2Numpy.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# `NumPy`: матрицы и операции над ними\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В этом ноутбуке из сторонних библиотек нам понадобится только `NumPy`. Для удобства импортируем ее под более коротким именем:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Создание матриц"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Приведем несколько способов создания матриц в `NumPy`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Самый простой способ — с помощью функции __`numpy.array(list, dtype=None, ...)`__.\n",
    "\n",
    "В качестве первого аргумента ей надо передать итерируемый объект, элементами которого являются другие итерируемые объекты одинаковой длины и содержащие данные одинакового типа.\n",
    "\n",
    "Второй аргумент является опциональным и определяет тип данных матрицы. Его можно не задавать, тогда тип данных будет определен из типа элементов первого аргумента. При задании этого параметра будет произведена попытка приведения типов.\n",
    "\n",
    "Например, матрицу из списка списков целых чисел можно создать следующим образом:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'>\n",
      "(3,)\n",
      "1 2 3\n",
      "[5 2 3]\n",
      "(2, 3)\n",
      "1 2 4\n",
      "[1 2 3 4]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([1, 2, 3])   # Создаем одномерный массив\n",
    "print(type(a))            # Prints \"<class 'numpy.ndarray'>\"\n",
    "print(a.shape)            # Prints \"(3,)\" - кортеж с размерностями\n",
    "print(a[0], a[1], a[2])   # Prints \"1 2 3\"\n",
    "a[0] = 5                  # Изменяем значение элемента массива\n",
    "print(a)                  # Prints \"[5, 2, 3]\"\n",
    "\n",
    "b = np.array([[1,2,3],[4,5,6]])    # Создаем двухмерный массив\n",
    "print(b.shape)                     # Prints \"(2, 3)\"\n",
    "print(b[0, 0], b[0, 1], b[1, 0])   # Prints \"1 2 4\"\n",
    "print(np.arange(1, 5)) #Cоздает вектор с эелементами от 1 до 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Матрица:\n",
      " [[1 2 3]\n",
      " [2 5 6]\n",
      " [6 7 4]]\n"
     ]
    }
   ],
   "source": [
    "matrix = np.array([[1, 2, 3], [2, 5, 6], [6, 7, 4]])\n",
    "print (\"Матрица:\\n\", matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Второй способ создания — с помощью встроенных функций __`numpy.eye(N, M=None, ...)`__, __`numpy.zeros(shape, ...)`__, __`numpy.ones(shape, ...)`__.\n",
    "\n",
    "Первая функция создает единичную матрицу размера $N \\times M$; если $M$ не задан, то $M = N$. \n",
    "\n",
    "Вторая и третья функции создают матрицы, состоящие целиком из нулей или единиц соответственно. В качестве первого аргумента необходимо задать размерность массива — кортеж целых чисел. В двумерном случае это набор из двух чисел: количество строк и столбцов матрицы.\n",
    "\n",
    "__Примеры:__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Единичная матрица:\n",
      " [[1. 0. 0. 0. 0.]\n",
      " [0. 1. 0. 0. 0.]\n",
      " [0. 0. 1. 0. 0.]\n",
      " [0. 0. 0. 1. 0.]\n",
      " [0. 0. 0. 0. 1.]]\n"
     ]
    }
   ],
   "source": [
    "b = np.eye(5)\n",
    "print (\"Единичная матрица:\\n\", b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Матрица, состоящая из одних единиц:\n",
      " [[1. 1. 1. 1. 1.]\n",
      " [1. 1. 1. 1. 1.]\n",
      " [1. 1. 1. 1. 1.]\n",
      " [1. 1. 1. 1. 1.]\n",
      " [1. 1. 1. 1. 1.]\n",
      " [1. 1. 1. 1. 1.]\n",
      " [1. 1. 1. 1. 1.]]\n"
     ]
    }
   ],
   "source": [
    "c = np.ones((7, 5))\n",
    "print (\"Матрица, состоящая из одних единиц:\\n\", c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[7 7]\n",
      " [7 7]]\n",
      "[[0.25744383 0.48056466]\n",
      " [0.13767881 0.40578168]]\n"
     ]
    }
   ],
   "source": [
    "d = np.full((2,2), 7)  # Создает матрицу (1, 2) заполненую заданным значением\n",
    "print(d)               # Prints \"[[ 7.  7.]\n",
    "                       #          [ 7.  7.]]\"\n",
    "\n",
    "e = np.random.random((2,2))  # Создает еденичную матрицу (2, 2) заполненую случаными числами (0, 1)\n",
    "print(e)                     # Might print \"[[ 0.91940167  0.08143941]\n",
    "                             #               [ 0.68744134  0.87236687]]\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Обратите внимание: размерность массива задается не двумя аргументами функции, а одним — кортежем!__ \n",
    "\n",
    "Вот так —  __`np.ones(7, 5)`__ — создать массив не получится, так как функции в качестве параметра `shape` передается `7`, а не кортеж `(7, 5)`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "И, наконец, третий способ — с помощью функции __`numpy.arange([start, ]stop, [step, ], ...)`__, которая создает одномерный массив последовательных чисел из промежутка __`[start, stop)`__ с заданным шагом __`step`__, и _метода_ __`array.reshape(shape)`__. \n",
    "\n",
    "Параметр __`shape`__, как и в предыдущем примере, задает размерность матрицы (кортеж чисел). Логика работы метода ясна из следующего примера:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Вектор-столбец:\n",
      " [ 0  2  4  6  8 10 12 14 16 18 20 22]\n"
     ]
    }
   ],
   "source": [
    "v = np.arange(0, 24, 2)\n",
    "print (\"Вектор-столбец:\\n\", v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Матрица:\n",
      " [[ 0  2  4  6]\n",
      " [ 8 10 12 14]\n",
      " [16 18 20 22]]\n"
     ]
    }
   ],
   "source": [
    "d = v.reshape((3, 4))\n",
    "print (\"Матрица:\\n\", d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Более подробно о том, как создавать массивы в `NumPy`, \n",
    "см. [документацию](http://docs.scipy.org/doc/numpy-1.10.1/user/basics.creation.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Индексирование "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для получения элементов матрицы можно использовать несколько способов. Рассмотрим самые простые из них."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для удобства напомним, как выглядит матрица __d__:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Матрица:\n",
      " [[ 0  2  4  6]\n",
      " [ 8 10 12 14]\n",
      " [16 18 20 22]]\n"
     ]
    }
   ],
   "source": [
    "print (\"Матрица:\\n\", d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Элемент на пересечении строки __`i`__ и столбца __`j`__ можно получить с помощью выражения __`array[i, j]`__. \n",
    "\n",
    "__Обратите внимание:__ строки и столбцы нумеруются с нуля!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Второй элемент третьей строки матрицы: 18\n"
     ]
    }
   ],
   "source": [
    "print (\"Второй элемент третьей строки матрицы:\", d[2, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Из матрицы можно получать целые строки или столбцы с помощью выражений __`array[i, :]`__ или __`array[:, j]`__ соответственно:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Вторая строка матрицы d:\n",
      " [ 8 10 12 14]\n",
      "Четвертый столбец матрицы d:\n",
      " [ 6 14 22]\n"
     ]
    }
   ],
   "source": [
    "print (\"Вторая строка матрицы d:\\n\", d[1, :])\n",
    "print (\"Четвертый столбец матрицы d:\\n\", d[:, 3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Еще один способ получения элементов — с помощью выражения __`array[list1, list2]`__, где __`list1`__, __`list2`__ — некоторые списки целых чисел. При такой адресации одновременно просматриваются оба списка и возвращаются элементы матрицы с соответствующими координатами. Следующий пример более понятно объясняет механизм работы такого индексирования:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Элементы матрицы d с координатами (1, 2) и (0, 3):\n",
      " [12  6]\n"
     ]
    }
   ],
   "source": [
    "print (\"Элементы матрицы d с координатами (1, 2) и (0, 3):\\n\", d[[1, 0], [2, 3]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2 3]\n",
      " [6 7]]\n",
      "2\n",
      "77\n"
     ]
    }
   ],
   "source": [
    "# Slicing\n",
    "\n",
    "# Создадим матрицу (3, 4)\n",
    "# [[ 1  2  3  4]\n",
    "#  [ 5  6  7  8]\n",
    "#  [ 9 10 11 12]]\n",
    "a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])\n",
    "\n",
    "# Используя слайсинг, созадим матрицу b из элементов матрицы а\n",
    "# будем использовать 0 и 1 строку, а так же 1 и 2 столебц\n",
    "# [[2 3]\n",
    "#  [6 7]]\n",
    "b = a[:2, 1:3]\n",
    "print(b)\n",
    "\n",
    "# ОБРАТИТЕ ВНИМАНИЕ НА ИЗМЕНЕНИЕ ИСХОДОЙ МАТРИЦЫ\n",
    "print(a[0, 1])   # Prints \"2\"\n",
    "b[0, 0] = 77     # b[0, 0] is the same piece of data as a[0, 1]\n",
    "print(a[0, 1])   # Prints \"77\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2]\n",
      " [3 4]\n",
      " [5 6]]\n",
      "\n",
      "[1 4 5]\n",
      "\n",
      "[1 4 5]\n"
     ]
    }
   ],
   "source": [
    "# Integer array indexing\n",
    "\n",
    "a = np.array([[1,2], [3, 4], [5, 6]])\n",
    "print(a)\n",
    "print()\n",
    "\n",
    "# Пример Integer array indexing \n",
    "# В результате получится массив размерности (3,)\n",
    "# Обратите внимание, что до запятой идут индексы строк, после - столбцов\n",
    "print(a[[0, 1, 2], [0, 1, 0]])  # Prints \"[1 4 5]\"\n",
    "print()\n",
    "\n",
    "# По-другому пример можно записать так\n",
    "print(np.array([a[0, 0], a[1, 1], a[2, 0]]))  # Prints \"[1 4 5]\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Примеры использования слайсинга:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  2  3]\n",
      " [ 4  5  6]\n",
      " [ 7  8  9]\n",
      " [10 11 12]]\n",
      "[ 1  6  7 11]\n",
      "\n",
      "[[11  2  3]\n",
      " [ 4  5 16]\n",
      " [17  8  9]\n",
      " [10 21 12]]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# Создадим новый маассив, из которого будем выбирать эллементы\n",
    "a = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])\n",
    "\n",
    "print(a)  # prints \"array([[ 1,  2,  3],\n",
    "          #                [ 4,  5,  6],\n",
    "          #                [ 7,  8,  9],\n",
    "          #                [10, 11, 12]])\"\n",
    "\n",
    "# Создадим массив индексов\n",
    "b = np.array([0, 2, 0, 1])\n",
    "\n",
    "# Выберем из каждой строки элемент с индексом из b (индекс столбца берется из b) \n",
    "print(a[np.arange(4), b])  # Prints \"[ 1  6  7 11]\"\n",
    "print()\n",
    "\n",
    "# Добавим к этим элементам 10\n",
    "a[np.arange(4), b] += 10\n",
    "\n",
    "print(a)  # prints \"array([[11,  2,  3],\n",
    "          #                [ 4,  5, 16],\n",
    "          #                [17,  8,  9],\n",
    "          #                [10, 21, 12]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[False False]\n",
      " [ True  True]\n",
      " [ True  True]]\n",
      "\n",
      "[3 4 5 6]\n",
      "[3 4 5 6]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([[1,2], [3, 4], [5, 6]])\n",
    "\n",
    "bool_idx = (a > 2)   # Найдем эллементы матрицы a, которые больше 2\n",
    "                     # В результате получим матрицу b, такой же размерности, как и a\n",
    "\n",
    "print(bool_idx)      # Prints \"[[False False]\n",
    "print()              #          [ True  True]\n",
    "                     #          [ True  True]]\"\n",
    "\n",
    "# Воспользуемся полученным массивом для создания нового массива, ранга 1\n",
    "print(a[bool_idx])  # Prints \"[3 4 5 6]\"\n",
    "\n",
    "# Аналогично\n",
    "print(a[a > 2])     # Prints \"[3 4 5 6]\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5 6 7 8] (4,)\n",
      "[[5 6 7 8]] (1, 4)\n"
     ]
    }
   ],
   "source": [
    "#Помните, что вы можете пользоваться сразу несколькими типами индексирования\n",
    "a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])\n",
    "\n",
    "row_r1 = a[1, :]\n",
    "row_r2 = a[1:2, :] \n",
    "print(row_r1, row_r1.shape)  # Prints \"[5 6 7 8] (4,)\"\n",
    "print(row_r2, row_r2.shape)  # Prints \"[[5 6 7 8]] (1, 4)\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Более подробно о различных способах индексирования в массивах\n",
    "см. [документацию](http://docs.scipy.org/doc/numpy/reference/arrays.indexing.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Векторы, вектор-строки и вектор-столбцы"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Следующие два способа задания массива кажутся одинаковыми: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([1, 2, 3])\n",
    "b = np.array([[1], [2], [3]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Однако, на самом деле, это задание одномерного массива (то есть _вектора_) и двумерного массива:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Вектор:\n",
      " [1 2 3]\n",
      "Его размерность:\n",
      " (3,)\n",
      "Двумерный массив:\n",
      " [[1]\n",
      " [2]\n",
      " [3]]\n",
      "Его размерность:\n",
      " (3, 1)\n"
     ]
    }
   ],
   "source": [
    "print (\"Вектор:\\n\", a)\n",
    "print (\"Его размерность:\\n\", a.shape)\n",
    "print (\"Двумерный массив:\\n\", b)\n",
    "print (\"Его размерность:\\n\", b.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Обратите внимание:__ _вектор_ (одномерный массив) и _вектор-столбец_ или _вектор-строка_ (двумерные массивы) являются различными объектами в `NumPy`, хотя математически задают один и тот же объект. В случае одномерного массива кортеж __`shape`__ состоит из одного числа и имеет вид __`(n,)`__, где __`n`__ — длина вектора. В случае двумерных векторов в __`shape`__ присутствует еще одна размерность, равная единице. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В большинстве случаев неважно, какое представление использовать, потому что часто срабатывает приведение типов. Но некоторые операции не работают для одномерных массивов. Например, транспонирование (о нем пойдет речь ниже):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = a.T\n",
    "b = b.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Вектор не изменился:\n",
      " [1 2 3]\n",
      "Его размерность также не изменилась:\n",
      " (3,)\n",
      "Транспонированный двумерный массив:\n",
      " [[1 2 3]]\n",
      "Его размерность изменилась:\n",
      " (1, 3)\n"
     ]
    }
   ],
   "source": [
    "print (\"Вектор не изменился:\\n\", a)\n",
    "print (\"Его размерность также не изменилась:\\n\", a.shape)\n",
    "print (\"Транспонированный двумерный массив:\\n\", b)\n",
    "print (\"Его размерность изменилась:\\n\", b.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Datatypes\n",
    "Все элементы в массиве numpy принадлежат одному типу. В этом плане массивы ближе к C, чем к привычным вам листам питона. Numpy имеет множество встренных типов, подходящих для решения большинства задач."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "int32\n",
      "float64\n",
      "int64\n"
     ]
    }
   ],
   "source": [
    "x = np.array([1, 2])   # Автоматический выбор типа\n",
    "print(x.dtype)         # Prints \"int64\"\n",
    "\n",
    "x = np.array([1.0, 2.0])   # Автоматический выбор типа\n",
    "print(x.dtype)             # Prints \"float64\"\n",
    "\n",
    "x = np.array([1, 2], dtype=np.int64)   # Принудительное выставление типа\n",
    "print(x.dtype)                         # Prints \"int64\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Математические операции\n",
    "К массивам (матрицам) можно применять известные вам математические операции. Следут понимать, что при этом у элементов должны быть схожие размерности. Поведение в случае не совпадения размерностей хорошо описанно в документации numpy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([[1,2],[3,4]], dtype=np.float64)\n",
    "y = np.array([[5,6],[7,8]], dtype=np.float64)\n",
    "arr = np.array([1, 2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 6.  8.]\n",
      " [10. 12.]]\n",
      "\n",
      "[[ 6.  8.]\n",
      " [10. 12.]]\n",
      "С числом\n",
      "[[2. 3.]\n",
      " [4. 5.]]\n",
      "C массивом другой размерности\n",
      "[[2. 4.]\n",
      " [4. 6.]]\n"
     ]
    }
   ],
   "source": [
    "# Сложение происходит поэлеметно\n",
    "\n",
    "# [[ 6.0  8.0]\n",
    "#  [10.0 12.0]]\n",
    "print(x + y)\n",
    "print()\n",
    "print(np.add(x, y))\n",
    "print('С числом')\n",
    "print(x + 1)\n",
    "print('C массивом другой размерности')\n",
    "print(x + arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-4. -4.]\n",
      " [-4. -4.]]\n",
      "[[-4. -4.]\n",
      " [-4. -4.]]\n"
     ]
    }
   ],
   "source": [
    "# Вычитание\n",
    "print(x - y)\n",
    "print(np.subtract(x, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.2        0.33333333]\n",
      " [0.42857143 0.5       ]]\n",
      "[[0.2        0.33333333]\n",
      " [0.42857143 0.5       ]]\n"
     ]
    }
   ],
   "source": [
    "# Деление\n",
    "# [[ 0.2         0.33333333]\n",
    "#  [ 0.42857143  0.5       ]]\n",
    "print(x / y)\n",
    "print(np.divide(x, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.         1.41421356]\n",
      " [1.73205081 2.        ]]\n"
     ]
    }
   ],
   "source": [
    "# Другие функции\n",
    "# [[ 1.          1.41421356]\n",
    "#  [ 1.73205081  2.        ]]\n",
    "print(np.sqrt(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. Умножение матриц и столбцов"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Напоминание теории.__ Операция __умножения__ определена для двух матриц, таких что число столбцов первой равно числу строк второй. \n",
    "\n",
    "Пусть матрицы $A$ и $B$ таковы, что $A \\in \\mathbb{R}^{n \\times k}$ и $B \\in \\mathbb{R}^{k \\times m}$. __Произведением__ матриц $A$ и $B$ называется матрица $C$, такая что $c_{ij} = \\sum_{r=1}^{k} a_{ir}b_{rj}$, где $c_{ij}$ — элемент матрицы $C$, стоящий на пересечении строки с номером $i$ и столбца с номером $j$.\n",
    "\n",
    "В `NumPy` произведение матриц вычисляется с помощью функции __`numpy.dot(a, b, ...)`__ или с помощью _метода_ __`array1.dot(array2)`__, где __`array1`__ и __`array2`__ — перемножаемые матрицы."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([[1, 0], [0, 1]])\n",
    "b = np.array([[4, 1], [2, 2]])\n",
    "r1 = np.dot(a, b)\n",
    "r2 = a.dot(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Матрица A:\n",
      " [[1 0]\n",
      " [0 1]]\n",
      "Матрица B:\n",
      " [[4 1]\n",
      " [2 2]]\n",
      "Результат умножения функцией:\n",
      " [[4 1]\n",
      " [2 2]]\n",
      "Результат умножения методом:\n",
      " [[4 1]\n",
      " [2 2]]\n"
     ]
    }
   ],
   "source": [
    "print (\"Матрица A:\\n\", a)\n",
    "print (\"Матрица B:\\n\", b)\n",
    "print (\"Результат умножения функцией:\\n\", r1)\n",
    "print (\"Результат умножения методом:\\n\", r2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Матрицы в `NumPy` можно умножать и на векторы:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = np.array([1, 2])\n",
    "r3 = b.dot(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Матрица:\n",
      " [[4 1]\n",
      " [2 2]]\n",
      "Вектор:\n",
      " [1 2]\n",
      "Результат умножения:\n",
      " [6 6]\n"
     ]
    }
   ],
   "source": [
    "print (\"Матрица:\\n\", b)\n",
    "print (\"Вектор:\\n\", c)\n",
    "print (\"Результат умножения:\\n\", r3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Обратите внимание:__ операция __`*`__ производит над матрицами покоординатное умножение, а не матричное!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = a * b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Матрица A:\n",
      " [[1 0]\n",
      " [0 1]]\n",
      "Матрица B:\n",
      " [[4 1]\n",
      " [2 2]]\n",
      "Результат покоординатного умножения через операцию *:\n",
      " [[4 0]\n",
      " [0 2]]\n"
     ]
    }
   ],
   "source": [
    "print (\"Матрица A:\\n\", a)\n",
    "print (\"Матрица B:\\n\", b)\n",
    "print (\"Результат покоординатного умножения через операцию *:\\n\", r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Более подробно о матричном умножении в `NumPy`\n",
    "см. [документацию](http://docs.scipy.org/doc/numpy-1.10.0/reference/routines.linalg.html#matrix-and-vector-products)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7. Объединение массивов\n",
    "Массивы можно Объединенять. Есть горизонтальное и вертикальное объединение.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[4. 0.]\n",
      " [1. 4.]]\n",
      "[[9. 7.]\n",
      " [2. 6.]]\n",
      "\n",
      "[[4. 0.]\n",
      " [1. 4.]\n",
      " [9. 7.]\n",
      " [2. 6.]]\n",
      "\n",
      "[[4. 0. 9. 7.]\n",
      " [1. 4. 2. 6.]]\n"
     ]
    }
   ],
   "source": [
    "a = np.floor(10*np.random.random((2,2)))\n",
    "b = np.floor(10*np.random.random((2,2)))\n",
    "\n",
    "print(a)\n",
    "print(b)\n",
    "print()\n",
    "\n",
    "\n",
    "print(np.vstack((a,b)))\n",
    "print()\n",
    "\n",
    "print(np.hstack((a,b)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Массивы можно переформировать при помощи метода, который задает новый многомерный массив. Следуя следующему примеру, мы переформатируем одномерный массив из десяти элементов во двумерный массив, состоящий из пяти строк и двух столбцов:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 1. 2. 3. 4. 5. 6. 7. 8. 9.]\n",
      "\n",
      "[[0. 1.]\n",
      " [2. 3.]\n",
      " [4. 5.]\n",
      " [6. 7.]\n",
      " [8. 9.]]\n",
      "\n",
      "[0. 1. 2. 3. 4. 5. 6. 7. 8. 9.]\n",
      "[0. 1. 2. 3. 4. 5. 6. 7. 8. 9.]\n",
      "[[0.]\n",
      " [1.]\n",
      " [2.]\n",
      " [3.]\n",
      " [4.]\n",
      " [5.]\n",
      " [6.]\n",
      " [7.]\n",
      " [8.]\n",
      " [9.]]\n",
      "[[0. 1. 2. 3. 4. 5. 6. 7. 8. 9.]]\n"
     ]
    }
   ],
   "source": [
    "a = np.array(range(10), float)\n",
    "print(a)\n",
    "print()\n",
    "\n",
    "# Превратим в матрицу\n",
    "a = a.reshape((5, 2))\n",
    "print(a)\n",
    "print()\n",
    "\n",
    "# Вернем обратно\n",
    "print(a.flatten())\n",
    "\n",
    "# Другой вариант\n",
    "print(a.reshape((-1)))\n",
    "# Превратим в марицу (9, 1)\n",
    "print(a.reshape((-1, 1)))\n",
    "# Превратим в марицу (1, 9)\n",
    "print(a.reshape((1, -1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Задания: (Блок 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задание 1: \n",
    "Решите без использования циклов средставми NumPy (каждый пункт решается в 1-2 строчки)\n",
    "1. Создайте вектор с эелементами от 12 до 42\n",
    "2. Создайте вектор из нулей длины 12, но его пятый елемент должен быть равен 1\n",
    "3. Создайте матрицу (3, 3), заполненую от 0 до 8\n",
    "4. Найдите все положительные числа в np.array([1,2,0,0,4,0])\n",
    "5. Умножьте матрицу размерности (5, 3) на (3, 2)\n",
    "6. Создайте матрицу (10, 10) так, чтобы на границе были 0, а внтури 1\n",
    "7. Создайте рандомный вектор и отсортируйте его\n",
    "8. Каков эквивалент функции enumerate для numpy массивов?\n",
    "9. *Создайте рандомный вектор и выполните нормализацию столбцов (из каждого столбца вычесть среднее этого столбца, из каждого столбца вычесть sd этого столбца)\n",
    "10. *Для заданного числа найдите ближайший к нему элемент в векторе \n",
    "11. *Найдите N наибольших значений в векторе"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "vec_1 = np.arange(12, 44, 2)\n",
    "vec_2 = np.arange(12)\n",
    "vec_2 = np.zeros_like(vec_2)\n",
    "vec_2[4] = 1\n",
    "mat_3 = np.arange(9)\n",
    "mat_3 = mat_3.reshape((3, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42]\n",
      "[0 0 0 0 1 0 0 0 0 0 0 0]\n",
      "[[0 1 2]\n",
      " [3 4 5]\n",
      " [6 7 8]]\n"
     ]
    }
   ],
   "source": [
    "print(vec_1)\n",
    "print(vec_2)\n",
    "print(mat_3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "vec_4 = np.array([1,2,0,0,4,0])\n",
    "for i in vec_4:\n",
    "    if i>0:\n",
    "        print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 10  13]\n",
      " [ 28  40]\n",
      " [ 46  67]\n",
      " [ 64  94]\n",
      " [ 82 121]]\n"
     ]
    }
   ],
   "source": [
    "mat_51 = np.arange(15)\n",
    "mat_51 = mat_51.reshape((5,3))\n",
    "mat_52 = np.arange(6)\n",
    "mat_52 = mat_52.reshape((3,2))\n",
    "result = mat_51 @ mat_52\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 1. 1. 1. 1. 1. 1. 1. 1. 0.]\n",
      " [0. 1. 1. 1. 1. 1. 1. 1. 1. 0.]\n",
      " [0. 1. 1. 1. 1. 1. 1. 1. 1. 0.]\n",
      " [0. 1. 1. 1. 1. 1. 1. 1. 1. 0.]\n",
      " [0. 1. 1. 1. 1. 1. 1. 1. 1. 0.]\n",
      " [0. 1. 1. 1. 1. 1. 1. 1. 1. 0.]\n",
      " [0. 1. 1. 1. 1. 1. 1. 1. 1. 0.]\n",
      " [0. 1. 1. 1. 1. 1. 1. 1. 1. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "mat_6 = np.ones((10,10))\n",
    "mat_6[:10,:1] = 0\n",
    "mat_6[:1,:10] = 0\n",
    "mat_6[:10,9] = 0\n",
    "mat_6[9,:10] = 0\n",
    "print(mat_6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.42285329 0.83524622 0.44042705 0.75412893 0.84078913 0.73904361\n",
      "  0.78118586 0.46654897 0.3052399  0.60999334]]\n"
     ]
    }
   ],
   "source": [
    "mat_7 = np.random.random((1,10))\n",
    "print(mat_7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# numpy.ndenumerate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задание 2:\n",
    "**Напишите полностью векторизованный вариант**  \n",
    "Дан трёхмерный массив, содержащий изображение, размера (height, width, numChannels), а также вектор длины numChannels. Сложить каналы изображения с указанными весами, и вернуть результат в\n",
    "виде матрицы размера (height, width). Считать реальное изображение можно при помощи функции\n",
    "`scipy.misc.imread` (если изображение не в формате png, установите пакет pillow: `conda install pillow`).\n",
    "Преобразуйте цветное изображение в оттенки серого, использовав коэффициенты np.array([0.299, 0.587,\n",
    "0.114])."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# загружаем картинку которая изображение вернет в виде трехмерного массива ,свертку проводим по image.dot([],(2,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "import imageio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "image = imageio.imread('ixCczpxl51M.jpg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(432, 768, 3)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "image.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "image = image.dot([0.299, 0.587, 0.114])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(432, 768)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "image.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x158abe61bc8>"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1)\n",
    "\n",
    "plt.imshow(image)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8. Транспонирование матриц"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Напоминание теории.__ __Транспонированной матрицей__ $A^{T}$ называется матрица, полученная из исходной матрицы $A$ заменой строк на столбцы. Формально: элементы матрицы $A^{T}$ определяются как $a^{T}_{ij} = a_{ji}$, где $a^{T}_{ij}$ — элемент матрицы $A^{T}$, стоящий на пересечении строки с номером $i$ и столбца с номером $j$.\n",
    "\n",
    "В `NumPy` транспонированная матрица вычисляется с помощью функции __`numpy.transpose()`__ или с помощью _метода_ __`array.T`__, где __`array`__ — нужный двумерный массив.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([[1, 2], [3, 4]])\n",
    "b = np.transpose(a)\n",
    "c = a.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Матрица:\n",
      " [[1 2]\n",
      " [3 4]]\n",
      "Транспонирование функцией:\n",
      " [[1 3]\n",
      " [2 4]]\n",
      "Транспонирование методом:\n",
      " [[1 3]\n",
      " [2 4]]\n"
     ]
    }
   ],
   "source": [
    "print (\"Матрица:\\n\", a)\n",
    "print (\"Транспонирование функцией:\\n\", b)\n",
    "print (\"Транспонирование методом:\\n\",  c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "См. более подробно о \n",
    "[numpy.transpose()](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.transpose.html) и \n",
    "[array.T](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.ndarray.T.html) в `NumPy`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В следующих разделах активно используется модуль __`numpy.linalg`__, реализующий некоторые приложения линейной алгебры. Более подробно о функциях, описанных ниже, и различных других функциях этого модуля можно посмотреть в его [документации](http://docs.scipy.org/doc/numpy-1.10.0/reference/routines.linalg.html#linear-algebra-numpy-linalg)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 9. Определитель матрицы"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Напоминание теории.__ Для квадратных матриц существует понятие __определителя__.\n",
    "\n",
    "Пусть $A$ — квадратная матрица. __Определителем__ (или __детерминантом__) матрицы $A \\in \\mathbb{R}^{n \\times n}$ назовем число \n",
    "\n",
    "$$\\det A = \\sum_{\\alpha_{1}, \\alpha_{2}, \\dots, \\alpha_{n}} (-1)^{N(\\alpha_{1}, \\alpha_{2}, \\dots, \\alpha_{n})} \\cdot a_{\\alpha_{1} 1} \\cdot \\cdot \\cdot a_{\\alpha_{n} n},\n",
    "$$\n",
    "где $\\alpha_{1}, \\alpha_{2}, \\dots, \\alpha_{n}$ — перестановка чисел от $1$ до $n$, $N(\\alpha_{1}, \\alpha_{2}, \\dots, \\alpha_{n})$ — число инверсий в перестановке, суммирование ведется по всем возможным перестановкам длины $n$.\n",
    "\n",
    "_Не стоит расстраиваться, если это определение понятно не до конца — в дальнейшем в таком виде оно не понадобится._\n",
    "\n",
    "Например, для матрицы размера $2 \\times 2$ получается:\n",
    "\n",
    "$$\\det \\left( \\begin{array}{cc} a_{11} & a_{12} \\\\ a_{21} & a_{22}  \\end{array} \\right) = a_{11} a_{22} - a_{12} a_{21}\n",
    "$$\n",
    "\n",
    "\n",
    "Вычисление определителя матрицы по определению требует порядка $n!$ операций, поэтому разработаны методы, которые позволяют вычислять его быстро и эффективно.\n",
    "\n",
    "В `NumPy` определитель матрицы вычисляется с помощью функции __`numpy.linalg.det(a)`__, где __`a`__ — исходная матрица."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([[1, 2, 1], [1, 1, 4], [2, 3, 6]], dtype=np.float32)\n",
    "det = np.linalg.det(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Матрица:\n",
      " [[1. 2. 1.]\n",
      " [1. 1. 4.]\n",
      " [2. 3. 6.]]\n",
      "Определитель:\n",
      " -1.0\n"
     ]
    }
   ],
   "source": [
    "print (\"Матрица:\\n\", a)\n",
    "print (\"Определитель:\\n\", det)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Рассмотрим одно интересное свойство определителя. Пусть у нас есть параллелограмм с углами в точках $(0, 0), (c,d), (a+c, b+d), (a, b)$ (углы даны в порядке обхода по часовой стрелке). Тогда площадь этого параллелограмма можно вычислить как модуль определителя матрицы $\\left( \\begin{array}{cc} a & c \\\\ b & d  \\end{array} \\right)$. Похожим образом можно выразить и объем параллелепипеда через определитель матрицы размера $3 \\times 3$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10. Ранг матрицы"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Напоминание теории.__ __Рангом матрицы__ $A$ называется максимальное число линейно независимых строк (столбцов) этой матрицы.\n",
    "\n",
    "В `NumPy` ранг матрицы вычисляется с помощью функции __`numpy.linalg.matrix_rank(M, tol=None)`__, где __`M`__ — матрица, __`tol`__ — параметр, отвечающий за некоторую точность вычисления. В простом случае можно его не задавать, и функция сама определит подходящее значение этого параметра."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([[1, 2, 3], [1, 1, 1], [2, 2, 2]])\n",
    "r = np.linalg.matrix_rank(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Матрица:\n",
      " [[1 2 3]\n",
      " [1 1 1]\n",
      " [2 2 2]]\n",
      "Ранг матрицы: 2\n"
     ]
    }
   ],
   "source": [
    "print (\"Матрица:\\n\", a)\n",
    "print (\"Ранг матрицы:\", r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "С помощью вычисления ранга матрицы можно проверять линейную независимость системы векторов.\n",
    "\n",
    "Допустим, у нас есть несколько векторов. Составим из них матрицу, где наши векторы будут являться строками. Понятно, что векторы линейно независимы тогда и только тогда, когда ранг полученной матрицы совпадает с числом векторов. Приведем пример:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([1, 2, 3])\n",
    "b = np.array([1, 1, 1])\n",
    "c = np.array([2, 3, 5])\n",
    "m = np.array([a, b, c])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "print (np.linalg.matrix_rank(m) == m.shape[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 11. Системы линейных уравнений"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Напоминание теории.__ __Системой линейных алгебраических уравнений__ называется система вида $Ax = b$, где $A \\in \\mathbb{R}^{n \\times m}, x \\in \\mathbb{R}^{m \\times 1}, b \\in \\mathbb{R}^{n \\times 1}$. В случае квадратной невырожденной матрицы $A$ решение системы единственно.\n",
    "\n",
    "В `NumPy` решение такой системы можно найти с помощью функции __`numpy.linalg.solve(a, b)`__, где первый аргумент — матрица $A$, второй — столбец $b$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([[3, 1], [1, 2]])\n",
    "b = np.array([9, 8])\n",
    "x = np.linalg.solve(a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Матрица A:\n",
      " [[3 1]\n",
      " [1 2]]\n",
      "Вектор b:\n",
      " [9 8]\n",
      "Решение системы:\n",
      " [2. 3.]\n"
     ]
    }
   ],
   "source": [
    "print (\"Матрица A:\\n\", a)\n",
    "print (\"Вектор b:\\n\", b)\n",
    "print (\"Решение системы:\\n\", x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Убедимся, что вектор __x__ действительно является решением системы:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[9. 8.]\n"
     ]
    }
   ],
   "source": [
    "print (a.dot(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Бывают случаи, когда решение системы не существует. Но хотелось бы все равно \"решить\" такую систему. Логичным кажется искать такой вектор $x$, который минимизирует выражение $\\left\\Vert Ax - b\\right\\Vert^{2}$ — так мы приблизим выражение $Ax$ к $b$.\n",
    "\n",
    "В `NumPy` такое псевдорешение можно искать с помощью функции __`numpy.linalg.lstsq(a, b, ...)`__, где первые два аргумента такие же, как и для функции __`numpy.linalg.solve()`__. \n",
    "Помимо решения функция возвращает еще три значения, которые нам сейчас не понадобятся."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([[0, 1], [1, 1], [2, 1], [3, 1]])\n",
    "b = np.array([-1, 0.2, 0.9, 2.1])\n",
    "x, res, r, s = np.linalg.lstsq(a, b, rcond=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Матрица A:\n",
      " [[0 1]\n",
      " [1 1]\n",
      " [2 1]\n",
      " [3 1]]\n",
      "Вектор b:\n",
      " [-1.   0.2  0.9  2.1]\n",
      "Псевдорешение системы:\n",
      " [ 1.   -0.95]\n"
     ]
    }
   ],
   "source": [
    "print (\"Матрица A:\\n\", a)\n",
    "print (\"Вектор b:\\n\", b)\n",
    "print (\"Псевдорешение системы:\\n\", x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12. Обращение матриц"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Напоминание теории.__  Для квадратных невырожденных матриц определено понятие __обратной__ матрицы. \n",
    "\n",
    "Пусть $A$ — квадратная невырожденная матрица. Матрица $A^{-1}$ называется __обратной матрицей__ к $A$, если \n",
    "\n",
    "$$AA^{-1} = A^{-1}A = I,\n",
    "$$ \n",
    "\n",
    "где $I$ — единичная матрица.\n",
    "\n",
    "В `NumPy` обратные матрицы вычисляются с помощью функции __`numpy.linalg.inv(a)`__, где __`a`__ — исходная матрица."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([[1, 2, 1], [1, 1, 4], [2, 3, 6]], dtype=np.float32)\n",
    "b = np.linalg.inv(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Матрица A:\n",
      " [[1. 2. 1.]\n",
      " [1. 1. 4.]\n",
      " [2. 3. 6.]]\n",
      "Обратная матрица к A:\n",
      " [[ 6.  9. -7.]\n",
      " [-2. -4.  3.]\n",
      " [-1. -1.  1.]]\n",
      "Произведение A на обратную должна быть единичной:\n",
      " [[1. 0. 0.]\n",
      " [0. 1. 0.]\n",
      " [0. 0. 1.]]\n"
     ]
    }
   ],
   "source": [
    "print (\"Матрица A:\\n\", a)\n",
    "print (\"Обратная матрица к A:\\n\", b)\n",
    "print (\"Произведение A на обратную должна быть единичной:\\n\", a.dot(b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 13. Собственные числа и собственные вектора матрицы"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Напоминание теории.__ Для квадратных матриц определены понятия __собственного вектора__ и __собственного числа__.\n",
    "\n",
    "Пусть $A$ — квадратная матрица и $A \\in \\mathbb{R}^{n \\times n}$. __Собственным вектором__ матрицы $A$ называется такой ненулевой вектор $x \\in \\mathbb{R}^{n}$, что для некоторого $\\lambda \\in \\mathbb{R}$ выполняется равенство $Ax = \\lambda x$. При этом $\\lambda$ называется __собственным числом__ матрицы $A$. Собственные числа и собственные векторы матрицы играют важную роль в теории линейной алгебры и ее практических приложениях.\n",
    "\n",
    "В `NumPy` собственные числа и собственные векторы матрицы вычисляются с помощью функции __`numpy.linalg.eig(a)`__, где __`a`__ — исходная матрица. В качестве результата эта функция выдает одномерный массив __`w`__ собственных чисел и двумерный массив __`v`__, в котором по столбцам записаны собственные вектора, так что вектор __`v[:, i]`__ соотвествует собственному числу __`w[i]`__."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([[-1, -6], [2, 6]])\n",
    "w, v = np.linalg.eig(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Матрица A:\n",
      " [[-1 -6]\n",
      " [ 2  6]]\n",
      "Собственные числа:\n",
      " [2. 3.]\n",
      "Собственные векторы:\n",
      " [[-0.89442719  0.83205029]\n",
      " [ 0.4472136  -0.5547002 ]]\n"
     ]
    }
   ],
   "source": [
    "print (\"Матрица A:\\n\", a)\n",
    "print (\"Собственные числа:\\n\", w)\n",
    "print (\"Собственные векторы:\\n\", v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Обратите внимание:__ у вещественной матрицы собственные значения или собственные векторы могут быть комплексными."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 14. Расстояния между векторами"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Вспомним некоторые нормы, которые можно ввести в пространстве $\\mathbb{R}^{n}$, и рассмотрим, с помощью каких библиотек и функций их можно вычислять в `NumPy`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### p-норма"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "p-норма (норма Гёльдера) для вектора $x = (x_{1}, \\dots, x_{n}) \\in \\mathbb{R}^{n}$ вычисляется по формуле:\n",
    "\n",
    "$$\n",
    "\\left\\Vert x \\right\\Vert_{p} = \\left( \\sum_{i=1}^n \\left| x_{i} \\right|^{p} \\right)^{1 / p},~p \\geq 1.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В частных случаях при:\n",
    "* $p = 1$ получаем $\\ell_{1}$ норму\n",
    "* $p = 2$ получаем $\\ell_{2}$ норму"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Далее нам понабится модуль `numpy.linalg`, реализующий некоторые приложения линейной алгебры. Для вычисления различных норм мы используем функцию __`numpy.linalg.norm(x, ord=None, ...)`__, где __`x`__ — исходный вектор, __`ord`__ — параметр, определяющий норму (мы рассмотрим два варианта его значений — 1 и 2). Импортируем эту функцию:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.linalg import norm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $\\ell_{1}$ норма"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\ell_{1}$ норма \n",
    "(также известная как [манхэттенское расстояние](https://ru.wikipedia.org/wiki/%D0%A0%D0%B0%D1%81%D1%81%D1%82%D0%BE%D1%8F%D0%BD%D0%B8%D0%B5_%D0%B3%D0%BE%D1%80%D0%BE%D0%B4%D1%81%D0%BA%D0%B8%D1%85_%D0%BA%D0%B2%D0%B0%D1%80%D1%82%D0%B0%D0%BB%D0%BE%D0%B2))\n",
    "для вектора $x = (x_{1}, \\dots, x_{n}) \\in \\mathbb{R}^{n}$ вычисляется по формуле:\n",
    "\n",
    "$$\n",
    " \\left\\Vert x \\right\\Vert_{1} = \\sum_{i=1}^n \\left| x_{i} \\right|.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ей в функции __`numpy.linalg.norm(x, ord=None, ...)`__ соответствует параметр __`ord=1`__."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Вектор a: [ 1  2 -3]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([1, 2, -3])\n",
    "print('Вектор a:', a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L1 норма вектора a:\n",
      " 6.0\n"
     ]
    }
   ],
   "source": [
    "print('L1 норма вектора a:\\n', norm(a, ord=1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $\\ell_{2}$ норма"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\ell_{2}$ норма (также известная как евклидова норма)\n",
    "для вектора $x = (x_{1}, \\dots, x_{n}) \\in \\mathbb{R}^{n}$ вычисляется по формуле:\n",
    "\n",
    "$$\n",
    " \\left\\Vert x \\right\\Vert_{2} = \\sqrt{\\sum_{i=1}^n \\left( x_{i} \\right)^2}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ей в функции __`numpy.linalg.norm(x, ord=None, ...)`__ соответствует параметр __`ord=2`__."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L2 норма вектора a:\n",
      " 3.7416573867739413\n"
     ]
    }
   ],
   "source": [
    "print ('L2 норма вектора a:\\n', norm(a, ord=2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Более подробно о том, какие еще нормы (в том числе матричные) можно вычислить, см. [документацию](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.linalg.norm.html). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 15. Расстояния между векторами"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для двух векторов $x = (x_{1}, \\dots, x_{n}) \\in \\mathbb{R}^{n}$ и $y = (y_{1}, \\dots, y_{n}) \\in \\mathbb{R}^{n}$ $\\ell_{1}$ и $\\ell_{2}$ раccтояния вычисляются по следующим формулам соответственно:\n",
    "\n",
    "$$\n",
    " \\rho_{1}\\left( x, y \\right) = \\left\\Vert x - y \\right\\Vert_{1} = \\sum_{i=1}^n \\left| x_{i} - y_{i} \\right|\n",
    "$$\n",
    "\n",
    "$$\n",
    " \\rho_{2}\\left( x, y \\right) = \\left\\Vert x - y \\right\\Vert_{2} = \n",
    " \\sqrt{\\sum_{i=1}^n \\left( x_{i} - y_{i} \\right)^2}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Вектор a: [ 1  2 -3]\n",
      "Вектор b: [-4  3  8]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([1, 2, -3])\n",
    "b = np.array([-4, 3, 8])\n",
    "print ('Вектор a:', a)\n",
    "print ('Вектор b:', b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L1 расстояние между векторами a и b:\n",
      " 17.0\n",
      "L2 расстояние между векторами a и b:\n",
      " 12.12435565298214\n"
     ]
    }
   ],
   "source": [
    "print ('L1 расстояние между векторами a и b:\\n', norm(a - b, ord=1))\n",
    "print ('L2 расстояние между векторами a и b:\\n', norm(a - b, ord=2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 16. Скалярное произведение и угол между векторами"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Вектор a: [ 0  5 -1]\n",
      "Вектор b: [-4  9  3]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([0, 5, -1])\n",
    "b = np.array([-4, 9, 3])\n",
    "print ('Вектор a:', a)\n",
    "print ('Вектор b:', b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Скалярное произведение в пространстве $\\mathbb{R}^{n}$ для двух векторов $x = (x_{1}, \\dots, x_{n})$ и $y = (y_{1}, \\dots, y_{n})$ определяется как:\n",
    "\n",
    "$$\n",
    "\\langle x, y \\rangle = \\sum_{i=1}^n x_{i} y_{i}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Длиной вектора $x = (x_{1}, \\dots, x_{n}) \\in \\mathbb{R}^{n}$ называется квадратный корень из скалярного произведения, то есть длина равна евклидовой норме вектора:\n",
    "\n",
    "$$\n",
    "\\left| x \\right| = \\sqrt{\\langle x, x \\rangle} = \\sqrt{\\sum_{i=1}^n x_{i}^2} =  \\left\\Vert x \\right\\Vert_{2}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Теперь, когда мы знаем расстояние между двумя ненулевыми векторами и их длины, мы можем вычислить угол между ними через скалярное произведение:\n",
    "\n",
    "$$\n",
    "\\langle x, y \\rangle = \\left| x \\right| | y | \\cos(\\alpha)\n",
    "\\implies \\cos(\\alpha) = \\frac{\\langle x, y \\rangle}{\\left| x \\right| | y |},\n",
    "$$\n",
    "\n",
    "где $\\alpha \\in [0, \\pi]$ — угол между векторами $x$ и $y$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Косинус угла между a и b: 0.8000362836474323\n",
      "Сам угол: 0.6434406336093618\n"
     ]
    }
   ],
   "source": [
    "cos_angle = np.dot(a, b) / norm(a) / norm(b)\n",
    "print ('Косинус угла между a и b:', cos_angle)\n",
    "print ('Сам угол:', np.arccos(cos_angle))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 17. Комплексные числа в питоне"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Напоминание теории.__ __Комплексными числами__ называются числа вида $x + iy$, где $x$ и $y$ — вещественные числа, а $i$ — мнимая единица (величина, для которой выполняется равенство $i^{2} = -1$). Множество всех комплексных чисел обозначается буквой $\\mathbb{C}$ (подробнее про комплексные числа см. [википедию](https://ru.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%BF%D0%BB%D0%B5%D0%BA%D1%81%D0%BD%D0%BE%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%BE))."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В питоне комплескные числа можно задать следующим образом (__j__ обозначает мнимую единицу):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 3 + 2j\n",
    "b = 1j"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Комплексное число a:\n",
      " (3+2j)\n",
      "Комплексное число b:\n",
      " 1j\n"
     ]
    }
   ],
   "source": [
    "print (\"Комплексное число a:\\n\", a)\n",
    "print (\"Комплексное число b:\\n\", b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "С комплексными числами в питоне можно производить базовые арифметические операции так же, как и с вещественными числами:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = a * a\n",
    "d = a / (4 - 5j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Комплексное число c:\n",
      " (5+12j)\n",
      "Комплексное число d:\n",
      " (0.0487804878048781+0.5609756097560976j)\n"
     ]
    }
   ],
   "source": [
    "print (\"Комплексное число c:\\n\", c)\n",
    "print (\"Комплексное число d:\\n\", d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Задания: (Блок 2)\n",
    "### Задание 3:\n",
    "Рассмотрим сложную математическую функцию на отрезке [1, 15]:\n",
    "\n",
    "f(x) = sin(x / 5) * exp(x / 10) + 5 * exp(-x / 2)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pylab as plt\n",
    "x = np.arange(1,15,0.1)\n",
    "y = np.sin(x / 5) * np.exp(x / 10) + 5 * np.exp(-x / 2)\n",
    "plt.plot(x,y)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Она может описывать, например, зависимость оценок, которые выставляют определенному сорту вина эксперты, в зависимости от возраста этого вина. Мы хотим приблизить сложную зависимость с помощью функции из определенного семейства. В этом задании мы будем приближать указанную функцию с помощью многочленов."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Как известно, многочлен степени $n$ (то есть $w_0$ + $w_1 x$ + $w_2 x^2$ + $\\ldots$ + $w_n x^n$) однозначно определяется любыми n + 1 различными точками, через которые он проходит. Это значит, что его коэффициенты $w_0$, ... $w_n$ можно определить из следующей системы линейных уравнений:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![eqs.png](eqs.png \"eqs.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "где через $x_1, ..., x_n, x_{n+1}$ обозначены точки, через которые проходит многочлен, а через $f(x_1), ..., f(x_n), f(x_{n+1})$ — значения, которые он должен принимать в этих точках."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Воспользуемся описанным свойством, и будем находить приближение функции многочленом, решая систему линейных уравнений.\n",
    "\n",
    "1. Сформируйте систему линейных уравнений (то есть задайте матрицу коэффициентов A и свободный вектор b) для многочлена первой степени, который должен совпадать с функцией f в точках 1 и 15. Решите данную систему с помощью функции scipy.linalg.solve. Нарисуйте функцию f и полученный многочлен. Хорошо ли он приближает исходную функцию?\n",
    "2. Повторите те же шаги для многочлена второй степени, который совпадает с функцией f в точках 1, 8 и 15. Улучшилось ли качество аппроксимации?\n",
    "3. Повторите те же шаги для многочлена третьей степени, который совпадает с функцией f в точках 1, 4, 10 и 15. Хорошо ли он аппроксимирует функцию? Коэффициенты данного многочлена (четыре числа в следующем порядке: w_0, w_1, w_2, w_3) являются ответом на задачу. Округлять коэффициенты не обязательно, но при желании можете произвести округление до второго знака (т.е. до числа вида 0.42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import linalg  \n",
    "\n",
    "def f(x):\n",
    "    return np.sin(x / 5) * np.exp(x / 10) + 5 * np.exp(-x / 2)\n",
    "\n",
    "A = np.array([[1, 1],[1,15]]) \n",
    "b_1 = f(1)\n",
    "b_15 = f(15)\n",
    "b = np.array([b_1,b_15])\n",
    "coef =  linalg.solve(A,b)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(1,15,0.1)\n",
    "y = np.sin(x / 5) * np.exp(x / 10) + 5 * np.exp(-x / 2)\n",
    "x1 = np.arange(1,15,0.1)\n",
    "y1 = coef[0] + coef[1]*x\n",
    "plt.plot(x,y)\n",
    "plt.plot(x1, y1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([[1, 1, 1],[1, 8, 64],[1, 15, 225]]) \n",
    "b_1 = f(1)\n",
    "b_8 = f(8)\n",
    "b_15 = f(15)\n",
    "b = np.array([b_1, b_8, b_15])\n",
    "coef =  linalg.solve(A,b)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(1,15,0.1)\n",
    "y = np.sin(x / 5) * np.exp(x / 10) + 5 * np.exp(-x / 2)\n",
    "x1 = np.arange(1,15,0.1)\n",
    "y1 = coef[0] + coef[1]*x + coef[2]*x**2\n",
    "plt.plot(x,y)\n",
    "plt.plot(x1, y1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([[1, 1, 1, 1],[1, 4, 16, 4**3],[1, 10, 100, 1000],[1, 15, 225, 15**3]]) \n",
    "b_1 = f(1)\n",
    "b_4 = f(4)\n",
    "b_10 = f(10)\n",
    "b_15 = f(15)\n",
    "b = np.array([b_1, b_4, b_10, b_15])\n",
    "coef =  linalg.solve(A,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(1,15,0.1)\n",
    "y = np.sin(x / 5) * np.exp(x / 10) + 5 * np.exp(-x / 2)\n",
    "x1 = np.arange(1,15,0.1)\n",
    "y1 = coef[0] + coef[1]*x + coef[2]*x**2 + coef[3]*x**3\n",
    "plt.plot(x,y)\n",
    "plt.plot(x1, y1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "как и ожидалось, с увеличением степени многочлена мы стали лучше приближаться к функции. В случае реальных задач нужно подбирать оптимальные значения, чтобы не потерять физ смысл"
   ]
  },
  {
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}