第4章 Numpy基础：数组和矢量计算.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NumPy基础: 数组和矢量计算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "np.random.seed(12345)\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rc('figure', figsize=(10, 6))\n",
    "np.set_printoptions(precision=4, suppress=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "my_arr = np.arange(1000000)\n",
    "my_list = list(range(1000000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 31.7 ms\n"
     ]
    }
   ],
   "source": [
    "%time for _ in range(10): my_arr2 = my_arr * 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 1.01 s\n"
     ]
    }
   ],
   "source": [
    "%time for _ in range(10): my_list2 = [x * 2 for x in my_list]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The NumPy ndarray: 一种多维数组对象"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.2047,  0.4789, -0.5194],\n",
       "       [-0.5557,  1.9658,  1.3934]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "# Generate some random data\n",
    "data = np.random.randn(2, 3)\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.4094,  0.9579, -1.0389],\n",
       "       [-1.1115,  3.9316,  2.7868]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data * 10\n",
    "data + data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape\n",
    "data.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 创建ndarrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6. , 7.5, 8. , 0. , 1. ])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data1 = [6, 7.5, 8, 0, 1]\n",
    "arr1 = np.array(data1)\n",
    "arr1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3, 4],\n",
       "       [5, 6, 7, 8]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data2 = [[1, 2, 3, 4], [5, 6, 7, 8]]\n",
    "arr2 = np.array(data2)\n",
    "arr2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 4)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr1.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int32')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros((3, 6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[9.3509e-312, 3.1620e-322],\n",
       "        [0.0000e+000, 0.0000e+000],\n",
       "        [0.0000e+000, 1.3955e-047]],\n",
       "\n",
       "       [[8.6917e-071, 2.3601e+180],\n",
       "        [1.1771e-047, 6.5841e-066],\n",
       "        [2.6303e-052, 2.9020e+180]]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.empty((2, 3, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ndarrays的数据类型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr1 = np.array([1, 2, 3], dtype=np.float64)\n",
    "arr1.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int32')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2 = np.array([1, 2, 3], dtype=np.int32)\n",
    "arr2.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int32')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.array([1, 2, 3, 4, 5])\n",
    "arr.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float_arr = arr.astype(np.float64)\n",
    "float_arr.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3.7, -1.2, -2.6,  0.5, 12.9, 10.1])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.array([3.7, -1.2, -2.6, 0.5, 12.9, 10.1])\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3, -1, -2,  0, 12, 10])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.astype(np.int32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.25, -9.6 , 42.  ])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#将数字格式的字符串转换成浮点型数据\n",
    "numeric_strings = np.array(['1.25', '-9.6', '42'], dtype=np.string_)\n",
    "numeric_strings.astype(float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 1., 2., 3., 4., 5., 6., 7., 8., 9.])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int_array = np.arange(10)\n",
    "calibers = np.array([.22, .270, .357, .380, .44, .50], dtype=np.float64)\n",
    "int_array.astype(calibers.dtype)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([         0, 1075314688,          0, 1075707904,          0,\n",
       "       1075838976,          0, 1072693248], dtype=uint32)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "empty_uint32 = np.empty(8, dtype='u4')\n",
    "empty_uint32"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 数组和标量之间的运算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 2., 3.],\n",
       "       [4., 5., 6.]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.array([[1., 2., 3.], [4., 5., 6.]])\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  4.,  9.],\n",
       "       [16., 25., 36.]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr * arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0.],\n",
       "       [0., 0., 0.]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr - arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.    , 0.5   , 0.3333],\n",
       "       [0.25  , 0.2   , 0.1667]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 / arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.    , 1.4142, 1.7321],\n",
       "       [2.    , 2.2361, 2.4495]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr ** 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  4.,  1.],\n",
       "       [ 7.,  2., 12.]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2 = np.array([[0., 4., 1.], [7., 2., 12.]])\n",
    "arr2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False,  True, False],\n",
       "       [ True, False,  True]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2 > arr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 基本的索引和切片"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(10)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 6, 7])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[5:8]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4, 12, 12, 12,  8,  9])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[5:8] = 12\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12, 12, 12])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr_slice = arr[5:8]\n",
    "arr_slice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([    0,     1,     2,     3,     4,    12, 12345,    12,     8,\n",
       "           9])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr_slice[1] = 12345\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4, 64, 64, 64,  8,  9])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr_slice[:] = 64\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 8, 9])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n",
    "arr2d[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[0][2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[0, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 1,  2,  3],\n",
       "        [ 4,  5,  6]],\n",
       "\n",
       "       [[ 7,  8,  9],\n",
       "        [10, 11, 12]]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d = np.array([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]])\n",
    "arr3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[42, 42, 42],\n",
       "        [42, 42, 42]],\n",
       "\n",
       "       [[ 7,  8,  9],\n",
       "        [10, 11, 12]]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "old_values = arr3d[0].copy()\n",
    "arr3d[0] = 42\n",
    "arr3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 1,  2,  3],\n",
       "        [ 4,  5,  6]],\n",
       "\n",
       "       [[ 7,  8,  9],\n",
       "        [10, 11, 12]]])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d[0] = old_values\n",
    "arr3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 8, 9])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d[1, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 7,  8,  9],\n",
       "       [10, 11, 12]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = arr3d[1]\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 8, 9])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 切片索引"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  2,  3,  4, 64])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr\n",
    "arr[1:6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 3],\n",
       "       [5, 6]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:2, 1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 5])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[1, :2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 6])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:2, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [4],\n",
       "       [7]])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:, :1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0],\n",
       "       [4, 0, 0],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:2, 1:] = 0\n",
    "arr2d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 布尔型索引"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'], dtype='<U4')"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names = np.array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'])\n",
    "names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.0929,  0.2817,  0.769 ,  1.2464],\n",
       "       [ 1.0072, -1.2962,  0.275 ,  0.2289],\n",
       "       [ 1.3529,  0.8864, -2.0016, -0.3718],\n",
       "       [ 1.669 , -0.4386, -0.5397,  0.477 ],\n",
       "       [ 3.2489, -1.0212, -0.5771,  0.1241],\n",
       "       [ 0.3026,  0.5238,  0.0009,  1.3438],\n",
       "       [-0.7135, -0.8312, -2.3702, -1.8608]])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = np.random.randn(7, 4)\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False,  True, False, False, False])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names == 'Bob'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.0929,  0.2817,  0.769 ,  1.2464],\n",
       "       [ 1.669 , -0.4386, -0.5397,  0.477 ]])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#只显示为true的列\n",
    "data[names == 'Bob']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.769 ,  1.2464],\n",
       "       [-0.5397,  0.477 ]])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[names == 'Bob', 2:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.2464, 0.477 ])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[names == 'Bob', 3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False,  True,  True, False,  True,  True,  True])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names != 'Bob'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.0072, -1.2962,  0.275 ,  0.2289],\n",
       "       [ 1.3529,  0.8864, -2.0016, -0.3718],\n",
       "       [ 3.2489, -1.0212, -0.5771,  0.1241],\n",
       "       [ 0.3026,  0.5238,  0.0009,  1.3438],\n",
       "       [-0.7135, -0.8312, -2.3702, -1.8608]])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#对条件进行否定\n",
    "data[~(names == 'Bob')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.0072, -1.2962,  0.275 ,  0.2289],\n",
       "       [ 1.3529,  0.8864, -2.0016, -0.3718],\n",
       "       [ 3.2489, -1.0212, -0.5771,  0.1241],\n",
       "       [ 0.3026,  0.5238,  0.0009,  1.3438],\n",
       "       [-0.7135, -0.8312, -2.3702, -1.8608]])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cond = names == 'Bob'\n",
    "data[~cond]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False,  True,  True,  True, False, False])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask = (names == 'Bob') | (names == 'Will')\n",
    "mask"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.0929,  0.2817,  0.769 ,  1.2464],\n",
       "       [ 1.3529,  0.8864, -2.0016, -0.3718],\n",
       "       [ 1.669 , -0.4386, -0.5397,  0.477 ],\n",
       "       [ 3.2489, -1.0212, -0.5771,  0.1241]])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[mask]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.0929, 0.2817, 0.769 , 1.2464],\n",
       "       [1.0072, 0.    , 0.275 , 0.2289],\n",
       "       [1.3529, 0.8864, 0.    , 0.    ],\n",
       "       [1.669 , 0.    , 0.    , 0.477 ],\n",
       "       [3.2489, 0.    , 0.    , 0.1241],\n",
       "       [0.3026, 0.5238, 0.0009, 1.3438],\n",
       "       [0.    , 0.    , 0.    , 0.    ]])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[data < 0] = 0\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[7.    , 7.    , 7.    , 7.    ],\n",
       "       [1.0072, 0.    , 0.275 , 0.2289],\n",
       "       [7.    , 7.    , 7.    , 7.    ],\n",
       "       [7.    , 7.    , 7.    , 7.    ],\n",
       "       [7.    , 7.    , 7.    , 7.    ],\n",
       "       [0.3026, 0.5238, 0.0009, 1.3438],\n",
       "       [0.    , 0.    , 0.    , 0.    ]])"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[names != 'Joe'] = 7\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 花式索引"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [2., 2., 2., 2.],\n",
       "       [3., 3., 3., 3.],\n",
       "       [4., 4., 4., 4.],\n",
       "       [5., 5., 5., 5.],\n",
       "       [6., 6., 6., 6.],\n",
       "       [7., 7., 7., 7.]])"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.empty((8, 4))\n",
    "for i in range(8):\n",
    "    arr[i] = i\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4., 4., 4., 4.],\n",
       "       [3., 3., 3., 3.],\n",
       "       [0., 0., 0., 0.],\n",
       "       [6., 6., 6., 6.]])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#输入一个用于指定顺序的整数列表或者ndarray\n",
    "arr[[4, 3, 0, 6]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5., 5., 5., 5.],\n",
       "       [3., 3., 3., 3.],\n",
       "       [1., 1., 1., 1.]])"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[[-3, -5, -7]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "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],\n",
       "       [20, 21, 22, 23],\n",
       "       [24, 25, 26, 27],\n",
       "       [28, 29, 30, 31]])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(32).reshape((8, 4))\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4, 23, 29, 10])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#最终选取的元素是（1,0），（5,3），（7,1）和（2,2）\n",
    "arr[[1, 5, 7, 2], [0, 3, 1, 2]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4,  7,  5,  6],\n",
       "       [20, 23, 21, 22],\n",
       "       [28, 31, 29, 30],\n",
       "       [ 8, 11,  9, 10]])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#筛选所有行，但是各行中的数值进行调整\n",
    "arr[[1, 5, 7, 2]][:, [0, 3, 1, 2]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 数据转置和轴对换"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3,  4],\n",
       "       [ 5,  6,  7,  8,  9],\n",
       "       [10, 11, 12, 13, 14]])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(15).reshape((3, 5))\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  5, 10],\n",
       "       [ 1,  6, 11],\n",
       "       [ 2,  7, 12],\n",
       "       [ 3,  8, 13],\n",
       "       [ 4,  9, 14]])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.8608,  0.5601, -1.2659],\n",
       "       [ 0.1198, -1.0635,  0.3329],\n",
       "       [-2.3594, -0.1995, -1.542 ],\n",
       "       [-0.9707, -1.307 ,  0.2863],\n",
       "       [ 0.378 , -0.7539,  0.3313],\n",
       "       [ 1.3497,  0.0699,  0.2467]])"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(6, 3)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 9.2291,  0.9394,  4.948 ],\n",
       "       [ 0.9394,  3.7662, -1.3622],\n",
       "       [ 4.948 , -1.3622,  4.3437]])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(arr.T, arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  1,  2,  3],\n",
       "        [ 8,  9, 10, 11]],\n",
       "\n",
       "       [[ 4,  5,  6,  7],\n",
       "        [12, 13, 14, 15]]])"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(16).reshape((2, 2, 4))\n",
    "arr\n",
    "arr.transpose((1, 0, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  1,  2,  3],\n",
       "        [ 4,  5,  6,  7]],\n",
       "\n",
       "       [[ 8,  9, 10, 11],\n",
       "        [12, 13, 14, 15]]])"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  4],\n",
       "        [ 1,  5],\n",
       "        [ 2,  6],\n",
       "        [ 3,  7]],\n",
       "\n",
       "       [[ 8, 12],\n",
       "        [ 9, 13],\n",
       "        [10, 14],\n",
       "        [11, 15]]])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.swapaxes(1, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 通用函数: 快速的元素级数组函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(10)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.    , 1.    , 1.4142, 1.7321, 2.    , 2.2361, 2.4495, 2.6458,\n",
       "       2.8284, 3.    ])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   1.    ,    2.7183,    7.3891,   20.0855,   54.5982,  148.4132,\n",
       "        403.4288, 1096.6332, 2980.958 , 8103.0839])"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.8626, -0.01  ,  0.05  ,  0.6702,  0.853 , -0.9559, -0.0235,\n",
       "       -2.3042])"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.random.randn(8)\n",
    "y = np.random.randn(8)\n",
    "x\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.8626,  1.0048,  1.3272,  0.6702,  0.853 ,  0.0222,  0.7584,\n",
       "       -0.6605])"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.maximum(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3.2623, -6.0915, -6.663 ,  5.3731,  3.6182,  3.45  ,  5.0077])"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(7) * 5\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.2623, -0.0915, -0.663 ,  0.3731,  0.6182,  0.45  ,  0.0077])"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "remainder, whole_part = np.modf(arr)\n",
    "remainder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3., -6., -6.,  5.,  3.,  3.,  5.])"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "whole_part"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3.2623, -6.0915, -6.663 ,  5.3731,  3.6182,  3.45  ,  5.0077])"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\program\\Anaconda\\lib\\site-packages\\ipykernel_launcher.py:1: RuntimeWarning: invalid value encountered in sqrt\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([   nan,    nan,    nan, 2.318 , 1.9022, 1.8574, 2.2378])"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\program\\Anaconda\\lib\\site-packages\\ipykernel_launcher.py:1: RuntimeWarning: invalid value encountered in sqrt\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([   nan,    nan,    nan, 2.318 , 1.9022, 1.8574, 2.2378])"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(arr, arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   nan,    nan,    nan, 2.318 , 1.9022, 1.8574, 2.2378])"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 利用数组进行数据处理"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [],
   "source": [
    "points = np.arange(-5, 5, 0.01) # 生成1000个间隔相等的点\n",
    "xs, ys = np.meshgrid(points, points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-5.  , -5.  , -5.  , ..., -5.  , -5.  , -5.  ],\n",
       "       [-4.99, -4.99, -4.99, ..., -4.99, -4.99, -4.99],\n",
       "       [-4.98, -4.98, -4.98, ..., -4.98, -4.98, -4.98],\n",
       "       ...,\n",
       "       [ 4.97,  4.97,  4.97, ...,  4.97,  4.97,  4.97],\n",
       "       [ 4.98,  4.98,  4.98, ...,  4.98,  4.98,  4.98],\n",
       "       [ 4.99,  4.99,  4.99, ...,  4.99,  4.99,  4.99]])"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99],\n",
       "       [-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99],\n",
       "       [-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99],\n",
       "       ...,\n",
       "       [-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99],\n",
       "       [-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99],\n",
       "       [-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99]])"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[7.0711, 7.064 , 7.0569, ..., 7.0499, 7.0569, 7.064 ],\n",
       "       [7.064 , 7.0569, 7.0499, ..., 7.0428, 7.0499, 7.0569],\n",
       "       [7.0569, 7.0499, 7.0428, ..., 7.0357, 7.0428, 7.0499],\n",
       "       ...,\n",
       "       [7.0499, 7.0428, 7.0357, ..., 7.0286, 7.0357, 7.0428],\n",
       "       [7.0569, 7.0499, 7.0428, ..., 7.0357, 7.0428, 7.0499],\n",
       "       [7.064 , 7.0569, 7.0499, ..., 7.0428, 7.0499, 7.0569]])"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = np.sqrt(xs ** 2 + ys ** 2)\n",
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Image plot of $\\\\sqrt{x^2 + y^2}$ for a grid of values')"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.imshow(z, cmap=plt.cm.gray); plt.colorbar()\n",
    "plt.title(\"Image plot of $\\sqrt{x^2 + y^2}$ for a grid of values\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 将条件逻辑表述为数组运算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "xarr = np.array([1.1, 1.2, 1.3, 1.4, 1.5])\n",
    "yarr = np.array([2.1, 2.2, 2.3, 2.4, 2.5])\n",
    "cond = np.array([True, False, True, True, False])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.1, 2.2, 1.3, 1.4, 2.5]"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result = [(x if c else y)\n",
    "          for x, y, c in zip(xarr, yarr, cond)]\n",
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.1, 2.2, 1.3, 1.4, 2.5])"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result = np.where(cond, xarr, yarr)\n",
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.5031, -0.6223, -0.9212, -0.7262],\n",
       "       [ 0.2229,  0.0513, -1.1577,  0.8167],\n",
       "       [ 0.4336,  1.0107,  1.8249, -0.9975],\n",
       "       [ 0.8506, -0.1316,  0.9124,  0.1882]])"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(4, 4)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2, -2, -2, -2],\n",
       "       [ 2,  2, -2,  2],\n",
       "       [ 2,  2,  2, -2],\n",
       "       [ 2, -2,  2,  2]])"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr > 0\n",
    "np.where(arr > 0, 2, -2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.5031, -0.6223, -0.9212, -0.7262],\n",
       "       [ 2.    ,  2.    , -1.1577,  2.    ],\n",
       "       [ 2.    ,  2.    ,  2.    , -0.9975],\n",
       "       [ 2.    , -0.1316,  2.    ,  2.    ]])"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(arr > 0, 2, arr) # set only positive values to 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 数学和统计方法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.1695, -0.1149,  2.0037,  0.0296],\n",
       "       [ 0.7953,  0.1181, -0.7485,  0.585 ],\n",
       "       [ 0.1527, -1.5657, -0.5625, -0.0327],\n",
       "       [-0.929 , -0.4826, -0.0363,  1.0954],\n",
       "       [ 0.9809, -0.5895,  1.5817, -0.5287]])"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(5, 4)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.19607051119998253"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.19607051119998253"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.9214102239996507"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.022 ,  0.1875, -0.502 , -0.0881,  0.3611])"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.mean(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3.1693, -2.6345,  2.2381,  1.1486])"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.sum(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  3,  6, 10, 15, 21, 28], dtype=int32)"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#对于各项进行累加\n",
    "arr = np.array([0, 1, 2, 3, 4, 5, 6, 7])\n",
    "arr.cumsum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5],\n",
       "       [6, 7, 8]])"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.array([[0, 1, 2], [3, 4, 5], [6, 7, 8]])\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2],\n",
       "       [ 3,  5,  7],\n",
       "       [ 9, 12, 15]], dtype=int32)"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.cumsum(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0,   0,   0],\n",
       "       [  3,  12,  60],\n",
       "       [  6,  42, 336]], dtype=int32)"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.cumprod(axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 用于布尔型数组的方法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "42"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(100)\n",
    "(arr > 0).sum() # 正值的数量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#any和all，any用于测试数组中是否存在一个或多个True，all用于检查数组中是否所有的值都为True\n",
    "bools = np.array([False, False, True, False])\n",
    "bools.any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bools.all()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 排序"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.6095, -0.4938,  1.24  , -0.1357,  1.43  , -0.8469])"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(6)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.8469, -0.4938, -0.1357,  0.6095,  1.24  ,  1.43  ])"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.sort()\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.6033,  1.2636, -0.2555],\n",
       "       [-0.4457,  0.4684, -0.9616],\n",
       "       [-1.8245,  0.6254,  1.0229],\n",
       "       [ 1.1074,  0.0909, -0.3501],\n",
       "       [ 0.218 , -0.8948, -1.7415]])"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(5, 3)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.2555,  0.6033,  1.2636],\n",
       "       [-0.9616, -0.4457,  0.4684],\n",
       "       [-1.8245,  0.6254,  1.0229],\n",
       "       [-0.3501,  0.0909,  1.1074],\n",
       "       [-1.7415, -0.8948,  0.218 ]])"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.sort(1)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.5311513550102103"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "large_arr = np.random.randn(1000)\n",
    "large_arr.sort()\n",
    "large_arr[int(0.05 * len(large_arr))] # 5% quantile"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 唯一化及其他的集合逻辑"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Bob', 'Joe', 'Will'], dtype='<U4')"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#枚举出names中出现的种类\n",
    "names = np.array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'])\n",
    "np.unique(names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4])"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ints = np.array([3, 3, 3, 2, 2, 1, 1, 4, 4])\n",
    "np.unique(ints)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Bob', 'Joe', 'Will']"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted(set(names))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False,  True,  True, False,  True])"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "values = np.array([6, 0, 0, 3, 2, 5, 6])\n",
    "np.in1d(values, [2, 3, 6])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 用于数组的文件输入输出"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.arange(10)\n",
    "np.save('some_array', arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.load('some_array.npy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.savez('array_archive.npz', a=arr, b=arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<numpy.lib.npyio.NpzFile at 0x1b8b8e9e240>"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arch = np.load('array_archive.npz')\n",
    "arch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arch['b']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.savez_compressed('arrays_compressed.npz', a=arr, b=arr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 线性代数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 2., 3.],\n",
       "       [4., 5., 6.]])"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([[1., 2., 3.], [4., 5., 6.]])\n",
    "y = np.array([[6., 23.], [-1, 7], [8, 9]])\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 28.,  64.],\n",
       "       [ 67., 181.]])"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#与下式结果相同\n",
    "x.dot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 28.,  64.],\n",
       "       [ 67., 181.]])"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6., 15.])"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(x, np.ones(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6., 15.])"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x @ np.ones(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.linalg import inv, qr\n",
    "X = np.random.randn(5, 5)\n",
    "mat = X.T.dot(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  933.1189,   871.8258, -1417.6902, -1460.4005,  1782.1391],\n",
       "       [  871.8258,   815.3929, -1325.9965, -1365.9242,  1666.9347],\n",
       "       [-1417.6902, -1325.9965,  2158.4424,  2222.0191, -2711.6822],\n",
       "       [-1460.4005, -1365.9242,  2222.0191,  2289.0575, -2793.422 ],\n",
       "       [ 1782.1391,  1666.9347, -2711.6822, -2793.422 ,  3409.5128]])"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#计算矩阵的逆\n",
    "inv(mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 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.]])"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat.dot(inv(mat))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.6914,  4.38  ,  0.1757,  0.4075, -0.7838],\n",
       "       [ 0.    , -2.6436,  0.1939, -3.072 , -1.0702],\n",
       "       [ 0.    ,  0.    , -0.8138,  1.5414,  0.6155],\n",
       "       [ 0.    ,  0.    ,  0.    , -2.6445, -2.1669],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.0002]])"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q, r = qr(mat)\n",
    "r"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pseudorandom Number Generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.5732,  0.1933,  0.4429,  1.2796],\n",
       "       [ 0.575 ,  0.4339, -0.7658, -1.237 ],\n",
       "       [-0.5367,  1.8545, -0.92  , -0.1082],\n",
       "       [ 0.1525,  0.9435, -1.0953, -0.144 ]])"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "samples = np.random.normal(size=(4, 4))\n",
    "samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "854 ms ± 15.1 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "from random import normalvariate\n",
    "N = 1000000\n",
    "%timeit samples = [normalvariate(0, 1) for _ in range(N)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "34.2 ms ± 1.64 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit np.random.normal(size=N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(1234)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.4714, -1.191 ,  1.4327, -0.3127, -0.7206,  0.8872,  0.8596,\n",
       "       -0.6365,  0.0157, -2.2427])"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = np.random.RandomState(1234)\n",
    "rng.randn(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 范例：随机漫步"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "position = 0\n",
    "walk = [position]\n",
    "steps = 1000\n",
    "for i in range(steps):\n",
    "    step = 1 if random.randint(0, 1) else -1\n",
    "    position += step\n",
    "    walk.append(position)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1b8b465ca20>]"
      ]
     },
     "execution_count": 165,
     "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": [
    "plt.plot(walk[:100])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(12345)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [],
   "source": [
    "nsteps = 1000\n",
    "draws = np.random.randint(0, 2, size=nsteps)\n",
    "steps = np.where(draws > 0, 1, -1)\n",
    "walk = steps.cumsum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-3"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "walk.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "31"
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "walk.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "37"
      ]
     },
     "execution_count": 171,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(np.abs(walk) >= 10).argmax()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 一次模拟多个随机漫步"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1,   0,   1, ...,   8,   7,   8],\n",
       "       [  1,   0,  -1, ...,  34,  33,  32],\n",
       "       [  1,   0,  -1, ...,   4,   5,   4],\n",
       "       ...,\n",
       "       [  1,   2,   1, ...,  24,  25,  26],\n",
       "       [  1,   2,   3, ...,  14,  13,  14],\n",
       "       [ -1,  -2,  -3, ..., -24, -23, -22]], dtype=int32)"
      ]
     },
     "execution_count": 172,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nwalks = 5000\n",
    "nsteps = 1000\n",
    "draws = np.random.randint(0, 2, size=(nwalks, nsteps)) # 0 or 1\n",
    "steps = np.where(draws > 0, 1, -1)\n",
    "walks = steps.cumsum(1)\n",
    "walks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "138"
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "walks.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-133"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "walks.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False,  True, False, ..., False,  True, False])"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hits30 = (np.abs(walks) >= 30).any(1)\n",
    "hits30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3410"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hits30.sum() # Number that hit 30 or -30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "498.8897360703812"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crossing_times = (np.abs(walks[hits30]) >= 30).argmax(1)\n",
    "crossing_times.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [],
   "source": [
    "steps = np.random.normal(loc=0, scale=0.25,\n",
    "                         size=(nwalks, nsteps))"
   ]
  },
  {
   "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}