From 369eca1ea838dc7f40bd5e12d4cc2f0809d80173 Mon Sep 17 00:00:00 2001 From: Khromov Date: Wed, 11 May 2022 21:06:09 +0300 Subject: [PATCH] task added --- check/test.ipynb | 382 +++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 382 insertions(+) create mode 100644 check/test.ipynb diff --git a/check/test.ipynb b/check/test.ipynb new file mode 100644 index 0000000..b9d6f6a --- /dev/null +++ b/check/test.ipynb @@ -0,0 +1,382 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "a204b887", + "metadata": {}, + "source": [ + "# Выполнил: Хромов Александр Эдуардович\n", + "# Группа: 3821Б1ПР2 \n", + "\n", + "# Задача 11. Аппроксимация данных. Радиоактивный распад\n", + "\n", + "https://web.lemoyne.edu/giunta/classicalcs/rutherhalf.html\n", + "\n", + "Закон радиоактивного распада, открытый Э.Резерфрдом и Ф.Содди, утверждает, что активность радиоактивного вещества \n", + "уменьшается во времени по экспоненциальному закону (геометрической прогресии). Таким образов, активность такого вещества можно характеризовать *периодом полураспада* – промежутком временем, в течении которого активность уменьшается в $2$ раза.\n", + "Здесь мы приводим данные, опубликованные в работе [Rutherford E. A Radioactive Substance emitted from Thorium Compounds // Philosophical Magazine. 1900. 49. 1–14]. Из сосуда с торием, был выкачан воздух. В результате была выделена эманация тория (газ радон-220, или торон).\n", + "Для измерения ее ионизирующей способности подавалось напряжение 100 В и измерялась сила тока, которая менялась во времени.\n", + "\n", + "```\n", + " Время, с Сила тока, А\n", + " 0 1.00 \n", + " 28 0.69\n", + " 62 0.51\n", + " 118 0.23\n", + " 155 0.14\n", + " 210 0.067\n", + " 272 0.041\n", + " 360 0.018\n", + "```\n", + "\n", + "* Изобразите данные на графике.\n", + "* Восстановите зависимость $y=c e^{\\alpha t}$. Воспользуйтесь двумя методами: \n", + " * логарифмированием сведите задачу к линейной задаче наименьших квадратов,\n", + " * нелинейным методом наименьших квадратов\n", + "* Изобразите графики построенных зависимостей.\n", + "* Насколько хорошо установленные зависимости приближают данные? Какая из них лучше?\n", + "* Определите период полураспада радона-220 и сравните его с данными из интернета. Чем обусловлено расхождение (если оно есть)?" + ] + }, + { + "cell_type": "markdown", + "id": "1f6615c5", + "metadata": {}, + "source": [ + "# Ход работы: " + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "97d67b40", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import math\n", + "from scipy import linalg\n", + "from scipy import optimize\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "id": "dca46f2e", + "metadata": {}, + "source": [ + "Импорт библиотек необходимых для работы." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "4f8bac48", + "metadata": {}, + "outputs": [], + "source": [ + "x = np.array([0, 28, 62, 118, 155, 210, 272, 360])\n", + "y = np.array([1.00, 0.69, 0.51, 0.23, 0.14, 0.067, 0.041, 0.018])" + ] + }, + { + "cell_type": "markdown", + "id": "5c370af1", + "metadata": {}, + "source": [ + "Инициализация массивов данных. Массив x - время, y - сила тока." + ] + }, + { + "cell_type": "markdown", + "id": "68a13a38", + "metadata": {}, + "source": [ + "# 1. Изображение данных на графике при помощи функции plot() ." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "1175aafd", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(x, y, color='tab:orange')\n", + "plt.plot(x, y, 'o', color='tab:red')\n", + "plt.grid()\n", + "pass" + ] + }, + { + "cell_type": "markdown", + "id": "ebf545b0", + "metadata": {}, + "source": [ + "*График 1*" + ] + }, + { + "cell_type": "markdown", + "id": "dcc1478f", + "metadata": {}, + "source": [ + "# 2. Восстановление зависимости $y=c e^{\\alpha t}$\n", + "\n", + "2.1 *Через линейную задачу наименьших квадратов*\n", + "\n", + "Т.к $y=c e^{\\alpha t}$ не линейная функция, при помощи логарифмирования приводим её к линейной форме:\n", + "\n", + "$$\n", + "\\ln y = \\ln c + \\alpha t.\n", + "$$\n", + "Обозначим\n", + "$$\n", + "y1 = \\ln y, \\qquad y2 = \\ln c.\n", + "$$\n", + "Теперь зависимость выглядит так:\n", + "$$\n", + "y1 = y2 + \\alpha t.\n", + "$$\n", + "\n", + "Затем, при помощи функции polyfit() проводим аппроксимацию данных, а функцией semilogy() отображаем полученные данные на графике:" + ] + }, + { + "cell_type": "code", + "execution_count": 89, + "id": "f5fcdf5d", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.23493308938370291, -0.5812246846111059)" + ] + }, + "execution_count": 89, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "alpha, y2 = np.polyfit(t, np.log(y), 1)\n", + "y2, alpha" + ] + }, + { + "cell_type": "code", + "execution_count": 90, + "id": "883eac42", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.2648241357390708" + ] + }, + "execution_count": 90, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c = np.exp(y2)\n", + "c" + ] + }, + { + "cell_type": "code", + "execution_count": 91, + "id": "d446e963", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "T = len(x)\n", + "t = np.arange(T)\n", + "c = np.exp(y2)\n", + "tt = np.linspace(0, T, 500)\n", + "yy = c*np.exp(alpha*tt)\n", + "plt.semilogy(tt, yy)\n", + "plt.semilogy(t, y, 'o')\n", + "plt.grid()\n", + "plt.xticks(t[::1], y[::1])\n", + "\n", + "pass" + ] + }, + { + "cell_type": "markdown", + "id": "63bfb2a2", + "metadata": {}, + "source": [ + "*График 2*" + ] + }, + { + "cell_type": "markdown", + "id": "c1491254", + "metadata": {}, + "source": [ + "2.2 Аппроксимация данных нелинейным методом\n", + "\n", + "Этот вид аппроксимации реализуется функцией curve_fit(), но перед её использованием необходимо создать функцию, реализующую зависимость" + ] + }, + { + "cell_type": "code", + "execution_count": 92, + "id": "efe2e128", + "metadata": {}, + "outputs": [], + "source": [ + "def expg(t, c, alpha):\n", + " return c * np.exp(alpha*t)\n", + "params, _ = optimize.curve_fit(exponential_growth, t, y)" + ] + }, + { + "cell_type": "code", + "execution_count": 93, + "id": "163360a3", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(1.0333524993007952, -0.4494511400319082)" + ] + }, + "execution_count": 93, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c, alpha = params\n", + "c, alpha" + ] + }, + { + "cell_type": "markdown", + "id": "afc846df", + "metadata": {}, + "source": [ + "Значения параметров c отличаются на 0.23, а значения alpha на 0.14" + ] + }, + { + "cell_type": "code", + "execution_count": 94, + "id": "35a96fbf", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "tt = np.linspace(0, T, 500)\n", + "yy = expg(tt, c, alpha)\n", + "plt.semilogy(tt, yy)\n", + "plt.semilogy(t, y, 'o')\n", + "plt.grid()\n", + "plt.xticks(t[::1], y[::1])\n", + "\n", + "pass" + ] + }, + { + "cell_type": "markdown", + "id": "64d81ec9", + "metadata": {}, + "source": [ + "*График 3*" + ] + }, + { + "cell_type": "markdown", + "id": "bed6676f", + "metadata": {}, + "source": [ + "Вывод:\n", + "\n", + "Исходя из графиков 2 и 3, и значений параметров можно сделать вывод, что метод линейной аппроксимации более точен в данной ситуации, т.к он наиболее точно отображает тренд из графика 1." + ] + }, + { + "cell_type": "markdown", + "id": "4c972b18", + "metadata": {}, + "source": [ + "# 3. Период полураспада\n", + "\n", + "Исходя из определения: \"период полураспада – промежуток времени, в течении которого активность вещества уменьшается в 2 раза.\"\n", + "\n", + "Если активность вещества уменьшится в 2 раза, то и сила тока, проходящего через газ, уменьшится в два раза. Это значит, что согласно таблице с измерениями, период полураспада радона-220 будет равен ~62с.\n", + "\n", + "Согласно Википедии, период полураспада радона-220 равен 55.6с. Разницу в 6,4с можно объяснить тем, что данные из таблицы были получены в 1900-м году. Измерительные приборы и электроника того времени несопоставима с современной, поэтому, можно предположить, что результаты не совпадают именно по этой причине." + ] + } + ], + "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": "3.9.7" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}