random_sampling.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br><br>\n",
    "**필요한 모듈 import**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1000000.txt 파일 불러오기**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(\"./W02/1000000.txt\", mode=\"r\") as file:\n",
    "    contents = []\n",
    "    indexs = []\n",
    "    while True:\n",
    "        sentence = file.readline()\n",
    "        content = []\n",
    "        \n",
    "        if sentence:\n",
    "            index, X, Y = sentence.split(\",\")\n",
    "            \n",
    "            indexs.append(int(index))\n",
    "            \n",
    "            content.append(float(X))\n",
    "            content.append(float(Y))\n",
    "            \n",
    "            contents.append(content)\n",
    "\n",
    "        else:\n",
    "            break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1000000.grid 파일 불러오기**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(\"./W02/1000000.grid\", mode=\"r\") as file:\n",
    "    stratNum = []\n",
    "    X_range = []\n",
    "    Y_range = []\n",
    "    i = 0\n",
    "    \n",
    "    while (i < 3):\n",
    "        sentence = file.readline()\n",
    "        \n",
    "        if sentence:\n",
    "            if (i == 0):\n",
    "                sections = sentence.split(\",\")\n",
    "                for section in sections:\n",
    "                    X_range.append(float(section))\n",
    "\n",
    "            elif (i == 1):\n",
    "                sections = sentence.split(\",\")\n",
    "                for section in sections:\n",
    "                    Y_range.append(float(section))\n",
    "\n",
    "            elif (i == 2):\n",
    "                nums = sentence.split(\",\")\n",
    "                for num in nums:\n",
    "                    stratNum.append(int(num))\n",
    "        else:\n",
    "            break\n",
    "            \n",
    "        i += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**두 점사이의 거리를 계산하는 함수 dist**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dist(point1, point2):\n",
    "    return math.sqrt((point1[0]-point2[0])**2 + (point1[1]-point2[1])**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**복원추출 랜덤샘플링 함수 WR_random_sampling**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def WR_random_sampling(n_sample_points):\n",
    "    sum_ = 0. #average_distance의 총합\n",
    "    average_distance_lists = [] #average_distance 100개 리스트\n",
    "    \n",
    "    varience = 0. #샘플평균의 분산\n",
    "    \n",
    "    #average_distance 100번 추정\n",
    "    for _ in range(100):\n",
    "        \n",
    "        sample_sum = 0. #샘플의 평균거리 총합\n",
    "        for i in range(0, n_sample_points):    \n",
    "            p1 = random.sample(contents, 1) #n_sample_points 개수만큼 인덱스 무작위 추출\n",
    "            p2 = random.sample(contents, 1)\n",
    "            while(True):\n",
    "                if(p1 != p2):\n",
    "                    break\n",
    "                p2 = random.sample(contents, 1)\n",
    "\n",
    "            sample_sum += dist(p1[0], p2[0])\n",
    "            \n",
    "        average_distance = sample_sum / n_sample_points\n",
    "        average_distance_lists.append(average_distance)\n",
    "        sum_ += average_distance\n",
    "       \n",
    "    #average의 평균(샘플평균 구하기)   \n",
    "    sample_mean = sum_ / 100\n",
    "    \n",
    "    variance = 0.\n",
    "    #샘플평균의 분산 구하기\n",
    "    for ad in average_distance_lists:\n",
    "        variance += ((sample_mean - ad) ** 2)\n",
    "    \n",
    "    variance /= 100\n",
    "    \n",
    "    print(\"sample mean: {}\".format(sample_mean))\n",
    "    print(\"variance: {}\".format(variance))\n",
    "\n",
    "    return variance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**샘플 개수를 1000, 2000, 4000, 8000, 16000개로 늘려가며 분산 계산**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sample mean: 0.394583155766402\n",
      "variance: 3.824550649465632e-05\n",
      "\n",
      "sample mean: 0.3964078118490852\n",
      "variance: 1.813327209220624e-05\n",
      "\n",
      "sample mean: 0.39543109263679826\n",
      "variance: 9.825234249383445e-06\n",
      "\n",
      "sample mean: 0.3956249766009944\n",
      "variance: 6.032525818108353e-06\n",
      "\n",
      "sample mean: 0.3956566359123172\n",
      "variance: 2.6790329958373234e-06\n",
      "\n"
     ]
    }
   ],
   "source": [
    "X = [1000, 2000, 4000, 8000, 16000]\n",
    "Y1 = []\n",
    "for num in X:\n",
    "    SRS_sample_variance = WR_random_sampling(num)\n",
    "    Y1.append(SRS_sample_variance)\n",
    "    print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3.824550649465632e-05,\n",
       " 1.813327209220624e-05,\n",
       " 9.825234249383445e-06,\n",
       " 6.032525818108353e-06,\n",
       " 2.6790329958373234e-06]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>**16개의 group별 좌표 계산**<br><br>\n",
    "ex)<br>\n",
    "G1 = 0.0 <= x < 0.25, 0.0 <= y < 0.25<br>\n",
    "G2 = 0.0 <= x < 0.25, 0.25 <= y < 0.5<br>\n",
    "    ...<br>\n",
    "G16 = 0.75 <= x < 1.0, 0.75 <= y < 1.0<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_range.insert(0,0.)\n",
    "grid = X_range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.0, 0.25, 0.5, 0.75, 1.0]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def list_by_group(v, grid):\n",
    "    list_ = []\n",
    "    size = len(grid) - 1\n",
    "    for i in range(size):\n",
    "        group1 = [grid[i], grid[i+1]]\n",
    "        \n",
    "        for j in range(size):\n",
    "            group2 = [grid[j], grid[j+1]]\n",
    "\n",
    "            group_list = []\n",
    "            \n",
    "            for vn in v:\n",
    "                if((group1[0]<=vn[0]<group1[1]) and (group2[0]<=vn[1]<group2[1])):\n",
    "                    group_list.append(vn)\n",
    "            list_.append(group_list)\n",
    "            \n",
    "    return list_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = list_by_group(contents, grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "G0's size: 224531\n",
      "G1's size: 153501\n",
      "G2's size: 72541\n",
      "G3's size: 23268\n",
      "G4's size: 153663\n",
      "G5's size: 106050\n",
      "G6's size: 49307\n",
      "G7's size: 15864\n",
      "G8's size: 71994\n",
      "G9's size: 49407\n",
      "G10's size: 23308\n",
      "G11's size: 7511\n",
      "G12's size: 23101\n",
      "G13's size: 15857\n",
      "G14's size: 7701\n",
      "G15's size: 2396\n",
      "\n",
      "total: 1000000\n"
     ]
    }
   ],
   "source": [
    "total = 0\n",
    "for i in range(16):\n",
    "    total += len(a[i])\n",
    "    print(\"G{}\\'s size: {}\".format(i,len(a[i])))\n",
    "\n",
    "print()\n",
    "print(\"total: {}\".format(total))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>**stratum별 사이즈, 사이즈 총합 계산**<br><br>\n",
    "ex)<br>\n",
    "S(1,1) : G1과 G1에서 만들수 있는 좌표쌍 수 => (G1 size) combination 2<br>\n",
    "S(1,2) : G1과 G2에서 만들수 있는 좌표쌍 수 => (G1 size) * (G2 size)<br>\n",
    "...<br>\n",
    "S(16,16) : G16과 G16로 만들수 있는 좌표쌍 수 => (G16 size) combination 2\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "total = 0\n",
    "strata_size = []\n",
    "\n",
    "for i in range(0, 16):\n",
    "    for j in range(i, 16):\n",
    "        L1 = len(a[i])\n",
    "        L2 = len(a[j])\n",
    "        if(i == j):\n",
    "            size = int((L1 * (L1-1))/2)\n",
    "            strata_size.append(size)\n",
    "            total += size\n",
    "            continue\n",
    "        size = L1 * L2\n",
    "        strata_size.append(size)\n",
    "        total += size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "499999500000"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**복원추출 층화샘플링 함수 WR_stratified_sampling**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def WR_stratified_sampling(n_sample_points):\n",
    "    average_distance_lists = []\n",
    "    sum_ = 0.\n",
    "      \n",
    "    stratum_size = []   \n",
    "              \n",
    "    for i in range(136):\n",
    "        stratum_size.append(int((strata_size[i]/total) * n_sample_points))\n",
    "   \n",
    "    for _ in range(100):\n",
    "        stratum_average_list = []\n",
    "        \n",
    "        n = 0\n",
    "        for i in range(0,16):\n",
    "            for j in range(i,16):\n",
    "                sample_sum = 0.\n",
    "                \n",
    "                #그룹 2개를 골라서\n",
    "                group1 = a[i]\n",
    "                group2 = a[j]\n",
    "                \n",
    "                temp = stratum_size[n]\n",
    "                if(temp == 0):\n",
    "                    stratum_average_list.append(0)\n",
    "                    continue;\n",
    "                    \n",
    "                #추출할 샘플 수만큼 반복   \n",
    "                for _ in range(temp):\n",
    "                    p1 = random.sample(group1, 1)\n",
    "                    p2 = random.sample(group2, 1)\n",
    "                    while(True):\n",
    "                        if(p1 != p2):\n",
    "                            break\n",
    "                        p2 = random.sample(group2, 1)\n",
    "                    distance = dist(p1[0], p2[0])\n",
    "                    sample_sum += distance\n",
    "                \n",
    "                stratum_average = sample_sum / temp\n",
    "                stratum_average_list.append(stratum_average)\n",
    "                n += 1\n",
    "        \n",
    "        #전체평균(averge distance) 구하기\n",
    "        entire_sample_sum = 0.\n",
    "        for i in range(len(stratum_average_list)):\n",
    "            entire_sample_sum += (stratum_average_list[i] * strata_size[i])\n",
    "        \n",
    "        average_distance = entire_sample_sum / total\n",
    "        average_distance_lists.append(average_distance)\n",
    "        sum_ += average_distance\n",
    "\n",
    "    #average의 평균(샘플평균 구하기)   \n",
    "    sample_mean = sum_ / 100\n",
    "    \n",
    "    variance = 0\n",
    "    #샘플평균의 분산 구하기\n",
    "    for ad in average_distance_lists:\n",
    "        variance += ((sample_mean - ad) ** 2)\n",
    "\n",
    "    variance /= 100\n",
    "    print()\n",
    "    print(\"sample mean: {}\".format(sample_mean))\n",
    "    print(\"variance: {}\".format(variance))\n",
    "    \n",
    "    return variance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**샘플 개수를 1000, 2000, 4000, 8000, 16000개로 늘려가며 분산 계산**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "sample mean: 0.23908585326820173\n",
      "variance: 5.2194549435904255e-06\n",
      "\n",
      "\n",
      "sample mean: 0.28096688893315613\n",
      "variance: 2.946412887599091e-06\n",
      "\n",
      "\n",
      "sample mean: 0.29787120083036717\n",
      "variance: 1.5548147033617568e-06\n",
      "\n",
      "\n",
      "sample mean: 0.2979080960173192\n",
      "variance: 8.054445035668533e-07\n",
      "\n",
      "\n",
      "sample mean: 0.39457099074134694\n",
      "variance: 4.3149591331540576e-07\n",
      "\n"
     ]
    }
   ],
   "source": [
    "Y2 = []\n",
    "for num in X:\n",
    "    ST_sample_variance = WR_stratified_sampling(num)\n",
    "    Y2.append(ST_sample_variance)\n",
    "    print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5.2194549435904255e-06,\n",
       " 2.946412887599091e-06,\n",
       " 1.5548147033617568e-06,\n",
       " 8.054445035668533e-07,\n",
       " 4.3149591331540576e-07]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**그래프 출력**<br>\n",
    "<li>파랑 선 : 랜덤샘플링</li>\n",
    "<li>주황 선 : 층화샘플링</li>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, Y1, marker='o')\n",
    "plt.plot(X, Y2, marker='s')\n",
    "plt.xlabel(\"x-axis\")\n",
    "plt.ylabel(\"y-axis\")\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}