pyspark.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c0a46d13",
   "metadata": {},
   "outputs": [],
   "source": [
    "## 필요한 라이브러리를 불러옵니다. \n",
    "import time\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np \n",
    "import pandas as pd\n",
    "from io import BytesIO\n",
    "## pyspark를 불러옵니다.\n",
    "from pyspark import SparkContext"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "35a91057",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def fig():\n",
    "    sc = SparkContext(master=\"local\", appName=\"first app\")\n",
    "    if sc is None: \n",
    "        sc = SparkContext(master=\"local\", appName=\"first app\")\n",
    "    else:\n",
    "        sc.stop()\n",
    "        sc = SparkContext(master=\"local\", appName=\"first app\")\n",
    "\n",
    "## 이미 spark context가 살아 있으면 죽이고, 있으면 그대로 사용합니다. \n",
    "## spark context는 한 번에 여러 개 돌리려면 세팅에 몇 개를 추가해야 한다.\n",
    "## 또한 스파크 컨텍스트를 제대로 구현하려면 여기에 넘겨야 하는 값들이 많이 있다. 하지만 간소하게 구현 \n",
    "    if sc is None: \n",
    "        sc = SparkContext(master=\"local\", appName=\"first app\")\n",
    "    else:\n",
    "        sc.stop()\n",
    "        sc = SparkContext(master=\"local\", appName=\"first app\")\n",
    "\n",
    "    ### peformance check \n",
    "    spark_time_lst = []\n",
    "    python_time_lst = []\n",
    "    python_np_time_lst = []\n",
    "    \n",
    "    n_lst = [5000*i for i in range(0, 10)]\n",
    "    \n",
    "    \n",
    "    for n in n_lst:\n",
    "        def each_k(k):\n",
    "            return 1/(16**k)*( 4/(8*k+1) - 2/(8*k+4) - 1/(8*k+5) - 1/(8*k+6))\n",
    "        ## with spark \n",
    "        start_time = time.time()\n",
    "        pi_approximated = sc.parallelize(range(0, n)).map(each_k).sum()\n",
    "        spark_time_lst.append(time.time()-start_time)\n",
    "        ## pure python\n",
    "        start_time = time.time()\n",
    "        pi_approximated = sum((each_k(k) for k in range(0, n)))\n",
    "        python_time_lst.append(time.time()-start_time)\n",
    "        ## with numpy \n",
    "        start_time = time.time()\n",
    "        pi_approximated = np.apply_along_axis(arr=np.array(range(0, 10)), func1d=each_k, axis=0).sum()\n",
    "        python_np_time_lst.append(time.time() - start_time)\n",
    "\n",
    "    ### plotting     \n",
    "    df = pd.DataFrame({\n",
    "        \"spark\":spark_time_lst.copy(), \n",
    "        \"pure python\":python_time_lst.copy(), \n",
    "        \"python with numpy\":python_np_time_lst.copy()\n",
    "    }, index = [5000*i for i in range(0, 10)])\n",
    "    plt.figure(figsize=(12, 6))\n",
    "    plt.plot(df['spark'], 'ro-'), plt.plot(df['pure python'], 'bo-'), plt.plot(df['python with numpy'], 'go-')\n",
    "    plt.legend(fontsize=25)\n",
    "    plt.xticks([5000*i for i in range(0, 10)], [5000*i for i in range(0, 10)])\n",
    "    img = BytesIO()\n",
    "    plt.savefig(img, format='png',dpi =200)\n",
    "    img.seek(0)\n",
    "    return 0\n",
    "    # return send_file(img, mimetype='image/png')\n",
    "   # plt.show()\n",
    "# if __name__ == '__main__':\n",
    "#     app.run(debug=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "077bcbe4",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig()"
   ]
  }
 ],
 "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": "3.8.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}