{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tutorial: ECT for Embedded Graphs\n", "\n", "\n", "\n", "This tutorial demonstrates how to use the `ect` package..." ] }, { "cell_type": "code", "execution_count": 120, "metadata": {}, "outputs": [], "source": [ "from ect import ECT, EmbeddedGraph\n", "\n", "import numpy as np\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Basic Usage\n", "\n", "\n", "\n", "First, let's create a simple graph\"\"\"\n", "\n" ] }, { "cell_type": "code", "execution_count": 121, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 121, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Construct an example graph\n", "# Note that this is the same graph that is returned by:\n", "# G = create_example_graph()\n", "\n", "G = EmbeddedGraph()\n", "\n", "G.add_node(\"A\", [1, 2])\n", "G.add_node(\"B\", [3, 4])\n", "G.add_node(\"C\", [5, 7])\n", "G.add_node(\"D\", [3, 6])\n", "G.add_node(\"E\", [4, 3])\n", "G.add_node(\"F\", [4, 5])\n", "\n", "G.add_edge(\"A\", \"B\")\n", "G.add_edge(\"B\", \"C\")\n", "G.add_edge(\"B\", \"D\")\n", "G.add_edge(\"B\", \"E\")\n", "G.add_edge(\"C\", \"D\")\n", "G.add_edge(\"E\", \"F\")\n", "\n", "G.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " The embedded graph class inherits from the networkx graph class with the additional attributes `coord_matrix` and `coord_dict`.\n", "\n", " The coordinates of all vertices can be accessed using the `coord_matrix` attribute." ] }, { "cell_type": "code", "execution_count": 122, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[1., 2.],\n", " [3., 4.],\n", " [5., 7.],\n", " [3., 6.],\n", " [4., 3.],\n", " [4., 5.]])" ] }, "execution_count": 122, "metadata": {}, "output_type": "execute_result" } ], "source": [ "G.coord_matrix\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " It's often useful to center the graph, so you can use the `center_coordinates` method shift the graph to have the average of the vertex coordinates be 0. Note that this does overwrite the coordinates of the points." ] }, { "cell_type": "code", "execution_count": 123, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-2.33333333 -2.5 ]\n", " [-0.33333333 -0.5 ]\n", " [ 1.66666667 2.5 ]\n", " [-0.33333333 1.5 ]\n", " [ 0.66666667 -1.5 ]\n", " [ 0.66666667 0.5 ]]\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 123, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "G.center_coordinates(center_type=\"mean\")\n", "print(G.coord_matrix)\n", "G.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " To get a bounding radius we can use the `get_bounding_radius` method." ] }, { "cell_type": "code", "execution_count": 124, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The radius of bounding circle centered at the origin is 3.2015621187164243\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 124, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# This is actually getting the radius\n", "r = G.get_bounding_radius()\n", "print(f\"The radius of bounding circle centered at the origin is {r}\")\n", "\n", "# plotting the graph with it's bounding circle of radius r.\n", "G.plot(bounding_circle=True)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " We can also rescale our graph to have unit radius using `scale_coordinates`" ] }, { "cell_type": "code", "execution_count": 125, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The radius of bounding circle centered at the origin is 0.9362075413977773\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "G.scale_coordinates(radius=1)\n", "G.plot(bounding_circle=True)\n", "\n", "r = G.get_bounding_radius()\n", "print(f\"The radius of bounding circle centered at the origin is {r}\")\n", "\n" ] }, { "cell_type": "code", "execution_count": 126, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of directions: 16\n", "Number of thresholds: 20\n" ] } ], "source": [ "myect = ECT(num_dirs=16, num_thresh=20)\n", "\n", "# The ECT object will automatically create directions when needed\n", "print(f\"Number of directions: {myect.num_dirs}\")\n", "print(f\"Number of thresholds: {myect.num_thresh}\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " We can override the bounding radius as follows. Note that some methods will automatically use the bounding radius of the input `G` if not already set. I'm choosing the radius to be a bit bigger than the bounding radius of `G` to make some better pictures." ] }, { "cell_type": "code", "execution_count": 127, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Thresholds chosen are: [-1.12344905 -1.00519125 -0.88693346 -0.76867567 -0.65041787 -0.53216008\n", " -0.41390228 -0.29564449 -0.17738669 -0.0591289 0.0591289 0.17738669\n", " 0.29564449 0.41390228 0.53216008 0.65041787 0.76867567 0.88693346\n", " 1.00519125 1.12344905]\n" ] } ], "source": [ "custom_bound_radius = 1.2 * G.get_bounding_radius()\n", "result = myect.calculate(G, override_bound_radius=custom_bound_radius)\n", "\n", "print(f\"Thresholds chosen are: {myect.thresholds}\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " If we want the Euler characteristic curve for a fixed direction, we use the `calculate` function with a specific angle. This returns an ECTResult object containing the computed values." ] }, { "cell_type": "code", "execution_count": 128, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ECT values for direction pi/2: [0 0 0 0 1 1 2 2 2 1 1 1 1 1 1 1 0 0 0 0]\n" ] } ], "source": [ "result = myect.calculate(G, theta=np.pi / 2)\n", "print(f\"ECT values for direction pi/2: {result[0]}\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " To calculate the full ECT, we call the `calculate` method without specifying theta. The result returns the ECT matrix and associated metadata." ] }, { "cell_type": "code", "execution_count": 129, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ECT matrix shape: (16, 20)\n", "Number of directions: 16\n", "Number of thresholds: 20\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 129, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "result = myect.calculate(G)\n", "\n", "print(f\"ECT matrix shape: {result.shape}\")\n", "print(f\"Number of directions: {myect.num_dirs}\")\n", "print(f\"Number of thresholds: {myect.num_thresh}\")\n", "\n", "# We can plot the result matrix\n", "result.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " ## SECT\n", "\n", "\n", "\n", " The Smooth Euler Characteristic Transform (SECT) can be calculated from the ECT. Fix a radius $R$ bounding the graph. The average ECT in a direction $\\omega$ defined on function values $[-R,R]$ is given by\n", "\n", " $$\\overline{\\text{ECT}_\\omega} = \\frac{1}{2R} \\int_{t = -R}^{R} \\chi(g_\\omega^{-1}(-\\infty,t]) \\; dt. $$\n", "\n", " Then the SECT is defined by\n", "\n", " $$\n", "\n", " \\begin{matrix}\n", "\n", " \\text{SECT}(G): & \\mathbb{S}^1 & \\to & \\text{Func}(\\mathbb{R}, \\mathbb{Z})\\\\\n", "\n", " & \\omega & \\mapsto & \\{ t \\mapsto \\int_{-R}^t \\left( \\chi(g_\\omega^{-1}(-\\infty,a]) -\\overline{\\text{ECT}_\\omega}\\right)\\:da \\}\n", "\n", " \\end{matrix}\n", "\n", " $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " The SECT can be computed from the ECT result:" ] }, { "cell_type": "code", "execution_count": 130, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 130, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sect = result.smooth()\n", "\n", "sect.plot()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " ## ECT for higher dimensions\n", "\n", "\n", "\n", " The `ECT` class can also be used for higher dimensional graphs." ] }, { "cell_type": "code", "execution_count": 131, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 131, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "# generate a 3d graph\n", "list_3d = [\n", " (\"A\", [0, 0, 0]),\n", " (\"B\", [1, 0, 0]),\n", " (\"C\", [0, 1, 0]),\n", " (\"D\", [1, 1, 0]),\n", " (\"E\", [0, 0, 1]),\n", " (\"F\", [1, 0, 1]),\n", " (\"G\", [0, 1, 1]),\n", " (\"H\", [1, 1, 1]),\n", "]\n", "graph_3d = EmbeddedGraph()\n", "graph_3d.add_nodes_from(list_3d)\n", "\n", "# add edges\n", "graph_3d.add_edge(\"A\", \"B\")\n", "graph_3d.add_edge(\"B\", \"C\")\n", "graph_3d.add_edge(\"C\", \"D\")\n", "graph_3d.add_edge(\"D\", \"E\")\n", "graph_3d.add_edge(\"E\", \"F\")\n", "graph_3d.add_edge(\"F\", \"G\")\n", "graph_3d.add_edge(\"G\", \"H\")\n", "graph_3d.add_edge(\"H\", \"A\")\n", "\n", "# plot the graph\n", "graph_3d.plot()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " lets center the graph" ] }, { "cell_type": "code", "execution_count": 132, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 132, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_3d.center_coordinates(center_type=\"mean\")\n", "graph_3d.plot()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Now we can compute the ECT of the 3d graph." ] }, { "cell_type": "code", "execution_count": 133, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 133, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ect_3d = ECT(num_dirs=16, num_thresh=20)\n", "result_3d = ect_3d.calculate(graph_3d)\n", "result_3d.plot()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Note that the each of the directions are appended in a list for the ECT result, so we won't see the same periodic behavior as in the 2d case.\n", "\n", " ECT results inherit from ndarrays but they store the associated directions and thresholds." ] }, { "cell_type": "code", "execution_count": 134, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 0.48609512, -0.71244342, -0.50609872],\n", " [ 0.00364975, -0.82190818, 0.56960831],\n", " [-0.77710663, -0.23260984, 0.5848059 ],\n", " [ 0.75362655, -0.61431121, -0.23381352],\n", " [-0.18133219, -0.98270096, -0.03764916],\n", " [-0.92728701, 0.26549447, 0.26391569],\n", " [-0.81397529, 0.14802792, 0.56172232],\n", " [ 0.54073592, -0.29337918, 0.78837385],\n", " [ 0.48363696, 0.74722911, -0.45578937],\n", " [ 0.99631892, 0.01735462, 0.08394891],\n", " [ 0.74179171, -0.62822234, -0.23469503],\n", " [ 0.09906268, -0.01998319, -0.99488052],\n", " [ 0.57301878, 0.71110718, -0.40740159],\n", " [ 0.93645869, -0.11437729, -0.33160663],\n", " [-0.19170715, 0.53609831, -0.82209913],\n", " [ 0.69801901, 0.38101835, -0.6062957 ]])" ] }, "execution_count": 134, "metadata": {}, "output_type": "execute_result" } ], "source": [ "result_3d.directions.vectors\n" ] }, { "cell_type": "code", "execution_count": 135, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-0.8660254 , -0.77486483, -0.68370427, -0.5925437 , -0.50138313,\n", " -0.41022256, -0.31906199, -0.22790142, -0.13674085, -0.04558028,\n", " 0.04558028, 0.13674085, 0.22790142, 0.31906199, 0.41022256,\n", " 0.50138313, 0.5925437 , 0.68370427, 0.77486483, 0.8660254 ])" ] }, "execution_count": 135, "metadata": {}, "output_type": "execute_result" } ], "source": [ "result_3d.thresholds\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " We can also define custom directions and thresholds for the ECT in case we need finer control. We use random sampling from the unit sphere for the directions and cosine sampling for the thresholds." ] }, { "cell_type": "code", "execution_count": 136, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 136, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from ect import Directions\n", "\n", "directions = Directions.random(16, dim=3)\n", "thresholds = np.cos(np.linspace(0, np.pi, 20))\n", "ect_3d = ECT(directions=directions, thresholds=thresholds)\n", "result_3d = ect_3d.calculate(graph_3d)\n", "result_3d.plot()" ] }, { "cell_type": "code", "execution_count": 137, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of direction vectors: 10000\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 137, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# another example sampling from the half sphere\n", "sample_size = 100\n", "theta = np.linspace(0, np.pi / 2, sample_size) # Only go up to pi/2 for half sphere\n", "phi = np.linspace(0, 2 * np.pi, sample_size)\n", "theta, phi = np.meshgrid(theta, phi)\n", "\n", "# Flatten the meshgrid arrays and create vectors\n", "half_sphere_vectors = np.column_stack(\n", " [\n", " np.sin(theta.flatten()) * np.cos(phi.flatten()),\n", " np.sin(theta.flatten()) * np.sin(phi.flatten()),\n", " np.cos(theta.flatten()),\n", " ]\n", ")\n", "\n", "# Normalize the vectors\n", "half_sphere_vectors = half_sphere_vectors / np.linalg.norm(\n", " half_sphere_vectors, axis=1, keepdims=True\n", ")\n", "\n", "directions = Directions.from_vectors(half_sphere_vectors)\n", "print(f\"Number of direction vectors: {len(directions)}\")\n", "ect_3d = ECT(directions=directions, num_thresh=20) # Reduced number of thresholds\n", "result_3d = ect_3d.calculate(graph_3d)\n", "result_3d.plot()\n" ] } ], "metadata": { "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 } }, "nbformat": 4, "nbformat_minor": 2 }