{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 参加者間のネットワークについて(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "参加者間のネットワークについて、マルコフモデルで統一的にそのモデル化ができることが示されたが、一方でその確率の決め方に今回のモデルの独自性が生まれると考える。そこで、これまでと同じように、距離の概念を入れて状態から状態への遷移確率が決まるとして考えてみる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(しかし、一般に言って、$i\\rightarrow j$と$j\\rightarrow i$の確率は同じである必要はなく、このような場合を考えるなら、それは\"距離\"としての定義を満たしていない。)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$i$と$j$の間の距離を$d_{ij}(=d_{ji})$とし、その重みを$d_{ij}$の関数として$w_{ij}=w(d_{ij})$とすると、遷移確率は\n",
    "$$p_{ij} = \\frac{w_{ij}}{\\sum_{j}{w_{ij}}}$$\n",
    "のようになる。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "以下には最初に考えたように各状態について位置の座標を定義して、その間のユークリッド距離のみで確率が決定するような場合を考える。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "from Tkinter import *\n",
    "import numpy as np\n",
    "from scipy.spatial.distance import euclidean as euc\n",
    "\n",
    "\n",
    "class Main:\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.N = 6\n",
    "        self.app = Calc(self.N)\n",
    "    \n",
    "    def run(self):\n",
    "        self.window = Window(self.N, main=self.app)\n",
    "        self.window.display()\n",
    "\n",
    "\n",
    "class Calc:\n",
    "    \n",
    "    def __init__(self, N):\n",
    "        self.members = dict()\n",
    "        self.N = N\n",
    "\n",
    "    def calc_P(self):\n",
    "        P = []\n",
    "        for key, v in self.members.items():\n",
    "            _P = []\n",
    "            for n in range(self.N):\n",
    "                d = euc(self.members[key].place, self.members[n].place)\n",
    "                w = self.g(d)\n",
    "                _P.append(w)\n",
    "            P += _P\n",
    "        P = np.array(P).reshape(self.N, self.N)\n",
    "        self.P = []\n",
    "        for _P in P:\n",
    "            s = np.sum(_P)\n",
    "            self.P.append(_P/s)\n",
    "        self.P = np.array(self.P)\n",
    "\n",
    "    def g(self, x):\n",
    "        # 発言者の物理的距離に対する関数\n",
    "        return np.exp(-x)\n",
    "\n",
    "class Person(object):\n",
    "\n",
    "    def __init__(self, place=np.array([0., 0.])):\n",
    "        # 発言者の実際の位置が2次元の座標として表せる\n",
    "        self.place = place\n",
    "\n",
    "\n",
    "class Window(object):\n",
    "\n",
    "    def __init__(self, N, main):\n",
    "        self.root = Tk()\n",
    "        self.main = main\n",
    "        self.width = 640\n",
    "        self.height = 480\n",
    "        canvas = Canvas(self.root, width=self.width, height=self.height)\n",
    "        self.var = StringVar()\n",
    "        self.oval(canvas, N)\n",
    "        canvas.bind('<Motion>', self.pointer)\n",
    "        canvas.pack()\n",
    "        label = Label(self.root, textvariable=self.var, font='Ubuntu 9')\n",
    "        label.pack(side='left')\n",
    "        b1 = Button(self.root, text='calc', command=self.b1_clicked)\n",
    "        b1.pack(side='right')\n",
    "        b2 = Button(self.root, text='save', command=self.b2_clicked)\n",
    "        b2.pack(side='right')\n",
    "\n",
    "    def oval(self, canvas, N=6):\n",
    "        self.members = dict()\n",
    "        deg = np.linspace(0., 360., N, endpoint=False)\n",
    "        radius = 20\n",
    "        self.r = int((min(self.height, self.width)/2-radius)*0.9)\n",
    "        self.centerx = int(self.width/2)\n",
    "        self.centery = int(self.height/2)\n",
    "        for n in range(N):\n",
    "            rad = np.radians(deg[n])\n",
    "            self.members[n] = Oval(canvas, n+1,\n",
    "                                   self.centerx+self.r*np.cos(rad),\n",
    "                                   self.centery+self.r*np.sin(rad),\n",
    "                                   radius, self.var)\n",
    "\n",
    "    def pointer(self, event):\n",
    "        self.var.set(\"(%d,%d)\" % (event.x, event.y))\n",
    "\n",
    "    def b1_clicked(self):\n",
    "        for n in range(self.main.N):\n",
    "            x = (self.members[n].x-self.centerx)/float(self.r)\n",
    "            y = (self.members[n].y-self.centery)/float(self.r)\n",
    "            self.main.members[n] = Person(place=np.array([x, y]))\n",
    "        self.main.calc_P()\n",
    "        self.root.destroy()\n",
    "        \n",
    "    def b2_clicked(self):\n",
    "        import tkFileDialog\n",
    "        import os\n",
    "\n",
    "        fTyp = [('eps file', '*.eps'), ('all files', '*')]\n",
    "        filename = tkFileDialog.asksaveasfilename(filetypes=fTyp,\n",
    "                                                  initialdir=os.getcwd(),\n",
    "                                                  initialfile='figure_1.eps')\n",
    "\n",
    "        if filename is None:\n",
    "            return\n",
    "        try:\n",
    "            self.canvas.postscript(file=filename)\n",
    "        except TclError:\n",
    "            print \"\"\"\n",
    "            TclError: Cannot save the figure.\n",
    "            Canvas Window must be alive for save.\"\"\"\n",
    "            return 1\n",
    "        \n",
    "    def display(self):\n",
    "        self.root.mainloop()\n",
    "\n",
    "\n",
    "class Oval:\n",
    "\n",
    "    def __init__(self, canvas, id, x, y, r, var):\n",
    "        self.c = canvas\n",
    "        self.x = x\n",
    "        self.y = y\n",
    "        self.var = var\n",
    "        self.tag = str(id)\n",
    "        self.c.create_oval(x-r, y-r, x+r, y+r, outline='', fill='#069', tags=self.tag)\n",
    "\n",
    "        self.c.tag_bind(self.tag, '<Button-1>', self.pressed)\n",
    "        self.c.tag_bind(self.tag, '<Button1-Motion>', self.dragging)\n",
    "\n",
    "    def pressed(self, event):\n",
    "        self.x = event.x\n",
    "        self.y = event.y\n",
    "\n",
    "    def dragging(self, event):\n",
    "        self.c.move(self.tag, event.x - self.x, event.y - self.y)\n",
    "        self.x = event.x\n",
    "        self.y = event.y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def cal_f(n, P, K):  \n",
    "    f = np.identity(n) + P\n",
    "    if K == 1:\n",
    "        return f\n",
    "    for k in range(2, K+1):\n",
    "        _k = 2\n",
    "        tmp = P\n",
    "        while _k < k+1:\n",
    "            tmp = np.dot(tmp, P)\n",
    "            _k += 1\n",
    "        f += tmp\n",
    "    return f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td> 0.333575</td>\n",
       "      <td> 0.161861</td>\n",
       "      <td> 0.125993</td>\n",
       "      <td> 0.111192</td>\n",
       "      <td> 0.119210</td>\n",
       "      <td> 0.148170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td> 0.133705</td>\n",
       "      <td> 0.275550</td>\n",
       "      <td> 0.173149</td>\n",
       "      <td> 0.135611</td>\n",
       "      <td> 0.134642</td>\n",
       "      <td> 0.147343</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td> 0.102755</td>\n",
       "      <td> 0.170949</td>\n",
       "      <td> 0.272049</td>\n",
       "      <td> 0.174709</td>\n",
       "      <td> 0.147433</td>\n",
       "      <td> 0.132106</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td> 0.092117</td>\n",
       "      <td> 0.136005</td>\n",
       "      <td> 0.177471</td>\n",
       "      <td> 0.276351</td>\n",
       "      <td> 0.182568</td>\n",
       "      <td> 0.135488</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td> 0.097598</td>\n",
       "      <td> 0.133445</td>\n",
       "      <td> 0.148002</td>\n",
       "      <td> 0.180420</td>\n",
       "      <td> 0.273100</td>\n",
       "      <td> 0.167436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td> 0.124496</td>\n",
       "      <td> 0.149872</td>\n",
       "      <td> 0.136102</td>\n",
       "      <td> 0.137414</td>\n",
       "      <td> 0.171837</td>\n",
       "      <td> 0.280279</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>6 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1         2         3         4         5\n",
       "0  0.333575  0.161861  0.125993  0.111192  0.119210  0.148170\n",
       "1  0.133705  0.275550  0.173149  0.135611  0.134642  0.147343\n",
       "2  0.102755  0.170949  0.272049  0.174709  0.147433  0.132106\n",
       "3  0.092117  0.136005  0.177471  0.276351  0.182568  0.135488\n",
       "4  0.097598  0.133445  0.148002  0.180420  0.273100  0.167436\n",
       "5  0.124496  0.149872  0.136102  0.137414  0.171837  0.280279\n",
       "\n",
       "[6 rows x 6 columns]"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pandas import DataFrame\n",
    "main = Main()\n",
    "def g(x):\n",
    "    return 1./(1+x)\n",
    "main.app.g = g\n",
    "main.run()\n",
    "DataFrame(main.app.P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td> 15.423693</td>\n",
       "      <td> 17.151696</td>\n",
       "      <td> 17.315426</td>\n",
       "      <td> 17.024868</td>\n",
       "      <td> 17.238498</td>\n",
       "      <td> 16.845818</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td> 14.168166</td>\n",
       "      <td> 18.278681</td>\n",
       "      <td> 17.380701</td>\n",
       "      <td> 17.064849</td>\n",
       "      <td> 17.264082</td>\n",
       "      <td> 16.843520</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td> 14.121725</td>\n",
       "      <td> 17.159921</td>\n",
       "      <td> 18.493416</td>\n",
       "      <td> 17.117771</td>\n",
       "      <td> 17.283518</td>\n",
       "      <td> 16.823649</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td> 14.104293</td>\n",
       "      <td> 17.114469</td>\n",
       "      <td> 17.388423</td>\n",
       "      <td> 18.234201</td>\n",
       "      <td> 17.329755</td>\n",
       "      <td> 16.828858</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td> 14.113258</td>\n",
       "      <td> 17.110581</td>\n",
       "      <td> 17.350238</td>\n",
       "      <td> 17.125873</td>\n",
       "      <td> 18.429867</td>\n",
       "      <td> 16.870184</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td> 14.154327</td>\n",
       "      <td> 17.132605</td>\n",
       "      <td> 17.332561</td>\n",
       "      <td> 17.068061</td>\n",
       "      <td> 17.313669</td>\n",
       "      <td> 17.998776</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>6 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           0          1          2          3          4          5\n",
       "0  15.423693  17.151696  17.315426  17.024868  17.238498  16.845818\n",
       "1  14.168166  18.278681  17.380701  17.064849  17.264082  16.843520\n",
       "2  14.121725  17.159921  18.493416  17.117771  17.283518  16.823649\n",
       "3  14.104293  17.114469  17.388423  18.234201  17.329755  16.828858\n",
       "4  14.113258  17.110581  17.350238  17.125873  18.429867  16.870184\n",
       "5  14.154327  17.132605  17.332561  17.068061  17.313669  17.998776\n",
       "\n",
       "[6 rows x 6 columns]"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K = 100\n",
    "DataFrame(cal_f(6, main.app.P, K))"
   ]
  }
 ],
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