{ "cells": [ { "cell_type": "markdown", "id": "c97b4906-3bd0-4cf9-bf67-12a876a3ecf9", "metadata": {}, "source": [ "# 2025-10-13 Global and Piecewise Interpolation\n", "\n", "* Runge phenomenon as ill-conditioning\n", "\n", "* Stability and Chebyshev polynomials\n", "\n", "* Piecewise methods\n", "\n", "See the [FNC](https://fncbook.com/overview-4)" ] }, { "cell_type": "code", "execution_count": 1, "id": "1691279d-21e8-49a4-8a8e-a4a158b965d7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "CosRange (generic function with 1 method)" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using LinearAlgebra\n", "using Plots\n", "using Polynomials\n", "default(lw=4, ms=5, legendfontsize=12, xtickfontsize=12, ytickfontsize=12)\n", "\n", "# Here's our Vandermonde matrix again\n", "function vander(x, k=nothing)\n", " if isnothing(k)\n", " k = length(x)\n", " end\n", " m = length(x)\n", " V = ones(m, k)\n", " for j in 2:k\n", " V[:, j] = V[:, j-1] .* x\n", " end\n", " V\n", "end\n", "\n", "# And Vandermonde with Newton polynomials\n", "function vander_newton(x, abscissa=nothing)\n", " if isnothing(abscissa)\n", " abscissa = x\n", " end\n", " n = length(abscissa)\n", " A = ones(length(x), n)\n", " for i in 2:n\n", " A[:,i] = A[:,i-1] .* (x .- abscissa[i-1])\n", " end\n", " A\n", "end\n", "\n", "# And a utility for points distributed via cos\n", "CosRange(a, b, n) = (a + b)/2 .+ (b - a)/2 * cos.(LinRange(-pi, 0, n))" ] }, { "cell_type": "markdown", "id": "b511de24-d6ae-4f99-a929-1989a308da39", "metadata": {}, "source": [ "## A well-conditioned polynomial basis\n", "\n", "Recall the Legendre basis from the assignment." ] }, { "cell_type": "code", "execution_count": 2, "id": "ba26d28c-0fcb-46da-bc6a-b75289cf7188", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "vander_legendre (generic function with 2 methods)" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function vander_legendre(x, k=nothing)\n", " if isnothing(k)\n", " k = length(x) # Square by default\n", " end\n", " m = length(x)\n", " Q = ones(m, k)\n", " Q[:, 2] = x\n", " for n in 1:k-2\n", " Q[:, n+2] = ((2*n + 1) * x .* Q[:, n+1] - n * Q[:, n]) / (n + 1)\n", " end\n", " Q\n", "end" ] }, { "cell_type": "code", "execution_count": 3, "id": "c1a39812-50d5-4a62-9256-c54671c77731", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's look at the condition number as we add columns\n", "vcond(mat, points, nmax) = [cond(mat(points(-1, 1, n))) for n in 2:nmax]\n", "\n", "# Plot\n", "plot(range(2, 20), [vcond(vander_legendre, CosRange, 20)], yscale=:log10, xlabel=\"rows\", xticks=range(2, 20, step=2), ylabel=\"cond(A)\", label=\"\\$cond(A)\\$\")" ] }, { "cell_type": "markdown", "id": "a8b6ad2e-6c1f-4812-b342-ce908eb62d42", "metadata": {}, "source": [ "## Different interpolation points\n", "\n", "The interpolation points we pick effect the conditioning of the interpolation." ] }, { "cell_type": "code", "execution_count": 4, "id": "d3d50fe9-cc3e-4417-bf92-eb045bfb85f3", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = 20\n", "plot(range(2, a), [vcond(vander, LinRange, a)], yscale=:log10, legend=:topleft, xticks=range(2, a, step=2), xlabel=\"# of columns\", ylabel=\"cond(A)\", label=\"Vander, LinRange\")\n", "plot!(range(2, a), [vcond(vander, CosRange, a)], yscale=:log10, label=\"Vander, CosRange\")\n", "plot!(range(2, a), [vcond(vander_legendre, LinRange, a)], yscale=:log10, label=\"Legendre, LinRange\")\n", "plot!(range(2, a), [vcond(vander_legendre, CosRange, a)], yscale=:log10, label=\"Legendre, CosRange\")" ] }, { "cell_type": "markdown", "id": "a7ab842c-34db-4b47-a2c0-ae8b37484235", "metadata": {}, "source": [ "## Ill-conditioning impact\n", "\n", "We can clearly see that the choice of basis polynomials and point locations changes the condition number, but why does this matter?\n", "Look at the following interpolating polynomials." ] }, { "cell_type": "code", "execution_count": 5, "id": "e9ac73c4-8397-43d7-8893-4613b77c2853", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "runge(x) = 1 / (1 + 10*x^2) # What's this \"Runge\"?\n", "\n", "# This is a good outcome\n", "x = CosRange(-1, 1, 20)\n", "y = runge.(x)\n", "plot(runge, xlims=(-1, 1), label=\"true\")\n", "scatter!(x, y, label=\"true\")" ] }, { "cell_type": "code", "execution_count": 6, "id": "75bf32ac-62ae-4e6d-8189-253990b24705", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's solve for a fit\n", "ourvander = vander_legendre # This is a good pick\n", "p = ourvander(x) \\ y;\n", "\n", "# And see how good it is\n", "scatter(x, y, label=\"data\")\n", "s = LinRange(-1, 1, 100)\n", "plot!(s, runge.(s), label=\"true\")\n", "plot!(s, ourvander(s, length(x)) * p, label=\"fit\")" ] }, { "cell_type": "markdown", "id": "f2ed0aaa-c50b-4e74-b49b-bb6ab5d36e7c", "metadata": {}, "source": [ "The singular values from the SVD show that this matrix is well-conditioned." ] }, { "cell_type": "code", "execution_count": 7, "id": "03feefde-3c7c-43d8-8fac-a70de4d78c70", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "20-element Vector{Float64}:\n", " 2.8563807370813343\n", " 2.8414668608815554\n", " 2.8202363866684848\n", " 2.782971972925489\n", " 2.7474280450222004\n", " 2.684651346430287\n", " 2.636781366412177\n", " 2.5450839711629127\n", " 2.486134057068077\n", " 2.3619485533713127\n", " 2.2916184164905107\n", " 2.1320708818800687\n", " 2.0460305389351454\n", " 1.8547347714535933\n", " 1.7347507488398972\n", " 1.5501994693431675\n", " 1.3481998183116588\n", " 1.2519073527674074\n", " 0.946254637146537\n", " 0.9419175178348704" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "svdvals(ourvander(s, length(x)) / ourvander(x))" ] }, { "cell_type": "markdown", "id": "fb4ce71f-0242-4a91-94f4-7eff4085563e", "metadata": {}, "source": [ "Let's compare that to the ill-conditioned set of points and Vandermonde matrix." ] }, { "cell_type": "code", "execution_count": 8, "id": "a4bcf36b-5e17-4ee7-8e83-350a411065be", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# This is a bad outcome\n", "x = LinRange(-1, 1, 20)\n", "y = runge.(x)\n", "plot(runge, xlims=(-1, 1), label=\"true\")\n", "scatter!(x, y, label=\"true\")" ] }, { "cell_type": "code", "execution_count": 9, "id": "117e0823-6158-471d-aadf-c8a28ca2acbe", "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAGQCAIAAAD9V4nPAAAABmJLR0QA/wD/AP+gvaeTAAAgAElEQVR4nOzdZ0BT19sA8HNvJhtEEAEXuBX3FrXuKi7ctu7R9l87rFZtq7ZVa2uXrba2b2vd24p7ggv3VsSJiFREGbIh6+be+35IuLkBDDch4YTk+X3KiTfJQ4ScnHOe8xyCZVkEAAAAOCsSdwAAAAAATtARAgAAcGrQEQIAAHBq0BECAABwatARAgAAcGrQEQIAAHBq0BECAABwatARAgAAcGrQEQIAAHBq0BECAABwalWsIzxy5MiJEycEXkzTNMMwNo0HlKbVanGH4IwoisIdgjOCtx0Lq3/IVLGO8OLFi1euXBF4sVarpWnapvGA0lQqFe4QnBG87VjA2175WJa1+ttexTpCAAAAwLqgIwQAAODUoCMEAADg1KAjBAAA4NSgIwQAAODUoCMEAADg1JyoI1RQSgWlxB0FAAAAM2hoTb66wKYv4Swd4aHE6CG7xw/ZPf5QYjTuWAAAAAhyM+1O5J5JQ6PG/9+tDbZ7FWfpCP+6tZFiKIqh/ry1XsvALnsAAKgC/r69qVBTxLDsjvt7XymzbfQqTtERMiyTr9GPrAs1RQ+yHuGNBwAAQLny1QWPsh/rbrOIzVPn2+iFxDZ6XrtCGw8Br7+MC/NriisYAAAQ4tq1a2+99ZYzF0zW0FQRVcQ1h/045Oa1G2Kx9bst5+gIWaOO8EZa3JQW43AFAwAAQqSkpISGhv7xxx+4A7EXzcOaq9Vq6AgtRLNGX6nuv3pURCncJK644gEAACHc3NxCQkJwR2EvSNJWa3lOsUZYYmqUZum4jHu4ggEAAGBXnKIj1DIlD6+6mRaHJRIAAAAWYm31xE7REZZYI0QIXYeOEAAAAELIaTrCkmlXybnPspQ5WIIBAABgV5yjIyy1g55F7A0YFAIAAHCWjrDU1CiCZUIAAAAIIWfpCMuqqXYt7XblRwIAAMDeOEdHWNaI8JUi61l+auUHAwAAwK44x4b619QoupF2u7ZnUCUHAwAAlSMpKenGjRtpaWmenp4hISGdO3e2RVmWSmOz3RNO0hGWNSJECN1IuxPZMKKSgwEAAFvbt2/fl18viY+7hRAiJTKGUiOEPH2qzXzv3fnz53t5eeEO0L443dSou9SNu30r/Q5TamcFAABUXUqlcty4tyIjI+/Tfuj9f9HKdOaPAvRnAVp4Ob/j1B9+WdWkWditW7es9XLjx49v1KiRtZ6tPLYaEzpHR8hLlgn1rusj138bKtQUPcxKxBQUAABYGU3Tw0eM/HffAfTudvrjQ6j1UOTqgxBCYhmq0waN+JZecjdTFhDevce9e9YpM1lUVJSXlyf8+pCQkMmTJ1vlpa3IOTpC3rBPTIrb1GjBNW9A7igAwFEsX778eHQ0/f5u1G5E2Vf4BGlnR2t8Q4YMG67RaCo3OoQQys3NLSoqKv+6yuUcHSFvRCgiRW0CWnJN2FYPAHAMmZmZ3y7/nu3zEWrS29R1MjfttM1Pnyb9/fffFryKQqE4cuTIrl27Hj9+XOYF2dnZp0+f3r59+4EDBzIyMrj7tVptUlISwzBFRUVJSUlJSUlPnz7l/jUtLS0mJmb79u1Hjx41a4hpFU6RLKPlrRGKCVG7mq245t3MhzRLiwgRjrgAAMBqoqKiVCoVenNu+ZfWbIzaRK5Zu/6DDz4w6yWuXLkSGRn58uVLgiBYlp05cybLGq3bzZ49+7ffftNq9eccSKXSr7766osvvkAIpaenh4aGIoSOHj2qu+Hi4qJQKBBCkZGR+/fv557Kw8Nj9erVEyZMMCu2inDGEWGAm7+H1F3XpBiqiFJgigsAAKwmOiaGqN8FufsKuZhtOTg+7lZWVpbw58/JyRk6dChN09HR0SqV6tatW2fOnDlx4gT/muDg4KioqJcvX9I0nZCQMGjQoAULFsTExCCEatasmZ2d7e3tPWTIkOzs7Ozs7BcvXugeFRYWFhMTk5mZSVHUrVu3WrVqNW3atEePHgmPrYKcoyPkjQh1gz8XsZy7R6VVY4gJAACs6ul/KbRffaFX16jPsuyzZ8+EP/+mTZvS09NXrlzZt29fqVTaqlWr7du364Z0nNmzZw8ZMiQgIIAkyQYNGmzbts3b23vr1q0IIZIkfXx8CIKQSqU+Pj4+Pj7e3t66Ry1ZsqR3797Vq1cXi8WtWrXasWMHRVG7du0SHlsFOcXUaIkRIUJIzusIlZQSQ0wAAGBVFEUhkeCPdJFE/xDBzp07JxKJhg8fzt0TFhbWpEmTEsPKR48excbGpqamqtVqhJBMJktMLD85/8aNG1euXHn58qUuJKlUKuRR1uIcHWHpEaEERoQAAIdSJzjo/vMUoVvtsp4hhIKCzCitlZGR4efnJ5VK+XfWqlWL3xEuWrTo22+/9fLyatasmY+Pj1wupyhKqTQ12GAYZvLkyZs3bw4ICGjYsKGPj4/uJUw/yrqcoyMsNSJ0EfFGhFoYEQIAqrzu3bsdX/wNTakQ74v+a909XrteqFkdoVwuLygoKHFnfn4+dzsuLu6bb76ZMmXKX3/9JZFIdHc2aNDA9NPu379/8+bNixcvXrhwIUmSCCGtVuvq6io8sIpzwjVCEhmPCJUwIgQAVH2jRo1CGhWKFbApIi9NdHXbxLfHmfX8TZs2LSoq4uewKBSKBw8ecE1dwZrJkydzvWBmZmZycjL/SaRSKZdTqnPz5k2E0LRp03S9IEIoLi7OrDnbinOSjtCwoV43NWq0RggjQgBA1RcSEjJ9+jTxoaUoLcHUdSxDbnnf3UU2Z84cs55/3LhxBEEsWrSIpvVDi+XLl+fm5nIX1KxZExV3hwghmqY//fTTEt1eUFBQQkICwzsIocSjFArFvHnzzAqs4pxialRbemoUskYBAA7nxx9/jD13IXFVhHbmXhTUvIwrtGpi8/9Q/NHtBw9ySZsCdezYcebMmb///ntSUlJ4ePi9e/fu3LnToUOH//77T3dBjx49mjZtOnfu3KtXr/r5+cXGxmo0msaNG/OfZOLEibNmzapXr15ISIibm9uhQ4dGjhz59ddfjx07dty4cVKpNDo6uk6dOpVcFtxJRoRGG+oRQi5iF+4eGBECAByDh4fHiehjTYN8Rd91RVELUNZ/hn/TKNDVneIlbSU3o7Zu2TJgwAALnn/lypV///23p6fnpUuX6tate+XKlcmTJ3M73+Vy+enTp99///3k5OTr168PGDDgwoULEydO5Ceafvzxx6dOnZo2bVqTJk3q1q2LEPL39798+fLYsWPv3r177969adOmHT58eOrUqX369KnIW2EWpxgRlpEsI5Zx98AaIQDAYQQFBV26cO7777//8ecVymM/Sv3rsF6BhDKPznhKa5Q9+7+54qeo5s3LGiwKQJLkjBkzZsyYwd3zv//9j3+Bv7//r7/+yr/n888/L/EkPXv27NmzJ/+ekJCQf/75h3/PihUrSr+6XZxHmJKScuPGjdu3b6tUqpEjR7Zr167ch1AU9ddffx0/fryoqKhly5Yff/yx7isAX0xMzIYNG168eBEYGDh16tTevU1WybOI8RohiYzXCFValdVfEQAAcHF1dV28ePHcuXOPHTt28+bNly9fenp6hoaGRkRE6GqbgRKEdoQ//fTT3LmGEnYNGzYstyOkKGrAgAEnT57s0aNHQEDAunXr1q9ff/bs2RYtDIc/rFixYs6cOQ0aNGjfvv21a9e2b9++YsWKWbNmWfCTmEAzhtXa4hEhTI0CAByZu7v7yJEjR44ciTuQKkDoGmHjxo2XLl165MiRlStXCnzIn3/+efLkye++++7MmTM7duy4du0awzDTpk3jKqsmJiZ+9tln3bt3j4+P37p1a3x8fHh4+Lx585KSkiz5UV6PPyIk9SNCw9QoJMsAAEBVgPtg3kGDBi1cuHDAgAG+voIquiKE/vrrL3d3d25417Bhw3Hjxl2/fl23awQhtH79eoqiPvvsM5lMhhCSyWSfffYZRVEbNmww74coj3GyjBgh5CLhjQihxBoAADgxW2WNvnr16v79+71795bLDatxAwcORAjFxsbqmmfPnpXL5fxV0169esnlcu4Ca4FkGQAAAK9jq6zRJ0+eIIRq1arFv7N27drcPyGEEhMT/fz8+D2lXC739/e3eq3V0skysEYIHMDzx5cPXtuepc5FCDEMS5IEQshd7NK3aUSztoNxRwcc0LFjx+Li4ubPn487ECuzVUeoK0lXrVo1/p26aVWuEkF+fn7Dhg1LPNDX1zch4bVlEZ4/f/7kyZOcnBxdkyCIOXPmvG5bqFqtJkmSpmkNpeHuZGhGpVKRDMHdo9AoVSpIHLUalUolFjvFthyMUh9f2X1jY7TolZZESFriH3P2PlwTdnvjpIaRYe2GI4Io8xmAVahUKq6cmNVVcpkxIfbs2bNmzRqMHaFKpRKJRGZ9yEgkEpGonKPXbfuBVeLwYl1hHq6gHEEQ/EI73DXE6/905XK5i4sL17/KZDIXF5fX/ZAikYgkSZFIxCDDq0hEEpFI5CZ14+5R0apy3yYgnEgkgvfTdp48iN16c9N5cS5j8uM3Xq759NnOlgn7324c2ab9COgObcSmv+3cRyXQY/VvuFlvu4kOhWOrjlA3SitxTlV2djZCyMfHh7um9PnI2dnZ3AWlVa9evVatWl988YWQGBiGIUlSIpGwvFwjqUQqkUg85PyOUG2773ROSCKRwPtpEyy7Zve8bZpHprtAvji5Ki55e68n0QvG/iGWupT/AGAmm/62l/isZxSFyvgLTGGejV6u1MuL5fVbSoIN+w4//vjjI0eOIIT69u2ru2fZsmUdOnRYsmTJrVu31q5du3DhQt2u8efPn0dFRf3zzz+6w5W4Zxg5cmSLFi2+/PJL7p7o6OiVK1fGxcUxDNO2bdsFCxZ06tTJRFASHiv+rLbqCOvXr08QRImNELomdypHw4YNz58/X1hY6O7urrunsLAwPT29e/fu1g2mrBPq+WuEMC8K7B3LMr/u+Hgf81+J+2vS0kFBXd3kHhqNRiqVUrQm5tm5BKKIf80pUVbBtunfjvk/qYtHJYYMrIlK+y/z9/lMYW75l1pPHkKeAyd59tMfUtGoUaPq1aunpqa2bdtWd4+uImh8fPzJkyf79OkjlUpHjBihG94kJyefOHGixJmCJRIhV61aNWvWrJYtW+qOnti+fXuPHj2OHDlii7IqptlwRNimTZszZ84UFRW5uemHX4cOHUIIcT9kr169Tp8+HR0dzVWii46OpiiqV69e1g2mrMoysI8Q2LvTp09Hn7nwIOm/Vo1CyJoJJ+VG0ye1tNKxIf0HhE/VfbcrKCjw8PBACI1G7996dGrr9U3XUDZ38TVJwYfbp4bmtLsa/7Smf/U+XdtHRETAUm4Vkrfv70ruBXXyj25ybfuG2LcmQuj999+/fft2XFzc8uXLS1xWUFDQrFmzjRs3Cp/Offz48Zw5c4YOHbp7927d2PfTTz9t06bNBx98cP/+fSHzmVYkNGitVpuTk5OTk1NUVIQQUigUuiZ3xMb9+/c7dOiwdOlS7iEzZ85UqVQLFy7UrRReuXJl586dPXv2bNq0qe6CqVOnuri4LF26VJc+k5ubu2TJEldX1ylTpljxJ0RlbZ+QiqS6jw+EkIbW8IeMAGBXUFDQuffAEcs2L89qeiR06lOPOH4v6EYTCxuM3TTx30HdZnC/xnytG/X66e0Nv7SdFaA1dHUPZeo4tyunag//neo84Z9zTdt3e/bsWWX8MMAaNM+f4HlhlqVeJAu58MsvvzRrUXPLli1arXbx4sXcDLCbm9s777zz8OFDq28cKJfQr4TXr1/v3Lkz1/zwww8//PBDhNCZM2d69OiBECosLLx27VqzZs24ayZNmnTy5Mlff/310KFD/v7+V69erVmz5tq1a7kLAgMD16xZM2XKlNDQ0ObNm8fHxxcWFm7cuFF3PJUVlZ4aRQjJxbIiSqG7rdKq3SSVeiAyACZEjp92o+F4qu0oKasaQ3+Q7KHg/smLJn7oMr9x/S7lPkmbxr1W+zf85OCsZ2J91vRzD23f2n/H0j+lN+tX+PRan6Fj7l87B+PCKkESUEudiGFEiBCS1KhV7jVSqdTcKqZ3795FCC1YsICftJ+eno4QSklJKfdce+sS+jcQEhLy119/lb6f2/9Qt27d33//vUmTJtw/kSS5efPmUaNGHT9+vLCwcMSIEVOmTCmRCPP222+3bNlyy5Ytz58/79Kly9tvv21xWXQTSo8IEUIuEheuI1RSSugIgZ149OjRnTQFNXgUQmg0/cF/HjncP3lq2GUd5wrpBXWqVwteNey397bPSPPQf1VPc9H0UH16kF6jrNc+rVb4gYMHh0dGWv1HAFbnNWR65urPWHVlb3p2f2O42D+43Mvc3NyEDAf5+wjUarVIJGratGmJWdCBAwcGB5f/itYltCP09/d/5513TF8wc+bMEncSBDF06NChQ4eaeGDz5s1LzzhbV5kjQhejQ+ohXwbYiwsXL2Y36IcQGqZe8czb0Av6aESPTwWnBavCmprxbIpC5sZO1O5t+UsX/S95mlwzPH/hVvLXgob9Dp86Dh1hlSCt3Sjg878VN84wioLKeUWCFEnrh8kbtbHs4brUEN1Smo5SqeS2gCOEgoODaZp+9913Q0JCBD6nXRzDVHXRvN2KouKvLdARAvuUX1BES92bUlcLPS9wd1ZXi69Q3+aqd/E/WYQoKioqYD0OM78PKfrwuVuh7s7nHim98redkjfKzzLv2QBGIm8/j96j8MZQvXp1hFBeXl65J8jXqVMHIXT79m1ukm/Pnj38jeODBw/+66+/Vq1aVeL8QiycoiPUsrxjmAxrhHAkIbBH9UPq+seeaSI7nFk81eRCozvUolRRqF9mQr16puZXSgsKCkKZSYWk5yHm196ad7KkDEKIJZDMbU+t3J5hDYV+GQcAIaTbOPHRRx8NGDBAJBKFh4e/LqUjPDzc3d19wYIFPj4+devWPXPmzPfff1+i9PSgQYN+++03lUo1efLkwMDA1NTUq1evHjp0KCYmppJ+nmJOUbmAv0YoJvV9P+ygAPapV69e/VvGZ8oM5bXEBf0SRc1RdopbVgL/OE8h3NzcmoXUJhLO5ZM+yar3xcWzS0ViNrzxiXEjzetWgZOLjIycN2/eyZMnx48fP3r06Fu3br3uSh8fn40bN+bm5g4aNKh58+bffvvtli1buC3jCCGCIHbv3j1r1qxNmzZ17ty5Tp06Xbp0+fLLL0sf3l4JnGJEWHofIULIlbenXgF1t4HduBZ/4FmI4VtavbzqG2XvotS71XfM2Lrudwv2V21Y/XPnfkNfRnx3q0nvsXnnXnjH6e5P9SFjH2xt0GCx1UIHjo4kye+///7777/n3/nvv/+WefHw4cMjIiLu3bun1Wpbt24tkUgyMzP5F8hksp9//vmbb765d+9eUVFRQEBASEgIlrpUztERlpU1CiNCYIfSM5N+eLSdLd4c6Ktkz//7qkZG1zo1/f/ZtT4sLMyC56xdu/a1U4enfzzvxuHPY32De49hnvnqX2Bb/q22d6NbN+9nrfgB4JPJZG3alJNu4+Li0q5dO2HPZ6t0GefoCHlZoyTBJcvASUzA7iw9trBQpP9rF7Po6w4f+A5oXrNmzQrWXw4MDDzy7xaE0IsXLxCd996p+XlihBCiCfTtjT831e/iIncv5ykAcFywRogQZI0C+xBzYUM8Wcg1J3q0btGif1BQkBVPIQgMDAys1WRu/VFE8XfrDDG96fj3Jh8EgINzjo6w7H2EhhEhZI0C7NQaxV+J+7hmC8p14uAvTVxfEd26ThgkMuxZjiqIe5mBqYIXAHbASTrCMpJlXIxGhLBGCDDbcvyHTLH+F1XMotnhnxCkDY91fC9iiXfxriI1gf488YPtXgs4Hl31abVaTdN0YWEhV3Ta1ljbLBM6R0dYdrIM7CME9iIrJ3V3riETPUJcp179jjZ9RXfP6pP8u3HNs8zLm/eibfqKwDHExsa2atXK1dW1WrVq69atO3v2rIeHx+7duyvn1elSZ7lbhVN0hFqmjA31LhJeZRkKOkKA0+rj3yhI/VddTy0xre9nlfCiw/p9EkLpU9VZAv1+Yy3D2q6IFXAEKpVqzJgxLMtu27YtJiZm8ODBusPPuRMkdu7cSRDEiRMnbBSAjU4KcpKsUX6JteIRoYg3IqShIwTYPEy8dJpO5ZrjfTt4+QZVwuuSIvGHzcbPfrSeJRBC6IlIeeTc2kHdp1fCS4Mq6vHjx+np6UuWLBk5cqTunuDgYI1GU2kB0IxN5mCdYkRYZrKMq4S3oZ6C7RMAm18v/sZ9UwvWiEb0n1NpL92mfWQn2ptr/pN8SKmqpJrOoMq5du1adHQ0Kj59/uTJkwihnJyckydP6o5PevLkSXx8PELo5s2bJ06cOHHiREJCgnVj4I9qrMg5RoRGa4T6vh821AN7cPzy5gciw5aJ/zUaKeZN2leCmT0+uX7+K4pACKEcEbMx+of3hiwt70GgstEsveb25gOPj3GHx9kaSZAt/JrO6fh+bU99gvHHH3986dIlhNB333333XfficViiqJu377dp0+f7du3jx07duPGjcuWLUMIzZ8/X/eQ2bNn//zzz1aMCtYILccYZY2WsX0CNtQDLCiaWvNoD9dsT7mHd3m7kmOoVbf1UHE9rhmVF5eRDSfX250Nd3Zsv7+n0npBhBDDMrcz7n566msNrZ/5vHjx4unTpxFCW7ZsYVmWoqgSD1myZMmOHTsQQjExMSzLsixr3V4Q2WyN0Ck6QjiPENing7F/ZYr1v5xiFn3Q9SMsYUwZsIDbSqEh0ZbTK7GEAUyIfnoay+umF2XEZdzD8tJlgo7QclrYPgHsD81od6Sc4pr9iaC6DTphicTdy3+8b2eueUz5OCvvBZZIwOtwtSGd6qVLg47QcsYl1rgRIWyoBzgdPrcuXawfiIkZNLH7BxiDGdbno+qU/lwLNYG2noJBoX15M6Q3ltcNdA9o4d8My0uXif9hbkVO0RHy1wi5bzcysYwsPtFGrVXDDipQmRiW2ZF8nGv2IQICauH8uJHI3Ub6tOWahwof5hZkYIwHlDCh+ajJYeN8XXwq7RXdpW6dAtv93HuJhLSjnEoGskYtQ7M0V5VHRIgIpO/8CETIRDLd6iCLWDWt5q8aAmBT0Rc3pYr1uQYilp3Q9T288SCEIvt8tPPfiTkShBBSk+yO06veG/IN7qCAHkmQU1qMm9JiHO5AyqE7g750Ho212Gj7hOOPCMusr6YDy4QACxaxWxMPcc2erH9wvXLObKsEcjfvSK+WXHN/7p2CwmyM8YCqqE6dOgihK1eu2Oj5YWrUQmVW3NaBxFGAxakr25+J9SnpJIve7jANbzycUX1meRWnjypEaOeZVVjDAVVPy5Yte/bsuXjxYn9//9DQUN22QiuCEmsWMjEihI4QYLH10T5U/JvYjakW0qgL1nAMXD18h7g326zSp8vvzb41TpHn5uqFNypgP0JCQpYvX966dWvunvr163///fetWrXSNXWFRk+cOJGYmFhQUNC+fXvrBmCjDfVO0BGWtYlQB+pug8p37uaeJyL9LxuJ0Pj2U/HGU8KYPrP27nunUMwihApF7O7Y1ZMGfIE7KGAvateuzVWN0alVq9a8efP495Ak2a9fv379+tkiANg+YSGTI0IoLgMq26a7u7jbHSmvhk26YwymNA+vGoNdG3DNqMwrSnURxngA4NNC0W3LmBgRQrIMqGQ370UniPRVsggWTW4/GWs4ZRvb62PX4j+aPBF76NwarOEAYMDAiNAykCwD7MfO2zu4220p98bN8OySNs3bt9YAaQjX3Jt6zkbHggNgLii6bSH+UFpsvDMUOkJQmVIzHl9lX3HNMc0iMQZj2uju74mL+75UMXXh5l6s4QCgB/sILWRyHyGcxAQqz86zfzL6cg6otkbUof1IrOGYEhDYuAtdjWv+ew86QmAXYB+hhUxOjUKyDKgkRcr8GEUi1xxRsxsqrvBnn0a3HM3dvk3mJSRfxxgMADqQNWohk8kyMCIElWRf7J+K4t8+Ly0a0N1eNtG/TlirgY01hj+Q3Vc24IsFAD0aQUdoEdhQD7BjWHZ/+mWuGeHWWFYVdqkPr9OLu31a8ywnPw1jMAAgSJaxmKkN9dARgkpx5sq2dO4AXgaN6PYO3ngE6tN9mn/x2UwaEu2N/QtvPADA9gkLQdFtgN3uhMPc7R7Ir3qN+hiDEU4klkZ4t+CaB7NvUVoNxngAsFGyjDOUWHt9sgyUWAO29/jptXuiQq45qs3bGIMx14g3Zu488I5udTNbzERf3BjRfQbuoJyIRqPJycnBHYW9YFlbbZ9wgo4Q1ggBVluvrOVuh2lcmjTrZeJie+PhHdBTHHyYfa5rRj2NgY6w0vj7+1+8eDE0NBR3IJVBy2i5ZSwxKeYvY3H/JPOWEyKbzGI6QUfIm1MmobIMqFxZOS/OUS+4JYjhIf2xhmOJ0R0nH738je57+BOx6va9k63ssiCO4wkPD8/KysIdRSVZeuHnE8mxutsLu87uW/cN7p/+uLlu54N9+oZtuiwnWCPkdYTikskysI8Q2Nb+C2u0xX9kNSiyR9cJWMOxRN3QDm0oD665985OjMEAR8XP0uB/MiPjJEfYUG8hrdHUqNHXCUiWATbFMMyRrFtcc0i11iKxBGM8FotsFMHdPk+nZeW+wBgMcEhKo45Qzv8n/pIWbKi3kNEaofHUKGyoBzZ17vq/mWL92r6UQYO62fsm+tfp2mlsTUr/YaQl0KEL6/DGAxyPqY7QaEQI+wgtYjQ1WrLotguB9NuklFollNgH1rXvkWHXRDeihrdPMMZgKoIgyAE+hn0Uh1/dYGzzeQSclskRoaGfYqDotmVMZI2SBCEV6aeqGJbV0FSlRgYc2ov0x7eJXK45vOUojMFU3LDu78qKvyimi+lLN/ZgDQc4Gv7ilNzEiBCmRjmWGl0AACAASURBVC1jYh8hgmVCYDNRF/7hzpqop5E0D+uHNZyK8vIJ7Iz8uObeRwcwBgMcD38nN3+HNyqxRgjJMpYxUWINwQ4KYBuUVh1T8JBrDg3sijEYaxkeNoK7fQPlvkh7hDEY4GBUNG9EKIIRobWZmBpF0BEC2zhxYWNe8cm2rjTq33Uy1nCso2XLgfWo4qUEAu27uAFrOMBxMCyrLq7eRxKETCzl/yt0hFZQzogQqqwBG9iffIq73Vta29W9momLq5BBAZ2428cL71MU5FoDK1BpVVyuolws53IYdfjJMpA1aiHTI0JYIwRWl5R07aFIwTWHtqtKxUVNG9htukvx31OuiD19eSvWcICDMJEpg2BEaBWmk2VgahRY3b/XNrHF32ibU64N6nfGGo41ubr59JTU4pr7k2IwBgMchom9EwiSZazCxIZ6BFXWgFU9f/784IGo0+r/uHsG161KJbaFGN5uPHf7nqho85aVjx8/xhgPcACmO0IxyS/ADR2hRYzWCMuYGuUXl4ERIbBQbm5u/+Hj2g6dsuHyfmXxb5mXlujddRLWuKyvQYPOjdX6vxqWQDHPL4ZPntc6vE9ycjLWuEAVpjSaGpWV+FeYGrUC08kyrrwRoQI6QmARhmHeiBh+smZkxv+OSEIM8wo+j1WJiUkYA7OFnJycvMuvuOarmqr8yRtuv7G028Dhubm5Jh4IwOuYqLiNoCO0CuOpUUiWAda389/dSb5t6daRYdTlly76REqCRZckU96f9yXe2Kxu6Y+/HmXHumv1q6BFYvYNahuq2y69ywdLfvgFb2ygijI9Nco/Pg/WCC1klCxTztQo5IIDS2zdd7Sg9RiEUEu0g7szWOH+OGjE/YREfHHZxIGjMfltxvkU1ebuqSaJRQhRbUYcPHYCX1ygClNShnmU0lmj/BrRMCK0kPDtE5AsAyyTnpGBvAJcUeErt+fcna+oNxBCyMWzqKgIV2C2oNJQSOJyg3yLKC49muqiaKi9jaSuSrUGa2igqlLRhkFIWVmjsI+wwrTlrBHyO0IYEQJL1PD3R7kve6s3KkT6zsFNS8RKxyCEkDLPzc0NZ3DWJpdJkEbxUNyuplL/t8MSqB29DWkULjKp6ccCUCYFb0RYRkcIa4QVxx8Rik2PCCkYEQJLTIgc6Hlzu7v0InePd1GoinBFT682a9QQY2C2MGxAP8mNfxFChRpDAdU8tySPWzuGDuiLLy5QhfGXpcrYUA/7CCvOOGu01D5CCT9ZBkaEwBKjRo4Il8e/cNEv+BMsuk6OQ6+S/aI++vPHpXhjs7qFc2cFXP6TSLpySjbRldanzBRI2P7M9kXzPsEbG6iijLJGJTAitAHjyjKwRgisjyTJHsMbctVkAvPJvB2/hO6YcGTr340aNcIamvV5e3ufO7Kn9fkl7v9M9Esz5JrVCK/h5eWFMTBQdZVTWQY6wooTfvoEjAiBZTSqonOUIU2mk7TB6T8WPr51qV3bthijsp06dercOBt9efuqfrXDuTvvSpQpz+IwRgWqrvJKrEGyTIWZcx4hjAiBJU5cWJ9ffOiSO43enfB106ZNCYIw/aiqrl69euPHflSfMqTMHLi6BW9IoIpSQtFtWzPnPEIYEQJLHEw5z93u7RIqkzlUmqhpA4MMJcWjixIoDVSlAGZTQdFtWyvv9Akoug0q5GnStQdiw6FLwxzo0CUhBnSd6srox765Yvbcle144wFVkeljmMS8EaHWNiNCcfmX8Dx58mTjxo3Jycn+/v5jxoxp3769iYvPnDmTkJBQ+v7atWu/+eabuts7duzIz88vccH06dNJ0mo9NJxHCGzqwPVtXJpMY61rSL12WMOpbK6uXt0lwcfoFF3zUNKJXt2m4A0JVDnGa4Slim7bfkRoRkcYHR0dGRlJkmSbNm2OHz/+yy+//PLLLx999NHrrt+wYcPGjRtL3z916lSuI1y0aFFiYskaVJMnT5ZKrbYzV8tqudul1wjFpEhCiilGixDSMjTFaCWkeV8OgDPTatWnlE+4P6NBtbpjDQePIa3HHrv+o+72LVFBasq9oFrN8IYEqhb+hnpXiWuJf+XP5GFeIywoKJgwYYKfn9+jR49iY2OTk5O7d+8+e/bs+/fvv+4hq1evzjY2ZcoUhNDEiRP5l4WHh5e4zIq9ICq5ob6MTg5mR4HFTp3flFv8O+VCoz6dJ2ANB49mjbrVo/R/swyBDl+DlBlgHn6JNbmo9IiQV2sU7xrhrl27MjIy5syZExgYiBBycXFZtmwZTdN//vnn6x7i5ubmw+Pi4rJv376QkJDu3Y2+NUskEh9jFfl5SjO9Roig7jaogMP/neZuvyGv6+LigTEYjAbU7MjdPl7wgKG1Ji4GoAR+VS8XiR0fw3T69GmE0KBBg7h7OnXq5Ofnd/LkSYHPsGfPnpycnOnTp5eZVs6ybOk7rcL0GiEyft+hyhoQ7mXq/TuiQq45tM0YjMHgFdF1mqz4L/iVmLl07V+s4YCqhEWsunhESCBCVsaI0G72ESYkJIhEojp16hgeSZJ169ZNTEwU2IetW7dOJBKNHz++xP3Xr1/39PQkSTIgIOCdd955+fKlwJAEMr2PEMGIEFhq/6WNxfmSKFQrb1K/q8nLHZm7e7XOZE2ueSjhKMZgQNWi1mqY4k5EJpaSpUZKlTAiFJoYkpub6+PjUyKZ09fXl6KooqIid3d30w9PTk4+ffr0gAEDatWqxb/f29u7Y8eODRo0oCjq7Nmza9asOXr06OXLl4OCgsp8nszMzKdPn3JjSrlcPm3aNFfXkourOhRFkSSpZQyzNCzNUhRV4jK5yJA4WqAqKH0BMAtFUc7wHjK0NqbwEZLom28GdMT7U2N/2yOaDjlz7y/d7atkbvrLxGrV65h+iAPA/rY7gHxVAXfbRSwv/X4yWsMokGZpqpjA5xeJROVuQxDaEbIsW/q5dPcwAsaq69atYxhm2rRpJe6/cuUK/2m/+eabRYsWffXVV//880+Zz6NWq5VKZXZ2NheASqWSyUoOpXVommZZVksbvkEQCNF0yS8UcpEhN6dIoyx9ATALTdPO8B5eurrzlUT/my9lUK92b+H9qbG/7S0a9w6KW5cqphBCWgIdubxx3IAFGOOpHNjfdgeg0Bi24cpEsjLeT96cI83QHIHPL2QzntCO0NPTMzk5mWVZ/gpfdna2SCQqdzjIMMzGjRv9/f35S4xlhvjFF1+sWLHi+PHjr3uq4ODgBg0aLFgg6A+MIAiSJFnC8C66yFzk8pK7Nd2khjogNEmXvgCYRavVOsN7eOzpSe6vp5skqLpvTZOX2xxFUdjf9v5+bdblXNHdjs67O1kmJcpKT3Mk9vC2V3WMyvAR7Sop4yNaylt9o1laLpfTtJU/qIX+moaGhmq12hILeCkpKfXq1Su3v42JiXn27NmECRMkEonpK0mSDA4OzsnJERiVEOUmy8AaITDXq/Ska6JcrjkkbCTGYOzHkPBp4uLpoRcS+ubNA1jDAVWD6bIyCCGSILiFQ4ZlGRtkVgrtCHV7Ho4eNayB3759OzU1tUePHuU+du3atQihqVOnlntlXl5eYmJicHCwwKiEKDdZBvYRAnMdvLSOLv7LDNJKWjbrhTceO+HjGdCB9OOaB+9DRwjKZ/roCR1b58sI7QjHjh3r4eGxcuXKgoIChBDDMMuWLUMITZ8+nbtm1qxZo0ePLvHArKysAwcOdO7cuWnTpiX+KS4uLj4+nmtmZ2dPmjRJqVSOGzfOgp/kdcrfPsEbEULdbVAulmWO597jmgNrtCeQgx80IdygJobljwvoVV5OKsZgQJUgqCO0cZU1oR1h9erVV69eff/+/WbNmk2YMKF169a7d++eO3dup06duGuOHz++e/fuEg/csmWLWq0uczh46dKlFi1ahIaG9uzZs2vXrnXr1t2/f3///v3nz59v8c9TWrkb6mFECMxy7VrUS4n+T1HMoIguUFrToHPrYX5a/WeWhkRHz2/AGg6oAsqdGkX2MyJECE2YMOHcuXO9e/d+9uxZo0aN9uzZ88MPP/AvmDFjxmeffVbiUe7u7vPnzx8zpoy9xhEREStWrNB1pRKJZMSIEVFRUUeOHLHuKqiAfYRQdxuY4cDDI9ztTiJ/H88aGIOxNyRB9PNpwTWPvLqBbFYrAzgG48MIy94CYOsRoXkFpjt37ty5c+fX/evs2bNL31l6ywSnVq1an3zyiVkBWIC/jxCSZUAF5bxKuUxmcc2hTYdhDMY+DesyZfuxW7pSA/9JtXfijrVoNQB3UMB+KU1W3NYpUXdbZO0DBB08uRkJKboNJdaAYAcv/EMVLwjW0IrbtYzAGo498q9ety0yVAw+cHcPxmCA/eNnZpQ+g0nHaGoU4xph1SVgjRCSZYAwLBudfYdrDazeunQ5KIAQGtzIMAQ8x6QX5KZhDAbYOUFrhPwDKPCuEVZRRlmjsH0CVMCNG/tSpPpfJxGLIjpDmkzZurUdVZ3W/62pROj4xQ1YwwF2Tdj2Cf7UqPXrbjtBR8jChnpgHQceHORudyD9/KpZc8OrIyFJUV8vw3apw+lXIWUGvI6QEaGY99GthalRc7GIZYq/PhCIIGH7BLBUfs6LS+gV1xzSpGS9QMA3rOsMsrjvS5Jq796NwRoOsF9VaUN9FcU/vEr0mlJwsEYIhDh8bq26+DeoOi3q1HII1nDsXUD1uq1Yb6558E4UxmCAPatKG+qrqHI3ESIYEQIhWPZo1i2uNdCnJVnWNDvgG9ygH3c7lnlZlP/KxMXAacGI0ObKra+GYI0QCBB369B/Uv2GVBGLBneejDWcqqFHh7HVtPpPGCWJoi+sxxsPsE/CskZte0i9o3eEAkaEUpGU+ycNrbHRCcigStt/bx93uy2q5l+9Lr5YqgwRKe7j2ZhrHn55GWMwwG7BiNDmhHSECAaFwKTC3PSLKJNrDm4MaTJCDe08hfuIeSyjHtw9gTMaYJegI7Q5IckyCIrLAJMOn1+rLP7d8dWS4W0isYZTlQQHNApjPLnmgTsli/IDwP/Iff3UKCTLVACD+GVlXjsidOW9+wrIlwF8LHsk8zrX6l+tBaTJmGVwfUPKzGntCwWkzABjRiNCCXSENlBuxW0do8RRCg6gAAY3bxxI5qXJRHYq/3xpwNer41uGlBkROnp+Ld54gF1RadXcVm8ZL12jBH5lGS1MjZqr3IrbOkZTozAiBDz7H+znbrcjqvv71cUXS5UkIsX8KjP7ocoM4OEPB115n8Ml8D+9YURotnIrbusYT43CiBDo5Wal8KvJDGsKm+gtEcmrMvOflIqPO4Y1HGBH+AMP/sxcCZAsUyECs0b5qUqQLAM4+8/+zVWTqaEVd2o1FGs4VVVNv3ptkKHKzL54qDID9BQUvyN87ZHsUHS7QoRsqEcwNQrKwjL00by7XDPCry0cumSxIY0Hc7fPoozc7OcYgwH2Q+DUKCTLVIjAEaErb0iugBEhQAghdOnKrpcS/e+PmEWDuk7DG0+V1q3tSD9tcdkKEh05vw5vPMBOKCmYGrU9S/YRwhohQAghdCDhKHe7iyjA1ysAYzBVHUkQb/q24JqHsm+xNvheD6oc/nY1GBHaiiVrhNARAoQy0x5fFeVwzWFhIzAG4xiGdZ0hKk6ZSZXQ12/sM3k5cApCysogGBFWkMA1Qv43EZgaBQihvRf+oYtXBINoaZvm/UxfD8pV3Se4I+HHNffzTjkGTssoWeY1u+kRFN2uIItGhNAROjtaS0UXPOSagwM6EgjSZKxgWDNDdbpLZPartCcYgwH2wChZBtYIbYT/lpV5PL2OCyTLAJ6zlzZnSvSzeDKGGNQF0mSso0OriECtfme0lkAHL0HKjLPjDzxeV2gUGXeE/Hph1uLgHSHDq2FhKmsUkmUAz77EGO52d0mQh3s1jME4EgIREf7tueahvHu0VoMxHoAdv6Sl0GQZ2EdoLv53B7GpWqMwNQr0khOv3JEWcc3INuMwBuN4hoa/I2P088yvJMzp8xvxxgPwUlhQWQayRs1ltEYocEM9FN12bruubuS+cDaiXZo17IYzGofj4eHbQxrMNfcln8QYDMCOv4/Q5IjQ0FUxMCI0F78jFBOvLboNxzABnaKCrFNaQ9GTyHp9MQbjqMZ0mMzdjpcoEh6exRcLwMx4RChojZB/uJ61OHpHaMnBvDAidF4HYv9PWfwX502TfTpPxBqOY6pfr30T2o1r7r25A2MwAC9L1ghhatRcgrdP8LJGtQrbxgTsFssefnWDaw30bC4RSzGG48CGhRiG2qe0zwvy0jEGAzCCDfWVQeCGegkplhSfd6VlaMoG6bnA/l26uitFwp3By0ZCcVGb6dtlIndar0qEDp79G288ABcFZRh4QK1RWxE4IkQlD6mHZUJntPfRIe52F8Lf368exmAcm4gUD/BuzjX3Z91gaCg96owEnz4BlWUqQOAaIYKTmJxeasq9a2Qe1xzecjTGYJzBiO7vi4v/OtMkzKVru7CGA/BQmp8sAyNCswkfERoljsKI0PlEXfqneHsbqquVtWneH2s4js/XJ7CLqAbX3PPoMMZgABYMy6qLKyqQBCETy153JSTLVIgZU6NQXMaJaZSFJ5SGupfDgmHvYGUY2Wosd/umOD/lv9sYgwGVT6lVskhf/MtF7GKioi+MCCuE/92BND01CiNCJ3bk7N95xbtM3WnizS5TsIbjLFo27R2q1Q8CGIR2X16PNx5QyQSmjCLjumBaGBGay4ypUYkrdxvWCJ0Ly+55cZ5r9XWp7+LigTEcpzK0Vg/udrT6aWFBFsZgQCUzOp7+9ZkyyPYjwtcWW3EMAotuIzib1yndu3fv78078vLj/+uqT9sgWTSy63S8UTmVAeHT1u2IyRWxCCGFCM3+dhKrbDph+KDu3bvjDg3YnNHx9K/fO4GMzw6CNUKzCaw1imBq1PksXv5Tj7dmripqS4cZ/gJbqdyCA5tgjMrZSKUu3cm6XDOzoXij+I1hn68aO/U9xgZZ8sCuGI0ITU6NGp8+AR2hmfjfHUycPoHgJCYnc+jwkZX7zmfNPNaoaeBzT8NZE3GHnqWkpGAMzNmoVKoNqy9Ji7u8bCnTs96LnCnbD2d6LPvxF6yhAZtTCNtEiIw/vWEfodnM2VAPJzE5kQXfrcgZ/gsiRe3ROu6vqqZCfibw4x9//wtnZE5m1+6opKCBNQprcvf4SmMQQoURX/2xbjPLW9oAjkd4sgxkjVaIhdsnoO62o0vPykHVgn2Zl2nuL7g7c6k+bMPuZy9dxRiYszlx4Zqi/hu3iIlEcZeX6qpsS51EYhnrWyc1NRVrdMC2lPz6aliTZRy9IxRcWQZOYnIqupFGb+r/NMW/FN4a8pTsbSSRa9RwZnrlUarUSCy7L+4QpHDn7mxC7EIIIYlcrVZjiwzYntHUqMlkGdhQXyHmjAh52ycgWcbRuUrFEnWO0u0+d49U0Ypipeh5fJNGDTEG5mzaNGsofnEXIfRSG8HdmeqeWZt+zKYnBgcHv/6hoMoz3j4BU6M2I/D0CQTbJ5zMlLdGDUz5LE+inzCQM+ik5B3Esj6nfpz1DpxBWHkmjB3lfelvRKnOSEbWUOp3c9EE0TX/p67tWslkr625BRyA8Rqh6REhFN2uAKg1Csr02eyP5HUzuaZ/QZ2cItZr6/Sx4U27hYdjDMzZBAcHL53zfrW/I9nMp1p1J+7+HP9Xq5YvwBgYqAQK4dsnYERYEWaMCCX8s3mhI3Rwt+8fe+mhL2xIsigh6kazXeP/fH/wHz8vxxuYE3pv+pSoX79sf3LO7TX/ulP6OxVidD5+N9a4gM2ZU2LNUPtFa4PzYh28sgzN8pJlCNPJMrCP0IlsvbMLFX8v6sB4f3/yANZwnN0bPbpfPdkdIfTH7rk71Y90d0ZlXBpFUyKRBGtowIYEHkaIjD+9+Z/q1uLoI0ILt0/AiNCRPXx8MY7M55pjwuDoQXsxqtv/JMX7KDLE9PELUIbbkRkfRghZozZjWYk1GBE6ti1X17LF5700oeRtWg/CGg4w8KsR0osM5Jo7kqK5Y3qA4+GvEZoeERrVGoU1QnPx84vE5VSWMZyGxT8lCziY5y8eXmQNaTLjGgzGGAwobULX98jiP77/JJoL12Gl0GGZUWuUgBFhBQgfEZIEIRNLdbcZllVrYSevY9p8bjVdPBwMosTdOr+NNRxQUq06rTqzPlxz2709GIMBNmVOrVFDOguMCM0mPGsUGU9Sw+yoQ8rKeXFK8x/XHBf0hunjmgEWE9pO4iqu3RMX3b53Ems4wFaMR4Swj9BmhCfLIDiJyQlsj13F1VTzpYg3u8/AGg4oW5OmvcK0hkpP225vwRgMsB2jZBmoNWo7ZnWEcEi9YytS5B3Jf8A1R/q2k8hM/e0BjN5qPIy7fZXNSky+gTEYYAsUo6WKdwSKSZGENLWXDzrCChFedBtB4qij2x27ukikn3Fzp9HQN97HGw8woXPHMQ00+jV7lkDbrqzFGw+wOqXR8fSuJq5EsH2igsybGpXA1KjD0mqp/RmG85WGuDZ28/DFGA8oB0GMqtOba52hnr/MSMIYDrA64RW3EYwIK8isZBl+cRnoCB3MwXN/Z4n10wMyBo3uMRNvPKBcfbpPCyhe0aUJtOPcH3jjAdalEFxfDUGyTAWZOSKErFHHRDPa7c9OcM1+omAfvzoY4wFCiMTSUf4dueZRZUJW3kuM8QDr4p9/bnrvBEKIQAT3Ac4i1uqDQgfvCLW8EaHYnBEhJMs4kiPn1qaL9b8JYga9Ff4/vPEAgYb0nFmN0u/6VBNo66lf8cYDrEh4fTUdmy4TOnhHKLzoNjKep+Z/WwFVGsMy25OjuWYfFBBYOwxjPEA4qavnSO/WXPNQ4cOcgnSM8QArEl5fTYdfZc3qlb8cvSPkHdghYB8hjAgd0NEL61LF+tN9RCw7Ifw9vPEAs4zoO8tHWzwoJNltp1bijQdYi/GIsJw1QmTjAygcvCNkEH/7hDkb6qEjdAgMy25/coxr9mT9g+u1wRgPMJfczXu4V0uueSD/bm5BBsZ4gLUIP55eh/8BbvUjCc07j/DOnTtHjhwpKipq1qxZZGSkTCYzffGjR49K3NmpU6datWrx70lLS9u7d29KSkqtWrWGDx9eo0YNs0IyzWgfYbkb6sUwNepooi9tShFrdLdFLDupCwwHq57RfT+J2j0pV4wQQioS7Tj923tDluIOClSUuVOjNq27bUZH+M0333z55Zdubm5eXl6pqanNmjU7ceJEQEDA667fsmXLjz/+WOLOHTt2jBkzhmueOHFi5MiRRUVFwcHBz58///zzz/fs2dOrVy9zf4zXEV50G0HWqMNhEbs18SB3AG8Pxq92aHusEQFLyN18Ij3C1ivjdc39uXFvFWV7ulXDGxWoIOHH0+sYJcvgyhqNiYlZtGjR0KFD09PTnz9/fujQoUePHk2dOrXcB966desJT0REBPdPOTk5Y8aMqVatWkJCwtOnTx89euTj4zN69Ojc3FwLf5pSzCuxBvsIHcuJK1ufifTDQZJFEzpMwxsPsNjo3rO8iifDFCK04zSsFFZ5ws9g0uGfo8fgSpb5+eefSZJcvXq1q6srQigiImLs2LFHjx69f/++6QfWrVs3hMfd3Z37p/Xr12dnZ3/99df16tVDCIWEhCxevDgrK2vjxo2W/jglmXf6hASSZRwHi9gtj/Zzze5MtZDGXTHGAyrC1ctvqFtTrrk3+1ZBUQ7GeEDF8fMwBE2NYt8+QVHU6dOn27dvHxhoODx66NChCKHjx49b/NrR0dEikWjQIMP54IMGDRKJRBV5zhLM2j7B/8+AEWFVd/rqzmSR/lBJkkUTYThYxY3t+4l78aefQoR2nvkNazigosxOlrFllTVBHWFSUpJGo2nUqBH/zsaNGyOEHj58aPqx/fv3DwoKatKkyYwZM0rkzjx48MDf379aNcNcf7Vq1WrUqPHgwYNST2MJhmWZ4o6QQARZ7j5CKLrtKBiWXfcwimt21XqHNu6GMR5QcW5eNSLljblmVPaN/KJsjPGACjKr1iiy8YhQULJMdnY2Qqh69er8O319fbl/ep3GjRs3bNiwVatWDx48+Oeff7Zt23bkyJEePXpwT1u3bt0SD/H19f3vv/9KPlGx/Pz8xMTEXbt26Zq6AaVEIinzYoqmuNsikmTKq1AnIw1JsApKWe71oEwMw2B/645c3JDCGw5OaDcJe0i2Zg9vu62N7PXh3sMzC8UIIaQg2Y0nfpo5+Bu8ITnD224jRbyOUC6Sl/s28keEWkYr/G0Xcvi2oI5Qq9UihMRio4ulUilCiKKosh+D0IIFC3744QeuefDgwcjIyKlTpz5+/FgXGU3TpfswqVSqe7kyZWZmxsfHcy8qEok6dOig65JLUygV3G0xKVapyhnkEbyXVWqV5V4PyqRSqUr8qlQyLa3d9OQQ96vdTetdK6Szw/9vqtXq130jdBhSV99hLo22UPqJpYP59yIzkqt5vjZxvRI4w9tuIwqN4fNZRJPlfz7zH6s04/NZKpWW+4kk6APLw8MDIZSTY7Q6rRsLenp6vu5RXl5e/ObgwYNHjhy5c+fO+Pj4li1b6p62xHMihLKysnQvV6bQ0NDmzZsvWLBASNgqRs3dFhEiXZqPCa7IVUSIdLPPalojc5GVm2gKSmMYpty32qZ2n/4tXaz/UiNi2enhH+CNp3LQNO0MP+b4AZ8f3jMlR8wihNQku/3C6rkjfsYYj5O87bag5n0++3j4lPs2SkSGLxxSudS6b7ugNUJdVufLl0al31NTUxFCISEhwl9Mt6yYkZHBPW1GRgZ//KfVajMyMsx6ThPM2juhIxcbZkdVWrWJK4F90lCqrSmnuGY/VLN2/Q4Y4wHW5eJRbYyXofroMeXj1IzHGOMBFuMfw+QqqMQa7mQZLy+vZs2axcbGqtWGviE6Ohoh1KVLF+EvpttrwdWO5EENdAAAIABJREFU6dKli0KhOH/+PHfB+fPnFQqFWc9pAsMa9pqUezy9jtEOCkgcrYJ2nFqZLdL/kUhYNKk7nDvoaEb2/7RG8TmFWgKtOwN7Cqsk42SZqrB9AiE0efLkgoKCtWvX6prZ2dmbNm2qU6dOz549dfekpKTMnj17x44duqZSqbx9+zb/Gfbs2RMVFVW/fv3mzZvr7pk4cSJBEKtWrWJZFiHEsuzKlStJkpw0aVLFfzBkZsVtHVcoN1qVKdSFu9Mvcs1BZO2atVuauB5URRIX93H+nbnmKc2zpOd3MMYDLMAilsvMJxBhbtFtLa4SazNnzty1a9dHH3108eLFoKCgf//9Nz09/cCBA9xC8cuXL3/55ZfJkyePHTsWIZSfn9+6deuwsLDGjRu7u7vfv3//ypUr7u7u69ev53J4WrVq9cknn6xYsaJHjx7dunU7d+7cuXPnPv3007Aw65ySY1Z9NR3jEaGDp1c4ns3RP+WJ9NMALjQ7se8neOMBNjKk78e7t156LmUQQgyB1p77fdm4v3EHBcyg1mq4vW0ysbTcvW3ITkqsubi4nDp1av78+Xfv3t27d2+LFi1iY2MHDBjAXeDr6ztu3LhOnTrpml5eXkuXLg0KCrp//35sbCxN05988kl8fHx4eDj/aX/66SfdKHPHjh0EQaxbt46faFpBxrvphXWE/CprMCKsUvIKXu3LvcU1I+UNq9UMxRgPsB2RVD4xuDfXvECnPUi6gjEeYC5zz2BCJUusWXnLihlp7u7u7suWLVu2bFmZ/xoaGrpt2zauKZfLFy5cWO5zEgQxdepUITVLLWBWfTUdOKS+6loX84OC1A8HPbTorYGf4o0H2FTfXu/t2Hg6SaZFCLEE+r+Lq1eGdMQdFBDK3LIyCCERaeit4IR6M5hVX02HX+AAqqxVISnpjw4pDEWORnuEefjUxBgPsDVSJJkaOphr3iZyL8YdwBgPMIu5ZzAhOJjXYhZsnzAeEcIaYZXxx8kfi48xR9UpYnS/OVjDAZWhW/fJzdSG/U5/xm1irP35CGzE3DOYkJ1kjVZF/FOMxaSgSWDYPlEV3Uk4e4kxnFo+uWYPuTscVucECOKDdtO5j7BnIs3+M/+HMx4gmLl7J5A97COsoizZRwjbJ6qg1Zf/YIuHg3U14oG9P8QaDqg8TVv076Y1fOlZnxJdpMzHGA8QyOgMJqFrhLxkGZgaFc6CqVF+RwiVZaqE6MtbHooMRQvfbTJaJIbaj07k/Z6fyoo/FfNEzJaYn7CGAwSxaETIXyOEEaFglqwRwpGEVQql1ax9tIdrdqA8unQaizEeUPkCajcfLDUUZdyddzv9VTK+cIAgCgvWCI2mRmFEKJgF2ydcYPtElbIz5uc0Q31t9E7n/+GNB2Ax5c0vvItzpTQkWnPyR7zxgHLxR4RCCo0i489wq1eWceiOsGJTozAitHP5Ba+2Z17mmv3JwAaNwk1cDxyVu5f/uGrtueZJbcrDpMsmrgfYGW+oFzQ1KoZkGcvQvJMbhZTwQSWmRmFEaN/WHP+20FBQDU3vMx9vPACjkf3nBGr0H5QMQn9c+B1vPMA0o6lRAcfTI0iWsZhxrVGzO0KoNWrPEpOvH1Ylcs3R7s19/ethjAfgJZa6vFPfsL8+jsw/eWkzxniAaUqjM5jMT5bBVXS7KuK/WUL3EcIaoX2jaTohIeHx48eHX22hi/dS16DItyNhOOjseoZPidpwPF6q/7Nd/Sgq76WsXr0GTZs2lclkph8LKpklWaP2UHS7KtJWbI0QKsvYm30HDtZu3u6Nmd/+dX7/Q5nhf+e9kCEyVy+MgQG7QBCfdPtEVLx7OEvC/Ht/b//PVtdp0fGnVavxhgZKsGQfoS2zRh15RMifRxYLPYYJkmXs1P5Dh6d+9WvOe8dcXSVisaFKe4N8sle3KRgDA/YjtH6nrtHeZ73ydM2MOkUe1ecmoYZLd85UKFVfzofCe/bCeERowfYJGBEKZlGtUVfuNkyN2g+WZT+c/2XOpK3IrdpQalmuVP8VR8yi+wfzn6Wk4A0P2AmKonasue9F6bdSaEnUmfgFiWX54/7v9w3bs7Oz8YYHOBadPgG1Ri1iwT5CMSmSkPq6JFqGpmjKJpEBMz148EDt1wi5+9bX3kn3eMzdXzO//nXfyCPHjmOMDdiPq1ev5tTsiIp6cfekuOf10uxApLio+ZBTp05hjA3wVfD0CQaxJq60gEN3hOaPCJHxOB2WCe1EWloa5RWEEOpI/KIt/p31psiD4s8o7+Cnz9NwBgfsRlpamtI98JD0vaAiw2erl0uUC1Ok8Ah+/gJ+T+yFBQfzwojQQvw1QoH7CJHxyi1sJbQTvr6+4oL0fuotKe6GksqaojfzSR9RQXpwjeoYYwP2w9fXV1aUwRLkffrd4kOaUZaUGUL9KC9KD/CH3xN7YcExTPzMf/7JQlbhyB0hf0O9wH2EyDiXF/Jl7ERYWJh37l256z7unkCF2zHZNISQz53db/brgy80YEc6deokTjiDtOo4Sbeggtrc/Vme8S2zj7zxxhv4QgMGDMuotRrdbZIgZGJBm1ug6LaFLJsadYWthPaHJMkRM5rmSvVf8kkW3dF+gFjW9fjyvm0aNmjQAG94wE7I5fJPZ77jtXMmoqkjos/cKUMB0mYjfGvU8McbHtBRalVs8SKfi9iFQITp63Wg6LaFLDiYF5VYI4TiMvYhLu7oZQ/DpKj/c++UE8f9fus1tkbOxj9XYgwM2Jt5sz6YF9Ha75dw9vAqJjGYuz/Rg9l//FeMgQGOBbvpkfHyFmvtZBlH3kdoYbIMjAjtjFaj/PnmGkaqb1aniB7eHSZOrdeu3cwaNWpgDQ3Yoy8+nTVzxpRr1649TnwSp8p8INd/nV2THhuePqx6jRDTDwe2pjCqryZogRDZOFnGkTtC/gn1wpNl4AAKe7P+wFf/SQ2D+7ktp3ZqPRRjPMD+eXl59enTp0+fPqnpPadEz1WTLEKoUMyuPLp46eSNuKNzdkYjQmGbCJHxYAaSZcxgQdFtVKLuNmyfwC058cou5UOu2VsUBL0gEC6oRsO3q3fkmmclOafPrsMYD0Al9k4Inho1rjUKa4SCGW2oN2NqlDcihKlRrFhG+9O5nzXFv6QeNPFhxNc4AwJV0Pj+80Jowx/170n7i/LSMcYDjAuNCp4aJWAfoUWMR4SCs0bhJCa7sfvQ8nip4b9gZugwHw9YFATmEZHiuV1ncdsKX0nYPw9+iTUiZ6fUqrnbAjcRIuN60TSCjlAwfkcoJgRnjRptqFdYOSYg2PMn19blXuWarZHPgK5QXBtYomlol6FuTbjmYeLl5QtbMcbj5JSU4XPVjKlRGBFaxsIN9WLYPoEfrVEvi/1eUfybL2OIef2+whoRqNrei/jSn9Z/G2YQ+ilhV0FWKt6QnJbC/FN5EawRWszSWqOQLIPfln2L7ss0XPOd4D6BfpD1Diwnl7p90fFDboI0U8r+cuALxFp5OxoQwrJ9hEZFt6EjFM6C0ycQVJaxA4/jYraoDZmiLQmfET0/wBgPcAytG/Uc4tGMa56U5kTH/IYxHqdlQaFRBEW3LWaF0ydgarTSUcr87278wWWKujLEFwO+EViECQDTPohYXJs2VLb87eWJjGf3MMbjnCw4gwkZf4YzCEaEglV8jRC2T1S+v6M+fyIzfIP5uOGYAJ9aGOMBjkQili5843Nx8YRovhj9eGIpS1t5dzYwzYIzmBCMCC3G/9ZgWdFtqCxTyW5f3BmFDMfNh0uC3uz4FsZ4gONpVLvNuOqduOZVmeLgoeUY43FClk2NivmVZeD0CeEsPH1C4srdhjXCypSXnvTto2108SSoD0POG/Qt1oiAY5rSf3591o1r/pF3NfnuaYzxOBvjqVFXE1fywYjQQvx6dMKTZYy2T0DWaGVhtdSPBxemSw1ZfHNazfBy9cEYEnBUIkK0qO9X0uIJI6UILbq6UpmbgTUoJ2I8NWrJ6RNwHqEZ+Cm2wkeEcrGcS81Q8c7NAja1c8+X51wKueYgj2bdwiIwxgMcW90ajd8LHcI1n8mYlXvnIsbKKRigTPwkRBdhp/Ii46P0YERoBi1jSdFt/onJDMuqedWAgI08uHFordqQvFeXcf0oYjHGeIAzGNFleg+p4RT7o9KcY4d/whiP8zCqNWrReYSMtccnjtwRWrZGiOAkpspV+CplSdwabr+EnCEWv/mNTCQ1+SAArODzYT8GMYbftJU555PvnsIYj5MwGhFaVmINpkaFs2xDPULIjbd+W6ApNHElqCCW1n63/7MXMt7SYJO36vrVxxgScB4uEpdFPb8QF0+IKkRoyZVVqtxMrEE5OBaxRfxao4LXCMWQLGMZi0eEnjIP7na+psCaMQFjO6MWnZcb3uGB7k36tRuDMR7gbJoEt3mn7kCu+UTO/Lp3HiwW2k6hpoj7ZHaVuEhIocchwIjQQvwT6s3qCL1lntztXFW+NWMCPNfOblyj4S0Nsq6fRCzBGA9wTmO6vddZEsg1j0qz9uz9Gl84Di5PbfhE9eJ90paLP6unhRGhcJadUI9gRFgpnj++sjQpSlu8a9CFJZb0WyoVnEIGgBUtHPKjPyPhmqsVt2+c34YxHgeWrzZ8ovI/acsFRbctxJ9HFgsegCPj7yn87y/AWhS5GYvOLc8r/uQhWDSn6fg6/g2wBgWcl7vcY1nPRTJG/71MS6LFiTteJF41/ShggVx1HnfbW+Yl/IH8ESF0hGaowBqhoSPkf38BVsHQ1LK9nyTxCoq+5de5b5tRGEMCoGFwq8/DJhPFyyl5EvT52e8UsMve2vJ4n6he5o0IRdwOb5qlrbvD27E7Qv6GejN+Uv5/D4wIrW7trvnnpYY/ho7imtP7fYYxHgB0eraKHF29PddMltHfRs2GktzWZfEaISqxldCqg0KH7ggt3T4BU6O2cypm9TYmkWvWZuRfD1tBEnDKErAL7/Vf2F5Ug2uek+ev3w3f0qypgDci9JCaMSJExjsorJsv49AdoVW2T8DUqPXEXd+3PO0490XOnSG+e3O5q8zN1GMAqEQkQSyOXBHMGJK2NmsTDh/9GWNIDiaXN7Twlps3IrRd3W0zUkiqHMuKbiMYEVrV+fPnz1y4/PR5WofGXofcrqmLE2RELPqqzcxgvxCs0QFQkpvM44c3v3/36OwCEYMQYhD6OevMsz/TbycQfj5eXdq16t+/v0hkxucJ4DNeI4SpUduzrOg2QshLyl8jhBGhhbKzs9u/0X/oV/8sSgo86dHmuMv1fEOCOppZa0CHZv3wRQfAawX5hXzZ9n3u/F6aIPa7PrjpFrQsrcFbf55o2KbL48ePsQZYhfGnRj3NnRolDCM3LWvNtVtH7giNkmXM20foyaUnFWgKrJ6q6yTeHPHW7Zb/yx63xrNN3y719mTx6qiN82o1osf/MMYGgGkdmvWb22AM96mhFBM1659s0KJ+3tDvkyL/7DNsrFIJVYgtwd8+4WXm1CjJ+xinrVr9x7E7Qt4+QsKMSWAxKeJqojMsW6gpsnJkTuD8+fNPyBrasAgJqx6MPk511XD/FPSfZsbArzDGBoAQb3Z8O+gOxTXzJGxz2WJ/5jkKDstoMXrthk0YY6u6KpI1arsqa47cEfJHcqQ52yeQ8f9QLiwTmu/oydjsRhEkS4+mP05xNxQuDyz0OnOy2uMEmFkC9o5hmOgDmQH5odw9WVKmJzHfnclTNR24/8RZjLFVUSxi+ccYeErdzXq47epuO3JHaPH2CWTcEULiqAWy8gqQi+co+pMUD0Mt/wCl7CD5KyX1ys+H7xbA3imVSkLm9q94ea2C6tydL11VEcSHMjcp/A5bQEEpuW0PcrFcauZpazAitITF2ycQJI5WWOOQWiNrbn7pkcrd46shz9A/FBGeoswntWvXNvFYAOyBm5sbUuSwiIgS/RKkMBzN9tK1aIjLogahdTDGVkVVZF4U2XL7hMN2hAzLcKdPkARp7pZt462E0BGajarxNKOmYSTtoyHuqRZliILRiwf+Mm1AQADG2AAQqGd4V9GdgyrC9TD7a6DSMHxJ91R5dMzSaNUYY6uK+If5eFvQEfJWuGjYPiGE0byomcNBVOIkJugIzbT66JJDmgSu6UGhp6pPEyQtUModv62Ttv7fSoyxASDcquWLA099S96Pzid9T9G/BCoNOXf3pUXzd79P0ZSJh4MSKjoihKlRc1l8BpMOFJex2PrYn3dlX+eanhSr3KdM+/evGiu7tzu7MHbftrCwMIzhASCcv7//tVNH+j3b5vdTR7Rt7sOd6sAiw0DkJp35ffQXFAPFSIUq4J1q5yEzL1MGlTyS0Jpvu8NWlqEt3U2vA2uEFmAR++uxxftyb3L3eGjRT60/qDGsY1paWkhIiFRq3to4ANjVqFHj6O6tNE0nJSV5eXkRVPbH0Z+lSvUfL5epF59HffDt8FXm5n04p1wrjghhH6EQFUkZRXA2r/kYll1+ZNG+LEMv6EqjbxtNbNSyv7e3d+PGjaEXBFWXSCRq0KCBv7+/X1DjX3stDVIbPjmvaV588u97Cgr215ePP6iwZI3Q6EhCmBoVoCIpo8j4PwmqrJWLZunFh+Yfy7nD3eOuZZfXf7tFp5EYowLAFvzrhP0UPj+Qlyhzl341Z8/7RZQCX1BVg8XH0+vwk2Xg9AlBKjwihKlRoShG++WheWfyH3L3eFLoh/oTWnYZgzEqAGwnsGHnlT0W11EZctHva7M+jHoXPitMs+L2CSi6LUgFR4TGG+rhl/u1lFrVvP2zzucbKsX4atgVjac26zoaY1QA2Jp/aOsVPb76//bOMyCKow3As3v9js5RBKnSRUFBrBhFRSVqLFhiYqxRozERo8YaS4xGTYzRxJho9NOoibF3E1sUFBRUqoB0pNfjgOt3+/1YXJYT8BocHPP82pmdGd6bO/bdmXmLi7BRF2bJaz49/0l5fXkrvbo42qSeADDotgZonJ4ep6nVaB3hkgghUy2q+fTCJ88E+USNtRjb4THXfcBEPUoFgbQPXLe+2weu86xvfLzkK2oXX1ySW52nR6k6MuRFhSZbo20WdFs9q1GpVPrff//l5ORYWVmNHDnS2Pgtn0QikTx58iQ7O5tKpbq7uwcEBKBNPRmSk5PFYmWn1L59+yJapywnG9dS1d8apaFUNo2FH4DLMXm9tN5YzbB4Bk9JXekXV1cUyBtf8exEYLf/UjPPIXqUCgJpT4wdfb432rHu5tpEo4bncgUQL70WsWPEpt7d/PQrWweEp52xDNpmfoRqKMKsrKxx48alpaVRKBS5XM7lcs+cOTNs2LCW2m/fvn337t08Ho+o8fHxOX36tK+vL1EzadKkzMxMpY5isVh7C0Mt3ScAAKYME8ISrEbMh4qQTGZl5sqba6pBY06JHgKwvd/ntv4j6urqWukIgRgYxk7eO8d+u/n62sfGDY/mOkS28u6mTYNXDXYerF/ZOhrkZITGaiYjBB0h6LZcLp88eXJBQcG1a9dkMlliYqKJicmkSZPKy1vcEI+NjR01atTly5ezs7Nzc3O3b9+elpY2btw4kUhEbubn53erKVSqDrwbtTSWAdCnvmWeFT1fdmMVWQv2rkW+H7LO1n+EHqWCQPQF29FrW/hPo/hMokYMFBujdl17cVmPUnU0BFIhEXyASWUwqQx1R2i7yDKqqpyrV68mJiZu2LAhLCwMANCrV689e/ZMnDjxwIEDmzY1n1vuxIkTHA6HKK5duzYzM/PIkSMPHjwIDW1MTW5hYTFy5EgtPkLzaK8IYSamZrmXcfubJz9JkcYF95Aa6vpxO9iOnnqUCgLRL3Su/dr3D1if+vykacNLsxzBdj0/nFGZ9XnwciLRd1emSUpe9fdFQUcIun3jxg0AwOTJk4ma0aNHczica9eutdSFrAVx/Pz8AADV1dVqi6k+WhrLAABM6TATkzL/e3xoy5N9UtA4t+N4jM1T90EtCIFQzLgLZv+yqNYKJZnWXci/t+3fzTAMGwCgVkzORKj2vijoCEG3U1JSEAQhR4lkMpkeHh4vXrxQ/Y/dv38fQRB/f39y5cuXL999993+/fuHh4cfP35cJtPNL0ZL9wkAgCmz8auC7kEyhfzbW1uPZl4h/scRDMziGa/44ADNqrs+JYNAOgwox+T9eT+vFDnRSU/p2+XPV176HLrb12hnMgo6QtDtiooKU1NTpdM7S0vL+vp6oVCl2EJnz549f/78/PnzPT2brB7odLpcLudwOHfu3Jk9e/bo0aOVDhHJiMXioqKip695/vw51oJjg5z0CkZBNTl0NKFDV8IGhDLRmksRN8oaQ2lTFeAzgd28uQcpZlZ6FAwC6WggdGbY3B+2oX1NZY2PpnjBq0/OLiytK9WjYHqHvDVqxjTVYIS22xpVVUNIJBIWi6VUideIxeI3bykRHx+/YMECNze33bt3k+uvX7/u7u6OX9fU1MyfP//cuXM7duzYsmVLs+NkZWXFxMRER0fjRQaDceLECRsbmzdb1gnqGwsKTANTRhbSeJZbXlfZZY0hy+rLN9/ZkIc1bg4bycBqxLfv9NUCBQLemJb6+noAaXfq6+u1dzqCqEtL097zvZU77h3fWnajhNlwN0/BX3RxyabB69ytuug5Qjm/krhmIUwNnqgKWeNCWyASqDgCk8l8qwGmqoqQw+EUFRUpVVZXVyMI8uZZoBIpKSmhoaEmJia3bt0yMzMj3yK0IADA1NT06NGj169fP336dEuK0MfHJyAgYP369W8VmM5vdMCgU+lGRmo7P1gZc4lroUKkwQidlMLCQty/s1evXkI6f929LdVI4/LaWgy22o33HvNxKyN0nbnqOGAYBqe9/Wll2nuOX7IvrseGZz+/fP2ArEakXz7curbPIm/LvomJiUKh0NfXt0ePHu0nrl4RI40u45ZGFhr8XJmMRrtcKo2qwx+8qorQyckpKSmppqbG1LRxSVtaWmpnZ0ej0Vrp+PLly1GjRlGp1Nu3bzs7O7f+V4yNjd3d3bOyslSUqhVkpB1kDRzqQZfMxFRaWjp1zuK08nqxY6CCQu9jcpgxDEhI2+c96sE2/0V2Qe/qT0YIpNNgEzh6r6X9tpsbH5k0PI7ECLbl+UFOgvRhpr+MxuIUHbOUVJw79qu3t7d+RW0Hmqan12hrVO/GMv369QMA3L17l6jJz8/PzMzE61siLy8vNDRUJpPdunXLw8PjrX9FLpfn5+ebm5urKFVrQ5F2kFGNrEa7mh+hUCgcPHrCQ5+F5Yuv8cO2DB7BpIQ00YL966h7R34DtSAEojocF98t036ZUNu4dsEQUOdPCxkjEI5aVTbndOq4/SET3y8oKNCjkO0DOZ+difpZeUFbJuZVVUPMmDGDQqEcPnyYME45dOgQhmEffPAB0eb48eN79+4livn5+cOGDauvr79z507Pnj3fHLO0tJQcXw3DsK1bt/J4vLFjx2ryUZoib7Ii1MRYxqyL+RHuO3ioyCdc4T2SiQmmyz4TGj8iv3FNElp8M+OwiStMLg+BqAfd0nbFvKNLFW4UkmVfpVHOVDCfqygGdj6lYdsiNnytRwnbBy1TT4CO4FDv4eERERHx3XffTZgwISwsLD4+/tChQ6NGjSJ7Fu7YsSM9PX358uV4cc6cObm5uW5ubitWrCAPtXjx4ilTpgAALly4sHHjxtGjR7u4uEgkkvv37z9+/NjR0bGlA0K10N6PkLwirJXUYgAzbK/Yvy5cFU466iZLD6JsKTBufEGhYqD3M9Hnuw8jFB1E/IFAuiAInTFt1p4ny8a/CAT1r/+Nitl1weJlhcJlT3xCH+75Sq8CtgdaJiMEbZmhXo1H286dO+3s7A4cOHDjxg0bG5sVK1Zs2bKFHEQ7ICDAyqrRmL5nz54USmuHc4GBgUOHDo2MjDx79qxCoXB2do6IiFi3bh2Xy22ll4po7z5Bp9CZVKZIJgIAyBRygVTIobG1F6zDUlVVPYYazaIfLyBFPuLIAZM34a+bB3/YA7UgBKIVlx9VW7hvdDQ6UMpoWBpWMjAz2r55lXE3NHpZ71zwRCT3Cc3OCNssQ70aTzcURSMiIiIiIlpqcOLECXJx//79rQ8YGBh47tw51QVQC+1XhAAAU4YJrggBADVivgErQkwimjua+8jseCVpqrhiSpZ4RQKzX3fkoP5Eg0AMBC6XGy3sUUT/Lli2voDT8GARoSCb+2huuKWcX0UxsdCvhG0KX0KKLKPRipDa5IwQZqhXAe1jjQKlY0KRwR4TinJTfzo0978+NDHp59Ct3uQ/2f4E2gA06cbw4EH6kw4CMRBmvDeG9fSvV1TnM+gRbp0LUa9AQJQnY9OJ+byE+3oUr00RykQSeUOYfjqFzqIyW2/fLPqPLNPp0D7EGlAyHJUYoCLE5LKCq799eX31WbN6jHQAalzf82/K4SrUBhSlWt/a8u1Xa/QnIwRiICyaP9c+4yqSekcKGOcp3yG1oeSopJGm8s+efPfi5NcKoQHG7tAyJS+O/o1lOh0yXawIm7gSGtyKUFqS9+z0N98ZF5eZNupAFAOyGHCvjMOg/GhcnGBRl3/+/Ck7Ozs9ygmBGAYMBiPq5qXJH32cEbVf4Ng/hsr0oLLtQgTC18E/8tjICnnskv1zQ8etYvoE6VVYHaO9EyHoOBnqOxEKXZwRkt9caiQG5EqokNfePXsl9sTR7ogEbdSCZoC+dfgGzgCjhIQEmUzm6zuuWb8XCASiGTY2Ng//uZyTkxMfHy8Wi318xpg7Way7uTZf1mBIIqSAH+zF2de2fvRijPn4+QjjLdErOwvaOxECuCLUAJ1sjZoaok+9tDCr5PQPv1Ny7zk2eT/wZnffNvprLtsSAODm5qYn6SAQw8fFxcXFpfGM8Lcph3b89+390md4UQHABTs0s+zm0p2PnCcuZfU2hDT32jsRgo6Qj7DToRNjGQOLsoZJRDUXf3t48LOVpnn3uE2WG/qIAAAgAElEQVS++kk9Qve/tw/XghAIpD1hUZlbRm5a4j+HQvJUTjJFVznV/XNhW9WxHfLa9sjh2qbUkJ0INUpGCOCKUAPIZ4SaxRoFAJgwDCc3ryg1tvLcz5dp5Wc8UTkpXj4dpUYELQnrMVKPskEgXRwEINN7Tva28tx0f3vV613EWir4wY0WW/Fw3s5ntuMWcPqHgk6bYIS8kNAsBxPoCLFGOx3kM0LNYo0CQ4myJudVVJ3cnfS/jV9ZVf7VnULWgo5GdgfH7oFaEALpCPS27nlo3H5/qyYH81FcdI2LKObqj2V7PpPkpulLNi3h62RFqPd8hJ0OGUaKLKMT94lOqAgxqaT2zt8V9/6+Yim/4kuXkt4HEICMcwv9NGA+UyOHHggE0hZwWRZ7Q7efS7t68NlR6euHWBkT+dqLGlSdM/OXFU4BY0zfnYNyNDxm0xdNzgiZGm+NkleEUBGqADwjFCY9qr546D+k9LQ3hUdrMgMWTLM1Az/vbxegL9kgEEhLIAAJ9xrvb9Pz64ff59a8wisxBDy2QBNMkQk5/4zfEWU5djZn4Big6ZOt/WmiCOkaG8s0Kiy4IlSJpiHWNF0R0juB1ejde/d+/+tCYnKKubnF0P59P1s030xcw7t06FlZ8unulGyO8lcc7DBgVf9PNTbcgkAg7YCbuetvY3/49fmx8+lXMdDgeC+iIH93p/wnFk67+/PABxctx34kd+vz65Fj/9yPLigs8PTwmD5u1LTwKeQQ0B0E7SNuAwCoSFuFWDNcRajQgfsEk8pgUhkimRgAIFXI6qWCDhVuFMOwmQuW/JNeWT1kKZjxFRDw8jNv2i2fzurF/tcaLfJU/nKt2NxP+swZ4TxUL9JCIBC1YFDonwV+PNRhwL64Q1m8XKK+jIH85Eo9KSkZ8e+3FvtFJ2XBz/usBSF2qaUZd/93Yu+vR+9eOctmd6AnFWgL9wm4NaoKcq0z1OOY0I1xRQgA4ItrO5Qi3LP/wLUSRu2ckwAAC1n1TOo5q54PL1sYC9/4uAwKfYbPpJk+4Uwqo5mBIBBIR8XfptfhsL1XMv85nHCCvK6qpiNn7SlUO05oVdxoseQUZUG+Yx++Y5/4R0cWfLby1OEDepT5TZo61OvijBCuCFVBJ2eEAABThkmZoAK/rhHzuxnZaCuZ7vjx0FHw6WFX9IwPdk/EKU1s4dc1zHHwkr5zbTjW7SsdBALRDSiCvuc+NsQp+EjiqUsvb5Df8mUIiLZEAUh2w5b3EZtnIMGFQwbc/fFIbW2tsbGG+kbniGRiYjlBQ6kaLyfgilBtdBJZBigbjurtmFCBKUrqy17xC/P5hQW1RQW1Rfm8Apcv7QDyFQCgWTMeKoIOdRwc7jW+J9ernaWFQCA6x5hu9Hngwkke755Nu/xv9h3h62QOODIEVDOrueAyF1wGq21mXlvkaunc3cSuu7Fdd2M7RxN7O+NuNI0ys2qPTpaDADrUa4BO8hECvboSVgmr7+VHPS9NzucXFNUWS0mphhtowbkWlTHRDOzv9b9ZsszbWkgIBNKeOJrYrwj6ZFGf2csOrMnmlGEsQbPN+PK6+LLk+LJkogZFUFuOtYOJfS8r7xCnYHvjbu0lsm4OCIGyHyEMuq0Cutoabf/gMnWS+shX0bdy7z8vTVKoEz3BRAqA1OUZZUJJXPFqq1yoBSEQQ4VDY4d1f2fuyef0cRMD5ec5lNRKxltWSApMUVRXUlRX8rjo6eGEE96WHiOchw53GsJltXk24KYmo1ooQrgiVBddbY2S31/aOiVhvVTw89Pf/835T6qQqtIeBcBCDFwEih51tHjKqJOmH9ajLCARc++P/PjKqTYVFQKB6JewsWON1n1dEvzJv8ZbqHLZlJKLwZKLRez6TCOknAHkbwvGllr5MrXy5YFnvw+wC4wI+sSazW07Ucl7aWY6WxFCRagCulsRNu5ot2mS+tyaVxsfbM/nF7bUwFQG7ASYrVhhK8JsxZitCNiIMakUOyZyWdv7qxqWFQAAlKRbnI/4atl8V1fXthMVAoHoHTab/ceBPe8vfa9i4vcyt0GnTcMvyt79KGnnOkWsGZNSzgAlTFDCQEuYSDETlDDRSjrA3hhEgWGPCmNfXH/51ZCVAbZ+bSSqTrLyArgi1ADdrQjJSerbamv0Xl7Uzph9QplIqd6dYzewGnhk5tuKFKym3zvKNjIKnUjrP5Z64DD3aDhTKKaiqLNj92/3bx4y2BDytkAgkNYZOSIk8uKJLzZtT7zyhRQDLBoVDAt23HCClv6YfueMbXUZAI1PDQkKSphInmO3aFtWkqBAgTWqRZ64ZuXdTR/7z3rfZzLSkumBFujqjJDsCAcd6lWCfJRK0SLOQltHWZNj8l+fH/s79RJGel2z49gMZzr3S8mxepX7ZheUY2IUPMHonYkoywgAsGX9l1vWf6lzwSAQSMfHy8vr2unjyrVW4zkDxwqf/ce/9ZesrACvoyuAowBzTCsKTgN8C/O4ni736fxMfj5+V4Epfn1+LLXi5ZqBn+vcW7pGF2FlQFtmnzBcRdix3SfkcnlJSYkp12xD5PbnpUnkWyOpDh89KaEIXr3Zi8q1Mxo+mRMUitDoupIEAoEYHgiFyu43kh0QIkx8WHv3rCQ/nXzXpKo6JLI6hEa77u/yJ5JPGOU9eBWdW/Pqu5AtMp7EysqKTtfNc6ZGV2eEcGtUXWQKHWSfAG3gPvH06dOFX6wvLK8GJja274hMezUmf6BiyPuv5GNKs97sRXdwNxr6HjsgBHS8KIIQCKSDgqIs/2CWf7A4O6XuwUVh4kNA9jqQSsNiX7oYI/s9GDVoQ30+v2DCL7PyL9AxfrkZk7Zr85oJ74ZpKYWutkZRGFlGXZr4EXYY94nbd+7OWLa2cuYRYOthRXloSt9D3LKUYMszpa71Tc6zEQqV2XuQ8dCJdBcfLf80BALpsjBcezJce8pKX9U+uCiIu4uJhcQt71psa7J4bw9qDqfhdJDZjc5cODVXOqO0pmTOpkVbXhUuW/yxNn+9VlxHXGuzNUolZ5+AK0JV0EnQbQAAi8qkU+gSuQQAIJFLhDIRS9MEfnK5fM6ylZULLgMTGwusoCf1Z0JXdxdi69OlJiSnCdTIjNM/1GjIOIo5DI0GgUB0ANXGwXzqMtPx84XP/qu9f1FW2nBAyBVjm9KkP7pRn5s2LLkcqWepYudM0wHVC/7+et/waZMm2NhoHl2S1yYO9VARqkCTM0LtthNNGMYVgkr8mi/ma6wIY2JipI5B76CFk1+dSO72KP21UDQF+DRLRmhBuouP0aB3WX2GIlSaNmJDIBDIm6BMNmdQGGfgWFFqbF3UVVFaHFAoaAqwKFu2xpfGo+HrQsyPuuvLPN/LJqH3A96/cOnK4oULNP6LfF0pQpiYV110tSIEAFgwzQhFWFxfpln0amlJHhJ5/qZHkVXupqvdKOnGjSJNL5A7CDEZSjMdMMpo8DiaPXQBhEAgbQyCMH2CmD5B8ppKQdydqrvnjet5i3PkO92pGAIAAOUMJNcy6UD2c5ElJSfVWJTiy/AKRChqq4waMZ9wDKNT6GwaS2ORmxjLwBWhKjRNw6TVx3QycXhZ1WDAksvL97f2Vb2vtDBLGB8lePafrLLYEQCAglwOcsa+8ev05StM632+5Iknjx00ZdoMbeSEQCAQdaGYWhqPmJZv7b1549djevuMKn/6r3XDYWGkJepXgw6slHtjvIpDm1EjM3afoSz/YIarL3hb5BqCHF4ece1k0l0bP8Wm2Seg+4QK6CroNgDA2cyRuM6pyVeli7QkTxgfKXh+X1baxAtCioJfXKiy178Eqpx+E9l8wNnT6uqondtWayMkBAKBaIynt/eDF2lnxxw1R+r7SldLaVV4/REninstxpVgAABFHa8u8nJd5GWUY8L06cf2D2Z69wNvM0XM5jU+M11Iz1INQBEUAQjucq3AFBjAdOX+b7iKUEch1gAArqQvL5v0dqOMQiHOSRElRQuTomWVxc02uWxLKWA1fnOJ8uUVVE/Go6ODfV27d++ujZAQCASiMVQq9ZO5s/Zc3Vg9cWeMYmMf8CUKJAAAAQU55Uj5LLNJ6htFPV8Qe0cQe4dibM70HcDqNZDh7t+Sc3MuafHgbKqVIgQAUFCUiCkjU8h1lVjKcBWhjhzqAQBctDE6e0pxWnR09MCBA4kaTCISpT8XJccIU2IUdTUtDYLQ6Iqegf8wk4C8IUFlSU3fiuRiixdze3MEp86e1EZCCAQC0ZJNa1a+WvbFpV/erQz4KMd7WA/rf/H6WAu0csAQq4R4hbBOqYu8tro++kZ99A2EwWJ6BbJ6D2R6BaKcRnOY9PT0OwmR4HWkGhO5kZZCUhCK7HXcODlUhG9FVyvCuKdPJ3y4wHWNM4UqBwDIKfKJG74N83T5betqcWqcKOWxOCsJk0pa6o5QaUyvAJZfMLPXwFOZ1+oT4vB6mpzm9aRgqit9zMzFQ4YM0Vg8CAQC0QkIgvz+056I5OSL124+T8gQBLMFTAEAQIGByw6sDeF/itKeCuMfiJIfK0T1Sn0xsVCYEClMiAQoSnfyZvUMYnr323vu5q5DpzxW2hJqZvHCTaLVoqmTJ2osJBWlil9nJNah4ajBKkKZLlaEdXV1732woHjuGVv0F2OQgVfOGBswJTuudNu8VjoiNDrTK4DlH8zsOQBlsgEAIpnoTNplosGcvjM+/GiqZlJBIBBIG+Hr6+vr6wsAiHwVs+HBdrzybl7knF4zHHwHsHwHYDKpOP2pID5SlPz4zTUiUCgkOSmSnJSaq0eHi4F4+thb1Mf4HTnGLPrg2pL1Y/v09nVzc9NMPHJwGbXStbaOwSrCpitCDY1ljp/8k9fn/V4cmYNQweM0VPpKY1zpzX8BKNuI6RPE6jWQ6RWIMJpYCV/MuMETN2yccmjsiR7aRi2CQCCQtmOIQ/8eZs5ZvFwAgAJTnHxxbs2AzwC+y9VzALPnAEwuE2ckiJKihcnR8prKN0ewZYC+0oe3XmsZEwk7CCt4PnrDN3t+PnrgB82kIq9qdJiAwnAVoXYrQllZgSgj3iHhRowtMM+8e8MGPcFpmKtXbGU7JSrXjunTj+U7kOHWq1kbKolccib1ElGc6vWeEZ3zZjMIBALpICAA+dB36pao3XjxVs692b7Tuxk1xpdBKFSmVwDTK8AsfKnk1UtRUozwxRNpUTYgJXgiPy2DaisW5KwRIIzkOkHt3bNMjz40e1fV3TBwyKsauDX6dsgrQhX9CKWl+ZLMJHFWojgzSc6vAgD0oQM8OVJ3UqLAAhYKgFyGAZqzj0mfISyfIKr1Www+r2T+WyFsMEdmUZmTPd9V78NAIBBIuzPMcchx09O4z5hMIf/zxfkVQZ800w5B6I6edEdPk3dny2sqRSmPRamxVfGPWBSkgNmo5+wFGACAjYmDLCg1lw/XAICyjOiuvgz33owevej2PVTJKNBGPvWGqQjFYrFU3mjvi8kVzX5QTC6TFmRKcl6Is5PF2S8UdbyWBuwubHzHyWVT5zmsyjyyPCPxGoXy9rWmTCE/nXqRKE72HKdNkCEIBAJpH1AEmdlzyjePGrYxr2fd+qBnuA3HqpUuFFNLzqAwzqCwd4KCzadsMzE5DEDDkZCDEFNqrBDWiVJiRCkxAACUyaa7+NCdfRg9fOmOngid0ez4Mknjg53H57UujOoYYE6fyKiHrv4DpPLGl4WeQe8kJibi14q6GlFKTM21/5X/tLpo7ZSyH5bzLv4mTHzUihbkUYyimQNRRcMXI0fkj/JTBg8ZrIoWBABcz7pVWl+GXzOpjKle72n4wSAQCKR9Gen8TndjO/xaqpD9nXax9fYE8z+a+fzRzRq6mKhJoA0qoVq01F4hEohS4/g3jjc+mS/8Knh+X17d8PAsKiryGxxSUtWYAmjk5PePnzqt9kdqDkNbEWZnZ09ZsKx8wSU3dBlRaTH56yMrF6+eNgYtyZVVFKkyDsJgMVx8GO7+Z55lrP47sjJ8ph84bApe4Hddi/7af+hS6yPgyBTyUy/OEcUJbmPMmabqfCAIBALRGyiCvu8zeffjn/Di5Yx/ZvqEW7LM39px2eKPL96f0nC2BIAUM1ljvMD0wcb5PYy3fDhO/DJenJWkqG8+wysml0ny0iR5aeA+AABQTC1pjp4HL98zGjRHZhQDQCHerGr2sYjdn9vbWI0YEaLlxzQ0Rfjl1p0V7+5AzK2JLwDFwKXqvcDHRJH8qHVjW4TBYrj6Mtx6MXr0pju642Yv80YAxz53Vn+9VB4gAwENFi7L1y0yMzNTRZ7bufeL60rxazqFPt1nkqafDAKBQPTAaNeQ48mnS+vLAW73l3ZpcZ85b+1FpVK//n7NxsgdeFGWX+F1acaXn348Z9YHAACjIeMBhklL8sQZCeKsJHFWUivRSOQ1lfKkRwtdGAulf64V0fJfG+AgdEbV+4c+Wz83BSpCJWJin2LL96FY4z4yqrwv3QSKqSXdxYfh6stw7Umzc232tHbkyBHPRo64+PL6D7EH8ZpCQfMR1N7kTFrjwjGsx0guq8WdAQgEAumA0FDqTJ8pxNPvSuY/s3vNUCUbXT6/gLieOWrS8nWLmtxGEFo3Z1o3Z6Oh7wEMk5a9kuS8EGenSLJTWtm3Ix9HsRWCegvvijqxWCxmMJo/U1QRQ1OEcgwDCIpiCIoBBQIAAEyFcs53mp0r3cWb7uRFd/amWtqqOLKLmRNxndNKxFES8WXJmdU5+DW+w6Di34JAIJCOQ1iPkf9L+qtaxAMA1Enq/8m+q4ondHZN43PyLeG2EYRm40izceQMGAMAkPOrJXmpktxUSU6qpCADkzQeNDLkGHgdaNtKxi+nAoRtxufzray0spoxNEXIotOBRCCjs7vXWecblwEAhlVgr+g28VTH8szYL7/9ju7g0VJw2NYhf5H5/EI5Jn+re+LZtCvEdbDDAFuNEhlCIBCIfqFT6BPcxxxL+gsvnku/+p7H2LdmfiAvGFzUCbdNMTFn9RrE6jUIAAAUcklh9pFd24VUc39G7dCKojRjAADoJmQ8ogQAADB+qYWFtjtthmY1Gj4hjPHkBADgFPVnBW8WqJ71rdGxQR6HV6Uj5iGTGa6+mmlBAIAJ3ZjY2JQqpAX8txjdlNSXPSx4TBSneI7X7O9CIBCI3nnPfSwR4TqfXxBb/Lz19jKF/BW/kCiSd9TUA6XQHdx9p8/fFlsQ4nZgsfWfUt5iak34JeywDKEiLyP9vD1VNOBv7Y9o2b+jsXF1RPf445SEKwqARjEmPmBOrKKY0B//0aM4cvH8uVoOrlZiwgvp14hQeG7mrn7WPbX86xAIBKIvLFnmwxwb0wOcS7vaevtXtYVSRYOtBpdtaUzXKu/EkCFD3nE24lzbUgdo0YxRd+nvixA2yI2zufzFbz/s0GZkHENThEZGRo/vXA8rv2T13QDuXwutTs2z2h00FXn28N8rNBpNy8FdTcnHhK0pQpFMfD3rNlEM94LLQQgE0rmZ6j2BuH5c9JRsC/Mm5H1R8pNTY/7+32/L/FjWu4Nsjn/APfup9b7hQdHboq6ddXZ21n5wQzsjBABYWlpe/uuYRCJJSEhgMBje3t7aq0CcpivC1uxl/sm5y5c0OH6aMUxHOAXrRAAIBALRF54Wbj5czxcV6QAADGAXXl7/PHBhS43J+Xi1TEyPQ6VSd2xe/81Xa7Ozs4uKigICAjgcnUVsNrQVIQGdTu/du7cOtSAAwMVUVcPRiy+vE9cT3MfQKRoeTEIgEEjHIZxk63Az+069VNBSy2zSnplaljKtg6Jojx49+vbtq0MtCAxYEbYFLmaOhKFUQW0xkR9Sidji59mv1SQVpUxwH91O8kEgEEhb8o7jYCs2F78WSIXkAyAlmpiMamwp015ARagGLCrT1qjBBUKBKV61sEV+Lr3Ra4L8u4FAIJBODRWljHdrfLM/l36l2ey4ErmkqK4Ev0YRxNnUoZ3k0xSoCNWDvMbPbs5eprC2+HHRU6IYDr0mIBCIAfGeR+NZT3FdaUxR3JttcmteEQrSlmPDVCEMjX6BilA93hpf5mTKWcXrvJRelu4+XM92kgwCgUDaHiXrvxPJjU88Ap1byrQ1UBGqh0urhqOJZSnkTXPoRA+BQAyPKSR/sJSKtKuZ/yg1yNY0poy+gIpQPciGo0pbo1K59LsnB7DXWS+cTR1CoNcEBAIxONzNXYd0708Uf40/ViWsJjcgu1l3fEsZABWhujiZdCdCjJbVl5cJKohbp16cy6t5hV8jAPkiaAkV1TbwDwQCgXRAPu+3iE1j4dd1kvp9Tw8Rt0QyUUZ1FlGEitAAoVFo9sbd8GsMYMv+XYPH08vnF/6RfIZoNs4ttDeMqQaBQAwUazZ3fu8PieK9vKjowjgAAF9cG3FnY+XrBSIFoTga2+tHRHWAilBtBtgHEtcl9WWf/rsmtfLl949/liqkeKUFy3xRn9l6kg4CgUDag8me73pZuhPFH2IP5tW8+vTWGjz0DE6ArR+NorOQJm0HVIRqs9BvVrDDAKLIE9d8+u+X8WXJRM2ygAVaRpiFQCCQDg6KoKv6LyWOikrry+Zd/4w4HgIAeFq4bRi8Qk/SqQdUhGpDo9C2Bq8Z5xZK1MgUcuJ6gF0gtJGBQCBdATdz16lejZG4yU/CAFu/vSO/MWWY6EMutYGKUBNQBF3Zf+ks32lK9UwqMyJosV5EgkAgkPZnbu+Z3YxslCqHOw3ZOewrwpqm4wMVoYYgAFng9+FngQtRpDFN87zeM2EaeggE0nVgUhkR/Zq8/U/2fPerwas6xdEgAVSEWjHFc9zGwSuZVAYAoF+3PjDvIAQC6Wr0twuY7DkOAIAi6AK/Dz8PXEReHnQK1MtHKBaLY2Nja2trfX19HRxUiqMqEoliY2Pr6ur8/Pzs7OyabZOQkFBUVGRnZ+fn56eWPB2BEKfgQFv/SmGVMyk3BQQCgXQdPg9cOMVzHINC76Q5BtRYEV6/ft3BwSE4ODgsLMzJyWn27NkSSfN5iAguXLhgb28/dOjQsLAwBweHhQsXymQycoPs7OyAgAB/f/+wsDB/f/9+/frl5uZq8DH0iwnD2MXMCWpBCATSZelubNdJtSBQXRGmpqaGh4dbW1s/fPgwPz9/7dq1x48fX7VqVStd4uPjZ8yY4eTkFBMTk5eXt3z58kOHDm3cuJFoIJVKJ0yYkJGR8eeffxYUFPz5559paWnjx49XUpYQCAQCgbQhmGrMmjULAPD8+XOiZsSIETQaraioqKUuU6ZMAQCkp6cTNYMHD2YymZWVlXjx+PHjAICdO3cSDXbu3AkAOHnyZEtjrl+/ftu2bSrKvGvXrqNHj6rYGKIrZs2a9ezZM31L0eUYOHBgbW2tvqXoWvB4vODgYH1L0eWIiYmZO3eubsdUaUWoUCiuXLni4eHh7+9PVE6bNk0qlV6/fr3ZLhKJ5MaNG35+fh4eHkTl1KlTRSLRzZs38eLly5fxcchjAgAuXbqknjJvgZKSkpKSEp0MBVGdwsLCioqKt7eD6JSMjAyhUKhvKboW9fX1mZmZ+paiy1FRUVFUVKTbMVVShPn5+TweLzAwkFzZr18/AEBiYmKzXbKysgQCQbNdkpKS8GJiYqKVlZWzszPRwNnZ2crKqqUxIRAIBALROSpZjZaWlgIAuNwmB6F4Eb+lYhdLS0tyl9LS0m7duil1tLS0bGlMAIBCoaiqqsrOzsaLDAbD3r4TRHSFQCAQSIdFJUUoFosBAGw2m1xpZGQEAGhpNwbvwuFwWukiFouVGgAAjI2NWzEcjY+Pj4qK+uuvv/AigiD79+9XUrcEBQUF9fX1kZGRLY0GaQt4PF5ycjKTydS3IF0LqVQaExNjZmamb0G6EBUVFRKJBD5h2pmUlJTq6mrVp93FxaV79+6tt1FJEeIqsKamhlzJ4/HAG6pOqQvehgAfgejCZrOVxsS7tDQmAMDd3f3ly5fk//ZvvvmmpcaVlZVUKjUuLq6lBpC2oKio6Pfffz958qS+BelaUCiUTZs2oSgMkdF+KBQKAEBERIS+BelaCIXC6upq1ac9PDx8zZo1rbdRSRHi6lTJAqK8vJy49Sb4jmXrXezt7V+9eqXUsby83MmpxUSOP/74448//qiKzBAIBAKBqIJK74+2trZ2dnZRUVH4GxDOgwcPAAB9+/Zttouzs7OFhYXS6lWpS0BAAI/HI5vGJCYm8ni8gIAANT8FBAKBQCAaoupGyrRp04qLi2/fvo0X5XL5yZMnTUxMwsLC8Jrq6upz5849ffq0YVwUDQ8Pz8nJiYqKwmukUumff/5paWk5atQoYkwAAO5NiINfT58+XduPBYFAIBCIiqjob1hcXGxjY8Plcn/++edLly6NGzcOAPD9998TDR4/fgwAmDNnDlGTl5dnaWlpa2v766+/Xrx4MTQ0FADwyy+/EA0UCsWoUaNQFP3yyy+vXr26evVqFEXHjBmjKx9JCAQCgUDeiqqKEMOwlJSUoUOHIggCALC2tt6zZw/5bnx8vKOj48qVK5UqBw0ahGvcbt26/fzzz0pj1tTUzJs3D7cwZDKZ8+fP5/P5Gn8YCAQCgUDUBcEwTK0VZG1tbW1tra2trer2aXw+v76+3tbWFmkhN4dYLK6oqOByuQwGQy1hIBAIBALRErUVIQQCgUAghoR6+Qg7OAqFIjU1NS4u7unTpyUlJX5+fuvXr39rLwzDjh079vvvvxcWFtra2s6ePXvhwoUtLV4hLXHy5MlDhw7l5+dbW1t/+OGHS5YsaWXPICsra+3atUqVQUFBK1eubGMxOyulpaVbt269d++eTCbr27fvxo0be/bs2XqXoqKizZs3R0VFyeXywMDAr776ytPTs32kNRjI096nT5+NGzf6+vq20n7Pnj0xMTFKld988427u3tbimk4iMXi+Pj4uLi458+f8/n8adOmhYeHv7WXSCTatWvXhQsX+FfCXcAAAAjHSURBVHy+h4dHREQEbpKiBnremtUpROg1CoUCABg9erQqvXBfyyFDhqxbt27EiBEAgE8//bStRTUwtm7dCgDo37//unXrRo8eDQCYP39+K+1jY2MBAI6OjgEklA6YIQTl5eXOzs4sFmvhwoVffPGFjY0Nh8NpPcVHUVGRvb09h8NZvHhxREQEl8s1MTFJTk5uN5kNAA2mferUqRQKJaApSUlJ7SZzZ+ePP/4gP8M3b9781i5SqTQkJARBkGnTpq1du9bb2xtBkFOnTqn1dw1KEVZWVu7bt+/hw4d4wBpVFGFKSgqFQgkLC5PL5RiGKRSK6dOnIwjy5MmTtpfXQMjKyqLRaCEhITKZDK+ZM2cOAODBgwctdcEV4cGDB9tLxs7N0qVLAQDXrl3Di1lZWUZGRgMHDmyly9y5cwEAd+/exYupqalMJnPEiBFtLqsBocG0T5061czMrF2kM0zi4+OPHDmSkJBw584dFRXhkSNHAABbt27Fi3V1dZ6enlwuVy27S4NShARSqVRFRYgvB2/cuEHUREdHAwCWLl3algIaFFu2bAEAnDt3jqhJSEgAALSSMwwqQtWRSCRmZmbu7u7kypkzZwIAUlNTm+0iEAjYbLafnx+5cuLEiQiC5OXltaGsBoQG045BRag77t+/r6IiHDp0KJVKJdLcYhj23XffgVbz2r5JV49MGB0dTaPRhg8fTtQEBQWZmZk9evRIj1J1LqKjoxEEIW/K9+7du1u3bm+dw9ra2qioqMjISJi/sBVevHjB4/GUzjzw/Wf8pe1NEhISBALBm12w1+95kLeSmpqq7rQTZGRk3L59OzExUS6Xt6GIEADkcvnjx4/79etnYWFBVOLfmlrPcIMyltGA7OxsS0tLstsGiqK2trY5OTl6lKpzkZOTY2xsjKcWIejWrVtycnLrHVetWoVfoCg6adKkAwcOWFtbt5WUnRY8GYtSwjK82NKvFK9XqwtECY3nkMfjEdnIbW1tt2/fjm9TQ9qC4uJisVis9DXhka7V+ql3AkWI73O2Ao1G03jwuro6W1tbpUoLC4uMjAyNxzQMVJ/2uro6c3NzpbsWFhYSiUQsFjfrG8pmsz/++OPRo0fb2tqWlJQcO3bs3LlzmZmZT548odPpOpHfYKitrQUAkF94wevUnnw+v9kudXV16naBKKHBtAMAevfuPWDAAF9fXzqd/uzZs127ds2bNw9F0dmzZ7e1wF0T/GtSev6YmZmhKKrWT72jK8KSkpI3k/cqIRQKNc5+R6FQJBKJUqVYLKZSO/rMtClqTXtLcwhem369iY+Pz2+//UYUp0yZ8tFHH/3xxx9nzpz54IMPtBLd4MB/ikozjE9vS6+A+LSr1QWihAbTDgDYsGEDcT1s2LDx48f36dNnw4YNH330EfTIagvwr0nprV0qlSoUCrV+6h39cW9iYrJr167W22jzv21hYYEnhyJTVVWl9CbY1VBr2i0sLFJTU5XuVlVVmZqaqv4+sWjRoj/++CM6OhoqQiXwn2JVVRW5Ei+29CvVoAtECZ3Mobu7e0hIyJUrVwoKChwcHHQuJERXP/WOrgjZbDZxktQWeHt7Z2RklJSUEBuktbW1hYWFgwcPbrs/2vFRa9q9vLzi4+Nzc3OdnZ3xGpFIlJub27rrsRJ4NuY3V5YQLy8vAEBaWhq5Ei/it3TSBaKEruYQ/2HjS0mIzrG0tORyuUpfE/5e7u3trfo4Xd1qNDQ0FMOwq1evEjU3b96USCS4eRhEFXAbrcuXLxM1d+7cqa+vV2sOr127BuBjujkcHR29vLz++ecf8sP00qVLdDqdbO1MxtPT08nJ6fr16zKZjNyFzWYPGTKkzSU2CDSY9jepra198OABh8NxdHRsGzEhIDQ0NDMzMyUlhajBn0XqPcPVd/Do0CQmJsbFxeE5oQYOHBgXFxcXF0f2nQoMDHRyciKKfD7fysrKwcEhPT0dw7Dc3Fw3NzdTU9Py8vL2F76TIhAI7O3tbW1t8cAlBQUFPj4+HA6nqKiIaKM07Tt27Lh+/XpVVRWGYdXV1Xv37mUwGGZmZqWlpe0uficAP09dsmSJWCxWKBQHDx4EAHzyySdEg0uXLllZWe3evZuo2bt3LwBgxYoV+HnJDz/8gBf1IX5npdlpX7x4MdFAadpTU1O3bNmSnp4ukUhkMll8fHxISAgAICIiQk+foPMhkUjwh/ahQ4cAAIsWLcKLhJtgaWmplZXV1KlTiS6xsbEoig4fPry6uhrDsPv377PZ7P79+ysUCtX/rqEpQicnpzeV/ZIlS4gGeMwkcpf//vvP3NycQqE4OTlRqVQTExOyfz1EFaKjo7lcLj6HNBqNw+FcunSJ3EBp2ocNG4Z/NSwWC7+wt7ePjIxsd8E7BwqFYuHChQAAMzMz3MPknXfeqaurIxqcPn0aNPU+lsvls2bNAgCYm5tbWVkBAEaNGiUQCPQhfmflzWkfOnRobW0t0UBp2okooyiK4sbSCIJ8+OGHYrFYT5+g81FQUNDsgu2PP/7AGxQVFQEARo4cSe71008/UalUFouFH8S6urpmZWWp9XcNLftEVFSUSCRSquzevTux53bv3j2xWDxmzBhyg/Ly8gsXLuTn59vb20+aNOlNhwrIW6mqqjp//nxubm63bt0mTpyIu/IQKE07n8+PiopKT08vLy83MjLq1atXaGgoTMLVOtHR0ffu3ZNKpYGBgWPGjCFb5BYXFz979szDw0MpuHNkZOSDBw9kMln//v1DQ0NVT50GISCmPSAgYOzYsa1Pe2pqakxMTEFBgUgksre3Hz58uFonVRCxWBwZGflmva+vL/5YFovFt2/ftrKyCgoKIjd4+fLl1atXq6urvby8Jk6ciB/Nqo6hKUIIBAKBQNQCviFCIBAIpEsDFSEEAoFAujRQEUIgEAikSwMVIQQCgUC6NFARQiAQCKRLAxUhBAKBQLo0UBFCIBAIpEsDFSEEAoFAujRQEUIgEAikSwMVIQQCgUC6NP8HtuL/oYBIPkwAAAAASUVORK5CYII=", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's solve for a fit\n", "ourvander = vander\n", "p = ourvander(x) \\ y;\n", "\n", "# And see how good it is\n", "scatter(x, y, label=\"data\")\n", "s = LinRange(-1, 1, 100)\n", "plot!(s, runge.(s), label=\"true\")\n", "plot!(s, ourvander(s, length(x)) * p, label=\"fit\")" ] }, { "cell_type": "markdown", "id": "fdceca0e-b83f-46cf-a31a-80ca14edf489", "metadata": {}, "source": [ "The singular values here show the ill-conditioning." ] }, { "cell_type": "code", "execution_count": 10, "id": "f6eca3cf-b684-40fa-94f3-7f147e22472c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "20-element Vector{Float64}:\n", " 4141.821777889664\n", " 756.1886115696186\n", " 11.201394442103451\n", " 5.200366811378892\n", " 2.3263899157608905\n", " 2.288653157584787\n", " 2.2826626548099376\n", " 2.2826582312605956\n", " 2.282657730773874\n", " 2.2826577307583387\n", " 2.2826577297322554\n", " 2.2826577141928723\n", " 2.282593863235459\n", " 2.282352200318817\n", " 2.2484549740292827\n", " 2.2449230243660097\n", " 1.9014541632683717\n", " 1.7794033223452121\n", " 1.0093167855538236\n", " 1.0064482710909068" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "svdvals(ourvander(s, length(x)) / ourvander(x))" ] }, { "cell_type": "markdown", "id": "20de1213-2306-499e-b4fa-c42314a5d49d", "metadata": {}, "source": [ "## Chebyshev interpolating polynomials\n", "\n", "Define\n", "\n", "$$ T_n \\left( x \\right) = \\cos \\left( n \\arccos \\left( x \\right) \\right) $$\n", "\n", "This is a polynomial, but it's not obvious why or how this can be true.\n", "\n", "Recall that\n", "\n", "$$ \\cos \\left( a + b \\right) = \\cos \\left( a \\right) \\cos \\left( b \\right) - \\sin \\left( a \\right) \\sin \\left( b \\right) $$\n", "\n", "Let $y = \\arccos \\left( x \\right)$ and check\n", "\n", "$$ \\begin{split} \\begin{split}\n", " T_{n+1} \\left( x \\right) &= \\cos \\left( \\left( n+1 \\right) y \\right) = \\cos \\left( ny \\right) \\cos \\left( y \\right) - \\sin \\left( ny \\right) \\sin \\left( y \\right) \\\\\n", " T_{n-1} \\left( x \\right) &= \\cos \\left( \\left( n-1 \\right) y \\right) = \\cos \\left( ny \\right) \\cos \\left( y \\right) + \\sin \\left( ny \\right) \\sin \\left( y \\right)\n", "\\end{split}\\end{split} $$\n", "\n", "Adding these together produces\n", "\n", "$$ T_{n+1} \\left( x \\right) + T_{n-1} \\left( x \\right) = 2 \\cos \\left( ny \\right) \\cos \\left( y \\right) = 2 x \\cos \\left( ny \\right) = 2 x T_n \\left( x \\right) $$\n", "\n", "which yields a recurrence relationship.\n", "\n", "### Chebyshev interpolating polynomials\n", "\n", "$$ \\begin{split}\\begin{split}\n", "T_0 \\left( x \\right) &= 1 \\\\\n", "T_1 \\left( x \\right) &= x \\\\\n", "T_{n+1} \\left( x \\right) &= 2 x T_n \\left( x \\right) - T_{n-1} \\left( x \\right)\n", "\\end{split}\\end{split} $$" ] }, { "cell_type": "markdown", "id": "685062f5-cbce-4a1e-9b93-f987773261f8", "metadata": {}, "source": [ "## Naturally, we need a Vandermonde matrix" ] }, { "cell_type": "code", "execution_count": 11, "id": "a238d844-6d33-4bce-90f1-8dc20191ea88", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "vander_chebyshev (generic function with 2 methods)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function vander_chebyshev(x, n=nothing)\n", " if isnothing(n)\n", " n = length(x) # Square by default\n", " end\n", " m = length(x)\n", " T = ones(m, n)\n", " if n > 1\n", " T[:, 2] = x\n", " end\n", " for k in 3:n\n", " T[:, k] = 2 * x .* T[:,k-1] - T[:, k-2]\n", " end\n", " T\n", "end" ] }, { "cell_type": "code", "execution_count": 12, "id": "795d6968-ddf2-4d2f-ae59-92f8243f83ca", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = LinRange(-1, 1, 50) \n", "plot(x, vander_chebyshev(x, 5), title=\"Chebyshev polynomials\", label=[\"\\$T_0\\$\" \"\\$T_1\\$\" \"\\$T_2\\$\" \"\\$T_3\\$\" \"\\$T_4\\$\"])" ] }, { "cell_type": "markdown", "id": "51093442-72d6-4081-b185-5dfebd6e4b66", "metadata": {}, "source": [ "### Well-conditioned\n", "\n", "The Chebyshev polynomials are well-conditioned." ] }, { "cell_type": "code", "execution_count": 13, "id": "64c1f100-4c3e-4ddd-957d-19d4ce5c8fcf", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = 20\n", "plot(range(2, a), [vcond(vander, LinRange, a)], yscale=:log10, legend=:topleft, xticks=range(2, a, step=2), xlabel=\"# of columns\", ylabel=\"cond(A)\", label=\"Vander, LinRange\")\n", "plot!(range(2, a), [vcond(vander, CosRange, a)], yscale=:log10, label=\"Vander, CosRange\")\n", "plot!(range(2, a), [vcond(vander_legendre, LinRange, a)], yscale=:log10, label=\"Legendre, LinRange\")\n", "plot!(range(2, a), [vcond(vander_legendre, CosRange, a)], yscale=:log10, label=\"Legendre, CosRange\")\n", "plot!(range(2, a), [vcond(vander_chebyshev, LinRange, a)], yscale=:log10, label=\"Chebyshev, LinRange\")\n", "plot!(range(2, a), [vcond(vander_chebyshev, CosRange, a)], yscale=:log10, label=\"Chebyshev, CosRange\")" ] }, { "cell_type": "markdown", "id": "4072a633-e30d-400f-99c3-0a51621ee185", "metadata": {}, "source": [ "## Piecewise polynomials\n", "\n", "Let's take a different approach.\n", "We'll re-examine the Lagrange polynomials as we vary the points." ] }, { "cell_type": "code", "execution_count": 14, "id": "bb076825-b250-49f3-b8e2-6e5ea2b7433d", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = LinRange(-1, 1, 11) # What about CosRange?\n", "s = LinRange(-1, 1, 100)\n", "A = vander_chebyshev(s, length(x)) /\n", " vander_chebyshev(x)\n", "plot(s, A[:,1:5], size=(1000, 600), label=[\"\\$l_0\\$\" \"\\$l_1\\$\" \"\\$l_2\\$\" \"\\$l_3\\$\" \"\\$l_4\\$\"])\n", "scatter!(x[1:5], ones(5), color=:grey, label=\"values\")\n", "scatter!(x, zero(x), color=:black, label=\"roots\")" ] }, { "cell_type": "markdown", "id": "c207d2ff-50dc-4e33-a95f-54d734e781ed", "metadata": {}, "source": [ "Let's look at a specific example that seems like it should be easy to fit but shows strange behavior." ] }, { "cell_type": "code", "execution_count": 15, "id": "d503f8aa-7c10-4ec2-a09b-e26863f67433", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Fit the function |x|\n", "y = abs.(x)\n", "plot(s, [abs.(s) A * y], label=[\"true\" \"fit\"])" ] }, { "cell_type": "markdown", "id": "ced9edf5-687c-4f63-9fcc-1198c6ab3b2a", "metadata": {}, "source": [ "Switching to a better set of points or basis doesn't fully fix the issue." ] }, { "cell_type": "code", "execution_count": 16, "id": "d4a3e584-b479-401e-a70b-9b4c515ff086", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = CosRange(-1, 1, 11)\n", "s = LinRange(-1, 1, 100)\n", "A = vander_chebyshev(s, length(x)) /\n", " vander_chebyshev(x)\n", "\n", "# Fit the function |x|\n", "y = abs.(x)\n", "plot(s, [abs.(s) A * y], label=[\"true\" \"fit\"])" ] }, { "cell_type": "markdown", "id": "c04255d0-d6e5-4204-a5ee-2b4b7892df7e", "metadata": {}, "source": [ "The effects of the higher order functions seem to be producing different behavior between the points we are fitting than we want.\n", "The absolute value function looks like two linear functions glued together.\n", "Let's try that." ] }, { "cell_type": "markdown", "id": "7afb7c96-98cd-4d76-854e-8b8e31f77581", "metadata": {}, "source": [ "### New interpolation matrix" ] }, { "cell_type": "code", "execution_count": 17, "id": "ff8216f7-21d7-4c00-85d2-87a0504220da", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4×3 Matrix{Float64}:\n", " 0.0 1.0 0.0\n", " 0.0 1.0 0.0\n", " 0.0 0.0 1.0\n", " 0.0 0.0 1.0" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function interp_nearest(x, s)\n", " A = zeros(length(s), length(x))\n", " for (i, t) in enumerate(s)\n", " loc = nothing\n", " dist = Inf\n", " for (j, u) in enumerate(x)\n", " if abs(t - u) < dist\n", " loc = j\n", " dist = abs(t - u)\n", " end\n", " end\n", " A[i, loc] = 1\n", " end\n", " A\n", "end\n", "interp_nearest(LinRange(-1, 1, 3), LinRange(0, 1, 4))" ] }, { "cell_type": "code", "execution_count": 18, "id": "73c8a506-a212-4541-b50a-4678e7242aac", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = LinRange(-1, 1, 11)\n", "A = interp_nearest(x, s)\n", "plot(s, A[:, 1:5], label=[\"\\$c_0\\$\" \"\\$c_1\\$\" \"\\$c_2\\$\" \"\\$c_3\\$\" \"\\$c_4\\$\"])\n", "scatter!(x, ones(length(x)), label=\"values\")" ] }, { "cell_type": "markdown", "id": "fccab8bc-2f6f-42a6-aa55-7be7241ac792", "metadata": {}, "source": [ "The condition number seems reasonable." ] }, { "cell_type": "code", "execution_count": 19, "id": "2253a2b4-768f-459c-ba42-27781f832d33", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "cond(A) = 1.224744871391589\n", "Singular values:\n" ] }, { "data": { "text/plain": [ "5-element Vector{Float64}:\n", " 1.7320508075688772\n", " 1.7320508075688772\n", " 1.7320508075688772\n", " 1.7320508075688772\n", " 1.7320508075688772" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "6-element Vector{Float64}:\n", " 1.4142135623730951\n", " 1.4142135623730951\n", " 1.4142135623730951\n", " 1.4142135623730951\n", " 1.4142135623730951\n", " 1.4142135623730951" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = LinRange(-1, 1, 40)\n", "A = interp_nearest(x, s)\n", "@show cond(A)\n", "println(\"Singular values:\")\n", "display(svdvals(A)[1:5])\n", "display(svdvals(A)[end-5:end]);" ] }, { "cell_type": "code", "execution_count": 20, "id": "4a3fda70-052e-42a1-ba6f-6817b6605075", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(s, A * runge.(x), label=\"fit\")\n", "plot!(s, runge.(s), label=\"true\")\n", "scatter!(x, runge.(x), label=\"data\")" ] }, { "cell_type": "markdown", "id": "afc3a02b-d44c-4253-a17f-8b8c53257253", "metadata": {}, "source": [ "This looks pretty good, but how accurate is it really?" ] }, { "cell_type": "code", "execution_count": 21, "id": "a8aabcd8-33fa-4262-b511-a83c2cce1fec", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "plot_convergence (generic function with 1 method)" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function interp_chebyshev(x, xx)\n", " vander_chebyshev(xx, length(x)) * inv(vander_chebyshev(x))\n", "end\n", "\n", "function interp_monomial(x, xx)\n", " vander(xx, length(x)) * inv(vander(x))\n", "end\n", "\n", "function interp_error(ieval, x, xx, test)\n", " \"\"\"Compute norm of interpolation error for function test\n", " using method interp_and_eval from points x to points xx.\n", " \"\"\"\n", " A = ieval(x, xx)\n", " y = test.(x)\n", " yy = test.(xx)\n", " norm(A * y - yy, Inf)\n", "end\n", "\n", "function plot_convergence(ievals, ptspaces; xscale=:log10, yscale=:log10, maxpts=40)\n", " \"\"\"Plot convergence rates for an interpolation scheme applied\n", " to a set of tests.\n", " \"\"\"\n", " xx = LinRange(-1, 1, 100)\n", " ns = 2:maxpts\n", " fig = plot(title=\"Convergence\",\n", " xlabel=\"Number of points\",\n", " ylabel=\"Interpolation error\",\n", " xscale=xscale,\n", " yscale=yscale,\n", " legend=:bottomleft,\n", " size=(1000, 700))\n", " for ieval in ievals\n", " for ptspace in ptspaces\n", " for test in [runge]\n", " errors = [interp_error(ieval, ptspace(-1, 1, n), xx, test)\n", " for n in ns]\n", " plot!(ns, errors, marker=:circle, label=\"$ieval, $ptspace\")\n", " end\n", " end\n", " end\n", " for k in [1, 2, 3]\n", " plot!(ns, ns .^ (-1.0*k), color=:black, label=\"\\$n^{-$k}\\$\")\n", " end\n", " fig\n", "end" ] }, { "cell_type": "code", "execution_count": 22, "id": "bb3cd1f7-0c1a-4552-85ff-3c3471d1c04c", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_convergence([interp_monomial, interp_chebyshev, interp_nearest], [LinRange, CosRange])" ] }, { "cell_type": "markdown", "id": "24583a2d-f1b4-4898-a55c-98725d8ca3e6", "metadata": {}, "source": [ "Piecewise interpolation seems to be not especially accurate, but it doesn't have the runaway Runge phenomenon.\n", "\n", "## Exploration\n", "\n", "Can you make a function that does peiecwise interpolation with higher order polynomials than constant functions?\n", "Perhaps linear or quadratic?" ] } ], "metadata": { "kernelspec": { "display_name": "Julia 1.11.6", "language": "julia", "name": "julia-1.11" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.11.6" } }, "nbformat": 4, "nbformat_minor": 5 }