From 498892780fb1c34bf8f1f193e98ca5f78f895042 Mon Sep 17 00:00:00 2001 From: Alexander Nozik Date: Sat, 18 Sep 2021 10:59:40 +0300 Subject: [PATCH] Update materials 2021 --- .gitignore | 3 +- .../python/estimates.ipynb | 2451 ++++++++- {ntebooks => notebooks}/python/examples.ipynb | 4871 ++++++++++++++++- notebooks/python/fitting.ipynb | 893 +++ notebooks/python/hypotesis.ipynb | 136 + notebooks/python/images/Chi-square_cdf.svg | 268 + notebooks/python/images/Nelder_Mead1.gif | Bin 0 -> 28867 bytes notebooks/python/images/two_hypothsis.png | Bin 0 -> 81761 bytes .../Теория вероятности.pptx | Bin 0 -> 1309275 bytes Теория оценок/estimates.docx | Bin 0 -> 28287 bytes Теория оценок/estimates.md | 66 + Теория решений/stat.pptx | Bin 0 -> 948734 bytes Теория решений/vaskin.png | Bin 0 -> 26760 bytes Теория решений/vaskin1.png | Bin 0 -> 24084 bytes .../теория решений.docx | Bin 0 -> 79915 bytes 15 files changed, 8456 insertions(+), 232 deletions(-) rename {ntebooks => notebooks}/python/estimates.ipynb (66%) rename {ntebooks => notebooks}/python/examples.ipynb (86%) create mode 100644 notebooks/python/fitting.ipynb create mode 100644 notebooks/python/hypotesis.ipynb create mode 100644 notebooks/python/images/Chi-square_cdf.svg create mode 100644 notebooks/python/images/Nelder_Mead1.gif create mode 100644 notebooks/python/images/two_hypothsis.png create mode 100644 Теория вероятности/Теория вероятности.pptx create mode 100644 Теория оценок/estimates.docx create mode 100644 Теория оценок/estimates.md create mode 100644 Теория решений/stat.pptx create mode 100644 Теория решений/vaskin.png create mode 100644 Теория решений/vaskin1.png create mode 100644 Теория решений/теория решений.docx diff --git a/.gitignore b/.gitignore index f73806e..d92c64f 100644 --- a/.gitignore +++ b/.gitignore @@ -1 +1,2 @@ -.ipynb_checkpoints/ \ No newline at end of file +.ipynb_checkpoints/ +.idea/ \ No newline at end of file diff --git a/ntebooks/python/estimates.ipynb b/notebooks/python/estimates.ipynb similarity index 66% rename from ntebooks/python/estimates.ipynb rename to notebooks/python/estimates.ipynb index 4834b42..b641a1c 100644 --- a/ntebooks/python/estimates.ipynb +++ b/notebooks/python/estimates.ipynb @@ -220,7 +220,7 @@ "\\end{equation}\n", "Здесь $L$ - функция правдоподобия, а $\\pi$ - априорная вероятность для параметра $\\theta$. Если нет никакой дополнительной информации оп параметре, то мы можем положить $\\pi = 1$. Мы получаем, что распределение значения реального параметра повторяет форму функции правдоподобия. Вероятность того, что параметр $\\theta$ лежит в диапазоне от $a$ до $b$ составляет \n", "\\begin{equation}\n", - " P(a < \\theta < b) = \\int_b^a{L(X | \\theta)}\n", + " P(a < \\theta < b) = \\int_b^a{L(X | \\theta)}.\n", "\\end{equation}\n", "#### Интервальная оценка в асимптотическом случае\n", "Согласно центральной предельной теореме, при достаточно большом количестве данных $X$ (и при разумных предположениях о форме распределения для этих данных), функция правдоподобия будет иметь вид нормального распределения. В этом случае центральный доверительный интервал можно вычислить, пользуясь аналитической формулой. Центральный доверительный интервал с уровнем значимости 68% будет соответствовать диапазону между значениями $\\theta$, такими, что значение функции правдоподобия в них отличается от максимума на 0.5.\n", @@ -326,19 +326,91 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## 3.4* Многопараметрические оценки" + "## 3.4 Многопараметрические оценки" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "**TBD**" + "Однопараметрические оценки очень просты для понимания и реализации, но довольно редко встречаются на практике. Даже при оценке параметров линейно зависимости вида $y = k x + b$ уже существует два параметра: $k$ - наклон прямой и $b$ - смещение. Все перечисленные выше математические методы отлично работают и в многомерном случае, но процесс поиска экстремума функции (максимума в случае метода максимума правдоподобия и минимума в случае методов семейства наименьших квадратов) и интерпретация результатов требуют использования специальных программных пакетов." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 3.4.1 Доверительные области в многомерном случае" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Принцип построения доверительной области в многомерном случае точно такой же, как и для одномерных доверительных интервалов. Требуется найти такую областью пространства параметров $\\Omega$, для которой вероятностное содержание для оценки параметра $\\hat \\theta$ (или самого параметра $\\theta$ в засимости от того, какой философии вы придерживаетесь) будет равно некоторой наперед заданной величине $\\alpha$:\n", + "\\begin{equation}\n", + " P(\\theta \\in \\Omega) = \\int_\\Omega{L(X | \\theta)}d\\Omega = \\alpha.\n", + "\\end{equation}\n", + "\n", + "Реализация на практике этого определения сталкивается с тремя проблемами:\n", + "\n", + "1. Взятие многомерного интеграла от произвольной функции - не тривиальная задача. Даже в случае двух параметров, уже требуется некоторый уровень владения вычислительной математикой и компьютерными методами. В случае большего числа параметров, как правило надо использовать специально разработанные для этого пакеты.\n", + "2. Определить центральный интервал для гипер-области гораздо сложнее, чем сделать это для одномерного отрезка. Единых правил для выбора такой области не существует.\n", + "3. Даже если удалось получить доверительную область, описать такой объект в общем случае не так просто, так что представление результатов составляет определенную сложность.\n", + "\n", + "Для решения этих проблем, пользуются следующим приемом: согласно центральной предельной теореме, усреднение большого количества одинаково распределенных величин дает нормально распределенную величину. Это же верно и в многомерном случае. В большинстве случаев, мы ожидаем, что функция правдоподобия будет похожа на многомерное нормальное распределение:\n", + "\\begin{equation}\n", + " L(\\theta) = \\frac{1}{(2 \\pi)^{n/2}\\left|\\Sigma\\right|^{1/2}} e^{-\\frac{1}{2} (x - \\mu)^T \\Sigma^{-1} (x - \\mu)}\n", + "\\end{equation}\n", + "где n - размерность вектора параметров, $\\mu$ - вектор наиболее вероятных значений, а $\\Sigma$ - [ковариационная матрица](https://ru.wikipedia.org/wiki/%D0%9A%D0%BE%D0%B2%D0%B0%D1%80%D0%B8%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%BD%D0%B0%D1%8F_%D0%BC%D0%B0%D1%82%D1%80%D0%B8%D1%86%D0%B0) распределения.\n", + "\n", + "Для многомерного нормального распределения, линии постоянного уровня (то есть поверхности, на которых значение плотности вероятности одинаковые) имеют вид гипер-эллипса, определяемого уравнением $(x - \\mu)^T \\Sigma^{-1} (x - \\mu) = const$. Для любого вероятностного содержания $\\alpha$ можно подобрать эллипс, который будет удовлетворять условию на вероятностное содержание. Интерес правда редставляет не эллипс (в случае размерности больше двух, его просто невозможно отобразить), а ковариацонная матрица. Диагональные элементы этой матрицы являются дисперсиями соответствующих параметров (с учетом всех корреляций параметров)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 3.4.2 Аналитическая оценка для линейной модели" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Линейная модель: $mu = kx + b$\n", + "\n", + "\\begin{equation}\n", + " Q = \\sum{(X_i - \\mu_i(\\theta))^2} = \\sum{(y_i - kx_i - b)^2}.\n", + "\\end{equation}\n", + "\n", + "Найдем минимум:\n", + "\n", + "\\begin{equation}\n", + " \\frac{\\partial Q}{\\partial k} = \\sum{-2x_i y_i +4 k x_i^2 + 2x_i b} = 0\n", + "\\end{equation}\n", + "\n", + "\\begin{equation}\n", + " \\frac{\\partial Q}{\\partial b} = \\sum{-2y_i +4 k x_i + 2 b} = 0\n", + "\\end{equation}\n", + "\n", + "Решение:\n", + "\\begin{equation}\n", + " k = \\frac{N \\sum{x_i y_i} - \\sum{x_i}\\sum{y_i}}\n", + " {N \\sum{x_i^2} - \\left( \\sum{x_i} \\right)^2}\n", + "\\end{equation}\n", + "\n", + "\\begin{equation}\n", + " b = \\frac{\\sum{y_i} - k\\sum{x_i}}{N}\n", + "\\end{equation}\n", + "\n", + "Аналитическое решеие может быть получено в случае любой полиномиальной модели, но не в общем случае." ] }, { "cell_type": "markdown", "metadata": { + "heading_collapsed": true, "slideshow": { "slide_type": "slide" } @@ -349,7 +421,9 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "hidden": true + }, "source": [ "## Установка и подготовка программного обеспечения\n", "При работе с интерактивными примерами предполагается использование интерактивной среды [Jupyter](http://jupyter.org/). Наиболее простым способом подготовки всего, необходимого для работы является установка дистрибутива [Anaocnda](https://www.anaconda.com/download/) (предполагается использование Python версии 3). Для работы необходимы пакеты `numpy`, `pandas` и `matplotlib`, которые входят в поставку Anaconda. Опытные пользователи python могут воспользоваться любым другим способом установки.\n", @@ -359,7 +433,9 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "hidden": true + }, "source": [ "## Инструменты" ] @@ -367,6 +443,7 @@ { "cell_type": "markdown", "metadata": { + "hidden": true, "slideshow": { "slide_type": "subslide" } @@ -377,26 +454,47 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2018-05-01T10:18:55.541135Z", "start_time": "2018-05-01T10:18:55.531132Z" }, + "hidden": true, "hide_input": false }, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "" + ], + "text/vnd.plotly.v1+html": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "import numpy as np # Библиотека для численных методов\n", "import pandas as pd # Библиотека для табличного представления данных\n", "import matplotlib.pyplot as plt # Библиотека для отрисовки графиков\n", "# Команда для интерактивной отрисовки графиков\n", - "%matplotlib inline " + "%matplotlib inline \n", + "\n", + "# Дополнительный паке plotly для интерактивных графиков\n", + "from plotly.offline import download_plotlyjs, init_notebook_mode, plot, iplot\n", + "import plotly.graph_objs as go\n", + "init_notebook_mode(connected=True)" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "hidden": true + }, "source": [ "### Генерация и отрисовка данных" ] @@ -404,6 +502,7 @@ { "cell_type": "markdown", "metadata": { + "hidden": true, "slideshow": { "slide_type": "subslide" } @@ -414,12 +513,13 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2018-05-01T10:18:55.573131Z", "start_time": "2018-05-01T10:18:55.544132Z" }, + "hidden": true, "hide_input": false }, "outputs": [], @@ -443,19 +543,22 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "hidden": true + }, "source": [ "#### Отрисовка функций" ] }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2018-05-01T10:18:55.592132Z", "start_time": "2018-05-01T10:18:55.576133Z" - } + }, + "hidden": true }, "outputs": [], "source": [ @@ -476,7 +579,9 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "hidden": true + }, "source": [ "### Параболический апроксиматор##\n", "Для нахождения оценок методом наименьших квадратов и обобщенным методом наименьших квадратов ($\\chi^2$) потребуется находить минимум функции, которую приближенно можно описать параболической зависимостью. Это можно сделать разными способами, но в одномерном случае это проще всего сделать аппроксимируя параболу по трем произвольным точкам (лучше брать этит точки как можно ближе к минимуму) или используя стандартную библиотечную функцию для полиномиального фита." @@ -484,12 +589,13 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2018-05-01T10:18:55.729149Z", "start_time": "2018-05-01T10:18:55.595133Z" - } + }, + "hidden": true }, "outputs": [], "source": [ @@ -548,26 +654,29 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "hidden": true + }, "source": [ "Проверим работу аппроксиматора:" ] }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2018-05-01T10:18:55.940160Z", "start_time": "2018-05-01T10:18:55.732142Z" - } + }, + "hidden": true }, "outputs": [ { "data": { - "image/png": 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h93A2J1/pTZH40OrBlTRq0tzqSC7L0SdbvxpYW770AYwxR40xx+2XlwDeIuJf\nC9u0nF/rQPZc/jyhtnRS3nvQ6jhKuaS0d+/G3+Rw8tr/auk7UG0U/3gqmeYRkbYiIvbL8fbtHaqF\nbTqFqIF/YpX/GPocmMf65YusjqOUS0n65h1ij/7Imo53cXFMf6vjuJUaFb+INAIGAwvKLJskIpPs\nV68HNohIKjATGGdqOrfkZCL/PJNdHkG0+emv5B4660WPUqoC+3ZtpcuaaWz1CiPu5qetjuN2alT8\nxpgTxphWxpjcMsveNMa8ab/8mjGmuzEmyhjTxxjze00DO5uGjZtSNPItWppcdsy5XU/XqNR5FBUW\ncPSDWxBjo8mN7+Hl7WN1JLejO8vWgs5Rl5LU5X565q1g1fznrI6jlFNLmvN/dC3ewrbezxLYKdzq\nOG5Ji7+W9L5xGimN+hKz5QXSkpdbHUcpp5T606f02f8Rq1qNotewP1sdx21p8dcS8fAg9I655EhL\nGi++k9zD2VZHUsqpHMj8gw7LH2CHRwhRd75hdRy3psVfi5q3asOR4W8RYMvmj3f+rPP9StkVFxVy\naO4tNDCFeI2bq597sZgWfy0LixtEUpf7iMlbzupP/211HKWcwpq5D9OtaAObej1Jh4ujrY7j9rT4\n60D8+GmkNOxDz80636/U+uWL6J3xLqtbDCN2xKTzr6DqnBZ/HfDw9CTkjrnkSAsaLb6To0fqzWfW\nlLogWXvTaffT/ez2DCLizjetjqPstPjrSAv/thwZ9iZtbFlsf/tWne9XbqewIJ9D746nkTkJN7yn\nh2RwIlr8dSgsfjCJXf5CTN6vrPxgqtVxlHKo5LcnE1a0ic29nyUkvErHDlMOosVfx3rfOI2kpgPp\nveN11v38udVxlHKI1QtfpXf2Ala2nUCvYXdYHUeVo8Vfx8TDg/C73yPdsyMhv9zPnh0brY6kVJ1K\nS15OVMoTbGgQTewdL1sdR1VAi98BGjVpToObPsEAhR+OJ+/YEasjKVUncg7uoemiP3NYWhB45yd6\nHB4npcXvIIGdwtk98HU6lOxmy1v6Zq+qf4qLCtk7+0ZamlyOjXqXlgHtrI6kKqHF70A9Lh/Nmovu\no9fxZaz68HGr4yhVqxJn/5WIghTW9ZxOl+jLrI6jzkGL38F63/QESU36E/fHq6z/ZcH5V1DKBSR+\n9Vbpwdf8xxA3aorVcdR51Lj4RSRdRNaLSIqInHWiXCk1U0S2i8g6EYmp6TZdmXh4ED7pfXZ7dqTD\nz1PISEu1OpJSNbJl9VIiEx9lo08Pet71X6vjqCqorWf8A4wx0ZWc6PdqoIv9ayLg9r8ZjZo0x+em\nTyjBE/l4LIez9lkdSalq2bNHKIIrAAASYUlEQVRjM62X3M4Bj9YETvwcnwa+VkdSVeCIqZ6RwPum\n1EqghYi4/bs+gZ3COTj8XQJs2eyfdR0F+SesjqTUBck9nE3xhzfgSQnc+Akt/NtaHUlVUW0UvwF+\nEJEkEZlYwe2BQEaZ65n2ZW4vLG4QG+KfI7xoI+vfuFn39FEuo6iwgN1v3kC7kr1kDn6b4C5RVkdS\nF6A2ir+fMSaG0imde0Xk8nK3SwXrnHXCdRGZKCKJIpKYlZVVC7FcQ6/hd7Iy5F5ij/7Iynf/bnUc\npc7L2GysfWsiPQrWkhI9ne79hlsdSV2gGhe/MWav/ftBYCEQX25IJhBc5noQsLeC+5lljIk1xsQG\nBATUNJZL6X3L06xpcTV9M94mcbHbvwWinNyqT56h96EvSWh3C/Gj77c6jqqGGhW/iDQWkaanLgND\ngA3lhi0GbrHv3dMHyDXG6LuZZYiHB1GT32OjTxSRSY+xKeFbqyMpVaGUpR8Tv/VF1ja+jN536uEY\nXFVNn/G3AVaISCqwGvjGGPOdiEwSkVNnXFgC7AC2A28D99Rwm/WSTwNfgiZ9wX7PtrT//k52bU2x\nOpJSZ9i86nvCVtzPdu8uhN8zDw9PT6sjqWoSY86abrdcbGysSUw86yMBbmHPjs00eH8oxXjBHd/T\nNriz1ZGUYufGVbT6bDS50pzGk3/Er7Xun+FsRCSpkl3qz6Kf3HUygZ3CyR0zj8Ymj4J3R+o+/spy\ne9O30uSzseTTAK/bvtTSrwe0+J3QRZGXkDH0XdqUHCDrrREcP3rY6kjKTR06kEnJ3FH4UMiJsZ/R\nrmNXqyOpWqDF76S69b2aLZe9Sqei7aS/Pko/4KUc7lhuDodnjcDfls2+YXP1LFr1iBa/E4seNJ7k\nnk8TUZDCxlfHUlJcbHUk5SYK8k+w643RhBTvZNsVrxMWP9jqSKoWafE7ubhR97Ly4r8Rk7ecpDdu\n00/3qjpXVFjAxlf/RERBCskxzxA18E9WR1K1TIvfBfS5cSoJgX8mPucrVr11j5a/qjPFRYWsn3kD\nMXm/svLih4gbqXtf10da/C6izx3/YVXA9fQ5ME/LX9WJ4qJCUmeOJeb4L6zs/H/0ufGfVkdSdUSL\n30WIhwfxk9/W8ld1oqS4mJRXx9Pr2E+svOgv9LlputWRVB3S4nchWv6qLpQUF5M8cxyxR38kIXQK\nfW5+0upIqo5p8bsYLX9Vm0qKi1n76gRijy4lIWQyfW99xupIygG0+F2Qlr+qDSXFxSS9djNxud+R\n0OFu+t72nNWRlINo8buos8r/zbuxlZRYHUu5iIL8E6S+PIb4I0tICL6LvrfPsDqSciAtfhd2qvxX\nth5Ln4OfkjRzHEWFBVbHUk4u79gRtr00vHTvnS4P0PeOF6yOpBxMi9/FiYcHvSe9SULIZOJyf2DT\nS9dyMu+Y1bGUk8o9dIDMV66iW34yq6Oeos+Ex62OpCygxV8PiIcHfW97jlXdpxFxYjW7Xh5Cbo77\nnL5SVU3W3nQOvz6I0KLtpF7yqp49y41Vu/hFJFhEfhaRzSKyUUT+UsGY/iKSKyIp9q9pNYurzqX3\nDQ+S2vdlOhVuI+e1K8nam251JOUkMrdvoOjtwQSUHGTb4HeJuepmqyMpC9XkGX8x8KAxJhzoQ+mJ\n1rtVMO5XY0y0/Ut3EK5jMUNvY9vgd2ldcoDiWYPI2L7e6kjKYmnJy/H9cDgNzUn2jPyUiEtHWB1J\nWazaxW+M2WeMWWu/fAzYDOgZGpxAxKUj2DvqM3wpoMmHV+s5fN3Y2u/eI+jL6yjCm6PjFnNxzBVW\nR1JOoFbm+EUkBOgJrKrg5r4ikioi34pI99rYnjq/Lj0v5/hNSzjm0YzO301g9Rd6Ymx3Ymw2EuY+\nSszKv7DbuxPek36mY1iM1bGUk6hx8YtIE+AL4K/GmKPlbl4LdDTGRAGvAl+e434mikiiiCRmZekb\nk7UhuHMPmt+3nK2+UcSvf5yV/52kx/R3AwX5J0h8ZRx9d75OYtMr6fjgT/i3DbY6lnIiNTrZuoh4\nA18D3xtj/lOF8elArDEm+1zj3Plk63WhuKiQpFmT6Z31OakN4+k0aT5Nm/tZHUvVgcNZ+9g/6zrC\nizaS0OFu+tz2HOKhO++5A4ecbF1EBJgNbK6s9EWkrX0cIhJv396h6m5TVY+Xtw+9753Nqm7/pPuJ\nRA69cjl7dmy2OpaqZTs3reHEG1cQWriNpLgX6Xv7DC19VaGa/Fb0A24GBpbZXXOYiEwSkUn2MdcD\nG0QkFZgJjDM1eYmhaqT3nx5iy+C5tLTl0Pj9QaT+9KnVkVQtWfPla7SdP4wGpoBd135Kr+F3Wh1J\nObEaTfXUFZ3qqVsZ29dT9PFNdLKlk9DuFmL//ALePg2sjqWq4WTeMda/PZH4I0vY6BNJm9s/wr9t\nB6tjKQs4ZKpHua7gzj1o/7ffWOU3gr773mf78/3Zn7Hd6ljqAmWkpbL/xUtLD7QWdDthf/9ZS19V\niRa/m/Jt1ITe939AYuzzdCjcQYPZ/XXqx4UkLZmN34dDaGE7xLorZtP3zpfw9PKyOpZyEVr8bi72\nmonk3PQDhz1aEbX8LhLeuleP8OnEjh89zKqZN9Nr9QNkeIdScMcyIgdcb3Us5WK0+BXBXaJKp35a\njaTvvg/Z/e8+/LHud6tjqXI2/vYNR1+KJ+7QV6xsO4GL/v4LbYM7Wx1LuSAtfgXYp37ue5/kS16n\neUkOHb64hoTZf6OwIN/qaG7vZN4xVr1+B92X3ogNT7YN+5Q+k97QN+RVtWnxqzP0HHITXlNWkdp8\nAH0z3iZjhj77t9KW1Us59EIcvbM+Z1XA9fg9uIqw3kOsjqVcnBa/OksL/7bEPvCF/dn/YX32b4Hj\nRw+z8r+TuPibG/CghA2DP6T3vbNp1KS51dFUPaDFryrVc8hNeN+3mtTmA+mb8Tb7/x1D6s+fWR2r\nXjM2G4mL3+Tkf3rS58A81viPoNn/rSai37VWR1P1iH6AS1VJ6s+f4bd8GsFmL6kNe+N33YsEd+5h\ndax65Y91v1P41d8IL9rINq+LYdjzXBzT3+pYykVcyAe4tPhVlRUW5LP2s2eJSHsLHwpZ224c3cc/\nrQd8q6HcQwfYMu8RYrMWclSaktbjQWJH3YeHp6fV0ZQL0eJXdSp7/252fPIwsYe/JUea80f3++k5\n4l58GvhaHc2l5B07wrqFLxK+Yw5NTR6Jra8jbPxzNPcLsDqackFa/Moh0pKXU7LkYcKKNrGPAHZ3\nn6x/AKrgZN4xUhe+yMXbZ+PHUVIbxtN0+NN0iuhtdTTlwrT4lcMYm431vyygwW8z6Fq8lf0EsKv7\nJHqOmKJ/AMrJP3GclC9fpvO2t/HnCOt8Y2kw6DG6xg60OpqqB7T4lcMZm431yxfSYMUMuhZvYT/+\n7Aq/i+5X302TZi2tjmepQwcySfv2DS5K/5gADrOhQTSeAx8lvPdVVkdT9YgWv7KMsdnY8OuXeK94\nnrCiTRw3DdkYcDVtrryXkPA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KKZVbjIE/P4AydZh8tAalixVhaHD+3lYxK7T4lVIqtxxeBef3cLLhaP44FMnIdtXxKuJ4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\nsaDUozzRsZbViZy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"text/plain": [ - "" + "
" ] }, "metadata": {}, @@ -575,7 +684,7 @@ } ], "source": [ - "function = lambda x: x*x + x\n", + "function = lambda x: (x*x + x)*np.exp(-x/100)\n", "x = np.linspace(-4,4)\n", "plt.plot(x, function(x), label = \"parabola\")\n", "plt.plot(x, ParabolicFunction().from_function(-1, 0, 1, function)(x), label = \"parabola-interpolation\")\n", @@ -584,14 +693,18 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "hidden": true + }, "source": [ "## Данные" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "hidden": true + }, "source": [ "### Генерируем и запоминаем данные\n", "В качестве модели берем $y = \\alpha x^2,$\n", @@ -600,19 +713,20 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2018-05-01T10:18:56.087163Z", "start_time": "2018-05-01T10:18:55.942155Z" - } + }, + "hidden": true }, "outputs": [ { "data": { - "image/png": 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RiwTNvnyYPtgL+V6jYORbCvkEpxa9SJBsWQGv3gS7N8NVf4VeI45+jASegl4kioY8txCo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\nfCfn3CRgEkBaWtq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errxyerr
01.04880911.8419941.9850471.048809
12.09761821.4613393.7620572.097618
23.14642739.00532813.8430413.146427
34.195235419.13697421.9822514.195235
45.244044530.26648138.2731925.244044
56.292853644.85523641.3337306.292853
67.341662758.98321256.6158437.341662
78.390471870.55098483.2323288.390471
89.439280980.30208993.2952879.439280
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" ], "text/plain": [ - " err x y\n", - "0 1.048809 1 1.841994\n", - "1 2.097618 2 1.461339\n", - "2 3.146427 3 9.005328\n", - "3 4.195235 4 19.136974\n", - "4 5.244044 5 30.266481\n", - "5 6.292853 6 44.855236\n", - "6 7.341662 7 58.983212\n", - "7 8.390471 8 70.550984\n", - "8 9.439280 9 80.302089" + " x y err\n", + "0 1 1.985047 1.048809\n", + "1 2 3.762057 2.097618\n", + "2 3 13.843041 3.146427\n", + "3 4 21.982251 4.195235\n", + "4 5 38.273192 5.244044\n", + "5 6 41.333730 6.292853\n", + "6 7 56.615843 7.341662\n", + "7 8 83.232328 8.390471\n", + "8 9 93.295287 9.439280" ] }, - "execution_count": 38, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } @@ -757,26 +872,31 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "hidden": true + }, "source": [ "## Метод наименьших квадратов" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "hidden": true + }, "source": [ "Вводим оценку наименьших квадратов. Функция воздействует на модель и набор данных и возвращает функцию одного переменного ( $\\chi^2(\\alpha)$ )." ] }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2018-05-01T10:18:56.124165Z", "start_time": "2018-05-01T10:18:56.102165Z" - } + }, + "hidden": true }, "outputs": [], "source": [ @@ -790,26 +910,29 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "hidden": true + }, "source": [ "Строим график для наименьших квадратов" ] }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2018-05-01T10:18:56.418182Z", "start_time": "2018-05-01T10:18:56.127164Z" - } + }, + "hidden": true }, "outputs": [ { "data": { - "image/png": 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AEHBGj1b8/Pg2PDEzm/W5B6p/g4iEtKU5+eQXltb556gAQsS95/YgPiaKu99ZSoXuGyAS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\npQIQEYlQKgARkQj1/wHIKJWpzGycPQAAAABJRU5ErkJggg==\n", 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"text/plain": [ - "" + "
" ] }, "metadata": {}, @@ -822,26 +945,29 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "hidden": true + }, "source": [ "Находим оценку наименьших квадратов" ] }, { "cell_type": "code", - "execution_count": 41, + "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2018-05-01T10:18:56.431184Z", "start_time": "2018-05-01T10:18:56.421182Z" - } + }, + "hidden": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "1.08760757649\n" + "1.2128183841151954\n" ] } ], @@ -852,26 +978,31 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "hidden": true + }, "source": [ "## Метод $\\chi^2$" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "hidden": true + }, "source": [ "Вводим оценку модифицированных наименьших квадратов ($\\chi^2$)" ] }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2018-05-01T10:18:56.454185Z", "start_time": "2018-05-01T10:18:56.434182Z" - } + }, + "hidden": true }, "outputs": [], "source": [ @@ -884,26 +1015,29 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "hidden": true + }, "source": [ "Строим график" ] }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2018-05-01T10:18:56.783205Z", "start_time": "2018-05-01T10:18:56.457184Z" - } + }, + "hidden": true }, "outputs": [ { "data": { - "image/png": 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" ] }, "metadata": {}, @@ -916,26 +1050,29 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "hidden": true + }, "source": [ "Находим оценку $\\chi^2$" ] }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2018-05-01T10:18:56.799223Z", "start_time": "2018-05-01T10:18:56.785206Z" - } + }, + "hidden": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "1.11018819489\n" + "1.243237812147532\n" ] } ], @@ -946,26 +1083,29 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "hidden": true + }, "source": [ "Строим более детальный график" ] }, { "cell_type": "code", - "execution_count": 45, + "execution_count": 14, "metadata": { "ExecuteTime": { "end_time": "2018-05-01T10:18:57.190229Z", "start_time": "2018-05-01T10:18:56.803205Z" - } + }, + "hidden": true }, "outputs": [ { "data": { - "image/png": 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RPcd/83YoERkNLAYuN8Ycdy5uai6lfOqmzfZrsLyrciEi/tQV/qvG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\nmYwT1C81kQAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": {}, @@ -978,7 +1118,9 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "hidden": true + }, "source": [ "## Утверждение!\n", "Сумма вида $\\chi^2 = \\sum {\\frac{y_i - \\mu(x_i)}{\\sigma_i^2}}$ в достаточно общем случае распределена по распределению $\\chi^2$. \n", @@ -988,21 +1130,22 @@ }, { "cell_type": "code", - "execution_count": 46, + "execution_count": 15, "metadata": { "ExecuteTime": { "end_time": "2018-05-01T10:18:57.213228Z", "start_time": "2018-05-01T10:18:57.193230Z" - } + }, + "hidden": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "259.090909 *x^2 + -575.279337 *x + 324.309668\n", + "259.090909 *x^2 + -644.223230 *x + 405.581501\n", "\n", - "0.0621260744197\n" + "0.06212607441973938\n" ] } ], @@ -1015,34 +1158,39 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "hidden": true + }, "source": [ "## Сравнение оценок" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "hidden": true + }, "source": [ "Сравниваем оценки" ] }, { "cell_type": "code", - "execution_count": 47, + "execution_count": 16, "metadata": { "ExecuteTime": { "end_time": "2018-05-01T10:18:57.234232Z", "start_time": "2018-05-01T10:18:57.215229Z" - } + }, + "hidden": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Оценка методом наименьших квадратов = 1.088\n", - "Оценка методом хи-квадрат = 1.110 +- 0.062\n" + "Оценка методом наименьших квадратов = 1.213\n", + "Оценка методом хи-квадрат = 1.243 +- 0.062\n" ] } ], @@ -1053,35 +1201,38 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "hidden": true + }, "source": [ "Строим распределения оценок. Заодно проверяем, что средняя ошибка методом $\\chi^2$ соответствует разбросу этой оценки" ] }, { "cell_type": "code", - "execution_count": 50, + "execution_count": 22, "metadata": { "ExecuteTime": { "end_time": "2018-05-01T10:21:55.257651Z", "start_time": "2018-05-01T10:20:04.092073Z" - } + }, + "hidden": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Стандартное отклонение оценки методом наименьших квадратов: 0.06516846169693595\n", - "Стандартное отклонение оценки методом хи-квадрат: 0.05951027223128111\n", - "Средняя ошибка методом хи-квадрат: 0.0592348877759137\n" + "Стандартное отклонение оценки методом наименьших квадратов: 0.15713530973827325\n", + "Стандартное отклонение оценки методом хи-квадрат: 0.09940335113972994\n", + "Средняя ошибка методом хи-квадрат: 0.10000000000000182\n" ] }, { "data": { - "image/png": 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JpXqiWFcUHSqjCcDMGgG/AP4DKAL+Zmbz3P3vmYyjNmnnLlL36Gqi5DLdAugL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\nRCSm/j/S37l+4SRoGAAAAABJRU5ErkJggg==\n", 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HkyMDgefMDKL39xlmts3dX8pvWJkXejWWzuUJXgJOBDCzjkRdMCtyGmV2pNP2\nlcDJAGZ2BFAAlOc0ytybBfwgPtplCLDB3dfmO6hcMLNDgN8Cl7n7J/mOJ1fcvYe7F7p7ITAT+KcQ\nkzkEXqF7LZcnMLN/AUrcfVY8briZfQRsB34cQuWSZtt/BDxhZjcTdTuM9viQgMbKzH5D1H3WMd43\nMBFoAeDujxPtKzgDWA78DbgiP5FmXhptnwB0AP4trla3eQBXIkyj3U2GTv0XEQlE6F0uIiJNhhK6\niEgglNBFRAKhhC4iEggldBGRQCihi4gEQgldRCQQ/x8dOJjnKvPqBAAAAABJRU5ErkJggg==\n", "text/plain": [ - "" + "
" ] }, "metadata": {}, @@ -1089,7 +1240,7 @@ } ], "source": [ - "num = 10000;\n", + "num = 1000;\n", "lqs = np.zeros(num)\n", "chi2s = np.zeros(num)\n", "\n", @@ -1107,7 +1258,7 @@ " # генерируем данные (попробовать заменить генератор ошибок на 0.1 * y)\n", " x = np.arange(1,10)\n", " y = parabola(x)\n", - " err = np.sqrt(y)\n", + " err = y*0.3 #np.sqrt(y)\n", " data = generate(x, y, err)\n", " # считаем оценку методом наименьших квадратов\n", " lqval = find_min(1, 0.1, sum_of_squares(model, data))\n", @@ -1134,6 +1285,2052 @@ "plt.legend();" ] }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "hidden": true + }, + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "data": [ + { + "name": "least squares", + "type": "histogram", + "uid": "06f12897-ed50-413e-85bc-07296d260170", + "x": [ + 1.0314938467997354, + 0.9519274519784201, + 0.9743354963608661, + 0.9866896840968007, + 1.081927970292236, + 1.049809675084462, + 1.115736678382606, + 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "lqs_plot = go.Histogram(x=lqs, name = 'least squares')\n", + "chi2s_plot = go.Histogram(x=chi2s, name = 'chi2')\n", + "\n", + "iplot([lqs_plot,chi2s_plot])" + ] + }, { "cell_type": "code", "execution_count": null, @@ -1144,6 +3341,7 @@ ], "metadata": { "anaconda-cloud": {}, + "hide_input": false, "kernelspec": { "display_name": "Python 3", "language": "python", @@ -1159,7 +3357,20 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.2" + "version": "3.6.3" + }, + "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 }, "widgets": { "application/vnd.jupyter.widget-state+json": { diff --git a/ntebooks/python/examples.ipynb b/notebooks/python/examples.ipynb similarity index 86% rename from ntebooks/python/examples.ipynb rename to notebooks/python/examples.ipynb index 07ae44b..a2a7a83 100644 --- a/ntebooks/python/examples.ipynb +++ b/notebooks/python/examples.ipynb @@ -11,7 +11,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 32, "metadata": { "ExecuteTime": { "end_time": "2017-09-22T06:34+0000", @@ -20,12 +20,29 @@ "hidden": true, "init_cell": true }, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "" + ], + "text/vnd.plotly.v1+html": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import math\n", - "%matplotlib inline" + "%matplotlib inline\n", + "\n", + "from plotly.offline import download_plotlyjs, init_notebook_mode, plot, iplot\n", + "import plotly.graph_objs as go\n", + "init_notebook_mode(connected=True)" ] }, { @@ -39,7 +56,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 34, "metadata": { "ExecuteTime": { "end_time": "2017-09-22T06:29+0000", @@ -50,9 +67,9 @@ "outputs": [ { "data": { - "image/png": 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XohQsex38Q6Dj/WanqZB0YbDCpysPkp2bx1P9nfCOys5jwbcmLH/D+IXSijW0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\n", 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zDUd0j2hndX56avUg6DPJ7GgqJZskBhEZLiLRIhIrIk9fYvkTIrJfRHaLyAoR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\nP8LmzyDyYWg3ius61mdwm3q882c0x1K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0.9672948630390291, + 0.991790013823246, + 1 + ] + } + ], + "layout": {} + }, + "text/html": [ + "
" + ], + "text/vnd.plotly.v1+html": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(0, 2*math.pi)\n", + "\n", + "sin_trace = go.Scatter(x = x, y = np.sin(x), name= \"sin\")\n", + "cos_trace = go.Scatter(x = x, y = np.cos(x), name= \"cos\")\n", + "\n", + "iplot([sin_trace, cos_trace], filename='basic-line')" + ] + }, { "cell_type": "markdown", "metadata": { @@ -89,7 +356,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2017-09-22T06:34+0000", @@ -100,8 +367,7 @@ }, "outputs": [], "source": [ - "def integrateR(func, a, b, numPoints = 400):\n", - " res = 0\n", + "def integrateR(func, a, b, numPoints = 100):\n", " points, step = np.linspace(a, b, numPoints, endpoint=True, retstep=True)\n", " return np.sum(func(points))*step" ] @@ -113,14 +379,12 @@ }, "source": [ "### Вариант 2: итеративный интеграл Симпсона \n", - "Используется [итеративный численный интегратор из библиотеки SciPy](https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.integrate.simps.html), \n", - "в основе которого лежит [квадратичная формула Симпсона](http://mathworld.wolfram.com/SimpsonsRule.html). Первый аргумент - сама функция, второй и третий - границы интегрирования. \n", - "Итеративная формула гарантирует точность интегрирования, но не гарантирует сходимости." + "[Квадратичная формула Симпсона](http://mathworld.wolfram.com/SimpsonsRule.html). Первый аргумент - сама функция, второй и третий - границы интегрирования. " ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2017-09-22T06:29+0000", @@ -130,23 +394,31 @@ }, "outputs": [], "source": [ - "# from scipy.integrate import simps\n", - "# def integrateS(func, a, b):\n", - " \n", - "# return simps(func( np.linspace(a,b, 5000, endpoint=True)), np.linspace(a,b, 5000, endpoint=True))\n", - "# # integrateS = {UnivariateFunction func, Number a, Number b -> new SimpsonIntegrator().integrate(5000,func,a,b)}" + "from scipy.integrate import simps\n", + "def integrateS(func, a, b, numPoints = 100):\n", + " x = np.linspace(a,b, numPoints, endpoint=True)\n", + " return simps(x = x, y = func(x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Вариант 3: \"Умное\" итеративное интегрирование\n", + "Используется [итеративный численный интегратор из библиотеки SciPy](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.quad.html).\n", + "Итеративная формула гарантирует точность интегрирования, но не гарантирует сходимости." ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "from scipy.integrate import quad\n", - "\n", "def integrateQ(func, a, b):\n", - " return quad(func, a,b)[0]" + " res = quad(func, a,b)\n", + " return res[0]" ] }, { @@ -163,7 +435,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 36, "metadata": { "ExecuteTime": { "end_time": "2017-09-22T06:34+0000", @@ -174,7 +446,7 @@ }, "outputs": [], "source": [ - "integrate = integrateR" + "integrate = integrateS" ] }, { @@ -192,12 +464,12 @@ "hidden": true }, "source": [ - "Итеративный интеграл:" + "Интеграл Римана 10 точек:" ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 37, "metadata": { "ExecuteTime": { "end_time": "2017-09-22T06:29+0000", @@ -209,16 +481,16 @@ { "data": { "text/plain": [ - "2.0" + "1.9995487365804032" ] }, - "execution_count": 7, + "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "integrateQ(np.sin,0, math.pi)" + "integrate(np.sin,0,math.pi,10)" ] }, { @@ -232,7 +504,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 39, "metadata": { "ExecuteTime": { "end_time": "2017-09-22T06:29+0000", @@ -247,7 +519,7 @@ "1.9998321638939927" ] }, - "execution_count": 8, + "execution_count": 39, "metadata": {}, "output_type": "execute_result" } @@ -262,12 +534,12 @@ "hidden": true }, "source": [ - "Интеграл Римана 400 точек:" + "Интеграл Римана 200 точек:" ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 40, "metadata": { "ExecuteTime": { "end_time": "2017-09-22T06:29+0000", @@ -279,16 +551,43 @@ { "data": { "text/plain": [ - "1.9999896675538067" + "1.9999584621373308" ] }, - "execution_count": 9, + "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "integrateR(np.sin,0,math.pi)" + "integrateR(np.sin,0,math.pi,200)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Интеграл Симпсона 10 точек" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.9995487365804032" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "integrateS(np.sin,0,math.pi,10)" ] }, { @@ -297,12 +596,12 @@ "hidden": true }, "source": [ - "Интеграл Римана 5000 точек:" + "Итеративный интеграл:" ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 42, "metadata": { "ExecuteTime": { "end_time": "2017-09-22T06:29+0000", @@ -314,16 +613,16 @@ { "data": { "text/plain": [ - "1.9999999341763102" + "2.0" ] }, - "execution_count": 10, + "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "integrateR(np.sin,0,math.pi,5000)" + "integrateQ(np.sin,0, math.pi)" ] }, { @@ -342,7 +641,7 @@ "hidden": true }, "source": [ - "[Сверткой](https://ru.wikipedia.org/wiki/%D0%A1%D0%B2%D1%91%D1%80%D1%82%D0%BA%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0B8%D0%B9_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7) \n", + "[Сверткой](https://ru.wikipedia.org/wiki/%D0%A1%D0%B2%D1%91%D1%80%D1%82%D0%BA%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8%D0%B9_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7)) \n", "двух функций называется следующее интегральное преобразование:\n", "$$\n", " h(x) = f(x) \\otimes g(x) = \\int {f(x-y) g(y) dy }\n", @@ -352,11 +651,18 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 43, "metadata": {}, "outputs": [], "source": [ - "convolute = lambda f, g, a, b: np.vectorize(lambda x: integrate(lambda y: f(x-y)*g(y), a, b))" + "convolute = lambda f, g, a, b: np.vectorize(\n", + " lambda x: integrate(lambda y: f(x-y)*g(y), a, b)\n", + ")\n", + "\n", + "# def convolute(f,g,a,b):\n", + "# def res (x):\n", + "# return integrate(lambda y: f(x-y)*g(y), a, b)\n", + "# return res" ] }, { @@ -379,7 +685,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 45, "metadata": { "ExecuteTime": { "end_time": "2017-09-22T06:29+0000", @@ -390,9 +696,1243 @@ "outputs": [ { "data": { - "image/png": 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G1+8etTizy5nMPW8uANcvuZ7DJw9XLJDQt15PqWq3jKoLTe4qaByOeg6olpXA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\n3G0ycdFxLNurT6yq6nmV3EV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" ] }, "metadata": {}, @@ -400,8 +1940,8 @@ } ], "source": [ - "wStep = 2; # Ширина ступеньки\n", - "sigma = 0.5;# Стандартное отклонение Гауссианы\n", + "wStep = 4; # Ширина ступеньки\n", + "sigma = 0.8;# Стандартное отклонение Гауссианы\n", "\n", "# ступенька\n", "f = lambda x: 1/wStep if (x >= -wStep/2 and x<= wStep/2) else 0.0 # нормировка на единицу\n", @@ -415,12 +1955,15 @@ "\n", "# автоматическое определение окна интегрирования и отрисовки\n", "wind = max(2*wStep, 4*sigma)\n", - "x = np.linspace(-wind, wind, 300)\n", - "plt.plot(x, f(x), label=\"f(x)\");\n", - "plt.plot(x, g(x), label=\"g(x)\");\n", - "plt.plot(x, convolute(f,g, -wind, wind)(x), label=\"convolution\");\n", - "plt.title( \"Convolution test plot\")\n", - "plt.legend();" + "x = np.linspace(-wind, wind, 200)\n", + "\n", + "traces = [\n", + " go.Scatter(x = x, y = f(x), name = \"f(x)\"),\n", + " go.Scatter(x = x, y = g(x), name = \"g(x)\"),\n", + " go.Scatter(x = x, y = convolute(f,g, -wind, wind)(x), name = \"convolution\")\n", + "]\n", + "\n", + "iplot(traces)" ] }, { @@ -446,7 +1989,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 46, "metadata": {}, "outputs": [], "source": [ @@ -479,14 +2022,14 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 47, "metadata": {}, "outputs": [ { "data": { - "image/png": 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mWh1HqSxTefRUTA44MmO81VE8ghZ3F7P4zcEEHbvBweZBBFYNsTqOUlnmnkbt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\nyW2HH1DuIzExkejoaK5du2Z1FI+UK1c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mWh1HqSxTefRUTA44MmO81VE8ghZ3F7P4zcEEHbvBweZBBFYNsTqOUlnmnkbt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\ncxPg79yYmWffu2MRAxWGj7c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" ] }, "metadata": {}, @@ -505,14 +2048,3066 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 48, "metadata": {}, "outputs": [ { "data": { - "image/png": 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thhH3qMcXc6/ioGh2pl5jMzYxBDYZbEdiI0hKr7K4m7CMfTHiHu34smUcZS2o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\nQwjxhWVivK7jnjtA28E6bHpgS4Qsq4C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" ] }, "metadata": {}, @@ -520,18 +5115,20 @@ } ], "source": [ - "plt.title(\"Testing function interpolation (step)\")\n", "x = np.linspace(-1, 1, 300, endpoint=True)\n", "# ступенька\n", "f = lambda x: 1 if (x >= -0.5 and x<= 0.5) else 0.0 # нормировка на единицу\n", "f = np.vectorize(f)\n", "\n", - "plt.plot(x, f(x), label=\"original\")\n", - "plt.plot(x, interpolate(f, -1, 1, 10)(x), label=\"10 points\")\n", - "plt.plot(x, interpolate(f, -1, 1, 100)(x), label=\"100 points\")\n", - "plt.plot(x, interpolate(f, -1, 1, 200)(x), label=\"200 points\")\n", - "plt.plot(x, interpolate(f, -1, 1, 300)(x), label=\"300 points\")\n", - "plt.legend();" + "traces = [\n", + " go.Scatter(x = x, y = f(x), name = \"original\"),\n", + " go.Scatter(x = x, y = interpolate(f, -1, 1, 10)(x), name=\"10 points\"),\n", + " go.Scatter(x = x, y = interpolate(f, -1, 1, 100)(x), name=\"100 points\"),\n", + " go.Scatter(x = x, y = interpolate(f, -1, 1, 200)(x), name=\"200 points\"),\n", + " go.Scatter(x = x, y = interpolate(f, -1, 1, 300)(x), name=\"300 points\"),\n", + "]\n", + "\n", + "iplot(traces)" ] }, { @@ -575,11 +5172,11 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 49, "metadata": {}, "outputs": [], "source": [ - "uniform = lambda a,b: np.vectorize(lambda x: 1/(b-a) if (x>=a and x<=b) else 0.0)\n" + "uniform = lambda a,b: np.vectorize(lambda x: 1/(b-a) if (x>=a and x<=b) else 0.0)" ] }, { @@ -591,14 +5188,14 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 50, "metadata": {}, "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "" + "
" ] }, "metadata": {}, @@ -607,11 +5204,11 @@ ], "source": [ "plt.title(\"Uniform distribution\")\n", - "x = np.linspace(-1,1, endpoint=True)\n", + "x = np.linspace(-1,1,300, endpoint=True)\n", "plt.plot(x, uniform(-0.5, 0.5)(x), label=\"d = 1\")\n", - "x = np.linspace(-1.5,1.5, endpoint=True)\n", + "x = np.linspace(-1.5,1.5,300, endpoint=True)\n", "plt.plot(x, uniform(-1, 1)(x), label=\"d = 2\")\n", - "x = np.linspace(-2,2, endpoint=True)\n", + "x = np.linspace(-2,2,300, endpoint=True)\n", "plt.plot(x, uniform(-1.5, 1.5)(x), label=\"d = 3\");\n", "plt.legend();" ] @@ -649,7 +5246,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 20, "metadata": {}, "outputs": [], "source": [ @@ -665,14 +5262,14 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 51, "metadata": {}, "outputs": [ { "data": { - "image/png": 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I9adRHwxTH2x6GUInsOUzCNVBvyPatl2/IwBjjbuvlHIM1yT9cNjYk6K3r6UP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\ny4FDjDGXisg04AxjzJkichDwHDAO6AP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I9adRHwxTH2x6GUInsOUzCNVBvyPatl2/IwBjjbuvlHIM1yT9cNjYk6K3r6UP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\ny4FDjDGXisg04AxjzJkichDwHDAO6AP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" ] }, "metadata": {}, @@ -727,7 +5324,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 22, "metadata": { "ExecuteTime": { "end_time": "2017-09-22T06:34+0000", @@ -749,7 +5346,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 52, "metadata": { "ExecuteTime": { "end_time": "2017-09-22T06:29+0000", @@ -759,9 +5356,9 @@ "outputs": [ { "data": { - "image/png": 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17l7tVF39GemkfxrGV9j0t/TDyOeFnwMwM2umyZFoXRUbG0t5eblO/BamlKK8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\nBQ32kO3eOVR5iHp3PRPSJ5g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I4uJiAB588EEWLVpk5K/t0h/y10se2YDH5+P5uy4G/L0Qiu57le9/ehL/MmdMRO9lMJyv\nGPnr8wcjf90Hmto8HRVG4N+P4BATMjIYDNFH1BuExtbTDYLDIX4JbLMPwWAwRBm2DIKIXCkiu0Vk\nr4jcG+T8XBF5X0Q8InJDl3NeESm1His6HR8tIhtFZI+IPCsiZ6Xov9HtITn29FSKX8/IeAgGgyG6\nCGsQRMQJ/B64CpgMLBGRyV2GlQO3An8NMkWLqhZbj2s6Hf8Z8GtVHQ/UArf3Yv19pqmLhwCQEmcU\nTw0GQ/Rhx0OYCexV1f2q2gYsAxZ3HqCqZaq6FfDZuan4i33nA4F6rCeAa22vOkL4fEpTm5fk+GAe\nggkZGQyG6MKOQRgOHOr0usI6Zpd4EdkiIhtEJPClnwnUqWrgWzfknCJyp3X9lsrKyh7cNjzN7X7p\n6+RO+xDA9EQwGAzRiR2DcObWPehJrepIq9zpC8BvRGRsT+ZU1UdUtURVS7Kzs3tw2/AEhO26hoxS\nE0zXNIPhXGMwyV8DFBQUdOxDKCk5VRFaU1PDwoULGT9+PAsXLqS2trbf1tAVOwahAhjR6XU+cMTu\nDVT1iPV3P7AWuACoAoaISOCbuEdzRoqu/ZQD+HsimJCRwWDoX9asWUNpaSmd91f99Kc/ZcGCBezZ\ns4cFCxbw058OnFSIHYOwGRhvVQXFAjcBK8JcA4CIpItInPU8C7gE2Kn+3XBrgEBF0i3A8p4uvq80\nhTIICS4aWj14fefPpj2DIVoYDPLX3bF8+XJuueUWAG655ZYOhdaBIKx0hap6ROQeYBXgBB5T1R0i\n8gCwRVVXiMgM4EUgHbhaRO5X1SnAJOBhEfHhNz4/VdWd1tTfAZaJyI+BD4BHI/7uwtBV+jpAwEA0\ntnpIs6QsDAaDn59t+hkf1XwU0TknZkzkOzO/Y2vsYJG/FhGuuOIKRISvfOUr3HnnnQAcP36c3Nxc\nwN83obNh6m9saRmp6kpgZZdjP+z0fDP+sE/X694BikLMuR9/BdNZoyGEh5Bo7UtoafMag2AwnGME\n5K/feustHA5HUPlrwJb8dUJCgm3565///Oc0NzdTU1PDlClTzjAIS5cuZenSpbbfx/r168nLy+PE\niRMsXLiQiRMnMnfu3D58Mn0nqsXtQnkIibH+qqPmNpNHMBi6YveXfH8xWOSv8/LyAMjJyeG6665j\n06ZNzJ07l6FDh3L06FFyc3M5evQoOTk5YT+TSBHV0hWnDMLpZacJHQbBO+BrMhgM3TMY5K+bmppo\naGjoeP7qq692yFxfc801PPHEEwA88cQTLF68+Izr+4uo9hAaW/1f+Clxp4eFAnLYLe3GIBgM5xqD\nQf76+PHjXHfddQB4PB6+8IUvcOWVVwJw7733cuONN/Loo48ycuRInn/++T7fzy5RLX/9y1W7+e+1\ne9n34KLTXMX3DtZy/R/e4YnbZnJZYWT3PhgM5yNG/vr8wchf95KA0mnXuGFHDqHV5BAMBkP0ENUG\nwd3uJSHGecbxRJNDMBgMUUhUG4RWj4+4mDM/go6ksskhGAyGKCLKDYKXeFcwDyGwD8GEjAwGQ/QQ\n1QbB3R7CQ4gxISODwRB9RLVBaPV4iQviITgdQpzLQYsxCAaDIYqIboPQ7iPOFfwjSIx1Gg/BYDiH\nGEzy17t376a4uLjjkZqaym9+8xvg3Je/HrS0enzEB6kyAn8ewRgEg8HQH0yYMKFjJ/N7771HYmJi\nx0a1c13+etDibvd26yG0tJukssFwrjHY5K/feOMNxo4dy6hRo4BzXP56MNPq6T5k1NRqPASDoSvH\nHnyQ1l2Rlb+OmzSRYd/7nq2xg0X+OsCyZctYsmRJx+tzXv56sNLq8YYMGSXEOk1S2WA4Bxks8tcA\nbW1trFixgoceeqiXn0ZkiWqD4O42qeziRMOZErcGQ7Rj95d8fzFY5K8BXn75ZaZPn87QoUM7jhn5\n67NEq8dLXDcegkkqGwznHoNB/jrAM888c1q4CIz89VlBVbvPIcSYkJHBcC4yGOSvAZqbm3nttdd4\n+OGHTztu5K9tEkn56zaPj8Lvv8y3PjWB/zNv3Bnnf7R8O38vPcKHP7oiIvczGM5njPz1+UO/y1+L\nyJUisltE9orIvUHOzxWR90XEIyI3dDpeLCLvisgOEdkqIp/vdO7PInJAREqtR7GdtUQKt8f/6z+U\nh5AQ6zIegsFgiCrChoxExAn8HlgIVACbRWSFqu7sNKwcuBX4ZpfLm4EvqeoeEckD3hORVapaZ53/\nlqr2z1bAMLS2+4DQBiEp1kmb14fH68PljOpUi8FgiBLs5BBmAntVdT+AiCwDFgMdBkFVy6xzvs4X\nqurHnZ4fEZETQDZQx1mmtcNDCJ1UBr8EdmrAINQcgBX/Ch43xCbDDY9BYsaArNdgMBj6Gzs/fYcD\nhzq9rrCO9QgRmQnEAvs6Hf6JFUr6tYjEhbjuThHZIiJbKisre3rbkLR6LA8hiNopnJLAbu68OW3f\nG1C2DlRh/xo4+E7E1mMwGAxnGzsG4czCXOhRJlpEcoGngC+rasCL+C4wEZgBZADfCXatqj6iqiWq\nWpKdHbn+xu727j2EU13TOslXVO8HVwLc/KL/ddXuiK3HYDAYzjZ2DEIFMKLT63zgiN0biEgq8E/g\n+6q6IXBcVY+qn1bgcfyhqQEjnIeQEKyNZvVeyBgD8amQOhwqPw56rcFgMJyP2DEIm4HxIjJaRGKB\nm4AVdia3xr8IPKmqz3c5l2v9FeBaYHtPFt5XwiWVAx5CS+c2mjX7IHOM/3nWeOMhGAwDyGCSvwa4\n7bbbyMnJYerUqacdDyV/rar827/9G+PGjWPatGm8//77EV9TWIOgqh7gHmAVsAt4TlV3iMgDInIN\ngIjMEJEK4HPAwyKyw7r8RmAucGuQ8tKnRWQbsA3IAn4c0XcWhkBSObT8dRcPweuB2jLIGOt/nTUB\nqvb48wkGg8HQQ2699VZeeeWVM46Hkr9++eWX2bNnD3v27OGRRx7h7rvvjviabNVTqupKVS1U1bGq\n+hPr2A9VdYX1fLOq5qtqkqpmquoU6/hfVDVGVYs7PUqtc/NVtUhVp6rqF1W1MeLvrhvcYTyEhJgu\nfZVPloPPA5nWJrbsQmhrhHrb0TODwRABBov89dy5c8nIOLNKMZT89fLly/nSl76EiDB79mzq6uo4\nevRon9fRmaiVrghXdnqGh1C93/83s5OHAP6wUVqPi64MhvOWdc99TNWhyP5+yxqRzJwbC22NHWzy\n110JJX99+PBhRow4lc7Nz8/n8OHDHWMjQRQbBL+HEB+q7DSui0GosaplAyGjbMsgVH4MY+djMBgG\nhsEkf93T992VYOqsfSF6DULYstNAyCjgIezzb0ZLtqRok7IhPs0klg1Rh91f8v3FYJK/DkYo+ev8\n/HwOHTq1JayiooK8vDzb89ohajUZwpadWsnmpkAOoWafv+Q08B+MiD9sZEpPDYYBZTDJXwcjlPz1\nNddcw5NPPomqsmHDBtLS0iIaLoJo9hA83SeVnQ4hzuU43UPI66K/l10IH7/an8s0GAxdGCzy10uW\nLGHt2rVUVVWRn5/P/fffz+233x5S/nrRokWsXLmScePGkZiYyOOPPx6RdXQmauWv//PV3fx/a/ay\n/8FFIeNwFzzwKp+Zlsd/XD0BfjwU5nwd5n//1ID1v4XXfgDfKYOE9Iisy2A4FzHy1+cP/S5/PRhx\nW81xukvKJMa6/Enl2oOg3lMJ5QBZVizVhI0MBsMgIGoNQmu7N2RCOUBCrJOWds+pCqPMLgZhiFUC\nVn+4H1ZoMBgMA0v0GoRu2mcGSAz0VQ584aeNOH1A8jD/38YTGAwGw/lOVBuEULIVARJiLIPQVO0/\nkJjZZUA6OFzQeLyfVmkwGAwDR9QaBHe7N6yHkBRntdFsroK4NHDFnj7A4YDkocYgGAyGQUHUGoRW\njy/kHoQACbFOfz+E5urQndGSc4xBMBgMg4IoNgjhk8qJHSGjKkjKCj4oeRg0GINgMPQ30SJ//a1v\nfYuJEycybdo0rrvuOurqTnUcfuihhxg3bhwTJkxg1apVEV9T9BqEdl9IHaMAHUnl5qoz8wcBjIdg\nMBh6QSj564ULF7J9+3a2bt1KYWEhDz30EAA7d+5k2bJl7Nixg1deeYWvfvWreL3eM67vC1FrENw2\nPISE2EAOoQYSQ3gIKcOgqdLfL8FgMPQ7g13++oorrsDl8otIzJ49m4qKCsAvt3HTTTcRFxfH6NGj\nGTdu3GnvKRJEr3RFu72y0zavF22qQpK68RBQvxeRMizyCzUYzjHW/PkRThzcH9E5c0aNYd6td9oa\nO9jlrzvz2GOP8fnPfx7wy1/Pnj2741xA/jqSRK9BsFF2mhjrJAk34m3tJmRkGYGGY8YgGAwDQLTI\nX//kJz/B5XJ1zGnkr/sRO2WnibEu0qXBehEqqTzU/9dsTjNECXZ/yfcXg13+Gvwqpy+99BJvvPFG\nx5qM/HU/YmenclKck0zq/S9CeQgpAYNwLIKrMxgMoRjs8tevvPIKP/vZz1ixYgWJiYkdx6+55hqW\nLVtGa2srBw4cYM+ePcycObPH7707bBkEEblSRHaLyF4RuTfI+bki8r6IeETkhi7nbhGRPdbjlk7H\nLxSRbdacv5VI+z5haPV4iQsbMurkIYQqO02yGuaYSiODYUBYunQpW7ZsoaSkhKeffrpP8tezZ88+\nTf56/PjxFBUVcffddweVv7722msjKn990UUXsXv3bvLz83n00UcBf76ioaGBhQsXUlxczF133QX4\nQ2A33ngjkydP5sorr+T3v/89Tmf332E9RlW7fQBOYB8wBogFPgQmdxlTAEwDngRu6HQ8A9hv/U23\nnqdb5zYBFwECvAxcFW4tF154oUYCn8+nBfe+pL9a9VG3497eU6lf/+63VX+Uqlq9P/TAh0aq/vOb\nEVmbwXAusnPnzrO9BINNgv1bAVs0zPerqtryEGYCe1V1v6q2AcuAxV2MSpmqbgV8Xa79FPCaqtao\nai3wGnCliOQCqar6rrXYJ4FrbVmwCNDm9aGKDQ/BSYaECRmBP4/QYEJGBoPh/MaOQRgOHOr0usI6\nZodQ1w63noedU0TuFJEtIrKlsrLS5m27J1y3tABJcS4ypAGvIwbiUkIPTBlqksoGg+G8x45BCBbb\nt7srI9S1tudU1UdUtURVS7Kzs23etnta2+0ZhMRYJxk00BqTfqqXcjCSh5qkssFgOO+xYxAqgM6N\nAPKBIzbnD3VthfW8N3P2mVaPf7t3uJBRUqyLDKnHHTOk+wmTLQ/hPGpHajAYDF2xYxA2A+NFZLSI\nxAI3AStszr8KuEJE0kUkHbgCWKWqR4EGEZltVRd9CVjei/X3CrddDyHOSYY00OQK0y85eSi0N0Nr\nQ6SWaDAYDANOWIOgqh7gHvxf7ruA51R1h4g8ICLXAIjIDBGpAD4HPCwiO6xra4D/wG9UNgMPWMcA\n7gb+B9iLv4rp5Yi+s27o8BDCaBnFOh1kSgONztTuJzSb0wwGwyDA1j4EVV2pqoWqOlZVf2Id+6Gq\nrrCeb1bVfFVNUtVMVZ3S6drHVHWc9Xi80/EtqjrVmvMeq9poQAgklcOpnYoIGdJAvSOt+wnN5jSD\nod+JFvnr++67j+HDh1NcXExxcTErV67sOGfkr/uBU0nlMJs6vO2k0sRJCeMhdGxOMx6CwWCwRyj5\na4Cvfe1rHTudFy1aBBj5637D3ZFUDvP2m/29lGsIZxCyTxtvMBj6j8Eufx0KI3/dT9gtOw18wVdr\nGIOQmAGIv7OawTDIqfvHPtqONEV0zti8JIZcPdbW2GiQv/7d737Hk08+SUlJCb/61a9IT08fEPnr\nqPQQAknlcPLXgS/4Km9S9+McTkhI9zfKMRgM/Ypa8tfTpk3j8ssvDyp/7XA4bMlfZ2Vl2Za/njVr\nFkVFRaxevZodO3acsa5Iidvdfffd7Nu3j9LSUnJzc/nGN77R8b67YuSvI4B9D8FvEE54u9mlHCAp\nq2O8wTCYsftLvr8Y7PLXQ4cO7Xh+xx138JnPfAYw8tf9ht2yU5r9FbLHPIndjwN/v4Qmk0MwGPqb\nwS5/ffTo0Y7nL774YkcV0kDIX0enhxDQMgqXVG6pA+BEe0L4SZOyoOrjHq1DVfnX1f/KtqptAHxx\n0he5Y9odPZrDYIg2li5dytVXX01JSQnFxcV9kr8uLy8/Tf569erVFBUVUVhYGFT+uqCgIKLy12vX\nrqWqqor8/Hzuv/9+br/9dr6Dk0eqAAAgAElEQVT97W9TWlqKiFBQUMDDDz8MnC5/7XK5+kX+Wgaw\n/L/PlJSU6JYtW/o8z+/X7OUXq3bz8Y+vIra7sNGqf6dt46OU+J5g632f6n7Sl74GO5fDt+33mv3g\nxAd86eUvMTd/LpXNlZQ3lPPG594gKSZMzsJgGGB27drFpEmTzvYyDDYI9m8lIu+pakm4a6MyZORu\n9yICMc4wCZmWOtyuFJrbvOHLzBKz/CEmn/264Od2P0dSTBK/mPsLfjD7BzS1N7F874ApeBgMBsNp\nRKVBCLTPDJuhb6mlLSYVj09p83Zt9dCFpCxAoaXW1hpq3bWsKlvF1WOuJjEmkaLsIqZlTeOZj57B\np2HuZTAYDP1AdBqEdm/4hDKAuw5PjF+2ork1zC//QItNm6Wny/cup93Xzo0Tbuw49oVJX6Csvox3\njrxjaw6DYSA5n8LL0Upf/42i0yB4fGF1jABoqcMb5zcITW2e7scmBgyCvdLTv+35G9NzpjM+fXzH\nsStGXUFWQhZ/+/hvtuYwGAaK+Ph4qqurjVE4h1FVqquriY+P7/UcUVll5O6Bh+AbUghAc5tND8HG\nXoQTzScoqy87zTsAiHHGcEneJbxZ8SaqGvFNJwZDb8nPz6eiooJIdS009A/x8fHk5+eHHxiCqDQI\nLe1e2x6C5vp7IYQ1CD3wELZV+stMi7KKzjh34dALWb5vOQfqDzAmbUz4NRoMA0BMTAyjR48+28sw\n9DNRGTJyt/tICCdb4WmD9iYkwd8trbk1XMgo0//XhkHYWrUVl8PFpMwzy/guyLkAgPePvx92HoPB\nYIgkUWoQvGHbZ+L2b0pzJvo9hKZwHoLT5dczshEy2la1jQnpE4hzxp1xblTqKDLiM/jgxAdh5zEY\nDIZIEp0GweMLL2xn7VJ2JgVCRmE8BLDkK7o3CF6flx1VO4KGi8CvpTI9Z7rxEAwGw4ATlQahtd1L\nfDhhO8tDiE3265U3hSs7BUvgrns9o30n99HsaWZa9rSQYy7IuYCKxgpONJuGOwaDYeCISoPgTyrb\n8xBiU/y5AXseQmbYfQjdJZQDTB86HYD3TxgvwWAwDBy2DIKIXCkiu0Vkr4jcG+R8nIg8a53fKCIF\n1vGlIlLa6eETkWLr3FprzsC5nEi+se5w26kysjyEeMsg2PMQssOGjLZVbSM1NpVRqaNCjpmYMZEE\nVwIfHDd5BIPBMHCENQgi4gR+D1wFTAaWiMjkLsNuB2pVdRzwa+BnAKr6tKoWq2oxcDNQpqqlna5b\nGjivqgMWH7FVZWRJUDgT04lzOWhut+EhJGVBSw34QktPbK3aSlFWUbd7DFwOF0VZRWyt3Br+ngaD\nwRAh7HgIM4G9qrpfVduAZcDiLmMWA09Yz18AFsiZ33hLgGf6sthI4e5ByIj4NJLiXOGlK8CfVFZf\nSD2jVm8r++r2MSVrStipCtML2Vu3F28PxPIMBoOhL9gxCMOBQ51eV1jHgo5RVQ9wEsjsMubznGkQ\nHrfCRT8IYkAAEJE7RWSLiGyJxC5Jn0/94nZ2yk5jk8EZQ2KsM7x0BYTVMzpYfxCf+hibFr7jVGF6\nIW6vm0MNh8KONRgMhkhgxyAE+6LuKmjS7RgRmQU0q+r2TueXqmoRMMd63Bzs5qr6iKqWqGpJdna2\njeV2T6A5TtgcQksdxPs3pSXF2vQQwshX7D/p75UwZkj4HcgTMiYA8HFtz5ruGAwGQ2+xYxAqgBGd\nXucDR0KNEREXkAbUdDp/E128A1U9bP1tAP6KPzTV77jb/V/s8eG0jNx1/o1mQGKcTQ8hsXsP4UDd\nAQShILUg7FRjh4zFIQ5jEAwGw4BhxyBsBsaLyGgRicX/5b6iy5gVwC3W8xuA1WrJIoqIA/gc/twD\n1jGXiGRZz2OAzwDbGQDcVj/lhFgbOYSETh5CuJ3K4K8ygpCVRvtP7icvOY94V3g1wjhnHAWpBeyu\n3R3+vgaDwRABworbqapHRO4BVgFO4DFV3SEiDwBbVHUF8CjwlIjsxe8Z3NRpirlAhap27i0ZB6yy\njIETeB34U0TeURjc7XZDRrWQ6Y/1J8Q6qWpsDT95YiYgIQ3CgZMHGJ1mXyCsML2wo9+ywWAw9De2\n1E5VdSWwssuxH3Z67sbvBQS7di0wu8uxJuDCHq41IvQsZBTwEJy0tNvwEJwuSMyApjMraL0+L2X1\nZczKnWV7rYXphbxS9goNbQ2kxKbYvs5gMBh6Q9TtVO4wCHbKTq2kcmKcy97GNLA2p52ZQzjSdIRW\nb2uPJK0DieW9dXttX2MwGAy9JeoMQuCXflx3ISNPK3haOpLKSbFOe9IVEHK38oGTBwB7FUYBCtP9\nzXl215g8gsFg6H+irkFOa0cOoRsPIbApzQoZJVpJZZ9PcTjCdDFLyoJjZ8b9AwZhdKr9HMLQxKGk\nxKb0S6WRp7KSqocfwdfUhCMhgcw77yBm2LCI38dgMJw/RJ1BCISMupWuCOw0DuxDiPOPbWn3khQX\n5iNLyoHGM0NG+0/uJyM+gyHWnHYQEQrTCyNuELx1dZTfdjttZWU4s7PwVlXTtH49I596kpicAZOU\nMhgM5xhRFzIKlJ126yG4z/QQAJu7lbOh9aQ/7NSJ/XX7e1RhFGDckHHsr9sfsebmvuZmyu/8Cm1l\nZYx4+I+MX72akX9+nPbKSspvuw1vXV1E7mMwGM4/os8g2Ck77dAxsnIIlodguycCnJZHUFX2n9zf\nqx7Jo9NG09DeQFVL+E5sdqh54gncW7cy/Nf/SdLFFwOQOH06I/7wB9oOlFH1hz9E5D4Gg+H8I+oM\nQkubjbLTLh5CanwMAA3u9vA36NicdipsVNdaR31bva0dyl0ZO8S/F2LfyX09vrYrvqYmav78BMmX\nXUbK5Zefdi5p1kzSFi+m9plltB8/3ud7GQyG84+oMwi2QkYdHoJlEBL8BqG+xUbIKNmKwXcyCOUN\n5QDd9kAIRUAIb3/d/jAjw1O77Fm8J0+SdfddQc9nffWrqCpVf/xjn+9lMBjOP6LPIFgho7juWmgG\nkspdPIR6Wx7CmXpG5fV+gzAidUSwK7olKyGLlJiUDmG83uJzu6l+/HGSLr6IhOLioGNi84cz5PrP\nUvfC32irONyn+xkMhvOPqDMIre1e4lyO7stHW2ohPg0cfi8iNcGfVK5v6V3I6FDDIQQhPzm/x+sV\nEcYMGcO+ur6FjOr/+U+8VVVkfiW4dxAg6667wOej7tll3Y4zGAyDj6gzCPaa49RAQkbHyx55CLHJ\n4Eo4I2SUm5RLrDO2V2seO2Rsnz2E+n/+k5iRI0mcOaPbcTHDhpF86aWcXPEP1Gua8xgM0UTUGYQW\nO/2UW2o7dikDJMY6cTrEXg5BxO8ldNqLcKj+UK/CRQHGpI2hxl1DrTt4J7ZweKqradqwkdRFV3Xb\nujNA2nXX4jl+nKYNG3p1P4PBcH4SdQbB3e4L7yE015xmEESE1HiXPQ8B/HmELiGjkSkje7NcgI5y\n1d56CfWrVoHPR+qiRbbGJ8+bhyM1lZN/X96r+xkMhvOTKDQI3u53KYPfQ0jMOO1QakKMvRwCnCZw\nV99WT21rbZ8MQqD0tNcGYeVK4saPI76w0NZ4R1wcqYuuouG11/A2NvbqngaD4fwj+gyCnX7KLad7\nCODPI9S7bQrcJZ8SuAv0RO5LyGhY0jASXAm9Kj1tP3aMli3v2fYOAgy59lrU7abh1dd6fM9wtDS0\ncXB7NQe3V1N9xBgcg+FcISq1jOK7Kzn1ecF98rSkMvgrjXrsIahyqN5vEPriITjEwei00b2qNGp4\n7XUAUq68skfXxX/iE8Tk5dHw+usM+ex1Pb5vMNSn7Hj7CO++uI+2TvmYSRfnctFnx5KQ3Luku8Fg\niAxRZxBa270MSezmi8d90v83iIewr8Hmr9mkbPC1g7uuY1NafkrPS047MzZtLJuOberxdY1vryO2\noIC40T3TURIRkufPp+755/E1N+NITOzxvTujPmXVn7az74NKhk9Ip2RRAa4YB/tLK/nw9UMc3F7N\n9d++kNSshD7dx2Aw9J6oCxmFrTJqrvH/DRYyslNlBH7FU4CmKsrry8lJyCHB1bcvujFDxnC8+TiN\nbfZDLL7WVpo3biJpzpxe3TNlwXy0tZWmd97p1fWd2fTSAfZ9UMnsa8ew+P8Vkz8hnWFj0rj4s+O4\n4bsleD0+Xvr9VlrtfsYGgyHiRJ1BCFtlFNilfEZSuYdVRgBNlRxq6FvJaYBApVGgr4IdmrdsQd1u\nkudc2qt7JpaU4EhNpeH1N3p1fYC9751gy8oyJl2cy/RPjTqj9DV7RApX3jmVk8ebWfWn7agvMsqu\nBoOhZ9gyCCJypYjsFpG9InJvkPNxIvKsdX6jiBRYxwtEpEVESq3HHztdc6GIbLOu+a3YKZCPAGGr\njFpCewjNbV7avb7wNwnsVm48QXlDeZ/yBwF6I3LXtO5tJDaWxBndb0YLhcTEkHzZZTSuXYt6evfL\nvbW5nTef2U1OQSqXLZkQch9E/sQM5nx+PId21vDRhqO9upfBYOgbYQ2CiDiB3wNXAZOBJSIyucuw\n24FaVR0H/Br4Wadz+1S12Hp01k34A3AnMN569Czr2UvC7lTu0DHqYhASAoqn9gXumusrqGqpYkRK\n3z2E4cnDiXHE9KjSqHHdOhJnzMCR0PtwVcqC+Xjr6mh+//1eXb9lZRnupnY++YUJOMNsCJwyZzi5\nY9N453/34W6y6Y0ZDIaIYcdDmAnsVdX9qtoGLAMWdxmzGHjCev4CsKC7X/wikgukquq76u/88iRw\nbY9X3wv8Zad2hO26GoQe6BklZoHDxSGrKmhkat89BJfDRUFage29CO2HD9O2bx9JvQwXBUi6dA7E\nxNC4Zm2Pr6073szWNRVMuiiX7JEpYceLQ5i7pJDWpnY2Lu+7uqvBYOgZdgzCcOBQp9cV1rGgY1TV\nA5wEMq1zo0XkAxF5U0TmdBpfEWbOiOP1KW0eX/e9EJprAPGL23WiR3pGDgckD6O8oe8lp50ZmzbW\ndulp4/r1ACRf2jeD4ExOIvHCC2l6e12Pr93w9304XQ5mLbbfGCgrP4WieflsX3eYmqNNPb6nwWDo\nPXYMQrBf+l2zfqHGHAVGquoFwNeBv4pIqs05/ROL3CkiW0RkS2Xlmb2Ke0KrrV4ItX7Za8fpY3rU\nEwEgNZfylhMAEQkZgT+xfLjxMG6PO+zY5g0bcWVnEzt2bJ/vmzxnDq179tJ+1H5sv+54M/tKK5k2\nP5+ktLge3a/kKn9J6nuvlPVwpQaDoS/YMQgVQOdvtHzgSKgxIuIC0oAaVW1V1WoAVX0P2AcUWuM7\nF+YHmxPrukdUtURVS7Kzs20sNzSBXggJ3YaMztylDD30EABScjnUVk9GfAbJsck9XmswxgwZg6KU\n1Zd1O05Vadq0icTZs22J2YUjea7fsWtcZ99LKH29HIdTmDav58YwISWWqXOHs2fTcepONPf4eoPB\n0DvsGITNwHgRGS0iscBNwIouY1YAt1jPbwBWq6qKSLaVlEZExuBPHu9X1aNAg4jMtnINXwL6XUnN\n3W7XQ8g443CPcggAqXmUqzti4SI4VXoaLmzUtm8f3qoqkmbNjMh9Y8eNw5WbS9O6t22Nb65v46MN\nx5g4axiJqb3bfVy8cCQOl4P3XznYq+sNBkPPCbtTWVU9InIPsApwAo+p6g4ReQDYoqorgEeBp0Rk\nL1CD32gAzAUeEBEP4AXuUlWrrpO7gT8DCcDL1qNfsW0QErPOONxzD2EY5U5hVlJuj9cZilGpo3CK\nM6xBaNq4EYDEWbMicl8RIXnOHOpXrkTb25GYmG7Hb3uzAm+7j+KFvTeGSWlxTL40jx1vHmbGZ0aT\nkhHf67n6i9pjR/j43bc5fmAvAPFJyYwtmc2oaRfgCvMZGQznIrakK1R1JbCyy7EfdnruBj4X5Lq/\nAX8LMecWYGpPFttXWjoMQpidypnjzzjco54IgDspm+MuFyNi08IPtkmsM5YRKSPCbk5r3rgJV14u\nMfl9k8voTNKcS6l77jlaSku73dfg9fjY8dZhRhVlkj4sqU/3LF4wgu1rK9j+1mEuurbvuZBI0Vhb\nw+v/89/s2+LvF5GeOxyH00ljTTXbVr9KQmoa8269k4kXz41IyM5gGCiiSsuoo59ytx5C3Rm7lKHn\nPREqYvwf7UiJ7C/bMWlj2Fu3N+R59flo3rSJ5E9+MqJfRkkXXQQuF41vrevWIJRtraKloZ2pc/te\nNJaalcDoT2Szc90RZiwqwBUbRqV2ANi7eQOr/vAbPG1tXHzjUqZctoDULP++E6+nnYPbSnn3hWdY\n+dtfsPudt7jq/3yDuD7qQBkMA0VUSVe0BjyEUGWnXg+0ngyaVIae9UQox3+vkRrZj3hc+jgONRyi\n1dsa9Hzrnj146+pInB2ZcFEAZ3IyicXFNK7vPo+w8+0jJKfHMXJKZrfj7DJtXj7upnY+3nw8IvP1\nhV1vr2XFrx4kbWguN//8t1x0/ZIOYwDgdMUw5oIZLPmPX3DZF29j//ubef4//p3m+pNncdUGg32i\nyiC4rbLThFC/NN11/r+hDEIPeiIc8vpr6Ee0Bf/i7i3j08fjVW/IHcvNVv4gKUL5g84kXXoprTt3\n4amqCnq+vqqF8l01TLw4F4cjMt5JXuEQMocnsXVNBf49jGeHXevWsPJ3vyJ/0hRu/NGDZOSFDsc5\nHE5Krv4si7/571QdKuO5+79LS0P9AK7WYOgd0WUQrJBRyBxCh9LpmSEj6FlPhPLm46T5fKQ11YQf\n3AMKh/i7nu2p2xP0fNOmTcSMGEFMbuSS2QGSrE1uodRPd73j36cw+ZK8iN1TxF+6Wl3RyNF9Z+eX\n9pGPP2LVH/+LEZOLuO7eHxEbb08KZOyFs/jsvfdTd+wIK/7zQbweI8dhOLeJMoMQJmQUQrYigN9D\nsGkQGsoZqU5oCLq9oteMTB1JrCOWj2s+PuOc+ny0bN7SazG7cMRPnoQzPZ0maxd0Z3w+5aN3jzJy\nckbEK4LGzxhKbLyTHesOR3ReOzTW1rDiPx8kOTOLq7/+XWLievbeRk6dxqfu+r9U7NzO6//z32fV\nyzEYwhFVSeWWcGWnHdLX3RgEm1VGhxoO8QlnItRHVrnT5XAxdsjYoB5C6549eE+eJHFm/xgEcThI\nuvhiGte/g/p8iOPU74nDH9fSWNvKxdePi/h9Y+KcFM4axq71R5lzYzvxSQNT0qk+H//87c9pbW7i\n+u89QEJyeD2mYEyaM4+aIxVs+N9nySucRNH8KyK80r7hbWrH/VENbeX1eKrdoIrEOIkZnkxcQSpx\nY4cgEQoBGs5tosxDCBMyCiF9HcBuT4R2bztHm44yMjYDGo71aq3dMT59PHtqzzQIzZs2A5DUTx4C\n+MNG3qoqWnfvPu347g3HiI13MnramXs4IsGUOXl4PT52b4j85xmK91/+BxU7tzP/y18he2RBn+a6\n+HNLGTl1Gqv//DA1RyrCXzAAeKpbqHnhY44+tIna5z+mubQSbfOiXsVT66ZhdTlVj27n2C+30LDu\nMOqxIf1uOK+JKg8h7MY0GyGjQE+EGGdoW3qo8RA+9TEyaRg0bgSfzy94FyHGDxnPin0rqHPXMSR+\nSMfx5s2bicnLI2Z4/+kEJl1yMQCN694mftIkANpbvez7oJLCkpx+Kw3Nyk9h6OhUdqw7zLT5+f1e\n319zpIK3n3mCMdNnMPWTC/s8nzgcXPl/vs6T3/43/vlfv+ALP/klTtfZ2bymXh8N6w5T/3o5IpB0\nYQ5JM3OJyU06zRPwtXpw766l8Z0jnPznfpo2HmXIdeOIHzukm9kN5zNR5SG0tnsRgThXqKRyNYgT\n4oJvJrPbEyGwcWx06mjweaCpb6J8XRmf7t841zlspKo0b95M4szIyFWEIiYnh7gJE2jqpGu0v7QS\nT6uXCbMjn8juzJQ5edQea+bo3v5NLqvPx6o//hZXbCwL7/zXiBmflIwsPvWVf+NE2T42vvh8RObs\nKd7GNiof2Ub9K2UkTEhn2LdKSL9uPLHDk88ICzniXCROyybnrk+QddtU1KdU/WkbJ1eVma52g5So\nMghuj484lyP0/+ANx/3NbUL8mg/oGZ0MU2kUMAgFWROteSObWA4YhI9rTyWW2/buxVtb228J5c4k\nz51D8wcf4G3093feveEoqVnx5I6N3K7sYIy70J9c3rk+sp9nV3a8+QZHdu/ksi/9C8npwSvOesu4\nGbOZeMllbHzxOaoODaxOU9vRJk78rpT2I41k3DSBzJsn40y1p0QbX5jOsK9NJ2nGMBrWHKLqzzvw\n2SzBNpw/RJVBaGkL0y2t8TgkDw15ekiiX6itpqn7vQUHTh4gJyGH5CFWH4AI5xGyE7JJi0s7LY/Q\ntNmfP+ivhHJnkubMAY+HpnffpamulYqPaimcOazfE48xcU7GzxzGvvdO0NrcPyWcLY0NvPX04+RN\nmMyUufP75R7zbr2TuMREXv3jb/H5vP1yj660HW6k8pGtqE/J/so0Eotzwl/UBYlxkn79eIZcN47W\nvXVU/s82vKaz3aAiqgyCu93bfXOcxmPdGoShKf6SwxP13RuEsvoyRqeNhlQrhFIf2XJJEaEwvfC0\nkFHzxk24ciOrXxSKxAsuwJGcTNNb69iz5TiqUDgz9OcWSSZfkoun3cfHm/pn5/L6ZU/hbmrk8tvv\nPq2KKpIkWlpHR/fu5sNXV4a/oI+0VTRQ+adtOOKc5Nz1CWLze1ctFSB5Vi6ZN0+i/VgTlY9sxdvQ\nFqGVGs420WUQPL7uhe0aT0BK6C+2HMu9Pl4fukGNqnLg5AEK0gr8xsUZC7WRDw0Upheyp3YPXp+3\nQ78oadasARFTk5gYki66iMZ16/h44zFyRqX0WcjOLjmjUskakczO9UciXtNfVV7G1tdfofhTnyZ7\n1OiIzt2ViZdcxsiiYtY/+xea6mr77T6eqhaqHt+OI95J9p3TcEVoj0jCpEyybp2Kt8ZN1WPb8dlt\nHGU4p4kqg9Dobic5PkRhlc/rT/524yFkJMbicggnGkJ7CNXuahraGvwegsMJ6QVQ2706aW+YkjmF\nFk8LB04e8O8/qK2NmNy1HZLmzuFkvVJ5qJHCmcMG7L7g3wlddaiRyvKGiM775l8eIy4xkYtu+EJE\n5w2GiLDgtrtob23lrb881i/38Da2Ufn4dlDIun1qxIxBgPhxQ8i8eTLtJ5qpemIHvraBCX8Z+o+o\nMggnW9pJSwhR6tdUBerr1iA4HEJ2ShzHuwkZdVQYpVm/MNNHQ03/GASAHdU7OukX9W+FUWeS58zh\n2NAZCMq4kp7Ho/tC4axhuGIc7Hg7csnlAx9soezD95l9/ZJeb0DrKRl5+cy45rPsXLeGip3bIzq3\nenxUP7kT78k2Mm+ZQkx2/yiuxhemk/H5CbQdrKf2hY/NTuzzHGMQAjRaid+U7n/t5qTGc6IhdMgo\nYBAC3c3IGOM3CBH+H2VU6igSXYnsqN5B04aNxIwcSUxe5DSEwuEaOpQTwy8my3Okxz2T+0pcgotx\nJTns2XSctghUuvi8Xt78y2MMGZZL8acWRWCF9pl13Y2kZGWz+vE/4vNG5he2qlL79720lTeQcWMh\ncaNSIzJvKBKnZZN25WhatlbR8EZ5v97L0L9EmUHwhDYIDVaSshsPAWBoSly3SeUDJw+Q4EogJ9H6\n1ZwxBtqb/PmJCOJ0OJmUOYmdJ7bTvHnzgHoHAEf3naTFlUbW3jfw1PZfDDwUU+YMp73Vy54IyGJv\nX/s61RXlzPnCrQO+WSwmLp7Lvng7leVlbH1jVUTmbNp4lOYtx0mZN4LEaX3rQ26X5LnDSZyeQ/3r\n5TRvi+y+G8PAETUGQVU52dJGWkKIHr+N9gxCTmocx7vzEOoPUJBagEOsjzbD8hRqgstV94WpmVNx\n79yJr6GBxFmzIz5/d+zeeAyXC7IrS2l8880BvTfA0NGpZOQlsbOPYaP2VjfvPv80uYUTGT/z4git\nrmcUzr6EEVOmsf7Zp/osk912uJG6f+wnfkI6qQtHRWiF4RER0j87ntiRKdQ+9zFthxsH7N6GyBE1\nBqGl3Uu7V8OHjMJ6CPHUNbfT6gnu3pedLDuVPwDIsJ73R2I5awqFZf468IHYfxDA0+5l33snGDN9\nKPGZaTS+sXrA7h1ARJh8aR4nDjb0Kbn8/soVNNbWMHfpl89au0sRYf6td9La3MT6557u9Ty+Vg81\nf92FMzmG9BsnDLggnbgcZN48GUdiDNVP7MBbb8pRzzeixiAEdheHNggnID4NYrqvxAiUngYLG7V4\nWjjSeOR0g5A2wi+H0Q8ewpTMKXzigOIekUNMzsAldg9uq6a12cOE2cNInj+PxvXr8bVGthGQHSZY\nyeXtb/ZOLK65/iSblr/A2JLZ5E+cEuHV9YyskQV8YuEitr72MpUHe/7jQVWpfXEvnho3GTdNxDlA\nirBdcabEknnLZHwtHqr/ugv1GkG88wlbBkFErhSR3SKyV0TuDXI+TkSetc5vFJEC6/hCEXlPRLZZ\nf+d3umatNWep9ejXb7SwBqGh+01pAXJSrc1pQcJGB04eQNHTDYIrFoaM6BeDMNyZyaRDysHJwcX4\n+ovdG4+RmBZL/sQMUhYsQJubad6wYUDXABCfFEPhzKF8vOk47l7smN34v8/S7nYzZ8kt/bC6nnPx\njUuJS05m9Z8f7nG1TvN7x2kprST18lHEje5fCZFwxOYlk37DeNrK6jn5z8h7xob+I6xBEBEn8Hvg\nKmAysEREJncZdjtQq6rjgF8DP7OOVwFXq2oRcAvwVJfrlqpqsfWIbNa1CyebbXgINgxCd7uVd9f4\nJaEnZkw8/UQ/lZ62bNlCjBc2jBy4X+ctDW0c3FZN4YyhOBxC4qxZOBITaXj9jQFbQ2emfjIfT7uP\nj97tWd+JkyeOUfrqSqbOu5zM/BH9tLqekZCcwqWfv5mKndvZ/e668BdYtJ9opm75PuLGppEy79x4\nL4mfyCH5kjwa3zlCc82OMQQAACAASURBVGm//q9tiCB2PISZwF5V3a+qbcAyYHGXMYuBJ6znLwAL\nRERU9QNVDWT9dgDxIjKwNYoWdZaHMCSxmxyCLQ8h9G7lXTW7SIpJYkRKl/8pM8b0i4fQuO5tvLEu\nVqcfpbm9OeLzB2P3xmP4fMrEi/2yHI7YWJLnzaPhtdfQ9oHXtckekcKwMWlsf/NwjxQ43172FA6n\nk4s+1/+b0HpC0YIryCkYy5t/eYw2d0vY8drupfrpXUisk4zPTzynGtmkLRpNbEEqtX/bQ9vRprO9\nHIMN7BiE4cChTq8rrGNBx6iqBzgJZHYZcz3wgap2/jn7uBUu+oGEyOiJyJ0iskVEtlRW9r6crduQ\nkaolWxF+x213u5U/qvmICekTTlUYdVw0Btx1p3o2R4imdevwXjCJFqeX0srSiM4dDFVl5/qjDB2d\nSmZecsfx1EVX4a2ro2nDxn5fQzCKPjmck5UtlO+y9/ke37+Xj9a/yfRF15CS0T8NfXqLw+Fk/m13\n0Vhdxcb/fTbs+LqX9uM53kzGjYU4U0NU0J0lxOkgc+kkJN5F9V92GnmL8wA7BiHYF3XXn2LdjhGR\nKfjDSF/pdH6pFUqaYz1uDnZzVX1EVUtUtSQ7u/c11fWWQUgNZhBaG6C92ZaHEGq3sk997K7ZfWa4\nCPql0qjt0CHaDh5k6LxP4RQnW45tidjcoThR1kDt0SYmXXx634OkOXNwpKRQv7L/hdqCMXZ6Dklp\nsZS+Fn5TlKry5lOPkpCaxszFnxuA1fWc4RMmMeWyBWx56e/UHAktjNi8tZKmjcdIviyf+AmRlemO\nFM6UWDK/OAlvbSs1z+42fRTOcewYhAqgcwwkH+ha/N0xRkRcQBpQY73OB14EvqSq+wIXqOph628D\n8Ff8oal+42RLOyKQEhdEyyiwacyGQYDgu5XL68tp9jSHMAiBvQiRMwhNb78NQPpl85mSNYXNxzZH\nbO5Q7HznCK4YB+NKTv+cHLGxpCxYQMPrr+NrG/hSQ6fLQdG8fCo+qqWqovsS1P3vb+bQzm1cdMMS\n4hL7R84hEsz5wq3ExMXxxqP/HTTB7KluofZve4gdkULaFQO336A3xI1KZchnxuD+qIaG1WYn87mM\nHYOwGRgvIqNFJBa4CVjRZcwK/EljgBuA1aqqIjIE+CfwXVVdHxgsIi4RybKexwCfASIr5tKFgGyF\nI1iMtUO2wp5BCLZb+aOaj4AgCWXwC9whUHVmH+Te0rBmDTH5+cQWFFAytITtVdv7NY/Q5vawZ/Nx\nxk7PIS7hTKOa+ulF+BoaOgzVQDNlznBccU5KXzsUcozX4+Gtpx8nPXc40xZcOYCr6zlJQ9K5dMkt\nlG//kI/eXnvaOfX4qH7mIxAhY8lEpJt2rucKSRflknhBDvVvlNOyO7KhU0PkCPtfkpUTuAdYBewC\nnlPVHSLygIhcYw17FMgUkb3A14FAaeo9wDjgB13KS+OAVSKyFSgFDgN/iuQb60pdc3c6RvZ2KQcI\ntlt5V80uXA4X44aMO/OCmATIngBHIxPn9zY00PTuBlIWLkREmDFsBh719Gse4eNNx2l3e5kyN3i/\n5qTZs3EOGUL9Sy/12xq6Iz4phskX57Jn83Eaa4PvJP/wtZXUHD7E3KVfxuk699uJf+LyK8kdN4G1\nTz1KS+Mpz+fkK2W0VzSSccP4iCuY9hciwpDrxhEzLImaZbvxVIdPmBsGHls/LVR1paoWqupYVf2J\ndeyHqrrCeu5W1c+p6jhVnamq+63jP1bVpE6lpcWqekJVm1T1QlWdpqpTVPX/qmq/aud2K2xnU8co\nQLDdyh/VfMS4IeOIcYa4R94FcOSDiIjcNa5dC+3tpFzhb/5+Qc4F/ZpHUFW2ra0ga0Qyw8YEF0qT\nmP+/vTMPj6q89/jnnT37MiEbW9gJIIiERbQuiGURkVastGhVXG61ltraa+XxtrV9rru3Wqv1iisi\nFZXKFUVEwBYFi+xbEpaAYUtC9n0mmZnz3j/OSUjCTDKTTDKDOZ/nOc+Zc857znzPe5bfebffz0zs\nnDnUbNgYEt9GAOOu6Y8Er6WE+uoqvv5gBQPHjmdIVs+5Ce8KwmBg+t0/x1FTzeblrwPgyCmjdssZ\noqemEzEmvBrEO8JgMWK/JRMklL2Tq7vLDkPCv6wZJNo3CIVqIJsI/wZ4tR2tLKXkUPkh79VFTaSP\nV0siNYH1l/cq9/MNmJKTiRg3DoAocxSj7d3XjlBwpJLygjouuqpfu+4d4m+6CelyUfXRR92ioyNi\nkyIYMSWVg1+doa6qdZXe1veW0+hwcPVtd4fMRUV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"text/plain": [ - "" + "
" ] }, "metadata": {}, @@ -772,7 +5369,7 @@ "plt.title(\"Poisson distribution\")\n", "for i, mean in zip([15,25,50,70,100,120,150], [5,10,20,35,50,75,100]):\n", " x = range(0,i)\n", - " plt.plot(x, poisson.pmf(x,i), '-', label=\"lambda = {:d}\".format(i))\n", + " plt.plot(x, poisson.pmf(x,mean), '-', label=\"lambda = {:d}\".format(i))\n", "plt.legend();" ] }, @@ -810,7 +5407,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 53, "metadata": {}, "outputs": [], "source": [ @@ -827,7 +5424,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 54, "metadata": { "ExecuteTime": { "end_time": "2017-09-22T06:29+0000", @@ -837,9 +5434,9 @@ "outputs": [ { "data": { - "image/png": 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0xuh7IaVyUzKSoqizNVBcVU+/2J6RbdNWYAHwyUzflJEBNhu2Awcw+2B8zU94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\nAUM6DWHl9JVM6jUpuJMNA9b8CIqOmXb8qKZ7wvz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Ws5WZtRlKrDDb4TGm36akgeY6eaA5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\nRU5ErkJggg==\n", 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I9Ew/uPxnfQlH5yS3K+o/PDoLEXhr/RFxCf2W2k8/JXrQIKzjj5yYJZ52GmI2U+1xkWpC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\nMqFJSXRZ9DgB8fFe035x+BQPrNjD4fxSpg/tyv1X9adHx2b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"text/plain": [ - "" + "
" ] }, "metadata": {}, @@ -848,7 +5445,7 @@ ], "source": [ "plt.title(\"Gaussian (Normal) distribution\")\n", - "x = np.linspace(-10,10)\n", + "x = np.linspace(-10,10, 200)\n", "plt.plot(x, gauss(0,1)(x), label=\"sigma = 1\")\n", "plt.plot(x, gauss(0,2)(x), label=\"sigma = 2\")\n", "plt.plot(x, gauss(0,3)(x), label=\"sigma = 3\")\n", @@ -881,7 +5478,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 26, "metadata": { "ExecuteTime": { "end_time": "2017-09-22T06:34+0000", @@ -903,7 +5500,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 27, "metadata": { "ExecuteTime": { "end_time": "2017-09-22T06:29+0000", @@ -913,9 +5510,9 @@ "outputs": [ { "data": { - "image/png": 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CV5SOyS+tdcskLvy5wzeQVvAY8/ajje+CxgXPaG5K160baLWqp+8BziT9JCC/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\nJ9QPH3zeUVFjxqBLSFDLN5uhkr7iNVJ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9Wq68D+o6q/r+QwMJvvHkfl49Psq1HXX8zcfW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\nYnNdWi/Ciw2bTbDINFKmY2prdsCMhxI5RlJ5egaTjKQKFEr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SypavLFLc6oUXXmDw4MEMHz6ciy++mBMn1MqRTWXbRvBpbST9tLgwjpVU06Bm8GA8dgyk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\nFYXULwAAAABJRU5ErkJggg==\n", "text/plain": [ - "" + "
" ] }, "metadata": {}, @@ -924,7 +5521,7 @@ ], "source": [ "plt.title(\"Cauchy distribution\")\n", - "x = np.linspace(-10,10)\n", + "x = np.linspace(-10,10,200)\n", "plt.plot(x, cauchy(0,1)(x), label=\"gamma = 1\")\n", "plt.plot(x, cauchy(0,2)(x), label=\"gamma = 2\")\n", "plt.plot(x, cauchy(0,3)(x), label=\"gamma = 3\")\n", @@ -941,7 +5538,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 55, "metadata": { "ExecuteTime": { "end_time": "2017-09-22T06:29+0000", @@ -951,9 +5548,9 @@ "outputs": [ { "data": { - "image/png": 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r1103GQ6st4Ob+Ref3frOTnX4aM42Xv9lM13uq5x9OIWYYTD/Tfj9FRj6o3tB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\nYKIxZp2IPC8iNzqzjcbes4kDHgXOaTq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r1103GQ6st4Ob+Ref3frOTnX4aM42Xv9lM13uq5x9OIWYYTD/Tfj9FRj6o3tB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\nYKIxZp2IPC8iNzqzjcbes4kDHgXOaTq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" ] }, "metadata": {}, @@ -973,7 +5570,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 29, "metadata": { "ExecuteTime": { "end_time": "2017-09-22T06:29+0000", @@ -983,9 +5580,9 @@ "outputs": [ { "data": { - "image/png": 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PyElcgGHZVtM3sSWUpD8c2OJ3v9Rb1p4rgJf97qeJSImILBGRs7oRozFhtbWq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\n2vQJE6recCdIs4ZGO6TQHXU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PyElcgGHZVtM3sSWUpD8c2OJ3v9Rb1p4rgJf97qeJSImILBGRs7oRozFhtbWq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\n2vQJE6recCdIs4ZGO6TQHXU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"text/plain": [ - "" + "
" ] }, "metadata": {}, @@ -1022,7 +5619,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 30, "metadata": { "ExecuteTime": { "end_time": "2017-09-22T06:29+0000", @@ -1032,9 +5629,9 @@ "outputs": [ { "data": { - "image/png": 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7j6BFizCPHdvjLt5JSQRceil177yDtloxGUykBCdxyMur625XGD03MYmRQ5K7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\nmC5iMrPXgddbPfZg2PYR4IaTG5rjOI4TL3f5muM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Jvn4x9Z98ir2xkTC/MMb4hJLn4wMFXzjrl+upYgiS4C5GjpM5HPTxYWKEc0FL\n/QcfgM1G2J139Lpb6E03oVtbafj4YwAmhKVwyMcHjm8e8CYLcaEkuIsRo66xjBKziVTXxdT6Vavx\ny8jAJzGx1/38MjLwGTuW2pUrAUiJyeK42UxbU3lnmZEx4i6GEwnuYsQ41Oqc4TIxfCLtx4/TmpdH\n8MKFfe6nlCJkyRJacnKxlpaSEpaCXcHR5qGz5F6Is0lwF15Nd1nElG9zJvtKDU+lfrVziCX4Ovdy\nhARdvQCAxrVrSQlzzi8/1O680bYMuYuhSIK7GBm0Jp82Ig1+RPpH0vD55/hnZmIePfqMYg6HprXR\nisNx5kCLz9ix+CQm0vD5GhKCEvDFwCF702CegRDnRYK7GBlaazliNjLBLxJbZSWt+/YReOW8zs0O\nu4Oc1YX85fEvef1HG1m2dBO7Pi/qDPJKKQLnz6dp2zZoamacTyiHjA6wWz10Qp4zUlP+rlu3jpCQ\nELKyssjKyuKZZ5656DoHklvBXSl1nVLqoFLqiFJqaQ9lblNK5Sml9iul/t6/zRTi4jgayzlmNjPW\nEkvjxi8BCHQltbLbHXzy2n6+ev8oo8aGcPmt44mMC2TTu0dY89e8zgAfNP8qsFpp+vJLUgJGOWfM\nuG6WPULWMI34lL+zZ89m165d7Nq1i6eeeqpf6hwofQZ3pZQReAVYCKQBdyql0s4qMwH4MXC51noy\n8OgAtFWIC1a27x+0GAyMDU6iaeMGjFGR+E6aBMCW9wo4uquCK74+ga89nEHWggSu/14mly5J5tBX\nZeR8dAwA/8xMDEFBNG3eTEpQEtVGI5V5Kz15WoNupKf8HU7cSRw2AziitT4KoJRaDtwAdP2c823g\nFa11DYDWuvycWoTwAI0za+PR0lwAxo6aQeOXTxG0YAFKKYoP1rB7zQmmzIsjc358535KKaYtTKKu\nvIXtqwpJnBJJTFIwlpmX0rRpM+P+7XtwYhXHTnyJ8pntkXNbu+xVyo8f7dc6oxPHcuV9D/a4fSSn\n/AXYsmULmZmZxMbG8uKLLzJ58uQ+2+Qp7gzLjAFOdHle7HqtqxQgRSm1SSm1VSl1XXcVKaUeVErl\nKKVyKipGZuIl4RlH25zDJ/G1gTjq67FcPguH3cGGtw4SHOnHrJvHnbOPUorZt6cQEOzD+r8fRDs0\nllmzsJaUEG+PBaCwVf6OO3h7yt+pU6dy/Phxdu/ezfe+970hnTQM3Ou5dzfT6+wRRhMwAZgHxAEb\nlVLpWuvaM3bS+lXgVYDs7OwRMkophoICWz2hZiOm3QcBsMyYQf7WUmpKm1n40BRMPt3n6PbxNzHr\npnF8vuwABTsrSJg1C4CAnYctzl6LAAAgAElEQVTxQ1HY7vwT1x4YdO+thz1QRnLK3+AuieUWLVrE\nww8/TGVlJZGRkX0e2xPc6bkXA/FdnscBJd2UeV9rbdVaHwMO4gz2QgwJx3Q7Y01BNG/bhk9yMoaI\nSHJXFxKdGERyZu//nBNmjCJsVAA5qwoxxcdjHjOGlq1bSTD4U+hoHqQzGBpGcsrf0tLSzjeIbdu2\n4XA4iIhw7wbrnuBOcN8OTFBKJSulfIA7gA/OKrMSuBJAKRWJc5imfwcDhbgAzux4do4aYaw5nObc\nXAKmT6doXxX1la1kXZ3Q2WPricGgyFqQQNXJRkoL6giYPp3mnFySTMEUKnuv+3qbkZzy99133yU9\nPZ3MzEy+//3vs3z58j7/djxJufMRSCm1CHgJMAJ/1lo/q5R6BmfqyQ+U8wz/P+A6wA48q7Ve3lud\n2dnZuuMKthADZeyPP+KRy8wsq/kh/9WWyeT/ziX2hRfYcCyOqpON3PPcLIzG032clsYGmqqrCIyI\nxM8S2Pm6td3OX5duIm5iODPD8zn105+x6YdpvGw+yE0hf+afu2vY87R7q10vxoEDB5jkmuUjvF93\nv2+lVK7WOruHXTq5dZs9rfUqYNVZrz3V5XsN/MD1JcSQ0tJ2GIDEYmcQbx+bQdFHR5hxfXJnYK+v\nrGDdX1/jyPataO3AYDQy4dLLufLeb2MJDcPsY2TS5bHsXnOCGd/JBGDCKRP2RIXDegQYuh/Pxcgk\nK1SF1/NtcC5aCjnWgDkxgUP57RgMirQrnDNeyo4V8MbS/+DY7lymL7mZxY8u5ZKFSziyfQtvLP0P\nqoqdk8WmzB2D1pqCYhPG8HAii5yrUy2N6yUrpBhyJLgLr9dsLcbocKAPnsQ/ezpHcspImByOJcSX\n+opy/vnszzD5+nLP879j9l33kXrZFcy7537ufva/cTgcvPvLn9BUW0NwpD+x40M5vL0M/6lTMR+t\nAcDafmRQz8cTM3PE4LvY37MEd+HVNFBJE5dUmnDUN9A0/lIaa9oYnx2Dw27nw9/+CrvNxq0/+SXh\nsXFn7BuVmMwtTz5Da1MTH/3PC2iHgwnZ0dSUNtM2cSb2klLG1kOFahy08/Hz86OqqkoCvJfTWlNV\nVYWfn98F1+HWmLsQw1m5oZ1Zp3yBdk5aR2MyN5KcGUnuRyspLTjM4kefIDz27HV5TtFJzhWbn736\ne/as+ZiUmQvY8PZhTvmMJRKYedLEvnF9z7HuL3FxcRQXFyOLAL2fn58fcXFxfRfsgQR34fVKjJrx\npwyo0HCOHW4hcUok7c11bH7374zLnknKzCt63X/KVddwcPN6Nr71V1Ium038xDCOFTYR6e/PxJMG\nPp9gHbRbMZnNZpKTkwfnYGJYk2EZ4dXMhkZqjQZGldhpybyKlgYrE6ZHs/ndv+Ow2Zl3z/19zlVW\nSjHv3gdpa27mqxXvMD47hobqNtqzrmTMSTsVRkC1D84JCeEmCe7Cq4WYThDQqgkoa6EyOhOjyUBo\ntJ396z4nY8F1hI4a3XclQFRCEmmzr2T3p6uISTaDgurR0wgsbcNkA39T6QCfiRDnR4K78GqBviWM\nO+UcMylti2BMaij71q5Ga0324pvOq67pS27B1t7Gwc2fMSo5hDIdg3JoksogwFQ8EM0X4oJJcBde\nbZzvflJOQnNADPX1mrhUC3s+/5iUSy8nJDrmvOqKjE8kOWsauz75iPi0YKpqFG0+IYw/pRln3jNA\nZyDEhZHgLryawVxF2kkHtROcecWbanbS3tJM9vU3X1B92dffTHNdLfa2AwDUJF3KxJMOfGRYRgwx\nEtyFV6s3tTGuBCqjMwkb7c+BjR8Tl5bOqHEXlrQ0fnIG0UnjOLh5NZYwH6rHzGDCKWgwD950SCHc\nIcFdeLcmO77tPlTbQgmNqqa+opzMqxddcHVKKTKvWURV8Qmi4lqoVDGE1xlos468G2WLoU2Cu/Ba\nVruVkEqoDR2PQyuaanbja7EwPnvmRdWbetkVmHx8aW3Yg81hoCEokaBKLatGxZAiwV14rZLaIySV\nQXVYKkq1U5Kfw8RZczD5+FxUvb4BFsZPn8mpg9vR2kZ1WCqJp6CqubKfWi7ExZPgLrxWceUBkkuh\nKnISlpAT2NrbSZszv1/qnjxvAW3NjViCS6iMmsT4Ek1x1YF+qVuI/iDBXXitourDxFf60+wXS3vT\nPsJi4xg9IbVf6k5IzyAwIhJH+34aLUkklZsorjrYL3UL0R8kuAuvVbl/PTa/FLRupL68gLTZV/bb\nbdEMBiNpV8yjruwgDm0F8zjK9n3WL3UL0R8kuAuvZTtWRk1YKnbrIYA+E4Sdr5SZV6C1A7u1gOqw\nVNqOFPVr/UJcDAnuwmuZS1upDkvFrguITEjqMa3vhYpOHkdwVAx2fYSa0FRMJ5v7tX4hLoYEd+GV\ntNaEVgbT7GdBt5wk5dLL+/0YSilSZl6Obi2kPjCawHJzvx9DiAslwV14paqWSoJbU7C3HwE0KTP7\nP7gDTJgxC7QDh/UYwS0TaLXJSlUxNEhwF16puGA7Nt/xOKz5EBpDRFzCgBxn9PgUdEAIdushHD7j\nOHl874AcR4jzJcFdeKWqHZupCY7DYStBJWUM2HGUwYA9IR2H9Tg1wUmU56wbsGMJcT4kuAuv1Lj/\nGE1m5wVOQ1L6gB7LETcJsFPv76Bhb96AHksId0lwF17JWmTEbj2K1eCLirrwmwy7Q48ah0MZsVuP\n01LQNqDHEsJdEtyFV7K3j8FhPcaxgASUGuA/c6OJ0oAx2K3HsLXEDuyxhHCTBHfhdewNDTT6BAPt\nHA4YOyjHLAgcB7qBRt8o7PX1g3JMIXojwV14naqdO2k0NwOKE/4DOyTTociSCECdr5Wm/TLuLjxP\ngrvwOgVb92O3FeIXasFq8KF/ssn0TAHNJgumAD9s9hMc27pvgI8oRN8kuAuvc/JwGdpRw5jUyEE9\nbmRyINpWwomD5YN6XCG6I8FdeJ2aJucq0cwpkwb1uJMnJwOasvqmQT2uEN1xK7grpa5TSh1USh1R\nSi3tpdytSimtlMruvyYK4T57UzNNqhGUD3GJgxfctYa01AxQJhpVE/YmCfDCs/oM7kopI/AKsBBI\nA+5USqV1Uy4I+D7wVX83Ugh3lWzei91Wgt0PVFD0oB7bJzgWq58Jm72YU5tl3F14ljs99xnAEa31\nUa11O7AcuKGbcr8AfgNI5iThMfmbdgLttEdWQLhzGmQ/3Z+jZx31x6TRFlkJupWDm3YN8EGF6J07\nwX0McKLL82LXa52UUpcA8Vrrf/VWkVLqQaVUjlIqp6Ki4rwbK0RfThQVAorgSb5ok9/gHtw3iIAJ\ndlc7jg/usYU4izvBvbt+j+7c6Fz+91vgh31VpLV+VWudrbXOjoqKcr+VQripvqUMowokOdQzf1+J\nIeEYVBB1rTJjRniWO8G9GIjv8jwOKOnyPAhIB9YppQqBmcAHclFVDLbyo6ewOyqwmxSJgf1716W+\ndPR2EgNicJgUNns5VUUS4IXnuBPctwMTlFLJSikf4A7gg46NWus6rXWk1jpJa50EbAWWaK1zBqTF\nQvRg77+cN6guC6smMSSp8/X+uil2T1SXD7eJwQmUhdQADvZ8+PmAHleI3vQZ3LXWNuC7wCfAAeAd\nrfV+pdQzSqklA91AIdx1PG8v4ENh/AlCguPRus9d+l10cCL5iScAE0X75cYdwnNM7hTSWq8CVp31\n2lM9lJ138c0S4vxoramrO4EvYfgHt4PFM2PuhsBofEKs+BBGTW2RR9ogBMgKVeElyo4ex+FoxMcB\niTYbBAxu6oHOQfeASBLsNny0wm6vo+rkqcFthxAuEtyFV9i3dhMAjX6VJFqtEJbkmYZETyTRaqXZ\nt9rZri82e6YdYsST4C68wvFdOShDKMeiikiKnQEmn0E79hnXa30sJERM4ljkCVAWjuVuG7R2CNGV\nBHcx7NmsVuoqj+Grwzk62kqSxXk3JI0HrqgCSf5RFMS24UskNWUFOBx2j7RDjGwS3MWwV5y3D61t\nhLbCqXBNfHCCR9uTHBjPyQgIaTPgcLRSWnDEo+0RI5MEdzHsHdi0DTAQqOqJ0XZ8LDGD3oaunxJC\ng8YQgoMg5cwMeWCj5NITg0+Cuxj2ivbtQpliqQ06QaLVds40yIFOHHZO9ZYoxrZbaQw6iTJGUbhn\n58A2QIhuSHAXw1pzXS2NVSfw1RHsj6hgrNXqsTnunSyRjLVayQsvx4doaksLaG9t8WybxIgjwV0M\na4W7nb3i8GYHh6IdjG+3gsU5x90TK1QBZ8/dauVAlJXQFkA7OCGrVcUgk+AuhrVDX20D5U9UXSlF\nUTh77iHxfe/Yz854I4lMIbndRlE0RNVXASYOfbV90NskRjYJ7mLY0lpzIm83BlMCfv7VWM2Ksak3\ngtGtrBoDx+zHuMS5tJsVgb41GExjKNorN+8Qg0uCuxi2KosKaW+ux8cwippRrUTb7AQHjjqnnOr2\nlgT9p7sLttGW0VgcmoaYFkzGMTRWn6K+Um5QIwaPBHcxbBXu3gFAWGM7h6KtjLO2d463e5oKjGas\n1cqxGE1os3PMpqO9QgwGCe5i2CrIzUUZIoisKyYntIZx7Z6bKXPOtVtLFMnt7ewKrSOyrhRUIEdz\n5RYHYvBIcBfDkrWtlVOH8zCYkwhtOMqhSCvjhsI0yA6WCMZZrewKqye07ihGcxJF+3bhsEsqAjE4\nJLiLYan4wH4cdhtmUxx+4XbazcrZcw+IOKfswC9i6uYAlijGttto9lMEBbZgNCdgbWvh1JFDA9sY\nIVwkuIthqXD3DlBGwltt1CaFAQyNBUwdLFHOTxJAU1I4oXYzoCjcnevZdokRQ4K7GJaO7dqBwRhH\nSNUhCkcbiXIoQhwagmM7y3hsERNA+DjG2Gz4a0XxaDOhFQUYTKM5tlOCuxgcEtzFsNNQVUlNyQkM\n5kRC6wrYG9HMWJsdpn4DDEaPtEmf/U5i8sEw+SYm2CEvooXQugIMpkTKjh2hub7OI20UI4sEdzHs\nFO5xTik0mRMIbixii6WECa3Ng39rvb4ERJLS1sbmoDJC6o5iMCeB1hyXBU1iEEhwF8PO8d07MZoD\nCVUKU8Io6gxtpLS19TjePsDXU3u+YGuJYkJLI8U+jfiE+hNsDsBg8ue4zHcXg0CCuxhWHA47x/fs\nAkMioVUHaBwbDUBqe/s5wd1Td2LqZIkkxXVRtXVCHOGuoZlju3ecO4wjRD+T4C6GlbKjR2htasBg\nSiC0ZDfFY3wxYnDNcffcsEy3odoSxYT2dgBKk4IILsoFQyLNtTVUHD82qO0TI48EdzGsHN2xHZTC\n5JNESF0B+yNaSfKLxFczdKZBdrBEEeLQxPiEkj/aQWjdYYzmREBSEYiBJ8FdDCtHc7fjGxBPhL8d\no3KwOfAUKa3Nzo099NwH/U5MHVztSbE5+CqkEh9bM2EBJnwCYiS4iwEnwV0MGw3VlZQXFmB3JBDW\nUIB5wjiKrGWktrU6C1iiPdvAs4UlAZBitZHfVoQ5OZnwliI0CZzMz6O9pdmz7RNeTYK7GDaO7XAm\n3jKYxxJ0ZAvNqXEApDY3Qvb9YDjzz9nj1yyNZphyGxNamrFpG7ZJSQQd3w6GJBx2m0yJFANKgrsY\nNgp2bMM3IByTTyRB5Qc4mRgIQGpDlcfH23t8I7FEkdLkXLRUlhRCcPFOjOYxmHwCKMj5avAaKEYc\nCe5iWLC2t1G0bzcm/3FEhVgxOmzsj2kn3DeUSLt9yORxP4clguTmOvyMvuTF2DDbWggPAd+g8RTs\n2C5ZIsWAkeAuhoXi/XuxtbXR3hZPRGsxhpAQcswlpATGOy9o9hLcB/pOTL1esbVEYQJSg5PZFnAK\n5etLpC7F2p5Aa0M9JQcPDGzbxIjlVnBXSl2nlDqolDqilFrazfYfKKXylFJ7lFJrlFKJ/d9UMZIV\n7NiO0eyLwRRHcFEOflMmc7juCBP9XBdRuxmW8fSQO9DZrjRLHPvrDuI7OY2QU3tQxiQMRhNHcmVo\nRgyMPoO7UsoIvAIsBNKAO5VSaWcV2wlka60zgHeB3/R3Q8XIpbXm6I5tBIaPx9ffF7+8L2lKiaPd\n0c5kH2e6X0+PufeoI7j7RtBia8GamoRl31pMZl+CIsdTkLNVVquKAeFOz30GcERrfVRr3Q4sB27o\nWkBrvVZr3TGvaysQ17/NFCNZZVEhDZUV2OyJjB4FBoeNwjgfANILNjkLDdng7hwumnzcOa/9ZGIA\nhpZGRo02o1UytaWnqD55wpMtFF7KneA+Buj611fseq0n9wOru9uglHpQKZWjlMqpqJA7wQv3HN62\nGZTCZo0n2nYSlGJnZAOhvqGMaSh3FvIP63F/jy1iAgiJByC5sQI/ox97YpzpCKKN5bS1OPtAR2TW\njBgA7gT37v52u/0cqZT6NyAbeKG77VrrV7XW2Vrr7KioIdrTEkPOoa2bCI0ZjzJYCDm6Gd+UFHa0\nHmZy5GRUUzXM+M7AR/ALZTBC1t2YmqpJDU9lB8cxjxlDWHEOyhBEcFQCBTlbPd1K4YXcCe7FQHyX\n53FAydmFlFILgJ8AS7TWbf3TPDHSVZcUU1VchMkvhfDYAPTOzfhMy6KgtoD0sEnQVtfjkMyQGcu2\nREJTBZMjJnOg+gD+2dMw5K4jKNwPH0sKp44coqm2xtOtFF7GneC+HZiglEpWSvkAdwAfdC2glLoE\n+D+cgb28/5spRqrDX20GoLFuDGOiHOiWFqomjsKu7aRbXJd2hsgc9x7fTAIiwd5GWnAyLbYWmtKT\ncNTUMCbeRHNjHGjdeZ5C9Jc+g7vW2gZ8F/gEOAC8o7Xer5R6Rim1xFXsBSAQ+IdSapdS6oMeqhPi\nvBzauonwMeOAQCKajwKQ54rp6X6uoD5UL6Z26Jgx4x8DQEGyHwBRtmLstjCCo2I5uGWjx5onvJPJ\nnUJa61XAqrNee6rL9wv6uV1CUFtWSnlhAXGTr6fdbsRyaBP2sWPZaTtKTEAMkTbnjTA83XPvc7jf\nFdzHGvyxmC3kGosZHxOD/9GtGI0LCYnJ4MT+T2ioriQofGh8ChHDn6xQFUPWwc0bAGhuiCcuJZS2\n3BwCpk9nf+V+0iPToanSWXDI99wjADA2V5ERmcGuit0EZGdjzdnKqPEhtLYmg9Yc2rLJww0V3kSC\nuxiStNbkbVxLdHIqzQ1+xEVZcTQ24shMpaihiCmRU2Dba87CPfTcB/tyam/JwwDI+TOZ0Zkcrj2M\ncWoGtooKEuKNNFT5Ez4mkYNbNgxaW4X3k+AuhqTywqNUnzxBUFQWSkFk9T4ADiaaAZgWMw0ay8Bg\nBt9gTza1b0Gxzsf6U2RFZeHQDorGBwEQ3XgIgNDRmZw6fJC68jJPtVJ4GQnuYkg68OU6DEYTzfXx\njB4fin3bBnzGjyPHcRRfoy+TIyZDcxVc2vccdzXAc+D7TExmMMDUb0BzJVOipgCww7cUc2ws5Kwn\nMj6Q9raxABzYuHZA2ypGDgnuYshxOOzkb1pP/OQsasocJKWF0Lw9h8ArZrOjbAdTIqdgtreDtdnj\nF1PdZomCpkqCTYGMDx3PrsrdWObMpnnLFpLTw6k8aSA2NZ3969cMnfn5YliT4C6GnKJ9e2iqqSYo\nMguA0Y4TaKsV02XZ5FfnMzVmKjS50lf0cjF1SMVISxRoO7TWkhmVyZ7yPQTMno2juZnRpjLQEB6X\nTW3ZKU7m7/d0a4UXkOAuhpy9az7BLzCI2ooYohKCYOcmlJ8fBxNN2LWdadHToKnKWXgIzZTp9b2k\no51NFUwfNZ0GawPFKaEosxnz3k2ERPvTVB+H2c+f/evXDEZzhZeT4C6GlKbaGo5s38K47DlUFrcw\nYXo0jevXEzBjOjtq9mJQBjKjM7v03IfLsIyrnU0VzBg1A4Cv6nYTMH06TRs3kDI9hlMFzYydehkH\nt3yJtbXVg40V3kCCuxhS9q9fg8Nuxy84CxQkhDdjPXGCoKvms6N8B6lhqVjMltPBPaDv4D7QKcXc\nul7b0c6mSqICohgbMpZtp7ZhmTOb9oICkhIUaAiMuARrawv5m2VapLg4EtzFkKEdDvau+YQxkyZz\n8pBiTEoojq/WglL4zLuCvRV7nVMgAbb9n/Nx2PTcXcMy2/8EwIxRM9hRvgO/K2YBYNq7maiEIMqL\nLEQlJLHz4w/lwqq4KBLcxZBxfN9uastOkZQ5j9qyZiZkx9D4+Rr8MzPZq0/Qam/lstjLnIWbKsFs\nAR9LzxUOcmzsNRgHum4H2Oicx37p6EtpsbVwKLgJn/HjaPjkEyZMj6GiqJGUWddQcfwYJw/IhVVx\n4SS4iyEj96OVBISE0tQQh8lsIGG0nda8PIIWzGdzyWZMBhPZMdnOaTBNlTDj255usvuUguz7O1Mm\nZMdko1B8deorgq+9juacHMaONWIwKNr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" ] }, "metadata": {}, @@ -1063,10 +5660,49 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 56, "metadata": { - "collapsed": true + "collapsed": true, + "jupyter": { + "outputs_hidden": true + } }, + "outputs": [ + { + "ename": "TypeError", + "evalue": "unsupported operand type(s) for +: 'vectorize' and 'vectorize'", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mTypeError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mf\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0muniform\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m0.5\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m0.3\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0muniform\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0.3\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0.5\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m;\u001b[0m\u001b[1;31m# Распределение, над которым мы экспериментируем\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 2\u001b[0m \u001b[0mwind\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m;\u001b[0m \u001b[1;31m# ширина окна интегрирования\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 3\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 4\u001b[0m \u001b[0mfs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m;\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 5\u001b[0m \u001b[0mx\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlinspace\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mwind\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mwind\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m300\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mTypeError\u001b[0m: unsupported operand type(s) for +: 'vectorize' and 'vectorize'" + ] + } + ], + "source": [ + "f = uniform(-0.5,-0.3) + uniform(0.3,0.5);# Распределение, над которым мы экспериментируем\n", + "wind = 1; # ширина окна интегрирования\n", + "\n", + "fs = [f];\n", + "x = np.linspace(-wind, wind, 300)\n", + "traces = []\n", + "traces.append(go.Scatter(x = x, y = f(x),name=\"Initial distribution\"))\n", + "\n", + "\n", + "for i in range(1,6):\n", + " wi = (i+1)*wind\n", + " fs.append(interpolate(convolute(fs[i-1],f,-wind,wind),-wi,wi))\n", + " x = np.linspace(-wi, wi, 300, endpoint=True)\n", + " traces.append(go.Scatter(x = x, y = fs[i](x), name = \"Convolution \"+str(i)))\n", + "\n", + "iplot(traces)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, "outputs": [], "source": [] } @@ -1098,7 +5734,20 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.2" + "version": "3.7.4" + }, + "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 }, "varInspector": { "cols": { @@ -94638,5 +99287,5 @@ } }, "nbformat": 4, - "nbformat_minor": 2 + "nbformat_minor": 4 } diff --git a/notebooks/python/fitting.ipynb b/notebooks/python/fitting.ipynb new file mode 100644 index 0000000..1c479f0 --- /dev/null +++ b/notebooks/python/fitting.ipynb @@ -0,0 +1,893 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "# Общий случай" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "## Постановка задачи" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Пусть есть параметрическая модель $M\\left( \\theta \\right)$, где $\\theta$ - параметры." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Функция правдоподобия $L\\left( X | M\\left( \\theta \\right) \\right)$ определят достоверность получения набора данных $X$ при заданном наборе параметров и данной модели." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "**Задача**: определить такой набор параметров $\\theta$, для которого функция принимает наибольшее значение." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "## Классификация\n", + "\n", + "По порядку производной:\n", + "\n", + "* Не использует производных $L$\n", + "\n", + "* Использует первую производную $\\frac{\\partial L}{\\partial \\theta_i}$ (градиент)\n", + "\n", + "* Использует вторые прозиводные $\\frac{\\partial^2 L}{\\partial \\theta_i \\partial \\theta_j}$ (гессиан)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Без производных" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Прямой перебор\n", + "(brute force)\n", + "* Строим сетку и ищем на ней максимум. \n", + "* Возможен только для одномерных, максимум двумерных задач. \n", + "* Точность ограничена размером ячкйки сетки." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "### Симплекс методы \n", + "1. Строим многоугольник в пространстве параметров с $n+1$ вершинами, где $n$ - размерность пространства. \n", + "2. Орпделеляем значения функции в каждой вершине. \n", + "3. Находим вершину с наименьшим значением и двигаем ее к центру масс многоугольника." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "![Nelder-mead](images/Nelder_Mead1.gif)" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Optimization terminated successfully.\n", + " Current function value: 0.000000\n", + " Iterations: 339\n", + " Function evaluations: 571\n" + ] + }, + { + "data": { + "text/plain": [ + " final_simplex: (array([[1. , 1. , 1. , 1. , 1. ],\n", + " [1. , 1. , 1. , 1. , 1. ],\n", + " [1. , 1. , 1. , 1.00000001, 1.00000001],\n", + " [1. , 1. , 1. , 1. , 1. ],\n", + " [1. , 1. , 1. , 1. , 1. ],\n", + " [1. , 1. , 1. , 1. , 0.99999999]]), array([4.86115343e-17, 7.65182843e-17, 8.11395684e-17, 8.63263255e-17,\n", + " 8.64080682e-17, 2.17927418e-16]))\n", + " fun: 4.861153433422115e-17\n", + " message: 'Optimization terminated successfully.'\n", + " nfev: 571\n", + " nit: 339\n", + " status: 0\n", + " success: True\n", + " x: array([1., 1., 1., 1., 1.])" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "from scipy.optimize import minimize\n", + "\n", + "\n", + "def rosen(x):\n", + " \"\"\"The Rosenbrock function\"\"\"\n", + " return sum(100.0*(x[1:]-x[:-1]**2.0)**2.0 + (1-x[:-1])**2.0)\n", + "\n", + "x0 = np.array([1.3, 0.7, 0.8, 1.9, 1.2])\n", + "minimize(rosen, x0, method='nelder-mead', options={'xtol': 1e-8, 'disp': True})" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Help on function minimize in module scipy.optimize._minimize:\n", + "\n", + "minimize(fun, x0, args=(), method=None, jac=None, hess=None, hessp=None, bounds=None, constraints=(), tol=None, callback=None, options=None)\n", + " Minimization of scalar function of one or more variables.\n", + " \n", + " Parameters\n", + " ----------\n", + " fun : callable\n", + " The objective function to be minimized.\n", + " \n", + " ``fun(x, *args) -> float``\n", + " \n", + " where x is an 1-D array with shape (n,) and `args`\n", + " is a tuple of the fixed parameters needed to completely\n", + " specify the function.\n", + " x0 : ndarray, shape (n,)\n", + " Initial guess. Array of real elements of size (n,),\n", + " where 'n' is the number of independent variables.\n", + " args : tuple, optional\n", + " Extra arguments passed to the objective function and its\n", + " derivatives (`fun`, `jac` and `hess` functions).\n", + " method : str or callable, optional\n", + " Type of solver. Should be one of\n", + " \n", + " - 'Nelder-Mead' :ref:`(see here) `\n", + " - 'Powell' :ref:`(see here) `\n", + " - 'CG' :ref:`(see here) `\n", + " - 'BFGS' :ref:`(see here) `\n", + " - 'Newton-CG' :ref:`(see here) `\n", + " - 'L-BFGS-B' :ref:`(see here) `\n", + " - 'TNC' :ref:`(see here) `\n", + " - 'COBYLA' :ref:`(see here) `\n", + " - 'SLSQP' :ref:`(see here) `\n", + " - 'trust-constr':ref:`(see here) `\n", + " - 'dogleg' :ref:`(see here) `\n", + " - 'trust-ncg' :ref:`(see here) `\n", + " - 'trust-exact' :ref:`(see here) `\n", + " - 'trust-krylov' :ref:`(see here) `\n", + " - custom - a callable object (added in version 0.14.0),\n", + " see below for description.\n", + " \n", + " If not given, chosen to be one of ``BFGS``, ``L-BFGS-B``, ``SLSQP``,\n", + " depending if the problem has constraints or bounds.\n", + " jac : {callable, '2-point', '3-point', 'cs', bool}, optional\n", + " Method for computing the gradient vector. Only for CG, BFGS,\n", + " Newton-CG, L-BFGS-B, TNC, SLSQP, dogleg, trust-ncg, trust-krylov,\n", + " trust-exact and trust-constr. If it is a callable, it should be a\n", + " function that returns the gradient vector:\n", + " \n", + " ``jac(x, *args) -> array_like, shape (n,)``\n", + " \n", + " where x is an array with shape (n,) and `args` is a tuple with\n", + " the fixed parameters. Alternatively, the keywords\n", + " {'2-point', '3-point', 'cs'} select a finite\n", + " difference scheme for numerical estimation of the gradient. Options\n", + " '3-point' and 'cs' are available only to 'trust-constr'.\n", + " If `jac` is a Boolean and is True, `fun` is assumed to return the\n", + " gradient along with the objective function. If False, the gradient\n", + " will be estimated using '2-point' finite difference estimation.\n", + " hess : {callable, '2-point', '3-point', 'cs', HessianUpdateStrategy}, optional\n", + " Method for computing the Hessian matrix. Only for Newton-CG, dogleg,\n", + " trust-ncg, trust-krylov, trust-exact and trust-constr. If it is\n", + " callable, it should return the Hessian matrix:\n", + " \n", + " ``hess(x, *args) -> {LinearOperator, spmatrix, array}, (n, n)``\n", + " \n", + " where x is a (n,) ndarray and `args` is a tuple with the fixed\n", + " parameters. LinearOperator and sparse matrix returns are\n", + " allowed only for 'trust-constr' method. Alternatively, the keywords\n", + " {'2-point', '3-point', 'cs'} select a finite difference scheme\n", + " for numerical estimation. Or, objects implementing\n", + " `HessianUpdateStrategy` interface can be used to approximate\n", + " the Hessian. Available quasi-Newton methods implementing\n", + " this interface are:\n", + " \n", + " - `BFGS`;\n", + " - `SR1`.\n", + " \n", + " Whenever the gradient is estimated via finite-differences,\n", + " the Hessian cannot be estimated with options\n", + " {'2-point', '3-point', 'cs'} and needs to be\n", + " estimated using one of the quasi-Newton strategies.\n", + " Finite-difference options {'2-point', '3-point', 'cs'} and\n", + " `HessianUpdateStrategy` are available only for 'trust-constr' method.\n", + " hessp : callable, optional\n", + " Hessian of objective function times an arbitrary vector p. Only for\n", + " Newton-CG, trust-ncg, trust-krylov, trust-constr.\n", + " Only one of `hessp` or `hess` needs to be given. If `hess` is\n", + " provided, then `hessp` will be ignored. `hessp` must compute the\n", + " Hessian times an arbitrary vector:\n", + " \n", + " ``hessp(x, p, *args) -> ndarray shape (n,)``\n", + " \n", + " where x is a (n,) ndarray, p is an arbitrary vector with\n", + " dimension (n,) and `args` is a tuple with the fixed\n", + " parameters.\n", + " bounds : sequence or `Bounds`, optional\n", + " Bounds on variables for L-BFGS-B, TNC, SLSQP and\n", + " trust-constr methods. There are two ways to specify the bounds:\n", + " \n", + " 1. Instance of `Bounds` class.\n", + " 2. Sequence of ``(min, max)`` pairs for each element in `x`. None\n", + " is used to specify no bound.\n", + " \n", + " constraints : {Constraint, dict} or List of {Constraint, dict}, optional\n", + " Constraints definition (only for COBYLA, SLSQP and trust-constr).\n", + " Constraints for 'trust-constr' are defined as a single object or a\n", + " list of objects specifying constraints to the optimization problem.\n", + " Available constraints are:\n", + " \n", + " - `LinearConstraint`\n", + " - `NonlinearConstraint`\n", + " \n", + " Constraints for COBYLA, SLSQP are defined as a list of dictionaries.\n", + " Each dictionary with fields:\n", + " \n", + " type : str\n", + " Constraint type: 'eq' for equality, 'ineq' for inequality.\n", + " fun : callable\n", + " The function defining the constraint.\n", + " jac : callable, optional\n", + " The Jacobian of `fun` (only for SLSQP).\n", + " args : sequence, optional\n", + " Extra arguments to be passed to the function and Jacobian.\n", + " \n", + " Equality constraint means that the constraint function result is to\n", + " be zero whereas inequality means that it is to be non-negative.\n", + " Note that COBYLA only supports inequality constraints.\n", + " tol : float, optional\n", + " Tolerance for termination. For detailed control, use solver-specific\n", + " options.\n", + " options : dict, optional\n", + " A dictionary of solver options. All methods accept the following\n", + " generic options:\n", + " \n", + " maxiter : int\n", + " Maximum number of iterations to perform.\n", + " disp : bool\n", + " Set to True to print convergence messages.\n", + " \n", + " For method-specific options, see :func:`show_options()`.\n", + " callback : callable, optional\n", + " Called after each iteration. For 'trust-constr' it is a callable with\n", + " the signature:\n", + " \n", + " ``callback(xk, OptimizeResult state) -> bool``\n", + " \n", + " where ``xk`` is the current parameter vector. and ``state``\n", + " is an `OptimizeResult` object, with the same fields\n", + " as the ones from the return. If callback returns True\n", + " the algorithm execution is terminated.\n", + " For all the other methods, the signature is:\n", + " \n", + " ``callback(xk)``\n", + " \n", + " where ``xk`` is the current parameter vector.\n", + " \n", + " Returns\n", + " -------\n", + " res : OptimizeResult\n", + " The optimization result represented as a ``OptimizeResult`` object.\n", + " Important attributes are: ``x`` the solution array, ``success`` a\n", + " Boolean flag indicating if the optimizer exited successfully and\n", + " ``message`` which describes the cause of the termination. See\n", + " `OptimizeResult` for a description of other attributes.\n", + " \n", + " \n", + " See also\n", + " --------\n", + " minimize_scalar : Interface to minimization algorithms for scalar\n", + " univariate functions\n", + " show_options : Additional options accepted by the solvers\n", + " \n", + " Notes\n", + " -----\n", + " This section describes the available solvers that can be selected by the\n", + " 'method' parameter. The default method is *BFGS*.\n", + " \n", + " **Unconstrained minimization**\n", + " \n", + " Method :ref:`Nelder-Mead ` uses the\n", + " Simplex algorithm [1]_, [2]_. This algorithm is robust in many\n", + " applications. However, if numerical computation of derivative can be\n", + " trusted, other algorithms using the first and/or second derivatives\n", + " information might be preferred for their better performance in\n", + " general.\n", + " \n", + " Method :ref:`Powell ` is a modification\n", + " of Powell's method [3]_, [4]_ which is a conjugate direction\n", + " method. It performs sequential one-dimensional minimizations along\n", + " each vector of the directions set (`direc` field in `options` and\n", + " `info`), which is updated at each iteration of the main\n", + " minimization loop. The function need not be differentiable, and no\n", + " derivatives are taken.\n", + " \n", + " Method :ref:`CG ` uses a nonlinear conjugate\n", + " gradient algorithm by Polak and Ribiere, a variant of the\n", + " Fletcher-Reeves method described in [5]_ pp. 120-122. Only the\n", + " first derivatives are used.\n", + " \n", + " Method :ref:`BFGS ` uses the quasi-Newton\n", + " method of Broyden, Fletcher, Goldfarb, and Shanno (BFGS) [5]_\n", + " pp. 136. It uses the first derivatives only. BFGS has proven good\n", + " performance even for non-smooth optimizations. This method also\n", + " returns an approximation of the Hessian inverse, stored as\n", + " `hess_inv` in the OptimizeResult object.\n", + " \n", + " Method :ref:`Newton-CG ` uses a\n", + " Newton-CG algorithm [5]_ pp. 168 (also known as the truncated\n", + " Newton method). It uses a CG method to the compute the search\n", + " direction. See also *TNC* method for a box-constrained\n", + " minimization with a similar algorithm. Suitable for large-scale\n", + " problems.\n", + " \n", + " Method :ref:`dogleg ` uses the dog-leg\n", + " trust-region algorithm [5]_ for unconstrained minimization. This\n", + " algorithm requires the gradient and Hessian; furthermore the\n", + " Hessian is required to be positive definite.\n", + " \n", + " Method :ref:`trust-ncg ` uses the\n", + " Newton conjugate gradient trust-region algorithm [5]_ for\n", + " unconstrained minimization. This algorithm requires the gradient\n", + " and either the Hessian or a function that computes the product of\n", + " the Hessian with a given vector. Suitable for large-scale problems.\n", + " \n", + " Method :ref:`trust-krylov ` uses\n", + " the Newton GLTR trust-region algorithm [14]_, [15]_ for unconstrained\n", + " minimization. This algorithm requires the gradient\n", + " and either the Hessian or a function that computes the product of\n", + " the Hessian with a given vector. Suitable for large-scale problems.\n", + " On indefinite problems it requires usually less iterations than the\n", + " `trust-ncg` method and is recommended for medium and large-scale problems.\n", + " \n", + " Method :ref:`trust-exact `\n", + " is a trust-region method for unconstrained minimization in which\n", + " quadratic subproblems are solved almost exactly [13]_. This\n", + " algorithm requires the gradient and the Hessian (which is\n", + " *not* required to be positive definite). It is, in many\n", + " situations, the Newton method to converge in fewer iteraction\n", + " and the most recommended for small and medium-size problems.\n", + " \n", + " **Bound-Constrained minimization**\n", + " \n", + " Method :ref:`L-BFGS-B ` uses the L-BFGS-B\n", + " algorithm [6]_, [7]_ for bound constrained minimization.\n", + " \n", + " Method :ref:`TNC ` uses a truncated Newton\n", + " algorithm [5]_, [8]_ to minimize a function with variables subject\n", + " to bounds. This algorithm uses gradient information; it is also\n", + " called Newton Conjugate-Gradient. It differs from the *Newton-CG*\n", + " method described above as it wraps a C implementation and allows\n", + " each variable to be given upper and lower bounds.\n", + " \n", + " **Constrained Minimization**\n", + " \n", + " Method :ref:`COBYLA ` uses the\n", + " Constrained Optimization BY Linear Approximation (COBYLA) method\n", + " [9]_, [10]_, [11]_. The algorithm is based on linear\n", + " approximations to the objective function and each constraint. The\n", + " method wraps a FORTRAN implementation of the algorithm. The\n", + " constraints functions 'fun' may return either a single number\n", + " or an array or list of numbers.\n", + " \n", + " Method :ref:`SLSQP ` uses Sequential\n", + " Least SQuares Programming to minimize a function of several\n", + " variables with any combination of bounds, equality and inequality\n", + " constraints. The method wraps the SLSQP Optimization subroutine\n", + " originally implemented by Dieter Kraft [12]_. Note that the\n", + " wrapper handles infinite values in bounds by converting them into\n", + " large floating values.\n", + " \n", + " Method :ref:`trust-constr ` is a\n", + " trust-region algorithm for constrained optimization. It swiches\n", + " between two implementations depending on the problem definition.\n", + " It is the most versatile constrained minimization algorithm\n", + " implemented in SciPy and the most appropriate for large-scale problems.\n", + " For equality constrained problems it is an implementation of Byrd-Omojokun\n", + " Trust-Region SQP method described in [17]_ and in [5]_, p. 549. When\n", + " inequality constraints are imposed as well, it swiches to the trust-region\n", + " interior point method described in [16]_. This interior point algorithm,\n", + " in turn, solves inequality constraints by introducing slack variables\n", + " and solving a sequence of equality-constrained barrier problems\n", + " for progressively smaller values of the barrier parameter.\n", + " The previously described equality constrained SQP method is\n", + " used to solve the subproblems with increasing levels of accuracy\n", + " as the iterate gets closer to a solution.\n", + " \n", + " **Finite-Difference Options**\n", + " \n", + " For Method :ref:`trust-constr `\n", + " the gradient and the Hessian may be approximated using\n", + " three finite-difference schemes: {'2-point', '3-point', 'cs'}.\n", + " The scheme 'cs' is, potentially, the most accurate but it\n", + " requires the function to correctly handles complex inputs and to\n", + " be differentiable in the complex plane. The scheme '3-point' is more\n", + " accurate than '2-point' but requires twice as much operations.\n", + " \n", + " **Custom minimizers**\n", + " \n", + " It may be useful to pass a custom minimization method, for example\n", + " when using a frontend to this method such as `scipy.optimize.basinhopping`\n", + " or a different library. You can simply pass a callable as the ``method``\n", + " parameter.\n", + " \n", + " The callable is called as ``method(fun, x0, args, **kwargs, **options)``\n", + " where ``kwargs`` corresponds to any other parameters passed to `minimize`\n", + " (such as `callback`, `hess`, etc.), except the `options` dict, which has\n", + " its contents also passed as `method` parameters pair by pair. Also, if\n", + " `jac` has been passed as a bool type, `jac` and `fun` are mangled so that\n", + " `fun` returns just the function values and `jac` is converted to a function\n", + " returning the Jacobian. The method shall return an ``OptimizeResult``\n", + " object.\n", + " \n", + " The provided `method` callable must be able to accept (and possibly ignore)\n", + " arbitrary parameters; the set of parameters accepted by `minimize` may\n", + " expand in future versions and then these parameters will be passed to\n", + " the method. You can find an example in the scipy.optimize tutorial.\n", + " \n", + " .. versionadded:: 0.11.0\n", + " \n", + " References\n", + " ----------\n", + " .. [1] Nelder, J A, and R Mead. 1965. A Simplex Method for Function\n", + " Minimization. The Computer Journal 7: 308-13.\n", + " .. [2] Wright M H. 1996. Direct search methods: Once scorned, now\n", + " respectable, in Numerical Analysis 1995: Proceedings of the 1995\n", + " Dundee Biennial Conference in Numerical Analysis (Eds. D F\n", + " Griffiths and G A Watson). Addison Wesley Longman, Harlow, UK.\n", + " 191-208.\n", + " .. [3] Powell, M J D. 1964. An efficient method for finding the minimum of\n", + " a function of several variables without calculating derivatives. The\n", + " Computer Journal 7: 155-162.\n", + " .. [4] Press W, S A Teukolsky, W T Vetterling and B P Flannery.\n", + " Numerical Recipes (any edition), Cambridge University Press.\n", + " .. [5] Nocedal, J, and S J Wright. 2006. Numerical Optimization.\n", + " Springer New York.\n", + " .. [6] Byrd, R H and P Lu and J. Nocedal. 1995. A Limited Memory\n", + " Algorithm for Bound Constrained Optimization. SIAM Journal on\n", + " Scientific and Statistical Computing 16 (5): 1190-1208.\n", + " .. [7] Zhu, C and R H Byrd and J Nocedal. 1997. L-BFGS-B: Algorithm\n", + " 778: L-BFGS-B, FORTRAN routines for large scale bound constrained\n", + " optimization. ACM Transactions on Mathematical Software 23 (4):\n", + " 550-560.\n", + " .. [8] Nash, S G. Newton-Type Minimization Via the Lanczos Method.\n", + " 1984. SIAM Journal of Numerical Analysis 21: 770-778.\n", + " .. [9] Powell, M J D. A direct search optimization method that models\n", + " the objective and constraint functions by linear interpolation.\n", + " 1994. Advances in Optimization and Numerical Analysis, eds. S. Gomez\n", + " and J-P Hennart, Kluwer Academic (Dordrecht), 51-67.\n", + " .. [10] Powell M J D. Direct search algorithms for optimization\n", + " calculations. 1998. Acta Numerica 7: 287-336.\n", + " .. [11] Powell M J D. A view of algorithms for optimization without\n", + " derivatives. 2007.Cambridge University Technical Report DAMTP\n", + " 2007/NA03\n", + " .. [12] Kraft, D. A software package for sequential quadratic\n", + " programming. 1988. Tech. Rep. DFVLR-FB 88-28, DLR German Aerospace\n", + " Center -- Institute for Flight Mechanics, Koln, Germany.\n", + " .. [13] Conn, A. R., Gould, N. I., and Toint, P. L.\n", + " Trust region methods. 2000. Siam. pp. 169-200.\n", + " .. [14] F. Lenders, C. Kirches, A. Potschka: \"trlib: A vector-free\n", + " implementation of the GLTR method for iterative solution of\n", + " the trust region problem\", https://arxiv.org/abs/1611.04718\n", + " .. [15] N. Gould, S. Lucidi, M. Roma, P. Toint: \"Solving the\n", + " Trust-Region Subproblem using the Lanczos Method\",\n", + " SIAM J. Optim., 9(2), 504--525, (1999).\n", + " .. [16] Byrd, Richard H., Mary E. Hribar, and Jorge Nocedal. 1999.\n", + " An interior point algorithm for large-scale nonlinear programming.\n", + " SIAM Journal on Optimization 9.4: 877-900.\n", + " .. [17] Lalee, Marucha, Jorge Nocedal, and Todd Plantega. 1998. On the\n", + " implementation of an algorithm for large-scale equality constrained\n", + " optimization. SIAM Journal on Optimization 8.3: 682-706.\n", + " \n", + " Examples\n", + " --------\n", + " Let us consider the problem of minimizing the Rosenbrock function. This\n", + " function (and its respective derivatives) is implemented in `rosen`\n", + " (resp. `rosen_der`, `rosen_hess`) in the `scipy.optimize`.\n", + " \n", + " >>> from scipy.optimize import minimize, rosen, rosen_der\n", + " \n", + " A simple application of the *Nelder-Mead* method is:\n", + " \n", + " >>> x0 = [1.3, 0.7, 0.8, 1.9, 1.2]\n", + " >>> res = minimize(rosen, x0, method='Nelder-Mead', tol=1e-6)\n", + " >>> res.x\n", + " array([ 1., 1., 1., 1., 1.])\n", + " \n", + " Now using the *BFGS* algorithm, using the first derivative and a few\n", + " options:\n", + " \n", + " >>> res = minimize(rosen, x0, method='BFGS', jac=rosen_der,\n", + " ... options={'gtol': 1e-6, 'disp': True})\n", + " Optimization terminated successfully.\n", + " Current function value: 0.000000\n", + " Iterations: 26\n", + " Function evaluations: 31\n", + " Gradient evaluations: 31\n", + " >>> res.x\n", + " array([ 1., 1., 1., 1., 1.])\n", + " >>> print(res.message)\n", + " Optimization terminated successfully.\n", + " >>> res.hess_inv\n", + " array([[ 0.00749589, 0.01255155, 0.02396251, 0.04750988, 0.09495377], # may vary\n", + " [ 0.01255155, 0.02510441, 0.04794055, 0.09502834, 0.18996269],\n", + " [ 0.02396251, 0.04794055, 0.09631614, 0.19092151, 0.38165151],\n", + " [ 0.04750988, 0.09502834, 0.19092151, 0.38341252, 0.7664427 ],\n", + " [ 0.09495377, 0.18996269, 0.38165151, 0.7664427, 1.53713523]])\n", + " \n", + " \n", + " Next, consider a minimization problem with several constraints (namely\n", + " Example 16.4 from [5]_). The objective function is:\n", + " \n", + " >>> fun = lambda x: (x[0] - 1)**2 + (x[1] - 2.5)**2\n", + " \n", + " There are three constraints defined as:\n", + " \n", + " >>> cons = ({'type': 'ineq', 'fun': lambda x: x[0] - 2 * x[1] + 2},\n", + " ... {'type': 'ineq', 'fun': lambda x: -x[0] - 2 * x[1] + 6},\n", + " ... {'type': 'ineq', 'fun': lambda x: -x[0] + 2 * x[1] + 2})\n", + " \n", + " And variables must be positive, hence the following bounds:\n", + " \n", + " >>> bnds = ((0, None), (0, None))\n", + " \n", + " The optimization problem is solved using the SLSQP method as:\n", + " \n", + " >>> res = minimize(fun, (2, 0), method='SLSQP', bounds=bnds,\n", + " ... constraints=cons)\n", + " \n", + " It should converge to the theoretical solution (1.4 ,1.7).\n", + "\n" + ] + } + ], + "source": [ + "help(minimize)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Первые производные" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Наискорейший подъем (спуск)\n", + "Направление на максимум всегда в направлении градиента функции:\n", + "\n", + "$$ \\theta_{k+1} = \\theta_k + \\beta_k \\nabla L $$\n", + "\n", + "* Не понятно, как определять $\\beta$\n", + "* Не понятно, когда останавливаться." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Модификация метода - метод сопряженных градиентов на самом деле требует второй производной." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Вторые производные" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Главная формула:\n", + "\n", + "$$ L(\\theta) = L(\\theta_0) + \\nabla L( \\theta - \\theta_0) + \\frac{1}{2} (\\theta-\\theta_0)^T H (\\theta-\\theta_0) + o(\\theta-\\theta_0)$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Метод Ньютона\n", + "\n", + "$$\\nabla f(\\theta_k) + H(\\theta_k)(\\theta_{k+1} - \\theta_k) = 0$$\n", + "\n", + "$$ \\theta_{k+1} = \\theta_k - H^{-1}(\\theta_k)\\nabla L(\\theta_k) $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Можно добавить выбор шага:\n", + "\n", + "$$ \\theta_{k+1} = \\theta_k - \\lambda_i H^{-1}(\\theta_k)\\nabla L(\\theta_k) $$" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1.0000000000000016" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from scipy import optimize\n", + "optimize.newton(lambda x: x**3 - 1, 1.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Методы с переменной метрикой\n", + "\n", + "* Вычислять $\\nabla L$ и $H$ очень дорого\n", + "* Давайте вычислять их итеративно.\n", + "\n", + "Примеры: \n", + "* MINUIT\n", + "* scipy `minimize(method=’L-BFGS-B’)`" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "# Случай наименьших квадратов" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "В случае анализа спектров имеем:\n", + "\n", + "$$ L(X | \\theta) = \\prod p_i (x_i | \\theta)$$\n", + "\n", + "Или:\n", + "\n", + "$$\\ln{ L(X | \\theta)} = \\sum \\ln{ p_i (x_i | \\theta)}$$\n", + "\n", + "В случае нормальных распределений:\n", + "\n", + "$$\\ln{ L(X | \\theta)} \\sim \\sum{ \\left( \\frac{y_i - \\mu(x_i, \\theta)}{\\sigma_i} \\right)^2 }$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Метод Гаусса-Ньютона\n", + "Пусть:\n", + "$$r_i = \\frac{y_i - \\mu(x_i, \\theta)}{\\sigma_i}$$ \n", + "$$J_{ij} = \\frac{\\partial r_i}{\\partial \\theta_j} = - \\frac{\\partial \\mu(x_i, \\theta)}{\\sigma_i \\partial \\theta_j}$$\n", + "\n", + "Тогда:\n", + "\n", + "$$ \\theta_{(k+1)} = \\theta_{(k)} - \\left( J^TJ \\right)^{-1}J^Tr(\\theta)$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Алгоритм Левенберга — Марквардта\n", + "\n", + "$$ \\theta_{(k+1)} = \\theta_{(k)} + \\delta$$\n", + "\n", + "$$ (J^TJ + \\lambda I)\\delta = J^Tr(\\theta)$$\n", + "\n", + "При этом $\\lambda$ - фактор регуляризации, выбирается произвольным образом." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Метод квазиоптимальных весов\n", + "Идея:\n", + " Есть некоторая статистика (функция данных) $f(x)$. Для оптимального решения среднее от этой функции по экспериментальным данным и по модели должны совпадать:\n", + "$$ E_\\theta(f(x)) = \\sum_i{f(x_i)} $$\n", + "\n", + "Можно показать, что оптимальная эффективность получается когда\n", + "\n", + "$$ f = \\frac{\\partial \\ln L}{\\partial \\theta} $$\n", + "\n", + "В этом случае и если ошибки распределены по Гауссу или Пуассону, решение для оптмального $\\theta$ можно получить как:\n", + "\n", + "$$ \n", + "\\sum_{i}{\\frac{\\mu_{i}\\left( \\mathbf{\\theta},E_{i} \\right) - x_{i}}{\\sigma_{i}^{2}}\\left. \\ \\frac{\\partial\\mu_{i}\\left( \\mathbf{\\theta},E_{i} \\right)}{\\partial\\mathbf{\\theta}} \\right|_{\\mathbf{\\theta}_{\\mathbf{0}}}} = 0. \n", + "$$" + ] + } + ], + "metadata": { + "celltoolbar": "Slideshow", + "hide_input": false, + "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": "3.7.4" + }, + "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": 4 +} diff --git a/notebooks/python/hypotesis.ipynb b/notebooks/python/hypotesis.ipynb new file mode 100644 index 0000000..4ef619b --- /dev/null +++ b/notebooks/python/hypotesis.ipynb @@ -0,0 +1,136 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Проверка статистических гипотез\n", + "\n", + "Задача: есть некоторое статистическое утверждение (гипотеза) $H$ и есть набор экспериментальных данных $X$. Требуется сделать утверждение о степени достоверности гипотезы **H** при заданном наборе $X$.\n", + "\n", + "В большинстве случаев речь идет о проверке единственной гипотезы, которую принято называть нулевой $H_0$. В отдельных случаях стоит также задача выбора наиболее подходящей гипотезы из набора $H_0,~H_1,~H_2,~...$\n", + "\n", + "Для формализации процесса проверки гипотезы требуется ввести ФПВ: $f(X|H_0)$, характеризующее вероятность получить заданные наблюдаемые результаты в случае, если гипотеза верна.\n", + "\n", + "**Замечание** Вообще говоря, уже этого распределеня достаточно для того, чтобы понять, верна гипотеза или нет. Если вероятность получить набор данных велика, то гипотеза наверное не верна. С другой стороны, возникает проблема с тем, что сложно понять, на сколько именно (с какой достоверностью) верна или не верна гипотеза нормировки распределений часто вычисляются не верно.\n", + "\n", + "Для упрощения процесс принятия решения, используют функцию, называемую проверочной статистикой: $T(X)$, где T - число. Для такой статистики довольно легко построит ФПВ: $g(T|H_0)$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![](images/two_hypothsis.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Для критерия $T$ вводится понятие критического значения или критической области $T_0$. В случае, если значение $T$ превышает критическое значение (или выходит из критической области), то гипотеза считается не верной. Если значение в области, гипотеза считается верной.\n", + "\n", + "Величина\n", + "$$\n", + " \\alpha = \\int_{T_0}^\\inf {g(T|H_0)}\n", + "$$\n", + "показывает вероятность **ошибки I рода**. То есть вероятность отвергнуть гипотезу, когда она верна. Величину $1-\\alpha$ называют уровнем достоверности критерия.\n", + "\n", + "В случае, если существует единственная альтернативная (исключающая $H_0$) гипотеза $H_1$, то также можно определить величину **ошибки II рода**, то есть вероятность принять $H_0$ в случае если она не верна:\n", + "$$\n", + " \\beta = \\int_{-\\inf}^{T_0} {g(T|H_1)}\n", + "$$\n", + "\n", + "Величину $1-\\beta$ называют мощностью критерия при заданной достоверности $1-\\alpha$.\n", + "\n", + "Среди двух критериев предпочтительным является тот, для которого мощность при той же значимости выше. Критерий, который будет более мощным для всех возможных состояний природы, называют равномерно более мощным критерием." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Построение критической области критерия\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Визуально подбро критической области критерия можно сделать следующим образом: \n", + "\n", + "* Берем распределение $g(T|H_0)$.\n", + "* Интегрируем его и получаем интегральное распределение: $G(T|H_0) = \\int{g(T|H_0)}$. При необходимости перенормируем в диапазон [0,1].\n", + "* Проводим линию на уровне нужного уровня значимости (например C. L. 95%).\n", + "* Пересечение этой линии с графиком проектируется на ось T и это значение и будет означать критическую область." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Качество фита (стандартные критерии)\n", + "\n", + "### Критерий Пирсона\n", + "Проверочная статистика:\n", + "$$\n", + "\\chi^2 = \\sum{\\frac{ (O_i-E_i)^2}{E_i}}\n", + "$$\n", + "\n", + "Асимпототически приближается к $\\chi^2$ распределению.\n", + "\n", + "![](images/Chi-square_cdf.svg)\n", + "\n", + "### Критерий соотношения правдоподобия\n", + "\n", + "Пусть $\\Theta$ - пространство параметров $\\theta$, а $\\Omega*$ - область пространства парамеров, на принадлежность которой мы хотим проверить данные. В качестве проверочной статиситки выбирается:\n", + "$$\n", + "\\lambda = \\frac{L(X|\\theta \\in \\Omega)}{L(X|\\theta \\in \\Theta)}\n", + "$$\n", + "\n", + "Величина $-2ln\\lambda$ распределена как $\\chi^2(r)$, где r - количество фиксированных параметров в $\\Omega$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Сложные гипотезы\n", + "Положим что есть семейство гипотез $H_i$, среди которых надо выбрать наиболее достоверную. Выбор можно сделать двумя способами:\n", + "\n", + "* Выбираем ту гипотезу, для которой $g(T|H_i)$ максимален.\n", + "* Выбираем ту гипотезу, для которой $\\int_T^\\inf{g(T|H_i)}$ максимален.\n", + "\n", + "Если принять $T = L(X|\\theta)$, то решение по первому методу сводится к методу максимуму правдоподобия." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.7.4" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/python/images/Chi-square_cdf.svg b/notebooks/python/images/Chi-square_cdf.svg new file mode 100644 index 0000000..20e13d9 --- 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zztvlKiN6f_{Ec%l|Aqe}0Q4pQGFb38FTna2|7YmnOZ;UJ*>Bv0{V)7wNZCshFCzec zn>gV8%f#Ok!>_zVA2$o&$3DU|Bq<$CH&9L#NQ|wn6?HO z*vqZOm-Nf6mfyUW_FrAU*m!wq;pJYyZwvUke_8mwGw>3AxzhX%Kj{4h|6|?xl7Hy} z{^oOy{^CtRW!wJ8A$-ZdbOC9fFr;{y8Q6HUb8gYWBx7_ +**Замечание** +Тут важно заметить, что мы также негласно предполагаем, что природа вообще действует согласно нашей модели, но этот вопрос мы пока оставим за кадром. В какой-то мере мы вернемся к нему, в главе 5, когда будем обсуждать теорию проверки гипотез. + + +Предоставим теперь, что мы провели некоторую серию экспериментов $X = \{X_0, X_1,...X_N\}$, в которых мы тем или иным способом изучаем состояние природы (будем дальше называть результаты этих экспериментов экспериментальной выборкой). Нашей задачей в этой главе будет описание процедуры, при помощи которой можно на основе выборки сделать вывод об истинном состоянии природы $\theta_0$. Важно понимать, что в общем случае, результаты измерений являются случайными величинами, поэтому полученное нами на основании этих данных состояние природы также будет случайной величиной в противовес истинному состоянию природы $\theta_0$, которое вообще говоря, истинно случайной величиной не является. Полученную величину будем называть *точечной оценкой* состояния природы $\hat{\theta}$ или просто оценкой. Саму процедуру, в процессе которой получена оценка, будем называть оцениванием. + +

    + +В дальнейшем будем считать, что состояния природы описываются действительным числом или набором действительных чисел. Сама по себе теория этого не требует, но в противном случае довольно сложно сравнивать состояния между собой (требуется определять понятие близости в произвольном пространстве). В этом случае наша процедура оценивания: +$$ + \hat{\theta} = f(X) +$$ +является действительной функцией на пространстве векторов $X$, состоящих из случайных переменных. Такие функции еще называют статистиками. Очевидно, что далеко не людая такая функция будет давать тот результат, которого мы хотим. Поэтому вводятся дополнительные обязательные свойства оценок. + +##Свойства точечных оценок + +### Состоятельность +Естественное пожелание к оценщику, заключается в том, что качество оценки должно зависеть от объема выборки, числа измерений $n$ случайных переменных $X$: чем больше выборка, тем качественней оценка $\hat{\theta}$. Иными словами, мы хотим, чтобы с ростом объема выборки значение оценки приближалось к истинному значению параметра. При использовании сходимости по вероятности оценку $\hat{\theta}$ определяют как состоятельную, если при любых $\varepsilon > 0$ и $\eta > 0$, найдется такое $N$, что $P \left( \left| \hat{\theta} - \theta \right| \right) < \eta $ при всех $n > N$. + +
    +**Замечание** +Нужно заметить, что на практике оценки являются состоятельными только когда при построении оценки не учитывается систематическая ошибка. В противном случае, может наблюдаться сходимость по вероятности не к нулю, а к некоторой фиксированной константе. +
    + +### Несмещенность +Рассмотрим набор измерений, каждое из которых состоит из $k$ наблюдений $X$, характеризуемый функцией плотности вероятности $P(\hat\theta | \theta)$ при фиксированном $k$ и определим смещение как отклонение среднего по этому набору $\hat{\theta_k}$ от истинного + $$ + b = E[\hat{\theta_k}] - \theta + $$ +Оценка называется несмещенной, если $b = 0$. + +Заметим, что смещение не зависит от измеренных величин, но зависит от размера образца, формы оценщика и от истинных (в общем случае неизвестных) свойств ФПВ $f(x)$, включая истинное значение параметра. Если смещение исчезает в пределе $n \to \infty$, говорят об асимптотически несмещенной оценке. Заметим, что из состоятельности оценки не следует несмещенность. Это означает, что даже если $\hat{\theta}$ сходится к истинной величине $\theta$ в единичном эксперименте с большим числом измерений, нельзя утверждать, что среднее $\hat{\theta}$ по бесконечному числу повторений эксперимента с конечным числом измерений $n$ будет сходится к истинному $\theta$. Несмещенные оценки пригодны для комбинирования результатов разных экспериментов. В большинстве практических случаев смещение должно быть мало по сравнению со статистической ошибкой и им пренебрегают. + +### Эффективность +Для сравнения разных методов оценки, очень важным свойством является эффективность. Говоря простым языком, эффективность - это величина, обратная разбросу значений $\hat{\theta}$ при применении к разным наборам данных. Для того, чтобы хорошо разобраться в этом свойстве, надо вспомнить, что оценка, как случайная величина, распределена с плотностью $P(\hat\theta | \theta)$. Вид этого распределения может быть не известен полностью, но знать его свойства – низшие моменты – необходимо. Среднее по нему суть смещение, а дисперсия $\sigma_{\hat\theta}^2 = \int{ (\hat\theta - \theta} ) P(\hat\theta | \theta) d\hat\theta$ суть мера ошибки в определении оценки. Выбирая между различными методами, мы, естественно, хотим, чтобы ошибка параметра была минимальной из всех доступных нам способов его определения для фиксированного эксперимента. Разные методы обладают разной эффективностью и в общем случае при конечной статистике дисперсия распределения оценки никогда не будет равна нулю. Разумеется, встает вопрос о том, можно ли построить оценку с максимальной возможной эффективностью. + +## Интервальные оценки + +На практике применение точечных оценок сильно затруднено тем, что не известно, на сколько каждая такая оценка точна. Действительно, мы можем спокойно утверждать, что слон весит один килограмм если разброс нашей оценки составляет больше массы слона. Для того, чтобы решить эту проблему есть два пути. +Первый путь - это на ряду с точечной оценки указывать меру эффективности этой оценки или ее разброс$\sigma_{\hat\theta}$. Но тут любой внимательный слушатель заметит, что для определения эффективности, вообще говоря, надо знать истинное значение параметра $\theta$, которого мы, разумеется не знаем. Следовательно приходится использовать не эффективность, а оценку этой эффективности, которая сама по себе является случайной величиной. Кроме того, часто случается, что распределение оценки является не симметричным и описать его одним числом не удается. + +Более корректным способом является построение интервальной оценки (доверительного интервала). Формально определение интервальной оценки будет отличаться в зависимости от того, какое определение вероятности вы будете использовать. + +**Частотная интерпретация**: интервальной оценкой параметра или группы параметров $\theta$ с уровнем достоверности $\alpha$ называется такая область на пространстве параметров (в одномерном случае - интервал), которая при многократном повторении эксперимента с вероятностью (частотой) $\alpha$ перекрывает истинное значение $\theta$. + +**Субъективная интерпретация**: доверительным интервалом для параметров $\theta$ будем называть такую область в пространстве параметров, в которой интегральная апостериорная вероятность нахождения истинного значения параметра равна $\alpha$. + +Для точного описания результата проведения анализа как правило в качестве результата приводят как точечную оценку, так и интервальную оценку с некоторым уровнем достоверности (в английском варианте Confidence Level или C. L.). В некоторых случаях приводят несколько интервальных оценок с разным уровнем достоверности. В случае, когда речь идет об определении верхней или нижней границы какого-то параметра, точечная оценка как правило не имеет смысла и в качестве результата дается только интервальная оценка. + +
    +**Замечание** +Точечная оценка также не имеет смысла в случае, когда распределение оценки, скажем имеет вид однородного распределения на отрезке. В этом случае все параметры на этом отрезке равновероятны и не понятно, какой из них называть результатом. +
    + +
    +**Замечание** +Вполне очевидно, что для одних и тех же данных с использованием одного и того же метода оценивания можно построить бесконечное множество интервальных оценок с фиксированным уровнем достоверности. Действительно, мы можем двигать интервал в разные стороны таким образом, чтобы его вероятностное содержание не менялось. Обычно, если не оговорено иначе, используются так называемые центральные доверительные интервалы, в которых вероятностные содержание за границами интервалов с обеих сторон равны. **Добавить картинку** +
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