{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# The HFM library - A fast marching solver with adaptive stencils\n", "\n", "## Part : Algorithmic enhancements to the fast marching method\n", "## Chapter : Geodesic computation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The fast marching method is a numerical scheme devoted to solving a Partial Differential Equation (PDE), the eikonal equation, which characterizes the arrival time of a front in a domain. In order to extract the corresponding minimal paths, a subsequent step is necessary, which involves solving an Ordinary Differential Equation (ODE). \n", "\n", "The HFM library and the Eikonal module offer state of the art implementations these two methods, written in C++ and cuda respectively. However, for pedagogical purposes, we also illustrate these tools with a Python implementation. The present notebook is devoted to geodesic computation, whereas the fast marching method is introduced in this other [notebook](../Notebooks_NonDiv/EikonalEulerian.ipynb)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[**Summary**](Summary.ipynb) of volume Fast Marching Methods, this series of notebooks.\n", "\n", "[**Main summary**](../Summary.ipynb) of the Adaptive Grid Discretizations \n", "\tbook of notebooks, including the other volumes.\n", "\n", "# Table of contents\n", " * [1. Theoretical tools](#1.-Theoretical-tools)\n", " * [1.1 Integrating the geodesic flow](#1.1-Integrating-the-geodesic-flow)\n", " * [1.2 Solving Hamilton's equations of motion](#1.2-Solving-Hamilton's-equations-of-motion)\n", " * [2. Isotropic metrics and the Brachistochrone problem](#2.-Isotropic-metrics-and-the-Brachistochrone-problem)\n", " * [2.1 Explicit solution: the cycloid.](#2.1-Explicit-solution:-the-cycloid.)\n", " * [2.2 Numerical solution using the fast marching method](#2.2-Numerical-solution-using-the-fast-marching-method)\n", " * [2.3 Solving Hamilton's equations of motion](#2.3-Solving-Hamilton's-equations-of-motion)\n", " * [2.4 Initial momentum from the PDE solution](#2.4-Initial-momentum-from-the-PDE-solution)\n", " * [2.5 The geodesic flow](#2.5-The-geodesic-flow)\n", " * [3. Riemannian metrics, and the fastest slide on a landscape](#3.-Riemannian-metrics,-and-the-fastest-slide-on-a-landscape)\n", " * [3.1 Numerical solution using the fast-marching method](#3.1-Numerical-solution-using-the-fast-marching-method)\n", " * [3.2 Integrating the flow](#3.2-Integrating-the-flow)\n", " * [3.3 Geodesic shooting](#3.3-Geodesic-shooting)\n", "\n", "\n", "\n", "This Python® notebook is intended as documentation and testing for the [HamiltonFastMarching (HFM) library](https://github.com/mirebeau/HamiltonFastMarching), which also has interfaces to the Matlab® and Mathematica® languages. \n", "More information on the HFM library in the manuscript:\n", "* Jean-Marie Mirebeau, Jorg Portegies, \"Hamiltonian Fast Marching: A numerical solver for anisotropic and non-holonomic eikonal PDEs\", 2019 [(link)](https://hal.archives-ouvertes.fr/hal-01778322)\n", "\n", "Copyright Jean-Marie Mirebeau, University Paris-Sud, CNRS, University Paris-Saclay" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 0. Importing the required libraries" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:32.919508Z", "iopub.status.busy": "2024-04-30T09:14:32.919098Z", "iopub.status.idle": "2024-04-30T09:14:32.929037Z", "shell.execute_reply": "2024-04-30T09:14:32.928238Z" } }, "outputs": [], "source": [ "import sys; sys.path.insert(0,\"..\") # Allow import of agd from parent directory (useless if conda package installed)\n", "#from Miscellaneous import TocTools; print(TocTools.displayTOC('HamiltonianShooting','FMM'))" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:32.932328Z", "iopub.status.busy": "2024-04-30T09:14:32.932030Z", "iopub.status.idle": "2024-04-30T09:14:33.187026Z", "shell.execute_reply": "2024-04-30T09:14:33.186632Z" } }, "outputs": [], "source": [ "from agd import Eikonal\n", "from agd import LinearParallel as lp\n", "from agd import Metrics\n", "from agd.ODE.hamiltonian import GenericHamiltonian,MetricHamiltonian\n", "from agd import AutomaticDifferentiation as ad\n", "from agd import FiniteDifferences as fd\n", "from agd.Plotting import savefig; #savefig.dirName = 'Images/HamiltonianShooting'\n", "from agd import Interpolation\n", "\n", "norm_infinity = ad.Optimization.norm_infinity\n", "Interp = Interpolation.UniformGridInterpolation" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.188710Z", "iopub.status.busy": "2024-04-30T09:14:33.188590Z", "iopub.status.idle": "2024-04-30T09:14:33.279998Z", "shell.execute_reply": "2024-04-30T09:14:33.279696Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import scipy.integrate\n", "from matplotlib import pyplot as plt" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.281718Z", "iopub.status.busy": "2024-04-30T09:14:33.281606Z", "iopub.status.idle": "2024-04-30T09:14:33.284260Z", "shell.execute_reply": "2024-04-30T09:14:33.284030Z" } }, "outputs": [], "source": [ "def reshape_input_flatten_output(f,vdim):\n", " return lambda q,*args,**kwargs : f(q.reshape((vdim,q.size//vdim)),*args,**kwargs).flatten()\n", "\n", "def add_patches(hfmIn):\n", " \"\"\"Draws a bounding rectangle, and scatters the seeds\"\"\"\n", " plt.gca().add_patch(plt.Rectangle(hfmIn['origin'],*(hfmIn['dims']*hfmIn['gridScale']),\n", " linewidth=1,edgecolor='black',facecolor='none'))\n", " plt.gca().add_patch(plt.Circle(np.array(hfmIn['seeds']).T,3*hfmIn['gridScale']))" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.285651Z", "iopub.status.busy": "2024-04-30T09:14:33.285573Z", "iopub.status.idle": "2024-04-30T09:14:33.287548Z", "shell.execute_reply": "2024-04-30T09:14:33.287303Z" } }, "outputs": [], "source": [ "def reload_packages():\n", " from Miscellaneous.rreload import rreload\n", " global ad,lp,fd,Metrics,Interp,GenericHamiltonian,MetricHamiltonian\n", " ad,lp,fd,Metrics,Interp,GenericHamiltonian,MetricHamiltonian = rreload([ad,lp,fd,Metrics,Interp,GenericHamiltonian,MetricHamiltonian],rootdir=\"../..\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 0.1 Optional configuration\n", "Uncomment the following line to use the GPU eikonal solver. (Comment it for the CPU eikonal solver.)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "editable": true, "execution": { "iopub.execute_input": "2024-04-30T09:14:33.288825Z", "iopub.status.busy": "2024-04-30T09:14:33.288710Z", "iopub.status.idle": "2024-04-30T09:14:33.290304Z", "shell.execute_reply": "2024-04-30T09:14:33.290080Z" }, "slideshow": { "slide_type": "" }, "tags": [ "EikonalGPU_config" ] }, "outputs": [], "source": [ "#Eikonal.dictIn.default_mode = 'gpu_transfer'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Theoretical tools\n", "\n", "In order to define minimal path problem, one needs several ingredients.\n", "Consider a domain $\\Omega \\subset R^d$, and a metric $F : \\Omega \\times R^d \\to R_+$ denoted\n", "$$\n", " (q,v) \\mapsto F_q(v).\n", "$$\n", "Assume that $F$ is $1$-homogeneous, convex, and definite (vanishes only at the origin) w.r.t. the second variable.\n", "\n", "Let also $q_* \\in \\Omega$, referred to as the seed point, and define $u : \\Omega \\to R$ as the length of the shortest path from $q_*$ to any given point, w.r.t. the metric. For any $q \\in \\Omega$\n", "$$\n", " u(q) := \\min_{\\gamma \\in \\Gamma( q_* , q) } \\int_0^1 F_{\\gamma(t)}(\\gamma'(t)) \\mathrm{d}t.\n", "$$\n", "We denoted by $\\Gamma(q_0,q_1)$ the collection of all paths $\\gamma : [0,1] \\to \\Omega$ with Lipschitz regularity and such that $\\gamma(0) = q_0$ and $\\gamma(1)=q_1$.\n", "\n", "It is known that $u$ is the unique viscosity solution to the eikonal equation\n", "$$\n", " F_q^*(\\nabla u(q)) = 1\n", "$$\n", "for all $q \\in \\Omega\\setminus\\{q_*\\}$, with $u(q_*)=0$ and outflow boundary conditions on $\\partial \\Omega$. We denoted by $F_q^*$ the dual metric, defined by \n", "$$\n", " F_q^*(p) := \\sup\\{; F_q(v)\\leq 1\\}.\n", "$$\n", "Solving the eikonal equation is the purpose of a PDE solver, such as the fast marching method, see [notebook](../Notebooks_NonDiv/EikonalEulerian.ipynb). In this notebook, we assume that $u$ has already been numerically computed, and that one would like to find the minimal geodesic path from the seed $q_*$ to a given $q \\in \\Omega$.\n", "\n", "Two approaches can be considered:\n", "* Integrating the geodesic flow, which is a sort of gradient descent of the function $u$ distorted by the metric. This is the most robust method, in particular in the presence of obstacles, and a variant of it is implemented in the HFM library.\n", "* Solving Hamilton's equations of motion, with an initial momentum proportional to $\\nabla u(q)$. The originality of this ODE is that it is completely autonomous: the solution $u$ to the eikonal equation is only used to provide the initial condition.\n", "\n", "We describe these approaches in more detail below, and prepare some tools needed for the implementation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.1 Integrating the geodesic flow\n", "\n", "This approach to geodesic computation is based on the observation that geodesics follow the direction of greatest slope of the value function, w.r.t the metric.\n", "More precisely, the geodesic $\\gamma$ from a seed $q_*$ to a given tip $q$, parametrized at constant speed w.r.t the metric, obeys the ordinary differential equation\n", "$$\n", " \\gamma'(t) = V(\\gamma(t)), \n", "$$\n", "with terminal condition $\\gamma(T) = q$. \n", "We denoted by $T = u(q)$ is the geodesic distance from the seed $q_*$ to the tip $q$, and by $V : \\Omega \\to R^d$ the geodesic flow, gradient of the distance *w.r.t the metric*. In the Riemannian case\n", "$$\n", " V(q) = M(q)^{-1} \\nabla u(q),\n", "$$\n", "where $\\nabla$ denotes the usual Euclidean gradient. The fast marching algorithm produces, as a byproduct, an upwind approximation of this vector field.\n", "We illustrate below a such an approach for geodesic computation. \n", "\n", "**Note on the HFM implementation.**\n", "The implementations of geodesic computation presented below and in the HFM library are related but also have significant differences. The HFM implementation only uses a first order interpolation of the flow, but has mechanisms designed to improve robustness in the presence of obstacles, and for problems whose distance maps are discontinuous (e.g. [Dubins model](Curvature.ipynb)), etc. It also has different stopping criteria.\n", "\n", "**Note on interpolation of $V$ and regularity.**\n", "The geodesic flow $V : \\Omega \\to R^d$ and the value function $u:\\Omega \\to R^d$ have a singularity at the seed $q_*$. In order to extend $V$ from the computation grid to the domain, the function below uses the quotient \n", "$$\n", " I(u V)/\\sqrt{I(u^2)}\n", "$$\n", "of the interpolations of $uV$ and $u^2$. Let us explain why $u^2$ and $u V$ are good candidates for interpolation. \n", "\n", "The squared distance $u^2$ is smooth, far from the cut-locus, in the absence of obstacles, and when the metric is Riemannian. This follows from the expression (notice the squares)\n", "$$\n", " u(q)^2 = \\min_{\\gamma \\in \\Gamma(q_*,q)} \\int_0^1 F_{\\gamma(t)}(\\gamma'(t))^2 \\mathrm{d} t\n", "$$\n", "which has better properties that the above definition of $q$ (without squares). E.g. the lack of invariance to reparametrization (so that there is a unique minimizer) and the smoothness of $v\\mapsto F_q(v)^2$ (when $F$ is a Riemannian metric).\n", "\n", "Likewise, the product $u V$ of the flow times the distance to the seed point $u : \\Omega \\to R_+$ is smooth, under the same assumptions. Indeed, it is the gradient of the path energy $u^2$, which is smooth, see the next section. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.291578Z", "iopub.status.busy": "2024-04-30T09:14:33.291485Z", "iopub.status.idle": "2024-04-30T09:14:33.293813Z", "shell.execute_reply": "2024-04-30T09:14:33.293572Z" } }, "outputs": [], "source": [ "def value_flow_i(hfmIn,hfmOut,**kwargs):\n", " \"\"\"Returns the distance to the seed, and the upwind geodesic flow, interpolated.\"\"\"\n", " grid = hfmIn.Grid()\n", " value = hfmOut['values']\n", " flow = hfmOut['flow']\n", " \n", " flowXvalue_i = Interp(grid, flow*value,**kwargs)\n", " valueXvalue_i = Interp(grid,value*value,**kwargs)\n", " \n", " def value_i(q): return np.sqrt(np.maximum(0.,valueXvalue_i(q)))\n", " def flow_i(q,t=None,mult=1): return mult*flowXvalue_i(q)/value_i(q)\n", " \n", " return value_i,flow_i" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Possible improvements.**\n", "Some numerical methods use the path computed by the above numerical method as a first guess, which is then improve to reduce length and more closely satisfy Hamilton's equations of motion using e.g. a homotopy method (small deformations of the path)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.2 Solving Hamilton's equations of motion\n", "\n", "The hamiltonian associated to a (minimal) geodesic problem reads \n", "$$\n", " H(q,p) := \\frac 1 2 F_q^*(p)^2,\n", "$$\n", "where $F^*$ is the dual metric, see above. It is known that geodesics obey Hamilton's equations of motion\n", "$$\n", " \\frac {dq}{dt} = \\frac {\\partial H}{\\partial p}, \\quad \\frac {dp}{dt} = -\\frac {\\partial H}{\\partial q},\n", "$$\n", "where $q(t) = \\gamma(t)$ is the geodesic path, and $p(t) = \\eta(t)$ is the impulsion which can also be regarded as an optimal control. \n", "\n", "**Initial momentum**\n", "Hamilton's equations are autonomous ODEs, and are also considered in this [notebook on dense automatic differentiation](../Notebooks_Algo/Dense.ipynb), and this [notebook on the wave equation](../Notebooks_Div/Time1D_Div.ipynb). In the context of minimal geodesic computation, from a seed $q_*$ to a given point $q$, the difficulty lies in finding the correct initial momentum, or final momentum if the equation is solved backwards in time.\n", "\n", "For that purpose, the numerical solution of the eikonal PDE provides valuable information. Indeed, one shows that the adequate final momentum is precisely\n", "$$\n", " p = \\nabla U(q),\n", "$$\n", "where $U = \\frac 1 2 u^2$ and $u: \\Omega \\to R_+$ is the distance map from the seed $q_*$. If the terminal condition is $(q,\\nabla U(q))$ at time $t=1$, for some $q\\in \\Omega$ the the geodesic goes through the seed $q_*$ at time $t=0$. The quantity $U(q)$ is often referred to as the energy of the minimal path from $q_*$ to $q\\in \\Omega$.\n", "\n", "As discussed in the previous section, $U$ is smooth far from the cut-locus, including at the seed point, under suitable assumptions (Riemannian metric, without obstacles). It is therefore a good candidate for interpolation.\n", "\n", "**Limitation.** This approach only works if the Riemannian geodesic between the seed and tip remains in the computational domain interior at all times, and does not meet any obstacles." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.295221Z", "iopub.status.busy": "2024-04-30T09:14:33.295139Z", "iopub.status.idle": "2024-04-30T09:14:33.297290Z", "shell.execute_reply": "2024-04-30T09:14:33.297074Z" } }, "outputs": [], "source": [ "def energy_impulsion_i(hfmIn,hfmOut,**kwargs):\n", " \"\"\"Returns the energy x -> u(x)^2/2, and its euclidean gradient referred to as the impulsion, interpolated.\"\"\"\n", " grid = hfmIn.Grid()\n", " values = hfmOut['values']\n", " \n", " energy_i = Interp(grid,0.5*values**2,**kwargs)\n", " \n", " def impulsion_i(q):\n", " q_ad = ad.Dense.identity(constant=q,shape_free=q.shape[:1])\n", " return energy_i(q_ad).gradient()\n", " \n", " return energy_i,impulsion_i" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Possible improvement.**\n", "In practical applications, the final momentum $p=\\nabla U(q)$ extracted from the numerical solution to the eikonal equation, is usually only used as a first guess. An iterative optimization method refines this guess afterwards.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Isotropic metrics and the Brachistochrone problem\n", "\n", "A brachistochrone curve, in mathematics and physics, is a curve of fastest descent, between two points in a uniform gravity field, and neglecting friction. The standard brachistochrone problem assumes that the curve can be constructed without constraints in free space and admits an explicit solution: the cycloid. See [Wikipedia](https://en.wikipedia.org/wiki/Brachistochrone_curve).\n", "\n", "In this section, we recover this explicit solution numerically.\n", "Consider a point of mass $m$, at altitude $h$, with velocity $v$, and denote by $g$ the intensity of the gravity field. The total energy (kinetic + potential) of this point is \n", "$$\n", " E = m g h + \\frac 1 2 m \\|v\\|^2,\n", "$$\n", "and it is conserved along the motion, provided there is no friction.\n", "\n", "For simplicity, but without loss of generality, we assume that $m = 1$ and $g=1$, and denote $z = -h$. Up to a vertical translation, we may also assume that the conserved energy equals zero. Then we obtain $-z+\\frac 1 2 \\|v\\|^2=0$, equivalently\n", "$$\n", " \\frac {\\|v\\|^2}{2 z} = 1.\n", "$$\n", "Thus the brachistochrone problem amounts to find a geodesic, between two given points, for an isotropic metric whose (half squared) expression is given above. More explicitly, denoting by $q=(x,z)$ the position, and $v$ the speed\n", "$$\n", " F_q(v) := \\frac {\\|v\\|}{\\sqrt z}.\n", "$$\n", "The matrix form, the Riemannian metric at $q=(x,z) \\in R \\times R_{++}$ reads\n", "$$\n", " M(q) = M(x,z) = \\frac {\\mathrm{Id}} z.\n", "$$\n", "\n", "**A closely related model.** The Poincare model of the hyperbolic plane is posed on the same domain $R\\times R_{+++}$ and involves the metric $M(x,z) = \\mathrm{Id} / {z^2}$ (note the square in the denominator). One significant difference is that the Poincare model is geodesically complete, whereas the Brachistochrone model isn't (geodesics reach the boundary $R \\times \\{0\\}$ in finite time).\n", "The Poincare half plane model naturally arises in the context of [Fisher-Rao metrics](FisherRao.ipynb)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1 Explicit solution: the cycloid.\n", "An explicit geodesic is known for the brachistochrone metric, known as the cycloid, see [Wikipedia](https://en.wikipedia.org/wiki/Brachistochrone_curve), and reading\n", "$$\n", " (x(t),z(t)) = (t-\\sin t, 1-\\cos t),\n", "$$\n", "for $t \\in ]0,2 \\pi[$.\n", "All other geodesics are dilations and horizontal translations of this particular solution $\\gamma(t)=(x(t),z(t))$\n", "$$\n", " \\lambda \\gamma(t/\\lambda) + (x_0,0),\n", "$$\n", "where $\\lambda>0$ and $x_0 \\in R$." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.298772Z", "iopub.status.busy": "2024-04-30T09:14:33.298695Z", "iopub.status.idle": "2024-04-30T09:14:33.300467Z", "shell.execute_reply": "2024-04-30T09:14:33.300258Z" } }, "outputs": [], "source": [ "def Cycloid(t): return ad.array((t-np.sin(t),1.-np.cos(t)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note : recall that the vertical axis is reversed, a.k.a. $z=-h$, w.r.t the physical brachistochrone problem." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.301836Z", "iopub.status.busy": "2024-04-30T09:14:33.301751Z", "iopub.status.idle": "2024-04-30T09:14:33.389839Z", "shell.execute_reply": "2024-04-30T09:14:33.389552Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title('The cycloid curve, solution to the Brachistochrone problem.')\n", "plt.axis('equal')\n", "T = np.linspace(0,2*np.pi)\n", "plt.plot(*Cycloid(T));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We introduce a slightly reduced interior interval, since the Brachistochrone problem becomes singular when the object velocity vanishes." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.391332Z", "iopub.status.busy": "2024-04-30T09:14:33.391222Z", "iopub.status.idle": "2024-04-30T09:14:33.392979Z", "shell.execute_reply": "2024-04-30T09:14:33.392726Z" } }, "outputs": [], "source": [ "Tint = np.linspace(0.2,2*np.pi-0.4) #Interior interval" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us emphasize that the Cycloid is not parametrized at constant Euclidean velocity. Indeed\n", "$$\n", " x(t) = \\frac{t^3} 6+ O(t^5), \\quad z(t) = \\frac {t^2} 2 + O(t^4)\n", "$$\n", "Hence the endpoints of the Cycloid on this interval are extremely close to the singularity of the metric at $z=0$.\n", "This raises a substantial difficulty for fast marching and shooting methods." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.394363Z", "iopub.status.busy": "2024-04-30T09:14:33.394264Z", "iopub.status.idle": "2024-04-30T09:14:33.396368Z", "shell.execute_reply": "2024-04-30T09:14:33.396117Z" } }, "outputs": [ { "data": { "text/plain": [ "array([0.00133067, 0.01993342])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Cycloid(Tint[0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.2 Numerical solution using the fast marching method" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.397751Z", "iopub.status.busy": "2024-04-30T09:14:33.397647Z", "iopub.status.idle": "2024-04-30T09:14:33.400025Z", "shell.execute_reply": "2024-04-30T09:14:33.399791Z" } }, "outputs": [], "source": [ "hfmIn = Eikonal.dictIn({\n", " 'model':'Isotropic2',\n", " 'seed':Cycloid(0.2),\n", " 'tip': Cycloid(2.*np.pi-0.2)\n", "})\n", "dx = 0.4 # Use a slightly larger domain, containing the trajectory in its interior\n", "hfmIn.SetRect([[-dx,2.*np.pi+dx],[0,2+dx]],dimx=300)\n", "X,Z = hfmIn.Grid()" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.401404Z", "iopub.status.busy": "2024-04-30T09:14:33.401304Z", "iopub.status.idle": "2024-04-30T09:14:33.403029Z", "shell.execute_reply": "2024-04-30T09:14:33.402805Z" } }, "outputs": [], "source": [ "hfmIn['cost'] = 1./np.sqrt(Z)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.404411Z", "iopub.status.busy": "2024-04-30T09:14:33.404305Z", "iopub.status.idle": "2024-04-30T09:14:33.422503Z", "shell.execute_reply": "2024-04-30T09:14:33.422165Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.004651 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 8.45\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.424117Z", "iopub.status.busy": "2024-04-30T09:14:33.423949Z", "iopub.status.idle": "2024-04-30T09:14:33.492468Z", "shell.execute_reply": "2024-04-30T09:14:33.492198Z" } }, "outputs": [ { "data": { "image/png": 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g5+eHxYsXm8z38fddGJ07d0bnzp2RmZmJgwcPYvLkyejVqxd8fX1Rv359ODg4IDo6Otfrchp7Pv5+H/Xo55Lz5QgU7EsvP/b29lAoFM9cU1FwcHCAVqvFvXv3TL5YhRCIiYkxHmkqLvb29sa/2IcNG5bnNH5+fk+dT0xMTL7DHv9xy2s7XrBgAd566y189dVXJsPj4uJQrlw54/OCbNvPq1GjRmjUqBF0Oh2OHj2KH3/8EaNGjYKLiwt69uyZ7+sKsz0Vx/vIa70+zz6Xl5zpP/74Y3Tt2jXPaSpXrvzU+eS3vajVapOjSUDu91XYfaYw22aOotovXlY8IlIEWrZsiVatWmHSpEm50reLiwvMzc1x6tQpk+HPczVJfjp06ICrV6/CwcEBYWFhuR45V3sUVrt27bBz584nHiKVJAlqtdpkJ4+JiSmS96nRaNCkSRNMmTIFAHDixAkAhsP3586dy3U49K+//oIkSWjWrFm+88xZF49/LmvXrs1z+QU5QmFlZYW6detixYoVJtPr9XosWLAAnp6eqFSp0lPnUxD5/RXbokULAIYf4kctX74cqampxvGFnW9BWVpaolmzZjhx4gSqV6+e53aY35f1o7Zv325ytYdOp8PixYvh7+9foL/8JUkyCZgAsH79+lyn+Nq1a4dLly69kNN4SqUSdevWNV4lkbPd5rfOC7M9FWQfLQrPs8/lpXLlyqhYsSJOnjyZ57YSFhZmciowPytWrDA5IpCcnIy1a9eiUaNGJqeG8ntPQMH3mbNnz+bqtmHhwoWwsbFBzZo181xGUe0XLyseESkiU6ZMQa1atRAbG4ugoCDjcEmS0Lt3b/z555/w9/dHSEgIDh8+jIULFxZ5DaNGjcLy5cvRuHFjvPfee6hevTr0ej2ioqKwZcsWvP/++6hbt26h5ztp0iRs3LgRjRs3xieffIJq1aohISEBmzZtwujRo1GlShV06NABK1aswDvvvINu3brh5s2b+Pzzz+Hm5obLly8Xepnjx4/HrVu30KJFC3h6eiIhIQEzZsyASqVCkyZNAADvvfce/vrrL7zyyiuYNGkSfHx8sH79esycORNDhw594o9++/btUb58eQwcOBCTJk2CmZkZ5s6di5s3b+aatlq1ali0aBEWL16MChUqwNzcHNWqVctzvpMnT0arVq3QrFkzjBkzBmq1GjNnzsSZM2fwzz//FLrXzfzkLH/KlClo164dlEolqlevjlatWqFNmzYYO3YskpKS0KBBA5w6dQoTJkxAaGgo+vTp80zzzTn8WxAzZsxAw4YN0ahRIwwdOhS+vr5ITk7GlStXsHbt2gL96Ds6OqJ58+b49NNPYWVlhZkzZ+LChQu5LuHNT4cOHTB37lxUqVIF1atXx7Fjx/Dtt9/mCjGjRo3C4sWL0blzZ3z00UeoU6cO0tPTsXv3bnTo0KHQP6yP++WXX7Bjxw688sor8Pb2RkZGhvGIZU67FBsbG/j4+GD16tVo0aIFypcvD0dHR/j6+hZ4eyrIPloUnmefy8+vv/6Kdu3aoU2bNujXrx88PDzw4MEDnD9/HsePH8fSpUufOg+lUolWrVph9OjR0Ov1mDJlCpKSkgrUOV9h9xl3d3d06tQJEydOhJubGxYsWICtW7diypQpsLS0zHc5RbFfvLRkbChbKj161czjevXqJQCYXDUjhBCJiYli0KBBwsXFRVhZWYmOHTuKyMjIfK/kuHfvnsnr+/btK6ysrHIt7/ErdIQQIiUlRfzf//2fqFy5slCr1cbLxd577z2TqxAAiGHDhuX5Hh+vSwghbt68KQYMGCBcXV2FSqUS7u7uonv37uLu3bvGab7++mvh6+srNBqNqFq1qvjtt9/yvDqlIFfNrFu3TrRr1054eHgItVotnJ2dRfv27cWePXtMprtx44bo1auXcHBwECqVSlSuXFl8++23uVra5/WeDh8+LMLDw4WVlZXw8PAQEyZMEL///nuuq2YiIyNF69athY2NjfGyOiHyvyJqz549onnz5sLKykpYWFiIevXqibVr15pMk992lNNifufOnU9cP5mZmWLQoEHCyclJSJJkUnN6eroYO3as8PHxESqVSri5uYmhQ4eK+Pj4J87zafPNb5vJ6/O8fv26GDBggPDw8BAqlUo4OTmJ8PBw8cUXXzy1hpzlzJw5U/j7+wuVSiWqVKki/v77b5PpnrQvxsfHi4EDBwpnZ2dhaWkpGjZsKPbs2SOaNGmS6wqo+Ph4MXLkSOHt7S1UKpVwdnYWr7zyivEy35zP+dHLMx+t9UlXYx04cEC8+uqrwsfHR2g0GuHg4CCaNGki1qxZYzKfbdu2idDQUKHRaAQAk/VZkO1JiKfvoznb1qOXQD/6/h7djvP6bslRkH2uMOtMCCFOnjwpunfvLpydnYVKpRKurq6iefPm4pdffsmzhseXM2XKFPHZZ58JT09PoVarRWhoqNi8ebPJtPl9vwpR8H3Gx8dHvPLKK2LZsmUiKChIqNVq4evrK6ZPn55nXY9/NxRkv8jvc8pve3/S+yotJCFk7IaQiIjoGUVGRsLPzw/ffvstxowZI3c59IzYRoSIiIhkwyBCREREsuGpGSIiIpINj4gQERGRbBhEiIiISDYMIkRERCSbEt2hmV6vx507d2BjY1NkHUERERFR8RJCIDk5Ge7u7lAonnzMo0QHkTt37sDLy0vuMoiIiOgZ3Lx586m3ZSjRQSTnHgM3b96Era2tzNUQERFRQSQlJcHLy6tA9woq0UEk53SMra0tgwgREVEpU5BmFWysSkRERLJhECEiIiLZMIgQERGRbEp0GxGioiSEgFarhU6nk7sUIqJST6VSQalUPvd8GESoTMjKykJ0dDTS0tLkLoWI6KUgSRI8PT1hbW39XPNhEKGXnl6vx/Xr16FUKuHu7g61Ws0O8oiInoMQAvfu3cOtW7dQsWLF5zoywiBCL72srCzo9Xp4eXnB0tJS7nKIiF4KTk5OiIyMRHZ29nMFETZWpTLjad0MExFRwRXVkWV+MxMREZFsGESIiIhINgwiRFTiRUZGQpIkRERE5DvN3LlzUa5cuRdWU+PGjbFw4cIXtryiVpB1WhpMnDgRLi4ukCQJq1atkrucXPr164cuXboU6zJ27doFSZKQkJBQZPOMjY2Fk5MTbt++XWTzzA+DCFEJ1q9fP0iSlOtx5cqV55pvYb64mjZtCkmS8PXXX+ca1759e0iShIkTJz5XPUWhR48euHTp0gtZ1rp16xATE4OePXsah82ePRtNmzaFra3tM/0olNQf0pLs/Pnz+Oyzz/Drr78iOjoa7dq1e+55FnWgnTFjBubOnVtk82vatClGjRplMiw8PBzR0dGws7MrsuU4OzujT58+mDBhQpHNMz8MIkQlXNu2bREdHW3y8PPze6E1eHl5Yc6cOSbD7ty5gx07dsDNze255p3T0dzzsrCwgLOz83PPpyB++OEH9O/f36QBdFpaGtq2bYtPPvnkhdRQUFlZWaVy3gVx9epVAEDnzp3h6uoKjUYjaz2P0ul00Ov1sLOzK/YjdWq1Gq6urkXeLUH//v3x999/Iz4+vkjn+zgGESqThBBIy9LK8hBCFKpWjUYDV1dXk4dSqcT06dNRrVo1WFlZwcvLC++88w5SUlKMr7tx4wY6duwIe3t7WFlZISgoCBs2bEBkZCSaNWsGALC3t4ckSejXr98Ta+jQoQPu37+Pffv2GYfNnTsXrVu3zvXjv2DBAoSFhcHGxgaurq7o1asXYmNjjeNzjsZs3rwZYWFh0Gg02LNnD/R6PaZMmYKAgABoNBp4e3vjyy+/NJn3tWvX0KxZM1haWiIkJAQHDhwwqefRL/yJEyeiRo0amD9/Pnx9fWFnZ4eePXsiOTnZOE1ycjLefPNNWFlZwc3NDd99912ef3E+Ki4uDtu2bUOnTp1Mho8aNQofffQR6tWrl+frsrKyMHz4cLi5ucHc3By+vr6YPHkyAMDX1xcA8Oqrr0KSJOPzvJw+fRrNmzeHhYUFHBwcMHjwYJPPPedUwOTJk+Hu7o5KlSoBAA4fPozQ0FCYm5sjLCwMJ06cyDXvc+fOoX379rC2toaLiwv69OmDuLg44/imTZti+PDhGD16NBwdHdGqVat863xUzme+fft2hIWFwdLSEuHh4bh48aLJdLNmzYK/vz/UajUqV66M+fPn5zvPiRMnomPHjgAMV8Tl/AgfOXIErVq1gqOjI+zs7NCkSRMcP37c5LUJCQkYPHgwXFxcYG5ujuDgYKxbtw67du1C//79kZiYaDz6mHO0Lz4+Hm+99Rbs7e1haWmJdu3a4fLly8Z55mx/69atQ2BgIDQaDW7cuGFyaibndNjjj6ZNmwIA7t+/jzfeeAOenp6wtLREtWrV8M8//xiX0a9fP+zevRszZswwvjYyMjLPI5zLly9HUFAQNBoNfH19MW3aNJN14Ovri6+++goDBgyAjY0NvL29MXv2bJNpqlWrBldXV6xcuTLfz6EosB8RKpPSs3UIHL9ZlmWfm9QGlurn3/UUCgV++OEH+Pr64vr163jnnXfw4YcfYubMmQCAYcOGISsrC//++y+srKxw7tw5WFtbw8vLC8uXL8drr72GixcvwtbWFhYWFk9cllqtxptvvok5c+agQYMGAAxfvN98802u0zJZWVn4/PPPUblyZcTGxuK9995Dv379sGHDBpPpPvzwQ0ydOhUVKlRAuXLl8PHHH+O3337Dd999h4YNGyI6OhoXLlwwec24ceMwdepUVKxYEePGjcMbb7yBK1euwMws7/V59epVrFq1CuvWrUN8fDy6d++Or7/+2hhwRo8ejX379mHNmjVwcXHB+PHjcfz4cdSoUSPfdbF3715YWlqiatWqT1xnj/vhhx+wZs0aLFmyBN7e3rh58yZu3rwJwPDj6ezsjDlz5qBt27b59smQc9SlXr16OHLkCGJjYzFo0CAMHz7c5PD/9u3bYWtri61bt0IIgdTUVHTo0AHNmzfHggULcP36dYwcOdJk3tHR0WjSpAnefvttTJ8+Henp6Rg7diy6d++OHTt2GKebN28ehg4din379hU6VI8bNw7Tpk2Dk5MThgwZggEDBhjD7cqVKzFy5Eh8//33aNmyJdatW4f+/fvD09PTGJwfNWbMGPj6+qJ///6Ijo42Dk9OTkbfvn3xww8/AACmTZuG9u3b4/Lly7CxsYFer0e7du2QnJyMBQsWwN/fH+fOnYNSqUR4eDi+//57jB8/3hiScnoN7devHy5fvow1a9bA1tYWY8eORfv27XHu3DmoVCrj5zN58mT8/vvvcHBwyBXSvby8TGqNiYlBy5Yt0bhxYwBARkYGatWqhbFjx8LW1hbr169Hnz59UKFCBdStWxczZszApUuXEBwcjEmTJgH4ry+PRx07dgzdu3fHxIkT0aNHD+zfvx/vvPMOHBwcTP7omDZtGj7//HN88sknWLZsGYYOHYrGjRujSpUqxmnq1KmDPXv2YMCAAQX/oAtLlGCJiYkCgEhMTJS7FCrF0tPTxblz50R6erpxWGpmtvAZu06WR2pmdoFr79u3r1AqlcLKysr46NatW57TLlmyRDg4OBifV6tWTUycODHPaXfu3CkAiPj4+KfW0KRJEzFy5Ehx8uRJYWNjI1JSUsTu3buFs7OzyMrKEiEhIWLChAn5vv7w4cMCgEhOTjZZ9qpVq4zTJCUlCY1GI3777bc853H9+nUBQPz+++/GYWfPnhUAxPnz54UQQsyZM0fY2dkZx0+YMEFYWlqKpKQk47APPvhA1K1b17hMlUolli5dahyfkJAgLC0txciRI/N9P999952oUKFCvuPzW7cjRowQzZs3F3q9Ps/XARArV67Md75CCDF79mxhb28vUlJSjMPWr18vFAqFiImJEUIYthkXFxeRmZlpnObXX38V5cuXF6mpqcZhs2bNEgDEiRMnhBBCfPrpp6J169Ymy7t586YAIC5evCiEMGwLNWrUeGKNeclZJ9u2bTOpG4BxvwwPDxdvv/22yetef/110b59+3znu3LlSvG0nzGtVitsbGzE2rVrhRBCbN68WSgUCuN7etzj25EQQly6dEkAEPv27TMOi4uLExYWFmLJkiXG1wEQERERJq/t27ev6Ny5c67lpKeni7p164oOHToInU6Xb/3t27cX77//vvF5zv74qMe3uV69eolWrVqZTPPBBx+IwMBA43MfHx/Ru3dv43O9Xi+cnZ3FrFmzTF733nvviaZNm+ZZW17frTkK8/vNIyJUJlmolDg3qY1syy6MZs2aYdasWcbnVlZWAICdO3fiq6++wrlz55CUlAStVouMjAykpqbCysoK7777LoYOHYotW7agZcuWeO2111C9evV8l/P333/jf//7n/H5xo0b0ahRI+Pz6tWro2LFili2bBl27tyJPn36GP8SfNSJEycwceJERERE4MGDB9Dr9QCAqKgoBAYGGqcLCwsz/v/8+fPIzMxEixYtnrguHq0/p21KbGysyV9wj/L19YWNjY3Ja3JOE127dg3Z2dmoU6eOcbydnR0qV678xBrS09Nhbm7+xGny0q9fP7Rq1QqVK1dG27Zt0aFDB7Ru3bpQ8zh//jxCQkKM2wAANGjQAHq9HhcvXoSLiwsAwyF1tVqd63WP9ixcv359k3kfO3YMO3fuzPO+IVevXjWe4nn0cyus/D4/b29vnD9/HoMHDzaZvkGDBpgxY0ahlhEbG4vx48djx44duHv3LnQ6HdLS0hAVFQUAiIiIgKenp/H9FMT58+dhZmaGunXrGoc5ODigcuXKOH/+vHGYWq1+4j72qIEDByI5ORlbt241tjXS6XT4+uuvsXjxYty+fRuZmZnIzMw0+bwLWm/nzp1NhjVo0ADff/89dDqd8Yjbo7VKkgRXV1eT06iAoe1Vcd+ji0GEyiRJkork9MiLYGVlhYCAAJNhN27cQPv27TFkyBB8/vnnKF++PPbu3YuBAwciOzsbADBo0CC0adMG69evx5YtWzB58mRMmzYNI0aMyHM5nTp1Mvmi9fDwyDXNgAED8PPPP+PcuXM4fPhwrvGpqalo3bo1WrdujQULFsDJyQlRUVFo06ZNroaNj365Pu3UUI5Hg09Om4CcoPO06XNekzO9eHha4fEGfuIppxscHR2fqfFezZo1cf36dWzcuBHbtm1D9+7d0bJlSyxbtqzA8xBC5Nsg8dHhj/9wPe09AYb12LFjR0yZMiXXuEcbJBf2R/FRT/v88vosCtsAs1+/frh37x6+//57+Pj4QKPRoH79+sbtr6Db2uN15Df80fosLCwKVO8XX3yBTZs24fDhwyZBedq0afjuu+/w/fffG9t/jRo1qtCNgvNab3m9hyftHzkePHgAJyenQi2/sNhYlagUOnr0KLRaLaZNm4Z69eqhUqVKuHPnTq7pvLy8MGTIEKxYsQLvv/8+fvvtNwAw/rWs0+mM09rY2CAgIMD4yOsLu1evXjh9+jSCg4NNjm7kuHDhAuLi4vD111+jUaNGqFKlSq6/sPJSsWJFWFhYYPv27QVeB8/L398fKpXKJFAlJSWZNEDMS2hoKGJiYp4pjNja2qJHjx747bffsHjxYixfvhwPHjwAYPhRePTzyEtgYCAiIiKQmppqHLZv3z4oFIon/oUfGBiIkydPIj093Tjs4MGDJtPUrFkTZ8+eha+vr8l2EBAQ8Fzho6CqVq2KvXv3mgzbv39/odvi7NmzB++++y7at29vbKz5aIPb6tWr49atW/le6q1Wq3N9DoGBgdBqtTh06JBx2P3793Hp0qVC17d8+XJMmjQJS5Ysgb+/f67aO3fujN69eyMkJAQVKlTItT3mVd/jAgMD81yXlSpVKvQ9Yc6cOYPQ0NBCvaawGESISiF/f39otVr8+OOPuHbtGubPn49ffvnFZJpRo0Zh8+bNuH79Oo4fP44dO3YYvzR9fHwgSRLWrVuHe/fumVx18ST29vaIjo7ONzB4e3tDrVYb61qzZg0+//zzp87X3NwcY8eOxYcffoi//voLV69excGDB/HHH38UqK5nYWNjg759++KDDz7Azp07cfbsWQwYMMDkCoy8hIaGwsnJyeQKIsDQ8DAiIsLYx8vp06eNp6cA4LvvvsOiRYtw4cIFXLp0CUuXLoWrq6vxSh9fX19s3779iSHnzTffhLm5Ofr27YszZ85g586dGDFiBPr06WM8LZOXXr16QaFQYODAgTh37hw2bNiAqVOnmkwzbNgwPHjwAG+88QYOHz6Ma9euYcuWLRgwYMBTf/iKwgcffIC5c+fil19+weXLlzF9+nSsWLECY8aMKdR8AgICMH/+fJw/fx6HDh3Cm2++aRKqmzRpgsaNG+O1117D1q1bjUepNm3aBMDwOaSkpGD79u2Ii4tDWloaKlasiM6dO+Ptt9/G3r17cfLkSfTu3RseHh65ToE8yZkzZ/DWW29h7NixCAoKQkxMDGJiYozbSEBAALZu3Yr9+/fj/Pnz+N///oeYmBiTefj6+uLQoUOIjIxEXFxcnkcE33//fWzfvh2ff/45Ll26hHnz5uGnn34q9LpMS0vDsWPHCn0KsbAYRIhKoRo1amD69OmYMmUKgoOD8ffffxsvBc2h0+kwbNgwVK1aFW3btkXlypWNV9R4eHjgs88+w0cffQQXFxcMHz68wMsuV65cvn8hOzk5Ye7cuVi6dCkCAwPx9ddf5/rBy8+nn36K999/H+PHj0fVqlXRo0ePAh1NeR7Tp09H/fr10aFDB7Rs2RINGjRA1apVn9gGRKlUYsCAAfj7779Nhv/yyy8IDQ3F22+/DcDQ82poaCjWrFkDwHD1xZQpUxAWFobatWsjMjISGzZsMLYPmDZtGrZu3QovL698/wK1tLTE5s2b8eDBA9SuXRvdunVDixYt8NNPPz3xfVpbW2Pt2rU4d+4cQkNDMW7cuFynYNzd3bFv3z7odDq0adMGwcHBGDlyJOzs7J56w8h+/foZL0F9Vl26dMGMGTPw7bffIigoCL/++ivmzJlT6Pn++eefiI+PR2hoKPr06YN3330319Ury5cvR+3atfHGG28gMDAQH374oTFshYeHY8iQIejRowecnJzwzTffAADmzJmDWrVqoUOHDqhfvz6EENiwYUOe7aTyc/ToUaSlpeGLL76Am5ub8dG1a1cAhn2gZs2aaNOmDZo2bQpXV9dcvbKOGTMGSqUSgYGBxlOfj6tZsyaWLFmCRYsWITg4GOPHj8ekSZOeepn+41avXg1vb2+TtmLFQRIFOXkok6SkJNjZ2SExMRG2trZyl0OlVEZGBq5fvw4/P79namRIZUdqaio8PDwwbdo0DBw4MN/p7t69i6CgIBw7dgw+Pj4vsMKSqWnTpmjatGmJ6GGXik6dOnUwatQo9OrVK8/xT/puLczvd+lorUdEVAxOnDiBCxcuoE6dOkhMTDT2zfC0w+0uLi74448/EBUVVeaDSHJyMq5evYp169bJXQoVodjYWHTr1g1vvPFGsS+LQYSIyrSpU6fi4sWLUKvVqFWrFvbs2QNHR8envq4wbQNeZjY2NsaO2ejl4ezsjA8//PCFLItBhIjKrNDQUBw7dkzuMojKNDZWJSIiItkwiBAREZFsGESIiIhINgwiREREJBsGESIiIpINgwgRERHJhkGEiODr64vvv//+ueaxa9cuSJKEhISEIqmJiMoGBhGiUmD//v1QKpVo27at3KUAMHTpPWrUKJNh4eHhiI6Ohp2dnTxFEVGpxCBCVAr8+eefGDFiBPbu3ZvnTa5KArVaDVdX1yfeuZaI6HEMIlQ2CQFkpcrzKOR9JlNTU7FkyRIMHToUHTp0wNy5c43jck6HbN++HWFhYbC0tER4eDguXrxonObq1avo3LkzXFxcYG1tjdq1a2Pbtm35Lm/AgAHo0KGDyTCtVgtXV1f8+eef6NevH3bv3o0ZM2ZAkiRIkoTIyMg8T83s27cPTZo0gaWlJezt7dGmTZt8b3FPRGVTsXbxPmvWLMyaNQuRkZEAgKCgIIwfPx7t2rUrzsUSPV12GvCVuzzL/uQOoLYq8OSLFy9G5cqVUblyZfTu3RsjRozAp59+anLkYdy4cZg2bRqcnJwwZMgQDBgwAPv27QMApKSkoH379vjiiy9gbm6OefPmoWPHjrh48SK8vb1zLW/QoEFo3LgxoqOj4ebmBgDYsGEDUlJS0L17d7z22mu4dOkSgoODjTeJc3JyMu7nOSIiItCiRQsMGDAAP/zwA8zMzLBz507j7daJiIBiDiKenp74+uuvERAQAACYN28eOnfujBMnTiAoKKg4F0300vjjjz/Qu3dvAEDbtm2RkpKC7du3o2XLlsZpvvzySzRp0gQA8NFHH+GVV15BRkYGzM3NERISgpCQEOO0X3zxBVauXIk1a9Zg+PDhuZYXHh6OypUrY/78+cabXs2ZMwevv/46rK2tARhOw1haWsLV1TXfur/55huEhYVh5syZxmHc74noccUaRDp27Gjy/Msvv8SsWbNw8OBBfiGRvFSWhiMTci27gC5evIjDhw9jxYoVAAAzMzP06NEDf/75p0kQqV69uvH/OUcxYmNj4e3tjdTUVHz22WdYt24d7ty5A61Wi/T09Ce2NRk0aBBmz56NDz/8ELGxsVi/fj22b99eqLcZERGB119/vVCvIaKy54XdfVen02Hp0qVITU1F/fr185wmMzMTmZmZxudJSUkvqjwqaySpUKdH5PLHH39Aq9XCw8PDOEwIAZVKZdLWQqVSGf+fc8pGr9cDAD744ANs3rwZU6dORUBAACwsLNCtWzdkZWXlu9y33noLH330EQ4cOIADBw7A19cXjRo1KlTtFhYWhZqeiMqmYm+sevr0aVhbW0Oj0WDIkCFYuXIlAgMD85x28uTJsLOzMz68vLyKuzyiEkur1eKvv/7CtGnTEBERYXycPHkSPj4++Pvvvws0nz179qBfv3549dVXUa1aNbi6uuZqz/E4BwcHdOnSBXPmzMGcOXPQv39/k/FqtfqpbT2qV69e6KMoRFT2FHsQqVy5MiIiInDw4EEMHToUffv2xblz5/Kc9uOPP0ZiYqLxcfPmzeIuj6jEWrduHeLj4zFw4EAEBwebPLp164Y//vijQPMJCAjAihUrjCGmV69exqMlTzJo0CDMmzcP58+fR9++fU3G+fr64tChQ4iMjERcXFye8/v4449x5MgRvPPOOzh16hQuXLiAWbNmIS4urmArgIjKhGIPImq1GgEBAQgLC8PkyZMREhKCGTNm5DmtRqOBra2tyYOorPrjjz/QsmXLPDsIe+211xAREYHjx48/dT7fffcd7O3tER4ejo4dO6JNmzaoWbPmU1/XsmVLuLm5oU2bNnB3N73CaMyYMVAqlQgMDISTk1Oe7U0qVaqELVu24OTJk6hTpw7q16+P1atXw8zshZ0RJqJSQBKikJ0aPKcWLVrAy8vLpC+E/CQlJcHOzg6JiYkMJfTMMjIycP36dfj5+cHc3FzuckqNtLQ0uLu7488//0TXrl3lLoeISpgnfbcW5ve7WP80+eSTT9CuXTt4eXkhOTkZixYtwq5du7Bp06biXCwRPQe9Xo+YmBhMmzYNdnZ26NSpk9wlEdFLrFiDyN27d9GnTx/j/SeqV6+OTZs2oVWrVsW5WCJ6DlFRUfDz84Onpyfmzp3LUylEVKyK9RumoI3piKjk8PX1xQs+Y0tEZRjvNUNERESyYRChMoN/5RMRFZ2i+k5lEKGXXk6vo2lpaTJXQkT08sjpnVmpVD7XfNgKjV56SqUS5cqVQ2xsLADA0tLS5M61RERUOHq9Hvfu3YOlpeVzN2hnEKEyIecusTlhhIiIno9CoYC3t/dz/2HHIEJlgiRJcHNzg7OzM7Kzs+Uuh4io1FOr1VAonr+FB4MIlSlKpfK5z2cSEVHRYWNVIiIikg2DCBEREcmGQYSIiIhkwyBCREREsmEQISIiItkwiBAREZFsGESIiIhINgwiREREJBsGESIiIpINgwgRERHJhkGEiIiIZMMgQkRERLJhECEiIiLZMIgQERGRbBhEiIiISDYMIkRERCQbBhEiIiKSDYMIERERyYZBhIiIiGTDIEJERESyYRAhIiIi2TCIEBERkWwYRIiIiEg2DCJEREQkGwYRIiIikg2DCBEREcmGQYSIiIhkwyBCREREsmEQISIiItkwiBAREZFsGESIiIhINgwiREREJBsGESIiIpINgwgRERHJhkGEiIiIZMMgQkRERLJhECEiIiLZMIgQERGRbBhEiIiISDYMIkRERCQbBhEiIiKSDYMIERERyYZBhIiIiGTDIEJERESyYRAhIiIi2TCIEBERkWwYRIiIiEg2DCJEREQkGwYRIiIikg2DCBEREcmGQYSIiIhkwyBCREREsmEQISIiItkUaxCZPHkyateuDRsbGzg7O6NLly64ePFicS6SiIiISpFiDSK7d+/GsGHDcPDgQWzduhVarRatW7dGampqcS6WiIiISglJCCFe1MLu3bsHZ2dn7N69G40bN37q9ElJSbCzs0NiYiJsbW1fQIVE9Di9XiA5U4vkjGwkpWuRlJGN5AwtktKzkZqlRZZWj0ytHllaPbJ0hn+zdXoU5ptFbaaAlVoJS40ZrNRKWGnMYKk2g5VGCUu1Gaw1ZrA0DldCY6aAJEnF96aJ6LkU5vfb7AXVBABITEwEAJQvXz7P8ZmZmcjMzDQ+T0pKeiF1EZUlKZlaxCRm4G6S4RGTlIHYpEwkpWcjKSMbSQ9DRnKGIXSkZGpNQoUZtLBFGmylVNghFbZSGmyRBjspFbZIhaOUClukwUpKx/NEhcyHjwcA0oQGSbBEkrBCIqyQKlkh08wG2SpbZKtsoTe3hdCUg7mFJRytNXC20cDJxvCvs605nGw0cLLWQG3GZnFEJc0LCyJCCIwePRoNGzZEcHBwntNMnjwZn3322Ysqieilo9XpcSs+HdfjUnHjfipikjIR+zBs5ASOlEytyWvUyIaHFAcvKRZe0j1UkxJgi1TYPgwUtqo02CEVdlIq7KQ0WCJDpneXh+yHjzTD0wyhQiKskCSskARLJAorRMISJ4UVkmCFdJU9Uiw8kGXjBVHOB+XsysHZ1hwe5SzgXd4SXuUtYGOukvMdEZU5L+zUzLBhw7B+/Xrs3bsXnp6eeU6T1xERLy8vnpoheoReL3A3OQPX76XiWlwqIuNScf3hI+pBGrR6011aAT1c8QBe0j14KQxhw08ZBz+zOHggFuV096HAM3wNaGwBc7uHj3KGfy3K/fdcYw1IRXAEQgggOxVIT4A+PRG6tHjo0xMgMhIhZSRAmZkEZVYSpGd4D3HCFreEE24KJ9wUzrgpnBCvdoPezgfmjj5wc7CFn4MVApytEeBsjXKW6ud/P0RlQIk7NTNixAisWbMG//77b74hBAA0Gg00Gs2LKImoxMvW6XElNgXno5Nw9V4Krsel4tq9VNy4n4b0bJ3JtLZIRQUpGu2kWPip41DFPB5+yji46GNgl3UXSqHNvYBHZ6GyBMr5APY+gK27IUg8GipyhQxbQPlCz+wCMLSuzzPa6PVAVjKQngBkJAIZD/99+FykJyAz5QGyE6OBhBvQJN+EOjsJjpLhUQNX/5uXAJAA6OIlxFwuj1vCCZHCGXv0hpAi2ftA41oJru4+CHC2hr+zNdztzNlmhegZFesRESEERowYgZUrV2LXrl2oWLFioV7PxqpUViSkZeFcdBLORyfj3J0knI9OwuXYZGTrcu+eDkhEiDIS4Va3UcPsBvy1V2GfdefJC1CoADtPQ9DICRzlfAB7X8O/Vo5AWfshTU8AEqKAhBtA/A0g4Qa09yOhexAJs6QoKHVPPgUVK8rhjN4XZ4Qvrij8oXWuBmevigj2LIdqHnbwd7KCmZJtUqhsKszvd7EGkXfeeQcLFy7E6tWrUblyZeNwOzs7WFhYPPX1DCL0MsrU6nDmdhKO3XiAo5HxOHM7EXcS8/rREwjQJKJ1+bsIU0chQHcVzqkXYZ5+N+8Z27jnETQe/mvrDiiUxfq+XipCAKn3jAEF8ZHIvh+JzHvXgIQoWKbdhgL6XC9LEFYPw4kfLkoVkOkYDEfvqgjyLIdaPuXh72TFIydUJpSYIJLfDjdnzhz069fvqa9nEKGXwYPULBy/EY+jN+Jx7MYDnLyViCyt6Y+YBD3q2CWhuV00aqpvwC/7KuwTz0OZ8SCPOUqAQwDgFvLfw7UaYJn31WhUDLJSgbtngeiT0N85iaxbJ6C+fwGKPE6BpQhznBM+OKv3xXVVABQeNeAREIJaFZwR7G7HK3nopVRigsjzYhCh0kYIgWtxqTgWGY+jNx7g6I14XLuXuwM/V0ugm8sdNFefR0DGGdjEn4OUlZx7hpIScK5qGjpcgg0NQalk0WYCseeB6JMQ0SeRefMEVPfOQqnPzDVpplDhvPDCKVRCjENdWFRsguoB3qjpXY5X7dBLgUGE6AURQuDS3RTsuXwPB689wPGoeDxIzco1XUVHc3RyjkMT9TkEpByDRcwRSNrHTscoNYBL0MPAUd3wr3MQoDJ/Qe+GipxOC9y/DESfhO52BNKijkFz7yzUOtNwqhUKnBIVsF8fjFvl6sDKvx5qVHBDbd/ycLXj50+lD4MIUTGKT83Cnitx2HPpHvZcjkNMkmmgUJspEOJhi1YuyWisPIsKKcegvrnXcBXHo6ycgQpNAN9GgEctwKkyoORfwy89vR6Ivw5x5wSSzu+EIvJf2KRFmUySIVQ4oq+M/fpgRNqFwa1KXTSp4oa6fuVhrmJbHyr5GESIipBWp8eJmwnYffEe9ly+h1O3E016GtWYKVC3ggPaeGrRQHkWXglHoIz8F0iONp2RxhbwbQj4NTEEEKcqZe9KFcpbQhRw/V+kX9wO6fq/MM+MMxmdKCxxQB+Ew1Iw0j0bonJgTTSp4gI/RyuZCiZ6MgYRoueUka3D3stx2Hw2BtsvxOY63VLZxQatKpijvfUlVEo7DrPI3cD9K6YzUWoArzpAhaaGh1sNWfreoFJGCODeBeDabmRf2QlE7oVKm2IySYywxz59EC5a1ISqUgvUqR6E+hUc2PCVSgwGEaJnkJiWjR0X72LzmbvYfemeSadhdhYqNK7khBa+ajTDUdhdWw9c3QHos/+bgaQwhI0KTQxHPbzrAaqnX6ZO9EQ6LRAdAXFtF9Iu7oAm+gjM9P8FY72QcExUxHYpHMkV2qNOSDCaVXGGLRu9kowYRIgKKCYxA1vOxWDL2bs4eO2+Sffo7nbmaB3kinYB5gjLOADl+dXA1Z2m4cMhAPBvbggevg0NvY8SFafsdCDqILKu7ET6he2wiz9jMvqovhI2i7q469kW4aHV0SbIFfZW7JqeXiwGEaInuJ+SifWno7HqxG0cj0owGVfJxRptglzR1t8cgYn/Qjq3Gri2yzR8OFUBArsAQV0Ml9YSySnxFvRnVyMtYjmsY4+ZjDqmr4iN+nq459UG4TVD0DqQoYReDAYRosekZ+mw5VwMVkfcwb+X7hmPfEgSUNPbHq0DXdDWXwOf2J3AuVUPw8cjnVM5VTUEj8AugHMVGd4BUQEk3gbOr0HGyeUwjz5iMuq4PgCb9PVwz7sdGoXVQJsgV1hp2GaJigeDCBEMV7vsv3ofq07cxuazMUjN+q/NRzUPO3Su4Y5OlczhfHsbcHYVcH23afhwDvzvyIdT5cdnT1SyJd0BzhlCiSb6iMndiU/oA7AF9ZBRsQOa1g1DA38H3heHihSDCJVpF2KSsOTILaw5eQdxKf/1aulV3gJdanigczUnBNzfBZxYkDt8uAQbwkdgZ8Cp0guvnahYJEUD59ci/eRymN85ZBJKIvT+2GTWHFJID7wSVgnBHnYyFkovCwYRKnPSs3RYd+oOFh6OwolH2n3YW6rQobo7uoS6o6ZNIqTjfwEn5htuaJbDpRoQ1BkIfBVwDHjxxRO9SMkxEOfWIOXEMljFHIbiYShJFRqs1oXjkENn1K7fHJ1ruLO7eXpmDCJUZlyIScLCQ1FYeeI2kjMMRzbMFBJaBbqgWy1PNPK3h/raVuDon8CV7UDOX4LWrkDNPkD1ngwfVHYl34Xu9DJkHPgdVsnXjIMj9BWwDK2gD+qK1+pVRk3vcrxrMBUKgwi91DKydVh/KhoLDt0wOfrhXd4SPet4oVstTzjr7wPH/zI8ku/892L/5kCt/kDlduxOnSiHEMCN/cg69DuUF9ZCKQxXiSUJC6zUNcT+cp3QsEFjvFrTE9Zs4EoFwCBCL6U7Cen4+9ANLDp8E/cf9nRqppDQOsgFver4INyvHBTXdxqOflzaBAi94YWWjkBob6BWX6B8BRnfAVEpkBoHceJvZB76A+bJN4yDj+grYYXUGpY1uuKNBpUQ4GwjY5FU0jGI0EtDCIEjkfH4c+91bDkXg5z+xtztzPFmPR90D/OCExIM7T6OzzPcsyOHbyOgVj+gakfATCNH+USll14PXN+N7EN/QHl5AxTCcNVZvLDGMl1jXHDvijZNGqFlVRcoFDxtQ6YYRKjUE0Jg18V7+HnnFRy9EW8cXr+CA/qG+6BlFWeY3dwHHPkDuLDuvytfzMsBNd40BBBe9UJUNJJjoD8+H1mH/oR52n+nOvfrArHFsj0CGr+BrrV9YanmaRsyYBChUkunF9h4Jho/77yK89FJAAC1UoHXanmgX7gfKjtbGU677JkK3H6kF0mvuoa2H0FdeH8XouKi1wFXtiP9wG/QXN8GBQynP2/onTFX8Sqs6/RG74aV4GJrLnOhJDcGESp1srR6rDpxG7N2X8X1uFQAgKVaid71fDCwoR9crFXA2ZXAnulA7FnDi8wsgNA3gbABgEuQjNUTlUGJt5B1eC50R36HRZbhqGW0KI8/9B2QFtwb/ZsGoqIL25GUVQwiVGqkZ+mw6EgUZv97DdGJGQAMd7rt38AXfev7wl4D4NRiYO93wIOrhhepbYA6bwP13gGsneQrnoiArDToj81F1u7vYJ4RCwCIE7b4U9sOUQG9MLBFCEK97WUukl40BhEq8RLTs7Hg4A38sfc6Hjy8AsbZRoO3G1XAG3W9Ya3IBo7PB/b/ACTeNLzIwt4QPuq8bfg/EZUc2kwgYiEyd02DJsWwzyYJS8zVtcYl394Y2DqMgaQMYRChEisuJRN/7r2O+QduIDnT0MDUq7wFhjTxx2s1PWGuTzNcfrv/JyDV8NcVrF2A8BGGNiAaaxmrJ6Kn0mmBM8uRtetbqOMvAzD02vq3riXO+PRBvzb1UJOB5KXHIEIlzr3kTPy88wr+ORyFTK2hgVslF2u80zQAHaq7wSwzATg8Gzg4C8hIMLzIzgtoMBII7QOo2PiNqFTR64ELa5G58xto7p0BAGQKFZbomiDCuy/ebNuIgeQlxiBCJUZKpha//XsNv+25hrSHd78N8SqHYU39Df0PpN0DDvwMHPkdyEoxvKi8P9BoNFC9B3s/JSrthAAub0XGzikwjz4KAMgWSqzWN8ARz37o0a45A8lLiEGEZJel1eOfw1H4YftlYy+oIZ52GNOmMhoGOELKTjOcftn3PZCdZniRcxDQ+H3D3W8VStlqJ6JiIAQQuRfpO6bA4uYeAIBOSFisa4bDfkPxv/b1UNWN3/MvCwYRko1eL7DudDSmbr6IqAeGgOHnaIUP2lRGu2BXSEIYroLZPum/e8C4hwKNPwQqtQUUChmrJ6IX4tZRpG2bDMvIbQCAFGGOmbrOiA0cgHfbVIe3g6XMBdLzYhAhWRyJfIBJa8/h9O1EAICjtQajWlZEj9peUCkVQOQ+YPMnQHSE4QV23kCriUBQV4B39iQqe27sR8b6j2AeexIAcEs44lvdG7Cv3RPvtqyE8lZqmQukZ8UgQi/UnYR0fL3xAtacNBzhsNaYYUiTChjQ0M/Q5fP9q8C2CcD5tYYXqG0Mp2DqDmUjVKKyTq8HTi9F9pYJUKVGAwCO6wMwXeqHhs3bo38DX2jMeKq2tGEQoRciI1uH2f9ew6xdV5GerYMkAT1re2NM60pwsNYA6fHAv1OBQ78C+mxAUhjuAdP0E3ZERkSmstKAAz9Dt2c6lFrDad21unr427o/BnVshhZVnSHxyGmpwSBCxUoIgU1nYvDlhvO4FZ8OAKjta48JHYMQ7GEH6LINfYHsmmwIIwDg3wJo/QXgEihj5URU4iXHQOz4AjixABIEMoUKf+ra4oTvQHzYKQwBzuw2vjRgEKFiczEmGRPXnMWBa/cBAG525vi4fVV0rO4GCQAubQa2/B9w39CREZyqAK2/BCq2lK1mIiqFok9Bu+kTmN0wXGETJ2zxve51aOr0w8jWVWFrzkv7SzIGESpy6Vk6zNh+Gb/vuQatXkBjpsD/GlfAkKb+hnYgMWcMDVGv7za8wNIRaPYJULMvoOStwYnoGQgBXNqE7I2fQJVwDQBwUe+Jn1T90LJjL3QKcefpmhKKQYSK1M4Lsfh09RnjaZjWgS74tEMgvMpbAtkZwO6vgX0/AEIHKNWG+8E0Gg2Y28lcORG9FB6e7s3e/hVUWQkAgNW6cGz0HIkPujaEvxNv/VDSMIhQkYhNysBna89h/WlDS3aPchb4rFMQWga6GCa4cQBYMxy4f8XwvGonoPXngL2vPAUT0cstPR7anV9DcXg2FNDjvrDBF7p+8GzUG8OaV4S5ilfXlBQMIvRchBBYHXEHE9acRWJ6NpQKCQMb+mFki4qw0pgBmcmGDskO/wZAGG5K98p0oGoHuUsnorLg9nFkrXgH6vvnAQDbdKGYZT0c73VtioYVHWUujgAGEXoO95IzMW7laWw5dxcAUM3DDlNeq45A94fr/8o2YO0oINFwm2+E9jZcDWPBe0UQ0QukzYLYOx1i91QoRDaShAW+0r4JhL6FcR0CYcPGrLJiEKFnsvbkHYxffQbxadlQKSWMbFER/2vib+gVNe0BsHkccHKhYeJy3kDHHwD/ZvIWTURlW+x56FYNg/LOMQDAfl0gvrcYjlE92iDcn0dH5MIgQoVyPyUT41efNbYFCXSzxbTuIf/dgOrcamD9GCA1FoAE1B0CNP8/QMMGYkRUAuh1wKFfoNs2CUpdBtKFGlO1r0NfZwg+bBcECzXbjrxoDCJUYJvOxGDcytO4n5oFM4WEYc0CMLx5gOEoSPJdYMMY4Pwaw8SOlYBOPwHedeUtmogoLw+uQbd6BJQ39gIAIvT+mGE1EsN7dkQtn/IyF1e2MIjQU6Vn6TBp3Tn8czgKAFDF1QZTXw8x9IwqBHDyH2DTx0BGAiApgYbvAY0/4L1hiKhkEwI4Pg/aTeNglp2CLKHETF0XZNV/DyPbBPK+NS8Igwg90YWYJIxYeAKXY1MgScD/GvvjvVYVDTtoahywaihweYthYtfqQOefAbfq8hZNRFQYSXeQvWYUVFc2AwDO670x1XYs3nujo+EPLipWDCKUJyEEFhyKwhfrziFTq4eTjQbf96iBBgEPG3RF7gOWDwSSowGlBmj6ERD+LntGJaLSSQjgzHJkrR0DdVY80oQGE3T94dF0IIY1e3gKmooFgwjlkpCWhbHLT2HzWcNluc0qO2Hq6yGGu+TqdcCe6cCurwChN7QFeX0u4BIkb9FEREUh+S6ylw6CKupfAMAyXWMscx2Fb9+ob+ghmoocgwiZOBL5ACP/OYE7iRlQKSWMbVsFAxr4QaGQgJRYYPmg/+4RE/IG0H4qr4ghopeLXgfsmQaxczIk6HFF744PFKMx+LUOaFfNTe7qXjoMIgTAcCpm1u6rmLr5IvQC8HWwxI9v1EQ1z4fnR6/tNoSQ1FhAZWkIIKFvyls0EVFxitwL3dIBUKbeRYZQYby2H1S13sKnHYPYRXwRYhAhpGZqMWbpSWw8EwMA6BrqgUldgmGtMTP8ZbB7CrD7GwACcKpqOBXjXEXWmomIXoiUe9CvGAzFtR0AgJW6Bphn/y6m9eEN9IoKg0gZF3U/DYPnH8WFmGSolBI+6xSMXnW9DSOTYwxHQSL3GJ6H9gbafQuoeZ6UiMoQvR7Y9x3Eji8hCR2u6t3wofQe3n69M9oGu8pdXanHIFKG7bsSh2ELjyMhLRuO1hr82qfmfx35XNkOrBgMpMUBKiugw3dASA95CyYiktONA9At7Q9lSjQyhQqfad+CbYO3MaZNZZjxqppnVpjfb67ll4QQAnP2Xcdbfx5GQlo2qnvaYe2IBoYQotMa7pa74DVDCHEJBgbvYgghIvKpD+XQfdAHtIJGysZXqj8QfGAU/vf7TtxPyZS7ujKBQeQlkJGtwwfLTuGzteeg0wt0DfXAkv/Vh5udBZAeDyx4FdgzDYAAavUHBm0DnCrJXTYRUclg5QBFryVAq8+hl8zQQXkQn9wehiEzluDkzQS5q3vp8dRMKXc3KQP/m38METcToJCAT9pXxcCGfpAkCXhwDfi7O3D/suFUTKcfgGrd5C6ZiKjkunkY2Yv7QpVyB/HCGsN076Prq93RrZan3JWVKjw1U0acvJmAjj/uRcTNBNhZqDBvQB0MalTBEEJuHAB+a2EIIbYewMDNDCFERE/jVQeq/+2Czi0U9lIK5iq/wP7lP2LSwyPOVPQYREqpnRdj0XP2QcQmZ6KiszVWD2uARhWdDCNPLgb+6gSkPwDcagBv7wBcq8laLxFRqWHjAmX/DRBVO0Mt6TBd/QvsD03B23MPITkjW+7qXjoMIqXQ8mO38Pa8o0jP1qFRRUesHNYAvo5Whvsq7PwKWDkY0GUBVToA/TcANrwUjYioUNSWkF6fCzQcDQAYYbYKr16fgDdm7sTNB2ny1vaSYRApRYQQ+GX3Vby/9CS0eoEuNdzxR9/ahk7KsjMM/YPsnmKYuMFIoPt8QG0lb9FERKWVQgG0nAB0/hl6hQodlQcxKeFjDPhpPY7deCB3dS8NBpFSQq8X+HzdeXy98QIA4O1GfpjevQbUZgogNc5wKubMMkBhBnT6EWg1ybATERHR8wntDUWfldBryqGm4grm6D7Cp78tw/pT0XJX9lLgL1UpkKnVYeTiCPy57zoAYFz7qhj3SqDhpnWxF4DfmgM3DwHmdkDvFUDNt2SumIjoJePXCIq3t0NvXwGeUhwWKcdjyaI5mLc/Uu7KSj0GkRIuOSMbA+YewdqTd2CmkPB9jxp4u3EFw8irO4E/WgMJNwB7X2DgNqBCE1nrJSJ6aTkGQDFoG4R3fdhK6fhD9S0ur/8e326+gBLcE0aJxyBSgt1LzkTP2Qex78p9WKqV+LNfbXQJ9TCMPLXE0FNqZiLgVQ8YtIOdlBERFTcrB0hvrYYI6QkzSY8vVHNguedLfLLiNPS8vPeZMIiUUHeTMtDj1wM4eycJDlZqLBpcD40rPbw89/h8wz1jhA6o9jrQdw1g5SBvwUREZYWZBlKXX4Bm/wcAGGa2BgEnvsLYZSfZ18gzYBApgWISM9Bz9kFci0uFRzkLLBsajuqe5QwjD/8GrBkOQABhA4FXZwNmGjnLJSIqeyQJaPIB8Mo0AMBAs40IOTUJHy49wTBSSAwiJUx0Yjp6zj6A6w9DyKLB9eDn+PAS3AM/AxvGGP5f7x3DDsArY4iI5FN7ENDpJwhI6G22HXVPT8T7i49Bq9PLXVmpUay/Yv/++y86duwId3d3SJKEVatWFefiSr3bCeno8etBRN5Pg1d5Cyz+Xz14lbc0jPx3KrD5E8P/G44G2nxlSORERCSvmn0gdZ0NvaREd7PdaHruU4aRQijWIJKamoqQkBD89NNPxbmYl8Kt+DT0nH0AUQ/S4F3eEosG14envaWht9QdXwI7PjdM2Gwc0GI8QwgRUUlSvTsUr8+BXjJDF+V+tDn/CUb/cwTZDCNP9cLuvitJElauXIkuXboU+DVl5e670YnpeP2XA7gVnw4fB0ssGlwPbnYWhhCydTyw/wfDhC0/AxqOkrVWIiJ6gosboV/cBwp9NrbpQrEy4Ct892Y9Q+eTZUipvftuZmYmkpKSTB4vuwepWejzx2Hcik+Hr4MlFg+u/18I2Tj2vxDSdgpDCBFRSVe5HRS9FkGn1KCl8gR6XPkQ7y3Yjywtj4zkp0QFkcmTJ8POzs748PLykrukYpWckY1+cw7jSmwK3OzMsWBQXbjamQN6PbBuFHD4VwAS0OF7oN4QmaslIqICCWgJZe/l0JlZorHyNHpf/QCj/tqLTK1O7spKpBIVRD7++GMkJiYaHzdv3pS7pGKTka3D238dxalbiShvpcb8gXUNbUL0emDNCODYXEBSAF1mAmH95S6XiIgKw68RlG+thNbMGvWV5zAg8n2MmLcXGdkMI48rUUFEo9HA1tbW5PEyytbpMXzhcRy89gDWGjPM618HAc7WhpHbxgMRCwBJCXT9DajRS95iiYjo2XjXg1n/NdCqbRGmuIQ3Ij/F0L8O8cjIY0pUECkL9HqBD5edwrbzsdCYKfB73zBU87QzjNz3A7D/R8P/O/8EVOsmX6FERPT8PGrBrM9y6JTmaKY8iY6RX2L0ouPs9OwRxRpEUlJSEBERgYiICADA9evXERERgaioqOJcbIklhMCkdeew8sRtmCkkzHyzJupVeNg1e8Q/wNZPDf9vNYlHQoiIXhZedaDsMR9CUqKrci9CLnyHcStP80Z5DxVrEDl69ChCQ0MRGhoKABg9ejRCQ0Mxfvz44lxsifXjjiuYuz8SkgRM6x6CFlVdDCMubQFWDzP8v/5woMFI+YokIqKiV6k1pC4zAQCDzdbD9vhMfL3pgsxFlQxmxTnzpk2bMvE9tOrEbUzfegkAMKlTEDrXeHgX3ZuHgSVvGW5gV70n0OpzGaskIqJiE9ITSL0HbPk/fKL6B+/vscMvloMxpIm/3JXJim1EXoCjkQ/w4bJTAIAhTfzRp76vYUTsBeDv1wFtOhDQytAuhPeOISJ6eYWPMDwATFHNxqHN/2DNyTsyFyUv/uoVs6j7aRg8/xiydHq0DXLFh20qG0Yk3gIWdAUyEgDP2kD3eYBSJWutRET0ArScBIS8ATNJj5mqGfh76RIcjXwgd1WyYRApRonp2Rgw7wgepGahuqcdvutRAwqFBKQ9AOZ3BZJuA46VgF5LALWV3OUSEdGLoFAAnX6ECGgNCykLvyq/weR5K3HjfqrclcmCQaSY6PQC7/5zAldiU+Bqa47f3wqDhVoJZKcDC3sAcRcBWw+g9wrAsrzc5RIR0YukVEHqPhc6jzCUk1Lxk/4LjJ2zCUkZ2XJX9sIxiBSTqVsuYvelezBXGfoKcbY1N9w/Zt17wK3DgHk5Qwgp93J3Y09ERPlQW0H55lJoy1eCm/QAHyV9gff+PgRtGbtjL4NIMdh0Jhqzdl0FAHzTLQTBHg87LDs8Gzj5j6HX1O5/Ac5VZKySiIhkZ1keZn2WQqsphxqKa2hz/Rt8uf6c3FW9UAwiRSzqfho+eHiFzNuN/NApxN0wInIvsOljw/9bfw5UaCJThUREVKLY+8Ks+xwIKNDdbDeyD/2OZcduyV3VC8MgUoQytToM/+c4kjO0qOVjjw/bPjzikXgLWNLX0FdIte5AvXfkLZSIiEoW/+aQWk0EAEww+wsrVi3FhZgkeWt6QRhEitDkDRdw6lYiylmq8OMboVApFYbGqYt7A2lxgGs1oOMMQJLkLpWIiEqa8HchgrpCJekwQ/EdPv1rK5LLQONVBpEisulMNObujwQATO8eAvdyFg8bp44G7pwALOyBHn8Dakt5CyUiopJJkiB1/glax0A4SYn4JOUr/N/SYy99D+UMIkXg0XYh/2tSAc2rPLyHzOHfgJMLAUkBdJsD2PvIWCUREZV4aiuY9VoIrdoOoYorqH9xMubuuy53VcWKQeQ5Pd4uZEzrhz2nRu4DNj9snNpqEuDfTL4iiYio9CjvB7Puc6CHAj3NduHqpp9wPCpe7qqKDYPIc8qzXUjSHWBpX0CvBYJfM9xRl4iIqKACWkBqYbhT/XjlXPwy/x88SM2SuajiwSDyHPJsF6LXA6veMdxh0SUY6PQjG6cSEVGhSQ1HIbtKZ6glHf4vczo++mc/9PqXr70Ig8gzik/NwriVZwA83i5kNnBtJ2BmYWgXwnvIEBHRs5AkqLr8iGxrT3gr7qFF5HeYveea3FUVOQaRZ/Tp6jO4n5qFSi7WeL/Vw3YhsReAbRMM/2/9OeBUSb4CiYio9DO3g6rbbAhI6GG2C6e2/o2LMclyV1WkGESeweazMVh3KhpKhYSpr4dAbaYAtFnAircBbQbg3wKoPUjuMomI6GXg2wAIfxcA8LlyNj5ftBNZ2pfnfjQMIoWUlJGN8asNp2QGN66A6p7lDCN2TQZiThn6C+n8M9uFEBFRkZGaj0O2UxAcpGQMuD8NP22/JHdJRYZBpJC+2XQBd5My4etgiZEtKhoG3jgA7Pve8P+OMwBbN9nqIyKil5CZBqrX/4BOoUZzZQQe7PkVJ28myF1VkWAQKYSjkQ+w4GAUAOCrrtVgrlICGUnAyv8BQg+E9AICO8tcJRERvZScq0LZ6jMAwCfKvzF90XpkZOtkLur5MYgUUKZWh7HLDb2ndg/zRLi/o2HEpo+BhBuAnTfQboqMFRIR0Uuv7hBk+zSGpZSJ95KnYtb2C3JX9NwYRArol13XcPVeKhyt1fikfVXDwEubgYgFACSg66+Aua2sNRIR0UtOoYCq6y/IVtmihuIasO87XLpbuq+iYRApgJsP0jBz1xUAwPiOQShnqQay0oANYwwT1B8G+ITLWCEREZUZdh4w6zAVADBUsQrfLd1aqjs6YxApgC/Xn0emVo/6FRzQsfrDhqh7pwMJUYCtJ9D0Y3kLJCKiMkWq3h2ZXg1hLmXjtbs/4J8jUXKX9MwYRJ7iwNX72HQ2BkqFhAmdAiFJEhB3Bdg3wzBB28mAxlreIomIqGyRJGg6fQedZIaWyhM4uGEBYpMy5K7qmTCIPIEQAlM2GRoC9arjjSqutoAQhlMyuiwgoCVQtaPMVRIRUZnkVAlS+AgAwFj8ie82npS5oGfDIPIEW87dRcTNBFiolBjRIsAw8Nwqw71klBqg3TfsuIyIiGSjaPIBMq084CnFwfP0zzhzO1HukgqNQSQfOr3A1M0XAQADG/rB2cYcyEw2XK4LAA3fAxz8ZayQiIjKPLUVNB2+AQC8rVyH31dthhClq+Eqg0g+Vp64jcuxKbCzUOHtxhUMA3d9DSRHA/Z+QMNRstZHREQEAKjyCjL8WkIt6dAt5ntsPhMtd0WFwiCSh0ytDt9tNfTj/05Tf9hZqAx31j04yzBB+28BlYWMFRIRET0kSTDvOBVahQYNlWdxYO0fyNSWnh5XGUTy8PfBKNxOSIeLrQZ9w30NA3d8DggdUPkVoGIrWesjIiIyUd4P+vCRAIC+GQvw9/5rMhdUcAwij8nS6vHL7qsAgHdbVDTcT+b2MeDCOgAS0GK8vAUSERHlQd3oXWSo7VFBEYNbO/9AaqZW7pIKhEHkMWtO3kFsciZcbDV4vZaXYeCOLwz/hvQEnKvIVxwREVF+NDZQNTH0+D1QvwTz916UuaCCYRB5hBACv/1rOJzVv4Ef1GYK4Poe4OoOQKECmn4kc4VERET5U9YZhHQLV3hI95G4ZzYS07PlLumpGEQe8e/lOFy8mwwrtRJv1PE2dF6243PDyFp9AXtfWesjIiJ6IpU5NC0M3UwMFCswd+cZmQt6OgaRR+QcDelZx9twpczlrcDNQ4CZBdD4A5mrIyIiejpF6JtItfaBo5QEHPoFSRkl+6gIg8hDV2JTsPdKHJQKCf0b+AJ6PbBjkmFk3cGAjaus9RERERWIUgWL1p8CAPpjDZbvLdlHRRhEHlpy9CYAoFllZ3jaWwKXNgExpwGNLdBglLzFERERFYIi+DUk2FSErZSG7AOzkKXVy11SvhhEAGTr9Fhx/BYAoEfth1fKHPjZ8G/YAMCyvEyVERERPQOFAtYtxwIAXtVuxNpjJbdfEQYRANvPxyIuJQtONho0q+wE3IkAbuwFFGZAncFyl0dERFRoZsFdkKxxhZOUhOu75kGvL5n3oGEQwX+nZV6r6QkzpQI4ONMwIqgrYOchY2VERETPSKmCKnwIAKBD6krsvhQrc0F5K/NBJD41C7sv3QMAdA/zBJLuAGeWG0bWf0fGyoiIiJ6PeZ3+yFJYoIriJk7sWil3OXkq80Fk6/m70OkFAt1sUcHJGjj8G6DXAj4NAPdQucsjIiJ6dhblkBb0BgCg5u2FiE5Ml7mg3Mp8ENl42nC75LbBrkBWKnD0T8OIejwaQkREpV+5ZiOgh4SmypPYunu33OXkUqaDSHJGNvZduQ8AaBfsCpxbDWQkGHpQrdxO1tqIiIiKRPkKuOvWHACgPjkfWl3JupS3TAeR07cSkaXTw8VWg4ouNkDEQsOI0N6AQilvcUREREXEsfHbAICW2n+x5+IdmasxVaaDyPGoeABALR97ICEKiNxjGFG9h4xVERERFS1VpZZIMbOHo5SEy/tXy12OiTIdRA5cM5yWCfawA04tNgz0bQSU85axKiIioiKmVCG1clcAgM/N1UjP0slc0H/KbBDR6wUuRCcDAOr62gMnFxlGhLwhY1VERETFw7lhXwBAUxzDv6cuy1zNf8psELl6LwX3U7OgMVMgUH8ZuH8FUFkCgZ3kLo2IiKjISW4hiLUMgEbSIu7gP3KXY1Rmg8iluykAgKputrC4vNYwsMorgMZGxqqIiIiKj76aoQ2kX+w2ZGSXjNMzZTaIXLxrOC1TycXacKddAKjSQcaKiIiIipdLndcAALWl8zhyIVLeYh4qs0Hk8sMgEmbzwHBaRqEC/JvLXBUREVHxkRz8EavxhkrSIfr4BrnLAVCGg8jtBEM3tyFphwwDfBsA5rYyVkRERFT8Un1aAgBsb26XuRKDMhtE7qdkAQDc7u4yDKjUVr5iiIiIXhCX2l0AALWzj+JmXLK8xaAMB5H4tCxokAWb2KOGARVby1sQERHRC2BZIRypkiUcpGRcPXNA7nLKZhDJyNYhLUuH6tI1SPpswNoFKF9B7rKIiIiKn1KFOzbVAQBpV/bJXEwZDSIPUg2nZeqYXTIM8KoLSJKMFREREb04Os86AADr2GMyV1JGg0halhYAUEf5sGc573oyVkNERPRiOQU2BgBUzDwre3fvZTKIZGQbboEciGuGAZ61ZayGiIjoxXKoFA49JLhJDxB547qstZTJIJKp1cMWKXCC4e67cK4qb0FEREQvktoKsUpXAMD9yNOylvJCgsjMmTPh5+cHc3Nz1KpVC3v27HkRi81XplaHAOmO4YmtJ7t1JyKiMifOwg8AIO5dkLWOYg8iixcvxqhRozBu3DicOHECjRo1Qrt27RAVFVXci85XllYPH+mu4YkDr5YhIqKyJ9XaFwBglvCSn5qZPn06Bg4ciEGDBqFq1ar4/vvv4eXlhVmzZhX3ovMV6G6L/9W0NDyx9ZCtDiIiIrlItm4AAFXaPVnrKNYgkpWVhWPHjqF1a9POwlq3bo39+/fnmj4zMxNJSUkmj+LgbGOOKnYPWwlb2BfLMoiIiEqyqhV8AAA1nOSto1iDSFxcHHQ6HVxcXEyGu7i4ICYmJtf0kydPhp2dnfHh5eVVfMV51QFqvw141y++ZRAREZVQNl7BQNhAmFVtL2sdZi9iIdJjnYUJIXINA4CPP/4Yo0ePNj5PSkoqvjBS5RXDg4iIqCzyqGV4yKxYg4ijoyOUSmWuox+xsbG5jpIAgEajgUajKc6SiIiIqAQp1lMzarUatWrVwtatW02Gb926FeHh4cW5aCIiIioFiv3UzOjRo9GnTx+EhYWhfv36mD17NqKiojBkyJDiXjQRERGVcMUeRHr06IH79+9j0qRJiI6ORnBwMDZs2AAfH5/iXjQRERGVcJIQQshdRH6SkpJgZ2eHxMRE2Nrayl0OERERFUBhfr/L5L1miIiIqGRgECEiIiLZMIgQERGRbBhEiIiISDYMIkRERCQbBhEiIiKSDYMIERERyYZBhIiIiGTDIEJERESyYRAhIiIi2TCIEBERkWwYRIiIiEg2DCJEREQkGwYRIiIikg2DCBEREcmGQYSIiIhkwyBCREREsmEQISIiItkwiBAREZFsGESIiIhINgwiREREJBsGESIiIpINgwgRERHJhkGEiIiIZMMgQkRERLJhECEiIiLZMIgQERGRbBhEiIiISDYMIkRERCQbBhEiIiKSDYMIERERyYZBhIiIiGTDIEJERESyYRAhIiIi2TCIEBERkWwYRIiIiEg2DCJEREQkGwYRIiIikg2DCBEREcmGQYSIiIhkwyBCREREsmEQISIiItkwiBAREZFsGESIiIhINgwiREREJBsGESIiIpINgwgRERHJhkGEiIiIZMMgQkRERLJhECEiIiLZMIgQERGRbBhEiIiISDYMIkRERCQbBhEiIiKSDYMIERERyYZBhIiIiGTDIEJERESyYRAhIiIi2TCIEBERkWwYRIiIiEg2xRpEvvzyS4SHh8PS0hLlypUrzkURERFRKVSsQSQrKwuvv/46hg4dWpyLISIiolLKrDhn/tlnnwEA5s6dW5yLISIiolKqWINIYWVmZiIzM9P4PCkpScZqiIiIqLiVqMaqkydPhp2dnfHh5eUld0lERERUjAodRCZOnAhJkp74OHr06DMV8/HHHyMxMdH4uHnz5jPNh4iIiEqHQp+aGT58OHr27PnEaXx9fZ+pGI1GA41G80yvJSIiotKn0EHE0dERjo6OxVELERERlTHF2lg1KioKDx48QFRUFHQ6HSIiIgAAAQEBsLa2Ls5FExERUSlQrEFk/PjxmDdvnvF5aGgoAGDnzp1o2rRpcS6aiIiISgFJCCHkLiI/SUlJsLOzQ2JiImxtbeUuh4iIiAqgML/fJeryXSIiIipbGESIiIhINgwiREREJBsGESIiIpINgwgRERHJhkGEiIiIZMMgQkRERLJhECEiIiLZMIgQERGRbBhEiIiISDYMIkRERCQbBhEiIiKSDYMIERERyYZBhIiIiGTDIEJERESyYRAhIiIi2TCIEBERkWwYRIiIiEg2DCJEREQkGwYRIiIikg2DCBEREcmGQYSIiIhkwyBCREREsmEQISIiItkwiBAREZFsGESIiIhINgwiREREJBsGESIiIpINgwgRERHJhkGEiIiIZMMgQkRERLJhECEiIiLZMIgQERGRbMzkLuBJhBAAgKSkJJkrISIiooLK+d3O+R1/khIdRJKTkwEAXl5eMldCREREhZWcnAw7O7snTiOJgsQVmej1ety5cwc2NjaQJKnI55+UlAQvLy/cvHkTtra2RT7/0ozr5sm4fvLHdfNkXD9PxvWTv9K0boQQSE5Ohru7OxSKJ7cCKdFHRBQKBTw9PYt9Oba2tiX+Q5UL182Tcf3kj+vmybh+nozrJ3+lZd087UhIDjZWJSIiItkwiBAREZFsynQQ0Wg0mDBhAjQajdyllDhcN0/G9ZM/rpsn4/p5Mq6f/L2s66ZEN1YlIiKil1uZPiJCRERE8mIQISIiItkwiBAREZFsGESIiIhINgwiREREJJsyG0RmzpwJPz8/mJubo1atWtizZ4/cJZUI//77Lzp27Ah3d3dIkoRVq1bJXVKJMXnyZNSuXRs2NjZwdnZGly5dcPHiRbnLKjFmzZqF6tWrG3t9rF+/PjZu3Ch3WSXS5MmTIUkSRo0aJXcpJcLEiRMhSZLJw9XVVe6ySpTbt2+jd+/ecHBwgKWlJWrUqIFjx47JXVaRKJNBZPHixRg1ahTGjRuHEydOoFGjRmjXrh2ioqLkLk12qampCAkJwU8//SR3KSXO7t27MWzYMBw8eBBbt26FVqtF69atkZqaKndpJYKnpye+/vprHD16FEePHkXz5s3RuXNnnD17Vu7SSpQjR45g9uzZqF69utyllChBQUGIjo42Pk6fPi13SSVGfHw8GjRoAJVKhY0bN+LcuXOYNm0aypUrJ3dpRUOUQXXq1BFDhgwxGValShXx0UcfyVRRyQRArFy5Uu4ySqzY2FgBQOzevVvuUkose3t78fvvv8tdRomRnJwsKlasKLZu3SqaNGkiRo4cKXdJJcKECRNESEiI3GWUWGPHjhUNGzaUu4xiU+aOiGRlZeHYsWNo3bq1yfDWrVtj//79MlVFpVFiYiIAoHz58jJXUvLodDosWrQIqampqF+/vtzllBjDhg3DK6+8gpYtW8pdSolz+fJluLu7w8/PDz179sS1a9fkLqnEWLNmDcLCwvD666/D2dkZoaGh+O233+Quq8iUuSASFxcHnU4HFxcXk+EuLi6IiYmRqSoqbYQQGD16NBo2bIjg4GC5yykxTp8+DWtra2g0GgwZMgQrV65EYGCg3GWVCIsWLcLx48cxefJkuUspcerWrYu//voLmzdvxm+//YaYmBiEh4fj/v37cpdWIly7dg2zZs1CxYoVsXnzZgwZMgTvvvsu/vrrL7lLKxJmchcgF0mSTJ4LIXINI8rP8OHDcerUKezdu1fuUkqUypUrIyIiAgkJCVi+fDn69u2L3bt3l/kwcvPmTYwcORJbtmyBubm53OWUOO3atTP+v1q1aqhfvz78/f0xb948jB49WsbKSga9Xo+wsDB89dVXAIDQ0FCcPXsWs2bNwltvvSVzdc+vzB0RcXR0hFKpzHX0IzY2NtdREqK8jBgxAmvWrMHOnTvh6ekpdzklilqtRkBAAMLCwjB58mSEhIRgxowZcpclu2PHjiE2Nha1atWCmZkZzMzMsHv3bvzwww8wMzODTqeTu8QSxcrKCtWqVcPly5flLqVEcHNzyxXmq1at+tJcYFHmgoharUatWrWwdetWk+Fbt25FeHi4TFVRaSCEwPDhw7FixQrs2LEDfn5+cpdU4gkhkJmZKXcZsmvRogVOnz6NiIgI4yMsLAxvvvkmIiIioFQq5S6xRMnMzMT58+fh5uYmdyklQoMGDXJ1FXDp0iX4+PjIVFHRKpOnZkaPHo0+ffogLCwM9evXx+zZsxEVFYUhQ4bIXZrsUlJScOXKFePz69evIyIiAuXLl4e3t7eMlclv2LBhWLhwIVavXg0bGxvjUTU7OztYWFjIXJ38PvnkE7Rr1w5eXl5ITk7GokWLsGvXLmzatEnu0mRnY2OTqy2RlZUVHBwc2MYIwJgxY9CxY0d4e3sjNjYWX3zxBZKSktC3b1+5SysR3nvvPYSHh+Orr75C9+7dcfjwYcyePRuzZ8+Wu7SiIe9FO/L5+eefhY+Pj1Cr1aJmzZq8BPOhnTt3CgC5Hn379pW7NNnltV4AiDlz5shdWokwYMAA4z7l5OQkWrRoIbZs2SJ3WSUWL9/9T48ePYSbm5tQqVTC3d1ddO3aVZw9e1buskqUtWvXiuDgYKHRaESVKlXE7Nmz5S6pyEhCCCFTBiIiIqIyrsy1ESEiIqKSg0GEiIiIZMMgQkRERLJhECEiIiLZMIgQERGRbBhEiIiISDYMIkRERCQbBhEiIiKSDYMIERERyYZBhIiIiGTDIEJERESy+X/3oyk4sq0RxwAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title(\"Numerical solution to the brachistochrone problem\") \n", "plt.plot(*hfmOut['geodesics'][0],label=\"Fast-Marching (1st order, no factorization)\")\n", "plt.plot(*Cycloid(T),label=\"Analytic\")\n", "plt.axis('equal'); plt.legend();" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.493983Z", "iopub.status.busy": "2024-04-30T09:14:33.493882Z", "iopub.status.idle": "2024-04-30T09:14:33.495800Z", "shell.execute_reply": "2024-04-30T09:14:33.495551Z" } }, "outputs": [], "source": [ "hfmIn2 = hfmIn.copy()\n", "hfmIn2.update({\n", " # Improve accuracy\n", " 'order':2,\n", " 'factoringRadius':20,\n", " \n", " # Export relevant data\n", " 'exportGeodesicFlow':True,\n", " 'exportValues':True,\n", "})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Introducing source factorization and a higher order method yields a more accurate trajectory." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.497202Z", "iopub.status.busy": "2024-04-30T09:14:33.497101Z", "iopub.status.idle": "2024-04-30T09:14:33.517102Z", "shell.execute_reply": "2024-04-30T09:14:33.516762Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field seedRadius defaults to 2\n", "Field factoringPointChoice defaults to Seed\n", "Field exportFactoring defaults to 0\n", "Fast marching solver completed in 0.005468 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 8.45\n" ] } ], "source": [ "hfmOut = hfmIn2.Run()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.518688Z", "iopub.status.busy": "2024-04-30T09:14:33.518568Z", "iopub.status.idle": "2024-04-30T09:14:33.586870Z", "shell.execute_reply": "2024-04-30T09:14:33.586593Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title(\"Numerical solution to the brachistochrone problem\") \n", "plt.plot(*Cycloid(T),label=\"Analytic\")\n", "plt.plot(*hfmOut['geodesics'][0],label=\"Fast-Marching (2st order, factorization)\")\n", "plt.axis('equal'); plt.legend();" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.588447Z", "iopub.status.busy": "2024-04-30T09:14:33.588334Z", "iopub.status.idle": "2024-04-30T09:14:33.652282Z", "shell.execute_reply": "2024-04-30T09:14:33.651995Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title('Traveltime using the Brachistochrone')\n", "plt.contourf(X,Z,hfmOut['values'])\n", "plt.axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.3 Solving Hamilton's equations of motion\n", "\n", "Recall that the Hamiltonian is defined as the half square dual metric. For the brachistochrone, it reads\n", "$$\n", " H(q,p) := \\frac z 2 \\|p\\|^2,\n", "$$\n", "where $q=(x,z)$ is the position, and $p$ is the momentum. In this simple case, the velocity and momentum at a point $q=(x,z)$ are related by the equation\n", "$$\n", " v = \\frac {\\partial H}{\\partial p} = z p.\n", "$$\n", "\n", "For generality, we illustrate this experiment with both the analytic expression of the Hamiltonian, and an interpolated metric." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.653837Z", "iopub.status.busy": "2024-04-30T09:14:33.653731Z", "iopub.status.idle": "2024-04-30T09:14:33.655627Z", "shell.execute_reply": "2024-04-30T09:14:33.655378Z" } }, "outputs": [], "source": [ "def Brach_A_(q,p):\n", " \"\"\"Analytic Hamiltonian for the brachistochrone problem\"\"\"\n", " return 0.5 * q[1] * (p**2).sum(axis=0)\n", "Brach_A = GenericHamiltonian(Brach_A_)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.657067Z", "iopub.status.busy": "2024-04-30T09:14:33.656971Z", "iopub.status.idle": "2024-04-30T09:14:33.661341Z", "shell.execute_reply": "2024-04-30T09:14:33.661088Z" } }, "outputs": [], "source": [ "Brach_I = MetricHamiltonian(Metrics.Isotropic(hfmIn['cost']),grid=hfmIn.Grid(),order=3)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.662878Z", "iopub.status.busy": "2024-04-30T09:14:33.662792Z", "iopub.status.idle": "2024-04-30T09:14:33.665397Z", "shell.execute_reply": "2024-04-30T09:14:33.665140Z" } }, "outputs": [ { "data": { "text/plain": [ "array([0.01993342, 0.19866933])" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Cycloid(ad.Dense.identity(constant=0.2)).gradient(0)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.666881Z", "iopub.status.busy": "2024-04-30T09:14:33.666786Z", "iopub.status.idle": "2024-04-30T09:14:33.669962Z", "shell.execute_reply": "2024-04-30T09:14:33.669699Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Exact hamiltonian flow: (array([0.01993342, 0.19866933]), array([ -0. , -50.16700053]))\n", "Interpolated hamiltonian flow: (array([0.01727088, 0.17213274]), array([ -0. , -54.81308574]))\n" ] } ], "source": [ "t_ad = ad.Dense.identity(constant=0.2)\n", "Cyc_ad = Cycloid(t_ad)\n", "q0 = Cyc_ad.value\n", "v0 = Cyc_ad.gradient(0) # Initial velocity\n", "p0 = v0/q0[1] # Initial impulsion\n", "\n", "print(f\"Exact hamiltonian flow: {Brach_A.flow(q0,p0)}\")\n", "print(f\"Interpolated hamiltonian flow: {Brach_I.flow(q0,p0)}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When using external ODE solvers, which ignore the Hamiltonian structure, one often needs a function which takes as input the concatenated position and impulsion, and returns their concatenated derivatives - the Hamiltonian flow.\n", "This is the purpose of the `.flow_cat` member of the `Hamiltonian` class." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.671438Z", "iopub.status.busy": "2024-04-30T09:14:33.671352Z", "iopub.status.idle": "2024-04-30T09:14:33.692781Z", "shell.execute_reply": "2024-04-30T09:14:33.692550Z" } }, "outputs": [], "source": [ "QP_A,dict_A = scipy.integrate.odeint(Brach_A.flow_cat,np.concatenate((q0,p0)),Tint,full_output=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The computation is a bit longer with the interpolated hamiltonian. Indeed, the `odeint` routine introduces substantial refinement, due to the lesser smoothness of the interpolated flow." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:33.694238Z", "iopub.status.busy": "2024-04-30T09:14:33.694151Z", "iopub.status.idle": "2024-04-30T09:14:34.010233Z", "shell.execute_reply": "2024-04-30T09:14:34.009959Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 309 ms, sys: 17.6 ms, total: 326 ms\n", "Wall time: 314 ms\n" ] } ], "source": [ "%%time\n", "QP_I,dict_I = scipy.integrate.odeint(Brach_I.flow_cat,np.concatenate((q0,p0)),Tint,full_output=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The ODE with an exact hamiltonian is, clearly, accurate to a very high order. In contrast, the spline interpolation introduces a slight deviation." ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:34.011783Z", "iopub.status.busy": "2024-04-30T09:14:34.011675Z", "iopub.status.idle": "2024-04-30T09:14:34.071371Z", "shell.execute_reply": "2024-04-30T09:14:34.071099Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(*Cycloid(T),label=\"Analytic\")\n", "plt.plot(*QP_A[:,:2].T,label=\"ODE, exact hamiltonian\")\n", "plt.plot(*QP_I[:,:2].T,label=\"ODE, interpolated hamiltonian\")\n", "plt.axis('equal'); plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Hamiltonian class provides some ODE integration schemes, in particular semi-implicit symplectic schemes. They do take into account the *Hamiltonian* structure, and may therefore offer an interesting alternative to `odeint` in some cases." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:34.072927Z", "iopub.status.busy": "2024-04-30T09:14:34.072812Z", "iopub.status.idle": "2024-04-30T09:14:34.431855Z", "shell.execute_reply": "2024-04-30T09:14:34.431593Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 352 ms, sys: 15.3 ms, total: 367 ms\n", "Wall time: 357 ms\n" ] } ], "source": [ "%%time\n", "Ttot = Tint[-1]-Tint[0]\n", "# Semi-implicit Euler (symplectic, first order scheme)\n", "Q_Ep,_,_ = Brach_I.integrate(q0,p0,scheme='Euler-p',T=Ttot,niter=3*len(Tint),path=True)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:34.433217Z", "iopub.status.busy": "2024-04-30T09:14:34.433136Z", "iopub.status.idle": "2024-04-30T09:14:34.987097Z", "shell.execute_reply": "2024-04-30T09:14:34.986827Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 546 ms, sys: 9.48 ms, total: 555 ms\n", "Wall time: 552 ms\n" ] } ], "source": [ "%%time\n", "# Semi-implicit Verlet (symplectic, second order scheme)\n", "Q_Vp,_,_ = Brach_I.integrate(q0,p0,scheme='Verlet-p',T=Ttot,niter=3*len(Tint),path=True)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:34.988647Z", "iopub.status.busy": "2024-04-30T09:14:34.988555Z", "iopub.status.idle": "2024-04-30T09:14:35.228903Z", "shell.execute_reply": "2024-04-30T09:14:35.228612Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 235 ms, sys: 11.3 ms, total: 246 ms\n", "Wall time: 238 ms\n" ] } ], "source": [ "%%time\n", "# Runge-Kutta (non-symplectic, fourth order scheme)\n", "Q_RK4,_,_ = Brach_I.integrate(q0,p0,scheme='Runge-Kutta-4',T=Ttot,niter=3*len(Tint),path=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here, the Verlet scheme seems to be the most accurate." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:35.230460Z", "iopub.status.busy": "2024-04-30T09:14:35.230377Z", "iopub.status.idle": "2024-04-30T09:14:35.292902Z", "shell.execute_reply": "2024-04-30T09:14:35.292646Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(*Cycloid(T),label=\"Analytic\")\n", "plt.plot(*Q_Ep,label=\"Euler semi-impl\")\n", "plt.plot(*Q_Vp,label=\"Verlet semi-impl\")\n", "plt.plot(*Q_RK4,label=\"Runge-Kutta-4 explicit\")\n", "\n", "plt.axis('equal'); plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.4 Initial momentum from the PDE solution\n", "\n", "As discussed in the theoretical section, we use the gradient of the squared distance function as a proxy for final momentum. Since Riemannian metrics are symmetric, we can solve forward in time, only reversing the momentum. " ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:35.294515Z", "iopub.status.busy": "2024-04-30T09:14:35.294399Z", "iopub.status.idle": "2024-04-30T09:14:35.298511Z", "shell.execute_reply": "2024-04-30T09:14:35.298267Z" } }, "outputs": [], "source": [ "energy_i,impulsion_i = energy_impulsion_i(hfmIn2,hfmOut,order=3)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:35.299986Z", "iopub.status.busy": "2024-04-30T09:14:35.299903Z", "iopub.status.idle": "2024-04-30T09:14:35.313322Z", "shell.execute_reply": "2024-04-30T09:14:35.313085Z" } }, "outputs": [], "source": [ "q0 = np.array([3.,1.])\n", "p0 = -impulsion_i(q0)\n", "QP = scipy.integrate.odeint(Brach_A.flow_cat,np.concatenate((q0,p0)),np.linspace(0,1.))" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:35.314713Z", "iopub.status.busy": "2024-04-30T09:14:35.314636Z", "iopub.status.idle": "2024-04-30T09:14:35.360621Z", "shell.execute_reply": "2024-04-30T09:14:35.360349Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(*QP[:,:2].T)\n", "plt.axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function `scipy.integrate.odeint` requires flattened inputs. If independent components of the inputs are correctly specified, by setting the `shape_free` parameter of the hamiltonian, then one can integrate multiple geodesics simultaneously.\n", "\n", "" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:35.362342Z", "iopub.status.busy": "2024-04-30T09:14:35.362221Z", "iopub.status.idle": "2024-04-30T09:14:35.385214Z", "shell.execute_reply": "2024-04-30T09:14:35.384950Z" } }, "outputs": [], "source": [ "np.random.seed(42); nSamples = 10\n", "q0 = np.array([np.random.uniform(0.,2.*np.pi,nSamples),np.random.uniform(0.2,2,nSamples)])\n", "p0 = -impulsion_i(q0)\n", "T = np.linspace(0,1)\n", "Brach_A.shape_free = (2,) # Number of independent components\n", "\n", "#Flatten position and impulsion, as required by odeint. Note the args argument, to inform about internal reshaping.\n", "QP = scipy.integrate.odeint(Brach_A.flow_cat,np.concatenate((q0,p0),axis=0).flatten(),T)\n", "#Expand back the solution\n", "Q = QP[:,:2*nSamples].reshape((len(T),2,nSamples))\n", "P = QP[:,2*nSamples:].reshape((len(T),2,nSamples))" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:35.386706Z", "iopub.status.busy": "2024-04-30T09:14:35.386618Z", "iopub.status.idle": "2024-04-30T09:14:35.452850Z", "shell.execute_reply": "2024-04-30T09:14:35.452559Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title(\"Geodesics computed from Hamilton's equations,\\n with numerically computed initial impulsion.\")\n", "plt.axis('equal'); add_patches(hfmIn)\n", "for i in range(nSamples):\n", " plt.plot(*Q[:,:,i].T)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that one of the geodesics displayed above does *not* correctly reach the seed point. Indeed, that the exact geodesic reaching this tip for this model goes outside of the computational domain. Therefore the numerical geodesic is perturbed by the presence of the domain boundary, which acts as an obstacle. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.5 The geodesic flow\n", "\n", "As discussed in the theoretical section, we integrate the geodesic flow to extract the geodesic." ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:35.454436Z", "iopub.status.busy": "2024-04-30T09:14:35.454327Z", "iopub.status.idle": "2024-04-30T09:14:35.462861Z", "shell.execute_reply": "2024-04-30T09:14:35.462610Z" } }, "outputs": [], "source": [ "value_i,flow_i = value_flow_i(hfmIn2,hfmOut,order=3)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:35.464361Z", "iopub.status.busy": "2024-04-30T09:14:35.464275Z", "iopub.status.idle": "2024-04-30T09:14:35.553688Z", "shell.execute_reply": "2024-04-30T09:14:35.553416Z" } }, "outputs": [], "source": [ "q0 = [3.,1.]\n", "T = np.linspace(0,value_i(q0))\n", "Q = scipy.integrate.odeint(flow_i,q0,T[:-1],args=(-1,)) # dropping last time step, to avoid leaving domain" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:35.555296Z", "iopub.status.busy": "2024-04-30T09:14:35.555201Z", "iopub.status.idle": "2024-04-30T09:14:35.602289Z", "shell.execute_reply": "2024-04-30T09:14:35.602036Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(*Q.T)\n", "plt.axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is often more convenient to compute several geodesics simulatenously. In Python, and using tensor based programming, this may also be more computationally efficient. However, one needs for that purpose some flattening and reshaping utilities, given the constraints of the `scipy.intergrate.odeint` routine." ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:35.603880Z", "iopub.status.busy": "2024-04-30T09:14:35.603765Z", "iopub.status.idle": "2024-04-30T09:14:35.605441Z", "shell.execute_reply": "2024-04-30T09:14:35.605229Z" } }, "outputs": [], "source": [ "flow_r = reshape_input_flatten_output(flow_i,2) # Flow reshaped" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:35.606886Z", "iopub.status.busy": "2024-04-30T09:14:35.606787Z", "iopub.status.idle": "2024-04-30T09:14:35.840016Z", "shell.execute_reply": "2024-04-30T09:14:35.839642Z" } }, "outputs": [], "source": [ "np.random.seed(42); nSamples = 10\n", "q0 = np.array([np.random.uniform(0.,2.*np.pi,nSamples),np.random.uniform(0.2,2,nSamples)])\n", "T = np.linspace(0,1)\n", "Q = scipy.integrate.odeint(flow_r,q0.flatten(),T[:-1],args=(-value_i(q0),)) #Dropping last time step to avoid leaving domain" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "All the computed geodesics end at the desired endpoint, including the one perturbed by the presence of the domain boundary. This is in contrast with the approach based on geodesic shooting using Hamilton's equations of motion, which fails in such cases, see the previous subsection." ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:35.841730Z", "iopub.status.busy": "2024-04-30T09:14:35.841644Z", "iopub.status.idle": "2024-04-30T09:14:35.904340Z", "shell.execute_reply": "2024-04-30T09:14:35.904060Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title(\"Geodesics backtracked from the geodesic flow.\")\n", "plt.axis('equal'); add_patches(hfmIn)\n", "for i in range(nSamples):\n", " plt.plot(Q[:,i],Q[:,i+nSamples])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Riemannian metrics, and the fastest slide on a landscape\n", "\n", "We consider a variant of the Brachistochrone problem, where the purpose is to build the fastest slide between two given points *on a given landscape* (two dimensional). Again, we neglect friction.\n", "\n", "The total energy of a point of mass $m$, at height $h$, velocity $\\mathbf{v}$, in a gravitational field g, as before\n", "$$\n", " E = m g h + \\frac 1 2 m \\|\\mathbf{v}\\|^2\n", "$$\n", "The total energy is conserved along the trajectory (no friction assumption), and the object velocity is therefore determined by its height. Denoting by $\\mathbf{z}$ the vertical coordinate, possibly shifted, inverted and rescaled w.r.t. the height $h$, one finds that\n", "$$\n", " \\frac{\\|\\mathbf{v}\\|^2}{\\mathbf{z}}\n", "$$\n", "is constant and positive along the trajectory. In particular, positions for which $z\\leq 0$ are not accessible. (These positions are too elevated, a.k.a have an excessive potential energy to be accessed. Note that the vertical axis was reversed.)\n", "\n", "Let us introduce a two dimensional domain $\\Omega$, and a landscape function $z : \\Omega \\mapsto R$. \n", "The vertical coordinate $\\mathbf{z}$ and three dimensional velocity $\\mathbf{v}$ are determined by the planar position $q \\in \\Omega$ and velocity $v \\in R^2$ by \n", "$$\n", " \\mathbf{z} = z(q), \\qquad \\mathbf{v} = \\begin{pmatrix} v \\\\ <\\nabla z(q),v> \\end{pmatrix}.\n", "$$\n", "\n", "As a result, the (squared) Riemannian metric underlying the brachistochrone on a landscape problem reads\n", "$$\n", " F_q(v)^2 = \\frac{\\|\\mathbf{v}\\|^2}{\\mathbf{z}} = \\frac{ \\|v\\|^2 + <\\nabla z(q),v>^2}{z(q)},\n", "$$\n", "in matrix form\n", "$$\n", " M(q) := \\frac{\\mathrm{Id} + \\nabla z(q) \\nabla z(q)^T}{z(q)}.\n", "$$\n", "Note that the hamiltonian is defined as the half-squared dual metric.\n", "\n", "\n", "**Implementation note.** We use here an analytic height map, and compute its gradient via automatic differentiation.\n", "Alternatively, one can estimate the gradient using finite differences, see the closely relateted example in the [notebook on Riemannian metrics](Riemannian.ipynb)." ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:35.905920Z", "iopub.status.busy": "2024-04-30T09:14:35.905810Z", "iopub.status.idle": "2024-04-30T09:14:35.908803Z", "shell.execute_reply": "2024-04-30T09:14:35.908532Z" } }, "outputs": [], "source": [ "def Slide_Z(q):\n", " \"\"\"(Opposite of the) landscape elevation where the slide is built\"\"\"\n", " return 2+2*np.sin(q[0])*np.sin(q[1])\n", "\n", "def Slide_M(q,ret_walls=False,ztol=1e-2,z0=0) : \n", " \"\"\"Riemannian metric of the slide on landscape problem, in matrix form. (Analytic expression)\"\"\"\n", " # Differentiate elevation\n", " q_ad = ad.Dense.identity(constant=q,shape_free=(2,))\n", " z_ad = z0+Slide_Z(q_ad)\n", " \n", " # Deal with inaccessible regions\n", " if ztol is not None:\n", " walls = z_ad<=ztol\n", " z_ad[walls]=1. # Dummy non-zero value\n", " \n", " # Produce riemannian tensor\n", " Id = fd.as_field(np.eye(2),q.shape[1:])\n", " M = ( Id + lp.outer_self(z_ad.gradient()) ) / z_ad.value\n", " \n", " return (M,walls) if ret_walls else M\n", "\n", "def Slide_A_(q,p,**kwargs):\n", " \"\"\"Hamiltonian of the slide on landscape problem. (Analytic expression).\"\"\"\n", " return lp.dot_VV(p, lp.solve_AV(Slide_M(q,**kwargs),p)) / 2." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.1 Numerical solution using the fast-marching method\n", "\n", "The computational domain is $[-2\\pi,2\\pi]^2$." ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:35.910226Z", "iopub.status.busy": "2024-04-30T09:14:35.910125Z", "iopub.status.idle": "2024-04-30T09:14:35.963945Z", "shell.execute_reply": "2024-04-30T09:14:35.963628Z" } }, "outputs": [], "source": [ "hfmIn = Eikonal.dictIn({\n", " 'model':'Riemann2',\n", " 'arrayOrdering':'RowMajor',\n", " 'seeds': [(0,2)],\n", "})\n", "\n", "hfmIn.SetRect([[-2*np.pi,2*np.pi],[-2*np.pi,2*np.pi]],dimx=800)\n", "grid = hfmIn.Grid()\n", "hfmIn.SetUniformTips((6,6)) # Regularly spaced tips\n", "\n", "metric_tensors,hfmIn['walls'] = Slide_M(grid,ret_walls=True,z0=-0.5)\n", "hfmIn['metric'] = Metrics.Riemann(metric_tensors)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Riemannian metric is (not so strongly) anisotropic. See below largest length distortion, at any given point, depending on the direction." ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:35.965650Z", "iopub.status.busy": "2024-04-30T09:14:35.965565Z", "iopub.status.idle": "2024-04-30T09:14:36.057178Z", "shell.execute_reply": "2024-04-30T09:14:36.056890Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Largest local anisotropic length distortion : 2.2359576383209347\n" ] } ], "source": [ "print(f\"Largest local anisotropic length distortion : {np.max(hfmIn['metric'].anisotropy())}\")" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:36.058640Z", "iopub.status.busy": "2024-04-30T09:14:36.058561Z", "iopub.status.idle": "2024-04-30T09:14:36.706498Z", "shell.execute_reply": "2024-04-30T09:14:36.706118Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.218663 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 8.45\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:36.708059Z", "iopub.status.busy": "2024-04-30T09:14:36.707967Z", "iopub.status.idle": "2024-04-30T09:14:36.834743Z", "shell.execute_reply": "2024-04-30T09:14:36.834458Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(4,4)); plt.axis('equal')\n", "plt.title(\"Numerical solution to the \\n brachistochrone on a landscape problem.\") \n", "plt.contourf(*grid,Slide_Z(grid),cmap='Greys')\n", "for geo in hfmOut['geodesics']: plt.plot(*geo)" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:36.836352Z", "iopub.status.busy": "2024-04-30T09:14:36.836235Z", "iopub.status.idle": "2024-04-30T09:14:36.937402Z", "shell.execute_reply": "2024-04-30T09:14:36.937047Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(4,4)); plt.axis('equal')\n", "plt.title('Accessible region (white) for the \\n brachistochrone on a landscape problem')\n", "plt.contourf(*grid,hfmIn['walls'],cmap='Greys');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As usual, one can improve the accuracy of the fast marching method by using source factorization, a second order accurate scheme, and spreading the seed over a few pixels." ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:36.939033Z", "iopub.status.busy": "2024-04-30T09:14:36.938915Z", "iopub.status.idle": "2024-04-30T09:14:36.941216Z", "shell.execute_reply": "2024-04-30T09:14:36.940811Z" } }, "outputs": [], "source": [ "hfmIn2 = hfmIn.copy()\n", "hfmIn2.update({\n", " # Improve accuracy\n", " 'order':2,\n", " 'factoringRadius':30,\n", " \n", " # Export relevant data\n", " 'exportGeodesicFlow':True,\n", " 'exportValues':True,\n", "})" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:36.942919Z", "iopub.status.busy": "2024-04-30T09:14:36.942779Z", "iopub.status.idle": "2024-04-30T09:14:37.696554Z", "shell.execute_reply": "2024-04-30T09:14:37.696221Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field seedRadius defaults to 2\n", "Field factoringPointChoice defaults to Seed\n", "Field exportFactoring defaults to 0\n", "Fast marching solver completed in 0.247063 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 8.45\n" ] } ], "source": [ "hfmOut = hfmIn2.Run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.2 Integrating the flow\n", "\n", "As before, integrating the flow the most robust approach to computing the minimizing geodesics - when the eikonal equation has been solved.\n", "\n", "Spline nterpolation in degree >1 requires that the array contains neither infinite nor nan values." ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:37.698271Z", "iopub.status.busy": "2024-04-30T09:14:37.698153Z", "iopub.status.idle": "2024-04-30T09:14:37.838566Z", "shell.execute_reply": "2024-04-30T09:14:37.838253Z" } }, "outputs": [], "source": [ "hfmOut['values'] [hfmIn['walls'] ] = 0. # Insert dummy values in inaccessible places, to allow interpolation\n", "value_i,flow_i = value_flow_i(hfmIn2,hfmOut,order=3)\n", "\n", "flow_r = reshape_input_flatten_output(flow_i,2) # Flow reshaped" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We only consider the tips which lie in the accessible regions. Numerical integration with scipy tends to be a bit long, up to a minute, possibly due to the lack of smoothness of the interpolated flow." ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:37.840319Z", "iopub.status.busy": "2024-04-30T09:14:37.840235Z", "iopub.status.idle": "2024-04-30T09:14:38.407114Z", "shell.execute_reply": "2024-04-30T09:14:38.406809Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 560 ms, sys: 842 µs, total: 561 ms\n", "Wall time: 564 ms\n" ] } ], "source": [ "%%time\n", "walls = Interp(grid,hfmIn['walls'],order=1)\n", "q0 = hfmIn['tips'].copy().T\n", "q0 = q0[:,walls(q0)==0.]\n", "nSamples=q0.shape[1]\n", "\n", "T = np.linspace(0,1)\n", "Q = scipy.integrate.odeint(flow_r,q0.flatten(),T[:-1],args=(-value_i(q0),)) # Dropping last time step" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:38.408626Z", "iopub.status.busy": "2024-04-30T09:14:38.408531Z", "iopub.status.idle": "2024-04-30T09:14:38.481358Z", "shell.execute_reply": "2024-04-30T09:14:38.481087Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title(\"Geodesics backtracked from the geodesic flow.\")\n", "plt.axis('equal'); add_patches(hfmIn)\n", "for i in range(nSamples):\n", " plt.plot(Q[:,i],Q[:,i+nSamples])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.3 Geodesic shooting\n", "\n", "**Using the analytic hamiltonian** Let us introduce the analytic Hamiltonian, as well as the energy of the paths and its gradient the impulsion." ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:38.482950Z", "iopub.status.busy": "2024-04-30T09:14:38.482844Z", "iopub.status.idle": "2024-04-30T09:14:38.484786Z", "shell.execute_reply": "2024-04-30T09:14:38.484551Z" } }, "outputs": [], "source": [ "Slide_A = GenericHamiltonian(lambda q,p:Slide_A_(q,p,z0=-0.5,ztol=None),\n", " shape_free=(2,), disassociate_ad=True)" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:38.486209Z", "iopub.status.busy": "2024-04-30T09:14:38.486103Z", "iopub.status.idle": "2024-04-30T09:14:38.529943Z", "shell.execute_reply": "2024-04-30T09:14:38.529625Z" } }, "outputs": [], "source": [ "energy_i,impulsion_i = energy_impulsion_i(hfmIn2,hfmOut,order=3)" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:38.531656Z", "iopub.status.busy": "2024-04-30T09:14:38.531568Z", "iopub.status.idle": "2024-04-30T09:14:39.087185Z", "shell.execute_reply": "2024-04-30T09:14:39.086868Z" } }, "outputs": [], "source": [ "p0 = -impulsion_i(q0)\n", "T = np.linspace(0,1)\n", "\n", "QP = scipy.integrate.odeint(Slide_A.flow_cat,np.concatenate((q0,p0),axis=0).flatten(),T)\n", "Q = QP[:,:2*nSamples].reshape((len(T),2,nSamples))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Most geodesics obtained from geodesic shooting reach the initial seed, but not all. Long paths that come close to the inaccessibe regions raise most difficulties." ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:39.088941Z", "iopub.status.busy": "2024-04-30T09:14:39.088852Z", "iopub.status.idle": "2024-04-30T09:14:39.163757Z", "shell.execute_reply": "2024-04-30T09:14:39.163489Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title(\"Geodesics computed from Hamilton's equations,\\n with numerically computed initial impulsion.\")\n", "plt.axis('equal'); add_patches(hfmIn)\n", "for i in range(nSamples):\n", " plt.plot(*Q[:,:,i].T)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Interpolated hamiltonian.** Using the interpolated metric does note work so well in the above example. This might be due to the discontinuities in the metric at the boundaries of the inaccessible, which pollute the interpolation.\n", "\n", "For this reason, we modify the problem using a positive value of $z_0$, so that all points in the domain are accessible." ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:39.165398Z", "iopub.status.busy": "2024-04-30T09:14:39.165279Z", "iopub.status.idle": "2024-04-30T09:14:51.834694Z", "shell.execute_reply": "2024-04-30T09:14:51.834285Z" } }, "outputs": [], "source": [ "metric_tensors = Slide_M(grid,z0=1)\n", "\n", "hfmIn2['metric'] = Metrics.Riemann(metric_tensors)\n", "hfmIn2.pop('walls',None);\n", "\n", "Slide_I = MetricHamiltonian(hfmIn2['metric'],grid=grid)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The metric anisotropy is unchanged, but it is now everywhere defined, and there are no obstacles." ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:51.836488Z", "iopub.status.busy": "2024-04-30T09:14:51.836383Z", "iopub.status.idle": "2024-04-30T09:14:51.930989Z", "shell.execute_reply": "2024-04-30T09:14:51.930705Z" } }, "outputs": [ { "data": { "text/plain": [ "2.2359576383209347" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.max(hfmIn2['metric'].anisotropy())" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:51.932672Z", "iopub.status.busy": "2024-04-30T09:14:51.932549Z", "iopub.status.idle": "2024-04-30T09:14:52.675990Z", "shell.execute_reply": "2024-04-30T09:14:52.675613Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field seedRadius defaults to 2\n", "Field factoringPointChoice defaults to Seed\n", "Field exportFactoring defaults to 0\n", "Fast marching solver completed in 0.277328 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 8.45\n" ] } ], "source": [ "hfmOut = hfmIn2.Run()" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:52.677611Z", "iopub.status.busy": "2024-04-30T09:14:52.677492Z", "iopub.status.idle": "2024-04-30T09:14:52.833614Z", "shell.execute_reply": "2024-04-30T09:14:52.833134Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(4,4)); plt.axis('equal')\n", "plt.title(\"Numerical solution to the \\n brachistochrone on a landscape problem.\") \n", "plt.contourf(*grid,Slide_Z(grid),cmap='Greys')\n", "for geo in hfmOut['geodesics']: plt.plot(*geo)" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:52.836042Z", "iopub.status.busy": "2024-04-30T09:14:52.835853Z", "iopub.status.idle": "2024-04-30T09:14:52.896740Z", "shell.execute_reply": "2024-04-30T09:14:52.896372Z" } }, "outputs": [], "source": [ "energy_i,impulsion_i = energy_impulsion_i(hfmIn2,hfmOut,order=3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use the standard Runge-Kutta fourth order to solve Hamilton's equations of motion. Indeed, strangely, `scipy.odeint` produces impredictable and often very long run times on this test case." ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:52.898957Z", "iopub.status.busy": "2024-04-30T09:14:52.898778Z", "iopub.status.idle": "2024-04-30T09:14:53.160682Z", "shell.execute_reply": "2024-04-30T09:14:53.160375Z" } }, "outputs": [], "source": [ "q0 = hfmIn['tips'].copy().T\n", "p0 = -impulsion_i(q0)\n", "nSamples=q0.shape[1]\n", "\n", "# Runge-Kutta (non-symplectic, fourth order scheme)\n", "Q_RK4,_,_ = Slide_I.integrate(q0,p0,scheme='Runge-Kutta-4',T=1,niter=200,path=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As before, more geodesics reach the initial seed. Yet some of the longest ones, going through regions where the metric varies strongly, are misled. For those, a more accurate (final) impulsion would be needed to meet the seed, or a refinement using an optimization method of this numerical approximation." ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:53.162409Z", "iopub.status.busy": "2024-04-30T09:14:53.162322Z", "iopub.status.idle": "2024-04-30T09:14:53.164892Z", "shell.execute_reply": "2024-04-30T09:14:53.164612Z" } }, "outputs": [ { "data": { "text/plain": [ "(2, 36, 201)" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Q_RK4.shape" ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:14:53.166378Z", "iopub.status.busy": "2024-04-30T09:14:53.166261Z", "iopub.status.idle": "2024-04-30T09:14:53.296953Z", "shell.execute_reply": "2024-04-30T09:14:53.296656Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title(\"Geodesics computed from Hamilton's equations,\\n with numerically computed initial impulsion.\")\n", "plt.axis('equal'); add_patches(hfmIn)\n", "for i in range(nSamples):\n", " plt.plot(*Q_RK4[:,i])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Format de la Cellule Texte Brut", "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": "3.10.8" }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }