zokuwaka11_5to11_8plot.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "plt.style.use(\"fivethirtyeight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def crp_table(alpha, n):\n",
    "    \"\"\"\n",
    "    return using table size list\n",
    "    \"\"\"\n",
    "\n",
    "    s = [1] # current sitting person's number list\n",
    "    c = [] # using table's number\n",
    "    c.append(len(s))\n",
    "    for i in range(2, n+1):\n",
    "        p = [] # crp's sitting distribution\n",
    "        for sitting_human_number in s:\n",
    "            p.append(sitting_human_number / (i - 1 + alpha))\n",
    "        p.append(alpha / (i - 1 + alpha))\n",
    "        new_table_id = np.nonzero(np.random.multinomial(1, p))[0][0]\n",
    "        if new_table_id == len(s): # new table\n",
    "            s.append(1)\n",
    "        else: # already someone sitting table\n",
    "            s[new_table_id] += 1\n",
    "        c.append(len(s))\n",
    "    return c, s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "c_10, s  = crp_table(10, 1000)\n",
    "c_2, s  = crp_table(2, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11105bda0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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/3Z48tLa2YsuWLZg1a1Y3/qKOMYFwUNdsw0dll7Dzn9J/zIUjwjG+r3wjZ4mI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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ec58c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = range(1,1001)\n",
    "plt.plot(x, c_10, label=r\"$\\alpha=10$\")\n",
    "plt.plot(x, c_2, label=r\"$\\alpha=2$\")\n",
    "ax = plt.subplot(111)\n",
    "plt.title(\"fig 11.5\")\n",
    "ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x111b86e48>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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N5eDBgz77e3t7WbFiBVFRUVitVjIyMmhtbR2+kYiIyKg2aCDV1dWxePFidu7c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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11169e160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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RI0dYsWIF+/fvp66uDrPZzB133IHL5fLWlJWVUV5eTnFxMXa7HYvFQkZGBt3d\n3d6avLw89u3bR1VVFfX19XR1dZGZmYnH4xmZmYmIyLhicrlcl5QI3d3dzJw5k1/96lfcdtttACQk\nJLBq1SrWrVsHgNvtJi4ujoKCArKzs+ns7CQ2Npby8nKWLVsGQEtLC0lJSdTU1LBw4cIBzxccfPXl\nzm1AdXVnWLCgt1+7w+EgLi5u2M8nIiKDu+RrSF1dXfT19REcHAxAc3MzbW1tPqHi7+9PWloajY2N\nABw7dozz58/71FitVuLj4701IiIysV1yIOXl5TF37ly+853vANDe3o7JZMJisfjUWSwW2tvbAXA6\nnfj5+REaGjpgjYiITGzmSyl+7LHHOHr0KL/5zW8wmUwjNSYREZmAhhxIjz76KHv37uWVV15h5syZ\n3vawsDA8Hg9OpxOr1eptdzqdhIWFeWt6e3vp6OjwWSU5nU7S0tKGYx6X5Ny5czgcH12wz+FwjPJo\nREQmjotdpx9SIG3cuJGXX36ZV155hZiYGJ++qKgowsPDsdvtJCcnA19samhoaKCgoACA5ORkzGYz\ndrvdZ1NDU1MTqamplzWpKzFlypQL/lC0qUFEZOwMGkiPPPII//Ef/8ELL7xAUFCQ95pPQEAAAQEB\nAOTm5lJaWkpsbCwxMTGUlJQQGBjoDZ+goCCWL1/O5s2bmTZtGsHBweTn55OUlITNZhvB6YmIyHgx\naCDt2rULk8nED37wA5/2jRs3snHjRgDWrl2L2+1mw4YNuFwuUlJSqK2t9QYWQFFREWazmZycHNxu\nNzabjYqKCl2LEhER4DLuQxptug9JRGRi0LPsRETEEBRIIiJiCAokERExhEu6Mfar7uzZ6Rw86Ddi\nx4+M7CM62tCX7ERExowC6a+0tV3F3XcHjtjx6+rOEB3dfzOFiIjoIzsRETEIBZKIiBiCAklERAxB\ngSQiIoagQBIREUNQIImIiCEokERExBAUSCIiYggKJBERMQQFkoiIGIICSUREDEGBJCIihqBAEhER\nQ1AgiYiIIQwpkI4cOUJWVhbXXXcdISEhvPjii/1qCgsLSUxMJCIigvT0dI4fP+7T39PTw/r164mJ\nicFqtZKVlUVra+vwzEJERMa9IQVSd3c3s2fPpqioiKlTp/brLysro7y8nOLiYux2OxaLhYyMDLq7\nu701eXl57Nu3j6qqKurr6+nq6iIzMxOPR3+wTkREhhhIt956K/n5+SxduhSTydSvf+fOnaxbt470\n9HQSEhJp3FBPAAAE3UlEQVQoLy/nzJkzVFdXA9DZ2cnu3bvZtm0bNpuNOXPmUFFRwTvvvMOBAweG\ndUIiIjI+XfE1pObmZtra2li4cKG3zd/fn7S0NBobGwE4duwY58+f96mxWq3Ex8d7a0REZGK74kBq\nb2/HZDJhsVh82i0WC+3t7QA4nU78/PwIDQ0dsEZERCY27bITERFDMF/pAcLCwvB4PDidTqxWq7fd\n6XQSFhbmrent7aWjo8NnleR0OklLS7vSIVyyc+fO4XB8dIGeb4zReUVEJoa4uLgB+644kKKioggP\nD8dut5OcnAyA2+2moaGBgoICAJKTkzGbzdjtdpYtWwZAS0sLTU1NpKamXukQLtmUKVMu+EP58MOe\nMTmviIgMMZC6u7s5ceIEHo+Hvr4+Tp48ydtvv01ISAiRkZHk5uZSWlpKbGwsMTExlJSUEBgY6A2f\noKAgli9fzubNm5k2bRrBwcHk5+eTlJSEzWYb0QmKiMj4MKRAOnbsGEuWLPFu+S4sLKSwsJCsrCye\ne+451q5di9vtZsOGDbhcLlJSUqitrSUgIMB7jKKiIsxmMzk5Objdbmw2GxUVFRfcRi4iIhOPyeVy\nGfrO1ODgq4f9mHV1Z1iwoLdf+/79Pdx9t+UCrxjZ8374oYmTJ0dmf0lkZB/R0Yb+JxYRAYbhGpJc\nuZMnJ7FkSeCIHLuu7gzR0f1DUETEaLTtW0REDEGBJCIihqCP7CYoXbcSEaNRIE1Qum4lIkajj+xE\nRMQQFEgiImIICiQRETEEBZKIiBiCAklERAxBu+xk1IzkVnPQdnOR8U6BJKNmJLeag7abi4x3CiT5\nytNNwCLjgwJJvvLG4iZghaDIpVMgiYwAPQlD5NJpl52IiBiCAklERAxBgSQiIoagQBIREUMY9UCq\nrKxk7ty5TJ8+nZtvvpmGhobRHoKIiBjQqAZSbW0tjz76KI888ggHDx7kO9/5DnfddRctLS2jOQwR\nETGgUQ2kHTt28MMf/pDly5cTFxfH008/TXh4OFVVVaM5DBERMaBRuw/p888/53//93/5yU9+4tN+\nyy230NjYOFrDEPnK0rMCZbwbtUD69NNP6e3tJSwszKfdYrHw+9//frSGIfKVNVbPCtRTKWS4mFwu\n16j8a586dYrExEReffVVbrjhBm/7008/TXV1NUePHh2NYYiIiEGN2jWka665Bj8/P9rb233anU5n\nv1WTiIhMPKMWSF/72tdITk7mwIEDPu12u53U1NTRGoaIiBjUqD5c9YEHHmD16tXMmzeP1NRUdu3a\nRVtbG/fff/9oDkNERAxoVAMpIyODzz77jGeeeYa2tjYSExPZs2cPkZGRozkMERExoFHb1CAiInIx\nE/5ZdkeOHCErK4vrrruOkJAQXnzxxbEekojIhDThA6m7u5vZs2dTVFTE1KlTx3o4IiIT1oT/i7G3\n3nort956KwBr1qwZ49GIiExcE36FJCIixqBAEhERQ1AgiYiIISiQRETEEBRIIiJiCBN+l113dzcn\nTpzA4/HQ19fHyZMnefvttwkJCdETJERERtGEf1LDoUOHWLJkCSaTyac9KyuL5557boxGJSIy8Uz4\nQBIREWPQNSQRETEEBZKIiBiCAklERAxBgSQiIoagQBIREUNQIImIiCEokERExBAUSCIiYggKJBER\nMYT/BwMJR8Lvqi/pAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11169e978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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KSj2DJCIiXsNa1PB1pUt2IiLjb/yX44iIiKBAEhERg1AgiYiIISiQRETEEBRIIiJiCAok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\niCEokERExBAUSCIiYgj/D0LrWSYIlHdnAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b061400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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3EhERGdJ6DaR9+/YxZ84cduzYwfbt2zGbzcyYMQOXy+WtKS4upqSkhIKCAhwO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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b121dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Q+gykoqIibr31VsaMGYPNZuPee+/lo48+6lWXl5dHbGwsERERpKSksH//fp/t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\nISiQRETEEBRIIiJiCAokERExhP8H+gc4zcnXQUQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b154550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mJhoaGkhJSRnwumfrvGZIIiLGNG7cuHP++TzoQPqP//gPFi5c2Ou3spycHEpKSrDZbMTE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\nQBIREUP4f1oU3krqnfBjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ba3bf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fig11-6 \n",
    "fig = plt.figure()\n",
    "plt.xticks(list(range(1,1000,100)))\n",
    "plt.ylim(0, 800)\n",
    "c, s  = crp_table(2, 1000)\n",
    "plt.bar(range(len(s)),sorted(s,reverse=True), label=\"table size \" + str(len(s)))\n",
    "plt.legend()\n",
    "\n",
    "fig = plt.figure()\n",
    "plt.xticks(list(range(1,1000,100)))\n",
    "plt.ylim(0, 800)\n",
    "c, s  = crp_table(2, 1000)\n",
    "plt.bar(range(len(s)),sorted(s,reverse=True), label=\"table size \" + str(len(s)))\n",
    "plt.legend()\n",
    "\n",
    "fig = plt.figure()\n",
    "plt.xticks(list(range(1,1000,100)))\n",
    "plt.ylim(0, 800)\n",
    "c, s  = crp_table(2, 1000)\n",
    "plt.bar(range(len(s)),sorted(s,reverse=True), label=\"table size \" + str(len(s)))\n",
    "plt.legend()\n",
    "\n",
    "\n",
    "fig = plt.figure()\n",
    "plt.xticks(list(range(1,1000,100)))\n",
    "plt.ylim(0, 800)\n",
    "c, s  = crp_table(10, 1000)\n",
    "plt.bar(range(len(s)),sorted(s,reverse=True), label=\"table size \" + str(len(s)))\n",
    "plt.legend()\n",
    "\n",
    "fig = plt.figure()\n",
    "plt.xticks(list(range(1,1000,100)))\n",
    "plt.ylim(0, 800)\n",
    "c, s  = crp_table(10, 1000)\n",
    "plt.bar(range(len(s)),sorted(s,reverse=True), label=\"table size \" + str(len(s)))\n",
    "plt.legend()\n",
    "\n",
    "fig = plt.figure()\n",
    "plt.xticks(list(range(1,1000,100)))\n",
    "plt.ylim(0, 800)\n",
    "c, s  = crp_table(10, 1000)\n",
    "plt.bar(range(len(s)),sorted(s,reverse=True), label=\"table size \" + str(len(s)))\n",
    "plt.legend()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def pitman_yor_process(alpha, beta, n):\n",
    "\n",
    "    s = [1] # current sitting person's number list\n",
    "    c = [] # using table's number\n",
    "    c.append(len(s))\n",
    "    for i in range(2, n+1):\n",
    "        p = [] # crp's sitting distribution\n",
    "        for sitting_human_number in s:\n",
    "            p.append((sitting_human_number - beta) / (i - 1 + alpha))\n",
    "        p.append((alpha + beta * len(s) ) / (i - 1 + alpha))\n",
    "        new_table_id = np.nonzero(np.random.multinomial(1, p))[0][0]\n",
    "        if new_table_id == len(s): # new table\n",
    "            s.append(1)\n",
    "        else: # already someone sitting table\n",
    "            s[new_table_id] += 1\n",
    "        c.append(len(s))\n",
    "    return c, s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x111ab0b70>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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6Gg0NDRg/fjy2b9+OZ555xmn30Wg0ANre1lwqODjYfMwera2tyMvLw3fffYeM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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112245828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "b_4,s = pitman_yor_process(2,0.4, 1000)\n",
    "b_3,s = pitman_yor_process(2,0.3, 1000)\n",
    "b_2,s = pitman_yor_process(2,0.2, 1000)\n",
    "b_0,s = pitman_yor_process(2,0.0, 1000)\n",
    "\n",
    "x = range(1,1001)\n",
    "plt.plot(x, b_4, label=r\"$\\beta=0.4$\")\n",
    "plt.plot(x, b_3, label=r\"$\\beta=0.3$\")\n",
    "plt.plot(x, b_2, label=r\"$\\beta=0.2$\")\n",
    "plt.plot(x, b_0, label=r\"crp $\\beta=0.0$\")\n",
    "\n",
    "ax = plt.subplot(111)\n",
    "plt.title(\"fig 11.7\")\n",
    "ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10b1bcd30>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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3ZT6+K/PxXRFRdVHlEkODwgIoondBuWcz5ElX73uqrlFLpHbph9Wewfj1ug73fmClDHir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\nERHdxcKQiIiIiAAA/wewiZd0uVB7KAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111c96cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 処理に時間かかる\n",
    "b, s_0 = pitman_yor_process(2, 0.0, 100000)\n",
    "b, s_8 = pitman_yor_process(2, 0.8, 100000)\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "\n",
    "\n",
    "plt.plot(range(len(s_8)), sorted(s_8, reverse=True), label=r\"crp$(\\beta=0.8)$\")\n",
    "plt.plot(range(len(s_0)), sorted(s_0, reverse=True) , label=r\"pitman yor$(\\beta=0.0)$\")\n",
    "\n",
    "ax = plt.subplot(111)\n",
    "plt.title(\"fig 11.8\")\n",
    "ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}