{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "# Математические инструменты"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:34+0000",
     "start_time": "2017-09-22T06:34+0000"
    },
    "hidden": true,
    "init_cell": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<script type=\"text/javascript\">window.PlotlyConfig = {MathJaxConfig: 'local'};</script><script type=\"text/javascript\">if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}</script><script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window._Plotly) {require(['plotly'],function(plotly) {window._Plotly=plotly;});}</script>"
      ],
      "text/vnd.plotly.v1+html": [
       "<script type=\"text/javascript\">window.PlotlyConfig = {MathJaxConfig: 'local'};</script><script type=\"text/javascript\">if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}</script><script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window._Plotly) {require(['plotly'],function(plotly) {window._Plotly=plotly;});}</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "%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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "### Проверка отрисовки графика"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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zDUd0j2hndX56avUg6DPJ7GgqJZskBhEZLiLRIhIrIk9fYvkTIrJfRHaLyAoR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\nP8LmzyDyYWg3ius61mdwm3q882c0x1K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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Plot test frame\")\n",
    "x = np.linspace(0, 2*math.pi, 10)\n",
    "plt.plot(x, np.sin(x), label=\"sin(x)\")\n",
    "plt.plot(x, np.cos(x), label=\"cos(x)\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "data": [
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         "type": "scatter",
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        {
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      ]
     },
     "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": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "## Численное интегрирование"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "### Вариант 1: простой интеграл Римана\n",
    "Фиксированное количество точек. Интеграл всегда сходится, но точность результата зависит от функции."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:34+0000",
     "start_time": "2017-09-22T06:34+0000"
    },
    "hidden": true,
    "init_cell": true
   },
   "outputs": [],
   "source": [
    "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "### Вариант 2: итеративный интеграл Симпсона \n",
    "[Квадратичная формула Симпсона](http://mathworld.wolfram.com/SimpsonsRule.html). Первый аргумент - сама функция, второй и третий - границы интегрирования. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "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": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.integrate import quad\n",
    "def integrateQ(func, a, b):\n",
    "    res = quad(func, a,b)\n",
    "    return res[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "### Интегратор по умолчанию\n",
    "В качестве интегратора по умолчанию выбираем интегратор Римана. Если захотим использовать другой, надо переопределить переменную `integrate,` например вот так:\n",
    "\n",
    "`integrate = integrateS`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:34+0000",
     "start_time": "2017-09-22T06:34+0000"
    },
    "hidden": true,
    "init_cell": true
   },
   "outputs": [],
   "source": [
    "integrate = integrateS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "### Проверяем, что интегратор работает"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "Интеграл Римана 10 точек:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9995487365804032"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate(np.sin,0,math.pi,10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "Интеграл Римана 100 точек:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9998321638939927"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrateR(np.sin,0,math.pi,100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "Интеграл Римана 200 точек:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9999584621373308"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "Итеративный интеграл:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    },
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrateQ(np.sin,0, math.pi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "## Свертка"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "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%D0%B8%D0%B9_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7)) \n",
    "двух функций называется следующее интегральное преобразование:\n",
    "$$\n",
    "  h(x) = f(x) \\otimes g(x) = \\int {f(x-y) g(y) dy }\n",
    "$$\n",
    "Интегрирование ведется по всей области определения функций. Очевидно, что переменные под интегрированием можно менять местами."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "### Проверяем работу свертки"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "Проверяем работу свертки, взяв в качестве одной функции ступеньку, а в качестве другой Гауссиану. Параметры `wStep` и `sigma` можно менять по своему усмотрению для получения различного результата."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    },
    "hidden": true
   },
   "outputs": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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",
    "f = np.vectorize(f)\n",
    "\n",
    "# Функция Гаусса\n",
    "g = lambda x : 1/np.sqrt(2*math.pi)/sigma*np.exp(-x*x/2/sigma/sigma)\n",
    "\n",
    "# Plot plot = new Plot(title: \"Convolution test plot\", showLegend: true)\n",
    "\n",
    "\n",
    "# автоматическое определение окна интегрирования и отрисовки\n",
    "wind = max(2*wStep, 4*sigma)\n",
    "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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "## Интерполяция"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "При использовании численных методов часто нужно уметь не только вычислить функцию, но и сохранить ее значения в виде таблицы для дальнейших вычислений.\n",
    "В данном случае используется кубический сплайн-интерполятор из библиотеки commons-math. Сплайн-интерполяторы характерны тем, что выдают гладкую функцию, проходящую через все заданные точки. \n",
    "Легко видно, что для функций с большой степенью гладкости такой интерполятор будет выдавать хорошее приближение даже при сравнительно маленьком количестве узлов."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.interpolate import CubicSpline\n",
    "\n",
    "def interpolate(func, a, b, numPoints=300):\n",
    "    xs = np.linspace(a,b, numPoints, endpoint=True)\n",
    "    spline = CubicSpline(xs, func(xs), extrapolate=False)\n",
    "    \n",
    "    def my_spline(x):\n",
    "        if x<a:\n",
    "            return spline(a)\n",
    "        elif x>b:\n",
    "            return spline(b)\n",
    "        else:\n",
    "            return spline(x)\n",
    "        \n",
    "    return np.vectorize(my_spline)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "### Проверка работы интерполятора"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mWh1HqSxTefRUTA44MmO81VE8ghZ3F7P4zcEEHbvBweZBBFYNsTqOUlnmnkbt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\ncxPg79yYmWffu2MRAxWGj7c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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Testing function interpolation (sin)\")\n",
    "x = np.linspace(0, math.pi, 300, endpoint=True)\n",
    "plt.plot(x, np.sin(x), label=\"original\")\n",
    "plt.plot(x, interpolate(np.sin, 0, math.pi, 10)(x), label=\"10 points\")\n",
    "plt.plot(x, interpolate(np.sin, 0, math.pi, 100)(x), label=\"100 points\")\n",
    "plt.plot(x, interpolate(np.sin, 0, math.pi, 200)(x), label=\"200 points\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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",
    "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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Распределения"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Равномерное распределение"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Равномерное распределение говорит о том, что величина может принимать любое значение в заданном интервале $(a,b)$ с равной вероятностью.\n",
    "\n",
    "*Распределение:* \n",
    "$$\n",
    "  f(x) = 1/(b-a),  a < x < b\n",
    "$$\n",
    "\n",
    "Равномерное распределение с конечными пределами указывает на то, что величина лежит строго в заданном интервале, но ее точное значение в этом интервале неизвестно.\n",
    "В случае бесконечных пределов нормировка равномерного распределения расходится, но его все равно можно использовать.\n",
    "\n",
    "*Среднее значение:* \n",
    "$\n",
    "  \\mu = (b-a)/2\n",
    "$\n",
    "\n",
    "*Дисперсия:* \n",
    "$\n",
    "  D = (b-a)^2/12\n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Демонстрация равномерного распределения"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UVR8t4/Ru+Ti5WyV8YtCstZzcrVLuuOfjNVStKCd3q4TLMsUMNJOzu+Xk5G6VcI4yay0n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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Uniform distribution\")\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(-1.5,1.5,300, endpoint=True)\n",
    "plt.plot(x, uniform(-1, 1)(x), label=\"d = 2\")\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();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Биномиальное распределение"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Биномиальное распределение описывает вероятность получить число \"успехов\" $k$ при проведении $n$ экспериментов при условии, что вероятность успеха в одном эксперименте равна $p$.\n",
    "\n",
    "*Распределение:* \n",
    "$$\n",
    "   p(k) = \\frac{n!}{k! (n-k!)} p^k (1-p)^{n-k}\n",
    "$$\n",
    "\n",
    "*Среднее значение:* \n",
    "$\n",
    "  \\mu  = np\n",
    "$\n",
    "\n",
    "*Дисперсия:* \n",
    "$\n",
    "  D = np(1-p)\n",
    "$\n",
    "\n",
    "Для вычислений используется [библиотечная функция](https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.binom.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import binom"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Демонстрация биномиального распределения"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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I9adRHwxTH2x6GUInsOUzCNVBvyPatl2/IwBjjbuvlHIM1yT9cNjYk6K3r6UP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\nRJO+Ukq5yP8D8NwtZkrIINgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Binomial distribution (p = 0.5)\")\n",
    "p =0.5\n",
    "x = range(0,10)\n",
    "plt.plot(x, binom.pmf(x,10,p), label=\"n = 10\")\n",
    "x = range(0,50)\n",
    "plt.plot(x, binom.pmf(x,50,p), label=\"n = 50\")\n",
    "x = range(0,100)\n",
    "plt.plot(x, binom.pmf(x,100,p), label=\"n = 100\");\n",
    "x = range(0,100)\n",
    "plt.plot(x, binom.pmf(x,150,p), label=\"n = 150\");\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Распределение Пуассона"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Распределение Пуассона описывает вероятность насчитать количество событий $k$ при условии, что все события равновероятны, а сренее количество таких событий равно $\\lambda$. \n",
    "Это распределение - одно из самых распространенных в физике, поскольку описывает отклонение от среднего в процессе достаточно произвольного вида.\n",
    "\n",
    "*Распределение:* \n",
    "$$\n",
    "   p(k) = \\frac{\\lambda^k}{k!} e^{-\\lambda}\n",
    "$$\n",
    "\n",
    "*Среднее значение:* \n",
    "$\n",
    "  \\mu  = \\lambda\n",
    "$\n",
    "\n",
    "*Дисперсия:* \n",
    "$\n",
    "  D = \\lambda\n",
    "$\n",
    "\n",
    "Для вычислений используется [библиотечная функция](http://commons.apache.org/proper/commons-math/javadocs/api-3.5/org/apache/commons/math3/distribution/PoissonDistribution.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:34+0000",
     "start_time": "2017-09-22T06:34+0000"
    },
    "init_cell": true
   },
   "outputs": [],
   "source": [
    "from scipy.stats import poisson"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Демонстрация распределения Пуассона"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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I4uJiAB588EEWLVpk5K/t0h/y10se2YDH5+P5uy4G/L0Qiu57le9/ehL/MmdMRO9lMJyv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\nOjo6Ohr/Dysb0SqDIuQlAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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,mean), '-', label=\"lambda = {:d}\".format(i))\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Нормальное распределение"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Нормальное или Гауссово распределение - наиболее часто встречается в физике (и не только). Оно является предельным случаем распределение Пуассона при больших $\\lambda$, \n",
    "а также всегда всплывает при усреднеии случайных величин в силу *центральной предельной теоремы*.\n",
    "\n",
    "*Распределение:* \n",
    "$$\n",
    "   f(x, \\mu, \\sigma) = \\frac {1}{\\sqrt{2\\pi} \\sigma} e^{-\\frac{(x-\\mu)^2}{2 \\sigma^2}}\n",
    "$$\n",
    "\n",
    "*Среднее значение:* \n",
    "$\n",
    "  \\mu \n",
    "$\n",
    "\n",
    "*Дисперсия:* \n",
    "$\n",
    "  D = \\sigma^2\n",
    "$\n",
    "\n",
    "Параметр $\\sigma$ называют стандартным отклонением и именно он в большинстве случаев используется для оценки погрешности эксперимента."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Функция Гаусса\n",
    "gauss = lambda mu, sigma: lambda x : 1/np.sqrt(2*math.pi)/sigma*np.exp(-(x-mu)*(x-mu)/2/sigma/sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Демонстрация распределения Гаусса"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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I9Ew/uPxnfQlH5yS3K+o/PDoLEXhr/RFxCf2W2k8/JXrQIKzjj5yYJZ52GmI2U+1xkWpC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\nOfcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Gaussian (Normal) distribution\")\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",
    "plt.plot(x, gauss(5,1)(x), label=\"sigma = 1, mu = 5\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Распределение Коши"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Распределение Коши (или Лорнца или Брейта-Вигнера) описывает резонансные процессы в физике.\n",
    "\n",
    "*Распределение:* \n",
    "$$\n",
    "   f(x, \\mu, \\gamma) = \\frac {1}{\\pi} \\frac{\\gamma}{ (x-\\mu)^2 + \\gamma^2}\n",
    "$$\n",
    "\n",
    "*Среднее значение:*  не определено\n",
    "\n",
    "*Дисперсия:*  распеделение Коши имеет бесконечную дисперсию (интеграл расходится)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:34+0000",
     "start_time": "2017-09-22T06:34+0000"
    },
    "init_cell": true
   },
   "outputs": [],
   "source": [
    "cauchy = lambda mu,gamma : lambda x : 1/math.pi * gamma/ ((x-mu)*(x-mu)+gamma*gamma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Демонстрация распределения Коши"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SypavLFLc6oUXXmDw4MEMHz6ciy++mBMn1MqRTWXbRvBpbST9tLgwjpVU06Bm8GA8dgyk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\nFYXULwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Cauchy distribution\")\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",
    "plt.plot(x, cauchy(5,1)(x), label=\"gamma = 1, mu = 5\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Сравнение распределений"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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r1103GQ6st4Ob+Ref3frOTnX4aM42Xv9lM13uq5x9OIWYYTD/Tfj9FRj6o3tB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\nYKIxZp2IPC8iNzqzjcbes4kDHgXOaTq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N+9aAaYWscXDFTfbkckA+Dc2tfLbnCB9treST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\nrkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambda_ = 10\n",
    "\n",
    "plt.title(\"Comparison of Poisson and Gaussian distribution for lambda = \" + str(lambda_));\n",
    "xg = np.linspace(0, 2*lambda_, 300)\n",
    "xp = range(2*lambda_ + 1)\n",
    "plt.plot(xp, poisson.pmf(xp, lambda_), label=\"Poisson\")\n",
    "plt.plot(xg, gauss(lambda_, np.sqrt(lambda_))(xg), label=\"Normal\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PyElcgGHZVtM3sSWUpD8c2OJ3v9Rb1p4rgJf97qeJSImILBGRs7oRozFhtbWq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\n2vQJE6recCdIs4ZGO6TQHXU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2QH0VNFT53d4DTR2MZJiStX/nzMx3wxZkDoaBh7gk76vJ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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sigma = 1;\n",
    "gamma = 1.75;\n",
    "xg = np.linspace(-4*sigma, 4*sigma)\n",
    "xc = np.linspace(-6*gamma, 6*gamma)\n",
    "plt.title(\"Comparison of Gaussian and Cauchy distribution\");\n",
    "plt.plot(xg, gauss(0, sigma)(xg),label=\"Normal\")\n",
    "plt.plot(xc, cauchy(0, gamma)(xc),label=\"Cauchy\" )\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Центральная предельная теорема"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Центральная предельная теоремма утверждает, что если некоторая случайная величина $x$ имеет распределение со средним $\\mu$ с конечной дисперсией $D$, то сумма большого количества таких случайных величин\n",
    "$\\sum_{i=1}^{n}{x_i}$ будет иметь нормальное распределение со средним $n \\mu$ и дисперсией $n D$ не зависимо от формы исходного распределения.\n",
    "\n",
    "Центральная предельная теорема в общем случае не говорит о том, каким должно быть $n$, обычно это надо определять экспериментально для каждого типа распределения."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-22T06:29+0000",
     "start_time": "2017-09-22T06:29+0000"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Jvn4x9Z98ir2xkTC/MMb4hJLn4wMFXzjrl+upYgiS4C5GjpM5HPTxYWKEc0FL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\nZMdko1B8deorgq+9juacHMaONWIwKNr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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = uniform(-0.5,0.5);# Распределение, над которым мы экспериментируем\n",
    "wind = 1; # ширина окна интегрирования\n",
    "\n",
    "fs = [f];\n",
    "# fs << f;\n",
    "x = np.linspace(-wind, wind, 300)\n",
    "plt.title(\"Central limit theorem\");\n",
    "plt.plot(x, f(x),label=\"Initial distribution\")\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",
    "    plt.plot(x, fs[i](x), label = \"Convolution \"+str(i))\n",
    "\n",
    "\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
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   "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<ipython-input-56-534616c956b3>\u001b[0m in \u001b[0;36m<module>\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": []
  }
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