{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Foundations of Computational Economics #31\n", "\n", "by Fedor Iskhakov, ANU\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "## Function approximation in Python\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "\n", "[https://youtu.be/liNputEfcXQ](https://youtu.be/liNputEfcXQ)\n", "\n", "Description: How to approximate functions which are only defined on grid of points. Spline and polynomial interpolation." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Interpolation problem\n", "\n", "- $ f(x) $ is function of interest, hard to compute \n", "- Have data on values of $ f(x) $ in $ n $ points\n", " $ (x_1,\\dots,x_n) $ \n", "\n", "\n", "$$\n", "f(x_1), f(x_2), \\dots f(x_n)\n", "$$\n", "\n", "- Need to find the approximate value of the function $ f(x) $ in\n", " arbitrary points $ x \\in [x_1,x_n] $ " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Approaches\n", "\n", "1. *Piece-wise* approach (connect the dots) \n", "\n", "\n", "- Which functional form to use for connections? \n", "- What are advantages and disadvantages? \n", "\n", "\n", "1. Use a *similar* function $ s(x) $ to represent $ f(x) $\n", " between the data points \n", "\n", "\n", "- Which simpler function? \n", "- What data should be used? \n", "- How to control the accuracy of the approximation? " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Distinction between function approximation (interpolation) and curve fitting\n", "\n", "- Functions approximation and interpolation refers to the situations\n", " when **data** on function values is matched **exactly** \n", " - The approximation curve passes through the points of the data \n", "- Curve fitting refers to the statistical problem when the data has\n", " **noise**, the task is to find an approximation for the central\n", " tendency in the data \n", " - Linear and non-linear regression models, econometrics \n", " - The model is *over-identified* (there is more data than needed to\n", " exactly identify the regression function) " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Extrapolation\n", "\n", "Extrapolation is computing the approximated function outside of the\n", "original data interval\n", "\n", "**Should be avoided in general**\n", "\n", "- Exact *only* when theoretical properties of the extrapolated function\n", " are known \n", "- Can be used with extreme caution and based on the analysis of the model \n", "- Always try to introduce wider bounds for the grid instead " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Spline interpolation\n", "\n", "Spline = curve composed of independent pieces\n", "\n", "**Definition** A function $ s(x) $ on $ [a,b] $ is a spline of\n", "order $ n $ ( = degree $ n-1 $) iff\n", "\n", "- $ s $ is $ C^{n-2} $ on $ [a,b] $ (has continuous derivatives\n", " up to order $ n-2 $), \n", "- given *knot* points $ a=x_0=fdata[0][0],xd<=fdata[0][-1])]\n", " if ifunc:\n", " plt.plot(xdi,ifunc(xdi),color=color,label=label)\n", " if label:\n", " plt.legend()\n", " elif label:\n", " plt.title(label)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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\n", 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oSImIiPgRBakHEBQES5YMbTjXyj0RERH/oSD1gJxOuHABqqqs6b3a2lr6+vrsLktERERGgILUA+rvk9q+3Vq519PTQ2Njo71FiYiIyIhQkHpAU6dCfLwVpNRwLiIi4l8UpB5QQAAsW2YFqcTERAIDA9UnJSIi4icUpNzA6YSSEqisDCQpKUmHF4uIiPgJBSk3uLFPKjk5WUFKRETETyhIucGkSeBwDAaptrY2Wltb7S5LREREhpmClBsYxmCfVFJSMoBGpURERPyAgpSbOJ1QUQHt7SmAgpSIiIg/UJByk/4+qf37w4mOjlaQEhER8QMKUm4yfjykpKjhXERExJ8oSLmJYVijUv19UvX19fT29tpdloiIiAwjBSk3cjqhpgY6OrLo6+ujoaHB7pJERERkGClIuVF/n9TZs9ZRMZreExER8W0KUm40ZgxkZMChQ1E6KkZERMQPKEi5UX+f1M6dBomJDurq6uwuSURERIaRgpSbOZ1QXw/d3eM0IiUiIuLjFKTcrL9PqrR0tI6KERER8XEKUm6Wk2PdTp9OAtRwLiIi4ssUpIaB0wmHD0fQ16cgJSIi4ssUpIaB0wlNTQatrblqOBcREfFhClLDoL9PqrZ2ohrORUREfJiC1DDIyIBx4+DSpSwdFSMiIuLDFKSGidMJp0+PwuUyaWxstLscERERGQYKUsPE6YRr1wKprk5Rn5SIiIiPUpAaJsuWWW9LS0crSImIiPgoBalhkpIC+flQVZWnICUiIuKjFKSGkdMJxcVpVFc32F2KiIiIDIMHDlKGYWQahrHdMIwzhmGcNgzjz91RmC9wOqGzM5jTp8Po7u62uxwRERFxM3eMSLmAvzRNMx+YB3zFMIyJbnher3djn1RDg0alREREfM0DBynTNKtN0zx6/c/XgDNA+oM+ry9ITISJE12UlOSoT0pERMQHubVHyjCMHGA6cMCdz+vNVqwIpKIii4oKBSkRERFf47YgZRhGFPBfwF+Yptlym/evNwzjsGEYh+vr6931sh5v+XKDnp5gDh407S5FRERE3MwtQcowjGCsELXRNM1Nt3uMaZobTNOcZZrmLIfD4Y6X9QpLl4JhmBw6FG13KSIiIuJm7li1ZwA/A86YpvnDBy/Jt8THw7hxbZw7l0pHR4fd5YiIiIgbuWNEaiHwB8BywzA+un5b6Ybn9RkLF/ZQUZFJebn6pERERHyJO1bt7TFN0zBNc4ppmtOu395xR3G+4tGYI/T2BvHhmu9CTg5s3Gh3SSIiIuIG2tl8uG3cyKMb/gDD6GNX7xIoK4P16xWmREREfICC1HB78UXiOmrIiK/kVMdk61p7O7z4or11iYiIyANTkBpu5eUAjIu4QPnVLMybrouIiIj3UpAabllZABQYJ2lpjaUsMnvIdREREfFeClLD7aWXICKCWd2HAdgTswgiIqzrIiIi4tUUpIbbunWwYQMLIy8BcDhuCWzYYF0XERERr6YgNRLWrWP0pf1ERbVxMvUxhSgREREfoSA1grKyWiguDrO7DBEREXETBakRNHZsN5cvx9LXpwOMRUREfIGC1AiaPNmguzuUkyev2l2KiIiIuIGC1AiaOdOa1issvGZzJSIiIuIOClIjaP78WACOH++xuRIRERFxBwWpEZSaGkpMTBtnzujTLiIi4gv0E32EZWZeo6Qk3O4yRERExA0UpEbYuHHdVFfH43L12V2KiIiIPCAFqRFmrdwL4eTJZrtLERERkQekIDXCZsywVu4dONBqcyUiIiLyoBSkRtiCBf0r91w2VyIiIiIPSkFqhCUnhxAT08rZs/rUi4iIeDv9NLdBVtY1Skoi7C5DREREHpCClA3Gju2mujpOK/dERES8nIKUDSZPDri+ck9n7omIiHgzBSkb9J+5p5V7IiIi3k1Bygbz5sUAOnNPRETE2ylI2SAlJfT6yr1Au0sRERGRB6AgZRNr5Z7O3BMREfFmClI2GTu2m8uXtXJPRETEmylI2WTyZIOeHq3cExER8WYKUjbRmXsiIiLeT0HKJjpzT0RExPspSNkkOTlUZ+6JiIh4Of0Ut5FW7omIiHg3BSkbaeWeiIiId1OQstHgyr0Wu0sRERGR+6AgZSOduSciIuLdFKRsNH9+/8o9nbknIiLijRSkbDS4ck9n7omIiHgjBSmbZWW1UFyslXsiIiLeSEHKZuPGdVNdHauVeyIiIl5IQcpmkyZp5Z6IiIi3UpCymc7cExER8V4KUjbTyj0RERHvpSBls5SUMGJjr3HmjFbuiYiIeBsFKQ+gM/dERES8k4KUBxgzxlq519tr2l2KiIiI3AMFKQ/Qf+beiRNauSciIuJNFKQ8wEzXcQAOPPHXkJMDGzfaW5CIiIjcFQUpu23cyLx//zMAjgdPhbIyWL9eYUpERMQLKEjZ7cUXSblaRmxUM2f7JljX2tvhxRftrUtEREQ+kYKU3crLAciOKeN8a94t10VERMRzKUjZLSsLgCkRJ6i+kkoL0UOui4iIiOdSkLLbSy9BRARzOYBJANsjl0FEhHVdREREPJqClN3WrYMNG1gafQaAnQmrYMMG67qIiIh4tCC7CxBg3TrGPv00iVn1HMx8DtaNsrsiERERuQsakfIQ4eHh5OTUcupUBKY2OBcREfEKClIeZPLkVq5eDaO01O5KRERE5G4oSHmQmTNdAOzfryEpERERb6Ag5UFmzw4nOLibXbu67S5FRERE7oKClAdJTXWQlnaZ/fv77C5FRERE7oJW7XkQh8NBRsYRDhzIorMTwsLsrkg8UXNzM2VlZdTV1dHa2gpAYGAgsbGxJCQkkJ6eTlxcHIZh2FypiIjvU5DyIOHh4Ywb18jevQEcOwbz59tdkXgK0zQ5c+YMBw4coPz68UGBgYFERUVhGAYul2sgVAHExsaSl5fH5MmTyczMVKgSERkmClIeZvr0bn7xCygsVJASS2NjI5s3b6ayspJRo0axYsUKxo0bR1JS0pCA1NPTQ2NjI+Xl5ZSUlHDs2DEOHTpEbGwss2fPZsaMGYSHh9v4NxER8T0KUh5m3Lgo4uKaKSyMBTSK4O+KiorYsmULgYGBrF69mqlTpxIQcPvWxuDgYFJSUkhJSWHOnDl0dXVx/vx5jh49yrZt29i5cydTp05l0aJFxMbGjvDfRETENylIeRiHw0F6eiX79sWgIOXfjh49yltvvUVGRgbPPfccMTEx9/TxoaGhFBQUUFBQQG1tLYWFhRw9epRjx44xa9YsFi9eTGRk5DBVLyLiHxSkPExSUhIZGUWcPj2Zy5chLc3uisQOp06d4q233mLs2LF8+tOfJjg4+IGeLzk5mTVr1rB06VJ27tzJwYMHOXbsGEuWLGHevHkEBga6qXIREf+i7Q88jLVyrxKAAwdsLkZsUVlZyebNm8nOzmbt2rUPHKJuFBcXx5o1a/iTP/kTcnJy2LZtGz/5yU8oLi5222uIiPgTBSkPY63cayUoqJfCQrurkZHW0dHBG2+8QUxMDJ/+9KcJChqeQePExESef/55nn/+eXp7e3nllVfYsmULnZ2dw/J6IiK+SlN7Hig1dRSZmQ0UFibbXYqMsHfeeYe2tja++MUvEhERMeyvl5eXR25uLjt37mTv3r0UFxezZs0acnNzh/21RUR8gUakPJDD4SA1tYxDh0xcLrurkZFy9uxZTp06xdKlS0kbwea4oKAgVqxYwQsvvEBwcDCvvPIK77zzDi795xMR+UQKUh7IClLldHQYnDxpdzUyEnp6enj//fdJSkpi0aJFttSQkZHBl7/8ZebOncuhQ4f4+c9/zpUrV2ypRUTEWyhIeSCr4bwKUMO5v9i3bx/Nzc089thjd9wnaiQEBwfz2GOP8elPf5rGxkY2bNjAuXPnbKtHRMTTKUh5IIfDQVxcM/Hx3Wo49wPt7e3s27eP/Px8Ro8ebXc5AOTn5/PlL3+Z+Ph4fvWrX7Fjxw5M07S7LBERj6Mg5YEiIiKIiopk3LhGBSk/sG/fPrq7u3E6nXaXMkR8fDwvvPACU6dOZefOnWzatEl9UyIiN1GQ8lBJSUmkp1dy7hw0NdldjQyXtrY2Dh48SEFBAQ6Hw+5ybhEUFMSaNWtYsWIFp06d4j//8z+HHI4sIuLvFKQ8VGJiIqNGnQfg4EGbi5Fhc/DgQXp6eliyZIndpdyRYRgsWrSI5557jpqaGn72s5+pCV1E5Dq3BCnDMF42DKPOMIxT7ng+sUakkpLKCQgwNb3no1wuF0eOHCEvL4/ExES7y/lEEydO5POf/zxdXV28/PLL1NXV2V2SiIjt3DUi9QvgMTc9l2A1nIeGdjNunBrOfdWpU6doa2tj7ty5dpdy19LT0/n85z+PYRj8/Oc/p7Ky0u6SRERs5ZYgZZrmLkCdPG7U3y8zYcIVDhyAvj6bCxK3Mk2TAwcO4HA4PGal3t1KSkriC1/4AuHh4fzyl7+ktLTU7pJERGyjHikPFRERQWRkJFlZ1TQ3w/nzdlck7lReXk5NTQ1z587FMAy7y7ln8fHxfOELXyAuLo7XXnuNsrIyu0sSEbHFiAUpwzDWG4Zx2DCMw/X19SP1sl7N4XDgcFwC0PSej/noo48ICQmhoKDA7lLuW3R0NH/4h39ITEwMr732GhUVFXaXJCIy4kYsSJmmucE0zVmmac7yxGXensjhcBAQcIHYWDWc+5Lu7m5Onz7NpEmTCAkJsbucBxIVFcXnPvc5oqKiePXVV6mqqrK7JBGREaWpPQ/mcDhwubqZOdOlIOVDioqK6OnpYdq0aXaX4hbR0dF87nOfIzIykldffVWr+UTEr7hr+4PXgf3AeMMwKg3D+KI7ntffJSUlATBx4jVOngTtg+gbjh8/Tnx8PJmZmXaX4jYxMTH84R/+IcHBwbz66qtcvXrV7pJEREaEu1btPW+aZqppmsGmaWaYpvkzdzyvv+ufAs3JqaGvDw4ftrkgeWDNzc2UlpYydepUr2wy/zhxcXGsW7eO7u5uXn31Vdrb2+0uSURk2Glqz4P1r9xLSioF1HDuC06ePAnA1KlTba5keCQnJ/P8889z5coVXn/9dXp6euwuSURkWClIeTiHw0FX12Xy8uDAAburkQdVVFREeno6cXFxdpcybLKzs3nmmWeoqqpi06ZNmKZpd0kiIsNGQcrDORwO6uvrmTvXZP9+0M8k79XU1ERNTQ0TJ060u5Rhl5+fz6OPPsrZs2f5/e9/b3c5IiLDRkHKwzkcDrq7u5k6tZPaWigvt7siuV9nzpwB8IsgBTBnzhxmzpzJ3r17+eijj+wuR0RkWChIebj+hvOxYxsA9Ul5s6KiItLS0nx6Wu9GhmHw+OOPM3r0aN566y3K9VuAiPggBSkP178FwqhRVYSHK0h5q+bmZi5fvuw3o1H9AgMDee6554iPj+fXv/41V65csbskERG3UpDycBEREURERNDUVMusWQpS3qp/Wi8/P9/mSkZeeHg4zz//PH19ffz617/WSj4R8SkKUl4gKSmJhoYG5s2Do0ehq8vuiuReXbhwAYfDwahRo+wuxRYJCQk888wz1NbW8vbbb2sln4j4DAUpL3Djyr3ublDfrnfp6uqirKyMcePG2V2KrcaOHcuyZcs4ceIEhw4dsrscERG3UJDyAtZeUl1MnmydEaPpPe9y6dIl+vr6yMvLs7sU2y1ZsoS8vDzef/99Kioq7C5HROSBKUh5gf6Ve4GBtWRmKkh5mwsXLhAWFuZTZ+vdL8MweOqpp4iNjeXNN9+kVQdIioiXU5DyAv1Bqr6+nnnzFKS8iWmaXLhwgTFjxhAQoC83gLCwMNauXUtHRwf/9V//RV9fn90liYjcN31n9wKRkZFEREQMBKnSUqipsbsquRvV1dW0tbX5fX/UzZKTk1m5ciWlpaXs3r3b7nJERO6bgpSX6G84nzfPuq9z97zD+fPnAavRWoaaNm0aBQUF7Ny5k7KyMrvLERG5LwpSXqI/SE2bZhIcrOk9b3HhwgUyMjKIjIy0uxSPYxgGq1atIj4+nk2bNtHe3m53SSIi90xBykv0r9xzua4xbZqClDdob2/n8uXLGo36GKGhoTz77LO0tbWxZcsW7S8lIl5HQcpL9B8V0z+9d+gQuFw2FyUfq6SkBIAxY8bYXIlnS01N5RMz3swAACAASURBVOGHH+b8+fMc0Jy1iHgZBSkv0b9yr66ujnnzoK0NTp+2uSj5WMXFxYSGhpKWlmZ3KR5vzpw5jB8/ng8++IDq6mq7yxERuWsKUl7i5pV7oOk9T1dcXExOTo62PbgLhmGwZs0aIiMj2bRpk87jExGvoe/wXqS/4Xz0aHA4FKQ82ZUrV2hubiY3N9fuUrxGeHg4Tz75JA0NDWzbts3uckRE7oqClBfpD1JgamNOD1dcXAygIHWPcnNzmTt3LgcPHuTixYt2lyMi8okUpLxI/8q9a9euMW8enD0LV67YXZXcTnFxMdHR0SQkJNhditdZsWIFDoeDLVu2aEsEEfF4ClJe5OajYgAOHrSxILkt0zQpKSkhNzcXwzDsLsfrBAcH8/TTT9Pe3s7bb7+tLRFExKMpSHmRG7dAmD0bDEPTe56opqaGjo4OTes9gJSUFJYvX86ZM2c4fvy43eWIiNyRgpQXiYiIIDw8nLq6OqKjYfJkBSlP1N8fNXr0aJsr8W7z588nOzubd999lyuawxYRD6Ug5UUMwyApKYmGhgYA5s2zztzr67O5MBmirKyMxMREoqOj7S7FqwUEBPDkk09iGAabN2+mT//RRcQDKUh5GYfDQV1dHaZprdy7cgUuXLC7KunX19dHeXk52dnZdpfiE+Li4nj88ccpLy/Xruci4pEUpLxMUlISXV1dtLS0aGNOD1RTU0NXV5eClBtNmTKFvLw8Pvzww4HRWBERT6Eg5WX6G87r6uqYMAFiYhSkPElZWRkAOTk59hbiQwzD4IknniAoKIgtW7Zoik9EPIqClJe5MUgFBMDcuQpSnqSsrIxRo0apP8rNoqOjWblyJZWVlezfv9/uckREBihIeZnw8HCio6Opq6sDrIbzEyesQ4zFXqZpUlZWpmm9YTJ58mTy8/PZvn379R3+RUTspyDlhZKTk4cEqb4+OHzY5qKE2tpaOjs7FaSGiWEYrFq1itDQUK3iExGPoSDlhfrP3Ovr62PuXOuapvfsp/6o4RcZGcnKlSu5fPkye/bssbscEREFKW+UnJxMb28vjY2NJCTAuHEKUp6grKyMuLg4YmNj7S7Fp02aNIlJkyaxc+dOamtr7S5HRPycgpQXurHhHKzpvcJC0JFk9lF/1MhauXIl4eHhbN68md7eXrvLERE/piDlhRITEzEMY0iQqqmB8nKbC/Nj9fX1tLe3K0iNkIiICJ544glqamrYvXu33eWIiB9TkPJCwcHBjBo1akiQAk3v2Un9USNvwoQJTJkyhd27d1NdXW13OSLipxSkvFRSUtJAkCoogPBwBSk7lZeXEx0dTVxcnN2l+JXHHnuMiIgINm/ejMvlsrscEfFDClJeKikpiaamJrq7uwkOhlmzFKTsVF5eTmZmJoZh2F2KXwkPD+dTn/oUdXV17Nq1y+5yRMQPKUh5qeTkZICBs8fmzYOjR6Gry86q/NPVq1dpaWkhMzPT7lL8Ul5eHtOmTWPPnj1UVVXZXY6I+BkFKS/Vv3Kvf/n3vHnQ3Q0ffWRnVf6poqICgKysLJsr8V+PPvooUVFRbNmyRVN8IjKiFKS8VHx8PEFBQWo49wAVFRUEBwcPjBLKyAsLC2P16tXU19ezY8cOu8sRET+iIOWlAgICcDgcA0EqLQ0yMxWk7FBRUUF6ejqBgYF2l+LXxo4dy/Tp09m3bx+VlZV2lyMifkJByovduHIPBjfmlJHT3d1NTU2N+qM8xKOPPkp0dDSbN2+mp6fH7nJExA8oSHmxpKQkWltbaW9vB6wgVVpqbc4pI6OqqgrTNBWkPERoaChr1qyhsbGR7du3212OiPgBBSkvdrujYgAOHLCrIv9Tfn07eQUpz5Gbm8vMmTPZv3//wL+PiMhwUZDyYv3Nzf1Bavp0CA7W9N5IqqioICkpibCwMLtLkRs8/PDDxMXFsWXLFk3xiciwUpDyYlFRUYSHhw9sgRAeDtOmKUiNFNM0qaysJCMjw+5S5CahoaGsXr2apqYmfv/739tdjoj4MAUpL2YYxm0bzg8dAm2lM/zq6uro6urS/lEeavTo0cyePZsDBw4MnIUoIuJuClJerj9ImaYJWEGqrQ1On7a5MD/QvxGn+qM810MPPUR8fDxbtmyhu7vb7nJExAcpSHm5pKQkuru7uXr1KqCNOUdSRUUFkZGRxMfH212K3EFISAhr1qzhypUrbNu2ze5yRMQHKUh5uZtX7o0eDQ6HgtSw2rgRcnKo2LGDrNOnMV57ze6K5GNkZ2czd+5cDh06RElJid3liIiPUZDycjefuWcY2phzWG3cCOvX09rYyJVRo8g4dw7Wr7eui8dasWIFo0aN4re//S1dOtlbRNxIQcrLhYWFERsbe0vD+dmzcOWKjYX5qhdfhPZ2zqSN54MPVvBO0UqK2rMx//ZFuyuTjxEcHMyTTz5Jc3MzH3zwgd3liIgPUZDyASkpKdTcsJ15f5/UwYM2FeTLrm/w+J3OF9m7dxEvXf1/mUQRueXb+cpX4J13oKPD5hrltjIzM5k/fz5Hjhzh0qVLdpcjIj5CQcoHJCcn09jYOLDx4OzZ1hSfpveGwfWtDg5dm82ktFNUkMF/sJ4p4Rf5xS9g1SpISIAnnoB/+zfQqnvP4nQ6SUxMZMuWLXQo8YqIGyhI+YDk5GRM0xyY3ouOhsmTFaSGxUsv0RCdweUracwMO0IGVayP2MiW/6+OxkZ4/3340pesqdWvfAVycqx/i7/+a9i5E7TJtr2Cg4N5+umnaWtr4+233x7YNkRE5H4pSPmAlJQUYLDhHKzpvQMHoK/Prqp81Lp1vPvFDZgEsKx7B2Rnw4YNsG4dYWHwyCPwL/8CFy5YYeqHP4SUFPjnf4Zly6wVlWvXwi9/CTe0tckISk1Nxel0UlRUxPHjx+0uR0S8nIKUD4iPjyckJOSWPqkrV6wf6OJeHzZPxDD6WHn4X6G0FNatu+UxhgHjx8PXvgbbtkFDA/zXf8Ezz8CuXfC5z1kBa+5c+Md/hCNHFHpH0oIFC8jOzubdd9/lilZliMgDUJDyAYZhkJycfMuIFGh6bzgcPhxCenojyckRd/0xMTHw9NPws59BVZUVnP7n/7QC17e+BbNmQXo6vPCCFbhaWoavfoGAgACeeuopDMNg06ZN9CnFish9UpDyEf1Bqr/nY8IE64e3gpR7uVwmFy6MoqCg9b6fIyAAZsyAv/s769+nttaa6lu6FP77v+HZZyExEVasgB/8wJoiVCuP+8XGxrJq1SoqKyvZvXu33eWIiJdSkPIRycnJdHV1DRwVExBgTRspSLnXnj1X6OoKZeFCw23P6XDAH/wB/OpXUF9vTf19/etWD9U3vgH5+TB2LPzZn8F770Fnp9te2u8VFBRQUFDAzp07qaystLscEfFCClI+or/h/OY+qRMnrEOMxT1+9ztrJOqxx2KG5fmDgmDxYvjud+HkSasF69//HSZOhJ/+FB5/3NpeYfVq+I//gOvnJssDWLlyJTExMWzatEm7novIPVOQ8hE3HxUDVpDq64PDh+2qyvfs328QHd3K9Okjc1Bxdjb88R/DW29BY6O14ecLL8CpU9b1rCyYMgX+5m9gzx5wuUakLJ8SFhbGU089RXNzM1u3btWWCCJyT4LsLkDcIyQkhFGjRg0JUnPnWm8LC63+G3lwp05Fk59/hYCAqBF/7fBwa0Tq8cfhxz+2eqe2brXC1fe/b41ixcfDo49aG4M+9pjVayWfLDs7m6VLl7Jjxw5ycnKYMWOG3SWJj+jr66Ozs5OOjg56enro6+ujt7eXvr4+TNMkKChoyC00NJSwsDAMw33tAzK8FKR8SEpKCtXV1QP3ExJg3Dj1SblLcXEbDQ1xrF1r/3J5w7B6p/LzrT6qq1fhgw8Gg9WvfjV4gPXKlVawmjbNuia3t3jxYsrKynj33XfJyMgYGOUV+Tg9PT3U19dTV1dHc3MzV69eHXjb3t5+X9PFhmEQERFBREQEkZGRxMbGEhsbS1xc3JCbwpZnUJDyIcnJyRQVFdHV1UVoaChg/SD94ANr1Ze+5h7MO+9cASJZsSLc7lJuERtrrfZ79llrOvfoUStUbd1qrQ78u7+DtDQrVK1cCQ89ZO2AL4MCAgJ4+umn+clPfsKbb77Jl770JUJCQuwuSzxIT08Ply9fpqKigqqqKurq6mhqahrymOjoaGJjY0lLSyMyMpLw8PCBW3BwMAEBAQQGBhIQEIBhGPT29uJyuXC5XPT09NDV1UV7ezttbW10dHTQ2tpKSUkJLTftiRIUFITD4Ri4JSUlkZycTExMjALWCFOQ8iHJyckA1NXVkZmZCVhB6pVXrLN2s7PtrM777drlIjDQxSOPePZ8WUCAtS/VrFnwD/9gba/w3ntWqHrjDatpPTjYmu5dtcoKVnl5dlftGaKionj66ad55ZVXeOedd3jyySftLkls1NvbS0VFBRcvXqSkpISampqBPcdGjRpFSkoKU6ZMISkpCYfDQXx8PIGBgcNWS0tLC83NzVy5cmVgFKykpIQTJ04MPC4yMpK0tDTS09MH3kZE3P2ed3LvFKR8yI0r924MUmBN7ylIPZhjx8LJyWkkMjLZ7lLuSXKytZP65z5nnfW3d+/gFODXvmbdxo61QtWqVbBkCVwf0PRLubm5LFmyhF27dpGTk8O0adPsLklGUFtbG2fOnOHChQuUlpbS3d1NQEAAGRkZLFiwgMzMTDIyMkY8nAQGBhIfH098fDyjR48e8r6Ojg7q6+upqanh8uXLVFVVceGGYy3i4+PJysoiOzub7Oxs4uPjNWrlRgpSPiQmJoawsLAhWyAUFFhNyoWF1hlvcn/a2lyUlibw5JPevddQcLB15t+yZfBP/wQlJVag2rrV2k7hX/4FIiOtqb/+0ar0dLurHnlLly6lvLycrVu3kpycTGpqqt0lyTBqbW3lzJkzFBUVUVZWhmmaxMfHM2XKFMaMGcPo0aMH2iU8UXh4OFlZWWRlZQ1c6+rqorq6mqqqKiorKzl//vzA2ZJRUVEDoSo7OxuHw6Fg9QAUpHzI7Y6KCQ62pnjUcP5gPvigEZcrmSVLfOtLZvRo+MpXrFt7O2zfPthbtWWL9ZipUwdHq+bOhWGaufAoAQEBPPvss2zYsIE33niDL33pS5oe8TEul4vz589z7NgxLl26hGmaJCYmsnjxYiZOnEhSUpJXh4vQ0FBycnLIyckBwDRNGhoaKCsro7y8nNLSUk6fPg1Y04G5ubkDt5iY4dknz1cZduyZMmvWLPOwNjcaFu+99x5Hjx7lm9/8JgEB1jZhf/VX1khDS4t/T9k8iK9+tZT/+39zuHixjTFjIu0uZ9iZJhQVDYaqvXuht9daCfrYY9ZI1WOPwahRdlc6vKqqqvj5z39OdnY269atG/iaEu9VV1fH0aNHOXHiBB0dHcTExDBlyhQKCgr8amTGNE2am5spLS2lpKSE4uJi2q7v3pyQkDAQqnJycggLC7O5WvsZhnHENM1Zt32fgpRvOXbsGL/97W/50z/9UxISEgDYtAmeecYalerfW0ruzdy5FVy6FENDQ6zdpdjiypXB7RXefdc6yiYgAObPHxytKijwzZWh/V9TCxcu5KGHHrK7HLkPfX19nD9/ngMHDlBaWkpAQAATJkxg+vTp5ObmKiBjBau6ujqKi4spLi6mrKyMnp4eDMMgPT2d0aNHk5ubS2Zm5tCG+o0b4cUXrRVNWVnw0kuwbp19f5Fh8nFByrfmKWRIw3l/kLqx4VxB6t719ZmcORPPjBlXAP8MUvHx8OlPW7e+Pjh0aLC36m//1rplZAzuWbVihdVr5QumT59OVVUVe/fuJTU1lUmTJtldktylrq4ujh07xsGDB7ly5QoxMTGsWLGCGTNmaKr2Jv2tIcnJycyfP5/e3l4qKysHgtWePXvYvXs3wcHBZGdnWyNWZ86Q9NWvYrS3W09SVgbr11t/9sEwdScakfIxLpeL73znOyxatIjly5cPXM/KgoUL4fXXbSzOSx071syMGXF885tl/O//raWPN6uutkaptm61Rq2uXYOQEKuhvX+0aswYu6t8ML29vfziF7+gtraWz3/+86SlpdldknyMtrY2CgsLOXToEF1dXWRmZjJ37lzy8/M1+nSfOjs7KS0tpbi4+PpWEE00NY2itSqK3ouBPNX73zx0eRuxLS3WEvHSUrtLdqthH5EyDOMx4F+AQOCnpml+1x3PK/euf5O2G1fugTUqpYbz+/Puu1eBOB55ZOSPhfEGqanW+X8vvADd3daZf/29VX/+59YtL28wVC1ebAUtbxIYGMjatWv56U9/yuuvv84f/dEfERvrn6OTnqylpYV9+/Zx5MgRXC4XkyZNYsGCBQq+98k0oaEBzp2Ds2fDOHt2AufOTeDsWSgpMentHZzLb10TxanPTCGhoYHc4mJyz571m/6qBx6RMgwjEDgPPAxUAoeA503TLLrTx2hEanht3ryZS5cu8Zd/+ZcD1374Q/jLv7RGD67P/sldWrWqhN//Po3W1hCCgnywCWgYXbo0OAW4Ywd0dVk7qj/88OAu6960s0BdXR0vv/wycXFxfOELX/DoJfH+pLm5md27d3P8+HH6+vqYMmUKixYtIlGHTd6Vnh7ra9UKTEPf3rhxe1iYdezYhAkwfjxM+Pc/Z0LjHsZxns6kCC7l5lKSm0vp6NH0BAdjGAZpaWkDjesZGRkEBXlnR9GwNpsbhjEf+JZpmo9ev/83AKZp/u87fYyC1PA6cOAA7733Hl//+teJvn4OyL591tTe5s2wZo3NBXqL602UGa17iA+7ysnvfeRX8/7u1tYGv//9YLCqvL4l14wZg3tWzZ7t+dsrXLx4kddee42xY8fymc98RlNFNuro6GD37t0cPHgQgGnTprFw4ULi4+NtrswzNTbeGpTOnoXiYnC5Bh+Xmno9KE0Y+jYr66avz40brZ6o/h4pgIgIev/jP6hcvHigv6qqqgrTNAkMDCQ9PZ3MzEyysrLIzMwkPNzzjty6neGe2ksHKm64XwmopdlG/ZsHVldXDwSp6dOtPaUKCxWk7sr1bxA1vVFc7k7jkczfwfqvWu9TmLovkZGwerV1M004eXJwh/WXXoL/9b8gMREef9wKVo88YjW5e5qxY8eycuVKtm7dynvvvcfjjz/uN0vmPYXL5eLAgQPs2bOHzs5Opk2bxrJlyzTdijW6VFJy+8DU2Dj4uJAQa8q9oACee24wMOXlWWd33pX+74U3rdoLXLeObCA7Oxun00lnZydlZWWUlZVRUVHB/v372bt3LwBJSUlDgpU3HsbsjiB1u7/xLcNchmGsB9YDQ3ZfFffrP3OvurqavOuHqIWHw7Rp6pO6ay++CO3tvJO2FvNyAM6uD63ful58UUHKDQwDpkyxbn/zN9b0wfvvDwarV16xfvNdsGCwt2rSJM/ZXmHWrFk0NTWxf/9+oqKiWLJkid0l+QXTNDlx4gTbt2/n6tWrjB07loceemjge54/aWq6/VTcxYtDR5eSk62A9MwzQ0eYsrPdNPq7bt0nfk8MCwtj/PjxjB8/HrAOf66qqqK8vJzy8nJOnjzJkSNHBh6blpZGamoqaWlppKWlERsb69Hhyh1BqhLIvOF+BnD55geZprkB2ADW1J4bXlfuIDQ0lISEhNs2nL/8svVF5qXT1COnvByA7SFODKOPlY3vDLku7jVqFDz/vHXr7YWDBwcb1r/5TeuWlTW4vcLy5WD36vWHH36YtrY2tm/fTnh4OLNnz7a3IB936dIltm3bRk1NDampqaxZs+aWM+d8jctlLX67MSz1/7m+fvBxwcFW71J+Pjz11NDpuLg428q/o+Dg4CG7rvf19VFbW8vly5cHbvv37x84IDo8PJyUlBQcDsfAAdEOh8NjpgXd0SMVhNVsvgKowmo2/39M0zx9p49Rj9Tw27RpE2VlZXzta18buPbaa9YvDh99ZB37IR8jJwfKypiYcpo2VyRlDTnWdR9c1uvpqqqGbq/Q1mY1vTqdg8HKrp+nvb29vPHGG5w/f56nn36agoICewrxYTU1NXzwwQcUFxcTFxfH8uXLmTx5skePUNyr5ubbjy5duGBN1fVzOG7tW5owwfp25Wu/HLtcriHhqq6ujvr6enpu+IRERUWRlJTE4sWLB0LZcBnWHinTNF2GYfwp8D7W9gcvf1yIkpGRkpLCyZMnaWtrI/L6zog3bsypIPUJXnqJzi//KRcbx/J46rvWtYgIq5lHRlR6OvzRH1m3ri7YvXtwtOqrX7Vu+fmDDeuLFlm/oY+EwMBAnn32WTZu3MjmzZsJCQkZmL6QB9Pc3Mz27ds5ceIEYWFhPPLII8yePdtrV3319lq/g90uMN1wPCpBQTB2rBWQPvWpwcA0frzvH8l0o6CgINLT00m/4dR00zS5evXqQKjqv9lNG3L6qJKSEn75y1/y2c9+ljHXd0M0TWu+fNUq+PnPbS7QC7zzd1tY9e01/FPGN/hG4G989ugDb3bhwmBf1c6d1j5WMTFWo/qqVVbj+ki0z3R2dvLKK69QU1PDc889x4QJE4b/RX1UR0cHe/bs4cCBAwDMnTuXRYsWecw0zie5etUKRzcHposXrV8E+iUk3H50afTokftFQO6eztrzQ52dnXzve99jxYoVLFq0aOD66tXWD58zZ2wszkt87Wul/OhHORQVXSM/P9rucuQTtLbCtm2Dwery9U7NWbMGG9ZnzrTOCBwOnZ2dvPrqq1RXV/Pss8+Sn58/PC/ko1wuFwcPHmT37t10dnYydepUnE6nR67E6+212iVvtzLuxtbUwEBrV/+bA9P48dYKVfEeClJ+6sc//jGpqak899xzA9e+8x1r4VlTk2cuLfck8+dXcO5cLE1NMXaXIvfINOH48cEpwMJC61pS0tDtFdz9M7qzs5ONGzdy+fJlnnnmGSZOnOjeF/BBpmly8uRJPvzwQ65evcqYMWN46KGHBs4NtdO1a7cfXbpwATo7Bx8XH2+FpJsDU26u9+3iL7enQ4v9VGpqKtXV1UOu9fdJHTwIjz5qQ1Feoq/PpKgonilTmgAFKW9jGNZ2H9OmWb84NDQMbq/w29/Cf/6n1YuyaNFgw3p+/oNvrxAWFsZnP/tZNm7cyG9+8xueeOIJZsyY4Z6/lA8qLi7mgw8+oKamhpSUFFavXk1ubu6I1tDXBxUVtx9dunzD+vOAACsYTZhgfe+8MTAlJnrO1hwy8hSkfFhKSgpFRUV0dnYOnHc0e7b1BV9YqCD1cU6evEZLSwzz5zfYXYq4QWLi4HY3Lpf1/79/h/W/+ivrlpMz2LDudFp7r92P0NBQPvvZz/Lmm2/y1ltv0dLSwtKlS31qldmDqq2tZdu2bVy8eJHY2FieeuopCgoKhvVz1NoK58/fGpjOn4eOjsHHxcZaAenhh4eGpTFjQCcCye0oSPmw/h3Oa2pqBpaGRkfD5MnamPNjbdzIOy+VAX/LI7/9a5i6Wk3mPqR/JGrRImuqu6LCClXvvGMtwvjXf7VC1PLlg71V97qHcEhICJ/5zGd4++232blzJy0tLTzxxBN+f5xMc3MzO3bs4Pjx44SFhfHwww8zZ84ct63E6+uzjh663cq4/iOJwBpdGj3aCkgrVgwNTElJGl2Se6Mg5cNuPCrmxj025s2D3/zG+qbj59/Xb3X9aJhdCW8SGtrJ0vObYP3b1vsUpnxSZiZ8+cvWrbPTWv3X31u1dav1mEmTBkPVggV3t2dPYGAgq1evJjo6mt27d3P16lWeffZZr1l95k7t7e3s3r2bQ4cOATB//nwWL15835+LtjZrJOnmwHT+/NBj32JirIDkdA7tXxo7VqNL4j5qNvdx//zP/0x2djZPP/30wLWXX4YvftH6xqMtb25yfSPO9FGVJIQ1cuLy9Q23tBGn3zFN6wdzf6DatcuaFoyNtabF+7dXcDg++bmOHTvG1q1biY6OZu3atR7RSD0Suru7KSwsZN++fXR3dzN16tS7PhPPNK3NWG8OS2fPWqOI/QzD+rLtD0k3BqbkZI0uiXuo2dyPfVzDeWGhgtQtysupDUmiuimVR3PeH3Jd/IthDC5V//rXoaVl6PYKb7xhPWb27MHRqunTbz/KO336dBwOB2+88QY/+9nPeOKJJ5gyZYrP9k319vZy9OhRdu7cSVtbGxMmTGD58uU4bpM6OzruPLrU2jr4uKgoKxwtWXLr6JIfDvKJB1GQ8nEpKSmcO3eO7u5uQq6vw50wwRryLiyEz33O5gI9TVYWW7uWY9YEsLzrwyHXxb/FxMDTT1u3vj7rqKX+0apvfQv+4R8gJcVqVl+50mpWjrlhwWdGRgbr16/nN7/5DZs3b+bixYusWrVqYCGIV9q40VoWWV4OWVm4vv1tPpowgT179nD16lWys7P5zGc+Q3p6BtXV8OGHtwam8nJr9Klfdrb1PWrRoqGBKTVVo0vimTS15+POnz/P66+/zuc//3mys7MHrj/yiHXo5bFjNhbniTZuZN3fBfCr0k9TH5TIqJ5m62iYDRvUIyV3VFcH771njVS9/751dlpwMCxePDhalZdnBYG+vj727NnDjh07iImJ8d7Dd6/3E9LejisoiKPTp7N9npMyVw6mmUdY2DTq60dx7pzBuXPWnkz9IiMHR/tuDEvjxtl/GLXI7WhDTj/W2trKD37wAx555BHmz58/cP3v/9468aSlxfqmJoMm5JbT2QqlDTnWSJSOhpF74HLBvn2DU4CnTlnXc3MHQ9XSpdDYWMWmTZtoampi6tSpPPzwwwPnYnoilwuqq63+pIoKKP/j71ByLZbTMZMpDsnlSms8bW1RQz4mM/P2x6Ckp2t0SbyLeqT8WFRUFLGxsVRVVQ25Pm+eNT1x+LD1TV0sra0uLlWksWZNBfymz+5yxAsFBVl9PEuWwPe+B2Vlg3tW/fSn8H/+jzXqsmJFOo899ifk5e3n5MntnD9/XY/gRAAAGo1JREFUHqfTyYwZMwgMDBzRmk3TGqGuqLCm2vrD0kBoKrdCVG/vjR/1t4SGdBIT1EJKUA2LjD3kU0QeFxl/9HXy8vRLmvgHBSk/kJ6ezuUbt+gF5s613hYWKkjdaOvWRlyuZFas0JeGuEd2NvyP/2HdOjpgx47B3qq33goEFjFx4jxycoo4e/YwU6Yc4KGHljFp0iSrGf2mPqT7GSG9evXOAamiwtpj6cYDdcHaHiAz07otXw4ZGSZhYXW0tZ2lpeU08VFXmHXxCPMKC0mtumFBS3Y2TH/gT5uI19BPCz+QlpZGUVER7e3tRFxvQEhIsPoRtDHnDTZu5L1/DMAw1rLmB09BzNc0pSduFR5ubZnw+OPWyNSZM/2jVUH87ncFuFxTiIjo5Gc/u8DMmb/nDyaWs+SlrxHc0mI9QVmZ1ZcEA/83OzruHJD6bzf2J4F1mG5amhWSZs2Cp56yMlp/cMrMtLZ1MAxoamri2LFjHD9+nGvXrpGQEMEjj8xkdkUF0f/6naEbN0VEWEFPxI8oSPmB9PR0AC5fvszYsWMHrs+bBx98YA3r+32/wvXG2cKow2QmVpB26cgtP7BE3MkwYOJE6/aNb8DVqwa/+x28804ov/3tBE6dKuA/MclOW47TsZ059QdpaYmhoj2Tii8lUfEDKyQ13OYUo6QkKwyNHw8PPTQ0IGVmWivgPm5T0cbGRvbsKeLMmTNUV1djGAZjx47l8ccfJy8vb3DqMSjogUfLRLydms39QFdXF9/97ndZtmwZS2+Yx/u3f4OvfMXaZ/KGBX3+KSeH9vI6YgOu8qmst9hU8ox1XRtxig2s/kWT1x75F94OfIJLTYO/AEUGtpIZUMHohyaQlWUMhKP+EaX0dLjXHRU6OjooKSkZuDU2NgLWL2H5+fkUFBQQE6PDu8V/qdncz4WGhuJwOG7pk7pxY06/D1Ll5bwT/xSupmBW9P5+yHWRkRYQAHPmGMyJ+xE/KvsaxeE5HBozh4bpiTTkWnNuISEhZGZmkpKSQnJyMomJiURHRxMSEgHcuiuoaZp0dnbS3NzMlStXaGpqoqamhurqapqamgAIDg4mOzubWbNmkZ+ff1c7kIv4OwUpP5GWlsbFixcxTXNgN+WCAqtno7AQ1v7/7d17cFTnecfx76O7RFAkLATWhRUgyRYGjLhYcpz4UjtxqLnYjpMmwRmnaeu0UzdOnUydlk7SGRdPx0ldp3UnM56kcTsmSR3bDBSMEY1xgk0NtkWwACGBQBYIkLgbXdD17R9HEiwWWKx296zY32dGI+nd1TnPnJG0vz3ve57zRz4X6LcpU3itdyFm/Sw+uSZoXMQ3K1bAww8zraORaTsbYSd0TJhA45NPsj8/n+bmZt5++236LriczsxIS0sjMTFx6CbJXV1ddHd3c/EMRFZWFtdeey1z5syhqKiIvLy8qF8xKDLWKUjFifz8fHbs2MGHH3449C4zOdlbaKoF58CKFWx5rJyCiYeY0jpwm3gtnBW/Da43umAdUsaKFcxYtowZA0/p6+vjxIkTnDhxgra2Ns6ePUtnZyf9/f3093stPFJSUkhNTSU9PZ2srCyysrLIzs4e213VRWKEglScyMvLA6C5uTnodH1lJfz4x96lz/F8N/TO+7/K3q/3cU/JBjhmWjgrsWPZssv+HiYmJpKbm0tubm4UixKRQcPcXlOuRpMmTSIxMXHYxpzd3d59w+LZhg1n6O1N4o5vXu+t9G1sVIgSEZGPpSAVJ5KSkpg0adJlF5zHs1df7cCsnyVLJvhdioiIjCEKUnFksMP54LoJON+UL96D1JYtyeTnt1JUlOV3KSIiMoYoSMWR/Px8uru7OX5RB7/KyvgOUp2djrq6bMrLPxy6olFERGQkFKTiSEFBAQCHDh0KGq+s9JYEHT3qQ1Ex4De/aae3N4nbb/e7EhERGWsUpOLIhAkTSE9P5+DBg0Hjg+uktm71oagYsHZtG2b9LFqkaT0REbkyClJxxMwoLCz8yBmp8nLvllnxOr335ptJ5OW1UlIy0e9SRERkjFGQijMFBQUcP36czs7OobH0dJgzJz6DlLc+Kou5c7U+SkRErpyCVJwpLCwEhl8n9c470NvrR1X+2bjxrNc/6g6FKBERuXIKUnEmLy8PMxt2nVR7O+za5VNhPhlcH7V06TV+lyIiImOQglScSUlJYfLkycOekYL4m9576y2vf9TUqdl+lyIiImOQglQcKigooLm5Oagx57RpkJMTX0Gqs9NRX5/N3LlntT5KRERCoiAVhwoLC+nu7qa1tXVozCz+GnO+9tppenuT+IM/0J+BiIiERq8gcWiwMedw66T27IFTp/yoKvrWrWvHrJ97783xuxQRERmjFKTiUFZWFuPGjbvkOqlt23woygdbtqRQUHCMQOCTfpciIiJjlIJUHBpszHnxGakFC7wpvniY3uvo6Gfv3gnMm3fW71JERGQMU5CKUwUFBZw6dYq2trahscxMuOGG+AhS69eforc3iTvvTPK7FBERGcMUpOLUlClTgOHXSW3dChdc0HdVevXVDvWPEhGRUVOQilN5eXkkJSXR2NgYNF5Z6S0237vXn7oibuVKKCpiy9o2CiY2U/i7NX5XJCIiY5iCVJxKTEyksLCQpqamoPGrujHnypXw8MO0HTzGvhPFzB/3Djz8sDcuIiISAgWpOBYIBDh69GjQDYzLyry1UldlkFq+HDo6eDHnS/T2JfO57iro6PDGRUREQqAgFccCgQAQvE4qIQFuuukqDVJNTRygiO+cfpqsrFN8qfW/h8ZFRERCoSAVx/Lz80lMTBx2ndT773s3Mb6anMyfxULW020p/M3tTzGh57T3wMDCexERkSulIBXHkpOTyc/PH3adVH8/vPuuT4VFwLlzsDRjI40U8UdffZFPn3jLeyAjA1as8Lc4EREZsxSk4lwgEODw4cN0dXUNjVVUeJ+vlum9/n546CF4sz6XJ/50M4FAE9MbGiAQgOeeg2XL/C5RRETGKAWpOBcIBHDOBd0uJicHiouvniD1+OPw4ovwwx9C8R+2kZGRwbWHDkFjo0KUiIiMioJUnCssLMTMhl0n9fbb4Jw/dYXLs8/Cj34EjzwCjz3maGhoYNq0aZiZ36WJiMhVQEEqzqWkpJCXlzfsOqmjR8f2BW2rV8Ojj8LSpfDMM9Da2kJ7ezvTp0/3uzQREblKKEgJgUCA5uZmenp6hsbGemPOrVvhK1+B+fPhF7+AxERoaGgAUJASEZGwUZASAoEAfX19QeukZs+GtLSxGaQaGmDxYrj2Wvif//EuzPPGG8jNzWX8+PH+FigiIlcNBSkhEAhgZuzfv39oLDnZO5sz1oLU8eOwcKF3pd769ZCb6413dXXR1NSks1EiIhJWClJCamoqBQUFQUEKvOm97dvhgs4IMa2zE5Ys8dZ1rVkDpaXnH9u/fz99fX2UXjgoIiIySgpSAsC0adM4fPhw0H33Kiu9ELVjh4+FjVBfHzz4oHcGbeVK+NSngh+vr68nLS2NKepiLiIiYaQgJYAXpICgNghjacH5d78Lr7wCTz8NX/hC8GPOOerr6ykuLiYhQb/yIiISPnpVEcC7715KSsrQlW3eGBQUxH6QeuYZ7+PRR+Hb3/7o483NzXR0dGhaT0REwk5BSgBITEykqKiIAwcOBI0PNuaMVS+/DI89BvffD//8z8M/p76+HjOjuLg4usWJiMhVT0FKhkybNo2TJ09y+vTpobHKSjhwAFpafCzsErZs8dZFVVbCCy94vaKGU19fz5QpU0hPT49ugSIictVTkJIhg+ukLrx6b3Cd1NatflR0afX13hV6BQXeFXqXykhnzpyhpaVF03oiIhIRClIyJCcnh/HjxwcFqblzISkptqb3Wlu9XlFmXq+onJxLP7e+vh5AQUpERCIiye8CJHaYGdOnT2fPnj309/eTkJBAejrMmRM7Qaqjw+tafuQIbNoEH7fsqb6+nuzsbK655proFCgiInFFZ6QkSHFxMefOnQu6XUxlJWzb5vVq8lNfH3z1q/DOO9798yoqLv/8rq4uDhw4QGlpKWYWnSJFRCSuKEhJkOnTp5OQkDA0JQZekGpvh127/KvLOa+1werV8K//Cvfe+/E/s3fvXvr6+igrK4t8gSIiEpcUpCTIYPfvvXv3Do3FQmPOp5+GZ5+F73wHHnlkZD9TW1vLuHHjKCwsjGxxIiIStxSk5CNKSkpobW3lzJkzAEyb5i3o9itI/frXXufyL34RnnpqZD/T09PD3r17KSsrUzdzERGJGL3CyEeUlJQADJ2VMvOvMeebb8LXvgaf/jT813/BSDPRvn376Onp0bSeiIhElIKUfEROTg5ZWVkfmd6rrYULenVGXF2d1yuqqMhbG5WWNvKfra2tJT09naKiokiVJyIioiAlH2VmlJSUsH//fnp7e4Hz66S2bYtODS0tXq+o5GR49VWYMGHkP9vb20t9fT3XXXedpvVERCSi9CojwyotLaW3t3fo3nsLFnhTfNGY3mtvh0WLvDC1dq23RutK7N+/n66uLmbMmBGZAkVERAYoSMmwioqKSE1Npba2FoDMTLjhhsgHqd5e+PKXoboafvUrL8BdqV27dpGWlsbUqVPDX6CIiMgFFKRkWElJSZSWlg51OYfzC86di8w+nYNvfcs7C/Xss14H8yvV3d1NbW0tZWVlJCWpcb+IiESWgpRcUllZGZ2dnTQ2NgJekDp1Ci5Ygx5WTz0FP/kJPP44/MVfhLaNuro6enp6mD17dniLExERGYaClFxScXExycnJQ9N7kWzM+ctfwve+503rPflk6NupqakhMzOTQCAQvuJEREQuQUFKLik5OZmSkpKh6b2yMm+tVLiD1G9/C1//Otx2Gzz//Mh7RV2so6ODhoYGZs6cqXvriYhIVChIyWWVlZXR1tbGwYMHSUiAm24Kb5Davdu7b9706bBqFaSmhr6tXbt20d/fz6xZs8JXoIiIyGUoSMlllZSUkJiYGDS99/77XouC0TpyxOsVlZYG69dDdvbotldTU8PEiROZNGnS6IsTEREZAQUpuazU1FSKi4vZvXs3/f39VFZCXx+8997ottvWBvfcAydOwLp1MNolTSdOnODgwYPMmjVL03oiIhI1owpSZvZFM9tlZv1mNj9cRUlsmTlzJmfPnqWxsZGKCm9sNNN7vb3wpS95Z7Z+/WuYO3f0NVZXV2NmzJkzZ/QbExERGaHRnpHaCdwP/C4MtUiMuu6660hNTaWmpoacHCguDj1IOee1Nli/3mt1sHDh6Ovr6+tjx44dlJaWMn78+NFvUEREZIRGFaScc7XOubpwFSOxKTk5mbKyMnbv3k1PTw+VlfB//xdaY84nn4Sf/hSWL4c/+7Pw1FdfX097eztzw3FqS0RE5ApEbY2UmT1sZu+a2bvHjh2L1m4lTG688Ua6u7vZs2cPlZVw9CgcPHhl23jhBfj7v4cHH4QnnghfbdXV1YwfP57i4uLwbVRERGQEPjZImdn/mtnOYT6WXsmOnHPPOefmO+fmT5w4MfSKxReBQIDMzEzef//9kBpzvv46fOMbcMcd8LOfeTdADofTp0+zb98+ysvLSQi1AZWIiEiIPvaVxzl3l3Nu5jAfq6NRoMQGM+PGG2+koaGBQOAMaWkjD1I7d8J990FpKbzyCqSkhK+u7du3A1BeXh6+jYqIiIyQ3sLLiM2dOxfnHDU11cyfP7Ig1dzsLSj/xCe8BeZZWeGrp7e3l/fee4+SkhKywrlhERGRERpt+4P7zOwQcDOwzsw2hKcsiUVZWVkUFxezfft2Kioc1dXQ1XXp53/4odcr6vRpr1dUYWF466mpqaG9vZ3KwblGERGRKBvtVXurnHMFzrlU59wk59zd4SpMYtO8efM4e/YsU6YcpqsLduwY/nk9PfDAA9603ksvQbjbOznn2Lp1K7m5uUydOjW8GxcRERkhTe3JFTnfq8mb1xtues85+OY3YeNGeO45uDsC8bqxsZGWlhYqKirUyVxERHyjICVXJCEhgXnz5nHq1E7y8vqGDVJPPAE//zl8//velXqRsGXLFjIyMpg9e3ZkdiAiIjICClJyxRYsWEBSUhJFRUc/EqSefx5+8AN46CH4h3+IzP6bm5vZt28fN998M0lJSZHZiYiIyAgoSMkVy8jIoLy8nMzM3Rw4AC0t3vjGjV638rvu8qb0IjXjtnnzZtLS0liwYEFkdiAiIjJCClISkptvvpn8/EMAbN3qLTr/whdgxgx4+eXw9oq60NGjR6mrq6OyspLU1NTI7ERERGSEFKQkJNnZ2dxR/CEJCX389/0ruWfeETKTOli3DjIzI7ffN954g9TUVCoqKiK3ExERkRFSkJLQrFzJZ3/yNJMnH+UXfcs425fB+s7bKfjtyojtsrGxkbq6Om655RbS0tIith8REZGRUpCS0CxfTm5TE/PS3yMhoY8X0h9k1rl3YPnyiOzOOUdVVRWZmZlqwCkiIjFDlzxJaJqaAPi3E39F0TcbsSYH686Ph1tNTQ1HjhzhvvvuIzk5OSL7EBERuVI6IyWhmTIFgMDpJj7/wQaq582jJTd3aDycOjs7qaqqIi8vj1mzZoV9+yIiIqFSkJLQrFgBGRkA3L5pE2nnzrFuyRLcP/5j2HdVVVVFR0cHixcvVhdzERGJKQpSEpply7xmUYEAGefO8dnqag4WFLB9xoyw7qahoYHf//733HLLLUyePDms2xYRERktBSkJ3bJl0NgI/f3MqaqiqKiIDRs2cPLkybBsvr29ndWrV3PNNddw2223hWWbIiIi4aQgJWFhZtx7772YGatWraKvr29U23POsWrVKjo6OnjggQd0KxgREYlJClISNp/85CdZvHgxhw4dYu3atTjnQtqOc47XXnuNhoYGFi5cqCk9ERGJWXqbL2F1ww030NLSwubNm8nOzubWW2+94m289dZbbNu2jcrKSubNmxeBKkVERMJDQUrC7o477uD06dNs2rQJ5xy33nrriK62c86xadMmNm/ezMyZM/nc5z4XhWpFRERCpyAlYTe4XiohIYE33niDY8eOsXjx4sveZLijo4M1a9ZQV1dHeXk5ixYtUqsDERGJeQpSEhEJCQksXbqUnJwcXn/9dRobG/nMZz7DrFmzyBjoPwXQ1tbG9u3b2bJlCz09Pdx9991UVFQoRImIyJhgoS4IHo358+e7d999N+r7FX8cPnyYqqoqPvjgA8yMnJwcMjIyaG9v5/jx4wCUlJRw5513MmnSJJ+rFRERCWZm7znn5g/7mIKURINzjiNHjlBbW8vx48fp6Ohg3LhxTJ48meuvv57c3Fy/SxQRERnW5YKUpvYkKsyMvLw88vLy/C5FREQkbNRHSkRERCREClIiIiIiIVKQEhEREQmRgpSIiIhIiBSkREREREKkICUiIiISIgUpERERkRApSImIiIiESEFKREREJEQKUiIiIiIhUpASERERCZGClIiIiEiIFKREREREQqQgJSIiIhIiBSkRERGREClIiYiIiIRIQUpEREQkRApSIiIiIiEy51z0d2p2DPgg6jv2Rw5w3O8iYoiOx3k6FsF0PILpeJynYxFMxyNYNI5HwDk3cbgHfAlS8cTM3nXOzfe7jlih43GejkUwHY9gOh7n6VgE0/EI5vfx0NSeiIiISIgUpERERERCpCAVec/5XUCM0fE4T8cimI5HMB2P83Qsgul4BPP1eGiNlIiIiEiIdEZKREREJEQKUlFkZt81M2dmOX7X4icz+6GZ7TGz981slZll+V1TtJnZ582szsz2mdn3/K7HT2ZWaGabzKzWzHaZ2aN+1+Q3M0s0s+1mttbvWvxmZllm9tLA/4xaM7vZ75r8YmZ/PfA3stPMfmlmaX7XFE1m9h9m1mpmOy8Ym2BmG81s78Dn7GjXpSAVJWZWCHwWaPK7lhiwEZjpnJsN1AN/63M9UWVmicC/AwuBGcBXzGyGv1X5qhf4jnOuDKgE/jLOjwfAo0Ct30XEiB8DrznnrgduJE6Pi5nlA98C5jvnZgKJwJf9rSrqngc+f9HY94DfOOdKgN8MfB9VClLR8y/A3wBxvyjNOVflnOsd+PZtoMDPenxwE7DPObffOdcN/ApY6nNNvnHOHXHOVQ98fRbvhTLf36r8Y2YFwD3AT/2uxW9mlgncCvwMwDnX7Zw77W9VvkoC0s0sCcgADvtcT1Q5534HnLxoeCnwnwNf/ydwb1SLQkEqKsxsCdDsnNvhdy0x6BvAer+LiLJ84OAF3x8ijoPDhcysCCgHtvpbia+ewXvT1e93ITFgGnAM+PnAVOdPzWyc30X5wTnXDPwIb1bjCHDGOVflb1UxYZJz7gh4b8qA3GgXoCAVJmb2vwPz1hd/LAWWA9/3u8Zo+pjjMfic5XjTOiv9q9QXNsxY3J+pNLNPAC8D33bOfeh3PX4ws0VAq3PuPb9riRFJwFzgJ865cqAdH6ZuYsHA2p+lwFQgDxhnZg/6W5WA90sqYeCcu2u4cTObhfeLv8PMwJvGqjazm5xzR6NYYlRd6ngMMrOHgEXAnS7+enAcAgov+L6AODtFfzEzS8YLUSudc6/4XY+PbgGWmNkfAmlAppm94JyL1xfMQ8Ah59zgGcqXiNMgBdwFHHDOHQMws1eATwEv+FqV/1rM7Frn3BEzuxZojXYBOiMVYc65GudcrnOuyDlXhPePYe7VHKI+jpl9HngcWOKc6/C7Hh+8A5SY2VQzS8FbMLrG55p8Y947jJ8Btc65p/2ux0/Oub91zhUM/K/4MvB6HIcoBv5PHjSz6waG7gR2+1iSn5qASjPLGPibuZM4XXh/kTXAQwNfPwSsjnYBOiMlfngWSAU2Dpyle9s59+f+lhQ9zrleM3sE2IB35c1/OOd2+VyWn24BvgbUmNnvB8b+zjn3qo81Sez4K2DlwJuO/cAf+1yPL5xzW83sJaAab0nEduKsw7mZ/RK4Hcgxs0PAD4B/Al40sz/BC5tfjHpd8TerIiIiIhIemtoTERERCZGClIiIiEiIFKREREREQqQgJSIiIhIiBSkRERGREClIiYiIiIRIQUpEREQkRApSIiIiIiH6f9NyiBr65S3DAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy import interpolate # Interpolation routines\n", "fi = interpolate.interp1d(x,func(x)) # returns the interpolation function\n", "plot1(fi,label='interp1d')" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on class interp1d in module scipy.interpolate.interpolate:\n", "\n", "class interp1d(scipy.interpolate.polyint._Interpolator1D)\n", " | interp1d(x, y, kind='linear', axis=-1, copy=True, bounds_error=None, fill_value=nan, assume_sorted=False)\n", " | \n", " | Interpolate a 1-D function.\n", " | \n", " | `x` and `y` are arrays of values used to approximate some function f:\n", " | ``y = f(x)``. This class returns a function whose call method uses\n", " | interpolation to find the value of new points.\n", " | \n", " | Note that calling `interp1d` with NaNs present in input values results in\n", " | undefined behaviour.\n", " | \n", " | Parameters\n", " | ----------\n", " | x : (N,) array_like\n", " | A 1-D array of real values.\n", " | y : (...,N,...) array_like\n", " | A N-D array of real values. The length of `y` along the interpolation\n", " | axis must be equal to the length of `x`.\n", " | kind : str or int, optional\n", " | Specifies the kind of interpolation as a string\n", " | ('linear', 'nearest', 'zero', 'slinear', 'quadratic', 'cubic',\n", " | 'previous', 'next', where 'zero', 'slinear', 'quadratic' and 'cubic'\n", " | refer to a spline interpolation of zeroth, first, second or third\n", " | order; 'previous' and 'next' simply return the previous or next value\n", " | of the point) or as an integer specifying the order of the spline\n", " | interpolator to use.\n", " | Default is 'linear'.\n", " | axis : int, optional\n", " | Specifies the axis of `y` along which to interpolate.\n", " | Interpolation defaults to the last axis of `y`.\n", " | copy : bool, optional\n", " | If True, the class makes internal copies of x and y.\n", " | If False, references to `x` and `y` are used. The default is to copy.\n", " | bounds_error : bool, optional\n", " | If True, a ValueError is raised any time interpolation is attempted on\n", " | a value outside of the range of x (where extrapolation is\n", " | necessary). If False, out of bounds values are assigned `fill_value`.\n", " | By default, an error is raised unless ``fill_value=\"extrapolate\"``.\n", " | fill_value : array-like or (array-like, array_like) or \"extrapolate\", optional\n", " | - if a ndarray (or float), this value will be used to fill in for\n", " | requested points outside of the data range. If not provided, then\n", " | the default is NaN. The array-like must broadcast properly to the\n", " | dimensions of the non-interpolation axes.\n", " | - If a two-element tuple, then the first element is used as a\n", " | fill value for ``x_new < x[0]`` and the second element is used for\n", " | ``x_new > x[-1]``. Anything that is not a 2-element tuple (e.g.,\n", " | list or ndarray, regardless of shape) is taken to be a single\n", " | array-like argument meant to be used for both bounds as\n", " | ``below, above = fill_value, fill_value``.\n", " | \n", " | .. versionadded:: 0.17.0\n", " | - If \"extrapolate\", then points outside the data range will be\n", " | extrapolated.\n", " | \n", " | .. versionadded:: 0.17.0\n", " | assume_sorted : bool, optional\n", " | If False, values of `x` can be in any order and they are sorted first.\n", " | If True, `x` has to be an array of monotonically increasing values.\n", " | \n", " | Attributes\n", " | ----------\n", " | fill_value\n", " | \n", " | Methods\n", " | -------\n", " | __call__\n", " | \n", " | See Also\n", " | --------\n", " | splrep, splev\n", " | Spline interpolation/smoothing based on FITPACK.\n", " | UnivariateSpline : An object-oriented wrapper of the FITPACK routines.\n", " | interp2d : 2-D interpolation\n", " | \n", " | Examples\n", " | --------\n", " | >>> import matplotlib.pyplot as plt\n", " | >>> from scipy import interpolate\n", " | >>> x = np.arange(0, 10)\n", " | >>> y = np.exp(-x/3.0)\n", " | >>> f = interpolate.interp1d(x, y)\n", " | \n", " | >>> xnew = np.arange(0, 9, 0.1)\n", " | >>> ynew = f(xnew) # use interpolation function returned by `interp1d`\n", " | >>> plt.plot(x, y, 'o', xnew, ynew, '-')\n", " | >>> plt.show()\n", " | \n", " | Method resolution order:\n", " | interp1d\n", " | scipy.interpolate.polyint._Interpolator1D\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __init__(self, x, y, kind='linear', axis=-1, copy=True, bounds_error=None, fill_value=nan, assume_sorted=False)\n", " | Initialize a 1D linear interpolation class.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | __dict__\n", " | dictionary for instance variables (if defined)\n", " | \n", " | __weakref__\n", " | list of weak references to the object (if defined)\n", " | \n", " | fill_value\n", " | The fill value.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from scipy.interpolate.polyint._Interpolator1D:\n", " | \n", " | __call__(self, x)\n", " | Evaluate the interpolant\n", " | \n", " | Parameters\n", " | ----------\n", " | x : array_like\n", " | Points to evaluate the interpolant at.\n", " | \n", " | Returns\n", " | -------\n", " | y : array_like\n", " | Interpolated values. Shape is determined by replacing\n", " | the interpolation axis in the original array with the shape of x.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from scipy.interpolate.polyint._Interpolator1D:\n", " | \n", " | dtype\n", "\n" ] } ], "source": [ "help(interpolate.interp1d)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fi = interpolate.interp1d(x,func(x),kind='linear')\n", "plot1(fi,label='Linear')" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for knd, clr in ('previous','m'),('next','b'),('nearest','g'):\n", " fi = interpolate.interp1d(x,func(x),kind=knd)\n", " plot1(fi,label=knd,color=clr)\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for knd, clr in ('slinear','m'),('quadratic','b'),('cubic','g'):\n", " fi = interpolate.interp1d(x,func(x),kind=knd)\n", " plot1(fi,color=clr,label=knd)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Max error with slinear splines is 1.05142e+00\n", "Max error with quadratic splines is 3.89974e-01\n", "Max error with cubic splines is 4.35822e-01\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Approximation errors\n", "# x = np.sort(np.random.uniform(-5,10,11)) # generate new data\n", "for knd, clr in ('slinear','m'),('quadratic','b'),('cubic','g'):\n", " fi = interpolate.interp1d(x,func(x),kind=knd,bounds_error=False)\n", " xd = np.linspace(-5,10,1000)\n", " erd=np.abs(func(xd)-fi(xd))\n", " plt.plot(xd,erd,color=clr)\n", " print('Max error with %s splines is %1.5e'%(knd,np.nanmax(erd)))" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Max error with slinear splines is 4.63043e-01\n", "Max error with quadratic splines is 3.48546e-01\n", "Max error with cubic splines is 1.89578e-01\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Approximation errors for regular grid\n", "for knd, clr in ('slinear','m'),('quadratic','b'),('cubic','g'):\n", " fi = interpolate.interp1d(xr,func(xr),kind=knd,bounds_error=False)\n", " xd = np.linspace(-5,10,1000)\n", " erd=np.abs(func(xd)-fi(xd))\n", " plt.plot(xd,erd,color=clr)\n", " print('Max error with %s splines is %1.5e'%(knd,np.nanmax(erd)))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Accuracy of the interpolation\n", "\n", "How to reduce approximation errors?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- Number of nodes (more is better) \n", "- Location of nodes (regular is better) \n", "- Interpolation type (match function of interest) \n", "\n", "\n", "*In economic models we usually can control all of these*" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Polynomial approximation/interpolation\n", "\n", "Back to the beginning to explore the idea of replacing original\n", "$ f(x) $ with simpler $ g(x) $\n", "\n", "- Data set $ \\{(x_i,f(x_i)\\}, i=0,\\dots,n $ \n", "- Functional form is polynomial of degree $ n $ such that $ g(x_i)=f(x_i) $ \n", "- If $ x_i $ are distinct, coefficients of the polynomial are uniquely identified \n", "\n", "\n", "Does polynomial $ g(x) $ converge to $ f(x) $ when there are\n", "more points?" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from numpy.polynomial import polynomial\n", "degree = len(x)-1 # passing through all dots\n", "p = polynomial.polyfit(x,func(x),degree)\n", "fi = lambda x: polynomial.polyval(x,p)\n", "plot1(fi,label='Polynomial of degree %d'%degree,extrapolation=True)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# now with regular grid\n", "degree = len(x)-1 # passing through all dots\n", "p = polynomial.polyfit(xr,func(xr),degree)\n", "fi = lambda x: polynomial.polyval(x,p)\n", "plot1(fi,fdata=(xr,func(xr)),label='Polynomial of degree %d'%degree,extrapolation=True)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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OjUbDPikiIqIIE9FBCvAt7wW6tKdSqeBwODgjRUREFGEiPkgZcg2YaJ6AdyqwRvGZhnNJkmSqjIiIiIIdg1SOAfAC442BN5xPTExgaGhIpsqIiIgo2EV8kJJz5x7AhnMiIqJIEvFBauYsqUB37jkcDgghGKSIiIgiSMQHKW2cFpp4TcA797RaLex2O3fuERERRZCID1LA+Z17Ac5IAb9tOCciIqLIwCAF3869QHukAF+QGhkZwejoqAxVERERUbBjkIKvT2qydRIelyegcWYazjkrRUREFBkYpHDBzr0GXhVDREREc8cgBd/SHhD4EQh6vR6xsbGckSIiIooQDFL47REIrrOB7dwDfLNSXV1dAY9DREREwY9BCoDGrEFUShRcZwIPUg6HA319fZienpahMiIiIgpmDFLnGfONcJ2WZ0YKALq7uwMei4iIiIIbg9R5M0Eq0EuHExISAIDLe0RERBGAQeo8Y74RniEPprqmAhonJiYGUVFRbDgnIiKKAAxS5xnzzh+BcCawnXtCCCQkJHBpj4iIKAIwSJ1nzPcFKTn6pBISEtDZ2RnwMiEREREFNwap83QpOqhMKtmC1OTkJIaHh2WojIiIiIIVg9R5QiVgzJVn595Mwzn7pIiIiMIbg9QF5DoCweFwAODOPSIionDHIHUBY74RE80T8IwHdnmxTqdDbGwsgxQREVGYY5C6gDHfCEjAeF1gO/cA3/IegxQREVF4Y5C6wMwRCHL1SfX39/OqGCIiojDGIHUBQ44BEPIFKUmSeJ4UERFRGGOQuoDaqIY+Qy/L5cW8KoaIiCj8MUhdRK6de7GxsbwqhoiIKMwxSF3EkGfwXV7sDexUciEEHA4Hl/aIiIjCGIPURYz5RnhdXky2TQY8Fq+KISIiCm8MUheZvXNPpj4pXhVDREQUvhikLiL35cUAG86JiIjCFYPURaISoqC2qmW9KoZ9UkREROGJQeoiQgjZdu7p9XpYrVYGKSIiojDFIHUZxnwjxs8Efk0MAO7cIyIiCmMMUpdhzDNisnUS7hF3wGM5HA709vbC6/XKUBkREREFk4CDlBAiTQixXwhRK4Q4JYT4YzkKU9JMw/n42cBnpRwOBzweD/r7+wMei4iIiIKLHDNSbgB/KknSMgDXAnhSCFEgw7iKkXPnHhvOiYiIwlfAQUqSpA5JkirP/3oEQC2AlEDHVZJhqQFQA2O1YwGPZbPZIIRgkCIiIgpDsvZICSGWAFgJoFzOcRebKkoFw1IDXLWBz0hptVrExcUxSBEREYUh2YKUEMIM4HUAT0uSdMlR3kKIx4UQFUKIip6eHrledsGYCkwYOxX4jBTAnXtEREThSpYgJYTQwheiXpYk6Y3LPUaSpOckSSqVJKnUbrfL8bILylRownj9OLyTge+2s9vt6O/vx/T0tAyVERERUbCQY9eeAPCfAGolSfrHwEsKDsYCI+ABXHXyXBUjSRJ6e3tlqIyIiIiChRwzUusAPAjgZiHEsfMft8owrqJMBSYAgKuGO/eIiIjo8jSBDiBJ0mcAhAy1BBVDngFQQZY+qbi4OKjVagYpIiKiMMOTzX8PtV4NQ7ZBlhkplUoFm82GUGiyJyIiorljkLoCY4ERYzXy7dzr6uqSZSwiIiIKDgxSV2AqMGH87Di8U4Hv3HM4HBgeHsbExIQMlREREVEwYJC6AlOhCZJbwni9PHfuAeDyHhERURhhkLoCY4Hvzj05lve4c4+IiCj8MEhdgTHPCAh5jkCIjo5GVFQUgxQREVEYYZC6ArVRDX2WXpYjEIQQvCqGiIgozDBIXYWpwCTLjBTguyqGQYqIiCh8MEhdhbHACNcZF7xueXbuuVwujI6OylAZERERKY1B6ipMhSZI0/Lu3OOsFBERUXhgkLoKOe/cS0hIAMAgRUREFC4YpK7CmC/fEQgmkwlGo5FBioiIKEwwSF2F2qSGfoletoZz7twjIiIKHwxSc2AsNMpyBALg27nX29sLSZJkGY+IiIiUwyA1B6YCE1yn5dm5Z7fbMTk5iZGRERkqIyIiIiUxSM2BqdAEaUrCREPgFw5z5x4REVH4YJCaA1Oxb+fe6InAz3+y2+0AeHkxERFROGCQmgPjMiOgAsZOBN4nZTQaYTKZGKSIiIjCAIPUHKgNahhyDLIEKcA3K8UgRUREFPoYpObIXGyWPUhx5x4REVFoY5CaI1ORCeMN4/CMeQIeizv3iIiIwgOD1ByZik2AJM8J52w4JyIiCg8MUnM0s3Nv7CSDFBEREfkwSM2RIcsAlUElS58U79wjIiIKDwxScyTUAqZCk6wN5729vbKMRURERMpgkJoHU7FJlkM5AV+Q6u7u5s49IiKiEMYgNQ+mIhOmu6Yx1TMV8FgzO/dGR+UJZkRERLT4GKTmYbbhXIblvZmGc/ZJERERhS4GqXmQM0jNXF7MnXtEREShi0FqHqISoqC1aWU5AsFoNMJgMDBIERERhTAGqXkQQsjWcC6EgMPhYJAiIiIKYQxS82QqMmHs5Bgkb+C77Ww2G+/cIyIiCmEMUvNkKjbBO+bFxLmJgMdyOByYmJjgzj0iIqIQxSA1Twuxc4/Le0RERKGJQWqeTIW+ICVHnxSDFBERUWhjkJonjUUDfZYeY8fluXPPYDDwLCkiIqIQxSDlB/MKM0ar5dm5xzv3iIiIQheDlB/MJWaM143DPeoOeCzeuUdERBS6GKT8YC4xA5J8DecTExMYGwt8LCIiIlpcDFJ+MK8wA4Asy3u8c4+IiCh0MUj5QZeugyZGg9FjgQcp3rlHREQUuhik/CCEgLnELEuQMplM0Ov1DFJEREQhiEHKT6YVJoydGIPkCaxJnHfuERERhS4GKT+ZS8zwurwYrx8PeCzeuUdERBSaGKT8ZC4533Auw/Ke3W7H+Pg4d+4RERGFGAYpP5mWmSA0Qpade2w4JyIiCk0MUn5S6VQwFhhlm5ECGKSIiIhCDYNUAOTauWc2m6HX63mWFBERUYhhkAqAucSMqY4pTHVPBTQO79wjIiIKTQxSAZD7hHPeuUdERBRaGKQCMBukZNy553K5Ah6LiIiIFgeDVAC08Vro0nS8c4+IiChCMUgFyLxCnoZz7twjIiIKPQxSATKXmOE67YJnwhPQOBaLBTqdjkGKiIgohDBIBchcYgY8wNiJwE4ln9m5xyBFREQUOhikAmRe5Ws4Hzk6EvBYDFJEREShhUEqQPoMPTSxGoxWynNVjMvl4p17REREIYJBKkBCCFhWWWSbkQLYcE5ERBQqGKRkYF5lxtiJMXgnvQGNwyMQiIiIQotG6QLCgWWVBdK0hLGTY7Cssvg/Dnfu0Rx4PB50dHSgq6sLIyO+mVC1Wg2r1Yr4+HgkJCRAq9UqXCURUWRgkJKB5RpfeBqpHAkoSHHnHl1JV1cXysvLcerUKUxN/f77HdVqNVJTU5GTk4PCwkLExMQsYpVERJGFQUoG+iw9NDEaX5/UNwMby26348yZM/IURmFhYmICu3fvRlVVFbRaLQoLC5GTk4Pk5GRYLBaoVCq43W4MDQ2ht7cXTqcTTU1N2Lt3L/bu3Yu0tDSsXr0ay5Ytg1qtVvrTISIKKwxSMhBCwHyNGaNH5TnhvKqqCmNjYzCZTDJUR6Gso6MDu3btwvDwMK699lqsX78eBoPhksdptVrYbDbYbDbk5+cDAAYGBnDq1ClUVVXh9ddfh8ViwerVq1FWVgadTrfYnwoRUVhikJKJZZUFrf/SCu+UF6oo/3v4L9y5xyAV2Zqbm/HKK69Ar9fj4YcfRlpa2ryeHxsbi+uvvx7r1q1DXV0dysvLsW/fPhw6dAjXX389ysrKoNHwLYCIKBB8F5WJZZUF0pSEsVNjsKz0v0/K4XAA8AWpJUuWyFQdhZq2tja89NJLiImJwYMPPgir1er3WEII5ObmIjc3F21tbfj444+xe/duHDp0CJs2bUJRURGEEDJWT0QUOXj8gUzM1/hOOA/0YE7u3KOhoSH8+te/htlsxkMPPRRQiLpYSkoKHnzwQTz00EMwm81444038OKLL/LIDSIiPzFIycSQbYDaqg74YE7u3ItsHo8Hu3btgtvtxgMPPACz2bwgr7NkyRJ84xvfwG233Yauri787Gc/w/79++HxBHb5NhFRpGGQkolQCViuke+Ec84QRKaDBw+ivb0d27dvn+2XWygqlQqlpaX4zne+g+LiYhw4cAC/+MUv0NXVtaCvS0QUThikZGReZcZo9Si804GfcM479yJPR0cHDhw4gOXLl6OgoGDRXtdoNOKuu+7CH/zBH2BkZATPPfccPvvsM0iStGg1EBGFKgYpGVmusUCalOCqdQU0Du/cizySJOG///u/YTAYsG3bNkVqyM/PxxNPPIG8vDzs27cPr7zyClyuwL6WiYjCHYOUjGZONQ90eY9BKvKcOHECTqcTGzduhF6vV6wOo9GIe++9F7feeiuamprw85//HK2trYrVQ0QU7BikZGTIMUBtCbzh3Gq1cudeBHG73fj444+RlJSElStXKl0OhBAoKyvDo48+CpVKheeffx5Hjx5VuiwioqDEICUjofKdcD5SwZ17NHdVVVUYGhrCxo0bg+o8p+TkZDz++OPIzMzEe++9h927d8PrDaz/j4go3DBIycy62orRqlF4pwL7hmOz2RikIoDb7cZnn32GtLQ0ZGVlKV3OJQwGAx544AGUlZXh0KFD2LVr1xUvTCYiijQMUjKzrPadcD56PLCDOR0OB8bGxtjsG+aOHz+O4eFhbNiwIahmoy6kUqlw6623Ytu2bTh79iyef/557iglIjpPliAlhPilEKJbCHFSjvFCmXW17xTqkXI2nNOVSZKE8vJyJCQkBOVs1MVWr16N+++/H729vXj++ecxNDSkdElERIqTa0bqBQBbZRorpOnSdNAmaDF8eDigcWaCFA/mDF/nzp1Dd3c31qxZE7SzURfLycnBgw8+iNHRUfzyl79Eb2+v0iURESlKliAlSdIBAP1yjBXqhBCwrrZi5HDgO/eioqI4IxXGysvLYTQaUVxcrHQp85Keno6HH34YHo8Hzz//PDo7O5UuiYhIMeyRWgCW1Ra4TrvgHnL7PQZ37oW3/v5+nDlzBqtWrYJGo1G6nHlLTEzEI488Ao1GgxdffJHXyhBRxFq0ICWEeFwIUSGEqAj3cDDbJxXgMQgMUuHr2LFjEEKgtLRU6VL8Fh8fj4ceemg2TPFrlYgi0aIFKUmSnpMkqVSSpNKFvoxVaZZS3wnncvRJcede+JEkCdXV1cjOzobValW6nIDExcXhoYcegkqlwq9+9Sv2TBFRxOHS3gLQxmlhyDEE3CflcDgAcOdeuGlqasLw8DBWrFihdCmymJmZAoAXX3wRg4ODCldERLR45Dr+4NcADgHIE0K0CiEek2PcUGZdY8Vw+TAkSfJ7DB6BEJ6qq6uh0+mQn5+vdCmysdls+PrXv47p6Wm89NJLnEUloogh1669+yVJSpIkSStJUqokSf8px7ihzLLagqmOKUy2Tfo9BnfuhZ/JyUnU1NSgqKgoJJvMr8ThcOD+++/H0NAQXnnlFZ6ATkQRgUt7C2S24TyA5T3u3As/tbW1cLvdYbOsd7H09HTcc889aG9vx29+8xt4PB6lSyIiWlAMUgvEtMIEoRWyNJzzUM7wUVtbi+joaKSmpipdyoLJz8/Hbbfdhvr6erz33nsBLW8TEQU7BqkFotarYV5hDrjhnDv3wsfExAQaGhqwbNmykDnJ3F+rVq3CDTfcgGPHjuHQoUNKl0NEtGAYpBaQZbUFIxUjkDxsOCfg7Nmz8Hg8KCgoULqURXHTTTehoKAAe/bswZkzZ5Quh4hoQTBILSDrais8Ix64Tvs/m8QjEMJHTU0NrFZrWC/rXUgIgR07diApKQlvvPEGTz8norDEILWArNf6Gs6Hv/S/T4o798LD5OQk6uvrI2JZ70JarRb33XcfdDodfv3rX2N0dFTpkoiIZMUgtYAMuQZo4jQY+mLI7zG4cy881NXVRdSy3oWsVivuu+8+jI2NcScfEYUdBqkFJISA9Torhr8IfOceg1Roq6urg9FojJhlvYslJydj+/btaGlpwZ49e5Quh4hINgxSCyx6bTRcp12Y7pv2ewy73Y7R0fXtxnoAACAASURBVFGMj4/LWBktFq/Xi7q6OixduhQqVeT+lysuLsaaNWtQXl6OEydOKF0OEZEsIvddfZFY1wbeJ8Wde6Gtra0N4+PjyMnJUboUxW3atAlpaWl49913eT4aEYUFBqkFZi2zAmoE1Cc1E6T4jSc0nT17FkIILF26VOlSFKdWq3HvvfdCp9Ph1VdfxcTEhNIlEREFhEFqgalNaphLzBg+5P+MVHR0NHfuhbC6ujqkp6dDr9crXUpQsFgsuPfeezE4OIi3336bJ58TUUhjkFoE0WujMVw+DK/b69fzhRCw2WwMUiFoaGgIXV1dXNa7SHp6OjZu3IjTp0/jyJEjSpdDROQ3BqlFYF1rhdflxdjxMb/HcDgcDFIhqK6uDgCQm5urcCXB57rrrkNOTg52796Nzs5OpcshIvILg9QiiF4bDSCwPimbzcadeyGorq4OMTExsNlsSpcSdGZOPjcajXjttdcwNTWldElERPPGILUIdGk6RKVEBXSeFK+KCT0ejwdNTU1YunRpRJ1mPh9GoxF33303+vv78f777ytdDhHRvDFILQIhBKKvi5Zl5x6DVOhobW3F9PQ0srOzlS4lqC1ZsgTr16/H8ePHcezYMaXLISKaFwapRWJda8Vk8yQm2yf9en50dDS0Wi2DVAhpbGyEEAJLlixRupSgt379emRkZOCDDz5AX1+f0uUQEc0Zg9QimemT8vcYBN65F3oaGxuRnJzMYw/mQKVS4e6774ZGo8Ebb7zB+/iIKGQwSC0S80ozhE4EvLzHQzlDw8TEBNra2pCVlaV0KSHDarXi9ttvR3t7Ow4cOKB0OUREc8IgtUhUUSpYy6wY+jywIMWde6GhubkZkiQxSM1TQUEBVqxYgYMHD8LpdCpdDhHRVTFILaLoG6IxenQUnjH/li3YcB46GhsbodFokJqaqnQpIWfbtm2Ijo7Gm2++ySMRiCjoMUgtouj10ZDckt8XGPMIhNDR2NiIjIwMaDQapUsJOTqdDjt27MDAwAA+/PBDpcshIroiBqlFFL02GlABgwcG/Xs+d+6FhOHhYfT29nJZLwAZGRlYt24dqqqqcObMGaXLISL6vRikFpHGqoF5pRlDB/zrk+LOvdDQ1NQEAAxSAbrpppuQmJiId955B6Ojo0qXQ0R0WQxSiyxmfQyGvxyGd9K/C4wZpILfuXPnYDAYkJCQoHQpIU2tVuPuu+/G1NQU3n33XUiSpHRJRESXYJBaZNHro+Gd8GKkYsSv59vtdoyMjHDnXhBrbm5GRkYGr4WRgd1ux8aNG3H27FlUV1crXQ4R0SXYCbvIoq/3Hcw5eGAQ0eui5/38CxvO09PTZa2NAjc8PIyBgQGsXr1a6VLCxpo1a3D69Gl8+OGHyMrKgtVqVbqkK5K8EtwDbkx1TcEz6oHH5YF33AtpWoLQCAitgNAIaKI10Nq00Nq0UBvVSpdNRH5ikFpkUbYoGAuNGPx0EBl/njHv588Eqa6uLgapIHTu3DkAvmZpkocQAnfeeSf+/d//He+88w527typ+GyfJEmYaJrA6PFRjJ8Zh+uMC66zLkycm8B01zQk9/yWIVUGFXSpOhiWGmY/TIUmmK8xQxurXaDPgojkwCClgJj1Mej6ry543V6oNPNbXbVardDpdDzhPEg1NzdDp9OxP0pmsbGx2LRpEz744ANUVlZi1apVi/r63kkvhr4YwtDBIQyXD2Pk8Aime6dn/16boIUxz4i4TXGISoxCVGIUtA4tNFYNVAYVVEYVVFoVJLcE77Rvdso95MZ07/Tsx2TzJMYbxjF0cAie0d+eNafP1sOyygLrdVbEboyFqcikeJAkot9ikFJA9PpotP97O0aPjcJaOr9lCiEEHA4Hg1SQmumPUqnYfii30tJS1NbWYvfu3cjOzkZMTMyCvt54wzj63u9D/+5+DO4fhNflBQRgXGZE/B3xsK6xwrzSDGOeEZpo+d5KJUnCdPc0Ro+PYuToCEYqRjBcPoyeXb5NJlq7FjE3xyBuSxxs223QxnPGikhJDFIKiLnB9w1g6MDQvIMU4FveO3XqFCRJ4k+mQWR0dBR9fX245pprlC4lLAkhsH379tklvgcffFD2r//xc+Po2dWD7le7MVrpO3LBsNSAxEcSEbclDjHrY2QNTZcjhEBUQhTiNsUhblPc7J9PtExg4OMBDO4bxMC+AfS82oMz6jOIuTEG9rvtsN1lgy5Jt6C1EdGlGKQUoEvRQZ+tx+CBQaT9Sdq8n5+QkICjR49iZGQk6BtvI0lzczMA9kctpJiYGGzevBnvvfceKioqUFZWFvCYHpcH3bu60fEfHRj+wnfrgGW1Bdl/nw3bXTYYsgwBv4Yc9Ol6JD2chKSHkyBJEkYrR9HzRg96Xu9B3ZN1qPujOsRtjUPiI4mw3WGDSsdZUaLFwCClkJj1Meh9uxeSV4JQze+n6pmG8+7ubgapIHLu3DlERUUhKSlJ6VLC2jXXXIPa2lrs2bMHS5cuRWxsrF/jjJ4cRfvP2tH1Uhc8Qx4Y843I+mEW7F+1w5AZHOHp9xFCwLLKAssqC7KezcJYzRi6XupC54udqLm3Bpp4DRIfTETyk8kwLjUqXS5RWOOPLAqJXh8Nd78bYzVj837uhTv3KHg0NzcjPT2d/VELbGaJT6VS4e23357XQZ2SJGHg4wFUb61GRXEFOn7RAdsdNpQcKEFZTRnS/yw96EPU5ZgKTMj62yxc13wdln+4HLEbY9H2b204nHsYJ7afwMC+AR5oSrRA+I6vkJgNvj6pwf3zv3fPYDDAYrHwhPMg4nK50NPTw2W9RWK1WrF161Y0NzejvLz8qo+XvBK6d3XjaOlRVG+sxmjVKDKfzcTatrVY9l/LEHNDTFj0Gwq1QNyWOBS+Wohrm69Fxv/KwPCXw6i+pRoVJRXo3tUNycNARSQnBimFGDIN0C/RY/Bj/y4wdjgcnJEKIuyPWnwrVqxATk4O9u3bh76+vss+RpIk9L7di4qSCtT8QQ08ox7kPpfrCxl/kRHWO950STpk/nUmrm25Fnm/zIM0LaHmD2pwpOgIul72Hb9CRIFjkFJQzM0xGPxk0K+fEB0OB3p6euD18s0wGDQ3N0Oj0SA5OVnpUiKGEAJ33HEHNBoN3n777Uv+L/Tv6Uflmkqc3HES3nEvlr28DKtrViP5m8lQ6yPnJHG1Xo2kR5JQdqIMBa8WQGgFar9WiyMFR9D9WjeX/IgCxCCloNiNsXAPujFSNf979xwOBzweD/r7+xegMpovp9OJlJQUqNWR8w06GFgsFmzbtg1OpxNf3nEHoFLBlbIGx1d+iOObj2Oqawp5/5mHstoyJDyQAKEO/eU7fwm1gOOrDpQeK0XhG4UQUQI199ag8rpKDB7wb2aciBikFBVz8/k+qX3zfxObOTmbB3Mqb3p6Gp2dnUhLm/9RFhS44uPHkVdXh08LynBS/zSOtP8Nho55kXXfENacXYOkR5PmfYNAOBMqAftddpRVlyHvl3mYbJ3EsQ3HcGL7CYydnv/mF6JIx3cXBekSdTAWGjHw8cC8n2uz2SCEYJ9UEGhra4PX62WQUsoz/wvXvjaM0p9eh57xO5CAPViDryH90B/zLKUrEGqBpEeSsObsGmT+bSYGPx1ExfIKNHyvAe5Rt9LlEYUMvssoLPbmWAwdHIJ3cn69TlqtFnFxcdy5FwScTicAMEgpYLxxHMdbvoNzk38Cg9SGyscr0bvuC0RhAGhpUbq8kKA2qpHx5xlYU7cGCTsT4Pz/nTiyjP1TRHPFIKWw2I2x8I57MVw+PO/ncudecHA6nbDb7TAYQu/8oVDldXvR8vctOFJ0BMOiEDn4J6wd/wbSBg/jk5tuQrfdDqSnK11mSIlyRCH/+Xys/GwlNPEa1Nxbg+NbjmO8cVzp0oiCGoOUwqI3RAMqYGDf/Jf3HA4H+vv7MT09ffUH04KQJAlOp5OzUYto7NQYKtdUovG7jYjdFIuyfx5EinEvVJBw2/vvQzc5ibfuuQeev/kbpUsNSdHrorGqYhWW/mQphr8cxpHiI2j9cSskL2eniC6HQUph2hgtLKssfgcpAFzeU1Bvby8mJiYYpBaB5JXQ+i+tqFhVgUnnJAp2FaDorSLon7ofeO45ICMDJpcLtx4+jI7ERHzOGSm/qTQqpH4nFWWnyhCzIQb1f1yPqvVVcJ11KV0aUdBhkAoCsRtjMVI+Mu8GT+7cU17L+T4cBqmFNdk2ieNbjqP+6XrEbYpD2YkyOO51/PY08p07gXPnAK8XhZ98gsLCQnz66adc+g6QPk2P4veLkf9CPlynXKhYUYGWH7XwdHSiCzBIBYGYjTGQ3BKGDg7N63mxsbHQaDQMUgpyOp0wGo2Ii4tTupSw1fN6D44UH8HQF0PI/Xkuit4pQlRC1BWfc+utt8JgMOCtt96Cx+NZpErDkxACiQ8loqymDLFbYtH4Pxtx7KZjmGiZULo0oqDAIBUEotdFQ0SJeS/vqVQq2O12BikFOZ1OpKenh8U9bcHGO+VF3VN1OPWVUzDkGFB6rBTJjyfP6d/aaDTitttuQ2dnJw4ePLgI1YY/XZIORW8WIf9X+Rg9Noojy4+g+1W+9xAxSAUBtUGN6LXRfh3MyZ17yhkbG0N/fz9SU1OVLiXsTDRPoOqGKrT9pA2p/yMVKw+uhDHHOK8xli1bhuLiYhw8eBAdHR0LVGlkEUIg8euJKD1WCtMyE2ruq0HtQ7VwD/PcKYpcDFJBInZTLEaPjWKqe2pez3M4HBgdHYXLxSbQxTZzflQ6m5pl1fteLypWVsB12oXCNwqx9B+XQhXl31vVtm3bYDQaucQnM0OWASUHS5DxlxnoeqkLFSsrMHxk/ke4EIUDBqkgEbfV12PTv3t+d+fN7Nzj8t7ia2lpgVqtRlJSktKlhAXJI6HxLxpx8o6T0C/Ro7SyFPa77AGNaTAYcPvtt6O7uxuffvqpTJUS4NvZl/mDTKw8sBKSW0LV9VVo+2kbD/GkiMMgFSTMJWZoHVr0f8ggFSqcTieSk5Oh0WiULiXkuYfcOHHnCbT8XQuSvpmElV+shCFbngNO8/LysGLFCnz22Wdob2+XZUz6reh10SitLEXsLbGoe7IOtTtrecUMRRQGqSAhVAJxW+Iw8NHAvA6+s1gs0Ov17JNaZG63Gx0dHTz2QAauOhcqr63EwEcDyPlpDvKey4Nar5b1NbZu3Qqz2Yy33noLbje/yctNG69F8bvFyHw2E92vdqNydSXGangBMkUGBqkgErclDtO90xipHJnzc4QQSEhI4IzUImtvb4fH42GQClD/7n5Urq7EVM8UVuxdgZRvpyzI6+j1etxxxx3o6enhEt8CESqBjL/IwIo9KzDdN42jZUfR9Qp/wKPwxyAVRGI3xwIC817eS0hIQFdXF3sTFhEvKg6MJPlOKT++7Th0aTqsOrIKMRtiFvQ1c3JysHLlSnz++edobW1d0NeKZLE3x6K0qhSWVRbU7qxFw3cbeIAnhTUGqSASZY+CZZVl3kEqMTER09PT6O+f3/PIf06nE/Hx8TCZTEqXEnIkj4T6p+tR/3Q9bHfafP1QmYtz4fPmzZthsVjw1ltvYWpqfjtkae50yTqs2LcCyU8mw/n3Tpy4/QSmB3knKIUnBqkgE7c1DsNfDs/rTWfmqhj2SS0OXlTsP4/Lg1P3nkLbj9uQ+iepKHytEBrz4jXr6/V63HXXXejr68NHH320aK8biVRaFXL/NRe5z+ViYN8AKtdUYuw0+6Yo/DBIBZm4rXGAB/M6nNPh8N051tnZuYCV0Yz+/n64XC4GqXma6plC9cZq9L7Vi6X/shRL/2EphGrxT4RfsmQJ1q5di8rKSpw+fXrRXz/SJH8zGSs+XgH3gBuVayrR90Gf0iURyYpBKshY1ligjlbPa3lPo9HAZrNxRmqR8KLi+XPVuVB5XSVGj42i8PVCpD6l7GnwN998MxITE/Huu+9idHRU0VoiQcz1MVhVsQqGbANO3H4CLf+nhT2dFDYYpIKMSqNC7C2x6P+wf15vNAkJCZyRWiROpxMGgwE2m03pUkLCcPkwqtZWwTPkwYr9KwI+ZFMOarUad999N6ampvD222/zm/oi0KfrsfKzlbB/1Y7GP2vEmW+egXfaq3RZRAFjkApCcVvjMNk6CVfN3K99SUhIwPDwMMbHxxewMgJ8QSo1NZUXFc9B/95+HNt4DGqrGisPrUT0tdFKlzTLbrdj8+bNqK+vx5EjR5QuJyKojWoU/LoAGf87A53/2YkTt56Ae4jnelFoY5AKQnFbfNfFzKeXIDExEQAbzheay+VCb28vl/XmoOeNHpy47QQMWQas/GwljEvnd+nwYigtLUVOTg727NmDnp4epcuJCEIIZP51JvKez8PgJ4OoXFeJieYJpcsi8huDVBDSp+lhWm5C33tzD1IzO/e4vLewZs4f4kXFV9bxfAdO3XsKllUWlHxaAl2STumSLksIge3btyMqKgqvv/46Tz1fREkPJ2H5R8sx2TqJymsrMXJ07gcREwUTBqkgFX9HPIY+H8J0/9yOQTCbzTAajZyRWmAtLS1QqVRITk5WupSg5fwnJ848egaxt8RixZ4V0MZqlS7pisxmM+688050dXVhz549SpcTUWJvjsU1X1wDlV6FqvVV6H27V+mSiOaNQSpI2e6wAR6g/7/ntntPCIHExEQGqQXmdDqRlJQErTa4w4ESJElC0/9uQsOfNMB+rx3F7xRDbZL3zryFkpubizVr1uDw4cOora1VupyIYiow4Zovr4GpyISTd51E60/C79R5r9cLl8uF4eFhDA4Ooq+vDz09Peju7kZ/fz+Gh4fhcrkwNTXFjQ8hiNfWBylLmQXaBC163+1Fws6EOT0nISEBhw8fhtfrhUrFjCw3j8eD9vZ2lJaWKl1K0JEkCY3/sxHOv3ci8bFE5P08D0IdWs34mzZtgtPpxNtvv43ExETExsYqXVLEiEqIQsn+EtTurEX9U/WY6phC5rOZIbGhw+v1YmBgAD09PRgcHMTQ0NDsh8vlwvj4OCYnJ+c8nkqlgtFonP0wm82Ijo5GTEwMYmJiZn/NH+aCB4NUkBIqgfjb4tHzWg+8U16ooq4ejBISEuDxeNDb2wuHw7EIVUaWjo4OuN1uNppfRJIkNPxJA1r/uRXJTyYj5yc5IfEN8GJqtRpf+cpX8POf/xyvv/46HnnkEajVoTGjFg7URjUKXyvE2SfOouXvWjDVNYXcn+dCpQmeHwq9Xi+6urrQ2tqKtrY2dHd3o6en53d66zQazWzgsdls0Ov1MBgMMBgM0Gg0UKlUUKvVUKlUEELA7XbPfkxPT2NiYgIul2v2o62tDTU1NfB6f/eoiJiYGDgcDtjtdtjt9tlfazT8tr7Y+C8exOLviEfnLzsxdHAIsRuv/tPxhTv3GKTkx4uKLyVJEuqfqkfbv7Yh5Y9TsPSfloZkiJoRGxuLO++8E7t27cLevXuxZcsWpUuKKEItkPuzXEQlRaH5B82Y7p5GwasFUBuVCbSSJKGjowP19fVoampCW1sbpqd9fasmkwmJiYkoLS2Fw+GAw+FAbGwsDAaD7P8HJEnCyMgIBgcHMTg4ODsD1tPTg/r6+tmQpVKpkJCQgOTkZCQnJyMlJQV2u50rFAuMQSqIxW2Kg9AJ9L7bO6cgZbPZoFKp0NnZieLi4kWoMLI4nU7ExMTAYrEoXUpQkLwS6p6sQ/vP2pH6p6nI/lF2SIeoGcuWLUNZWRm+/PJLLFmyBHl5eUqXFFGEEMj8fiaiEqNQ90Qdqm+pRvF7xdDGLc5S1sTEBM6cOYP6+no0NDTMns2XmJiIlStXIjU1FWlpaYiOjl60r3chBKxWK6xW6yU7hj0eD/r7+9Hd3Y2Ojg60t7fj5MmTOHr0KABAq9UiOTkZ6enpyMjIQFpaGqKiohal7kjBIBXE1CY1YjfGou/dvjn9pK9Wq2G329lwvgBmLirOyspSupSgIHklnP3Ds+j4RQfS/iwNWX+XFRYhasbmzZvR2tqKN998E48//jji4uKULinipHwrBVH2KNQ8UIOq66uw/KPl0KfpF+S1ZsLTqVOn0NDQAK/XC5PJhJycHGRnZyM7Oxsmk2lBXjtQM+/7drsdhYWFAHzvV/39/Whra0NbWxtaW1vx2Wef4eDBgxBCICkpCRkZGcjIyEB6ejoMBoPCn0VoY5AKcvF3xKP/g364al0wFVz9P3JiYiIaGhoWobLIMjg4iNHRUS7rAZA8Es584ww6X+hE+jPpyPz/QqMpeD40Gg2++tWv4rnnnsOrr76Kxx57jD/FK8B+jx0rdq/Aie0nULW2Css/XA5ToTyBxuv1or6+HseOHcOZM2fg9XoRHR2N1atXo7CwECkpKSH7dS2EQHx8POLj47F8+XIAwOTkJFpbW9Hc3Izm5mYcPnwYhw4dAgAkJycjMzMTWVlZSE9PZ5/VPPFfK8jF3x6Pum/Xofed3jkFqYSEBFRXV2NsbCxof4IKRbyo2Efy/jZEZfxVBpb81ZKQ/WZzNTExMbjnnnvw8ssv45133sE999wTtp9rMIvZEIOVB1bi+NbjqLq+CsUfFCP6Ov+vGurv70dVVRWqq6sxMjICo9EYFuHpanQ63ezsGgC43W60tbWhqakJTU1NOHToED7//HNoNBqkp6cjKysLWVlZSExMDNt/E7kwSAU5faoellILet/oRcb3Mq76+AtPOJ/5D0OBczqd0Ol0sNuVv3BXKZIk4ey3z6LzhU4s+f4SLPmrJUqXtOCys7OxceNG7N27F0lJSVi3bp3SJUUk8wozVn6xEsc3H0f1LdUoersIcbfMfblVkiQ0NjaivLwcdXV1EEJg6dKl2LZtG3JzcyNyd6ZGo5ld3rvxxhsxOTmJ5uZmNDY2oqmpCXv37gUAGAyG2dmqrKwsHgtyGQxSIcB2jw1Nf96EiZYJ6NOv3CNw4c49Bin5zFxUHKm7XyRJQv3T9eh4rgPp30tHxl9ePdSHi7Vr16K9vR379u1DYmIi/18pxJBpQMnBEhzffBwnbjuBgv9bAPtdV/7BZnp6GtXV1SgvL0dvby9MJhM2bNiAVatWcdPIRXQ6HXJzc5GbmwsAGBkZQVNTExobG9HY2IiamhoAvp2tM8EqMzMTRmPw3aG52BikQoD9Hjua/rwJvW/2IvWPU6/4WKPRCIvFwjv3ZDQxMYHu7m4UFBQoXYoiJElC4/ca0fbjNqQ+nYrMvw2/nqgrEULgzjvvRE9PD1577TU89thjsNlsSpcVkXSJOpR8WoITt57Aqa+cQv4v85H4UOIljxsfH0d5eTkOHz6M8fFxJCUlYceOHSgsLGT/zxxZLBYsX74cy5cvhyRJ6O3tnQ1Wp06dQmVlJQAgKSlpdrYqLS0tIg8KleUrSgixFcC/AFAD+IUkST+UY1zyMeYYYSo2oef1nqsGKcD3hc0gJZ+Zi4ojtT/q3A/Owfl/nEj+djKy/zE8jjiYr6ioKNx///34xS9+gVdeeQXf+MY3+JO4QrSxWizfsxwnd5zE6YdPw73vS6QeeBpoacFYbi4OffvbOHL+upW8vDysXbsWaWlpEfl1KxchxOzOwNWrV8Pr9aKtrW12GfDi/qqZGaukpKSI+HcPOEgJIdQA/g3AJgCtAI4IId6RJKkm0LHpt2x329D8182Y7JyELlF3xccmJiairq4OU1NT3GkkA6fTCSEEUlOvHmLDTfMPm9H8g2YkPpKInH8NzRPL5RIbG4v77rsPv/rVr/Dqq6/iwQcf5OyGQjRmDZa/vxw113+E+v+KwVjUJjRubkVl6Sq4BwZQZLHg+kcfne0ZJXmpVCqkpaUhLS0NGzZswNTU1Gx/VWNjI/bt24d9+/Zd0l8VExMTlu8hcrwLrAZQL0lSIwAIIf4vgDsBMEjJyH6PHc0/aEbvW71I+VbKFR+blJQESZLQ1dUVsbMocnI6nUhISIi4UOr8Zyea/rwJjvsdyPuPPAhV+L0BzldaWhp27NiB119/He+++y527NgRlt8YQoFKp0L2wNPoTnoCHR070TfYgqITb+D6zz9DvNkM/OmfKl1ixIiKikJOTg5ycnIAAKOjo7OzVQ0NDbP9VTMHiqalpSE9PR0OhyMs+k7lCFIpAJwX/L4VwBoZxqULmIpMMOQY0PvG3IIU4LsbjkEqMF6vF62trSgpKVG6lEXV/vN2NPyPBtjusSH/xfyQu4B4IRUVFaG/vx/79+9HbGwsbrzxRqVLijgejwcVFRX49J4dGNcPYs3Lx5BaXoJE5CIO7wL9/UqXGNHMZvPv9Ff19fWhqakJLS0taG5uxsmTJwH4GtxnZrYyMjKQlJQUkj+wyhGkLvcOK13yICEeB/A4gEuOuKerE0LAfo8dzr93Yrp/+orXJVitVhiNRnR0dCxiheGpq6sL09PTEfU12/2bbpz99lnE3RaHglcKgurS2GBxww03oL+/H59++inMZjNKS0uVLikiSJKEU6dO4eOPP8bAwAAyBwex6d3/QmJHB87hITTjYXhgxLK0l8Cv2uAghIDNZoPNZkNZWRkkScLQ0BBaWlpmP+rr63/nsTN3BSYnJyMhIeHyDewvvww88wzQ0gKkpwPPPgvs3LnIn52PHEGqFcCF0x6pANovfpAkSc8BeA4ASktLLwladHW2u21o+WELet/pRdLDSb/3cTNXALDhPHCRdhDnwMcDqP1aLaxrrSjcVQhVFL8dXY4QAnfccQdcLhfef/996PV6FBUVKV1WWDt37hz27NmD9vZ2JCQkYOfOncj+8kuIl14CAGTiV9BgDA14Eu7oa1E05oHaFHnnQwU7IQRiYmIQExMze+r6+Pg4nE4n2tvb0d7ejvr6elRXV88+3uFwICEhYbbh3XHoEGKefBLC5fIN2twMPP6479cKhCk5gtQRADlCiEwAbQDuA/CADOPSRSylFugydOjZ1XPFIAX4Gs4PHToEt9vNhtgArZu3EwAAIABJREFUOJ1OWK1WREf7f5JyqBipHMHJO0/CkGNA8bvFUBv5TehK1Go17r33Xrz00kt48803odfrsXTpUqXLCjvd3d3Yu3cv6urqYLVaceedd2L58uW+3pqlSwEhZmcm0tKPQLN5AGf+MxbVW85fdhwTedvxQ43BYPidM6wkScLIyMhssOro6MC5c+dw/Pjx2edon34aSfWTSPksDytGfoSEkTrf10EoBilJktxCiO8A+Ai+4w9+KUnSqYAro0sIIeC4z4HWf2jFVO8Uomy/fy05KSkJXq8X3d3dSE5OXsQqw4vT6YyI2ShXvQvHtx2HJk6DFR+tgDaW33zmQqvV4v7778cLL7yAXbt24Wtf+1pELQMvpOHhYXzyySc4duwYoqKicMstt2D16tWXLvPs3Pk73zyTAKg3d6P2gVpU31SN5R8tR5Qj9PpuIpkQAlarFVarFfn5+bN/PjExgZ6eHvTs2IEeux3TDXdB05UFrX7C94DzKwiLTZZ5e0mSPpAkKVeSpGxJkp6VY0y6vIT7EyC5JfS81nPFx13YcE7+GRoawvDwcNgHqcmOSRzffBySR8Lyj5ZDl3Ll4zXod+n1enzta1+D1WrFSy+9hObmZqVLCmmTk5P4+OOP8ZOf/ATV1dVYs2YNnnrqKaxbt27Ohz06vuJA8bvFcJ1xoWp9FSacEwtcNS0GvV6PtLQ0XNPXhxs/OgJLfSZSPe8hbuz8fjeFfohhA0SIMS03wbjMiO5fd1/xcbGxsdDpdAxSAXA6ff85wzlIuYfcOL7tOKa6p7D8g+Uw5fOia3+YzWY89NBDiI6Oxssvv4xz584pXVLI8Xg8KC8vx49//GMcPHgQ+fn5+M53voMtW7b4dfhp3JY4LN+9HFMdU6i6vgquOtcCVE2KePZZtGoegAQ10rDL92fG/9fencfXVdf5H399773Z9z252be2SZM0TVdboMWi0MpWlimCLDqWCoqI428EdNxGHZ0ZcQFkBFFEAcUKgtCyBEUo3dOkSZq0afZ935o9997v7490oXRPk3vuTT7Px6MP6E1yzrvnkeWd8/2e79d3YsK5AaRIuZljw3t97/cx0njm37JkwvnFa2howMPD4/j+hTONfcROyXUlDJUNkfVSFoFLA42O5NYCAgK48847CQ4O5vnnn6empsboSG7h2JN4jz/+OG+88QaRkZFs3LiRG2+88aI3yA2+JJjcf+TiGHJQeGkhA8UDU5RaGGnskzfTZF5PlN9OfFQLJCbCk08a9tSeFCk3FPnpSNDQ8aezD+9FR0fT2tqK3W53UrKZpaGhgdjY2BmxYNxHabum/NZy+v7Zx7zfzSP0k6FGR5oRjt2ZOlamysvLjY7k0urq6nj66afZvHkzHh4e3Hrrrdxxxx1TOq8zIC+A3PdzURZF0aoi+nb2TdmxhTEaH2nEMWYiseABcDigttawEgVSpNySb7ov/ov8aXuh7azvFxMTg91up7Oz00nJZo6xsTFaW1tn5LCe1pqKeyrofLmTtJ+nEfVp2UZjKvn5+XHXXXcRHR3Nn//8Z/bs2WN0JJfT0dHBCy+8wDPPPEN/fz/XXXcdmzZtIj19erYh8pvnx8JtC7GEWdh/xX563umZ8nMI5xjvGqfpsSYib4nEd65r7HcpRcpNRX06ioGCgbOO+8uE88lrbGxEaz0jn8Cq/VYtLU+1kPBwAnFfnn37BzqDr68vd9xxB+np6WzZsoV33nkHrWX5vP7+fv72t7/xxBNPUFdXx5o1a7jvvvvIzc2d9ju/Pkk+LHx/IT7JPhSvK6bzFfkF0x01/qwR+6CdxG8kGh3lOClSbipiQwQozjrpPCwsDA8PDylSk3BsovlM26i48dFG6r5fR8znY0j+frLRcWY0Dw8PNmzYQF5eHtu2beOll15ifHzc6FiGGB4eJj8/n0cffZSioiKWLFnCl7/8ZS655JLzfhJvKnjFeJH7z1z8c/0pvbGU1j/IHFJ3Mt4zTuMvGom4KQK/+a7zYIys1OimvOO8CV4dTOuzrST+R+Jpb4ebTCaio6OlSE1CQ0MDkZGReHt7Gx1lyrT/qZ3K+ysJvz6c9CemZwhFnMxkMnH11VcTEhLCO++8Q0dHBxs2bLjoSdTuYnx8nN27d7Nt2zZGRkbIyclh9erVhv77PUI9WJC/gNLrSzl4+0Hs/XZi7z37/qXCNTT8pAF7v53Eb7rO3SiQO1JuLfquaEaqRuj74MyTJ489uedwOJyYzL0d26h4Js2P6n67m/Lbywm6JIiM5zNk/zwnUkpxySWXcNttt9HX18dTTz3F4cOHjY41rRwOBwUFBTz66KPk5+cTHx/PF77wBdavX+8SJdISYCH79WzCrgnj8BcPU/cjWfvL1Y22jNL400Yib4nEP8ff6Dgnke+mbiz8hnBMfiZanznz7emYmBjGx8fp6upyYjL31tHRwejo6IwpUv17+ildX4pvhi9Zr2Zh9pGtX4yQlpbGxo0bCQgI4Pnnn2fr1q0zbqjPbrdTWFjIY489xmuvvUZQUBB33XUXt956K1FRrvVQg9nbzPy/zCfytkhqHqqh6sEqmcfmwuq+V4ce0y45JUGG9tyYxd9C5M2RdLzYQfov0k+7N9qHJ5xHREQ4O6JbOrYydWKia90+noyhQ0OUrCvBM8KTnDdyZN8xg4WGhrJx40by8/PZtWsXNTU1rF+//vjXqbuy2+3s37+f999/n97eXmJiYtiwYQNz58516SFkk4eJjGczsARYaPhxA/Y+O+mPp6NMrpt5NhqqGKL5qWZi74nFJ9XH6DinkCLl5qLviqb1mVY6X+4k6rZTf+OLiIjAw8ODpqam4ztti7Orr6+fERsVjzaPsv/K/aAg560cvGJk6xdXYLFYuOqqq0hLS+OVV17hqaeeYtmyZVx++eV4errXnnBjY2MUFRWxfft2+vr6sFqtrF27dtqWMZgOyqRI/2U6lmAL9T+qx9ZvY94z8zB5yICNq6j5Rg1mHzOJ/+Gav9xKkXJzQZcG4Z3sTeszractUiaTiZiYGJqbmw1I53601tTV1ZGcnOw2PwhOZ7xnnOIri7F12ch9NxffdNdYb0WckJaWxr333kt+fj47d+6krKyMT37yk2RmZrr8515fXx+7d+9m3759jIyMEBcXx9VXX01qaqrLZz8dpRQp/5WCOchMzUM12I/YyXwxE7O3DIMbrX93Px2bO0j8dqLLbj4tRcrNKZMi+s5oar9by0j9CN4Jpz5lZrVa2bNnD3a7HbNZvjGcTU9PDwMDA269fpR92E7ptaUMHRoie0s2AYsCjI4kzsDHx4drrrmG3NxcXnvtNTZv3ozVamXNmjWkpKQYHe8kWmtqa2spKCigrKwMgIyMDJYvXz5j5hMmPpiIJcjC4S8epmRdCVmvZGEJkB+TRtEOTeX9lXhEeRD/b677OSafITNA1B1R1H6nltZnW0n6ZtIpb4+NjWXnzp20t7e7/VyM6ebu86McNgdlG8ro+6CPzD9mEnqFbP3iDuLj49m0aRPFxcW8++67/P73vychIYHly5czd+5cQ7cp6uvro6ioiKKiInp7e/Hy8mL58uUsXbqU4OBgw3JNl9h7YrEEWii/s5z9V+wn+/VsPMNd807ITNf6bCv9O/uZ98w8ly60rptMnDefZB+CLw+m9elWEh9OPGWiZGzsxBopTU1NUqTOoa6uDl9fX8LDw42OcsG01lRsqqDrb12kP5ZO5L9EGh1JXACTyURubi5ZWVkUFBSwY8cOXnzxRUJCQli0aBHZ2dkEBjpnY+m+vj7Ky8spLy+nvr4egOTkZC6//HIyMjKcuoimEaJui8IcYKZsQxmFKwvJeTMHnyTXm+Q8k9n6bFR/vZrAjwUSdbtrPfH5UVKkZgjrJitlt5TR/VY3YVeFnfS24OBgfHx8aGpqYvHixQYldA/19fUkJCS45TyPmodraP3NxAKtsV+UBQbdlcViYdmyZSxZsoSDBw+ya9cu8vPzyc/PJzExkYyMDFJTUwkLC5uyz9OxsTHq6+uprq6mpqaG1taJJVUiIyNZtWoVCxYscIn1n5wp/NpwFuQvoOSaEgo/VjgxTL5QhsmdpfY7tYx3jJOzNcfln6KUIjVDhK8PxyPCg5ZftZxSpJRSxMbGyoTzc+jv76enp4elS5caHeWCNfysgfof1RNzdwxJ300yOo6YAiaTiczMTDIzM+nu7qa0tJSSkhLeeOMNAAICAkhMTCQqKoqoqCjCw8Px9/c/690im81GX18fPT09dHV10draSmtrK+3t7TgcDsxmM3FxcaxZs4aMjAzCwsLOeKzZIGhlEAu3LaT4qmKKVhUx/6X5MlzuBIMHBml8tJGYjTEE5Ll+eZUiNUOYPE1Efy6ahv9tYLRpFK/Ykx91t1qtVFVVMTY25naPWDvLsSEMd5to3vZcG1UPVBF+QzhzfjnHLe+mibMLDQ3lsssu47LLLqOnp4fq6mqqq6tpaGigtLT0pPf18vLCx8cHs9mM2WxGa83o6OjxPx/m6+tLTEwMK1asICkpiYSEhBk/bHeh/DL9yNuRR/HaYkrWlTDvmXlE3eraQ03uTDs0h+4+hCXQQvIPXG/xzdORIjWDWO+20vDjBlqebiHpW0knvS02NhatNS0tLW47kXq61dXV4enpSXR0tNFRzlvXG10cvOsgwauDyXguA2WWEjXTHZsztWjRIgBGRkZob2+nu7ubI0eOMDAwwPDwMA6H4/jWUF5eXscLVnBwMMHBwYSEhBAQECDF+zx4xXqR+14updeXUn5bOWMtYy79FJk7a/plE/3b+5n3u3luM8lfitQM4pPiQ8gnQ2h5qoWEhxNO2k/NarUC0NzcLEXqDOrq6khISDD0CakL0b+rnwM3HsAvy4+sV7JkzZtZytvbm4SEBLe7k+puPII9yHkjh4N3HKTqa1WMNo6S+pNUl5+/405G6kaofrCakCtDXH6C+Ye5x08Mcd6sX7Ay2jhK99buk1739/cnKCiIpqYmg5K5tqGhITo6Otzmh9HgwUGKP1WMZ7Qn2VuzsQTK70RCTDezt5nMP2YSe38sjT9r5MCNB7AP2o2ONSNorTm06RAAc3/l2lsLfZQUqRkm7OowPK2eND1+amGSCedndmx+lDvcrRtpHKH4k8Uoi2LBWwvwipatX4RwFmVSpP00jbSfp9H5aieFlxYy2jR67g8UZ9X8f830vNlDyo9S8E48dWFpVyZFaoYxeZiw3mOl580eBssHT3qb1Wqlp6eHoaEhg9K5rrq6Osxm8/EhUFc13n1065deGzlbc1xyA08hZjqlFHFfjiP71WyGDw9TsLSAI/uOGB3LbQ2WD1L11SpCrgxxy6VbpEjNQNZNVpSXovHnjSe9/uGFOcXJ6uvriYuLw2Jx3SEy+5CdkqtLGK4cJuuVLFnTRgiDhX0qjIUfLERZFIWXFtLx1w6jI7kdx5iD8tvKMfubmffbeW41pHeMFKkZyDPCk+jbo2l7to3xrvHjr1utVpRSNDY2nuWjZ5/R0VFaWlpcen6UY9zBgZsP0L+zn8znMwm5fHYtjiiEq/LP8SdvVx5+2X4cuOEA9f9dj9ba6Fhuo/qhagYKB5j767l4xbjnNAUpUjNU7P2xOIYdND95Yk6Up6cnUVFRNDQ0GJjM9TQ0NKC1dtn5UdqhOfT5Q3Rv6WbOE3OIuDHC6EhCiA/xivYi9x+5RNwcQfXXqym/vRz7kExCP5f2ze00PtKI9V4r4de537Zcx0iRmqH8s/wJ+UQITY814Rh3HH89Li6Opqam4+vLCKipqcFkMrnkHSmtNVVfq6Lt2TaSvpuEdZNrz+ESYrYy+5jJfCGTpP9Mov35dgpXFjJcM2x0LJc1eHCQQ589RMCyANIeSTM6zkWRIjWDxX0ljrHmMTr+fGLcPj4+nrGxMdrb2w1M5lpqa2uJi4tzyRWd639UT+NPG4m9L5bE/3DNO2ZCiAnKpEj6ZhLZr2UzUjtCwaICut/sPvcHzjK2fhsHbjyAydvE/D/Px+Tl3lXEvdOLswq9KhSfuT40/G/D8TH7+PiJ1XhlntSEkZERWlpaSE52va0Imp9qpubhGiJvjSTtZ2luOQlTiNkobF0Yi/YuwivOi+K1xdT9V53MmzrKYXNw4F8OMFwxTOafMvGOd6+lDk5HitQMpkyKhH9PYKBw4PhvRcHBwfj5+ck8qaPq6ia+wblaker4SwcVX6ggdG3oxJMssnqyEG7FJ9WHvB15RG6IpObhGkqvLWWsc8zoWIbSWnP4S4fpebOH9CfSCfn4zHhoRorUDBf1mSi84r2o/8HEgpNKKeLj4+WO1FE1NTVYLJbjS0O4gp53eii7tYzAZYETt7095ctUCHdk9jOT8XwGaY+m0f1WN3sX7KXn3R6jYxmm4b8baPlVCwkPJmD9/MyZ7ynfoWc4k6eJ+P8XT9+2Pnrf6wUmJpx3d3czODh4jo+e+WpqakhISHCZ9aP69/ZTen0pPuk+ZL+WjdlP9s8Twp0ppYj7Uhx5u/Iw+5vZ//H91Hy7Bodtdj3w0/TLJqofrCbylkiSf+BaIwAXS4rULBDzrzF4RHhQ98M6QOZJHTM4OEh7eztJSUlGRwEmnmIpWVuCR7gHC95cgEeo601+F0JMTkBuAIsKFhF1RxR136tj/+X7Ga6aHU/1tf6ulcNfPEzYNWHMe3bmTVWQIjULmH3NxH01jp43e+jf209MTAwmk2nWz5Oqra0FcIn5USMNE/vnYYKct3LwinXPhemEEGdm8beQ8UwG834/j4HiAfbk7KHp8Sa0Y+ZORG/5bQsHP3eQkE+EkPliJiaPmVc7Zt6/SJxW7D2xmIPM1H2/Dg8PD2JiYmb9Hamamho8PT0N319vrHPsxP55b+Tgm+5raB4hxPSK/kw0Sw4sIejSIA5/6TD7r9jPcO3MuzvV8NMGDn3uECFXhJD1chZm75k5VUGK1CxhCbIQ/0A8Xa900b+n//jCnHb77F19t7a2lsTEREwm474MxnsnNiEerh4m61XZP0+I2cI7zpucrTnMeWoOR/YeYU/WHhp/0Tgj5k5ph6b6oWqqvlpFxE0RZL86s+d7SpGaReIeiMMSZqHmGzXEx8djs9lobW01OpYh+vv76erqMnRYzzZgo+RTJQyWDJL1UhYhq2fGo8BCiPOjlML6eStLSpcQdEkQlfdXUrC4gL4P+oyONmm2IzZKbyil/kf1xNwdQ+YfM91+wc1zmdn/OnESS6CFxIcT6Xm7h+CaYADq6+sNTmUMo+dH2YftlF5XOrEJ8QuZhK0LMySHEMJ43gkTd6fmb56PrctG4SWFHPzsQcba3GvdqaFDQxSuKKTrtS7SfpHGnP+bgzLPrInlpyNFapax3mPFM9aTth+2ERIcMmuLVE1NDT4+PkRFRTn93I4xBwduOkDvP3qZ98w82YRYCIFSiogbI1h6cCkJDybQ9lwbO1N3UvPtGmz9NqPjnZXWmuanmtmbt5fRllFy3sgh7r64WbMbgxSpWcbsYybpW0n07+gntT31+Mres4nWmurqapKSkpz+he6wOSi/rZzuLd3MeWIO0bdHO/X8QgjXZvYzk/JfKSwpXULYujDqvlfHrtRdNP68EfuQ681pHakfofT6UiruriDwY4EsKV5C6BWhRsdyKilSs1D0Z6PxSfMh4E8BDA8M09HRce4PmkE6Ozvp7+8nNTXVqefVDs2hzx2iY3MHqY+kYt00c1b2FUJMLd85vsx/cT55u/Pwy/Gj8iuV7EzaSe33axnvGTc6Ho4xB/X/U8/ujN30vN1D6k9SWfDWAryss2/pFilSs5DJw0TKj1NwVDmwFliPzxeaLaqqqgCcWqS0Q1NxbwVtv28j6XtJxD8Q77RzCyHcV+CSQBbkLyD3vVwClgZQ+x+17IjfweH7DjNQPOD0PA6bg5bftLBrzi6q/72akCtCWFq+lPivxs+4hTbPl2vsiyGcLnx9OMGXB5P8z2QaDjSwdOlSoyM5TVVVFWFhYQQHBzvlfNqhOfzFw8f3mEr8ZqJTziuEmBmUUgRfGkzwpcEMlAzQ8N8NND/ZTNNjTQQsDSDmX2MIvyEcz3DPacsw3jVOy9MtND/RzEjtCAFLApj7q7mEXjm7hvFOR+5IzVJKKdJ+loZ52IztN7ZZM0/KZrNRW1vrtLtRx0pU8/81E//1eJJ/mDxrJmAKIaaef7Y/Gb/PYEXzClJ/mop9wE7Fpgq2R2+n6ONFND7ayGDZ4JR8T7f122h7oY3Sm0rZHrud6q9X45XoRdarWeTtypMSdZTckZrF/HP88VzvSeRLkTTvaCZ2RazRkaZdfX09NpvNKUXq2HDesTtRUqKEEFPFI8yD+K/EE3d/HAP7Buh4qYPOlzup/HLlxNsjPAi6JAj/XH98M33xy/TD0+qJJchyyvchrTW2PhvDlcMMHRxioHCAvvf7OLLvCNjBM9oT60YrMZti8M/yN+Kf69KkSM1yqd9PpeT1Eqq/Wo11h3XG/6CvqqrCZDJN+0bF2qGpuKeClielRAkhpo9SioBFAQQsCiDlBykMVw3T+89eet/rpW9bH51/7YQP3ZxSFoUlzILJc2JAyjHqwNZtQ9tOvJPyUgQuDSThwQRCrwwlaGXQrJ3/dD6kSM1yUXOjePOqN0n8ayJtz7UR/ZmZ/Th+VVUVCQkJeHpO31yCk0rUQwkk/0BKlBDCOXxSffBJ9SHmczEA2IfsDB0aYqh8iLG2McY7xhnvHD9enJSHwiPMA49wD7xTvPGd54tPis/xoiXOTYrULKeUwvcWXwaKBqj8SiWhV4biGTF9JcNIAwMDtLW1sWbNmmk7h8PmoOLuClp/2yolSghhOLOvmYCFAbKP5zSSyilITE6kfF059n47VV+tMjrOtJnuZQ8cYw7KP11O629bSfxWopQoIYSYBaRICRITExmKHMLzs560/aGNrje6jI40LaqqqvD19SU6euqHL+1DE3vndWzuIPUnqSR/V0qUEELMBlKkBJGRkfj5+dHy8RZ8M3yp2FSBrc+193a6UA6Hg6qqKlJTU6e84Nj6bBRfVUz3m93MeWoO8V+VxTaFEGK2kCIlUEqRkpJCdUM1c387l9GmUSq+WGF0rCnV1NTE0NAQc+bMmdLjjnWOUbSmiP4d/WS+kIn187LtixBCzCZSpAQAycnJDA4OMpI0QtK3k2h/rp2259uMjjVlKioqJhYhTUubsmMOVw9TuLKQwdJBsv6aReSGyCk7thBCCPcgRUoAkJKSAkB1dTUJDyUQuCKQinsqGK4dNjjZ1KioqCAxMRFvb+8pOV7/3n72fWwf4x3j5L6TS9inwqbkuEIIIdyLFCkBQFBQEGFhYdTU1GCymMj4QwYAZTeXYR+xG5zu4vT29tLe3j5lw3pdW7ooWl2EycfEwu0LCVoZNCXHFUII4X6kSInjUlJSqK2txW6345Psw7xn5nFk7xEq7680OtpFqaiYmO81FUWq+dfNlFxbgu9cX/J25uE3z++ijymEEMJ9SZESx6WkpDA+Pk5jYyMAEesjSHgwgZYnW2j5bYvB6SavoqKCsLAwwsImP/ym7ZrKr1VSsbGC0E+EkvtuLl7RXlOYUgghhDuSIiWOS0pKQilFdXX1idf+M4ngNcFU3FNB3wd9BqabnNHRUWpra0lPT5/0McZ7xym5uoTGnzQSe18sWa9mYQmQTQGEEEJIkRIf4u3tjdVqPalImSwm5v9pPt4J3pRcV8LQ4SEDE1646upq7HY7c+fOndTHD1UMsW/5Pnrye5jz5BzSf5GOyUO+bIQQQkyQnwjiJKmpqcfXXDrGI8yD7C3ZKKUoWVfCWOeYgQkvTEVFBV5eXsTHX/gimZ2vdFKwtABbl40F7yzAulHWiBJCCHEyKVLiJOnp6Witj+9Ld4xvmi9Zr2Yx2jhK8VXFjPeOG5Tw/DkcDioqKkhLS8NsNp//x407qPy3SkqvL8Un1Ye83XkEXxY8jUmFEEK4KylS4iSxsbH4+vpy+PDhU94W9LEg5m+ez2DxICVrS7Adce1tZOrr6xkaGiIjI+O8P2akYYSiVUU0PtKI9V4rCz9YiE+yzzSmFEII4c6kSImTKKVIT0+nsrISh8NxytvDPhVG5p8y6d/TT8mnSrD1u26ZKisrw2KxnPdE846/dLB34V4GSwfJ/GMmcx6fg9n7/O9kCSGEmH2kSIlTpKenMzw8fHwZhI+KWB9B5vOZ9O/op2h1EWNtrjdnSmvNwYMHSUtLw9PT86zvO947Tvnt5Ry46QDeSd4s2rtItnsRQghxXqRIiVOkpqailDrt8N4xkf8SSdarWQwdGmLfyn0MV7nWVjKNjY0cOXLknMN63W91szd7L20vtJH47UTyduThO8fXSSmFEEK4OylS4hTe3t4kJCSctUgBhK0NY8E7C7D12ChYWkD3291OSnhu5eXlmEymM65mPto6StmtZRRfWYzJz0TejjySv5MsSxsIIYS4IPJTQ5xWeno6bW1t9PWdfRHOoOVBLNq9CK9YL4qvKqb+x/Voh3ZSytPTWlNeXk5KSsopmxRru6bpiSZ2z9tNx186SPpOEouLFhO4JNCgtEIIIdyZFClxWscmaJ/rrhQwsUTAjjwibo6g+sFq9n9iPyP1I9Md8YxaWlro7e09aVhPa03na53sWbCHw/ceJmBxAEtKlpD07SSZUC6EEGLSpEiJ04qIiCA0NJTy8vLzen+zn5nMFzKZ8+Qcjuw+wp7sPTT/qhltd/7dqQMHDmAymZg3bx4Afdv7KFpVROk1pegxTeafM1nw9gKZCyWEEOKiSZESp6WUIiMjg9raWoaHz28iuVIK60Yri4sX47/Qn4ovVFCwuIDe93qnOe1Rzz2HTkqidOtWUmvrGP7OFgpXFVK4spChQ0Ok/zKdJQeWEHlTJEop52QSQggxo0mREmeUkZGBw+Hg0KFDF/RxPsk+5P4jl8w/ZjLeNU7RqiKK1hTR804CvzuNAAAMxUlEQVQPWk/THarnnoO776ba4U9AeSbxz32ckv8JZ6S0i9RHUllWtYzYe2JlMrkQQogpJVvYizOyWq0EBQVRVlZGbm7uBX2sUorIDZGEXRNG0y+baHykkf1X7Mcvx4/oz0YTdVsUnhFnX9/pfNn6bHR95VU6h/4f7SOXkNZgwUcdJI5nifQ/jOmBqnMfRAghhJgEKVLijI4N7+3Zs4fR0VG8vLwu+BhmXzMJX0sg9kuxtP2+jZYnW6h6oIqqr1URtCKI0KtCCV4djF+OHxb/8/t0HO8d58juI/Rt76Pv/Yk/evwePOihLbcJ3+BtrP77ryfeuUGG8IQQQkwfKVLirDIyMti5cycVFRVkZ2dP+jhmbzPWjVasG60MlA7Q/nw73W90U/ONmol3UBNP/3kleOEZ44lHqAfKosAE9iN2bD02xlrGGKoYYrz96IbJJvDL9iPuK3GEP7uJ5uBm8q/dwG1/ePfEiRMSJv+PF0IIIc5BipQ4q/j4ePz9/SkrK7uoIvVh/ln++P/Qn5QfpjDWNkb/7n4GigYYLB5ktGmU/g/6Ge8ZB/vEuk/mADMeoR54RHoQdk0Yvum++C/yJ3BpIJbAo5/CCz7LW6+9hu/gICnV1ROv+frCD34wJZmFEEKI05EiJc7q2PBeYWHhpIf3zsYzypPwa8IJvyb8oo4zfMMNHKqqYtGBA5i0hsTEiRJ1221TlFQIIYQ41UU9wqSUulkpdUAp5VBKLZ6qUMK1ZGdnY7PZzntNKSPs378fu9Ys/PnPweGA2lopUUIIIabdxT4LXgrcALw3BVmEi4qLiyMkJITi4mKjo5yW1prCwkKsVivR0dFGxxFCCDGLXFSR0lqXa60vbJEh4XaUUuTk5FBTU0N/f7/RcU7R1NREe3s7eXl5RkcRQggxyzhtdUKl1N1Kqb1Kqb0dHR3OOq2YIscmmpeUlBic5FQFBQV4eHiQlZVldBQhhBCzzDmLlFIqXylVepo/113IibTWT2qtF2utF0dEREw+sTBEWFgYcXFxFBcXT9/q5JMwOjrKgQMHyMrKmvKJ8EIIIcS5nPOpPa31Fc4IIlzfggULeP3112lqaiIuLs7oOMDEHbLx8XEZ1hNCCGEI2XhMnLfs7Gw8PDwoKCgwOgowMcl8165dREdHExsba3QcIYQQs9DFLn+wXinVCHwMeF0p9ebUxBKuyMvLi+zsbEpLSxkZGTE6DlVVVXR2drJ8+XKUkq1ghBBCON/FPrX3stY6TmvtpbWO0lpfOVXBhGtavHgxNpuN/fv3Gx2FXbt24e/vL5PMhRBCGEaG9sQFiYmJwWq1UlBQYOik846ODiorK1myZAlms9mwHEIIIWY3KVLigi1ZsoSOjg6qj+1pZ4Dt27djsVhYtGiRYRmEEEIIKVLigmVlZeHv78/27dsNOX9vby/FxcXk5eXh5+dnSAYhhBACpEiJSbBYLCxbtozq6mpaWlqcfv5t27ahlGLlypVOP7cQQgjxYVKkxKQsXrwYT09PduzY4dTz9vf3U1RURG5uLoGBgU49txBCCPFRUqTEpHh7e5OXl0dpaSnd3d1OO+97772H1ppLLrnEaecUQgghzkSKlJi0lStXYrFYePfdd51yvo6ODvbt28fixYsJDg52yjmFEEKIs5EiJSbN39+fZcuWUVJSQmtr67SfLz8/H09PT1atWjXt5xJCCCHOhxQpcVFWrFiBt7c3f//736f1PDU1NVRUVHDppZfi6+s7recSQgghzpcUKXFRfHx8WLlyJYcPH6aqqmpazmGz2Xj99dcJDg5m2bJl03IOIYQQYjKkSImLtnz5ckJDQ9myZQs2m23Kj//Pf/6Trq4urr76aiwWy5QfXwghhJgsKVLiolksFtatW0d3dzfvv//+lB67tbWV7du3s2DBAlJTU6f02EIIIcTFkiIlpkRqaio5OTm8//77NDY2Tskxx8bGeOmll/Dx8eHKK2U/bCGEEK5HipSYMmvXriUwMJCXX36Z0dHRizqW1potW7bQ0dHBDTfcgI+PzxSlFEIIIaaOFCkxZby9vVm/fj29vb1s3rwZh8Mx6WNt376d/fv3c9lll5GSkjKFKYUQQoipI0VKTKnExETWrl1LZWUlW7ZsQWt9wccoKioiPz+f+fPns3r16qkPKYQQQkwReQRKTLnFixfT29vLBx98AMC6deswmc6vs+/evZutW7eSnJzM9ddfj1JqOqMKIYQQF0WKlJgWa9asQSnFtm3b6O7u5oYbbsDf3/+M7z82NsbWrVspKipi7ty53HTTTbLUgRBCCJenJjP0crEWL16s9+7d6/TzCucrLCxky5YtmM1mVqxYwcKFCwkICDj+9uHhYUpKSti2bRtHjhzh0ksvZfXq1ed9B0sIIYSYbkqpAq314tO+TYqUmG6dnZ3k5+dz6NAhAMLDw/Hz82N4eJiOjg601iQkJHDFFVcQHx9vcFohhBDiZGcrUjJ2IqZdeHg4t9xyCx0dHZSVldHW1sbg4CChoaHMnTuXuXPnYrVaZT6UEEIItyNFSjhNREQEq1atMjqGEEIIMWVkIooQQgghxCRJkRJCCCGEmCQpUkIIIYQQkyRFSgghhBBikqRICSGEEEJMkhQpIYQQQohJkiIlhBBCCDFJUqSEEEIIISZJipQQQgghxCRJkRJCCCGEmCQpUkIIIYQQkyRFSgghhBBikqRICSGEEEJMkhQpIYQQQohJkiIlhBBCCDFJUqSEEEIIISZJipQQQgghxCRJkRJCCCGEmCSltXb+SZXqAOqcfmJjhAOdRodwIXI9TpBrcTK5HieT63GCXIuTyfU4wVnXIlFrHXG6NxhSpGYTpdRerfVio3O4CrkeJ8i1OJlcj5PJ9ThBrsXJ5Hqc4ArXQob2hBBCCCEmSYqUEEIIIcQkSZGafk8aHcDFyPU4Qa7FyeR6nEyuxwlyLU4m1+MEw6+FzJESQgghhJgkuSMlhBBCCDFJUqScSCn1NaWUVkqFG53FSEqp/1FKHVRKFSulXlZKBRudydmUUlcppQ4ppSqVUg8ancdISql4pdQ/lFLlSqkDSqn7jc5kNKWUWSlVqJR6zegsRlNKBSulNh/9nlGulPqY0ZmMopR64OjXSKlS6gWllLfRmZxJKfUbpVS7Uqr0Q6+FKqXeVkodPvrfEGfnkiLlJEqpeOATQL3RWVzA20CW1joHqAAeMjiPUymlzMDjwFogE/i0UirT2FSGsgH/prXOAJYDX5zl1wPgfqDc6BAu4ufAG1rrecACZul1UUrFAl8GFmutswAzcIuxqZzuGeCqj7z2IPCO1jodeOfo351KipTz/BT4d2DWT0rTWr+ltbYd/etOIM7IPAZYClRqrau11mPAH4HrDM5kGK11i9Z639H/P8LED8pYY1MZRykVB3wK+LXRWYymlAoELgOeBtBaj2mte41NZSgL4KOUsgC+QLPBeZxKa/0e0P2Rl68Dfnf0/38HXO/UUEiRcgql1LVAk9Z6v9FZXNDngK1Gh3CyWKDhQ39vZBYXhw9TSiUBC4FdxiYx1M+Y+KXLYXQQF5ACdAC/PTrU+WullJ/RoYygtW4C/peJUY0WoE9r/ZaxqVxClNa6BSZ+KQMinR1AitQUUUrlHx23/uif64BvAN8yOqMzneN6HHufbzAxrPOccUkNoU7z2qy/U6mU8gf+AnxFa91vdB4jKKWuBtq11gVGZ3ERFiAPeEJrvRAYxIChG1dwdO7PdUAyYAX8lFKfMTaVgIlPUjEFtNZXnO51pVQ2E5/4+5VSMDGMtU8ptVRr3erEiE51putxjFLqTuBqYI2efWtwNALxH/p7HLPsFv1HKaU8mChRz2mtXzI6j4FWAtcqpdYB3kCgUuoPWuvZ+gOzEWjUWh+7Q7mZWVqkgCuAGq11B4BS6iVgBfAHQ1MZr00pFaO1blFKxQDtzg4gd6Smmda6RGsdqbVO0lonMfGNIW8ml6hzUUpdBXwduFZrPWR0HgPsAdKVUslKKU8mJoy+anAmw6iJ3zCeBsq11o8YncdIWuuHtNZxR79X3AL8fRaXKI5+n2xQSs09+tIaoMzASEaqB5YrpXyPfs2sYZZOvP+IV4E7j/7/ncArzg4gd6SEER4DvIC3j96l26m1/oKxkZxHa21TSn0JeJOJJ29+o7U+YHAsI60EbgdKlFJFR197WGu9xcBMwnXcBzx39JeOauCzBucxhNZ6l1JqM7CPiSkRhbjAqt7OpJR6AVgNhCulGoFvAz8CXlRK/SsTZfNmp+eafaMqQgghhBBTQ4b2hBBCCCEmSYqUEEIIIcQkSZESQgghhJgkKVJCCCGEEJMkRUoIIYQQYpKkSAkhhBBCTJIUKSGEEEKISZIiJYQQQggxSf8fw5rOuel/xeEAAAAASUVORK5CYII=\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# how number of points affect the approximation (with degree=n-1)\n", "for n, clr in (5,'m'),(10,'b'),(15,'g'),(25,'r'):\n", " x2 = np.linspace(-5,10,n)\n", " p = polynomial.polyfit(x2,func(x2),n-1)\n", " fi = lambda x: polynomial.polyval(x,p)\n", " plot1(fi,fdata=(x2,func(x2)),label='%d points'%n,color=clr,extrapolation=True)\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# how locations of points affect the approximation (with degree=n-1)\n", "np.random.seed(2025)\n", "n=8\n", "for clr in 'b','g','c':\n", " x2 = np.linspace(-4,9,n) + np.random.uniform(-1,1,n) # perturb points a little\n", " p = polynomial.polyfit(x2,func(x2),n-1)\n", " fi = lambda x: polynomial.polyval(x,p)\n", " plot1(fi,fdata=(x2,func(x2)),label='%d points'%n,color=clr,extrapolation=True)\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# how degree of the polynomial affects the approximation\n", "for degree, clr in (7,'b'),(9,'g'),(11,'m'):\n", " p=polynomial.polyfit(xr,func(xr),degree)\n", " fi=lambda x: polynomial.polyval(x,p)\n", " plot1(fi,fdata=(xr,func(xr)),label='Polynomial of degree %d'%degree,color=clr,extrapolation=True)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Least squares approximation\n", "\n", "We could also go back to **function approximation** and fit polynomials\n", "of lower degree\n", "\n", "- Data set $ \\{(x_i,f(x_i)\\}, i=0,\\dots,n $ \n", "- **Any** functional form $ g(x) $ from class $ G $ that best\n", " approximates $ f(x) $ \n", "\n", "\n", "$$\n", "g = \\arg\\min_{g \\in G} \\lVert f-g \\rVert ^2\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Orthogonal polynomial approximation/interpolation\n", "\n", "- Polynomials over domain $ D $ \n", "- Weighting function $ w(x)>0 $ \n", "\n", "\n", "Inner product\n", "\n", "$$\n", "\\langle f,g \\rangle = \\int_D f(x)g(x)w(x)dx\n", "$$\n", "\n", "$ \\{\\phi_i\\} $ is a family of orthogonal polynomials w.r.t.\n", "$ w(x) $ iff\n", "\n", "$$\n", "\\langle \\phi_i,\\phi_j \\rangle = 0, i\\ne j\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Best polynomial approximation in L2-norm\n", "\n", "Let $ \\mathcal{P}_n $ denote the space of all polynomials of degree $ n $ over $ D $\n", "\n", "$$\n", "\\lVert f - p \\rVert_2 = \\inf_{q \\in \\mathcal{P}_n} \\lVert f - q \\rVert_2\n", "= \\inf_{q \\in \\mathcal{P}_n} \\left[ \\int_D ( f(x)-g(x) )^2 dx \\right]^{\\tfrac{1}{2}}\n", "$$\n", "\n", "if and only if\n", "\n", "$$\n", "\\langle f-p,q \\rangle = 0, \\text{ for all } q \\in \\mathcal{P}_n\n", "$$\n", "\n", "*Orthogonal projection is the best approximating polynomial in L2-norm*" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Uniform (infinity, sup-) norm\n", "\n", "$$\n", "\\lVert f(x) - g(x) \\rVert_{\\infty} = \\sup_{x \\in D} | f(x) - g(x) |\n", "= \\lim_{n \\rightarrow \\infty} \\left[ \\int_D ( f(x)-g(x) )^n dx \\right]^{\\tfrac{1}{n}}\n", "$$\n", "\n", "Measures the absolute difference over the whole domain $ D $" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Chebyshev (minmax) approximation\n", "\n", "What is the best polynomial approximation in the uniform (infinity, sup) norm?\n", "\n", "$$\n", "\\lVert f - p \\rVert_{\\infty} = \\inf_{q \\in \\mathcal{P}_n} \\lVert f - q \\rVert_{\\infty}\n", "= \\inf_{q \\in \\mathcal{P}_n} \\sup_{x \\in D} | f(x) - g(x) |\n", "$$\n", "\n", "Chebyshev proved existence and uniqueness of the best approximating polynomial in uniform norm." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Chebyshev polynomials\n", "\n", "- $ [a,b] = [-1,1] $ and $ w(x)=(1-x^2)^{(-1/2)} $ \n", "- $ T_n(x)=\\cos\\big(n\\cos^{-1}(x)\\big) $ \n", "- Recursive formulas: \n", "\n", "\n", "$$\n", "\\begin{eqnarray}\n", "T_0(x)=1,\\\\\n", "T_1(x)=x,\\\\\n", "T_{n+1}(x)=2x T_n(x) - T_{n-1}(x)\n", "\\end{eqnarray}\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Accuracy of Chebyshev approximation\n", "\n", "Suppose $ f: [-1,1]\\rightarrow R $ is $ C^k $ function for some\n", "$ k\\ge 1 $, and let $ I_n $ be the degree $ n $ polynomial\n", "interpolation of $ f $ with nodes at zeros of $ T_{n+1}(x) $.\n", "Then\n", "\n", "$$\n", "\\lVert f - I_n \\rVert_{\\infty} \\le \\left( \\frac{2}{\\pi} \\log(n+1) +1 \\right) \\frac{(n-k)!}{n!}\\left(\\frac{\\pi}{2}\\right)^k \\lVert f^{(k)}\\rVert_{\\infty}\n", "$$\n", "\n", "📖 Judd (1988) Numerical Methods in Economics\n", "\n", "- achieves *best polynomial approximation in uniform norm* \n", "- works for smooth functions \n", "- easy to compute \n", "- but *does not* approximate $ f'(x) $ well " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### General interval\n", "\n", "- Not hard to adapt the polynomials for the general interval\n", " $ [a,b] $ through linear change of variable \n", "\n", "\n", "$$\n", "y = 2\\frac{x-a}{b-a}-1\n", "$$\n", "\n", "- Orthogonality holds with weights function with the same change of\n", " variable " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Chebyshev approximation algorithm\n", "\n", "1. Given $ f(x) $ and $ [a,b] $ \n", "1. Compute Chebyshev interpolation nodes on $ [-1,1] $ \n", "1. Adjust nodes to $ [a,b] $ by change of variable, $ x_i $ \n", "1. Evaluate $ f $ at the nodes, $ f(x_i) $ \n", "1. Compute Chebyshev coefficients $ a_i = g\\big(f(x_i)\\big) $ \n", "1. Arrive at approximation \n", "\n", "\n", "$$\n", "f(x) = \\sum_{i=0}^n a_i T_i(x)\n", "$$" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy.polynomial.chebyshev as cheb\n", "for degree, clr in (7,'b'),(9,'g'),(11,'m'):\n", " fi=cheb.Chebyshev.interpolate(func,degree,[-5,10])\n", " plot1(fi,fdata=(None,None),color=clr,label='Chebyshev with n=%d'%degree,extrapolation=True)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Multidimensional interpolation\n", "\n", "- there are multidimensional generalization to all the methods \n", "- curse of dimensionality in the number of interpolation points when number of dimensions increase \n", "- sparse Smolyak grids and adaptive sparse grids \n", "- irregular grids require computationally expensive triangulation in the general case \n", "- good application for machine learning! \n", "\n", "\n", "**Generally much harder!**" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Further learning resources\n", "\n", "- [https://docs.scipy.org/doc/scipy/reference/tutorial/interpolate.html](https://docs.scipy.org/doc/scipy/reference/tutorial/interpolate.html) \n", "- [https://docs.scipy.org/doc/numpy/reference/generated/numpy.interp.html](https://docs.scipy.org/doc/numpy/reference/generated/numpy.interp.html) \n", "- M.H. Mudde’s thesis on Chebyshev approximation [http://fse.studenttheses.ub.rug.nl/15406/1/Marieke_Mudde_2017_EC.pdf](http://fse.studenttheses.ub.rug.nl/15406/1/Marieke_Mudde_2017_EC.pdf) " ] } ], "metadata": { "celltoolbar": "Slideshow", "date": 1612589586.138697, "download_nb": false, "filename": "31_approximation.rst", "filename_with_path": "31_approximation", "kernelspec": { "display_name": "Python", "language": "python3", "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": "3.7.6" }, "title": "Foundations of Computational Economics #31" }, "nbformat": 4, "nbformat_minor": 4 }