{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Implement your own Riemannian Geometry" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lead author: Nina Miolane.\n", "\n", "Geomstats provides several Riemannian manifolds in its `geometry` folder. Yet, the manifold that you are interested in might not be available there.\n", "\n", "This notebook shows how to use Riemannian geometry on any manifold defined by an immersion into a Euclidean space, such as high-dimensional surfaces immersed in a Euclidean space. \n", "\n", "Specifically, we focus on the case of an embedded manifold $M$ that can be defined by a map \n", "$f: M \\rightarrow \\mathbb{R}^n$ \n", "called the immersion, whose differential $df_x$ is injective for all $x \\in M$.\n", "\n", "This immersion allows to define the pull-back metric $g$ on $M$, as:\n", "\n", "$$g : T_xM \\times T_x M \\rightarrow \\mathbb{R}\\\\\n", "u, v \\rightarrow $$\n", "\n", "where $<,>$ represents the Euclidean inner-product of the embedding space. \n", "\n", "The pull-back metric gives a structure of Riemannian manifold to $M$. In particular, we can compute the Riemannian exp and log maps, the Riemannian distance, the Riemannian parallel transport, etc.\n", "\n", "This notebook illustrates the computation of the pull-back metric, using the class `PullbackMetric` from geomstats, on two embedded manifolds:\n", "\n", "- the 2-sphere $S^2$ embedded in $\\mathbb{R}^3$,\n", "\n", "- a surface defined by: $x, y \\rightarrow z = x^2 + y^2$ embedded in $\\mathbb{R}^3$.\n", "\n", "We also illustrate the use of the class`PullbackDiffeoMetric` to compute the pull-back metric induced via a diffeomorphism, on a function that warps the plane $\\mathbb{R}^2$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "INFO: Using autograd backend\n" ] } ], "source": [ "import time\n", "import matplotlib.pyplot as plt\n", "\n", "import geomstats.visualization as viz" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import geomstats.backend as gs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We import the main structures used in this notebook: the `ImmersedSet` and the `PullbackMetric`:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from geomstats.geometry.base import ImmersedSet\n", "from geomstats.geometry.pullback_metric import PullbackMetric" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Immersed manifolds: the example of the 2-sphere" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We first consider the simple example of the 2-sphere. We define the immersion of the 2-sphere $S^2$ into the Euclidean space $\\mathbb{R}^3$ as follows:\n", "$$\n", "\\begin{align}\n", "f : S^2 &\\rightarrow \\mathbb{R}^3\\\\\n", "(\\theta, \\phi) &\\mapsto (\\cos\\phi.\\sin\\theta, \\sin\\phi.\\sin\\theta, \\cos\\theta)\n", "\\end{align}\n", "$$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "from geomstats.geometry.euclidean import Euclidean\n", "\n", "\n", "class SphereIntrinsic(ImmersedSet):\n", " def __init__(self, equip=True):\n", " super().__init__(dim=2, equip=equip)\n", "\n", " def immersion(self, point):\n", " theta = point[..., 0]\n", " phi = point[..., 1]\n", " return gs.stack(\n", " [\n", " gs.cos(phi) * gs.sin(theta),\n", " gs.sin(phi) * gs.sin(theta),\n", " gs.cos(theta),\n", " ],\n", " axis=-1,\n", " )\n", "\n", " def _define_embedding_space(self):\n", " return Euclidean(dim=self.dim + 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the purpose of visualizing the results in the embedding space $\\mathbb{R}^{3}$, we will need the jacobian of the immersion. Notice that `ImmersedSet` already takes care of it if we want to rely on automatic differentiation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use the `PullbackMetric` structure to define the Riemannian metric on $S^2$ from the immersion. \n", "\n", "Note that the Riemannian metric on the sphere is already implemented in Geomstats using closed forms with the class `Hypersphere`. However, this notebook showcases how we can recover the computations of Riemanian geometry by only relying on the immersion." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "sphere = SphereIntrinsic(equip=False)\n", "\n", "sphere.equip_with_metric(PullbackMetric)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we can access the methods from any Riemannian metric, i.e. the Riemannian exp and log maps, the parallel transport, etc." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We first show the computation of the Riemannian exp map of a tangent vector at a point." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 1.57079633 -0.52359878]\n" ] } ], "source": [ "point_a = gs.array([gs.pi / 2.0, -gs.pi / 2.0])\n", "tangent_vec = gs.array([0.0, gs.pi / 3.0])\n", "\n", "end_point = sphere.metric.exp(tangent_vec=tangent_vec, base_point=point_a)\n", "print(end_point)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And visualize the result of the Riemannian exp map in the embedding space $\\mathbb{R}^3$:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\n", "# We immerse the points and the tangent vector in R^3\n", "\n", "immersed_point_a = sphere.immersion(point_a)\n", "immersed_tangent_vec = sphere.tangent_immersion(tangent_vec, point_a)\n", "immersed_end_point = sphere.immersion(end_point)\n", "\n", "# We plot our results\n", "\n", "fig = plt.figure(figsize=(8, 8))\n", "ax = fig.add_subplot(111, projection=\"3d\")\n", "\n", "viz.plot(immersed_point_a, ax=ax, space=\"S2\", label=\"Initial point\", s=80)\n", "\n", "arrow = viz.Arrow3D(immersed_point_a, vector=immersed_tangent_vec)\n", "arrow.draw(ax, color=\"black\", label=\"Tangent vector\")\n", "\n", "viz.plot(immersed_end_point, ax=ax, space=\"S2\", label=\"End point\", s=80)\n", "\n", "ax.set_title(\"Riemannian Exp map on the sphere\")\n", "ax.legend()\n", "ax.grid(False)\n", "plt.axis(\"off\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we show the computation of the parallel transport on the sphere. Note that `step`, `n_steps`, `tol` and `alpha` are integration parameters that control the efficiency-accuracy tradeoff of the computation." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Computing time for parallel transport: 0.48 secs\n" ] }, { "data": { "text/plain": [ "{'transported_tangent_vec': array([0.78539816, 1.04719755]),\n", " 'end_point': array([ 1.57079633, -0.52359878]),\n", " 'trajectory': [[]]}" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "point_a = gs.array([gs.pi / 2.0, -gs.pi / 2.0])\n", "tangent_vec = gs.array([0.0, gs.pi / 3.0])\n", "tangent_vec_to_transport = gs.array([gs.pi / 4.0, gs.pi / 3.0])\n", "\n", "time_start = time.perf_counter()\n", "\n", "\n", "sphere.metric.exp_solver.integrator.step = \"euler\"\n", "sphere.metric.exp_solver.integrator.n_steps = 1\n", "sphere.metric.log_solver.optimizer.tol = 1e-6\n", "\n", "parallel_transport = sphere.metric.ladder_parallel_transport(\n", " tangent_vec=tangent_vec_to_transport,\n", " direction=tangent_vec,\n", " base_point=point_a,\n", " alpha=1,\n", ")\n", "\n", "time_elapsed = time.perf_counter() - time_start\n", "print(f\"Computing time for parallel transport: {time_elapsed:5.2f} secs\")\n", "\n", "display(parallel_transport)\n", "\n", "transported_tangent_vec = parallel_transport[\"transported_tangent_vec\"]\n", "end_point = parallel_transport[\"end_point\"]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We visualize the result of the parallel transport in the embedding space $\\mathbb{R}^3$:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "is_tangent = True\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\n", "# We first immerse the points and tangent vectors into the embedding space R^3\n", "\n", "immersed_point_a = sphere.immersion(point_a)\n", "immersed_end_point = sphere.immersion(end_point)\n", "\n", "immersed_tangent_vec = sphere.tangent_immersion(tangent_vec, point_a)\n", "immersed_tangent_vec_to_transport = sphere.tangent_immersion(tangent_vec_to_transport, point_a)\n", "immersed_transported_tangent_vec = sphere.tangent_immersion(transported_tangent_vec, end_point)\n", "\n", "# We verify manually that the immersed tangent vector is actually tangent to the sphere\n", "# as the plot can be sometimes misleading. We use the method of the Hypersphere class.\n", "\n", "from geomstats.geometry.hypersphere import Hypersphere\n", "\n", "sphere = Hypersphere(dim=2)\n", "is_tangent = sphere.is_tangent(\n", " immersed_transported_tangent_vec, base_point=immersed_end_point\n", ")\n", "print(\"is_tangent = \", is_tangent)\n", "\n", "# We plot the results\n", "\n", "fig = plt.figure(figsize=(8, 8))\n", "ax = fig.add_subplot(111, projection=\"3d\")\n", "\n", "viz.plot(immersed_point_a, ax=ax, space=\"S2\", label=\"Initial point\", s=80)\n", "\n", "arrow = viz.Arrow3D(immersed_point_a, vector=immersed_tangent_vec)\n", "arrow.draw(ax, color=\"black\", label=\"Tangent vector\")\n", "\n", "arrow = viz.Arrow3D(immersed_point_a, vector=immersed_tangent_vec_to_transport)\n", "arrow.draw(ax, color=\"red\", label=\"Tangent vector to transport\")\n", "\n", "viz.plot(immersed_end_point, ax=ax, space=\"S2\", label=\"End point\", s=80)\n", "\n", "arrow = viz.Arrow3D(immersed_end_point, vector=immersed_transported_tangent_vec)\n", "arrow.draw(ax, color=\"orange\", label=\"Transported tangent vector\")\n", "\n", "ax.set_title(\"Riemannian parallel transport on the sphere\")\n", "ax.legend()\n", "ax.grid(False)\n", "plt.axis(\"off\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Immersed manifolds: the example of a surface defined by its graph" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We consider the example of a 2D surface immersed in $\\mathbb{R}^3$. The surface is defined by its graph:\n", "\n", "$$ x, y \\rightarrow z = x^2 + y^2$$\n", "\n", "which leads to the following immersion into $\\mathbb{R}^3$:\n", "$$\n", "\\begin{align}\n", "f : S^2 &\\rightarrow \\mathbb{R}^3\\\\\n", "(x, y) &\\mapsto (x, y, x^2 + y^2)\n", "\\end{align}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We first implement the graph and the immersion:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "class Surface(ImmersedSet):\n", " \n", " def __init__(self, equip=True):\n", " super().__init__(dim=2, equip=equip)\n", " \n", " def _define_embedding_space(self):\n", " return Euclidean(dim=self.dim + 1)\n", " \n", " def graph(self, x, y):\n", " return x**2 + y**2\n", " \n", " def immersion(self, point):\n", " x = point[..., 0]\n", " y = point[..., 1]\n", " return gs.transpose(gs.array([x, y, self.graph(x, y)]))" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "surface = Surface(equip=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the purpose of visualizing the results in the embedding space ℝ3 , we will need the jacobian of the immersion, which we compute here. Notice that `ImmersedSet` already takes care of it if we want to rely on automatic differentiation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also add a utility function to visualization the surface in 3D:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\n", "def plot_surface(surface, alpha=1.0, ax=None):\n", " if ax is None:\n", " fig = plt.figure()\n", " ax = fig.add_subplot(111, projection=\"3d\")\n", "\n", " x = y = gs.arange(-3.0, 3.0, 0.1)\n", " X, Y = gs.meshgrid(x, y)\n", " zs = gs.array(surface.graph(gs.flatten(X), gs.flatten(Y)))\n", " Z = gs.reshape(zs, X.shape)\n", "\n", " ax.plot_surface(gs.to_numpy(X), gs.to_numpy(Y), gs.to_numpy(Z), alpha=alpha)\n", "\n", " ax.set_xlabel(\"X\")\n", " ax.set_ylabel(\"Y\")\n", " ax.set_zlabel(\"Zm\")\n", " return ax\n", "\n", "\n", "ax = plot_surface(surface)\n", "ax.grid(False)\n", "plt.axis(\"off\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use the `PullbackMetric` structure to define the Riemannian metric on the surface from the immersion. " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "surface.equip_with_metric(PullbackMetric)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we can access the methods from any Riemannian metric, i.e. the Riemannian exp and log maps, the parallel transport, etc." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We show the computation of the Riemannian exp map:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-1.82332926 -0.85879156]\n" ] } ], "source": [ "point_a = gs.array([-2.0, -2.0])\n", "tangent_vec = gs.array([0.0, 1.0])\n", "\n", "end_point = surface.metric.exp(tangent_vec=tangent_vec, base_point=point_a)\n", "print(end_point)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And visualize the result:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\n", "# We first immerse the points and tangent vector into the embedding space R^3\n", "\n", "immersed_point_a = surface.immersion(point_a)\n", "immersed_tangent_vec = surface.tangent_immersion(tangent_vec, point_a)\n", "immersed_end_point = surface.immersion(end_point)\n", "\n", "two_points = gs.vstack([immersed_point_a, immersed_end_point])\n", "\n", "# We plot the results\n", "\n", "ax = plot_surface(surface, alpha=0.3)\n", "\n", "ax.plot(\n", " immersed_point_a[0],\n", " immersed_point_a[1],\n", " immersed_point_a[2],\n", " label=\"Initial point\",\n", " marker=\"o\",\n", " linestyle=\"None\",\n", ")\n", "\n", "arrow = viz.Arrow3D(immersed_point_a, vector=immersed_tangent_vec)\n", "arrow.draw(ax, color=\"black\", label=\"Tangent vector\")\n", "\n", "ax.plot(\n", " immersed_end_point[0],\n", " immersed_end_point[1],\n", " immersed_end_point[2],\n", " label=\"End point\",\n", " marker=\"o\",\n", " linestyle=\"None\",\n", ")\n", "\n", "ax.set_title(\"Riemannian exponential map on a surface\")\n", "ax.legend()\n", "ax.grid(False)\n", "plt.axis(\"off\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we show the computation of the parallel transport on the surface. Again, note that `step`, `n_steps`, `tol` and `alpha` are integration parameters that control the efficiency-accuracy tradeoff of the computation." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Computing time for parallel transport: 7.07 secs\n" ] }, { "data": { "text/plain": [ "{'transported_tangent_vec': array([-0.39054548, 0.74638966]),\n", " 'end_point': array([-1.83662524, -0.86671498]),\n", " 'trajectory': [[]]}" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "point_a = gs.array([-2.0, -2.0])\n", "tangent_vec = gs.array([0.0, 1.0])\n", "tangent_vec_to_transport = gs.array([-0.6, 0.6])\n", "\n", "time_start = time.perf_counter()\n", "\n", "surface.metric.exp_solver.integrator.step = \"rk4\"\n", "surface.metric.exp_solver.integrator.n_steps = 20\n", "surface.metric.log_solver.optimizer.tol = 1e-14\n", "\n", "parallel_transport = surface.metric.ladder_parallel_transport(\n", " tangent_vec=tangent_vec_to_transport,\n", " direction=tangent_vec,\n", " base_point=point_a,\n", " alpha=2,\n", ")\n", "time_elapsed = time.perf_counter() - time_start\n", "print(f\"Computing time for parallel transport: {time_elapsed:5.2f} secs\")\n", "\n", "display(parallel_transport)\n", "\n", "transported_tangent_vec = parallel_transport[\"transported_tangent_vec\"]\n", "end_point = parallel_transport[\"end_point\"]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We visualize the result of the parallel transport." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "tags": [ "nbsphinx-thumbnail" ] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\n", "# We first immerse the points and tangent vectors into the embedding space R^3\n", "\n", "immersed_point_a = surface.immersion(point_a)\n", "immersed_tangent_vec = surface.tangent_immersion(tangent_vec, point_a)\n", "immersed_tangent_vec_to_transport = surface.tangent_immersion(tangent_vec_to_transport, point_a)\n", "immersed_end_point = surface.immersion(end_point)\n", "immersed_transported_tangent_vec = surface.tangent_immersion(transported_tangent_vec, end_point)\n", "\n", "# We plot the results\n", "\n", "ax = plot_surface(surface, alpha=0.3)\n", "\n", "ax.plot(\n", " immersed_point_a[0],\n", " immersed_point_a[1],\n", " immersed_point_a[2],\n", " label=\"Initial point\",\n", " marker=\"o\",\n", " color=\"orange\",\n", ")\n", "\n", "arrow = viz.Arrow3D(immersed_point_a, vector=immersed_tangent_vec_to_transport)\n", "arrow.draw(ax, color=\"orange\", label=\"Tangent vector to transport\")\n", "\n", "arrow = viz.Arrow3D(immersed_point_a, vector=immersed_tangent_vec)\n", "arrow.draw(ax, color=\"black\", label=\"Tangent vector\")\n", "\n", "ax.plot(\n", " immersed_end_point[0],\n", " immersed_end_point[1],\n", " immersed_end_point[2],\n", " label=\"End point\",\n", " marker=\"o\",\n", " color=\"green\",\n", ")\n", "\n", "\n", "arrow = viz.Arrow3D(immersed_end_point, vector=immersed_transported_tangent_vec)\n", "arrow.draw(ax, color=\"green\", label=\"Transported tangent vector\")\n", "\n", "ax.set_title(\"Riemannian parallel transport on a surface\")\n", "ax.legend()\n", "ax.grid(False)\n", "plt.axis(\"off\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Pullback via diffeomorphism: Warping of the plane $\\mathbb{R}^2$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We consider the example of a diffeomorphism that warps the plane $\\mathbb{R}^2$. \n", "\n", "The warp is given by \n", "$$\n", "\\begin{align}\n", "\\varphi : \\mathbb{R}^2 &\\to \\mathbb{R}^2 \\\\\n", "\\vec{x} &\\mapsto \\vec{u} = \\tanh(R_\\theta\\cdot \\vec{x})\n", "\\end{align}\n", "$$\n", "\n", "where $\\theta$ is the angle by which grid lines near the origin are rotated and $\\tanh(\\cdot)$ is applied element-wise" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "from geomstats.geometry.special_orthogonal import SpecialOrthogonal\n", "\n", "def get_warp(angle):\n", " rot_mat = SpecialOrthogonal(2).matrix_from_rotation_vector(gs.array([angle * gs.pi / 180]))\n", " def warp(point):\n", " transformed_point = gs.einsum('ij,j...->i...', rot_mat, point)\n", " transformed_point = gs.tanh(transformed_point)\n", " return transformed_point\n", " return warp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The inverse diffeomorphism $\\varphi^{-1}$ is given by \n", "$$\n", "\\begin{align}\n", "\\varphi^{-1} : \\mathbb{R}^2 &\\to \\mathbb{R}^2 \\\\\n", "\\vec{u} &\\mapsto \\vec{x} = R_{\\theta}^{-1}\\cdot \\tanh^{-1}(\\vec{u})\n", "\\end{align}\n", "$$" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "def get_inverse_warp(angle):\n", " inv_rot_mat = SpecialOrthogonal(2).matrix_from_rotation_vector(gs.array([-angle * gs.pi / 180]))\n", " def inverse_warp(transformed_point):\n", " transformed_point = gs.einsum('...i', transformed_point)\n", " point = gs.arctanh(transformed_point)\n", " point = gs.einsum('ij,j...->i...', inv_rot_mat, point)\n", " return point\n", " return inverse_warp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set the angle to $\\theta = 15^{\\circ}$" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "theta = 15\n", "warp = get_warp(theta)\n", "inverse_warp = get_inverse_warp(theta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We visualize the warping of the plane:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def plot_grid_warped(grid_warped, color, interval=1, show_axis=False):\n", " \"\"\"Plot the given warped grid.\n", "\n", " This function plots a given warp grid with the specified color and interval between grid lines.\n", " It also provides the option to include or exclude axes in the plot.\n", "\n", " Parameters\n", " ----------\n", " grid_warped : array-like, shape = [width, height, 2]\n", " A W x H x 2 dimensional array representing the transformation grid.\n", " color : str\n", " A string indicating the color to be used for plotting the grid lines.\n", " interval : int, optional\n", " The interval between grid lines, default is 1.\n", " show_axis : bool, optional\n", " Whether or not to include axes in the plot, default is False.\n", "\n", " Returns\n", " -------\n", " ax : matplotlib.axes.Axes\n", " The Axes object with the plot drawn onto it.\n", " \"\"\"\n", " \n", " if show_axis is False:\n", " plt.axis('off')\n", " ax = plt.gca()\n", " ax.invert_yaxis()\n", " ax.set_aspect('equal')\n", "\n", " for x in range(0, grid_warped.shape[0], interval):\n", " plt.plot(grid_warped[x, :, 0], grid_warped[x, :, 1], c=color)\n", " for y in range(0, grid_warped.shape[1], interval):\n", " plt.plot(grid_warped[:, y, 0], grid_warped[:, y, 1], c=color)\n", " return ax\n", "\n", "x = gs.linspace(-4, 4, 100)\n", "y = gs.linspace(-4, 4, 100)\n", "x_grid, y_grid = gs.meshgrid(x, y)\n", "grid = gs.stack((x_grid, y_grid), axis=-1)\n", "x_grid_warped, y_grid_warped = warp((x_grid, y_grid))\n", "\n", "\n", "grid_warped = gs.stack((x_grid_warped, y_grid_warped), axis=-1)\n", "\n", "fig = plt.figure(figsize=(12, 12))\n", "ax_template = fig.add_subplot(121)\n", "ax_template = plot_grid_warped(grid, \"darkblue\", show_axis=True)\n", "ax_warped = fig.add_subplot(122)\n", "\n", "ax_warped = plot_grid_warped(grid_warped, \"red\", show_axis=True)\n", "\n", "# Set x and y limits\n", "ax_template.set_xlim((-1, 1))\n", "ax_template.set_ylim((-1, 1))\n", "\n", "ax_warped.set_xlim((-1, 1))\n", "ax_warped.set_ylim((-1, 1))\n", "\n", "# Ensure that the aspect ratio is the same\n", "# 'equal' means that one unit on the x-axis is equal to one unit on the y-axis\n", "ax_template.set_aspect(\"equal\", adjustable=\"box\")\n", "ax_warped.set_aspect(\"equal\", adjustable=\"box\")\n", "\n", "ax_template.set_title(\"Template\");\n", "ax_warped.set_title(\"Warped\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We import the structure `PullbackDiffeoMetric`" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "from geomstats.geometry.pullback_metric import PullbackDiffeoMetric" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "class PlaneWarpMetric(PullbackDiffeoMetric):\n", " def __init__(self):\n", " super().__init__(space=Euclidean(dim=2))\n", " def _define_embedding_space(self):\n", " return Euclidean(dim=2)\n", " def diffeomorphism(self, base_point):\n", " return warp(base_point)\n", " def inverse_diffeomorphism(self, base_point):\n", " return inverse_warp\n", "\n", "pullback_diffeo_metric = PlaneWarpMetric()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use the pullback metric to compute the distance between the origin and $(1,1)$" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.3811819105129122\n" ] } ], "source": [ "point_a = gs.array([0.0,0.0])\n", "point_b = gs.array([3.0,4.0])\n", "distance = pullback_diffeo_metric.dist(point_a,point_b)\n", "print(distance)" ] } ], "metadata": { "backends": [ "autograd", "pytorch" ], "celltoolbar": "Tags", "kernelspec": { "display_name": "Python 3", "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": "3.8.8" } }, "nbformat": 4, "nbformat_minor": 4 }