Python科学计算基础包-Numpy

亦凉 2022-05-29 08:29 295阅读 0赞

## 一、Numpy概念 ##

Numpy（Numerical Python的简称）是Python科学计算的基础包。它提供了以下功能：

1.  快速高效的多维数组对象ndarray。
2.  用于对数组执行元素级计算以及直接对数组执行数学运算的函数。
3.  用于读写硬盘上基于数组的数据集的工具。
4.  线性代数运算、傅里叶变换，以及随机数生成。
5.  用于将C、C++、Fortran代码集成到Python的工具。

除了为Python提供快速的数组处理能力，Numpy在数据分析方面还有另外一个主要作用，即作为在算法之间传递数据的容器。对于数值型数据，Numpy数组在存储和处理数据时要比内置的Python数据结构高效的多。此外，由低级语言（比如C和Fortran）编写的库可以直接操作Numpy数组中的数据，无需进行任何数据复制工作。

## 二、Numpy的突出优势 ##

与Python的基本数据类型相比，其具有以下突出优势：

1.  提供功能更强大的高维数组（N-dimensional）对象 
2.  强大的广播功能（broadcasting），便于矢量化数组操作（直接对数组进行数据处理，而不需要编写循环） 
3.  集成了 C/C++ 以及 Fortran代码编写的工具 
4.  包含常用的线性代数、傅里叶变换，以及随机数生成 
5.  提供易用的C API，可以将数据传递到使用低级语言编写的外部库，也可以使外部库返回NumPy数组数据到Python 
6.  通用的数组算法，例如：sorting，unique和set等操作

NumPy提供了两种基本的对象：ndarray（N-dimensional array object）和ufunc（universal function object）。ndarray用来存储单一数据类型的多维数组，ufunc是对数组进行处理的函数。

## 三、ndarray对象 ##

Numpy的核心是ndarray对象，它封装了同质数据类型的n维数组，与python序列有以下区别：

ndarray在创建时有固定大小：不同于python中的列表，更改ndarray的大小将创建一个新的数组并删除原始数据 ndarray中的元素有相同的数据类型 ndarray便于对大量数据进行高级数学操作：通常会比python内置序列更高效也更简单 越来越多的基于python的科学和数学软件使用ndarray数组：只知道python的内置序列类型是不够的，还需要知道如何使用ndaray数组

### ndarray数据类型 ###

Numpy支持比Python更多种类的数值类型，参见：数据类型

<table style="border-width:0px;margin:0px;padding:0px;color:rgb(51,51,51);font-family:Simsun;font-size:14px;list-style-type:none;list-style-image:none;background-color:rgb(249,249,249);"> 
 <thead> 
  <tr style="border-top-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"> 
   <th align="left">numpy数据类型</th> 
   <th align="left">python类型</th> 
   <th align="left">描述</th> 
  </tr> 
 </thead> 
 <tbody> 
  <tr style="border-top-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"><strong>bool_</strong></td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">bool</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">布尔（True或False），存储为一个字节</td> 
  </tr> 
  <tr style="border-top-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"><strong>int_</strong></td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">int</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">默认整数类型（与C long相同；通常为int64或int32）</td> 
  </tr> 
  <tr style="border-top-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">intc</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">&nbsp;</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">与C int（通常为int32或int64）相同</td> 
  </tr> 
  <tr style="border-top-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">intp</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">&nbsp;</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">用于索引的整数（与C ssize_t相同；通常为int32或int64）</td> 
  </tr> 
  <tr style="border-top-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">int8</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">&nbsp;</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">字节（-128到127）</td> 
  </tr> 
  <tr style="border-top-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">int16</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">&nbsp;</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">整数（-32768到32767）</td> 
  </tr> 
  <tr style="border-top-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">int32</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">&nbsp;</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">整数（-2147483648至2147483647）</td> 
  </tr> 
  <tr style="border-top-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">int64</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">&nbsp;</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">整数（-9223372036854775808至9223372036854775807）</td> 
  </tr> 
  <tr style="border-top-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">uint8</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">&nbsp;</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">无符号整数（0到255）</td> 
  </tr> 
  <tr style="border-top-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">uint16</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">&nbsp;</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">无符号整数（0到65535）</td> 
  </tr> 
  <tr style="border-top-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">uint32</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">&nbsp;</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">无符号整数（0至4294967295）</td> 
  </tr> 
  <tr style="border-top-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">uint64</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">&nbsp;</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">无符号整数（0至18446744073709551615）</td> 
  </tr> 
  <tr style="border-top-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"><strong>float_</strong></td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">float</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">float64的简写。</td> 
  </tr> 
  <tr style="border-top-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">float16</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">&nbsp;</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">半精度浮点：符号位，5位指数，10位尾数</td> 
  </tr> 
  <tr style="border-top-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">float32</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">&nbsp;</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">单精度浮点：符号位，8位指数，23位尾数</td> 
  </tr> 
  <tr style="border-top-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">float64</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">&nbsp;</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">双精度浮点：符号位，11位指数，52位尾数</td> 
  </tr> 
  <tr style="border-top-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"><strong>complex_</strong></td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">complex</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">complex128的简写。</td> 
  </tr> 
  <tr style="border-top-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">complex64</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">&nbsp;</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">复数，由两个32位浮点（实数和虚数分量）</td> 
  </tr> 
  <tr style="border-top-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;"> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">complex128</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">&nbsp;</td> 
   <td align="left" style="border-width:0px;margin:0px;padding:0px;list-style-type:none;list-style-image:none;">复数，由两个64位浮点（实数和虚数分量）</td> 
  </tr> 
 </tbody> 
</table>

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     <div style="margin:0px;border:0px;list-style-type:none;list-style-image:none;padding:0px 1em;width:auto;height:auto;line-height:1.1em;font-size:1em;vertical-align:baseline;float:none;white-space:pre;min-height:auto;"> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;"># 作为类型名称设置数组中元素的类型，为了向后兼容，也可以使用</code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:rgb(0,102,153);line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;font-weight:bold;vertical-align:baseline;float:none;min-height:auto;">float</code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">或字符串</code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#0000FF;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">'float'</code> 
     </div> 
     <div style="margin:0px;border:0px;list-style-type:none;list-style-image:none;padding:0px 1em;width:auto;height:auto;line-height:1.1em;font-size:1em;vertical-align:baseline;float:none;white-space:pre;min-height:auto;"> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">x = np.array([</code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:rgb(0,153,0);line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">1</code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">,</code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:rgb(0,153,0);line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">2</code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">,</code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:rgb(0,153,0);line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">3</code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">],dtype=np.</code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:rgb(0,102,153);line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;font-weight:bold;vertical-align:baseline;float:none;min-height:auto;">float</code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">)</code> 
     </div> 
     <div style="margin:0px;border:0px;list-style-type:none;list-style-image:none;padding:0px 1em;width:auto;height:auto;line-height:1.1em;font-size:1em;vertical-align:baseline;float:none;white-space:pre;min-height:auto;"> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">print x</code> 
     </div> 
     <div style="margin:0px;border:0px;list-style-type:none;list-style-image:none;padding:0px 1em;width:auto;height:auto;line-height:1.1em;font-size:1em;vertical-align:baseline;float:none;white-space:pre;min-height:auto;">
       &nbsp; 
     </div> 
     <div style="margin:0px;border:0px;list-style-type:none;list-style-image:none;padding:0px 1em;width:auto;height:auto;line-height:1.1em;font-size:1em;vertical-align:baseline;float:none;white-space:pre;min-height:auto;"> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;"># 查看数据类型</code> 
     </div> 
     <div style="margin:0px;border:0px;list-style-type:none;list-style-image:none;padding:0px 1em;width:auto;height:auto;line-height:1.1em;font-size:1em;vertical-align:baseline;float:none;white-space:pre;min-height:auto;"> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">print x.dtype</code> 
     </div> 
     <div style="margin:0px;border:0px;list-style-type:none;list-style-image:none;padding:0px 1em;width:auto;height:auto;line-height:1.1em;font-size:1em;vertical-align:baseline;float:none;white-space:pre;min-height:auto;">
       &nbsp; 
     </div> 
     <div style="margin:0px;border:0px;list-style-type:none;list-style-image:none;padding:0px 1em;width:auto;height:auto;line-height:1.1em;font-size:1em;vertical-align:baseline;float:none;white-space:pre;min-height:auto;"> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;"># 作为单值类型转化函数</code> 
     </div> 
     <div style="margin:0px;border:0px;list-style-type:none;list-style-image:none;padding:0px 1em;width:auto;height:auto;line-height:1.1em;font-size:1em;vertical-align:baseline;float:none;white-space:pre;min-height:auto;"> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">print np.int32(</code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:rgb(0,153,0);line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">1.3</code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">)</code> 
     </div> 
     <div style="margin:0px;border:0px;list-style-type:none;list-style-image:none;padding:0px 1em;width:auto;height:auto;line-height:1.1em;font-size:1em;vertical-align:baseline;float:none;white-space:pre;min-height:auto;">
       &nbsp; 
     </div> 
     <div style="margin:0px;border:0px;list-style-type:none;list-style-image:none;padding:0px 1em;width:auto;height:auto;line-height:1.1em;font-size:1em;vertical-align:baseline;float:none;white-space:pre;min-height:auto;"> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;"># 转换数组的类型，会产生新的副本</code> 
     </div> 
     <div style="margin:0px;border:0px;list-style-type:none;list-style-image:none;padding:0px 1em;width:auto;height:auto;line-height:1.1em;font-size:1em;vertical-align:baseline;float:none;white-space:pre;min-height:auto;"> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">print x.astype(np.</code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:rgb(0,102,153);line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;font-weight:bold;vertical-align:baseline;float:none;min-height:auto;">int</code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">)</code> 
     </div> 
    </div></td> 
  </tr> 
 </tbody> 
</table>

结果：

[?][Link 1]

<table style="background:none;margin:0px;border:0px;width:613px;list-style-type:none;list-style-image:none;padding:0px;height:auto;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;"> 
 <tbody style="background:none;margin:0px;padding:0px;width:auto;height:auto;line-height:1.1em;font-size:1em;vertical-align:baseline;float:none;min-height:auto;"> 
  <tr style="background:none;margin:0px;border-top:0px;list-style-type:none;list-style-image:none;padding:0px;width:auto;height:auto;line-height:1.1em;font-size:1em;vertical-align:baseline;float:none;min-height:auto;"> 
   <td style="background:none;margin:0px;border-width:0px;list-style-type:none;list-style-image:none;padding:0px;width:auto;height:auto;color:rgb(175,175,175);line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;"> 
    <div style="margin:0px;border-right:3px solid rgb(108,226,108);list-style-type:none;list-style-image:none;padding:0px .5em 0px 1em;width:auto;height:auto;text-align:right;line-height:1.1em;font-size:1em;vertical-align:baseline;border-top-width:0px;border-bottom-width:0px;border-left-width:0px;float:none;white-space:pre;min-height:auto;">
      1 
    </div> 
    <div style="margin:0px;border-right:3px solid rgb(108,226,108);list-style-type:none;list-style-image:none;padding:0px .5em 0px 1em;width:auto;height:auto;text-align:right;line-height:1.1em;font-size:1em;vertical-align:baseline;border-top-width:0px;border-bottom-width:0px;border-left-width:0px;float:none;white-space:pre;min-height:auto;">
      2 
    </div> 
    <div style="margin:0px;border-right:3px solid rgb(108,226,108);list-style-type:none;list-style-image:none;padding:0px .5em 0px 1em;width:auto;height:auto;text-align:right;line-height:1.1em;font-size:1em;vertical-align:baseline;border-top-width:0px;border-bottom-width:0px;border-left-width:0px;float:none;white-space:pre;min-height:auto;">
      3 
    </div> 
    <div style="margin:0px;border-right:3px solid rgb(108,226,108);list-style-type:none;list-style-image:none;padding:0px .5em 0px 1em;width:auto;height:auto;text-align:right;line-height:1.1em;font-size:1em;vertical-align:baseline;border-top-width:0px;border-bottom-width:0px;border-left-width:0px;float:none;white-space:pre;min-height:auto;">
      4 
    </div></td> 
   <td style="background:none;margin:0px;border-width:0px;width:581px;list-style-type:none;list-style-image:none;padding:0px;height:auto;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;"> 
    <div style="background:none;margin:0px;border:0px;list-style-type:none;list-style-image:none;padding:0px;width:auto;height:auto;line-height:1.1em;font-size:1em;vertical-align:baseline;float:none;min-height:auto;"> 
     <div style="margin:0px;border:0px;list-style-type:none;list-style-image:none;padding:0px 1em;width:auto;height:auto;line-height:1.1em;font-size:1em;vertical-align:baseline;float:none;white-space:pre;min-height:auto;"> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">[ </code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:rgb(0,153,0);line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">1</code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">.&nbsp; </code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:rgb(0,153,0);line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">2</code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">.&nbsp; </code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:rgb(0,153,0);line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">3</code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">.]</code> 
     </div> 
     <div style="margin:0px;border:0px;list-style-type:none;list-style-image:none;padding:0px 1em;width:auto;height:auto;line-height:1.1em;font-size:1em;vertical-align:baseline;float:none;white-space:pre;min-height:auto;"> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">float64</code> 
     </div> 
     <div style="margin:0px;border:0px;list-style-type:none;list-style-image:none;padding:0px 1em;width:auto;height:auto;line-height:1.1em;font-size:1em;vertical-align:baseline;float:none;white-space:pre;min-height:auto;"> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:rgb(0,153,0);line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">1</code> 
     </div> 
     <div style="margin:0px;border:0px;list-style-type:none;list-style-image:none;padding:0px 1em;width:auto;height:auto;line-height:1.1em;font-size:1em;vertical-align:baseline;float:none;white-space:pre;min-height:auto;"> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">[</code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:rgb(0,153,0);line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">1</code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:rgb(0,153,0);line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">2</code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:rgb(0,153,0);line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">3</code> 
      <code style="background:none;margin:0px;border:0px;padding:0px;width:auto;height:auto;color:#000000;line-height:1.1em;font-family:Consolas, 'Bitstream Vera Sans Mono', 'Courier New', Courier, monospace;font-size:1em;vertical-align:baseline;float:none;min-height:auto;">]</code> 
     </div> 
    </div></td> 
  </tr> 
 </tbody> 
</table>

## ##

感谢阅读上海尚学堂文章，获取更多内容或支持请点击 [*上海python培训*][python]

[Link 1]: https://www.2cto.com/kf/201712/707488.html#
[python]: http://www.shsxt.com/it/python