From 7cd113c899dc6793c3d9a8d5765a7df5e9891813 Mon Sep 17 00:00:00 2001 From: Burdyuja Alexandr Date: Tue, 3 May 2022 18:19:13 +0300 Subject: [PATCH 1/3] added solution of my final task. Variant 14 --- Final Project/Untitled.ipynb | 433 +++++++++++++++++++++++++++++++++++ 1 file changed, 433 insertions(+) create mode 100644 Final Project/Untitled.ipynb diff --git a/Final Project/Untitled.ipynb b/Final Project/Untitled.ipynb new file mode 100644 index 0000000..038eb5b --- /dev/null +++ b/Final Project/Untitled.ipynb @@ -0,0 +1,433 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 4, + "id": "17120ee3", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Requirement already satisfied: matplotlib in c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages (3.5.1)\n", + "Requirement already satisfied: fonttools>=4.22.0 in c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages (from matplotlib) (4.33.3)\n", + "Requirement already satisfied: pyparsing>=2.2.1 in c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages (from matplotlib) (3.0.8)\n", + "Requirement already satisfied: python-dateutil>=2.7 in c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages (from matplotlib) (2.8.2)\n", + "Requirement already satisfied: packaging>=20.0 in c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages (from matplotlib) (21.3)\n", + "Requirement already satisfied: pillow>=6.2.0 in c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages (from matplotlib) (8.3.1)\n", + "Requirement already satisfied: cycler>=0.10 in c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages (from matplotlib) (0.11.0)\n", + "Requirement already satisfied: kiwisolver>=1.0.1 in c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages (from matplotlib) (1.4.2)\n", + "Requirement already satisfied: numpy>=1.17 in c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages (from matplotlib) (1.21.6)\n", + "Requirement already satisfied: typing-extensions in c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages (from kiwisolver>=1.0.1->matplotlib) (4.2.0)\n", + "Requirement already satisfied: six>=1.5 in c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages (from python-dateutil>=2.7->matplotlib) (1.16.0)\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING: You are using pip version 21.2.4; however, version 22.0.4 is available.\n", + "You should consider upgrading via the 'c:\\users\\user\\appdata\\local\\programs\\python\\python37\\python.exe -m pip install --upgrade pip' command.\n" + ] + } + ], + "source": [ + "!pip install matplotlib" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "c7ccc6cf", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "from scipy import linalg\n", + "from scipy import interpolate" + ] + }, + { + "cell_type": "markdown", + "id": "a8bfc70e", + "metadata": {}, + "source": [ + "
Представим начальные данные след. образом:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "cfcf41be", + "metadata": {}, + "outputs": [], + "source": [ + "v = np.array([0, 10, 20, 30, 40, 50, 60])\n", + "d = np.array([0, 5.0, 20, 46, 70, 102, 153])" + ] + }, + { + "cell_type": "markdown", + "id": "c337f5c2", + "metadata": {}, + "source": [ + "
Построим график кусочно-линейной функции и найдем максимальную доступную скорость:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "b4f15d4a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array(35.83333333)" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "h = interpolate.interp1d(d, v, kind = 'linear')\n", + "h(60)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "42c30ac3", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages\\ipykernel_launcher.py:4: UserWarning: color is redundantly defined by the 'color' keyword argument and the fmt string \"or\" (-> color='r'). The keyword argument will take precedence.\n", + " after removing the cwd from sys.path.\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "dd = np.linspace(0, 150, 500)\n", + "vv = h(dd)\n", + "plt.plot(dd, vv, color = 'tab:blue')\n", + "plt.plot(d, v, 'or', color = 'tab:orange')\n", + "pass" + ] + }, + { + "cell_type": "markdown", + "id": "778d7316", + "metadata": {}, + "source": [ + "
Теперь построим график для кусочно-кубической интерполяции:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "d7d80941", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages\\ipykernel_launcher.py:5: UserWarning: color is redundantly defined by the 'color' keyword argument and the fmt string \"or\" (-> color='r'). The keyword argument will take precedence.\n", + " \"\"\"\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "f = interpolate.interp1d(d, v, kind = 'cubic')\n", + "dd = np.linspace(0, 150, 500)\n", + "vv = f(dd)\n", + "plt.plot(dd, vv, color = 'tab:blue')\n", + "plt.plot(d, v, 'or', color = 'tab:orange')\n", + "pass" + ] + }, + { + "cell_type": "markdown", + "id": "0037a3a1", + "metadata": {}, + "source": [ + "
Теперь надо вычислить значение в требуемой точке:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "23c6cc90", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array(36.00342639)" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "f(60)" + ] + }, + { + "cell_type": "markdown", + "id": "60ef58d4", + "metadata": {}, + "source": [ + "
То есть, методом кубической интерполяции мы выяснили, что для выполнения данного условия скорость должна быть не меньше 36.003.
Найдем для функции интерполяционный многочлен и вычислим с его помощью искомое значение" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "96c533f0", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-9.09170761e-10 3.71982217e-07 -5.69439974e-05 4.10077119e-03\n", + " -1.43048892e-01 2.61961353e+00 -3.43756686e-13]\n" + ] + } + ], + "source": [ + "f = np.polyfit(d, v, 6)\n", + "print(f)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "4be66686", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "36.80827351484006" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.polyval(f, 60)" + ] + }, + { + "cell_type": "markdown", + "id": "6a28a335", + "metadata": {}, + "source": [ + "
С помощью интерполяционнго многочлена, мы получили более возможное значение скорости: 36.808.
График интерполяционного многочлена:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "a12c1ac7", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "dd = np.linspace(0, 159, 50)\n", + "plt.plot(dd, np.polyval(f, dd))\n", + "plt.plot(d, v, 'o')\n", + "pass" + ] + }, + { + "cell_type": "markdown", + "id": "83d8a3e0", + "metadata": {}, + "source": [ + "
Наблюдаем сильный скачек на одном из данных промежутков, который далек от истины.
Найдем требуемую величину с помощью обратной кубической интерполяции." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "a8ab7a9e", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages\\ipykernel_launcher.py:5: UserWarning: color is redundantly defined by the 'color' keyword argument and the fmt string \"or\" (-> color='r'). The keyword argument will take precedence.\n", + " \"\"\"\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "u= interpolate.interp1d(v, d, kind = 'cubic')\n", + "vv = np.linspace(0, 60, 500)\n", + "dd = u(vv)\n", + "plt.plot(vv, dd, color = 'tab:green')\n", + "plt.plot(v, d, 'or', color = 'tab:orange')\n", + "pass" + ] + }, + { + "cell_type": "markdown", + "id": "8c96f6da", + "metadata": {}, + "source": [ + "
Далее сравним результаты прямой и обратной кубической интерполяции:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "6929e837", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array(60.32398532)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "u(36.00342639)" + ] + }, + { + "cell_type": "markdown", + "id": "201bd54d", + "metadata": {}, + "source": [ + "
Получим результат примерно на 0.3 больше требуемого значения.
Подставим результат, полученный интерполяционным многочленом:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "fe647d72", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array(62.20781598)" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "u(36.808273514842234)" + ] + }, + { + "cell_type": "markdown", + "id": "7505c5ba", + "metadata": {}, + "source": [ + "
И тут мы получаем разницу заметно больше, на 2 единицы скорости...
\n", + "

Вывод:

\n", + "
\n", + "
    \n", + "
  1. Пользуясь различными методами интерполяции, получаем не одинаковые значения;
    2. \n", + "
  2. Интерполяционный многочлен удобен в применении, но при высоком значении степени некоторые точки осц
    3. \n", + "
  3. \n", + "
\n", + "
" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "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": "3.7.0" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From 4848605058fa8599c5c4efecf549d12a02f0d822 Mon Sep 17 00:00:00 2001 From: Burdyuja Alexandr Date: Fri, 6 May 2022 11:13:50 +0300 Subject: [PATCH 2/3] added final solution for the task --- ...d.ipynb => Sasha_Burduzha_3821B1PR3.ipynb} | 85 ++++++++++--------- 1 file changed, 43 insertions(+), 42 deletions(-) rename Final Project/{Untitled.ipynb => Sasha_Burduzha_3821B1PR3.ipynb} (97%) diff --git a/Final Project/Untitled.ipynb b/Final Project/Sasha_Burduzha_3821B1PR3.ipynb similarity index 97% rename from Final Project/Untitled.ipynb rename to Final Project/Sasha_Burduzha_3821B1PR3.ipynb index 038eb5b..9c809e9 100644 --- a/Final Project/Untitled.ipynb +++ b/Final Project/Sasha_Burduzha_3821B1PR3.ipynb @@ -3,7 +3,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "17120ee3", + "id": "456b4e80", "metadata": {}, "outputs": [ { @@ -38,8 +38,8 @@ }, { "cell_type": "code", - "execution_count": 6, - "id": "c7ccc6cf", + "execution_count": 18, + "id": "dd066a80", "metadata": {}, "outputs": [], "source": [ @@ -52,7 +52,7 @@ }, { "cell_type": "markdown", - "id": "a8bfc70e", + "id": "026bc4ce", "metadata": {}, "source": [ "
Представим начальные данные след. образом:" @@ -60,8 +60,8 @@ }, { "cell_type": "code", - "execution_count": 7, - "id": "cfcf41be", + "execution_count": 19, + "id": "e65e507b", "metadata": {}, "outputs": [], "source": [ @@ -71,7 +71,7 @@ }, { "cell_type": "markdown", - "id": "c337f5c2", + "id": "023c8749", "metadata": {}, "source": [ "
Построим график кусочно-линейной функции и найдем максимальную доступную скорость:" @@ -79,8 +79,8 @@ }, { "cell_type": "code", - "execution_count": 8, - "id": "b4f15d4a", + "execution_count": 20, + "id": "6ffb3d21", "metadata": {}, "outputs": [ { @@ -89,7 +89,7 @@ "array(35.83333333)" ] }, - "execution_count": 8, + "execution_count": 20, "metadata": {}, "output_type": "execute_result" } @@ -101,8 +101,8 @@ }, { "cell_type": "code", - "execution_count": 9, - "id": "42c30ac3", + "execution_count": 21, + "id": "6a022373", "metadata": {}, "outputs": [ { @@ -136,7 +136,7 @@ }, { "cell_type": "markdown", - "id": "778d7316", + "id": "56142c08", "metadata": {}, "source": [ "
Теперь построим график для кусочно-кубической интерполяции:" @@ -144,8 +144,8 @@ }, { "cell_type": "code", - "execution_count": 10, - "id": "d7d80941", + "execution_count": 22, + "id": "f754c604", "metadata": {}, "outputs": [ { @@ -180,7 +180,7 @@ }, { "cell_type": "markdown", - "id": "0037a3a1", + "id": "8e024ddd", "metadata": {}, "source": [ "
Теперь надо вычислить значение в требуемой точке:" @@ -188,8 +188,8 @@ }, { "cell_type": "code", - "execution_count": 11, - "id": "23c6cc90", + "execution_count": 23, + "id": "5c8f05bc", "metadata": {}, "outputs": [ { @@ -198,7 +198,7 @@ "array(36.00342639)" ] }, - "execution_count": 11, + "execution_count": 23, "metadata": {}, "output_type": "execute_result" } @@ -209,7 +209,7 @@ }, { "cell_type": "markdown", - "id": "60ef58d4", + "id": "c16c1e9b", "metadata": {}, "source": [ "
То есть, методом кубической интерполяции мы выяснили, что для выполнения данного условия скорость должна быть не меньше 36.003.
Найдем для функции интерполяционный многочлен и вычислим с его помощью искомое значение" @@ -217,8 +217,8 @@ }, { "cell_type": "code", - "execution_count": 12, - "id": "96c533f0", + "execution_count": 24, + "id": "f4bc9f4e", "metadata": {}, "outputs": [ { @@ -237,8 +237,8 @@ }, { "cell_type": "code", - "execution_count": 13, - "id": "4be66686", + "execution_count": 25, + "id": "df479f4f", "metadata": {}, "outputs": [ { @@ -247,7 +247,7 @@ "36.80827351484006" ] }, - "execution_count": 13, + "execution_count": 25, "metadata": {}, "output_type": "execute_result" } @@ -258,7 +258,7 @@ }, { "cell_type": "markdown", - "id": "6a28a335", + "id": "46c7c239", "metadata": {}, "source": [ "
С помощью интерполяционнго многочлена, мы получили более возможное значение скорости: 36.808.
График интерполяционного многочлена:" @@ -266,8 +266,8 @@ }, { "cell_type": "code", - "execution_count": 14, - "id": "a12c1ac7", + "execution_count": 26, + "id": "00fd25d2", "metadata": {}, "outputs": [ { @@ -292,7 +292,7 @@ }, { "cell_type": "markdown", - "id": "83d8a3e0", + "id": "9368f710", "metadata": {}, "source": [ "
Наблюдаем сильный скачек на одном из данных промежутков, который далек от истины.
Найдем требуемую величину с помощью обратной кубической интерполяции." @@ -300,8 +300,8 @@ }, { "cell_type": "code", - "execution_count": 15, - "id": "a8ab7a9e", + "execution_count": 27, + "id": "20566e46", "metadata": {}, "outputs": [ { @@ -336,7 +336,7 @@ }, { "cell_type": "markdown", - "id": "8c96f6da", + "id": "da7c5ae6", "metadata": {}, "source": [ "
Далее сравним результаты прямой и обратной кубической интерполяции:" @@ -344,8 +344,8 @@ }, { "cell_type": "code", - "execution_count": 16, - "id": "6929e837", + "execution_count": 28, + "id": "7d107c29", "metadata": {}, "outputs": [ { @@ -354,7 +354,7 @@ "array(60.32398532)" ] }, - "execution_count": 16, + "execution_count": 28, "metadata": {}, "output_type": "execute_result" } @@ -365,7 +365,7 @@ }, { "cell_type": "markdown", - "id": "201bd54d", + "id": "def5fa77", "metadata": {}, "source": [ "
Получим результат примерно на 0.3 больше требуемого значения.
Подставим результат, полученный интерполяционным многочленом:" @@ -373,8 +373,8 @@ }, { "cell_type": "code", - "execution_count": 17, - "id": "fe647d72", + "execution_count": 29, + "id": "449a4309", "metadata": {}, "outputs": [ { @@ -383,7 +383,7 @@ "array(62.20781598)" ] }, - "execution_count": 17, + "execution_count": 29, "metadata": {}, "output_type": "execute_result" } @@ -394,16 +394,17 @@ }, { "cell_type": "markdown", - "id": "7505c5ba", + "id": "4d2c8865", "metadata": {}, "source": [ "
И тут мы получаем разницу заметно больше, на 2 единицы скорости...
\n", "

Вывод:

\n", + "
\n", "
\n", "
    \n", "
  1. Пользуясь различными методами интерполяции, получаем не одинаковые значения;
    2. \n", - "
  2. Интерполяционный многочлен удобен в применении, но при высоком значении степени некоторые точки осц
    3. \n", - "
  3. \n", + "
  4. Интерполяционный многочлен удобен в применении, но при высоком значении степени некоторые точки осциллируют, тем самым понижая точность вычислений;
    5. \n", + "
  5. Наиболее точным оказался метод кубической интерполяции. Он наиболее плавен и близок к реальным знчениям начальных данных;
    6. \n", "
\n", "
" ] From 981f6129e964274a321ac03ea9fabe8beac4ff6b Mon Sep 17 00:00:00 2001 From: Burdyuja Alexandr Date: Fri, 6 May 2022 11:18:50 +0300 Subject: [PATCH 3/3] rework solution --- Final Project/Sasha_Burduzha_3821B1PR3.ipynb | 61 +++++--------------- 1 file changed, 14 insertions(+), 47 deletions(-) diff --git a/Final Project/Sasha_Burduzha_3821B1PR3.ipynb b/Final Project/Sasha_Burduzha_3821B1PR3.ipynb index 9c809e9..7e7aaa3 100644 --- a/Final Project/Sasha_Burduzha_3821B1PR3.ipynb +++ b/Final Project/Sasha_Burduzha_3821B1PR3.ipynb @@ -2,43 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 4, - "id": "456b4e80", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Requirement already satisfied: matplotlib in c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages (3.5.1)\n", - "Requirement already satisfied: fonttools>=4.22.0 in c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages (from matplotlib) (4.33.3)\n", - "Requirement already satisfied: pyparsing>=2.2.1 in c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages (from matplotlib) (3.0.8)\n", - "Requirement already satisfied: python-dateutil>=2.7 in c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages (from matplotlib) (2.8.2)\n", - "Requirement already satisfied: packaging>=20.0 in c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages (from matplotlib) (21.3)\n", - "Requirement already satisfied: pillow>=6.2.0 in c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages (from matplotlib) (8.3.1)\n", - "Requirement already satisfied: cycler>=0.10 in c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages (from matplotlib) (0.11.0)\n", - "Requirement already satisfied: kiwisolver>=1.0.1 in c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages (from matplotlib) (1.4.2)\n", - "Requirement already satisfied: numpy>=1.17 in c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages (from matplotlib) (1.21.6)\n", - "Requirement already satisfied: typing-extensions in c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages (from kiwisolver>=1.0.1->matplotlib) (4.2.0)\n", - "Requirement already satisfied: six>=1.5 in c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages (from python-dateutil>=2.7->matplotlib) (1.16.0)\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "WARNING: You are using pip version 21.2.4; however, version 22.0.4 is available.\n", - "You should consider upgrading via the 'c:\\users\\user\\appdata\\local\\programs\\python\\python37\\python.exe -m pip install --upgrade pip' command.\n" - ] - } - ], - "source": [ - "!pip install matplotlib" - ] - }, - { - "cell_type": "code", - "execution_count": 18, + "execution_count": 1, "id": "dd066a80", "metadata": {}, "outputs": [], @@ -60,7 +24,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 2, "id": "e65e507b", "metadata": {}, "outputs": [], @@ -79,7 +43,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 4, "id": "6ffb3d21", "metadata": {}, "outputs": [ @@ -89,7 +53,7 @@ "array(35.83333333)" ] }, - "execution_count": 20, + "execution_count": 4, "metadata": {}, "output_type": "execute_result" } @@ -101,7 +65,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 5, "id": "6a022373", "metadata": {}, "outputs": [ @@ -109,13 +73,13 @@ "name": "stderr", "output_type": "stream", "text": [ - "c:\\users\\user\\appdata\\local\\programs\\python\\python37\\lib\\site-packages\\ipykernel_launcher.py:4: UserWarning: color is redundantly defined by the 'color' keyword argument and the fmt string \"or\" (-> color='r'). The keyword argument will take precedence.\n", + "c:\\Users\\User\\AppData\\Local\\Programs\\Python\\Python37\\lib\\site-packages\\ipykernel_launcher.py:4: UserWarning: color is redundantly defined by the 'color' keyword argument and the fmt string \"or\" (-> color='r'). The keyword argument will take precedence.\n", " after removing the cwd from sys.path.\n" ] }, { "data": { - "image/png": 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\n", 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", 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\n", 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", 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\n", 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", 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\n", 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", 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" ] @@ -411,8 +375,11 @@ } ], "metadata": { + "interpreter": { + "hash": "82d4c6f819cf47785f735f902f00da8643513d08dab4f4c7470bccf934b8d2d6" + }, "kernelspec": { - "display_name": "Python 3 (ipykernel)", + "display_name": "Python 3.7.0 64-bit", "language": "python", "name": "python3" },