{ "cells": [ { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "# Вычислительные методы в физике\n", "\n", "## Фитирование\n", "Пусть есть набор экспериментальных точек $(x_i, y_i)$ (полученных, естественно, с некоторой погрешностью) и есть некоторая функция $F(x,\\theta)$, которая предположительно описывает нашу экспериментальную зависимость при некотором $\\hat{\\theta}$. Процедура поиска значения параметра или набора параметров $\\theta^*$, при которых функция $(x,\\theta)$ наилучшим образом описывает экспериментальные точки, называется фитированием.\n", "\n", "Фитирование важная процедура и многие математический библиотеки имеют функции для проведения этой операции.\n", "\n", "\n", "### Определение положения пика\n", "\n", "Фитирование может применяться для определения положения пика. В качестве примера можно рассмотреть график, иллюстрирующий открытие бозона Хиггса: \n", "![](./example_fit.jpg)\n", "Красной линией на верхнем графике показан результат фитирования экпериментальных данных с помощью суммы двух функций: описывающей фоновую подложку и форму пика.\n", "Проведя процедуру фитирования можно получить точное положения максимума пика и его ширину. \n", "\n", "\n", "### Пример 1\n", "\n", "Пусть есть истиная функция $y = x^2 - x + 1$, и результат измерения этой зависимости (файл `example_fit.dat`). Предположим, что нам из каких-то теоретических предположений известно, что зависимость должна быть параболической, и мы пытаемся восстановить параметры этой параболы. Для этого мы воспользуемся функцией `curve_fit` из модуля `scipy.optimize`" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "name": "#%%\n", "is_executing": true } }, "outputs": [], "source": [ "# Импротируем необходимые функции\n", "import numpy as np # работа с массивами и линейной алгеброй\n", "import matplotlib.pyplot as plt # для отрисовки графиков\n", "import pandas as pd # для чтения и работы с данными\n", "from scipy.optimize import curve_fit # фитирующая процедура" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [ "# #Так были сгенерированны данные\n", "# from tabulate import tabulate\n", "# n = 15\n", "# x = np.linspace(0, 1, n)\n", "# y_true = x**2 - x + 1\n", "# error = y_true*0.1*np.random.sample(n)\n", "# y = np.random.normal(y_true, error)\n", "# with open('example_fit.txt', 'w') as fout:\n", "# text = tabulate(zip(x,y, error), headers = ('x', 'y', 'y_error'), tablefmt='plain')\n", "# fout.write(text)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [ "data = pd.read_table('example_fit.txt', # имя или путь к файлу \n", " sep = '\\s+' # Здесь указывается разделитель между значениями, используемыми в файле\n", " )" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [ "# Создадим переменные с короткими именами\n", "x = data['x']\n", "y = data['y']\n", "yerr = data['y_error']" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [ { "data": { "text/plain": [ "0.0" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x[0] # получить одно значение" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [ { "data": { "text/plain": [ "array([ 0.35714286, 0.42857143, 0.5 , 0.57142857, 0.64285714])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x[5:10] # выбрать диапазон значений" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [ "def parabolla(x, a, b, c):\n", " \"\"\"\n", " Параметрическая парабола\n", " \"\"\"\n", " return a*x**2 + b*x + c" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [ "result = curve_fit(f = parabolla, # функция, для которой ищутся параметры\n", " xdata= x, ydata=y, # вводим экспериментальные точки\n", " )" ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "Функция `curve_fit` имеет большой список параметров. Например, кроме экспериментальных точек можно указать их ошибки, и тогда будет применен алгоритм фитирования, учитывающий величины ошибок, или начальную точку для поиска значения параметров. " ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [ "popt, pcov = result # декомпозиция кортежа по отдельным переменным" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [ "import matplotlib as mpl\n", "mpl.rcParams['font.size'] = 16 # Управление стилем, в данном случаем - размером шрифта " ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize= (7,7)) # Настраиваем размер холста\n", "plt.plot(x, parabolla(x, *popt), label='Результат фитирования') # Строим график\n", "plt.errorbar(x,y, yerr=yerr, fmt='.', label='Экспериментальные точки') # Строим график с \"крестами\"\n", "plt.plot(x, parabolla(x, 1,-1,1), label=\"Истиная зависимость\")\n", "plt.legend(); # Активируем легенду" ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "### Пример 2: \n", "\n", "Для приближения функции многочленом можно использовать `numpy.polyfit()`" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 3.00601091 4.85432505 6.48622882]\n", "[[ 2.11152260e-02 -4.35855647e-18 -2.15062487e-01]\n", " [ -4.35855647e-18 1.66836354e-01 5.77114466e-20]\n", " [ -2.15062487e-01 5.77114466e-20 3.88971042e+00]]\n", "a = 3.01 ± 0.15\n", "b = 4.85 ± 0.41\n", "c = 6.49 ± 1.97\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "z = np.linspace(-5, 5, 1000)\n", "\n", "# Данные\n", "x = np.linspace(-5, 5, 10)\n", "y = 3*x**2 + 5*x + 1 + 10*np.random.sample(len(x))\n", "\n", "# Фитируем многочленом второй степени с рассчетом матрицы ошибок\n", "params, cov = np.polyfit(x, y, 2, cov=True)\n", "plt.plot(x, y, 'o', markersize=2)\n", "plt.plot(z, params[0] * z**2 + params[1] * z + params[2])\n", "print(params)\n", "print(cov)\n", "print(f\"a = {params[0]:.3} \\u00B1 {np.sqrt(cov[0][0]):.2}\")\n", "print(f\"b = {params[1]:.3} \\u00B1 {np.sqrt(cov[1][1]):.2}\")\n", "print(f\"c = {params[2]:.3} \\u00B1 {np.sqrt(cov[2][2]):.3}\")" ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "### Пример 3" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 45.40114559 341.39906678 88.62304246]\n", "[[ 17.35905932 -6.77377934 0.75023018]\n", " [ -6.77377934 4.29974581 -2.95671194]\n", " [ 0.75023018 -2.95671194 10.18644967]]\n", "a = 45.4 ± 4.2\n", "b = 3.41e+02 ± 2.1\n", "c = 88.6 ± 3.19\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.optimize import curve_fit\n", "\n", "# Функция, которой нужно приблизить зависимость\n", "def fit_func(x, a, b, c):\n", " return c*np.exp(-x*1.9*11.34/a)+b\n", "\n", "# Данные\n", "z = np.linspace(0, 9, 1000)\n", "x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n", "y = [428., 401., 376., 360., 356., 345., 345., 346.5, 344., 345.]\n", "\n", "# Получение параметров и ошибок по функции и точкам, с указанием начальных параметров\n", "params, cov = curve_fit(fit_func, x, y, p0 = [30, 345, 100])\n", "print(params)\n", "print(cov)\n", "\n", "plt.plot(x, y, 'o', markersize=2)\n", "plt.plot(z, fit_func(z, params[0], params[1], params[2]))\n", "\n", "print(f\"a = {params[0]:.3} \\u00B1 {np.sqrt(cov[0][0]):.2}\")\n", "print(f\"b = {params[1]:.3} \\u00B1 {np.sqrt(cov[1][1]):.2}\")\n", "print(f\"c = {params[2]:.3} \\u00B1 {np.sqrt(cov[2][2]):.3}\")" ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "## Гистограммы и распределения\n", "\n", "### Закон больших чисел\n", "\n", "ЗБЧ говорит нам о сходимости среднеего по выборке из распределения к математическому ожиданию от этого распределения. Привеженный ниже код эмулирует бросок игрального кубика. \n", "Изучите как меняется среднее от размера выборки. Выполняется ли ЗБЧ?" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 50 # Размер выборки\n", "np.random.seed(10) # Фиксирует состояниее ГПСЧ, для повторяемости случайных последовательностей\n", "sample = np.random.randint(1,7,size=n) # Правая граница не включается\n", "means = np.cumsum(sample)/np.arange(1, n+1)\n", "\n", "plt.ylabel(\"Среднее значение\")\n", "plt.xlabel('Размер выборки')\n", "plt.plot(means);" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python [default]", "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": "3.6.7" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": false, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": false, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }