{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 3. Trust Region\n", "For this training course we'll be using the optimization routines in SciPy." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy.optimize as opt\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also need to define a callback function so that we can plot the optimization steps." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def callback(x):\n", " global xprev\n", " plt.plot([xprev[0],x[0]],[xprev[1],x[1]],'b.-')\n", " xprev = x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3.1 Trust Region Subproblem\n", "Consider the trust-region subproblem given by\n", "\n", "$\n", "\\begin{align}\n", "&\\min_{s \\in \\mathbb{R}^n} s^Tg + \\frac{1}{2}s^THs \\\\\n", "&\\text{ s.t. } \\lVert s \\rVert_2 \\le \\Delta \n", "\\end{align}\n", "$\n", "\n", "and recall that any global minimizer $s$ satisfies\n", "\n", "$\n", "\\begin{align}\n", "(H + \\lambda I)s = -g \\\\\n", "(H + \\lambda I) \\succeq 0 \\\\\n", "\\lambda \\left(\\lVert s \\rVert_2 - \\Delta \\right)=0\n", "\\end{align}\n", "$\n", "\n", "from the relevant optimality conditions. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.1.1 Solving the Subproblem\n", "\n", "#### Coding Task:\n", "\n", "Define the secular function as\n", "\n", "$\n", "\\begin{align}\n", "\\phi(\\lambda) = \\lVert s(\\lambda) \\rVert_2 = \\lVert -(H + \\lambda I)^{-1}g \\rVert_2\n", "\\end{align}\n", "$\n", "\n", "and plot the following on the same plot: \n", "\n", "1. $\\phi(\\lambda)$ against $\\lambda$\n", "\n", "2. the trust region radius $\\Delta$\n", "\n", "3. $-\\lambda_1$ (minus the smallest eigenvalue) of $H$\n", "\n", "4. $\\lambda = 0$\n", "\n", "Use your plot to estimate:\n", "\n", "1. the optimal $\\lambda^*$ and thus the optimal solution $s^*$ to the trust-region subproblem \n", "\n", "2. if the optimal solution $s^*$ is constrained or unconstrained\n", "\n", "for the following input data:\n", "\n", "$\n", "\\begin{align}\n", "H = \n", "\\begin{pmatrix}\n", "1 & 0 & 0 \\\\\n", "0 & 2 & 0 \\\\\n", "0 & 0 & 2\n", "\\end{pmatrix},\\qquad\\quad\n", "g = \n", "\\begin{pmatrix}\n", "1 \\\\\n", "0 \\\\\n", "1\n", "\\end{pmatrix},\\quad\n", "\\text{ and } \\Delta = 2 \n", "\\end{align}\n", "$\n", "\n", "$\n", "\\begin{align}\n", "H = \n", "\\begin{pmatrix}\n", "1 & 0 & 0 \\\\\n", "0 & 2 & 0 \\\\\n", "0 & 0 & 2\n", "\\end{pmatrix},\\qquad\\quad\n", "g = \n", "\\begin{pmatrix}\n", "1 \\\\\n", "0 \\\\\n", "1\n", "\\end{pmatrix},\\quad\n", "\\text{ and } \\Delta = 5/12 \n", "\\end{align}\n", "$\n", "\n", "$\n", "\\begin{align}\n", "H = \n", "\\begin{pmatrix}\n", "-2 & 0 & 0 \\\\\n", "0 & -1 & 0 \\\\\n", "0 & 0 & -1\n", "\\end{pmatrix},\\quad\n", "g = \n", "\\begin{pmatrix}\n", "1 \\\\\n", "0 \\\\\n", "1\n", "\\end{pmatrix},\\quad\n", "\\text{ and } \\Delta = 5/12 \n", "\\end{align}\n", "$\n", "\n", "$\n", "\\begin{align}\n", "H = \n", "\\begin{pmatrix}\n", "-2 & 0 & 0 \\\\\n", "0 & -1 & 0 \\\\\n", "0 & 0 & -1\n", "\\end{pmatrix},\\quad\n", "g = \n", "\\begin{pmatrix}\n", "0 \\\\\n", "0 \\\\\n", "1\n", "\\end{pmatrix},\\quad\n", "\\text{ and } \\Delta = 1/2 \n", "\\end{align}\n", "$\n", "\n", "$\n", "\\begin{align}\n", "H = \n", "\\begin{pmatrix}\n", "-2 & 0 & 0 \\\\\n", "0 & -1 & 0 \\\\\n", "0 & 0 & -1\n", "\\end{pmatrix},\\quad\n", "g = \n", "\\begin{pmatrix}\n", "0 \\\\\n", "0 \\\\\n", "1\n", "\\end{pmatrix},\\quad\n", "\\text{ and } \\Delta = \\sqrt{2} \n", "\\end{align}\n", "$\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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tv30jgrgLaw2p7N/lUEG3DgQ2kkwmnTbBMkqVeVir2YqbcSJVvsZRoW0LEtWlyEr3ZQlU9u9yqKBbBwIbUaFcbSlKbShbq9myqaEyewiutO0plMKwGq8LcwQq+3c5VNCtA4GN9Pb2Om2CZZSaGlqr2aoNZUamhgIWTEuVwo2H16vs3+VQQbcOBDZS8bi4BiZ/gw2sGRGs1Rz0eUllJJmseVMnlcpfX2nbxhyBC88sVtm/y6GCbh0IbCSmcAKx1KqhtZrzUzhm1vwpdiBOMXLTUvaMCLJZ99U0Utm/y6GCbh0IbKSpqclpEyyjVCBYq9mKHb6JdPaa8tfFsHPVkMfjvj8tlf27HCrodp+3Okh/f7/TJlhGIp3B6xH41pSYWKvZipo/VU0N2bRqKBQK2dJOPaGyf5dDBd06ENjIxMSE0yZYRqklnGs1W3FAjPENZfZNDSUSCVvaqSdU9u9yqKBbBwIbiUajTptgGaWeytdqvlIO2sSpoZTBDWU2JotVqD9TLSr7dzlU0K0DgY2oXJo4WWIJ51rNlk0NGdlH4PfYdjCNp0zdI1VR2b/LoYJuHQhsZGBgwGkTLKPUpq61mq1JFlczNWRTjkCBBGK1qOzf5VBBtw4ENjI5Oem0CZaRSGevOYsArtVsTY6gig1lNuUIki7MEajs3+VQQbcOBDYyPz/vtAmWUWp6Zq3m/DJPs57MpZQr01LGN5RJG+oApV2YI1DZv8uhgm4dCGxE5fozuemZa/Wt1Wz21JCR84pXty0lpDLWBwL3ZQjU9u9yqKBbBwIbGRwcdNoEyyi1fHSt5iuBwJwRgZHziq+0nR+NWP+03tzcbHkb9YbK/l0OFXTrQGAjU1NTTptgGaWWj67VXJgaMilHYOS84ittmxuEyqFCaeJqUdm/y6GCbh0IbGR2dtZpEyyj1NTQWs2mTw0ZOK/42ratDwSpdNryNuoNlf27HCro1oFAYwpJo2v5rZoaMlJraCVQ2bWXQKNpFHQgsJGhoSGnTbCMUlNDazWbvaGs1IE4xbBiD0Mp3JgjUNm/y6GCbh0IbESFIWQpEunsNWcRwLWa/V6BEGaOCIznCAIW7GEoRTqVsryNekNl/y6HCrp1ILCR6elpp02wjNyZANdOz6zVLIQw9ZSy2lYN2ZAsdmEgUNm/y6GC7roIBEKIdiHEF4UQzwshhoUQdzptk6Y6jJaCBnMPka9qH4EFBe80GhXwOW3ACn8DfFNK+XohRABQcoJ1586dTptgCelMlnRWFn0qL6bZzCqg+SMyq8oR2DA11OzCWkOq+nclVNDteCAQQrQBrwDeDiClTAJKLsJWoVxtMZKZ0k/lxTTnTgpTe2rIjSUmVPXvSqig2/FAAGwHZoBPCiFeAhwC3i2lXFp9kRDiAeABgO7ubqamppidnS3Mz+3cuZNoNFooADUwMEAymWR8fBy4copQ/qDpvr4+AoEAo6OjAPT09BAOhzlx4gQAXV1dRCIRhoeHAYhEInR3dzMyMkImk6G9vZ2enh5GR0dJJpOEw2F6e3sZGxsjFovR1NREf38/ExMTRKNRAoEAFy5cIBaLMT8/j9frZXBwsKADcqsPGk3TwMAAI2O5gzkmzpxmejp8laa5uTkymcxVmkQmzcT5C+zbt2/dmk5Hc0/eRw7+mIlmT1lN45dyB8pPz17iwIGzZTVNTk7W3E+JUIhoNMq+ffvqqp/Wo8lIPz3zzDOF61XRZKSfvvGNbzA5OdkQmkoipXT0C9gDpIG9K6//BvhAud/ZvXu3bEQef/xxp02whMn5mNz24KPyof1nrvlZMc0//eEn5Ds+9bQpbX9m/5jc9uCjcupyrOK15+eX5bYHH5X/cuBaO83knsOH5UsU7etyqOrflWgk3cBBWeSeWg/J4glgQkp5YOX1F4HbHLTHMlSoW16Mcmv5i2k2dWooVf3UkB0byppceGaxqv5dCRV0Ox4IpJQXgHEhRL5y06uA4w6aZBmq1p8prOUvkiMoptnUZHGV1Udzv2P9/H3WhlLX9Yaq/l0JFXQ7HghW+F3gISHEs8AtwP921hxryM/bqUb+ZlzsYJpims08KSx/Uy/W9lrs3FDmxsPrVfXvSqigux6SxUgpj5LLFWgakCsjAmN12YM+T2HZ5/rbzp2M5vFUPgHA5xF4TNzVrNGoQr2MCFxBPoOvGuUqgBbTHPR7TZunL3UOQjFyu5q9tkwNhYJBy9uoN1T170qooFsHAs26SVRR+C1/nZlTQ0byA4W2/ea1rdGogg4ENlJxLW+DcqXw27VTQ8U0m11ryMiKoavatiFHEHdhjkBV/66ECrqrDgRCiBYhROMf0qkxjWpW7oD5tYaMjkQKbetaQxrNVVT8CxJCeIQQvyKE+JoQYhp4HpgUQhwXQvy5EGKH9WaqQV9fn9MmWEK5qaFims2cnkmkMkXLX5ci6PMUSmJYSdCFOQJV/bsSKug28hf0ODAAvB+4TkrZJ6XsAl4G7Ac+JIR4i4U2KkMgEHDaBEsoV++nmOb8zTibXf9a+0Q6a3i1EqwEIRumhjyi8iom1VDVvyuhgm4jgeDVUsoPSCmflVIW/oKklHNSyoellL8MfM46E9UhX7NENfJLQYs9mRfTXNjha8KTee6sZOMjgoDXnmRxLB63vI16Q1X/roQKuiv+BUkpK56wYeQajbrUsmoIzNnYpXMEGs36qWpDmRCiD7gRuAl4MXCjlFJvBDNIT0+P0yZYQrlAUEzz1QfE+NfXdipLpKW6qaGlpfS62jSCCtMF1aKqf1dCBd1GksW/KYR4UggxD5wAfgNoBb4C/Iq15qlFOBx22gRLSKRzCVtRZF68mGYzzwWoeh+BTctHfV73LaxT1b8roYJuI39B7wfeC+wGHgVCwCdW8gMnrDRONfJ1zFWj3O7eYprz18ZNKDMRr2Jnca5te6aGlmMxy9uoN1T170qooNvIX9D9UsoDUspRKeUbgL8FviqEeK8QQm9I01S9qWtjc27aZG5p/VUbLy0nC59nBDN3NWs0qmAkWfyTNa+/AdwOdAA/ssguJenq6nLaBEtIpEqv3CmmuWtDbo39dHR9u28XE2mWkxm6wsbX7If8XmImFbwrR8C/vtxHI6Kqf1dCBd1GcgTXTPxKKRNSyv8CvK3UNZpriUQiTptgCReXknS2Fn8qL6a5O5w7tGVqYX1LLPO/373B+CEwHS0BLsdSpCzeVOZzYSBQ1b8roYJuQxvKhBC/K4TYuvpNIUQA6BVCfJqVgKApT/68VtWYiSbYVOKpvJjmDU0+gj7PukcE+UCQH2EYYVM4iJTmTEuVY3l52dLPr0dU9e9KqKDbSCC4D8gAnxVC5EtLnAZOAm8GPiyl/JSFNmrqnJlogs5W4zdjIQRdG4JMr3NEMLMSSLrCxkcEeTtn1hmENBqVqLiPQEoZBz4KfFQIEQbCwLKUct5i25RDhSHkWjJZydxS6RFBKc3d4RBTC+aMCLqrHBEAzCxaGwj8vro488lWVPRvI6ig2/CqHyHEu4Ax4MfAU0KId1pllKp0d3c7bYLpzC0lyUpKBoJSmrs3hJiKrjdHkKA54KU1aPymm08sWz0icOOGMhX92wgq6DaSLP4bIcTbgPcAQ1LKXuAVwI1CiA9YbJ9SjIyMOG2C6eRvqJtKTA2V0rwpHGRmnSOC6WiCrnCw6Ea2Utg1NeTGHIGK/m0EFXRXU320E3hSCHEY+HNgFHiTEGKjhfYpRSajXo2b/BRLqRFBKc3dG0JEE2mWErWXe5haiNNVxYohgKaAl3DQZ3kgWH9d1cZDRf82ggq6jewj+JKU8r+SKzn9OuDVwKeANLm9BN8TQjR++T0baG9vd9oE07m4ckMtlSwupTk/RbOelUPTC/Gq9hDk6QwHuWhxjsCNJSZU9G8jqKC7mozWO4HPA0eBY8AQcExKee/KUlJNBVQoTrWWSiOCUprza/+nF+Js72ypul0pJdPRRFV7CPJsag1anyNw4cE0Kvq3EVTQbThZLKU8CewFvkiu3tCzwC+u/MzaRdmKoELd8rXMRHMJ25YSCdtSmvMrfaZqvCHndxVXs2Ioz6Zw0PJVQ3EX1hpS0b+NoILuqta4rdzwv7bypamSZFK9eFluMxmU1pxf+1/rXoLpGvYQ5NkUDvLESWsDQVa6L0ugon8bQQXdumicjahQrnYtFxfLbyYrpXm9u4tr2VWcp7M1QDSeNqX6aSm8LswRqOjfRlBBtw4ENtLb2+u0CaYzE02UXDoKpTULIXJ7CWodEawsPa0pR7AygrEyYezGw+tV9G8jqKBbBwIbGRsbc9oE05lZLD81VE5zVzhYuKFXy/TKZrRaVg1tsmFTWdyFZxar6N9GUEG3DgQ2ElMsgZhMZ5lfTpUNBOU0r2d3cS27ivNsas2NIqwMBNms+848UM2/jaKCbh0IbKSpqclpE0xldqn80lEor3nTOkYEUyt7CGqpgH5lasi6JJ/H474/LdX82ygq6HaftzpIf3+/0yaYykyFzWRQXnP3hhCLNe4uno4mqt5VnCeycnaClSOCUKg22xoZ1fzbKCro1oHARiYmJpw2wVQKdYbKjAjKae5ex0ll0wvxmhLFAH6vh43NfmYWrZvHTyTcV+ZaNf82igq66yYQCCG8QogjQohHnbbFKqLRqNMmmIqRQFBOc1eNJ5VJKZlaSNSUKM6zKWzt7mIV6s9Ui2r+bRQVdNdNIADeDTT+UT9lUK00cX75ZaljKqG85lpHBIuJNLFUbbuK82wKB63NEbjw9FbV/NsoKuiui0AghOgFfhb4R6dtsZKBgQGnTTCVmWiCDSEfQV/pzVPlNHdtqG138dQ69hDk6bS43lBIgQRitajm30ZRQXe9HKP0YeB95E4/K4oQ4gHgAcgdBDE1NcXs7CzT09MA7Ny5k2g0yuTkJJDrnGQyyfj4OHAloZNf89vX10cgECjUCenp6SEcDnPixAkAurq6iEQihfNII5EI3d3djIyMkMlkaG9vp6enh9HRUZLJJOFwmN7eXsbGxojFYjQ1NdHf38/ExATRaJRAIEAsFmNycpL5+Xm8Xi+Dg4MFHQBDQ0MNpWl4LElHs4+jR4+W1JTJZEpqklIS8ApGzk6xb99Zw5pG5nM+cX70eY4HLtekKb04x4XLcfbv38/27duv6qeBgYF19VMiFGJxcZF9+/bVRT+ZocmI7508ebKQJFdFk5F++upXv8qOHTsaQlNJpJSOfgH3Ax9d+f5e4NFKv7N7927ZiDz++ONOm2Aqr/+7H8k3/sOTZa+ppPnlH/qefNdnD1fV7r8dnpDbHnxUvjAdrer3VvP3+16Q2x58VEbjqZo/oxT3HD4sX6JYXxtBNf82SiPpBg7KIvfUepgauhv4eSHEGPCvwCuFEJ9x1iRrUK3+zMXFJJsqFH2rpLkrHKw6WVyoM7TOZDFcOU/BbNyXIVDPv42igm7HA4GU8v1Syl4pZT/wJuB7Usq3OGyWJQwODjptgqlUqjMElTV3bwhVnSyejta+qziP1YfYNzc3W/K59Yxq/m0UFXQ7HgjcxNTUlNMmmMZyMs1iIk1nuPyKiUqauzZUv7t4amUPQS27ivNYfXaxCqWJq0Ul/64GFXTXVSCQUu6TUt7vtB1WkU/4qMDFaO5GV2lEUElzV7j63cXTC+UL3RnB6sJzqXTtZzE3Kir5dzWooLuuAoGmcah0RKVRatlLMB2tfVdxno3NAbweYfnZxRpNI6ADgY0MDQ05bYJpGNlVDJU1X9eWu6GPzy0bajeVyTJ5Oc5169hMBuD1CCItActGBG7MEajk39Wggm4dCGxEhSFknsKIYJ1TQy/e0oZHwMGxOUPtHjt3mUQ6y61bNxoztAxWbipLp1KWfG49o5J/V4MKunUgsJH8JhAVmIkmEAI6WsoniytpDof83LSljf2njQWCA6dy192+vcOYoWWw8hD7pAsDgUr+XQ0q6NaBQFMTFxcTRFoC+Lzrd6G92zs4Oj5v6AzhA6dn2dHVWrb0tVE2hYOW7SPQaBoJHQhsZOfOnU6bYBrTC3FDN2Mjmvduj5BMZzk6Pl/2unQmy8GxS+w1YTQAV0YEmaw05fNW0+zCWkMq+Xc1qKBbBwIbUaFcbZ6RqSg7ulorXmdE80u3dyDElWmfUhyfXGAxkWbv9RHDdpZjx6ZWUhnJ6YtLpnzeatK6DLVrUEG3DgQ2ki8M1ehcjqUYn4sx1LOh4rVGNLc1+Rm6bgMHTpdPuuUDxR0mjQjy9h+fXDDl81bjxg1lqvh3taigWwcCTdU8v3Lj3LW5ciAwyt7rOzh89hLJdOlD3w+cnmV7Z0vNR1SuZUdXK36v4Ph58wOBRtNI6EBgIyrULYcrT9A3GhgRGNW8d3uEeCrLsxPzRX+eyUp+fHrOtPwAQMDn4YausCUjgiYXnlmsin9Xiwq6dSCwEVWmC4YnF+hsDRjaVWxUc3456IESy0ifv7DAQjzN3uvNCwSQG9UMWxAIstL8BHS9o4p/V4sKunUgsJH8YRGNzvHJBYZ6Nhgq+mZUc0dLgMHuMPtPFc8T5PMDe7ebkyjOM9SzgZlogumouQfZu/HwelX8u1pU0K0DgaYqUpksJy4sssvAtFC17L2+g0NnLpHKXJsnOHB6lr6OJja3m7ssM69jeLLxV35oNLWiA4GN5I+Na2RGZxZJZrKGE8XVaL59ewfLyQwHxy5d9X4smeHHp+e4vd/c0QBcCQRmJ4xDwfVveGs0VPDvWlBBtw4EmqrI3zCNLB2tlpffsIlN4SC//4VnCgfaZ7KS93zuCPOxFL902xbT22xr9rOlvcmShLFG0yjoQGAjFQ+QbgCGJxcI+Dxc39li6PpqNLc1+fnk21/KpeUk/+HTT7OUSPNnXx/mW89N8Sc/u4u7d3TWaHV5hnrMTxjHXZgjUMG/a0EF3ToQaKri+OQCL7oubEqNoWLctKWNj/zKrRw/v8DPfeSH/OMPT/P2u/p5x8u2W9Ie5FYOnZpZJJZ0325gjQZ0ILCVvr4+p01YF1JKjp9fqCpRXIvmV76om//+ups4NbPEa3Z181/u31X1Z1TDrp4NZGWubIZZBF2YI2h0/64VFXTXfvq3pmoCgfIlm+udCwtxLi2nqsoP1Kr5rXds49a+dm7obsXrqf1sYiOsThjf0tduymd61nGecqPS6P5dKyro1iMCGxkdHXXahHUxXENpifVovmlLG0Gft+bfN0rvxibCQZ+peYJY3Nx9CY1Ao/t3raigWwcCjWHyK4ZedF3YYUvMxeMRDPVs0CuHNK5FBwIb6enpcdqEdXF8coGtHc2EQ37Dv9Momod6wgxPLpA16WwCFaYLqqVR+tpsVNCtA4GNhMON+ySdL/pW7Rx6o2i+ZWs7y8kMx85dNuXzfF7rp7TqjUbpa7NRQbcOBDZy4sQJp02omSNnL3FxMclrdnVX9XuNovmnBrvwegTfPn7BlM9bjsVM+ZxGolH62mxU0K0DgcYQjx2fwu8V3Du4yWlTLKG9OcDt/R08dnzKaVM0GtvRgcBGurq6nDahJqSUfOu5C9w50FlVfgAaS/Nrb+zmxNSiKUdXBvzV/T+pQCP1tZmooFsHAhuJRMwvmmYHL0wvMja7XPW0EDSW5ry+x0yYHvK5MBA0Ul+biQq6dSCwkeHhYadNqIlvr0yXvGao+kDQSJp7Nzazq2eDKdNDy8vLJljUWDRSX5uJCrp1INBU5NvHp3hJXzvXtal//OJrb+zm4JlLXFx0X9E4jXvRgcBGGnEIObUQ55nxeV5bw7QQNJ7m1+zqRkr43vD0uj7H73Nf9ZZG62uzUEG3DgQ20t1d283USfLTJLUGgkbTvKtnA1vam9a9jNSNG8oara/NQgXdjgcCIUSfEOJxIcRxIcRzQoh3O22TVYyMjDhtQtV8+/gU2ztb2NHVWtPvN5pmIQSvvbGbH5y8yFIiXfPnuDFH0Gh9bRYq6HY8EABp4PeklLuAO4B3CiGsrTvsEJlMY9W7H51Z5AcnZ/i5m3sMHVRfjEbTDPDzL9lMIp3l8wdrP5TcnEIVjUUj9rUZqKBbSFlfLiuE+DLwESnlY6Wu2RXeJR/a/ZCNVpnD4uIira21PVk7wemZJWYWE9y6dSN+b22BoNE05zl+foFEOsstfe1UGwOfWVwkk8lwW1ubNcbVKY3a1+ulkXTf9v3bDkkp96x9v64yWkKIfuBW4ECRnz0APABwvf96UskUqXSKVDIFQFNzE5l0hmQyCUCoKYTMShIrRwYGQ7mDQhLxldfBIMIjiMdy5YIDgQBen5fYcq40gD/gx+/zF4b4Pr+PQCCQey3B6/MSDASJxWPIrMTr9RIMBonH42SzWTweD6FQiEQiQSaTQXgEXq+XxcVFMukMCGhubiaZTJJO5aYgmpub60ZTMp1lZjFLpMVPfGmR5RKamkJNJJKJkpp8fh/Ly8t1ocloPzWFmugIwZn5LOMz8/RsbKmqn7IegQQuz1+uK03l+skM32OVZlU0GemneDxOJp1pCE2lqJsRgRCiFfg+8L+klI+Uu3bPnj3y4MGD9hhmIk8++SR33XWX02YY4s++PszHf3CKfb//U2yNNNf8OY2keTVSSu778A+QSL757lfgqeJwnHuPHGFhYYHD99xjoYX1R6P29XppJN1CiKIjgnrIESCE8AMPAw9VCgKNTD5q1zuXYykeOnCW+2/evK4gAI2jeS1CCH7r3us5MbXI4yPVLyXN1skDlp00al+vFxV0Ox4IRC4L+U/AsJTyr5y2x0oapVztZ/afYTGR5jfvuX7dn9Uomotx/82b2dLexN9/v/oTqLy6DLVrUEG344EAuBt4K/BKIcTRla+fcdooK+jt7XXahIpcWkryTz88zSt2buLGzetPdjaC5lL4vR7+48u38/TYJb5/Yqaq33Xj4fWN3NfrQQXdjgcCKeUPpZRCSnmzlPKWla+vO22XFYyNjTltQkU+8OhxFmIp/vC+F5nyeY2guRxvun0rA5ta+KNHjlW1ryDuwjOLG72va0UF3Y4HAjcRq/PDSh5/fppHjpzjt+8dqOqA+nLUu+ZKhPxe/s/rb+b85Rj/55vPG/69bDZroVX1SaP3da2ooFsHAhtpampy2oSSROMp/vjfjnFDVyvvfOUO0z63njUbZfe2Dt52Zz//vP8MT4/NGfodj8d9f1oq9HUtqKDbfd7qIP39/U6bUJIPffN5JhfifOj1NxP0mZforGfN1fAH/26QLe1NPPjws8RTlXeShkLqV2pdiyp9XS0q6NaBwEYmJiacNqEoXzw0wWf2n+Udd2/ntq0bTf3setVcLS1BHx/8pZs5NbPEH3zxWbLZ8stD8xt63IQqfV0tKujWgcBGotGo0yZcw5OjF3n/I89y944I7zMpQbyaetRcKy+7oZMH73sRX33mPH/5WPlCYyrUn6kWlfq6GlTQXVclJlSn3koTn5yK8pv/7xD9kRY++qu7CfjMfy6oN83r5bfuuZ6zc0v87eOjbO1o5o0v3Vr0Ok+NRfoaGdX62igq6NaBwEYGBgacNqHA2dll3v7Jpwn6vHzy119KW5M1Z+zWk2YzEELwP153ExOXYvzRv/2EtqYA99103TXXhRRIIFaLan1tFBV066khG5mcnHTaBACeO3+ZX/q7J1lKpvnk219K78b1lZEoR71oNhO/18NHf/U2Xryljd9+6BCf/fHZa65JujBHoGJfG0EF3ToQ2Mj8/LzTJvDk6EXe+A/7CXgFX/ytO3lxr7WlkutBsxWEQ37+5T/u5RU7N/H+R47xf797ktUFHNMuzBGo2teVUEG3DgQ24mT9GSkln/zRad7+iafZ3B7i4d++ix1d1tdIUbnmTnPAx8d/bQ+/dNsW/uqxE7znc0eJxnPlgd2XIVC7r8uhgm6dI7CRwcFBR9qdW0ryB194hu8+P82rh7r4yzfcQluzNTmBtTil2S78Xg9/+YaXsD3Swl9/5wRHx+dZenkrzc3WTbfVK6r3dSlU0K1HBDYyNTVla3tSSr5xbJL7PvwEPzh5kf/2c7v4+K/tsS0IgP2anUAIwe++6gY+/5t3ks5Inju/wPilZUMbz1TCDX1dDBV060BgI7Ozs7a1NTqzyK994sf8p4cO09ES4EvvvJu337295rOHa8VOzU6zp7+Dr7/r5URaA0wvZXjNX3+f7xxv/JuEUdzU16tRQbeeGlKMycsxPvr4KP/69FlCfi//7ed28ZY7tuHz6phvB23NfnZsaqVZzBP0efiNfz7Iy3Z08t7X3MDubR1Om6fRFEUHAhsZGhqy7LPH55b5+A9O8a8/HkciecOePt776p1sCjtbF99KzfVMZ1sL33j3Hv75qTP83b4X+OW/e4qX39DJ7/zUDm7f3mH7yMwO3NrXKujWgcBGZmdn6e7uNu3zpJQ8NTrLJ58c4zvDU3iF4A17+njnTw1YujegGszW3CikUyn8Xg/veNl23nx7H5/Zf4Z/+P4p3vix/Qz1bODX7+rn52/ZTMjf+CtO8ri1r1XQrQOBjUxPT7Nr1651f8743DKPHD7HI0cmODO7TEdLgHfeu4NfvWMrPW31taPVLM2NRjKVKnzfHPDxwCsGeOsd/Xz56Dk+9eQY73v4WT7wtePcf/NmXr97C7dt3djwowS39rUKunUgaBDG55b55k8u8M3nLnDozCUA7rw+wrteeQM/e3OPUk+WqtIU8PKm27fyxpf2sf/UHF84OM6Xjpzjsz8+S19HEz99Uw/33XQdt/S24/E0dlDQNBY6ENjIzp07DV+bymQ5dOYSj49M8/2RGZ6/kKtweOPmDfz+a3fyC7duqZvpn3JUo1klmsvUGhJCcOdAhDsHIvyPX0jzjWOTPPrsJJ/80Wk+9sQpusJB7tm5iXsHu3jZDZ2W1YEyG7f2tQq6dSCwkXLlahPpDD85t8CB07M8NTrLwbFLxFIZ/F7Bnm0d/PHPDPHvbryOrZH6v/mvRoUSvbVgtMREa9DHG/b08YY9fVyOpfje81N8Z3iabz13gS8cmsAj4MbNbdw5EOGO6zu4betG2pvrs9qlW/taBd06ENjI5OQkg4ODSCkZm13m2Yl5jk1c5sh47t9kJnfO7WB3mH+/p5e7dnRy945OWoON2015zW4jmUxW/TttTX5+8dZefvHWXtKZLEfH5/nByYs8dWqWT/1ojI89cQqAHV2t3La1nZt727m5t40XXbfBkhLi1eLWvlZBd+PeYRqEhXiKk1OLnJyK8tjxBB99/imGLywQjacBCPo83LSljV+/u5/btm1k97aNdLY6u+RT4zw+r4c9/R3s6e/gvUA8leHI2XkOn73E4TOXeOz4FJ8/mDsZy+8V7OgKM9QTZlfPBnZ2h9nZHaZ7Q7DhE9Aae9CBwARSmSwTl2KMzS5x5uISpy4uMTqzyKmZJSYvxwvXNfk97Nosed0tm7lpcxs397ZzQ3crfoU3e6lQq70Wmkw+szjk9xbyCpBbOjxxKcaxc5d5duIyw5ML/PDkRR45fK7wOxtCPga6Wrm+s5WBrha2R1rYFmlhW6SZFgtGmW7taxV060BggEQ6w9TlBOcvxzh3Kca5+dy/Z+eWGb+0zPn5GKuPsA2HfFy/qZU7r4+wo7uVnV25J7TEpfPcsGOHc0IcoJYpEhXIyvJnGq8XIQR9Hc30dTTzMy/uKbw/u5jgxNQiJ6ainJiKcmpmiR++MMPDh68+V7ezNUDvxma2djTTu7GJLRub2NLexOb2JnraQoRD1Seo3drXKuh2dSBIpDNcXEwyE01wMZpgKhpneiHBdDTB1EKcC5fjTEfjXFy8tqM7W4Ns7Whi97aN/MItW+jvbKE/0sy2SAudrYGiQ/J9xyZcFwjGx8eVeGKqFqcOr4+0BrmzNVgYOeRZTKQ5M7vE2MVlxmaXGF95iDkyfomvH5sknb06cLUGfVzXFqJ7Q5DuDSG6N4ToCgfpCofo2hCkszVIZ2uA1qCv4Otu7WsVdLsqEPzFt0bYf2qW2aUkFxcThXn6tURaAnRvCHFdW4iX9LXR05Z7Suppyz059bSF9Lp9TUPRGvRx4+Y2btx87UFEmaxkOhrn3KUY5y/HmZyPMXk59yA0FY2zf3SW6WjimmABuRxXZ2uQSGsA4nG+Mn2UjuYAG1sCdLQE2Njsp705QHuzn43NAdqa/Ppvpw5xVSCIpzIEVpKzkZYAkZYAm8K5p5tN4WDhSceqOfv+/n5LPreecaNmgFCwcRL+Xo9Yedgpvfchm5VcWk4yHU3kRtCLV/6dXUoyu5hkMu7nwKk55paSxMqU4A76PLQ1+QtfG1b+DYd8bAjl/g0X/s19tQb9tIZ8tAZ8tAS9dVVEUQUfd1Ug+JP7G3sbuEbjFB6PINIaJNIaZKin+DVjY2OFm2IsmeHScpJLy0nml1O5r1ju+4VY7vXlWIqFeIqphTgnpqJE42mi8RRFBh7XEPR5aA36aAn6aA54aQ36aA76aAl4aV4JFk0BLy0BH03+3PfNK18hf+6a3PseQn5v4ZqQz+vKXd2uCgROs/oPxS24UTNA3IWH16/u66aAl6ZALvlcDVJKlpIZFleCwkI8zVIizWIi93oxkSm8XkykWU6kWUxkWE6muRxLMTkfYzmZe72UzJBMZ6vWEfB6CPlzASL3tfK9z0vQ7yG48m/+9cyF8wz0xwn6PAT9HgJeD0G/l6DXQ8DnIejL/Rvw5X6W/z7o8xL0efCvvOf3ity/Ho/twUgHAo1GUzcIIWgN+grJ6vWSzmSJpTLEkpmVAJEhlkqznMwQT+V/liaeyhJPZYilMoXvr3xliadz3y8m0lxcTJJIZ0iksiTSGZbiab5/7nRNQacUfq/A7/UUvgJegX8laPzT2/awLdJiWlugA4Gt9PX1OW2C7bhRM0CwgXIEZlGPfe3zegh7PTUthzXK6OgoAwMDZLOSZCZLIp0LEMl07vtk/iuTXXnv6p+lMpJU5uprkpks6VXf569JZbKWJNvrIhAIIe4D/gbwAv8opfygwyZZQiBQnzVirMSNmgE8LtzR69a+zuv2eAQhj3flRt0YhQLzOJ56F0J4gb8FfhrYBbxZCKFkVnd0dNRpE2zHjZoBYvF45YsUw619rYJuxwMBcDvwgpTylJQyCfwr8DqHbdJoNBrXUA9TQ1uA8VWvJ4C9ay8SQjwAPADQ3d3N1NQUs7OzTE9PA7ma4NFolMnJSSBX/yOZTDI+nvvo/GqGsbExIDefGQgECtG8p6eHcDjMiRMnAOjq6iISiTA8PAxAJBKhu7ubkZERMpkM7e3t9PT0MDo6SjKZJBwO09vby9jYGLFYjKamJvr7+5mYmCAajRIIBPD7/Rw9epT5+Xm8Xi+Dg4MFHZA7+7TRNA0MDDA5OVlSk9/v5/jx40ppqtRPiVAImc2yb98+ZTQZ6SegoFkVTUb66ezZs+zbt68hNJVCSItrolRCCPF64D4p5W+svH4rsFdK+TulfmfPnj3y4MGDdploGufPn2fz5s1Om2ErbtR875EjJJNJntx7zfOM0rixr6GxdAshDkkp96x9vx6mhs4Bq5cb9K68pxz5Jwk34UbNAMuxmNMm2I5b+1oF3fUQCJ4GbhBCbBdCBIA3AV9x2CaNRqNxDY7nCKSUaSHE7wDfIrd89BNSyuccNssSurq6nDbBdtyoGSDgb6zlg2bg1r5WQbfjgQBASvl14OtO22E1kUik8kWK4UbNAD4XBgK39rUKuh1PFteCEGIGOOO0HTXQCVx02gibcaNmcKduN2qGxtK9TUq5ae2bDRkIGhUhxMFiGXuVcaNmcKduN2oGNXTXQ7JYo9FoNA6iA4FGo9G4HB0I7OVjThvgAG7UDO7U7UbNoIBunSPQaDQal6NHBBqNRuNydCDQaDQal6MDgUMIIX5PCCGFEJ1O22I1Qog/F0I8L4R4Vgjxb0KIdqdtsgohxH1CiBEhxAtCiD902h47EEL0CSEeF0IcF0I8J4R4t9M22YUQwiuEOCKEeNRpW9aDDgQOIIToA14LnHXaFpt4DLhJSnkzcAJ4v8P2WIKbDllaQxr4PSnlLuAO4J0u0Q3wbmDYaSPWiw4EzvDXwPsAV2TqpZTfllKmV17uJ1dhVkVceciSlHJSSnl45fsouRvjFmetsh4hRC/ws8A/Om3LetGBwGaEEK8Dzkkpn3HaFof4D8A3nDbCIoodsqT8DXE1Qoh+4FbggMOm2MGHyT3QZR22Y93URdE51RBCfAe4rsiP/hj4I3LTQkpRTrOU8ssr1/wxuWmEh+y0TWMPQohW4GHgPVLKBaftsRIhxP3AtJTykBDiXofNWTc6EFiAlPLVxd4XQrwY2A48I4SA3BTJYSHE7VLKCzaaaDqlNOcRQrwduB94lVR384prDllaixDCTy4IPCSlfMRpe2zgbuDnhRA/A4SADUKIz0gp3+KwXTWhN5Q5iBBiDNgjpWyUyoU1IYS4D/gr4B4p5YzT9liFEMJHLhn+KnIB4GngV1Q9XyOPyD3VfBqYk1K+x2FzbGdlRPD7Usr7HTalZnSOQGMHHwHCwGNCiKNCiL932iArWEmI5w9ZGgY+r3oQWOFu4K3AK1f69+jKk7KmQdAjAo1Go3E5ekSg0Wg0LkcHAo1Go3E5OhBoNBqNy9GBQKPRaFyODgQajUbjcnQg0Gg0GpejA4FGo9G4HB0INBqTEEK8WAhxRgjxn5y2RaOpBh0INBqTkFIeA94E/JrTtmg01aADgUZjLtPAjU4bodFUgw4EGo25fBAICiG2OW2IRmMUHQg0GpMQQvw00AJ8DT0q0DQQOhBoNCYghAgBHwJ+GzgG3OSsRRqNcXQg0GjM4U+Af5ZSjqEDgabB0IFAo1knQohB4DXkzrAFHQg0DYY+j0Cj0Whcjh4RaDQajcvRgUCj0Whcjg4EGo1G43J0INBoNBqXowOBRqPRuBwdCDQajcbl6ECg0Wg0Luf/A2e7nVknpKbjAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Parameters\n", "g = np.array([1,0,1]) \n", "#g = np.array([0,0,1]) \n", "H = np.array([[1,0,0],[0,2,0],[0,0,2]])\n", "#H = np.array([[-2,0,0],[0,-1,0],[0,0,-1]])\n", "I = np.eye(3)\n", "Delta = 2\n", "\n", "# Secular function\n", "psi = lambda l: np.linalg.norm(np.linalg.solve(H+l*I,-g))\n", "\n", "# Evaluate secular function\n", "X = np.arange(-5,5,0.1)\n", "Y = np.array([psi(l) for l in X])\n", "\n", "# Mask poles\n", "X[Y>100] = np.inf\n", "Y[Y>100] = np.inf\n", "\n", "# Plot secular function\n", "plt.figure()\n", "plt.plot(X,Y)\n", "plt.xlabel(r'$\\lambda$')\n", "plt.ylabel(r'$\\phi(\\lambda)$')\n", "plt.grid()\n", "\n", "# Plot minus leftmost eigenvalue\n", "plt.axvline(0,color='c')\n", "\n", "# Plot trust region radius\n", "plt.axhline(Delta,color='m')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.1.2 Subproblem Evolution\n", "Solve the trust-region subproblem with \n", "\n", "$\n", "\\begin{align}\n", "H = \n", "\\begin{pmatrix}\n", "1 & 0 \\\\\n", "0 & 3\n", "\\end{pmatrix},\\quad\n", "g = \n", "\\begin{pmatrix}\n", "1 \\\\\n", "1\n", "\\end{pmatrix}\n", "\\end{align}\n", "$\n", "\n", "as the trust-region radius $\\Delta$ increases and plot the solution trajectory. Hint: carefully use the fact that\n", "\n", "$\n", "\\begin{align}\n", "s(\\lambda) = -(H + \\lambda I)^{-1}\n", "\\end{align}\n", "$\n", "\n", "For what value of the trust-region radius does the solution become unconstrained?\n", "\n", "What about when we change the problem to the following?\n", "\n", "$\n", "\\begin{align}\n", "H = \n", "\\begin{pmatrix}\n", "-3 & 0 \\\\\n", "0 & -1\n", "\\end{pmatrix},\\quad\n", "g = \n", "\\begin{pmatrix}\n", "1 \\\\\n", "1\n", "\\end{pmatrix}\n", "\\end{align}\n", "$\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Parameters\n", "g = np.array([1,1]) \n", "H = np.array([[1,0],[0,3]])\n", "I = np.eye(2)\n", "Delta = 1\n", "\n", "# Constrained solution\n", "s = lambda l: np.linalg.solve(H+l*I,-g)\n", "\n", "# Evaluate solution trajectory until unconstrained solution\n", "X = np.linspace(0,50,100)\n", "Y = np.array([s(l) for l in X])\n", "\n", "# Plot solution trajectory\n", "plt.figure()\n", "plt.plot(Y[:,0],Y[:,1])\n", "plt.grid()\n", "\n", "# Evaluate trust-region function\n", "fun = lambda s: s[0]*g[0] + s[1]*g[1] + 0.5*s[0]*H[0,0]*s[0] + 0.5*s[1]*H[1,1]*s[1]\n", "X = np.linspace(-2,2)\n", "Y = np.linspace(-2,2)\n", "Z = fun(np.meshgrid(X,Y))\n", "\n", "# Plot trust-region function\n", "plt.contour(X,Y,Z,20)\n", "plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3.2 Trust Region Methods\n", "Consider the Rosenbrock function defined as\n", "\n", "$\n", "f(x) = (a - x_1)^2 + b(x_2 - x_1^2)^2\n", "$\n", "\n", "where usually $a=1$ and $b=100$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.2.1 Trust Region Exact\n", "\n", "A trust-region algorithm that solves the trust-region subproblem exactly, using Newton's method on the secular equation (as discussed in lectures):\n", "\n", "$\n", "\\begin{align}\n", "&\\text{Factorize } H + \\lambda I = LL^T \\\\\n", "&\\text{Solve } Lu = -g \\\\\n", "&\\text{Solve } L^Ts = u \\\\\n", "&\\text{Solve } Lw = s \\\\\n", "&\\text{Set } \\lambda = \\lambda + \\left( \\frac{\\lVert s \\rVert_2 - \\Delta}{\\Delta} \\right)\\left( \\frac{\\lVert s \\rVert^2_2}{\\lVert w \\rVert^2_2} \\right)\n", "\\end{align}\n", "$\n", "\n", "with suitable safeguards and special handling of the hard case.\n", "\n", "#### Coding Task: \n", "Now apply Scipy's trust-exact starting from $x^0 = (-a,a)$ to solve the above problem for $a=1$ and $b=100$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " fun: 5.4669467408061773e-05\n", " hess: array([[ 813.7116442 , -402.90327443],\n", " [-402.90327443, 200. ]])\n", " jac: array([ 0.07132719, -0.02820072])\n", " message: 'Optimization terminated successfully.'\n", " nfev: 14\n", " nhev: 14\n", " nit: 13\n", " njev: 12\n", " status: 0\n", " success: True\n", " x: array([1.00725819, 1.01442805])\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Parameters\n", "a = 1\n", "b = 100\n", "\n", "# Initial guess\n", "x0 = np.array([2,2])\n", "\n", "# Objective function, gradient and Hessian\n", "fun = lambda x: (a-x[0])**2 + b*(x[1]-x[0]**2)**2\n", "jac = lambda x: np.array([-2*(a-x[0])-2*x[0]*2*b*(x[1]-x[0]**2),2*b*(x[1]-x[0]**2)])\n", "hess = lambda x: np.array([[2-4*b*x[1]+12*b*x[0]**2,-4*b*x[0]],[-4*b*x[0],2*b]])\n", "\n", "# Plot function contours\n", "plt.figure()\n", "X = np.linspace(-2,2.5)\n", "Y = np.linspace(-2,3.5)\n", "Z = np.meshgrid(X,Y)\n", "plt.contour(X,Y,fun(Z),20)\n", "plt.colorbar()\n", "\n", "# Call Scipy's CG\n", "xprev = x0 # for plotting\n", "res = opt.minimize(fun, x0, method='trust-exact', jac=jac, hess=hess, tol=1e-1, callback=callback)\n", "\n", "# Print results and show plot\n", "print(res)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.2.2 Trust Region CG\n", "\n", "A trust region algorithm that solves the trust-region subproblem approximately using CG (as discussed in lectures). Essentially this applies CG to solve\n", "\n", "$\n", "\\begin{align}\n", "(H + \\lambda I)s = -g\n", "\\end{align}\n", "$\n", "\n", "truncating to the trust region radius $\\Delta$ before encountering negative curvature or exceeding $\\Delta$.\n", "\n", "#### Coding Task: \n", "Now apply Scipy's trust-ncg starting from $x^0 = (-a,a)$ to solve the above problem for $a=1$ and $b=100$." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " fun: 0.0004252132652748247\n", " hess: array([[ 835.3084499 , -408.24645045],\n", " [-408.24645045, 200. ]])\n", " jac: array([0.02350248, 0.00868582])\n", " message: 'Optimization terminated successfully.'\n", " nfev: 22\n", " nhev: 17\n", " nit: 21\n", " njev: 18\n", " status: 0\n", " success: True\n", " x: array([1.02061613, 1.04170071])\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Parameters\n", "a = 1\n", "b = 100\n", "\n", "# Initial guess\n", "x0 = np.array([2,2])\n", "\n", "# Objective function, gradient and Hessian\n", "fun = lambda x: (a-x[0])**2 + b*(x[1]-x[0]**2)**2\n", "jac = lambda x: np.array([-2*(a-x[0])-2*x[0]*2*b*(x[1]-x[0]**2),2*b*(x[1]-x[0]**2)])\n", "hess = lambda x: np.array([[2-4*b*x[1]+12*b*x[0]**2,-4*b*x[0]],[-4*b*x[0],2*b]])\n", "\n", "# Plot function contours\n", "plt.figure()\n", "X = np.linspace(-2,2.5)\n", "Y = np.linspace(-2,2.5)\n", "Z = np.meshgrid(X,Y)\n", "plt.contour(X,Y,fun(Z),20)\n", "plt.colorbar()\n", "\n", "# Call Scipy's CG\n", "xprev = x0 # for plotting\n", "res = opt.minimize(fun, x0, method='trust-ncg', jac=jac, hess=hess, tol=1e-1, callback=callback)\n", "\n", "# Print results and show plot\n", "print(res)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.2.3 Trust Region Krylov\n", "\n", "A trust region algorithm that solves the trust-region subproblem approximately using Lanczos (as discussed in lectures).\n", "\n", "#### Coding Task: \n", "Now apply Scipy's trust-krylov starting from $x^0 = (-a,a)$ to solve the above problem for $a=1$ and $b=100$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " fun: 0.002305467938203958\n", " hess: array([[ 880.57544587, -419.19753274],\n", " [-419.19753274, 200. ]])\n", " jac: array([0.03582087, 0.0287057 ])\n", " message: 'Optimization terminated successfully.'\n", " nfev: 13\n", " nhev: 11\n", " nit: 12\n", " njev: 13\n", " status: 0\n", " success: True\n", " x: array([1.04799383, 1.0984346 ])\n" ] }, { "data": { "image/png": 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8+cEyVgbuIDlZEB098zpKcmvp6RogfKdh6UVKXardkFWYmel/C7xa3MjIyBghRnb4txshhDOwA3gGQEo5AozoLv8CpU7pu5OGGLSRwC7grJSyQzfvWeAQk+qeTmVeNXUhhC8QAqRMubQCqJ30e52ubUaj3tPRN5/LU7kJOLk5cOjJbRx6chvd7X2UZFdRkV9HRX4d5fm1JJ7IwZRytBaW5izxdMFzlTtPffVegnesZ13wqrv24NNUenvh73+Hxx7T3zHPJ3Z2EB2NnpHu64OsrAkjn5EB77xjATxMYZLk0l5FCprJsKfFFWNmJozmT29q7KKluYfHnoyZdi0rT9HTt2ycP6PeP1pFcuMz8zWdH9AK/E0IEQRkAJ8H9gH1UsqcKXKlMRtprN0o82bUhRAOwFvAF6SUPTcwz7PAswBOFkvpauvF5SZlZVOZX5yXOBC+dxPheyeq3Az0DdFY1crQwAgjgyMMD44wPDTK8OAI9k62uHu5stTLFZeljpgZct9QmZGXX4aeHvjMZ27tfR0clEPZ7dsn2vZHZHMubQtSmjEyonjczGbUN4SswtHZsFSXk6kEFgUZKG2XnVvLGj8PHB1v2wG5uxAifdLvL0opJzuJWgChwGellClCiF8B30HZvR+4mQubF6MuhLBEMej/lFK+baBLPTD5keqta5uG7h/mRQBnSw+ZcDyLe5427u6ksrCxc7BhzaaF+RV5sSOlckC6dStE3uYTKo1Gi7blCpbmm9BihpUV7NplvH9Hay9lhQ0888WDRvvkZFbj4mLHKj93vfaR0XE9PWieVq9gb+lL1PK/m9j7H21SyukuORPUAXVSynHV4k0Uo+4HjO/SvYFMIUQExm1kPYoEM7n90kwru+Gtke7U9i9AkZTy50a6vQd8VChEAd2z6ekAVtYWJHyQdaNLVFG5IzlwAAoLFT39FnqWGuRqRiVWg4X88gelfP/7s0svGbpI5bDt6wxel1KSk1XN5pBV07yqrpY0MTIyRtCmheufLqVsAmqFEONhzXuBTCmlh5TSV0rpi2L4Q3V9jdnI08ABIYSrEMIVZZdvIMxsgvnYqccCTwF5QohsXds3gZW6D/cH4ASKq04ZirvOx0yZ2MHZjpyEEno6+nByc5iHpaqo3Bl85CNw7pzyPjkZnnxSkWJuF6ln8jAzN+Ojn16FgwlephlXSnB1d2T1esOJ1poau2ht7uFDBvT0nHxFYt6yyfuG1nwL+CzwT53nSwUz2z2DNlJK2SGE+D6Qpuv3vfFDU2PMh/dLPLMkF9ad6D4/17ntne3QtmtJOZPH/sdnOUpXUbmLeP99/d9Pnrw96xgn9Vw+myLX4uBsN2tfjUZLZkIpkbs3GI1tyNSVrgsOna6n5+bX4bfKHecbcJu9FUgps1FcEY1d95303qiNlFL+Ffirqfdd0CdTNnZWeHi7Ea9KMCoqejhO8R04fPj2rAOgubadqqJ6Ig5sNql/aX4dvd2DbN1mWHoBSEsux2OZEyt99fX0MY2WvMI6gtRzGqMsaKMOEHMkmMzLRQz0Dd3upaioLAiuXoWGBti8WQnv/8hHbq/0knY+H4CIfZtm6amQEV+KEIKQGMNVjkZHNWSlVxIevXbaTr6svJnBwdHFIL3cNha8UY8+FMTYyBiZlwpn76yichfwi1+AtbVyGNnefnsNOkDauQI8V7njvdY0R/mspDLWbvQympWxML+OgYERwg0UzcjJrwMgSDXqRlnwRn1j5BocXe1JPpV7u5eionLbaW2Fl16Cj35Uyc1yuxkZGiUnvpjwvZtMyv3T3zdEUXaN0YAjgPSUcszNzQgO8512LbegjhXLXXBfosauGGPBG3VzC3Mi9m0i9Vw+mjHN7V6Oispt5Q9/UPKzfOELt3slChkXCxkeHCHSRD09L7UCrUZLaMwMRj25go1bvLG3t9Zr12i0ZOfVEDQlK6PmDqmrO18seKMOEHVoC72d/RSklN/upaio3DaGhpRgo8OHIdC0es43ncvvpOO0xMHkKlOZiWXY2FmxPtiwj3lnRx9lJU2EGZBeikub6OsbJjzEV6/9X8fTp/W9m1kU+dS37g7EwsqC1HN5bIk1fmKuonIn88or0NICX/rS7V6JwtDACMmnc9n7aCQWlqbl6MlMKGXTVl+sjNSNzdC5Mm41UNouLbMKISB0SgbI9IKaaX2vh86RWt6sXiD/uDfAotip29rbsCXGn9Sz+bd7KSoqtwUp4ec/Vzxe9u693atRSDuXx/DgCDuObjWpf0tDF/VVbTNKLxmpFTi72LF2nef0a9lV+K9ZhsskX/jRMQ3ZxQYzjty1LIqdOijuUn/4zzdoqGrFy3cBnBCpqNxCzp2D/Hz4299uf0qAceLey8R1qROboo0b6cmkXCwCIGyH8dQAGakVhIb7TUu1OzA4QsHVBh57MFyvPb+0keGR+ams7WrlwyOrjGU6mcov5uWeN4NFsVMHCN+vHMSknc27zStRUbn1/PznSuWiJ5643StRGOwfIu1cHtvuCzG5YEnShUJW+LrjM6XgxTiV5S10dvQTGu437VpOXi1jY1rCpujp6YU1mC2Up9wCYdEYdS/fpfj4e5J8WnVtVLm7KCiAU6eU9LrW1rP3vxWkns1neHCU7febJr309w6Rl1ZJ9B7jJ7wz6ekZ2VVYWVmwaUox64yCGtb73aRE8ouURWPUAWLvCSY3sZTOlutO166isuj45S/B1la/tujtJvF4Ni7ujgRGTPdSMUT6lRLGRjVE7d1gtE9WeiU+q5aw1MNp+visajYHrsB60gHr0PAo+WWNhAaqKQMms6iM+q4Hw9FqtFx5X61ZrXJ30NIC//d/8PTT4O4+e/9bwfDgCKnn8ok5Emyy9JJ8sRAnV3vWBxl2ZRwd1ZCXXWNQeuno7Keyum2a9JJTUs+YRstW1ajrsaiM+qr1XvgFruDS22mzd1ZRuQP4/e9heHjhBBsBZF0uYmhgmJh7gk3qPzaqIT2umMhd640+BIry6xgaGiU0bLpRz8xRKiCFTnkgZBbWYm5uRlDAjNXd7joWlVEH2PVQOEXpFTRVt93upaio3FSGhuB3v4N774UA02J7bgkJJ7JxcLYlKNa0RRVkVtHXM0TkLsMFpgEy0ysxMxNsMVC6LjO7GgcHa/zX6GvnGYW1BK72xM7Gam4f4A5n0Rn1nUeV9MSqBKNyp/PPfyq5XhZKsBGAZkxDypk8Ig9sMTngKPXSVSwszWfM95KVXsW69ctxMFBzNDO3hpAtK/V2+QNDIxRVNKnSiwHmxagLIf4qhGgRQhiMDhJC7BJCdAshsnWv/7reey1buYSAEF+uvJdx/QtWUVngjAcbhYTMXOvzVlOQWk5vZz9Rh7aYPCb1cjFbIlZja2/YdWegf5jiwgaDCbwam7pobOomNEh/B59b0oBGKwnZsHCzNQohqoQQeTqblz6p/bNCiKtCiAIhxE8mtX9DCFEmhCgWQhyc1H5I11YmhPj6bPedr53634FDs/S5IqUM1r2+dyM32350K6U5NTRUtd7INCoqC5bTp5X6o1/60sIJNgJIPpWLhZUFobtMSz7TUN1GXWUrETuNSzX5ubVoNFpCtvpOu5aZq6QACNliWE/f4r/g9fTdOpsXBiCE2A0cBYKklBuBn+naA4HHgY0otvQFIYS5EMIc+B1wGAgEntD1Ncq8RJRKKeOEEL7zMZcpbLs3hD9/5y2uvJvBhz4/27NERWXx8fOfg5cXPPbY7V7JBFJKkk7lELw9ADuH6TKJIVIvFwMQvtO4np6VXoWlpTmBm6dLKVk5Nbi62OG7colee2aRoqfb2ljO4RPMTMtwI78pvaH9pil8GviRlHIYQErZoms/Cryqa68UQpQBEbprZVLKCgAhxKu6vkYLTNxKTT1aCJEjhDgphNhorJMQ4lkhRLoQIr211fBOfJnPEgJCfUk4rpa5U7nzyMuDs2fhs58FqwV0BlhT3EhTdRvRh4JMHpMWV4y331K8phjlyWSkVhC42RubKQZaSkmWTk+fnKt9XE8Pvb3Si/u4ndK9njXQRwJnhBAZk66vA7YLIVKEEJeFEON5D1YAtZPG1unajLUb5VblfskEVkkp+4QQR4B3AIOnJlLKF4EXAcLCwqSxCWPvCeGv3z9Gc207y3yM/w+jorKYeO65iUpGCyV6dJzxaG5Tc6cPDY6Ql1bJvU9EGu3T0tRNZXkLz35mepay+oZO2tr7pkkveaXjevr8HpJ6WC/ns/6mHfd9jm+3jUsqM7BNSlkvhPAAzgohrqLYXDcgCggHXhdCTA+hvQFuyU5dStkjpezTvT8BWAohbiiUIlbnI5t4IvtGl6eisiB48UX44x+hv1/5/UtfUtoWCpffSWf9Vj+WeLqY1D83pYLRkTHCthvX01MSywCINJC5MStP2aAGb9E33llFdZibCTb7e5m48tuDlLJe97MFOIYip9QBb0uFVEALuAP1wOQP6q1rM9ZulFti1IUQnkL3/UkIEaG7b/uNzOnl54Ff4ArVqKvcMfzhD9Pb3nrr1q/DEJUFdVQW1rPnkYjZO+tIiyvG2taSTQaiRMdJSSxluZcLPqumf9vOyqlhiZs9Pivc9Nqzr9YR4LsMe9sFpE1NQQhhL4RwHH8PHADyUVSK3br2dYAV0Aa8BzwuhLAWQvihKBmpQBrgL4TwE0JYoRymvjfTvedFfhFCvALsQtGZ6oBvA5YAUso/AI8AnxZCjAGDwONSSqPSiqnE3hPMP392gs6WHlwN5ItQUVksSKkUkZ7Kww/f+rUY4sLbaZhbmLHj6GyKg4KUkvT4EoIi1xgtiDE0NEpWehVH7g+ZVt9USkl2Xg3Bm/X19OGRMQrKm3j0QPB1f5ZbxDLgmG7tFsC/pJSndIb5rzr37xHgaZ0tLBBCvI5yADoGPC+l1AAIIT4DnAbMgb9KKQtmuvF8eb/MmBBUSvlb4Lfzca/JRB8O5uWfHif1bB4HPxI739OrqNwy3nkHamrgmWcgNVUx8l/4Ajxr6PjtFqPVarl8LI2tuwJxXuJg0piG6naaajt4+JltRvvkZFYzMjJGRMzaaddq6zto7+gnZEpqgMLyJkbHNASvX7j+6QA6b5VpJ8pSyhHgSSNjfgj80ED7CeCEqfdeNEUyDOEXuAIPHzcST+aoRl1l0fLkk/Dqq+DoCH/6E1gssL/KwtRyWus7+di3HjB5THp8CQBbZ9DT05LLsLa2IMhAaoD0LCXfy9RD0qyrdQB6+V6qmztNXtfdwKJLEzAZIQTRB4PIiitisH/odi9HRWXOPPmkkg5Ao4HeXmWnvtC4+HYa1rZWc4oiTbt8lRWrlrDcx83gdSklqYllBG/1xcp6+lMsNb2CFV4ueHu56rVnX61jjY87zg6219reiMsxeV13A4vaqAPEHAlmdHhMrV+qsig5MeVL9cmTt2cdxhgb1RD/fiZRB7dga29awFFv9yDZyeVE7zUajkJ9bQeNDV1ERE+XXoZHxsjKrSVi6+pp7Tkl9YROcWVMK65FZYJFb9Q3Rq1lyXIXLryRcruXoqIyZ1ZNUR4OH7496zBG9pWr9HT0s/MB0w5IAVIvFaEZ0xJ7wLhRT00qByA8anqRjbyCOoaGR4ncqu81k1tSz/DIGJGbJ/7ROnsHKK1XM7ZOZtEbdXNzM/Y8HEH6xUK1IpLKoqKjAyorYcUKcHODj3xkIvBooRD3bgZ2jjZs3W1arheAxHOFuHs6s26z8cPM9NRyvFe6sXyF67RraZmVWFqYT/NPT82vxtzcTC/oKL2kzuR13S0ssCOZ62Pvo5G88dszXH4nnQee3XO7l6OiYhI/+hH09MCVK7DZtCDNW8rYqIakUzlEHwrCysQcK0MDI2TEl3Dg4TDMzAzvGUeGx8jNrObwfSEGr6ekV7J54wpsp+RJT8uvYfPa5Xr+6WnFtdhZz0/+l/rBZr6V+8t5met2suh36qBURFq7xYcLb6oSjMrioK4OfvMbeOqphWnQQZFe+roGTC4uDZARX8Lw0Cix+41LL3k5NQwPjxFmQHppbeulsrqN8FB96aW7d5DiqmYiNuvrVWnFtYT6L2z3xlvNHbFTB9jzSCQv/teb1JQ0snLd8tu9HBWVGfnud0GrVX4uVK68l4mdow0hM2RYnErCuQKcXOzYZCCN7jhpyeVYWpqzJWR6vdL0rCoAIqbo6WkFNUgJ4ZsmjHpLVx/VLZ08tH1+noorbJfxwy1fMKnvf/PFebnnzWBB79RHhsdM7rvzgTDMzASXjqXP3llF5TZy9Sr89a/w6U+Dr+/tXo1hNGMakk/nEHlgC1YmyhtjoxrSLl8lYtd6zC2MV0XKTKtkU5APtgbC/NMyq3BztWe171K99vSCGuxtrdiw2nOirUTxegkPUKsfTWZBG/XOtl6T+7otc2ZzzDouH0tjHjIQqKjcNL71LbC3V34uVPKTy+jp6L+WOM+kMRlKLdKoPcYPVdvbeqksb2FrxPTEhFqtJCO7mq3BqzAz008bkJZfTegGHywmlbRLL67D0dYa/xU3lBvwjmNBG/X+3iHGRjUm99/1YBgNla2U5tTcxFWpqFw/KSnw9tvwH/8BS5fO3v92kXA8G2tbS7aaWOEIIOl8AVbWFmydoRZpZlolgEGjXl7ZQlf3AGGhvnrtDS3d1Ld0E7ZRX65JL6ll6zpvzI0cyN6tLOh/DY1GS25qhcn9Y+8NwcLSnMvH0m7iqlRUro+vfU2pN2prC19cuJIsWq2WxJPZbN29ERsjdUWnIqUk+UIRwdFrsbEznj0xI6UCF1d7Vq9dNu1aWmYVAGHBUw5DC5SUARGT9PSmjl7q2roJW6cekk5lQRt1MzNBwtkZE5Lp4ehiT+iuQK68n6lKMCoLiq99DX7yExgagsFB+MEPbveKjJOXWEp7Yxfb7jXscmiIqpImWhq6iJ5BetFqJRlplYSG+06TVwAysqvxW+WO+xJH/faCWpa42OM7KQVveqmip4etU/X0qSxoo27nYEPS+QI0Gq3JY7bfH0prfSdXMypv4spUVObG22/P/PtC4uyrSdg52hBzJNjkMckXrwLMWGC6orSZrs5+QsOnSy/DI2PkFtSxdcouXUpJemENWwN99FLwZpbU42RnzVovVU+fyoI26g5OtnS29XF1Dhp51MEtWFiaE/9+5k1cmYrK3HjooZl/Xyj09w4S/0EmOx8Iw3oORShSLxWxbrM3bjPUNUiKL0EIiIie7p9eUFjPyMjYNKNeVd9BR/fAdD29VPFPN7Tjv9uZF6MuhPirEKJFl/jd0HUhhPi1EKJMCJErhAg1ZV57RxssLM1JOGN6si4HZztCdwUS/0GWKsGoLBh+/GP46ldh7Vrl549/fLtXZJgr72YwPDjK/sejTR7T1d5HcW4dEbP4syfFl7BhkzeubtNzsqdnV2NuJgjerC+npBcqG7qwwAmj3tzZS11r94IPOhJCmAshsoQQH+h+3yuEyBRCZAsh4oUQa3Xt1kKI13T2MUUI4Ttpjm/o2ouFEAdNue987dT/Dhya4fphlPJM/sCzwO9NmdTMTBAas5bEc4VzMtDb7w+lpa6DYt3Bi4rKQuDHP4bS0oVr0AHOvZ6Mj78n67caL0E3lbS4YqSURO7eYLRPa0sPpcVNRBvxjMnIrmJDgBd2dvoHs+kFNXi6O+Hl4XytLbNUKdG51X8FC5zPA0WTfv898BEpZTDwL+A/de0fBzqllGuBXwA/BhBCBKKUr9uIYl9fEEIYDwDQMV+Vj+ImP10McBR4SVe2KVkI4SKEWC6lbJxt7ui9G0m9XExlcROr15sWKRp5YLMiwXyQOaf/OVVU7maaqtsoSCnnmW8enVZebiZSLl1lyTIn1mww/veZHF8KQPSO6Zp7b98QJWXNPDXl24FWK8m6WseOrfpyTUZpHQ621qzznl+f0Or+Np5L+dO8zCWE8AbuQalk9CVdswTG9SlnoEH3/ijwHd37N4Hf6mo6HwVelVIOA5VCiDKU4tVJM937VmnqK4DJSY/rdG3TEEI8K4RIF0Kkt7a2Erl7PUIIks7P0Qtm5wYuHUuf0yGrisrdzMW3UgHY9VC4yWNGR8bITCglfEfAjA+CpPgSvFa4stJAgemcvFq0WknolNJ1ZTWt9PQNsXWDfntmWT3Ba7xut3+6+7id0r2mFh78JfBVYLIB+gRwQlfH+SngR7r2a/ZRSjkGdANLmIPdnMyCy/0ipXwReBEgLCxMuro7siF4JUnni/jI8/tMnmf/E9GkfvxPZFwsJGLfppu1XBWVOwIpJeffTGFTtD/LfKYbXmPkpJQz2D88o/QyODBCdkYV9z8UZtDwZ+RUY21tQeB6L/32IsWebQ2c0Nnbe/qpaurg/ugJ18mKlg6T1zsTq+zd+UPkJ03q+0eebZNSGkwyL4S4F2iRUmYIIXZNuvRF4IiUMkUI8RXg5yiGfl65VY+6emDyCYi3rs0kovcGUl7UQHO96bUIIw9swXmJA2f+lWD6KlVU7lJKsqupL29h7yMRcxoXdyoPOwdrQmeIIs1Iq2B0VEP0dsN90jOrCNrkg5Wl/h4zs7AW72UueEzyW88qU8xG6NqJQ9I3knPntOZbQCxwvxCiCngV2COEOA4ESSnHU8m+BsTo3l+zj0IICxRppp3rtJu3yqi/B3xU5wUTBXSboqePE7VH2QWkXCqapecEllYW7HkkkpQzeXS39811vSoqdxWXj6VjYWlO7BwCjkZHxkg6V0D0nkCsrIx/6U9JKMXewZqNW6YHCtU1dFJT10HUFN91jVZL1tU6vV06KIekNlYWbFjlca0tuWxhlbOTUn5DSuktpfRFOei8gKKPOwsh1um67WfiEPU94Gnd+0eAC7rzx/eAx3XeMX4ojiaps91/vlwaX0ER7wOEEHVCiI8LIZ4TQjyn63ICqADKgD8B/z6X+b39lrLC150UXYCDqez/UBRjoxouqWkDVFSMotVqiXs3nbA9G3F0sTd5XFZSGX09Q+w4bLwgtVYrSU0qJyxyDRYGMjcmpylpQKLD9Q9DS6tb6RsYnlaPNL20ji1+y7E0V+Zq7xugtGnhl7PTaeWfBN4SQuSgaOpf0V3+C7BEdxD6JeDrujEFwOtAIXAKeF5KOWsyrPnyfnlilusSeP5G7hG5ewPvvZxIf98Q9g6mFcD12+jNms0+nHstiaOf2H0jt1dRuWPJTy6jvambT3zb9DqkAPGn87F3tCEkZnrx6HHKSproaO8j0kif5LRyVvq44bXcRa89Na8KmK6nl9W38dkHYq+1pZUvrF36VKSUl4BLuvfHgGMG+gwBjxoZ/0MUDxqTWdARpZOJ3LWesVENmQmlcxq3/0NRlOXWUlmg1jJUUTHE5XfSsba1Iuqg8R33VEZHxkg6X0D03kAsZ5JeEksRwnCB6YHBEbJza4kKm542ICm3inWrluLuOhGolHJVCUSKXD8RdZpSVou9temRr3cDi8aobwxdhYOzLSkXTdfVAXY9FIG5hRnn1VJ3KirT0IxpiP8gi8j9m03OyAiQnVxOX88Q2w/OXHUoNamc9YErcHGdLutk5VQzOqaZJr30D46QW9JA5BZfvfaUohqc7W1Y7zOhp6eW1xK2esEHId1SFo1RN7cwJ3LnelIuXWV0xPSKSM5LHAjbs1H1WVdRMUBOQgk97X3seHBu0kvCmXzsHKwJnkF66ersp7iwnnADuV5A0dNtbS3ZvFE/3D+joAaNRkvUlonAQSklKVdriAjwuZbvpbm7j+q2LiLWqJkaJ7NojDrAjiNb6OsenLMEs/vhCNobu8hLLLlJK1NRWZxceDMFWwcbwnabXgxDM6Yh6XwhEbvWz+j1kp5SgZQQET3d8EspSUmvZGvQKiwt9Q9Qk/OqsLOxZMu6Cb/1quZOWrr6iNwwIb2k6vR01ajrs6iMekj0Whydbbl8cm5+qZEHtmDrYMPFt1QvGBWVcXq7+rnyXia7Hw6fU0bGvPQqeroGiN0/c1BfWnIZLq72+AdMTx9QXdtOc2sPkVP0dCklyTlVhAb6YDnJWyalSCmUEbl+Iro0tbwWJ1trApYv4BJSt4EFF1E6E5ZWFsQe2MSl4zkMD41ibWNaQVwbOyu23RtC/AeZPP+jx7EycZyKyp3MhTdTGRka5fBT2+c0LvFsPtY2loRtW2e0j0ajJT2lgojotQbT46akK66MU416XXMXDa3dfPjIVv3+V2vwdndmhftEYq+08jrCVs9f+t3K3naevPTSvMx1O1lUO3WAHYe3MDQwQnpc8ZzG7XwwjIHeIdIumJ5DRkXlTkVKyel/JuAftJK1m02XL6SUJJ4vJDTWf8aydSVXG+npHjTo9QKQkl6J78olLJuSfz0lT7cjn3RIOqbRklFSR8SkXXpjZw91Hd2Er1nY6XdvB4tqpw6wJdwPZzd74k7lEXvA9JwuwdsCcHF35PKxNGLnUNFFReVOpDSnhsrCep7/8eNzG1dQT3tzDzFf2Dhjv/TkcszMBGGR090VB4dGyM2v4wED0aupeVV4LXXGe5nLtbaimmb6hkaIWD/x8EmrUFyUw1fPn57u57iEl3d91KS+/7wWALrwWHQ7dXMLc2L3byLlUhFDgyNzGrf9/lBSzuQx0Dd0E1eoorLwOf2vBKxtLdn1oOkZGQGSzhViZm42Y9k6ULIyrg9cgZOz3bRrOXm1jI5piAzTT4s9NqYhvaCWyM2r9BJ/jfunh6/TN+pOttas81TL2U1l0Rl1gB2HNzM8OEra5blJMLsfimBkaJRLb6sHpip3L0MDI1x6O41t94biYMDozkTiuQI2h/niZMDvfJymxi5Ki5vYtsuw4U/NqMLKyoItU1wZ88sbGRgaIXyzfkm71Ku1+K9wx9VxYq3zraffSSxKo74pzA+XJQ7En86b07j1YX74Ba7g5P9duUkrU1FZ+CSeyGagd4gDT8TM3nkS9VVt1JS3EL13ZvfHBN1mK9ZAQQyAtMxKgjf7YG2t77CQlleNmRB69UiHR8fIrWjQ19O7ehU9fbWqpxtiURp1c3MzovcGkhpXzPDQqMnjhBAcfmobZbm1lGRX38QVqqgsXM69nswynyVsMuA/PhNJFwoBiNozm1G/it8aD7y83aZda27poaaug/BQ32nXUvNrWL96GU72E7mdcisaGRnTEB4wIb2k6/T0MNWoG2RRGnWA2AMbGRoYmXMg0p5HIrG2teLkS+puXeXuo7Whk+y4q+x9LBKzOVYOunIqj7WBXixb4Wq0T2dHH/m5tcQa0dzTs6oACA/V19P7B4YpLG8kfJO+9JJWXIu5mSB07UQqgIyKOhxtrFm3XNXTDbFojXpQxBocnG1JOJM/p3H2TrbsfCCMS8fS6e8dvEmrU1FZmFx8MxUpJXsfi5rTuPqqNkry6th1b/CM/ZKulCAlbNu53uD1tMxK3Jc44LtSv7pS5tU6NFpJxDSjXsOGlctwsJ3IS5NeUU+o30Q5uzNFc9vY3eksWqNuYWlO9J5Aki8WzSkXDMCRj25naGCYy8fSb9LqVFQWHlJKzr2RzMbINXj5zi0K89LxbIQQ7DwycybH+LhiPL1cWL3WY9o1jUZLRnY1YSG+08rapeVXY21lwWb/iejTgaERCqqaCVs3IbO09fZT1dbJVr+JttOqUddjvopkHBJCFAshyoQQXzdw/RkhRKsQIlv3Mqku32wuizH7AunvHSIvrXJO610XsgrfDSs486/EOY1TUVnMlOfVUlvSxJ5HIuc0TkrJxQ9y2BLhh/syZ6P9BvqHyU6vImb7OoO1SItLm+jpHSIsxHfatfSCGoIDVuiVtMuuaGBMqyU8YOKQNKNSqeY2fkgqpSS5amHmVBdCmAshsoQQH+h+9xNCpOjs5GtCCCtdu7Xu9zLddd9Jc3xD114shDhoyn1v2KgLIcyB3wGHgUDgCSGEoZOU16SUwbrXn02Zu7NzYMbrITFKVFviublFiQohOPBENMVZVVQVmVwqVUVlUXPhzVQsrCzYfn/onMaVFzZQX9XGziNBM/ZLT1FqkcZsN5w+IDGlHHMzMc0/vb2rn4q6dj2vF4CMkjoszMwIWj2xe8+oqMfWypL1K5RvGuVtHbT1z2wnbiOfZ6JkHcCPgV9IKdcCncDHde0fBzp17b/Q9UNnRx8HNgKHgBd09nZG5iOiNAIok1JW6BbyKko9vsIbnbi/b4iR4TGsrA0v09rGkq3b1pF0vpB//3/3z+ngZ/fDEfz1+8c480oSz37vkRtdqorKgma8rGPEvk1zKlkHcOlEDhaW5mybJYI78Uoxjk62bNqy0uD1hJQyNm/yxsnRVq89vUAXXGTgkHSj7zLsbCbSEaRV1BK8aqKc3Xzu0iu6O/jQyVfmZS4hhDdwD0rVoi8J5avLHuDDui7/AL4D/B7FXn5H1/4m8Ftd/6PAq1LKYaBSV+4uAqV0qFHmQ35ZAUz+l63TtU3lYSFErhDiTSGE0dheIcSzQoh0IUS6VitJT62Y8eYx+wLpaO3las7c/uO6uDsSeXAL599MmbMmr6Ky2Eg6lUNnSw/7H4+e0zitVsvlE7mExvrj6GI8UEkzpiU1sYzImLWYW0w3K41NXVRUtRIbOd2NMr2gBid7G/xXTej8/UMjFNU0EzYpirS1p4/Spnai1k48NJIra1nhrJ8/5hbhPm6ndK9np1z/JfBVYLyIwxKgS1erFPTt5DUbqrveretvqm3V41blfnkfeEVKOSyE+BTKU2qPoY5SyheBFwFcnX1k/OWrRr/OgVK71MragovvZxMYsspoP0MceDyahA+ySD9fQPThmb9aqqgsZj7462WW+SwhfJ/p+ZIAirJraGvq5mNfmlnOzc+tobd3yOjfakJKOQCxUfpGXUpJcm4VWwN9rnmzAGSWKt4wkw9Jk8sU+xbtrxh1rZSk1dSxZ90aLs7pUxlmtbMbrx2esdzyNV7nw21SSoOVRYQQ9wItUsoMIcSueVjanJiPnXo9MHnn7a1ru4aUsl33FQLgz4B+Xk0j2DtYk3ylhLEx4wW07R1siNoTSNzJ3DnvuEN3BeLi7sj5N5LnNE5FZTFRXdxIbmIJ9zyzA3PzufumW1pZzBpwlBRfiqWlOVsjpifwAkhMKWOVzxJWLNf3cS+tbqW1s4/YEP1xSYXV2FhaEDzJPz2ptBoXOxvWeymeNcXNrXQNDhHpu+CCkGKB+4UQVcCrKBvYXwEuQojxjfRkO3nNhuquOwPtmGBbDTEfRj0N8Ned7FqhCPvvTe4ghJicJf9+9A8PjOLgYENv7xC52TUz9ttzXzA9XQNkzDEQycLSnF0PhZNyJo/ezv45jVVRWSwc/3scltYWc04LoNVquXIqj/AdAdjNUr80OaGULSGrDPbrHxgmJ7+WmMjpaXgTshV5NTpI//A0sbCKsAAfrHXeMFJKkktriFy78lq+l5QqJbI0yndhVT6SUn5DSuktpfRFsYcXpJQfAS4C4wd4TwPv6t6/p/sd3fULUkqpa39c5x3jB/gDqbPd/4aNuk4D+gxwGsVYvy6lLBBCfE8Icb+u2+eEEAVCiBzgc8Azpsxt72CNjY0l8Zeuzthv67Z1OLnac+G9rDmvf+9jUYyNarj8ruqzrnLnMdA3xLnXk9lx/1aclzjMaWxhZjUdrb1sPzRzcena6nbqazuI2uZv8HpqRiVjY1piDOjpidmVbFi9jCWTDm9rW7uoaekiJnBCTq1o6aClp/+a9ALKIekqNxc8nRzn9LluI19DOTQtQ9HM/6Jr/wuwRNf+JeDrAFLKAuB1FKeTU8DzUkrjsoWOefFTl1KekFKuk1KukVL+UNf2X1LK93TvvyGl3CilDJJS7pZSzmyldQghCI9aQ0JcMVqtNNrPwtKcnUe2kHyhiP45ptVds8lbl+QrHuXhqKJy53Dp7TQG+4a45+kdcx4bdyoPK2sLIncZjg4dJ1n3DTk61rBRT0otx8nRho3rvfTau3sHKShrJCZYX3pJLlTyMkUH+k7MUap8Wx836hqtlvSaeiJXLTjpRQ8p5SUp5b269xVSyggp5Vop5aPjkrSUckj3+1rd9YpJ43+os6sBUsqTptxzwUeUxuwIoKOtj+Kihhn77b4niNGRMZLOzc2TUgjBvR/bSUV+HQWp5TeyVBWVBcepl+Px3bCC9VN8w2dDq9WSeLaAsO0B2M4ivaQkluK3xoNly12mXdNotCSnVRAZtnqanp+SV4VWSmKC9deWVFSN1xInVnpMzJdSVoO3mzMr3JTgp6vNrfQODxOxamFJLwuBBW/UI2PWYmYuSLwyc+709cErWbbClUvHs+d8jz0PR+DgYsd7f56PM3QVlYVBWV4tpTk1HHoy1mCE50xczamlvaWH2AMzVzjq6x0iP6eWyFjDGR+vljbR3TNIVPj0A9TE7EpcHG3Z4Od5rW1UoyGtuJaoDROFMsY0WtIq6vSkl9RqRU+PWOA79dvBgjfqjk62BIWsIjGuZMZ+Qgh23RNEVlI5XR19c7qHjb01hz4SS8LxbFrrO25kuSoqC4ZTL8djZWPJnkci5jw24Uw+FpbmRO7aMGO/pPgSNBotMdsNZ2VMTlXK2kVs1d+Na7WSlLwqIrf46hW6yKtopH9ohOhJenpBnVLOLnLtxK48paoOXzcXljnN7ZzgbmDBG3VQJJiaqjZqq9tn7LfzniC0Gi1XTs6teAbAvc/sBCk5/ve4612misqCYah/mItvpbL9vtA5R5BKKYk/k09orD/2jjYz9r18vhCPZU6sD/QyeD0prZyNG1ZMiyK9WtlMZ88gMVO8XpKLajATgohJ+dOTyxQ9PWKN0jaup6u7dMMsDqO+TQloSE6Yebfut86TlWs8iDs1d6O+bOUSIg9s4dQ/E9QIU5VFT/zxLKW60Yfn5sYIUJhVTUtDF9sOzhyo1Nc7REZqBTv2BBqUd9o7+igtbyEqbLr0kpxbiRAQMaV0XXJRNRt9PXG0m3iYpJbXsm65O24OSkRrcXMbvcPDhKtG3SC3KqL0hvDwdGaN/zKSrpTw6IdnDnPecXgL//zdedpbeljiMbfw4SNPbyfpVA4Jx7PmXJBXRWUhceaVRLz8lrI52rBHykycO5aJjZ0V2/bPnutlbEzLjj2GJZqUdCV7qiE9PSmnig1+nrg6TaQe6OkforC6mY8fnpCLhkbHyKpq4PHoiYjv1Bp9Pb1neJj5oKKzkyfeem1e5rqdLIqdOkD09nUU5NXR0z1zRrYdhzcrXx/nWL8UIHTXBjxXLuH4P9SqSCqLl4bKFvISS9n/ePScD0iHh0aJO5VL7P6Ns3q9xF0omlF6SU6vwH2JA2v89HO39/QPUVDWSFSQr157WnEtWimJ2jCxe8+pbmBkTKOnp6dV1+Hj6nzNP/1v2Rlz+Yh3PItipw4QFevPy3+9QkpiGfsPG0/U77PaA78AT+JO5XH0qdg53cPMzIzDH93O337wDtXFjawKWD77IBWVBcbJlxMwMxNzrm4EkHS+gIG+YfY9MHMmj3Hp5egj4QYfHGNjGjKyqtgZOz23elp+tWK8t/jqtSdfrcbexopNk7xhUsqUcnZb/ZR0AVopSa+pZ8+6iejUpNr5ydS42tWVVx7+kEl9X+XxebnnzWDR7NT9A5azxN2RpCsz6+oA2w9toTCzmtbGrjnf58ATMVhYmqs1TFUWJYP9Q5z6vyvE3BPCUi/jtUSNcf7dLJYud2ZLxMx+7UnxJTNKLwVXG+jrHybSoJ5ehYOdNYFr9DdNKVdr2OrvfS2tLkBKeS2bvD1xsFG+NZS1ttM1OET4KsXID46OktU0cwzL3caiMepmZoKY7etISy5ncJaKSNt1Bzzxc6xfCkpK3pjDwVx4K5WRodHrWquKyu3i3GvJ9HUP8uCnDCZBnZGO1l4yE0rZc1/IrLUJEi4X477UkfWBhjPBpqRXYm5uRlior167lJKU3CrCN67EYlIwUn1bN3Wt3URtmPBFHxgeoaC2mfA1EweiaTW6ykcrlbb0xnpGtVpUJlg0Rh1g175AhoZGSY6fOXGXt99SVq9fzuUTOdd1n4NPxtLb2U/iyezrGq+icjvQarW8+6eLBIT4ssHADnk2Lp/IQauV7L4veMZ+gwMjpCWXs23nej0f88kkppSxeeMK7O30dfmqhg5aOvqInCK9pF7VuS2unzDqmVVKObtxV0aA9Oo6PJ0c8HZRnCCS62qxmENxnLuBRfWvsSloJUvcHbl8fvZUAHuPhlCcW0d1WfOc7xO8PYBlPks49XLC9SxTReW2kHo2n/qKFh741J45H5ACXHgvi7WBXqxau2zm+ySXMTIyxrZdhgOOauraqaxuY0fM9NzqKblVwHRXxpSrNSx1tsfP023iPuW1WJibEeKrHMRqpSSluo7wld7XPl9SbS1ByzxRmWBRGXUzM8HOvRtITSqbNXHXnvtCMLcw48zbcz8ZNzMz4+CHY8iJL6aufO4PBRWV28E7L17A3cuVbffOrQYpQE15C2WFDey5P2TWvvGXruLsYsemIMNl664kKt+ktxtwp0zJq8bH0xWvpRMFrLVaSWpxLZHrV+o9jFLLa9ni44mtlSUAJc1ttPcPELNauW/v8DB5LU1Eeav5XyazqIw6wM49gYyOakic5cDUZYkDETvXc/H9LDQzFNkwxuGntmFpbcGxP5y/3qWqqNwyqosbyYkv5t5ndmBhOWtt4mlc+iBb2TTNUlx6ZGSM1MQyorevM1pw40piKQH+nngs1Y8TGRkdI7Oolsgt+rv00vpWuvoGiZikp/cNDVNY16InvSRWKhJNrJ8yPr2xHo2URHsbfrjcrSw6o75+4wqWLnMi7uLsdTb2PRBKZ1sfGbNo8IZwWerEvseiOPd6Ml2tPdezVBWVW8YHf7uEpbUFBz8yNzdeUA4vL53IYUvEatyWzpybPCezmoGBEbbtMCy9tLb1UlTSyPaY6bv0rKt1DI+MEbnZV689tVhxSYwMmDDO6RV1aKXUOyRNqKxmjbvbtXwvyXW1WJmZE7pcdT2ezLwYdSHEISFEsRCiTAjxdQPXrYUQr+mupwghfK/3XmZmgh27N5CRUjGrBBO+IwAnFzvOvZt5Xfd66Lm9jA6P8f7fLl/XeBWVW0F/7yDnX09h5wNhuLjPvWBESX4djTUd7Lo3eNa+CXHF2NpZEWIklW98chlgWHqJz6zA2tKC8I36O+uUohp8Pd1Y6jKRnCuhpBpbS4trevrI2Bjp1fXE+E0qklFXS7DncmwsLGdd961GCGEjhEgVQuToCgR9V9f+T52tzBdC/FUIYalrF0KIX+tsZK4QInTSXE8LIUp1r6eN3XOcGzbqQghz4HfAYSAQeEIIMbWg4ceBTinlWuAXwI9v5J479mwwSYKxtLJg933BJJ0vpLdr5khUQ3iv9STq4BY++NtlhgZmdqNUUbldnH89hcH+Ye77t13XNf7y8RwsLM2J3T9zml2tVpJ0pYTwqDVYWRuOW7ySWILPCldW+SzRa5dSciWznPDNK7GxnjDCgyOjZJTW6lU5AogvriJirQ9WFsp9MusaGRobI1pn1HuGhylobVnIevowsEdKGQQEA4eEEFHAP4H1wGbAFviErv9hlHJ1/sCzwO8BhBBuwLeBSCAC+LYQYsYAhPmIKI0AysardQghXgWOopRgGuco8B3d+zeB3wohhJyl1JAxf/QNG1fgoZNgZoouBdh3NJR3/y+RuFN53PN4pCmfR4+HPr2XpFM5XHgzhSMf3T7n8SoqNxMpJR/8/TIBIb6sC141+4ApaDRaLp/IJXxHAA5OtjP2vVpQT0d7H7FGpJfeviGy82p57MGwad43ZbVtNLX18MxR/b/B9OJahkc1xG6c2PnXtHdR297NU9smDnyTKmowF+Javpe0BkWemU+jXtneyVMvvTEvc+ls23gOcEvdS0opT4z3EUKkohSTBsVGvqQblyyEcNHVdt4FnJVSdujGnAUOAa8Yu/d8yC8rgMlxunW6NoN9dDVNu1Fq9E1DCPGsECJdCJHe1NJp8IZCCLbtWk9GagX9/TMn81kT6MXKNR5ceH/u9UsBNkauZe0WH97980W13J3KgiM/uYzakibueWbu5eoACjKq6GjtnfWAFBTpxcLCjMgYwwUxUtIr0Gi0bIsyJL0oVcW2hej7z8fnV2FrbclW/wmTkVislLOLXTfxkEqqqmHLCk8cdZGlKXW1WJmbE+J52/R093E7pXs9O7WDEMJcCJENtKAY5pRJ1yyBp1Bqj4JxO2qKfdVjweV+kVK+CLwI4OzqI4dHxrC2mr7M7bvW8/ZrqaQklLLngPFsckII9h4N4W8/P01jbQfLfdyM9jU2/ugn9/C/n/0HWXFXCd05c9EAFZVbyfG/x+HgbMv2+2fO1WKMC+9lYW1rOWsdUq1WculcASHhftg7GM6xnpBchquLHRsM5EyKz6wgcLUn7q4TurmUkoSCSiLXr8TKcuJvPKGkCm83J1a6uwDQOzRMXkMzn4qdyN6YUl9HiOdyrC3mz4T5LXHl/z76qEl9X36aNill2Ex9dEWig4UQLsAxIcQmKeV4mPsLQJyUct7zkczHTr0emPwdyFvXZrCPEMICcAZmrniB8j9SelaVwWuBm31wc3cg/tLsNax36w6ALl7nbn3H0a24LnXi3RcvXNd4FZWbQWt9B/EfZLLvQ9HY2FnNefxA/zCXT+ay83DQrOML82ppae5hr5EN1OiohpT0CqIj1kxzdWzv7qewopFtofq79MqmDhrae4jd6Dsxj0ZDSlkt0f4T5exSqxWpJdpPMTPjenrEisWRT11K2QVcRJFNEEJ8G1gKfGlSN2N21BT7qsd8GPU0wF8I4SeEsAIeB96b0uc9YPzU9hHgwmx6OoC5uRmX4w3XJjUzE8TuCCA1qYyhWXK0LF3uwpaI1Vx4L+u6JBQra0uOPL2d1HNKxJ6KykLgrd+fA+DBT+29rvGXj+cwNDDCoUdm3HACcOFMAdbWFkbL1mXn1dI/MMK2qOnSTFJ2JVLCtpA1eu0JBVUAenp6TnUjAyOjxAb4ToyvqsHGwoIQb+UbQHpDPVopiVyh2LrCjoX3NymEWKrboSOEsAX2A1eFEJ8ADgJPSCknJ615D/iozgsmCuiWUjYCp4EDQghX3QHpAV2bUW7YqOs08s/oblQEvC6lLBBCfE8Icb+u21+AJUKIMpSn0zS3R0PY21uTmFLOmJHgoW271jM8PEZ6Svmsc+25L5j66nbKCq8vo9uRj27H3MJMLXensiDo6ejj1MsJ7H44Ag/vuUmK45x5O52VazxYHzxz8M7YmIa4i0VEb1uHrZEdfWJqGVZWFmwN9p12LT6rAg83B/xX6edVT8ivZK3XEjzdJtwwk0prMDcTRE4KOkqprCVs5YprnjCp9bVYmpld09NfK8k16fPeYpYDF4UQuSgb37NSyg+APwDLgCQhRLYQ4r90/U8AFUAZ8Cfg3wF0B6Tf182RBnxv/NDUGPPipy6lPCGlXCelXCOl/KGu7b+klO/p3g9JKR+VUq6VUkaMe8rMhqO9Db19Q+Tk1xm8viV4JY5OtiRcNrybn0zM/k1YWJpftwTjtsyZ2HtCOPtqIkOzHM6qqNxs3v/rJYYHR3jk+QPXNb66rJmrObUcfGS6p8pUstKr6O4aYNc+wy6PUkoSU8rZGrwKGxt9n/HRMQ2peVXEBK/Wu8/A0AhZ5Q3ETJJeABJLqtns44mjrXIg2tbXT0lrO5G+E0Y+tb6eLcs8sbVU7pXYWG3y575VSClzpZQhUsotUspNUsrv6dotdHYyWPcab5dSyud11zZLKdMnzfVXne1cK6X822z3XtARpfb2VthYWxJnpDaphYU5Udv8SU4oNbqbH8fR2ZbwHQFcPpGLRnN9qTrv+7ed9HUPcvHttOsar6IyHwz1D/Puny8RdXDLdRdyOfN2BuYWZuy5b/ZcLxfPFWDvYE149BqD1yur22hq7iYmcvr1rKt1DAyNEjvF6yWtuJbRMQ0xgb7X2roHhiioaybaf8LrJbVa2dBF6fT0/pER8lqarkkvLQN9lHbNejx3V7GgjboQgoitfsQnl6LVGtbCt+1cT1/vEFnpVbPOt/u+YDpae8lKnHvaAFDcG9ds9uGtF85e94NBReVGOf2vBHo7+3nssweva/zYqIbz72YStXsDLkscZuw7MjxGwuViYncEYGXACw0gUSd/xkRMN+qJWRVYWZoTFqgv8SQWVmFnbUnI2gnvvJSyGrRSEjPZlbGyBkdrawI9PQDIbGxAIyWRukPSpMYaEz7x3cWCNuoA22P8aWvv42pJo8HrYZGrcXC04YIJBTEid2/AydWeU29c305bCMGHPn+I+ooWrryn1kVUufVoxjQc++MFNkauYYOBgs6mkBZXTHdHP/sfnN0NMj2lnIH+YaPSCyh6esDaZbgvmZ6iIDGnktANPthOkmUUV8YqwgN8sLSYSD6WVFqDvbUVm30mlbOrriNs5YprOdNTG+owF4KQ5Ur6gKSmGhytZq6lerex4I16dPgazM3EtZwSU7GysmDH7g3EX746a0UkKysL9j8YSvLFIjpari9JV+w9wfj4e/Lar06jVSuuqNxiEk/m0FzbzkPP7bvuOc4ey8DV3YGw7dPznU/l8oVCnJxtCQnzNXi9q3uAwqsNxERO93qpbeqkprGTmGD9PDE1LV00tPfoSS+gGPWINd7XKiI1dvdS3dFF1CQ9PaW+jo0ey3CwUg5skxpriFy2YFMF3BYWvFF3dLQheMtK4pOMSyZ7D25iaHDUpPqlhx4JRzOm5ew715fky8zMjMc+d5CqonpSz+Rd1xwqKtfLsT+cZ7nvUiIPzpwewxhdHX2kXr7K7vtCMLeYOUXv8PAoSfGlbNu5HgsjfeMSSxR3RQMJvJJyKgGIDtI36kmFVUr7pHwvte1d1HV06+npKVVKIOW4Ue8bGSG7qZFoXWqA+r4eqnu7iF6upt6dzIKLKDVEbNRafv2H89TWdeBjwH1rU9BKli5z4vzp/BmjS0EpdbclYjWn3kjl0U/smLUWoyF2PRjOyz/5gFd/eYrIg1uuq8qMispcKUqroCi9gk//94eM5jKfjcvHc9CMadn3wOyFNFKTyhkcGGHnXuNR1JeuFOOzwpU1fkunXUvMrmTlcld8PPXzTyUWVuOz1AXvpS7X2pJLFW08yn/CQKdU1+Jia8O6Ze7KeurrGNNq2bZSMfzjevp8GfWq1k6e+cP85H65nSz4nTpwLZfEFSO7dTMzwd4Dm0hPLaers3/W+Q4/FkFTXSfZSbP7txvCwtKcRz97gOKsKnKMBEepqMw3x148j4OzLfsfj7ruOc69k8naQC/81s1eAi7uQiHOLnYEhfgavN7VPUB2bg27tq2ftrEZGh4lq6hu2i59ZHSM9JJavV06KNLLMmcH/JZOPABSquqIWOWNmW7u+NpqrM0tCFuuHK4mN9XgYm3DetfpD5S7mUWxU1/m4cTa1R4kppbz4UcNZ1rcvX8jr/5fIlcuXuW+h2Y+AIrZF4iDsy2n30onNHb610ZT2P+haF7+yQe89cJZgrfPnDdDReVGaa5tJ+GDLB769D5s7Q3nXpmN6tJmygobeO6b987ad3h4lJTEMvbs34i5hZEKR0mlaLSSXQaiTDOLahkeHSNmilHPLm9gaGRMz6hrtZLU8lp2bpjwZa/t7Ka+u4d/i574W06sqSbca8W1fC/JTbVEea68ZvRvFN+lrvz9OdNyv/zj0/Nyy5vCotipgyLBFBTV09VtOC+63xoPVvm5c+Hs7F4wVtaW7LkvmMRzBfSYsLM3OIeNJfd/YjfpFwqpLDAcHKWiMl+89cI5hJm47pzpAOffy8LM3MykjIwZKRUMDoywfffM0ssKLxfD0ktOJTbWFgSv18/PklxUjYW5GeHrJg43ixtb6RoYInLtRFuSrnTduJ7e0t9HSUc7sSsVqaW2t5u6vm6iPNVD0qksHqMeuRatVpKcZjgYVQjB7n0byc+ppaWpe9b5Dj4cztiohosfZF/3mu59Zgc2dtbXcnCoqNwMWus7OPlyPPs/FH3dKQE0Gi0X3s8ibJv/rL7pAHEXi3B0siUo1HCO9u6eQbJyqg1KL1JKrmSUE75x1bQMq8lFNQSt9sLOZiLdQNK4nr52QhuPL6/C08mBNe7K502s1dUn9VHWk9ykG+OpHpJOZdEY9XVrl7F0iQMJRlwbQZFgAC6dLzTaZ5zV65fjv3EFp99Kn7WvMRxd7Tn4kRguHUujtX7GdAwqKtfNa78+DVLy+BcOX/ccaZev0t7cw/6HZk/eNTI8RlJ8KbE71hn1eolP1kkv26a7RV6tbKa5vZdd4frSZkfPAFdrW4jaoP+gSC6rYbWHGx7OysNmTKslsbKW7Wt8rz0wEmprcLGxIXCpEoSU3FSLq7Ut61zdZ//wdxmLxqgLIdgW7U9KRgUDRvzRvbzdCNjgZZJRBzjw0FYqi5soL7q+JF+gZMiTEt7988XrnkNFxRitDZ2c/lci+x+PZtlKg3VlTOKDV5JZ4uFE1AxyyjhJCSUM9A+zc+/UqpQTxCWU4LnMGf81y6Zdu5RehrmZmF4Qo0BxcYzZOGHUB0ZGSa+o0yuIkVPfSO/wMLGrlTYpJYm11UR7T+jnyU01RHr6zJuefiexaIw6wO4dSlbGxBTju/WdewMpvdpIfd3sO+edR4KwsDTn7LHrjw5d5rOE7feFcuKleHq7rk+fV1Exxpu/PYPUavnQ5w5d9xwNNe1kxJdy+LFwLCxn9k0HOHcyD/eljkaLS/f1D5OeVcXO2HUG3Xkvp5USssEHZ0f98niXcyvwcHFgvY/HtbbUslpGxjTs2DBxr/jyasyEuFZkurKrk8a+PmJ8lN/r+rqp7+shUqenZ7WrZ1qTWVRGfXOgN0uXOHAxznhhjJ17lJ3IZRN2644udkTt2cDFD3IYHRm77nU99rmDDPYN8dYLqrauMn90NHdz8uV49j0WdUO79JOvpWJmbsbBR8Jn7dvZ0Udqchl7D2426guflFrO2JiWHTHTpZfqhg6qGjrYsVU/D8zw6BhJhVXs3KKfrTHuaiW2VpZs9ZvIAZNQUc0WL0+cbRUvn3E9fdyopzQpQUnjRv3tqpxZP9fdxKIy6mZmgl3bA0hJr6S3b8hgHw9PZwI3eZtk1AH2P7CVns5+0k2IRjXG6o3e7Di6lXf/dJGu1utLP6CiMpU3f3cWzZiWxz5//bv0keFRzrydTvTeQNyXOc/a/8KZArQayf7Dm432iUsoYYmbPYHrvaZdu5yhfIveGaafNiCtuJahkTF2bJkw9lJKrlytJNp/5bVc6V2DQ+Q1NBO7euIANLG2huUOjvg6uwCKUXe2mvBPT26tmvVz3U3ckFEXQrgJIc4KIUp1P12N9NPoEsJnCyGmVkWaE7t3bGB0TEPCLBJMRVkLNVVts863dZs/ru4OnHrzxtLpPvXVexkZGuGN3565oXlUVAC62no58VIcux8Ox8v3+oNr4s/k09M1wD0fMhzfMZVzp/LwX7+cVQbcFEHxX0/NqGRbtD9mZoaklzLW+y1j2RInvfa43ApsrS0JWzfh4lje3E5jVy/bJ1c5qlQyNcauUfR0rZQk19cS47Py2g4/pamW8GVKUFLjQDfVfQvPSUEI4SOEuCiEKBRCFAghPj/l+peFEFII4a77XQghfi2EKBNC5AohQif1fVpnY0uFEE9PvddUbnSn/nXgvJTSHziP8YpGg5OSwt9vpM80+gamF6MIDFiOx1JHLl0xHsm5Y896hFDcsmbD3MKcgw+Hk3a5mMba6/+fw3utJ7sfieCDv8fR0Ty7S6WKyky89+eLjAyNXXd63XFOvp6G18olBEXNntGxqqKVspIm9h8yvktPy6xiaHjUoPTS1tlHQXnjNOlFSsmV/AqiNqzCelKB6birVQBsXz+hpydWVONgbUXQCiVP/NW2VrqGhojxVnbuTf29VPd2XfNPX8C79DHgy1LKQCAKeF4IEQiKwUcpSzc5b/BhwF/3ehb4va6vG/BtIBKIAL5tbPM8zo1GlB4Fdune/wO4BHztBue8Rlfv4LQ2IQQ7YwN454Ms+vqHcbCfnnbTfakTm4JWcuF0Ph95ZtusuVmOPB7J63++zPFXk/nEV45c93o//KUjXHwrjdd/c5rnfvDYdc+jcncz0DfE+3+9RPThIFauu74iGAC1FS3kp1fysS8dMinH0fkzeZiZC3btM+71ciWpFAcHa4I3Tw/6ic9SYkh2bNWXXkrr22ju7ONT9+ofvMYXV+HvuQRPFyVlr5SShIoaon1XXku1O66nR+mSeKU06+vpyS1VuFjpH8heL9XNnXzy5/OT+0VXX7RR975XCFEErAAKgV8AXwXenTTkKPCSrnZzshDCRQixHMW+nh0vYSeEOItSwPoVY/e+0Z36Mt3iAZpQau8ZwkYIkS6ESBZCPDDThEKIZ3V90/sGhuk34L64a3uAIsHM4LN+4MgWamvaKcqfsfA2AEs9nYndv5HTb6UzNEv63pnw8vNg76ORnHjpCu1NXdc9j8rdzYmXrtDXPXjDu/RTb6ZjbmHG/gdnT96l1UounM5na8RqXN0MByeNabQkpZYTHb7GoP96XEYZXkudWeOj7zsel6sY++2bJox6/9AImVX1bJskvVR3dFHf3UPMJD09qa4WPxdXljsqhj+1qQ4HSys2uHkgpSSltZrIpYYDpG4y7uN2Svd61lhHIYQvEAKkCCGOAvVSyqmnuyuA2km/1+najLUbZdaduhDiHGAo+8+3Jv8ipZRCCMPliWCVlLJeCLEauCCEyJNSGsymJaV8EXgRwGGJj0zMrmB/tH5ulcAAL0WCib/Kwb2Gk/fv2L2B3/38NKeP5xC42dtgn8nc9+ForpzK4+L72Rx+LGLW/sZ44ouHufBmCq//+jSf/u8PXfc8KncnQ/3DvP37cwRtCyAg1Pe65xkZGePcsQyi9wbi6j69eMVU8nNqaGnu4eOf3mO0T15BHd09g2w3kGZ3YGiE9IIaHtobNO2bcVxeBZt8PVniZH+tLbmshjGNlu0BE4Y+oUKpNTrunz6m1ZJWX8f96yd865Obagjz8MbCzIyavk4aBrr5xLpofjvrJ5ydVctc+dOXTMv98ucv0yalnDWSSwjhALwFfAFFkvkmivRy05h1py6l3KcrnDr19S7QrPuKgO5ni5E56nU/K1AkmtkLIwLm5mZcSpuemdHMTLAzdh1pGVX0G9DdAezsrdm+ez2XzhcyPDw66702hfniu86T46+moHwDuj6W+y5l76NRnPpnAh0tqrauMjeO/fE8nS09fPTr993QPMnnC+npGuCQCW6MABfOFmBjY0n0DIUzriSWYmVpTvjW6f7rqXnVjIxq2B6qr6d39AxQUN3E9s3TpRc7K0tCfCc8aBIra/B2cWKVmwsA+S3N9I2OEKOTXhr7eynv7mCbl2L0U3R6epSHr0mf8VYjhLBEMej/lFK+DawB/IAcIUQV4A1kCiE8gXpgsqblrWsz1m6UG5Vf3gPGT2OfRl8jAkAI4SqEsNa9dwdiUXSlWXG0syYxu5JhAz7kO2IVCSYp1Xj63P2HtzDQP0xi3OzuikII7nk8kvKiBopza2ftPxMf+vxBxkbGeFvNCaMyB7raennjd2eJORJMYLjhIs+mcvqtdDyWuxAcPb0i0VRGRzXEXSgievs6bG2tDPbRaLRcvHKVqPA12BnocyWzHEc7a4IC9JWBxMIqpYjGJOlFSklCSTVR/iuvlbMb02pJrqq9FnAEkFSn6OkRuiLT8Q1VAMReM+rVuFvbs8Zx4aUKEMrXlb8ARVLKnwNIKfOklB5SSl8ppS+KlBIqpWxCsaUf1XnBRAHdOmn7NHBAZ0ddUXb5p2e6940a9R8B+4UQpcA+3e8IIcKEEH/W9dkApAshcoCLwI+klKYZdXsbBodHSc2vnnZt04YVuLnaE5dg3GAHhfriscyJsydzTfowe+4PwdbOiuOvppjU3xhefh7sfDCc43+/Qnd73w3NpXL38MrPTzA8OMIz3zx6Q/M013eSlVjG/oe2mlRMIyO1gt6ewRkLzGTl1tDR2c/eXdPTDGi0WhKzK4gO8pumtV/Jr8TdyY4A74ko0qrWTho6e/RSA+Q3NNM3PEL0JKOeXFfLOrcluNvZAZDQUI27jR3rXZfq9PQqIpauWqhFamKBp4A9k9y5Z/LCOAFUAGXAn4B/B9AdkH4fSNO9vjd+aGqMGzLqUsp2KeVeKaW/Tqbp0LWnSyk/oXufKKXcLKUM0v38i6nz29lY4WBnzeV0wxLM9hh/ktMrGBwyfLhpZibYd2gzGakVtLX2zn4/e2v23B9C3Mnc607JO86HPn+I4cER3nzh7A3No3J30FjVyomXrnDwwzH4+M9ewGImTutiLkwpLA1w4Uw+jk62bI0w7vZ4/nIRdrZWRBsodl1Q1khnzyDbQvWvjWo0JBVWE7vJT8+nPb6kCoDYSYekCRXVCCBKZ9RHNBrSG+qveb1IKYlvrCbWSzHiNf2dNA/2Erl0Yo6FhJQyXkoppJRbJrlzn5jSx1dK2aZ7L6WUz0sp1+jsZPqkfn+VUq7Vvf42270XdESpEBAbsporGeWMaaYXed4VG8Dw8Bip6ZVG59h/JAitVnLRhDzrAPc8EcXI8Bjn38u67nUDrApYzp5HI3j3Txdorm2/oblU7nxe/ukHmFuY8eRXZi9gMRPDQ6Mcfy2ViF3rWbZiRndmAAYHR0i6UsKO3euxNJIXZmR0jLiEErbH+GNtbTntenxmBeZmgqgpBTFyKxrpGxzWk14AEour8XV3xdttIsI1qbKGDZ4euNkp7om5zU0Mjo0RpfNPL+5so22wn9jlE9ILQMTt8XxZ0Cxoow5KuHF33xC5JdPPBrZs9sHJ0cZomTsAbx831m9cwblTphWJ9lvnyfogH06+kXZDB6YAT3/9foQQ/P2/px01qKhco/pqAxffSuO+j+/GzYRQ/pm49EE2PZ39PPh0rEn9UxJKGRoavZa22hBpGZX09Q+zd6fhDI8JWRUEBXjjNKUiU0J+JRZmZkSun5BUhkfHSKuoIyZAP1Njdl2jnp5+paYKMyGuFZlOaNR5xnj5ApDaWoW7tT2rHa8/J86dyoI36lFbfLGyNCcufbpPuoW5GbFR/iSmlDE6qjE6x75Dm6koa6GirNmkex5+LILa8hYKMqdr+XNh6Qo3HvzUXi69nUZxVtUNzaVy5/J/P/0AG3trHn1+/w3NI6XknZcS8AvwZMsMUspkzpzMxX2pI5uCjBebOH/5Ks5OtmwNnr4rrm/poryubZr0ApBQUEXwWi8cbCcCBLOqGhgaHdPT09Nr6hnVavX09LjqKoKXeeJsozwoEhqq8HNyZYWDE1JKUltrrunpzYNdJn3Wu4UFb9TtbKwI37SKyxllBnfOO2L86R8YIX0Go7lrbyDm5macP22aBLPj0BbsHKw59Xrq9S77Go997iAu7o78+btv3/DOX+XOoyy3Rqk9+txenIwE/ZhKTkoFVaXNPPj07FHUAC3N3aQnl3Pw3iCjB6qDQyMkJJexM9ZwwYwLKYqjwq4wfd/15s5eSuvbiN2oL70klFQp5exWT8SOJFXVYGluztaVintjx+AAuc1NbF/lC8CoVkNKUy0xOumltr+TpsGea9LLGzXJs37Wu4kFb9RBkWAaW3sorW6ddi081A8nRxvOXTLuUOPsYkdE9FrOn85HY0Cbn4qNnRW77w0m7lTeDR+Y2jnY8ORX7yU/qZTkU6Z54ajcPbz04/dxcLHjwU/tveG53nkpAZclDuw8ssWk/qeP5yAlHLzHeM3SpNQKhoZH2b3DcHH1C6klbFi9DC8PfdkosaAKgNiNvnrtCSXVhKzyws56wi0yobyaEO/l2Foqen1CbQ0S2LFSGZvT2kj/2KieKyNM6OnpHYZLXN6t3Gjul1tCbMhqhFB8Ydf5euhds7Q0Z9e2AM5cKGRgcMSgDy3A3oObSIovITer2mjy/8nc+0QUx19N4fhrqTzx3O4bWv+hj8Ry7I/n+cf/vEvEAeN5qlXuLgrTykk7l88z3zyKvdON5S9pqusg9dJVHn9uN1YGDjOnotVKzhzPITTcj+Vexg9UL125ipurPUGbpud6aWjtpqiimecf3z7tWnx+JZ6ujqzxmtC8W3v6KGls4wuHJ/T+pp5eilva+MreiTmu1FThbG3DlmWKF1BiYw0CiNbVI01trcbN2o41ju70jQ5xtXv2VCCmUNPYyad/8Nq8zHU7WRTWZYmzPZvWLudKpuFAo327AxkaHiUh2fiBadQ2f+zsrLhwxjQJxnedJ2Hb1/H+PxMZuYECGqBkgnz66/dTXdzIxbduXNJRWfxotVr+8K3XWeLpzP2f2HXD833wSjLCTHDkQ6aluMjJrKKpsXvGXfrA4AhJaRXs3BZgcCNyMVX5e9sTqR+FOjgySlJhNTuD1kwpiFEFwLZJqQHiypS2nWt9AV1Gx+pqYn1WYq5L6pXQWE2gmweuNsqDL72thnB3JRVvVmclWlRZczKLYqcOsH3rWl549Qot7b14LNHPZbE50JtlS504e7GI/bsNn+JbW1sSu2s9cRev8tkvH8bKevaP/tAz2/nmx//CxfezOfjw7AV7ZyL23hD8g1byfz95nx1Ht5q0m1K5czn7ShKlOTV85Xcfw3aK18hcGRoc4fRb6cTu32hSIQyA0x/k4OBoQ+zOAKN9klLLGRkZY/d2w30uppYQ4OvBCg8X/XGF1QyNjrE7SD8q9lJhOctdHAlYPhEBermsEi9nR9YuVXb0pR3tNPf3sX2lIq0Mjo2S1dLAM4FKUrL6/i7qB7r52LooANLbK7A2mx8ztnK5K7//T9PyNf3h/z0+L/e8GSyKnTpwLadEnIHdupmZYN+uDaRnVtI5Q53QfQc3MdA/TPxl4+XwJhMcvYbV65fz9t+u3PAhp5mZGc986wFaajs48Y8rNzSXyuKmr3uAv/3wHQIj1rD7YdNys8zE5eM59HUPcv9Hok27f+8QVy5dZff+jQb9zse5eOUqS9zs2Rw4PSFec3sP+WWN7ImYnivmQlYpzvY2hPpPjBsaHSOptIZdgRPl7EbGxkisrGHnWr9rbXHVVQBs0x2SZrTUM6LVEK07JE1t0+np7hN6+mYX4547dyOLxqj7ernhvcyF+BkkGI1Wzlg8I3irH55eLpw0MbBICMFDz2yjpryFzETj0o6phOxYT9C2AF755Un6ugdueD6VxckrPz9BT0c/n/7hYzcc4i6l5L1/JeG7zpONW31NGnPpfAEjI2MzSy8Dw6TopBdDFY4upSkuxrunSC+jGg1X8irZsXk1FpMkm5SyGoZGx9i1YcL1MaO2gYGRUXasnVh3Qm01q11dWeGoVE5KbKzBQpgRsUx5QKS11uBsacM6Zw+6RgYo7W1k6xLT3DfvFhaNURdCsCvcn7SCGroNFM9Y7bsUv1XunL9svNqRmZng8H3BZGdWU2dilaPth7fg6u7IO/9IuO61jyOE4BPfeZi+zn5e+tENVfVTWaTUV7Tw3l8usf/xaNZuufEd5tWcWiqKGrnvw1EmPyDOHM/Fd/VS1q03XoAjKa2CkVENu7YZl17W+Liz0lP/kDWztJ7ewWF2B+snErtUWIGdlSXhayZ275fLKrE0NyfKV/l3GB4bI6W+ju06rxeAxMZqgpYux95ScYBIaa0mzH0lZkKQpfN6CXO7seRndxqLxqgD7IsKULLFGUjHC7B35wbyCutpbjFe/PngPUGYmQuTd+tWVhbc83gk6VdKqK0wmFl4Tqzd7MM9z+zk+N/jKMutmX2Ayh3FX773NpZWFjz9DZOrOs7I8VeSsbW3Zve9wSb1r61up6igngNHtsz4ELgcX4ybqz2bNkyvx9De1U9OST27w6fnVb+UU46NpQWRGyYeWFJK4q5WErNu1bUC06AckoavXIGdlSIBZTQ2MDQ2xjYfRVrpHRkmr62JmOXKXDV9ndT2dxK9TDlozeioxMbckkDnGWtG3HUsKqMe4OuB9zIXziUbllj27FR8aS/EGd+tL3F3JDp2HWdO5M4YhTqZex6PxMLSnPdeTpr7og3w0a/fh/MSR377tVfQamf3m1e5M8iJLybpZA6Pfe7gDacDAOho6eHyyVz2HQ3B1kBZR0OcOZmDmbmYMSPjwOAIyekV7IhZZ9Dr5XJ6GVLCrilGXUrJpZwyogNXYWs1odVfbWilubuPnZOkl/quHsrbOvSkl/iaaiWtgC41QFpzHRopr7kyJrYoOZ5iPZR5MjoqCHJZheU8HZTeKSxoo97WrX/oKYRgX1QAmYW1dBjQpFcsd2XDuuUzSjAAh+8Poauzn+T42fOsA7gscWD3vcGcfSeD3u7p0s9ccXC24xPfeYjizCrO/CvxhudTWfhoNFpe/PabeHi7zUugEcCxlxLQarQ8+Mx0P3Fjazh/Ko+wiDUsmaEaUlxiCcPDYwbT7AJcSivFx9N1Wtm6opoWmjv72DnF6+VyUQVCwPb1vhP3KFcM9I41E23xtdUEey7HwUqRWhIbq7EyNyfUQ4k0TWqpYJmtI6sdl9A50kd5XzNb3VQ9fSoL2qj3Dk6varQ3KgCtlAYrIgHs3rGe0vIW6uqNa+ZhkatZ6uHIyQ+yTV7L/U/GMDw4yrljGSaPmYndD0cQGLGGv//3u+qh6V3AhTdSqMiv42PfegBrIwFyc6G/d4jjr6aw7eBmlvu4mTQmJ6ua1pZeDswScXrmfAFeni5sDpwua/T0D5FRVMuu8LXT5JvLueWYCcH2zfqG9nJRJZt9PHF3nChnd6WsmhXOTqx2V9beOThIQUvzNekFIKmxhtClXthYWKKVkqSWKmI9FO+ZrI4qAEJVoz6NGzLqQohHhRAFQgitEMKoI7cQ4pAQolgIUSaE+Lqp8w+OjNLQrl8Sbq2POyuXu3Ih1fAue9yn9kKccbdFc3MzDhwJIiOlgtYZ9He9+wZ6ERi6ivdfSZoXyUQIwaf/+0P0dPTzr/89MfsAlUVLb1c/f/vBOwSE+LLzwRuLdxjn+KspDPYP8+gndpo85tzJXOwdrInaNl0LH6eltYfMnGoO7t1oUHNPyKpAo9GyM2z6HJdzKwha44Wrw0R0bHvfAPl1TexYPxFwNKLRkFxVy7Y1EwUukupqkUDsSkVq6RoepLCjhWidnl7U1UTXyCDRutJ1GR0VC1pPF0L8VQjRIoTIn9L+WSHEVZ3d/Mmk9m/o7GOxEOLgpPY5284b3annAw8BccY6CCHMgd8Bh4FA4AkhRKCpN7iQpZ+dUQjB3kjjEozHUic2B66Y0aiDcmCq1UrOnDA9H8v9H4mhsaaD9CumyTazsXazDwc/Est7f7lITUnjvMypsvD4y3ffprujj8/85Il5qdIzMjzKOy8lEBKzlrWBXrMPAPr7h7ly6So7dm+Y0Tf97MVCpIQDewwH8V1OL8PdxZ7A1fqFPBraeyipa2XXFOkl/molUqJn1LPrGukfGdGTXhJqq3GwtCJomeKRk9yoGPmpenq0hzJPZkclQS6+WJiZk9tl3I35NvJ34NDkBiHEbuAoECSl3Aj8TNceCDwObNSNeUEIYX69tvOGThiklEW6Rc3ULQIo0xWdRgjxKsoHm7WknY2lJeezSnlyn34Flz2R6/jbO8lcSivloX3TfW1371jPr/9wnqqaNnxXGq5fuHyFK8FbfTn9QTZPfDTWoC/uVGL3b2TJMife/tsVInYaTnA0V57+xv1ceS+DP/6/N/jBq59dqKW5VK6T3IQSTv8rkUc+c2BeXBgBzr+bRWdbL1/5yWMmjzl3Ko+hwVHuORpqtI+UktPnC9i80Ruv5S7Trg+NjJKcW8mR7Run/b3E5SnuhTu3TJdePJzs2bBiImfTlbIqLMzMiPKbyCeTUFNNlLcPFrrUAJfrK3GwtCLkmp5eib/TUjxsHa/p6QeXK3/7l1vTmQ9q6zr4/NdemZe5pJRxQgjfKc2fRinnOazrM+5OdxR4VddeKYQoQ7GbcB2281Zo6iuAyZWc63RtBhFCPCuESBdCpJvLMXIrG6cdmK71cWfVclcuphneMe/aFoAQcHGW3fqhe4NobOgiL8c010ILS3MeemYbOSkVFGXdWK71cVzcHfnIf9xD5qUiNYvjHcbI8Ci//so/8Vzlzke+fM+8zKnVann77/Gs2eBFcJRp/tlSSj44loH/+uUEzLCzLy1vprq2nQO7DW8GU/OqGRoeY2fY9GLWcbnl+Hq6sdJjwm99VKMhsbSabQF+epuV+AolK6ODteKxU9vdTU1PNzE+K6+tN66hkujlK7E0M2dEM0Z6Ww1ROukl+5qeruzac7vm55vzHHEft1O617MmjFkHbBdCpAghLgshxsOJjdnIOdnOcWbdqQshzgGGiiZ+S0o57yV9pJQvAi8CbA4KllLCpdxyHtk+cbgjhGBXxDpefj+Vrt4BXBzt9OZY4uZA0GYfzl4q5JmPxBrd/cbuXI+d3UnOHM8hKMS0sliHH43gtT9e4tUXL/Hd3z99nZ9Sn/v+bRdn/pXI777+Cptj/HFwtpt9kMqC543fnKa+vIUfvPpZbOxu/HAUID2uhLrKVr7yE9OjUQtya6mqaOVL35j5wXLmQiEWFmbsMpLr5VJaKY521mzdoJ+xsW9wmPSSOj68J0SvPbuqkb6hEXZsmJBe2vr6KWxq4Yu7JzI1JtYqG6RtunwvFT0d1Pf18NzmSGWejnqGNGMT0ktnJdZmlmxwXkHzUBstw/NTLtLH241f/fgJk/r++icfbpNSzvWAxAJwA6KAcOB1IcS8n/TOulPXFZTeZOBlqkGvByb/X+Cta5sVa0sLfJa6cDF7etWjPRH+aLSSuAzDaQMO7d1EfUMX+YXGb2VjY8nOvYHEXSxicMBw8eqp2Npbc/SpGFIvXaXi6vzo4BaW5nzxVx+ls7WXF//rzXmZU+X2UlfezKu/Os3OB8LYamTnez28/fcruHs6s+OQaTnTAd4/loG9gzW79hkvWafRaDl/uYio8DU4OU5PAzw0MsqltDJ2hftPK5aRVFjNmEbLjileL1eKK7EwNyNq7SSZpUL5Vhy7ekKKSqitwcPenjWuiidMXH0VADtXKEY8qaUSM8S1fC+ZHVVscV2JpZkFeV03nr7jFlIHvK0rMp0KaAF3jNvI67Kdt0J+SQP8hRB+QggrlAMBk2PkdwevIa24dpp747pVHqzwcL5WeWUqO7cFYGtjycmzM9cmPXBPEEODo8RdnNm3fTL3fSQGW3trXnvxksljZmNd8Coe/cwBzr6aRNp509IDqyxMpJT89quvYG1jybPff2Te5i0rbCAnpYKjT8ZgYaRI9FS6Ovu5cvEq+w9twXYGV8rMnBo6OvuNSi+JWZUMDI2wP2b6WVJcXgXO9jZsWa0v7cQVVbLVbwUONhOBUQkV1bjY2rBx+TIAxrRartRUs32l77VvHlfqK/F1dGGlowugGPVNrstxsrKhZ3SQst4mQl0Vg5/XXYKzpXGf+wXGO8BuACHEOsAKaEOxh48LIayFEH6AP5DKddrOG3VpfFAIUQdEA8eFEKd17V5CiBMAUsox4DPAaaAIeF1KWWDqPXYHr2VMoyU+r3Lqva/lguntH5o2zs7Wip3bArh4pZihoVGj82/c7I33SjdOvGta2gAAR2db7vtwFFdO5dFQ3WbyuNn48JePsDJgOb/+j38x0Df9M6ksDi6+lUpOfDHPfOsobh43Hjk6zrG/X8HWzopDj5qe2XE8cvreB40fkAKcu1SIvZ0VURGGdfozSVdxc7Zja6C+9KLRaknIryR2o69eAq/Gzh7KmtvZPil3ulZKEiqqiV29CjOdAc9uaqR7eIhdq5R+w5oxkppq2a7bpfeNDpPb0TChp3dWIZGEuPkipSS3u4TNzsZdNG8XQohXgCQgQAhRJ4T4OPBXYLXOzfFV4Gndrr0AeB3lAPQU8LyUUnO9tvOGjLqU8piU0ltKaS2lXCalPKhrb5BSHpnU74SUcp2Uco2U8odzucdm3+UscbLjUu50mWV3xDo0Gi3xWYbLWR3at4mBwRGuJBn/iiaE4L4Ht1KYX0dpselyytGnYjG3MOOtv8WbPGY2rKwt+cLPn6S9sYu//3DejytUbgG9Xf386dtvERDiy5GPmhbpaQptzd1cPpnLgYfDcDCxSpKUkhPvZbEpyIdVfkuN9hseHiUuoYQdsQFYW00/ZusfGCYxu4K9kQHXCleMk13WQFf/EDu36D8MrhRXAfpRpMXNrbT1D7BtzcT51eXqSsyFYPsqnbTS0sDg2Cg7VijjMtpqGZPaa3p6VkclVmYWbHT2oWGohY6RbjY7T0//e7uRUj4hpVwupbTU2ci/SClHpJRP6uTrUCnlhUn9f6izjwFSypOT2udsOxd0RCkomRV3bFlNQn4lI6P6FYgCV3uy1NXBaHRp0CYfPD2cOD2LnHHgSBA2Npa895bprlFuSx3Z90AoZ49l0NnWa/K42dgQtpr7/m0nH/ztMkVpau3FxcYLX3+Vns5+PvPTD2NmNn9/Xsf+Ho/USo4+FTt7Zx25WdXU13Zw5P6QGfslp1UwMDjCPiNpAeIyyhkZ1XDAgPRyNrMEG0sLtm3SLxEZV1SJl6sTqz0mol0vlFQg0E8NcKmqktDlXjhZK4VCrjRUYSHMiNL5pye3VmFpZk7oEuUbQkZHJRudvbE2t7ymp292WXg79dvJgjfqALuD1jIwPEpaSZ1eu5mZYGf4WpJzqxg0ILGYmQkO7N1IRnY1rTMYXgdHG/Ye2syFMwX0zCFk/+GPbWdsVMO7L89v/panv3kUdy8Xfvnllxm9wVJ6KreOi2+lculYOk/+xz2s3Ty9puf10tHay/FXU9h9X7DJKQEAjr+bhYOjDTv2GDbW45y7VISbqz0hRvzozyZfxdPdiU1r9VP1arRaLmSVErvJF9tJAU0DwyMkllaze1JBDFCMetCK5bg7KOkCmvv6KGhtYZfvxAPhSn0lIR5eOFopOnxySyUhbt7YWljSNTJAcU8D4UuUbwX53aW4WjnhZaNft/huZ1EY9fAAH2ytLbmUM90LZneYP8MjYyRkG97VHtyzEa1WcvbizLFORx8OY2RkjJPvZ5u8Lm+/pcTsC+T4K8kM9E/PU3O92DnY8JkfP0FNcSOv/+b0vM2rcvNore/gd19/lcDw1Tz2uYOzD5gDb/01jtGRMZ54bo/JY3q6B4i/dJV9hzbPGEHa1z9Mclo5e3asN5iRsbt3kJS8avZFBUxzocwub6CtZ4B9ofryR3xxFSNjGvZtmthBN/f2kd/YzO51Ex4yl6uVc7JxPb1jaID89ma2e/kC0DUySGFX0zU9PaOjHIkkYslapJTkd5ey2XmdGrA3hUVh1K0tLYgJXEVcbgVarX5ZueAN3ix1deB0gmHvFe8Vbmzc4MWZCwUzlqTzW+PB5uCVHH8nc9o9ZuKRj++gr2eI02+kmTzGFCL2b2bnA2G8+ouTlObMT6CTys1Bq9Xyiy/8H5oxLV/+7TOYW5jmmWIKXe19yi793mBW+BqOjjbEuVN5jI5qZpVeriSWMDKqYe9OIxkZ00vRaLTsi5ruu34+sxRrS3O2T5FezheU42JnQ4jvhDfM5VLFgO/2n2zUq1hm78B6d0XvT2ioRgLbdEY9tVX5PXKp7vf2cuzNrQl09qZ+sJnO0Z4FeUh6u1kURh1gZ9AaWrv7uVrbrNdubmbGvqgAknIq6e4znBb3wJ6NVFa3UTZLkYv7HtxKY0MXGamma9nrg1ayaasvx16Kn3ep5PkfPY6rhxM/+tRfVG+YBczxv8eRFXeVT373Ybx8jR9IXg9v/e0KoyNjPP7cbpPHSCk5+V426zeuwG/NzNLEqXP5rPByYUOA4SpI55NL8F7mQoCv/jxareRCdhkxG/2ws5lwlRzVaIgrqmRX4Bo9b5gLJRWscHZinYdSYHpMqyW+ppodqyZcGeMbqnC0smaLuxLrmNJahY25BUFuysMhrb2MUDc/LMzMyevW6ekL8JD0drNojPq2jX6Ymwku5Uw3uIe2bWBMozXqs757+3osLMxmlWC27VqPi6s97789t/S6j35yJ62N3Zx9J3NO42bD0dWer77wMZqq2/jdPOWkUJlf6ita+Mv33mbr7kAOP7VtXufu7uzng1eS2XFkC94zeK9MpaignqrKVg7fFzxjv7r6DrLzajmy33AVpM6eATIKa9hrQHrJq2qkpauPvSH6KQPSyuvoHRpm78YJb5ih0TGSKmvY5T+RLiCrqYHekWF26qQXKSXxDdXEeK68lv8lpaWK0CU+WJlbUD/QQd1ABxFLlPsVdJexxMoFTxt36gfUb7KTWTQlQ1wcbAles4KL2WX8+/0xetfWrfLA18uN0wlFPLh3eoIvZydbosJWc+5SIZ/62E6D2iGApaU5h+4L4vWXk2hp6sbD0zQf4/AdAWwIXskrv7/AvqMhWM2gYc6VTVH+fPjLR3j5p8cJ2bmBfY9FzdvcKjeGRqPlfz/7DyytLPjCL56ad233nX8kMDw4yuOfMn2XDvD+2xnY2lmxa+/MkawnzuRhZiY4ZCTS9FJaKRqtNCq9WFqYT8udfqGgHFtLC6LXTbgtJlfVMDQ2pqenx1VXYS4E23Spdqt6Oqnv7+G5LUpqgI7hfkp6WrnHR6nQlNauuDSHu6+5pqdvcVEeNknt1zwDb4i6mna+/PxL8zLX7WTR7NQB9ob6U97YTkWjfq4HIQQHYzeQXVxPU5vh/Oj792ykvaOfzFmSd917NFTx733f9GAkIQQf/fwB2pq6OTnP2jrA4188wqZof174+qs0VLXO+/wq18dbvztLUXoFn/7vx3E3kNXwRujrGeS9fyay7eAmVq1dZvK4jvY+Lp0r4OCRIOxmKHE3ptFy6nw+kWGrcV9iOCLzfEoJK5e7snZKhSMpJeezyohcvxJHW2u99ouF5cQE+GJjObFfvFhaiZ2lJRGrJhWdrq4iZJIrY3yjLv/LcuVhkNRSBXAtf3paexnu1o742XtQP9hC52gPm5yVXXtpn8mxjHcFC3qn3tqrn51xb8hafvr6Rc5klPDcvdF61/ZHr+ePbyRwLrmYJ++dHnEXHbEGezsrzl0qJDzU1+g9ly13ISxqDafez+Gpj+3A3MK0515Q5Go2h/vx2h8vceiRcKxt5m+3bm5uxld++wz/vvsH/Oz5v/PTd780r4dxKnMnL6mUf/zoPbbfH8ruh02P8DSVD15JZqBvmA89u2tO494/loFGo+XoLFGnaRmVtHf0c+TAZoPXO7oHyCys5emjkdO+gVytbaGxo4dn79H/1lhQ10xzdx+fOzixI5dScrm0kpjVK7HWFZ1uGxggv6WZL0dP+NwnNFSzwsEJXycly2N8czlOljZscvVCK7Wkd1QQ5e6PEIKCHkVP3+i8lp7RLpqGTEolNSveK5fwv7/7qEl9f/7C/CTzuxks6J361HwvS50d2OrvzZmMkmmeLN7LXAhc48mZJMPpdq2tLNi5LYC4hJIZ0waAsltvb+slJdH0ZEFCCJ78zD4623o58VqKyeNMxcPbjc/85AmK0it49ZcnZx+gctNob+rifz75Z5b7uvP5nz8577LL0OAIx/6RQPiOANZsMK0IBsDIyBgfHMskMsYf71n82U+cycPF2Y7ocMNpAeIyytBKyZ6I6d4lF7LKMNcFBU7mYmEFZkKwY1KB6ZKWdhp7etnlP+EhE19TBcAOnZ6u0WpJbKxm23KlEpKUkitNFcQu88PCzIzyvmY6R/oJdxv3Ty/D1VLxTy/rm7Usw13HgjbqgyOj1Hfol7PbH7qOqqYOyhqmp9s8EL2ekqoWqgxcA8ULZmBwhLjEmfMvR8b44+buwPE55IMB2BKxmqCoNbzx58sMDZqW9XEu7HownD2PRPCv/z1Bfsp0n32Vm8/YqIb//uSfGegb4v/99VPYG8hoeKOcfjONns5+PvSpXXMad+lcAV2d/Tz42My79K7uARJSyjiwJxBLI4nBzqcU4+PpytqV0w9oL2SXEervrVe2DhQ9PdTXC1f7ifZLpYpjw461E0Y9rrqKJba2bFyqeNTktzfTMzJMjJcivZT2tNIy1Mu2ZYoRH9fTw5YoenpBdxmbnJVde2lvITZm8//fYDGzoI06wLl8feO1N8QfMyE4kz69hJUSIAFnEw3v1oM3+7DCy4X3T+bMeE9zCzMO3xtMWnIZjQ2dc1qvsltXfItvBv/+P4/jucqd//74n2id49pUbpy/fO9tClPL+cIvnmTVetN30aYyPDTKG3+JY9NWXzbOIBNORUrJsdfT8PVbSkiY34x9z14sRKPRcnj/zNLLngj/ad9CKhrbqWzqYHewvtdLXUc3pU1t7N6ov/O/VFZJoKcHyxwdACWp15WaKmJXTiT1GtfTY3R6+pVmxYhvW6bs+NPbK/CxW4KnrQtNQ220j3SxUaenl/QVsMZh5ojZu40FbdRtLC2nGXU3Jzu2rvPmXGbpNAnG3dWB0A0+nEsuNhhoJITg3oNB5BbUUV07c2L9ex8MxczMjGOvz+3gc9NWX0Ki1/LWX+Nuym7d3smW//rHpxkaHOH7H/sjwzfhHiqGSTiexTsvXuD+j+9i14Pzr6MDvPdyIu3NPTz1uf1zGleYX0dZSRP3PxI2qxx06lw+Af6erDbiU3826SoareRAzHRjeTFbMbh7phj1S4XKjnx34IRR7xocIruukZ2TdumFrS20Dw6yc+UkOaa+ivWuS1lqq6QPSGiuYK2TO8vtnBnTasjqqCRMlxqgoFuxB5uc/ekaaadtuAl/R+N54u9GFrRRd7K1Jru6gbYpB6b7Q/2pbumktH562tt9UQFUN3ZSVmPYS+TQvk2Ym5tx/PTMpePclzqxa18gpz7Ipq93boE/H/73PXS29XHqJnjCAKwKWM5XfvsMpdnV/OYr/5oxUlZlfmiobOHnn3+JgBBfPvGdh2/KPXq7Bnj9T5eI2BnAloi5FcR554007B2s2XfQ8O57nNLyZsoqWji8b5PRPifjCwnw9WCNz/QI1ks5ZWzy9cTDxUG/vbCc1R5urHR3udaWUF6NVkp2+vtea7ui09PHqxz1jgyT1lzHLm/l8w5pRklrrWGbh2LEi3rq6dcMT+R76SnF2dIBb9tllOr0dH91p67HgjbqjrbWSAkXC/TT7u4JViSYc5nTDzJ3R/hjbiY4m2S4wribqz2xkWs5dS6f0VHNjPd/5IkoBgdGOPHe3LT1TWF+bIlYzZt/iWNkeOZD2esl+nAQT371Xs6/kcI7f5wfP10VwwwPjvDDT/wJM3MzvvGnT2BpID3tfPD6ny7T3zvMM186NHvnSbS39XLl4lUO3ROM7Sxl806fz8fCwow9RtICVNS1cbWymSPbp+9+mzt7KahuZnewvsTSOzhMekU9uwOnFJ0uq8TF1oYtXhPVMK9UV7PBfSlL7XW78oZqxqSW3TqjntFWy7B2jNhJ0gvAVjc/pJTkdZcS6LQWIQRlfUXYmdvjZWtaKcq7hRstkvGoEKJACKEVQhit1yeEqBJC5AkhsoUQJue3tbG0wGeJs0EJJtTfm3OZ071gXBztCN+0yqgEA3DvoS109wwSnzyzd8vadZ4Eb/Xl2OupjI3N/ACYyhOf3kN7S89N8Vu/do8vHibmSDB//u5bZF02vXKTiuloNFp++vzfqCyo5z9+8wzLfJbclPu0NnXz3j8T2XN/MH7rDJUENs6Jd7PQaLTc9/DWGfuNjWk4e7GI2Mi1OBvJyX4yvhBzM8H+6Olpdi/mKJur3UH60kt8cRVjWi07Jxl1rZRcKa9i+xrfaznY+0dGyGisZ/sq34k568pxtLIm1EM5n4hvrsDSzJzwpUpQUnpHOWsdPXG1cqBhqIW24U6CXJRgqNJeRU83EwtzbyqE+KLOPuYLIV4RQtjoqhilCCHKhBCv6Soaoat69JquPUUI4Xu9973Rf4184CEgzoS+u6WUwXMt1rp341pSyqeXs9sf6k9Vc+e0QCRQJJiG1m6KKpqnXQMIC/Fl2VKnWSUYUHbrba29xF2Ym9EMilzNlojV/OuFC/TPUb4xFTMzM778m6fx8ffkfz71F5rmsQqTisJfvvs2Ccez+eR3HybSiE/3fPCvF86j1Uqe+uzctPSxMQ0fvJtJeNQaVnjP7MaYklFJV/cAB41IL1qt5FR8EVFb/HAzUPz8XGYJfp5u+Hrq3+dSYQWu9rYErZzIH5Pf0EzHwCA71vpea0uorWZUq2XHSqVNSsml+kq2e/liaaZ44cQ3l7N1iQ92FlaMaMfI7awmTOfKmNOlfPsOdllPx0gb7SMtrHWYv/qv84kQYgXwOSBMSrkJMEcpR/dj4BdSyrVAJ/Bx3ZCPA5269l/o+l0XN1r5qEhKaVjnmCf2blLK2Y1XUhlnd/BahIDzWdNd+3aErcXC3IxzyYa9YMzNzTi0fxPpWVU0txiOQB0nPGoN3ivdODbHHbcQgk989Qg9nf288efLcxo7F+wcbPivfzyH1Gr57tN/oG8O+eBVZubdP1/k2B/Pc/QTu3nwU3tv2n0aqts483YGRz4UwbIVrnMamxBXTEdbH0cfnn2vdPp8AS7OdkRuNewdk1VUS2tnH4e2TZdmmjt7ySqr51C4fsoA5W+zkh3r/fSqIl0uq0QA2ycVxDhfWYGjlTXhXisAKOpspXmg75qe3jrUR3F3yzXpJb+rhmHtGGFLlN9zuorxsF6Cp4075X3KJst/gRp1HRaArRDCArADGoE9wHh1+X8AD+jeH9X9ju76XnGdARC3KqJUAmeEEBL4o5TyRVMHblnpyRIHOy4UlHEkeOJ/KHdne4JWe3Euq3RaZJuTvQ1RQb6cTSrm+Sd2TCvBBXB4/2b+8a9ETp7L45kPG68mY2YmeODRCH77v6cozK8jcJO30b5T8d+4gj33BXPsH/Ec+VAkHl4uJo+dC15+HnzjT5/k2x/5Hd956gV+8OrnsJlFW1WZmaSTOfzxP98g+nAQn/ze/BWPNsT//fYclpbmfOjZueV4ASXPi+dyZ8KiDAcRjdPVPUBichn3HwnGwkg08qmEIuxsrNgeOn0uJeAPDobpyzIZlXX0DA6za4qefrGkgmDv5bjaKTKPVkouVlWwc5UvlubK/S/VKXr5Ll090sRm5ffJeroZghBXXzRSS15XCTHuIdf80+3M7Vlu60Npz/xsmuoqW/nqR002TTMipawXQvwMqAEGgTNABtClqz0KUAes0L1fAdTqxo4JIbqBJSiFqefErDt1IcQ5nSY09XV0DvfZJqUMBQ4Dzwshdsxwv2eFEOlCiPTW1lbMzczYHbiaK1erGBnTT227N8Sfsvo2alqm+2vfs2MTrZ19pOYZzuC2fJkzW4NXcfJs/qz50w8c3oK9gzXHXkud/ZNO4ekvHERKeOlXZ+Y8di6E7tzAV373MQpTK/ifT/6JsVkOgVWMU5xVxY8//Rf8g1by1Rf+zWgCuPmgqqSJy8dzuf/JGNyWGs7BYoySq43kZFZz/8Nhs67xxJk8Rsc03Hd4esI7gOGRMS6klrA7wh8bAwnpTqVdJXDVMlZ6uOi1n84txdbSgm0Bvtfa6rt6KGhqYV/AhPae29xE28AAe1dPPDAu1VUQ6OaBh53iSZPQUomLlS2BLsqZQnpHBQFOXjha2lLeV0O/ZvCanl7WV3hNTy/rnb86wXPAfdxO6V7PTr4o/n975x0W1Zn2/88zQ4ehKiAgRaUIghqxKyrYu4mml03ZZLMmm1/c3yZrsvtmN3WTbNpmk2zybpJNMYlx1dgLYsUuFlCRKtKk917mef84I8VhpKkgzue6uGTOnDoy93nO97nv+yuEA8ro2wdwA6yBzs2Ad5F2R+pSyundPYiUMkv3b54QYj0wBgM6vG4U/wVAaGioBJgWNJj/HjvL0eQMJgc0PzpGjPTlvf/uI+pUEo/OGtNqP5NGDsLOxoIt+88xfnjbj5tzZwbz2jubORWbzqgRhmfQLa3MmLNgJOt+PsqTeWX0d7bt8LU7u9mz+OGJrPn3PhY/Mokhgde/YOUKYYtGUVFaxcd/+IEPn/+OFf94+Lr6ZN4O5KYX8teHPsOhvy1/+e63N/yJ59t/RGJpbcayxw2Ocwyy+vtDWNuYM3fRHddcT6uVbNp2hpAgD3y82jbaOHgqlcrqOmZN1JdeLuUWE5+ex4q7Wp9jo1bLrrPJhA31wdKs+UawK0GRRKf7NwfwqIspqIVgim6StKyulpi8LJ4KVroySik5lJvKBGcfVEJQ01jHuZIM7vFWOrJe0dND7P0oriuksC6PsP6zkFKSWXX6mtffUTx8+vPOt0+2vyLw7ndPFbQzPzgduCilzAcQQqwDJgL2QggT3WjdA7jSuCYLGAhk6uQaO+DaxTQGuOHfeCGEtRBCc+V3YCbKBGuHGTfEE0szU/acb91L3dVRQ5CXC7vb0NVNTdTMGB/A/phkyivbnqicPN4XG2tztkXGtXsOi5aGgoTN6zvXax3g7l9PQWNnyX8+2N7pbTvL3Icn8/CLC4hac5QvX11/w4/Xl8jPLualuz+ivq6ev65ajkMnbt5dISEug8NR57nzV5PR2OtPTF6LrMwiovdeYMGSUVhfoxsjQMzpNLJzSlg0b4TBdXYciqefvTWjAvW9VXfGJCAEzAxtrafHXMyiqKKKmSGtjSp2JaTg198Jb6fm+YHdF1MJdXPH3kKRYw5lX6JRyibpJaW8gLyaiibp5UzxJeplI6GOyuvYkgR8rN2xM9U09XsZYhNIUV06VY29srI6HRgnhLDSaeMRwHlgD3BFz3sE2KD7faPuNbr3d8suFqB0N6VxiRAiExgPbBFC7NAtdxNCbNWt5gJECyHOAMeALVLKTkU3c1MTJvp5sfd8ip5UEjHSl3OXcrlcpD/hOXdyEHX1jUQZMM8wNzclfMpQ9h9KpKIdj1HXAfaMm+jLlg2nqKvtnMORja0l9zw1jZjoJE4fSWl/g25y7/NzWPDYVNZ9tov/fhp5w4/XF8jPKuLFJR9QUlDOqz88g6df205A1wspJZ+/uRl7JxsWP2J4TscQa388ilqtYnE73RgBNmw9jZ2tJWET23YJKqus4dDpi0wfH9Dm/NOOEwmMGOyuV3AUGZeEhalJq6fn4qpqTqRnEdFCeskqLyO+IJ9wnxZWdlmpaEzNGKlLZTyUq9jdTXBW9nWkIAlToWakgw+1jXXEl6USYqfcVFIq4rFUW+Nm6XndRunXGynlUZQJz5NAHEqs/QJ4EVghhEhG0cy/1G3yJeCkW74C+GNXj93d7Jf1UkoPKaW5lNJFSjlLtzxbSjlX93uqlHK47idISvlGV441LWgweWWVnM9qnaYYPlLpIrfzhH7gHjrIBW83R7bsN9xvec70YdTWNrDnQNuZMi1ZvGw0pSVV7NnV+f7NC+4fR/8Bdnz9/vYbXgEqhOCp15cRtnAUX/51HZu+2ntDj3erk59VxAtLPqC0sJw3Vv+OoaGdq+bsCns2nSb+dDqPrpiFtY1Fp7YtLqpkx5YzzJgTglO/a+vw+QXlHDqSzNyZwZiZtq227j2eRH1DI7Mm6OemJ2cVkHq5iFlXjdK1WklkXBKTA7yxaiG97E1KRSsl0wOapZc9F5Un7HBv5XOVUrIv6yITW6QyHspLxcvGEXdre0AJ6iMcvbE0MSO+PJV62UBIk54ez2Brf1RCRUblKTQmHe83fzORUr4ipQyQUg6TUj4kpazVxcMxUsohUsplUspa3bo1utdDdO933FPzKm4ZwXVKgKK1XS3BeDrbM8zblW3H9YOyEIK5YUHEJWWTntP2I9pQ/wF4ezq12+QLYMQob3wGO7Pmh8OdMqcGMDM35aFnZ5AYl0n0zk6pT11CrVbx+38+wrhZIXy6crWxXa8BrgT0sqIK3lj9OwIMpPtdT6ora/ny79vwC/Zg+uJr6+FtsWHtcerrG1h6X/suWFt2xtKolQYnSAF2HrrAQFcHAnz0g+OOEwmohNCzrVPad1QxI1hfehlgqyHItdnTdHdaKl529gxyUPLbk0sLya4sZ4pOeqnXNnI0/1LTKD2vppSUilzG9VMGbLElCaiFiiC7IZTWF5Ffm8Ngm6FIqSWrOhYP6xHtfg63E706qNc1Nmdw2FtbcoePO1Fn9fXzOaMDSMzMJyVbP/tn9sShCAHbo9vuuyyEYPG8kSQk5RCfcPma5yOE4N6HJnDpYgGHD1y7fW9bhC8cidcQF775cOd1N6luCzNzU17+8knCl47hm7c28vXrvxj7xLQgP7u4KaC/+fNzNyWgg9IOoCi/nN+snN/piezq6jo2ro1hwmR/Bnpdu7q1sVHLlh2xhI70xn1A2/nv+cUVxJxPZ+Z4fR9SKSWRJxMJ9fPAyda61XuRcUmYmaiZ0kJ6qa6vJzrlEhH+g5v2VV1fz+GMDKb5DGpati9TkVrCdEE9riibyoa6JpejYwXKd3ys05WgnoivjTeWanNSKpTB2xDNUApqL1LTWMZAK8M3rNuRXh3UCytaF9LMDPYlObeQlNzWk8IzQ/1QCcH24/p1UM6OGkKDPNkeHW8woM2MCMLS0pR1m9o3jp4SHsgAN3t+/PZgpwOkWq3isf8/m6y0An759mCntu0qJqZqfv/xI8x9ZDI/f7yDT1f+hFarvSnH7s1kp+XzYosRun8n2tx2h9ysYtZ+fYCp84czdGTne5ZEbo2lvKyapfeNbXfd4yfTyMsvv+YoXWmnQZsdGRMz80nPK2HGqNajcSklu84mM8HXC2uL5uygQ6mKF2lECy/SQ5np1DY2MM27Ofjvy7rIEDsn3G2UiehDeUqh0rgWerqTuQZfjSuVDdWkVKQTYq+cQ3JFPOYqS9wtvcmsUp6u3Y1BvRW9OqiX1tSgbRE4Z4b4KqPuM61HyU621owJ8GT78QttBto5kwLJzi/lTGLbtlfWVubMjhjGnv0XKGmnIlNtouKeByeQEJ/NqZi0Tl/TmCkBjI8IZNWnUeRfLun09l1BpVLxzNv3sXT5DDZ/vZ/3f/ctjZ3sZdOXOHs0mefnvE1FaRWv//TsTRuhA3z13nZUKsFjnWzaBcrIe+3qowQEuhEUop+lcjWbtp/Bwd6KiWOHtPm+lJLN+84SOMgVLzf9FgORJ5NQq4Rem92zmblcLilnenDr5VGJKWjMzRndwot0T5rOn9RNWVbdUM/R3AzC3L2b1onOTSXIYQD2ZpZopZajhcmMdVKadp0rTUaLJMROF9TLzzPIxh+1UJNZdRo70wHYmvZOTb2n6NVBvUGr5UxWsyTST2NNqI8H22P1G3nNHRNAVmEZsRf1JZSpo32xMDdhe7Th/i2L54+kvqGxQ/1gZswNwbGfDT9+07XR9lMr54OEL97e0qXtu4IQgsf+vISH/7iQqDVHee3Rz6ksr75px+8t7P7vMVYu/QiNgzUfbH3hpkyKXuHcyTT2b4vlrscm078LRtVHopPIzixm6X3j2u2ZXlhUweGjycyePsygu1F8ai4pGQUsmKrfC0ZKSWRMIqP9B+KgaZ1uueusYmfXsnd6o1bLnsRUpgxprhiVUrLnYiqTBno1+ZMezcmgrrGxSXopqavmdGEmU1yVG0RC2WVK66ua9fTSBMxUpvjb+lBSV0hubTb+mmFoZSNZVbF4WI3owCd3e9Grg7pAsDO+tYY+e7gfF/OKSMxprZ9PHT4Yc1N1mxKMlYUZU0J9iTqSQF1921q2t2c/RoZ4snHraRobry1PmJmZsOy+cZyOSSP+XOdNb13cHbjnqWlE7zjLyYMd90HtLkII7nt+Dsv/di/Ho87x/Jx3yEjKuWnH70mklHz3zibeXf41gaGD+GDLC7gPcm5/w+uEVqvli79twcnZlmWPT+nSPtb+dAQXVzsmTdHPUrmarZFxNGol82eFGFxn0944zM1M2uzImJCZT0Z+CdPv0JdeouKSGT14IHZWzVk7Z7JyKKqqJtyvOdAnFBZwuaK8lfSyP+siZmo1Y12VJ43o3BS0SMJ0Qf1ogfJ9uNI/PbYkkQDNIMxUpiSUKwkGfjbDKKhNpVZbgYdRetGjVwd1G3MzIhOSW43Kpwfr7OxiWwdDG0tzJgcPIjImkYY2gvKcSYGUV9Vy6PRFg8dbNG8EOXllHIsxvM4V5i26A43Ggp9XHe7EFTVz16OTGODpyL/e2nzTS/rnPzqFt9Y8R1lRBc/NfptDW0/f1OPfbOpq6nnn6a/44b2tzLh3PK+vfhaNg3X7G15H9m2NJTEuk0een9mlKtWE89nEncngznvGoDa59tdWq5Vs3RHHiJCBeLi33bmxpraenYcvED7GDxsr/eKlyJhEZTR+lfSSkltIWkEx04e1Xr47MQUTlapVV8a9acr3aKp389PQ/qw0xroMxNJESYPcn5OCvZklIY5KvvrRwiT8NANwMtdQWl/OparsJj09sfwsNia2DLAc2EpPL629PubTmSm5vLDk/Q799GZ6dVC3tTAno7iUhLzmUbmTjRWhgzzY2YYEMyvUn6LyKmISM/T2FRrkiYOtFTsOGpZgJo/3xdHBmg1b2jfFsLQyY8Gdozi47wIZlzpfzWtmbsqTf5xPRkoem7p4Y+gOIRP9+HjXS3j6uvLao5/znzc3tPuEciuSnniZFfPfZe/6Ezz68mKe//ChG2ZyYYjKihq+/Ps2Bg91I2LhyC7t44dvorHRWDBr/oh21z0Vm052TgnzZxkexe45nkRldR3zp7Qtvew6maRIL1eZS0fpDGvCA1s3/dqdmMpoL3c0Fs03iL1pFwns1x8XG6VoKbuijOTSwiY9XSsl+3OSmewyGLVQUd1Qx5nidMb0U24YZ0uVgVuInR9SShLLz+KnGYZKqMiqOoOdqRsa0/5klK9r9zO5nbi5f92dRGNhTg2w60IyAS7NfoqzQnx5bf1uknIK8RvQ3MtiYpAP1hZmbD+RwNihrTMLTNQqZk4IYN2uM5RX1qCx1i/4MDFRM39WCN+tPszl3FIGuNhd8/wWLxvDf388ypofDrNi5fxOX9/YqQGETvbj+092MXX+cBzaKSS53vR3c+CdX1bw2UurWf3RdlLi0lnx0SM3vDz+ZiClZPPX+/j3X9dhYW3OK9/8hnGze+ZR/ZsPdlCUV86fPnqgS714khNyOHQgkYefCGu3JQDA+s0nsdVYEDbB1+A6W/afw93ZjpEB+l1H49Nzycgv4ZGZ+q1Nos4mM9xzAM52zdWlaYXFpBQUce+oZqmnrLaGmMtZPDWquSdTVKZyQ7jSavdc8WWKaqsIc1VuEKeKL9IgGxnrpAT1uJIkLNTmDLbxJKcmk7KGEvw1w5T89KqzDNFMAqCopvON9trCY7AL76xf0aF13xW/vy7HvBH06pG6iUrFHQPd2Hmhta5+RYLZEds6C8bCzIRpwwcTdSq5Te18zqRA6hsarzlaXzBnOEKIDhUjOThaM2vecHZtj6OwoLyDV9WMEIKnVs6nrraBrz/Y0entrwdmFqY89/6D/O7vD3A6OpGnwl4lcvXhWzqfvSi3lP954BM+XbmakIl+fLb3Tz0W0ONPXWLzj0dZ+OB4AoZ7dmkf3321HxuNBUuWjWl33cs5JRw8ksyCOSMwb6PbIkB2XiknzqUzL2wYKpX+hOvmI/GYmaiZcUfrm8Ll4jLOZ+URMaz1KH1Pks502rdZZolOT1d6u7TQ06PSU/DS2DPETsmv35eTrPRc1wX1IwXJmKlMGO7gDUBcaSJBtoMxUamb9XRNsE5PL8fDajg1DflU1He5+LJP0quDOsCMgCEk5BWQUVzStOyKBBMZpz/JOCvUn4rqWg7H67fc9fd2xs+rPxv2xBkMWs79bRk3ehDbIuM6ZGG39L6xNDZq+aWLtnUePv1Z9NAEItfFkBCrLxvdLOY8NIlPol5ioK8r7//uW16++x9cTmvbvLu3IqUkevNJnp76GrEHE/ntW/fw6qrlODpf+4nrRtFQ38g/XlmPk4stDz83s0v7SEnK5dCBRJYsG42Npv12Aus3n0KgZHMZYuuBcwgBcyfrG0zUNzay40QCYSGD0Fi1Pt4V6SUi6Go9PRW//k4MdGj+nPekpWJrbs4IV6WHTlV9HYdyLhE+sLkw6UBOCsEObjiaK/MbxwuTGeHgjYXalMLaEjKrcxmmS2VMKj9LP3NXHM36tdDTQyi8TqP0vkSvD+oRutn0qITWd+MZwUNIzSvSK0QaM9QTWytzdsboV3wKIVg4LYSk9HyDVncAC+eMoKi4kugj+tWrV+Pm4cjEKQFsWh9DZUXXbOvuezocx/4aPvzzuptSaWoIT78BvLthBcvfvpcLJ9N4euprrP1s1y2R0556LpOXln3EG4//Ly4DnfjnrpdY8NjUdlP/biTrv4kmLSmX3/5pIVYdkE3aYtV/orGyMmPJ3e2P0quq69iyI5awiX44G5DytFrJ1gPnCQ3yxLWfvsx2+PwliiuqmTdWvxhpR2wivq5OePVvrk4tra4hJj2LaS0Kjhq0WnZfTGGqtw8mOrnpQPYl6hobmT5QuSGU1FVzpiirKeuloKaMlIpcxlyRXkqV72+IvR+NspGkinj8bBQz7KyqWGxNXdGYOlNUfQwT1c2VLXs7vT6oezra4+fcr6lH8xUighQ7u6uzYEzVasJH+LLvTAo1bQTI2ROHYm5mwoY9hvPRx4zywaW/LRs7mBVy/8MTqayoZe1PRzu0/tVY21jw7F8Wk5aYw+ov9nZpH9cLlUrF/F9N4fMD/8OIyQH8+y9rWR7+Bgc2xvTKStSCyyW8/9y3PBPxJilnM/nN68t4f8sLDPTtnHnz9SYns4hVn0QxPiKQ8RFds1xLS80nem88i5eNRmPAKLolO3efo6KylqWLDLf5Pp2QSXZ+KfPC2vYp3XI0HnsbSyYEebdanl1cxqm0bOaMaJ3+uDsxhUYpWxlixGRnUVxTw8xBzfLN7oxkNKZmjHZRNPyDuam6VEZl0Ha8SHkKGON0RV+Px87UhkHWHqRXpVCrrcavSU+PbaoiLaw5hqNFp2yP+zy9PqgDzPAfTExGNkWVzdWeznY2jPRyI/KsvgQzM9SPqtp6Dp7TT020sTInYqw/kYcvUFVT1+bx1GoV82aFEHP6EhmZRe2e3xB/VyZNDWDt6mOUlXWtoGdceCBT5w/np8/3kHrh2j1obgb93Rx45dun+dNXT6KVkjd//W9+O/V19m+I6RVZMpVl1Xz3ziaeGP8Ke9Yd586nI/jq6Kss+nU4JgaKbW4WUko+eXUDKpXg6ZcXdHk/P3wTjbmFKXfe035LACklazfG4D/EhaChho1Ytuw/h5WFGVND9atMy6tr2XcmhVmh/k0FRFfYdlqp/2hpKQmwPT4JNzsNwW7NVZ07UpMxU6ubDDG0UhKVmUqYuw9muv3uz0nG3syS4CupjAXJ2Jla4Wc7AK3UcqrkAsPtA1AJFYk6Pd1XE0hhbRo12nI8LEOobrhMVUMGThbtP8XcTtwSQT3Cf7DicZjUOkjPCPYl8XIBl/Jbd2AM9VNSsXaeaNsTe9G0YKpq6tl1xLBn9oI5wzE1UbNmw4kOnePDj4dRXVXLmh+6np749EsL0NhZ8eGf1vYKyUMIwcR5I/ls75958V+PoZWSt578N09PeY2oNUeprW77pnijkFISfyKV95/7lgdCXuSH97YydmYw/xv9Ck+8chc2dp0zmrhRRO88y4kDiTz07IwuVY4CZGYUsS/qPAvvDMWuAwYaMacvkZ5RxJ2LRhmUnKpq6th9NJGIcX5tWtZFnUqirqGxTell25kEQjxd8XBs1s3La2o5mJrOzADfpmNKKYlMSWaypxfWZko+flxBDgXVlUTopBetlETnpjLRZRBqoUJKyfHCFEY7DUYlVKRVZlNaX85Ie+WpIKn8HO6WXtiY2JJVrTxhu1uFUFStzGM5WbTfU/524pYI6oGuzgyw1RCV0Npg4koBxK6rOjeaqFXMCvVnX2wqZW24HoX4ueE1wIFNew23wHV0sGZGeCDbd52lrAPl9D6DnZkSHsgva45TWnLt/jGGsHWw5umXF5B0Lov1N6nhV0dQq1VMXTKaz/b+mZVfPIFareLvz/yH+4Je4N3lX3MsMu6GzgVUlFax6au9LA9/gxXz3uXAxpNMu2ssH0euZOUXT+BqwKKtJ6isqOHzNzczaOgAFj44vsv7Wf39IUxM1B1q3AWwftNJ7O2sCA8zXG2673gy1bX1zJsc1Ob7W49ewNPZniCv1r1UUvOKuJCdz5yrRum7E1Opb2xkdmCzzBJfkE9WeRkzBjU/CURlpiCAqR5KJsyF0lzyayqY7KJILWmV+eTXljXp6adKlOy0EQ5DqdPWcbEyCd8WerqNSX9sTV0prDmGqcoOjVnb5h+3K911PnpXCHFBCBErhFgvhLA3sN5sIUSCECJZCNFpRw8hBOF+gziYeonq+vqm5QMcbBk20KVNCWbB+EDqGhrZGaM/GhdCsGBqMHFJ2VzMMlw4tGxxKLW1DWzooLb+4ONh1NbUd7nKFGDy7GDGhQ/l+493kZ3eJYvCG4ZarSJs0Sg+2fMyb655jimLQzm26yyvPPgp9we/yEcrvid680ly0wu7lRJZW13H6QMX+PZvG/n9/He5N/APfLpyNSamap59935Wxf2N5957gCEhXUsRvJF8/tZmigvKefaVxahNuiYD5eWWsmtbLLMXjMDB0abd9S/nlnLoWAoLZg83aIQBsOWAkps+3N9d773c4nJikjKYO2ao3kh/+xnFzm7WVb3Td8Qn4aKxYbh7s0vUzpRkpf+6TwuTjIwU7nB2x9FCeeKIzlEGZ5N01nXHCpVBWVNQL47H28odRzM7LlYm0iDrm/T0zKozeFgpaceFNSdwtAhFiN45Nu1u3Osq3S0+igRWSikbhBBvAytR7JqaEEKogU+AGUAmcFwIsVFK2ana3gj/waw6cYZDqelEtDC0nT5sCB9uO8jl4jIGODTP5gcMdGaIez82HYlnaZh+jvKcyYF89nM0m/ed5dn72+7FMci7P6Pv8GbdxpPcc+foa35hALy8+zFtRhAb155g6X3jcHDsfCm6EILl/7OIp+Z/wD9eWc9bXz3eoxkcbaFSqRgZFsDIsAB++7d7ObUvnn2/nGDfLyfYvkp5wrB1tGZwsCdDggfiPdQdGztLLKzNsdT9mFuZU1VWTUFOCYWXlZ+CnBIyk3KJj0mlvrYBlVqF73BP7np6BpMWjMR3eOdb1d5MDu48S+S6GO59alqXc9IB1qw6gpRw9/3tm2AAbNiipDEunGs4Fz87r5SY8+k8vmR8m39P248rLXhnj2490pdSsu1MIqE+Hq0Kjipq6ziQksY9o4JRtdhfZGoyowa44WSlBPC8qgriCnP5w6hm0+oDuSkE2LngbKlkrRwrSMbd0hE3KwdqGmuJL0thvttUQJFeVKgYbBNAQW0q1Y2leFrfQXV9NtUNmfjYPtihz+hmc73iXlfoVlCXUu5s8fIIzYaqLRkDJF+xZxJC/AQsQjFhvSYtTTJGe3ng5WhPSXVrOWVmiB8/HjpDZlHroC6EYOG4QHbGJFJdW4/lVRqik501U0YNobTi2tLK3UtG894/d5J9uRRvz2ubEgA8+GgYJ49d5GJqHg6OXWvp2s/Fjsf/MJfV/9pDQW4Z/V17Js+6I5iamTBmRjBjZgRTV1PPxfNZJMelk3wmneS4dNZ/HtXh3ja2jta4ePZjwWNTGT7Rj6BxQ7DWtJ/10Vs4eSgJ3yB3Hlge0eV9SCnJzipm+uxgXDqoxxeXVDFpgh/O/Q1XAl+6XISTnTULpwa3+X5ZVQ2hfh54Orc+Zll1LVZmpswe3nqUnlVShpudhtlDm6WX6vp6LExMmDm4eVlWZRleGnvCdVWkWilRCxXTBvg2Xa8QgsnOys2koLYYd0vnJj1dK7X4a4KxUFuSW1OCrakrA63uoKYxC2tTHxwtR9PQmNehz6k9MhOy+f20V67LvuhG3Osu4npVDgohNgGrpZTfX7V8KTBbSvmE7vVDwFgp5TMG9vMk8KTu5TDgxnu/9Q76AfrWTX2X2+l6b6drhZ65Xi8pZf/2VzOMEGI7yrl3BAug5QjzCynlFy321am4dz1pd6QuhNgFtJX0+7KUcoNunZeBBmBVd09I98F8odvvCSnlbZGEejtdK9xe13s7XSvcutcrpey8c0kvpN2gLqWcfq33hRC/AuYDEbLtYX8W0NKmxUO3zIgRI0b6Kj0W97qb/TIbeAFYKKU0lMd3HPAVQvgIIcyAe4GN3TmuESNGjPRyeizudTcX6J+ABogUQpwWQvwLQAjhJoTYCiClbACeAXYA8cDPUspzHdz/F+2v0me4na4Vbq/rvZ2uFW6/69Wjm3GvW1y3iVIjRowYMdLz9M6sfSNGjBgx0iWMQd2IESNG+hC9Oqh3tA1BX0EIsUwIcU4IoRVC3HIpYR2hp0qnewIhxFdCiDwhRJ+vtRBCDBRC7BFCnNf9DT/X0+d0u9KrgzpKG4JhUsoQIBGlDUFf5ixwJ7C/p0/kRtCidHoOEAjcJ4ToWrPxW4P/AH0i97kDNAC/l1IGAuOA5X38/7bX0quDupRyp24WGZQ2BPouuX0IKWW8lNJwP+Bbn6bSaSllHXCldLpPIqXcD7TfkL8PIKW8LKU8qfu9HCXjQ79zmJEbTq8O6lfxGLCtp0/CSLdwB1oasWZi/OL3OYQQ3sBIoGtWYEa6RXe7NHabm92GoKfpyPUaMXKrIoSwAdYC/09KWdbT53M70uNB/Tq0IbilaO96+zjGlhF9GCGEKUpAXyWlXNfT53O70qvllw62ITBy62BsGdFHEUqT9i+BeCnl+z19PrczvTqoY6ANQV9FCLFECJEJjAe2CCF29PQ5XU96snS6JxBC/AgcBvyFEJlCiMd7+pxuIBOBh4Bw3Xf1tBBibk+f1O2IsU2AESNGjPQhevtI3YgRI0aMdAJjUDdixIiRPoQxqBsxYsRIH8IY1I0YMWKkD2EM6kaMGDHShzAGdSNGjBjpQxiDuhEjRoz0If4Pu1nToFo5xkgAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Parameters\n", "a = 1\n", "b = 100\n", "\n", "# Initial guess\n", "x0 = np.array([2,2])\n", "\n", "# Objective function, gradient and Hessian\n", "fun = lambda x: (a-x[0])**2 + b*(x[1]-x[0]**2)**2\n", "jac = lambda x: np.array([-2*(a-x[0])-2*x[0]*2*b*(x[1]-x[0]**2),2*b*(x[1]-x[0]**2)])\n", "hess = lambda x: np.array([[2-4*b*x[1]+12*b*x[0]**2,-4*b*x[0]],[-4*b*x[0],2*b]])\n", "\n", "# Plot function contours\n", "plt.figure()\n", "X = np.linspace(-2,2.5)\n", "Y = np.linspace(-2,2.5)\n", "Z = np.meshgrid(X,Y)\n", "plt.contour(X,Y,fun(Z),20)\n", "plt.colorbar()\n", "\n", "# Call Scipy's CG\n", "xprev = x0 # for plotting\n", "res = opt.minimize(fun, x0, method='trust-krylov', jac=jac, hess=hess, tol=1e-1, callback=callback)\n", "\n", "# Print results and show plot\n", "print(res)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Exercises: \n", "\n", "1. Compare the number of objective function, gradient and Hessian evaluations across the different trust-region methods above (these are reported as nfev, njev and nhev in the outputs above). How do these compare to linesearch?" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.8.7" } }, "nbformat": 4, "nbformat_minor": 4 }