{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 近距離であることによる反応の抑制化"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "意見を提出する際に個人として感じることは何か、ということを考えると、他の人が自分と似たような意見を出すのではないか、という点から発言を控えるという場面が考えられる。また、これを代謝系などの化学反応に落とし込んだ際には、このような近い位置の意見はすべて同一の物質を表しているというように考えることもできる。そのように考えれば、似たような性質が縮約されてしまうので全体としての効率が下がってしまうという結果をもたらすのかもしれない。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: 化学反応でも同じように1分子での反応とよく混ざった多数の粒子の反応の間でエネルギー的な差に有無があるのかについて調べる必要がある。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "これを今まで会議のモデルとして考えてきたものに適応するときには、意見の近いもの(閾値よりも近い距離にある意見)は同じ意見を指すと考え、このような意見は以前に発言されているときには次の発言者はそのような意見は選びにくい、ということを反映したモデルであることが求められる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "具体的なモデルとして、有限個数の意見が状態空間上に分布しているときに、ある閾値$r$よりも近い距離にある点同士をノードでつないでいき、そうして連結されたノードとリンクを一つのクラスターとする。そして意見の選び方は、ある時刻に選ばれた意見から一番近い位置にノードをもつようなクラスターの中から選ぶこととする。このときクラスターの内部でどの意見を選ぶかの規則については、それぞれの人の発言力との関係で決めることにする。一度意見が選ばれたクラスターはもう一度選ばれることはなく、そのためクラスターを作るのに必要なパラメータの値によっては、例3で考えたものと全く同じになることが考えられる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "以上の設定を考えて、シミュレーションを行ってみる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.spatial.distance import euclidean as euc\n",
    "import collections\n",
    "import operator\n",
    "import random\n",
    "import bisect\n",
    "from itertools import chain\n",
    "from scipy.optimize import leastsq\n",
    "from ipython_doctester import test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def uniq_list(seq):\n",
    "    seen = set()\n",
    "    seen_add = seen.add\n",
    "    return [x for x in seq if x not in seen and not seen_add(x)]\n",
    "\n",
    "def accumulate(iterable, func=operator.add):\n",
    "    \"\"\"Return running totals\n",
    "    \n",
    "    Usage:\n",
    "    accumulate([1,2,3,4,5]) --> 1 3 6 10 15\n",
    "    accumulate([1,2,3,4,5], operator.mul) --> 1 2 6 24 120\n",
    "    \"\"\"\n",
    "    it = iter(iterable)\n",
    "    total = next(it)\n",
    "    yield total\n",
    "    for element in it:\n",
    "        total = func(total, element)\n",
    "        yield total\n",
    "\n",
    "def weighted_choice(d):\n",
    "    choices, weights = zip(*d)\n",
    "    cumdist = list(accumulate(weights))\n",
    "    x = random.random() * cumdist[-1]\n",
    "    return choices[bisect.bisect(cumdist, x)]\n",
    "\n",
    "class Person:\n",
    "    \n",
    "    def __init__(self, master, id, ideas, w):\n",
    "        \"\"\"Initialize argmunets.\n",
    "        \n",
    "        Keyword arguments:\n",
    "        master    : Master class (call from \"Meeting\")\n",
    "        self.id   : Id for each person [0, 1, ..., N-1]\n",
    "        self.ideas: ideas in space [0,1] × [0,1]\n",
    "        self.w    : probability weight for the person to speak\n",
    "        \"\"\"\n",
    "        self.id = id\n",
    "        self.ideas = ideas\n",
    "        self.w = w\n",
    "        # add_ideas : place, tag : (x, y), [person_id, cluster_id]\n",
    "        master.ideas += [[(i1, i2), [self.id, 0, self.w]] for i1, i2 in self.ideas]\n",
    "\n",
    "\n",
    "class Cluster:\n",
    "    \n",
    "    def __init__(self, ideas, r):\n",
    "        \"\"\"make cluster with self.r\n",
    "        \n",
    "        cluster_link:        \n",
    "        \"\"\"\n",
    "        self.ideas = ideas\n",
    "        self.r = r\n",
    "        self.l = 0\n",
    "        self.cluster_link = []\n",
    "        self.clustering()\n",
    "        \n",
    "    def clustering(self):\n",
    "        self.cell_num = int(1./self.r)\n",
    "        lr = 1./self.cell_num\n",
    "        \n",
    "        self.cell = dict() # key: (cellx,celly), value: list of ids\n",
    "        self.rcell = []\n",
    "        for i, idea in enumerate(self.ideas):\n",
    "            cellx = int(idea[0][0]/lr)\n",
    "            celly = int(idea[0][1]/lr)\n",
    "            if self.cell.has_key((cellx, celly)):\n",
    "                self.cell[(cellx, celly)] += [i]\n",
    "            else:\n",
    "                self.cell[(cellx, celly)] = [i]\n",
    "            self.rcell.append((cellx, celly))\n",
    "        num = 1\n",
    "        for i in range(len(self.ideas)):\n",
    "            num += self.find_nearest(i, num)\n",
    "        return self.cluster_link\n",
    "\n",
    "    def find_nearest(self, idea_id, num):\n",
    "        \"\"\"find nearest idea\n",
    "\n",
    "        idea_id: index in self.ideas\n",
    "        \"\"\"\n",
    "        cx, cy = self.rcell[idea_id]\n",
    "        place = self.ideas[idea_id][0]\n",
    "        CX = uniq_list([max(0, cx - 1), cx, min(cx + 1, self.cell_num - 1)])\n",
    "        CY = uniq_list([max(0, cy - 1), cy, min(cy + 1, self.cell_num - 1)])\n",
    "        tmp = [self.cell[(i, j)] for i in CX for j in CY if self.cell.has_key((i, j))]\n",
    "        tmp = list(chain.from_iterable(tmp))\n",
    "        tmp.remove(idea_id)\n",
    "        if len(tmp) == 0:\n",
    "            self.ideas[idea_id][1][1] = num\n",
    "            return 1\n",
    "        \n",
    "        nearest = []\n",
    "        cid = [num]\n",
    "        for k in tmp:\n",
    "            if euc(self.ideas[k][0], place) > self.r:\n",
    "                continue\n",
    "            nearest.append(k)\n",
    "            prenum = self.ideas[k][1][1]\n",
    "            if prenum == 0:\n",
    "                cid.append(num)\n",
    "                self.cluster_link.append((idea_id, k))\n",
    "            elif prenum < num:\n",
    "                cid.append(prenum)\n",
    "                if not (k, idea_id) in self.cluster_link:\n",
    "                    self.cluster_link.append((idea_id, k))\n",
    "        self.l += len(nearest)\n",
    "        cluster_id = min(cid)\n",
    "        if cluster_id < num:\n",
    "            ans = 0\n",
    "        else:\n",
    "            ans = 1\n",
    "        self.ideas[idea_id][1][1] = cluster_id\n",
    "        for i in nearest:\n",
    "            self.ideas[i][1][1] = cluster_id\n",
    "        cid.remove(num)\n",
    "        if len(cid) == 0:\n",
    "            return ans\n",
    "        cid.remove(cluster_id)\n",
    "        if len(cid) == 0:\n",
    "            return ans\n",
    "        for i in cid:\n",
    "            for x in self.ideas:\n",
    "                if x[1][1] == i:\n",
    "                    x[1][1] = cluster_id\n",
    "        return ans\n",
    "\n",
    "        \n",
    "class Meeting:\n",
    "    \n",
    "    def __init__(self, K, N, S=20, r=0.06, draw=True):\n",
    "        self.K = K\n",
    "        self.N = N\n",
    "        self.S = S\n",
    "        self.r = r\n",
    "        self.ideas = []\n",
    "        self.minutes = []\n",
    "        self.ave_l = 0\n",
    "        self.draw = draw\n",
    "        \n",
    "    def gather_people(self, ideass=None, weights=None):\n",
    "        \"\"\"Gather participants.\n",
    "        \n",
    "        Keyword arguments:\n",
    "        ideas  : list of ideas for each person\n",
    "               ex) [((0.3,0.1),(0.2,0.5)), ((0.5,0.6))] when N = 2\n",
    "        weights: list of weights for the probability of the person to speak\n",
    "        \"\"\"\n",
    "        if not ideass:\n",
    "            x = np.random.rand(self.N, self.S*2)\n",
    "            ideass = []\n",
    "            for _x in x:\n",
    "                ideass.append([(i,j) for i,j in zip(_x[::2], _x[1::2])])\n",
    "        if not weights:\n",
    "            weights = [1.] * self.N\n",
    "        for i, ideas, w in zip(range(self.N), ideass, weights):\n",
    "            Person(self, i, ideas, w)\n",
    "\n",
    "    def init(self):\n",
    "        self.gather_people()\n",
    "        cluster = Cluster(self.ideas, self.r)\n",
    "        self.cluster_link = cluster.cluster_link\n",
    "        self.ave_l = cluster.l/float(len(self.ideas))\n",
    "        if self.draw:\n",
    "            colors = ['b', 'g', 'r', 'c', 'm', 'y', 'k']\n",
    "            self.fig = plt.figure(figsize=(9, 9))\n",
    "            self.ax = self.fig.add_subplot(1, 1, 1)\n",
    "            self.labels = []\n",
    "            self.s1 = []\n",
    "            for idea, tag in self.ideas:\n",
    "                x = idea[0]\n",
    "                y = idea[1]\n",
    "                s = self.ax.scatter(x, y,\n",
    "                                    c=colors[tag[0]%len(colors)],\n",
    "                                    alpha=0.2)\n",
    "                self.s1.append(s)\n",
    "            data = []\n",
    "            for link in self.cluster_link:\n",
    "                ix = self.ideas[link[0]][0][0]\n",
    "                iy = self.ideas[link[0]][0][1]\n",
    "                jx = self.ideas[link[1]][0][0]\n",
    "                jy = self.ideas[link[1]][0][1]\n",
    "                data += [(ix, jx), (iy, jy), 'k']\n",
    "            self.ax.plot(*data, alpha=0.5)\n",
    "            \n",
    "    def progress(self):\n",
    "        self.init()\n",
    "        preidea = self.ideas[np.random.choice(range(len(self.ideas)))]\n",
    "        self.minutes.append(preidea)\n",
    "        l = list(self.ideas)\n",
    "        self.k = 1\n",
    "\n",
    "        while self.k < self.K + 1:\n",
    "            \n",
    "            # remove ideas in the same cluster\n",
    "            l = [idea for idea in l if idea[1][1] != preidea[1][1]]\n",
    "\n",
    "            # if no one can speak: meeting ends.\n",
    "            if len(l) == 0:\n",
    "                break\n",
    "\n",
    "            # confirm cluster id which is nearest from the preidea\n",
    "            distance = [(euc(preidea[0], i[0]), i) for i in l]\n",
    "            minclusterid = min(distance)[1][1][1]\n",
    "            \n",
    "            # gather ideas in the cluster\n",
    "            tmp = [idea for idea in l if idea[1][1] == minclusterid]\n",
    "            d = dict()\n",
    "            for t in tmp:\n",
    "                d[t[1][0]] = d.get(t[1][0], 0) + t[1][2]\n",
    "            d = [(k, v) for k, v in d.items()]\n",
    "            # chose whose ideas to be chosed from the cluster\n",
    "            whois = weighted_choice(d)\n",
    "            \n",
    "            # gather ideas\n",
    "            who = [idea for idea in tmp if idea[1][0] == whois]\n",
    "            p = [(idea, idea[1][2]) for idea in who]\n",
    "            # chose the next idea from the id is \"whois\"\n",
    "            idea = weighted_choice(p)\n",
    "\n",
    "            self.minutes.append(idea)\n",
    "            preidea = idea\n",
    "            self.callback()\n",
    "            self.k += 1\n",
    "        self.after()\n",
    "\n",
    "    def callback(self):\n",
    "        if self.draw:\n",
    "            ix = self.minutes[-2][0][0]\n",
    "            iy = self.minutes[-2][0][1]\n",
    "            jx = self.minutes[-1][0][0]\n",
    "            jy = self.minutes[-1][0][1]\n",
    "            l1 = self.ax.plot([ix, jx], [iy, jy], color='b', alpha=0.5)\n",
    "            self.ax.text((ix+jx)/2, (iy+jy)/2, self.k)\n",
    "        else:\n",
    "            pass\n",
    "\n",
    "    def after(self):\n",
    "        if self.draw:\n",
    "            plt.show()\n",
    "        else:\n",
    "            pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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gct8+U+uSc4uJiaEofzxH9/aQFnGQArudCQUFZpcl50mhRESChtVqZeHChXz0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\nSAQolIhMQ2trKy6Xi2XLlpldiswCTuflG/Ht3buXu+++G4D77ruPvXv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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8468000250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "meeting = Meeting(K=20, N=4, S=20, r=0.07, draw=True)\n",
    "meeting.progress()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 16, 18, 19, 20, 21, 22, 23, 25, 26]\n",
      "[(0, 36), (1, 77), (1, 44), (1, 76), (1, 56), (3, 17), (3, 41), (4, 75), (5, 26), (6, 16), (6, 22), (6, 50), (6, 52), (8, 71), (8, 29), (8, 67), (9, 53), (9, 58), (9, 59), (10, 29), (10, 67), (10, 51), (10, 62), (11, 68), (11, 19), (12, 13), (14, 44), (15, 37), (16, 22), (16, 33), (16, 50), (17, 41), (18, 47), (18, 48), (20, 22), (20, 52), (21, 35), (21, 43), (21, 37), (21, 64), (21, 57), (22, 33), (22, 50), (23, 55), (25, 46), (25, 49), (27, 79), (27, 69), (27, 38), (28, 32), (29, 71), (29, 67), (30, 53), (30, 56), (30, 61), (30, 58), (31, 73), (34, 35), (34, 43), (35, 43), (35, 57), (37, 64), (38, 60), (40, 52), (40, 64), (42, 63), (43, 57), (44, 76), (45, 62), (46, 66), (47, 48), (47, 49), (49, 77), (50, 52), (53, 56), (53, 61), (53, 58), (56, 76), (56, 61), (58, 61), (58, 59), (64, 65), (66, 72), (67, 71), (69, 79), (76, 77)]\n",
      "2.15\n"
     ]
    },
    {
     "data": {
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       " (15, 1, (0.96744124846013835, 0.078418261875894513)),\n",
       " (15, 2, (0.88962638115936798, 0.04539049236789694)),\n",
       " (16, 1, (0.68761047534364972, 0.64918608670064326)),\n",
       " (18, 1, (0.80121711959545239, 0.42653342658277726)),\n",
       " (18, 1, (0.80187805723956129, 0.52583274790107759)),\n",
       " (18, 3, (0.72852663213127911, 0.37628648179783108)),\n",
       " (18, 3, (0.78179613448732854, 0.42496439463717328)),\n",
       " (18, 3, (0.78311718940759023, 0.56941770392782298)),\n",
       " (19, 1, (0.91768358288503415, 0.61059572441061327)),\n",
       " (19, 1, (0.9279229423963673, 0.58245458683053131)),\n",
       " (20, 1, (0.86322781257252634, 0.73916431889739587)),\n",
       " (20, 3, (0.8419152483438278, 0.73785405745071431)),\n",
       " (21, 1, (0.61344701984242944, 0.44821935555722947)),\n",
       " (22, 2, (0.21561835981849842, 0.068401539998441563)),\n",
       " (22, 3, (0.28895337169425228, 0.093477423024687867)),\n",
       " (23, 2, (0.38847352923601031, 0.96358073404884115)),\n",
       " (24, 3, (0.93938848026074784, 0.99901379507312937)),\n",
       " (25, 3, (0.065369284870898103, 0.18285788846524653)),\n",
       " (26, 3, (0.99679804461878541, 0.18361492890179043))]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print sorted([x[1][1] for x in meeting.minutes])\n",
    "print meeting.cluster_link\n",
    "print meeting.ave_l\n",
    "sorted([(x[1][1], x[1][0], (x[0])) for x in meeting.ideas])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "下のやり方ではクラスターの数をちゃんと数えたことにならない。(クラスター同士の融合を考えることができない)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "26"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max([x[1][1] for x in meeting.ideas])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "正しい数え方"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(uniq_list([x[1][1] for x in meeting.ideas]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "閾値$r$を変えたときに意見の総数に対するクラスターの数との関係。横軸$r$、縦軸$1- (\\text{クラスターの数})/(\\text{意見の総数})$の通常のプロット(上段)と両対数プロット(下段)。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "trial = 100\n",
    "\n",
    "r = np.logspace(-2, np.log10(0.2), num=50)\n",
    "phi1 = []\n",
    "for _r in r:\n",
    "    _phi = 0.\n",
    "    for t in range(trial):\n",
    "        meeting = Meeting(K=50, N=6, r=_r, draw=False)\n",
    "        meeting.init()\n",
    "        _phi += len(uniq_list([x[1][1] for x in meeting.ideas]))/float(len(meeting.ideas))\n",
    "    phi1.append(1 - _phi/trial)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def myplot1(x, y, xfit=np.array([]), yfit=np.array([]), param=None,\n",
    "            scale=['linear', 'linear', 'log', 'log']):\n",
    "    \"\"\"my plot function\n",
    "    \n",
    "    x: {'label_x', xdata}\n",
    "    y: {'label_y', ydata}\n",
    "    param: {'a': 10, 'b': 20}\n",
    "    \"\"\"\n",
    "    if param:\n",
    "        s = [r'$%s = %f$' % (k, v) for k, v in param.items()]\n",
    "        label = s[0]\n",
    "        for _s in s[1:]:\n",
    "            label += \", \" + _s\n",
    "    label_x, xdata = x.items()[0]\n",
    "    label_y, ydata = y.items()[0]\n",
    "    fig = plt.figure(figsize=(8, 12))\n",
    "    ax1 = fig.add_subplot(211)\n",
    "\n",
    "    ax1.plot(xdata, ydata)\n",
    "    if len(xfit):\n",
    "        ax1.plot(xfit, yfit, label=label)\n",
    "        ax1.legend(loc='best')\n",
    "    ax1.set_xlabel(label_x)\n",
    "    ax1.set_ylabel(label_y)\n",
    "    ax1.set_xscale(scale[0])\n",
    "    ax1.set_yscale(scale[1])\n",
    "    \n",
    "    ax2 = fig.add_subplot(212)\n",
    "    ax2.plot(xdata, ydata)\n",
    "    if len(xfit):\n",
    "        ax2.plot(xfit, yfit, label=label)\n",
    "        ax2.legend(loc='best')\n",
    "    ax2.set_xlabel(label_x)\n",
    "    ax2.set_ylabel(label_y)\n",
    "    ax2.set_xscale(scale[2])\n",
    "    ax2.set_yscale(scale[3])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def myfit(fit_func, parameter, x, y, xmin, xmax):\n",
    "    \"\"\"my fitting and plotting function.\n",
    "    \n",
    "    fit_func: function (parameter(type:list), x) \n",
    "    parameter: list of tuples: [('param1', param1), ('param2', param2), ...]\n",
    "    x, y: dict\n",
    "    xmin, xmax: float\n",
    "    \"\"\"\n",
    "    xkey, xdata = x.items()[0]\n",
    "    ykey, ydata = y.items()[0]\n",
    "\n",
    "    def fit(parameter, x, y):\n",
    "        return y - fit_func(parameter, x)\n",
    "\n",
    "    # use x : xmin < x < xmax\n",
    "    i = 0\n",
    "    while xdata[i] < xmin:\n",
    "        i += 1\n",
    "    imin, imax = i, i\n",
    "    while xdata[i] < xmax:\n",
    "        i += 1\n",
    "    imax = i - 1\n",
    "\n",
    "    paramdata = [b for a, b in parameter]\n",
    "    paramkey = [a for a, b in parameter]\n",
    "    res = leastsq(fit, paramdata, args=(xdata[imin:imax], ydata[imin:imax]))\n",
    "    for p in res[0]:\n",
    "        print xkey + \": \" + str(p)\n",
    "    fitted = fit_func(res[0], xdata[imin:imax])\n",
    "\n",
    "    fittedparam = dict([(k, v) for k, v in zip(paramkey, res[0])])\n",
    "    myplot1(x, y, xdata[imin:imax], fitted, param=fittedparam)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "$r$: 1.73018673432\n",
      "$r$: 1.81957023866\n"
     ]
    },
    {
     "data": {
      "image/png": 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E8dYzcC4wG5gHPJDF64cCo4ApwHSgY4Elk3Kpa9fIhYe6dQs7iSTlXqz0DBQF5gAtgGXA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2632594210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "param = [('a', 1.5), ('b', 0.)]\n",
    "xmin, xmax = 0., 0.07\n",
    "x = {r'$r$': r}\n",
    "y = {r'$\\phi$': phi1}\n",
    "def fit_func(parameter, x):\n",
    "    a = parameter[0]\n",
    "    b = parameter[1]\n",
    "    return np.power(x, a)*np.power(10, b)\n",
    "myfit(fit_func, param, x, y, xmin, xmax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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gxHvhBTjoIHj7bdcVkKQluTdBQ4aBFOrdG/bdF37/+9iVSFLyGAYaMgykzJQpUFkZ5gys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\nSZIkSZIkSZIkSZKk5vn/AQvTW8ZTR3hCAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa957226350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "myplot1({r'$r$': r}, {r'$\\phi$': phi1})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "このグラフから、クラスターの作り方に関する閾値$r$に関してクラスターの数との関係を見ることができる。$r$が大きくなるほどクラスターができやすく、またクラスター同士の融合も起こりやすいため、$r=0.15$ほどで系の中にあるクラスターの数は1となって、すべてが同じクラスター内に所属することになる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "両変数を対数にした状態で直線としてフィットしてみる。得られたパラメータによるフィッティング関数のプロットは、元の状態に戻してから行う。後に示す直接べき関数として求めた場合に比べて、$r$の小さい領域での直線の傾きがよく合っているように見える。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "傾き: 1.86089133868\n",
      "切片: 2.00299872509\n"
     ]
    },
    {
     "data": {
      "image/png": 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RJBWGaDlMUFg8TFDEer7Tk9VzmtBgzW089VTYaSRJXrVQxWrDtg28s+AdFo7u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\nSZIkSZIkSZIkSZIkSYfm/wHcKIYUwiHoIgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa956f6cb90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 1.5\n",
    "b = 0.\n",
    "param = [a, b]\n",
    "rmin, rmax = 0., 0.07\n",
    "\n",
    "def fit_func(parameter, x):\n",
    "    a = parameter[0]\n",
    "    b = parameter[1]\n",
    "    return a*np.log10(x) + b\n",
    "\n",
    "def fit(parameter, x, y):\n",
    "    return np.log10(y) - fit_func(parameter, x)\n",
    "\n",
    "i = 0\n",
    "while r[i] < rmin:\n",
    "    i += 1\n",
    "imin, imax = i, i\n",
    "while r[i] < rmax:\n",
    "    i += 1\n",
    "imax = i - 1\n",
    "\n",
    "res = leastsq(fit, param, args=(r[imin:imax], phi1[imin:imax]))\n",
    "print u\"傾き: \" + str(res[0][0])\n",
    "print u\"切片: \" + str(res[0][1])\n",
    "R1 = np.power(10, fit_func(res[0], r[imin:imax]))\n",
    "\n",
    "myplot1({r'$r$': r}, {r'$\\phi$': phi1}, r[imin:imax], R1, param={'a': res[0][0], 'b': res[0][1]})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "両変数をそのまま用い、ベキ関数で最小2乗法でフィッティングした場合。先の場合に比べて、$r$の小さい領域で直線とデータの間の差は大きく見える。これは$r$の小さい時にはその差も小さくなっているために、エラーの値としては小さくなっているために起こっていることだと思われる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "傾き: 1.72659903811\n",
      "切片: 1.81357538307\n"
     ]
    },
    {
     "data": {
      "image/png": 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Ua8/M7EObw6/nT2X+FHYokqQocgChcmXONxtZddhgUi+fG3YokqQoszKgXOk+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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa957032390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 1.5\n",
    "b = 0.\n",
    "param = [a, b]\n",
    "rmin, rmax = 0., 0.07\n",
    "\n",
    "def fit_func(parameter, x):\n",
    "    a = parameter[0]\n",
    "    b = parameter[1]\n",
    "    return np.power(x, a)*np.power(10, b)\n",
    "\n",
    "def fit(parameter, x, y):\n",
    "    return y - fit_func(parameter, x)\n",
    "\n",
    "i = 0\n",
    "while r[i] < rmin:\n",
    "    i += 1\n",
    "imin, imax = i, i\n",
    "while r[i] < rmax:\n",
    "    i += 1\n",
    "imax = i - 1\n",
    "\n",
    "res = leastsq(fit, param, args=(r[imin:imax], phi1[imin:imax]))\n",
    "print u\"傾き: \" + str(res[0][0])\n",
    "print u\"切片: \" + str(res[0][1])\n",
    "R2 = fit_func(res[0], r[imin:imax])\n",
    "\n",
    "myplot1({r'$r$': r}, {r'$\\phi$': phi1}, r[imin:imax], R2, param={'a': res[0][0], 'b': res[0][1]})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "S字型の曲線であるので、\n",
    "\n",
    "$$\\rho (L) = \\frac{2}{\\omega}L \\exp \\left[ -  \\left( \\frac{L}{\\omega} \\right)^{2} \\right]$$\n",
    "\n",
    "を参考にして、この関数系でフィットしてみる。この場合、$r$の比較的大きい領域のデータを含んでもよい。\n",
    "\n",
    "$$\\phi (r) = 1 - \\exp \\left[ -  \\left( \\frac{r}{\\omega} \\right)^{a} \\right]$$\n",
    "\n",
    "としてパラメータ$\\omega$に関して最小2乗法でフィッティングを行う。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "omega: 0.0710580799788\n",
      "a: 2.09805559422\n"
     ]
    },
    {
     "data": {
      "image/png": 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95vWidNHSfN7mc6qXynyfrbtw5mLA0126dIkGDRoQFRWFj4+P1XFciooBx6kYEI918SKE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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2632503850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "omega = 0.06\n",
    "a = 2.0\n",
    "param = [omega, a]\n",
    "rmin, rmax = 0.01, 0.2\n",
    "\n",
    "def fit_func(parameter, x):\n",
    "    omega = parameter[0]\n",
    "    a = parameter[1]\n",
    "    return 1 - np.exp(-(x/omega)**a)\n",
    "\n",
    "def fit(parameter, x, y):\n",
    "    return y - fit_func(parameter, x)\n",
    "\n",
    "i = 0\n",
    "while r[i] < rmin:\n",
    "    i += 1\n",
    "imin, imax = i, i\n",
    "while r[i] < rmax:\n",
    "    i += 1\n",
    "imax = i - 1\n",
    "\n",
    "res = leastsq(fit, param, args=(r[imin:imax], phi1[imin:imax]))\n",
    "print u\"omega: \" + str(res[0][0])\n",
    "print u\"a: \" + str(res[0][1])\n",
    "R3 = fit_func(res[0], r[imin:imax])\n",
    "\n",
    "myplot1({r'$r$': r}, {r'$\\phi$': phi1}, r[imin:imax], R3, param={'\\omega': res[0][0], 'a': res[0][1]})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "また、シグモイド関数の一般形としてのロジスティック関数\n",
    "\n",
    "$$f(x) = \\frac{K}{1+\\exp \\left[ rK(x_{0}-x)\\right]}$$\n",
    "\n",
    "に関してもフィッティングしてみる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "K: 0.981918027574\n",
      "r: 58.6818506045\n",
      "x0: 0.0601203071207\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "-c:11: RuntimeWarning: overflow encountered in exp\n"
     ]
    },
    {
     "data": {
      "image/png": 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YAuwDfsUcPNgn5iY2cvIk7NwJbdrA2ZtnWXp0KT2r97Q6loiIPCS7HCZwFB0m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\nFy9+qLYH5w442jNw70P//PnzZMuWDV9fX9544w0Arly5wuTJk8mdOze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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa95720ae50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "K = 1.\n",
    "_r = 1.\n",
    "x0 = 0.\n",
    "param = [K, _r, x0]\n",
    "rmin, rmax = 0.01, 0.2\n",
    "\n",
    "def fit_func(parameter, x):\n",
    "    K = parameter[0]\n",
    "    _r = parameter[1]\n",
    "    x0 = parameter[2]\n",
    "    return K/(1+np.exp(_r*K*(x0-x)))\n",
    "\n",
    "def fit(parameter, x, y):\n",
    "    return y - fit_func(parameter, x)\n",
    "\n",
    "i = 0\n",
    "while r[i] < rmin:\n",
    "    i += 1\n",
    "imin, imax = i, i\n",
    "while r[i] < rmax:\n",
    "    i += 1\n",
    "imax = i - 1\n",
    "\n",
    "res = leastsq(fit, param, args=(r[imin:imax], phi1[imin:imax]))\n",
    "print u\"K: \" + str(res[0][0])\n",
    "print u\"r: \" + str(res[0][1])\n",
    "print u\"x0: \" + str(res[0][2])\n",
    "R4 = fit_func(res[0], r[imin:imax])\n",
    "\n",
    "myplot1({r'$r$': r}, {r'$\\phi$': phi1}, r[imin:imax], R4, param={'K': res[0][0], 'r': res[0][1], 'x_{0}': res[0][2]})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$r$の小さい領域ではフィットは良くないように見える。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $r$を固定して参加者の人数を変更したときのクラスター数と意見の総数に対するクラスターの数との関係"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "横軸を参加者の数$N$、縦軸を$1-(\\text{クラスタ数}/\\text{総意見数})$としたときのグラフを書いてみることにする。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "trial = 100\n",
    "\n",
    "N = np.arange(1, 20)\n",
    "phi6 = []\n",
    "for _N in N:\n",
    "    _phi = 0.\n",
    "    for t in range(trial):\n",
    "        meeting = Meeting(K=50, N=_N, r=0.07, draw=False)\n",
    "        meeting.init()\n",
    "        _phi += len(uniq_list([x[1][1] for x in meeting.ideas]))/float(len(meeting.ideas))\n",
    "    phi6.append(1 - _phi/trial)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dBa+8ErsSSVJaJWVqoFhSNTVw9NGwySZw8cWxK5EkJZVnDdSVmiCQy8GJJ8K7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\nPxz+9S/YccfY1UiStHQGgSL66CPYf3+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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa956ac6610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "myplot1({r'$N$': N}, {r'$\\phi$': phi6})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "このとき、意見の総数と参加者の数、一人あたりの意見の数の間には比例の関係が成り立っており、この数のみに依存して、どちらを変えるかは問題ではない。したがって、より刻みを多く取ることのできる一人あたりの意見の数$S$を変えて計算した場合を見てみることにする。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "trial = 100\n",
    "\n",
    "S = np.arange(10, 70)\n",
    "phi7 = []\n",
    "for _S in S:\n",
    "    _phi = 0.\n",
    "    for t in range(trial):\n",
    "        meeting = Meeting(K=50, S=_S, N=6, r=0.07, draw=False)\n",
    "        meeting.init()\n",
    "        _phi += len(uniq_list([x[1][1] for x in meeting.ideas]))/float(len(meeting.ideas))\n",
    "    phi7.append(1 - _phi/trial)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JkvLHOQKr8dvfwujRzguQJMWfcwRybOBA+Mc/nBcgSUoHg0AtM2fCBRc4L0CS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\nJEmSJEmSJEmSJEmSJCnF/j/XzhTdXDWp9gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2651306150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "myplot1({r'$S$': S}, {r'$\\phi$': phi7})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "グラフの形から、\n",
    "\n",
    "$$\\phi(S) = 1- \\exp\\left[- \\left( \\frac{S}{\\omega} \\right)^{a}\\right]$$\n",
    "\n",
    "であるとしてフィッティングを行ってみる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "omega: 20.6143107436\n",
      "a: 1.17886589316\n"
     ]
    },
    {
     "data": {
      "image/png": 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8vTE9qvZguNsKOrYoTrVqcPw4jBqlJEBE8i5r6RpIxJgVsBpjBsEMjIGCI1Ne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\nJEmSJEmSpBD7f1D+mz8jdbi3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2632a40f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "omega = 20.\n",
    "a = 1.\n",
    "param = [omega, a]\n",
    "\n",
    "def fit_func(parameter, x):\n",
    "    omega = parameter[0]\n",
    "    a = parameter[1]\n",
    "    return 1. - np.exp(-(x/omega)**a)\n",
    "\n",
    "def fit(parameter, x, y):\n",
    "    return y - fit_func(parameter, x)\n",
    "\n",
    "res = leastsq(fit, param, args=(S, phi7))\n",
    "print u\"omega: \" + str(res[0][0])\n",
    "print u\"a: \" + str(res[0][1])\n",
    "R5 = fit_func(res[0], S)\n",
    "\n",
    "myplot1({r'$S$': S}, {r'$\\phi$': phi7}, S, R5, param={r'\\omega': res[0][0], r'a': res[0][1]})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### パーコレーション閾値での振る舞い"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "また、パーコレーションとしてこの現象をとらえたとき、ある$r$の値において系のサイズと同程度の大きさのクラスターが出現するようになり、このときのクラスターのサイズ分布を求めれば、それはべき分布に従うことが予想される。\n",
    "\n",
    "以下のセルでそのことを調べてみる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(1, 5.262), (2, 4.921), (3, 4.607), (4, 4.615), (5, 4.118), (6, 4.118), (7, 4.061), (8, 3.678), (9, 3.718), (10, 3.555), (11, 3.392), (12, 3.334), (13, 3.172), (14, 2.841), (15, 2.959), (16, 2.902), (17, 2.723), (18, 2.633), (19, 2.573), (20, 2.461), (21, 2.429), (22, 2.313), (23, 2.184), (24, 2.295), (25, 2.084), (26, 2.034), (27, 2.091), (28, 1.971), (29, 1.801), (30, 1.872), (31, 1.732), (32, 1.684), (33, 1.662), (34, 1.592), (35, 1.543), (36, 1.567), (37, 1.533), (38, 1.455), (39, 1.436), (40, 1.362), (41, 1.357), (42, 1.313), (43, 1.249), (44, 1.156), (45, 1.117), (46, 1.02), (47, 0.908), (48, 0.777), (49, 0.667), (50, 0.559), (51, 0.472), (52, 0.349), (53, 0.241), (54, 0.19), (55, 0.126), (56, 0.077), (57, 0.056), (58, 0.037), (59, 0.019), (60, 0.013), (61, 0.005), (62, 0.003), (63, 0.001), (64, 0.001), (65, 0.001), (66, 0.001), (67, 0.001), (68, 0.001)]\n"
     ]
    }
   ],
   "source": [
    "trial = 1000\n",
    "_r = 0.07\n",
    "_phi = collections.Counter()\n",
    "for i in range(trial):\n",
    "    meeting = Meeting(K=50, N=6, r=_r, draw=False)\n",
    "    meeting.init()\n",
    "    _phi = _phi + collections.Counter([x[1][1] for x in meeting.ideas])\n",
    "phi = [(k, v/float(trial)) for k, v in dict(_phi).items()]\n",
    "print phi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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0vklR5Zy/pO02cuQj/OpXN7N+fTFDhpzKbbfd8q3LCq9cubLqI4fzgCzi8bnc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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f14012b4050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8, 12))\n",
    "ax = fig.add_subplot(211)\n",
    "ax.scatter([x[0] for x in phi], [x[1] for x in phi])\n",
    "ax.set_xlabel(r'$l$')\n",
    "ax.set_ylabel(r'$\\phi$')\n",
    "ax.set_xscale('linear')\n",
    "ax.set_yscale('linear')\n",
    "ax = fig.add_subplot(212)\n",
    "ax.scatter([x[0] for x in phi], [x[1] for x in phi])\n",
    "ax.set_xlabel(r'$l$')\n",
    "ax.set_ylabel(r'$\\phi$')\n",
    "ax.set_xscale('log')\n",
    "ax.set_yscale('log')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "閾値$r$を変えたときの最大クラスターのサイズと全要素数との間の関係。クラスターサイズとはここでは同じクラスター内に含まれる要素の数。\n",
    "\n",
    "横軸$r$、縦軸$(\\text{最大クラスターサイズ})/(\\text{全要素数})$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Counter({12: 6, 15: 6, 27: 6, 2: 5, 19: 5, 25: 4, 8: 3, 10: 3, 16: 3, 20: 3, 26: 3, 30: 3, 38: 3, 1: 2, 3: 2, 5: 2, 6: 2, 7: 2, 11: 2, 18: 2, 32: 2, 37: 2, 42: 2, 47: 2, 50: 2, 51: 2, 4: 1, 9: 1, 13: 1, 14: 1, 17: 1, 21: 1, 22: 1, 23: 1, 28: 1, 29: 1, 31: 1, 33: 1, 34: 1, 35: 1, 36: 1, 39: 1, 40: 1, 41: 1, 43: 1, 44: 1, 45: 1, 46: 1, 48: 1, 49: 1, 52: 1, 53: 1, 54: 1, 55: 1, 56: 1, 57: 1, 58: 1, 59: 1, 60: 1, 61: 1, 62: 1, 63: 1, 64: 1, 65: 1, 66: 1, 67: 1, 68: 1})\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.05"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print collections.Counter([x[1][1] for x in meeting.ideas])\n",
    "max([v for v in collections.Counter([x[1][1] for x in meeting.ideas]).values()])/float(len(meeting.ideas))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "trial = 100\n",
    "\n",
    "r = np.linspace(0.01, 0.2, num=50)\n",
    "phi2 = []\n",
    "for _r in r:\n",
    "    _phi = 0.\n",
    "    for t in range(trial):\n",
    "        meeting = Meeting(K=50, N=6, r=_r, draw=False)\n",
    "        meeting.init()\n",
    "        _phi += max([v for v in\n",
    "                     collections.Counter([x[1][1] for x in meeting.ideas]).values()]\n",
    "                    ) \\\n",
    "                / \\\n",
    "                float(len(meeting.ideas))\n",
    "    phi2.append(_phi/trial)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def myplot2(x, y, xfit=np.array([]), yfit=np.array([]), param=None):\n",
    "    myplot1(x, y, xfit, yfit, param, scale=['linear', 'linear', 'linear', 'log'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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YBKTkMQxIKguXE0rJZRiQVHITJ4ZzEBx7bOxKJK2IYUBSyd14I5x1FrRtG7sSSStiA6Gk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\nHyurhgadXjn3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa956ac63d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "myplot2({r'$r$': r}, {r'$\\phi$': phi2})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "横軸r、縦軸(最大クラスターサイズ)/(全要素数)で縦軸に対数を取ったときに直線に乗っている(ように見える)。\n",
    "\n",
    "なぜか?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "フィッティング関数として\n",
    "\n",
    "$$f(x) = 10^{ax + b}$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a: 12.4841338989\n",
      "b: -1.14418617506\n"
     ]
    },
    {
     "data": {
      "image/png": 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BcYRZ22ZxV+W7KJS3kOkoPqMhAhFxlz4mxBGmbXXmKYU6i0BE3KFiQILe2dSzzNk+hw7V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\nL82bNwdg7969bNmy5dKB6qmnniI6Opo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dO3QaSbIMKEFue+U2Xl35Kq90eYV9qu8TOk5K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\nj4e+faO7EloEJKnyOGdAKWHKFOjVKxoROPnk0GkkKX0kYs6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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f13fbe14250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 10.\n",
    "b = 20.\n",
    "param = [a, b, c]\n",
    "rmin, rmax = 0.01, 0.10\n",
    "\n",
    "def fit_func(parameter, x):\n",
    "    a = parameter[0]\n",
    "    b = parameter[1]\n",
    "    return np.power(10, a*x + b)\n",
    "\n",
    "def fit(parameter, x, y):\n",
    "    return y - fit_func(parameter, x)\n",
    "\n",
    "i = 0\n",
    "while r[i] < rmin:\n",
    "    i += 1\n",
    "imin, imax = i, i\n",
    "while r[i] < rmax:\n",
    "    i += 1\n",
    "imax = i - 1\n",
    "\n",
    "res = leastsq(fit, param, args=(r[imin:imax], phi1[imin:imax]))\n",
    "print u\"a: \" + str(res[0][0])\n",
    "print u\"b: \" + str(res[0][1])\n",
    "R5 = fit_func(res[0], r[imin:imax])\n",
    "\n",
    "myplot2(r, phi2, r[imin:imax], R5, res[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 解析的アプローチ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "点の分布する範囲は$\\Omega = [0,1]\\times [0,1]$であり、この中の面積$S$の領域の中に点を見出す確率は$S$である。\n",
    "\n",
    "次に、領域内のある点$\\vec x=(x,y)$を中心として半径$r$($0 < r \\le 0.5$)の領域$B(\\vec x, r)$内に点を見出す確率$p(\\vec x)$は、境界の影響をうけない領域($\\Omega ' = \\{(x,y) | r \\le x \\le 1-r, r \\le y \\le 1-r \\}$)では$\\pi r^{2}$であり、境界の影響を受ける領域($\\Omega'' = \\Omega / \\Omega'$)において点を見出す確率は、領域を\n",
    "\n",
    "$$\\begin{align}\n",
    "\\Omega''_{x} &= \\{(x,y) | 0 \\le x < r, r< y < 1-r\\} \\\\\n",
    "\\Omega''_{1-x} &= \\{(x,y) | 1-r < x \\le 1, r< y < 1-r\\} \\\\\n",
    "\\Omega''_{y} &= \\{(x,y) | r < x < 1-r, 0 \\le y < r\\} \\\\\n",
    "\\Omega''_{1-y} &= \\{(x,y) | r < x < 1-r, 1-r < y \\le 1\\} \\\\\n",
    "\\Omega''_{x,y} &= \\{(x,y) | 0 \\le x < r, 0 \\le y < r\\} \\\\\n",
    "\\Omega''_{1-x,y} &= \\{(x,y) | 1-r < x \\le 1, 0 \\le y < r\\} \\\\\n",
    "\\Omega''_{x,1-y} &= \\{(x,y) | 0 \\le x < r, 1-r < y \\le 1\\} \\\\\n",
    "\\Omega''_{1-x, 1-y} &= \\{(x,y) | 1-r < x \\le 1, 1-r < y \\le 1\\}\n",
    "\\end{align}$$\n",
    "\n",
    "のようにあらわし、$\\Omega''_{i} = \\{\\Omega''_{x}, \\Omega''_{1-x}, \\Omega''_{y}, \\Omega''_{1-y}$\\}、また$\\Omega''_{i,j} = \\{\\Omega''_{x,y}, \\Omega''_{1-x,y}, \\Omega''_{x,1-y}, \\Omega''_{1-x,1-y}\\}$でまとめて書くことにすると、\n",
    "\n",
    "$$p(\\vec x \\in \\Omega''_{i}) = i \\sqrt{r^{2}-i^{2}} + r^{2} \\left[ \\pi -\\arccos \\frac{i}{r} \\right]$$\n",
    "\n",
    "$$\\begin{align}p(\\vec x \\in \\Omega''_{i,j}) = &\\frac{1}{2}\\left\\{ \\sqrt{r^{2}-i^{2}} + \\min \\left(j, \\sqrt{r^{2}-i^{2}}\\right) \\right\\}i + \\frac{1}{2}\\left\\{ \\sqrt{r^{2}-j^{2}} + \\min \\left( i, \\sqrt{r^{2}-j^{2}}\\right) \\right\\}j \\\\\n",
    "&+ \\frac{1}{2}r^{2} \\left\\{ 2\\pi -\\arccos \\frac{i}{r}-\\arccos \\frac{j}{r}-\\min \\left( \\frac{\\pi}{2}, \\arccos \\frac{i}{r} +\\arccos \\frac{j}{r} \\right) \\right\\}\n",
    "\\end{align}$$\n",
    "\n",
    "のようにあらわすことができる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "確率$p$をすべての領域について積分した値は、領域$\\Omega$から一様乱数によって一つの点を選び、その点を中心とした$r$による範囲に1つの点を見出す確率の期待値となる。\n",
    "\n",
    "この確率を$p'(r)$とし、$0\\le r \\le 0.5$のときは\n",
    "\n",
    "$$p'(r) = p'(r)_{\\Omega''} + 4p'(r)_{\\Omega''_{i}} + 4p'(r)_{\\Omega''_{i,j}}$$\n",
    "\n",
    "とできる。それぞれの領域について積分を実行する。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$p'(r)_{\\Omega'} = \\int_{r}^{1-r} \\int_{r}^{1-r}\\pi r^{2}\\mathrm{d}x\\mathrm{d}y = (1-2r)^{2}\\pi r^{2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\begin{align}\n",
    "p'(r)_{\\Omega'_{i}} = p'(r)_{\\Omega'_{x}} &= \\int_{0}^{r} \\int_{r}^{1-r}\\mathrm{d}x\\mathrm{d}y\\ x\\sqrt{r^{2}-x^{2}} + r^{2}\\left[\\pi - \\arccos\\frac{x}{r}\\right]\\\\\n",
    "&= (1-2r)\\left\\{ \\frac{r^{3}}{3} + r^{2}\\pi\\cdot r - r^{2}\\cdot r \\right\\}\\\\\n",
    "&= (1-2r)r^{3}\\left( \\pi-\\frac{2}{3} \\right)\n",
    "\\end{align}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "NOTE1:\n",
    "\n",
    "$$\\begin{align}\n",
    "&\\int_{0}^{r}\\mathrm{d}x\\ x\\sqrt{r^{2}-x^{2}} \\\\\n",
    "&\\ \\ \\ \\ \\ \\left[x = r\\cos \\theta \\right]\\\\\n",
    "&= \\int_{\\frac{\\pi}{2}}^{0}\\mathrm{d}\\theta\\ (-r\\sin\\theta)\\ r\\cos\\theta\\ r\\sin\\theta\\\\\n",
    "&= r^{3}\\left[ \\frac{\\sin^{3}\\theta}{3}\\right]^{\\frac{\\pi}{2}}_{0} \\\\\n",
    "&= \\frac{r^{3}}{3}\n",
    "\\end{align}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "NOTE2:\n",
    "\n",
    "$x = \\cos t \\ (0< t< \\pi)$とすると\n",
    "$$\\frac{\\mathrm{d}x}{\\mathrm{d}t} = - \\sin t < 0$$\n",
    "\n",
    "$t = \\arccos x$であるから、\n",
    "\n",
    "$$\\begin{align}\n",
    "\\frac{\\mathrm{d}}{\\mathrm{d}x}\\arccos x &= \\frac{1}{\\frac{\\mathrm{d}}{\\mathrm{d}t}\\cos t} = -\\frac{1}{\\sin t}\\\\\n",
    "&=- \\frac{1}{\\sqrt{\\sin^{2}t}} = - \\frac{1}{\\sqrt{1- \\cos^{2}t}} \\\\\n",
    "&= - \\frac{1}{\\sqrt{1- x^{2}}}\n",
    "\\end{align}$$\n",
    "\n",
    "したがって、\n",
    "\n",
    "$$\\begin{align}\n",
    "\\int \\arccos x \\mathrm{d}x\\  &= x\\arccos x + \\int \\frac{x}{\\sqrt{1-x^{2}}}\\mathrm{d}x\\\\\n",
    "&=x\\arccos x - \\sqrt{1-x^{2}} + C\n",
    "\\end{align}$$\n",
    "\n",
    "($C$は積分定数)\n",
    "\n",
    "今の場合、\n",
    "\n",
    "$$\\begin{align}\n",
    "\\int^{r}_{0} \\arccos \\frac{x}{r} \\mathrm{d}x &= \\int^{1}_{0}\\arccos t \\cdot r\\mathrm{d}t\\\\\n",
    "&= r \\left[ t \\arccos t - \\sqrt{1-t^{2}} \\right]^{1}_{0}\\\\\n",
    "&= r ( 1\\arccos1 -\\sqrt{1-1} - 0 \\arccos0 + \\sqrt{1-0})\\\\\n",
    "&= r\n",
    "\\end{align}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$p'(r)_{\\Omega''_{i,j}}$を以下のように分解してそれぞれ計算する。\n",
    "\n",
    "$$\\begin{align}\n",
    "p'(r)_{\\Omega''_{i,j}} &= p'(r)_{\\Omega''_{x, y}}\\\\\n",
    "&= p'(r)_{\\Omega''_{x, y}1}  +p'(r)_{\\Omega''_{x, y}2}\\\\\n",
    "&= p'(r)_{\\Omega''_{x, y}1'} - p'(r)_{\\Omega''_{x, y}1''} + p'(r)_{\\Omega''_{x, y}2}\n",
    "\\end{align}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\begin{align}\n",
    "p'(r)_{\\Omega''_{x,y}1'} &= \\int^{r}_{0}\\int^{r}_{0}\\mathrm{d}x\\mathrm{d}y\\ x\\sqrt{r^{2}-x^{2}} + y \\sqrt{r^{2} -y^{2}} + \\frac{1}{2}r^{2}\\left( 2\\pi -2\\arccos\\frac{x}{r} -2\\arccos\\frac{y}{r} \\right) \\\\\n",
    "&= r\\int^{r}_{0}\\mathrm{d}x\\ \\left\\{x\\sqrt{r^{2}-x^{2}} - r^{2}\\arccos\\frac{x}{r} \\right\\} \n",
    "+ r\\int^{r}_{0}\\mathrm{d}x\\ \\left\\{x\\sqrt{r^{2}-x^{2}} - r^{2}\\arccos\\frac{x}{r} \\right\\} + \\pi r^{2}\\cdot r^{2}\\\\\n",
    "&= r\\left( \\frac{r^{3}}{3} -r^{3} \\right) + r\\left( \\frac{r^{3}}{3} -r^{3} \\right) + \\pi r^{4}\\\\\n",
    "&=  \\left(\\pi -\\frac{4}{3}\\right)r^{4}\n",
    "\\end{align}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\begin{align}\n",
    "p'(r)_{\\Omega''_{x,y}1''} &= \\int^{r}_{0}\\int^{\\sqrt{r^{2}-x^{2}}}_{0}\\mathrm{d}x\\mathrm{d}y\\ \\left[ x\\sqrt{r^{2}-x^{2}} + y \\sqrt{r^{2} -y^{2}} + r^{2}\\left(\\pi -\\arccos\\frac{x}{r} -\\arccos\\frac{y}{r}\\right) \\right]\\\\\n",
    "&= \\int^{r}_{0}\\mathrm{d}x\\left[ \\left\\{ x\\sqrt{r^{2}-x^{2}} + r^{2}\\pi -r^{2}\\arccos\\frac{x}{r} \\right\\}\\sqrt{r^{2}-x^{2}} + \\int^{\\sqrt{r^{2}-x^{2}}}_{0}\\mathrm{d}y\\ y\\sqrt{r^{2}-y^{2}} -r^{2}\\arccos\\frac{y}{r}\\right]\\\\\n",
    "&= \\int^{r}_{0}\\mathrm{d}x\\left[ x(r^{2}-x^{2}) + r^{2}\\pi\\sqrt{r^{2}-x^{2}} -r^{2}\\arccos \\frac{x}{r} \\sqrt{r^{2}-x^{2}} + \\frac{r^{3}}{3} - \\frac{x^{3}}{3} - r^{2}\\frac{\\pi}{2}\\sqrt{r^{2}-x^{2}} + r^{2}\\arccos\\frac{x}{r}\\sqrt{r^{2}-x^{2}} +r^{2}x - r^{3}\\right] \\\\\n",
    "&= \\int^{r}_{0}\\mathrm{d}x \\left[-\\frac{4}{3}x^{3} + 2r^{2}x - \\frac{2}{3}r^{3} + \\frac{\\pi}{2}r^{2}\\sqrt{r^{2}-x^{2}} \\right]\\\\\n",
    "&= \\left[ -\\frac{4}{3}\\frac{x^{4}}{4} + r^{2}x^{2} - \\frac{2}{3}r^{3}x \\right]^{r}_{0} + \\frac{\\pi}{2}r^{2}\\cdot \\frac{1}{4}\\pi r^{2}\\\\\n",
    "&= -\\frac{r^{4}}{3} + r^{4} -\\frac{2}{3}r^{4} + \\frac{\\pi ^{2}}{8}r^{4}\\\\\n",
    "&= \\frac{\\pi^{2}}{8}r^{4}\n",
    "\\end{align}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "NOTE1:\n",
    "\n",
    "$y=r\\cos \\theta$とおく。\n",
    "\n",
    "$y$の積分領域$[0, \\sqrt{r^{2}-x^{2}}]$は$\\theta$の範囲としては$[\\pi/2, \\theta' = \\arcsin(x/r)]$となる。\n",
    "\n",
    "(図)\n",
    "\n",
    "$$\\begin{align}\n",
    "\\int^{\\sqrt{r^{2}-x^{2}}}_{0}\\mathrm{d}y\\ y\\sqrt{r^{2}-y^{2}} &= \\int^{\\theta'}_{\\frac{\\pi}{2}}-r^{3}\\sin^{2}\\theta\\ \\cos\\theta \\mathrm{d}\\theta\\\\\n",
    "&= r^{3}\\left[ \\frac{\\sin^{3}\\theta}{3} \\right]^{\\frac{\\pi}{2}}_{\\theta'}\\\\\n",
    "&= \\frac{r^{3}}{3} - r^{3}\\frac{\\left( \\frac{x}{r} \\right)^{3}}{3}\\\\\n",
    "&= \\frac{r^{3}}{3} - \\frac{x^{3}}{3}\n",
    "\\end{align}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "NOTE2:\n",
    "\n",
    "$t = x/r$とおいて積分する。\n",
    "\n",
    "$$\\begin{align}\n",
    "r^{2}\\int^{\\sqrt{r^{2}-x^{2}}}_{0}\\mathrm{d}y\\ \\arccos \\frac{y}{r} &= r^{2}\\int^{\\frac{\\sqrt{r^{2}-x^{2}}}{r}}_{0}r\\mathrm{d}t\\ \\arccos t\\\\\n",
    "&= r^{3}\\left[ t\\arccos t - \\sqrt{1-t^{2}} \\right]^{\\frac{\\sqrt{r^{2}-x^{2}}}{r}}_{0}\\\\\n",
    "&= r^{3}\\left[ \\frac{\\sqrt{r^{2}-x^{2}}}{r}\\left( \\frac{\\pi}{2} - \\arcsin \\frac{x}{r} \\right) - \\frac{x}{r} + 1 \\right]\\\\\n",
    "&= r^{2}\\frac{\\pi}{2}\\sqrt{r^{2}-x^{2}} - r^{2}\\sqrt{r^{2}-x^{2}}\\arccos\\frac{x}{r} - r^{2}x + r^{3}\n",
    "\\end{align}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\begin{align}\n",
    "p'(r)_{\\Omega''_{x, y}2} &= \\int^{r}_{0}\\int^{r}_{0}\\mathrm{d}x\\mathrm{d}y\\ \\frac{1}{2}x\\sqrt{r^{2}-x^{2}} + \\frac{1}{2}y\\sqrt{r^{2} -y^{2}} + xy + \\frac{1}{2}r^{2}\\left( 2\\pi - \\arccos\\frac{x}{r} - \\arccos\\frac{y}{r} - \\frac{\\pi}{2} \\right)\\\\\n",
    "&= \\int^{r}_{0}\\mathrm{d}x\\int^{\\sqrt{r^{2}-x^{2}}}_{0}\\mathrm{d}y\\ \\frac{1}{2}x\\sqrt{r^{2}-x^{2}} + \\frac{1}{2}y\\sqrt{r^{2} -y^{2}} + xy + \\frac{1}{2}r^{2}\\left( 2\\pi - \\arccos\\frac{x}{r} - \\arccos\\frac{y}{r} - \\frac{\\pi}{2} \\right)\\\\\n",
    "&= \\int^{r}_{0}\\mathrm{d}x\\left[ \\left\\{ \\frac{1}{2}x\\sqrt{r^{2}-x^{2}} + \\frac{3}{4}\\pi r^{2} - \\frac{1}{2}r^{2}\\arccos\\frac{x}{r} \\right\\}\\sqrt{r^{2}-x^{2}} + \\int^{\\sqrt{r^{2}-x^{2}}}_{0}\\mathrm{d}y\\ \\frac{1}{2}y\\sqrt{r^{2}-y^{2}} + xy - \\frac{1}{2}r^{2}\\arccos\\frac{y}{r}\\right]\\\\\n",
    "&= \\int^{r}_{0}\\mathrm{d}x\\left[ \\frac{1}{2}xr^{2} - \\frac{x^{3}}{2} + \\frac{3}{4}\\pi r^{2}\\sqrt{r^{2}-x^{2}} - \\frac{1}{2}r^{2}\\arccos \\frac{x}{r} \\sqrt{r^{2}-x^{2}} \\right.\\\\\n",
    "&\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ + \\left. \\frac{r^{3}}{6} - \\frac{x^{3}}{6} + \\frac{1}{2}xr^{2} - \\frac{x^{3}}{2} - \\frac{\\pi}{4}r^{2}\\sqrt{r^{2}-x^{2}} + \\frac{1}{2}r^{2}\\arccos\\frac{x}{r}\\sqrt{r^{2}-x^{2}} + \\frac{1}{2}r^{2}x - \\frac{r^{3}}{2}\\right] \\\\\n",
    "&= \\int^{r}_{0}\\mathrm{d}x\\left[- \\frac{7}{6}x^{3} - \\frac{r^{3}}{3} + \\frac{3}{2}r^{2}x + \\frac{\\pi}{2}r^{2}\\sqrt{r^{2}-x^{2}} \\right]\\\\\n",
    "&= -\\frac{7}{24}r^{4} - \\frac{r^{4}}{3} + \\frac{3}{4}r^{4} + \\frac{\\pi}{2}r^{2}\\cdot \\frac{\\pi}{4}r^{2}\\\\\n",
    "&= \\left( - \\frac{7}{24} - \\frac{1}{3} + \\frac{3}{4} + \\frac{\\pi^{2}}{8}\\right)r^{4}\\\\\n",
    "&= \\left( \\frac{\\pi^{2}}{8} + \\frac{1}{8} \\right)r^{4}\n",
    "\\end{align}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\begin{align}\n",
    "p'(r)_{\\Omega''_{i,j}} &= p'(r)_{\\Omega''_{x, y}}\\\\\n",
    "&= p'(r)_{\\Omega''_{x, y}1}  +p'(r)_{\\Omega''_{x, y}2}\\\\\n",
    "&= p'(r)_{\\Omega''_{x, y}1'} - p'(r)_{\\Omega''_{x, y}1''} + p'(r)_{\\Omega''_{x, y}2}\\\\\n",
    "&= \\left(\\pi -\\frac{4}{3}\\right)r^{4} - \\frac{\\pi^{2}}{8}r^{4} + \\left( \\frac{\\pi^{2}}{8} + \\frac{1}{8} \\right)r^{4}\\\\\n",
    "&= \\left(\\pi -\\frac{29}{24}\\right)r^{4}\n",
    "\\end{align}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "これまでの結果をすべて合わせると、\n",
    "\n",
    "$$\\begin{align}\n",
    "p'(r) &= p'(r)_{\\Omega''} + 4p'(r)_{\\Omega''_{i}} + 4p'(r)_{\\Omega''_{i,j}}\\\\\n",
    "&= (1-2r)^{2}\\pi r^{2} + (1-2r)r^{3}\\left( 4\\pi-\\frac{8}{3} \\right) + \\left(4\\pi -\\frac{29}{6}\\right)r^{4}\\\\\n",
    "&= \\pi r^{2} - 4\\pi r^{3} + 4\\pi r^{4} + 4\\pi r^{3} -\\frac{8}{3}r^{3} - 8\\pi r^{4} + \\frac{16}{3}r^{4} + 4\\pi r^{4} - \\frac{29}{6}r^{4}\\\\\n",
    "&= \\frac{1}{2}r^{4} -\\frac{8}{3}r^{3} + \\pi r^{2}\n",
    "\\end{align}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "実際に数えてみる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "trial = 100\n",
    "\n",
    "r = np.linspace(0.01, 0.5, num=50)\n",
    "phi3 = []\n",
    "for _r in r:\n",
    "    _phi = 0.\n",
    "    for t in range(trial):\n",
    "        meeting = Meeting(K=50, N=6, r=_r, draw=False)\n",
    "        meeting.init()\n",
    "        _phi += meeting.ave_l\n",
    "    phi3.append(_phi/trial)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lyhBkJNhbsezBfm7P8WgsAS8iIgYV7ywmpywHj/Ee3P717ZTmBzFnz2qOObqQ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\niIiIiIiIiIiIiIiIiIiIyF3wP57mSr8vGO+LAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1d37256610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8,6))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "r = np.linspace(0.01, 0.5, num=50)\n",
    "def func(x):\n",
    "    return (1./2*x**4 - 8/3.*x**3 + np.pi*x**2)*(120-1)\n",
    "y = func(r)\n",
    "def func2(x):\n",
    "    return np.sqrt((-0.25*x**8 + 8/3.*x**7 - (64/9.+np.pi)*x**6 + 16/3.*np.pi*x**5\n",
    "                   + (0.5-np.pi**2)*x**4 - 8/3.*x**3 + np.pi*x**2)*(120-1)/(trial))\n",
    "\n",
    "delta = func2(r)\n",
    "y1 = y + delta\n",
    "y2 = y - delta\n",
    "y3 = np.zeros(50)\n",
    "y3[y2>0] = y2[y2>0]\n",
    "ax.fill_between(r, y1, y3, facecolor='green', alpha=0.2)\n",
    "ax.plot(r, phi3)\n",
    "ax.plot(r, y)\n",
    "ax.set_xlabel(r'$r$')\n",
    "ax.set_ylabel(r\"Average number of edges for each time: $l$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "OK"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 平均の頂点間の距離と人数(アイデアの個数)との間の関係"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.151907351898\n"
     ]
    }
   ],
   "source": [
    "tmp = 0\n",
    "for p0, p1 in zip(meeting.minutes[:-1], meeting.minutes[1:]):\n",
    "    tmp += euc(p0[0], p1[0])\n",
    "ave_dist_btw_nodes = tmp/float(len(meeting.minutes)-1)\n",
    "print ave_dist_btw_nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'np' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-1-2b008740037e>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mtrial\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m10\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      6\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 7\u001b[1;33m \u001b[0mN\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m15\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      8\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      9\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mwrapper\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0marg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'np' is not defined"
     ]
    }
   ],
   "source": [
    "import multiprocessing as mp\n",
    "cp = mp.cpu_count() * 2\n",
    "pool = mp.Pool\n",
    "\n",
    "trial = 10\n",
    "\n",
    "N = np.arange(1, 15)\n",
    "\n",
    "def wrapper(arg):\n",
    "    return arg[0](arg[1], arg[2])\n",
    "\n",
    "def calc_N_phi(N, trial):\n",
    "    _phi = []\n",
    "    for t in range(trial):\n",
    "        meeting = Meeting(K=50, N=_N, r=0.07, draw=False)\n",
    "        meeting.progress()\n",
    "        tmp = []\n",
    "        for p0, p1 in zip(meeting.minutes[:-1], meeting.minutes[1:]):\n",
    "            tmp.append(euc(p0[0], p1[0]))\n",
    "        _phi.append(np.average(np.array(tmp)))\n",
    "    return np.average(np.array(_phi))\n",
    "\n",
    "jobs = [(calc_N_phi, _N, trial) for _N in N]\n",
    "phi4 = pool(cp).map(wrapper, jobs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2X7gUnXZa2Dl28cWxk6gclEK/MFgMS9GsXh2GVpxxBhx8cHHf25VhSVKhuDJc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\ng73HgPHdRxkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffc277e5c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,12))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "ax.plot(N, phi4)\n",
    "ax.set_xlabel(r'A number of participants: $N$')\n",
    "ax.set_ylabel(r\"Average length of each edges: $\\phi$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "trial = 1000\n",
    "\n",
    "S = np.arange(10, 60, 5)\n",
    "phi5 = []\n",
    "for _S in S:\n",
    "    _phi = 0.\n",
    "    for t in range(trial):\n",
    "        meeting = Meeting(K=50, N=5, S=_S, r=0.07, draw=False)\n",
    "        meeting.progress()\n",
    "        tmp = 0\n",
    "        for p0, p1 in zip(meeting.minutes[:-1], meeting.minutes[1:]):\n",
    "            tmp += euc(p0[0], p1[0])\n",
    "        try:\n",
    "            result = tmp/float(len(meeting.minutes)-1)\n",
    "        except ZeroDivisionError:\n",
    "            result = 0.\n",
    "        _phi += result\n",
    "    phi5.append(_phi/trial)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ERERERERERCTz/D8By6ULvr2rswAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9f24319550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(S*5, phi5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0 </th>\n",
       "      <td> 0.001000</td>\n",
       "      <td> 0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1 </th>\n",
       "      <td> 0.011474</td>\n",
       "      <td> 0.023056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2 </th>\n",
       "      <td> 0.021947</td>\n",
       "      <td> 0.081389</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3 </th>\n",
       "      <td> 0.032421</td>\n",
       "      <td> 0.181667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4 </th>\n",
       "      <td> 0.042895</td>\n",
       "      <td> 0.283333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5 </th>\n",
       "      <td> 0.053368</td>\n",
       "      <td> 0.406111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6 </th>\n",
       "      <td> 0.063842</td>\n",
       "      <td> 0.522222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7 </th>\n",
       "      <td> 0.074316</td>\n",
       "      <td> 0.635278</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8 </th>\n",
       "      <td> 0.084789</td>\n",
       "      <td> 0.711667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9 </th>\n",
       "      <td> 0.095263</td>\n",
       "      <td> 0.788056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td> 0.105737</td>\n",
       "      <td> 0.833611</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td> 0.116211</td>\n",
       "      <td> 0.869444</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td> 0.126684</td>\n",
       "      <td> 0.900833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td> 0.137158</td>\n",
       "      <td> 0.920556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td> 0.147632</td>\n",
       "      <td> 0.955000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td> 0.158105</td>\n",
       "      <td> 0.972500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td> 0.168579</td>\n",
       "      <td> 0.977778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td> 0.179053</td>\n",
       "      <td> 0.982500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td> 0.189526</td>\n",
       "      <td> 0.988333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td> 0.200000</td>\n",
       "      <td> 0.991389</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>20 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           0         1\n",
       "0   0.001000  0.000000\n",
       "1   0.011474  0.023056\n",
       "2   0.021947  0.081389\n",
       "3   0.032421  0.181667\n",
       "4   0.042895  0.283333\n",
       "5   0.053368  0.406111\n",
       "6   0.063842  0.522222\n",
       "7   0.074316  0.635278\n",
       "8   0.084789  0.711667\n",
       "9   0.095263  0.788056\n",
       "10  0.105737  0.833611\n",
       "11  0.116211  0.869444\n",
       "12  0.126684  0.900833\n",
       "13  0.137158  0.920556\n",
       "14  0.147632  0.955000\n",
       "15  0.158105  0.972500\n",
       "16  0.168579  0.977778\n",
       "17  0.179053  0.982500\n",
       "18  0.189526  0.988333\n",
       "19  0.200000  0.991389\n",
       "\n",
       "[20 rows x 2 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "pd.DataFrame(np.array([r, phi]).T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n",
      "[1, 2, 3, 4, 5, 6, 7]\n"
     ]
    }
   ],
   "source": [
    "a = [1,2,3,4,5,6,7]\n",
    "preidea = np.random.choice(a)\n",
    "print preidea\n",
    "print a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16\n",
      "0.0625\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{(0, 1): [80],\n",
       " (0, 4): [59],\n",
       " (0, 5): [11],\n",
       " (0, 7): [114],\n",
       " (0, 11): [115],\n",
       " (0, 13): [78],\n",
       " (0, 15): [43, 70, 117],\n",
       " (1, 1): [67],\n",
       " (1, 6): [8],\n",
       " (1, 9): [39],\n",
       " (2, 1): [108],\n",
       " (2, 2): [113],\n",
       " (2, 4): [10],\n",
       " (2, 5): [18],\n",
       " (2, 7): [63],\n",
       " (2, 8): [81],\n",
       " (2, 9): [35, 74],\n",
       " (2, 13): [48],\n",
       " (2, 15): [103],\n",
       " (3, 0): [91],\n",
       " (3, 4): [4, 42],\n",
       " (3, 10): [58, 73],\n",
       " (3, 11): [0],\n",
       " (3, 15): [96],\n",
       " (4, 5): [34],\n",
       " (4, 6): [46],\n",
       " (4, 9): [16],\n",
       " (4, 11): [86],\n",
       " (4, 12): [89],\n",
       " (5, 2): [75],\n",
       " (5, 3): [76, 107],\n",
       " (5, 4): [99],\n",
       " (5, 9): [28],\n",
       " (5, 10): [72],\n",
       " (5, 11): [5],\n",
       " (5, 12): [51, 53],\n",
       " (5, 13): [31],\n",
       " (5, 14): [92, 106],\n",
       " (5, 15): [102],\n",
       " (6, 1): [77, 87],\n",
       " (6, 3): [2],\n",
       " (6, 6): [50, 112, 116],\n",
       " (6, 8): [25],\n",
       " (6, 9): [45],\n",
       " (6, 13): [22],\n",
       " (7, 1): [79],\n",
       " (7, 2): [66],\n",
       " (7, 3): [64],\n",
       " (7, 5): [84],\n",
       " (7, 6): [14, 109],\n",
       " (7, 7): [19],\n",
       " (7, 9): [23],\n",
       " (7, 13): [104],\n",
       " (7, 14): [1],\n",
       " (7, 15): [54],\n",
       " (8, 4): [111],\n",
       " (8, 7): [20, 62],\n",
       " (8, 9): [33],\n",
       " (8, 10): [9],\n",
       " (8, 11): [94],\n",
       " (8, 14): [85],\n",
       " (9, 0): [52, 83],\n",
       " (9, 2): [47],\n",
       " (9, 6): [3, 38],\n",
       " (9, 7): [105],\n",
       " (9, 8): [44],\n",
       " (9, 11): [57],\n",
       " (9, 12): [61],\n",
       " (9, 13): [119],\n",
       " (10, 0): [101],\n",
       " (10, 2): [100],\n",
       " (10, 3): [95],\n",
       " (10, 5): [69],\n",
       " (10, 7): [60],\n",
       " (10, 10): [56],\n",
       " (10, 13): [12],\n",
       " (10, 14): [7],\n",
       " (11, 1): [21],\n",
       " (11, 7): [88, 93],\n",
       " (11, 8): [110],\n",
       " (11, 9): [6],\n",
       " (12, 0): [26, 41],\n",
       " (12, 2): [49],\n",
       " (12, 5): [37],\n",
       " (12, 6): [13],\n",
       " (12, 8): [24],\n",
       " (12, 10): [40],\n",
       " (12, 12): [118],\n",
       " (12, 13): [15],\n",
       " (13, 4): [27, 65],\n",
       " (13, 6): [17],\n",
       " (13, 9): [36],\n",
       " (13, 13): [32],\n",
       " (13, 15): [90],\n",
       " (14, 0): [29],\n",
       " (14, 2): [97],\n",
       " (14, 4): [55],\n",
       " (14, 14): [68, 71],\n",
       " (14, 15): [82],\n",
       " (15, 0): [98],\n",
       " (15, 1): [30]}"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ideas = meeting.ideas\n",
    "r = 0.06\n",
    "cell_num = int(1./r)\n",
    "print cell_num\n",
    "lr = 1./cell_num\n",
    "print lr\n",
    "cell = dict()\n",
    "rcell = []\n",
    "for i, idea in enumerate(ideas):\n",
    "    cellx = int(idea[0][0]/lr)\n",
    "    celly = int(idea[0][1]/lr)\n",
    "    if cell.has_key((cellx, celly)):\n",
    "        cell[(cellx, celly)] += [i]\n",
    "    else:\n",
    "        cell[(cellx, celly)] = [i]\n",
    "    rcell.append((cellx, celly))\n",
    "cell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[[], [], [], [], [], [], [], [], [], [], [], [], [], []],\n",
       " [[], [], [], [], [], [], [], [], [], [], [], [], [], []],\n",
       " [[], [], [], [], [], [], [], [], [], [], [], [], [], []],\n",
       " [[], [], [], [], [], [], [], [], [], [], [], [], [], []],\n",
       " [[], [], [], [], [], [], [], [], [], [], [], [], [], []],\n",
       " [[], [], [], [], [], [], [], [], [], [], [], [], [], []],\n",
       " [[], [], [], [], [], [], [], [], [], [], [], [], [], []],\n",
       " [[], [], [], [], [], [], [], [], [], [], [], [], [], []],\n",
       " [[], [], [], [], [], [], [], [], [], [], [], [], [], []],\n",
       " [[], [], [], [], [], [], [], [], [], [], [], [], [], []],\n",
       " [[], [], [], [], [], [], [], [], [], [], [], [], [], []],\n",
       " [[], [], [], [], [], [], [], [], [], [], [], [], [], []],\n",
       " [[], [], [], [], [], [], [], [], [], [], [], [], [], []],\n",
       " [[], [], [], [], [], [], [], [], [], [], [], [], [], []]]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cell_num = 14\n",
    "[[[]]*cell_num]*cell_num"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "      <p style=\"color:green;font-size:250%;font-weight=bold\">Success!</p>\n",
       "      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@test\n",
    "def uniq_list(seq):\n",
    "    \"\"\"\n",
    "    >>> a = [1, 2, 5, 6, 7, 3, 2, 0]\n",
    "    >>> uniq_list(a)\n",
    "    [1, 2, 5, 6, 7, 3, 0]\n",
    "    \"\"\"\n",
    "    seen = set()\n",
    "    seen_add = seen.add\n",
    "    return [x for x in seq if x not in seen and not seen_add(x)]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Blue'"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def accumulate(iterable, func=operator.add):\n",
    "    \"\"\"Return running totals\n",
    "    \n",
    "    Usage:\n",
    "    accumulate([1,2,3,4,5]) --> 1 3 6 10 15\n",
    "    accumulate([1,2,3,4,5], operator.mul) --> 1 2 6 24 120\n",
    "    \"\"\"\n",
    "    it = iter(iterable)\n",
    "    total = next(it)\n",
    "    yield total\n",
    "    for element in it:\n",
    "        total = func(total, element)\n",
    "        yield total\n",
    "\n",
    "\n",
    "def weighted_choice(d):\n",
    "    import random\n",
    "    import bisect\n",
    "\n",
    "    choices, weights = zip(*d)\n",
    "    cumdist = list(accumulate(weights))\n",
    "    x = random.random() * cumdist[-1]\n",
    "    return choices[bisect.bisect(cumdist, x)]\n",
    "\n",
    "weighted_choices = [(k,v) for k,v in {'Red': 3, 'Blue': 2, 'Yellow': 1, 'Green': 4}.items()]\n",
    "weighted_choice(weighted_choices)"
   ]
  }
 ],
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