vander_plus_2_NumPy_7.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "dd7b6c2b",
   "metadata": {},
   "source": [
    "## Сортировка массивов"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe378ea5",
   "metadata": {},
   "source": [
    "### Быстрая сортировка в библиотеке NumPy:\n",
    "###     np.sort и np.argsort"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "604142c0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# ф-ии np.sort и np.argsort намного быстрее встроенных ф-ий Python sort и sorted"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60f799a0",
   "metadata": {},
   "source": [
    "##### np.sort  по умолчанию использует алгоритм quiqsort имеет сложность O(N log N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fa908af0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7cd104a8",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([9,8,7,6,5,4,3,2,1,2,3,4,5,6,7,6,5,4,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9ad3a5be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 9])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sort(x)  # сортировка без изменения самого массива"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "cff65dfb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7679b9a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = np.sort(x)  # копия массива"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "40ca839c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 9])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b6ce49d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "x[1] = 99"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c83c9e06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 9, 99,  7,  6,  5,  4,  3,  2,  1,  2,  3,  4,  5,  6,  7,  6,  5,\n",
       "        4,  3])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c23a38d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 9])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3a61e736",
   "metadata": {},
   "outputs": [],
   "source": [
    "#  можно отсортировать массив с перезаписью\n",
    "x.sort()  # как метод класса массивов NumPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b4de9930",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  2,  2,  3,  3,  3,  4,  4,  4,  5,  5,  5,  6,  6,  6,  7,  7,\n",
       "        9, 99])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "e3b683fc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# имеестя возможность возврата индексов отсортированных эл-тов\n",
    "x = np.array([9,8,7,6,5,4,3,2,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7311ffd7",
   "metadata": {},
   "outputs": [],
   "source": [
    "i = np.argsort(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "7bdd31a2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([8, 7, 6, 5, 4, 3, 2, 1, 0], dtype=int64)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "ecd216f8",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = np.array([9,8,7,6,5,4,3,2,1,2,3,4,5,6,7,6,5,4,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "289e7c0a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 8,  9,  7, 10,  6, 18, 17, 11,  5,  4, 12, 16,  3, 13, 15,  2, 14,\n",
       "        1,  0], dtype=int64)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i_y = np.argsort(y)\n",
    "i_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b8d90dbc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# возвращает индексы эл-тов, для заполнения отсортированного массива с помощью прихотливой индексации\n",
    "# первый индекс соответствует min эл-ту и т.д."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "5628b72e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 9])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y[i_y]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "d87697e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y[8]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e333380a",
   "metadata": {},
   "source": [
    "##### Сортировка по строкам и столбцам многомерного массива"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "f4fc13a7",
   "metadata": {},
   "outputs": [],
   "source": [
    "rand = np.random.RandomState(42)\n",
    "X = rand.randint(0, 10, (4,6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "9bff75b0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6, 3, 7, 4, 6, 9],\n",
       "       [2, 6, 7, 4, 3, 7],\n",
       "       [7, 2, 5, 4, 1, 7],\n",
       "       [5, 1, 4, 0, 9, 5]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "79d28b7f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 4, 6, 6, 7, 9],\n",
       "       [2, 3, 4, 6, 7, 7],\n",
       "       [1, 2, 4, 5, 7, 7],\n",
       "       [0, 1, 4, 5, 5, 9]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# сортировка всех строк\n",
    "np.sort(X, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "098732ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 1, 4, 0, 1, 5],\n",
       "       [5, 2, 5, 4, 3, 7],\n",
       "       [6, 3, 7, 4, 6, 7],\n",
       "       [7, 6, 7, 4, 9, 9]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# сортировка всех столбцов\n",
    "np.sort(X, axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9926ee30",
   "metadata": {},
   "source": [
    "### Частичные сортировки: секционирование  np.partition\n",
    "Для случаев, когда сортировка всего массива не требуется, а нужно найти К наименьших значений в нем\n",
    "np.partition принимает в качестве агрумунтов массив и число К\n",
    "результатом является массив с К наименьших значений до точки разбиения, и все остальные после..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "5f2b7ced",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([9,8,7,6,5,4,3,2,1,2,3,4,5,6,7,6,5,4,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "2c168cd0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 2, 3, 1, 2, 3, 4, 4, 4, 5, 5, 5, 7, 6, 7, 6, 8, 6, 9])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.partition(x, 6)\n",
    "# вначале идут первые 6 мин элементов не по порядку, затем все остальные\n",
    "# при этом эл-ты не отсортированы"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "de688585",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 4, 6, 7, 6, 9],\n",
       "       [2, 3, 4, 7, 6, 7],\n",
       "       [1, 2, 4, 5, 7, 7],\n",
       "       [0, 1, 4, 5, 9, 5]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.partition(X, 2, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9b40eae3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# np.argpartition вычисляет индексы для секций"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "141449a6",
   "metadata": {},
   "source": [
    "### Пример: К ближайших соседей"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "11fc45e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "Y = rand.rand(10, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "e160354b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.00706631, 0.02306243],\n",
       "       [0.52477466, 0.39986097],\n",
       "       [0.04666566, 0.97375552],\n",
       "       [0.23277134, 0.09060643],\n",
       "       [0.61838601, 0.38246199],\n",
       "       [0.98323089, 0.46676289],\n",
       "       [0.85994041, 0.68030754],\n",
       "       [0.45049925, 0.01326496],\n",
       "       [0.94220176, 0.56328822],\n",
       "       [0.3854165 , 0.01596625]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "78ddf2bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "9d09ee2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x28eb27c6a00>"
      ]
     },
     "execution_count": 39,
     "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": [
    "#import seaborn\n",
    "#seaborn.set()\n",
    "plt.scatter(Y[:,0], Y[:,1], s=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "098e729a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x28eb295f4f0>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn\n",
    "seaborn.set()\n",
    "plt.scatter(Y[:,0], Y[:,1], s=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "a728be60",
   "metadata": {},
   "outputs": [],
   "source": [
    "dist_sq = np.sum((Y[:,np.newaxis,:] - Y[np.newaxis,:,:])**2, axis=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "45878d8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        , 0.40999909, 0.90538547, 0.05550496, 0.50287983,\n",
       "        1.14976739, 1.15936537, 0.19672877, 1.16632222, 0.14319923],\n",
       "       [0.40999909, 0.        , 0.55794316, 0.18090431, 0.00906581,\n",
       "        0.21465798, 0.19098635, 0.15497331, 0.20095384, 0.16679585],\n",
       "       [0.90538547, 0.55794316, 0.        , 0.81458763, 0.67649219,\n",
       "        1.13419594, 0.74752753, 1.08562368, 0.9704683 , 1.03211241],\n",
       "       [0.05550496, 0.18090431, 0.81458763, 0.        , 0.23387834,\n",
       "        0.70468321, 0.74108843, 0.05338715, 0.72671958, 0.0288717 ],\n",
       "       [0.50287983, 0.00906581, 0.67649219, 0.23387834, 0.        ,\n",
       "        0.14021843, 0.1470605 , 0.16449241, 0.13755476, 0.18859392],\n",
       "       [1.14976739, 0.21465798, 1.13419594, 0.70468321, 0.14021843,\n",
       "        0.        , 0.06080186, 0.48946337, 0.01100053, 0.56059965],\n",
       "       [1.15936537, 0.19098635, 0.74752753, 0.74108843, 0.1470605 ,\n",
       "        0.06080186, 0.        , 0.61258786, 0.02046045, 0.66652228],\n",
       "       [0.19672877, 0.15497331, 1.08562368, 0.05338715, 0.16449241,\n",
       "        0.48946337, 0.61258786, 0.        , 0.54429694, 0.00424306],\n",
       "       [1.16632222, 0.20095384, 0.9704683 , 0.72671958, 0.13755476,\n",
       "        0.01100053, 0.02046045, 0.54429694, 0.        , 0.60957115],\n",
       "       [0.14319923, 0.16679585, 1.03211241, 0.0288717 , 0.18859392,\n",
       "        0.56059965, 0.66652228, 0.00424306, 0.60957115, 0.        ]])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist_sq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "c2843ea6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0.        ,  0.        ],\n",
       "        [-0.51770836, -0.37679855],\n",
       "        [-0.03959936, -0.95069309],\n",
       "        [-0.22570504, -0.06754401],\n",
       "        [-0.6113197 , -0.35939957],\n",
       "        [-0.97616458, -0.44370047],\n",
       "        [-0.8528741 , -0.65724511],\n",
       "        [-0.44343295,  0.00979746],\n",
       "        [-0.93513545, -0.54022579],\n",
       "        [-0.3783502 ,  0.00709617]],\n",
       "\n",
       "       [[ 0.51770836,  0.37679855],\n",
       "        [ 0.        ,  0.        ],\n",
       "        [ 0.478109  , -0.57389455],\n",
       "        [ 0.29200332,  0.30925454],\n",
       "        [-0.09361135,  0.01739898],\n",
       "        [-0.45845623, -0.06690192],\n",
       "        [-0.33516575, -0.28044657],\n",
       "        [ 0.07427541,  0.38659601],\n",
       "        [-0.4174271 , -0.16342725],\n",
       "        [ 0.13935816,  0.38389472]],\n",
       "\n",
       "       [[ 0.03959936,  0.95069309],\n",
       "        [-0.478109  ,  0.57389455],\n",
       "        [ 0.        ,  0.        ],\n",
       "        [-0.18610568,  0.88314908],\n",
       "        [-0.57172035,  0.59129353],\n",
       "        [-0.93656522,  0.50699263],\n",
       "        [-0.81327474,  0.29344798],\n",
       "        [-0.40383359,  0.96049056],\n",
       "        [-0.89553609,  0.4104673 ],\n",
       "        [-0.33875084,  0.95778927]],\n",
       "\n",
       "       [[ 0.22570504,  0.06754401],\n",
       "        [-0.29200332, -0.30925454],\n",
       "        [ 0.18610568, -0.88314908],\n",
       "        [ 0.        ,  0.        ],\n",
       "        [-0.38561467, -0.29185556],\n",
       "        [-0.75045955, -0.37615646],\n",
       "        [-0.62716907, -0.5897011 ],\n",
       "        [-0.21772791,  0.07734147],\n",
       "        [-0.70943042, -0.47268178],\n",
       "        [-0.15264516,  0.07464018]],\n",
       "\n",
       "       [[ 0.6113197 ,  0.35939957],\n",
       "        [ 0.09361135, -0.01739898],\n",
       "        [ 0.57172035, -0.59129353],\n",
       "        [ 0.38561467,  0.29185556],\n",
       "        [ 0.        ,  0.        ],\n",
       "        [-0.36484488, -0.0843009 ],\n",
       "        [-0.2415544 , -0.29784555],\n",
       "        [ 0.16788676,  0.36919703],\n",
       "        [-0.32381575, -0.18082623],\n",
       "        [ 0.23296951,  0.36649574]],\n",
       "\n",
       "       [[ 0.97616458,  0.44370047],\n",
       "        [ 0.45845623,  0.06690192],\n",
       "        [ 0.93656522, -0.50699263],\n",
       "        [ 0.75045955,  0.37615646],\n",
       "        [ 0.36484488,  0.0843009 ],\n",
       "        [ 0.        ,  0.        ],\n",
       "        [ 0.12329048, -0.21354465],\n",
       "        [ 0.53273163,  0.45349793],\n",
       "        [ 0.04102913, -0.09652532],\n",
       "        [ 0.59781438,  0.45079664]],\n",
       "\n",
       "       [[ 0.8528741 ,  0.65724511],\n",
       "        [ 0.33516575,  0.28044657],\n",
       "        [ 0.81327474, -0.29344798],\n",
       "        [ 0.62716907,  0.5897011 ],\n",
       "        [ 0.2415544 ,  0.29784555],\n",
       "        [-0.12329048,  0.21354465],\n",
       "        [ 0.        ,  0.        ],\n",
       "        [ 0.40944115,  0.66704258],\n",
       "        [-0.08226135,  0.11701932],\n",
       "        [ 0.4745239 ,  0.66434129]],\n",
       "\n",
       "       [[ 0.44343295, -0.00979746],\n",
       "        [-0.07427541, -0.38659601],\n",
       "        [ 0.40383359, -0.96049056],\n",
       "        [ 0.21772791, -0.07734147],\n",
       "        [-0.16788676, -0.36919703],\n",
       "        [-0.53273163, -0.45349793],\n",
       "        [-0.40944115, -0.66704258],\n",
       "        [ 0.        ,  0.        ],\n",
       "        [-0.4917025 , -0.55002326],\n",
       "        [ 0.06508275, -0.00270129]],\n",
       "\n",
       "       [[ 0.93513545,  0.54022579],\n",
       "        [ 0.4174271 ,  0.16342725],\n",
       "        [ 0.89553609, -0.4104673 ],\n",
       "        [ 0.70943042,  0.47268178],\n",
       "        [ 0.32381575,  0.18082623],\n",
       "        [-0.04102913,  0.09652532],\n",
       "        [ 0.08226135, -0.11701932],\n",
       "        [ 0.4917025 ,  0.55002326],\n",
       "        [ 0.        ,  0.        ],\n",
       "        [ 0.55678525,  0.54732197]],\n",
       "\n",
       "       [[ 0.3783502 , -0.00709617],\n",
       "        [-0.13935816, -0.38389472],\n",
       "        [ 0.33875084, -0.95778927],\n",
       "        [ 0.15264516, -0.07464018],\n",
       "        [-0.23296951, -0.36649574],\n",
       "        [-0.59781438, -0.45079664],\n",
       "        [-0.4745239 , -0.66434129],\n",
       "        [-0.06508275,  0.00270129],\n",
       "        [-0.55678525, -0.54732197],\n",
       "        [ 0.        ,  0.        ]]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# расшифорвка\n",
    "# для каждой пары точек вычисляем разности их координат\n",
    "diff = Y[:, np.newaxis, :] - Y[np.newaxis, :, :]\n",
    "diff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "77071668",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 10, 2)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "4c9d32ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[0.00706631, 0.02306243]],\n",
       "\n",
       "       [[0.52477466, 0.39986097]],\n",
       "\n",
       "       [[0.04666566, 0.97375552]],\n",
       "\n",
       "       [[0.23277134, 0.09060643]],\n",
       "\n",
       "       [[0.61838601, 0.38246199]],\n",
       "\n",
       "       [[0.98323089, 0.46676289]],\n",
       "\n",
       "       [[0.85994041, 0.68030754]],\n",
       "\n",
       "       [[0.45049925, 0.01326496]],\n",
       "\n",
       "       [[0.94220176, 0.56328822]],\n",
       "\n",
       "       [[0.3854165 , 0.01596625]]])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y[:, np.newaxis, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "161d5305",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[0.00706631, 0.02306243],\n",
       "        [0.52477466, 0.39986097],\n",
       "        [0.04666566, 0.97375552],\n",
       "        [0.23277134, 0.09060643],\n",
       "        [0.61838601, 0.38246199],\n",
       "        [0.98323089, 0.46676289],\n",
       "        [0.85994041, 0.68030754],\n",
       "        [0.45049925, 0.01326496],\n",
       "        [0.94220176, 0.56328822],\n",
       "        [0.3854165 , 0.01596625]]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y[np.newaxis, :, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "25260b80",
   "metadata": {},
   "outputs": [],
   "source": [
    "# далее возводим разности координат в квадрат\n",
    "sq_diff = diff**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "26fb3a08",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[0.00000000e+00, 0.00000000e+00],\n",
       "        [2.68021941e-01, 1.41977145e-01],\n",
       "        [1.56810915e-03, 9.03817359e-01],\n",
       "        [5.09427629e-02, 4.56219322e-03],\n",
       "        [3.73711781e-01, 1.29168048e-01],\n",
       "        [9.52897288e-01, 1.96870105e-01],\n",
       "        [7.27394233e-01, 4.31971139e-01],\n",
       "        [1.96632778e-01, 9.59902985e-05],\n",
       "        [8.74478311e-01, 2.91843907e-01],\n",
       "        [1.43148872e-01, 5.03556687e-05]],\n",
       "\n",
       "       [[2.68021941e-01, 1.41977145e-01],\n",
       "        [0.00000000e+00, 0.00000000e+00],\n",
       "        [2.28588213e-01, 3.29354951e-01],\n",
       "        [8.52659388e-02, 9.56383688e-02],\n",
       "        [8.76308468e-03, 3.02724521e-04],\n",
       "        [2.10182111e-01, 4.47586710e-03],\n",
       "        [1.12336078e-01, 7.86502769e-02],\n",
       "        [5.51683628e-03, 1.49456475e-01],\n",
       "        [1.74245380e-01, 2.67084648e-02],\n",
       "        [1.94206961e-02, 1.47375156e-01]],\n",
       "\n",
       "       [[1.56810915e-03, 9.03817359e-01],\n",
       "        [2.28588213e-01, 3.29354951e-01],\n",
       "        [0.00000000e+00, 0.00000000e+00],\n",
       "        [3.46353231e-02, 7.79952305e-01],\n",
       "        [3.26864154e-01, 3.49628036e-01],\n",
       "        [8.77154416e-01, 2.57041522e-01],\n",
       "        [6.61415808e-01, 8.61117171e-02],\n",
       "        [1.63081567e-01, 9.22542111e-01],\n",
       "        [8.01984893e-01, 1.68483405e-01],\n",
       "        [1.14752131e-01, 9.17360279e-01]],\n",
       "\n",
       "       [[5.09427629e-02, 4.56219322e-03],\n",
       "        [8.52659388e-02, 9.56383688e-02],\n",
       "        [3.46353231e-02, 7.79952305e-01],\n",
       "        [0.00000000e+00, 0.00000000e+00],\n",
       "        [1.48698673e-01, 8.51796660e-02],\n",
       "        [5.63189529e-01, 1.41493681e-01],\n",
       "        [3.93341038e-01, 3.47747392e-01],\n",
       "        [4.74054435e-02, 5.98170350e-03],\n",
       "        [5.03291514e-01, 2.23428068e-01],\n",
       "        [2.33005455e-02, 5.57115682e-03]],\n",
       "\n",
       "       [[3.73711781e-01, 1.29168048e-01],\n",
       "        [8.76308468e-03, 3.02724521e-04],\n",
       "        [3.26864154e-01, 3.49628036e-01],\n",
       "        [1.48698673e-01, 8.51796660e-02],\n",
       "        [0.00000000e+00, 0.00000000e+00],\n",
       "        [1.33111784e-01, 7.10664207e-03],\n",
       "        [5.83485269e-02, 8.87119701e-02],\n",
       "        [2.81859633e-02, 1.36306447e-01],\n",
       "        [1.04856638e-01, 3.26981242e-02],\n",
       "        [5.42747911e-02, 1.34319127e-01]],\n",
       "\n",
       "       [[9.52897288e-01, 1.96870105e-01],\n",
       "        [2.10182111e-01, 4.47586710e-03],\n",
       "        [8.77154416e-01, 2.57041522e-01],\n",
       "        [5.63189529e-01, 1.41493681e-01],\n",
       "        [1.33111784e-01, 7.10664207e-03],\n",
       "        [0.00000000e+00, 0.00000000e+00],\n",
       "        [1.52005422e-02, 4.56013156e-02],\n",
       "        [2.83802994e-01, 2.05660374e-01],\n",
       "        [1.68338952e-03, 9.31713829e-03],\n",
       "        [3.57382037e-01, 2.03217612e-01]],\n",
       "\n",
       "       [[7.27394233e-01, 4.31971139e-01],\n",
       "        [1.12336078e-01, 7.86502769e-02],\n",
       "        [6.61415808e-01, 8.61117171e-02],\n",
       "        [3.93341038e-01, 3.47747392e-01],\n",
       "        [5.83485269e-02, 8.87119701e-02],\n",
       "        [1.52005422e-02, 4.56013156e-02],\n",
       "        [0.00000000e+00, 0.00000000e+00],\n",
       "        [1.67642059e-01, 4.44945800e-01],\n",
       "        [6.76692953e-03, 1.36935214e-02],\n",
       "        [2.25172936e-01, 4.41349345e-01]],\n",
       "\n",
       "       [[1.96632778e-01, 9.59902985e-05],\n",
       "        [5.51683628e-03, 1.49456475e-01],\n",
       "        [1.63081567e-01, 9.22542111e-01],\n",
       "        [4.74054435e-02, 5.98170350e-03],\n",
       "        [2.81859633e-02, 1.36306447e-01],\n",
       "        [2.83802994e-01, 2.05660374e-01],\n",
       "        [1.67642059e-01, 4.44945800e-01],\n",
       "        [0.00000000e+00, 0.00000000e+00],\n",
       "        [2.41771352e-01, 3.02525583e-01],\n",
       "        [4.23576427e-03, 7.29697339e-06]],\n",
       "\n",
       "       [[8.74478311e-01, 2.91843907e-01],\n",
       "        [1.74245380e-01, 2.67084648e-02],\n",
       "        [8.01984893e-01, 1.68483405e-01],\n",
       "        [5.03291514e-01, 2.23428068e-01],\n",
       "        [1.04856638e-01, 3.26981242e-02],\n",
       "        [1.68338952e-03, 9.31713829e-03],\n",
       "        [6.76692953e-03, 1.36935214e-02],\n",
       "        [2.41771352e-01, 3.02525583e-01],\n",
       "        [0.00000000e+00, 0.00000000e+00],\n",
       "        [3.10009818e-01, 2.99561334e-01]],\n",
       "\n",
       "       [[1.43148872e-01, 5.03556687e-05],\n",
       "        [1.94206961e-02, 1.47375156e-01],\n",
       "        [1.14752131e-01, 9.17360279e-01],\n",
       "        [2.33005455e-02, 5.57115682e-03],\n",
       "        [5.42747911e-02, 1.34319127e-01],\n",
       "        [3.57382037e-01, 2.03217612e-01],\n",
       "        [2.25172936e-01, 4.41349345e-01],\n",
       "        [4.23576427e-03, 7.29697339e-06],\n",
       "        [3.10009818e-01, 2.99561334e-01],\n",
       "        [0.00000000e+00, 0.00000000e+00]]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sq_diff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "25b99194",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        , 0.40999909, 0.90538547, 0.05550496, 0.50287983,\n",
       "        1.14976739, 1.15936537, 0.19672877, 1.16632222, 0.14319923],\n",
       "       [0.40999909, 0.        , 0.55794316, 0.18090431, 0.00906581,\n",
       "        0.21465798, 0.19098635, 0.15497331, 0.20095384, 0.16679585],\n",
       "       [0.90538547, 0.55794316, 0.        , 0.81458763, 0.67649219,\n",
       "        1.13419594, 0.74752753, 1.08562368, 0.9704683 , 1.03211241],\n",
       "       [0.05550496, 0.18090431, 0.81458763, 0.        , 0.23387834,\n",
       "        0.70468321, 0.74108843, 0.05338715, 0.72671958, 0.0288717 ],\n",
       "       [0.50287983, 0.00906581, 0.67649219, 0.23387834, 0.        ,\n",
       "        0.14021843, 0.1470605 , 0.16449241, 0.13755476, 0.18859392],\n",
       "       [1.14976739, 0.21465798, 1.13419594, 0.70468321, 0.14021843,\n",
       "        0.        , 0.06080186, 0.48946337, 0.01100053, 0.56059965],\n",
       "       [1.15936537, 0.19098635, 0.74752753, 0.74108843, 0.1470605 ,\n",
       "        0.06080186, 0.        , 0.61258786, 0.02046045, 0.66652228],\n",
       "       [0.19672877, 0.15497331, 1.08562368, 0.05338715, 0.16449241,\n",
       "        0.48946337, 0.61258786, 0.        , 0.54429694, 0.00424306],\n",
       "       [1.16632222, 0.20095384, 0.9704683 , 0.72671958, 0.13755476,\n",
       "        0.01100053, 0.02046045, 0.54429694, 0.        , 0.60957115],\n",
       "       [0.14319923, 0.16679585, 1.03211241, 0.0288717 , 0.18859392,\n",
       "        0.56059965, 0.66652228, 0.00424306, 0.60957115, 0.        ]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# суммируем квадраты расстояния по координатным осям, для получения квадрата расстояния м/у (.)\n",
    "dist_sq = sq_diff.sum(-1)\n",
    "dist_sq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "76decf7f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# диагональ такой матрицы должна быть = 0 (сами с собой)\n",
    "dist_sq.diagonal()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "41f153ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 3, 9, 7, 1, 4, 2, 5, 6, 8],\n",
       "       [1, 4, 7, 9, 3, 6, 8, 5, 0, 2],\n",
       "       [2, 1, 4, 6, 3, 0, 8, 9, 7, 5],\n",
       "       [3, 9, 7, 0, 1, 4, 5, 8, 6, 2],\n",
       "       [4, 1, 8, 5, 6, 7, 9, 3, 0, 2],\n",
       "       [5, 8, 6, 4, 1, 7, 9, 3, 2, 0],\n",
       "       [6, 8, 5, 4, 1, 7, 9, 3, 2, 0],\n",
       "       [7, 9, 3, 1, 4, 0, 5, 8, 6, 2],\n",
       "       [8, 5, 6, 4, 1, 7, 9, 3, 2, 0],\n",
       "       [9, 7, 3, 0, 1, 4, 5, 8, 6, 2]], dtype=int64)"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nearest = np.argsort(dist_sq, axis=1)\n",
    "nearest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b00b19cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# крайние слева столбцы будут представлять собой индексы ближайших соседей\n",
    "# первый столбец говорит о том, что ближайший сосед точки она сама (нулевая диагональ)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "c861a17b",
   "metadata": {},
   "outputs": [],
   "source": [
    "K = 2\n",
    "nearest_partition = np.argpartition(dist_sq, K + 1, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "762dc321",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 0, 9, 7, 1, 4, 2, 5, 8, 6],\n",
       "       [1, 4, 7, 9, 3, 5, 6, 2, 8, 0],\n",
       "       [2, 1, 4, 6, 3, 0, 5, 7, 8, 9],\n",
       "       [3, 9, 7, 0, 1, 5, 6, 2, 8, 4],\n",
       "       [1, 8, 4, 5, 7, 6, 9, 3, 2, 0],\n",
       "       [5, 8, 6, 4, 1, 7, 9, 3, 2, 0],\n",
       "       [6, 8, 5, 4, 1, 7, 9, 3, 2, 0],\n",
       "       [7, 9, 3, 1, 4, 5, 6, 2, 8, 0],\n",
       "       [8, 5, 6, 4, 1, 7, 9, 3, 2, 0],\n",
       "       [3, 9, 7, 0, 1, 5, 6, 2, 8, 4]], dtype=int64)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nearest_partition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "e1f32e75",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(Y[:,0], Y[:,1], s=100)\n",
    "for i in range(Y.shape[0]):\n",
    "    for j in nearest_partition[i, :K+1]:\n",
    "        plt.plot(*zip(Y[j], Y[i]), color='black')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "84476a0e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}