Numpy.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.00160242,  1.40986346,  0.56378413],\n",
       "       [ 0.26148908,  0.93617709, -1.87600515]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#4.1 Numpy 的ndarray：一种多维数组对象\n",
    "import numpy as np\n",
    "#Generate some random data\n",
    "data = np.random.randn(2,3)\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 6.60056143,  7.59472989, -5.27268652],\n",
       "       [-2.16448272,  8.61174371,  0.14576085]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data*10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.32011229,  1.51894598, -1.0545373 ],\n",
       "       [-0.43289654,  1.72234874,  0.02915217]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data+data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6. , 7.5, 8. , 0. , 1. ])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#创建ndarray(序列型对象)\n",
    "import numpy as np\n",
    "data1 = [6,7.5,8,0,1]\n",
    "arr1 = np.array(data1)\n",
    "arr1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3, 4],\n",
       "       [5, 6, 7, 8]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#嵌套序列\n",
    "import numpy as np\n",
    "data2 = [[1,2,3,4],[5,6,7,8]]\n",
    "arr2 = np.array(data2)\n",
    "arr2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 4)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr1.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int32')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "np.zeros(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros((3,6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[9.54599745e-312, 2.47032823e-322],\n",
       "        [0.00000000e+000, 0.00000000e+000],\n",
       "        [0.00000000e+000, 1.04082753e-047]],\n",
       "\n",
       "       [[4.97167527e-091, 5.99520995e-066],\n",
       "        [3.63574746e+174, 4.25310541e+174],\n",
       "        [3.99910963e+252, 4.03629024e+175]]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.empty((2,3,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 1., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 1., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 1., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 1., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 1., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0., 1., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0., 0., 1., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0., 0., 0., 1., 0.],\n",
       "       [0., 0., 0., 0., 0., 0., 0., 0., 0., 1.]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.eye(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#ndarray的数据类型\n",
    "import numpy as np\n",
    "arr1 = np.array([1,2,3],dtype=np.float64)\n",
    "arr2 = np.array([1,2,3],dtype=np.int64)\n",
    "arr1.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int64')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int32')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#转换数据类型\n",
    "import numpy as np\n",
    "arr = np.array([1,2,3,4,5])\n",
    "arr.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float_arr = arr.astype(np.float64)\n",
    "float_arr.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3.7, -1.2, -2.6,  0.5, 12.9, 10.1])"
      ]
     },
     "execution_count": 19,
     "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": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3, -1, -2,  0, 12, 10])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.astype(np.int32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.25, -9.6 , 42.  ])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_eric_strings = np.array(['1.25','-9.6','42'])\n",
    "num_eric_strings.astype(float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 1., 2., 3., 4., 5., 6., 7., 8., 9.])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int_array = np.arange(10)\n",
    "calibers = np.array([.22,.270,.357,.380,.44,.50])\n",
    "int_array.astype(calibers.dtype)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([         0, 1075314688,          0, 1075707904,          0,\n",
       "       1075838976,          0, 1072693248], dtype=uint32)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "empty_uint32 = np.empty(8,dtype='u4')\n",
    "empty_uint32"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 2., 3.],\n",
       "       [4., 5., 6.]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Numpy数组的运算\n",
    "arr = np.array([[1.,2.,3.],[4.,5.,6.]])\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  4.,  9.],\n",
       "       [16., 25., 36.]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr*arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0.],\n",
       "       [0., 0., 0.]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr-arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.5       , 0.33333333],\n",
       "       [0.25      , 0.2       , 0.16666667]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1/arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 1.41421356, 1.73205081],\n",
       "       [2.        , 2.23606798, 2.44948974]])"
      ]
     },
     "execution_count": 32,
     "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": "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": [
    "#基本的索引和切片\n",
    "import numpy as np\n",
    "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": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4, 12, 12, 12,  8,  9])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[5:8] = 12\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12, 12, 12])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr_slice = arr[5:8]\n",
    "arr_slice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([    0,     1,     2,     3,     4,    12, 12345,    12,     8,\n",
       "           9])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr_slice[1] = 12345\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4, 64, 64, 64,  8,  9])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr_slice[:] = 64\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 8, 9])"
      ]
     },
     "execution_count": 46,
     "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": 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": [
       "3"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[0,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 1,  2,  3],\n",
       "        [ 4,  5,  6]],\n",
       "\n",
       "       [[ 7,  8,  9],\n",
       "        [10, 11, 12]]])"
      ]
     },
     "execution_count": 53,
     "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": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[42, 42, 42],\n",
       "        [42, 42, 42]],\n",
       "\n",
       "       [[ 7,  8,  9],\n",
       "        [10, 11, 12]]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "old_values = arr3d.copy()\n",
    "arr3d[0] = 42\n",
    "arr3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 8, 9])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d[1,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 7,  8,  9],\n",
       "       [10, 11, 12]])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = arr3d[1]\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 8, 9])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4, 64, 64, 64,  8,  9])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#切片索引\n",
    "import numpy as np\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  2,  3,  4, 64])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[1:6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 3],\n",
       "       [5, 6]])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:2,1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 5])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[1,:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 6])"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:2,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [4],\n",
       "       [7]])"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:,:1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0],\n",
       "       [4, 0, 0],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:2,1:] = 0\n",
    "arr2d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Bob', 'Joe', 'Will', 'Bob', 'Will'], dtype='<U4')"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#布尔型索引\n",
    "import numpy as np\n",
    "names = np.array(['Bob','Joe','Will','Bob','Will'])\n",
    "data = np.random.randn(7,4)\n",
    "names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.74300719,  0.08968585, -2.19784319, -0.12625833],\n",
       "       [ 0.02701389,  0.52510093, -0.44675143,  1.07837882],\n",
       "       [-0.63809503, -0.22134761, -0.51813752, -0.127262  ],\n",
       "       [ 1.22067228, -1.31660962, -0.57547406, -1.40810589],\n",
       "       [-0.76417018, -0.9057833 ,  0.13843215, -0.75950265],\n",
       "       [ 1.09035921,  0.03810573,  0.4228162 ,  1.71877001],\n",
       "       [ 0.82538824,  0.09432466,  0.90292365, -0.44623205]])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False,  True, False])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names == 'Bob'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "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": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#花式索引\n",
    "import numpy as np\n",
    "arr = np.empty((8,4))\n",
    "for i in range(8):\n",
    "    arr[i] = i\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "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": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[[4,3,0,6]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5., 5., 5., 5.],\n",
       "       [3., 3., 3., 3.],\n",
       "       [1., 1., 1., 1.]])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[[-3,-5,-7]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "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": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(32).reshape((8,4))\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4, 23, 29, 10])"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[[1,5,7,2],[0,3,1,2]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "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": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[[1,5,7,2]][:,[0,3,1,2]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "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": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#数组转置与轴对换\n",
    "import numpy as np\n",
    "arr = np.arange(15).reshape((3,5))\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "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": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.69306685,  0.10577455, -0.29956033],\n",
       "       [ 0.21236179, -0.9005502 ,  1.53338829],\n",
       "       [ 2.59179414, -1.0973871 ,  2.80785805],\n",
       "       [-0.03858067, -1.32608771,  0.48899554],\n",
       "       [ 0.07338376, -0.35643257, -1.26529761],\n",
       "       [ 1.21549738,  0.01201184, -1.00798873]])"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(6,3)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 8.72714357, -2.92252972,  6.05848203],\n",
       "       [-2.92252972,  3.91213442, -4.70345166],\n",
       "       [ 6.05848203, -4.70345166, 13.1812188 ]])"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(arr.T,arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "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": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(16).reshape((2,2,4))\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "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": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.transpose((1,0,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "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": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "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": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.swapaxes(1,2)\n",
    "#swapaxes返回源数据的视图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#4.2通用函数：快速的元素级数组函数\n",
    "import numpy as np\n",
    "arr = np.arange(10)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 1.        , 1.41421356, 1.73205081, 2.        ,\n",
       "       2.23606798, 2.44948974, 2.64575131, 2.82842712, 3.        ])"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.00000000e+00, 2.71828183e+00, 7.38905610e+00, 2.00855369e+01,\n",
       "       5.45981500e+01, 1.48413159e+02, 4.03428793e+02, 1.09663316e+03,\n",
       "       2.98095799e+03, 8.10308393e+03])"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.29997895, -1.13023467,  0.04080098, -0.6270586 ,  0.02874077,\n",
       "       -0.18159788,  1.13263641, -1.58742233])"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.random.randn(8)\n",
    "y = np.random.randn(8)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.79597933,  0.02837327, -0.34180716,  0.31262398,  0.10355968,\n",
       "        0.89357148, -0.83900659,  0.48357737])"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.29997895,  0.02837327,  0.04080098,  0.31262398,  0.10355968,\n",
       "        0.89357148,  1.13263641,  0.48357737])"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.maximum(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0.75574086, -11.52865753,   0.81363629,   3.57720021,\n",
       "         7.9850385 ,   1.14871948,   6.84214931])"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(7)*5\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.75574086, -0.52865753,  0.81363629,  0.57720021,  0.9850385 ,\n",
       "        0.14871948,  0.84214931])"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "remainder,whole_part = np.modf(arr)\n",
    "remainder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0., -11.,   0.,   3.,   7.,   1.,   6.])"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "whole_part"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0.75574086, -11.52865753,   0.81363629,   3.57720021,\n",
       "         7.9850385 ,   1.14871948,   6.84214931])"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "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": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#4.3利用数组进行数据处理\n",
    "import numpy as np\n",
    "points = np.arange(-5,5,0.01)\n",
    "xs,ys = np.meshgrid(points,points)\n",
    "ys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[7.07106781, 7.06400028, 7.05693985, ..., 7.04988652, 7.05693985,\n",
       "        7.06400028],\n",
       "       [7.06400028, 7.05692568, 7.04985815, ..., 7.04279774, 7.04985815,\n",
       "        7.05692568],\n",
       "       [7.05693985, 7.04985815, 7.04278354, ..., 7.03571603, 7.04278354,\n",
       "        7.04985815],\n",
       "       ...,\n",
       "       [7.04988652, 7.04279774, 7.03571603, ..., 7.0286414 , 7.03571603,\n",
       "        7.04279774],\n",
       "       [7.05693985, 7.04985815, 7.04278354, ..., 7.03571603, 7.04278354,\n",
       "        7.04985815],\n",
       "       [7.06400028, 7.05692568, 7.04985815, ..., 7.04279774, 7.04985815,\n",
       "        7.05692568]])"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = np.sqrt(xs ** 2 + ys ** 2)\n",
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x1c1e90d62b0>"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.imshow(z,cmap=plt.cm.gray);plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Image plot of $\\\\sqrt{x^2 +y^2}$ for a grid of values')"
      ]
     },
     "execution_count": 130,
     "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.title(\"Image plot of $\\sqrt{x^2 +y^2}$ for a grid of values\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.1, 2.2, 1.3, 1.4, 2.5]"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#讲条件逻辑表述为数组运算\n",
    "import numpy as np\n",
    "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])\n",
    "result = [(x if c else y)\n",
    "          for x,y,c in zip (xarr,yarr,cond)]\n",
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.1, 2.2, 1.3, 1.4, 2.5])"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result = np.where(cond,xarr,yarr)\n",
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.29963475, -0.60766528,  1.23503376, -1.18626118],\n",
       "       [-0.05074228, -0.51019625, -0.49160973,  0.82988911],\n",
       "       [-0.11682229, -0.04759952, -1.08689021,  1.11413842],\n",
       "       [-0.52398286,  0.04424767, -1.56030486,  2.0857034 ]])"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(4,4)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ True, False,  True, False],\n",
       "       [False, False, False,  True],\n",
       "       [False, False, False,  True],\n",
       "       [False,  True, False,  True]])"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr > 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "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": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(arr > 0,2,-2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.        , -0.60766528,  2.        , -1.18626118],\n",
       "       [-0.05074228, -0.51019625, -0.49160973,  2.        ],\n",
       "       [-0.11682229, -0.04759952, -1.08689021,  2.        ],\n",
       "       [-0.52398286,  2.        , -1.56030486,  2.        ]])"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(arr > 0,2,arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.5992689 , -1.69864394,  1.561818  , -0.53395186],\n",
       "       [-1.71298856, -0.94139098, -0.32612384, -1.12102302],\n",
       "       [-0.071833  ,  0.4600608 ,  0.20233416,  0.58837811],\n",
       "       [ 1.57594721,  0.87444476, -0.64955072, -0.40976553],\n",
       "       [ 1.21241387, -0.90363265, -1.00081511,  0.56469417]])"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#数学和统计方法\n",
    "import numpy as np\n",
    "arr = np.random.randn(5,4)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.1964448521542647"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.1964448521542647"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-3.9288970430852936"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.56751168, -1.0253816 ,  0.29473502,  0.34776893, -0.03183493])"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.mean(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.59572939, -2.20916201, -0.21233751, -0.91166813])"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.sum(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  3,  6, 10, 15, 21, 28], dtype=int32)"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.array([0,1,2,3,4,5,6,7])\n",
    "arr.cumsum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5],\n",
       "       [6, 7, 8]])"
      ]
     },
     "execution_count": 146,
     "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": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2],\n",
       "       [ 3,  5,  7],\n",
       "       [ 9, 12, 15]], dtype=int32)"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.cumsum(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0,   0,   0],\n",
       "       [  3,  12,  60],\n",
       "       [  6,  42, 336]], dtype=int32)"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.cumprod(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "53"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#用于布尔型数组的方法\n",
    "import numpy as np\n",
    "arr = np.random.randn(100)\n",
    "(arr > 0).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bools = np.array([False,False,True,False])\n",
    "bools.any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bools.all()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.40191351, -0.40635211, -0.91622923, -1.30847631, -2.07000455,\n",
       "       -0.47327965])"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#排序\n",
    "import numpy as np\n",
    "arr = np.random.randn(6)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2.07000455, -1.30847631, -0.91622923, -0.47327965, -0.40635211,\n",
       "        0.40191351])"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.sort()\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.37438646, -0.7049088 , -0.51239477],\n",
       "       [ 0.84855863, -0.0462446 , -0.60550334],\n",
       "       [ 1.51910966,  0.35563551, -0.74311457],\n",
       "       [-0.4214869 , -1.34728708, -0.93430907],\n",
       "       [ 0.01429564,  0.0452119 , -0.08273392]])"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(5,3)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.7049088 , -0.51239477, -0.37438646],\n",
       "       [-0.60550334, -0.0462446 ,  0.84855863],\n",
       "       [-0.74311457,  0.35563551,  1.51910966],\n",
       "       [-1.34728708, -0.93430907, -0.4214869 ],\n",
       "       [-0.08273392,  0.01429564,  0.0452119 ]])"
      ]
     },
     "execution_count": 159,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.sort(1)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.5767760032976605"
      ]
     },
     "execution_count": 161,
     "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": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Bob', 'Joe', 'Will'], dtype='<U4')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#唯一化以及其它的集合逻辑\n",
    "import numpy as np\n",
    "names = np.array(['Bob','Joe','Will','Bob','Will'])\n",
    "np.unique(names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4])"
      ]
     },
     "execution_count": 4,
     "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": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Bob', 'Joe', 'Will']"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted(set(names))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False,  True,  True, False,  True])"
      ]
     },
     "execution_count": 6,
     "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": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#4.4用于数组的文件输入输出\n",
    "import numpy as np\n",
    "arr = np.arange(10)\n",
    "np.save('some_array',arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.load('some_array.npy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.savez('array_archive.npz',a=arr,b=arr)\n",
    "arch = np.load('array_archive.npz')\n",
    "arch['b']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.savez_compressed('arrays_compressed.npz',a=arr,b=arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#4.5线性代数\n",
    "import numpy as np\n",
    "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": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 6, 23],\n",
       "       [-1,  7],\n",
       "       [ 8,  9]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 28,  64],\n",
       "       [ 67, 181]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.dot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 28,  64],\n",
       "       [ 67, 181]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6., 15.])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(x,np.ones(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6., 15.])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x @ np.ones(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.01406200e-01,  2.88270174e-02,  1.74241550e-01,\n",
       "        -1.58925680e-03, -7.58480644e-02],\n",
       "       [ 2.88270174e-02,  1.20319976e+00,  9.18038971e-01,\n",
       "         3.71126702e-01, -1.02964326e+00],\n",
       "       [ 1.74241550e-01,  9.18038971e-01,  1.87332065e+00,\n",
       "         5.78580778e-01, -1.56544758e+00],\n",
       "       [-1.58925680e-03,  3.71126702e-01,  5.78580778e-01,\n",
       "         4.49081836e-01, -6.96134555e-01],\n",
       "       [-7.58480644e-02, -1.02964326e+00, -1.56544758e+00,\n",
       "        -6.96134555e-01,  1.74286717e+00]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from numpy.linalg import inv,qr\n",
    "x = np.random.randn(5,5)\n",
    "mat = x.T.dot(x)\n",
    "inv(mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.00000000e+00,  2.11962104e-16,  5.01935486e-16,\n",
       "         1.67060854e-17,  5.36340576e-16],\n",
       "       [ 6.91705175e-18,  1.00000000e+00, -2.07572381e-16,\n",
       "         2.59348420e-17,  3.99857385e-16],\n",
       "       [-1.19051172e-16,  5.36579226e-16,  1.00000000e+00,\n",
       "         2.05329605e-16,  4.44285233e-16],\n",
       "       [ 1.45318957e-17, -1.64945351e-16, -5.72275262e-16,\n",
       "         1.00000000e+00,  1.00014210e-15],\n",
       "       [ 3.49539812e-17,  6.79979343e-16,  1.19856977e-16,\n",
       "         3.67614845e-16,  1.00000000e+00]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat.dot(inv(mat))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-14.6502084 ,  -0.50154123,   3.65196985,  -2.45531293,\n",
       "          1.40644469],\n",
       "       [  0.        ,  -2.15321447,  -1.5454658 ,  -3.40606032,\n",
       "         -4.35064115],\n",
       "       [  0.        ,   0.        ,  -2.77405524,  -2.69865997,\n",
       "         -3.84628781],\n",
       "       [  0.        ,   0.        ,   0.        ,  -5.41860519,\n",
       "         -2.16601286],\n",
       "       [  0.        ,   0.        ,   0.        ,   0.        ,\n",
       "          0.37692308]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q,r = qr(mat)\n",
    "r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.30115001, -1.25048429,  1.6359591 , -0.1109819 ],\n",
       "       [-1.047847  ,  1.90394927, -0.10815803, -0.60077574],\n",
       "       [ 0.93111775,  0.73946753, -0.97415372, -0.40649315],\n",
       "       [ 0.02979956, -0.1704346 , -0.52887129, -0.69423006]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#4.6伪随机数生成\n",
    "import numpy as np\n",
    "samples = np.random.normal(size=(4,4))\n",
    "samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(1234)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.47143516, -1.19097569,  1.43270697, -0.3126519 , -0.72058873,\n",
       "        0.88716294,  0.85958841, -0.6365235 ,  0.01569637, -2.24268495])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = np.random.RandomState(1234)\n",
    "rng.randn(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x224e285e278>]"
      ]
     },
     "execution_count": 29,
     "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": [
    "#4.7示例：随机漫步\n",
    "import numpy as np\n",
    "import random\n",
    "import matplotlib.pyplot as plt\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)\n",
    "plt.plot(walk[:100])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nsteps = 1000\n",
    "draws = np.random.randint(0,2,size=nsteps)\n",
    "steps = np.where(draws > 0,1,-1)\n",
    "walk = steps.cumsum()\n",
    "walk.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "47"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "walk.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "21"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(np.abs(walk) >= 10).argmax()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -1,  -2,  -1, ..., -18, -19, -18],\n",
       "       [  1,   0,  -1, ...,  24,  23,  22],\n",
       "       [ -1,   0,   1, ...,  14,  15,  16],\n",
       "       ...,\n",
       "       [ -1,   0,  -1, ...,  30,  29,  30],\n",
       "       [  1,   0,  -1, ...,  18,  19,  20],\n",
       "       [ -1,   0,   1, ...,  -6,  -7,  -8]], dtype=int32)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#一次模拟多个随机漫步\n",
    "nwalks = 5000\n",
    "nsteps = 1000\n",
    "draws = np.random.randint(0,2,size=(nwalks,nsteps))\n",
    "steps = np.where(draws > 0,1,-1)\n",
    "walks = steps.cumsum(1)\n",
    "walks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "137"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "walks.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-137"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "walks.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True, ...,  True,  True, False])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hits30 = (np.abs(walks) >= 30).any(1)\n",
    "hits30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3431"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hits30.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "267.0"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crossing_times = (np.abs(walks[hits30]) >= 30).argmax()\n",
    "crossing_times.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.06626308, -0.05580706,  0.00894138, ..., -0.16706321,\n",
       "         0.06556504, -0.25535347],\n",
       "       [-0.30144803, -0.04668555,  0.39323052, ..., -0.13938766,\n",
       "         0.05117242,  0.18862323],\n",
       "       [ 0.43825982, -0.09105661, -0.12766657, ..., -0.13850272,\n",
       "        -0.2132949 ,  0.44987438],\n",
       "       ...,\n",
       "       [-0.10667613,  0.15201926,  0.10808834, ...,  0.54424086,\n",
       "         0.01814818, -0.10079955],\n",
       "       [-0.09886624,  0.18707354, -0.11160941, ..., -0.1337319 ,\n",
       "         0.12325044, -0.35940792],\n",
       "       [-0.20215048, -0.13240065, -0.21375584, ...,  0.10644227,\n",
       "         0.1328109 ,  0.22751891]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "steps = np.random.normal(loc=0,scale=0.25,size=(nwalks,nsteps))\n",
    "steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#4.8结论\n",
    "import pandas as pd\n",
    "from pandas import Series,DataFrame"
   ]
  }
 ],
 "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}