{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tutorial: Sub-Riemannian geometry on the Heisenberg group" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lead author: Morten Pedersen." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "INFO: Using autograd backend\n" ] } ], "source": [ "import geomstats.backend as gs\n", "import geomstats\n", "\n", "from geomstats.geometry.sub_riemannian_metric import SubRiemannianMetric\n", "from geomstats.geometry.heisenberg import HeisenbergVectors" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We import modules for plotting," ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import matplotlib\n", "from mpl_toolkits.mplot3d import Axes3D" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Heisenberg group" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We instantiate the 3D heisenberg group, " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "heis = HeisenbergVectors(equip=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "'heis' is an object representing a manifold, without any sub-Riemannian structure associated to it. \n", "\n", "In geomstats, a sub-Riemannian structure is constructed via the SubRiemannianMetric-class. \n", "We now instantiate a SubRiemannianMetric corresponding to the heisenberg group. \n", "\n", "In geomstats, a sub-Riemannian metric can be instantiated by supplying either \n", "\n", "- a function which at an input point outputs the matrix representing the cometric, or\n", "- a function which at an input point outputs a matrix whose columns are frame-vectors spanning the distribution at that point. This frame is then implicitly assumed to be orthonormal, so it determines both the distribution and the metric on the tangent bundle." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Defining the Heisenberg sub-Riemannian structure via a frame-field" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will construct the sub-Riemannian Heisenberg group by supplying a frame-function. Mathematically, we represent the distribution $\\Delta$ in a standard way; at the point $p \\in heis$ the distribution is $$\\Delta_p = \\text{span}(F_X(p), F_Y(p)),$$ where $F_X = L^{\\star}_p(X)$, $F_Y = L^{\\star}_p(Y)$ and $X = (1,0,0)$, $Y=(0,1,0)$. So e.g. $F_X$ is the tangent left translation to point $p$ of the standard basis vector X in the Lie-algebra. In geomstats, this can be done concisely as follows," ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def heis_frame(point):\n", " translations = heis.jacobian_translation(point)\n", " return translations[..., 0:2]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Given the frame, we now instantiate the sub-Riemannian metric for the Heisenberg group" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "heis_sr = SubRiemannianMetric(heis, frame=heis_frame)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can illustrate the distribution by plotting the frame-vectors along a line:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "line = gs.array([k * gs.array([1.0, 1.0, 1.0]) for k in gs.linspace(0, 10, 10)])\n", "line = gs.array([k * gs.array([1.0, 0.0, 0.0]) for k in gs.linspace(0, 10, 10)])\n", "\n", "quiver_length = 0.1\n", "\n", "\n", "fig1 = plt.figure()\n", "ax = plt.axes(projection=\"3d\")\n", "\n", "for i in range(line.shape[0]):\n", " point = line[i, :]\n", " frame_at_point = heis_sr.frame(point)\n", "\n", " frame1 = frame_at_point[:, 1]\n", " frame2 = frame_at_point[:, 0]\n", "\n", " ax.quiver(\n", " point[0],\n", " point[1],\n", " point[2],\n", " frame1[0],\n", " frame1[1],\n", " frame1[2],\n", " length=quiver_length,\n", " normalize=True,\n", " color=\"orange\",\n", " alpha=0.8,\n", " linestyle=\"-\",\n", " )\n", " ax.quiver(\n", " point[0],\n", " point[1],\n", " point[2],\n", " frame2[0],\n", " frame2[1],\n", " frame2[2],\n", " length=quiver_length,\n", " normalize=True,\n", " color=\"blue\",\n", " alpha=0.8,\n", " linestyle=\"-\",\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Everything is now set up to generate sub-Riemannian geodesics. A sub-Riemannian geodesic on a manifold $M$ is determined by an initial point $p \\in M$ and an initial cotangent $\\lambda \\in T_p M$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "base_point = gs.array([0.0, 0.0, 0.0])\n", "initial_cotangent = gs.array([1.0, 1.0, 1.0])\n", "\n", "times = gs.linspace(0.0, 10.0, 50)\n", "\n", "path = heis_sr.geodesic(\n", " initial_point=base_point, initial_cotangent_vec=initial_cotangent, n_steps=1000\n", ")\n", "\n", "path_1_1 = path(times)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig1 = plt.figure()\n", "ax = plt.axes(projection=\"3d\")\n", "ax.scatter(0, 0, 0, marker=\"+\", color=\"black\")\n", "\n", "ax.plot3D(\n", " path_1_1[:, 0],\n", " path_1_1[:, 1],\n", " path_1_1[:, 2],\n", " \"-\",\n", " linewidth=1.5,\n", " markersize=0,\n", " marker=\".\",\n", " color=\"green\",\n", " alpha=0.7,\n", ")\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sub-Riemannian structures as limits of Riemannian structures" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If the distribution $\\Delta$ is of the same dimension as the manifold at every point, the structure is actually Riemannian. In geomtats, if the manifold is $n$-dimensional and we pass a frame function with $n$ linearly independent vectors at every point, this will generate the Riemannian structure with a metric that makes these vectors orthonormal at every point. \n", "\n", "For the heisenberg group, we can use the frame given by left-translation of the standard basis in the Lie algebra, $$\\{F_X(p), F_Y(p), \\epsilon\\cdot F_Z(p)\\},$$ where $\\epsilon \\in [0,1]$. For $\\epsilon=0$ the geodesics will be those of the standard Heisenberg group. For $\\epsilon = 1$ the geodesics will be those of the left-invariant Riemannian metric which on the algebra is simply the euclidean metric.\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def heis_frame_riemannian(point, epsilon):\n", " frame_matrix = heis.jacobian_translation(point)\n", " scale_matrix = gs.array([gs.ones((3,)), gs.ones((3,)), gs.ones((3,)) * epsilon]).T\n", " return gs.einsum(\"...ij,...ij -> ...ij\", frame_matrix, scale_matrix)\n", "\n", "\n", "heis_epsilon_1 = SubRiemannianMetric(\n", " heis, frame=lambda point: heis_frame_riemannian(point, 1)\n", ")\n", "heis_epsilon_0 = SubRiemannianMetric(\n", " heis, frame=lambda point: heis_frame_riemannian(point, 0)\n", ")" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "tags": [ "nbsphinx-thumbnail" ] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "base_point = gs.array([0.0, 0.0, 0.0])\n", "initial_cotangent = gs.array([1.0, 1.0, 1.0])\n", "\n", "times = gs.linspace(0.0, 10.0, 50)\n", "\n", "path_epsilon_1 = heis_epsilon_1.geodesic(\n", " initial_point=base_point, initial_cotangent_vec=initial_cotangent, n_steps=1000\n", ")\n", "\n", "path_epsilon_0 = heis_epsilon_0.geodesic(\n", " initial_point=base_point, initial_cotangent_vec=initial_cotangent, n_steps=1000\n", ")\n", "\n", "\n", "path_1 = path_epsilon_1(times)\n", "path_0 = path_epsilon_0(times)\n", "\n", "fig1 = plt.figure()\n", "ax = plt.axes(projection=\"3d\")\n", "ax.scatter(0, 0, 0, marker=\"+\", color=\"black\")\n", "\n", "ax.plot3D(\n", " path_1[:, 0],\n", " path_1[:, 1],\n", " path_1[:, 2],\n", " \"-\",\n", " linewidth=1.5,\n", " markersize=0,\n", " marker=\".\",\n", " color=\"green\",\n", " alpha=0.7,\n", " label=\"epsilon = 1\",\n", ")\n", "\n", "ax.plot3D(\n", " path_0[:, 0],\n", " path_0[:, 1],\n", " path_0[:, 2],\n", " \"-\",\n", " linewidth=1.5,\n", " markersize=0,\n", " marker=\".\",\n", " color=\"red\",\n", " alpha=0.7,\n", " label=\"epsilon = 0\",\n", ")\n", "\n", "ax.legend()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the spiralling structure is similar for the Riemannian ($\\epsilon=1$) and the sub-Riemannian ($\\epsilon=0$) geodesics, in fact only their z-coordinates differ. Let's check that the sub-Riemannian geodesic is horizontal wrt. to the distribution $\\Delta_p = \\text{span}(F_X(p), F_Y(p))$ (i.e. it's tangent vectors lies in $\\Delta$), whereas the Riemannian one isn't." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "base_point = gs.array([0.0, 0.0, 0.0])\n", "initial_cotangent = gs.array([1.0, 1.0, 1.0])\n", "\n", "times = gs.linspace(0.0, 1.0, 50)\n", "\n", "path_epsilon_1 = heis_epsilon_1.geodesic(\n", " initial_point=base_point, initial_cotangent_vec=initial_cotangent\n", ")\n", "\n", "path_epsilon_0 = heis_epsilon_0.geodesic(\n", " initial_point=base_point, initial_cotangent_vec=initial_cotangent\n", ")\n", "\n", "\n", "path_1 = path_epsilon_1(times)\n", "path_0 = path_epsilon_0(times)\n", "\n", "\n", "fig1 = plt.figure()\n", "ax = plt.axes(projection=\"3d\")\n", "ax.scatter(0, 0, 0, marker=\"+\", color=\"black\")\n", "\n", "ax.plot3D(\n", " path_1[:, 0],\n", " path_1[:, 1],\n", " path_1[:, 2],\n", " \"-\",\n", " linewidth=1.5,\n", " markersize=0,\n", " marker=\".\",\n", " color=\"green\",\n", " alpha=0.7,\n", " label=\"epsilon = 1\",\n", ")\n", "\n", "ax.plot3D(\n", " path_0[:, 0],\n", " path_0[:, 1],\n", " path_0[:, 2],\n", " \"-\",\n", " linewidth=1.5,\n", " markersize=0,\n", " marker=\".\",\n", " color=\"red\",\n", " alpha=0.7,\n", " label=\"epsilon = 0\",\n", ")\n", "\n", "ax.legend()\n", "\n", "quiver_length = 1\n", "\n", "exp_curve = path_1\n", "\n", "for i in range(exp_curve.shape[0]):\n", " if i % 10 == 0:\n", " point = exp_curve[i, :]\n", " frame_at_point = heis_sr.frame(point)\n", "\n", " frame1 = frame_at_point[:, 1]\n", " frame2 = frame_at_point[:, 0]\n", "\n", " ax.quiver(\n", " point[0],\n", " point[1],\n", " point[2],\n", " frame1[0],\n", " frame1[1],\n", " frame1[2],\n", " length=quiver_length,\n", " normalize=True,\n", " color=\"orange\",\n", " alpha=0.8,\n", " linestyle=\"-\",\n", " )\n", " ax.quiver(\n", " point[0],\n", " point[1],\n", " point[2],\n", " frame2[0],\n", " frame2[1],\n", " frame2[2],\n", " length=quiver_length,\n", " normalize=True,\n", " color=\"blue\",\n", " alpha=0.8,\n", " linestyle=\"-\",\n", " )\n", "\n", "\n", "quiver_length = 1\n", "\n", "exp_curve = path_0\n", "\n", "for i in range(exp_curve.shape[0]):\n", " if i % 10 == 0:\n", " point = exp_curve[i, :]\n", " frame_at_point = heis_sr.frame(point)\n", "\n", " frame1 = frame_at_point[:, 1]\n", " frame2 = frame_at_point[:, 0]\n", "\n", " ax.quiver(\n", " point[0],\n", " point[1],\n", " point[2],\n", " frame1[0],\n", " frame1[1],\n", " frame1[2],\n", " length=quiver_length,\n", " normalize=True,\n", " color=\"pink\",\n", " alpha=0.8,\n", " linestyle=\"-\",\n", " )\n", " ax.quiver(\n", " point[0],\n", " point[1],\n", " point[2],\n", " frame2[0],\n", " frame2[1],\n", " frame2[2],\n", " length=quiver_length,\n", " normalize=True,\n", " color=\"yellow\",\n", " alpha=0.8,\n", " linestyle=\"-\",\n", " )\n", "\n", "ax.view_init(3, -96)\n", "\n", "plt.show()" ] } ], "metadata": { "backends": [ "autograd" ], "celltoolbar": "Tags", "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.11.3" } }, "nbformat": 4, "nbformat_minor": 4 }