{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 08wk-2: Pandas (2)\n", "\n", "최규빈 \n", "2023-04-26\n", "\n", "\n", "\n", "# 강의영상\n", "\n", "> youtube:\n", "> \n", "\n", "# import" ], "id": "8d2675f6-8f62-439f-bab1-65cd2c7ae1cf" }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd" ], "id": "e81630d3-04aa-449d-9195-b8b45f5bbe51" }, { "cell_type": "markdown", "metadata": {}, "source": [ "# pandas 공부 3단계\n", "\n", "`-` df자료형의 메소드를 알아보자.\n", "\n", "## 전치" ], "id": "47744033-ad48-4107-be18-e48515f3e5db" }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "arr = np.arange(2*3).reshape(2,3)\n", "df = pd.DataFrame(arr)\n", "df" ], "id": "46606936" }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "df.T" ], "id": "d3514ad4" }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 합" ], "id": "8cc29e90-d9a9-4c68-a72d-944f3105b5e2" }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "df" ], "id": "82621565" }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "df.sum(axis=0)" ], "id": "99e22eab-0cef-4c80-92f2-0f8c0375ee73" }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "df.sum(axis=1)" ], "id": "71fb404f-b55c-4c16-93d7-2989e0c16c42" }, { "cell_type": "markdown", "metadata": {}, "source": [ "## cumsum" ], "id": "918b6f6f-c968-4a46-ac75-95237f8094ac" }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "df" ], "id": "e207a37c-2c24-4419-ae72-00154d8e648d" }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "df.cumsum(axis=1) " ], "id": "c7b68db2" }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 형태변환" ], "id": "5d01525f-e6dd-4a5b-ace4-125e4a344830" }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "df" ], "id": "428fa1f1" }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "df.to_dict()" ], "id": "58527f7e-7836-434b-9ae6-6a78a992d36a" }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "df.to_numpy()" ], "id": "d425a4c1-8a46-4dc6-b16f-707b781d111a" }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [ "df.to_numpy().tolist()" ], "id": "138ffbce-20d9-4b02-9fd9-e63b2acaa89e" }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 기타메소드.. 생략…\n", "\n", "# pandas 공부 4단계" ], "id": "183e50d4-194b-40cc-9b39-5e6b15ace250" }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [], "source": [ "np.random.seed(43052)\n", "att = np.random.choice(np.arange(10,21)*5,20)\n", "rep = np.random.choice(np.arange(5,21)*5,20)\n", "mid = np.random.choice(np.arange(0,21)*5,20)\n", "fin = np.random.choice(np.arange(0,21)*5,20)\n", "key = ['2022-12'+str(s) for s in np.random.choice(np.arange(300,501),20,replace=False)]\n", "df = pd.DataFrame({'att':att,'rep':rep,'mid':mid,'fin':fin},index=key)\n", "df.head()" ], "id": "15801715-efeb-4f09-8d18-48575b002bd0" }, { "cell_type": "markdown", "metadata": {}, "source": [ "## query ($\\star$)\n", "\n", "`-` 예제1: att==90 and fin\\>30" ], "id": "0aef14c1-3ecd-4afe-ba63-8ecb08ccdb59" }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "df.query('att ==90 and fin >30')" ], "id": "45b4a0ea" }, { "cell_type": "markdown", "metadata": {}, "source": [ "`-` 예제2: att\\=60" ], "id": "dc5ff946-61da-4c3a-b40a-8b7474e1896f" }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [], "source": [ "df.query('(mid+fin)/2>=60')" ], "id": "d51a0b33" }, { "cell_type": "markdown", "metadata": {}, "source": [ "`-` 예제6: att \\> mean(att)" ], "id": "b6e3e506-ce20-4493-bcbf-e795f00f5edf" }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [], "source": [ "_mean = df['att'].mean() \n", "_mean " ], "id": "ad9f2c38" }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [], "source": [ "df.query('att> @_mean')" ], "id": "7eaf06fb" }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 시계열자료\n", "\n", "`-` 시계열자료" ], "id": "9e35a50f-6c9e-4baf-9e6f-4c882e1eb0aa" }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [], "source": [ "pd.date_range('20211226',periods=10)" ], "id": "dd64bbeb-f548-4e57-b8ef-6e1f5e1b3b31" }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [], "source": [ "df=pd.DataFrame(np.random.normal(size=(10,4)),columns=list('ABCD'),index=pd.date_range('20211226',periods=10))\n", "df" ], "id": "4f523f3e-95fd-41ae-922b-7f93856ff239" }, { "cell_type": "markdown", "metadata": {}, "source": [ "`-` 예제1: 시계열자료에서의 인덱싱" ], "id": "5889bcf2-e212-4c05-88b8-82dc8fd318b8" }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [], "source": [ "df.loc['2021-12-28':'2022-01-02',:]" ], "id": "e2fd19bf" }, { "cell_type": "markdown", "metadata": {}, "source": [ "`-` 예제3: 스트라이딩 (샘플링)" ], "id": "781b1f8f-2889-4c15-8521-f942e3934ec0" }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [], "source": [ "df.loc[::3,:]" ], "id": "b672bab5" }, { "cell_type": "markdown", "metadata": {}, "source": [ "`-` 예제4: query를 이용한 인덱싱" ], "id": "031966fd-7def-4cb1-935c-21c5a015ecb0" }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [], "source": [ "df.query(\"index <= '2021-12-30' or index=='2022-01-02'\")" ], "id": "9ddd67ea" }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 더러운 자료 (1)\n", "\n", "***예비학습: 하나의 col을 선택하는 가장 좋은 방법***" ], "id": "0e127560-4bc1-49ba-ad7b-c081a43da8bc" }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [], "source": [ "np.random.seed(43052)\n", "att = np.random.choice(np.arange(10,21)*5,20)\n", "rep = np.random.choice(np.arange(5,21)*5,20)\n", "mid = np.random.choice(np.arange(0,21)*5,20)\n", "fin = np.random.choice(np.arange(0,21)*5,20)\n", "key = ['2022-12'+str(s) for s in np.random.choice(np.arange(300,501),20,replace=False)]\n", "df = pd.DataFrame({'att':att,'rep':rep,'mid':mid,'fin':fin},index=key)\n", "df.head()" ], "id": "0d8a6d94-a50b-4be0-8986-2c40fc417658" }, { "cell_type": "markdown", "metadata": {}, "source": [ "`-` att 선택" ], "id": "00f33cdd-8722-4657-bf89-f901ad6fc37c" }, { "cell_type": "code", "execution_count": 93, "metadata": {}, "outputs": [], "source": [ "df.att" ], "id": "b0e18c88" }, { "cell_type": "markdown", "metadata": {}, "source": [ "`-` 단점: 칼럼이름에 스페이스가 있으면 쓸 수 없음.\n", "\n", "***예비학습끝***\n", "\n", "------------------------------------------------------------------------\n", "\n", "`-` 누가 자료를 아래와 같이 주었다고 하자. (엑셀특)" ], "id": "e14c86e5-7f4f-42a7-bfd4-c63fcc9a67e8" }, { "cell_type": "code", "execution_count": 115, "metadata": {}, "outputs": [], "source": [ "df.columns = pd.Index(['att score', 'rep score', 'mid score', 'fin score'])\n", "df.head()" ], "id": "6c65c76d" }, { "cell_type": "markdown", "metadata": {}, "source": [ "`-` 출석점수를 뽑고 싶다면?" ], "id": "a71978ed-b0b7-4f8b-92bb-4fee8d3b262b" }, { "cell_type": "code", "execution_count": 102, "metadata": {}, "outputs": [], "source": [ "df['att score']\n", "# df.att score # 이코드는 실행불가능" ], "id": "d6456f23" }, { "cell_type": "markdown", "metadata": {}, "source": [ "`-` 출석점수가 90보다 작은 학생을 뽑고 싶다면?" ], "id": "b112bb0b-b29e-4d2b-a6e3-c852f0464221" }, { "cell_type": "code", "execution_count": 108, "metadata": {}, "outputs": [], "source": [ "df.loc[df['att score'] < 90, :] \n", "# df.query('att score < 90')" ], "id": "bd9f51d3" }, { "cell_type": "markdown", "metadata": {}, "source": [ "`-` 그냥 컬럼이름을 바꾸고 하는것도 방법임" ], "id": "01fea4af-d859-42fb-8d6c-9d309de5d111" }, { "cell_type": "code", "execution_count": 125, "metadata": {}, "outputs": [], "source": [ "df.columns = pd.Index([l.replace(' ','_') for l in list(df.columns)])\n", "df.head()" ], "id": "2c751ad4" }, { "cell_type": "code", "execution_count": 126, "metadata": {}, "outputs": [], "source": [ "df.query('att_score<90')\n", "df.att_score" ], "id": "d648d385" }, { "cell_type": "markdown", "metadata": {}, "source": [ "`-` 그렇지만 col이름을 바꾸는게 항상 만능은 아니다.\n", "\n", "## 개인습관\n", "\n", "`-` row의 이름은 없는게 낫다고 생각함 // 시계열자료는 예외" ], "id": "c3c7fe9a-71d6-4c6e-a037-b3d9311ff093" }, { "cell_type": "code", "execution_count": 127, "metadata": {}, "outputs": [], "source": [ "np.random.seed(43052)\n", "att = np.random.choice(np.arange(10,21)*5,20)\n", "rep = np.random.choice(np.arange(5,21)*5,20)\n", "mid = np.random.choice(np.arange(0,21)*5,20)\n", "fin = np.random.choice(np.arange(0,21)*5,20)\n", "key = ['2022-12'+str(s) for s in np.random.choice(np.arange(300,501),20,replace=False)]\n", "df = pd.DataFrame({'att':att,'rep':rep,'mid':mid,'fin':fin},index=key)\n", "df.head()" ], "id": "6f026262-f8c2-4fc2-859f-d5b6baa10122" }, { "cell_type": "code", "execution_count": 132, "metadata": {}, "outputs": [], "source": [ "df2 = df.reset_index().rename(columns={'index':'student_id'})\n", "df2.head()" ], "id": "efd9a418" }, { "cell_type": "markdown", "metadata": {}, "source": [ "`-` 편해" ], "id": "219bb730-85c7-475b-a6aa-95e6a1f1495b" }, { "cell_type": "code", "execution_count": 142, "metadata": {}, "outputs": [], "source": [ "#df2.loc[0,'student_id':'rep'] \n", "#df2.loc[[0],'student_id':'rep'] \n", "#df2.loc[[0,4,5],'student_id':'rep'] \n", "#df2.loc[range(5),'student_id':'rep'] \n", "#df2.loc[5::2,'student_id':'rep'] " ], "id": "ba09f9f4-173b-4b24-96c8-ceb35b2c2405" }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 새로운 열의 추가 ($\\star\\star\\star$)\n", "\n", "`-` 자료" ], "id": "7c34d9e0-f9f7-4376-97f7-6ea11e45e697" }, { "cell_type": "code", "execution_count": 143, "metadata": {}, "outputs": [], "source": [ "np.random.seed(43052)\n", "att = np.random.choice(np.arange(10,21)*5,20)\n", "rep = np.random.choice(np.arange(5,21)*5,20)\n", "mid = np.random.choice(np.arange(0,21)*5,20)\n", "fin = np.random.choice(np.arange(0,21)*5,20)\n", "student_id = [ '2023-12362', '2022-12471', '2023-12333', '2022-12400', '2022-12377',\n", " '2022-12469', '2023-12314', '2022-12363', '2023-12445', '2023-12336',\n", " '2023-12426', '2022-12380', '2023-12422', '2022-12488', '2022-12370',\n", " '2023-12443', '2022-12463', '2023-12491', '2023-12340', '2022-12312' ]\n", "df = pd.DataFrame({'student_id':student_id,'att':att,'rep':rep,'mid':mid,'fin':fin})\n", "df" ], "id": "56eb7528-1677-47a7-8471-47ad2c6fd9c6" }, { "cell_type": "markdown", "metadata": {}, "source": [ "`-` 방법1: assign을 이용한 추가" ], "id": "e24e2732-45be-45a1-85f6-8192f1c64eb5" }, { "cell_type": "code", "execution_count": 149, "metadata": {}, "outputs": [], "source": [ "df.assign(total = df.att*0.1 + df.rep*0.2 + df.mid*0.3 + df.fin*0.4) " ], "id": "af2e45ec" }, { "cell_type": "markdown", "metadata": {}, "source": [ "`-` 방법2: eval을 이용한 추가" ], "id": "7526b0ec-9d9b-4353-a750-0b80ef31720b" }, { "cell_type": "code", "execution_count": 150, "metadata": {}, "outputs": [], "source": [ "df.eval('total = att*0.1 + rep*0.2 + mid*0.3 + fin*0.4') " ], "id": "bb7b7f64" }, { "cell_type": "markdown", "metadata": {}, "source": [ "`-` 방법3: `df['total']` 을 이용한 할당 // 추천X" ], "id": "dd624b16-b06a-41f0-9f73-61a936f407af" }, { "cell_type": "code", "execution_count": 154, "metadata": {}, "outputs": [], "source": [ "df['total'] = df.att*0.1 + df.rep*0.2 + df.mid*0.3 + df.fin*0.4\n", "df" ], "id": "75ae65d1" }, { "cell_type": "markdown", "metadata": {}, "source": [ "`-` 아래의 자료에서 입학년도를 추가하고 싶다면?" ], "id": "d5f68755-5844-48d4-90fe-25ca4383e505" }, { "cell_type": "code", "execution_count": 155, "metadata": {}, "outputs": [], "source": [ "np.random.seed(43052)\n", "att = np.random.choice(np.arange(10,21)*5,20)\n", "rep = np.random.choice(np.arange(5,21)*5,20)\n", "mid = np.random.choice(np.arange(0,21)*5,20)\n", "fin = np.random.choice(np.arange(0,21)*5,20)\n", "student_id = [ '2023-12362', '2022-12471', '2023-12333', '2022-12400', '2022-12377',\n", " '2022-12469', '2023-12314', '2022-12363', '2023-12445', '2023-12336',\n", " '2023-12426', '2022-12380', '2023-12422', '2022-12488', '2022-12370',\n", " '2023-12443', '2022-12463', '2023-12491', '2023-12340', '2022-12312' ]\n", "df = pd.DataFrame({'student_id':student_id,'att':att,'rep':rep,'mid':mid,'fin':fin})" ], "id": "f4488030-4b32-4fc4-8ebb-9948a8bc0a72" }, { "cell_type": "code", "execution_count": 166, "metadata": {}, "outputs": [], "source": [ "df.assign(year=[l.split('-')[0] for l in list(df.student_id)]).query('year==\"2022\"')" ], "id": "aaa329bf" }, { "cell_type": "markdown", "metadata": {}, "source": [ "# HW\n", "\n", "아래는 전북대 통계학과 학생들이 R과 Python을 공부한 평균 시간이다." ], "id": "d125354e-b5b6-4ead-a21f-040a5d18f7ed" }, { "cell_type": "code", "execution_count": 212, "metadata": {}, "outputs": [], "source": [ "np.random.seed(20230426)\n", "day = ['2023-04-24(Mon)','2023-04-25(Tue)','2023-04-26(Wed)','2023-04-27(Thu)','2023-04-28(Fri)',\n", " '2023-05-01(Mon)','2023-05-02(Tue)','2023-05-03(Wed)','2023-05-04(Thu)','2023-05-05(Fri)',\n", " '2023-05-08(Mon)','2023-05-09(Tue)','2023-05-10(Wed)','2023-05-11(Thu)','2023-05-12(Fri)']\n", "hours1 = np.random.randn(15).cumsum()*2\n", "hours1 = hours1 - hours1.min() +1\n", "hours2 = np.random.randn(15).cumsum()*2\n", "hours2 = hours2 - hours2.min() +1\n", "\n", "df = pd.DataFrame({'hours(R)':hours1, 'hours(Python)':hours2},index=day)\n", "df" ], "id": "cea8600a-ec2b-4348-9a91-b40bcf4c0a76" }, { "cell_type": "markdown", "metadata": {}, "source": [ "`(1)` 데이터프레임을 변형하여 아래와 같이 만들어라." ], "id": "61cab58e-0a62-47e3-b13a-479b55317a25" }, { "cell_type": "code", "execution_count": 213, "metadata": {}, "outputs": [], "source": [ "#" ], "id": "a1f02496-3633-44c6-b97e-f797b1fbdf00" }, { "cell_type": "markdown", "metadata": {}, "source": [ "(풀이)" ], "id": "e7cfcbc1-90f1-43cf-85e5-a1a74f0ef61b" }, { "cell_type": "code", "execution_count": 211, "metadata": {}, "outputs": [], "source": [ "index = [l.replace(')','').split('(') for l in df.index]\n", "df = df.assign(\n", " day=[day for day, _ in index],\n", " weekday=[weekday for _,weekday in index]\n", ").reset_index().loc[:,'hours(R)':]\n", "df" ], "id": "69b08397-e956-4d45-8fed-7087f863fabe" }, { "cell_type": "markdown", "metadata": {}, "source": [ "`(2)` 4월달에 전북대학교 학생들은 R과 Python중 어떤 과목을 더 많이\n", "공부하였는가?\n", "\n", "(풀이)" ], "id": "283789ae-fd11-4e45-91eb-548a1b96c8c5" }, { "cell_type": "code", "execution_count": 179, "metadata": {}, "outputs": [], "source": [ "df.query('day <= \"2023-04-28\"')['hours(R)'].sum()" ], "id": "8eb8520a-99b7-4b12-8dc3-924d9cdb09d3" }, { "cell_type": "code", "execution_count": 180, "metadata": {}, "outputs": [], "source": [ "df.query('day <= \"2023-04-28\"')['hours(Python)'].sum()" ], "id": "5770bca2-f7c0-43cf-938d-d63690442262" }, { "cell_type": "markdown", "metadata": {}, "source": [ "`(3)` ‘월-금’ 사이의 요일중 R을 가장 열심히 공부한 요일은 어느 요일인가?\n", "\n", "(풀이1)" ], "id": "c38f60e0-652f-4bc6-aa70-9f1313f14072" }, { "cell_type": "code", "execution_count": 144, "metadata": {}, "outputs": [], "source": [ "{s:df.loc[df.weekday == s,'hours(R)'].sum() for s in set(df.weekday)}" ], "id": "fa9c7970-4d53-4a50-8255-f7fd57fa6c62" }, { "cell_type": "markdown", "metadata": {}, "source": [ "월요일에 가장 많이함\n", "\n", "(풀이2) – groupby를 이용하여 풀어도 무방 (이 수업에서는 설명하지 않은\n", "방법임)\n", "\n", "`(4)` ’월-금’사이의 요일중 Python과 R의 합계학습량이 가장 큰 요일은 어느\n", "요일인가?\n", "\n", "(풀이)" ], "id": "72b4e168-3627-419e-a086-6279243c591c" }, { "cell_type": "code", "execution_count": 190, "metadata": {}, "outputs": [], "source": [ "{s:df.loc[df.weekday == s,'hours(R)',].sum()+df.loc[df.weekday == s,'hours(Python)'].sum() for s in set(df.weekday)}" ], "id": "1084cfd8-54b4-491e-85da-ab485dc5315e" }, { "cell_type": "markdown", "metadata": {}, "source": [ "`(5)` R과 Python의 학습량 차이를 계산하고 (R-Python을 계산) maplotlib 을\n", "이용하여 시각화하라.\n", "\n", "(풀이)" ], "id": "4df324f5-a7a6-4226-8a79-0aa596f69990" }, { "cell_type": "code", "execution_count": 177, "metadata": {}, "outputs": [ { "output_type": "display_data", "metadata": {}, "data": { "image/png": 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0qGvrlTsMl+0+bsKTO4tR1njmu4iV02Px5i3nQKshfPu5r/DUrmLuJdOvpP/F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\ny6YakZWsx9OfeH9WPrDMlc4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} } ], "source": [ "y = df['hours(R)'] - df['hours(Python)']\n", "plt.plot(y,'--o')" ], "id": "8ff611b9-0dcd-41c8-96e4-552932be8834" }, { "cell_type": "markdown", "metadata": {}, "source": [ "`(6)` R과 Python의 학습량 차이를 ${\\bf y}=(y_1,\\dots,y_n)$라고 할때,\n", "아래와 같은 변환을 이용하여\n", "$\\tilde{\\bf y}=({\\tilde{y}_1}, \\dots, {\\tilde{y}_n})$를 계산하라.\n", "\n", "- $\\tilde{y}_1= \\frac{1}{3}(2y_1 + y_2)$\n", "- $\\tilde{y}_i= \\frac{1}{3}(y_{i-1}+y_i+y_{i+1})$, for\n", " $i=2,3,\\dots,n-1$\n", "- $\\tilde{y}_n= \\frac{1}{3}(y_{n-1}+2y_{n})$\n", "\n", "결과를 시각화하라.\n", "\n", "(풀이)" ], "id": "001b8254-9d8b-4cbf-917c-4dcae49e1e73" }, { "cell_type": "code", "execution_count": 196, "metadata": {}, "outputs": [], "source": [ "n = len(y)\n", "M = np.array([abs(i-j)<2 for i in range(n) for j in range(n)]).reshape(n,n)/3\n", "M[0,0] = 2/3\n", "M[-1,-1] = 2/3 " ], "id": "f7f330d3-4f07-4e6c-b0d2-41ae54951fca" }, { "cell_type": "code", "execution_count": 209, "metadata": {}, "outputs": [ { "output_type": "display_data", "metadata": {}, "data": { "image/png": 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tejUjb43pj4G7Lxi0RrDdLTNP0TEMBsH95zWv+FdUUcP4Z9dx94z+/HlSnB2U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\nYII=\n" } } ], "source": [ "plt.plot(y,'--o',label=r'$y$=hours(R)-hours(Python)')\n", "plt.plot(M@y,'--o',label=r'$M@y$:= smoothed $y$ = $\\tilde{y}$')\n", "plt.legend()" ], "id": "0d9734c1-4e01-45d9-92ea-b7bed97d77e8" } ], "nbformat": 4, "nbformat_minor": 5, "metadata": { "kernelspec": { "name": "python3", "display_name": "Python 3 (ipykernel)", "language": "python" }, "language_info": { "name": "python", "codemirror_mode": { "name": "ipython", "version": "3" }, "file_extension": ".py", "mimetype": "text/x-python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.16" } } }