03-numpy/03.04-array-types.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 数组类型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "之前已经看过整数数组和布尔数组，除此之外还有浮点数数组和复数数组。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 复数数组"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "产生一个复数数组："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = np.array([1 + 1j, 2, 3, 4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Python**会自动判断数组的类型："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('complex128')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对于复数我们可以查看它的实部和虚部："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  2.,  3.,  4.])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.real"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  0.,  0.,  0.])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.imag"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "还可以设置它们的值："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a.imag = [1,2,3,4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "查看 `a`："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.+1.j,  2.+2.j,  3.+3.j,  4.+4.j])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "查看复共轭："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.-1.j,  2.-2.j,  3.-3.j,  4.-4.j])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.conj()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "事实上，这些属性方法可以用在浮点数或者整数数组上："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([0.,1,2,3])\n",
    "a.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  1.,  2.,  3.])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.real"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.,  0.,  0.])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.imag"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  1.,  2.,  3.])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.conj()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "但这里，虚部是只读的，并不能修改它的值：因为此ndarray数组是float型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "array does not have imaginary part to set",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-12-3db28f506ec9>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m# 会报错\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0ma\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mimag\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m4\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m: array does not have imaginary part to set"
     ]
    }
   ],
   "source": [
    "# 会报错\n",
    "a.imag = [1,2,3,4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "array does not have imaginary part to set\n",
    "数组不是复数形式，不存在虚部"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 指定数组类型"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "之前已经知道，构建数组的时候，数组会根据传入的内容自动判断类型："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = np.array([0,1.0,2,3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对于浮点数，默认为双精度："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "查看所用字节（`8 bytes * 4`）："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "32"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.nbytes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "当然，我们也可以在构建的时候指定类型："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = np.array([0,1.0,2,3],\n",
    "         dtype=np.float32)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "此时类型为单精度浮点数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float32')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "查看所用字节（`4 bytes * 4`）："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.nbytes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "除此之外，还可以指定有无符号，例如无符号整数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('uint8')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([0,1,2,3],\n",
    "         dtype=np.uint8)\n",
    "a.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`uint8` 只使用一个字节，表示 `0` 到 `255` 的整数。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "还可以从二进制数据中读取。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "先写入二进制数据："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = np.array([102,111,212], \n",
    "          dtype=np.uint8)\n",
    "a.tofile('foo.dat')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "从数据中读入，要指定类型："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'str' object has no attribute '__buffer__'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-33-0f1d6158612b>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mb\u001b[0m \u001b[1;33m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfrombuffer\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'foo.dat'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0muint8\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAttributeError\u001b[0m: 'str' object has no attribute '__buffer__'"
     ]
    }
   ],
   "source": [
    "b = np.frombuffer('foo.dat', dtype=np.uint8)\n",
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "清理数据文件："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import os\n",
    "os.remove('foo.dat')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`0-255` 的数字可以表示ASCⅡ码，我们可以用 ord 函数来查看字符的ASCⅡ码值："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "102"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ord('f')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "83"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ord('S')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numpy 类型"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "具体如下：\n",
    "\n",
    "|基本类型|可用的**Numpy**类型|备注|\n",
    "|--|--|:--|\n",
    "|布尔型|`bool`|占1个字节|\n",
    "|整型|`int8, int16, int32, int64, int128, int`| `int` 跟**C**语言中的 `long` 一样大|\n",
    "|无符号整型|`uint8, uint16, uint32, uint64, uint128, uint`| `uint` 跟**C**语言中的 `unsigned long` 一样大|\n",
    "|浮点数| `float16, float32, float64, float, longfloat`|默认为双精度 `float64` ，`longfloat` 精度大小与系统有关|\n",
    "|复数| `complex64, complex128, complex, longcomplex`| 默认为 `complex128` ，即实部虚部都为双精度|\n",
    "|字符串| `string, unicode` | 可以使用 `dtype=S4` 表示一个4字节字符串的数组|\n",
    "|对象| `object` |数组中可以使用任意值|\n",
    "|Records| `void` ||\n",
    "|时间| `datetime64, timedelta64` ||\n",
    "\n",
    "任意类型的数组："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = np.array([1,1.2,'hello', [10,20,30]], \n",
    "          dtype=object)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "乘法："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 2.4, 'hellohello', [10, 20, 30, 10, 20, 30]], dtype=object)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a * 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 类型转换"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "转换数组的类型："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.5, -3. ], dtype=float32)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([1.5, -3], \n",
    "         dtype=np.float32)\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### asarray 函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用 `asarray` 函数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.5, -3. ])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.asarray(a, dtype=np.float64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1, 253], dtype=uint8)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.asarray(a, dtype=np.uint8)#将负数去反"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`asarray` 不会修改原来数组的值："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.5, -3. ], dtype=float32)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "但当类型相同的时候，`asarray` 并不会产生新的对象，而是使用同一个引用："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "b = np.asarray(a, dtype=np.float32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b is a "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这么做的好处在与，`asarray` 不仅可以作用于数组，还可以将其他类型转化为数组。\n",
    "\n",
    "有些时候为了保证我们的输入值是数组，我们需要将其使用 `asarray` 转化，当它已经是数组的时候，并不会产生新的对象，这样保证了效率。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.asarray([1,2,3,4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### astype 方法"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`astype` 方法返回一个新数组："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.5, -3. ])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.astype(np.float64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1, 253], dtype=uint8)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.astype(np.uint8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "astype也不会改变原来数组的值："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.5, -3. ], dtype=float32)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "另外，`astype` 总是返回原来数组的一份复制，即使转换的类型是相同的："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.5 -3. ]\n",
      "[ 1.5 -3. ]\n"
     ]
    }
   ],
   "source": [
    "b = a.astype(np.float32)\n",
    "print (a)\n",
    "print (b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a is b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### view 方法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array((1,2,3,4), dtype=np.int32)\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`view` 会将 `a` 在内存中的表示看成是 `uint8` 进行解析："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 4, 0, 0, 0], dtype=uint8)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = a.view(np.uint8)#内存的占用的方法\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1073741824,          2,          3,          4])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[0] = 2**30\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "修改 `a` 会修改 `b` 的值，因为共用一块内存："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  0,  0, 64,  2,  0,  0,  0,  3,  0,  0,  0,  4,  0,  0,  0], dtype=uint8)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  }
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