vander_plus_2_NumPy_6.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "00ac21c5",
   "metadata": {},
   "source": [
    "## \"Прихотливая (причудливая)\" индексация\n",
    "## fancy indexing\n",
    "Вместо скалярных значений передаются массивы индексов\n",
    "Что дает возможность очень быстрого доступа и модификации сложных подмножеств значений массива"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "65210cf0",
   "metadata": {},
   "outputs": [],
   "source": [
    "Суть прихотливой индексации заключается в передаче массива индексов с целью одновременного доступа к нескольким эл-там массива"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2f651415",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5deb4059",
   "metadata": {},
   "outputs": [],
   "source": [
    "rand = np.random.RandomState(42)  # установили нач. значение рандомайзера"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2be2303f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomState(MT19937) at 0x249F33A3740"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rand"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "46569950",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = rand.randint(100, size=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a7b93e9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([51, 92, 14, 71, 60, 20, 82, 86, 74, 74])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "60137d6c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[71, 86, 14]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# обычный способ обращения к нескольким эл-там\n",
    "[x[3], x[7], x[2]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "0ebaa22c",
   "metadata": {},
   "outputs": [],
   "source": [
    "ind = [3, 7, 4]  # список индексов"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "07f0445b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([71, 86, 60])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[ind]  # прихотливая индексация"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fd329811",
   "metadata": {},
   "outputs": [],
   "source": [
    "Форма результата отражает форму массива индексов, а не форму индексируемого массива"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a6a3ebe7",
   "metadata": {},
   "outputs": [],
   "source": [
    "ind = np.array([[3,7],\n",
    "                [4,5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "1e7b83b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[71, 86],\n",
       "       [60, 20]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[ind]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a1f711e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.arange(12).reshape((3,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "4fa13d72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "e58070ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2,  5, 11])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row = np.array([0, 1, 2])\n",
    "col = np.array([2, 1, 3])\n",
    "X[row, col]  # первый индекс - строка, второй - столбец\n",
    "# пары индексов X[0, 2] X[1, 1] X[2, 3] подчиняются правилам транслирования массивов"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "2cbac4d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  1,  3],\n",
       "       [ 6,  5,  7],\n",
       "       [10,  9, 11]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[row[:, np.newaxis], col]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "e96449a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 0],\n",
       "       [2, 1, 3],\n",
       "       [4, 2, 6]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# каждое строчное значение соединяется с каждым вектором-столбцом точно так же, как при транслировании арифметических операций\n",
    "row[:, np.newaxis]*col"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66fb7605",
   "metadata": {},
   "source": [
    "##### Возвращаемое значение отражает транслируемую форму индексов, а не форму индексируемого массива!!!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9914e67",
   "metadata": {},
   "source": [
    "### Комбинированная индексация:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "b790de27",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "1f624fcd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10,  8,  9])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[2, [2, 0, 1]]  # где 2 - это номер строки\n",
    "# совместное использование простой и прихотливой индексации"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "50736f8a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 6,  4,  5],\n",
       "       [10,  8,  9]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[1:, [2, 0, 1]]  # совместное использование прихотливой индексации и срезов"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "a5876137",
   "metadata": {},
   "outputs": [],
   "source": [
    "# одновременное использование прихотливой индексации и МАСКИРОВАНИя\n",
    "mask = np.array([1, 0, 1, 0], dtype=bool)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "e7efac17",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False,  True, False])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "45e4b785",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  2],\n",
       "       [ 4,  6],\n",
       "       [ 8, 10]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[row[:, np.newaxis], mask]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "c0caf605",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a0b688a",
   "metadata": {},
   "source": [
    "### Пример: выборка случайных точек"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "15830a95",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 2)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean = [0, 0]\n",
    "cov = [[1, 2],\n",
    "       [2, 5]]\n",
    "X = rand.multivariate_normal(mean, cov, 100)\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "86e9873c",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn\n",
    "seaborn.set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "17d64725",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x249f82fd670>"
      ]
     },
     "execution_count": 33,
     "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": [
    "plt.scatter(X[:, 0], X[:, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "949e54e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([92, 39, 79, 95, 55, 70, 62, 43, 58, 26, 75, 54,  7, 83, 16, 53,  1,\n",
       "       23, 60, 21])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ind = np.random.choice(X.shape[0], 20, replace=False)\n",
    "ind"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "16d95df3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.12065651,  1.13236323],\n",
       "       [-0.90649669, -0.93486441],\n",
       "       [-0.31332021, -1.7895623 ],\n",
       "       [-0.69144553, -1.56919875],\n",
       "       [ 0.69226246,  1.21504303],\n",
       "       [-1.16586444, -2.24482237],\n",
       "       [ 0.10259314,  1.24690575],\n",
       "       [ 0.37785618,  0.51409383],\n",
       "       [ 0.42044896,  1.85189522],\n",
       "       [ 0.32124996,  0.33137032],\n",
       "       [-1.03637857, -1.18469125],\n",
       "       [-0.34226126, -1.10666237],\n",
       "       [ 0.35282131,  1.49875397],\n",
       "       [ 0.74577693,  1.95834451],\n",
       "       [-3.0236127 , -6.00766046],\n",
       "       [ 0.6074983 ,  1.47089233],\n",
       "       [ 0.7376352 ,  1.21236921],\n",
       "       [-1.11518048, -1.87508012],\n",
       "       [-1.83106042, -2.91352836],\n",
       "       [ 0.99305043,  2.54294059]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "selection = X[ind]\n",
    "selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "9a3c67e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20, 2)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "selection.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "6c8082db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x249f994eee0>"
      ]
     },
     "execution_count": 50,
     "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": [
    "plt.scatter(X[:, 0], X[:, 1], alpha=0.8)\n",
    "plt.scatter(selection[:, 0], selection[:, 1], facecolor='red', s=100, alpha=0.3)\n",
    "# X[:, 0] - первый столбец - это координаты по х\n",
    "# X[:, 1] - второй столбец - это координаты оп у\n",
    "# подобная стратегия часто используется для быстрого секционирования наборов данных, часто требуемого при разделении \n",
    "# на обучающую/тестовую последовательности для проверки статистических моделей"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aeeb3422",
   "metadata": {},
   "source": [
    "### Изменение значений с помощью прихотливой индексации"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "d2e62c66",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "0d6a87d1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "12f3cf00",
   "metadata": {},
   "outputs": [],
   "source": [
    "i = np.array([2, 1, 8, 4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "c0bfa72e",
   "metadata": {},
   "outputs": [],
   "source": [
    "x[i] = 99"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "a00ba3c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0, 99, 99,  3, 99,  5,  6,  7, 99,  9])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "eef80209",
   "metadata": {},
   "outputs": [],
   "source": [
    "x[i] -= 10  # сработает любой оператор присваивания"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "8b2236ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0, 89, 89,  3, 89,  5,  6,  7, 89,  9])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "22f013af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6., 0., 0., 0., 0., 0., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# повторные индексы присваиваются по порядку:\n",
    "x = np.zeros(10)\n",
    "x[[0, 0]] = [4, 6]\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "3448b8b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6., 0., 1., 1., 1., 0., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i = [2,3,3,4,4,4]\n",
    "x[i] += 1\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cda08922",
   "metadata": {},
   "outputs": [],
   "source": [
    "# при этом инкрементация не выполнилась несколько раз, она как бы запомнила начальные данные,\n",
    "# и провела все операции с ними по отдельности"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "de84a6c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# если мы хотим реализовать инкремент пропорционально кол-ву вхождений индекса, \n",
    "# то следует использовать метод .at() или .reduceat() операции .add <==>+:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "8c6b5b29",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 1., 2., 3., 0., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.zeros(10)\n",
    "np.add.at(x, i, 1)\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "332fc031",
   "metadata": {},
   "source": [
    "### Пример: Разбиение данных на интервалы"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7f0ec98a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# пусть есть 100 значений, необходимо понять как они распределяются по массиву интервалов"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "c9d8c340",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "x = np.random.randn(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "aeb50085",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.49671415, -0.1382643 ,  0.64768854,  1.52302986, -0.23415337,\n",
       "       -0.23413696,  1.57921282,  0.76743473, -0.46947439,  0.54256004,\n",
       "       -0.46341769, -0.46572975,  0.24196227, -1.91328024, -1.72491783,\n",
       "       -0.56228753, -1.01283112,  0.31424733, -0.90802408, -1.4123037 ,\n",
       "        1.46564877, -0.2257763 ,  0.0675282 , -1.42474819, -0.54438272,\n",
       "        0.11092259, -1.15099358,  0.37569802, -0.60063869, -0.29169375,\n",
       "       -0.60170661,  1.85227818, -0.01349722, -1.05771093,  0.82254491,\n",
       "       -1.22084365,  0.2088636 , -1.95967012, -1.32818605,  0.19686124,\n",
       "        0.73846658,  0.17136828, -0.11564828, -0.3011037 , -1.47852199,\n",
       "       -0.71984421, -0.46063877,  1.05712223,  0.34361829, -1.76304016,\n",
       "        0.32408397, -0.38508228, -0.676922  ,  0.61167629,  1.03099952,\n",
       "        0.93128012, -0.83921752, -0.30921238,  0.33126343,  0.97554513,\n",
       "       -0.47917424, -0.18565898, -1.10633497, -1.19620662,  0.81252582,\n",
       "        1.35624003, -0.07201012,  1.0035329 ,  0.36163603, -0.64511975,\n",
       "        0.36139561,  1.53803657, -0.03582604,  1.56464366, -2.6197451 ,\n",
       "        0.8219025 ,  0.08704707, -0.29900735,  0.09176078, -1.98756891,\n",
       "       -0.21967189,  0.35711257,  1.47789404, -0.51827022, -0.8084936 ,\n",
       "       -0.50175704,  0.91540212,  0.32875111, -0.5297602 ,  0.51326743,\n",
       "        0.09707755,  0.96864499, -0.70205309, -0.32766215, -0.39210815,\n",
       "       -1.46351495,  0.29612028,  0.26105527,  0.00511346, -0.23458713])"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "f88fa394",
   "metadata": {},
   "outputs": [],
   "source": [
    "bins = np.linspace(-5, 5, 20)\n",
    "counts = np.zeros_like(bins)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "7d17312b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-5.        , -4.47368421, -3.94736842, -3.42105263, -2.89473684,\n",
       "       -2.36842105, -1.84210526, -1.31578947, -0.78947368, -0.26315789,\n",
       "        0.26315789,  0.78947368,  1.31578947,  1.84210526,  2.36842105,\n",
       "        2.89473684,  3.42105263,  3.94736842,  4.47368421,  5.        ])"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "0c0eeddf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "       0., 0., 0.])"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "3689116c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bins.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "7c1ff9d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counts.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "b9791c8a",
   "metadata": {},
   "outputs": [],
   "source": [
    "i = np.searchsorted(bins, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "990cb485",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([11, 10, 11, 13, 10, 10, 13, 11,  9, 11,  9,  9, 10,  6,  7,  9,  8,\n",
       "       11,  8,  7, 13, 10, 10,  7,  9, 10,  8, 11,  9,  9,  9, 14, 10,  8,\n",
       "       12,  8, 10,  6,  7, 10, 11, 10, 10,  9,  7,  9,  9, 12, 11,  7, 11,\n",
       "        9,  9, 11, 12, 12,  8,  9, 11, 12,  9, 10,  8,  8, 12, 13, 10, 12,\n",
       "       11,  9, 11, 13, 10, 13,  5, 12, 10,  9, 10,  6, 10, 11, 13,  9,  8,\n",
       "        9, 12, 11,  9, 11, 10, 12,  9,  9,  9,  7, 11, 10, 10, 10],\n",
       "      dtype=int64)"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "ac8a01f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.add.at(counts, i, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "83c1e046",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.,  0.,  0.,  0.,  1.,  3.,  7.,  9., 23., 22., 17., 10.,\n",
       "        7.,  1.,  0.,  0.,  0.,  0.,  0.])"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "fe875752",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x249fa442340>]"
      ]
     },
     "execution_count": 113,
     "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": [
    "plt.plot(bins, counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "b117ee28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 0.,  0.,  0.,  0.,  1.,  3.,  7.,  9., 23., 22., 17., 10.,  7.,\n",
       "         1.,  0.,  0.,  0.,  0.,  0.]),\n",
       " array([-5.        , -4.47368421, -3.94736842, -3.42105263, -2.89473684,\n",
       "        -2.36842105, -1.84210526, -1.31578947, -0.78947368, -0.26315789,\n",
       "         0.26315789,  0.78947368,  1.31578947,  1.84210526,  2.36842105,\n",
       "         2.89473684,  3.42105263,  3.94736842,  4.47368421,  5.        ]),\n",
       " <BarContainer object of 19 artists>)"
      ]
     },
     "execution_count": 114,
     "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": [
    "plt.hist(x, bins)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b2f8923a",
   "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
}