{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9047b87b",
   "metadata": {},
   "source": [
    "# Numpy索引：index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "da02a90c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4,)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# 查看形状，会返回一个元组，每个元素代表这一维的元素数目：\n",
    "a = np.array([1, 2, 3, 5])\n",
    "# 1维数组，返回一个元组\n",
    "a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a1309e98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 查看元素数目：\n",
    "a.size"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93aebc68",
   "metadata": {},
   "source": [
    "使用fill方法设定初始值\n",
    "\n",
    "可以使用 fill 方法将数组设为指定值："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "edc572fd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3 5]\n",
      "[-4 -4 -4 -4]\n"
     ]
    }
   ],
   "source": [
    "print(a)\n",
    "a.fill(-4)\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "80d0abb2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[12 13]\n"
     ]
    }
   ],
   "source": [
    "# 切片，支持负索引：\n",
    "a = np.array([11, 12, 13, 14, 15])\n",
    "print(a[1:-2])  # [12 13]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0b61a551",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[11 13 15]\n",
      "[14 15]\n"
     ]
    }
   ],
   "source": [
    "# 省略参数：\n",
    "print(a[::2])  # [11 13 15]\n",
    "print(a[-2:])  # array([14, 15])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "236f13a3",
   "metadata": {},
   "source": [
    "假设我们记录一辆汽车表盘上每天显示的里程数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "13288500",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([180,  60, 860, 300])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rec = np.array([21000, 21180, 21240, 22100, 22400])\n",
    "dist = rec[1:] - rec[:-1] # 后一天减去前一天的\n",
    "dist"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9202e4ee",
   "metadata": {},
   "source": [
    "### 多维数组的索引"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c5856ff3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([[1, 2, 3], [7, 8, 9]])\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f150460c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 3)\n",
      "6\n",
      "2\n",
      "8\n",
      "[1 2 3]\n"
     ]
    }
   ],
   "source": [
    "# 查看形状：\n",
    "print(a.shape)\n",
    "\n",
    "# 查看总的元素个数：\n",
    "print(a.size)\n",
    "\n",
    "# 查看维数：\n",
    "print(a.ndim)\n",
    "\n",
    "# 对于二维数组，可以传入两个数字来索引：\n",
    "print(a[1, 1])\n",
    "\n",
    "# 索引一整行内容：\n",
    "print(a[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35ea1b11",
   "metadata": {},
   "source": [
    "多维数组的复杂一点的例子:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "cf7936fe",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3 4]\n",
      "[[44 45]\n",
      " [54 55]]\n",
      "[ 2 12 22 32 42 52]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([[0, 1, 2, 3, 4, 5],\n",
    "               [10, 11, 12, 13, 14, 15],\n",
    "               [20, 21, 22, 23, 24, 25],\n",
    "               [30, 31, 32, 33, 34, 35],\n",
    "               [40, 41, 42, 43, 44, 45],\n",
    "               [50, 51, 52, 53, 54, 55]])\n",
    "\n",
    "# 想得到第一行的第 4 和第 5 两个元素：\n",
    "print(a[0, 3:5])  # [3 4]\n",
    "\n",
    "# 得到最后两行的最后两列：\n",
    "print(a[4:, 4:])  # [[44 45][54 55]]\n",
    "\n",
    "# 得到第三列：\n",
    "print(a[:, 2])  # [ 2 12 22 32 42 52]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "619af4f6",
   "metadata": {},
   "source": [
    "取出3，5行的奇数列："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7944d8bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[20, 22, 24],\n",
       "       [40, 42, 44]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = a[2::2, ::2]\n",
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7aa17a25",
   "metadata": {},
   "source": [
    "**切片在内存中使用的是引用机制**\n",
    "\n",
    "引用机制意味着，Python并没有为 b 分配新的空间来存储它的值，\n",
    "而是让 b 指向了 a 所分配的内存空间，因此，改变 b 会改变 a 的值："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "61730af8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 3])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([0, 1, 2, 3, 4])\n",
    "b = a[2:4]\n",
    "\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5d34cccb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10,  3])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[0] = 10\n",
    "\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "2490fff8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1, 10,  3,  4])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "592be095",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0  1 12  3  4]\n",
      "[ 0  1 12  3  4] [10  3]\n"
     ]
    }
   ],
   "source": [
    "# 而这种现象在列表中并不会出现：\n",
    "b = a[2:3]\n",
    "b[0] = 12\n",
    "print(a)\n",
    "\n",
    "# 解决方法是使用copy()方法产生一个复制，这个复制会申请新的内存：\n",
    "b = a[2:4].copy()\n",
    "b[0] = 10\n",
    "print(a, b)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9513c2dc",
   "metadata": {},
   "source": [
    "### 一维花式索引\n",
    "与 range 函数类似，我们可以使用 arange 函数来产生等差数组。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "e3275859",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0, 10, 20, 30, 40, 50, 60, 70])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(0, 80, 10)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "8f34f5fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10, 20, 50])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 花式索引需要指定索引位置：\n",
    "indices = [1, 2, -3]\n",
    "y = a[indices]\n",
    "\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "19e40629",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10, 20, 50, 70])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 还可以使用布尔数组来花式索引：\n",
    "mask = np.array([0, 1, 1, 0, 0, 1, 0, 1], dtype=bool)\n",
    "a[mask]  # [10 20 50 70]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fd30b8a",
   "metadata": {},
   "source": [
    "选出了所有大于0.5的值："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d820532c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.68881917, 0.94978704, 0.20051132, 0.7950809 , 0.20974509,\n",
       "       0.28850105, 0.48678931, 0.21979243, 0.22952482, 0.49433356])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from numpy.random import rand\n",
    "\n",
    "a = rand(10)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "991aec54",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.68881917, 0.94978704, 0.7950809 ])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask = a > 0.5\n",
    "a[mask]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ca71325",
   "metadata": {},
   "source": [
    "### “不完全”索引\n",
    "只给定行索引的时候，返回整行："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "dffa4d28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3,  4,  5],\n",
       "       [10, 11, 12, 13, 14, 15],\n",
       "       [20, 21, 22, 23, 24, 25]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([[0, 1, 2, 3, 4, 5],\n",
    "           [10, 11, 12, 13, 14, 15],\n",
    "           [20, 21, 22, 23, 24, 25],\n",
    "           [30, 31, 32, 33, 34, 35],\n",
    "           [40, 41, 42, 43, 44, 45],\n",
    "           [50, 51, 52, 53, 54, 55]])\n",
    "b = a[:3]\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "980e22e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10, 11, 12, 13, 14, 15],\n",
       "       [20, 21, 22, 23, 24, 25],\n",
       "       [40, 41, 42, 43, 44, 45]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 这时候也可以使用花式索引取出第2，3，5行：\n",
    "condition = np.array([0, 1, 1, 0, 1, 0], dtype=bool)\n",
    "c = a[condition]\n",
    "c"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9fb12d78",
   "metadata": {},
   "source": [
    "### where语句\n",
    "\n",
    "where(array)\n",
    "\n",
    "where 函数会返回所有非零元素的索引。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "150fdbf7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False,  True,  True])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([1, 2, 4, 6])\n",
    "a > 2  # [False False  True  True]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "882c0748",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([2, 3]),)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.where(a > 2)\n",
    "b # 返回的是索引位置"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "b5050079",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 3]\n",
      "[4 6]\n"
     ]
    }
   ],
   "source": [
    "# 注意到 where 的返回值是一个元组。\n",
    "index = np.where(a > 2)[0]\n",
    "print(index)  # [2 3]\n",
    "\n",
    "# 可以直接用 where 的返回值进行索引：\n",
    "loc = np.where(a > 2)\n",
    "b = a[loc]\n",
    "print(b)  # [4 6]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "827af5cf",
   "metadata": {},
   "source": [
    "考虑二维数组："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "7cb19acb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([0, 0, 1, 1]), array([1, 3, 2, 3]))\n",
      "[12 20 11 15]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([[0, 12, 5, 20],\n",
    "           [1, 2, 11, 15]])\n",
    "loc = np.where(a > 10)\n",
    "print(loc)  # (array([0, 0, 1, 1]), array([1, 3, 2, 3]))\n",
    "\n",
    "# 也可以直接用来索引a：\n",
    "b = a[loc]\n",
    "print(b)  # [12 20 11 15]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa7e4a76",
   "metadata": {},
   "source": [
    "或者可以这样："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "081ed508",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 1 1]\n",
      "[1 3 2 3]\n",
      "[12 20 11 15]\n"
     ]
    }
   ],
   "source": [
    "rows, cols = np.where(a > 10)\n",
    "print(rows)\n",
    "print(cols)\n",
    "print(a[rows, cols])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "038fbe5b",
   "metadata": {},
   "source": [
    "例子："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "3391aebb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11],\n",
       "       [12, 13, 14, 15],\n",
       "       [16, 17, 18, 19]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(20)\n",
    "a.shape = 5, 4\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "e12d1f68",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False, False, False, False],\n",
       "       [False, False, False, False],\n",
       "       [False, False, False, False],\n",
       "       [False,  True,  True,  True],\n",
       "       [ True,  True,  True,  True]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a > 12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "4c0b15c3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([3, 3, 3, 4, 4, 4, 4]), array([1, 2, 3, 0, 1, 2, 3]))"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.where(a > 12)\n",
    "b\n",
    "# (array([3, 3, 3, 4, 4, 4, 4]), array([1, 2, 3, 0, 1, 2, 3]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "d02922d8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([13, 14, 15, 16, 17, 18, 19])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[b]  # [13 14 15 16 17 18 19]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c691a5a",
   "metadata": {},
   "source": [
    "本节完。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bb1592c0",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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