{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# High Order Taylor Maps II\n", "(by Dario Izzo)\n", "\n", "In this notebook we consider the system of differential equations $\\dot{\\mathbf y} = \\mathbf f(\\mathbf y)$:\n", "\n", "$$\n", "\\begin{array}{l}\n", "\\dot r = v_r \\\\\n", "\\dot v_r = - \\frac 1{r^2} + r v_\\theta^2\\\\\n", "\\dot \\theta = v_\\theta \\\\\n", "\\dot v_\\theta = -2 \\frac{v_\\theta v_r}{r} + T\n", "\\end{array}\n", "$$\n", "\n", "which describe, in non dimensional units, the motion of a mass point object around some primary body perturbed by a fixed thrust $T$ acting in the direction perpendicular to the radius vector.\n", "We show how we can build a high order Taylor map (HOTM, indicated with $\\mathcal M$) representing the final state of the system at the time $T$ as a function of the initial conditions. \n", "\n", "In other words, we build a polinomial representation of the relation $\\mathbf y(T) = \\mathbf f(\\mathbf y(0), T)$. Writing the initial conditions as $\\mathbf y(0) = \\overline {\\mathbf y}(0) + \\mathbf {dy}$, our HOTM will be written as:\n", "\n", "$$\n", "\\mathbf y(T) = \\mathcal M(\\mathbf {dy})\n", "$$\n", "\n", "and will be valid in a neighbourhood of $\\overline {\\mathbf y}(0)$." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# We use numpy for arrays and pyaudi for the differential algebra machinery\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline \n", "from pyaudi import gdual_double as gdual\n", "from pyaudi import sin, cos" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# This is a simple Runga Kutta fourth order numerical integrator with fixed step.\n", "# It is programmed to work both with floats and gduals. It infers the type from the initial conditions\n", "def rk4(f, t0, y0, h, N):\n", " t = t0 + np.arange(N+1)*h\n", " y = np.array([[type(y0[0])] * np.size(y0)] * (N+1))\n", " y[0] = y0\n", " for n in range(N):\n", " xi1 = y[n]\n", " f1 = f(t[n], xi1)\n", " xi2 = y[n] + (h/2.)*f1\n", " f2 = f(t[n+1], xi2)\n", " xi3 = y[n] + (h/2.)*f2\n", " f3 = f(t[n+1], xi3)\n", " xi4 = y[n] + h*f3\n", " f4 = f(t[n+1], xi4)\n", " y[n+1] = y[n] + (h/6.)*(f1 + 2*f2 + 2*f3 + f4)\n", " return y" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# The Equations of Motion of Keplerian motion in non dimensional spherical coordinates.\n", "T = 1e-3\n", "def eom_kep_polar(t,y):\n", " return np.array([y[1], - 1 / y[0] / y[0] + y[0] * y[3]*y[3], y[3], -2*y[3]*y[1]/y[0] - T])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### We perform the numerical integration using floats (the standard way)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Fixed step size\n", "step = 0.01\n", "# Number of steps\n", "n_steps = 30000\n", "# The initial conditions\n", "ic = [1.,0.1,0.,-1.]\n", "# The intitial time (irrelevant as the system is autonomous)\n", "it = 0.\n", "y = rk4(eom_kep_polar, it, ic, step, n_steps)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0,0.5,'y')" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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POKbhnS6Pl12NJjbuMbK2oo0NlW1YnR6EgJFJYczNj2dufjwjk8KO2TXa23vj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\njlQZrFzy33UAvHvj9CExmmi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ul2fAcwWGIhqhZGR7paLwM2NCmJQeyc4GE8WNJsamhHPH\nmblsqGzj+VWV6Pz9uHt+HldOSeOtTTX89bNd+AnBHxaO4JKJKQgh+K6khbuXbsPq8PCPS8bsF6fv\n9Ur+ubyUp1dWMHt4LE9dMb5Xc+OXOxr55ZuFTExXsoL7c+/WGm1c8NQa9EFaPvn1rAFpf7q72cz8\nf/3AtTMz+cO5I4778Y4lQ0UhzAYswKsnikLwen0jgSYTX94++6AF1k4UWkx2zn9qDQL46Fczj9jH\n0bMu/JOXHzoRx+OV/O7D7by9qZZLJ6XwlwtG7zcjsbs8/P6jHSwtqOOMPMX/EK5TEsue/q6cf31T\nRkJYEE8sHsf4tEheWrOHf3xVSqBWw+/OySchXMcfP9nJHoOVeSPiSQgL4pNtDXR2ubrr77T68gpU\n+o5GgD7IHyGgw+bytRUN4+viFppMdi6dlMJlk9N4bEUpa8rbmJUTw98vHoPbI7l76TY27DGycGwS\nDy8aTUiglhaznZtf30JBdTu3nJbNnWfm7jdwentjDb/7aAd5CXpeu25qr87mZdsauO3tQmZkx/DC\nkkn9KqeyqcrI4ufWc9bIeJ66YsKAdCa8d2kRHxbW882dpw6p3IS+KoRBDZmRUv4AGAdThgN5a1MN\nG6uM/OHcESe0MnC6vdz4egEdNhfPL5l0xMrA6fZy42sFrKts49FLxx5SGTjdXm59u5C3N9Xy6zNy\neOSiMfspA6PVyeLn1rO0oI5b5wzjhZ9NIlynOCaveWkjj67YzTmjE/ni9lNIitCx+Ll1/OWzXczK\nieH9m2ewvtLIkhc3AnDbnGHUtNl4bX01kcH+JIUH0Wp2qMrgCPFKxdRic3pIidRR2Wrh9fU1TEiP\n4PIpqby/pZ4bXyvg8ilp/O3C0Wypaeesf/1AYW07b10/jbvPyuWzogbOf2oN5S1m4vRBvHn9VC6f\nksrTKyu4+fWC/cqAL56SxgtLJlHeYuGK59djsBz8e1s4Nom/XzyW1eUG7nx3G95+OIEmZ0Rx91m5\nfL69iVfXVR/1NeoLv5k3HI0GHl1eOiDHG2hO7BjKAabZZOfhz0uYkR3NJQOcKt9fHl1eSmFNB/+8\nZOwRN+SRUvL7j7bz/e5W/nbhoePDXR4vt7xRwGdFjdy/II87z8zdb0RWa7Rx8bNrKW408cyVE7hj\n3nA0GsHuZjPnP7WGDZVGHrloNE8sHseW6nbOeXIVxQ0mHr1kLNfNyuRnL27kk20NXDcrk/FpETzx\nTRmtFgfD4kJp6LDT0Gk/onNU2R+n26uUDUcpArh8p9JP4uZTs0kID+RXbxayucrI0ptmkBuv57a3\nt/LAJzu5/pQsXr9uKu1WJ+f/Zw3flbYQqPXjoUVjeGDhCJYXN7PkxY2Y7Puqxp6eG8eL10ymqs3K\nZf9d16syv3hiCvedncdn2xt5bMXufp3PDadkMScvjr9+tovdvpahx5OE8CCWTM/gk20NVBmsx/14\nA82gO5WFEBnAp72ZjIQQNwA3AKSlpU2srj5+I4GbXivgu9IWvrp99qD1eu0L35W2cO1Lm7hqWhp/\nuWD0Ee9nbwLbrWfkcMeZub2u5/FKbn9nK8u2NfDn80dy9fSM/ZaXNZu58oUN2F0eXlgyudtfsKqs\nlZteK0AXoOW/V09kQloE//q6jCe/LSM3Xs9/rhjPB1vqeXqlUg7j6unpvLSmirp2G+PTIqlrt9Fs\nOrFmBLH6QHLj9WTHhpAdF0p0SCABWg1aP4G/RimT7XB7sLu8dDk9WJ1uZg+LxWhz0mp2UNpkZnWZ\ngY1VJ8bEeFhcKDanh/qOLhaMTiAxXMeLa/aQGR3CvxaP49OiRp77oZLxaRE8c+VEAH7x6iZ2NZr5\nywWjuiNuPt5az13vbWNYnJ43fjF1P6fr+so2rnlpIzlxobx9w/SDOpCllNz3gWKKfOzS/vU4brM4\nmPf4D6RG6nj/5hnHvUJpi8nOrL9/x0UTUnho0ZH//gaSIeFDgMMrhJ4cTx/C2nIDV7ywgbvPyuWX\npw9cJmR/MVgcnPX4D8TqA/nolzOPuIT18p1N3PBaAeeNTeKJxeN6tb8qs4gdvLGhhnvn53Hzadn7\nLa9otXDZf9cjBLx+3dTuqJPPtzdy29uFZMeG8tK1k4kKCeCepUV8vLWBRROSueesPO55v4gfdrdy\nycQUYvSBPPdDJTGhASRH6Cis7RjUyKHZw2NZOCaR0SlKxdGjyfY+FB02J8UNJtZUGHhxddWglNYI\n1/mTExfK1toOUiJ1XD0tnedXVdJuc/GPi8fg76fh7ve2Ea7z55WfTyEpQsctb2zh+92t/GbucG6b\nq0Thfb+7letf3UxuvJ7XfzGVcN0+R++3Jc1c/2oBM7Kj+d+SyQeNhHN5vFz9vw1sre3gk1/NYng/\nKgnvrSbw27PzuOnU7MNvcJTc/+F2lm6uY/W9p/8oE/9ERFUI/cDjlfw/e+cdHlWZ9uH7zExm0nvv\nhRSSQCihNxWk20DFhr3gZ3ft3XV3LevauyIWFJCiCAooXTpJSEICSUjvvU0yydTz/TGTgZDeIBHu\n6/JaNjNnzsnknPd53+gCvMEAACAASURBVOd9nt9v4Yf7qG/SsuMfM/rsEzCQPLTqGNtSStn8cM8e\nmDMpqFax4IO/CHCxYe2ySZ3+vi0148tmhPDMvIhWr+VVNXL95wfR6UXW3DeRYe7G6/kproBn1icz\n2t+Jr28bBwLc+10ch3OqeXJOOPOiPbl9xVFK65p5am44h3Oq+fNEGeODnKlp1HCqvOGc9xTcPTWI\nBSO9iPZxOOduXWeiN4icLKnnt+MlfLo765yee3yQM7mVjdSqtDwxJ4ztJ8o5klvNo7NCmTXcgzu+\nOYpaq2f57eMY5efI0+uT2ZBQxCMzQ3ns8jDAuHq997s4Rvg48P1dE7A5YzXwU1wBT61L5oZxfryx\neGS711CubGb++3/hZC1n44NTut2jIIoiy1bGszu9gp1PXDLg+3+5lY1c8vbuVgFxMDMkNpUFQVgF\nHATCBUEoFAThrvNxHevjCzlZUs8z8yIGdTDYfqKMTUnFPHDpsF4HA43OwIM/JiACH980ptPfd2da\nGW9uTWPhSC+ents6pVTdqGHp8iOodQZW3j3BHAx+TSrm6fXJTBnmyvd3jQcBli4/TEJ+De/fMIpp\noa5c+9lBGtU63r4+hp/iCtiZVs7sSA9OlSnJrGgABj4Y2Mil/O+6GJJenk3uGwt4YWEko/2dzmsw\nAGOndbSPA0/PjSD3jQUcenZmm0A8UBzJqcbZRk6ohy3/+T2N0QGOLBrjw3vbT/HtgVzWLZuEq62C\nW746TFxuDf+9NoZrx/ry/g5jCTIY9w0+vHEMSYV1PLI6sVXX+PWxfjxwaQirjxaw+kh+u9fgbmfJ\ne0tGk1nRwL9/O9ntazdqKhlLQd/cktaHb6F7BLraMC3UlZ/iCv5WnfHnu8roRlEUvURRtBBF0VcU\nxeXn+hqatXre/iOdMf6OLBzZuXDb+aRRreOFX1II97Brk7bpCe/vyCCpsI7/XjsSf5eOy+ayKxp4\nZFUikV72/PfamFYpJbVOz7Lv4ymtb+br28eZhc92ppXx+JpExgU688XSWLR6kaXLD3OypJ7PbhmL\nu50lN35xCGu5lNcXjeDfv52grF7NNaN92JlmtHmUD/CA/My8CBJfupzUf85l8VjfVmmNwYingyXL\nZoSQ+8YCtj06nVnDPQbsXNZyKRllShrUOqYMc+HzPdkgwoOXDmNtfCHv/JnB6nsnEuBizV3fHuVY\nfg1vLh7JojE+vPNnBj8dLQBgbrQnLy2MZPtJo5rtmTx+eTjTQl15aWMqyYW17V7H1FBX7poSxA+H\n8zmUXdXt6/d1sube6cH8mlRMfN7A79HcON6fotom9p6qGPBznSsu+Cqj1UfyKVeqeWpuxDmpY+4t\nX+zNprS+mf8siu51J3JKUR2f7cnmurG+zI3uOPhpdAYeWZ2ITCrwxa2xrRqGRFHk+Z9TOJJbzdvX\nxZh1a1KK6vi/HxIY7mXP8ttiEQS465uj5mDgaC3nrm+P4uNkxStXRPH0+mREEWZGuLMuvhBLCyka\nvaFLu8reYKuQseqeieS8Pp9lM0JwtB5aXaYthHva8dVtsSS/MpuHL+v/fS6VRo9cJqGktpn00gYW\njPBiw7Ei8qtV/OPyMDYmFvPPzSf4/q4JeNpbcvuKo6SV1vPm4pFMD3Pj2Z+PszfDODjeNjmQpRMD\n+HxvNhsTi8znkEoEPrhhNK62ch5dk9iqVPVMHp8dhp+zFc9uON7he9pj2YwQ3OwU/O+PnlUr9YZZ\nwz1wsZGzLr5wwM91rrigA0KzVs+ne7KYEOTMxGCX8305HVJW38wXe7NZMNKLsQGdW1V2hFZv4Kl1\nyTjbyHlhQeddlu9uz+B4UR1vLB7ZJhe7PqHI2Gdw2TCujDH2LFQ2qLnv+3icreWsuGMcNnIZ/1ib\nRFxeDe8tGY2XgxV3rDiCu52Cl6+I4h9rk7BRyLgk3I0Nx4rwdrBEozfaUPYnrrYKtj46jZRX5zAp\nxGVQB/yeYG9pweOzw0l7bS6PzQrr189u1hqwUUhp0ug4mF3FNaN9+DWpmIzyBp6aG87m5BI+25PF\nj/dMxM5Sxj3fxlGj0vDJzWMI87DjgR8TKDCpzb50RSSxAU48/3MK+Wd4QzvZyHnr2hiyKxp5e1v7\n9fzWchmvXzOSnMpGvvoru9vXb6OQcd/0YA5kVQ34KkEukzAn2pNdaeU9ClqDmQs6IKyNK6CsXs0j\n59B0oze880cGeoPI03N6n0v+8XA+J0rqee2qaBysO06THMuv4bM9Wdw43q+NK1x2RQMvbUxhQpAz\nj5gGIp3ewAM/JFDZoOaLW2NxtVXw7vYMfksu4dl5EcQGOnH7iiPYKGS8sXgkj61JRCGTcGm4Oz/F\nFeLtYElVo6bfg8HaZZOIe2EWEZ72Xb95iGJpIeWRWaEkvHg5syP7L5VUo9Iik0rQ6gzszajg+lhf\nNiUVU9Wg4c4pQazYn8vm5GK+vDWWGpWWe76Lx0Iq8MXSsQjAgz8moNEZsJBKeO+GUQgCPLz6GLoz\nPKOnhrpyy0R/lu/PISG/pt3rmBrqyuxIDz7bk91hY1t73DTBH2cbOR/uzOzrV9El86O9UGn07Mn4\ne6SNLtiAYDCIfLUvhzH+jkwKGbyrg8IaFesTCrlpgn+nOf/OqGvS8t72DCaHuDAnquOBQ28QeXFj\nCu52Cp4/axVh1KNPQi4zPuQtMgWf783mcE41ry8aQbSPA3szKvhoVybXjfXl9imBLFsZT4Nax0c3\njeaFX1Jo1upZPNaX7w/lEeJmQ22Ttl/TRE/OCSfrP/MZF9i7ldRQxNlGzhe3xrL+/kn99pl1TVoc\nrC3Q6A0cyanmqlHeLN+XQ4CLNfOiPfnP7ydRNut4d0kMSQW1vLU1HT9na/57XYxxj2qbce/A18ma\n/1wzgsSCWr45kNvqHM/OG467nYJXN53osEP56XkRNGn1vL/9VLev3Vou447JgexOryDbVKQwUEwI\ndsbR2oJtKaUDep5zxQUbEHZnlJNXpeKOKUGDOpXw5d5sBAHum9G58mhnfLIrk9omLc8vGN7p7/rD\n4TxSiup5cWFkm+ahHw/nkVhQy8tXROLlYEwjpRTV8e6fGSwY6cU1o30oVzbz+E+JhLrb8s+rovnX\n5pPmbuqv/sohu6KB+y8ZxvJ9Ofg7W1Oj0varQN1fT13KA5cOG9RihAPJ2ABn0l6by4J+Ko4orGnC\n1VZBcV0zxbVNTA9z47XNJ7hlYgCBrjY8tOoYYwKcuHVSAMv35bA7vZw5UZ7cNMGf5ftySCowbhov\nHOnFzAh33vkzg+La0w52NgoZT82JIKmglp+PFbV7DSFutiwZ58eaowWU13e/W33JeD9kEoFVHVQz\n9RcWUglTh7ma7FyHfrXRBRsQvjmQh4e9grnRnl2/+TxR1WB0BVs02tc8CPeU6kYN3x3M4+pRPp1K\nXDSodby3/RSTQ1xYcJZNZoVSzVtb05kyzIWrR/kAxhXDsxuO42Qj519XRSMIAi9vTEXZrOPjm8Zw\nOKeK7w/lcffUIErqmtmSUsq900P45kAOztZyJILx2vqDK2O8yfjXvCElNjZQWFpI+fimMbx9XUy/\nfF5OZSOj/Bw5mluDv7MVHvaWPL0+mTcXj6RBreW5DSk8N384YR62PLvhOI1qHc/Mi8DVVsEzG46j\n1RsQBIFXrozCIIq8flZJ6DWjfRjp68C72zPQ6ttfKd47LRitwdBmhdEZ7naWXB7pwbr4QtS6gc3v\nTw5xpaxeTfbfQMriggwIOZWN7M2o4OYJAee97rwzjDezgXum994u8NsDxu7X/+uiVPXbA0Z/3faq\nrT7aeQqVVs8/TQM/GPdfjhfV8cKC4TjZyNl+oowtKaU8PDMUd3tLnlqXTJiHLdfG+vLW1jRmRriT\nU9lATaOWYDcbcqv6x+bytauj+eDG0YPe2vRcc+1YXzY+MKVfPisxv5ZoH3t+OJzPLRMDKKlrZl1c\nIY9fHsb2k2XsTCvn9UUjKalr5oMdp4wWqldGcbKknrVxxgocP2dr7poaxKakYk6W1Js/WyIRePiy\nUAprmswGSGcT6GrD3ChPVh7KQ6XRdfu6rx/nR41Ky18ZlX37ArqgJeV8MKv7JbKDlQvyKfr5WBGC\nYGyUGayIosjqowWMD3Q2N331lCaNnm8P5jJruAehnTSyNah1fL4ni5kR7ozyc2z1WmGNih+P5HN9\nrK/ZiKRBreO/29IZF+jElTHeqHV6Xv41lTAPW+6ZFswHJmG6/14bw4u/pKCQSRgX5My21DKmhrpy\nIKsKux4YonTEV7fGsnRiQJ8/5+9KjJ8j2x+f3ufP0YsiDc06fJ2sWHUkn6UTA1gTV0C0jwMjfBx4\n+ddUIjztuD7Wl+X7csipbGRutCdj/B35YMcpcwXOvdNCsLOU8e5ZAnYzh7sT4WnHp3uyOky73D45\nkPpmHdtSu5+rnxLiip2ljK09OKY3BLpY42orJ7Gg/b6KocQFFxBEUeSXY0VMCXHF02HwapAczqkm\np7KRG8b3PmhtTS2hVqXlrqmdrzB+PlZEfbOO/2tHw+nT3VkICDx0hmvcD4fyqGrU8Nx8457EqsP5\nFNU28eLCSApqVHx7IJclsX7kVas4mlvDI7PC+OqvHCK97MmuaEAhk/RZs+eLpWOZ1Y+VNX9Xhrnb\nse3RvgUFS5mE3CoVAc425FersLSQ4utkxT83neCVK6OoUKr5el8OT86JQCYV+HDnKQRB4Mk5EZTW\nN/PDYWMe38HagjsmB/LnyTLyqk6nVwRB4K6pQWSWN3A0t/2Ko3GBzvg5W7Ehof29hvaQyyTMjHBn\n+8myVhVO/Y0gCAz3sm+18hmqXHABISG/lvxqFVeP9jnfl9IpvyWXYGUhZV4nDWRdsTauEH9nayYG\nd1xxI4oi3x/MJdrHnjH+rVcHdU1aNiQUcfVob7xN/QjNWj1f/pXNtFBXRvs70azV89EuYy/H1GGu\nvL/9FAqZhEdmhfL2tnQiPO0oq2+mskGNv7M1uVUqHKws0PWh3f/1RSOYHTV4934GG+Gedqxb1vsK\npBa70mP5NUwMdmbF/hxunxxIWqmS4tomZkd68MXebORSCbdMCOCXY0XkVDYyKcSFcYFOfHsg1yzv\ncPPEAKSCwMpDrVWLF4z0wlYhY42p2/lsJBKBa0b7si+zskeeGLMiPahVaUkuquv1798dIr3sOVXW\n0OE+yFDhggsIvyWXGBtKOim/PN8YDCLbUku5NMKt15aYRbVNHMiq4lqT7WFHHCuoJaOsgaUTA9q8\nb318IU1aPbeeIXe9ObmEygYN95sUJX9NKqayQc0js0IpqG5ic3IxN08MYHd6BfnVKu6bEcx3B3OZ\nNdydg9lVuNkpKO+Dyc0VMd5D0uT8fBMb6Nwn20eZRKBJq8dWYYFWb6CsvpkwD1ve33GKR2aFolTr\nWBOXz70zgpFKTg/4t00OJL9axe70cgA87C2ZE+XJ2vjCVoOntVzGFTFebEkp6bDJa3akB6JIj2r+\nJwQZ8/tHcwa2SS3Cyw6N3tBq5TMUueACws60MiaHuHTo8zoYOFZQS7lS3aYxrCdsP1EGGAfQzvg9\nuQS5VMK8EW1XIusTConxcyTa53R10k9HCwhytTFvpK08lEeYhy2Tgl1YcSAHqUQwNS8ZU0Q5FY2m\n7lcZdU3aPmsVvX1d+yqZF+maO6cEEunVu0a9GpUWD3tL9mVWMD3MjR8P53PjeH8yyxuoU2kZH+TM\ndwfzcLFRcHmkBxsSjNU9c6I8cbWVt0r1XD3ah1qVts0m7OwoT1QafYf6RVHe9rjZKczBpTu42SkI\ndrXh6AD7T/g5GSvcimqHtpHTBRUQsisayK1ScVmE+/m+lE7Zn1mJIMAlYb2/zp1p5QS72hDUidGP\nKIpsSSllWqhrG5Py/CoVqcX1XHFGTXt+lYojudXmVUd6qZLkwjpunhCAziCyMbGY2VGe5FQ2klHW\nwK2TAvjhcD6XhrtxJKcaf2driuuazr6MbrPh/yYPmC/BhYAgCHy+dGyvj5cIAs1aA07Wcho1evQG\nEQcrC34wbTQX1jRxJKeaG8b5U6PSsiutAguphDlRnuxMK6fJ1HMyLdQVG7mULWc1c00KdsHKQsqO\nk+0P+IIgMG2YK4eyq3pU8z/Kz5GUooHN77ekVM/ssxiKXFABYWea8Ua7NHxwB4TDOVUM97TvVGKi\nM5q1eg5mV3FJF7/nqfIGimqbmN1O+mxraglAq1XKjjTTqsPku7wlpQRBgHkjPNmbUUF1o4ZrRhm1\nb6zlUuytLKhq1OBhb0lJXTMyidBr05sZYW5mIb2L9B4/Z2vumda7MubS+mZ8naxILa4j3MOOzckl\nXD3Km+0njKtuSwsJW1JKmBTigp2ljJ2m+2X+CC+atHr2ZRrLPy0tpEwNdWV/ZutyUEsLKeOCnDud\nzY/yd6SyQUNJDyxVQz3sKK1vbmXv2d+42ymQCFByMSAMHQ5lVxHkajOoG5g0OgPxeTVmG8recKKk\nHo3O0OVnHDHlVdsT9juUXU2IW+vvald6BcFuNmYJjT9PlDHW3wl3O0u2nyzHTiFjaqgrf6SWclmE\nO9tPlOFobYFKo8fByqJPlUUvXdH7/PdFWnNfLx3F9AYRqUQgo6yBUX6OJBbUMsrfEbXOQGJBLdND\n3dh+ogwLqYQZYW7sSq9AFEXGBjghl0o4knM6FTQu0Jn8ahVlZ3Ufj/JzJKNMSaO6/X6DEab0ZUfS\n2e0R6m4slz5VNnAyFjKpBFuFjPrm7vdJDEYumIAgiiLxeTXEBgzuWWZWRQPNWgOjz6r46QnH8o0P\nS1efcTS3Gnc7Bf5nBUiDQSQut7pVQNEbRI7mVDNtmCsAymYtJ0rqmRpq/P8HsyqZEOxMZnkDVY0a\nZg334K/MSqYMc+VAViWeplVCb1RCgl1tzD0QF+k7rrbGPH9vUJgaAFs2hLU6EWu5lL0ZFUwKcTHL\nXEwKcaFCqaawpglLCykxfg6tSkpjTVpTx84StovxdcAgGic17dFi0dqTruCWSU1JH9KV3cFWIaOh\ng0A2VLhgAkJWRSM1Ki2xgYM7IGSUKQH6pNKZWlyHu50Cjy68Xk+W1DPS16FNdVFOVSP1zTpGn5Gi\nya5ooEmrZ6SvMcgkmjyPxwY4UV7fTG6VionBLsSZlvvONnIqlGpcbeRUNmiwtDDear1JGT00c/B6\nXA9VbuplpVZhTROe9pao9QbsLWUkFdYS7e1ASnE9sSZp9oT8GqJNMimpxcZyzyhvBzLKlObcf8us\nPaui9cDeEvjzO+hkt5bLcLaRU1jT/cHd1dbof1HZh+q27mCjkHW4shkqXDABISHPOBPprZ/AuSKj\nTIlMInS6GdwVeVWqLo/XG0RyK1XtzrxzTA9py0MLkFpsnLFF+RgDVVqJMXCN8HEgw7QUj/Sy53hR\nPW52CmqbjPnaFkkJvSj2Wl5iWqhbr467SMdM6KQ3pTNUGj1ONnJSiuqI8LQno0xJlI89J4rrCXE3\n3nM5FY2Ee9ohCJBWarxPgt1sUGn05pJjG4UMNztFmzJNL0dLBIFOB3wfRyuKehAQnKzlSCUClQ39\no53VEVKJgGGIC9ydb0/luYIgpAuCkCkIwjMDea60UiWWFhKC+zDQngvyqlT4Oln1SZsnr0pFQBdS\n2cW1TWj0BoLd2n4fuaaHNNDl9GtFps2ylp/lV6uwt5ThaC0ns9z40A9ztyW/upEgVxuyKxoQBOOe\niFwmQRTpdbeoq62iV8ddpGOs5TLzqq27tCwk9QYDhTVNBLvZkFXRSICzNU1aPSqNHk97S3M3s4uN\n3BwAWsoyzxzovR2t2mwOK2TG40o7UTa1t+pZakYiEbCUSQbcxEZnEJFJhvYc+7xdvSAIUuBjYB4Q\nCdwoCMKA7RyeKlcS6m6HZJBLI5cr1bjb9V5SQ6c3UNmgNpfBdUSVSWnUza7tYFtW34ylhQQnG3mr\nnzlYWWBpYSz7LKptwtf0kJcr1cgkAm52CgprmvB1Ms7gPOwsqW3S4mGvoLi2qVdBrrd18xfpmuk9\nXHm1TH5lEom587hWpcHFFLArlGrc7U83HrraKiivN/7b3uRdrTyj0sfesv0Ui5Vc2ungbWUh67Fs\nulQi9Kk7vju0bLoPZc5nOBsPZIqimC2KogZYDVw1UCfLKFMS6jH4NyYrlGrc7Hs/I26ZOZ3dV3A2\ntSpjQHCwausv3KDWtWncq27U4HJGgDC+xyhQV9+sxd7KAkEQaGjWYW9pYX69ulGDs40CZbOO3jyP\nI307luy+SN/oabXd2QUBxhSJsT8BQNmsw9Li9GBuLZeapadb7pUzZ/Y28vZn+lYWUnPPQnsoLCQ9\nlrSWSgRzEBsoGtU6rCyGdp/M+QwIPsCZwiWFpp+1QhCEewVBiBMEIa6ionc2dSqNjrJ69ZCoVKlR\naXDugwm80lT21vIAdkSj2vhAnW2EA9Cg1mNzlmTG2bOfJo3eLKuhUuuxNv27SWv8d6PG+L86vYiA\ncTkt7UWJkeUQf8AGMz2dzbasEDoaWCUCyKWSdvV8WnLrkjPuAZ1BRNpOisUgdn5taq2hxw2KqjPu\n14FAFEXjs2vb+2d3MHA+A0J7f/E2d5ooil+IohgrimKsm1vvNhdb8pTejoNX3bQFrSnn3ltalsUy\naecPe8vzJrb9ypEIbf8QeoPY6mGWmGaHYNw4bvFElkmNMzGFTIJGLyKRGGeWgtD+ubri72JePhjp\nqY91y5+/5d5q+fu33EsSiUCDWoeNaZKhO+OeUWuN5zpz30Kt07e7j6FS68wTjPZo1rZ/XEdodAbU\nOkO/SK53RH2zDq1ebLWKHoqcz4BQCJyp7ewLtO+Q0UfKTAGhqzLMwYBG37eAIDM9nVp954NvywxM\n18772luyW8ulqLSnl/e2Cqk5/2tpITU3ndkqLFCqddjIja/bW1pQ36TFViHrVcoopXhgVSovZNJN\nFUDdpWWFcKYHtqWFBKXpPnCzVRjTh6Z0Y4VSbS4IqDNVndkqTqci60z3xdkom08HlfaobdJ0mRI9\nk5Zzt+xjDAQt9p5DvQDifAaEo0CoIAhBgiDIgRuAXwfiRC0rBM8hEBCMOdneH9/iANeVDK+1vG1O\n98zXGtS6VnoxzjYKqs8o23OwsqDmjI1pZbMOlUZnrCypV+Nub0lpfTPudgrK6tV42Fv2KmU00Bo0\nFzIHOxCR6wq5qSu3rkmDt6MVpabnq6WowNvREoNBNG8yw+nqIl+n08UORTWnCxNaqGvSolTr8Omk\nKKK4trnLookzaamQ68kxPSXH1CjXl3LxwcB5CwiiKOqAB4FtwEngJ1EUUwfiXC018U59yM2fK6zl\n0j4ZzzuYZkG1qs51WzxMD2p7UtTejpaoNHrzzAqMD3ujRm+uEvFztqagRoXeIJo3JwuqmwhytSGn\nsoEgVxs0OgMWUol5g7m3WvEtG+AX6T+qGnrfpNWs1RPhaUdaqZJgVxvSy5T4OFpRoVSj0RkIcbMl\nt6oRnUEk6IwyZZlEMK/SVRodVY2aVgECTjekdbTh3aTRU92owacH6d/8auNndlWK3RdaAkLgxYDQ\ne0RR/F0UxTBRFENEUfz3QJ2nyeTD2tkydLBgI+9bt6OVXIqdQtaliYi76cEsa0ckrGXWVlB9umZ8\nWIseTLmxCS3IxQatXqSwRmXu7cgoUxLibkNelcpcd96SmtIbRPSiaE5p9YRdPZA7vkj32JfZO59h\nH1PvgL+LNdkVjYz2dyLJpGmUXGhM74V72pFiamSMPkN7KMLLznw/tDQ6hp9l7Xqq/HQjW3uklRqP\n64mtbEtPjJ/TwAWEU+UNuNrKzROyocrQ7qLoJo0aPRZSYUgYsdtZylrNzHuDu72iS90We0ujBEBW\nRVvBrxDTw5hedjrH3PLgtuSdR5jKQRMLagn3tMPKQmrSinJGZxDRGgwoZBLqm7XIZRIEwah02pta\n8M92Z/f4mIt0zkc7M3t1nNRklNOCl4MlhTVNjPZz5FB2FTZyKdE+DsTnVmNpISHUwxa9QSS5sK6V\nX3eiSW8r5iwP74T8GmwVsg4rAlNMzmfRPt3vTzleWEeIm+2AVhklFdSahfeGMoN/hOwHmjT6IVO+\n6NVO92ZPCXGzNc/kO0IQBCK97NsVEQtxs8VOISOx4LTwmK+TFc42crM0cYSnPbYKGUdyqrGQShjt\nbxwQYgOdkAgQl1tNbKATR3NrmBjsQlWDGjuFrFfidullSrLbCVwX6R3ZFQ1d3h+doZBJUKn1OFlb\nUGXaV5o53IM9GRWMC3JGJhHYmV7OlBBXLKQSEgtqaFDrGB90WlX3cE4Vfs5WbRojE/JqGeXn2GHZ\n6bGCWpxt5J3uMZyJKIokFdYS49t7sciuqG/WklnRwCi/wa2T1h0uiIDQm0HofOHjaNlnk40ITzty\nKxu7LNmM9LYnrVTZpslHIhGI8XMkPq+21c8mh7iwP7MSUTT2JEwIcma3SeL4knA30kqV1DRqmRTi\nwpbjpcyN8iSzvAE/JytjB7Ozda/9EF7fkta7Ay/Shlc3nejVcXYKGTUqDROCXdiXWcms4R5sSy0l\nzMOWuiYt+dUq5o/wIqOsgYLqJmYONyqq/nGiDJlEYEaYsWy8SaPnr1OVzIxorbhaVt/MiZJ6sxvf\n2YiiyL5TlUwKcenUFvZMcqtUVDZoGNUH9eCuSDIJPQ7kOc4VF0RAkEkEDAPcpdhf+DpZU9mg6ZOM\nbqS3facSwi1MCHI2+i/k1rR5bcowV06W1LcKTtNCXSmrV5vzv3OjPSmqbeJ4UR3zTRacm48Xc8VI\nb7IrG/F3sUEmEdDpRawspD3uLj2TP0+UkVTQfQ38i7RPQn5NjzyJz8RKLjWWhMqlNKh1jA1wIi6v\nhuvG+rEhoRC5yR1tbVwBMonA5ZEeGAwivx83mua05Nf3nqpArTO0keD+02T7OrsDae60UiXlSrU5\nsHSHFrvNGQMokLg3owK5VDLopfW7wwURECTnQMekvxjuZczVn+xiMO+MFq35w9md+8hODHbBQiqw\n91TbDcaWh3X77qSqkwAAIABJREFUyTLzz2ZHemIhFfjlWJH5PRZSgQ0JRfg6WRMb4MRPRwuYG+2J\ntVzKr4nFzIn25PfjJVwW4U5JbXO3l/rtcdXH+3vcTHWR06h1ehZ9cqBXx8okAs1avbGqqFTJCB8H\nEgtqsbQwBoF18YUsjPHC0kLC+oRC5kR54man4K/MSgqqm7gu9nTL0dq4AtzsFG0MnH5LLiHI1cZc\nwHA2W1JKEQR6GBAqCHY9beo0EOxOr2B8kPOQKFrpigsiIChkUjR6w5BYJUR6mXTki3rfkOVqqyDM\nw7bLOnMbhYzYAGf+PFHaxqN2mLstIW42bEo63SvoZCPnknB3NiYVo9UbcLSWM3+EF+vjC2lU67ht\nciC5VSricmu4PtaPX5OKuGaUD0q1DluFrE8rhBZe2pjS58+4UHl2/fFeH2tlIaW+WWesLqps5IoY\nL9bFF3LtWF82JRej0ui5e2ow6+ILqVFpuWmC0W/h+4N5ONvImWOyaS2pa2JnWjnXx/qae2bAWLZ5\nMLuKxWN82k0HiaLIL8eKmBzi0u0G01qVhoNZVQPqoV5Yo+JUeQOXhP89JNoviIDgaGWBKDKgnqr9\nhYe9AldbOUmFfevQnRbqxqHsqlbqku1xRYw3WRWNHG8nAF0f68fR3BqzaQ/ADeP8qFCq+f240XP5\ntsmBKNU61sYZVwZeDpZ8uieLO6YEIorGktFpoa5sNdlqntm92htWHy1gXXxhr4+/UFl9JJ8NppVd\nT5FKBNQ6A8PcbTlZUs8oP0dSi+uRSQVunhDAZ3uyuCzCnRB3Gz7emckYf0cmh7iQWlzH9pNlLJ0Y\nYNYe+mZ/LgA3jGtt0LPqSD5SicD1sX5nnx6AuLwa8qtVXDPat9vXvTm5BI3ewNWj20ik9Rstz8Gs\n4b1zoBtsdBkQBEF4UBCEIZ0cc7Ix5i6rGwd/g5MgCEwIduFAVmWbWXtPmBftiUZnYMfJzmv4F4zw\nQi6VsCGh7WBx7Vhf5FIJPxzKM//s0nB3Qtxs+GxPNqIoMtrPkfGBzny8OwudXuShy0KJz6shrVTJ\nTRP8WX20gBvH+6Ns1iIIAhbSvpuIPLE2iX3tpLku0j5bU0p5ZkPvVwcGUURnMOBoZUFZvZpZw93Z\nmFjMnVOCWH0kH5VGz3PzI1h5KJ/iumYeuzwMQRB4b/sp7Cxl3Dk1CDA2w313MI8rY7xbNZ7VqbSs\nOpzPnCgPc3/M2azYn4O9pYx50Z7dvu4NCYWEe9gR5T1wEuo/HytmlJ/jkG9Ia6E7KwRP4KggCD+Z\nDG2GUM2OEUdTh3LNEOl4nTrMuHnbXo9Adxnj74SnvSWbkzuXh3KwtmBOtCfr4wvbrCZcbBVcEePN\nmrgCc6ObRCJw3/QQTpbU88eJMgRB4Mm54VQo1aw4kMP1sb6EuNnw5pY07r8kBGsLKd8dzOXmCQHs\nOFnGJRHubaS0e8Mtyw+zK+1iw1pX/HmijGUr4/v0GaIII30dic+vYUmsH+viC/F3tmZaqBvfH8rj\nxvF+2Fla8O6fGcwIc2OqyUf7zxNl3DMt2LyZ/OnuLNQ6PQ9eFtrq81ccyEGp1vHgpaHtnZ78KhVb\nU0q5eWJAt/P0qcV1JOTXsnhs+ymo/iCttJ6TJfVcM4ArkHNNlwFBFMUXgFBgOXA7cEoQhP8IghAy\nwNfWb7RoGBXX9q2+/1wx1WRkvzu9d9UgYBy4rx7tw8608i6b1O6ZFoRSrWPN0YI2rz142TA0OgNf\n7M0y/2zRGB+GudvyxpY0NDoD4wKdmTXcnY92ZlKmVPPiwkiyKxv54VA+LywczqHsarwdrfB2tCKp\noJbhXvbGhjVp3zKWd3xzlJ+PXUwfdcQ3+3O457u4Pn+Oj6MVBdVGJz+N3kBulYpXr4zi+V+O42lv\nyVNzI3h1UypavYF/XhWFVi/y4i8p+Dtbc+/0YAAyyxv45kAu1471bbVpXN2oYfm+HGZHehDZwUz+\ns71ZSCUCt08O7PY1f/VXDjZyKUvG9c47ujusOWqsplo40mvAznGu6dYTKRpzF6Wm/3SAE7BOEIS3\nBvDa+g1/0/K0RdNksOPnbE2klz2/mfKTveXmCf6IwKrD+Z2+b6SvIxOCnFm+L6dN70KQqw1Xj/bh\nu4N5FNYYvz+ZVMLz84eTU9nItwdyAXjlyihEEV78JYUZYW4sHuPLp3uyiPRyYFqoKx/sOMWyGSEU\n1TZhq5Biq5ChMxj6JOQH8NiaJJ5elzzg5idDCY3OwONrEnmll/0GZ2IjlyIIRhHEuVGe/HysiPtm\nBLMjrYzsikbeujaGbSml/H68lIdnhhLgYsPHuzLJqmjk1auisLSQIooir/yairVcytNzI1p9/n+3\npdGk0fPknPB2z59V0cCaowXcMM6/25vJxbVNbEoqZsk4/wGTklA2a1kbV8jCkV5mx7i/A93ZQ3hY\nEIR44C1gPzBCFMX7gbHA4gG+vn7BRiHD1VZuFs4aCiwY6cWx/FrzINwb/JytuTTcnR+PFHTZpPbI\nzFBK6pr57mBum9eemB2ORBB4bfPpAeaScDdmDXfnf3+mk1vZiK+TNf+YHcbOtHLWxhfy0sJIXG3l\nPLgqgZcWRmKjkPH1vhyWzQjhaG4Nw03WmP0xjK+JK2DEK9v69F39XciraiTshS293kA+E5lEwNFa\nTmFNE9fH+rHyUD7jg5zxc7Jm5aF87psejJejJS//msrEYGfT37aaD3ee4prRPlwabqzuWXWkgH2Z\nlTw5J7zV4JlcWMvqowXcNjmQUI/2tYne2pqGpUzCI7PaTye1x0e7MhEEuHNqYJ9+/85YG1dIg1pn\n3h/5u9CdFYIrsEgUxTmiKK4VRVELIIqiAVg4oFfXjwS42JBjMo8fClwx0huAjYl9s4i4d3owlQ1q\nfuhilTB5mCuXhLvx0c7MNuqi3o5WPDRzGNtSy8x5e0EQ+Pc1I5BLJTxlmqHfMSWIySEuvLQxhTJl\nMx/fNIaimibe3JrOxzeNJr9aRXqpkvkjPDmYXcXEYJdedy6fjUqjZ+qbu/j+UF6fNuOHKjq9gU92\nZzLjv7v77TM97C0pqm3iihhvNicX426v4I7Jgfxz0wmmhbpy34wQ7vk2DoVMwntLRlPfpOWRVcfw\nc7bmtaujAaNMxmubje+/eUKA+bObtXqeWJuEm62iw8F+b0YF21LLWDYjpNuVaS0ripsnBLSR1u4v\ntHoD3xzIZWyAEyMHUBLjfNCdPYSXRFHM6+C1k/1/SQPDcC87ThbXD4leBAB/F2smBbvw4+H8PqVD\nJga7MCnYhU93Z3XqUwvwzLwIGtQ63tya3ua1u6cGE+Zhy9Prk80+CB72lrx8RRRHcqt5f3sGUonA\nezeMwlZhwf0r4wnztOO5+cPZfrKMnenlvHxlFDvTypEIAuMCnTmcU93vgmAv/pJC0LO/X1BdzQn5\nNQx7fgtvtfN36y0OVhYU1TZxWYQ7CXk1SCUCT8+N4Kl1yfg6W/HO9aN44IcECmpUfL40FmcbOctW\nxlPZoOGDG0Zjq5DRpNHz8OpjKCwkvH1dDJIz8oNvb0sno6yBt64d2a7ZTaNax3M/HyfYzYZ7TPsQ\n3aFlRfHgZcP65Xtojw0JheRXq7h/xpDZRu02F0QfAkC0twNKtY6CIZRWuHVSAEW1xkaevvDY5WFU\nNqj5en9Op++L8LTn7mnBrDqSz6GzmtrkMgnvLhlFjUrDsxuOm2fhi8f6ct1YXz7YmcmutHLc7Sz5\n8EbjauD+lfHcMjGApRMD+HxPNhqdgUdnhbI5uYQgFxuive1JL1US6dX/ZYFXfbyfee//RWYfRNwG\nO+mlSqa8sbPX3ccdYSOXUtekZVKwsZegQa3j+QXDefGXFOytLPj2jvG88msqB7OreHPxSMYFOvHs\nhuMczqnmrWtHEuPniCiKPLU+mdTiet65PqZV/n9PRgVf7cth6cQALglvv2ns7T/SKaxp4o1FI7st\nTLk7vbzHK4qeotbp+WBHJqP8HJk5fOAa3s4XF05AMM1E22vAGqzMivTAw17Bii4G8q4YH+TMnCgP\nPtqZ2aVw3mOzwvB3tuaZ9cltfBmivB34x+xwtqaW8o1pMxngtaujGe5lz8Orj5FWahQne2PRSPZn\nVvHMhmReviKSuVGevLb5BK62Cu6YEsiauAJ8na0Z7mVHWmn9gDhNnSypZ9Y7e7js7d1m2eShjiiK\nHMmpZsJ/tjPnvb1mN7D+pFGjZ3qYGxllSvQGkefmR/DPTSeQSAS+vXM8/92Wzm/HS3hhwXCuGe3D\nm1vTWZ9QyCMzQ81NYB/tzGRTUjFPz43gsjNE7HIrG3noxwQiPO14dn5Eu+fflVbOiv25LJ0Y0Ebe\noiNUGh0v/JJCiJsN987o/oqip6w5WkBRbROPm3ot/m5cMAEhzMMOhUxCQt7QSSVYSCXcNTWIA1lV\nxOd1rkvUFS8siMQgivz7t86zfFZyKW8uHkletYqXNrY1sLt3WjCzhnvwr99OcsBksmJpIeWr22Kx\nlku5/eujFNc2sXisL/+4PIwNCUW8uDGF924YxcwId174JQUfRyvuvySE35JLcLNTMDHYhZzKRvyd\nrbGQ9v9Dll3ZyMIP9xH4zG+sOpLf5Qb7YKS+Wcs3+3MIevZ3rv/8IGX1vXc86wyZRGB8kDNHcqqw\ntJDy8MxQXt10AltLGT/ePYH3d5ziV9NAf/e0YN79M4PP9mRx8wR/HjXtBaw8lMf//sxg0Wgf7jsj\n3dOg1nHv93FIJAJfLI0127ieSUldE4//lEiEpx3PLxje7et+988MCmuaeH3RSHNXdH9T06jhnT8z\nmBTswrRQ1wE5x/nmggkIcpmEcYHOHMgaWh2ut0wMwMVGznvbT/Xpc/ycrXnw0mH8dryEbamlnb53\nUogLD18WyvqEwjYyERKJwLtLYgh2teH/fkwwp2R8HK349s7xNKp13Pr1ESqUah68bBgPXTaMVUcK\neHljKh/fPIZ50Z7867eTWEgEnpobzvaT5TSodcyMcCe/WoW1XNbn/oTOeHbDcSJe3Mr0t3bx54my\nftFXGiga1Tq2ppQw/a1djHzlj34pI+0MBysLRvk5ciSnmmhvB64Z7cOrm07g52TNitvH8eLGFDYl\nFfPsvAiWzQjmra1pfLAzkyWxfrx2VTSCIPDzsUJe3JjCzAh33rx2pHkWrdbpue/7ODLLG/joxjHt\nis2pdXoe/PEYap2Bj28e0+1U0f7MSr7al8NNE/y7vaLoDf/7Mx1ls45Xroz6W64O4DwFBEEQrhME\nIVUQBIMgCLHn6ryTQlxIK1X2yU/2XGMtl3Hv9GD+OlVpNqfpLffNCCHK257nNhynsovv4OGZoUwM\ndub5n4+TeNYGrZ2lBV/dFotMInDr8sPmtEWEpz1f3hZLUU0TN3xxkHKlmscvD+Phy4axJq6Ax9Yk\n8t/rYrg+1rjnkFpUz/+ui+FUWQOpxfUsifVDpdEhlQjYDrByZH61inu+iyP8ha2EPPc7n+/JIqey\n8bxWKBkMIumlSj7fk0XgM78R9fI2lq1MOCf9M94OlljLpcTl1XDVKG98nKz4aFcml0W4886SGP7v\nhwTi82p4b8ko7pwaxJPrkvlkdxY3jvfn9UUjkEgE1sUX8sTaZCYFu/DxzWPM4nV6g8ijqxPZn2nc\nc5jazuxaFEWeWX+c+Lwa3lw8skPHtLOpalDz2JpEgl1teKEHK4qeklJUxw+H81k6MYBwz+7bdw41\nhPPxAAiCMBwwAJ8DT4ii2K12ytjYWDEurvedlwn5NSz65AAf3TSahaayzqGASqPjsrf34Gon59cH\npraq1ugpGWVKFn64j+mhrnx5a2ynM52qBjVXf7KfJo2BXx6Y3KaML7W4jhs+P4SbnYKflk0yb+Qd\nyanmjhVHcLNTsPLuCfg4WrF8Xw7//v0ko/wc+erWWNYnFPL6ljSivR144NJhvLb5BGX1zVwW4U5q\ncT1FtU1GL4XzVBV226QALo1wZ5i7Ld4OVn36ztvDYBApqFGRVqpkb0ZFl2XBA4VMIhDgYk1JXTNS\nQeCmCf7sSCsns7yBR2eFMtzLnifWJiERBD69eQxR3g48tPoYezMqeHRWKI/MDEUQBL76K5t//XaS\naaGufHbLWLPEhN4g8tS6ZNYnFPLiwkju6qBu//3tp3h3ewb/uDyMh2Z2r+dAbxC5+9uj7M+s4pcH\npnTY6dxXNDoDV328nwqlmh3/mDEkfZMFQYgXRbHLyfd5CQjmkwvCbs5hQNDpDYz793ZmhLnx3g2j\ne/0554ONiUU8sjqRNxeP6HM7/tf7cvjn5hM8My+CZV2Uzp0qU7Lo0wN4OVjy032TzLpQLRzNrWbp\n8sP4OFqx8u4JeDkY/Q7i82q4fcURFDIpy2+LJcbPkS3HS3h0TSKutgo+uXkMFUo1j/2UCCI8Mz+C\nA1lV/JZcwkhfBxysLPjrVCVSiTBoupBlEoFoHwdG+DgQ6W2Pk7UcG4UUG4UMK1N6wyCKZu9oZbMW\nZbOOqkYN2RUNHMuvbbPaOp84WhsHtlqVltH+jkR62fNTXAEuNgpeXzSCg9lVfLE3mxE+Dnxy8xiU\nzTqWrYynpK6J166K5obx/ugNIm9uTeOLvdksGOHFO0tizDl8jc7AY2sS+e14iXGl2MFA/93BXF7a\nmMriMb68fd3Ibqdj3tiSxmd7snjt6miWTgzo+oBe8s6fGXyw4xRfLB3L7Kjui+sNJv42AUEQhHuB\newH8/f3H5uW12xLRbZ5al8SW46XEv3g5ctnQ2UIRRZHrPjtIblUj2x+f0WZg7ulnPbjqGFuOl/D9\nXROYMqzzDbL9mZXcseIoEV52rLx7Qpu68cPZVdz1bRwOVhb8cPcEs/LjqTIld3xzlMoGNe8tGcXc\naC8SC2p54IcEKpRqXrwikkvC3Hh49TGO5ddyfawv4Z72vPNHOnpRJMbXkfxqVZ89pi/SGmMHsgV1\nTVosLaTMifIkpaiONFPT4E3jA3ht8wnSy5TcPMGfFxdGsimpmBc3puBoJeeTW8Ywxt+JuiYtD686\nxp6MCm6dFMDLV0SZvZBVGh0P/JDArvQKXlgwnLuntV/5s/pIPs9sOM7lkR58ckaaqSs2JBTy+E9J\n3DzBn39fM6LfvpuzOV5Yx9Wf7OeqGG/eWTJqwM4z0Jz3gCAIwnaMSqln87woihtN79nNOVwhAOxM\nK+POb+L45o5xHdZAD1ZSi+u46qP9XBHjzbt9vDkb1Tqu+cS4DF5//2SCu8jZbjepZo70deC7uya0\nyfEnF9Zy29dHkEokfHnrWEb7GxXTK5Rq7vkujsSCWpbNCOGJ2WEom3U89lMiu9MrmBPlwatXRvPd\nwVw+25OFq62C/7skhIPZVWxLLSPQxRp3e0sSC2ovuqX1EYkAMokErcGAKBotURUyKTvSyvCws+Sp\nueHkVDby6e4snG3kvLF4BDG+jjz383G2pZYxMdiZD28cg5udgrTSeu5fmUBBtYp/XhVtNsQBKK1r\n5u7vjnKiuJ5/XT2i1WtnsuaoMRhMD3Xji1vHdrs66EBWJbevOMoYf0e+v2tCt4NIT1E2a7niw300\naw1se3Q6DtZDL1XUQncDwoBNkUVRnCWKYnQ7/20cqHN2hynDXLFVyPgtuW/CceeDKFO+/edjRWb/\n2d5io5DxxVLjHsJtK46Y5a07YlakBx/eOJqkwjpu+eqwuVu5hZG+jqxdNgkruYQlXxwy22y62SlY\nfe9Ebhzvz2d7srjxy0OodQa+vm0cz86LYFd6BfPe30uktz0bH5iKq62CVzadQBThhQXD0eqNdfd+\nTlZEeNrxNy3uOCdIJQIavYEYX0dmDffgWH4tu9LLuXNKEE/MCed/f2Tw4c5Mrojx5o/HpqPRicx5\nby+70ip4bn4EP9w9EVdbOd/sz+HKj/ajbNbx4z0TWw34yYW1XPnRPnIrVXx1W2y7wUAURT7dncXT\n648zdZgrny/tfjBILqzlnm/jCHSx5tObxw5YMBBFkafXJ1NQ08QHN44e0sGgJwz6lNGZ9McKAeDp\ndclsSi7m6POzhpwP6pkbXFsfndbnjszEglpu/OIQIe42rL53UpfVPdtSS3lo1TH8na357s7xeJ/l\nkVzdqOH+lfEczqnmvhnBPDE73PzQbkws4tkNx5HLJLx6ZRRXxniTWd7AE2uTSCqsY9ZwD56bH8G2\n1DI+3HkKrd7AjeP9sbOU8f3BPJRqHRGe9jRr9eRUDh1dqsFChKcd7vaWpBbVUdWoYW6UJ/NGeLI2\nrpB9mZWEe9jxypVR+Dha8cqmVHamlRPpZc+7S0YR7mlHubKZp9clsyu9gkvD3fjvdTHm+08URX44\nnM8/N5/A3U7B8tvGtVuNYzCI/Of3k3y1L4crYrz533Ux3U7dZpYrue6zg9goZKy/f3K31U97wzf7\nc3hlU/f22YYC5z1l1OlJBeEa4EPADagFEkVRnNPVcf0VEOLzqln86UHeWjyS68e1b9k3mDlZUs/V\nH+9nfJAz39wx3py37S270sq5+7s4xvo7seKOcV0GyUPZVdzzbRy2ljK+ui2WKO/WekQanYFXN6Xy\nw+F8xvg78sGNo80VStkVxgCQkF/L7EgP/nVNNM7Wcr7al8MHO06hM4gsmx7M4rG+fLIri5/iC3Cw\nsuC6sb40avT8cqwIlUaPr5MVcpmEgmoVWv3g2HQerIzwccBKLiWtpJ76Zh2TQ1y4apQ3O9OMUg/2\nljIevzyMRWN9Wf5XDp/uycJCIvDorDBunxKIVBBYE1fA67+fpFln4Pn5w7l1UoB587e+Wcuz64/z\n2/ESZoS58c71Me1KQjeodTy+JpE/TpRxm2nPobvVW+mlSm7+6jAA65ZNGlCHsv2Zldz29RFmhLnx\n5a2x/V5hdj4Y1AGht/RXQBBFkVnv7MHRWs76+yf3w5Wde1YdyefZDcc7rd7oCZuSinl0TSJj/B1Z\nccf4LlcKqcV13PVNHHVNWt6+LoYF7ZiEbEoq5rkNxxEEeH3RSPN79AaRr/fl8PYf6ShkEh6/PIxb\nJgZQ2aDhP7+f5NekYjztLXlo5jBG+Djw3vZT7Ewrx95SxqIxRk/dXxKLqFVp8XKwRGcQUal1NHYh\n3nchYaeQ4etsjQBkVjSg1RuYE+nJpBAXjuRW8/vxEmzlRnvLWycFsDm5hA93ZlLZoGbhSC9eWBCJ\np4Mlp8qUPPfzcY7m1jAhyJn/LBrRqkfgUHYVT65Lori2mSfnhHPvtOB2B9C8qkbu+S6OrIpGnps/\nnDunBHa7muh4YR1Lvz6MQibhh7sntjLY6W8yyxtY9Ml+PB0sWXf/5HaF94YiFwNCF3y5N5t//36S\n3x6e2maGOxQQRZHHf0ril8QiVtzePxvkvyWX8PDqY4zyc+Tr28d1WW9drmzm/pXGhqUHLg3h8cvD\n26xW8qtUPLQqgaTCOuZFe/LqVVG42xmX+lkVDbzyayp/nTKmK16+MpLJIa4czq7iza1pJOTX4uds\nxSMzwxjmbssnuzL540QZlhYSZkd6YqOQEp9XQ0ZZA1YWUpysLdDoDVQ3ahgklarnHF8nK2wVMpTN\nOopqm7BTyLhilDe+TlbsPFlOXF4NdgoZSycFcPvkQHanV/DhrlMUVDcxIciZp+ZGMDbAicoGNe9v\nP8WPR/KxVch4fv5wrov1NQ/iDWodb2w5ycpD+fg7W/PukhjGBrTfJbzjZBmP/5QEwMc3jWm3Ma0j\njuRUc9c3R3GwtuDHuye22+HcX1Q3arj64/2oNDp+/r8prXyfhzoXA0IX1DVpmfz6DmZHefa5Yud8\n0ajWcd1nB8mvVrH+/sn90kG55bgxKAS72rLijnFt9gjORq3T88qvqaw6UsD4QGfevWEUPmcdo9Ub\n+PKvbN7bfgorCykvLoxk8Rij160oivxxoozXNp+gsKaJmRHuPHZ5GFHe9uxOr+DtP9JJLa7Hx9GK\nO6cGMcrPkbVxBfySWESz1sD4IGdC3W2pbFCzK70Cjc6ApYUEC6kEmUSgvlk3aPoYBgofRyskEjAY\noLiuCVGEUX6OTBnmQpPGwJaUEkrqmvFztuKOyUHMG+HJxsRivt6XQ7lSTbSPPU/OiWB6qCtNWj0r\n9uca5dK1em4a788js0Jb7RXsOFnOy7+mUlzXxJ1TgvjH7LB2dYmatXre2JLGNwdyGe5lz2e3jCHA\npfupnl+OFRnltp2MPS5d3Yt9oUGt45avDnOypJ5V905kjKlK7u/CxYDQDV7dlMr3B/P46+lLzQ1V\nQ42Suiau+mg/FlIJPz8w2Tz77gv7MytZ9n08NgoZ39w5jgjPrjtAfz5WyAs/pyCVCK3SQ2eSWd7A\nM+uTicurYYy/Iy9fEUWMn9FgpFmrZ/m+HD7fk0V9s475Izx5bJZxZfDniTK+/Cubo7k12FnKuGm8\nP/NHeHEou4rvD+VRWNOEjVxqrCCzlFHZoGF/ZiV6g4ilhQS9QUQQBARA/TcoXbW0kLRK6VU1ahBF\nCPOwZXKIKxZSgaSCOo7kViMRYHqYGzeM8yfAxZo1RwtYF290+5o6zJX7ZgQzdZgrjRo93x3MZflf\nOVQ1arg80oOn50a0Ss+cKlPyz80n+OtUJaHutryxeCRjA9ofONNLlTyy+hhppUrunBLE0/PCu11J\nJIoi7+84xXvbTzEhyJnPl47tU99NVzRr9dy+4ghHc2v49OYxQ7b5rDMuBoRuUFCtYsZ/d3H3tGCe\nmz9wOigDzfHCOq7//CChHrb8cPcE7Poh73mypJ47VhylUa3jnSWjuDzSo8tj8qoaeXh1IkkFtVw1\nypuXFka22Vw0GETWJxTy5tZ0KhvULB7jy5NzwvF0MAayuiYty/fl8PW+HBo1OmZGeHDv9GDGBTqR\nWFDLV3/lsCWlBIMIk0NcuD7WDycbOb8nl/D78RKUah2utnJG+TkhCMbVSXxuDUq1USNJZiq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TVz+McN1dO64/hEB/pcfOp3u+l3BfjaDQtOqs56KVIJ4Tzcu7GN7/61lZ99cCnXLrp4ViFEYhrf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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Here we transform from polar to cartesian coordinates \n", "# to then plot\n", "cx = [it[0]*np.sin(it[2]) for it in y]\n", "cy = [it[0]*np.cos(it[2]) for it in y]\n", "plt.plot(cx,cy)\n", "plt.title(\"Orbit resulting from the chosen initial conditions\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### We perform the numerical integration using gduals (to get a HOTM)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# Order of the Taylor Map. If we have 4 variables the number of terms in the Taylor expansion in 329 at order 7 \n", "order = 6\n", "# We now define the initial conditions as gdual (not float)\n", "ic_g = [gdual(ic[0], \"r\", order), gdual(ic[1], \"vr\", order), gdual(ic[2], \"t\", order), gdual(ic[3], \"vt\", order)]" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "--- 183.67201781272888 seconds ---\n" ] } ], "source": [ "import time\n", "start_time = time.time()\n", "# We call the numerical integrator, this time it will compute on gduals\n", "y = rk4(eom_kep_polar, it, ic_g, step, n_steps)\n", "print(\"--- %s seconds ---\" % (time.time() - start_time))\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\[ 0.528727{dt}^{3}+812961{dr}{dt}^{3}{dvt}-76468.3{dr}{dt}^{3}{dvr}-4.15449e+11{dr}^{2}{dvr}^{3}+2.8007e+12{dr}^{3}{dt}{dvt}-516.738{dt}^{3}{dvt}-7.651e+07{dr}^{2}{dt}^{3}{dvr}-5.40986e+08{dr}^{3}{dt}^{3}+1.54096e+12{dt}{dvr}^{2}{dvt}^{3}+6.053e+14{dr}^{2}{dt}{dvt}^{3}-1380.12{dt}^{2}{dvt}+4.15004e+11{dr}{dvr}^{3}{dvt}-3.72337e+08{dr}{dt}{dvr}^{3}-1.68326{dt}^{2}-3.17062e+14{dr}{dvr}^{3}{dvt}^{2}+2.6941e+07{dvr}^{5}-1.63654e+10{dr}^{2}{dt}{dvr}^{2}-1.47832e+09{dr}^{3}{dt}^{2}+48.4846{dt}^{3}{dvr}+1.98873e+06{dt}^{3}{dvr}^{2}{dvt}+\\ldots+\\mathcal{O}\\left(7\\right) \\]\n", "xf (latex):\n" ] }, { "data": { "text/latex": [ "\\[ 0.528727{dt}^{3}+812961{dr}{dt}^{3}{dvt}-76468.3{dr}{dt}^{3}{dvr}-4.15449e+11{dr}^{2}{dvr}^{3}+2.8007e+12{dr}^{3}{dt}{dvt}-516.738{dt}^{3}{dvt}-7.651e+07{dr}^{2}{dt}^{3}{dvr}-5.40986e+08{dr}^{3}{dt}^{3}+1.54096e+12{dt}{dvr}^{2}{dvt}^{3}+6.053e+14{dr}^{2}{dt}{dvt}^{3}-1380.12{dt}^{2}{dvt}+4.15004e+11{dr}{dvr}^{3}{dvt}-3.72337e+08{dr}{dt}{dvr}^{3}-1.68326{dt}^{2}-3.17062e+14{dr}{dvr}^{3}{dvt}^{2}+2.6941e+07{dvr}^{5}-1.63654e+10{dr}^{2}{dt}{dvr}^{2}-1.47832e+09{dr}^{3}{dt}^{2}+48.4846{dt}^{3}{dvr}+1.98873e+06{dt}^{3}{dvr}^{2}{dvt}+\\ldots+\\mathcal{O}\\left(7\\right) \\]" ], "text/plain": [ "0.528727*dt**3+812961*dr*dt**3*dvt-76468.3*dr*dt**3*dvr-4.15449e+11*dr**2*dvr**3+2.8007e+12*dr**3*dt*dvt-516.738*dt**3*dvt-7.651e+07*dr**2*dt**3*dvr-5.40986e+08*dr**3*dt**3+1.54096e+12*dt*dvr**2*dvt**3+6.053e+14*dr**2*dt*dvt**3-1380.12*dt**2*dvt+4.15004e+11*dr*dvr**3*dvt-3.72337e+08*dr*dt*dvr**3-1.68326*dt**2-3.17062e+14*dr*dvr**3*dvt**2+2.6941e+07*dvr**5-1.63654e+10*dr**2*dt*dvr**2-1.47832e+09*dr**3*dt**2+48.4846*dt**3*dvr+1.98873e+06*dt**3*dvr**2*dvt+..." ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# We extract the last point\n", "yf = y[-1]\n", "# And unpack it into some convinient names\n", "rf,vrf,tf,vtf = yf\n", "# We compute the final cartesian components\n", "xf = rf * sin(tf)\n", "yf = rf * cos(tf)\n", "# Note that you can get the latex representation of the gdual\n", "print(xf._repr_latex_())\n", "print(\"xf (latex):\")\n", "xf" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Final x from the gdual integration 3.3665168110417256\n", "Final y from the gdual integration -3.1723626941974543\n", "\n", "Final x from the float integration 3.3665168110875494\n", "Final y from the float integration -3.172362694145616\n" ] } ], "source": [ "# We can extract the value of the polinomial when $\\mathbf {dy} = 0$\n", "print(\"Final x from the gdual integration\", xf.constant_cf)\n", "print(\"Final y from the gdual integration\", yf.constant_cf)\n", "# And check its indeed the result of the 'reference' trajectory (the lineariation point)\n", "print(\"\\nFinal x from the float integration\", cx[-1])\n", "print(\"Final y from the float integration\", cy[-1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### We visualize the HOTM" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "--- 7.01151704788208 seconds ---\n" ] } ], "source": [ "# Let us now visualize the Taylor map by creating a grid of perturbations on the initial conditions and\n", "# evaluating the map for those values\n", "Npoints = 20 # 10000 points\n", "epsilon = 1e-3\n", "grid = np.arange(-epsilon,epsilon,2*epsilon/Npoints)\n", "nxf = [0] * len(grid)**4\n", "nyf = [0] * len(grid)**4\n", "i=0\n", "import time\n", "start_time = time.time()\n", "for dr in grid:\n", " for dt in grid:\n", " for dvr in grid:\n", " for dvt in grid:\n", " nxf[i] = xf.evaluate({\"dr\":dr, \"dt\":dt, \"dvr\":dvr,\"dvt\":dvt})\n", " nyf[i] = yf.evaluate({\"dr\":dr, \"dt\":dt, \"dvr\":dvr,\"dvt\":dvt})\n", " i = i+1\n", "print(\"--- %s seconds ---\" % (time.time() - start_time))" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5,1,'Stretch')" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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29PSg+xLiYMJ9HcI4GmOMOVWgFv5pGS7Tt7IOSC6ZRO+2tSxQOw3LsBU1xw7C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uAFD2LtJSRF8mG3a15w+36hUuojpVRZrbV3n/pQY/ssaYZdvByMWJor9WoNX1jkVayVLh7Bva2q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\nYTOzl4DN0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f, axarr = plt.subplots(1,3,figsize=(15,5))\n", "# Normal plot of the final map\n", "axarr[0].plot(nxf,nyf,'.')\n", "axarr[0].plot(cx,cy)\n", "axarr[0].set_title(\"The map\")\n", "\n", "# Zoomed plot of the final map (equal axis)\n", "axarr[1].plot(nxf,nyf,'.')\n", "axarr[1].plot(cx,cy)\n", "axarr[1].set_xlim([cx[-1] - 0.1, cx[-1] +0.1])\n", "axarr[1].set_ylim([cy[-1] - 0.1, cy[-1] +0.1])\n", "axarr[1].set_title(\"Zoom\")\n", "\n", "# Zoomed plot of the final map (unequal axis)\n", "axarr[2].plot(nxf,nyf,'.')\n", "axarr[2].plot(cx,cy)\n", "axarr[2].set_xlim([cx[-1] - 0.007, cx[-1] + 0.007])\n", "axarr[2].set_ylim([cy[-1] - 0.007, cy[-1] + 0.007])\n", "axarr[2].set_title(\"Stretch\")\n", "#axarr[1].set_xlim([cx[-1] - 0.1, cx[-1] + 0.1])\n", "#axarr[1].set_ylim([cy[-1] - 0.1, cy[-1] + 0.1])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### How much faster is now to evaluate the Map rather than perform a new numerical integration?\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "# First we profile the method evaluate (note that you need to call the method 4 times to get the full state)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "20 µs ± 966 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n" ] } ], "source": [ "timeit xf.evaluate({\"dr\":epsilon, \"dt\":epsilon, \"dvr\":epsilon,\"dvt\":epsilon})" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "# Then we profile the Runge-Kutta 4 integrator" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "774 ms ± 16.7 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n" ] } ], "source": [ "timeit rk4(eom_kep_polar, 0, [it + epsilon for it in ic], step, n_steps)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0,0.5,'Error in estimating the final state (x)')" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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CrwBbi9aHbQ9pmdnpKZaPAkZlFqorj5as2cxvnpzI5EVr+PUhXbnyqJ7U8HHA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\nXFZFqYhfIeks4Olw/nSCxvI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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# It seems the speedup is 2-3 orders of magnitude, but did we loose precision?\n", "# We plot the error in the final result as computed by the HOTM and by the Runge-Kutta\n", "# as a function of the distance from the original initial conditions\n", "out = []\n", "pert = np.arange(0,2e-3,2*1e-4)\n", "for epsilon in pert:\n", " res_map_xf = xf.evaluate({\"dr\":epsilon, \"dt\":epsilon, \"dvr\":epsilon,\"dvt\":epsilon})\n", " res_int = rk4(eom_kep_polar, 0, [it + epsilon for it in ic], step, n_steps)\n", " res_int_x = [it[0]*np.sin(it[2]) for it in res_int]\n", " res_int_xf = res_int_x[-1]\n", " out.append(np.abs(res_map_xf - res_int_xf))\n", "plt.semilogy(pert,out)\n", "plt.title(\"Error introduced by the use of the polynomial\")\n", "plt.xlabel(\"Perturbation of the initial conditions\")\n", "plt.ylabel(\"Error in estimating the final state (x)\")" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 2 }