{
 "metadata": {
  "celltoolbar": "Slideshow",
  "name": "",
  "signature": "sha256:5a26d730ae77686ee5f57b359193cfdcda1dd1ae4e5b329f72af3c15da8ce497"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "# \u7b2c4\u7ae0 \u7dda\u5f62\u8b58\u5225\u30e2\u30c7\u30eb #"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "## \u6f14\u7fd2\u554f\u984c3.1 ##\n",
      "\n",
      "* $\\tanh(a) = 2\\sigma (2a) - 1$\u3092\u793a\u305b\n",
      "\n",
      "$$\\sigma(a) = \\frac{1}{1+e^{-a}} $$\n",
      "\n",
      "* \u3057\u305f\u304c\u3063\u3066\n",
      "$${\\rm tanh}(x)=\\frac{{\\rm sinh}(x)}{{\\rm cosh}(x)}=\\frac{\\frac{e^x-e^{-x}}{2}}{\\frac{e^x+e^{-x}}{2}} $$\n",
      "$$\\iff \\frac{1-e^{-2x}}{1+e^{-2x}} = \\frac{1}{1+e^{-2x}}-\\frac{e^{-2x}}{1+e^{-2x}} + \\left(\\frac{1}{1+e^{-2x}} - \\frac{1}{1+e^{-2x}}\\right)$$\n",
      "$$\\iff \\frac{2}{1+e^{-2x}}-\\frac{1+e^{-2x}}{1+e^{-2x}} = 2\\sigma(2x) - 1$$\n",
      "\n",
      "* \u30ed\u30b8\u30b9\u30c6\u30a3\u30af\u30b7\u30b0\u30e2\u30a4\u30c9\u95a2\u6570\u306e\u7dda\u5f62\u7d50\u5408\u304ctanh\u95a2\u6570\u306e\u7dda\u5f62\u7d50\u5408\u3068\u7b49\u4fa1\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u3001\u4fc2\u6570\u306e\u95a2\u4fc2\u3092\u793a\u305b\n",
      "$$y(x, {\\bf w})=w_0+\\sum_{j=1}^{M}w_j\\sigma\\left(\\frac{x-\\mu_j}{s}\\right) $$\n",
      "$$y(x, {\\bf u})=u_0+\\sum_{j=1}^{M}u_j{\\rm tanh}\\left(\\frac{x-\\mu_j}{2s}\\right) $$\n",
      "\n",
      "    * $\\sigma(a)=\\frac{1+\\tanh(a/2)}{2} $\u3067\u3042\u308b\u306e\u3067\u3001\n",
      "$$y(x,{\\bf w})=w_0+\\sum_{j=1}^{M}w_j\\left(\\frac{1+\\tanh((x-\\mu_j)/(2s))}{2}\\right)$$ $$=w_0+\\sum_{j=1}^M\\frac{w_j}{2}+\\sum_{j=1}^{M}\\frac{w_j}{2}\\tanh((x-\\mu_j)/2s)$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# \u6e96\u5099\n",
      "# slide\u306b\u3057\u305f\u6642\u306blatex\u304c\u5909\u63db\u3055\u308c\u306a\u3044\u5834\u5408\u306e\u5bfe\u51e6 https://gist.github.com/damianavila/ba6a308bd0e605db0e6e\n",
      "%matplotlib inline\n",
      "import numpy as np\n",
      "import scipy as sp\n",
      "import matplotlib.pyplot as plt\n",
      "import matplotlib.image as mpimg\n",
      "from IPython.display import display, Image\n",
      "\n",
      "# os\u304cDarwin\u306e\u3068\u304d\u306f\u30ed\u30fc\u30ab\u30eb\u3068\u5224\u5b9a\n",
      "os = !uname -s\n",
      "use_local = os == \"Darwin\"\n",
      "\n",
      "# \u30ed\u30fc\u30ab\u30eb\u3058\u3083\u306a\u3044\u5834\u5408\u306f\u4f5c\u8005\u306e\u30da\u30fc\u30b8\u304b\u3089\u53d6\u3063\u3066\u304f\u308b\n",
      "base_url = \"./figure\" if use_local else \"http://research.microsoft.com/en-us/um/people/cmbishop/PRML/prmlfigs-png\"\n",
      "\n",
      "# \u56f3\u8868\u793a\u7528\n",
      "disp_figure = lambda nfig: display(Image(\"{0}/Figure{1}.png\".format(base_url, nfig), width=\"500px\", embed=True))"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u5185\u5bb9 ###\n",
      "\n",
      "* 3\u7ae0\u306e\u56de\u5e30\u30e2\u30c7\u30eb\u3068\u985e\u4f3c\u306e\u30e2\u30c7\u30eb(\u7dda\u5f62\u8b58\u5225\u30e2\u30c7\u30eb)\u3067\u5206\u985e\u3092\u884c\u3046\n",
      "* \u5206\u985e\n",
      "    * \u5165\u529b\u30d9\u30af\u30c8\u30eb${\\bf x}$\u3092K\u500b\u306e\u96e2\u6563\u30af\u30e9\u30b9${\\cal C}_k$\u306b\u5272\u308a\u5f53\u3066\u308b\u3053\u3068(k=1,...,K)\n",
      "    * \u5404\u30af\u30e9\u30b9\u306f\u4e92\u3044\u306b\u91cd\u306a\u3089\u305a\u5404\u5165\u529b\u306f\u4e00\u3064\u306e\u30af\u30e9\u30b9\u306b\u5272\u308a\u5f53\u3066\u3089\u308c\u308b\n",
      "        * \u5165\u529b\u7a7a\u9593\u306f\u6c7a\u5b9a\u9818\u57df(decision region)\u306b\u5206\u96e2\n",
      "        * \u6c7a\u5b9a\u9818\u57df\u306e\u5883\u754c\u3092\u6c7a\u5b9a\u5883\u754c(decision boundary)\u307e\u305f\u306f\u6c7a\u5b9a\u9762(decision surface)\u3068\u547c\u3076"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u7dda\u5f62\u8b58\u5225\u30e2\u30c7\u30eb ###\n",
      "\n",
      "* D\u6b21\u5143\u5165\u529b\u7a7a\u9593\u306b\u5bfe\u3057\u3066\u5165\u529b\u30d9\u30af\u30c8\u30eb${\\bf x}$\u3092\u672a\u77e5\u6570\u3068\u3059\u308b\u65b9\u7a0b\u5f0f\u3067\u8868\u3055\u308c\u308b\u6c7a\u5b9a\u9762\u304cD-1\u6b21\u5143\u306e\u8d85\u5e73\u9762\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u3082\u306e\n",
      "* \u7dda\u5f62\u6c7a\u5b9a\u9762\u306b\u3088\u3063\u3066\u6b63\u3057\u304f\u5404\u30af\u30e9\u30b9\u306b\u5206\u96e2\u3067\u304d\u308b\u30c7\u30fc\u30bf\u96c6\u5408\u3092\u7dda\u5f62\u5206\u96e2\u53ef\u80fd(linearly separable)\u3068\u3044\u3046"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u5206\u985e\u554f\u984c\u306e\u8868\u73fe\u6cd5 ###\n",
      "\n",
      "* \u76ee\u7684\u5909\u6570${\\bf t}$\n",
      "    * \u56de\u5e30\u554f\u984c\u3067\u306f\u5b9f\u6570\u5024\u30d9\u30af\u30c8\u30eb\n",
      "    * 2\u30af\u30e9\u30b9\u5206\u985e -> 2\u5024\u8868\u73fe $t \\in \\{0,1\\}$\n",
      "        * t=0: ${\\cal C}_1$, t=1:${\\cal C}_2$\u3067\u3042\u308a\u3001t\u306e\u5024\u306f${\\cal C}_1$\u3092\u53d6\u308b\u78ba\u7387\u3068\u3057\u3066\u89e3\u91c8\u53ef\u80fd\n",
      "    * \u591a\u30af\u30e9\u30b9\u5206\u985e -> 1-of-K\u7b26\u53f7\u5316\u6cd5\n",
      "        * 5\u30af\u30e9\u30b9\u5206\u985e\u306e\u5834\u5408\u306e\u4f8b ${\\bf t}=(0,1,0,0,0)^T.$\n",
      "    * \u975e\u78ba\u7387\u30e2\u30c7\u30eb\u3092\u63a1\u7528\u3059\u308b\u5834\u5408\u306f\u5225\u306e\u8868\u73fe\u304c\u826f\u3044\u5834\u5408\u3082\u3042\u308b\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u5206\u985e\u554f\u984c\u306b\u5bfe\u3059\u308b3\u3064\u306e\u30a2\u30d7\u30ed\u30fc\u30c1 ###\n",
      "\n",
      "1. \u8b58\u5225\u95a2\u6570(discriminant function)\u306e\u69cb\u7bc9\n",
      "    * \u5165\u529b\u30d9\u30af\u30c8\u30eb${\\bf x}$\u304b\u3089\u76f4\u63a5\u30af\u30e9\u30b9\u3092\u63a8\u5b9a\n",
      "2. \u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u5206\u5e03$p({\\cal C}_k|{\\bf x})$\u306e\u30e2\u30c7\u30eb\u5316\n",
      "    1. \u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u30e2\u30c7\u30eb\u3067\u76f4\u63a5\u30e2\u30c7\u30eb\u5316\u3057\u3001\u5b66\u7fd2\u30c7\u30fc\u30bf\u96c6\u5408\u3067\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u6700\u9069\u5316\n",
      "    2. \u751f\u6210\u7684\u30a2\u30d7\u30ed\u30fc\u30c1 \n",
      "        * $p({\\cal C}_k|{\\bf x})=\\frac{p({\\bf x}|{\\cal C}_k)p({\\cal C}_k)}{p({\\bf x})}$\n",
      "\n",
      "\u672c\u7ae0\u3067\u306f\u3053\u308c\u30893\u3064\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u3059\u3079\u3066\u306e\u4f8b\u306b\u3064\u3044\u3066\u8ff0\u3079\u3066\u3044\u304f"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u4e00\u822c\u5316\u7dda\u5f62\u30e2\u30c7\u30eb(generalized linear model) ###\n",
      "\n",
      "* \u5206\u985e\u554f\u984c\u3067\u6271\u3046\u30e2\u30c7\u30eb\u3067\u306f\u96e2\u6563\u5024\u3092\u53d6\u308b\u30af\u30e9\u30b9\u30e9\u30d9\u30eb\u3084\u3082\u3063\u3068\u4e00\u822c\u7684\u306b\u9818\u57df(0,1)\u306e\u5024\u3092\u3068\u308b\u4e8b\u5f8c\u78ba\u7387\u3092\u4e88\u6e2c\u3057\u305f\u3044\n",
      "    * \u30d1\u30e9\u30e1\u30fc\u30bf${\\bf w}$\u306e\u7dda\u5f62\u95a2\u6570\u3092\u975e\u7dda\u5f62\u95a2\u6570\u306b\u3088\u308a\u5909\u63db\n",
      "$$y({\\bf x})=f({\\bf w}^T{\\bf x}+w_0).$$\n",
      "\n",
      "    * f: \u6d3b\u6027\u5316\u95a2\u6570(activation function)\n",
      "        * \u9006\u95a2\u6570\u306f\u7d71\u8a08\u5b66\u306e\u5206\u91ce\u3067\u306f\u9023\u7d50\u95a2\u6570(\u30ea\u30f3\u30af\u95a2\u6570; link function)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u4e00\u822c\u5316\u7dda\u5f62\u30e2\u30c7\u30eb\u306e\u7279\u5fb4 ###\n",
      "\n",
      "* \u6c7a\u5b9a\u9762\u306f$y({\\bf x})={\\bf w}^T {\\bf x} + w_0=\u5b9a\u6570$\u306b\u76f8\u5f53\n",
      "    * \u6c7a\u5b9a\u9762\u306f${\\bf x}$\u306e\u7dda\u5f62\u95a2\u6570\n",
      "* \u30d1\u30e9\u30e1\u30fc\u30bf\u306b\u5bfe\u3057\u3066\u306f\u3082\u306f\u3084\u7dda\u5f62\u3067\u306f\u306a\u3044\n",
      "* \u7dda\u5f62\u30e2\u30c7\u30eb\u3088\u308a\u306f\u8907\u96d1\u3060\u304c\u4e00\u822c\u7684\u306a\u975e\u7dda\u5f62\u30e2\u30c7\u30eb\u306b\u6bd4\u3079\u305f\u3089\u76f8\u5bfe\u7684\u306b\u7c21\u5358\n",
      "* \u56de\u5e30\u30e2\u30c7\u30eb\u3068\u540c\u69d8\u306b\u57fa\u5e95\u95a2\u6570$\\phi({\\bf x})$\u3082\u5229\u7528\u53ef\u80fd\n",
      "    * \u307e\u305a\u5165\u529b\u7a7a\u9593${\\bf x}$\u3067\u5206\u985e\u3059\u308b\u3053\u3068\u3092\u8003\u3048\u308b\u304c4.3\u7bc0\u3067\u306f\u57fa\u5e95\u95a2\u6570\u3092\u7528\u3044\u308b"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "## 4.1 \u8b58\u5225\u95a2\u6570(\u5224\u5225\u95a2\u6570) ##\n",
      "\n",
      "* \u8b58\u5225\n",
      "    * \u5165\u529b\u30d9\u30af\u30c8\u30eb${\\bf x}$\u3092K\u30af\u30e9\u30b9\u306e1\u3064${\\cal C}_k$\u306b\u5272\u308a\u5f53\u3066\u308b\u95a2\u6570\n",
      "* \u6c7a\u5b9a\u9762\u304c\u8d85\u5e73\u9762\u3068\u306a\u308b\u7dda\u5f62\u8b58\u5225(\u7dda\u5f62\u5224\u5225; linear discriminant)\u306e\u307f\u306b\u6ce8\u76ee\n",
      "* 2\u30af\u30e9\u30b9\u3092\u6700\u521d\u306b\u8003\u3048\u3001\u305d\u306e\u5f8c\u3067K>2\u30af\u30e9\u30b9\u3078\u62e1\u5f35"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### 4.1.1 2\u30af\u30e9\u30b9 ###\n",
      "\n",
      "* \u6700\u3082\u7c21\u5358\u306a\u7dda\u5f62\u8b58\u5225\u95a2\u6570\n",
      "$$y({\\bf x})={\\bf w}^T{\\bf x}+w_0.$$\n",
      "\n",
      "    * ${\\bf w}$: \u91cd\u307f\u30d9\u30af\u30c8\u30eb(weight vector)\n",
      "    * $w_0$: \u30d0\u30a4\u30a2\u30b9\u30d1\u30e9\u30e1\u30fc\u30bf(bias parameter)\n",
      "        * \u7d71\u8a08\u5b66\u306b\u304a\u3051\u308b\u30d0\u30a4\u30a2\u30b9\u3068\u7570\u306a\u308b\n",
      "* $y({\\bf x}) \\ge 0$\u306a\u3089\u3070\u5165\u529b\u30d9\u30af\u30c8\u30eb${\\bf x}$\u306f${\\cal C}_1$\u306b\u5272\u308a\u5f53\u3066\u3089\u308c\u3001\u305d\u308c\u4ee5\u5916\u306f${\\cal C}_2$\u306b\u5272\u308a\u5f53\u3066\u3089\u308c\u308b"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u6c7a\u5b9a\u5883\u754c ###\n",
      "\n",
      "* $y({\\bf x})=0$\u3067\u5b9a\u7fa9\n",
      "    * D\u6b21\u5143\u5165\u529b\u7a7a\u9593\u4e2d\u306eD-1\u6b21\u5143\u8d85\u5e73\u9762\u306b\u5bfe\u5fdc\n",
      "* \u6c7a\u5b9a\u5883\u754c\u4e0a\u306e\u30d9\u30af\u30c8\u30eb${\\bf x}_A, {\\bf x}_B$\u306b\u5bfe\u3057\u3001$y({\\bf x}_A)=y({\\bf x}_B)=0$\n",
      "    * ${\\bf w}^T({\\bf x}_A-{\\bf x}_B)=0$\u3067\u3042\u308b\u306e\u3067${\\bf w}$\u306f\u6c7a\u5b9a\u9762\u4e0a\u306b\u3042\u308b\u3059\u3079\u3066\u306e\u30d9\u30af\u30c8\u30eb\u306b\u76f4\u4ea4\n",
      "    * ${\\bf w}$\u306f\u6c7a\u5b9a\u9762\u306e\u65b9\u5411\u3092\u6c7a\u5b9a"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u539f\u70b9\u304b\u3089\u6c7a\u5b9a\u9762\u307e\u3067\u306e\u8ddd\u96e2 ###\n",
      "\n",
      "* ${\\bf x}$\u304c\u6c7a\u5b9a\u9762\u4e0a\u306b\u3042\u308b\u5834\u5408\u3001$y({\\bf x})=0$\n",
      "    * $\\therefore {\\bf w}^T{\\bf x}+w_0=0 \\iff {\\bf w}^T{\\bf x}=-w_0$\n",
      "* \u539f\u70b9\u304b\u3089\u6c7a\u5b9a\u9762\u307e\u3067\u306e\u8ddd\u96e2\u306f\u539f\u70b9\u304b\u3089\u6c7a\u5b9a\u9762\u3078\u306e\u5782\u7dda\u306e\u5927\u304d\u3055\n",
      "    * ${\\bf w}$\u3068${\\bf x}$\u306e\u306a\u3059\u89d2\u3092$\\theta$\u3068\u3059\u308b\u3068\u3001\u4e0a\u8a18\u7d50\u679c\u3092\u7528\u3044\u3066\n",
      "    $$||{\\bf x}||cos\\theta=||{\\bf x}||\\frac{{\\bf w}^T{\\bf x}}{||{\\bf w}||||{\\bf x}||}=\\frac{{\\bf w}^T{\\bf x}}{||{\\bf w}||}=-\\frac{w_0}{||{\\bf w}||}$$\n",
      "    * \u3088\u3063\u3066\u30d0\u30a4\u30a2\u30b9\u30d1\u30e9\u30e1\u30fc\u30bf$w_0$\u306f\u6c7a\u5b9a\u9762\u306e\u4f4d\u7f6e\u3092\u6c7a\u5b9a\u3059\u308b"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# D=2\u306e\u5834\u5408\n",
      "disp_figure(\"4.1\")"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "subslide"
      }
     },
     "outputs": [
      {
       "metadata": {
        "png": {
         "width": "500px"
        }
       },
       "output_type": "display_data",
       "png": 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mcYy7XAAAAACQlWgBhHDXxuKTbnHMNOVJFylJFwAAAACIFsD9zt1SotyNKHSL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\njBYAAAAAAMAQjBYAAAAAAMAQ/gf1yGfZ5zf4FQAAAABJRU5ErkJggg==\n",
       "text": [
        "<IPython.core.display.Image at 0x104ab22d0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u6c7a\u5b9a\u9762\u304b\u3089\u4efb\u610f\u306e\u70b9${\\bf x}$\u3078\u306e\u76f4\u4ea4\u8ddd\u96e2 ###\n",
      "\n",
      "* $y({\\bf x})$\u306e\u5024\u304c\u76f4\u4ea4\u8ddd\u96e2\u3092\u4e0e\u3048\u308b\n",
      "* \u4efb\u610f\u306e\u70b9${\\bf x}$\u306b\u5bfe\u3057${\\bf x}_{\\bot}$\u3092\u6c7a\u5b9a\u9762\u4e0a\u3078\u306e\u76f4\u4ea4\u5c04\u5f71\u3068\u3059\u308b\u3068\u3001\n",
      "$${\\bf x}={\\bf x}_\\bot + r\\frac{{\\bf w}}{||{\\bf w}||}$$\n",
      "* \u4e21\u8fba\u306b${\\bf w}^T$\u3092\u5de6\u304b\u3089\u639b\u3051\u3001$w_0$\u3092\u8db3\u3059\u3068\u3001\n",
      "$${\\bf w}^T{\\bf x}+w_0={\\bf w}^T{\\bf x}_\\bot + w_0 + r\\frac{{\\bf w}^T{\\bf w}}{||{\\bf w}||}$$\n",
      "$$\\iff y({\\bf x})=0+r||{\\bf w}||$$\n",
      "* \u5f93\u3063\u3066\n",
      "$$r=\\frac{y({\\bf x})}{||{\\bf w||}}$$\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# D=2\u306e\u5834\u5408\n",
      "disp_figure(\"4.1\")"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "subslide"
      }
     },
     "outputs": [
      {
       "metadata": {
        "png": {
         "width": "500px"
        }
       },
       "output_type": "display_data",
       "png": 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mcYy7XAAAAACQlWgBhHDXxuKTbnHMNOVJFylJFwAAAACIFsD9zt1SotyNKHSL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\njBYAAAAAAMAQjBYAAAAAAMAQ/gf1yGfZ5zf4FQAAAABJRU5ErkJggg==\n",
       "text": [
        "<IPython.core.display.Image at 0x104ab2310>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u30c0\u30df\u30fc\u5165\u529b\u306e\u5c0e\u5165 ###\n",
      "\n",
      "* $x_0=1$\u3092\u5c0e\u5165\u3057$\\tilde{{\\bf x}}=(x_0, {\\bf x})$\u3068\u5b9a\u7fa9\u3059\u308b\u3068\n",
      "$$y({\\bf x})=\\tilde{{\\bf w}}^T\\tilde{{\\bf x}}$$\n",
      "* \u3053\u306e\u5834\u5408\u6c7a\u5b9a\u9762\u306fD+1\u6b21\u5143\u306e\u5165\u529b\u7a7a\u9593\u306e\u539f\u70b9\u3092\u901a\u308bD\u6b21\u5143\u306e\u8d85\u5e73\u9762\n",
      "    * \u8d85\u5e73\u9762\u304c\u539f\u70b9\u3092\u901a\u308b$\\iff y({\\bf x})=0$\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "## 4.1.2 \u591a\u30af\u30e9\u30b9 ##\n",
      "\n",
      "* K=2\u30af\u30e9\u30b9\u306e\u7dda\u5f62\u8b58\u5225\u3092K>2\u30af\u30e9\u30b9\u3078\u62e1\u5f35\n",
      "* 2\u30af\u30e9\u30b9\u8b58\u5225\u5668\u306e\u7d44\u307f\u5408\u308f\u305b\u3067K\u30af\u30e9\u30b9\u8b58\u5225\u3092\u69cb\u6210\n",
      "    * \u3044\u304f\u3064\u304b\u306e\u91cd\u5927\u306a\u554f\u984c\u70b9\u6709"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### 1\u5bfe\u4ed6\u5206\u985e\u5668(one-versus-the-rest classifier) ###\n",
      "\n",
      "* \u7279\u5b9a\u306e\u30af\u30e9\u30b9${\\cal C}_k$\u306b\u5165\u308b\u70b9\u3068\u305d\u306e\u30af\u30e9\u30b9\u306b\u5165\u3089\u306a\u3044\u70b9\u3068\u306b\u5206\u985e\u3059\u308b2\u30af\u30e9\u30b9\u554f\u984c\u3092\u89e3\u304f\u5206\u985e\u5668\u3092K-1\u500b\u5229\u7528\n",
      "* 3\u30af\u30e9\u30b9\u5206\u985e\u306b\u304a\u3044\u3066\u66d6\u6627\u306a\u5206\u985e\u9818\u57df\u304c\u767a\u751f"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "disp_figure(\"4.2a\")"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "subslide"
      }
     },
     "outputs": [
      {
       "metadata": {
        "png": {
         "width": "500px"
        }
       },
       "output_type": "display_data",
       "png": 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Fp4EFAAAALMpsMAsNLACKUsICAOAl1wYTEWABAAAAyzEbzMUVQgBKc44QAICvzAYz8gYW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\nWAAAAACE9j9Rnx9TnVJiYAAAAABJRU5ErkJggg==\n",
       "text": [
        "<IPython.core.display.Image at 0x104ab2d50>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### 1\u5bfe1\u5206\u985e\u5668(one-versus-one classifier) ###\n",
      "\n",
      "* \u3059\u3079\u3066\u306e\u53ef\u80fd\u306a\u30af\u30e9\u30b9\u306e\u7d44\u306e2\u30af\u30e9\u30b9\u8b58\u5225\u95a2\u6570\u3092\u8003\u3048\u3001K(K-1)/2\u500b\u306e2\u30af\u30e9\u30b9\u8b58\u5225\u95a2\u6570\u3092\u5c0e\u5165\n",
      "* \u3053\u306e\u5834\u5408\u3082\u66d6\u6627\u306a\u9818\u57df\u304c\u5b58\u5728"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "disp_figure(\"4.2b\")"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "subslide"
      }
     },
     "outputs": [
      {
       "metadata": {
        "png": {
         "width": "500px"
        }
       },
       "output_type": "display_data",
       "png": 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AqrNOCABoTRICAAAACEcSAgDomHVCAEAZkhAAAABAOJIQAEAL1gkBAE1JQgAAAADhSEIA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\n",
       "text": [
        "<IPython.core.display.Image at 0x104ab2510>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u5358\u72ec\u306eK\u30af\u30e9\u30b9\u8b58\u5225\u306b\u3088\u308b\u89e3\u6c7a ###\n",
      "\n",
      "* K\u500b\u306e\u7dda\u5f62\u95a2\u6570\u3067\u69cb\u6210\u3055\u308c\u308b\u5358\u72ec\u306eK\u30af\u30e9\u30b9\u8b58\u5225\n",
      "$$y_k({\\bf x})={\\bf w}_k^T{\\bf x}+w_{k0}.$$\n",
      "\n",
      "* \u3059\u3079\u3066\u306e$j\\neq k$\u306b\u5bfe\u3057\u3066$y_k({\\bf x})>y_j({\\bf x})$\u3067\u3042\u308b\u5834\u5408\u70b9${\\bf x}$\u306f\u30af\u30e9\u30b9${\\cal C}_k$\u306b\u5272\u308a\u5f53\u3066\u3089\u308c\u308b\n",
      "    * \u30af\u30e9\u30b9${\\cal C}_k$\u3068\u30af\u30e9\u30b9${\\cal C}_j$\u9593\u306e\u6c7a\u5b9a\u5883\u754c\u306f$y_k({\\bf x})=y_j({\\bf x})$\n",
      "    * \u6c7a\u5b9a\u5883\u754c\u306f\u4ee5\u4e0b\u306e\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u308b(D-1)\u6b21\u5143\u306e\u8d85\u5e73\u9762\n",
      "$$({\\bf w}_k-{\\bf w}_j)^T{\\bf x}+(w_{k0}-w_{j0})=0.$$\n",
      "        * 4.1.1\u7bc0\u306e2\u30af\u30e9\u30b9\u306e\u5834\u5408\u306e\u6c7a\u5b9a\u5883\u754c\u3068\u540c\u69d8\u306e\u5f62\u3092\u3057\u3066\u3044\u308b\u305f\u3081\u985e\u4f3c\u306e\u5e7e\u4f55\u5b66\u7684\u7279\u6027\u304c\u9069\u7528\u53ef\u80fd"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u8b58\u5225\u9818\u57df ###\n",
      "\n",
      "* \u8b58\u5225\u5668\u306e\u6c7a\u5b9a\u9818\u57df\u306f\u5e38\u306b1\u3064\u306b\u9023\u7d50\u3057\u3066\u3044\u3066\u51f8\u9818\u57df\n",
      "* \u6c7a\u5b9a\u9818\u57df${\\cal R}_k$\u306b\u3042\u308b2\u70b9${\\bf x}_A$\u3068${\\bf x}_B$\u3092\u7d50\u3076\u76f4\u7dda\u4e0a\u306b\u3042\u308b\u4efb\u610f\u306e\u70b9$\\hat{{\\bf x}}$($0\\leq\\lambda\\leq 1$)\n",
      "$$\\hat{{\\bf x}}=\\lambda{\\bf x}_A + (1-\\lambda){\\bf x}_B$$\n",
      "* \u8b58\u5225\u95a2\u6570\u306e\u7dda\u5f62\u6027\u304b\u3089\u4ee5\u4e0b\u304c\u6210\u7acb\n",
      "$$y_k(\\hat{{\\bf x}})=\\lambda y_k({\\bf x}_A) + (1-\\lambda)y_k({\\bf x}_B)$$\n",
      "    * \u3059\u3079\u3066\u306e$j\\neq k$\u306b\u5bfe\u3057\u3066$y_k({\\bf x}_A)>y_j({\\bf x}_A)$, $y_k({\\bf x}_B)>y_j({\\bf x}_B)$\u304c\u6210\u308a\u7acb\u3064\u306e\u3067$y_k(\\hat{{\\bf x}})>y_j(\\hat{{\\bf x}})$\n",
      "    * \u5f93\u3063\u3066\u4efb\u610f\u306e\u70b9$\\hat{{\\bf x}}$\u3082\u6c7a\u5b9a\u9818\u57df${\\cal R}_k$\u306b\u5c5e\u3057\u3001\u6c7a\u5b9a\u9818\u57df${\\cal R}_k$\u306f\u5358\u4e00\u7d50\u5408\u3057\u3066\u304a\u308a\u51f8\u9818\u57df\n",
      "* 2\u30af\u30e9\u30b9\u306e\u8b58\u5225\u306e\u5834\u5408\u306f$y_1({\\bf x})$\u3068$y_2({\\bf x})$\u306b\u57fa\u3065\u304f\u5b9a\u5f0f\u5316\u3067\u30821\u3064\u306e\u8b58\u5225\u95a2\u6570$y({\\bf x})$\u306b\u57fa\u3065\u304f\u5b9a\u5f0f\u5316\u306e\u3069\u3061\u3089\u3067\u3082\u826f\u3044"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "disp_figure(\"4.3\")"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "subslide"
      }
     },
     "outputs": [
      {
       "metadata": {
        "png": {
         "width": "500px"
        }
       },
       "output_type": "display_data",
       "png": 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Lw3LeLeCfXgkvv+zKq+VeIPA6hOXY9QAAMDhbHhbyd6lfYxl/JUwAAAAwOkFhFb0+auHn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\n",
       "text": [
        "<IPython.core.display.Image at 0x104ab2790>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u7dda\u5f62\u8b58\u5225\u95a2\u6570\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u5b66\u7fd2\u3059\u308b3\u3064\u306e\u30a2\u30d7\u30ed\u30fc\u30c1 ###\n",
      "\n",
      "* \u6700\u5c0f\u4e8c\u4e57\n",
      "* \u30d5\u30a3\u30c3\u30b7\u30e3\u30fc\u306e\u7dda\u5f62\u5224\u5225\n",
      "* \u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "## 4.1.3 \u5206\u985e\u306b\u304a\u3051\u308b\u6700\u5c0f\u4e8c\u4e57 ##\n",
      "\n",
      "* 3\u7ae0\u3067\u306e\u56de\u5e30\u554f\u984c\u3068\u540c\u3058\u304f\u6700\u5c0f\u4e8c\u4e57\u306b\u57fa\u3065\u304f\u5b9a\u5f0f\u5316\u3092K\u30af\u30e9\u30b9\u306e\u5206\u985e\u554f\u984c\u306b\u3082\u9069\u7528\n",
      "* \u76ee\u7684\u5909\u6570\u30d9\u30af\u30c8\u30eb${\\bf t}$\u306b\u306f1-of-K\u7b26\u53f7\u5316\u6cd5\u3092\u7528\u3044\u308b\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u6700\u5c0f\u4e8c\u4e57\u3092\u5229\u7528\u3059\u308b\u7406\u7531 ###\n",
      "\n",
      "* \u5165\u529b\u30d9\u30af\u30c8\u30eb\u304c\u4e0e\u3048\u3089\u308c\u305f\u969b\u306e\u76ee\u7684\u5909\u6570\u5024\u306e\u6761\u4ef6\u4ed8\u304d\u671f\u5f85\u5024$\\mathbb{E}({\\bf t}|{\\bf x})$\u3092\u8fd1\u4f3c\u3059\u308b\u305f\u3081\n",
      "* 2\u5024\u8868\u8a18\u6cd5\u3067\u306f\u6761\u4ef6\u4ed8\u671f\u5f85\u5024\u306f\u30af\u30e9\u30b9\u4e8b\u5f8c\u78ba\u7387\u306e\u30d9\u30af\u30c8\u30eb\u306b\u3088\u3063\u3066\u4e0e\u3048\u3089\u308c\u308b\n",
      "    * \u3057\u304b\u3057\u63a8\u5b9a\u3055\u308c\u305f\u78ba\u7387\u306f\u8fd1\u4f3c\u304c\u60aa\u304f\u78ba\u7387\u306e\u5024\u304c(0,1)\u306e\u7bc4\u56f2\u3092\u8d8a\u3048\u308b\u3053\u3068\u3082\u3042\u308b\n",
      "        * \u7dda\u5f62\u30e2\u30c7\u30eb\u306e\u67d4\u8edf\u6027\u304c\u4f4e\u3044\u3053\u3068\u304c\u7406\u7531"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u7dda\u5f62\u30e2\u30c7\u30eb\u306b\u3088\u308b\u8868\u73fe ###\n",
      "\n",
      "* \u5404\u30af\u30e9\u30b9${\\cal C}_k$\u306f\u5404\u30af\u30e9\u30b9\u6bce\u306e\u7dda\u5f62\u30e2\u30c7\u30eb\u3067\u8a18\u8ff0(k=1,...,K)\n",
      "$$y_k({\\bf x})={\\bf w}_k^T{\\bf x}+w_{k0}.$$\n",
      "\n",
      "* D+1\u6b21\u5143\u30d9\u30af\u30c8\u30eb$\\tilde{{\\bf w}}_k=(w_{k0},{\\bf w}_k^T)^T$\u3092k\u5217\u76ee\u306b\u6301\u3064\u884c\u5217$\\tilde{{\\bf W}}$, \u30c0\u30df\u30fc\u5165\u529b$x_0=1$\u3092\u52a0\u3048\u305f\u5165\u529b\u30d9\u30af\u30c8\u30eb$(1,{\\bf x}^T)$\u3092\u7528\u3044\u308b\u3068\u7e8f\u3081\u3066\u8868\u8a18\u53ef\u80fd\n",
      "$${\\bf y}({\\bf x})=\\tilde{{\\bf W}}^T\\tilde{{\\bf x}}$$\n",
      "\n",
      "* \u65b0\u305f\u306a\u5165\u529b${\\bf x}$\u306f$y_k=\\tilde{{\\bf w}}_k^T\\tilde{{\\bf x}}$\u304c\u6700\u5927\u3068\u306a\u308b\u30af\u30e9\u30b9\u306b\u5272\u308a\u5f53\u3066\u3089\u308c\u308b\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u4e8c\u4e57\u548c\u8aa4\u5dee\u95a2\u6570\u306e\u6700\u5c0f\u5316\u306b\u3088\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u884c\u5217$\\tilde{{\\bf W}}$\u306e\u6c7a\u5b9a ###\n",
      "\n",
      "* \u5b66\u7fd2\u30c7\u30fc\u30bf\u96c6\u5408$\\{{\\bf x}_n, {\\bf t}_n\\}$     (n=1,...,N)\n",
      "* n\u756a\u76ee\u306e\u884c\u304c\u30d9\u30af\u30c8\u30eb${\\bf t}_n^T$\u3067\u3042\u308b\u884c\u5217${\\bf T}$\u3068n\u756a\u76ee\u306e\u884c\u304c$\\tilde{{\\bf x}}_n^T$\u3067\u3042\u308b\u884c\u5217$\\tilde{{\\bf X}}$\u3092\u5b9a\u7fa9\n",
      "* \u4e8c\u4e57\u548c\u8aa4\u5dee\u95a2\u6570\u306f\u4ee5\u4e0b\u3067\u4e0e\u3048\u3089\u308c\u308b\n",
      "$$ E_D(\\tilde{{\\bf W}})=\\frac{1}{2}{\\rm Tr}\\left\\{ (\\tilde{{\\bf X}}\\tilde{{\\bf W}}-{\\bf T})^T(\\tilde{{\\bf X}}\\tilde{{\\bf W}}-{\\bf T}) \\right\\} $$\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### $\\tilde{{\\bf W}}$\u306b\u3088\u308b\u5fae\u5206\u3068\u8b58\u5225\u95a2\u6570 ###\n",
      "\n",
      "* (C.27)\u3067B=I\u3068\u307f\u306a\u3057\u3066\u8a08\u7b97\n",
      "$$ \\frac{\\partial E_D(\\tilde{{\\bf W}})}{\\partial{\\bf \\tilde{{\\bf W}}}}=\\frac{1}{2}\\left\\{ 2(\\tilde{{\\bf X}}\\tilde{{\\bf W}}-{\\bf T})^T\\tilde{{\\bf X}} \\right\\} = 0$$\n",
      "$$ \\iff (\\tilde{{\\bf X}}\\tilde{{\\bf W}}-{\\bf T})^T\\tilde{{\\bf X}} = 0$$\n",
      "$$ \\iff (\\tilde{{\\bf X}}\\tilde{{\\bf W}})^T\\tilde{{\\bf X}}-{\\bf T}^T\\tilde{{\\bf X}} = 0$$\n",
      "$$ \\iff (\\tilde{{\\bf X}}\\tilde{{\\bf W}})^T\\tilde{{\\bf X}} = {\\bf T}^T\\tilde{{\\bf X}}$$\n",
      "$$ \\iff \\tilde{{\\bf X}}^T(\\tilde{{\\bf X}}\\tilde{{\\bf W}}) = \\tilde{{\\bf X}}^T{\\bf T}$$\n",
      "$$ \\iff \\tilde{{\\bf W}}=(\\tilde{{\\bf X}}^T\\tilde{{\\bf X}})^{-1}\\tilde{{\\bf X}}^T{\\bf T}=\\tilde{{\\bf X}}^{\\dagger}{\\bf T}$$\n",
      "\n",
      "* $\\tilde{{\\bf X}}^{\\dagger}$\u306f3.1.1\u7bc0\u3067\u51fa\u3066\u304d\u305f\u64ec\u4f3c\u9006\u884c\u5217(pseudo-inverse matrixt)\n",
      "* \u7d50\u5c40\u3001\u8b58\u5225\u95a2\u6570\u306f\n",
      "$${\\bf y}({\\bf x})=\\tilde{{\\bf W}}^T\\tilde{{\\bf x}}={\\bf T}^T(\\tilde{{\\bf X}}^\\dagger)^T\\tilde{{\\bf x}}.$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u6700\u5c0f\u4e8c\u4e57\u89e3\u306e\u7279\u6027 ###\n",
      "\n",
      "* \u5b66\u7fd2\u30c7\u30fc\u30bf\u306b\u304a\u3051\u308b\u76ee\u7684\u5909\u6570\u30d9\u30af\u30c8\u30eb\u304c\u3042\u308b\u5b9a\u6570${\\bf a}$\u3068b\u306b\u5bfe\u3057\u3066\u7dda\u5f62\u5236\u7d04\u3092\u6301\u3063\u3066\u3044\u308b\u5834\u5408\u306f\u30e2\u30c7\u30eb\u306e\u4e88\u6e2c\u3082\u540c\u3058\u7dda\u5f62\u5236\u7d04\u3092\u6301\u3064\n",
      "$${\\bf a}^T{\\bf t}_n+b=0$$\n",
      "$${\\bf a}^T{\\bf y}({\\bf x})+b=0$$\n",
      "\n",
      "* 1-of-K\u7b26\u53f7\u5316\u6cd5\u3092\u4f7f\u7528\u3059\u308b\u5834\u5408\u3001\u30e2\u30c7\u30eb\u306b\u3088\u308b\u4e88\u6e2c\u306e\u7279\u6027\u3068\u3057\u3066\u4efb\u610f\u306e${\\bf x}$\u306b\u5bfe\u3057${\\bf y}({\\bf x})$\u306e\u8981\u7d20\u306e\u548c\u304c1\n",
      "    * \u548c\u51fa\u529b\u304c(0,1)\u306e\u7bc4\u56f2\u306b\u5165\u308b\u5236\u7d04\u304c\u7121\u3044\u305f\u3081\u78ba\u7387\u3068\u3057\u3066\u306f\u89e3\u91c8\u51fa\u6765\u306a\u3044\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u8b58\u5225\u95a2\u6570\u306b\u304a\u3051\u308b\u6700\u5c0f\u4e8c\u4e57\u89e3\u306e\u554f\u984c ###\n",
      "\n",
      "* \u6700\u5c0f\u4e8c\u4e57\u89e3\u306f\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u6c42\u3081\u308b\u305f\u3081\u306e\u89e3\u6790\u89e3\u3092\u4e0e\u3048\u308b\n",
      "    * \u3057\u304b\u3057\u6700\u5c0f\u4e8c\u4e57\u89e3\u306f\u5916\u308c\u5024\u306b\u5bfe\u3057\u3066\u9811\u5065\u3067\u306a\u3044\n",
      "* \u8b58\u5225\u95a2\u6570\u306b\u304a\u3044\u3066\u554f\u984c\u3068\u306a\u308b\n",
      "    * \u56f34.4\u3067\u306f\u30c7\u30fc\u30bf\u306e\u8ffd\u52a0\u306b\u3088\u308a\u6c7a\u5b9a\u5883\u754c\u306e\u4f4d\u7f6e\u304c\u8457\u3057\u304f\u5909\u5316\n",
      "        * \u300c\u6b63\u3057\u904e\u304e\u308b\u300d\u4e88\u6e2c\u306b\u30da\u30ca\u30eb\u30c6\u30a3\u3092\u79d1\u3059\n",
      "    * 2.3.7\u7bc0\u3067\u3082\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306b\u3088\u308b\u89e3\u304c\u5916\u308c\u5024\u306b\u5f31\u3044\u8a18\u8ff0\u6709\n",
      "* 7.1.2\u7bc0\u3067\u5916\u308c\u5024\u306b\u5bfe\u3057\u3066\u904e\u654f\u3067\u3042\u308b\u6b20\u70b9\u3092\u907f\u3051\u308b\u305f\u3081\u306e\u5225\u306e\u8aa4\u5dee\u95a2\u6570\u304c\u7d39\u4ecb"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "disp_figure(\"4.4a\")"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "subslide"
      }
     },
     "outputs": [
      {
       "metadata": {
        "png": {
         "width": "500px"
        }
       },
       "output_type": "display_data",
       "png": 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LglM1H8qKW8+TN0MymdY2J60NAKAzuQ2ARRXks57Frf+F0irH0drmpLUBAPQntwGwouJw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\nSUVORK5CYII=\n",
       "text": [
        "<IPython.core.display.Image at 0x104ab24d0>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "disp_figure(\"4.4b\")"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "subslide"
      }
     },
     "outputs": [
      {
       "metadata": {
        "png": {
         "width": "500px"
        }
       },
       "output_type": "display_data",
       "png": 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FIeXJpzy9r+MkvsaQPRYKNnwI39lg6gJ7Lv2lJR7VwV8vf9LagEuYzgbAIbfB\nRqKm+QxeHM6fXuBBSHm4xEFyxwnc2WDqAnsuq7UdittqtDagP6ENgDu5DfYQuKTuuKg4pDemT08v\n8dtz58eFbNRQPE6NhQtsbmu7/2/FbQlaG9CZdaMAPPn5dc0Q5+fP6zTHllGEL6m7f3F/xU+vUWtL\n/8bEJ5O+jjXL67CxBfbtQ1yl8jMc9VHhIlob0I3pbADT6dZt5LZIchsjKkgP6xW31q0t8dsTn8z5\nOCFbJWQdkME/D09Cnq3iNi2tDehDaAOYlNw2JbmN4bSeC/b6jX20mK9Xv8dC1CAn41ROScvKZwV5\n7higQA31dtOX1ga0prIBzE5um5Lcxlj6LKn79O2txa6FDFzCGbIvQeU7Uq9m8enlp77K+YOJ41z+\nMvmT1gY0JbQBrKFbt7FVAiyqPo7kbn/ZWeDTSzzDVt5Hf+rWdkRsVdHN+VMN2QFWaxuM1ga0YxsE\nAArIbbC382qwQ3HL6ibFxW321nb/TyN/Hh59eqq5meztOFrbYLQ2oAXT2QCoIbfBolLKSEo1+DrO\nyPOYUr690SM+Freeq3pDbu7W9CG6eX2qZZ/Vp3G0tsFobUA4oQ2Aeu7dFsm92xhOyJK6k3EG+ZCX\nBaCaJ59+H7f+d9AL2br03MgF9sn9qVY+q9s4Q700tDYgmnWjAMuzVcKU5DZGFLKk7u04Q33CcxtT\n/ZPvsFdDh41lz5/AicELLBvQ2oAoprMB7MNWCUCQTZbU1c8ja/qIX4d6VfNycp9b1KLa0T4VrEtr\nA0IIbQA0IrfBBh7LSE0QuY8ze1WJ2jqz/14N6d/e4SZrgxdY1qW1AfWsGwWgKbkN9hCVQoZNKrlp\naZDi1qi13f9rh+IGfWltQA3T2QDoQ24D5lcWlS4vbpWxLGRj2cRxYAxaG1BMaAOgJ7kNmFzNBK4L\ni1tlLEt/2ufPTWtjHlobUMa6UQD6k9uAmdUvlrykuFXGstwn/Om5aW3MQ2sDcpnOBsCF5DZgWlE3\nJgspbu3ukhayI0HUBrVwBa0NyCK0AXA5uQ2YU2zeqixurTdqeN0TtiDAvd2gNmTLWmhJawMSqWwA\njENuAyaUmLduCSnxi4uLW5+NGh6/+OkR04d6+rLHcaIW1UIorQ1IIbQBMBq5DZhNVms7cu6qVpCc\n+m/U8PYRQ575AsUtZLKeGX/D0NqAr2yDAMCY5DZgKrmt7f5/WxS3/hs1nDxiyDP/Okj9XeSiBjkf\nNmSu4gL9cWZaG3DCdDYABvfz61oizs+fV7COLQQra9O7K/cAACAASURBVG25334yQtloIQ+X+Igh\nzzz9AIbMzgs5VYZsvWr/1mFobcAnQhsANbp1G7PbgElUtrYjZ45b1JNJHy3qLJ81PS1rkJBFrFEr\nYVOGzR05ZBAiaG3AW9aNAjARuQ2YREos+5pFQopb7iy54sJV5mSo4tcesog1aiVs+rDpI4cMQgSt\nDXhiOhsAM7KYNJLFpNDcSRaJuuda/eyw13Hqp+bVPHrl94YsYo1aCVsw7NeRo94dqmltwCOhDYBw\nFpMCvPNpelrWWfJkjluL1nb+iE/jnz+B4j0fmra214d7/a/XajHjj2haG3Bn3SgAszO7LZLZbdDJ\nUyKp34MyZZz6nRaumuNW+cyv/favLpnxRzStDThMZwOgvW7dRm6LJLdBmNtPU8qEqa9fkzjrKipy\n9Vm32GJOVsj0tLLJceeP/lXTFb6H1tbcAq2tZoU6cAhtAPRiMSmwsfsZ8GQNYHqQqhkkV8iAl1ya\nt1jE2q1nFTw9rW0Y87a29A9RVtiHrahsAKzK7LZIZrdBgNw1nu0GSRk26yGitgsIn9pWv7Xo64D9\ne1bnGX9EmLG11X/QfKzgENoAuIjZbcCW3l7Ift1AoMUgbxXvsZDu6/O8qrUdmZPIYh/967rgI7Px\npRBFGpuutUV9vlKWwsPCbIMAwA7MbotkdhtUCbn7UYdbKNVMnau8d9uFra3Fcyh4T7vd1c4JvLFt\nW9sTHzT2YTobACOwVcKU5DYoF7LQMmq15lc1t2IqLm4jtLabkGdS3E87FDdn78a0tic+caxNaANg\nHHLblOQ2KFe/ZedEN78veLHjtLabyudTOVexaXGr/3ikLH3d2FytrXVou/N5YUnWjQIwGrltSnIb\nlKuMZRO1tpus4jZaa7spflZ91gVfVdxsQnlKazvh88IyTGcDYFhy25TkNqhSnMyma203nS/lnwxe\n3LotLi4ePPERh/rIXU1r+8rnhdkJbQAMTm6bktwGtQrC2aSt7UZxqxkz5fn3LG6td62d3Fyt7Sj6\n7BT/Q8DJIDAL60YBmEK3bvNXo3EBSvz+pl6h/vxkfPEx6iVs1ksIdzuGoz36IK3tyDw+J4917XEe\nw9qt7dPbW/CPAjAd09kA4C2z2yKZ3QYxxrxVWTvzznEL3wN0nNYW/liDfwhbWri1Zb2rs//rADwR\n2gCYkdltwMZi53yNf+U66Ry3kOf8+OgDtrYj4fiYuXRqutaWqOCHJn3jExMiGZnKBgAp5DZgSFEF\n6vECt/L6NWSQT6YrbuE9a8zWdh/w0+MGPu0VzdjaWk9VvPZnHWoIbQCQzmLSSBaTQrDKq9LXySTF\nP5Uhg2Q9Sn8h9ylr6pLWdvLoWtsprW2EB4IQtkEAYBkWkwLUzQN5u3CrbI1WyCDjS3xde7a24+X4\naG2nZmxtKaLeT3PcmILpbABQTG4DxlZ2VXpyk6TcWBYySPEDdTbsfcoub233h0i//9ahtX23Z2u7\nj3b+OVo17DMFoQ0AKsltwPByi9vXIJJ+FRsySOUDdVZ/n7Ljis0ucjd9LH56dpeMM1prG+enEC5k\n3SgAhJDbgBV9vW5OiWUhg6QY7Sr/7evKzUyxm12cK0hgrdfybdzaEqe2jdbavmrxllpSyjhMZwOA\nWHIbMLzc69HErz+PZd0ugqe42i6b0lXfEhq1tvv/bXTwtbZvpmttsDChDQBakNuAsfW8+X2fB73k\ngW4S11E+HZOa5ZP1m12cq1za2aK4aW3fzNja2r2r559Bt2+jKetGAaAduQ0YWM+b3xc8aOV18CWt\n7fh2fR9+NIqTVmBpOBmn/23mFjV7a5timimEMJ0NADqQ24BR9Zxidq8ky7e2+/99+wSKp6edH412\nxS1l5K/vVM/bzC1q9tYGmxDaAKAbuQ0YUucadcs6m7S2+x8+PY3i6WkpR+Oq4pb4TvW5zdyitLZK\nNkygA+tGAaAzuQ0YzyWXnqO1tg5Trh4f4nV+X+KmB+c3vyuYNvh2tLLilvVOaR5FtDYYmelsAHAV\nuQ0YTFb26t9HurW2o8uUq5M7tT1FrrdP5utGE7nTBj8pKG4F71TNU93ynvZaGwxLaAOAa8ltwEhy\np5h1Lm49W9v9fzfd2fPR6wOdF7fETV2j3qCs4lb8TiluybQ2GJDKBgCDkNuAYZQt5+xW3LJKSnH3\nefz6mtdV39ruf/72aCe2tlgpxa2e4pZAawtkETMhhDYAGIrcBoyh5tZpHYpbWWs7/uwvWXsOjNDa\n7v/1qbgVDHLiNmDit3foWZWfpQ2Km9YGQ7ENAgAMSG4DplK8e2aLB33rfElm4p4DPae7pDzW14RU\nv+I1/R1s2rNCjvzSxU1rg0GYzgYAI5PbgHmUbU9Z9mWJD/okZUnm1z0HOmwsEDtm1N3lLi9ugZVz\n0eK2cGuzMy0TEdoAYHw/vyteD1zl589f1R1byJO+0LJykEa57euwn5pao3ltgc/8ZMzwnRxqnkyN\nrI0sCna9mN/Cre0m5Aw0xYMyL+tGAaBSt25jdhswjMSFlpWD5OahxGlKuUsy3+45EDu7Jn2CVfG0\nsha7pl4yyyg3nyU+yYXmuC3f2mBkprMBwHTMbotkdhsEOF9oWTlIizx08qBZQzVqTO3muF1+MKPO\nscVv3DZz3DZpbVnzUyd9RKYjtAFArG7dRm6LJLdBjE8LLSsHqexZTYtb0/lcLYpbsagnc3lrC/n2\nGWzS2m469y+57XIjvwXWjQJAC3LblOQ2GFdISGpU3CaKXN2exk394uKy8bMebunitlVrO/rGl5FD\nz/IKznPd3g7T2QCgKfduA4gTlZBSbsWVe1evmufWYivPdrdOK/ib7Osurh1EveMT2q21HQlvZtTt\n+Bb9yIyu5rC/3mwznNAGACsxuy2S2W0wovDr2sA5biFPo8VWnvXP/ykm1pwPQxYXpwz+arSlrx1t\n2NpuOtw2sOedCbm55O+BRCobAPRkMemU5DYYTlaKiu1WPVdljlbc5jr7RS1Zbb30taNtW9tN0/XB\nSy8+HtQ4E3afCG0A0J/cNiW5DcZSEKGmKG5vH3qc4jbjqS9qyerlS18jbN7ajjY/TO2G5cRQN8Z8\nZBsEALiK3DYluQ0GUnxpO3hxO3nQEYrbvOe9qCWrTZe+tpfY2o6lc9uR+cH/+j7HjkaibjfIS3/L\nTGcDgMvJbVOS22AUleFp2OIWclkftUayfuTRRN0LvcM91dvQ2h7Vb165z/TQAXXejOLruya0AcAg\n7EwKUKo+D8XuNdlz58rwx8oaLWrXxqtEPfk5D4LW9qTghylqixEq9d/49eTkZ90oAOxJbgOWk3iV\nfH5dO2Zx+9qzUh4lPYoVPOfZi9uutLbL+bmJEjKpsP7kZzobAGxObgNW9DVvpVzahgwS7qRnxW55\nWNwHFbfZaG2f3D7I/adK0c3JFOebgndfaAMADrkNWNZJLEuPQSGDHNHX62971iCt7f7titsktLav\nWi8H97MSKPxWk1nJ1bpRAOBObgPW9fYqOffStn6QFlfqTz1rqNZ2H0RFGJ7WlqhdcfNTEij2RPj6\nLZ/G/+cwnQ0AeCa3AUt7ukouu7StGaTdrJh7zxqwtd2H0hIGprVlabGw1M9HfzXH/LW6Cm0AwCdy\nG7C6kCvaskFa3/MpfN1U+BNW3EaltZWJim5+LMLVb5CT4l7cokKbygYAq/r59RtfnJ8/f9dzbGFr\n49xfPby15SYHJ8PBaG0hCn7E/Si08/XtCDn4tkEAgNl16zZmtwE0sHxrO3JuZ2WO20i0tiiJWwT7\n7I+g/l2wDQIAkEVuA4iWla5G2PKweJ6a4jYbra0Dn/T+2p1HTWcDAMrIbQChctPV5VseVq4JVdzm\nobWxp7ITj9AGANSQ2wDilKWrFsUtPGydDNh6jh4RtDZIZN0oAFBPbgMIUjNNLLZYZbW2lIf+OmDI\nIDSjtbGw83NP+okncDrbf46/j8PPEgBsTW4DiFC/TeeFc8TOHzrxajVkEBrQ2uBceGgDAJDbADo6\nr05Rxa3gLmmfHjpkopzWdh2tDU5EhTaVDQB4IrcBRIhaTTlUcSvIZCGD5Lo/YuVj3cZZKA5qbZew\nrnp8prMBAK3JbQBBolZTDlLcipNAyCDpHo9Vzean93FW2UFVa+sp60f28YuX+KzNJH6/UfvEAADv\nyG0AcaJWU15b3Op1SwivR6kslj2NM39x09q6qfxJnf+zNrTHY2u/UQCgJ7kNIFTUasoLi9ssPh2f\n3Jf8dpyZj9tira3nXMksUVubDPsCF/Dzc/xzRE9nAwBIILcBRAtZTRm4S+nM5eij8+OT/pJPxpnz\nuM3e2s7fkFdXvUUtthGe8xM3rg6h7ardpAGA8cltAA2E3LM/5VESv3Kx6/iUV53ykr+OM9txm7e1\nFWeL/lPDmhaWyu06TJQ7ulQ2AICv5DaAwaS3tmPj4pbi/CUvNy9l0tYWuCSz884cTR+lcnZm//2B\nRyC0AQDjkNsARpLV2u7/e7fiVv+SC47z2DZvbY+jtXvTehba2Fa8/F6oUaFNZQMAovz8Lvlr10V+\n/vz917EF8tQ0oPTr72VOTcUvWWsbQOt0Ff7uXTIb8vVVRD2NeT7dZ6I2Gz2KQtv5e7HGEQaA9XTr\nNma3AYyhsgGZ43bi8SVrbQPokK5iP+ZlT7gs8z59S+4nN33kY6aP+bNrQxsAwFdyG8A8zi+O0/PT\nMnKLm9Y2gG4f0qvC8kkSv6lZChprxvYeFdoqK9tu51oAIJfcBjCGrzEo5bI4pShNd3l9Lqu4JQ44\nCa0t5eHq38/whdq3L4v92BabZZrbXNPZxj+eAEBrchvAME7KUfrV23l+WvIqMHBa3zzHR2tLf9Ca\nd7VdpM2Kbq2NPM1twNA2yLsGAIxMbgMYydtylHsd/Ck/DXs9XS+kuM1zfDZpbZ/ekILFmE3f25rB\nN1wCni4qtP3n+F9lC/kUeL8AgBRyG9DX/UolZMLJPH0kw9P1d9lrfL2IX/JYParsFvMcnxlbW5av\nb0Wj3QNepYxf/8EZpLiNs6o0cDrbPbTd1IfXPh8JAGABchvQ0eOVSvF1T8ggg7tff0dNm1nyKL0q\n7hbzHJ9JW1ujJZnp6zEbnSqixqwvblEzAa/VLrTd1XwS5jqYAMC1fn7nucYY38+fv4g5tvCHkOWN\nu62RHND48xNzr4nn+fxM2tqO9nOCWozff9ORwPW2NYP3/4HoUNleZb3MkY8eAJClW7eR2yLJbfBR\nyM37d9sBYEAhC1Q7rHJd8eJYa+v8KIPntpAfvtjBC7TYBiH2MHZ4UwCAnrp1G4tJgfbOr1cS1/aE\nDEKN17eg4LCHDBJokk/OvK0tRcg70PkOaI2WprbOYYPcJ+6IC22vm41mvcZPE22bzjQEAHYgtwGN\nhdxX6cKbM3Hz6S3IOuwhgxQ/ysnXj/3Jmbq19Zwj9rWzDP9WJ6l8CSk1qt2BajGdLcQgFRIAWIbc\nBmSq3zTz07Br3Ot7SRPNTyz7tAycYaZubV+FH/Wo2Vvng1z4YZlxJuBNz9C2wFRHAGB2chuQ4+kK\nJiVSpF/3vB1txZtwTWai+Yk1V9hDFre1WxtPOheibjMB260bPTHOslkAYE9yG5Ds7bVL0+KmtU3k\n8vmJ9Y8yWHFboLVdMkfs/Hwz2Ju8ssvXjd7e6KanH58lAOATuQ1IU3n9WlDctLZBTDE/MeqSepgY\ns0BrY3Dt5n9dHtoetXuZY5wqAIBByW1AgpAba2dVm3SueDoYfH5i7MX0AMVNa7vQVfuyXLLyMXwm\n4CXrRr8Kn+Z29RkCAJiA3AYECbl7Vy4XPd0MOz8x8VGyntKlxW2T1tb0ABdMaKr8+s1PRUNNZ/sk\nKrpt/l4DAInkNiBO57t3uejpbMD5iVmt7aheGNveJq1tKIE7mW54TpoitD0qjm4bvrkAQA25DUjQ\n7e5d6Vz6XCL8Nkg9W9v9/45a3LS2zsLPTAMsRM5W/DM95rrRROn/MDTdGwoADEJuA9J0uHtX1pPh\nKoHFrX9ru//heMVtvdZ2yc3I0jV6estPc5tuOluWhd84AKAzuQ1I1vTuXVlPg2uFFLerWtv9P41U\ng9ZrbYNr/ebPOM3tq7VDGwBALLkNyNHo7l1ZT4ARVOaqyvcx5dEDt8odxlytbdgD3OdZZRW3MQ/U\njcoGAFDg59e1a5yfP39fdmxZVuClYdYVuZ+p0ZR9EqLex5NHj+ocXT5yiVPb5mptNyFvUfhD95T4\nMuvna9b49Oj/HEIbALCabt3G7DYgX9SsldxxllygNbWCT0LgO/jp0bMe4uQlaG1USzxpjTYTMCq0\nqWwAwLbkNqBI/dVh2QiK22iunZ/4+ugFD/H2JWhtjTX9UR4qXU100jKdDQAgitwGlKopbjXfO9HF\n6w4un5/4+FkqHvzpA6m17e3+/kdlu5APftNPpdAGABDLvdsiuXcbOyq4Hr18X0uiXHvvtplt0tou\nuTNe4B4eKRtyRN12rX7zjzJROyGobADAFNy7DZhEbjuLukeROW6XMz+x1Cat7fj24z7aB6Hgydxe\nQsqPwvmL7b/61X6jAABNyW1AtayCFnhZOdrF+lYq38eN37t9WluK8A9C7ITLlHNbenE7GeGrwKMk\ntAEAdCC3AdUuvC35xtXmSuYnltLaBlT/MUwsbq8f+ax/p6h/ntaNAgB0I7cBdVq0tttlZeLIW1ab\nK5mfWGrP1va1QwV+ChqdjRLXiubK/ZbiA2U6GwBAf3IbUKFdazty1qhuVm2uFP6Ob/Pe7dnaEoV8\nCtrt2xF1w8m7bhOChTYAgKvYmTSSnUnZS9PWVvAofuJay30vvHf/0tpa356swx65Fy6af5TynFU2\nAIBP7EwKjK1PazvMcRtGQTvz3h3HobUdx5G858CRH90GqWDdnP+sCG0AAIOQ24B83Vrb/T91vqS+\nP1zIfJsFQlLxPLXti5vWlis9ulWeFXI/bv3PQ5+8/VmJCm3/Of4+ljhpAQBcS24DMiVecWZdm369\ntksZrcXt1osbUMggg6h8Hzcublrbo6xTwkmsvrB5DVjcAqez3UIbAAAh5DYgR3prO6I7y/lo7bY2\nLGhAIYNMZ6j5iQPQ2l4VfBBG++Dk3paw7CFSxm8X2pY5V50fxmVeJgAwJlslRLJVAovLam253/X6\njenPoV1rK3iIDk2wv5Cphd3mJw5AazsxQkG7aiPUr+5P7GT8f47IdaOfnsCkOmyaAQBMzVYJwGDK\nWtvRfo5bh9Z2JE9PCxlkQCFTC/vMTxyA1raD8GluX38Coirb8Xnd6NQ/hTXvRdk2HQAAJ8xui2R2\nG8sqbm25I5wP8jpan9Z2d/5wIYOMLGRqYdP5iQPQ2hK1nuPWs+6227ThNnKH0Pb1mYws9rM06UEA\nABKZ3QbM5vw8FXj3rpB5CGWDnExPG2GBXGshUwvbzU8cgNaWrukN/Tp/popnunWb0ZayDcKkP4jh\nnyIz3QCAEGa3RTK7jZWF3HS6/u5djyMU/4i9HaRm/l3s3L3BhUwtDJ+fOACtrUCL4pbyM936c1d5\nvuy83+ikP4UdJkgCAOsxuw0YzMlclPQzVOX6rqfvLbsV2qdBiu8xt1VrO4JexRqH4oHWVib2DmgL\nfKw6h7Zj2oPWYT7xvDfbBABGILcByd4GqdzLkU9VK7e13f8w6wmcD1JQ3HZrbbyjtVWqj26B68Iv\n0b+y3Qx1ENJ1W7s/2ucEAJiI3AbkeApSZRciBXfvOrm6Sr8eShkkq7ilc8W2Lq0tSu6c0Ul/qp6e\nttCWq/N9MhU3AKCM3MYYYu8GVTkO5+5BquYgP1atmtZ2/4LAQcJv4e7TuK7E1kauqX9oEs8fUaEt\nq7IdexzbJ2Wr/x+/ZeqDBgBcwlYJkWyVUChkm8L6RY4MK/Hy6OQdL1jy6W5SfJPe2kxtu0rIFi+x\nDxq12ehxHH///v314W7WOA+FTyk2RxkANmSrBLbx+ttuwb8jh9zVawRm+dX49I6X3V4tZI7bVsd/\nM1obb52cNsJD243TzJOszXuO7qtTAYBNmN0Wyey2bDWbVKYMkjXO5czyO1G8I0HlVgY9b97OPLS2\nWXz9CQ7/MX37iFGh7bGy7aZ+lvNVgwMAQ+nWbeS2SHJbnpDLoGVW0ZRt1pkySME4Y2q6IDRkIWri\ngExOa5tLz+L29FiNprNtqEMOU9wAYBMWk7K6lF9sv64GXWYFyKcXkrUeNmTvzpFl7RmatRT0/OAU\nrCpd4GjzgdbGJ4/nCaGtv8rzroWlAEAsuY2LJCaMk060zC/F5y8ksZSF7N05vqzilj5m4OMmDsic\ntLYlhZwd72cI60bDDTWLfY2/SwGADuQ2rlNT3JZpH2b55QrZweBxtBRZj+hqbFFa26RSzhm3Lyj+\nwf35MZ3tSoFn3Ni/YQCAnbl3WyT3bitRcLuUZVrbTeUNYxY7GolCrodatLbcwZmE1ja7dnfm+u+P\n0NZW//2QltmBCQB45d5tbCN3jtt6dcksvwL1MxCatrbDHLelaG37yJrmFhXaVLYTA841c3YHAFLI\nbQwgvTdljTmRsuK2bWu7qSlurVvb/duXPPKb0drWkHXCuH/l259g09nG0egUa0kpAFBPbmMMl9yQ\nayhm+RUo+9j0aW33QRY+/hvQ2lZScMJ4+no3aAMAIJHcxjCiitu8dcMsvwK5H5uere0+1PLvwqK0\ntvWU/T2jsgEAkEtuYyTdbsg1LLP8RhC+iEhxm5DWtqqss6zQNrKmp1XrSQGASnIbg+lwQ67BmeWX\npWBt2PmRyV2lm/j1ittUtLa1pZxlo0KbygYAsCe5jfE0vSHXFMzyS1R2lE7KV8Ed8dLfrKzi9jhm\nzbt5fst33tHadvCplpvOBgBACLmNITW6IddEzPI7/r0Urk9jb7/3ddji3SfCi9vTaMUz4x7HMb0u\njda2rW6h7fxs4cd0Ck6oAMBXchvzW/V33s1n+d1fe2UaOxn/cdjKnV4Di9vbcQqu7V7HcYH4jda2\nm9sPxH9/mq8bTT/BRE1spSlvDQDwldzGkLJiiohw9/Y4nM8RG9P59K6o+1cXfHJOvj7kpnsnIxSv\nRS0eZDNa226iKtsRFNo+fa8fWQCAGcltjKfg6mTJiJB7HE5a2zHVITqf3hW7V1zWYfn6lSnF7WSQ\nr99btha1bJDNaG1bGT+0vY7jpxYAYC4/v36Di/Pz5y/Xjm2JmguUlQ542XF4OgKvg4x/iGJrWqKU\nkFc/s+zrIImvvcMgm9Ha9tFh3ehNozPZhj+4V93qzi32AGBV3bqN2W2MpPICZZlpO8XH4fEIRN0C\nrKdLWtvx72E5mZuWddA+jRN15EN2VuVfWtsO+kxnu2n6Uzj4KRwAgDu5jWGEXKMscC0S0hyjbgG2\nj5PiVnC4XsdJGaRyv4XK3R62pLUVmGsCZc/QdnQp3k7hAABTsJg0ksWk5WKvUeY98t1mJw17iK6d\nn/W6qrTmQN3HyRqkrJppbfm0tixzLfTvXNluOp+9NvlRrrkf5lwPCgD0YTEpO8kqBSlf7F//vxr2\nEIXs71nsPsctRNk4BXPctLZ8Wlu6qB13+3z6Lgltx9X/UrCwa/9OeMt5FABIIbdxtdxSoLiFGPng\nXHh1NchhySpuWcNyHIfWlix8H+Cj5cew2zYIrxrtbfP1Qf1MHw2Ow2h1DwCYlNzGpcpm5axa3Kwk\nvbukuA11WMKPwFCv7lJaW4qJisNV09nuoqL3+T43nx7aT/YRehwm+uQDAIOT27hOzQq49Yqb1vak\nUW8K2Xu0j8AjMOCru4jWlqL13ppH0Efy8tCWK/FVZ60Rn+hvuWIp58Jux2H5ow0ARJHbuEj93aZW\nKm5a21stelPU3qN9hByBYV9dd1pbij5no8oT84XrRp+026d1wHuWDa7yQ+VoAwCx5DbGdv678xqX\nI1rbiRa96WnMwQ9L5REY/NV1pLWl6HlCLYgj001nuyn+KUyc5jbFPypVav3va+2yKQCwrXVy28+H\n35Xa7epKlZTfnVPeu6/jDP4BWCAXttaiN93HHPzjcVN8BKZ4dV1obSn6n43S48iYoS3liNX/FK7x\n70r12hU3hxcAaGH63Papsj19geg2ovPfndPfspNxvO9raNGb5vpsFByBuV5gS1pbioKfsLcfsfDt\nNcdZN1og6qfw6wlghwlu6dL/McXezgBAOz9Td6in1vb6Wr5+Qefnwxtvf9stOHQT3ZDrSZ9/WJ/l\naJzQm+rveLgfrS1R+IerMmSMOZ3tUcj87GEfblj1//JirjAAbK5bt5k1t71Oavv0QnomMLmt0NO7\nWXzcJroh15Ovs/wqk9xcR+PEzr1JbcyntSVqd+OqgpHHD203/W9jMPWNEwL1X/u5z7EFgB3IbWfS\nW9vbr294NOW2YvdDV3nQJroh15Ovs/yKrzBmPBpv7bzsx3yMfFpbotY3iU8ff651o6PltkYPOqae\nxW2fowoAm5DbzhQcnT4HVG6jytdZflF3V5qR115mmYOQSWtL1+d+/yeP8s8xx3S2R1dNNDPB7c5t\nGACAMt26zXxbJZQdmt/f38dv/PmZsjOyuMe7YYd8Ppf5kJddV61x8/DKa8o1DkImrS1dn9b2SVRo\nu2QbBK7VYcPW/c6dAECkyXLb131I4Q8ha0tjE9i5k4fY9sNf88Jnj00hb/rsByGT1harxd6aM05n\nG0SHxjSRdkdjp1MmANDKZLntSdYMNRPctnN/u2tyw+Pv8hdmi22nd9VfS817EAKvI+c9CJm0tlix\nn5rAu7MdA4e2PX7URhGymdDbMQEAKs2U28KntiluK3v6tJTlhteP3CXZYtvpXVE/8jMehPA5GzMe\nhExaW66e86Tm2gZhUhv8lL8XFd32PHoAQCMz5TZI9faX7twLkU+/uXe+oNl2eldsCZjrIKS/9qyr\nzLkOQiatLVzIh2WH6WwMoia6rXtqBAAuM01ue53aVjAx7Wk9KWs6eYvTc8P556Rbtth2eleL3jTL\nQch97UfOHYxmOQiZtLYBCW1c4vEMZyNXAOBCj4vcLgAAIABJREFU0+S2RqwnXc3X6JCSGwZpN9tO\n72rXm8Y/CAWv/f5/dy1uWlsLNZ8R60YZxFqnOgBgMrvnNnZ0nhsGmf+YlV1W6iyte9PIB6H4td//\ncKVPQhqtrVj4qc50NgAAuJsjt1kBSqrK5lLZO6LkPo1lOkuf3jT4Qfjq5MmnfxKWoLW9Snn/wz/+\ngaHtP8ffU/90XsuhAwAYxxy5rSnrSVdT3FwmbW33/71GcUtR35vGPAgpT/7r0w4ZZAZa26OsyhqY\nZKNC23+OdaazjXl2AQCgM7mNFRU0l6lb2/1Pdihua/em8yef+LRDBhmb1nZ3yXTG2OlsUUPtYKfZ\nqwAAc5s1txXPR7M56S6yitsgrS3dp6cxe3H7+vx36E2fnnzW0w4ZZH5rtzahDQAAhjVrboPv0otb\n+oAjOH8aia96kNfy6uT579ObXp98wdMOGWRIiVPbFm5t/UNb+DYIs/+z1/mJttE/Z8x+0AAAtjJB\nbuswGc3t25YVeOf4Pp+QkOldUXPErvL2+e/Wmx6ffPHTDhlkMFpb5+bSYr9R2aiFVX7EAQAWMUFu\ngyohxa3ndUzI9K6oOWJXeXr+e/amkCc83as+pbX1DFVRoe1e2bYSPsFNowQAmMsEs7rezm6redrh\nA34aefxju5GaK5VL3seQ6V0hg8AYtLY+weWfI34625OpZ98+6rkpy7wbwAAADKVbtzG7raHEZbCq\nXA/Fc9yuendCpndFzRGDq2ltHVpbh9C2m6g5blobAMBXo+2KKbexjYLidu0VjLWEcByH1lbU2l5/\n9E8GiQptKZVtmaltR9rfKvXFbbDfGwEASCK3sZOs4jbXZR8sSmvLqi0n5637f7oPaDpbH8XFLfGt\n95cVAMCA5DZ2YpIATEVrS5e1k0qL/UZTrHcOTvxHnNvXZHWx9Y4VAMBW5Da2kXvtEr6xHJBDazsa\nzG+6cL9RNyBLjG5R8xkBALiQ3NaQPRAGUjZPQHGDi2ht6VLOUldNZ9tB7n1B71/89MaF3KEPAGBb\niQWm244KchsbqPlxCilun66urhoHxqa13aScur6eDAYJbWsvjSzb+7rymPh7AABgZHIbq6u/yKss\nbo9PoGaoqHFgbFpbupPTQGBl+8/x9/ljndvkfv9lxa3m4QAAGJncxtKirn4CN5YrGypqHBib1nZX\nfKez8NB2fz4hp663TkYu2GTgKt2K2xRHAwBgc3Ib64q97im41vz0BHKHihoHxqa1pXv7ox8V2h4r\n26Os8lV8w8yUPx/2zNehuA372gEAeDRBbvv9/e12KzvWkf6ZuV27pHx9Vt46HzB9qKhxYGxaW7FG\n09k++XoPydy/sQsS1ePXj3YKbFfcRnulAACcmCC3dWAL0dXktrYj+QopMW9FDSU0swet7cn5j/79\nzBG7DUJN86pROc6Aq03T/xEnd0wAAGYht7GcgtZ2/79RmSxkKK2NPWhtBaJC2+Nmo51v9h9r2Oh2\n2IEUAGBLP1NM7HpdTFr8tN+uS406CE+DT3FsV1Pc2nJHiJrj9mmoTTbzY3ta21ufTgD/HJHT2bIe\nehZjnhTLjuqYrwUAYGrdus2ss9t+fuYIhQzq5MMzwhw3rY09aG3pOoS2NQw4ze348/kkrhQGAGBq\nc+Q2uyUQKSSTJV4SFRQ3rY09aG2JokLb2pXtyci7yAz7xAAACDRHbmvKLLmlfM1bIZks6zOTVdy0\nNvagtX11yXQ2/7AFAAAhplmSGXX7tsDbwH0dfJZju6BPl4y578jbccre1sCrWJ8rJqe1nYvdb/Tr\n16yd2JwvAQB45N5tz6wnJcPbaWIFP0Wv4xT/KEbt+efakckltrY9tdhv9ESfv1TLTn6Vm9kAAMC1\npsltrwp2S2g6tY2xPF3hhWSyyk9LfXHzcWVy6a1tq6ltnaezHR1DW/i35N7lcuSbuAEAsLCJcxt8\nEXWNFXitVlPcXDIyOa3tVf/QdjRrbZXz0XLPcLevj9pHGgAAYs2U28LXk5raxgViF1bBJLS2R5dU\ntqPxpLaaqnX5Mn0AAIg1U257lbWe1K3fGEXuBaLWxuS0trurQtvRZQHpa3FLedAOy/RNcAMAoLPJ\nclvgBDdT27hSenHzQWVyWttNVGj7z/H3EbTNcgu5YSvkDGeOGwAAo5kstx0vxS1xglu3rV4hSfql\noVkZzExrC5zOdgttBTqnqPtJ6+vj9rwxplMpAAA9zZfbjvziZhkpY8n9QLpMZE6bt7amoS39rHDJ\nX4ApT89ZDQCAhU2Z246c4vba2kxt40pl176KG7PZubXFrhutEdjachds9s98lpQCADCOWXPbkVbc\nrCFlLDXXgoob89iztcVvg1C3OjK8PSUuEU0fqjMnUQAAupk4tx3/5rN7UztfNKq1cbH6i1QXi8xg\nw9Z21X6jIaeElElhj48SGN3CmeAGAMAg5s5tN0/R7e1/hYtFXQIqboxtt9YWFdreVraUePTplJBy\nyrmNX3ZyErYAAODECrntRlZjXIlXpYnXr4obo9qntV01ne2tslNCei/7NHhxcWt6AtMBl3H+Pvpr\nEAAY3Dq5DQaVdUWruDGtTVpb59CWfko4HgJE+rdU6ta27o/izLe29I/T41f6VAAAA5LboKWC2SOK\nGxNavrVdOJ0tPWm1KF9fTzONitunMd/+uXPhAuwkBAAsRm6DZopXailuTGXt1jbUutHOrto/tPhb\nnBFnFJJrfQYAgNHIbdBGn7siKW5cbeHW1nQbhCyX3I8s/dQS8vRimwtTaDcv0l+MAMDl5DZooLK1\n3f+ra0fGtmRrG3M6W+fzQW6tqHl6znN7avq++6coAOBychs0kHLpmXIpoLgxsPVa25ih7a7b+aBn\np3CG21OH911xAwCuJbdBG+dXxlHLtFxMcJHFWts460bP3X7im6YKrY3Wur3vihsAcCG5DZr5VMqi\nlmm5jOAiy7S2waezfdJomtv5GeXxESvPPSrbzjq/+4obAHAVuQ1aer0sLvvFP2ocqLZGa5s0tN2F\nT3N7PaOcDP76n35/51j7HhgNKVDwCXl6m8o2rvVeAwD9yW3Q2OM1aM2v/FHjQIUFWtss60ZThES3\n+pxR/xwuYQvLzrI+JCe7dhcMqLgBAP3JbdBe1K/5Lhe41NStbfbpbCfKolvWdLYLvT3tBT5V0a2P\n9Lcs6tamAADXktsA+G7e1rZwaHuUEt1OQsZo2eLTU230PM1+GkTBrU2PtE+FtxgA6ExuA+CLSVvb\nSutG2xkttB3dW9vj4IpMCylvXNS9FgAABiG3AXBmuta2yXS2EKNFisvn35kDdYn6Y55S3Ly5AEBP\nchsAH83V2kxny5rmo7V9eixRJtDX9y7w7qajfaQBgJ3JbQC8N0trM50t0WNIGi1MDNLa7o+ouM3o\na3HzzgIA3chtALwxRWsT2sqM1tpOXPVUdZk+wg+yOW4AwCDkNgCejd/arBstlhsj3gaR8KLxdqcC\n3WR2xVvlAgDMTm4D4A8jtzbT2SplBaz+O4TeRx4hxJjgNqnzCW7eVgCgD7kNgP8zbGsT2hKFLKbr\nH9o6P1DiUZJmAAAoI7cB8D9jtjbrRju7vLX14SZf19IxAYC1yW0AHMd4rc10tmLFIWmo7UErpRyE\nlK8xwW1GWioAcDm5DYCxWpvQNpq5ykVKHbtHNF2mHQcWANiZ3Aawu3Fam3WjUQoq0hprSAtmoilu\nAACEk9sAtjZCazOd7XLbtrYU1pMCAJBLbgPY1+WtTWhrJ2vS1uxFqfLJm+AGAEAsuQ1gUxe2NpWt\nj9zidv+upz9p/dA1pq6EAACsSm4D2NFVrW3J0JbSla6qQgXZqz6Ttd6FoMXBNMEtnEMKAOxMbgPY\nziWtbbFtEIob1vKzsZq+wKuO3uyLbXcj8wEAl5PbAPbSubWtN52t8kr+9u2rtpvc15U1Aerag/b2\nea76PnagYAIAa5PbADbSs7UJbV+HWiw3vL6clJp2yZLDp6da/ASWfB8BAKgntwHsoltrW2zd6E2L\nJLRSrKl5FS2KW+KAIY+70vvYU6MJbufvqbcJAOhDbgPYQofWtt50tpvWc69mX1VX8+RzX3vsLfBi\n31nR7ZXdEgCAbclttBF1SeTyBSK0bm2rhraj1z3XJy1ugc85pcs8fsH5ndSyhoo16Vt5lfDDpe4B\nAIOQ22jg6ZKo+Ffp+zguX6CLgta25LrRu56X7nOd5wKfauALHyS1+HeiLD0/AN4UAKAbuY1or7/t\nlv0q/TTOXFeiMJLEqW1ZrW3h6Wx3/dvNJee59BlhT18faMkT/JIvqkC39aSDxFYAgBu5jVCfftst\nvj1PzSBAg9a2Q2gr9nqKyk0AF57nUrpb7nNLf/lLthJ/ayWqP1Apnx/vBQDQk9xGnPPfdtN/mz4Z\nx7UL5AhsbbtVtqz6c3Jayp07djQ4z7ldfb3bO1JwGP2tdeTcmK/sWPl4AwADktsIkvLbbsplR8qv\n5K5dIEFUa9sttB05V+/pZ6PiXtOac2q6gnhKlpCp8G/5kAMAnclt9HX+q7QrGAgS0trW3gahUtnV\ne+JEswsTWOBpeOEzelY8FTSPnCmWidPcFv50AQBrkNsIkvWr9Nvfoy+8TTespbK1bTid7VHrm0AN\nuLRTDzr36eCkRzdH+Mj85N+/8um4lf3sOPgAQH9yG3FqipvWBkFqWtvmoS1R/Xko8VZWgSe89NNz\nVA0cLSm2M2A/HVbBsao/tn5xAAAuIbcRqqy4aW0QpLi1WTd68/VsFHUeGq3RxNa9oV5aB/376bw6\nf/IdcwDgKnIb0XKLm9YGQQpam+lsWTpvGNo50EQ93GKtLfGYjNZPR9btWPnFAQC4kNxGA7m3RE4Z\nEDiV29qEtlf9c0nPRhMyAyvlC7Y1Wj8dWYdPvkMNAFxLbqONwF+l/coM32S1NutGy2xyKqo5c6/X\n2jZ50y/Rrrh51wCAEfz8+q0kzs+fvzk6tm5xDB0ktrZ/fv6JesRVQ9v5Gavd2ajn44YEjprNpSdS\nduSv+hTNK/aT4wgDAOe6dRuz22ip8h+v/dYM33RubauGtn20mFI0YGhzJ7WJ3P6q989zAMBi5DYa\nK77o8YszfNOttalsF56Qns6gI5was/a5ucSF7eb8yLh92yfF0c3xBADGJLfRXsFlmV+f+7i9L5VH\nO2QQ8vVpbfuEtq83uT/afMxzz46PX1/2fEJKWVkWGbnQPep2PrPy9MnjS3ZwAICpyW10kXWZ5Zfo\nPu7vSM10i5BByNe6tals518c8mGPal4FT6Z/+Zro9ND6qaYf+fq0OrUNXzIAsBK5jfEINx08XfCV\nHfOQQcjXtLUJbenfW5+pQ5Q9mZ7FrfLmXPeX1uEJh5zDGt0gz/kVAGAichtdFCyXcmHRztu3I/eY\nhwxCvnatTWgrGyf3I9+oGRX88PUpbpWnhMdvb/2EBz97xU6uBACgKbmN9souj4SbRkJu4u1O4Bdp\n0dr2qWw3jfblrP/R6fxMbqI2hTwfP3bAds92lhtROssCAIxPbqOxyvVaLilifX07Uo55yCD8f/bu\nNVlxJEvUKKTF6Krm29Ojf5BFkjyEu2v7ey1ru9cs8hwhxCNKX2yX8oW3NqEtduPH7/pmKzcHGXOL\nWpX57Q83j25T7CQAwM7kNmoKuRK484koiS/H8TGf5c6Cy4ltbbuFtkuTd+5BAWn8uSkrbpe4/Xx/\n9LI7mf78r6Lb4HsIALCt683/Uotz/ff/8N/92AaeBm1+JAOdvD+s28t2EtXaNqxsd93vwtklUw9y\nJ4cyg1wR71J0GLu/3wAA+KZZtzHdRh3hN95zPhEifc3Y+zHX2pr7v+v/XS6X/97+m/LDx61t29B2\n6RGPXj49J3eg5X05Xx6x5YOe0XeZ8PvPN+ZvSACAAcltVJB4tpG1Fsj5RJSy4qa1tXUPbZfk1nZg\n59B2GaAW1Rjzbfmt2Tf2/dRmr2r//VP8TxvPv+KrFwBgKBaTRrKY9HLJbG1Zv3KRcuJkHXMvUEOP\n0HbJaW3vo22bV7a7vq0t5P4D568EF/uhrH1IB2xtDyn7FvvS5D5BX8AAAD9ZTMqcClrb5dwKR8pk\nHfP0bVLqubLdFbc2oa1A4gxX7khulO4zeg817mH6vPGRBd58NvGZ1r4dBAAA9Zhui7T7dFtZa8v9\n9YMtkMvtLAbwHtoupa1NaHtW9oX087faL648L/zTWeO5j3NvhGMn79tc+/4VvokBAI6ZbmM2508F\nqk5N8FHUMXeGl+9jZbvLbW0qW7Gym07ef2vnb6zuU1fh/1KQvsFvM24Nltlu+34DAJiR3EaQlFOB\nn6e2zifaO3/MtbZMB6HtktnahLZviueMcq9VOMU3VqVV+L2iW40XqM1zOfkqpDwdV1wAABiE3Eac\n41OB9GvVpFw86dhjC2dOO0I2MoUzzWD5gxPqOLRdclrb7XK7OPYnnP9umGvGrV6FKbvtzbvYPUzf\n1PPjJr6a77va8ratU7zfAABw7bZIu1+77e7jqUDUVXkK7gxX9iqEbGQuBedwOxyWCD8r211ea+O7\n84O2uYvjZykg3T+ygf+YkridSpfwK3iUwIN//h0OALAt125jWu//+F7w9v34L/hlp2IFIxMhG5lO\n7tTE8gckQmJou2htc3oec5vC4N9kIbtX/C8sz7+Y9XU4S2wFAKAluY0Kns9Uik+eXk53zow9ZJ3D\nhWyE7aWHtovW1lbK53jh2jL4N9nx7uVOdWW9NC/x9Od7oOM/T1hSCgAwPrmNOkLOLbI28vPE6Pw6\npcHPU0/KPXtb+2iUyqpsd1pbrPPLFR8/uWrR6PjZbXlUyx5olonF4yPp6xkAoDu5jSWUXd26xkYm\nVXxiuuTRKFIQ2i5a29gGLG7fPnAr1fLifYu6acP5X38x7KEGAKAeuY2dHJzGjXZW3dI4dxOcU1lo\nu2htMxikuP38kE1004aUQ/pxxGzS5b3bf0ECAGxKbmMJ6efEH/NQ+snZemdO509Mdy1uxZXtTmub\nRd/iVu+zNf6S0qw9vP/kUKHtsuLfGAAAJJLbWEVxcdPaQraz3sH57mRou2htnUTduKWZnT5Vn6Vf\nSW200NbAIKOXAAB8JLexkILiprUFbm29Q/Rv5yvbndY2o/Zpo8HnafwBt7vwK6mpVAAA1Ca3sZas\n4pa12cVkdcYzC3WXEBXaLlrbzFouV2z2SZqluIU/9GXLgTgAAJqR21hO+Dncegkpd6Zv4+IWFdr+\nc/vP5XK5XlKPvNY2rAalZq3P0JG+M4PG3AAAqEduY0WBZ1HrnfiWrZ/drLgFjrPdQ9tFa1tL8Z1A\nJZ4XLQ/I+zfTRHd0BQBgLnIbiwo5h5s/G706c626PYpbjdB20drGUOONmXvblZ8/c2YPy77zun9e\nGxS3n09wxgw63Q4DAGxFbmNdJ8+fpg1GX52/L8SMp6TJYteNPtPaSLTet06iql8tiUe1+IbV634p\nAgBQTm5jacVnQkue9SYejePnvtzJZaVxtgetbRNrfSw6qPTVUvZd/vJbxTvWfXIQAIBe5DZWV3AO\nt/Dp0c+jkfLcQzYygNqh7aK1jWfh/LFA74u9DcWqL/TdAi83AMDa5DY2kFXc1j5FuxwejfTnHrKR\nfuqtG32mtbU3dYOo+tGZaCz1fHSLPZKzHLdnM3wNAwAsTm5jA1lnSwtPvzx8PPPOfdYhG2mrwTjb\ng9bWTG4Nuf/8YkWm+w6Ey72S2rDfPTX+Slnv5QYAWI/cxuoKzks2LG7F1zc6v5EmWoa2i9bWxMni\nEPgp794+zt/tdPDvvNhFpuF+Tg4OfngBAKhBbmNpLnB9IOQJDn+U2qwbfTZUa3t8AoZ/ofKElJc1\nDs6wEaqxSt/ZA16mMuUVrzHCCQBAFrmNdY0z/UJzjcfZHrq3tm/v+o9/PuMbvEZdOtMm+tauqVdZ\n5hr58nNtBtzK1k3fLfM2AACYhdzGoqKmX57PopyvzKBXaLt0bW1l7/fp3tpVa8txEPn4X8dvbVsJ\n/yeS2CN8ZvfO74l5NwCAxuQ2VhR4kvS8KfNuA+tY2e56tbbAZZUjv7vbpKWXwH5+HyoNZIXfaXnk\nlz5Ly0vyvTxQymtd8EEbJ/kBAJBFbmM5HQdg6KF7aLt0am3h7/Rh390tx7jCHyu9uP0cNjTOlpi0\n2i/bzN144h6OtnQaAIB0chtryZ36cN/SmbW/DcJHa7S25816g4fouHLwfQeWSXUNilvxFfFy0+rx\n4uWq/D0GAFCb3MZCClZYla31cqbS1QjjbA/tW1uDbjLUG/zM8+14cf3nA1jc9qN2YEPF7+GTL1PW\nW+7bPGPLpdMAAFQit7GK4qsZKW7zGCq0XRZtbY8H6v4Gj7o8/Ia6v3ZVJX5n545qRl0Rr+CvlF5v\n1BE+5gAAq5LbWELWycr7GUbHGRjSDLJu9NnCre3xcL1OxRf4OHb8msm9g+rawSUlui3wfiumuAEA\nVCK3saXzp8JOUJoYbZztYfnW9njQ9u/0ZdrHx6+ZS+UnuMk3U+4XduAxTznCLZcP59bVd4obAEAN\nchtLKFu9U3yG4dSkvmFD26XTvRFyRd3dsvGp+DKt7a7l0dvtfqZdhpKzXs0Ge/jtjg13WVeR89ca\nAEAsuY1VnCxuUZft4bQB140+G/w+pD/fngVv+TZG258oDVaVnrnB5dTfZ42LW8GxqreHow3ZAQDw\nQm5jIcXFTWsbwMjjbA8jt7bc92b6qXiDyZe1i0C9AzjmJckqvWO/baTXms2sX2wWWD/+8CAfcwCA\nrVxv/udVnOu//yetY9tHvXMvL2gdU4S2S781pCnv6DPvzZZx5OQ+TO3lAJ58yj9fjtpvm+IH/abB\ne7hY1IE6v5+1j5K/5QCA5TXrNqbbWM7zP+UHTj44C4k2S2W7W7W1XQa4MW/uo49wkbLnfWjwuFkv\ncftXM+QRU24h+k29VZOxX/zF+znXJCAAABfTbbFMtw2q70QBb+YKbZeu90Zodu2tXpMvUa3tzDbP\nP3TZhGCNmyE3Xhk/WuHquGazTOPP3drX8gMASNGs28htkeS2cfVa48S/DX4bhI92aG1dHi7lEc/s\nQ27MOv75kMz3vpGoI9Alew27cH+uf2E5/8YLfLgajwgAMBSLSSFU8SoaZx4Rphtne+jY2tpbbK3Z\ngE8n5C6lzZ7U8wOFhMLchz55d4JLndnJWO3fogN+LgAAliS3sY2Ckwyt7bR5Q9tl+NbWJQ20XNf2\nruDuqy0X65WFjCnyx0v/arPD599vPycBB/+OH3z3AAA4ILexk6zzWic658y4bvRZ99bWJcFMkX4q\nCXnuPzcSmywb63IThvDDNe/xj3L8Lp36LQoAMA65jZ1sGxIamnqc7aF7a/v9uJOfDw/1WYztC8Vz\ntEMdk3GoPwAAzEhuYxsFV0hykpdjjdCWZYHrtTGOJUcLQ27ssOeX8YZPGQBgJXIbeyg7i93zJC/f\n7OtGXySOtq3a2paMPrNY5uAff3EWXAPOl3GsZd5pAADDktvYwJmzCid53y05zjZFa5v9Ldnl3po/\nf7LZetLjx5p9YWnWYZz9yZ607RMHANiB3Mbqzp/QKG5vlgxtl0laW18+DW1M2qHK3huJk1beewAA\nTERuY2lRZ6vO8/5nsXWjz7Q2RvP8rVMjvYVcWO1gU7m/Pl1eBACAb+Q21hV76rZ3cVt1nO1BaxtE\nx0tKDd56fn79pO9/+IXVmtn7axgAgJnIbSwq99TTWqYvFh5ne9DaZjHRR7BxN4xqbe8/2fJZuH4/\nAADLkNtYUcGpp6sH/dvy42wPWluWPd7+a6r62kV9Nf78Jl7pO9gsJwDAwuQ2llM85qG4XS6XnULb\nZdrWtvp78EiX517wiKONtjU4aDu/LQEA4IXcxlpOLqnau7jtsG702aStrbbuYy9WFGYZpLUF8ga4\nW/TvGQCAXchtbOngJGa/4rbVONuD1javhT58LThWvFAzAQAakNvYz8+zz5TitsQp7J6h7bJEa9s8\nObV8+lMf59ydf/7mK5gya3MFt33e/LMsnQYA4J3cxlp+niAmnkkcb2f+05Hd1o0+m6W1dVlSN8jY\nS9Rz77UsMeRL6PwDndzCIG+GtbV/i3pZAQDakNtYzsHpS9Zp7rftzNzath1ne5iltaVoP/ky1OX2\n75/O2rs088f9aOc1l1nsM8oHALAYuY0VfSxlBacs79uZ9rxHaLus1druYk/Fh0ow815EcajD+K72\n7g34iswu8JDucZkEAIAhyG0s6uVkvfgc4nk7c56I7Lxu9NmMra3lQrPBI9GBen1nzk/8kXlf5YWl\nfMxD3uRefQCAluQ21hV1rjznObdxtmcztrZEzc7DAz8HiRfCT6+NBwtLG18ba5zpoZcHklpmd/KT\n3vgzDgCA3AarEdpeTN3aEidfLidOlQc8Dy8obpdL8BxqwUaGTVrD7hh3tZdOewMAALQnt8EiVLaP\npm5tWQpOxac4CS8YTzv/vCq1tthqmTX6xxpy23r6q2+0DQAgltwG0xPavlmjtYWsqfz2w4k7EO7n\nk3quh40XhJpro72CQc7AO89qbQAA4eQ2mJjbIBxYo7XdBa6pnOg8vEtxq9fa2h9JrW0uuW9yry8A\nwMjkNpiPcbafVmptd13WVFaVe0PGNsVtognBYyFdtddb6PhxFx7FajzI+XhQAADCyW0wE6EtxXqt\n7a79qfgI5+FdZtxiJwQHd/Aqlx3wkLvlbmv8pdMAAKSQ22AO1o0mWrW1tdfgPDz9hoyX/+3P/f9t\n1iNCHqjSkTzfZeq9xGeK22I1s8DIS6cBAEgkt8HQjLNlSWxt82oWm5qdh+feCOL+K42j2xnDFo1h\nd4xL/eLm1QcAqE1ug0EJbbnSW9vso21VT8XHPw+forLdjXkws/aq+M1WNuD287HGPKQ11PuY73MM\nAQA6kttgONaNFtintd1VOhXvch4+0ahaFlEj13rvgZPCPxrekwAAzchtMArjbMV2a213safi58/D\nU/ZkkLP9x25sOCRYsGNdbpf50bBHtarT+NV1AAAgAElEQVSQT/qehw4AoCO5DfoT2s7Ys7U9nD8V\nP3Menvu4zz//8rhdLg9f40Fbdo3c/W/cXNLXkw6S80ZW3IiFNgCALuQ26EZlO2/z1vbwfEbdZsrs\nfB95vt/oXYNVpe9PPLa4rZo26sXQ9M2uemxzfTwOzzcSAQBgBHIbdCC0hdDaPqp9vh2bXT5Gt8aX\npes7IdjMUDtZcLTf3yo8OCwAAKOR26Apt0GIorW1V2/u7GXVYZfL0r38WOKjd88c41xY7aP39aQn\n91Z0AwBgCnIbtGCcLZbW1l7tpvPeZfoOnQk6z868CjXeOaIbAACDk9ugLqEtnNbWXpv5qY9X1s+9\nLN1lvwqTOOCWfuOC918cU/EzAgCA2uQ2qMW60Rq0tvZa1pbjgPJxWaLgcskpbpecIzZsaHvwHgAA\nYExyGwQzzlaP1tZe++CSPrIkspT5majGr2wvjLkBADAauQ3CCG1VaW3tFWSXj9UjdzvqSQPTNbVj\n3jMAAAxFboMA1o3WprUN7rh0PP5reuJRT8jlPQMAwDjkNihnnK0Nra2LGvclOH+zUYYS/oJ+vDxf\nOsUNAIBByG1QQmhrRmvrouo9QGvfSZM2Al+db5sqmIsEAIARyG2Qx7rRlrS2kZ2pLYlTUYrbmBqE\ntvcfSyxu3jMAAIxAboMkxtna09p6SekaIUUjvaHwU7ODGfXSl/2KuUgAAKYgt8EPQlsXWtvItIw9\nRb3uJ+ciJVoAAMYnt8FnKltHWtvIYlvbz3piUmkEBy9Bbvw6/2qmFDdvGwAA+pLb4JXQ1pfW1lf7\n0SHzSs3kHurwYhU4H+c9AwDAyOQ2+IfbIHSntQ3OxNDIUiLUx1fw8Vu5r2/HeKe4AQAwMrkNjLON\nQmvb1nE6sTAwyrcjWXZ4+w7K/eRtAwBAR3IbWxPaxqG1jU+8GMq9dhXMo4W8jiNMlhlwAwBgWHIb\nm7JudChaGxz71pVe/rzNbQTa3x4BAADmIrexF+NsA9LaxtFxVsik0jdZhyXxh88Ut6FeJm8bAADG\nJLexC6FtTFobfFS7IhWvRZ2Iy7cBANCL3Mb6rBsdltYG71omrfQgNVdoAwCAvuQ2lmWcbXBaG7xr\nX7Uej/ixu53fH/NlAABsSG5jQULb+LQ2eNd3gsz8GgAARJHbWIfKNgutDd6pXQAAsAy5jRUIbRPR\n2kbW8T6Pm8emzZ8+AAAsRm5jbm6DMBetDd5pbQAAsBi5jSkZZ5uR1ja79LtYkm6B1nY8FOltAwDA\nhuQ2JiO0TUpr48Bxclo41sze2gZ/aQbfPQAAFia3MQ3rRueltS3DpFIgre282Y8hAACrktsYnXG2\n2Wltc2l/t4Q9i8liz9p6UgAAeCa3MS6hbQFa23qkk/OGam3FgfX5t7q8JYY6jAAA8ExuY0TWja5B\na1tVYHH7WUzWS3sFkejlIMRmpvureXKbP3+9faVd750DAMBE5DYGYpxtJVrbvFLiS0g92XA6Kesp\nfzvCz38ecgxnfCFm3GcAAPYhtzEEoW0xWtsOTha3lFyy2IBSeiFKf+Ltr7VXrOVQJAAA9CW30ZPK\ntiStbQGJEacsoGglx3IP6f3npziqzZaULhZqAQCYjtxGH0LbqrS23dwrT3rdqDHhNYXaOWyWMbcG\nQ5EAANCd3EZrboOwMK1tJVn55vGT30pKbiVZrLWlO/PEJypul6Jnmvjstn3zAAAwDrmNRoyzLU9r\nW09BvgnJPevlkmYVbJbidskcc9t2KBIAgEnJbVQntO1Aa1vVRPmGu/CX7CVgBW7851Bk7MMBAEAz\nchsVWTe6Ca1tVV1Kh+mk80KK27cX4vHnNbrbSd48AAAMQm4jnnE2PtLaptBxmGjVVjLpfNbzbn98\naUa7I+qq7x8AAGYktxFJaNtQ4mib1ja+vt1EK7mEHoTYJaXfNnW7jRLdvH8AABiK3EYM60b3pLWt\nQSuhzOMeo32v8ef9AwDAaOQ2TjHOtjOtbQ2G2saRdbPOcXgLAQDAi3Vy2/XL/96/+V/idQhtm9Pa\n1mAiaWHL31XWWwgAgGFNn9u+Vbb3H9Ddolg3ita2BjceZV7eSAAAjGzu3Paztb38sOJ2hnE27rS2\nNTRubdt++649X9bFtu8lAAAmMmtuywptL78luuUS2njQ2tbQvgFNelWy9nY4UI8nmPU+XP6wAACw\nkilzW1lre/51xS2FysYLrW0NBd+g71+ZhrY47/h95S9qAADmNV9uO9naSCG08U5rW0PUPFHBgNIO\nc1vvCu5XMM6BetmNqL9+D57gIE8cAABOmi+3vfs4qnZc5Qy4feM2CHykta0hPZekf0HefzJxy+OE\nJA78bGH+2QsAAI5NltueI9pxL7v/14Poprg9M87GAa1tNwVfjVnRjZ9CumTIquGDH/NyAwDAN5Pl\ntofEUvYzuiG0cUxrW0bKF+HJxJOycNKAW6LGB0pjBQCAQDPltkc1y51Ku91uits760b5SWvbSkjc\nKbhUGd80K25nHsUrDgAA72bKbeH2XE9qnI1EWttKWgaRn/3FgFu64mNV4zp9B1tQ3AAA4Nk0ua14\ntO3xWwbchDbSaW27ie1f+suzk0ejap2M2rJXHAAAnk2T2+42HEYLYd0oWbS23bT/ZjXgluVeshKP\nWMu5tpetKW4AAHA3WW47Y8MBN+NsFNDaCCG+hHscz4+ZzNEGAIBxzJHb7pnMaFs6oY0yWtuSjkOM\nb9YGYuPjsGVNYwUAgLs5cpvQlkhl4wytDQAAAM6bI7fxk9DGSVob4cw6PRvwaNS4gl7K0/QvaAAA\nLG/r3LbG0JzbIHCe1ratJb4FpzFgcQMAAGrYOrdNzTgbUbQ2unBz0hF4FQAAoAa5bT5CG4ESWxsQ\nYsABN8UNAADCbZTbrv8+xZlxJal1o8RKb21G2yDKgMUtkAu3AQDAZavcNi/jbNSgtUEvoxW3qAG3\noZ4UAAB0tGluazPadk078zjYGaGNSrQ2utt8ymm94jbU0wEAYDeJBaaZTXPb+KwbpR6tjQfX7epo\npeI21BMBAIDudsltz5lz5Ku2GWejNq0NxjFgcbtkDh4Otf8AADCIXXLb+IQ2GtDaaEmISXFvW7HH\n6mTFS4xuXl8AAPhmi9w2+GibdaO0obXxkfWkI4iKboEv5WNnXrapsgEAwE9b5LaHxq3t+OGMs9GS\n1razLisWRZkCZ6Lby184gS964Esp7AIAUEli8Gl2R4X1c9vjUI4z12acjca0No61H3Ab5vt4RM8H\n5/h/DDiMAAAwpsVz21CtzTgbXWhttGe0LcoAf3cBAADZknJbs1m7hxHqWCChjV60Nu5+Li0MHHDT\n2gYx2m1P1/qLHQAAjqw83TbCaJt1o3SktZElpLil9B3ZBQAAWNuyuW2Z1ia0UUZr40XKrNPJ4jbU\nLBWJRhuCAwCABayZ20ZobecJbRTT2ihWXNwSk83M38rzyWqsVaOb1x0AgK0smNtmb20qGydpbXyT\nOMd0/5n0b9D0TDPnt/L67sWtQXQDAIBNJOW2ibrV1K1NaOM8rY1j6SsHHz928G0qzYwvt7F+e7nP\nvNYT/oUMAACnLDXdNm9rE9oIobVRQ1RTm+2LeR25jfXjK/X8h1lvCa87AAAbWie3zdjaVDYCaW0k\n6nJp/Hm+mPk62GiYEQAAEq2T2+5maW1CG7G0NrI0Lm6TfDGvrOwVP/8m8dIDALCnRXLbfbRtitYm\ntBFOa6NAs+I2wxfzFjRWAABoZoXcNkVrU9moRGujWIM7UY79xbydLuuIAQBgQ9PntpDWdr1e69U6\noY16tDbOq5RghLYxtSluXn0AADZXMTM1ENXazm/keVMPUx9bxqe1ESuwwmz45ffz6I12TCpFt9Ge\nJgAAPGvWbSaebgtsbTAdrY1wIWtLt6otWcfq+YdHOEo1xtxGeF4AADCCWXNbbGszhsZctDbqKYtu\n9b5Ex5waOxmqrtchytRjH9yBFAAAYk2Z2x6ZzGwaG9LaaOBjPXl849ZuK2VTY22KT9RfO413+9j5\nwcaPvzvCUwMAgC7my23hic1oGxPR2uiowZfl+eJTdSdr/BPPIJNul9Bht/ftDPIcAQCgjclym3E2\ndqa1sbDYxBMed6r+5dMgFGZ535PzT3+05wgAAFXNlNtqtDajbcxCa2NVlUbGLnFxp80/9Iwz5vYs\n9rmLbgAAbOKv3juQylwbO9PaWFWDqbERNjLgY6WotD+jPU0AAAg3R27T2tiZ1saqGny1n7+FaGPj\n/HU3fgkFAIBhzbGY1JJPtqW1sapmwaV4AWPZHr48UMFGuq8qbbZ49mJhKQAAi5ojt8GetDZWtd5w\n07dsFH67z9pm2U8AABiZ3AaD0tpYVZepsdyRsfTtJ272/mOJm+0+4NbMPs8UAICtyG0wIq2NVWVl\nsoMQUzA1ll52ErdZ0InSo1uXDlVQQt93snYJBQCA8c1xqwTYitYGl5ypsfRYE7hS8kwhGrMu5ZbQ\nb0f+4D+FPDQAAIxPboOxaG0sLH1qLDdIBQaslJ08/3ApW2gZobIWz9YooQAAsBK5DQaitUFxoEmM\nO+cbVlRCmi5FleWzZq8LAACMQ26DUWhtrG2cqbFxtj9IcWvw0ihuAABsRW6DIWht0Gxq7CDrjFZ8\nBtmfkJdmkLYIAAANyG3Qn9bG8n5moylaTI2d7P7EW740Z0ooAABMRG6DzrQ2CE9O3RsWAACwM7kN\netLaoJLj4vZxiup4tKpewivY1WaUUAAAKCC3QTdaGzu4Xq0QHNeAL82AuwQAALn+9N4B2JTWxsJy\ni8nzz5t+Gkel1+J209QAAFic6TboQGtjVedn2QKn4ZQ7AACgC7kNxqW1MZHYRaOjLUHdsNxVfcob\nHk8AALYit0FriaNtWhsTqZTGqhY3OQ8AAKhEboOmtDbWs08Uq2eTpwkAAJuQ26AdrY31NOhEIyws\n7b4DW3G0AQCYndwGjWhtrKdlFpFgAACAWcht0ILWxnr0LypxJTsAAGYnt0F1Whvr6dLaYh9U0wEA\nACqR26AurY31ZGWvn1UrK3tVzXzHe1LvoY+3LAsCAMB05DaoSGtjPenV6XZLTUXpP5m1A5a7nuGG\nswAAUExug1q0NnZWMJOVFd26qBGJhCcAAFiP3AZVaG0sKaUNvVezrEWaKcUtZTfKMtZovW+0/QEA\nAFLIbRBPa2NbIXmoQWMqfojYYbTuo21dLlfnWnUAACxPboNgWhuranmvgJ/N5XhnprjuWPfWBgAA\nVCK3QSStjZ0dNLKT+aylqNWs57cwwpxX+OsyzgsNAAD1yG0QRmtjZ+fbUMFF3FK28y4kY53JRkO1\ntpYltM1LAwAA3cltEENrY23nm0vB1FjBlcVC2lBi9Llesx+u4FdGELLPMz5xAAAoI7dBAK2NzQUO\nJRVHmcSSlbir6c8o8XGzQlvjIa8G62eHGugDAIDa5DY4S2uDRFWnxsJl1Z/7Pr/vxrc/j3rcls6U\nUAAA2Mqf3jsAc9PaoJJ7o7ndIm9C2qBkTZqWfh7nu8eLkmjYgT4AAKhKboNyWhtcMkNJYtZ56Nva\ncvf2pFmS0+OYfNvhSZsjAABEkdugkNYGZRo3rMeDFv/iJvGo4JlGHZlZOiMAACRy7TYoobXBGQPe\nCuD412vvcIOHSNyNTR4UAACqktsgm9YG5zWLLFEPVG+Hh+pNc5VQAAAYk9wGebQ2iNIgtcQ+RPgM\n2iBDbS+mK6EAADAauQ0yJLY2IFHVkbFKGw/Z8pih7WG6EgoAAENxqwRIld7ajLZBunt2ib0dQbNa\nVLDbs2SmGq/L85YBAGBhchsk0drgm+s1ZtrrsbWQ7bTx7eFensW8gSk2us17HAAAIIvcBr9pbdDM\nGlNjQ+3MebdbQHFb7JgAAMABuQ1+0NqgvcRhNwWnmeLxQ68RAAAbktvgiNYGd8fzTSHrST9ultF8\nfKEfr5S4BgAAF7kNDmhtMDJlZxxeCwAAePZX7x2AQWltkCV8Es1oGwAAMCm5DT7Q2uDdzwmmwED2\nc1PGqQAAgGHJbfBKa4NiIcXNXBsAADA1uQ3+RWuDAykzZSdjmdYGAADMTm6Df2htEKI4mSX+opWk\nAADAyNyZFP6mtUGK2y0pit1/Jr2LpRe6g2264hsAADACuQ0uF60N6nj0rzONLPEhcn9YegMAACqR\n20Brg6Ro9ehTiQNuudtP8dzIQjqd6AYAAIST29id1sa2ziSzguJ23iONBT606AYAAIST29ia1sae\nzueqXq2t0uNer4obAAAQxp1J2ZfWxp7al7Lzqra2u+t1yiMDAAAMSG5jU1obG5q0KDVobQ8zHh8A\nAGA0chs70trY0Iwh6XZr2truZjxQAADAUOQ2tqO1saEZE1KNGyMkmvFwAQAA43CrBPaitbGh6eLR\n810LCnb+400PCm7D6uYJAABAGbmNjWhtbKhLaytbAXoybx3/esGsnOIGAACUkdvYhdbGsFICUFn3\nCRkNKw52P6fMfj6pxIfOOjjtLwYHAADsRm5jC1oboylY23iXnpayHuJgs7FzYeH7XxYib7ek7Rtw\nAwAACshtrE9rYygn56oKutux9O1kzYW1CVVnHiKxuAEAAOSS2yaXtS6r6kZGpbUxjti4c9yz6o2G\ntVmMWW+B7csWfj6QATcAACDXX713gBNeThPLTn9DNjIqrY1x1PhsXa+fN5vYqk6Ohv1U9euk/XAf\nAABAIrltWsUn2eEbGZXWxiC+RbHA7ecKaUz1itvP34ptZFF3bAAAALiT2+Z0cPKXdTHz8xsZldbG\nINp8mHp9ZI2GAQAAvJPbJpRyqaE2GxmV1sYgWn6MHo812mhYuBqPqBsCAACB3CphNiE3BRzqzoLR\ntDYG0T5Zp3xk23+m34/DhN8rAAAAGeS22aTcSO/u25l3egOY8JxYa2NzXcZS07+W7r79cMo9T+t9\nLR0/izn/9QEAAOjDYtIJpZ/zvZ87am2Xy0Vro74xV2MP/rGufU8JAACANuS2OZUVN63tcrlobdSn\nGQEAAOxMbptWbnHT2i6Xi9YGAAAAVCa3zezMqtLz2xyG1sZQhh1tq/ThbrkCtPb304TffwAAwIjk\ntsnFnh1OeK6ptTGUYVtbJbs9XwAAgBTuTDq/3JsCHmxnNlobyzj4/ElaD7VvD+pQAwAAIeS2JZwv\nblob9JDyybv/zGglaLT9AQAAGIfctoozxU1rgwhZH8Hcj91Q0a1sN16e8iDPBQAAIJxrty2krJpp\nbdBc8cduws/r3973/Hb7+/8AAAAWI7etpWxgZipaG7M7+bEr/vWoabKC7Rzvc1Z06zUTN+GXJQAA\n0I3cxky0NmYXUm06pp96tav7pJvFrQAAQBS5bS2554tTnV9qbcwuMCetOmyV8rym+t4CAAB2JLct\npOwcdJIzV62Nwf38JIUHsoINnvy4t/m26FISJ/kiBAAA5iC3reLMyeLwJ5paG2zlZ3GL/dJqn0oB\nAIC1yW1LOH/qOXxxS6G1MaxKvablgFvxLw7eqpb48gMAAMYit82v4+0Gm0gcbdPaYCWNB9wODJ4L\nAQCAAcltk2u8pKo5rQ3CjfdBL3S9nl1Gv8yhAAAAhiK3zSz9TDF9PGOks0+tDX4qm72aYjQs8Xer\n3iTGaBsAAFBAbptWbmubrbhpbVBV1gd9jG+Fr7Lm1NJ/WGsDAADKyG1zKptrm6e4aW3QQO0P+vlc\nlbWFnx3N6lEAAKCNP713gHxn1pDebqm/fr32Gu3Q2lhPv8/TD/fvgxr71uv5RgW1MV8vAABgCqbb\nZnP+em1jz7hpbZAl5GN6H/sy+fWgtQEAAGeYblvU8cli+oxbW1obCxt2wO2Z0bDL5DsPAACMwHTb\nbFJOBFv+TBytDXL9rGNdytHUuWrqnQcAAAYht03o5+Ra4+1E0NrYQZeh0sb9aOpcNfXOAwAA45Db\n5nT+umyx2zlHa2MfgcXt/IUcw02dq6beeQAAYChy27Q+3nW043ZKaW3sJurmBllut+qf7HlzVYOD\nAwAAbEVum9nzCeKZk8Wo7eTT2tjTyeJW/OuVPt+T5qr7bs+45wAAwODcmXRyUWeKPc44tTZWknu/\n3+IblZ5cQ3r/wyFvTZzt/QkmPi+JDQAAqEpuow+tDe5tKD39BDay2OhWnA5TtpzlZTdyjzAAAEAI\nuY0OtDZ4+JmE6k2irTTp9pHQBgAAdCG30ZrWxqpy15M+C29e6aXp408+709Klasx4LZwBwQAANYm\nt9GU1gZTGH8ubPw9BAAAtuXOpLSjtbG8QRpQjd34uc3YYTSjbQAAwLzkNhrR2tjEIMWti8B7LwAA\nAMxLbqMFrQ2aqdf7UrZ8vpSlbGHnpgkAAIxPbqM6rY3ddIxBI3SoM8VNawMAABYgt1FXYmuDxXRJ\nQg0eNPEhrtfs6FbwKwAAAGOS26govbUZbWM9qw5hpT+vxIKWFdpWPaoAAMBK/vTeAZaltcHt1m5i\na9gO9TgCL3tYcGSGfY4AAADP5Daq0NrgrkFxax+hyp6UtaIAAMAmLCYlntYGz6rmsF4DX40f93Yz\n2gYAAExDbiOY1gbvKqWivgVK/wIAAPjIYlIiaW3wzT1ORS2oHCR1LblUFgAA4CS5jTBaG/x0PrqN\nlp9iM+LHjQMAAMxFbiOG1gbpnitSSqgavzrVGHMb/1kDAAB8JLcRQGuDYstEpccTOd/dljkmAADA\nnuQ2ztLagGfFk24qGwAAsAa5jVO0NuBd1mpZlQ0AAFiM3EY5rQ34SU0DAAB281fvHWBWWhsAAADA\nO7mNElobAAAAwEdyG9m0NgAAAIBv5DbyaG0AAAAAB9wqgQxaG6zhcbdQ9zEAAAAIJ7eRSmuDeV2/\nfHw//rkGBwAAcIbcRhKtDWb0rbIl/pbuBgAAUEBu4zetDaZTFto+bkR0AwAAyCK38YPWBnMJCW3v\nGxTdAAAAErkzKUe0NphLeGtrsGUAAIDFyG18pbXBXGoXMcUNAAAghdzGZ1obzKVNC7teRTcAAIAf\n5DY+0NpgLhIYAADAOOQ2XmltMJf2rU3dAwAAOODOpPyL1gZzyS1fBzcYzdrU9epepQAAAJ+ZbuMf\nWhss7Hb7Ech+/sALM24AAAAfmW7jb1obTCcxeGVFtPsPS2kAAADFTLdxuWhtMKGUIpY7sJb7i6oc\nAADAO7kNrQ3WdP7aaq7OBgAAUEBu253WBjP6OVYWVcp+bseAGwAAwAu5bWtaGwAAAEAsuW1fWhtM\nqtloW+LWDLgBAAA8k9s2pbXBqmpccM1F3AAAANLJbTvS2gAAAAAqkdu2o7XB1I5XbtYbQzvesvWk\nAAAAD3LbXrQ2AAAAgKrkto1obQAAAAC1yW270NoAAAAAGpDbtqC1AQAAALQht61Pa4NN1LtPQpvt\nAwAArEFuW5zWBgAAANCS3LYyrQ22ck39xA+6fQAAgDXIbcvS2gAAAADak9vWpLUBAAAAdCG3bU1r\nAwAAAIglty0ocbRNa4MZHd8etN7l1Y637KalAAAAD3LbarQ2AAAAgI7ktqVobUCNATf3JAUAAEgn\nt61DawMAAADoTm5bhNYG+/h5obTYYbSfW3PhNgAAgGdy2wq0NuBFVHGzjBQAACCX3DY9rQ02lDJQ\ndr6UpWzBaBsAAMALuW1uWhtw4ExxM9cGAABQRm6bmNYGO0scKyurZom/ZbQNAADg3Z/eO0AhrQ1I\ndG9n4XlOawMAAPhIbpuS1gZcLpfbLaOOPX7yYyazdBQAACCK3DYfrQ14yCpudyFlzWgbAADAN67d\nNhmtDXjRvnxpbQAAAAfktplobcBHLfuX1gYAAHBMbpuG1gYcaFPBtDYAAICf5LY5aG3AT7db3Rym\ntQEAAKSQ2yagtQHpakSx2iEPAABgJe5MOjqtDch1T2PuQAoAANCF3DY0rQ0odjK6CW0AAABl5LZx\naW3Aec/V7Gd6k9gAAADOk9sGpbUB4dQ0AACABtwqYURaGwAAAMCk5LbhaG0AAAAA85LbxpLY2gAA\nAAAY0y7Xbrs+XSH8Nurli9Jbm9E2AAAAgDGZbhuF1gYAAACwgC1y2/No25i0NgAAAIA1rJ/btDYA\nAAAAmlk/tw1OawMAAABYyeK5bfDRNq0NAAAAYDEr5zatDQAAAIDGls1tWhsAAAAA7S2b20amtQEA\nAACsas3c9hhtu92Gy1VaGwAAAMDCFsxtWhsAAAAAvSyY2+60NgAAAADaWy23DXuHBK0NAAAAYAdL\n5bZhl5FqbQAAAACbWCq33WltAAAAAPSyTm4bcxmp1gYAAACwlUVy25jLSLU2AAAAgN2skNvGbG3p\ntDYAAACAZayQ26amtQEAAACsZPrcNvVom9YGAAAAsJi5c5vWBgAAAMBQ5s5t89LaAAAAAJb0p/cO\nlJtgtO37jUmfb1o67v4DAAAADO/RiAYx63TbBK0NAAAAgP3MmtvutDYAAAAAhjJlbhttRBAAAAAA\n7ubLbZaRAgAAADCsyW6VMFlruz3+/xn2FgAAAGBCiZmo2XLJ+abbpqO1AQAAAOxjpum2yUbbhDYA\nAACA/STltva3JngPatO1NgAAAAA2ZDEpAAAAAISZI7cZbQMAAABgChPkNq0NAAAAgFlMeauEGtvR\n8gAAAAA4Lym3SVEAAAAAkGKCxaQAAAAAMAu5DQAAAADCyG0AAAAAEGaCWyWcvHLc+40RXIoOAAAA\ngEpMtwEAAABAGLkNAAAAAMLIbQAAAAAQRm4DAAAAgDByGwAAAACEkdsAAAAAIIzcBgAAAABh5DYA\nAAAACCO3AQAAAEAYuQ0AAAAAwshtAAAAABDmT+8dqO52u/XeBQAAAAB2YboNAAAAAMLIbQAAAAAQ\nRm4DAAAAgDByGwAAAACEkdsAAAAAIIzcBgAAAABh5DYAAAAACCO3AQAAAEAYuQ0AAAAAwshtAAAA\nABBGbgMAAACAMHIbAAAAAISR2wAAAAAgjNwGAAAAAGHkNgAAAAAII7cBAAAAQBi5DQAAAADCyG0A\nAAAAEEZuAwAAAIAwchsAAAAAhN/GEXEAACAASURBVJHbAAAAACCM3AYAAAAAYeQ2AAAAAAgjtwEA\nAABAGLkNAAAAAMLIbQAAAAAQRm4DAAAAgDByGwAAAACEkdsAAAAAIIzcBgAAAABh5DYAAAAACCO3\nAQAAAEAYuQ0AAAAAwshtAAAAABBGbgMAAACAMHIbAAAAAISR2wAAAAAgjNwGAAAAAGHkNgAAAAAI\nI7cBAAAAQBi5DQAAAADCyG0AAAAAEEZuAwAAAIAwchsAAAAAhJHbAAAAACCM3AYAAAAAYeQ2AAAA\nAAgjtwEAAABAGLkNAAAAAMLIbQAAAAAQRm4DAAAAgDByGwAAAACEkdsAAAAAIIzcBgAAAABh5DYA\nAAAACCO3AQAAAEAYuQ0AAAAAwshtAAAAABBGbgMAAACAMHIbAAAAAISR2wAAAAAgjNwGAAAAAGHk\nNgAAAAAII7cBAAAAQBi5DQAAAADCyG0AAAAAEEZuAwAAAIAwchsAAAAAhJHbAAAAACCM3AYAAAAA\nYeQ2AAAAAAgjtwEAAABAGLkNAAAAAMLIbQAAAAAQRm4DAAAAgDByGwAAAACEkdsAAAAAIIzcBgAA\nAABh5DYAAAAACCO3AQAAAEAYuQ0AAAAAwshtAAAAABBGbgMAAACAMHIbAAAAAISR2wAAAAAgjNwG\nAAAAAGHkNgAAAAAII7cBAAAAQBi5DQAAAADCyG0AAAAAEEZuAwAAAIAwchsAAAAAhJHbAAAAACCM\n3AYAAAAAYeQ2AAAAAAgjtwEAAABAGLkNAAAAAMLIbQAAAAAQRm4DAAAAgDByGwAAAACEkdsAAAAA\nIIzcBgAAAABh5DYAAAAACCO3AQAAAEAYuQ0AAAAAwshtAAAAABDmT+8dAAAAACDe9fr7Z263+vux\nH7kNAAAAYB0ple3jD0tvUeQ2AAAAgBVkhbZvvy66nSe3AQAAAMztZGh735TodoZbJQAAAADM6nqN\nbG3Pm6WY3AYAAAAwpapRTHErJrcBAAAAzKdBDqs0Orc8uQ0AAABgMi0rmOKWS24DAAAAmEn7/qW4\nZXFnUgAAAIBpFJSv99uMymdVyW0AAAAAc8jKZO+V7f0/pW/wej3aIM8sJgUAAABYyu2WmsbSf/Ji\nJi6Z3AYAAAAwgcTaVTCDlhXd+EluAwAAABhdvdaW9bsG3FLIbQAAAAArOD+hZsYthNwGAAAAML2o\nUvZzOwbcfpLbAAAAAIb2s3DFTqWZcTtJbgMAAACYmDo2GrkNAAAAgH85TnjWkx6T2wAAAADGddy2\njLYNSG4DAAAAgDByGwAAAACvzM0Vk9sAAAAApqSIjUluAwAAACCPuyUckNsAAAAAIIzcBgAAAABh\n5DYAAAAACCO3AQAAAEAYuQ0AAACAPG6KekBuAwAAAJiS24OOSW4DAAAA4JWWV0xuAwAAAIAwchsA\nAADAuI6vklZpBs1o2xlyGwAAAMDE2qcx90k4JrcBAAAA8A+jbSfJbQAAAABD+zlNFhjItLbz5DYA\nAACA6TXLZFaS/iS3AQAAAIwuJXKdLG7Xq9G2GHIbAAAAwCKKe1niLxptSyG3AQAAAEwgMXXlDqkZ\nagsntwEAAADMIX24LDGiZYU2o22J/vTeAQAAAACqCBxb09rSmW4DAAAAmEaX7KW1ZZHbAAAAAGbS\nOH5pbbnkNgAAAIDJNEtgWlsBuQ0AAABgPg1CmNZWxq0SAAAAAKZ0z2GB90N42TJlTLcBAAAATCw8\njWltJ5luAwAAAJjbI5CdnHQT2kLIbQAAAACLKFteqrLFktsAAAAAlvIxn700OImtHrkNAAAAYFCJ\nc2op7Uxfa0ZuAwAAABhO1oJQk2tDkdsAAAAARnHyXgfPGxHdevmr9w4AAAAAcLleY1rb8wbpQm4D\nAAAA6KxSGlPcupDbAAAAAHqqGsXCh+b4SW4DAAAA6KZNC1PcWnKrBAAAAGAFM96ds2UFu17nOCYL\nkNsAAACAWR3kqo//aaje1H7iTHFrQ24DAAAAJlMcqh6/2L06FTyFj/ucux3FrQG5DQAAAJhG1ETY\nfTu9wlPWszjeycd/Td+m4lab3AYAAADMIXz1ZUh0S9mrsofI+q37D7slwgjkNgAAAGB0VStSwbRX\nwRLOXMWFLuWxDLhVJbcBAAAAQ2swsZWenxrszMkQZsytu7967wAAAADAV82y0c8Hul6XalgrPZfR\nyG0AAADAoBonoYOHa7YnUWs8rRXtyGJSAAAAYERlheslMxVcZO3kFs6IbWQ/r+PmCm6VyG0AAADA\ncHIj17ds9Pjz9A0+R6h5WxsdWUwKAAAATOx2SwpVWTHrXtkWuLqZhNeF3AYAAACMJbFzJYa2sp9v\n39oWqHvcWUwKAAAAzKd4buvnFc2KN/vu/JXjzjt+vi7fVoPcBgAAAAwkJVGdLET3Xw+Jbsd7cvLK\ncUzKYlIAAABgJoPUqKylqQVXjmNechsAAAAwip+lKbC1ndnUIMmPMW23mPT69sG9+YgAAADADBpf\n16zZbryzpHRqW+S298R2J7QBAAAAWbQEflo8t30MbSobAAAADOh40KzS2XzWgJuiQIplc5tFowAA\nAECgxl3BetJ5LZjbTLQBAAAA6cqu4AbfrJbbDLUBAADAerqf3HffASayTm4z1AYAAACsJGQ9aZcr\n4m3ur947EENrAwAAAEamUuxjhdymtQEAAAD1zNsYXJOui+lzm9YGAAAAwDjmzm1aGwAAADCLxsXi\n52ibglLJxLlNawMAAAD4yDLSjmbNbVobAAAA7GOZeDROuhhnT9bzp/cOAAAAAPS0TMu7W+zpzGjK\n6TajbQAAAMCkqgaMxNYmolRlug0AAAAYwu12VIuu11OR6H3LUySn9GedPtQ2xROf2ny5zWgbAAAA\nkOi43/VyHBZfPH7yY/ywdHRA8+U2AAAAYE81Rr1iHzdlU11+98HAUgOT5baPo20AAADAJn6Wr2HL\nwQg7prW1MVlu++hlJem3JGfBKQAAAAwuZZXlQXGrl7TODLiNENouWltDM+W2n6Ntxz/w+K+6GwAA\nAEztPX4NkrTeDbJjWkhLf/XegRjX6zV9nakVqQAAADCsgquztTnRz32U61Vr29R1olGv40z28YkU\n/MoZZSFvopcAAAAA2kg8w866xWeILvdqKLZJchgtyMy0mPSbg6Pz+E8m2gAAAGA97U/3Uy7iNkiE\n2KS1DWiaxaQnb4BQMPsGAAAA9DJyKjrOCd1jw+329//RyzS57aOsqT/FDQAAACYycjD6lhP6ZgaV\nbRAT57aCFbaukgYAAAATGfk8vt6dEB7jaSM/fQ6scO22k67XWveLUPcAAADgpJY3Q7ifx2c93OOH\no/bzpSW0vxfEjBILTLM1jhNPt5WRwAAAAGAuDU7ln0fJysbKarS2xx/OdTtUtsttAAAAwHSqFrdv\nkWsoo+0PB5IWk7a/n0DjGbR660kBAACAEAUrPRO3OYifO5OysPR6HetJ7cl0GwAAALCjlLzVTOJj\nSWlT2DG3GWQDAACAbWXd9LPxZeMSf/6YK7h1586kAAAAwPrGnL0Zc684SW4DAAAA5nA8t1UpXaVc\nMa1ss2d+1wjbyJJym9WXAAAAACFUluVNc+02yQ8AAADoIqRJZF0zLmVrB8y+9WUxKQAAAEAVZof2\nNM1027urVAsAAABcLhdhi5FMnNsCWakKAAAAQIiZcpsoBgAAAHAnkwxrptwGAAAAMAs5bFtz57ay\ny7e56BsAAABQm/ywrclyW431pNaoAgAAANOR84Y1WW57Z1QNAAAAkAcYx3y57eQw2kueM9oGAAAA\nHNPyyDJfbru8NbLiATetDQAAAIBYU+a2S2lxe/4xrQ0AAADmcnwqP+AMWr1dOt6y5tHXrLntkl/c\ntDYAAAAg14AVj8FNnNsun4rbx+j28udaGwAAACwpPI393ODPxlCj1imAg/vTewfOurez55p2MOYm\ntAEAAMDUbrcfsel6bb2UcrRdEj+6mz633T062rfWJrQBAADAJs7nrcTxsS6xwWjb+BbJbQ+yGgAA\nAKzt5zTZpbS45Zas9J+PGnDT2qYw97XbAAAAAD7KKlPXa/WSdX77KVswhjSC1abbAAAAgOWlDLhd\n/tenjgtUy3mxlP05+MWftLZBmG4DAAAAVnbQqrqszay3ZHUo94HBSXf+JNNtAAAAwHwSB9zunn/y\nPgLWNwM9Hv1gHi13D7uPtn3b4Y9/3n1vq5LbAAAAgCllFbeHoeatonamb7068yos2d3kNgAAAGBW\nZcWNECFHvvh6diOT2wAAAICJbV7cuoSq8AO+WHST2wAAAIC5NShuLyVokMC3Rmt73vIaxc2dSQEA\nAIDpVc007xu/3f7+v44Wa21ttt+G3AYAAACsoEb/+rnNXsVtydbW8lGqspgUAAAAWMejQ52vNolJ\n6/5jzSJRr8DXsoLNvqrUdBsAAACwoOJeU7ZQtEEe6rh8tf3E2dQzbqbbAAAAgDWlT7qFZKyUOzaU\n3dWh76hX7g4f7G3WpuadcZPbAAAAgJW1aW2PTR0/3EFCev7FcTJTViD7udu5C28nLW5yGwAAALCv\ncWrOOHtSIGvnG1/trj3XbgMAAAAIM3U1e5FSxIqvKJf4WzNWObkNAAAAWNZxrOmSxmbpR4mt7YyO\nN3+oSm4DAAAAiLRkQnrX7GnOEigf5DYAAAAAulmvTsptAAAAwI6qVp7ZE1LL27mmbG2uATe5DQAA\nAIAMs8fE2uQ2AAAAYE1zjURtbqWEJ7cBAAAA8I8Bb+c6F7kNAAAAgP6OQ95Es4p/eu8AAAAAQBW3\n20yNJlzj2x3wILcBAAAALCIrLz7/sPQWyGJSAAAAgOldr6dG+RJ/V5VLYboNAAAA2NH1WjEetVzE\nGvVYOy+8jWW6DQAAAGBWGtmATLcBAAAARGqTwIS2YZluAwAAAJZ1vFy0S7EKWcHaq7VpfCnkNgAA\nAIAwDYKU5jU4uQ0AAADY13TparodjjLRTVFduw0AAABY2e32I1EF3qL0Zws7+UBlre3lQYcNdsPu\nWC65DQAAANhdSHEbrRZ9e0aPPy/b4cA6uSqLSQEAAIDFpeShk7Es5debjbbdbkmPlfhjbYwWK8+Q\n2wAAAAAulxPTXuPcHqGgoBX8Svs0Nk4WTCG3AQAAAOtL7DW57Sxr4qy2Mw/Rt7itNNp2kdsAAACA\nTaQXpXt0O2hAP3+g+KG/PVzthyjYQlQjW6y1Xdwq4f/bu7ctxXEsiqK4R/z/L7sf6BFNQmBssyXr\nMudTVcalSPKUUqyQDQAAAMA7kRLU+Lm2p+9z9HBfFyWxMqfbAAAAgFl0F272yP6map5xG+9c253c\nBgAAAEykcnH7/j/XfpM6/RYTe/RYSOU2AAAAYC7VCk5Hl5F++T0P3clu/yf32Npu7t0GAAAATOje\nccodHOu0E33p9/n887ff/jG9FLkNAAAAmNTRdwbY/21Tth9euaj35TPTy1tMFCK3AQAAAH/4WEz6\nrSGPssfcxnhOWtD1Mym3AQAAAP9zqDo9fnLXceSWiG69PwNN6f3JlNsAAACAb4933b+890ry+PjH\nvpd/ywZ4SuU2AAAAmFrw5mVjRLe79n8XpR9hoRvbffyPDkBuAwAAgEkViinLMkg0oaaRZuY/Vz8A\nAAAA4AJFDy4tywUHo2ZT+hmu9qao6zpUa7vJbQAAADChOi1McRvb95lsvNB252JSAAAAmEvNCubC\n0uEdfX+JGeZBbgMAAICJ1D9xprjNwx/0ndwGAAAAszjR2v4MKEe/j+LGVNy7DQAAAHh2v6nWu0a2\n/dE/uY/bOdtPcrlntdr7JAzJ6TYAAACYws40c6ik3D9ZSoNHTrcBAADA+Eq0tqNfpcqVUOJZ9Sf1\nJbkNAAAAuN2+u0LQ1YXltPbctvZ4GiS3AQAAwOD2HFb6vqHs+Q6OTZWQfVb9GX1PbgMAAIDZpc4r\nOfd0lVQj09oi5DYAAAAY2ceAkm1kH7+boHNCnZODdU5BzkBuAwAAAGhd6eKmtQXJbQAAADCvEgFF\nlLnQshyObie+hG1yGwAAAEAH9nfMnQXtUGhTUfeT2wAAAGBY2zGlXEDZ/s7OUp126I/sXtNen+13\nv5767/Jz9QMAAAAAoCB9szKn2wAAAAC6Ufmg2bo62naY3AYAAADQE/2rcXIbAAAAzKh0spGEiqpw\n6My5ttPkNgAAAIAuXfVmF2yT2wAAAGBGpW+f7/b8dcTPoDnU9j25DQAAAKBvqUYmtEX8XP0AAAAA\nAAi4x7IT5wpVtiy5DQAAAGAc79rZU4aT2MqR2wAAAADGp69V495tAAAAMKztwlLu3Qy2v7Puw9jk\nNgAAAACIkdsAAABgXiUOuJU7NAddkNsAAABgZB+v3MzWsY/fzZWkDE9uAwAAAIAYuQ0AAAAGV+2A\nm6NtcJPbAAAAgFuiuLllG9zJbQAAADC+PcfKluVkMtv5hY62MQm5DQAAAPi/o8XNoTZ48nP1AwAA\nAABqWNe9aez30zbOox2tbI62MQ+5DQAAAGaxv7jdpU6uaW1MxcWkAAAAMJH65UtrYzZyGwAAAFCK\n1saE5DYAAACYy7pWqmBaG3OS2wAAAGBGpVuY1sa05DYAAACYVLkiprUxM+9MCgAAAPO6d7HUO5De\nhDaQ2wAAAIBIdBPa4E5uAwAAAG63h152qLupbPBEbgMAAAD+8WdB+21w+hpsk9sAAACAz1Q22Mk7\nkwIAAABAjNwGAAAAADFyGwAAAADEyG0AAAAAECO3AQAAAECM3AYAAAAAMXIbAAAAAMTIbQAAAAAQ\nI7cBAAAAQIzcBgAAAAAxchsAAAAAxMhtAAAAABAjtwEAAABAjNwGAAAAADFyGwAAAADEyG0AAAAA\nECO3AQAAAECM3AYAAAAAMXIbAAAAAMTIbQAAAAAQI7cBAAAAQIzcBgAAAAAxchsAAAAAxMhtAAAA\nABAjtwEAAABAjNwGAAAAADFyGwAAAADEyG0AAAAAECO3AQAAAECM3AYAAAAAMXIbAAAAAMTIbQAA\nAAAQI7cBAAAAQIzcBgAAAAAxchsAAAAAxMhtAAAAABAjtwEAAABAjNwGAAAAADFyGwAAAADEyG0A\nAAAAECO3AQAAAECM3AYAAAAAMXIbAAAAAMTIbQAAAAAQI7cBAAAAQIzcBgAAAAAxchsAAAAAxMht\nAAAAABAjtwEAAABAjNwGAAAAADFyGwAAAADEyG0AAAAAECO3AQAAAECM3AYAAAAAMXIbAAAAAMTI\nbQAAAAAQI7cBAAAAQIzcBgAAAAAxchsAAAAAxMhtAAAAABAjtwEAAABAjNwGAAAAADFyGwAAAADE\nyG0AAAAAECO3AQAAAECM3AYAAAAAMXIbAAAAAMTIbQAAAAAQI7cBAAAAQIzcBgAAAAAxchsAAAAA\nxMhtAAAAABAjtwEAAABAjNwGAAAAADFyGwAAAADEyG0AAAAAECO3AQAAAECM3AYAAAAAMXIbAAAA\nAMTIbQAAAAAQI7cBAAAAQIzcBgAAAAAxchsAAAAAxPxc/QBilmV596F1XWs+EgAAAACm1X1u26hs\nr5+juwEAAABQVMe57TW0/VnTHj/t/s+iGwAAAACF9HrvtqfWtq7ru4j2+qE9B+IAAAAA4IQuc9tr\na/v4JYobAAAAABX0l9tOtLajnwkAAAAA53SW24Kn0hxwAwAAACCus9z25OiBNQfcAAAAACiq79z2\nJQfcAAAAAMjqKbepYwAAAAA0rqfcBgAAAACNk9sAAAAAIEZuAwAAAICYvnObu7kBAAAA0JS+c9tR\nT3luXderHgkAAAAAQ+o+tzngBgAAAEA7espt7w6j7SxujrYBAAAAUFpPuW3D0TNuWhsAAAAAJXSW\n2zYy2XZxc80pAAAAABV0lttup4rb46+v6+poGwAAAACF9Jfbbp+K21N0e2ptBR8WAAAAANPrMrfd\nPoWze2J7TG8OtQEAAABQwdJ1hNp5R7Zqv8dzd4jr+o8AAAAA4FqtBZleT7fd7XlexCwAAAAAquk7\nt9121LTXu7kBAAAAQCHd57bbvvNrihsAAAAAFYyQ23ZS3AAAAAAo7efqBxCwv6PdP7Pa3dzcNg4A\nAACgtJ0FptpJrO5Ptz0+U+u6urAUAAAAgAt1nNue3gPhN7TtiW6KGwAAAAAl7LqYtH6cOtrLXj9/\nXdfth70si4s9AQAAAMjq8nTbx9a2/esAAAAAUEh/ue3QUbvtC0tdUgoAAABAVn+57cmeI2yKGwAA\nAAB1dJbbTtcxF5YCAAAAUMGut0potlUdemAf3zwBAAAAAL7U0+m272PZn3lOgwMAAAAgpafcBgAA\nAACNmy63NXthLAAAAAADmC63AQAAAEA5chsAAAAAxMhtAAAAABAjtwEAAABATE+57fVdDpZlKfFt\nAQAAAOCcnnIbAAAAADSus9z2/QG3p893tA0AAACAoM5yGwAAAAC0rL/c9s0BN0fbAAAAACiqv9x2\nO1vctDYAAAAASusyt93eFLd30e31Q1obAAAAACX8XP0Azrsns6eO9vGYm9AGAAAAQDkd57a733y2\nHdpUNgAAAAAq6D63/RLUAAAAALhcr/duAwAAAIAGyW0AAAAAECO3AQAAAECM3AYAAAAAMXIbAAAA\nAMTIbQAAAAAQI7cBAAAAQIzcBgAAAAAxchsAAAAAxMhtAAAAABAjtwEAAABAjNwGAAAAADFyGwAA\nAADEyG0AAAAAECO3AQAAAECM3AYAAAAAMXIbAAAAAMTIbQAAAAAQI7cBAAAAQIzcBgAAAAAxchsA\nAAAAxMhtAAAAABAjtwEAAABAjNwGAAAAADFyGwAAAADEyG0AAAAAECO3AQAAAECM3AYAAAAAMXIb\nAAAAAMTIbQAAAAAQI7cBAAAAQIzcBgAAAAAxchsAAAAAxMhtAAAAABAjtwEAAABAjNwGAAAAADFy\nGwAAAADEyG0AAAAAECO3AQAAAECM3AYAAAAAMXIbAAAAAMTIbQAAAAAQI7cBAAAAQIzcBgAAAAAx\nchsAAAAAxMhtAAAAABAjtwEAAABAjNwGAAAAADFyGwAAAADEyG0AAAAAECO3AQAAAECM3AYAAAAA\nMXIbAAAAAMTIbQAAAAAQI7cBAAAAQIzcBgAAAAAxchsAAAAAxMhtAAAAABAjtwEAAABAjNwGAAAA\nADFyGwAAAADEyG0AAAAAECO3AQAAAECM3AYAAAAAMXIbAAAAAMTIbQAAAAAQI7cBAAAAQIzcBgAA\nAAAxchsAAAAAxMhtAAAAABAjtwEAAABAzM/VDwC42LIsj/+6rutVjwQOMbp0yujSI3NLp4wunTK6\nA3C6DQAAAABi5DYAAAAAiJHbAAAAACBGbgMAAACAGLkNAAAAAGLkNgAAAACIkdsAAAAAIEZuAwAA\nAIAYuQ0AAAAAYuQ2AAAAAIiR2wAAAAAgRm4DAAAAgBi5DQAAAABilnVdr34M41iW5eqHAAAAAMBn\n5ZqY020AAAAAECO3AQAAAECMi0nzXFIKAAAA0KzSNczpNgAAAACIcboNAAAAAGKcbgMAAACAGLkN\nAAAAAGLkNgAAAACIkdsAAAAAIEZuAwAAAIAYuQ0AAAAAYuQ2AAAAAIiR2wAAAAAgRm4DAAAAgBi5\nDQAAAABi5DYAAAAAiJHbAAAAACBGbgMAAACAGLkNAAAAAGLkNgAAAACIkdsAAAAAIEZuAwAAAIAY\nuQ0AAAAAYuQ2AAAAAIiR2wAAAAAgRm4DAAAAgBi5DQAAAABi5DYAAAAAiJHbAAAAACBGbgMAAACA\nGLkNAAAAAGLkNgAAAACIkdsAAAAAIEZuAwAAAIAYuQ0AAAAAYuQ2AAAAAIiR2wAAAAAgRm4DAAAA\ngBi5DQAAAABi5DYAAAAAiJHbAAAAACDm5+oHMIVlWX7/eV3XCx8JPHkczkcGlcYZXbpjaBmSXS69\ne12cTTIXerdbuJnMDsltMKONdfzpEyzrNGXn6Jpb2mG9BWiNn3/Qmo+7hZsNQ4cWf1SlPf2f4wnn\ncntW80eGlkZ8XE6tt7TGesvYrLp0589l2ehyoZ3nKx3D7JHcVpb/K2jK0Rd+j4wuF9q/lnrtRyOs\ntwzPLpe+mFgadHTjaqPbF2+VALP45rXf918Opx3aHz99yNxyCestQDuWZdHaaNCJdmaj2xe5rSDT\nTztMI8P4uBexEeFaRo4ZmHN68Wdo09q43Olzaqa3I94qoRS7EBq386YATx+1vlPZub3Iuq6PX2h0\nuZb1lsHY5dIFt2mjWcFV1IahZXJbEXYhNOVxILeX4/tHNwbYgk5N1lK6Y71leFZmuqC10ZGjk/n0\nc2Wa5WJSmMj+k0G2IzTo0Fi6pJRrWW8BrqK1MRW73GbJbXm/425NpwWnB9IAc6341sFehNKstwzP\nLpf2aW00zo50HnJbmF0Iw/M3BEAd1luaYpdL+7Q2oB1yWxHWdBrx5c7YJHOVP99H7Og3McDUZL1l\nEmaVZmltQFPktiQ/haZN9hlwZ5WmNOsto7J+0jitDWiN3BbjgD1DMs8AdVhvaZZdLkA5fp4xKrkt\nzC6EdtwXbjNJd+w56I71lhmYcJrlaBtTeRp4o94suS3Di0MatK6rxReeWK4pwXrLwCybAKVZaYck\ntwU4YA8AwHjscmmfo2305d1w7ixujrZ1RG77ll0IszHq1Hd66owrXTPAXMsuF6Cmo2fcLM6Nk9sA\nAADoj0vw6NFGJtseaQPfl5+rH0Df/NAPIKvCNmJZFos2wDa7XPr1NLTvthZmmwut6/puMt/tVB8/\n3/R2QW47zy6EGbg7AEAd1lvaYZdLFz7+iG7nQSFzziW2i9vt38nU2nrkYlIAAADGsSzL/vPyLtDj\nKtvh7D6Zj8PsndD74nTbSX4YwoRMO0Ad1lsuZJdL715PBj196NCXQFEbZ9xuDrV1Tm47wy4EAIDx\n2OUygI3p/f2QE220Y7u4/X5OnQdDkItJzzPxDM+PUwDqsN7SFENI+758A4RDZ9+gtI9ze+j6aBoh\ntx1mygEAGI9dLr07VIoVfHd2YAAAA1NJREFUN5qyZ3rNZ1/ktmMcsGcejloA1GG9pQV2ufTuxOia\ndrqjuHVEbjvALoQ5GXiAOqy3XMUuF37JGVzi0HvpmtIuyG3AH2y7Aeqw3gJcyNpLC57OubuwdAxy\n2152w8zDtAPUYb2lBeYQ4CpPR9V+1+E90U1xa9zP1Q9gl/pj9DTZdiGccPncAgBss8uFV8uy+D+C\nCp5eML5O3bqu2y8qzWrLnG4D/mHbDVCH9RYApvWxtW3/Ou2T2z6zG2Yepp3LmT0mYb2lBeYQbuaf\nKxy6EGr7wlKXlDZLbvvALoR5mHYmYcK5nPWWFphDgEbsWYcVt+70ce+2FqQm+M/vY5fD5ey5Aeqw\n3tIau1yAmk6vuh9v5UZT+sht/p6mRx3Nrdd+jMqOhNZYbwGAR4e2BIpbR1xMCrPz2o/22VUwBust\nQIqFlE59v639c/jtlhskt8HUvPajQaaRIVlvAQDmIbcBXvsxEdPOtUwgQCFO9zAP24ku9HHvtgt9\nOcevi77/MWjHfT7NJEBp1lsaZJcL7xhm4HtOt8GkvPajZSaTkVhvAUqwrgItk9tgRpHXfk7sU9OJ\neXPyghZYbwEAJiS3wXS89gOow3oLUNO5BdMyC5Qgt8FcvPajF/GTaI62UZn1FqC0En+52zBQ1OuA\nRf6uN7cNkttgItnXftZ0Kju0FxEpuJb1FuASNgBAI7wzKczid/NhF0Iv1nVNjataQU3WW4Bqvtwt\nPH2tDQMVvA7tsiyHZs/cdsHpNphC/CWfNZ06niZt5yTbgnAh6y1AZed2Cx+/D8A35DYYn+MVdO3o\nHtrAcyHjB3CJ738+p7VR0zd3cPNz5V7IbTC4Eq/9rOlUtn8P/foh40o11luAC33z8zmLLfWdK25a\nW0fkNhiZcxYMY88e+nX/YQtCNdZbgMu97hbebRi0NlrwZ3F7t6N4/ZDRbZy3SoBhee3HYO5bip03\nobf/oCbrLUAjnnYLt80l2m6By71O7Ou/vvsqGnfs/S8AoAXvdiH+UgMAftkw0Bc/Th6J3AYAAAAA\nMe7dBgAAAAAxchsAAAAAxMhtAAAAABAjtwEAAABAjNwGAAAAADFyGwAAAADEyG0AAAAAECO3AQAA\nAECM3AYAAAAAMXIbAAAAAMT8Fw2JeYXuCfiYAAAAAElFTkSuQmCC\n",
       "text": [
        "<IPython.core.display.Image at 0x104ab2a90>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u6700\u5c0f\u4e8c\u4e57\u6cd5\u306e\u4ed6\u306e\u554f\u984c ###\n",
      "\n",
      "* \u9811\u5065\u6027\u306e\u6b20\u5982\u3060\u3051\u3067\u306f\u306a\u3044\n",
      "* \u56f34.5\n",
      "    * 2\u6b21\u5143\u5165\u529b\u7a7a\u9593$(x_1,x_2)$\u306b\u304a\u3051\u308b3\u30af\u30e9\u30b9\u306e\u4eba\u5de5\u7684\u306b\u4f5c\u6210\u3055\u308c\u305f\u30c7\u30fc\u30bf\u96c6\u5408\n",
      "        * \u7dda\u5f62\u6c7a\u5b9a\u5883\u754c\u306b\u3088\u3063\u3066\u6b63\u3057\u304f\u30af\u30e9\u30b9\u5206\u985e\u3055\u308c\u308b\n",
      "    * \u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u306b\u3088\u308b\u89e3(\u53f3)\u3067\u306f\u6b63\u3057\u304f\u5206\u985e\u3055\u308c\u308b\u304c\u6700\u5c0f\u4e8c\u4e57\u89e3(\u5de6)\u3067\u306f\u7dd1\u306e\u30af\u30e9\u30b9\u306f\u5c0f\u3055\u306a\u9818\u57df\u3057\u304b\u6b63\u3057\u304f\u5206\u985e\u3055\u308c\u306a\u3044\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# \u6700\u5c0f\u4e8c\u4e57\u89e3\u306b\u3088\u308b\u5206\u985e\u5883\u754c\n",
      "disp_figure(\"4.5a\")"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "subslide"
      }
     },
     "outputs": [
      {
       "metadata": {
        "png": {
         "width": "500px"
        }
       },
       "output_type": "display_data",
       "png": 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7pnNYeAgLHwogjhAGNEQLA6A1m0rNuTPCqsphx4ewdIkX22rF0yXPOr5pAMA0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\nAKALLQwAAACALrQwAAAAALr4P7JPww/h8RtEAAAAAElFTkSuQmCC\n",
       "text": [
        "<IPython.core.display.Image at 0x104ab2bd0>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# \u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u306b\u3088\u308b\u30af\u30e9\u30b9\u5206\u985e\n",
      "disp_figure(\"4.5b\")"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "subslide"
      }
     },
     "outputs": [
      {
       "metadata": {
        "png": {
         "width": "500px"
        }
       },
       "output_type": "display_data",
       "png": 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7IQwAAPhICAOYzb+zN6AiS+YD0KjH565rwQet5w9vJeMATEwIA5jQsPPCXB0JQKOeP3d9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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<IPython.core.display.Image at 0x104ab2710>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u6700\u5c0f\u4e8c\u4e57\u6cd5\u306e\u307e\u3068\u3081 ###\n",
      "\n",
      "* \u6700\u5c0f\u4e8c\u4e57\u6cd5\u306f\u6761\u4ef6\u4ed8\u78ba\u7387\u5206\u5e03\u306b\u30ac\u30a6\u30b9\u5206\u5e03\u3092\u4eee\u5b9a\u3057\u305f\u5834\u5408\u306e\u6700\u5c24\u6cd5\n",
      "    * \u4e00\u65b9\u30672\u5024\u76ee\u7684\u5909\u6570\u30d9\u30af\u30c8\u30eb\u306f\u660e\u3089\u304b\u306b\u30ac\u30a6\u30b9\u5206\u5e03\u304b\u3089\u304b\u3051\u96e2\u308c\u3066\u3044\u308b\n",
      "    * \u6700\u5c0f\u4e8c\u4e57\u6cd5\u304c\u4f7f\u3048\u306a\u3044\u306e\u306f\u5f53\u305f\u308a\u524d\n",
      "* \u9069\u5207\u306a\u78ba\u7387\u30e2\u30c7\u30eb\u3092\u63a1\u7528\u3059\u308c\u3070\u6700\u5c0f\u4e8c\u4e57\u6cd5\u3088\u308a\u3082\u826f\u3044\u7279\u6027\u3092\u6301\u3064\u5206\u985e\u6cd5\u3092\u5f97\u3089\u308c\u308b\n",
      "* \u305d\u306e\u524d\u306b\u78ba\u7387\u7684\u3067\u306a\u3044\u65b9\u6cd5\u306b\u3064\u3044\u3066\u3082\u3046\u5c11\u3057\u8ff0\u3079\u308b"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "## 4.1.4 \u30d5\u30a3\u30c3\u30b7\u30e3\u30fc\u306e\u7dda\u5f62\u5224\u5225 ##\n",
      "\n",
      "* \u6b21\u5143\u306e\u524a\u6e1b\u3068\u3044\u3046\u89b3\u70b9\u304b\u3089\u7dda\u5f62\u8b58\u5225\u30e2\u30c7\u30eb\u3092\u898b\u308b\n",
      "* 2\u30af\u30e9\u30b9\u306e\u5834\u5408\u306bD\u6b21\u5143\u5165\u529b\u30d9\u30af\u30c8\u30eb\u3092\u5f97\u30661\u6b21\u5143\u306b\u5c04\u5f71\n",
      "$$y={\\bf w}^T{\\bf x}. $$\n",
      "\n",
      "* $y \\geq -w_0$\u306e\u5834\u5408\u30af\u30e9\u30b9${\\cal C}_1$\u3001\u305d\u3046\u3067\u306a\u3044\u5834\u5408${\\cal C}_2$\u3068\u3059\u308b\u3068\u7dda\u5f62\u5206\u985e\u5668\u304c\u5f97\u3089\u308c\u308b\n",
      "    * 1\u6b21\u5143\u3078\u306e\u5c04\u5f71\u306f\u76f8\u5f53\u91cf\u306e\u60c5\u5831\u306e\u640d\u5931\u3092\u767a\u751f\n",
      "    * D\u6b21\u5143\u7a7a\u9593\u3067\u306f\u5206\u96e2\u3055\u308c\u3066\u3044\u305f\u30af\u30e9\u30b9\u304c1\u6b21\u5143\u7a7a\u9593\u3067\u306f\u5927\u304d\u304f\u91cd\u306a\u308b\u304b\u3082\u3057\u308c\u306a\u3044\u304c\u3001${\\bf w}$\u306e\u8981\u7d20\u306e\u8abf\u6574\u3067\u30af\u30e9\u30b9\u306e\u5206\u96e2\u3092\u6700\u5927\u5316\u53ef\u80fd\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u30af\u30e9\u30b9\u5206\u96e2\u5ea6\u306e\u6e2c\u5b9a ###\n",
      "\n",
      "* \u30af\u30e9\u30b9${\\cal C}_1$\u306e\u70b9\u304c$N_1$\u3001\u30af\u30e9\u30b9${\\cal C}_2$\u306e\u70b9\u304c$N_2$\u3042\u308b\u6642\u306e\u305d\u308c\u305e\u308c\u306e\u5e73\u5747\u30d9\u30af\u30c8\u30eb\n",
      "$${\\bf m}_1 =\\frac{1}{N_1}\\sum_{n\\in{\\cal C}_1}{\\bf x}_n, {\\bf m}_2 =\\frac{1}{N_{2}}\\sum_{n\\in{\\cal C}_2}{\\bf x}_n,$$\n",
      "* \u30af\u30e9\u30b9\u306e\u5206\u96e2\u5ea6\u3092\u5c04\u5f71\u3055\u308c\u305f\u30af\u30e9\u30b9\u306e\u5e73\u5747\u306e\u5dee\u3067\u6e2c\u5b9a\n",
      "$$m_2-m_1={\\bf w}^T({\\bf m}_2 -{\\bf m}_1)$$\n",
      "    * \u3053\u3053\u3067$m_k={\\bf w}^T{\\bf m}_k$\u306f${\\cal C}_k$\u304b\u3089\u5c04\u5f71\u3055\u308c\u305f\u30c7\u30fc\u30bf\u306e\u5e73\u5747\n",
      "    * \u3053\u306e\u5f0f\u3092\u6700\u5927\u5316\u3059\u308b${\\bf w}$\u3092\u9078\u629e\u3059\u308c\u3070\u5206\u96e2\u5ea6\u304c\u6700\u5927\u3068\u306a\u308b\n",
      "    * ${\\bf w}_k$\u3092\u5927\u304d\u304f\u3059\u308c\u3070$m_k$\u306f\u5e7e\u3089\u3067\u3082\u5927\u304d\u304f\u306a\u308b\u554f\u984c\n",
      "        * \u5358\u4f4d\u9577\u3067\u3042\u308b\u3068\u3044\u3046\u5236\u7d04\u3092\u52a0\u3048\u308b\u3053\u3068\u3067\u56de\u907f\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u5358\u4f4d\u9577\u306e\u5236\u7d04 ###\n",
      "\n",
      "* $\\sum_i w_i^2 = 1$\u306e\u5236\u7d04\u306e\u4e0b\u3067$m_2-m_1={\\bf w}^T({\\bf m}_2 -{\\bf m}_1)$\u3092\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u306e\u672a\u5b9a\u4e57\u6570\u6cd5\u3092\u4f7f\u3063\u3066\u89e3\u304f(\u6f14\u7fd24.4)\n",
      "* $f({\\bf w})=m_2-m_1-{\\bf w}^T({\\bf m}_2 -{\\bf m}_1)+\\lambda(\\sum_i w_i^2 - 1)=m_2-m_1-{\\bf w}^T({\\bf m}_2 -{\\bf m}_1)+\\lambda({\\bf w}^T{\\bf w} - 1)$\u3092${\\bf w}$\u3067\u5fae\u5206\u3057\u30660\u3068\u304a\u304f\n",
      "    * $\\frac{\\partial f({\\bf w})}{\\partial {\\bf w}}=({\\bf m}_2 -{\\bf m}_1)+\\lambda{\\bf w}=0$\n",
      "    * \u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306b\u306f\u307e\u3060\u56f34.6\u5de6\u56f3\u306e\u3088\u3046\u306a\u554f\u984c\u304c\u3042\u308b"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# \u56f34.6\u5de6\u56f3\n",
      "# \u30af\u30e9\u30b9\u5e73\u5747\u3092\u7d50\u3093\u3060\u76f4\u7dda\u4e0a\u3078\u5c04\u5f71\u3057\u3066\u3082\u91cd\u306a\u308a\u5408\u3046\u90e8\u5206\u304c\u591a\u3044\u3053\u3068\u3092\u793a\u3059\n",
      "# \u30af\u30e9\u30b9\u5206\u5e03\u306e\u975e\u5bfe\u89d2\u306a\u5171\u5206\u6563\u304c\u5f37\u3044\u305f\u3081\u306b\u8d77\u3053\u308b\u554f\u984c\n",
      "disp_figure(\"4.6a\")"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [
      {
       "metadata": {
        "png": {
         "width": "500px"
        }
       },
       "output_type": "display_data",
       "png": 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Z4L5QJ9e0pABAbQZiA8CrzKduD+dcoAI5txFvC6YlBQAa0IIEgCtGDBrytd87q7u29PFQ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\nAACgIQkSAAAAAGhIggQAAAAAGvo/k58OoEWltxgAAAAASUVORK5CYII=\n",
       "text": [
        "<IPython.core.display.Image at 0x106218910>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u30d5\u30a3\u30c3\u30b7\u30e3\u30fc\u306e\u63d0\u6848\u6cd5 ###\n",
      "\n",
      "* \u30af\u30e9\u30b9\u5e73\u5747\u9593\u306e\u5206\u96e2\u5ea6\u3092\u5927\u304d\u304f\u3059\u308b\u3068\u540c\u6642\u306b\u5404\u30af\u30e9\u30b9\u5185\u3067\u306f\u5c0f\u3055\u306a\u5206\u6563\u3092\u4e0e\u3048\u308b\u95a2\u6570\u3092\u6700\u5927\u5316\n",
      "    * \u30af\u30e9\u30b9\u9593\u306e\u91cd\u306a\u308a\u3092\u6700\u5c0f\u306b\u3067\u304d\u308b\n",
      "* \u30af\u30e9\u30b9${\\cal C}_k$\u304b\u3089\u5c04\u5f71\u3055\u308c\u305f\u30c7\u30fc\u30bf\u306e\u30af\u30e9\u30b9\u5185\u5206\u6563($y_n={\\bf w}^T{\\bf x}$\u3068\u3059\u308b)\n",
      "$$s_k^2=\\sum_{n \\in {\\cal C}_k}(y_n - m_k)^2$$\n",
      "    * \u5168\u30c7\u30fc\u30bf\u96c6\u5408\u306b\u5bfe\u3059\u308b\u7dcf\u30af\u30e9\u30b9\u5185\u5206\u6563$s_1^2+s_2^2$\n",
      "* \u30d5\u30a3\u30c3\u30b7\u30e3\u30fc\u306e\u5224\u5225\u57fa\u6e96\u306f\u30af\u30e9\u30b9\u5185\u5206\u6563\u3068\u30af\u30e9\u30b9\u9593\u5206\u6563\u306e\u6bd4\n",
      "$$J({\\bf w})=\\frac{(m_2-m_1)^2}{s_1^2+s_2^2}$$\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u4e00\u822c\u5316\u306e\u305f\u3081\u306e\u5f0f\u5909\u5f62 ###\n",
      "\n",
      "* $y={\\bf w}^T{\\bf x}$, $m_k={\\bf w}^T{\\bf m}_k$, $s_k^2=\\sum_{n \\in {\\cal C}_k}(y_n - m_k)^2$, $({\\bf w}^T{\\bf x})^2=({\\bf w}^T{\\bf x})({\\bf w}^T{\\bf x})={\\bf w}^T{\\bf x}{\\bf x}^T{\\bf w}$\u3067\u3042\u308b\u306e\u3067\n",
      "$$J({\\bf w})=\\frac{(m_2-m_1)^2}{s_1^2+s_2^2}=\\frac{({\\bf w}^T{\\bf m}_2-{\\bf w}^T{\\bf m}_1)^2}{\\sum_{n \\in {\\cal C}_1}({\\bf w}^T{\\bf x}_n - {\\bf w}^T{\\bf m}_1)^2+\\sum_{n \\in {\\cal C}_2}({\\bf w}^T{\\bf x}_n - {\\bf w}^T{\\bf m}_2)^2}$$\n",
      "$$ \\iff \\frac{\\{{\\bf w}^T({\\bf m}_2-{\\bf m}_1)\\}^2}{\\sum_{n \\in {\\cal C}_1}\\{{\\bf w}^T({\\bf x}_n - {\\bf m}_1)\\}^2+\\sum_{n \\in {\\cal C}_2}\\{{\\bf w}^T({\\bf x}_n - {\\bf m}_2)\\}^2}$$\n",
      "$$ \\iff \\frac{{\\bf w}^T({\\bf m}_2-{\\bf m}_1)({\\bf m}_2-{\\bf m}_1)^T{\\bf w}}{\\sum_{n \\in {\\cal C}_1}{\\bf w}^T({\\bf x}_n - {\\bf m}_1)({\\bf x}_n - {\\bf m}_1)^T{\\bf w}+\\sum_{n \\in {\\cal C}_2}{\\bf w}^T({\\bf x}_n - {\\bf m}_2)({\\bf x}_n - {\\bf m}_2)^T{\\bf w}}$$\n",
      "$$ \\iff \\frac{{\\bf w}^T({\\bf m}_2-{\\bf m}_1)({\\bf m}_2-{\\bf m}_1)^T{\\bf w}}{{\\bf w}^T\\left\\{\\sum_{n \\in {\\cal C}_1}({\\bf x}_n - {\\bf m}_1)({\\bf x}_n - {\\bf m}_1)^T+\\sum_{n \\in {\\cal C}_2}({\\bf x}_n - {\\bf m}_2)({\\bf x}_n - {\\bf m}_2)^T\\right\\}{\\bf w}}$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u4e00\u822c\u5316\u3055\u308c\u305f\u30d5\u30a3\u30c3\u30b7\u30e3\u30fc\u306e\u5224\u5225\u57fa\u6e96 ###\n",
      "\n",
      "$$J({\\bf w})=\\frac{{\\bf w}^T{\\bf S}_B{\\bf w}}{{\\bf w}^T{\\bf S}_W{\\bf w}}$$\n",
      "\n",
      "* \u30af\u30e9\u30b9\u9593\u5171\u5206\u6563\u884c\u5217(between-class covariance matrix)\n",
      "$${\\bf S}_B=({\\bf m}_2-{\\bf m}_1)({\\bf m}_2-{\\bf m}_1)^T$$\n",
      "\n",
      "* \u7dcf\u30af\u30e9\u30b9\u5185\u5171\u5206\u6563\u884c\u5217(within-class covariance matrix)\n",
      "$${\\bf S}_w=\\sum_{n\\in{\\cal C}_1}({\\bf x}_n-{\\bf m}_1)({\\bf x}_n-{\\bf m}_1)^{\\rm T}+\\sum_{n\\in{\\cal C}_2}({\\bf x}_n-{\\bf m}_2)({\\bf x}_n-{\\bf m}_2)^{\\rm T}$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u30d5\u30a3\u30c3\u30b7\u30e3\u30fc\u306e\u5224\u5225\u57fa\u6e96\u306e\u6700\u5927\u5316 ###\n",
      "\n",
      "* \u5224\u5225\u57fa\u6e96$J({\\bf w})=\\frac{{\\bf w}^T{\\bf S}_B{\\bf w}}{{\\bf w}^T{\\bf S}_W{\\bf w}}$\u3092${\\bf w}$\u306b\u95a2\u3057\u3066\u5fae\u5206\n",
      "$$\\frac{\\partial J({\\bf w})}{\\partial {\\bf w}}=2\\frac{({\\bf S}_B{\\bf w})({\\bf w}^T{\\bf S}_W{\\bf w})-({\\bf w}^T{\\bf S}_B{\\bf w})({\\bf S}_W{\\bf w})}{({\\bf w}^T{\\bf S}_W{\\bf w})^2}=0$$\n",
      "\n",
      "* \u5f93\u3063\u3066\u6700\u5927\u3068\u306a\u308b\u6761\u4ef6\u306f\n",
      "$$({\\bf w}^T{\\bf S}_B{\\bf w}){\\bf S}_w{\\bf w}=({\\bf w}^T{\\bf S}_w{\\bf w}){\\bf S}_B{\\bf w}.$$\n",
      "    * ${\\bf S}_B=({\\bf m}_2-{\\bf m}_1)({\\bf m}_2-{\\bf m}_1)^T$\u3067\u3042\u308b\u306e\u3067${\\bf S}_B{\\bf w}$\u306f\u5e38\u306b$({\\bf m}_2-{\\bf m}_1)$\u3068\u540c\u3058\u65b9\u5411\u3092\u6301\u3064\u30d9\u30af\u30c8\u30eb\n",
      "    * ${\\bf w}$\u306e\u65b9\u5411\u3060\u3051\u304c\u91cd\u8981\u3067\u5927\u304d\u3055\u306f\u8003\u616e\u3059\u308b\u5fc5\u8981\u304c\u306a\u3044\u306e\u3067\u3001\u30b9\u30ab\u30e9\u30d5\u30a1\u30af\u30bf$({\\bf w}^T{\\bf S}_B{\\bf w})$\u3068$({\\bf w}^T{\\bf S}_w{\\bf w})$\u306f\u7121\u8996\u3057\u3066\u3001\u5de6\u304b\u3089${\\bf S}_W^{-1}$\u3092\u639b\u3051\u308b\u3068\n",
      "$${\\bf w}\\propto{\\bf S}_w^{-1}({\\bf m}_2-{\\bf m}_1)$$\n",
      "    * \u30af\u30e9\u30b9\u5185\u5171\u5206\u6563${\\bf S}_w$\u304c\u7b49\u65b9\u7684\u3067\u3042\u308b\u3068\u3059\u308b\u3068${\\bf S}_w$\u306f\u5358\u4f4d\u884c\u5217\u306b\u6bd4\u4f8b\u3057${\\bf w}$\u304c\u30af\u30e9\u30b9\u5e73\u5747\u306e\u5dee\u306b\u6bd4\u4f8b\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u30d5\u30a3\u30c3\u30b7\u30e3\u30fc\u306e\u7dda\u5f62\u5224\u5225(Fisher's linear discriminant) ###\n",
      "\n",
      "$${\\bf w}\\propto{\\bf S}_w^{-1}({\\bf m}_2-{\\bf m}_1)$$\n",
      "\n",
      "* \u30c7\u30fc\u30bf\u30921\u6b21\u5143\u3078\u524a\u6e1b\u3059\u308b\u969b\u306e\u30c7\u30fc\u30bf\u306e\u5c04\u5f71\u65b9\u5411\u306e\u9078\u629e\n",
      "* \u3057\u304d\u3044\u5024$y_0$\u3092\u8a2d\u5b9a\u3059\u308b\u3053\u3068\u3067$y({\\bf x})\\geq y_0$\u306e\u5834\u5408\u306b\u306f\u30af\u30e9\u30b9${\\cal C}_1$\u306b\u5206\u985e\u3055\u308c\u3001\u305d\u3046\u3067\u306a\u3044\u5834\u5408\u306b\u306f\u30af\u30e9\u30b9${\\cal C}_2$\u306b\u5206\u985e\u3055\u308c\u308b\u3088\u3046\u306a\u8b58\u5225\u95a2\u6570\u3092\u69cb\u6210\u53ef\u80fd\n",
      "* \u3055\u3089\u306b\u30af\u30e9\u30b9\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u5bc6\u5ea6$p(y|{\\cal C}_k)$\u3092\u30ac\u30a6\u30b9\u5206\u5e03\u3067\u30e2\u30c7\u30eb\u5316\u3057\u30011.2.4\u7bc0\u306e\u624b\u6cd5\u3067\u6700\u5c24\u6cd5\u306b\u3088\u308a\u30ac\u30a6\u30b9\u5206\u5e03\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u6c7a\u3081\u30011.5.1\u7bc0\u306e\u5b9a\u5f0f\u5316\u306b\u3088\u308a\u8b58\u5225\u306e\u305f\u3081\u306e\u6700\u9069\u306a\u3057\u304d\u3044\u5024\u304c\u6c42\u307e\u308b\n",
      "    * \u30ac\u30a6\u30b9\u5206\u5e03\u3067\u3042\u308b\u3068\u3044\u3046\u4eee\u5b9a\u306f$y={\\bf w}^T{\\bf x}$\u304c\u78ba\u7387\u5909\u6570\u96c6\u5408\u306e\u548c\u3067\u3042\u308b\u3053\u3068\u306b\u3088\u308a\u4e2d\u5fc3\u6975\u9650\u5b9a\u7406\u304b\u3089\u6b63\u5f53\u5316\u3055\u308c\u308b"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# \u56f34.6\u306e\u5de6\u56f3\u304b\u3089w\u30d9\u30af\u30c8\u30eb\u306e\u65b9\u5411\u3092\u5206\u96e2\u5ea6\u304c\u6700\u5927\u3068\u306a\u308b\u3088\u3046\u306a\u65b9\u5411\u306b\u4fee\u6b63\n",
      "disp_figure(\"4.6b\")"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "subslide"
      }
     },
     "outputs": [
      {
       "metadata": {
        "png": {
         "width": "500px"
        }
       },
       "output_type": "display_data",
       "png": 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uHQDAmkSQAPDB19ZXE2xVYlWfgmYqexxL4gbiMwwAYE0iSAB4VXzqPTIJboqQPGaq1Ivt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\n9H8vbmj29Nov5QAAAABJRU5ErkJggg==\n",
       "text": [
        "<IPython.core.display.Image at 0x106218a10>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "## 4.1.5 \u6700\u5c0f\u4e8c\u4e57\u3068\u306e\u95a2\u9023 ##\n",
      "\n",
      "* \u6700\u5c0f\u4e8c\u4e57\u6cd5\n",
      "    * \u76ee\u7684\u5909\u6570\u5024\u306e\u96c6\u5408\u306b\u3067\u304d\u308b\u3060\u3051\u8fd1\u3044\u4e88\u6e2c\u3092\u3059\u308b\u3053\u3068\u3092\u76ee\u7684\n",
      "* \u30d5\u30a3\u30c3\u30b7\u30e3\u30fc\u306e\u5224\u5225\u57fa\u6e96\n",
      "    * \u51fa\u529b\u7a7a\u9593\u3067\u306e\u30af\u30e9\u30b9\u5206\u96e2\u3092\u6700\u5927\u5316\n",
      "* 2\u3064\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306e\u95a2\u4fc2\u306b\u3064\u3044\u3066\u8abf\u3079\u308b\n",
      "    * \u7279\u306b2\u30af\u30e9\u30b9\u5206\u985e\u554f\u984c\u306b\u304a\u3044\u3066\u30d5\u30a3\u30c3\u30b7\u30e3\u30fc\u306e\u5224\u5225\u57fa\u6e96\u304c\u6700\u5c0f\u4e8c\u4e57\u306e\u7279\u6b8a\u306a\u5834\u5408\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3059"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### 1-of-K\u7b26\u53f7\u5316\u6cd5\u3067\u306a\u3044\u76ee\u7684\u5909\u6570\u306e\u8868\u73fe ###\n",
      "\n",
      "* \u30af\u30e9\u30b9${\\cal C}_1$\u306b\u5bfe\u3059\u308b\u76ee\u7684\u5909\u6570\u5024\u3092$N/N_1$\u3068\u8868\u73fe\n",
      "    * \u30af\u30e9\u30b9${\\cal C}_1$\u306b\u5bfe\u3059\u308b\u4e8b\u524d\u78ba\u7387\u306e\u9006\u6570\u3092\u8fd1\u4f3c($N_1$\u306f\u30af\u30e9\u30b9${\\cal C}_1$\u306b\u5c5e\u3059\u308b\u30d1\u30bf\u30fc\u30f3\u306e\u500b\u6570\u3001N\u306f\u7dcf\u30d1\u30bf\u30fc\u30f3\u306e\u500b\u6570\n",
      "* \u30af\u30e9\u30b9${\\cal C}_2$\u306b\u5bfe\u3059\u308b\u76ee\u7684\u5909\u6570\u5024\u3092$-N/N_2$\u3068\u3068\u308b"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u4e8c\u4e57\u548c\u8aa4\u5dee\u95a2\u6570\u3068\u5c0e\u95a2\u6570 ###\n",
      "\n",
      "* \u4e8c\u4e57\u548c\u8aa4\u5dee\u95a2\u6570\n",
      "$$E=\\frac{1}{2}\\sum_{n=1}^N({\\bf w}^T{\\bf x}_n+w_0-t_n)^2$$\n",
      "\n",
      "* $w_0$\u3068${\\bf w}$\u306b\u95a2\u3059\u308b\u5c0e\u95a2\u6570\u30920\u3068\u304a\u3044\u305f\u3082\u306e\n",
      "$$\\sum_{n=1}^N({\\bf w}^T{\\bf x}_n + w_0-t_n)=0$$\n",
      "$$\\sum_{n=1}^N({\\bf w}^T{\\bf x}_n + w_0-t_n){\\bf x}_n=0$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### $w_0$\u306b\u95a2\u3059\u308b\u5c0e\u95a2\u6570\u306e\u4e0a\u8ff0\u306e\u8868\u8a18\u6cd5\u306b\u3088\u308b\u5909\u5f62 ###\n",
      "\n",
      "$$\\sum_{n=1}^N({\\bf w}^T{\\bf x}_n + w_0-t_n)=0$$\n",
      "$$\\iff {\\bf w}^T\\sum_{n=1}^N{\\bf x}_n + Nw_0 - \\sum_{n=1}^N t_n=0$$\n",
      "$$\\iff w_0 = -\\frac{1}{N}{\\bf w}^T\\sum_{n=1}^N{\\bf x}_n$$\n",
      "$$\\iff w_0=-{\\bf w}^T{\\bf m}.$$\n",
      "* \u3053\u3053\u3067\u4ee5\u4e0b\u306e\u5f0f\u3092\u5229\u7528\n",
      "$$\\sum_{n=1}^Nt_n=N_1\\frac{N}{N_1}-N_2\\frac{N}{N_2}=0.$$\n",
      "$${\\bf m}=\\frac{1}{N}\\sum_{n=1}^N{\\bf x}_n = \\frac{1}{N}(N_1{\\bf m}_1+N_2{\\bf m}_2)$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### ${\\bf w}$\u306b\u3088\u308b\u5c0e\u95a2\u6570\u306e\u5909\u5f62 ###\n",
      "$$\\sum_{n=1}^N({\\bf w}^T{\\bf x}_n + w_0-t_n){\\bf x}_n=0$$\n",
      "$$\\iff \\sum_{n=1}^N({\\bf w}^T{\\bf x}_n -{\\bf w}^T{\\bf m} -t_n){\\bf x}_n=0$$\n",
      "$$\\iff \\sum_{n=1}^N{\\bf w}^T({\\bf x}_n - {\\bf m}){\\bf x}_n - \\sum_{n=1}^N t_n {\\bf x}_n=0$$\n",
      "$$\\iff \\sum_{n=1}^N{\\bf w}^T({\\bf x}_n - \\frac{1}{N}(N_1{\\bf m}_1+N_2{\\bf m}_2)){\\bf x}_n - \\sum_{n=1}^N t_n {\\bf x}_n=0$$\n",
      "$$\\iff \\sum_{n=1}^N{\\bf w}^T({\\bf x}_n - \\frac{1}{N}(N_1{\\bf m}_1+N_2{\\bf m}_2)){\\bf x}_n - \\sum_{n\\in C_1} \\frac{N}{N_1} {\\bf x}_n + \\sum_{n\\in C_2} \\frac{N}{N_2} {\\bf x}_n=0$$\n",
      "\n",
      "\u6642\u9593\u306e\u90fd\u5408\u304b\u3089\u65ad\u5ff5\u3057\u307e\u3057\u305f(\u6f14\u7fd24.6)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u4e8c\u4e57\u548c\u8aa4\u5dee\u95a2\u6570\u306e\u6700\u5c0f\u5316\u306b\u3088\u308a\u540c\u3058\u5f0f\u304c\u5c0e\u51fa ###\n",
      "\n",
      "* \u7c21\u5358\u306a\u4ee3\u6570\u6f14\u7b97\u3092\u3057\u305f\u7d50\u679c\n",
      "$$\\left({\\bf S}_w+\\frac{N_1N_2}{N}{\\bf S}_B\\right){\\bf w} = N({\\bf m}_1 - {\\bf m}_2)$$\n",
      "\n",
      "* ${\\bf S}_B{\\bf w}$\u306f\u5e38\u306b$({\\bf m}_2-{\\bf m}_1)$\u3068\u540c\u3058\u65b9\u5411\u3068\u306a\u308b\u3053\u3068\u304b\u3089\n",
      "$${\\bf w}\\propto {\\bf S}_w^{-1}({\\bf m}_2-{\\bf m}_1)$$\n",
      "\n",
      "    * \u30d5\u30a3\u30c3\u30b7\u30e3\u30fc\u306e\u7dda\u5f62\u5224\u5225\u3068\u4e00\u81f4\n",
      "* \u30d0\u30a4\u30a2\u30b9$w_0=-{\\bf w}^T{\\bf m}$\u3067\u3042\u308b\u305f\u3081$y({\\bf x})={\\bf w}^T({\\bf w}-{\\bf m})>0$\u306e\u5834\u5408\u65b0\u305f\u306a\u30d9\u30af\u30c8\u30eb${\\bf x}$\u306f\u30af\u30e9\u30b9${\\cal C}_1$\u306b\u3001\u305d\u3046\u3067\u306a\u3044\u5834\u5408\u3001\u30af\u30e9\u30b9${\\cal C}_2$\u306b\u5206\u985e"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### 4.1.6 \u591a\u30af\u30e9\u30b9\u306b\u304a\u3051\u308b\u30d5\u30a3\u30c3\u30b7\u30e3\u30fc\u306e\u5224\u5225 ###\n",
      "\n",
      "* K>2\u30af\u30e9\u30b9\u3078\u306e\u30d5\u30a3\u30c3\u30b7\u30e3\u30fc\u5224\u5225\u306e\u4e00\u822c\u5316\n",
      "* (\u5165\u529b\u6b21\u5143\u6570D) > (\u30af\u30e9\u30b9\u6570K)\u3092\u4eee\u5b9a\n",
      "* D'>1\u3067\u3042\u308b\u7dda\u5f62\u300c\u7279\u5fb4\u300d$y_k={\\bf w}_k^T{\\bf x}$\u3092\u5c0e\u5165(k=1,...,D')\n",
      "    * \u30b0\u30eb\u30fc\u30d7\u5316\u3057\u3066${\\bf y}$\u3067\u8868\u73fe\n",
      "* \u91cd\u307f\u30d9\u30af\u30c8\u30eb$\\{{\\bf w}_k\\}$\u3092\u5217\u3068\u3059\u308b\u884c\u5217${\\bf W}$\u3092\u7528\u3044\u308b\u3068\n",
      "$${\\bf y}={\\bf W}^T{\\bf x}.$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u30af\u30e9\u30b9\u5185\u5171\u5206\u6563\u306e\u4e00\u822c\u5316 ###\n",
      "\n",
      "$${\\bf S}_W=\\sum_{k=1}^{K}{\\bf S}_k$$\n",
      "\n",
      "* \u3053\u3053\u3067\u4ee5\u4e0b\u3092\u5229\u7528($N_k$\u306f\u30af\u30e9\u30b9${\\cal C}_k$\u5185\u306e\u30d1\u30bf\u30fc\u30f3\u306e\u500b\u6570)\n",
      "$${\\bf S}_k=\\sum_{n\\in{\\cal C}_k}({\\bf x}_n-{\\bf m}_k)({\\bf x}_n-{\\bf m}_k)^T$$\n",
      "$${\\bf m}_k=\\frac{1}{N_k}\\sum_{n\\in{\\cal C}_k}{\\bf x}_n$$\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u30af\u30e9\u30b9\u9593\u5171\u5206\u6563\u884c\u5217\u306e\u4e00\u822c\u5316 ###\n",
      "\n",
      "* Duda and Hart(1973)\u306b\u3042\u308b\u4ee5\u4e0b\u306e\u7dcf\u5171\u5206\u6563\u884c\u5217\u3092\u8003\u3048\u308b\n",
      "\n",
      "$${\\bf S}_T=\\sum_{n=1}^N({\\bf x}_n-{\\bf m})({\\bf x}_n-{\\bf m})^T.$$\n",
      "\n",
      "* \u3053\u3053\u3067\u4ee5\u4e0b\u3092\u5229\u7528($N=\\sum_k N_k$)\n",
      "$${\\bf m}=\\frac{1}{N}\\sum_{n=1}^N{\\bf x}_n=\\frac{1}{N}\\sum_{k=1}^K N_k{\\bf m}_k$$\n",
      "\n",
      "* \u7dcf\u5171\u5206\u6563\u884c\u5217\u306f\u30af\u30e9\u30b9\u5185\u5171\u5206\u6563\u884c\u5217\u306e\u548c\u3068\u30af\u30e9\u30b9\u9593\u5171\u5206\u6563\u306e\u6e2c\u5ea6\u3068\u8003\u3048\u3089\u308c\u308b\u884c\u5217${\\bf S}_B$\u3092\u8db3\u3057\u305f\u3082\u306e\u306b\u5206\u89e3\u53ef\u80fd\n",
      "\n",
      "$${\\bf S}_T = {\\bf S}_W + {\\bf S}_B.$$\n",
      "\n",
      "* \u3053\u3053\u3067\n",
      "$${\\bf S}_B = \\sum_{k=1}^K N_k({\\bf m}_k - {\\bf m})({\\bf m}_k - {\\bf m})^T$$\n",
      "\n",
      "* TODO: \u5909\u5f62"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u5c04\u5f71\u5f8c\u306eD'\u6b21\u5143\u7a7a\u9593\u306b\u304a\u3051\u308b\u5b9a\u7fa9 ###\n",
      "\n",
      "$${\\bf S}_W = \\sum_{k=1}^K\\sum_{n\\in{\\cal C}_k}({\\bf y}_n - {\\mu}_k)({\\bf y}_n - {\\mu}_k)^T$$\n",
      "$${\\bf S}_B=\\sum_{k=1}^K N_k({\\bf \\mu}_k-{\\bf \\mu})({\\bf \\mu}_k-{\\bf \\mu})^T$$\n",
      "\n",
      "* \u3053\u3053\u3067\n",
      "$${\\bf \\mu}_k=\\frac{1}{N_k}\\sum_{n\\in{\\cal C}_k}{\\bf y}_n, {\\bf \\mu}=\\frac{1}{N}\\sum_{k=1}^K N_k{\\bf \\mu}_k$$\n",
      "\n",
      "* FIXME: \u8aa4\u690d\u3067\u306f\u306a\u3044\u304b"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u30d5\u30a3\u30c3\u30b7\u30e3\u30fc\u306e\u5224\u5225\u57fa\u6e96\u306e\u4e00\u822c\u5316 ###\n",
      "\n",
      "* \u30af\u30e9\u30b9\u9593\u5206\u6563\u304c\u5927\u304d\u304f\u3001\u30af\u30e9\u30b9\u5185\u5206\u6563\u304c\u5c0f\u3055\u3044\u5834\u5408\u306b\u5927\u304d\u304f\u306a\u308b\u30b9\u30ab\u30e9\u30fc\u3092\u69cb\u6210\n",
      "* \u4e00\u3064\u306e\u4f8b\n",
      "$$J({\\bf W})={\\rm Tr}\\{{\\bf S}_W^{-1}{\\bf S}_B\\}$$\n",
      "\n",
      "    * \u5c04\u5f71\u884c\u5217${\\bf W}$\u306e\u660e\u793a\u7684\u306a\u95a2\u6570\u3068\u3057\u3066\u8868\u73fe\u3059\u308b\u3068\n",
      "$$J({\\bf W})={\\rm Tr}\\{({\\bf W}^T{\\bf S}_W{\\bf W})^{-1}({\\bf W}^T{\\bf S}_B{\\bf W}) \\}$$\n",
      "\n",
      "* \u6700\u5927\u5316\u306f\u3084\u3084\u6df7\u307f\u5408\u3063\u3066\u3044\u308b(Fukunaga(1990)\u3092\u53c2\u7167)\n",
      "    * \u91cd\u307f\u306e\u5024\u306fD'\u500b\u306e\u6700\u3082\u5927\u304d\u306a\u56fa\u6709\u5024\u306b\u5bfe\u5fdc\u3059\u308b${\\bf S}_W^{-1}{\\bf S}_B$\u306e\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u306b\u3088\u3063\u3066\u6c7a\u5b9a"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u3059\u3079\u3066\u306e\u57fa\u6e96\u306b\u5171\u901a\u3059\u308b\u91cd\u8981\u306a\u7d50\u679c ###\n",
      "\n",
      "* ${\\bf S}_B=\\sum_{k=1}^K N_k({\\bf m}_k - {\\bf m})({\\bf m}_k - {\\bf m})^T$\u306fK\u500b\u306e\u884c\u5217\u306e\u548c\u3067\u69cb\u6210\n",
      "    * \u5404\u884c\u5217\u306f2\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u5916\u7a4d\u3067\u3042\u308a\u30e9\u30f3\u30af\u306f1\u3001\u307e\u305f${\\bf m}=\\frac{1}{N}\\sum_{n=1}^N{\\bf x}_n=\\frac{1}{N}\\sum_{k=1}^K N_k{\\bf m}_k$\u306e\u5236\u7d04\u3088\u308a(K-1)\u500b\u306e\u884c\u5217\u3060\u3051\u304c\u72ec\u7acb\n",
      "    * \u5f93\u3063\u3066${\\bf S}_B$\u306e\u30e9\u30f3\u30af\u306f\u9ad8\u3005(K-1)\u3067\u3042\u308a0\u3067\u306a\u3044\u56fa\u6709\u5024\u306e\u6570\u306f\u9ad8\u3005(K-1)\u500b\n",
      "* ${\\bf S}_B$\u306e\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3067\u5f35\u308b(K-1)\u6b21\u5143\u90e8\u5206\u7a7a\u9593\u3078\u306e\u5c04\u5f71\u304c$J({\\bf W})$\u306e\u5024\u3092\u5909\u3048\u306a\u3044\n",
      "    * \u3064\u307e\u308a\u3053\u306e\u65b9\u6cd5\u3067\u306fK\u500b\u4ee5\u4e0a\u306e\u7dda\u5f62\u300c\u7279\u5fb4\u300d\u3092\u767a\u898b\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "### \u30a2\u30a4\u30ea\u30b9\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8 ###\n",
      "\n",
      "* 1930\u5e74\u4ee3\u304b\u3089\u3042\u308b\u4f1d\u7d71\u7684\u306a\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\n",
      "* \u30a2\u30a4\u30ea\u30b9(\u30a2\u30e4\u30e1)\u3068\u3044\u3046\u82b1\u306b\u95a2\u3059\u308b\u3082\u306e\n",
      "    * 3\u3064\u306e\u7570\u306a\u308b\u54c1\u7a2e\u306e\u30b5\u30f3\u30d7\u30eb\u30c7\u30fc\u30bf(\u30b5\u30f3\u30d7\u30eb\u6570150)\u304b\u3089\u69cb\u6210\n",
      "    * \u82b1\u306e\u5f62\u72b6\u304b\u3089\u5206\u985e\u53ef\u80fd\n",
      "* \u4e2d\u8eab\u306f4\u3064\u306e\u8981\u7d20\u304b\u3089\u306a\u308b\n",
      "    * \u304c\u304f\u7247\u306e\u9577\u3055(Sepal length)\n",
      "    * \u304c\u304f\u7247\u306e\u5e45(Sepal width)\n",
      "    * \u82b1\u3073\u3089\u306e\u9577\u3055(Petal length)\n",
      "    * \u82b1\u3073\u3089\u306e\u5e45(Petal width)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.datasets import load_iris\n",
      "\n",
      "data = load_iris()\n",
      "\n",
      "features = data[\"data\"]\n",
      "feature_names = data[\"feature_names\"]\n",
      "target = data[\"target\"]\n",
      "target_names = data[\"target_names\"]\n",
      "labels = target_names[target]\n",
      "\n",
      "print \"150\u30b5\u30f3\u30d7\u30ebx4\u6b21\u5143\u306e\u7279\u5fb4\u91cf\u30c7\u30fc\u30bf\"\n",
      "print features.shape\n",
      "print features[0]\n",
      "\n",
      "print \"\"\n",
      "print \"\u7279\u5fb4\u91cf\u306e\u540d\u524d\u306e\u30ea\u30b9\u30c8\"\n",
      "print feature_names  # list\n",
      "\n",
      "print \"\"\n",
      "print \"\u6b63\u89e3\u30c7\u30fc\u30bf\" \n",
      "print target.shape\n",
      "print target[0:150]\n",
      "\n",
      "print \"\"\n",
      "print \"\u6b63\u89e3\u30c7\u30fc\u30bf\u306e\u540d\u524d\u306e\u30ea\u30b9\u30c8\"\n",
      "print target_names[0:150]\n",
      "\n",
      "print \"target_names[target] (target_names\u306fndarray)\"\n",
      "print labels"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "150\u30b5\u30f3\u30d7\u30ebx4\u6b21\u5143\u306e\u7279\u5fb4\u91cf\u30c7\u30fc\u30bf\n",
        "(150, 4)\n",
        "[ 5.1  3.5  1.4  0.2]\n",
        "\n",
        "\u7279\u5fb4\u91cf\u306e\u540d\u524d\u306e\u30ea\u30b9\u30c8\n",
        "['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']\n",
        "\n",
        "\u6b63\u89e3\u30c7\u30fc\u30bf\n",
        "(150,)\n",
        "[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
        " 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
        " 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2\n",
        " 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n",
        " 2 2]\n",
        "\n",
        "\u6b63\u89e3\u30c7\u30fc\u30bf\u306e\u540d\u524d\u306e\u30ea\u30b9\u30c8\n",
        "['setosa' 'versicolor' 'virginica']\n",
        "target_names[target] (target_names\u306fndarray)\n",
        "['setosa' 'setosa' 'setosa' 'setosa' 'setosa' 'setosa' 'setosa' 'setosa'\n",
        " 'setosa' 'setosa' 'setosa' 'setosa' 'setosa' 'setosa' 'setosa' 'setosa'\n",
        " 'setosa' 'setosa' 'setosa' 'setosa' 'setosa' 'setosa' 'setosa' 'setosa'\n",
        " 'setosa' 'setosa' 'setosa' 'setosa' 'setosa' 'setosa' 'setosa' 'setosa'\n",
        " 'setosa' 'setosa' 'setosa' 'setosa' 'setosa' 'setosa' 'setosa' 'setosa'\n",
        " 'setosa' 'setosa' 'setosa' 'setosa' 'setosa' 'setosa' 'setosa' 'setosa'\n",
        " 'setosa' 'setosa' 'versicolor' 'versicolor' 'versicolor' 'versicolor'\n",
        " 'versicolor' 'versicolor' 'versicolor' 'versicolor' 'versicolor'\n",
        " 'versicolor' 'versicolor' 'versicolor' 'versicolor' 'versicolor'\n",
        " 'versicolor' 'versicolor' 'versicolor' 'versicolor' 'versicolor'\n",
        " 'versicolor' 'versicolor' 'versicolor' 'versicolor' 'versicolor'\n",
        " 'versicolor' 'versicolor' 'versicolor' 'versicolor' 'versicolor'\n",
        " 'versicolor' 'versicolor' 'versicolor' 'versicolor' 'versicolor'\n",
        " 'versicolor' 'versicolor' 'versicolor' 'versicolor' 'versicolor'\n",
        " 'versicolor' 'versicolor' 'versicolor' 'versicolor' 'versicolor'\n",
        " 'versicolor' 'versicolor' 'versicolor' 'versicolor' 'versicolor'\n",
        " 'versicolor' 'virginica' 'virginica' 'virginica' 'virginica' 'virginica'\n",
        " 'virginica' 'virginica' 'virginica' 'virginica' 'virginica' 'virginica'\n",
        " 'virginica' 'virginica' 'virginica' 'virginica' 'virginica' 'virginica'\n",
        " 'virginica' 'virginica' 'virginica' 'virginica' 'virginica' 'virginica'\n",
        " 'virginica' 'virginica' 'virginica' 'virginica' 'virginica' 'virginica'\n",
        " 'virginica' 'virginica' 'virginica' 'virginica' 'virginica' 'virginica'\n",
        " 'virginica' 'virginica' 'virginica' 'virginica' 'virginica' 'virginica'\n",
        " 'virginica' 'virginica' 'virginica' 'virginica' 'virginica' 'virginica'\n",
        " 'virginica' 'virginica' 'virginica']\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import itertools\n",
      "    \n",
      "# \u53ef\u8996\u5316\n",
      "fig = plt.figure(1, figsize=(16,16))\n",
      "for t, marker, c in zip(range(3), \">ox\", \"rgb\"):  # \u54c1\u7a2e\u3054\u3068\u306b\u8272\u3068\u30de\u30fc\u30ab\u3092\u5909\u3048\u3066\u30d7\u30ed\u30c3\u30c8\n",
      "    for (i,j) in itertools.combinations(range(4), 2):\n",
      "        ax = fig.add_subplot(4, 4, 4*i + j + 1)\n",
      "        ax.set_xlabel(feature_names[i])\n",
      "        ax.set_ylabel(feature_names[j])\n",
      "        ax.scatter(features[target == t, i],\n",
      "                   features[target == t, j],\n",
      "                   marker=marker,\n",
      "                   c=c)"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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BdG7q6u5jwaIfwmDn+K77fkiXLts45ZSmbd8tW/7Kood+0hh4t+ihnzBy5EFJ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\nUeGdQnlmAWpra6nNs8o1bou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+DLQClgJjcap+veEnT53fRo7lh8wW7nzAFRWfK637ROSl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ZX8OFhEKkg2LWwlJSWl5IR6rXIS1yMb9Tg3k97buMfBcY9zo2TyODgfP3Oxy8gn1LNc8TQMQ8Mw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\n2H9/Jq233nJ5yW53rZHAYFmSJ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       "text": [
        "<matplotlib.figure.Figure at 0x10ba6a990>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# http://scikit-learn.org/stable/auto_examples/decomposition/plot_pca_vs_lda.html\n",
      "from sklearn import datasets\n",
      "from sklearn.decomposition import PCA\n",
      "from sklearn.lda import LDA\n",
      "\n",
      "iris = datasets.load_iris()\n",
      "\n",
      "X = iris.data\n",
      "y = iris.target\n",
      "target_names = iris.target_names\n",
      "\n",
      "pca = PCA(n_components=2)\n",
      "X_r = pca.fit(X).transform(X)\n",
      "\n",
      "lda = LDA(n_components=2)\n",
      "X_r2 = lda.fit(X, y).transform(X)\n",
      "\n",
      "# Percentage of variance explained for each components\n",
      "print('explained variance ratio (first two components): %s'\n",
      "      % str(pca.explained_variance_ratio_))\n",
      "\n",
      "plt.figure()\n",
      "for c, i, target_name in zip(\"rgb\", [0, 1, 2], target_names):\n",
      "    plt.scatter(X_r[y == i, 0], X_r[y == i, 1], c=c, label=target_name)\n",
      "plt.legend()\n",
      "plt.title('PCA of IRIS dataset')\n",
      "\n",
      "plt.figure()\n",
      "for c, i, target_name in zip(\"rgb\", [0, 1, 2], target_names):\n",
      "    plt.scatter(X_r2[y == i, 0], X_r2[y == i, 1], c=c, label=target_name)\n",
      "plt.legend()\n",
      "plt.title('LDA of IRIS dataset')\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "explained variance ratio (first two components): [ 0.92461621  0.05301557]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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06FSvV6d64/faaGho0CFuty5xgvwQd+f2wDCZEauHTaRA7xnvSaknTyyZuKHU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\nncLU0NCgngkeLR9Wrp7x8Se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xBc4CvTHGFDgL9MYYU+As0BtjTIH7f+rdIUE3pkYiAAAA\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b7d4690>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ut5uCwgKqc61CrilcQ+lynVApXrU0Z4pnH2hjaFQEEvmD2dCaedwpKysTp3Oi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\nhnJGAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b8691d0>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 4.1.7 \u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3 ###\n"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}