{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Cubic roots and excess surrogate risk\n", "\n", "This Jupyter notebook is meant to complement the technical contents of the appendix of the paper \"Classification using margin pursuit\", by Matthew J. Holland.\n", "\n", "- __The paper:__ To be presented at AISTATS 2019. See also the arXiv preprint.\n", "\n", "- __The code:__ my GitHub repository houses all the code used in this notebook.\n", "\n", "In addition to using `git clone` or some similar means to acquire our code, users are assumed to have Python 3.6+, as well as the `numpy` and `matplotlib` packages installed.\n", "\n", "\n", "__Contents:__\n", "\n", "- Initial setup\n", "\n", "- Getting roots, simplest case ($0 < \\gamma \\leq \\sqrt{2}/2$)\n", "\n", "- Getting roots, more complicated case ($\\gamma > \\sqrt{2}/2$)\n", "\n", "- Actual computation of desired functions ($H$ and $\\Psi$)\n", "\n", "___\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## Initial setup\n", "\n", "Please see the paper linked above for all formal definitions, they will not be repeated here. Basically, we have a function $\\phi(u) = \\rho(\\gamma - u)$ to be used as a surrogate loss instead of the popular surrogate $\\phi(u)=\\max(0,1-u)$. If we denote the risk of our surrogate loss as $R_{\\phi}$, then following the theory of Bartlett *et al.* (2006), as long as our $\\phi$ is \"classification calibrated\" as a surrogate loss for the 0-1 loss, there exists a function $\\Psi$, non-decreasing on the positive real line, such that $\\Psi(R(h)-R^{\\ast}) \\leq R_{\\phi}(h) - R_{\\phi}^{\\ast}$.\n", "\n", "The final goal of this demonstration is to actually compute this \"linking\" function $\\Psi$, to give additional empirical insights into how sharp our formal guarantees actually are." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Preliminary setup.\n", "import helpers as hlp\n", "import math\n", "import numpy as np\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "\n", "# Our scripts.\n", "import getroots as gtrt\n", "import linker as lnk\n", "\n", "# Image setup.\n", "saveImages = True\n", "forPrint = False\n", "imgDir = \"img/\"\n", "\n", "if forPrint:\n", " matplotlib.rcParams['pdf.fonttype'] = 42\n", " matplotlib.rcParams['ps.fonttype'] = 42\n", " matplotlib.rcParams['axes.unicode_minus'] = False\n", "else:\n", " matplotlib.rcParams['pdf.fonttype'] = 3\n", " matplotlib.rcParams['ps.fonttype'] = 3\n", " matplotlib.rcParams['axes.unicode_minus'] = True\n", "\n", "# Font size setup.\n", "FONTSIZE = \"xx-large\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the $\\rho$ function used here and its derivatives take the following form:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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c1hcLt3Dzh4vomBzDhFuPp0Oyaob4tnU5hVw+dh7hwYG0S4q2Hccr3P/Vcs4d8xubcotsR/FLag7rSNfmcZzfsxljZ21kg8ZLi59wHIdHJ2YQFRrEPSe2sx1HRDxcakIkJ3dK4oNrj6ORho+Jj8vOK+bSt+YSYAwfXHsczRpE2I7kFW4c0ppKl8Mlb81lyx5dQaxvag7r0L0ntyM0KJDHv1tlO4pIvZiSsZNZ63Zz94lpNNAeRSJyEI7jMGtdLgA9Uhrw6iU9iQjRNsvi23L2lXLp23MpLq/k/Wv60Credze3r2tpjaMZd3UfCkoruOzteeQVlduO5FfUHNahxOgwbh/ehmmZOUzPzLEdR8StSiuqePy7lbRrHM0lx6XYjiMiHshxHB6buIpL3prL3A27bccRqReFZZVc8c58dhWU8e7VfTTl4ih0ahrL2Ct7s3VvCde+N5/SCm1zUV/UHNaxK/u3IjU+kscmrqS80mU7jojbvPHrBrbsKeHhMzsQFKhSIiL/zXEcnvx+FWNnbeSq41vSp1VD25FE3K6yysWtHy1izc4Cxlzakx4pDWxH8lq9WjbkpQu7sTh7L3d8spgqbRlXL3REV8dCggJ48IwObMgt4t3fNtqOI+IW2/aW8OrP6zi1cxL9W8fbjiMiHsZxHJ6ZvJo3Z2zk8n4teOj0DlrJWPzCYxNX8vPqXTx2VicGpyXYjuP1TunchAdP68CUjJ08NnEljqMG0d006N8NhrZLZFh6IqOnruPs7k1JjA6zHUmkTj35/SocB+4/tb3tKCLigRZl7eG1X9ZzyXEpPHKmtrgR/zGkXSJxESFcrOkWdebqAa3YureEt2dupGNyDOf3am47kk/TlUM3efD0DpRVVvHs5NW2o4jUqbkbdjNx2XZuGtJaK6+JyEH1bNGQz27ox2NndVJjKH5hX80+10PTE7nrxDTLaXzPA6e2568nt+PkTkm2o/g8NYdu0io+kquPb8UXC7ewJHuv7TgidaKyysXDEzJoGhfODYNa244jIh5m8oodfyw806dVQwIC1BiK79uYW8SgZ6fzzeKttqP4rIAAw81D2hAdFkxpRRU795XajuSz1By60a3D2pAQHcqoCRm4NIlWfMDH87PJ3FHAA6e1Jzwk0HYcEfEgs9fv5vaPFzN62lrNCxK/khAdyskdk+jVUovPuJvjOFw3bgFXvjNfC9S4iZpDN4oOC+a+k9NZkr2Xr3U2Sbzc3uJynv9hNf1SG3GKhnWIyH5W7yjg+nELaNEogn9f3ENDScUvOI5DaUUVUaFBPH1uF021qAfGGK4bmMo9J6YRqJEJbqHm0M3+0r0pXZvH8fTkTArLKm3HETlqL/y4hn0lFTx8plYdFJH/yC0s4+p35xMeEsh7V/chLiLEdiSRejHml/Wc8+pv5BdX2I7iVwalJXBCh8ZAdf2RuqXm0M0CAgyjzujAroIyXp621nYckaOyavs+Ppizmcv6tiA9SZv5ish/vD97M7uLynjril4kx4XbjiNSL+Zu2M0/p6ymTWIUMeFa/N+GySt2MPCZ6SzV2h51Ss1hPeie0oDzejZj7MyNbMwtsh1H5Ig4jsMj32YQGx6sFdhE5H/cMbwt39xyPF2axdmOIlIv8orKueOTJbRoFMlTf+ms0TSW9E1tSMPIEG75aBH5Jbp6W1fUHNaTv57cjtCgQB6fuNJ2FJEj8v3yHczZkMc9I9ppuJiI/OHT+Vlk5xUTEGA0okD8huM43Pv5UvKKynn5ou5EheqqoS1xESG8fHF3duSX8tcvlmohrDqi5rCeJEaHcduwNkzNzGH66hzbcURqpaS8iie/X0X7JjFc1Ecb+opItemZOfztq+W8OWOD7Sgi9ertmRuZmpnD/aem06lprO04fq9HSgP+dko6UzJ28t5vm2zH8QlqDuvRVce3olV8JI99u5LySpftOCJ/6rVf1rN1bwmPnNlRq4KJCABZu4u545PFpCfF8PdT2tuOI1Jvlm/J55nJmZzYoTFX9G9pO47UuGZAK4alJ/LUpEzW7CywHcfrqTmsRyFBATx0egc25Bbp7IZ4vC17inntl/Wc0TWZPq0a2o4jIh6gpLyKGz9YCMBrl/bQfqfiN0orqrjz08U0igzlufO6aJ6hBzHG8My5XYgKDeLOT5boAswxUnNYz4amJzK0XQKjp65lV4GW3xXP9eT3qwgwhr+fkm47ioh4iH9PX8fK7ft4cWQ3WjSKtB1HpN6MX7KV9buKeO78Lpp/74ESokN5+twurNy+jxd+XGM7jldTc2jBg6d3oLSyiuemZNqOInJQv63P5fvlO7hlaGstTS8if7hpSGvGXNKDYemNbUcRqVcX9GrO1zf3Z2DbBNtR5BBO7NCYkb2b89mCbK1eegzUHFqQmhDFVce34vOFW7Q3i3iciioXD4/PoHnDcK4dmGo7joh4gI25RZSUVxEZGsQpnZvYjiNSb/aVVrB5dxHGGLqnNLAdR/7Eg6d34PvbBxIbHmw7itdSc2jJbcPa0CgylFHfZuByaeld8RzvztrE2pxCRp3RkbBgzScS8XcFpRVcMXYeN3240HYUkXr37ORMTn95JvnFuhLlDSJDg0iKDcPlcpi9frftOF5JzaEl0WHB3HdyOxZn7eWbJVttxxEBYEd+KS/+tIYT2icyvL2GjYn4O8dxeODrFWzdW8Jtw9rYjiNS724Z2oZHz+pIbISuRHmTcbM3cdGbc1ixNd92FK+j5tCic3s0o2vzOJ78PpN9pTojJfY98f0qKl0OD5/R0XYUEfEAny/cwoSl27jrhLb0bKFVi8V/lFVW4TgOTWLDOad7M9tx5Ahd2DuFl0Z2o2NyjO0oXkfNoUUBAYbHz+rE7qIyXvhBKyuJXb+ty+Xbpdu4eUgbmjeMsB1HRCxbl1PIw+Mz6JfaiJuG6Kqh+JcnvlvF5WPnUVmlbRG8UXhIIGd1a4oxhgJdgDkiag4t69wslkuPa8G42Zt06VusKa908dCEDFIaRnDDYC1CIyIQEhjAcakNeXFkNwIDtKeb+I/5m/IYN3szbRKjCArUobI3m7thN/2fnsairD22o3gN/cR7gP8b0Y4GESE8OH6FFqcRK96ZtZF1OYWMOrODFqEREQBSGkXw7lV9aBwTZjuKSL0prajivi+X0TQunP8b0c52HDlGHZvGEhMWzN++XEaFrgLXippDDxAbEczfT23P4qy9fL4w23Yc8TPb80t4aepaTmjfWHuXiQgz1u7i5g8Xap8w8Uv/nr6ODbuKeOovnYkMDbIdR45RVGgQj57VkTU7C3l75kbbcbyCmkMPcW6PpvRp2ZCnJ2Wyp6jcdhzxI49/t4oql8PDZ3SwHUVELMsvruDez5exZmchoUE6RBD/smFXIa//soGzuyUzKE2b3fuK4e0bM6JDY178aQ3ZecW243g8VX4PYYzh0bM7sq+0kmenZNqOI35i5tpcvlu2nVuGahEaEYGHJqwgt7CMf13QTUPMxa84jsPDEzIIDQrg/tPa244jdezhMzsSYAyjJmTgOJrCdThqDj1IelIMV/VvySfzszVxVtyuehGaFbRoFMH1g7QIjYi/m7hsG+OXbOP24W3p3CzWdhyRejV5xQ5mrM3l7hFpJEZrnq2vaRoXzl0npDE1M4cfVu60HcejqTn0MHeemEZidCgPfrOCKi1OI2709syNbNhVxKgzO+oKgYifq3I5vPDjGro2j+PmIa1txxGpV8XllTw6cSXtm8RwWd8WtuOIm1x5fEvSk6J5ZEIGRWWVtuN4LDWHHiYqNIgHT+9AxrZ9fDBns+044qOy84p5aeoaRnRozNB2ibbjiIhlgQGGT6/vxysXddfS/eJ3ggICuLJ/Sx4/u6N+/n1YcGAAT5zTmW35pfx7+jrbcTyW/gV4oNM6N2FAm3j++cNqcgpKbccRH+M4Dg+NX1E99v7MjrbjiIhlq3cUUOVySIgO1dxj8UshQQHcMLg1PVs0tB1F3KxniwY8cGp7zurW1HYUj6Xm0AMZY3jkrI6UVlTx1PdanEbq1vfLdzB99S7uGdGO5Lhw23FExKId+aWcN+Y3Hv9upe0oIvXOcRzu/nQJk1dstx1F6tF1g1JplxRtO4bHUnPooVonRHHDoNZ8vXgrM9fm2o4jPmJfaQWjvs2gU9MYruineRUi/sxxHB74ejkVLhdX9m9pO45IvdtbXMHanEJyCspsR5F6tre4nNs+XsyMtbtsR/E4ag492K3D2tAqPpL7v15OSXmV7TjiA56bvJrdhWU8dU4XzasQ8XMTlm5jamYO/zeiHS0aRdqOI1LvGkSGMP6W47nkOJ0s9TfhIYGs2VFAlvY9/B9uPzo0xgQZYx40xmw0xpQaYzKNMbcaY0wtXvuzMcY5yC+/WGIoLDiQJ87pRFZeMaOnrbUdR7zcoqw9fDB3M1f0b6ll6lFtEv+WW1jGqAkZdE+J46rjW9mOIwdQfXK/2et3s6eonIAAQ2DAn/61io8JDQrku9sH6MTAQQTVw2eMAa4F3gTmASOAl4GGwKO1eP0e4PYD7nPVZUBP1r91POf3bMYbv27gzK7JtG8SYzuSeKGKKhf3f7WcxtFh3DOine04nkK1SfxWbmEZidFhPHtuFx0YeybVJzfaW1zOjR8spF9qI167rKftOGJJUGAAjuMwLTOHni0aEBcRYjuSR3Brc2iM6Up1cfuX4zh319z9ljHmc+B+Y8ybjuP82SzgYsdxPnBnTk93/6ntmZaZw9++Ws5XN/XXF7kcsbEzN5K5o4DXL+tJVGh9nBPybKpN4u/Sk2KYdMdAAvR94nFUn9zv5Wnr2FdawR0ntLUdRSzbvLuYa8ct4LqBqdx/anvbcTyCu4eVXlhz+9IB978EhAJn1+ZNjDGBxpiY2gyn8EUNIkN46IwOLM3ey/uzN9mOI14mO6+Yf/20hhM7NOakjkm243gK1SbxS/klFTz/w2qKyyvVGHou1Sc32phbxLjZm7iwV3ONxhJaxkdyXo9mvDtrE9mafwi4vznsBex0HOfA3dznUT28oTbX8hsDBUA+sNcY844xxu927T6zazKD0hJ4bspqtu0tsR1HvMT+exo+oj0N96faJH7pye9W8erP69mwq8h2FDk01Sc3enrSKoIDA7h7RJrtKOIh7h6RhjHwwo9rbEfxCO5uDpOBrQfe6ThOObAb+LMdKDcCTwNXAiOBT4HLgVnGmLhDvcgYc70xZoExZsGuXb6xRK0xhifO7kSV4/DQ+Awcx7EdSbzAhKXbmL56F3efmKY9Df+bapP4nXkb8/h0QTbXDmhFp6ZalMqDqT65ydwNu5mSsZObBrcmMTrMdhzxEE1iw7l6QCu+XryVFVvzbcexzt3NYThwqM1jSmsePyTHca5yHOdBx3E+cxznU8dxrgduBNoAdx7mdW84jtPLcZxeCQkJR5vd4zRvGMHdJ6bx06qdTMnYYTuOeLjfVyPs1lyrER6EapP4lfJKF/d/vZymceGaZ+X5VJ/cwHEcnpqUSZPYMK4dmGo7jniYm4a0pkFEMM9MzrQdxTp3N4clVI+PP5iwmseP1FtUnzkbcbShvNnVx7eiQ5MYHhqfQX5Jhe044sFGTcigqKyKZ8/TaoQHodokfuXNGRtYl1PIY2d3JCJEi1J5ONUnN/hx5U6WZO/lzhPaEh4SaDuOeJiYsGBuHdaWGWtz+XWNb145ry13N4fbqB4e8V+MMSFAo5rHj4hTPZ4yC4g/5nReKCgwgGfO7cLuonKe+G6l7TjioaZk7GDisu3cNqwNaY2jbcfxRKpN4ldO6pjEPSemMSy9se0o8udUn+qY4zi88OMaUuMjObdHM9txxENd2jeF5g3DeWpSJi6X/07fcndzuBBIMsakHHB/75rPXnikb2iMCQBaATnHHs87dW4Wyw2DUvlswRZ+Xu23fw1yCPnFFfzjmxW0bxLDjUNa247jqVSbxK+0SYzituEaTuolVJ/qmDGGZ8/rwpN/6UxQoLsPfcVbhQYFcu9J6azavo9vlx3xORif4e5/IZ/V3B64EevtQDnwDYAxJsIYk26M+eOMljEm2hhzsLEv9wBxwHduyOs17jihLW0To/j7V8vZV6rhpfIfj3+3kryicp47rwvB+hI8FNUm8QsTlm6prDVSAAAgAElEQVTjxvcX6nvCu6g+uUGXZnH0TW1kO4Z4uNM7N+HZ87r49dZfbp144DjOYmPMWOBuY0w01cswjwAuAB5xHOf3trwPMB14BBhVc19P4F1jzHhgPeAAQ4FzgKXAaHdm93ShQYH88/yunPPqLJ6YuIpnzutiO5J4gF/W7OLzhVu4eUhrrUZ4GKpN4g/ySyp49NuVNIkNI1LzDL2G6lPd+mhuFouy9vD42Z0IC9ZcQzm8gADDBb2a245hVX18W9xI9Tj3q6heVnkTcAfw8p+8bhMwFzgdSAICqV6e+Qngacdx/H6Tpq7N47hhcGvG/LyeU7s0YXCa760uJrVXWFbJ/V8tp3VCJLdr+FhtqDaJT3tuSiZ5RWW8e1VvLUrlfVSf6sie4nJ27islNEgjaaT2pmfm8MavG3jv6j6E+NnPjtubQ8dxKqg+q/XIYZ7zM2AOuG8TcKE7s/mCO4a35ceVO/nbl8uYctcgYsKCbUcSS578fhXb8kv44sZ+OjtaC6pN4suWZu/lw7lZXNm/pUYReCHVp7pzy9A23DS4NcboBInUXkCAoaCsgp37SmneMMJ2nHrlX62wDwoLDuS587qwc18pT32/ynYcsWT66hw+mpvFdQNT6dmioe04ImLZP39YTXxUKHefmGY7iogV+0ormLUuF6g+0Bc5EoPaxvPtrQP8rjEENYc+oXtKA64blMrH87L9fm8Wf7SnqJz7vlhGu8bROhAUEQBeGtmd1y7tSbRGk4ifem/WJi55ay7rcgptRxEvZIzBGMOeonIWbMqzHadeqTn0EXedkEbrhEju/WIpe4vLbceReuI4Dv8Yv4I9xeW8cGFXDScV8XOlFVW4XA4NI0Po2aKB7TgiVhSWVfLWzI0MT0+kTWKU7Tjixe79Yik3frCIkvIq21HqjZpDHxEWHMhLI7uzu7CcB75eQfV+t+LrJizdxnfLtnPnCWl0TNa8IhF/9+T3qzj3td+oqHLZjiJizbjZm8gvqdDibHLMbhzcmtzCMsbN3mQ7Sr1Rc+hDOjWN5e4RaXy3fDtfL95qO4642Y78Uh78ZgU9UuK4YVCq7TgiYlnGtnw+mLOZLk1jtcep+K2iskremrGRIe0S6No8znYc8XK9WjZkUFoCr/+6geLySttx6oW+PXzMDYNa06dlQx4an0F2XrHtOOImjuNw7xdLqahyeP6CbgTpQFDErzmOw0PjM2gQEcLdI9rZjiNizYdzN5NXVM5tw3TVUOrGHcPbkFdUzkdzs2xHqRc6ovQxgQGG5y/oCsDdny2hyqXhpb7ogzmbmbE2l/tPa0+r+EjbcUTEsq8Xb2Xh5j3cd3I6seFahEb8U0l5FW/8uoGBbeM151bqTM8WDemX2og3ft1AaYXvzz1Uc+iDmjeM4NGzOjJ/0x5e+2W97ThSx9bsLODx71YxKC2BS49LsR1HRCxzHIdP5mXTrXkc5/VsZjuOiDUfzt1MbmE5d2iuodSxW4e1IaegjC8WbrEdxe3UHPqoc7o35bQuTfjXj2tYsTXfdhypI6UVVdz20WKiw4L45/ldtKmviGCM4f1r+zDm0h7az038VmlFFa//uoH+rRvRq6X2+5W61b91I7o1j+O1X9b7/IJfag59lDGGJ87uRHxUKLd/spiiMv+YROvrHv9uJat3FvD8Bd1IjA6zHUdELNueX0JxeSWhQYE0iQ23HUfEGseBK/u35C7t9ytuYIzhtmFt2LKnhPFLttmO41ZqDn1YXEQIL1zYlY25RTw4foXtOHKMJq/Yzgdzsrh+UCqD0xJsxxERyxzH4d7Pl3HumNnavkj8XnhIILcMbUNvXTUUNxmWnsgV/VqQ1ti3985Uc+jj+reO5/Zhbflq0VY+X5BtO44cpa17S/jrF8vo0iyW/9NKhCIC/LQqh5nrcrmwVzMNMRe/Nj0zh/FLtuLSInziRsYYHjmrE12a+fYWKWoO/cDtw9vSN7V6e4u1Owtsx5EjVFnl4s5PFlPlchg9sjshQfpnK+LvyiqreOK7lbRJjOKSvi1sxxGx6tP52Yz5eT06RyL1ITuvmBd/WuOzIzZ0lOkHAgMML43sTkRIILd8tIiSct9fhteXvPDjGuZv2sPj53SipbatEBHgvd82sWl3Mf84rb02vBe/9+olPXj3qj66gi71Yu7GPF6dvp7MHb55wUXfKH6icUwY/7qwG2tzCnl4guYfeosfV+7k1Z/Xc1Gf5pzTXUvUi0i1eRv3MLRdAkPaJdqOImJVSXkVAQGGpFgt0ib146xuycy8byjtm8TYjuIWag79yKC0BG4e0prPFmzxi31avN3m3UXc/dkSOjWN4eEzOtqOIyIe5M3Le/LyxT1sxxCxasGmPPo+NZVFWXtsRxE/EhwYQGJM9cmI0grfG42n5tDP3HVCGn1TG/LA18u1/6EHKymv4sYPFhFgDGMu6UlYcKDtSCLiATblFrEjvxRjDFGhQbbjiFj12i/rCTCQnhRtO4r4oWvfW8A9ny21HaPOqTn0M0GBAbxycQ8aRoZww/sLySsqtx1JDuA4Dv/4ZgWZO/bx4shuNG8YYTuSiHgAx3G478tlnDvmNyp9fBNmkT+zZmcBP63K4fJ+LYkI0YkSqX+tEyOZtGI7WbuLbUepU2oO/VB8VCivXdqTXYVl3PrRIh1keJiP52Xz5aIt3DasLUM1n0hEakzJ2MHcjXncOKQ1QVqERvzc679sICw4gCv6t7QdRfzUVf1bERhgeHvmBttR6pS+XfxU1+ZxPHF2J35bv5tnJmfajiM15m/K4+EJKxjYNp47hre1HUdEPERpRRVPfL+Kdo2juah3c9txRKzakV/K+CVbGdk7hYaRIbbjiJ9Kig3jzK5N+WzBFvb40Eg8NYd+7Pxezbm8XwvenLGRCUu32Y7j97Lzirnh/YU0bxDBKxf1IDBAS3KLSLWxszaSnVfCg6d30FVD8Xvvzd6Ey3G4ZkAr21HEz10/KJWSiio+nLvZdpQ6o28YP/eP0zrQu2UD/vrFUpZm77Udx28VllVy3bgFVFa5eOuKXsRGBNuOJCIeJGdfGSM6NGZA23jbUUSsKimv4qO5WYzokKQ5+WJdu6RoBqcl8O5vm31m5VI1h34uJCiAMZf2JD4qlGveW8CWPb41qdYbuFwOd36yhLU5hfz7kh6kJkTZjiQiHmbUmR159RJtXSHy5aIt5JdUcM1AXTUUz3DDoFRyC8v4ZvFW21HqhJpDIT4qlHeu7E1ZZRXXvLuAfaUVtiP5lWenrOanVTt56PQODGybYDuOiHiQ9bsK/9h2SMNJRWBp9l66NIulV4sGtqOIANCvdSM6Jsfw5owNuFyO7TjHTN80AkDbxtGMuaQn63cVcsuHi6jQCqb14rP52bz2y3ouOS6Fy/u1sB1HRDzMo9+u5NK351JS7hvDlUSO1XPnd+XDa4/DGM3LF89gjOHaga3YVVDG5jzvH4Gn5lD+MKBtPE+c04kZa3N5eEIGjuP9Zz882bTMnfz96+UMbBvPqDM76otORP7LzLW5/LJmFzcPaU14SKDtOCLW5RdXj2yKDtO8fPEsp3VOZs79w2kVH2k7yjFTcyj/5cLeKdw0pDUfzc3i1Z/X247js5Zk7+WWDxfToUkMYy7tSbCGi4nIflwuhye/X0WzBuFc3q+l7Tgi1q3eUUDvJ39i6qqdtqOI/I+QoAAiQoJwuRyKyyttxzkmOiKV/3HviHac2TWZ56as5uN5Wbbj+JyNuUVc/e584qNDGHtlb6JCg2xHEhEP8/Xirazcvo97T2pHWLCuGopEhwVxcZ8UeqRorqF4psoqF6eOnsGzk1fbjnJMdFQq/yMgwPDP87uyr7SCB75eTmx4MKd2bmI7lk/YkV/K5WPnAjDu6uNIiA61nEhEPFFReSV9UxtyRpdk21FEPEJyXDijzuxoO4bIIQUFBnBa5yZev+q8rhzKQYUEBTDmkp50T2nAnZ8sYebaXNuRvN6ugjIufmsOe4oqeOfK3j4xLl1E3OPyfi35+Lq+BARoLrLIpOXbmbcxz3YMkT912/C2nNbFuy+oqDmUQwoPCWTsFb1JTYjk+vcXqDAfgz1F5Vz29ly27y3lnat607V5nO1IIuKBdheWMXnFDhzH0SJVIkBFlYtR32bwyvR1tqOI1Mre4nLGzd7ktdtaqDmUw4qNCGbcNX1oEhvGle/MU4N4FPaVVnDFO/PYkFvEm5f3onfLhrYjiYiHGj11Lbd8tIjsvBLbUUQ8wo8rd7JzXxmX99V2T+IdZqzN5aHxGUxfnWM7ylFRcyh/KjE6jI+v60uSGsQjtre4nMvemsuq7ft47dIeDGgbbzuSiHioDbsK+XBuFiN7NyelUYTtOCIeYdzsTTSNC2doeqLtKCK1cnKnJBrHhPLub5tsRzkqag6lVhJjwvhkvwZx7obdtiN5vNzCMka+MYdV2wsYc0lPhqU3th1JRDzYM5MzCQ0K4M4T0mxHEfEIa3YWMGdDHpf2bUGg5t+KlwgODOCyvi2YsTaXtTsLbMc5YmoOpdb2bxAvHzuPaZnaa+hQdu4r5cLXZ7NpdxFvX9mLEzqoMRSRQ5u/KY8pGTu5YXBrrWIsUuP92ZsJCQrgwt7NbUcROSIX9UkhJDCAD+Zsth3liKk5lCOSGBPG5zf0I61xNNeNW8hXi7bYjuRxNuUWccHrs9mRX8p7V/VhYNsE25FExMMVllXStXkc1w5sZTuKiEcoKK3gq0VbOL1LExpGhtiOI3JEGkWFcmrnJL5atJWiskrbcY6ImkM5Yo2iQvn4+r4c16ohd3+2lLdmbLAdyWMsztrDX8b8xr6SCj649jiOS21kO5KIeIGh7RL55ub+RIRo+2ERoPqguryKy/u1tB1F5Khc2rcFBWWVTFi6zXaUI6LmUI5KVGgQ71zVm5M7JvH4d6sYNSGDyiqX7VhW/ZCxg4venENUaBBf3tSf7ikNbEcSEQ9XXunigzmbKaus0tYVIjUcx+H9OZvp0iyWbtr6SbxUzxYNSE+K5oM5m3Ec79nWQs2hHLXQoED+fUkPrhnQind/28TV7y0gv6TCdqx65zgOY2du5MYPFtIuKYavbu5PakKU7Vgi4gXen7OZf3yzQqtAi+ynvMrFmV2TuXlIa9tRRI6aMYZL+rYgY9s+lmTvtR2n1jR+RY5JYIDhwdM70DYxin98s4K/vDqLt6/oTcv4SNvR6kVJeRUPfL2crxZv5cQOjXlpZDcNCxORWskvruDlaWsZ2DaeAW20zY3I70KDArl9eFvbMUSO2dndkpm9PpeQIO+5Huc9ScWjjeyTwvvXHMfuonLOeGUmk1fssB3J7bLzijl3zG98vWQr95yYxuuX9lRjKCK19u+f15FfUsHfT2mvIaUiNXL2lfL98u2UV/r3VBXxDdFhwbx6SU86JsfajlJrag6lzvRr3Yhvbx1AanwkN36wkFETMiirrLIdyy2mZOzgjFdmsmVPMWOv6M1tw9sSoD2YRKSWsvOKeXfWJs7t0YwOyTG244h4jG+WbOXmDxexPb/EdhSROrN5d5HXTB/QZQ6pU80bRvD5jf15elImY2dtZOHmPbw0spvPzMErKqvk0W9X8umCbDomx/DqJT1o0cg/htCKSN0pKq+kW0oc94zQhvci+7tmQCo9WzTUd6v4lHs+W0p+SQU/3DXI40eKqDmUOhcSFMBDZ3Sgb2pD7v1iGae8NIO7T0zjmgGtCAr03ovVCzfv4e7PlpCVV8zNQ1pz5wlpXjWGXEQ8R3pSDJ/d0M92DBGPExhg6NlCq32Lb3n0rE40jAzx+MYQNKxU3GhExyR+vGsQg9MSeGpSJueO+Y3VOwpsxzpie4vLuf/r5Zz32m9UVjl8en0//npyuhpDETliv69unFdUbjuKiMe5/+vlvPbLetsxROpch+QYkmLDbMeoFR3dilslxoTx+mU9eeXi7mTvKeG00TMYNSGDPV5wYOQ4Dl8s3MLw53/h0/nZXH18K6bcNYg+rRrajiYiXmrqqhwenbiS75Z516bIIu6Ws6+UT+dne8XxgcjRyNiWzxVj55FTUGo7ymFpWKm4nTGG07sk0791PM//sJpxszfx9eKt3D68LZf1beGRV+Bmrs3l2SmZLNuST4+UON4/u7MWjRCRY1JZ5eKpSatIjY9kZJ8U23FEPMrnC7dQ5XK4sHdz21FE3CI0KIBf1uziy4VbucmD9/B0+1G5MSbIGPOgMWajMabUGJNpjLnV1HLQrTFmmDFmljGm2BizyxjzjjEmwd25pe41jAzhiXM6M/nOQXRtHsdjE1cy5LnpjJu9idIK+6uaOo7Db+tyufjNOVz69lx2F5bzz/O78sWN/dUY+iDVJqlvny7IZv2uIu47JZ1gL55/Le7nb/XJ5XL4ZH4WfVMb+swCdiIHapMYTe+WDfh0fhaO49iOc0j18e00BngU+BG4FVgGvAw8+GcvNMYMBqYAYcA9wCvAucB0Y0y4uwKLe6U1jmbc1X0Yd3UfkuPCeWh8BgOemc4LP66xsnR1aUUV45ds5cxXZnHxW3NZs7OQh07vwLT/G8x5PZtpiwrfpdok9aaSQP714xp6t2zAiA6NbccRz+dX9WnW+lyy80q4SFfUxceN7J3Cpt3FzNngudtauHVYqTGmK3At8C/Hce6uufstY8znwP3GmDcdx9l+mLd4EdgODHYcp7DmPRcAE4EbgX+5L72426C0BAa2jWfuxjxe+2U9L09by7+nr2Nou0TO6pbM8PaJbttU3uVyWLJlL+MXb+WbJdvIL6kgNSGSp//SmbO7NyUsONAtnyueQbVJ6luVCaRPq4ZcNzDVK1arE3v8sT59PC+LBhHBnNQxyXYUEbc6tXMTRn2bwSfzs+jXupHtOAfl7jmHF9bcvnTA/S8B5wFnU3127H8YY9KAbsCo34sbgOM43xlj1gMj8cACJ0fGGEPf1Eb0TW1E1u5iPpy3ma8XbeWnVTsJDw5kQNt4BraN5/g28aTGRx7TQdWugjLmb8pj1rpcfly5k5yCMkKCAji5YxIX9m5Ov9RGukroP1SbpF6FOuW8eklP2zHEO/hVfdpVUMYPGTu5sn9LnZgVnxceEsg53ZvyyfxsHikuJy4ixHak/+Hu5rAXsNNxnM0H3D8PcAGH+6bsVXM79yCPzQHON8YEOo5jf7Ka1ImURhH8/ZT2/PWkdOZtzOO75dv4efUufly5E4CYsCA6NY0lPSmGlIbhNG0QQXxUCFGhQZSYMBwMG3YVUlJRxa6CMnIKysjOK2b1jgLW7Cxg0+5iACJCAhmclsBJHZMYmp5IbHiwzT+22KHaJPVmc0gLGlXuth1DvIdX1addBWV/On8qJCjgj4PgXQVlhAYHEBMWjMvl8NLUNVS6HEb20UI04h9G9k5h3OzN/Hv6Oq4bmEqjqFACAwyFZZUUl1WSEB2KMYZ9pRWUlh/6n6oxhoTo0DrP5+7mMBnYeuCdjuOUG2N2A03/5LUc7PXANiAEiAd2Hi5AVlYWN910U+3SisfpBKQGRLA7MJ59ZbFkFMYyZ100LnPA2cWYEwAY9vwv/3W3cVxEuIqIchXSrnIvDat2E1OVD7scpsyqnpQhfkm1SepFQUA0K6MGEbtzkf5/S215VX2aGn0i5QGHP0BNrNhBz+IFfzy/ccV2OpWuwIVhSuxpNC/fzPMP/7VWnyd1Z83atQCqTRYkh3fjzRnw5oyNDNn3E+FOKWtD27IurB0n50/EACvCOpEd2vKQ7xHmKmFowdQ6z+bu5jAc2HeIx0prHj/cawHKDvHa/Z/zX4wx1wPXA8TGxv55SvFYBoh0FRPpyoKK6vscoNyEUBIQQbkJocoEsjVnNzgOyY0TCHBchDplhLrKCHVKCcRl848gnkm1SepFZlh7AqrKaLB9LqRqsQ2pFa+qT+mlK6k68ITtgaFc/1lsLr105R+/Nzj0LJpHQmVOrT9PxBd0KVlCUsV2ygJCCXaqD3ATK3IIdf7zTze5YhsxrkOVAgh00wAldzeHJcChTieF1Tx+uNdyiNeHHfCc/+I4zhvAGwC9evVyxow56NB88SG/n/UaM/pPF3ITH/Daa68d61uoNonbzVyby6S355JespJWqSno/7d/UH0Sb/HHsZP+X/uF2tYmd29lsY3/DHH4gzEmBGhU8/jhXsvBXl9zXzmQe6wBRcQvqTaJW7lcDk9+v4pmDcJJKd9kO454F9UnEbHG3c3hQiDJGHPgWJreNZ+98E9eC3DcQR7rAyzVgg8icpRUm8StyqtcDGwbz99Paa+h7XKkVJ9ExBp3N4ef1dzefsD9t1N99uobAGNMhDEm3RgT//sTHMdZDSwFrjbGRP5+vzHmFKAt8Kk7g4uIT1NtErcKCw7k76e257QuTWxHEe+j+iQi1rh1zqHjOIuNMWOBu40x0VQvwzwCuAB4xHGc34c/9AGmA48Ao/Z7i7uAH4FfjDFvAYnAPcAqDrHHj4jIn1FtEnf6cuEWEqJDGZSWYDuKeCHVJxGxyd0L0gDcCGQBVwFXApuAO4CX/+yFjuNMN8acDDxG9aatxVSfMfur4zjFbsorIv5BtUnq3O7CMh6ekEHf1EZqDuVYqD6JiBVubw4dx6mg+qzWI4d5zs9U71pwsMd+An5ySzgR8VuqTeIOo6eupaSiir+dkm47ingx1ScRscXdcw5FRET8woZdhXw4N4uRvZvTJjHKdhwREZEjpuZQRESkDjwzOZPQoADuPCHNdhQREZGjUh9zDkVERHya4zgMaBNPv9RGJEQfav9yERERz6bmUERE5BgZY7isX0vbMURERI6JhpWKiIgcgx8ydvDR3CyqXI7tKCIiIsdEzaGIiMhRKq2o4pFvV/LBnM22o4iIiBwzNYciIiJHadzsTWzdW8IDp7UnMOCguwqIiIh4DTWHIiIiR2FPUTkvT1vH0HYJHN8m3nYcERGRY6bmUERE5CiMnraWorJK/n5qe9tRRERE6oRWKxURETkKQ9olEh8VSlrjaNtRRERE6oSaQxERkaMwOC2BwWkJtmOIiIjUGQ0rFREROQILN+fxzORMisoqbUcRERGpU2oORUREaslxHB6buIqvFm3BaHFSERHxMWoORUREamnisu0syd7LPSPaERGimRkiIuJb1ByKiIjUQlllFc9MziQ9KZpzezSzHUdERKTOqTkUERGphXG/bWbLHm14LyIivktjYkRERGphUFoChWWVDGyrFUpFRMQ3qTkUERGphXZJ0bRL0p6GIiLiuzSsVERE5DA25RZxxyeL2bmv1HYUERERt1JzKCIichjPTM7kx5U7tXWFiIj4PDWHIiIihzB3w24mrdjBDYNakxgdZjuOiIiIW6k5FBEROYgql8OjE1fSJDaM6wel2o4jIiLidmoORUREDuLLRVvI2LaPv52STnhIoO04IiIibqfmUERE5CCGpSfy15PbcWbXZNtRRERE6oW2shARETmI+KhQbh7SxnYMERGReqMrhyIiIvvJzivmwtdnsy6nwHYUERGReqXmUEREZD9PT8pk2ZZ8IkM1uEZERPyLmkMREZEa8zbm8d3y7dw4uDVNYsNtxxEREalXag5FREQAl8vh0YkZ2rpCRET8lppDERER4Ntl21ixVVtXiIiI/1JzKCIiApzUMYlnz+uirStERMRvaba9iIj4PZfLISw4kAt6NbcdRURExBpdORQREb+WtbuYE174hYWb82xHERERsUrNoYiI+LXHvlvJjn2lNI2LsB1FRETEKjWHIiLit35encOPK3dy+/C2JMWG2Y4jIiJilZpDERHxS2WVVTzy7UpS4yO5+vhWtuOIiIhYpwVpRETEL323bDsbc4t47+o+hATpXKmIiIiaQxER8UvndG9Kclw4fVMb2Y4iIiLiEXSqVERE/E5+cQXGGDWGIiIi+1FzKCIifmXOht30f3oq8zdp6woREZH9qTkUERG/UVnlYtSEDOIiQuiUHGs7joiIiEdRcygiIn7jgzmbydxRwIOntyc8JNB2HBEREY+i5lBERPxCbmEZz/+4hoFt4zmpY5LtOCIiIh5HzaGIiPiF6Zk5lFW4ePiMDhhjbMcRERHxONrKQkRE/ML5vZozoG08TWLDbUcRERHxSLpyKCIiPq280kXGtnwANYYiIiKHoeZQRER82pszNnDGyzNZl1NgO4qIiIhHU3MoIiI+K2t3MaOnruWkjkm0SYy2HUdERMSjub05NMZ0M8b8YIwpMMbsNcZ8ZYxJreVrhxhjnEP8+oe7s4uI71Jt8n2O4/Dg+BUEBRgeOqOD7Tgitab6JCK2uHVBGmNMOvArkAM8AIQBdwEzjTHdHcfZWcu3ehv4+YD7ltRVThHxL6pN/mHSih38smYXD57eQXMNxWuoPomITe5erfQpwACDHcfZCmCMmUR1cbofuKOW7zPHcZwP3BNRRPyQapMf2F1YRo+UOK7o18J2FJEjofokIta4bVipMSYKOBX44vfiBuA4znJgOjDyCN8v0hgTWrcpRcTfqDb5j8v6teSLG/sTFKjp9eIdVJ9ExDZ3fmN2AUKAuQd5bA6QaIxpVsv3egEoBEqNMUuNMRfUUUYR8T+qTT5uSfZeJq/YDkBAgDa7F6+i+iQiVrlzWGlyze3Wgzy2rea2KbDlMO9RAYwHvge2Ay2B24BPjTEJjuP8+2AvMsZcD1wPkJKScsTBRcSnqTb5sLLKKu79fCmFZZUMTkskPCTQdiSRI6H6JCJW1ao5NMYEU12MaqPQcZxc4PfZ/2UHeU5pze1hVwhwHGcWMOuALG9TPe7+KWPMOMdx/mfjKsdx3gDeAOjVq5dTy9wi4mVUm+RAr05fz9qcQsZe2UuNoVil+iQi3qi2Vw7bActr+dwPgUuBkprfH2yse1jNbclBHjssx3GKjTEvA6OBfsAPR/oeIuIzVJvkD6t3FPDqz+s4q1syw9Ib244jovokIl6nts3hZuCMWj7396EOvw9/SD7Ic5IPeIAn8LsAAA29SURBVM6R2lxzG3+UrxcR36DaJABUuRz++uUyokKDeOh07WkoHkH1SUS8Tq2aw5rhBxOP8L2XUz3u/Tjg9QMeO47q/XsON2b+cNrU3OYc5etFxAeoNsnvAgxcfXxLQgIDaBSlxRnFPtUnEfFGbluttKYofg+cZ4xp8vv9xphOwFDgM8dxnP3uT6nZ+JX97mt44PvW3HcnsAeY7ab4IuKjVJt8j+M4GGM4q1tTTunc5M9fIOKhVJ/k/9u79yAr6/uO4+/vLstydeUWrgG8FDVEiHUx0lBMx0jTPwJOm+rES5XUEO1Q2hptq6kTwthOL9PJWKROiEbjJWlFGw2m045jjdaZImURpEGjqLCChJtc5abw6x/nhIUF1sOy5zzPnvN+/XPY5/fsme/+ePgcvvv8nueRslbOu5VC4WGtLwMvFte6NwJ/BmwB/qbdvg8Dl1F48OuvPB4Re4FlFJZRjAFuAoYCN6SUPihv+ZKqlNlUJVJKzHqkhcvGDeG6S33YvaqC+SQpM2VtDlNKqyPiMuDvKATaIeC/gNtTShtLeIunga9QuAXzmcAuCs/5+YeU0s/KUrSkqmc2VY8fLm3l2dWbmDpuSNalSF3CfJKUpXKfOSSltBy4ooT9Pn+CbfOB+WUoS1KNM5u6v9Zte/nrn77GlHMHc+0lPpdN1cN8kpSVsl1zKElSuRw6nLht0UrqI/j7L0+gri4+/pskSVKHbA4lSd3Oy+9sY+na9/nW9PGMOLPDZ4JLkqQSlX1ZqSRJXe03zhnMT+dM4VPDz8i6FEmSqoZnDiVJ3caHhw6zav1OAMaPaCLC5aSSJHUVm0NJUrex4Pk1zFjwEm9s2p11KZIkVR2bQ0lSt7Bs7fv803NvMuMzIxk3tH/W5UiSVHVsDiVJubdz34f8yb+sYNSAPsybMT7rciRJqkrekEaSlGspJe788So27drPopsn079XQ9YlSZJUlWwOJUm5N3FUExNHNXHR6AFZlyJJUtWyOZQk5VpEMGvqOVmXIUlS1fOaQ0lSLh346BDXP/Ayz722KetSJEmqCTaHkqRcuvuZ1/jvN7dy6HDKuhRJkmqCzaEkKXeeemUDjyxZx6ypZzNt/LCsy5EkqSbYHEqScuWNTbu5499WccnYgfz5b5+XdTmSJNUMm0NJUq4sXvkefRt7cO81F9Gj3o8pSZIqxbuVSpJy5dYrxnH9pWP4xBm9si5FkqSa4q9kJUm58GTLetZs3k1E2BhKkpQBm0NJUuZeeGMLtz+xkgXPv5V1KZIk1SybQ0lSptZs3sPsHy5n3ND+3H3lp7MuR5KkmmVzKEnKzM69H/K1h5fRs76O+29opm+jl8JLkpQVP4UlSZlZ8LM1rN++lx997VJGDeiTdTmSJNU0m0NJUma+MW0cl5//CZrHDsy6FEmSap7LSiVJFfdEy3p27D1IY496Pnv2oKzLkSRJ2BxKkirsX/+3ldsWreSBl97JuhRJknQUm0NJUsU8//pm7vzx/zF13BDmXP5rWZcjSZKOYnMoSaqIJW9v45bHWrhgeH/++dpfp6HejyBJkvLET2ZJUtkdPpyY+5OfM2pAH34w8xL6+cgKSZJyx09nSVLZ1dUFD86cRF0Eg/o1Zl2OJEk6Ac8cSpLK5vVf7mLe4tUcOpwY3tSboWf0yrokSZJ0EjaHkqSyWPHuDq7+7hL+fdVGtuw+kHU5kiTpY9gcSpK63P+8tY1rv7eEpt4NLLp5MsOaPGMoSVLeec2hJKlLPf/6Zm5+tIXRA/vw6E2fdSmpJEndhM2hJKlL9WqoZ8KoJr57fTMD+/bMuhxJklQil5VKkk7bocOJF9/YAsDkcwbx+Ncn2xhKktTN2BxKkk7LBwc+4uuPLOMPvr+UVet3AhARGVclSZJOlctKJUmdtmbzbm55dDlvb/2AeTPGc+GopqxLkiRJnWRzKEnqlKdXbOAvn1xF38Z6Hv7qJXzu3MFZlyRJkk6DzaEkqVP2HTzEhaOamP+Vi7wjqSRJVcDmUJJUsude28SeAx8x4zMjuXrSJ/n95k9SX+f1hZIkVQObQ0nSx3r3/b3Me2Y1z67eRPOYAUyfOIKIoN6+UJKkqmFzKEk6qR17D7Lwxbe5/6V36FEX/MUXz+cPp5zl3UglSapCNoeSpOOklIgI3ty8h/teeIvpE0dwx+9cwLAmry2UJKla2RxKkoBCQ7i8dTuPLmmlqXcDc6ePZ9LYgbxw228xelCfrMuTJEllZnMoSTXuldbtPL3iPf7z579k48799GvswbWXjj4ybmMoSVJtsDmUpJzbtGs/K97dQUoAiZQgAZPPHsSAvj159/29LG/dDlAcK+xz+QVDaerdwJrNu1neugMSHDx0mI0797F++z7+9ncn0LtnPYtXbuRHS1uZOm4It007jy9+ehh9G/14kCSp1vjpL0k517JuO3/02PLjtj95y2Qu7juQJW9v4/YnXj1u/D/+9Ddp6t3AS29uZe7i1Ue219cFw5t6se2DA4zq2YdbPn8O35g2zoZQkqQa5/8EJCnnPnfuYJ754ylEQBCF14DRAwvLPaeNH8ZFowcUxyEiCGD4mYWbx/zexaP4wqeGFh89EQzu15Me9XVH3n9I/8YMfipJkpQ3ZW0OI2Ia8GXgYuBCoAE4K6W09hTeowdwB/BVYDiwFrgXWJBSYZGVJJ2K7pZNTb0baBrZ1PF474aTjvfv1UD/Xicfl5Qf3S2fJFWXuo/f5bRcA9xA4fKYX3TyPe4D5gHPArOBV4H5wF1dUaCkmmQ2Scor80lSZsrdHH4TOCOl1Aw8farfHBETgZuA76SUZqWU7k8pXQU8AdwZEcO7tlxJNcJskpRX5pOkzJS1OUwpbUgpHTiNt7i6+HpPu+33AI3Alafx3pJqlNkkKa/MJ0lZKveZw9PVDGxKKa1rt30pcJjCenxJqjSzSVJemU+SOi3vzeEIYEP7jSmlg8A2YOSJvikiZkXEsohYtmXLljKXKKkGmU2S8sp8ktRpJd2tNCIaOEmYnMCelNLWzpd0jN7ArpOM7S+OHyeltBBYCNDc3OxduaQqZTZJyivzSVJ3VOqjLM4DVpW472PAdZ0r5zj7KKyPP5FexXFJtctskpRX5pOkbqfU5nAd8KUS913fyVpO5D0Kz/g5RkT0BAYVxyXVLrNJUl6ZT5K6nZKaw5TSbuCZMtdyIi3AFRExOqXUetT2SRSul2zJoCZJOWE2Scor80lSd5SbG9JExPCIOL+4Rv9XHi++zmm3+xzgIPBURYqTVLPMJkl5ZT5J6mqRUvmuOY6ICcD04pdfAC4D/hHYAexIKd171L4PATcAZ6WU1h61/QFgJvA9CrdhngZcBXw7pTS3hBq2UFjaUa0GA111EXt351y0qfa5GJNSGtLZbzabKqLaj8FT5Xy0qfa5MJ/yr9qPwVPhXLSp9rkoKZvK3RzeCDx4kuF1KaWxR+37ECcOuAbgTgohNxxYCywA5qdyFt9NRMSylFJz1nXkgXPRxrnomNlUfh6Dx3I+2jgXHTOfys9jsI1z0ca5KChrc6jy80Bu41y0cS6UNY/BYzkfbZwLZc1jsI1z0ca5KMjNNYeSJEmSpOzYHHZ/C7MuIEecizbOhbLmMXgs56ONc6GseQy2cS7aOBe4rFSSJEmShGcOJUmSJEnYHEqSJEmSsDmsKhExLSIWRkRLRByMiBQRY7Ouq5wiokdE3BUR70TE/oh4PSJmR0RkXVulRUS/iJgbEYsjYmPx7/+hrOuSzCazyWxSXplP5pP5dCybw+pyDYXnHSXgFxnXUin3AfOAZ4HZwKvAfOCuLIvKyGDgW8DFwLKMa5GOZjaZTWaT8sp8Mp/Mp6N4Q5oqEhEjga0ppQMRcTfwTdo9GLeaRMREYAXwnZTSrUdtXwR8icLPvjGr+iotIhqBwSmlDRHRA/gQ+EFK6cZsK1OtM5uObDebzCbljPl0ZLv5ZD4BnjmsKimlDSmlA1nXUUFXF1/vabf9HqARuLKy5WQrpXQgpbQh6zqk9symI8wmKWfMpyPMJwE2h+remoFNKaV17bYvBQ5TWCIgSZVmNknKK/NJHbI5VHc2Ajjutz0ppYPANmBkxSuSJLNJUn6ZT+pQj6wL0PEiooHS/3HuSSltLWc9OdYb2HWSsf3FcUldxGwqmdkkVZj5VDLzSR2yOcyn84BVJe77GHBdGWvJs30U1sefSK/iuKSuYzaVxmySKs98Ko35pA7ZHObTOgp3jCrF+nIWknPvARe23xgRPYFBxXFJXcdsKo3ZJFWe+VQa80kdsjnMoZTSbuCZrOvoBlqAKyJidEqp9ajtkyhcT9uSTVlSdTKbSmY2SRVmPpXMfFKHvCGNurPHi69z2m2fAxwEnqpsOZIEmE2S8st8Uoc8c1hFImICML345ZTi6+yI2AHsSCndm01l5ZFSeiUivg/cGhH9KdyGeRpwFfDtlFLNLY2IiNnAmbT94mdCRPxV8c8/SSm9mk1lqmVmk9lkNimvzCfzyXw6VqSUsq5BXSQibgQePMnwupTS2MpVUxnFu5PdCcwEhgNrgQXA/FSDB3dErAXGnGR4ZkrpocpVIxWYTWaT2aS8Mp/MJ/PpWDaHkiRJkiSvOZQkSZIk2RxKkiRJkrA5lCRJkiRhcyhJkiRJwuZQkiRJkoTNoSRJkiQJm0NJkiRJEjaHkiRJkiRsDiVJkiRJ2BxKkiRJkoD/B3vTjZmhNtLwAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x_range = np.linspace((-math.sqrt(2)-0.25), (math.sqrt(2)+0.25), 250)\n", "y_rho = hlp.rho_catnew(x_range)\n", "y_rho_g = hlp.psi_catnew(x_range)\n", "y_rho_gg = hlp.psi_catnew_deriv(x_range)\n", "\n", "myfig = plt.figure(figsize=(15,5))\n", "\n", "ax_1 = myfig.add_subplot(1,3,1)\n", "plt.axvline(x=0.0, color=\"xkcd:dark grey\")\n", "plt.axhline(y=0.0, color=\"xkcd:dark grey\")\n", "ax_1.plot(x_range, y_rho, \"-\")\n", "ax_1.tick_params(labelsize=FONTSIZE)\n", "\n", "ax_2 = myfig.add_subplot(1,3,2, sharey=ax_1)\n", "plt.axvline(x=0.0, color=\"xkcd:dark grey\")\n", "plt.axhline(y=0.0, color=\"xkcd:dark grey\")\n", "ax_2.plot(x_range, y_rho_g, \"--\")\n", "ax_2.tick_params(labelsize=FONTSIZE)\n", "\n", "ax_3 = myfig.add_subplot(1,3,3, sharey=ax_2)\n", "plt.axvline(x=0.0, color=\"xkcd:dark grey\")\n", "plt.axhline(y=0.0, color=\"xkcd:dark grey\")\n", "ax_3.plot(x_range, y_rho_gg, \"-.\")\n", "ax_3.tick_params(labelsize=FONTSIZE)\n", "\n", "plt.show()\n", "\n", "if saveImages:\n", " myfig.savefig(imgDir+\"rho_psi_deriv.pdf\", bbox_inches=\"tight\")\n", " myfig.savefig(imgDir+\"rho_psi_deriv.eps\", bbox_inches=\"tight\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## Getting roots, simplest case: $0 < \\gamma \\leq \\sqrt{2}/2$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us begin with some plots related to the *double-cube* condition, which is all we'll ever need as long as $\\gamma \\leq \\sqrt{2}/2$. First, we look at how the discriminant of this function depends on $\\gamma$ and $\\eta$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Small gamma = 0.1414213562373095\n", "max = -923.791209089676 min = -88739014952.46182\n", "--\n", "Medium gamma = 0.7071067811865476\n", "max = -1222.1605295237487 min = -117400252824.0\n", "--\n", "Large gamma = 0.6071067811865476\n", "max = -1193.3880176915707 min = -114636376817.63322\n", "--\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "eta_range = np.linspace(start=0.01, stop=0.99, num=200)\n", "\n", "myfig = plt.figure(figsize=(7,7))\n", "ax_1 = myfig.add_subplot(1,1,1)\n", "\n", "gamvals = [math.sqrt(2)/10, math.sqrt(2)/2, (math.sqrt(2)/2 - 0.1)]\n", "gamlabels = [\"Small gamma\", \"Medium gamma\", \"Large gamma\"]\n", "\n", "for i in range(len(gamvals)):\n", " \n", " gamval = gamvals[i]\n", " gamlabel = gamlabels[i]\n", " \n", " myA = lnk.coef_twocube_A(gam=gamval, eta=eta_range)\n", " myB = lnk.coef_twocube_B(gam=gamval, eta=eta_range)\n", " myC = lnk.coef_twocube_C(gam=gamval, eta=eta_range)\n", " myD = lnk.coef_twocube_D(gam=gamval, eta=eta_range)\n", " discrimvals = gtrt.discrim(a=myA, b=myB, c=myC, d=myD)\n", " \n", " print(gamlabel, \"=\", gamval)\n", " print(\"max =\", np.max(discrimvals),\n", " \"min =\", np.min(discrimvals))\n", " print(\"--\")\n", " \n", " ax_1.semilogy(eta_range, -discrimvals, \"-\", label=gamlabel)\n", " ax_1.tick_params(labelsize=FONTSIZE)\n", "\n", "plt.title(\"Log-scale Graph of (-1)*discriminant of double-cube\", size=FONTSIZE)\n", "plt.xlabel(\"Value of eta\", size=FONTSIZE)\n", "plt.axvline(x=0.0, color=\"blue\")\n", "plt.axvline(x=1.0, color=\"blue\")\n", "ax_1.legend(loc=1,ncol=1, fontsize=FONTSIZE)\n", "plt.show()\n", "\n", "if saveImages:\n", " myfig.savefig(imgDir+\"discrimvals_doublecube.pdf\", bbox_inches=\"tight\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we have the graph of the cubic polynomial itself (+root(s))." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Value of P(ustar) = 1.7763568394002505e-15\n", "Value of C_{eta}(ustar) = 0.22846483390112957\n" ] } ], "source": [ "\n", "gamval = math.sqrt(2)/2\n", "etaval = 0.6\n", "\n", "myA = lnk.coef_twocube_A(gam=gamval, eta=etaval)\n", "myB = lnk.coef_twocube_B(gam=gamval, eta=etaval)\n", "myC = lnk.coef_twocube_C(gam=gamval, eta=etaval)\n", "myD = lnk.coef_twocube_D(gam=gamval, eta=etaval)\n", "\n", "xvals = np.linspace(start=-2, stop=2, num=200)\n", "\n", "myfig = plt.figure(figsize=(7,7))\n", "\n", "yvals = lnk.cube(x=xvals, a=myA, b=myB, c=myC, d=myD)\n", "\n", "rootvals = gtrt.getroot(a=myA, b=myB, c=myC, d=myD)\n", "if ( len(rootvals) == 1 ):\n", " rootval = rootvals[0]\n", "\n", "ax_1 = myfig.add_subplot(1,1,1)\n", "ax_1.plot(xvals, yvals, \"--\")\n", "ax_1.tick_params(labelsize=FONTSIZE)\n", "plt.title(\"Graph of double-cube function\", size=FONTSIZE)\n", "plt.axvline(x=gamval, color=\"blue\")\n", "plt.axvline(x=(-gamval), color=\"blue\")\n", "plt.axvline(x=0.0, color=\"black\")\n", "plt.axhline(y=0.0, color=\"black\")\n", "plt.axvline(x=rootval, color=\"pink\")\n", "\n", "plt.show()\n", "\n", "print(\"Value of P(ustar) =\", lnk.cube(x=rootval, a=myA, b=myB, c=myC, d=myD))\n", "print(\"Value of C_{eta}(ustar) =\", lnk.condPhiRisk(u=rootval, eta=etaval, gam=gamval))\n", "\n", "if saveImages:\n", " myfig.savefig(imgDir+\"graph_doublecube.pdf\", bbox_inches=\"tight\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we have the value of the $H_{\\gamma}(\\eta)$ function over a range of $\\eta$ values, given small enough $\\gamma$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Small gamma = 0.282842712474619\n", "--\n", "Medium gamma = 0.47140452079103173\n", "--\n", "Large gamma = 0.7071067811865476\n", "--\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "eta_range = np.linspace(start=0, stop=1, num=200)\n", "\n", "myfig = plt.figure(figsize=(7,7))\n", "ax_1 = myfig.add_subplot(1,1,1)\n", "\n", "gamvals = [math.sqrt(2)/5, math.sqrt(2)/3, math.sqrt(2)/2]\n", "gamlabels = [\"Small gamma\", \"Medium gamma\", \"Large gamma\"]\n", "gamcolours = [\"red\", \"green\", \"black\"]\n", "linklabels = [\"Link fn (small)\",\n", " \"Link fn (medium)\",\n", " \"Link fn (large)\"]\n", "\n", "for i in range(len(gamvals)):\n", " \n", " gamval = gamvals[i]\n", " gamlabel = gamlabels[i]\n", " gamcolour = gamcolours[i]\n", " linklabel = linklabels[i]\n", " \n", " print(gamlabel, \"=\", gamval)\n", " print(\"--\")\n", " \n", " Hvals = lnk.Hfn(eta=eta_range, gam=gamval)\n", " linkvals = lnk.linkfn(theta=eta_range, gam=gamval)\n", " ax_1.plot(eta_range, Hvals, \"-\", label=gamlabel, color=gamcolour)\n", " ax_1.plot(eta_range, linkvals, \"--\", label=linklabel, color=gamcolour)\n", " ax_1.tick_params(labelsize=FONTSIZE)\n", "\n", "plt.axvline(x=0.0, color=\"blue\")\n", "plt.axvline(x=1.0, color=\"blue\")\n", "plt.axhline(y=0, color=\"black\")\n", "plt.title(\"Graphs of of H() and Psi() functions.\", size=FONTSIZE)\n", "ax_1.legend(loc=2,ncol=1, fontsize=FONTSIZE)\n", "plt.show()\n", "\n", "if saveImages:\n", " myfig.savefig(imgDir+\"Hfn_Linkfn_simplecase.pdf\", bbox_inches=\"tight\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One nice conclusion is that (as expected) the discriminant is always negative, and thus we easily can find solutions. Furthermore, the $H$ takes the concave form that we would expect from the cited literature." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## Getting roots, more complicated case: $\\gamma > \\sqrt{2}/2$\n", "\n", "Now we get into some computations related to the *single-cube* conditions. First, we look at how the discriminant of this function depends on $\\gamma$ and $\\eta$." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Small gamma = 0.8071067811865476\n", "Medium gamma = 1.4142135623730951\n", "Large gamma = 2.8284271247461903\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# PLOTS of quantities related to the single-cube conditions.\n", "\n", "## \n", "eta_range = np.linspace(start=0.01, stop=0.99, num=200)\n", "myfig = plt.figure(figsize=(14,7))\n", "\n", "gamvals = [(math.sqrt(2)/2 + 0.1),\n", " math.sqrt(2),\n", " 2*math.sqrt(2)]\n", "gamlabels = [\"Small gamma\", \"Medium gamma\", \"Large gamma\"]\n", " \n", "\n", "ax_1 = myfig.add_subplot(1,2,1)\n", "\n", "for i in range(len(gamvals)):\n", " \n", " gamval = gamvals[i]\n", " gamlabel = gamlabels[i]\n", " \n", " myA = lnk.coef_onecubeminus_A(gam=gamval, eta=eta_range)\n", " myB = lnk.coef_onecubeminus_B(gam=gamval, eta=eta_range)\n", " myC = lnk.coef_onecubeminus_C(gam=gamval, eta=eta_range)\n", " myD = lnk.coef_onecubeminus_D(gam=gamval, eta=eta_range)\n", " discrimvals = gtrt.discrim(a=myA, b=myB, c=myC, d=myD)\n", " \n", " #print(\"max =\", np.max(discrimvals))\n", " #print(\"min =\", np.min(discrimvals))\n", " print(gamlabel, \"=\", gamval)\n", " \n", " ax_1.plot(eta_range,\n", " np.log(np.abs(discrimvals))*np.sign(discrimvals),\n", " \"-\", label=gamlabel)\n", " ax_1.tick_params(labelsize=FONTSIZE)\n", "\n", "plt.title(\"Log (-1)*discriminant of (-) single-cube\", size=FONTSIZE)\n", "plt.xlabel(\"Value of eta\", size=FONTSIZE)\n", "plt.axvline(x=0.0, color=\"blue\")\n", "plt.axvline(x=1.0, color=\"blue\")\n", "plt.axhline(y=0.0, color=\"black\")\n", "plt.axvline(x=1/2, color=\"black\")\n", "ax_1.legend(loc=2,ncol=1, fontsize=FONTSIZE)\n", "\n", "ax_2 = myfig.add_subplot(1,2,2)\n", "\n", "for i in range(len(gamvals)):\n", " \n", " gamval = gamvals[i]\n", " gamlabel = gamlabels[i]\n", " \n", " myA = lnk.coef_onecubeplus_A(gam=gamval, eta=eta_range)\n", " myB = lnk.coef_onecubeplus_B(gam=gamval, eta=eta_range)\n", " myC = lnk.coef_onecubeplus_C(gam=gamval, eta=eta_range)\n", " myD = lnk.coef_onecubeplus_D(gam=gamval, eta=eta_range)\n", " discrimvals = gtrt.discrim(a=myA, b=myB, c=myC, d=myD)\n", " #print(\"max =\", np.max(discrimvals))\n", " #print(\"min =\", np.min(discrimvals))\n", " \n", " ax_2.plot(eta_range,\n", " np.log(np.abs(discrimvals))*np.sign(discrimvals),\n", " \"-\", label=gamlabel)\n", " ax_2.tick_params(labelsize=FONTSIZE)\n", "\n", "plt.title(\"Log (-1)*discriminant of (+) single-cube\", size=FONTSIZE)\n", "plt.xlabel(\"Value of eta\", size=FONTSIZE)\n", "plt.axvline(x=0.0, color=\"blue\")\n", "plt.axvline(x=1.0, color=\"blue\")\n", "plt.axhline(y=0.0, color=\"black\")\n", "plt.axvline(x=1/2, color=\"black\")\n", "ax_2.legend(loc=1,ncol=1, fontsize=FONTSIZE)\n", "plt.show()\n", "\n", "if saveImages:\n", " myfig.savefig(imgDir+\"discrimvals_singlecubes.pdf\", bbox_inches=\"tight\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "While the above graph can be a bit confusing (we have $\\log(|\\Delta|) \\, \\text{sign}(\\Delta)$ displayed), it *does* show clearly that the discriminant of the cubic functions of interest here take both positive and negative values, which means we'll have to deal with *multiple roots*. Numerically, the value of $\\gamma$ makes minimal difference to the discriminant.\n", "\n", "Let's plot the graph of the cubic polynomial itself, along with roots determined using our function `getroot`, to ensure our root-finding mechanism works as we desire." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "gamval = 2*math.sqrt(2) + 0.5\n", "deltaval = math.fabs((math.sqrt(2) - gamval))\n", "etaval = np.array([0.65])\n", "\n", "xvals = np.linspace(start=-4, stop=4, num=200)\n", "\n", "myfig = plt.figure(figsize=(14,7))\n", "\n", "myA = lnk.coef_onecubeminus_A(gam=gamval, eta=etaval)\n", "myB = lnk.coef_onecubeminus_B(gam=gamval, eta=etaval)\n", "myC = lnk.coef_onecubeminus_C(gam=gamval, eta=etaval)\n", "myD = lnk.coef_onecubeminus_D(gam=gamval, eta=etaval)\n", "yvals = lnk.cube(x=xvals, a=myA, b=myB, c=myC, d=myD)\n", "rootvals = gtrt.getroot(a=myA, b=myB, c=myC, d=myD)\n", "rootvals = np.array(rootvals)\n", "numroots = len(rootvals)\n", "\n", "ax_1 = myfig.add_subplot(1,2,1)\n", "ax_1.plot(xvals, yvals, \"--\")\n", "ax_1.tick_params(labelsize=FONTSIZE)\n", "plt.title(\"Graph of (-) minus single-cube function\", size=FONTSIZE)\n", "plt.axvline(x=gamval, color=\"blue\")\n", "plt.axvline(x=(-gamval), color=\"blue\")\n", "plt.axvline(x=0.0, color=\"black\")\n", "plt.axvline(x=deltaval, color=\"green\")\n", "plt.axvline(x=-deltaval, color=\"green\")\n", "plt.axhline(y=0.0, color=\"black\")\n", "for t in range(numroots):\n", " plt.axvline(x=rootvals[t], color=\"pink\")\n", "\n", "myA = lnk.coef_onecubeplus_A(gam=gamval, eta=etaval)\n", "myB = lnk.coef_onecubeplus_B(gam=gamval, eta=etaval)\n", "myC = lnk.coef_onecubeplus_C(gam=gamval, eta=etaval)\n", "myD = lnk.coef_onecubeplus_D(gam=gamval, eta=etaval)\n", "yvals = lnk.cube(x=xvals, a=myA, b=myB, c=myC, d=myD)\n", "rootvals = gtrt.getroot(a=myA, b=myB, c=myC, d=myD)\n", "rootvals = np.array(rootvals)\n", "numroots = len(rootvals)\n", "\n", "ax_2 = myfig.add_subplot(1,2,2)\n", "ax_2.plot(xvals, yvals, \"--\")\n", "ax_2.tick_params(labelsize=FONTSIZE)\n", "plt.title(\"Graph of (+) single-cube function\", size=FONTSIZE)\n", "plt.axvline(x=gamval, color=\"blue\")\n", "plt.axvline(x=(-gamval), color=\"blue\")\n", "plt.axvline(x=0.0, color=\"black\")\n", "plt.axvline(x=deltaval, color=\"green\")\n", "plt.axvline(x=-deltaval, color=\"green\")\n", "plt.axhline(y=0.0, color=\"black\")\n", "for t in range(numroots):\n", " plt.axvline(x=rootvals[t], color=\"pink\")\n", " \n", "plt.show()\n", "\n", "if saveImages:\n", " myfig.savefig(imgDir+\"graph_singlecubes.pdf\", bbox_inches=\"tight\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A brief legend:\n", "\n", "- Dashed curve: graph of the relevant cubic polynomial.\n", "\n", "- Solid vertical blue lines: $\\pm \\gamma$.\n", "\n", "- Solid vertical green lines: $\\pm \\delta$, where $\\delta = |\\gamma - \\sqrt{2}|$.\n", "\n", "- Solid vertical pink lines: roots of the polynomial computed by `getroot`.\n", "\n", "If appears that our root-finding mechanism is working well. Depending on whether $\\eta > 1/2$ or $\\eta < 1/2$, there always exists *at least* one root within the known feasible set of $[-\\gamma,\\gamma]$ for the relevant polynomial.\n", "\n", "With this in mind, to complete our computation of $H$ and $\\Psi$ for arbitrary settings, all that remains is for us to automatically determine *which* of these multiple roots is to be used. As is outlined in our more rigorous notes elsewhere, a few simple if/else conditions sort this all out.\n", "\n", "0. Is $\\gamma > \\sqrt{2}$? If so, choose the root that satisfies $|u| \\geq \\delta$, while of course satisfying $\\text{sign}(u) = \\text{sign}(\\eta - 1/2)$.\n", "\n", "0. If $\\gamma \\leq \\sqrt{2}$, then we need to check the condition ourselves. The quantity to compute is $Q = \\rho^{\\prime}(\\delta - \\gamma) / \\rho^{\\prime}(\\delta + \\gamma)$.\n", "\n", " 0. In $\\eta > 1/2$ case, check $Q < (\\eta - 1)/\\eta$.\n", " \n", " 0. In $\\eta < 1/2$ case, check $Q < \\eta / (\\eta-1)$. \n", " \n", "0. In either case, if the condition we check is TRUE, find a solution to the appropriate *single-cube* condition. If FALSE, then find the solution to the *double-cube* condition.\n", "\n", "Let's try using this procedure, and see if it leads us reliably to the correct root." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gamval = math.sqrt(2) - 0.5\n", "deltaval = math.fabs((math.sqrt(2) - gamval))\n", "etaval = np.array([0.1])\n", "\n", "xvals = np.linspace(start=-4, stop=4, num=200)\n", "\n", "myfig = plt.figure(figsize=(14,7))\n", "\n", "myA = lnk.coef_onecubeminus_A(gam=gamval, eta=etaval)\n", "myB = lnk.coef_onecubeminus_B(gam=gamval, eta=etaval)\n", "myC = lnk.coef_onecubeminus_C(gam=gamval, eta=etaval)\n", "myD = lnk.coef_onecubeminus_D(gam=gamval, eta=etaval)\n", "yvals = lnk.cube(x=xvals, a=myA, b=myB, c=myC, d=myD)\n", "rootvals = gtrt.getroot(a=myA, b=myB, c=myC, d=myD)\n", "rootvals = np.array(rootvals)\n", "numroots = len(rootvals)\n", "\n", "ax_1 = myfig.add_subplot(1,2,1)\n", "ax_1.plot(xvals, yvals, \"--\")\n", "ax_1.tick_params(labelsize=FONTSIZE)\n", "plt.title(\"Graph of (-) minus single-cube function\", size=FONTSIZE)\n", "plt.axvline(x=gamval, color=\"blue\")\n", "plt.axvline(x=(-gamval), color=\"blue\")\n", "plt.axvline(x=0.0, color=\"black\")\n", "plt.axvline(x=deltaval, color=\"green\")\n", "plt.axvline(x=-deltaval, color=\"green\")\n", "plt.axhline(y=0.0, color=\"black\")\n", "for t in range(numroots):\n", " plt.axvline(x=rootvals[t], color=\"pink\")\n", "if (etaval > 1/2):\n", " # Find the single solution root, and plot it in RED.\n", " if (gamval > math.sqrt(2)):\n", " rootval = np.copy(rootvals)\n", " rootval = rootval[(np.sign(rootval) == math.copysign(1.0,(etaval-1/2)))]\n", " rootval = rootval[np.abs(rootval) >= deltaval]\n", " rootval = rootval[np.abs(rootval) <= gamval]\n", " rootval = rootval[0] # should be just one left.\n", " plt.axvline(x=rootval, color=\"red\")\n", " else:\n", " # Check which conditions are relevant in this case.\n", " Q = hlp.psi_catnew(deltaval-gamval) / hlp.psi_catnew(deltaval+gamval)\n", " if (Q < (etaval-1)/etaval):\n", " # Solving the single-cube condition is enough.\n", " rootval = np.copy(rootvals)\n", " rootval = rootval[(np.sign(rootval) == math.copysign(1.0,(etaval-1/2)))]\n", " rootval = rootval[np.abs(rootval) >= deltaval]\n", " rootval = rootval[np.abs(rootval) <= gamval]\n", " rootval = rootval[0] # should be just one left.\n", " plt.axvline(x=rootval, color=\"red\")\n", " else:\n", " # None are relevant -- the double-cube condition should be solved.\n", " pass\n", "\n", "myA = lnk.coef_onecubeplus_A(gam=gamval, eta=etaval)\n", "myB = lnk.coef_onecubeplus_B(gam=gamval, eta=etaval)\n", "myC = lnk.coef_onecubeplus_C(gam=gamval, eta=etaval)\n", "myD = lnk.coef_onecubeplus_D(gam=gamval, eta=etaval)\n", "yvals = lnk.cube(x=xvals, a=myA, b=myB, c=myC, d=myD)\n", "rootvals = gtrt.getroot(a=myA, b=myB, c=myC, d=myD)\n", "rootvals = np.array(rootvals)\n", "numroots = len(rootvals)\n", "\n", "ax_2 = myfig.add_subplot(1,2,2)\n", "ax_2.plot(xvals, yvals, \"--\")\n", "ax_2.tick_params(labelsize=FONTSIZE)\n", "plt.title(\"Graph of (+) single-cube function\", size=FONTSIZE)\n", "plt.axvline(x=gamval, color=\"blue\")\n", "plt.axvline(x=(-gamval), color=\"blue\")\n", "plt.axvline(x=0.0, color=\"black\")\n", "plt.axvline(x=deltaval, color=\"green\")\n", "plt.axvline(x=-deltaval, color=\"green\")\n", "plt.axhline(y=0.0, color=\"black\")\n", "for t in range(numroots):\n", " plt.axvline(x=rootvals[t], color=\"pink\")\n", "if (etaval < 1/2):\n", " # Find the single solution root, and plot it in RED.\n", " if (gamval > math.sqrt(2)):\n", " rootval = np.copy(rootvals)\n", " rootval = rootval[(np.sign(rootval) == math.copysign(1.0,(etaval-1/2)))]\n", " rootval = rootval[np.abs(rootval) >= deltaval]\n", " rootval = rootval[np.abs(rootval) <= gamval]\n", " rootval = rootval[0] # should be just one left.\n", " plt.axvline(x=rootval, color=\"red\")\n", " else:\n", " # Check which conditions are relevant in this case.\n", " Q = hlp.psi_catnew(deltaval-gamval) / hlp.psi_catnew(deltaval+gamval)\n", " if (Q < etaval/(etaval-1)):\n", " # Solving the single-cube condition is enough.\n", " rootval = np.copy(rootvals)\n", " rootval = rootval[(np.sign(rootval) == math.copysign(1.0,(etaval-1/2)))]\n", " rootval = rootval[np.abs(rootval) >= deltaval]\n", " rootval = rootval[np.abs(rootval) <= gamval]\n", " rootval = rootval[0] # should be just one left.\n", " plt.axvline(x=rootval, color=\"red\")\n", " else:\n", " # None are relevant -- the double-cube condition should be solved.\n", " pass\n", "\n", "plt.show()\n", "\n", "if saveImages:\n", " myfig.savefig(imgDir+\"graph_singlecubes_withroot.pdf\", bbox_inches=\"tight\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note how in the above routines, we have incorporated all the relevant conditions such that a red vertical line is used to highlight the *valid* root that we seek from the single-cube functions. Getting the root from the double-cube functions is easy, and was handled in the previous section.\n", "\n", "The above tests (tried over a wide variety of $\\gamma$ and $\\eta$ values) show that in addition to the correct root-finding procedure, we can isolate which of the conditions to solve, and which of the potentially multiple roots to use, since only one will be relevant in the context of computing $H(\\eta)$ and $\\Psi(\\theta)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## Actual computation of desired functions ($H$ and $\\Psi$)\n", "\n", "In the previous sections, we covered all possible $\\gamma$ and $\\eta$ settings such that we can find the roots of cubic polynomials needed for the computation of $H$ and $\\Psi$.\n", "\n", "We have implemented these functions as `Hfn` and `linkfn` respectively, both contained in the `linker.py` file. Here we plot these functions over their domain." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Final computations of the H(eta) function in the general gamma case.\n", "eta_range = np.linspace(start=0, stop=1.0, num=500)\n", "\n", "myfig = plt.figure(figsize=(14,7))\n", "\n", "ax_1 = myfig.add_subplot(1,2,1)\n", "\n", "gamvals = [2*math.sqrt(2),\n", " math.sqrt(2)+0.11,\n", " math.sqrt(2)-0.11,\n", " math.sqrt(2)-0.4,\n", " math.sqrt(2)/2]\n", "gamlabels = [\"largest gamma\",\n", " \"large gamma\",\n", " \"mid-large gamma\",\n", " \"mid-small gamma\",\n", " \"small gamma\"]\n", "\n", "for i in range(len(gamvals)):\n", " \n", " gamval = gamvals[i]\n", " gamlabel = gamlabels[i]\n", " \n", " Hvals = lnk.Hfn(eta=eta_range, gam=gamval)\n", " ax_1.plot(eta_range, Hvals, \"-\", label=gamlabel)\n", " ax_1.tick_params(labelsize=FONTSIZE)\n", "\n", "plt.axvline(x=0.0, color=\"blue\")\n", "plt.axvline(x=0.5, color=\"grey\")\n", "plt.axvline(x=1.0, color=\"blue\")\n", "plt.axhline(y=0, color=\"black\")\n", "plt.title(\"H() function graph\", size=FONTSIZE)\n", "ax_1.legend(loc=1,ncol=1, fontsize=FONTSIZE)\n", "\n", "\n", "ax_2 = myfig.add_subplot(1,2,2)\n", "\n", "for i in range(len(gamvals)):\n", " \n", " gamval = gamvals[i]\n", " gamlabel = gamlabels[i]\n", " \n", " linkvals = lnk.linkfn(theta=eta_range, gam=gamval)\n", " ax_2.plot(eta_range, linkvals, \"--\", label=gamlabel)\n", " ax_2.tick_params(labelsize=FONTSIZE)\n", "\n", "\n", "ax_2.plot(eta_range, eta_range, \"-\", color=\"blue\") # identity graph\n", "\n", "plt.axvline(x=0.0, color=\"blue\")\n", "plt.axvline(x=1.0, color=\"blue\")\n", "plt.axhline(y=0.0, color=\"black\")\n", "plt.axhline(y=1.0, color=\"blue\")\n", "plt.title(\"Psi() function graph\", size=FONTSIZE)\n", "ax_2.legend(loc=1,ncol=1, fontsize=FONTSIZE)\n", "\n", "plt.show()\n", "\n", "\n", "if saveImages:\n", " myfig.savefig(imgDir+\"Hfn_Linkfn_generalcase.pdf\", bbox_inches=\"tight\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, from the perspective of providing learning guarantees, we are naturally interested in tradeoffs induced by modifying the value of $\\gamma$. Intuitively, we would expect that for the same excess surrogate risk (say $a$, matching figures below), achieving it with a larger $\\gamma$ is \"harder\", and thus the resulting excess risk should be as good or better than in cases of achieving $a$ with smaller $\\gamma$ settings. The following experiments highlight this monotonicity, as expected." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# Compute how the value of gamma impacts output.\n", "# Note: takes a bit of time to compute.\n", "\n", "eta_range = np.linspace(start=0, stop=1.0, num=2500)\n", "gam_min = math.sqrt(2)/2\n", "gam_max = 2*math.sqrt(2)\n", "gam_range = np.linspace(gam_min, gam_max, 500)\n", "\n", "mydict = {}\n", "a_vals = [0.1, 0.01, 0.001]\n", "for a in a_vals:\n", " out = np.zeros(gam_range.shape, dtype=np.float32)\n", " \n", " for i in range(gam_range.size):\n", " gamval = gam_range[i]\n", " y_vals = lnk.linkfn(theta=eta_range, gam=gamval, s=1.0)\n", " idx = np.nonzero(((y_vals-a) >= 0))[0][0] - 1\n", " out[i] = eta_range[idx]\n", " \n", " mydict[str(a)] = out" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot these results:\n", "myfig = plt.figure(figsize=(7,7))\n", "ax_1 = myfig.add_subplot(1,1,1)\n", "plt.axhline(y=0.0, color=\"black\")\n", "#plt.axvline(x=0.0, color=\"black\")\n", "plt.title(\"Impact of gamma on Psi-inverse(a)\", size=FONTSIZE)\n", "plt.xlabel(\"Gamma value\", size=FONTSIZE)\n", "for a in a_vals:\n", " ax_1.plot(gam_range, mydict[str(a)], label=(\"a = \"+str(a)))\n", "ax_1.tick_params(labelsize=FONTSIZE)\n", "ax_1.legend(loc=1,ncol=1, fontsize=FONTSIZE)\n", "plt.show()\n", "\n", "if saveImages:\n", " myfig.savefig(imgDir+\"gamma_inversePsi.pdf\", bbox_inches=\"tight\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we would like to consider the impact of $s>0$ in setting a loss $\\phi(u) = s^2 \\,\\rho((\\gamma-u)/s)$. This is easy via the `s` argument of`linkfn`." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Computations of the link function over a fixed range, for fixed\n", "# gamma value, with varying s values.\n", "\n", "# Final computations of the H(eta) function in the general gamma case.\n", "eta_range = np.linspace(start=0, stop=1.0, num=500)\n", "gamval = 2*math.sqrt(2)\n", "svals = [1, 2, 4, 8, 16]\n", "slabels = [\"s=1\", \"s=2\", \"s=4\", \"s=8\", \"s=16\"]\n", "\n", "myfig = plt.figure(figsize=(7,7))\n", "\n", "ax_1 = myfig.add_subplot(1,1,1)\n", "\n", "for i in range(len(svals)):\n", " \n", " sval = svals[i]\n", " slabel = slabels[i]\n", " \n", " linkvals = lnk.linkfn(theta=eta_range, gam=gamval, s=sval)\n", " ax_1.plot(eta_range, linkvals, \"--\", label=slabel)\n", " ax_1.tick_params(labelsize=FONTSIZE)\n", "\n", "\n", "ax_1.plot(eta_range, eta_range, \"-\", color=\"blue\") # identity graph\n", "\n", "plt.axvline(x=0.0, color=\"blue\")\n", "plt.axvline(x=1.0, color=\"blue\")\n", "plt.axhline(y=0.0, color=\"black\")\n", "plt.axhline(y=1.0, color=\"blue\")\n", "plt.title(\"Psi() function graph\", size=FONTSIZE)\n", "ax_1.legend(loc=1,ncol=2, fontsize=FONTSIZE)\n", "\n", "plt.show()\n", "\n", "\n", "if saveImages:\n", " myfig.savefig(imgDir+\"Linkfn_over_s.pdf\", bbox_inches=\"tight\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we look at $\\Psi_{s,\\gamma}^{-1}(\\varepsilon/s)$ as a function of $s$." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "scrolled": true }, "outputs": [], "source": [ "# Compute how the value of gamma AND s impacts output.\n", "\n", "eta_range = np.linspace(start=0, stop=1.0, num=5000)\n", "s_range = np.linspace(start=1.0, stop=15.0, num=250)\n", "epsilon = 0.5\n", "\n", "gamvals = [3*math.sqrt(2),\n", " 2*math.sqrt(2),\n", " math.sqrt(2)]\n", "gamlabels = [\"gam=3*sqrt(2)\",\n", " \"gam=2*sqrt(2)\",\n", " \"gam=1*sqrt(2)\"]\n", "\n", "perf_dict = {}\n", "\n", "for i in range(len(gamvals)):\n", " \n", " gamval = gamvals[i]\n", " gamlabel = gamlabels[i]\n", "\n", " out = np.zeros(s_range.shape, dtype=np.float32)\n", " \n", " for j in range(s_range.size):\n", " sval = s_range[j]\n", "\n", " upperbd = epsilon/sval\n", " rangemax = sval*hlp.rho_catnew(gamval/sval)\n", " if (upperbd <= rangemax):\n", " sanity = \"OK\"\n", " else:\n", " sanity = \"FAIL\"\n", "\n", " y_vals = lnk.linkfn(theta=eta_range, gam=gamval, s=sval)\n", " idx = np.nonzero(((y_vals-epsilon/sval) >= 0))[0][0] - 1\n", " out[j] = eta_range[idx]\n", "\n", " #print(\"Sanity check:\", sanity,\n", " # \"; max val =\", rangemax,\n", " # \"; upperbd =\", upperbd)\n", " \n", " perf_dict[gamlabel] = out # Store output.\n", " \n", " " ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot these results:\n", "myfig = plt.figure(figsize=(7,7))\n", "ax_1 = myfig.add_subplot(1,1,1)\n", "plt.axhline(y=0.0, color=\"black\")\n", "#plt.axvline(x=0.0, color=\"black\")\n", "plt.title(\"Graph of Psi-inverse(eps/s), eps = \"+str(epsilon),\n", " size=FONTSIZE)\n", "plt.xlabel(\"s value\", size=FONTSIZE)\n", "for gamlabel in gamlabels:\n", " ax_1.plot(s_range, perf_dict[gamlabel], label=gamlabel)\n", "ax_1.tick_params(labelsize=FONTSIZE)\n", "ax_1.legend(loc=1, ncol=1, fontsize=FONTSIZE)\n", "plt.show()\n", "\n", "if saveImages:\n", " myfig.savefig(imgDir+\"inversePsi_over_s.pdf\", bbox_inches=\"tight\")" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "___" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.8" } }, "nbformat": 4, "nbformat_minor": 2 }