2, "id": "3cc2507f", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "R = ex_rg.dancing_man()\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(14, 6))\n", "R.draw(ax=axes[0])\n", "axes[0].set_title('Reeb Graph', fontsize=14, fontweight='bold')\n", "\n", "bd = R.branch_decomp()\n", "bd.draw(ax=axes[1])\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "b0f9031f", "metadata": {}, "source": [ "The branch decomposition diagram shows each branch as a vertical line positioned at its function values. Labels next to each endpoint indicate which branch that endpoint is attached to:\n", "\n", "- **Purple (lower endpoint)**: the branch ID whose path contains this vertex\n", "- **Green (upper endpoint)**: the branch ID whose path contains this vertex\n", "\n", "When a label matches the branch's own ID, that endpoint is a local min or max (no other branch claims it)." ] }, { "cell_type": "markdown", "id": "813632e0", "metadata": {}, "source": [ "## Inspecting the branches\n", "\n", "The branches are stored as an $n \\times 4$ numpy array. Each row is one branch:\n", "\n", "| Column | Meaning |\n", "|--------|---------|\n", "| 0 | `f_low` — function value of the lower endpoint |\n", "| 1 | `f_high` — function value of the upper endpoint |\n", "| 2 | `low_attach` — branch ID owning the lower endpoint |\n", "| 3 | `high_attach` — branch ID owning the upper endpoint |" ] }, { "cell_type": "code", "execution_count": 3, "id": "9184fe25", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Branches (f_low, f_high, low_attach, high_attach):\n", "[[1. 7. 0. 0.]\n", " [4. 5. 1. 0.]\n", " [4. 6. 0. 0.]\n", " [5. 6. 2. 3.]]\n" ] } ], "source": [ "print(\"Branches (f_low, f_high, low_attach, high_attach):\")\n", "print(bd.branches)" ] }, { "cell_type": "code", "execution_count": 4, "id": "aead1647", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Branch 0: f=[1.0, 7.0] attaches=(0, 0) path=[7, 6, 2, 1, 0]\n", "Branch 1: f=[4.0, 5.0] attaches=(1, 0) path=[5, 2]\n", "Branch 2: f=[4.0, 6.0] attaches=(0, 0) path=[6, 3, 1]\n", "Branch 3: f=[5.0, 6.0] attaches=(2, 3) path=[3, 4]\n" ] } ], "source": [ "# You can also inspect individual branches and their vertex paths\n", "for i in range(len(bd.branches)):\n", " print(f\"Branch {i}: f=[{bd.branches[i,0]}, {bd.branches[i,1]}] \"\n", " f\"attaches=({int(bd.branches[i,2])}, {int(bd.branches[i,3])}) \"\n", " f\"path={bd.get_branch_path(i)}\")" ] }, { "cell_type": "markdown", "id": "69d80062", "metadata": {}, "source": [ "## Reconstructing the Reeb graph\n", "\n", "Once you have a branch decomposition, you can reconstruct the original Reeb graph exactly from it using `reconstruct()`." ] }, { "cell_type": "code", "execution_count": 5, "id": "ea7fd61d", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Original: ReebGraph with 8 nodes and 8 edges.\n", "Reconstructed: ReebGraph with 8 nodes and 8 edges.\n" ] } ], "source": [ "R2 = bd.reconstruct()\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(12, 5))\n", "R.draw(ax=axes[0])\n", "axes[0].set_title('Original', fontsize=13, fontweight='bold')\n", "R2.draw(ax=axes[1])\n", "axes[1].set_title('Reconstructed', fontsize=13, fontweight='bold')\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "print(f\"Original: {R}\")\n", "print(f\"Reconstructed: {R2}\")" ] }, { "cell_type": "markdown", "id": "0cb9074c", "metadata": {}, "source": [ "## Handling isolated vertices: the juggling man\n", "\n", "The `juggling_man` graph has isolated vertices (vertices with no edges), representing disconnected components. These are handled as **degenerate branches** where `f_low == f_high` and both attachment IDs point to the branch itself." ] }, { "cell_type": "code", "execution_count": 6, "id": "b22dd894", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "J = ex_rg.juggling_man()\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(16, 6))\n", "J.draw(ax=axes[0])\n", "axes[0].set_title('Juggling Man Reeb Graph', fontsize=14, fontweight='bold')\n", "\n", "bd_j = J.branch_decomp()\n", "bd_j.draw(ax=axes[1])\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "id": "514266b4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Degenerate branches (isolated vertices):\n", " Branch 4: vertex=[8], f=6.5, attaches=(4, 4)\n", " Branch 5: vertex=[9], f=6.5, attaches=(5, 5)\n", " Branch 6: vertex=[10], f=5.5, attaches=(6, 6)\n" ] } ], "source": [ "# Identify the degenerate branches (isolated vertices)\n", "print(\"Degenerate branches (isolated vertices):\")\n", "for i, (f_low, f_high, low_a, high_a) in enumerate(bd_j.branches):\n", " if f_low == f_high:\n", " print(f\" Branch {i}: vertex={bd_j.get_branch_path(i)}, f={f_low}, \"\n", " f\"attaches=({int(low_a)}, {int(high_a)})\")" ] }, { "cell_type": "markdown", "id": "f1867367", "metadata": {}, "source": [ "## Summary\n", "\n", "The `BranchDecomp` class provides:\n", "\n", "- `decompose(R)` — compute the decomposition from a `ReebGraph`\n", "- `branches` — the $n \\times 4$ array of branch data\n", "- `get_branch(i)` — return row $i$ of the branches array\n", "- `get_branch_path(i)` — return the list of vertices in branch $i$\n", "- `reconstruct()` — rebuild the original `ReebGraph` from the stored paths\n", "- `draw()` — visualise the decomposition\n", "\n", "You can also call `R.branch_decomp()` directly on any `ReebGraph` or `MapperGraph` as a shortcut." ] } ], "metadata": { "kernelspec": { "display_name": "cereeberus", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.12" } }, "nbformat": 4, "nbformat_minor": 5 }