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<!DOCTYPE html>
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<title>第 12 章 地理计算 | 数据工程讲义：经济学分册</title>
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<meta name="author" content="史冬波 续本达" />
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<li><a href="./">数据工程讲义</a></li>
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<li class="chapter" data-level="" data-path="index.html"><a href="index.html"><i class="fa fa-check"></i>前言</a>
<ul>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html#致谢"><i class="fa fa-check"></i>致谢</a></li>
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<li class="chapter" data-level="" data-path="author.html"><a href="author.html"><i class="fa fa-check"></i>作者简介</a></li>
<li class="chapter" data-level="1" data-path="intro.html"><a href="intro.html"><i class="fa fa-check"></i><b>1</b> 写在前面</a>
<ul>
<li class="chapter" data-level="1.1" data-path="intro.html"><a href="intro.html#为什么写本书"><i class="fa fa-check"></i><b>1.1</b> 为什么写本书</a></li>
<li class="chapter" data-level="1.2" data-path="intro.html"><a href="intro.html#如何使用本书"><i class="fa fa-check"></i><b>1.2</b> 如何使用本书</a></li>
</ul></li>
<li class="chapter" data-level="2" data-path="flow.html"><a href="flow.html"><i class="fa fa-check"></i><b>2</b> 数据工程：重塑经济学研究的流程</a>
<ul>
<li class="chapter" data-level="2.1" data-path="flow.html"><a href="flow.html#人工智能时代的社会科学研究机遇与挑战"><i class="fa fa-check"></i><b>2.1</b> 人工智能时代的社会科学研究：机遇与挑战</a>
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<li class="chapter" data-level="2.1.1" data-path="flow.html"><a href="flow.html#社会科学的三圈分类"><i class="fa fa-check"></i><b>2.1.1</b> 社会科学的三圈分类</a></li>
<li class="chapter" data-level="2.1.2" data-path="flow.html"><a href="flow.html#ai智能发展的三要素"><i class="fa fa-check"></i><b>2.1.2</b> AI智能发展的三要素</a></li>
<li class="chapter" data-level="2.1.3" data-path="flow.html"><a href="flow.html#ai对社会科学研究的冲击"><i class="fa fa-check"></i><b>2.1.3</b> AI对社会科学研究的冲击</a></li>
<li class="chapter" data-level="2.1.4" data-path="flow.html"><a href="flow.html#ai为社会科学研究创造的机遇"><i class="fa fa-check"></i><b>2.1.4</b> AI为社会科学研究创造的机遇</a></li>
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<li class="chapter" data-level="2.2" data-path="flow.html"><a href="flow.html#数据工程与数据科学"><i class="fa fa-check"></i><b>2.2</b> 数据工程与数据科学</a>
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<li class="chapter" data-level="2.2.1" data-path="flow.html"><a href="flow.html#数据工程的灵魂数据流"><i class="fa fa-check"></i><b>2.2.1</b> 数据工程的灵魂：数据流</a></li>
<li class="chapter" data-level="2.2.2" data-path="flow.html"><a href="flow.html#数据工程的钥匙数据结构"><i class="fa fa-check"></i><b>2.2.2</b> 数据工程的钥匙：数据结构</a></li>
<li class="chapter" data-level="2.2.3" data-path="flow.html"><a href="flow.html#数据工程师的工具箱"><i class="fa fa-check"></i><b>2.2.3</b> 数据工程师的工具箱</a></li>
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<li class="chapter" data-level="2.3" data-path="flow.html"><a href="flow.html#数据工程的四个指导原则"><i class="fa fa-check"></i><b>2.3</b> 数据工程的四个指导原则</a>
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<li class="chapter" data-level="2.3.1" data-path="flow.html"><a href="flow.html#可复现性原则"><i class="fa fa-check"></i><b>2.3.1</b> 可复现性原则</a></li>
<li class="chapter" data-level="2.3.2" data-path="flow.html"><a href="flow.html#模块化与正交分解原则"><i class="fa fa-check"></i><b>2.3.2</b> 模块化与正交分解原则</a></li>
<li class="chapter" data-level="2.3.3" data-path="flow.html"><a href="flow.html#最佳工具原则"><i class="fa fa-check"></i><b>2.3.3</b> 最佳工具原则</a></li>
<li class="chapter" data-level="2.3.4" data-path="flow.html"><a href="flow.html#一次原则"><i class="fa fa-check"></i><b>2.3.4</b> 一次原则</a></li>
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<li class="chapter" data-level="2.4" data-path="flow.html"><a href="flow.html#gnu-环境"><i class="fa fa-check"></i><b>2.4</b> GNU 环境</a>
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<li class="chapter" data-level="2.4.1" data-path="flow.html"><a href="flow.html#posix"><i class="fa fa-check"></i><b>2.4.1</b> POSIX</a></li>
<li class="chapter" data-level="2.4.2" data-path="flow.html"><a href="flow.html#gnu"><i class="fa fa-check"></i><b>2.4.2</b> GNU</a></li>
<li class="chapter" data-level="2.4.3" data-path="flow.html"><a href="flow.html#命令行"><i class="fa fa-check"></i><b>2.4.3</b> 命令行</a></li>
<li class="chapter" data-level="2.4.4" data-path="flow.html"><a href="flow.html#编辑器"><i class="fa fa-check"></i><b>2.4.4</b> 编辑器</a></li>
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<li class="chapter" data-level="2.5" data-path="flow.html"><a href="flow.html#版本控制"><i class="fa fa-check"></i><b>2.5</b> 版本控制</a>
<ul>
<li class="chapter" data-level="2.5.1" data-path="flow.html"><a href="flow.html#git"><i class="fa fa-check"></i><b>2.5.1</b> Git</a></li>
<li class="chapter" data-level="2.5.2" data-path="flow.html"><a href="flow.html#git的三种状态"><i class="fa fa-check"></i><b>2.5.2</b> Git的三种状态</a></li>
<li class="chapter" data-level="2.5.3" data-path="flow.html"><a href="flow.html#git仓库"><i class="fa fa-check"></i><b>2.5.3</b> Git仓库</a></li>
<li class="chapter" data-level="2.5.4" data-path="flow.html"><a href="flow.html#git命令实践"><i class="fa fa-check"></i><b>2.5.4</b> Git命令实践</a></li>
<li class="chapter" data-level="2.5.5" data-path="flow.html"><a href="flow.html#git目前的局限性"><i class="fa fa-check"></i><b>2.5.5</b> Git目前的局限性</a></li>
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<li class="chapter" data-level="3" data-path="basic.html"><a href="basic.html"><i class="fa fa-check"></i><b>3</b> R语言基础</a>
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<li class="chapter" data-level="3.1" data-path="basic.html"><a href="basic.html#r语言简介"><i class="fa fa-check"></i><b>3.1</b> R语言简介</a></li>
<li class="chapter" data-level="3.2" data-path="basic.html"><a href="basic.html#r语言的特点"><i class="fa fa-check"></i><b>3.2</b> R语言的特点</a></li>
<li class="chapter" data-level="3.3" data-path="basic.html"><a href="basic.html#r与rtudio的安装"><i class="fa fa-check"></i><b>3.3</b> R与Rtudio的安装</a>
<ul>
<li class="chapter" data-level="3.3.1" data-path="basic.html"><a href="basic.html#安装r"><i class="fa fa-check"></i><b>3.3.1</b> 安装R</a></li>
<li class="chapter" data-level="3.3.2" data-path="basic.html"><a href="basic.html#r安装rstudio"><i class="fa fa-check"></i><b>3.3.2</b> R安装RStudio</a></li>
<li class="chapter" data-level="3.3.3" data-path="basic.html"><a href="basic.html#组织r代码的三种方式"><i class="fa fa-check"></i><b>3.3.3</b> 组织R代码的三种方式</a></li>
<li class="chapter" data-level="3.3.4" data-path="basic.html"><a href="basic.html#r代码的组成"><i class="fa fa-check"></i><b>3.3.4</b> R代码的组成</a></li>
</ul></li>
<li class="chapter" data-level="3.4" data-path="basic.html"><a href="basic.html#r对文件和路径的相关操作"><i class="fa fa-check"></i><b>3.4</b> R对文件和路径的相关操作</a>
<ul>
<li class="chapter" data-level="3.4.1" data-path="basic.html"><a href="basic.html#路径操作"><i class="fa fa-check"></i><b>3.4.1</b> 路径操作</a></li>
<li class="chapter" data-level="3.4.2" data-path="basic.html"><a href="basic.html#文件操作"><i class="fa fa-check"></i><b>3.4.2</b> 文件操作</a></li>
<li class="chapter" data-level="3.4.3" data-path="basic.html"><a href="basic.html#特殊路径"><i class="fa fa-check"></i><b>3.4.3</b> 特殊路径</a></li>
</ul></li>
<li class="chapter" data-level="3.5" data-path="basic.html"><a href="basic.html#数据类型"><i class="fa fa-check"></i><b>3.5</b> 数据类型</a>
<ul>
<li class="chapter" data-level="3.5.1" data-path="basic.html"><a href="basic.html#数值型"><i class="fa fa-check"></i><b>3.5.1</b> 数值型</a></li>
<li class="chapter" data-level="3.5.2" data-path="basic.html"><a href="basic.html#逻辑型布尔型"><i class="fa fa-check"></i><b>3.5.2</b> 逻辑型/布尔型</a></li>
<li class="chapter" data-level="3.5.3" data-path="basic.html"><a href="basic.html#字符型"><i class="fa fa-check"></i><b>3.5.3</b> 字符型</a></li>
<li class="chapter" data-level="3.5.4" data-path="basic.html"><a href="basic.html#缺失值"><i class="fa fa-check"></i><b>3.5.4</b> 缺失值</a></li>
<li class="chapter" data-level="3.5.5" data-path="basic.html"><a href="basic.html#数据类型判断与转换"><i class="fa fa-check"></i><b>3.5.5</b> 数据类型判断与转换</a></li>
<li class="chapter" data-level="3.5.6" data-path="basic.html"><a href="basic.html#运算"><i class="fa fa-check"></i><b>3.5.6</b> 运算</a></li>
</ul></li>
<li class="chapter" data-level="3.6" data-path="basic.html"><a href="basic.html#变量"><i class="fa fa-check"></i><b>3.6</b> 变量</a></li>
<li class="chapter" data-level="3.7" data-path="basic.html"><a href="basic.html#数据结构"><i class="fa fa-check"></i><b>3.7</b> 数据结构</a>
<ul>
<li class="chapter" data-level="3.7.1" data-path="basic.html"><a href="basic.html#向量"><i class="fa fa-check"></i><b>3.7.1</b> 向量</a></li>
<li class="chapter" data-level="3.7.2" data-path="basic.html"><a href="basic.html#因子"><i class="fa fa-check"></i><b>3.7.2</b> 因子</a></li>
<li class="chapter" data-level="3.7.3" data-path="basic.html"><a href="basic.html#矩阵"><i class="fa fa-check"></i><b>3.7.3</b> 矩阵</a></li>
<li class="chapter" data-level="3.7.4" data-path="basic.html"><a href="basic.html#数据框"><i class="fa fa-check"></i><b>3.7.4</b> 数据框</a></li>
<li class="chapter" data-level="3.7.5" data-path="basic.html"><a href="basic.html#列表"><i class="fa fa-check"></i><b>3.7.5</b> 列表</a></li>
<li class="chapter" data-level="3.7.6" data-path="basic.html"><a href="basic.html#数据结构之间的转化"><i class="fa fa-check"></i><b>3.7.6</b> 数据结构之间的转化</a></li>
</ul></li>
<li class="chapter" data-level="3.8" data-path="basic.html"><a href="basic.html#数据读写"><i class="fa fa-check"></i><b>3.8</b> 数据读写</a>
<ul>
<li class="chapter" data-level="3.8.1" data-path="basic.html"><a href="basic.html#csv文件"><i class="fa fa-check"></i><b>3.8.1</b> csv文件</a></li>
<li class="chapter" data-level="3.8.2" data-path="basic.html"><a href="basic.html#hdf5"><i class="fa fa-check"></i><b>3.8.2</b> HDF5</a></li>
<li class="chapter" data-level="3.8.3" data-path="basic.html"><a href="basic.html#xml"><i class="fa fa-check"></i><b>3.8.3</b> XML</a></li>
<li class="chapter" data-level="3.8.4" data-path="basic.html"><a href="basic.html#json"><i class="fa fa-check"></i><b>3.8.4</b> JSON</a></li>
<li class="chapter" data-level="3.8.5" data-path="basic.html"><a href="basic.html#yaml"><i class="fa fa-check"></i><b>3.8.5</b> YAML</a></li>
<li class="chapter" data-level="3.8.6" data-path="basic.html"><a href="basic.html#专用数据文件"><i class="fa fa-check"></i><b>3.8.6</b> 专用数据文件</a></li>
</ul></li>
<li class="chapter" data-level="3.9" data-path="basic.html"><a href="basic.html#流程控制"><i class="fa fa-check"></i><b>3.9</b> 流程控制</a>
<ul>
<li class="chapter" data-level="3.9.1" data-path="basic.html"><a href="basic.html#条件判断"><i class="fa fa-check"></i><b>3.9.1</b> 条件判断</a></li>
<li class="chapter" data-level="3.9.2" data-path="basic.html"><a href="basic.html#循环"><i class="fa fa-check"></i><b>3.9.2</b> 循环</a></li>
</ul></li>
<li class="chapter" data-level="3.10" data-path="basic.html"><a href="basic.html#函数与包"><i class="fa fa-check"></i><b>3.10</b> 函数与包</a>
<ul>
<li class="chapter" data-level="3.10.1" data-path="basic.html"><a href="basic.html#函数的定义与调用"><i class="fa fa-check"></i><b>3.10.1</b> 函数的定义与调用</a></li>
<li class="chapter" data-level="3.10.2" data-path="basic.html"><a href="basic.html#变量作用域"><i class="fa fa-check"></i><b>3.10.2</b> 变量作用域</a></li>
<li class="chapter" data-level="3.10.3" data-path="basic.html"><a href="basic.html#函数模块化"><i class="fa fa-check"></i><b>3.10.3</b> 函数模块化</a></li>
<li class="chapter" data-level="3.10.4" data-path="basic.html"><a href="basic.html#包"><i class="fa fa-check"></i><b>3.10.4</b> 包</a></li>
</ul></li>
<li class="chapter" data-level="3.11" data-path="basic.html"><a href="basic.html#向量化"><i class="fa fa-check"></i><b>3.11</b> 向量化</a>
<ul>
<li class="chapter" data-level="3.11.1" data-path="basic.html"><a href="basic.html#apply"><i class="fa fa-check"></i><b>3.11.1</b> apply</a></li>
<li class="chapter" data-level="3.11.2" data-path="basic.html"><a href="basic.html#lapply"><i class="fa fa-check"></i><b>3.11.2</b> lapply</a></li>
<li class="chapter" data-level="3.11.3" data-path="basic.html"><a href="basic.html#sapply"><i class="fa fa-check"></i><b>3.11.3</b> sapply</a></li>
<li class="chapter" data-level="3.11.4" data-path="basic.html"><a href="basic.html#vapply"><i class="fa fa-check"></i><b>3.11.4</b> vapply</a></li>
<li class="chapter" data-level="3.11.5" data-path="basic.html"><a href="basic.html#mapply"><i class="fa fa-check"></i><b>3.11.5</b> mapply</a></li>
<li class="chapter" data-level="3.11.6" data-path="basic.html"><a href="basic.html#其他"><i class="fa fa-check"></i><b>3.11.6</b> 其他</a></li>
</ul></li>
<li class="chapter" data-level="3.12" data-path="basic.html"><a href="basic.html#代码风格"><i class="fa fa-check"></i><b>3.12</b> 代码风格</a></li>
</ul></li>
<li class="chapter" data-level="4" data-path="rmd.html"><a href="rmd.html"><i class="fa fa-check"></i><b>4</b> 文学式编程</a>
<ul>
<li class="chapter" data-level="4.1" data-path="rmd.html"><a href="rmd.html#什么是文学式编程"><i class="fa fa-check"></i><b>4.1</b> 什么是文学式编程</a></li>
<li class="chapter" data-level="4.2" data-path="rmd.html"><a href="rmd.html#markdown格式"><i class="fa fa-check"></i><b>4.2</b> Markdown格式</a>
<ul>
<li class="chapter" data-level="4.2.1" data-path="rmd.html"><a href="rmd.html#标题"><i class="fa fa-check"></i><b>4.2.1</b> 标题</a></li>
<li class="chapter" data-level="4.2.2" data-path="rmd.html"><a href="rmd.html#段落文本"><i class="fa fa-check"></i><b>4.2.2</b> 段落文本</a></li>
<li class="chapter" data-level="4.2.3" data-path="rmd.html"><a href="rmd.html#表格"><i class="fa fa-check"></i><b>4.2.3</b> 表格</a></li>
<li class="chapter" data-level="4.2.4" data-path="rmd.html"><a href="rmd.html#图片"><i class="fa fa-check"></i><b>4.2.4</b> 图片</a></li>
<li class="chapter" data-level="4.2.5" data-path="rmd.html"><a href="rmd.html#代码块"><i class="fa fa-check"></i><b>4.2.5</b> 代码块</a></li>
<li class="chapter" data-level="4.2.6" data-path="rmd.html"><a href="rmd.html#数学公式"><i class="fa fa-check"></i><b>4.2.6</b> 数学公式</a></li>
</ul></li>
<li class="chapter" data-level="4.3" data-path="rmd.html"><a href="rmd.html#rmarkdown"><i class="fa fa-check"></i><b>4.3</b> Rmarkdown</a>
<ul>
<li class="chapter" data-level="4.3.1" data-path="rmd.html"><a href="rmd.html#yaml头文件"><i class="fa fa-check"></i><b>4.3.1</b> YAML头文件</a></li>
<li class="chapter" data-level="4.3.2" data-path="rmd.html"><a href="rmd.html#代码块控制"><i class="fa fa-check"></i><b>4.3.2</b> 代码块控制</a></li>
<li class="chapter" data-level="4.3.3" data-path="rmd.html"><a href="rmd.html#rmarkdown特殊语法"><i class="fa fa-check"></i><b>4.3.3</b> Rmarkdown特殊语法</a></li>
<li class="chapter" data-level="4.3.4" data-path="rmd.html"><a href="rmd.html#格式转换"><i class="fa fa-check"></i><b>4.3.4</b> 格式转换</a></li>
</ul></li>
<li class="chapter" data-level="4.4" data-path="rmd.html"><a href="rmd.html#xaringan"><i class="fa fa-check"></i><b>4.4</b> Xaringan</a>
<ul>
<li class="chapter" data-level="4.4.1" data-path="rmd.html"><a href="rmd.html#安装与模板"><i class="fa fa-check"></i><b>4.4.1</b> 安装与模板</a></li>
<li class="chapter" data-level="4.4.2" data-path="rmd.html"><a href="rmd.html#其他学习资源"><i class="fa fa-check"></i><b>4.4.2</b> 其他学习资源</a></li>
</ul></li>
<li class="chapter" data-level="4.5" data-path="rmd.html"><a href="rmd.html#leanr"><i class="fa fa-check"></i><b>4.5</b> leanr</a>
<ul>
<li class="chapter" data-level="4.5.1" data-path="rmd.html"><a href="rmd.html#安装与模板-1"><i class="fa fa-check"></i><b>4.5.1</b> 安装与模板</a></li>
<li class="chapter" data-level="4.5.2" data-path="rmd.html"><a href="rmd.html#互动代码模块"><i class="fa fa-check"></i><b>4.5.2</b> 互动代码模块</a></li>
<li class="chapter" data-level="4.5.3" data-path="rmd.html"><a href="rmd.html#测试题"><i class="fa fa-check"></i><b>4.5.3</b> 测试题</a></li>
</ul></li>
<li class="chapter" data-level="4.6" data-path="rmd.html"><a href="rmd.html#bookdownblogdown以及pagedown"><i class="fa fa-check"></i><b>4.6</b> bookdown、blogdown以及pagedown</a></li>
<li class="chapter" data-level="4.7" data-path="rmd.html"><a href="rmd.html#quarto"><i class="fa fa-check"></i><b>4.7</b> Quarto</a></li>
</ul></li>
<li class="chapter" data-level="5" data-path="manipulate.html"><a href="manipulate.html"><i class="fa fa-check"></i><b>5</b> 数据整理</a>
<ul>
<li class="chapter" data-level="5.1" data-path="manipulate.html"><a href="manipulate.html#整齐数据tidydata"><i class="fa fa-check"></i><b>5.1</b> 整齐数据tidydata</a>
<ul>
<li class="chapter" data-level="5.1.1" data-path="manipulate.html"><a href="manipulate.html#分析单位unit-of-analysis"><i class="fa fa-check"></i><b>5.1.1</b> 分析单位(unit of analysis)</a></li>
</ul></li>
<li class="chapter" data-level="5.2" data-path="manipulate.html"><a href="manipulate.html#整齐数据"><i class="fa fa-check"></i><b>5.2</b> 整齐数据</a>
<ul>
<li class="chapter" data-level="5.2.1" data-path="manipulate.html"><a href="manipulate.html#整齐数据的缘起"><i class="fa fa-check"></i><b>5.2.1</b> 整齐数据的缘起</a></li>
<li class="chapter" data-level="5.2.2" data-path="manipulate.html"><a href="manipulate.html#整齐数据的定义"><i class="fa fa-check"></i><b>5.2.2</b> 整齐数据的定义</a></li>
<li class="chapter" data-level="5.2.3" data-path="manipulate.html"><a href="manipulate.html#数据的凌乱点"><i class="fa fa-check"></i><b>5.2.3</b> 数据的凌乱点</a></li>
</ul></li>
<li class="chapter" data-level="5.3" data-path="manipulate.html"><a href="manipulate.html#关系代数"><i class="fa fa-check"></i><b>5.3</b> 关系代数</a></li>
<li class="chapter" data-level="5.4" data-path="manipulate.html"><a href="manipulate.html#sql语言"><i class="fa fa-check"></i><b>5.4</b> SQL语言</a>
<ul>
<li class="chapter" data-level="5.4.1" data-path="manipulate.html"><a href="manipulate.html#mysql"><i class="fa fa-check"></i><b>5.4.1</b> MySQL</a></li>
<li class="chapter" data-level="5.4.2" data-path="manipulate.html"><a href="manipulate.html#postgresql"><i class="fa fa-check"></i><b>5.4.2</b> Postgresql</a></li>
</ul></li>
<li class="chapter" data-level="5.5" data-path="manipulate.html"><a href="manipulate.html#dplyr"><i class="fa fa-check"></i><b>5.5</b> dplyr</a>
<ul>
<li class="chapter" data-level="5.5.1" data-path="manipulate.html"><a href="manipulate.html#集合运算"><i class="fa fa-check"></i><b>5.5.1</b> 集合运算</a></li>
<li class="chapter" data-level="5.5.2" data-path="manipulate.html"><a href="manipulate.html#线性运算"><i class="fa fa-check"></i><b>5.5.2</b> 线性运算</a></li>
<li class="chapter" data-level="5.5.3" data-path="manipulate.html"><a href="manipulate.html#管道"><i class="fa fa-check"></i><b>5.5.3</b> 管道</a></li>
<li class="chapter" data-level="5.5.4" data-path="manipulate.html"><a href="manipulate.html#数据连接"><i class="fa fa-check"></i><b>5.5.4</b> 数据连接</a></li>
<li class="chapter" data-level="5.5.5" data-path="manipulate.html"><a href="manipulate.html#数据分组与汇总"><i class="fa fa-check"></i><b>5.5.5</b> 数据分组与汇总</a></li>
</ul></li>
<li class="chapter" data-level="5.6" data-path="manipulate.html"><a href="manipulate.html#宽数据与长数据的转换"><i class="fa fa-check"></i><b>5.6</b> 宽数据与长数据的转换</a>
<ul>
<li class="chapter" data-level="5.6.1" data-path="manipulate.html"><a href="manipulate.html#宽数据转长数据"><i class="fa fa-check"></i><b>5.6.1</b> 宽数据转长数据</a></li>
<li class="chapter" data-level="5.6.2" data-path="manipulate.html"><a href="manipulate.html#长数据转宽数据"><i class="fa fa-check"></i><b>5.6.2</b> 长数据转宽数据</a></li>
<li class="chapter" data-level="5.6.3" data-path="manipulate.html"><a href="manipulate.html#联系人数据表的案例"><i class="fa fa-check"></i><b>5.6.3</b> 联系人数据表的案例</a></li>
</ul></li>
<li class="chapter" data-level="5.7" data-path="manipulate.html"><a href="manipulate.html#其他定制操作"><i class="fa fa-check"></i><b>5.7</b> 其他定制操作</a>
<ul>
<li class="chapter" data-level="5.7.1" data-path="manipulate.html"><a href="manipulate.html#排序"><i class="fa fa-check"></i><b>5.7.1</b> 排序</a></li>
<li class="chapter" data-level="5.7.2" data-path="manipulate.html"><a href="manipulate.html#抽样"><i class="fa fa-check"></i><b>5.7.2</b> 抽样</a></li>
<li class="chapter" data-level="5.7.3" data-path="manipulate.html"><a href="manipulate.html#去重复"><i class="fa fa-check"></i><b>5.7.3</b> 去重复</a></li>
<li class="chapter" data-level="5.7.4" data-path="manipulate.html"><a href="manipulate.html#缺失值处理"><i class="fa fa-check"></i><b>5.7.4</b> 缺失值处理</a></li>
<li class="chapter" data-level="5.7.5" data-path="manipulate.html"><a href="manipulate.html#拆分与合并数据列"><i class="fa fa-check"></i><b>5.7.5</b> 拆分与合并数据列</a></li>
<li class="chapter" data-level="5.7.6" data-path="manipulate.html"><a href="manipulate.html#合并数据"><i class="fa fa-check"></i><b>5.7.6</b> 合并数据</a></li>
</ul></li>
<li class="chapter" data-level="5.8" data-path="manipulate.html"><a href="manipulate.html#数据库的连接"><i class="fa fa-check"></i><b>5.8</b> 数据库的连接</a></li>
<li class="chapter" data-level="5.9" data-path="manipulate.html"><a href="manipulate.html#data.table"><i class="fa fa-check"></i><b>5.9</b> data.table</a></li>
</ul></li>
<li class="chapter" data-level="6" data-path="visu.html"><a href="visu.html"><i class="fa fa-check"></i><b>6</b> 数据可视化</a>
<ul>
<li class="chapter" data-level="6.1" data-path="visu.html"><a href="visu.html#从一个可以画恐龙的包说起"><i class="fa fa-check"></i><b>6.1</b> 从一个可以画恐龙的包说起</a></li>
<li class="chapter" data-level="6.2" data-path="visu.html"><a href="visu.html#数据可视化的目的"><i class="fa fa-check"></i><b>6.2</b> 数据可视化的目的</a></li>
<li class="chapter" data-level="6.3" data-path="visu.html"><a href="visu.html#图形语法grammar-of-graphics"><i class="fa fa-check"></i><b>6.3</b> 图形语法（Grammar of Graphics）</a></li>
<li class="chapter" data-level="6.4" data-path="visu.html"><a href="visu.html#ggplot2"><i class="fa fa-check"></i><b>6.4</b> <code>ggplot2</code></a>
<ul>
<li class="chapter" data-level="6.4.1" data-path="visu.html"><a href="visu.html#ggplot2几何对象"><i class="fa fa-check"></i><b>6.4.1</b> <code>ggplot2</code>几何对象</a></li>
<li class="chapter" data-level="6.4.2" data-path="visu.html"><a href="visu.html#ggplot2的美术属性"><i class="fa fa-check"></i><b>6.4.2</b> <code>ggplot2</code>的美术属性</a></li>
<li class="chapter" data-level="6.4.3" data-path="visu.html"><a href="visu.html#ggplot2辅助"><i class="fa fa-check"></i><b>6.4.3</b> <code>ggplot2</code>辅助</a></li>
</ul></li>
<li class="chapter" data-level="6.5" data-path="visu.html"><a href="visu.html#案例did结果的可视化"><i class="fa fa-check"></i><b>6.5</b> 案例：DID结果的可视化</a></li>
<li class="chapter" data-level="6.6" data-path="visu.html"><a href="visu.html#动图"><i class="fa fa-check"></i><b>6.6</b> 动图</a></li>
<li class="chapter" data-level="6.7" data-path="visu.html"><a href="visu.html#大屏"><i class="fa fa-check"></i><b>6.7</b> 大屏</a>
<ul>
<li class="chapter" data-level="6.7.1" data-path="visu.html"><a href="visu.html#交互式"><i class="fa fa-check"></i><b>6.7.1</b> 交互式</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="7" data-path="reg.html"><a href="reg.html"><i class="fa fa-check"></i><b>7</b> 回归</a>
<ul>
<li class="chapter" data-level="7.1" data-path="reg.html"><a href="reg.html#一般线性回归"><i class="fa fa-check"></i><b>7.1</b> 一般线性回归</a>
<ul>
<li class="chapter" data-level="7.1.1" data-path="reg.html"><a href="reg.html#基础模型"><i class="fa fa-check"></i><b>7.1.1</b> 基础模型</a></li>
<li class="chapter" data-level="7.1.2" data-path="reg.html"><a href="reg.html#稳健性标准误"><i class="fa fa-check"></i><b>7.1.2</b> 稳健性标准误</a></li>
</ul></li>
<li class="chapter" data-level="7.2" data-path="reg.html"><a href="reg.html#因果推断的反事实框架"><i class="fa fa-check"></i><b>7.2</b> 因果推断的反事实框架</a>
<ul>
<li class="chapter" data-level="7.2.1" data-path="reg.html"><a href="reg.html#定义因果关系"><i class="fa fa-check"></i><b>7.2.1</b> 定义因果关系</a></li>
<li class="chapter" data-level="7.2.2" data-path="reg.html"><a href="reg.html#cef三定理"><i class="fa fa-check"></i><b>7.2.2</b> CEF三定理</a></li>
<li class="chapter" data-level="7.2.3" data-path="reg.html"><a href="reg.html#交互项还是分组回归"><i class="fa fa-check"></i><b>7.2.3</b> 交互项还是分组回归</a></li>
</ul></li>
<li class="chapter" data-level="7.3" data-path="reg.html"><a href="reg.html#匹配"><i class="fa fa-check"></i><b>7.3</b> 匹配</a>
<ul>
<li class="chapter" data-level="7.3.1" data-path="reg.html"><a href="reg.html#原理"><i class="fa fa-check"></i><b>7.3.1</b> 原理</a></li>
<li class="chapter" data-level="7.3.2" data-path="reg.html"><a href="reg.html#案例"><i class="fa fa-check"></i><b>7.3.2</b> 案例</a></li>
</ul></li>
<li class="chapter" data-level="7.4" data-path="reg.html"><a href="reg.html#工具变量"><i class="fa fa-check"></i><b>7.4</b> 工具变量</a>
<ul>
<li class="chapter" data-level="7.4.1" data-path="reg.html"><a href="reg.html#原理-1"><i class="fa fa-check"></i><b>7.4.1</b> 原理</a></li>
<li class="chapter" data-level="7.4.2" data-path="reg.html"><a href="reg.html#案例-1"><i class="fa fa-check"></i><b>7.4.2</b> 案例</a></li>
</ul></li>
<li class="chapter" data-level="7.5" data-path="reg.html"><a href="reg.html#双重差分"><i class="fa fa-check"></i><b>7.5</b> 双重差分</a>
<ul>
<li class="chapter" data-level="7.5.1" data-path="reg.html"><a href="reg.html#原理-2"><i class="fa fa-check"></i><b>7.5.1</b> 原理</a></li>
<li class="chapter" data-level="7.5.2" data-path="reg.html"><a href="reg.html#案例-2"><i class="fa fa-check"></i><b>7.5.2</b> 案例</a></li>
</ul></li>
<li class="chapter" data-level="7.6" data-path="reg.html"><a href="reg.html#断点回归"><i class="fa fa-check"></i><b>7.6</b> 断点回归</a>
<ul>
<li class="chapter" data-level="7.6.1" data-path="reg.html"><a href="reg.html#原理-3"><i class="fa fa-check"></i><b>7.6.1</b> 原理</a></li>
<li class="chapter" data-level="7.6.2" data-path="reg.html"><a href="reg.html#案例-3"><i class="fa fa-check"></i><b>7.6.2</b> 案例</a></li>
</ul></li>
<li class="chapter" data-level="7.7" data-path="reg.html"><a href="reg.html#包含高维分类变量的回归"><i class="fa fa-check"></i><b>7.7</b> 包含高维分类变量的回归</a></li>
<li class="chapter" data-level="7.8" data-path="reg.html"><a href="reg.html#formula-公式对象"><i class="fa fa-check"></i><b>7.8</b> formula (公式)对象</a>
<ul>
<li class="chapter" data-level="7.8.1" data-path="reg.html"><a href="reg.html#公式的生成"><i class="fa fa-check"></i><b>7.8.1</b> 公式的生成</a></li>
<li class="chapter" data-level="7.8.2" data-path="reg.html"><a href="reg.html#生成公式的运算符"><i class="fa fa-check"></i><b>7.8.2</b> 生成公式的运算符</a></li>
<li class="chapter" data-level="7.8.3" data-path="reg.html"><a href="reg.html#公式与字符串之间的转换"><i class="fa fa-check"></i><b>7.8.3</b> 公式与字符串之间的转换</a></li>
</ul></li>
<li class="chapter" data-level="7.9" data-path="reg.html"><a href="reg.html#表达式expression"><i class="fa fa-check"></i><b>7.9</b> 表达式expression</a></li>
<li class="chapter" data-level="7.10" data-path="reg.html"><a href="reg.html#表达式的生成与执行"><i class="fa fa-check"></i><b>7.10</b> 表达式的生成与执行</a></li>
<li class="chapter" data-level="7.11" data-path="reg.html"><a href="reg.html#表达式与字符串的转换"><i class="fa fa-check"></i><b>7.11</b> 表达式与字符串的转换</a></li>
<li class="chapter" data-level="7.12" data-path="reg.html"><a href="reg.html#使用stargazer输出表格"><i class="fa fa-check"></i><b>7.12</b> 使用stargazer输出表格</a>
<ul>
<li class="chapter" data-level="7.12.1" data-path="reg.html"><a href="reg.html#标准回归表"><i class="fa fa-check"></i><b>7.12.1</b> 标准回归表</a></li>
<li class="chapter" data-level="7.12.2" data-path="reg.html"><a href="reg.html#默认格式"><i class="fa fa-check"></i><b>7.12.2</b> 默认格式</a></li>
<li class="chapter" data-level="7.12.3" data-path="reg.html"><a href="reg.html#表格表头"><i class="fa fa-check"></i><b>7.12.3</b> 表格表头</a></li>
<li class="chapter" data-level="7.12.4" data-path="reg.html"><a href="reg.html#表格正文"><i class="fa fa-check"></i><b>7.12.4</b> 表格正文</a></li>
<li class="chapter" data-level="7.12.5" data-path="reg.html"><a href="reg.html#添加变量信息"><i class="fa fa-check"></i><b>7.12.5</b> 添加变量信息</a></li>
<li class="chapter" data-level="7.12.6" data-path="reg.html"><a href="reg.html#选择统计量"><i class="fa fa-check"></i><b>7.12.6</b> 选择统计量</a></li>
<li class="chapter" data-level="7.12.7" data-path="reg.html"><a href="reg.html#表格注释"><i class="fa fa-check"></i><b>7.12.7</b> 表格注释</a></li>
<li class="chapter" data-level="7.12.8" data-path="reg.html"><a href="reg.html#整体布局"><i class="fa fa-check"></i><b>7.12.8</b> 整体布局</a></li>
<li class="chapter" data-level="7.12.9" data-path="reg.html"><a href="reg.html#其他-1"><i class="fa fa-check"></i><b>7.12.9</b> 其他</a></li>
<li class="chapter" data-level="7.12.10" data-path="reg.html"><a href="reg.html#描述性统计表"><i class="fa fa-check"></i><b>7.12.10</b> 描述性统计表</a></li>
</ul></li>
<li class="chapter" data-level="7.13" data-path="reg.html"><a href="reg.html#回归结果的可视化"><i class="fa fa-check"></i><b>7.13</b> 回归结果的可视化</a>
<ul>
<li class="chapter" data-level="7.13.1" data-path="reg.html"><a href="reg.html#使用ggcoefstats可视化回归结果"><i class="fa fa-check"></i><b>7.13.1</b> 使用ggcoefstats可视化回归结果</a></li>
<li class="chapter" data-level="7.13.2" data-path="reg.html"><a href="reg.html#使用"><i class="fa fa-check"></i><b>7.13.2</b> 使用</a></li>
<li class="chapter" data-level="7.13.3" data-path="reg.html"><a href="reg.html#双重差分模型的可视化"><i class="fa fa-check"></i><b>7.13.3</b> 双重差分模型的可视化</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="8" data-path="py.html"><a href="py.html"><i class="fa fa-check"></i><b>8</b> Python基础</a>
<ul>
<li class="chapter" data-level="8.1" data-path="py.html"><a href="py.html#python简介"><i class="fa fa-check"></i><b>8.1</b> Python简介</a></li>
<li class="chapter" data-level="8.2" data-path="py.html"><a href="py.html#python安装与pycharm"><i class="fa fa-check"></i><b>8.2</b> Python安装与Pycharm</a>
<ul>
<li class="chapter" data-level="8.2.1" data-path="py.html"><a href="py.html#安装"><i class="fa fa-check"></i><b>8.2.1</b> 安装</a></li>
<li class="chapter" data-level="8.2.2" data-path="py.html"><a href="py.html#编辑器-1"><i class="fa fa-check"></i><b>8.2.2</b> 编辑器</a></li>
</ul></li>
<li class="chapter" data-level="8.3" data-path="py.html"><a href="py.html#变量-1"><i class="fa fa-check"></i><b>8.3</b> 变量</a></li>
<li class="chapter" data-level="8.4" data-path="py.html"><a href="py.html#数据类型-1"><i class="fa fa-check"></i><b>8.4</b> 数据类型</a>
<ul>
<li class="chapter" data-level="8.4.1" data-path="py.html"><a href="py.html#类型转换"><i class="fa fa-check"></i><b>8.4.1</b> 类型转换</a></li>
<li class="chapter" data-level="8.4.2" data-path="py.html"><a href="py.html#算术运算"><i class="fa fa-check"></i><b>8.4.2</b> 算术运算</a></li>
<li class="chapter" data-level="8.4.3" data-path="py.html"><a href="py.html#布尔运算"><i class="fa fa-check"></i><b>8.4.3</b> 布尔运算</a></li>
<li class="chapter" data-level="8.4.4" data-path="py.html"><a href="py.html#字符串"><i class="fa fa-check"></i><b>8.4.4</b> 字符串</a></li>
<li class="chapter" data-level="8.4.5" data-path="py.html"><a href="py.html#字符串的替换"><i class="fa fa-check"></i><b>8.4.5</b> 字符串的替换</a></li>
<li class="chapter" data-level="8.4.6" data-path="py.html"><a href="py.html#字符串的切片"><i class="fa fa-check"></i><b>8.4.6</b> 字符串的切片</a></li>
<li class="chapter" data-level="8.4.7" data-path="py.html"><a href="py.html#标准字符串操作"><i class="fa fa-check"></i><b>8.4.7</b> 标准字符串操作</a></li>
</ul></li>
<li class="chapter" data-level="8.5" data-path="py.html"><a href="py.html#标准输入输出"><i class="fa fa-check"></i><b>8.5</b> 标准输入输出</a>
<ul>
<li class="chapter" data-level="8.5.1" data-path="py.html"><a href="py.html#标准输入"><i class="fa fa-check"></i><b>8.5.1</b> 标准输入</a></li>
<li class="chapter" data-level="8.5.2" data-path="py.html"><a href="py.html#命令执行"><i class="fa fa-check"></i><b>8.5.2</b> 命令执行</a></li>
</ul></li>
<li class="chapter" data-level="8.6" data-path="py.html"><a href="py.html#数据结构-1"><i class="fa fa-check"></i><b>8.6</b> 数据结构</a>
<ul>
<li class="chapter" data-level="8.6.1" data-path="py.html"><a href="py.html#列表-1"><i class="fa fa-check"></i><b>8.6.1</b> 列表</a></li>
<li class="chapter" data-level="8.6.2" data-path="py.html"><a href="py.html#元组"><i class="fa fa-check"></i><b>8.6.2</b> 元组</a></li>
<li class="chapter" data-level="8.6.3" data-path="py.html"><a href="py.html#字典"><i class="fa fa-check"></i><b>8.6.3</b> 字典</a></li>
<li class="chapter" data-level="8.6.4" data-path="py.html"><a href="py.html#数据结构之间的转化-1"><i class="fa fa-check"></i><b>8.6.4</b> 数据结构之间的转化</a></li>
</ul></li>
<li class="chapter" data-level="8.7" data-path="py.html"><a href="py.html#流程控制-1"><i class="fa fa-check"></i><b>8.7</b> 流程控制</a>
<ul>
<li class="chapter" data-level="8.7.1" data-path="py.html"><a href="py.html#条件判断-1"><i class="fa fa-check"></i><b>8.7.1</b> 条件判断</a></li>
<li class="chapter" data-level="8.7.2" data-path="py.html"><a href="py.html#循环-1"><i class="fa fa-check"></i><b>8.7.2</b> 循环</a></li>
</ul></li>
<li class="chapter" data-level="8.8" data-path="py.html"><a href="py.html#函数与模块"><i class="fa fa-check"></i><b>8.8</b> 函数与模块</a>
<ul>
<li class="chapter" data-level="8.8.1" data-path="py.html"><a href="py.html#批量调用"><i class="fa fa-check"></i><b>8.8.1</b> 批量调用</a></li>
<li class="chapter" data-level="8.8.2" data-path="py.html"><a href="py.html#无名函数"><i class="fa fa-check"></i><b>8.8.2</b> 无名函数</a></li>
<li class="chapter" data-level="8.8.3" data-path="py.html"><a href="py.html#函数文档"><i class="fa fa-check"></i><b>8.8.3</b> 函数文档</a></li>
<li class="chapter" data-level="8.8.4" data-path="py.html"><a href="py.html#模块"><i class="fa fa-check"></i><b>8.8.4</b> 模块</a></li>
</ul></li>
<li class="chapter" data-level="8.9" data-path="py.html"><a href="py.html#数据读写与文件操作"><i class="fa fa-check"></i><b>8.9</b> 数据读写与文件操作</a>
<ul>
<li class="chapter" data-level="8.9.1" data-path="py.html"><a href="py.html#读入文件"><i class="fa fa-check"></i><b>8.9.1</b> 读入文件</a></li>
<li class="chapter" data-level="8.9.2" data-path="py.html"><a href="py.html#写出文件"><i class="fa fa-check"></i><b>8.9.2</b> 写出文件</a></li>
<li class="chapter" data-level="8.9.3" data-path="py.html"><a href="py.html#with关键字"><i class="fa fa-check"></i><b>8.9.3</b> with关键字</a></li>
</ul></li>
<li class="chapter" data-level="8.10" data-path="py.html"><a href="py.html#os模块"><i class="fa fa-check"></i><b>8.10</b> os模块</a></li>
<li class="chapter" data-level="8.11" data-path="py.html"><a href="py.html#案例获取高德地图地址信息"><i class="fa fa-check"></i><b>8.11</b> 案例：获取高德地图地址信息</a></li>
<li class="chapter" data-level="8.12" data-path="py.html"><a href="py.html#面向对象单独成一章"><i class="fa fa-check"></i><b>8.12</b> 面向对象单独成一章</a></li>
</ul></li>
<li class="chapter" data-level="9" data-path="regexp.html"><a href="regexp.html"><i class="fa fa-check"></i><b>9</b> 正则表达式</a>
<ul>
<li class="chapter" data-level="9.1" data-path="regexp.html"><a href="regexp.html#语法要素"><i class="fa fa-check"></i><b>9.1</b> 语法要素</a>
<ul>
<li class="chapter" data-level="9.1.1" data-path="regexp.html"><a href="regexp.html#元字符"><i class="fa fa-check"></i><b>9.1.1</b> 元字符</a></li>
<li class="chapter" data-level="9.1.2" data-path="regexp.html"><a href="regexp.html#重复"><i class="fa fa-check"></i><b>9.1.2</b> 重复</a></li>
<li class="chapter" data-level="9.1.3" data-path="regexp.html"><a href="regexp.html#常用字符集"><i class="fa fa-check"></i><b>9.1.3</b> 常用字符集</a></li>
<li class="chapter" data-level="9.1.4" data-path="regexp.html"><a href="regexp.html#分组"><i class="fa fa-check"></i><b>9.1.4</b> 分组</a></li>
<li class="chapter" data-level="9.1.5" data-path="regexp.html"><a href="regexp.html#非捕获组与断言"><i class="fa fa-check"></i><b>9.1.5</b> 非捕获组与断言</a></li>
</ul></li>
<li class="chapter" data-level="9.2" data-path="regexp.html"><a href="regexp.html#grep命令"><i class="fa fa-check"></i><b>9.2</b> grep命令</a></li>
<li class="chapter" data-level="9.3" data-path="regexp.html"><a href="regexp.html#sed命令"><i class="fa fa-check"></i><b>9.3</b> sed命令</a>
<ul>
<li class="chapter" data-level="9.3.1" data-path="regexp.html"><a href="regexp.html#应用情景"><i class="fa fa-check"></i><b>9.3.1</b> 应用情景</a></li>
<li class="chapter" data-level="9.3.2" data-path="regexp.html"><a href="regexp.html#文本替换"><i class="fa fa-check"></i><b>9.3.2</b> 文本替换</a></li>
<li class="chapter" data-level="9.3.3" data-path="regexp.html"><a href="regexp.html#定位行"><i class="fa fa-check"></i><b>9.3.3</b> 定位行</a></li>
<li class="chapter" data-level="9.3.4" data-path="regexp.html"><a href="regexp.html#替代"><i class="fa fa-check"></i><b>9.3.4</b> 替代</a></li>
</ul></li>
<li class="chapter" data-level="9.4" data-path="regexp.html"><a href="regexp.html#awk命令"><i class="fa fa-check"></i><b>9.4</b> awk命令</a>
<ul>
<li class="chapter" data-level="9.4.1" data-path="regexp.html"><a href="regexp.html#入门"><i class="fa fa-check"></i><b>9.4.1</b> 入门</a></li>
</ul></li>
<li class="chapter" data-level="9.5" data-path="regexp.html"><a href="regexp.html#r语言stringr包"><i class="fa fa-check"></i><b>9.5</b> R语言stringr包</a>
<ul>
<li class="chapter" data-level="9.5.1" data-path="regexp.html"><a href="regexp.html#stringr包"><i class="fa fa-check"></i><b>9.5.1</b> stringr包</a></li>
<li class="chapter" data-level="9.5.2" data-path="regexp.html"><a href="regexp.html#应用案例wos数据分析"><i class="fa fa-check"></i><b>9.5.2</b> 应用案例：wos数据分析</a></li>
<li class="chapter" data-level="9.5.3" data-path="regexp.html"><a href="regexp.html#应用案例数据合并与校对"><i class="fa fa-check"></i><b>9.5.3</b> 应用案例：数据合并与校对</a></li>
</ul></li>
<li class="chapter" data-level="9.6" data-path="regexp.html"><a href="regexp.html#python的re模块"><i class="fa fa-check"></i><b>9.6</b> Python的re模块</a>
<ul>
<li class="chapter" data-level="9.6.1" data-path="regexp.html"><a href="regexp.html#原生字符串"><i class="fa fa-check"></i><b>9.6.1</b> 原生字符串</a></li>
<li class="chapter" data-level="9.6.2" data-path="regexp.html"><a href="regexp.html#编译"><i class="fa fa-check"></i><b>9.6.2</b> 编译</a></li>
<li class="chapter" data-level="9.6.3" data-path="regexp.html"><a href="regexp.html#匹配-1"><i class="fa fa-check"></i><b>9.6.3</b> 匹配</a></li>
<li class="chapter" data-level="9.6.4" data-path="regexp.html"><a href="regexp.html#分割"><i class="fa fa-check"></i><b>9.6.4</b> 分割</a></li>
<li class="chapter" data-level="9.6.5" data-path="regexp.html"><a href="regexp.html#替换"><i class="fa fa-check"></i><b>9.6.5</b> 替换</a></li>
<li class="chapter" data-level="9.6.6" data-path="regexp.html"><a href="regexp.html#命名组"><i class="fa fa-check"></i><b>9.6.6</b> 命名组</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="10" data-path="cml.html"><a href="cml.html"><i class="fa fa-check"></i><b>10</b> 命令行</a>
<ul>
<li class="chapter" data-level="10.1" data-path="cml.html"><a href="cml.html#命令的基本概念"><i class="fa fa-check"></i><b>10.1</b> 命令的基本概念</a>
<ul>
<li class="chapter" data-level="10.1.1" data-path="cml.html"><a href="cml.html#常用命令"><i class="fa fa-check"></i><b>10.1.1</b> 常用命令</a></li>
<li class="chapter" data-level="10.1.2" data-path="cml.html"><a href="cml.html#标准输入与输出"><i class="fa fa-check"></i><b>10.1.2</b> 标准输入与输出</a></li>
<li class="chapter" data-level="10.1.3" data-path="cml.html"><a href="cml.html#管道与进程管理"><i class="fa fa-check"></i><b>10.1.3</b> 管道与进程管理</a></li>
<li class="chapter" data-level="10.1.4" data-path="cml.html"><a href="cml.html#别名"><i class="fa fa-check"></i><b>10.1.4</b> 别名</a></li>
<li class="chapter" data-level="10.1.5" data-path="cml.html"><a href="cml.html#脚本"><i class="fa fa-check"></i><b>10.1.5</b> 脚本</a></li>
<li class="chapter" data-level="10.1.6" data-path="cml.html"><a href="cml.html#传参"><i class="fa fa-check"></i><b>10.1.6</b> 传参</a></li>
</ul></li>
<li class="chapter" data-level="10.2" data-path="cml.html"><a href="cml.html#变量与数据结构"><i class="fa fa-check"></i><b>10.2</b> 变量与数据结构</a>
<ul>
<li class="chapter" data-level="10.2.1" data-path="cml.html"><a href="cml.html#数组"><i class="fa fa-check"></i><b>10.2.1</b> 数组</a></li>
<li class="chapter" data-level="10.2.2" data-path="cml.html"><a href="cml.html#字典-1"><i class="fa fa-check"></i><b>10.2.2</b> 字典</a></li>
</ul></li>
<li class="chapter" data-level="10.3" data-path="cml.html"><a href="cml.html#运算-1"><i class="fa fa-check"></i><b>10.3</b> 运算</a></li>
<li class="chapter" data-level="10.4" data-path="cml.html"><a href="cml.html#控制流程"><i class="fa fa-check"></i><b>10.4</b> 控制流程</a>
<ul>
<li class="chapter" data-level="10.4.1" data-path="cml.html"><a href="cml.html#选择结构"><i class="fa fa-check"></i><b>10.4.1</b> 选择结构</a></li>
<li class="chapter" data-level="10.4.2" data-path="cml.html"><a href="cml.html#循环-2"><i class="fa fa-check"></i><b>10.4.2</b> 循环</a></li>
</ul></li>
<li class="chapter" data-level="10.5" data-path="cml.html"><a href="cml.html#函数"><i class="fa fa-check"></i><b>10.5</b> 函数</a></li>
<li class="chapter" data-level="10.6" data-path="cml.html"><a href="cml.html#bash内建正则表达式"><i class="fa fa-check"></i><b>10.6</b> bash内建正则表达式</a></li>
<li class="chapter" data-level="10.7" data-path="cml.html"><a href="cml.html#应用案例"><i class="fa fa-check"></i><b>10.7</b> 应用案例</a></li>
<li class="chapter" data-level="10.8" data-path="cml.html"><a href="cml.html#通配符"><i class="fa fa-check"></i><b>10.8</b> 通配符</a></li>
<li class="chapter" data-level="10.9" data-path="cml.html"><a href="cml.html#sed"><i class="fa fa-check"></i><b>10.9</b> sed</a></li>
<li class="chapter" data-level="10.10" data-path="cml.html"><a href="cml.html#awk"><i class="fa fa-check"></i><b>10.10</b> awk</a></li>
<li class="chapter" data-level="10.11" data-path="cml.html"><a href="cml.html#正则表达式"><i class="fa fa-check"></i><b>10.11</b> 正则表达式</a></li>
<li class="chapter" data-level="10.12" data-path="cml.html"><a href="cml.html#r的命令行选项"><i class="fa fa-check"></i><b>10.12</b> R的命令行选项</a>
<ul>
<li class="chapter" data-level="10.12.1" data-path="cml.html"><a href="cml.html#linuxunix-shebang"><i class="fa fa-check"></i><b>10.12.1</b> Linux/Unix Shebang</a></li>
<li class="chapter" data-level="10.12.2" data-path="cml.html"><a href="cml.html#argparse包实例"><i class="fa fa-check"></i><b>10.12.2</b> argparse包实例</a></li>
</ul></li>
<li class="chapter" data-level="10.13" data-path="cml.html"><a href="cml.html#关于命令行与ide"><i class="fa fa-check"></i><b>10.13</b> 关于命令行与IDE</a></li>
</ul></li>
<li class="chapter" data-level="11" data-path="web.html"><a href="web.html"><i class="fa fa-check"></i><b>11</b> 网络数据采集</a>
<ul>
<li class="chapter" data-level="11.1" data-path="web.html"><a href="web.html#网络数据格式"><i class="fa fa-check"></i><b>11.1</b> 网络数据格式</a>
<ul>
<li class="chapter" data-level="11.1.1" data-path="web.html"><a href="web.html#csv"><i class="fa fa-check"></i><b>11.1.1</b> CSV</a></li>
<li class="chapter" data-level="11.1.2" data-path="web.html"><a href="web.html#xml-1"><i class="fa fa-check"></i><b>11.1.2</b> XML</a></li>
<li class="chapter" data-level="11.1.3" data-path="web.html"><a href="web.html#json-1"><i class="fa fa-check"></i><b>11.1.3</b> JSON</a></li>
</ul></li>
<li class="chapter" data-level="11.2" data-path="web.html"><a href="web.html#html"><i class="fa fa-check"></i><b>11.2</b> HTML</a>
<ul>
<li class="chapter" data-level="11.2.1" data-path="web.html"><a href="web.html#html的基本语法"><i class="fa fa-check"></i><b>11.2.1</b> HTML的基本语法</a></li>
<li class="chapter" data-level="11.2.2" data-path="web.html"><a href="web.html#常见html标签"><i class="fa fa-check"></i><b>11.2.2</b> 常见HTML标签</a></li>
<li class="chapter" data-level="11.2.3" data-path="web.html"><a href="web.html#dom树形数据结构"><i class="fa fa-check"></i><b>11.2.3</b> DOM树形数据结构</a></li>
</ul></li>
<li class="chapter" data-level="11.3" data-path="web.html"><a href="web.html#css"><i class="fa fa-check"></i><b>11.3</b> CSS</a>
<ul>
<li class="chapter" data-level="11.3.1" data-path="web.html"><a href="web.html#css的基本语法"><i class="fa fa-check"></i><b>11.3.1</b> CSS的基本语法</a></li>
<li class="chapter" data-level="11.3.2" data-path="web.html"><a href="web.html#id选择器"><i class="fa fa-check"></i><b>11.3.2</b> id选择器</a></li>
<li class="chapter" data-level="11.3.3" data-path="web.html"><a href="web.html#类选择器"><i class="fa fa-check"></i><b>11.3.3</b> 类选择器</a></li>
</ul></li>
<li class="chapter" data-level="11.4" data-path="web.html"><a href="web.html#javascript"><i class="fa fa-check"></i><b>11.4</b> JavaScript</a>
<ul>
<li class="chapter" data-level="11.4.1" data-path="web.html"><a href="web.html#javascript案例"><i class="fa fa-check"></i><b>11.4.1</b> JavaScript案例</a></li>
<li class="chapter" data-level="11.4.2" data-path="web.html"><a href="web.html#javascript的基本语法"><i class="fa fa-check"></i><b>11.4.2</b> JavaScript的基本语法</a></li>
<li class="chapter" data-level="11.4.3" data-path="web.html"><a href="web.html#ajax"><i class="fa fa-check"></i><b>11.4.3</b> AJAX</a></li>
</ul></li>
<li class="chapter" data-level="11.5" data-path="web.html"><a href="web.html#开发者工具"><i class="fa fa-check"></i><b>11.5</b> 开发者工具</a>
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<li class="chapter" data-level="11.5.1" data-path="web.html"><a href="web.html#打开开发者工具"><i class="fa fa-check"></i><b>11.5.1</b> 打开开发者工具</a></li>
<li class="chapter" data-level="11.5.2" data-path="web.html"><a href="web.html#查看器与样式"><i class="fa fa-check"></i><b>11.5.2</b> 查看器与样式</a></li>
<li class="chapter" data-level="11.5.3" data-path="web.html"><a href="web.html#其他功能"><i class="fa fa-check"></i><b>11.5.3</b> 其他功能</a></li>
</ul></li>
<li class="chapter" data-level="11.6" data-path="web.html"><a href="web.html#xpath"><i class="fa fa-check"></i><b>11.6</b> Xpath</a>
<ul>
<li class="chapter" data-level="11.6.1" data-path="web.html"><a href="web.html#基本查询"><i class="fa fa-check"></i><b>11.6.1</b> 基本查询</a></li>
</ul></li>
<li class="chapter" data-level="11.7" data-path="web.html"><a href="web.html#http"><i class="fa fa-check"></i><b>11.7</b> HTTP</a>
<ul>
<li class="chapter" data-level="11.7.1" data-path="web.html"><a href="web.html#http常见方法"><i class="fa fa-check"></i><b>11.7.1</b> HTTP常见方法</a></li>
</ul></li>
<li class="chapter" data-level="11.8" data-path="web.html"><a href="web.html#静态爬虫"><i class="fa fa-check"></i><b>11.8</b> 静态爬虫</a></li>
<li class="chapter" data-level="11.9" data-path="web.html"><a href="web.html#使用rselenium的动态爬虫"><i class="fa fa-check"></i><b>11.9</b> 使用RSelenium的动态爬虫</a>
<ul>
<li class="chapter" data-level="11.9.1" data-path="web.html"><a href="web.html#rselenium简介与安装"><i class="fa fa-check"></i><b>11.9.1</b> RSelenium简介与安装</a></li>
<li class="chapter" data-level="11.9.2" data-path="web.html"><a href="web.html#安装docker"><i class="fa fa-check"></i><b>11.9.2</b> 安装Docker</a></li>
<li class="chapter" data-level="11.9.3" data-path="web.html"><a href="web.html#rselenum语法"><i class="fa fa-check"></i><b>11.9.3</b> RSelenum语法</a></li>
<li class="chapter" data-level="11.9.4" data-path="web.html"><a href="web.html#案例1在链家搜索并获取相关信息"><i class="fa fa-check"></i><b>11.9.4</b> 案例1:在链家搜索并获取相关信息</a></li>
<li class="chapter" data-level="11.9.5" data-path="web.html"><a href="web.html#案例2登录豆瓣"><i class="fa fa-check"></i><b>11.9.5</b> 案例2:登录豆瓣</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="12" data-path="geo.html"><a href="geo.html"><i class="fa fa-check"></i><b>12</b> 地理计算</a>
<ul>
<li class="chapter" data-level="12.1" data-path="geo.html"><a href="geo.html#r中地理计算"><i class="fa fa-check"></i><b>12.1</b> R中地理计算</a></li>
<li class="chapter" data-level="12.2" data-path="geo.html"><a href="geo.html#地理数据结构"><i class="fa fa-check"></i><b>12.2</b> 地理数据结构</a>
<ul>
<li class="chapter" data-level="12.2.1" data-path="geo.html"><a href="geo.html#向量vector"><i class="fa fa-check"></i><b>12.2.1</b> 向量（Vector）</a></li>
<li class="chapter" data-level="12.2.2" data-path="geo.html"><a href="geo.html#栅格raster"><i class="fa fa-check"></i><b>12.2.2</b> 栅格（Raster）</a></li>
<li class="chapter" data-level="12.2.3" data-path="geo.html"><a href="geo.html#坐标系coordinate-reference-system"><i class="fa fa-check"></i><b>12.2.3</b> 坐标系（coordinate reference system）</a></li>
</ul></li>
<li class="chapter" data-level="12.3" data-path="geo.html"><a href="geo.html#地理数据操纵"><i class="fa fa-check"></i><b>12.3</b> 地理数据操纵</a></li>
<li class="chapter" data-level="12.4" data-path="geo.html"><a href="geo.html#地理数据可视化"><i class="fa fa-check"></i><b>12.4</b> 地理数据可视化</a></li>
<li class="chapter" data-level="12.5" data-path="geo.html"><a href="geo.html#地理数据运算"><i class="fa fa-check"></i><b>12.5</b> 地理数据运算</a>
<ul>
<li class="chapter" data-level="12.5.1" data-path="geo.html"><a href="geo.html#取子集"><i class="fa fa-check"></i><b>12.5.1</b> 取子集</a></li>
</ul></li>
<li class="chapter" data-level="12.6" data-path="geo.html"><a href="geo.html#地理数据读写"><i class="fa fa-check"></i><b>12.6</b> 地理数据读写</a></li>
<li class="chapter" data-level="12.7" data-path="geo.html"><a href="geo.html#地理数据计算"><i class="fa fa-check"></i><b>12.7</b> 地理数据计算</a></li>
</ul></li>
<li class="chapter" data-level="13" data-path="make.html"><a href="make.html"><i class="fa fa-check"></i><b>13</b> GUN Make的数据生产线</a>
<ul>
<li class="chapter" data-level="13.1" data-path="make.html"><a href="make.html#使用make的必要性"><i class="fa fa-check"></i><b>13.1</b> 使用Make的必要性</a></li>
<li class="chapter" data-level="13.2" data-path="make.html"><a href="make.html#数据流水线的构造目标"><i class="fa fa-check"></i><b>13.2</b> 数据流水线的构造目标</a></li>
<li class="chapter" data-level="13.3" data-path="make.html"><a href="make.html#make安装"><i class="fa fa-check"></i><b>13.3</b> Make安装</a></li>
<li class="chapter" data-level="13.4" data-path="make.html"><a href="make.html#快速上手make"><i class="fa fa-check"></i><b>13.4</b> 快速上手make</a></li>
<li class="chapter" data-level="13.5" data-path="make.html"><a href="make.html#make的工作方式"><i class="fa fa-check"></i><b>13.5</b> make的工作方式</a></li>
<li class="chapter" data-level="13.6" data-path="make.html"><a href="make.html#makefile-的高级写法"><i class="fa fa-check"></i><b>13.6</b> Makefile 的高级写法</a>
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<li class="chapter" data-level="13.6.1" data-path="make.html"><a href="make.html#特殊目标"><i class="fa fa-check"></i><b>13.6.1</b> 特殊目标</a></li>
<li class="chapter" data-level="13.6.2" data-path="make.html"><a href="make.html#使用变量"><i class="fa fa-check"></i><b>13.6.2</b> 使用变量</a></li>
<li class="chapter" data-level="13.6.3" data-path="make.html"><a href="make.html#分支与循环结构"><i class="fa fa-check"></i><b>13.6.3</b> 分支与循环结构</a></li>
<li class="chapter" data-level="13.6.4" data-path="make.html"><a href="make.html#函数-1"><i class="fa fa-check"></i><b>13.6.4</b> 函数</a></li>
</ul></li>
<li class="chapter" data-level="13.7" data-path="make.html"><a href="make.html#make的高级语法"><i class="fa fa-check"></i><b>13.7</b> Make的高级语法</a>
<ul>
<li class="chapter" data-level="13.7.1" data-path="make.html"><a href="make.html#并行计算"><i class="fa fa-check"></i><b>13.7.1</b> 并行计算</a></li>
</ul></li>
<li class="chapter" data-level="13.8" data-path="make.html"><a href="make.html#参考资料"><i class="fa fa-check"></i><b>13.8</b> 参考资料</a></li>
</ul></li>
<li class="chapter" data-level="14" data-path="net.html"><a href="net.html"><i class="fa fa-check"></i><b>14</b> 图数据分析</a></li>
<li class="appendix"><span><b>附录</b></span></li>
<li class="chapter" data-level="A" data-path="sound.html"><a href="sound.html"><i class="fa fa-check"></i><b>A</b> 余音绕梁</a></li>
<li class="chapter" data-level="" data-path="references.html"><a href="references.html"><i class="fa fa-check"></i>参考文献</a></li>
<li class="chapter" data-level="B" data-path="date.html"><a href="date.html"><i class="fa fa-check"></i><b>B</b> R日期时间</a>
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<li class="chapter" data-level="B.1" data-path="date.html"><a href="date.html#日期-时间数据类型"><i class="fa fa-check"></i><b>B.1</b> 日期-时间数据类型</a></li>
<li class="chapter" data-level="B.2" data-path="date.html"><a href="date.html#lubridate包"><i class="fa fa-check"></i><b>B.2</b> lubridate包</a>
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<li class="chapter" data-level="B.2.1" data-path="date.html"><a href="date.html#定义日期-时间变量"><i class="fa fa-check"></i><b>B.2.1</b> 定义日期-时间变量</a></li>
</ul></li>
<li class="chapter" data-level="B.3" data-path="date.html"><a href="date.html#从日期-时间中取出元素"><i class="fa fa-check"></i><b>B.3</b> 从日期-时间中取出元素</a></li>
<li class="chapter" data-level="B.4" data-path="date.html"><a href="date.html#日期-时间取整"><i class="fa fa-check"></i><b>B.4</b> 日期-时间取整</a></li>
<li class="chapter" data-level="B.5" data-path="date.html"><a href="date.html#日期-时间的数学运算"><i class="fa fa-check"></i><b>B.5</b> 日期-时间的数学运算</a>
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<li class="chapter" data-level="B.5.1" data-path="date.html"><a href="date.html#时间长度"><i class="fa fa-check"></i><b>B.5.1</b> 时间长度</a></li>
<li class="chapter" data-level="B.5.2" data-path="date.html"><a href="date.html#时间周期"><i class="fa fa-check"></i><b>B.5.2</b> 时间周期</a></li>
<li class="chapter" data-level="B.5.3" data-path="date.html"><a href="date.html#时间区间"><i class="fa fa-check"></i><b>B.5.3</b> 时间区间</a></li>
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<i class="fa fa-circle-o-notch fa-spin"></i><a href="./">数据工程讲义：经济学分册</a>
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<div id="geo" class="section level1 hasAnchor" number="12">
<h1><span class="header-section-number">第 12 章</span> 地理计算<a href="geo.html#geo" class="anchor-section" aria-label="Anchor link to header"></a></h1>
<blockquote>
<p>就是为了这点儿醋，我才包的这顿饺子。 <em>—邪不压正</em></p>
</blockquote>
<p>地理计算（geocomputation）指的是将编程语言应用于地理数据以解决地理与空间问题的过程。地理计算是地理学与计算科学的交叉领域，其核心一方面是以何种数据结构刻画具有空间属性的信息，这建立在地理信息系统（Geographic Information Systems，GIS）的基础上；另一方面是以何种方式对地理数据进行操纵、可视化与统计计算。本章的重点则是通过R语言处理地理数据来满足经济学分析的需要。</p>
<div id="r中地理计算" class="section level2 hasAnchor" number="12.1">
<h2><span class="header-section-number">12.1</span> R中地理计算<a href="geo.html#r中地理计算" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>2000之前，R语言社区便开发出了用于地理计算的包，例如<code>spatial, sgeostat,splancs</code>。2005年，<code>sp</code>包第一次开发出特定的空间数据结构，可以用于储存点、边、多边形和网格等空间数据。<code>sp</code>极大推动了R地理计算的发展，当前有600多个包依赖于<code>sp</code>，<code>sp</code>已经是R语言生态中必不可少的组成部分。<code>sp</code>的不足在于其对”栅格数据(raster)“的支持比较有限，这恰好被2010年开发的<code>raster</code>包补齐，其继承者<code>terra</code>则实现了对raster数据更高效和简洁的处理。</p>
<p>地理计算的另一个主要在R中制作各式样的地图，<code>ggmap,tmap, leaflet和mapview</code>主要是针对这一用途。</p>
<p>本章的主要内容是参考Robin Lovelace, Jakub Nowosad, Jannes Muenchow的著作<em>Geocomputation with R</em>[<a href="https://geocompr.robinlovelace.net/index.html" class="uri">https://geocompr.robinlovelace.net/index.html</a>]，我们认为这是目前用于地理计算的最佳工具。本章使用的主要包是<code>sf</code>与<code>terra</code>，数据则在<code>spData</code>与<code>spDataLarge</code>包中。</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="geo.html#cb1-1" tabindex="-1"></a><span class="fu">library</span>(sf) </span>
<span id="cb1-2"><a href="geo.html#cb1-2" tabindex="-1"></a><span class="fu">library</span>(terra) </span>
<span id="cb1-3"><a href="geo.html#cb1-3" tabindex="-1"></a><span class="fu">library</span>(spData) </span>
<span id="cb1-4"><a href="geo.html#cb1-4" tabindex="-1"></a><span class="fu">library</span>(spDataLarge) </span></code></pre></div>
<pre><code>## Warning: package 'spDataLarge' was built under R version 4.2.3</code></pre>
</div>
<div id="地理数据结构" class="section level2 hasAnchor" number="12.2">
<h2><span class="header-section-number">12.2</span> 地理数据结构<a href="geo.html#地理数据结构" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>在正式介绍地理数据结构之前，我们先仔细观察一下下面的地图。</p>
<p><img src="12-geo_files/figure-html/unnamed-chunk-3-1.png" width="672" /></p>
<p>可以发现，这幅非洲地图是由一块块如下图的图形组合而成的。</p>
<p><img src="12-geo_files/figure-html/unnamed-chunk-4-1.png" width="672" /></p>
<p>由于任何复杂的曲线在局部都可以近似表示为一段折线，因此上图中的图形可以近似看做一个多边形，组成这个多边形的基本要素包括点与线段，这便构成了地理数据基本数据结构–向量。</p>
<p>除此之外，栅格数据是另一类基本地理数据结构，以矩阵的方式刻画一个背景图片信息。</p>
<div id="向量vector" class="section level3 hasAnchor" number="12.2.1">
<h3><span class="header-section-number">12.2.1</span> 向量（Vector）<a href="geo.html#向量vector" class="anchor-section" aria-label="Anchor link to header"></a></h3>
<p>地理向量是sf包中刻画地理信息的数据结构，也是经济学中使用最多的地理数据结构。值得注意的是，地理向量并非R中的向量类。sf中的地理向量是包含了几何列（geometry columns）的数据框。</p>
<div id="简单要素" class="section level4 hasAnchor" number="12.2.1.1">
<h4><span class="header-section-number">12.2.1.1</span> 简单要素<a href="geo.html#简单要素" class="anchor-section" aria-label="Anchor link to header"></a></h4>
<p>sf中使用openGIS的简单要素（simple features）来刻画地理数据，最常用的7类简单要素如下为：</p>
<table>
<colgroup>
<col width="19%" />
<col width="19%" />
<col width="61%" />
</colgroup>
<thead>
<tr class="header">
<th>要素</th>
<th>生成函数</th>
<th>解释</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>点Point</td>
<td>st_point(vector)</td>
<td>二维或者三维的坐标点，例如(5 2)</td>
</tr>
<tr class="even">
<td>线段Linestring</td>
<td>st_linestring(matrix)</td>
<td>一列点按照顺序连接形成的线段，例如(1 5, 4 4, 4 1, 2 2, 3 2)</td>
</tr>
<tr class="odd">
<td>多边形Polygon</td>
<td>st_polygon(list)</td>
<td>多点相连形成的闭合图形，例如((1 5, 2 2, 4 1, 4 4, 1 5))</td>
</tr>
<tr class="even">
<td>点组合Multipoint</td>
<td>st_multipoint(matrix)</td>
<td>多个坐标点的组合，例如(5 2, 4 4)</td>
</tr>
<tr class="odd">
<td>线段组合Multilinestring</td>
<td>st_multilinestring(list)</td>
<td>多个线段的组合，例如((1 5, 4 4, 4 1, 2 2, 3 2), (1 2, 2 4))</td>
</tr>
<tr class="even">
<td>多边形组合Multipolygon</td>
<td>st_multipolygon(list)</td>
<td>多个多边形的组合，例如(((1 5, 2 2, 4 1, 4 4, 1 5), (0 2, 1 2, 1 3, 0 3, 0 2)))</td>
</tr>
<tr class="odd">
<td>图形组合Geometry collection</td>
<td>st_geometrycollection(list)</td>
<td>各类简单要素的组合，例如多点与线段的组合((5 2, 1 3, 3 4, 3 2), (1 5, 4 4, 4 1, 2 2, 3 2))</td>
</tr>
</tbody>
</table>
</div>
<div id="简单要素几何simple-feature-geometries-sfg" class="section level4 hasAnchor" number="12.2.1.2">
<h4><span class="header-section-number">12.2.1.2</span> 简单要素几何（<strong>Simple feature geometries, sfg）</strong><a href="geo.html#简单要素几何simple-feature-geometries-sfg" class="anchor-section" aria-label="Anchor link to header"></a></h4>
<p>st_为前缀的函数可以将一般数据结构转化为地理数据，即成为简单要素几何。例如，st_point可以将向量转化成为地理点，st_linestring可以将矩阵转化为线段，st_polygon可以将以矩阵为元素的列表转化为多边形。</p>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="geo.html#cb3-1" tabindex="-1"></a>pt <span class="ot"><-</span> <span class="fu">st_point</span>(<span class="fu">c</span>(<span class="dv">5</span>,<span class="dv">2</span>))</span>
<span id="cb3-2"><a href="geo.html#cb3-2" tabindex="-1"></a>lnstr <span class="ot"><-</span> <span class="fu">st_linestring</span>(<span class="fu">rbind</span>(<span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">5</span>), <span class="fu">c</span>(<span class="dv">4</span>, <span class="dv">4</span>), <span class="fu">c</span>(<span class="dv">4</span>, <span class="dv">1</span>), <span class="fu">c</span>(<span class="dv">2</span>, <span class="dv">2</span>), <span class="fu">c</span>(<span class="dv">3</span>, <span class="dv">2</span>)))</span>
<span id="cb3-3"><a href="geo.html#cb3-3" tabindex="-1"></a>plg <span class="ot"><-</span> <span class="fu">st_polygon</span>(<span class="fu">list</span>(<span class="fu">rbind</span>(<span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">5</span>), <span class="fu">c</span>(<span class="dv">2</span>, <span class="dv">2</span>), <span class="fu">c</span>(<span class="dv">4</span>, <span class="dv">1</span>), <span class="fu">c</span>(<span class="dv">4</span>, <span class="dv">4</span>), <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">5</span>))))</span></code></pre></div>
<p>使用<code>plot</code>函数可以将sfg可视化，例如：</p>
<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb4-1"><a href="geo.html#cb4-1" tabindex="-1"></a><span class="fu">plot</span>(plg)</span></code></pre></div>
<p><img src="12-geo_files/figure-html/unnamed-chunk-6-1.png" width="672" /></p>
</div>
<div id="简单要素列simple-feature-columns-sfc" class="section level4 hasAnchor" number="12.2.1.3">
<h4><span class="header-section-number">12.2.1.3</span> 简单要素列（<strong>Simple feature columns, sfc）</strong><a href="geo.html#简单要素列simple-feature-columns-sfc" class="anchor-section" aria-label="Anchor link to header"></a></h4>
<p><code>st_sfc</code> 函数可以将多个sfg合并成为以sfg为元素的列向量：</p>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="geo.html#cb5-1" tabindex="-1"></a>plg1 <span class="ot"><-</span> <span class="fu">st_polygon</span>(<span class="fu">list</span>(<span class="fu">rbind</span>(<span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">5</span>), <span class="fu">c</span>(<span class="dv">2</span>, <span class="dv">2</span>), <span class="fu">c</span>(<span class="dv">4</span>, <span class="dv">1</span>), <span class="fu">c</span>(<span class="dv">4</span>, <span class="dv">4</span>), <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">5</span>))))</span>
<span id="cb5-2"><a href="geo.html#cb5-2" tabindex="-1"></a>plg2 <span class="ot"><-</span> <span class="fu">st_polygon</span>(<span class="fu">list</span>(<span class="fu">rbind</span>(<span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">2</span>), <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">2</span>), <span class="fu">c</span>(<span class="dv">1</span>, <span class="dv">3</span>), <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">3</span>), <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">2</span>))))</span>
<span id="cb5-3"><a href="geo.html#cb5-3" tabindex="-1"></a>polygon_sfc <span class="ot">=</span> <span class="fu">st_sfc</span>(plg1, plg2)</span>
<span id="cb5-4"><a href="geo.html#cb5-4" tabindex="-1"></a><span class="fu">st_geometry_type</span>(polygon_sfc)</span></code></pre></div>
<pre><code>## [1] POLYGON POLYGON
## 18 Levels: GEOMETRY POINT LINESTRING POLYGON MULTIPOINT ... TRIANGLE</code></pre>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="geo.html#cb7-1" tabindex="-1"></a><span class="fu">plot</span>(polygon_sfc)</span></code></pre></div>
<p><img src="12-geo_files/figure-html/unnamed-chunk-7-1.png" width="672" /></p>
<p>上面代码中，st_geometry_type用于判断地理数据的类型，plot将多边形组合可视化。</p>
</div>
<div id="sf类" class="section level4 hasAnchor" number="12.2.1.4">
<h4><span class="header-section-number">12.2.1.4</span> sf类<a href="geo.html#sf类" class="anchor-section" aria-label="Anchor link to header"></a></h4>
<p>正如前文所述，地理向量是包括几何列（即sfc）的数据框，地理向量的其他列用于刻画地理数据的属性，使用st_sf函数可以将几何列与属性列合并成为最终的地理向量，即sf类。</p>
<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="geo.html#cb8-1" tabindex="-1"></a>sh_point <span class="ot">=</span> <span class="fu">st_point</span>(<span class="fu">c</span>(<span class="fl">121.47</span>, <span class="fl">31.23</span>)) </span>
<span id="cb8-2"><a href="geo.html#cb8-2" tabindex="-1"></a>sh_geom <span class="ot">=</span> <span class="fu">st_sfc</span>(sh_point, <span class="at">crs =</span> <span class="dv">4326</span>) </span>
<span id="cb8-3"><a href="geo.html#cb8-3" tabindex="-1"></a>sh_attrib <span class="ot">=</span> <span class="fu">data.frame</span>( </span>
<span id="cb8-4"><a href="geo.html#cb8-4" tabindex="-1"></a> <span class="at">name =</span> <span class="st">"Shanghai"</span>,</span>
<span id="cb8-5"><a href="geo.html#cb8-5" tabindex="-1"></a> <span class="at">temperature =</span> <span class="dv">19</span>,</span>
<span id="cb8-6"><a href="geo.html#cb8-6" tabindex="-1"></a> <span class="at">date =</span> <span class="fu">as.Date</span>(<span class="st">"2021-11-29"</span>)</span>
<span id="cb8-7"><a href="geo.html#cb8-7" tabindex="-1"></a> )</span>
<span id="cb8-8"><a href="geo.html#cb8-8" tabindex="-1"></a>sh_sf <span class="ot">=</span> <span class="fu">st_sf</span>(sh_attrib, <span class="at">geometry =</span> sh_geom) </span>
<span id="cb8-9"><a href="geo.html#cb8-9" tabindex="-1"></a><span class="fu">class</span>(sh_sf)</span></code></pre></div>
<pre><code>## [1] "sf" "data.frame"</code></pre>
<p>生成的sf类在R中以数据框的形式储存如下：</p>
<p><img src="images/Screen%20Shot%202021-11-29%20at%2010.02.29%20PM.png" /> 注意，<strong>sfc只能有一列几何列，为了方便，通常命名为geometry或者geom。</strong></p>
</div>
</div>
<div id="栅格raster" class="section level3 hasAnchor" number="12.2.2">
<h3><span class="header-section-number">12.2.2</span> 栅格（Raster）<a href="geo.html#栅格raster" class="anchor-section" aria-label="Anchor link to header"></a></h3>
<p>栅格数据以像素的方式储存一个或多个图层，<strong>terra</strong>包中的<code>raster</code> 函数用于生成栅格数据。</p>
<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="geo.html#cb10-1" tabindex="-1"></a>new_raster <span class="ot">=</span> <span class="fu">rast</span>(<span class="at">nrows =</span> <span class="dv">6</span>, <span class="at">ncols =</span> <span class="dv">6</span>, <span class="at">resolution =</span> <span class="fl">0.5</span>, </span>
<span id="cb10-2"><a href="geo.html#cb10-2" tabindex="-1"></a> <span class="at">xmin =</span> <span class="sc">-</span><span class="fl">1.5</span>, <span class="at">xmax =</span> <span class="fl">1.5</span>, <span class="at">ymin =</span> <span class="sc">-</span><span class="fl">1.5</span>, </span>
<span id="cb10-3"><a href="geo.html#cb10-3" tabindex="-1"></a> <span class="at">ymax=</span> <span class="fl">1.5</span>,<span class="at">vals =</span> <span class="dv">1</span><span class="sc">:</span><span class="dv">36</span>)</span>
<span id="cb10-4"><a href="geo.html#cb10-4" tabindex="-1"></a><span class="fu">plot</span>(new_raster)</span></code></pre></div>
<p><img src="12-geo_files/figure-html/unnamed-chunk-9-1.png" width="672" /></p>
</div>
<div id="坐标系coordinate-reference-system" class="section level3 hasAnchor" number="12.2.3">
<h3><span class="header-section-number">12.2.3</span> 坐标系（coordinate reference system）<a href="geo.html#坐标系coordinate-reference-system" class="anchor-section" aria-label="Anchor link to header"></a></h3>
<p>上述方法中生成的地理数据仍是欧几里得空间中的二维数据，为了描述与地球对应的地理属性，我们需要引入刻画地球的坐标系。地理信息系统中有两种坐标系：地理坐标系（Geographic coordinate system）与投影坐标系（Projected coordinate systems），前者是针对地球的建立的三维模型，包括球形坐标系与椭球坐标系，后者则是将地球投影在二维空间的坐标系，根据投影方式不同又有多种分类。</p>
<p>欧洲调查组织（European Petroleum Survey Group，EPSG）专门负责维护地球的上的所有测量坐标系统，并且给每组坐标系统都赋予了一个编号和一组描述。目前通用的地理坐标系为WGS84，其编号是EPSG:4326；互联网地图常用的伪墨卡托投影坐标系，编号就是EPSG:3857。</p>
<p><code>st_sfc</code>函数的crs参数可以在定义sfc时指定坐标系，<code>st_crs</code> 可以查看地理数据的坐标系，<code>st_set_crs</code>可用于修改地理数据的坐标系，例如：</p>
<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb11-1"><a href="geo.html#cb11-1" tabindex="-1"></a>sh_sf <span class="ot"><-</span> <span class="fu">st_set_crs</span>(sh_sf, <span class="st">"EPSG:4326"</span>)</span>
<span id="cb11-2"><a href="geo.html#cb11-2" tabindex="-1"></a><span class="fu">st_crs</span>(sh_sf)</span></code></pre></div>
<pre><code>## Coordinate Reference System:
## User input: EPSG:4326
## wkt:
## GEOGCRS["WGS 84",
## ENSEMBLE["World Geodetic System 1984 ensemble",
## MEMBER["World Geodetic System 1984 (Transit)"],
## MEMBER["World Geodetic System 1984 (G730)"],
## MEMBER["World Geodetic System 1984 (G873)"],
## MEMBER["World Geodetic System 1984 (G1150)"],
## MEMBER["World Geodetic System 1984 (G1674)"],
## MEMBER["World Geodetic System 1984 (G1762)"],
## MEMBER["World Geodetic System 1984 (G2139)"],
## ELLIPSOID["WGS 84",6378137,298.257223563,
## LENGTHUNIT["metre",1]],
## ENSEMBLEACCURACY[2.0]],
## PRIMEM["Greenwich",0,
## ANGLEUNIT["degree",0.0174532925199433]],
## CS[ellipsoidal,2],
## AXIS["geodetic latitude (Lat)",north,
## ORDER[1],
## ANGLEUNIT["degree",0.0174532925199433]],
## AXIS["geodetic longitude (Lon)",east,
## ORDER[2],
## ANGLEUNIT["degree",0.0174532925199433]],
## USAGE[
## SCOPE["Horizontal component of 3D system."],
## AREA["World."],
## BBOX[-90,-180,90,180]],
## ID["EPSG",4326]]</code></pre>
<p>sfc只能有一列几何列，为了方便，通常命名为geometry或者geom。</p>
<p>如何将多个地理数据框存放在一起呢？</p>
</div>
</div>
<div id="地理数据操纵" class="section level2 hasAnchor" number="12.3">
<h2><span class="header-section-number">12.3</span> 地理数据操纵<a href="geo.html#地理数据操纵" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>我们假设本书的读者的学习目标是利用R处理地理数据以服务于经济学或者其他社会科学的研究，而不是成为一名地理信息系统的专家。因此，在介绍地理数据的操纵之前，我们先设想一下在经济学研究中对地理数据有哪些需求？</p>
<p>首先是数据可视化，很多时候我们希望画一个酷炫的地图，甚至是一个酷炫的动画地图，这是最常见也是最容易满足的需求；</p>
<p>其次，我们有时候需要通过地理数据计算一些经济变量，最简单的是两点之间的距离，论文<em>Patent Citations as a Measure of Knowledge Flows: The Influence of Examiner Citations</em>使用的一个因变量是两个专利之间的地理距离；更复杂一些的情况下，我们会需要计算点与其他地理对象之间的距离，例如，在我的工作论文<em>Minimum Wages and Business Location in China: Estimates Based on a Refined Border Approach</em>，需要计算一家企业距离行政区划边界之间的距离；</p>
<p>第三，对地理数据的修改，例如合并，简化，从而生成一个新的地理对象，例如我们在做一些分析的时候可能需要把欧盟国家合并成为整个区域来进行处理，或者我们需要把不同的铁路段连接成为一整个铁路网络，进而计算一个城市距离最近铁路线路的距离。</p>
<p>以上三个需求分别对应：地理数据可视化、地理计算以及地理数据操纵。在熟悉地理数据结构的基础上，我们可以分别介绍上述三个功能如何实现。</p>
</div>
<div id="地理数据可视化" class="section level2 hasAnchor" number="12.4">
<h2><span class="header-section-number">12.4</span> 地理数据可视化<a href="geo.html#地理数据可视化" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>动态地图</p>
</div>
<div id="地理数据运算" class="section level2 hasAnchor" number="12.5">
<h2><span class="header-section-number">12.5</span> 地理数据运算<a href="geo.html#地理数据运算" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<div id="取子集" class="section level3 hasAnchor" number="12.5.1">
<h3><span class="header-section-number">12.5.1</span> 取子集<a href="geo.html#取子集" class="anchor-section" aria-label="Anchor link to header"></a></h3>
<p>地理数据可以通过属性列或者地理列的空间关系实现取子集运算。前者与普通的数据框相同，例如下面的代码可以取出来世界地图的非洲区域：</p>
<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb13-1"><a href="geo.html#cb13-1" tabindex="-1"></a>data <span class="ot"><-</span> world[<span class="st">"region_un"</span>]</span>
<span id="cb13-2"><a href="geo.html#cb13-2" tabindex="-1"></a>Africa <span class="ot"><-</span> data[data<span class="sc">$</span>region_un <span class="sc">==</span> <span class="st">"Africa"</span>,]</span>
<span id="cb13-3"><a href="geo.html#cb13-3" tabindex="-1"></a><span class="fu">plot</span>(Africa)</span></code></pre></div>
<p><img src="12-geo_files/figure-html/unnamed-chunk-11-1.png" width="672" /></p>
<p>后者需要依赖于<code>sf</code>包提供的空间关系函数，并通过[]运算符st_filter来取子集，例如下列代码可以取出与非洲大陆距离在100km范围内，且不接壤的所有国家或地区：</p>
<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb14-1"><a href="geo.html#cb14-1" tabindex="-1"></a><span class="fu">library</span>(dplyr)</span></code></pre></div>
<pre><code>##
## Attaching package: 'dplyr'</code></pre>
<pre><code>## The following objects are masked from 'package:terra':
##
## intersect, union</code></pre>
<pre><code>## The following objects are masked from 'package:stats':
##
## filter, lag</code></pre>
<pre><code>## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union</code></pre>
<div class="sourceCode" id="cb19"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb19-1"><a href="geo.html#cb19-1" tabindex="-1"></a>data <span class="ot"><-</span> world[<span class="st">"region_un"</span>]</span>
<span id="cb19-2"><a href="geo.html#cb19-2" tabindex="-1"></a>Africa <span class="ot"><-</span> data[data<span class="sc">$</span>region_un <span class="sc">==</span> <span class="st">"Africa"</span>,]</span>
<span id="cb19-3"><a href="geo.html#cb19-3" tabindex="-1"></a>Africa <span class="ot"><-</span> Africa <span class="sc">%>%</span> </span>
<span id="cb19-4"><a href="geo.html#cb19-4" tabindex="-1"></a> <span class="fu">group_by</span>(region_un) <span class="sc">%>%</span> </span>
<span id="cb19-5"><a href="geo.html#cb19-5" tabindex="-1"></a> <span class="fu">summarise</span>()</span>
<span id="cb19-6"><a href="geo.html#cb19-6" tabindex="-1"></a>data2 <span class="ot"><-</span> world[<span class="st">"iso_a2"</span>]</span>
<span id="cb19-7"><a href="geo.html#cb19-7" tabindex="-1"></a>country_wt <span class="ot"><-</span> <span class="fu">st_is_within_distance</span>(data2,Africa,<span class="at">dist=</span><span class="dv">1000000</span>,<span class="at">sparse=</span><span class="cn">FALSE</span>)</span>
<span id="cb19-8"><a href="geo.html#cb19-8" tabindex="-1"></a>country_af <span class="ot"><-</span> <span class="fu">st_intersects</span>(data2,Africa,<span class="at">sparse=</span><span class="cn">FALSE</span>)</span>
<span id="cb19-9"><a href="geo.html#cb19-9" tabindex="-1"></a>neighbor <span class="ot"><-</span> country_wt<span class="sc">&</span>(<span class="sc">!</span>country_af)</span>
<span id="cb19-10"><a href="geo.html#cb19-10" tabindex="-1"></a><span class="fu">plot</span>(data2[neighbor,])</span></code></pre></div>
<p><img src="12-geo_files/figure-html/unnamed-chunk-12-1.png" width="672" /></p>
<p>其他常见二元地理关系函数，以两个地理对象为输入，返回值为1或0。</p>
<table>
<colgroup>
<col width="18%" />
<col width="81%" />
</colgroup>
<thead>
<tr class="header">
<th>函数</th>
<th>返回1的条件</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>st_contains</td>
<td>第一个对象完全包含第二个对象，且B至少有一个点存在于A内部。</td>
</tr>
<tr class="even">
<td>st_contains_properly</td>
<td>第一个对象完全包含第二个对象内部。st_contains(A, A) = TRUE, 但是 st_contains_properly(A, A) = FALSE 。</td>
</tr>
<tr class="odd">
<td>st_covered_by</td>
<td>第二个对象完全包含第一个对象</td>
</tr>
<tr class="even">
<td>st_covers</td>
<td>第一个对象（含边界）完全包含第二个对象</td>
</tr>
<tr class="odd">
<td>st_crosses</td>
<td>两个对象的内部交集非空，且交集不等于任何一个输入对象的内部</td>
</tr>
<tr class="even">
<td>st_disjoint</td>
<td>两个对象的内部交集为空集</td>
</tr>
<tr class="odd">
<td>st_equals</td>
<td>两个对象相同</td>
</tr>
<tr class="even">
<td>st_intersects</td>
<td>两个对象的交集非空</td>
</tr>
<tr class="odd">
<td>st_is_within_distance</td>
<td>两个对象的距离在小于等于参数</td>
</tr>
<tr class="even">
<td>st_within</td>
<td>st_within(A,B) = st_contains(B,A)</td>
</tr>
<tr class="odd">
<td>st_touches</td>
<td>两个对象交集非空，但内部交集为空</td>
</tr>
<tr class="even">
<td>st_overlaps</td>
<td>两个对象的交集非空，交集与输入对象相同维度，且不等于任何一个输入对象</td>
</tr>
</tbody>
</table>
<p>raster就当成矩阵来做处理即可 global(grain, sd)函数做summary</p>
</div>
</div>
<div id="地理数据读写" class="section level2 hasAnchor" number="12.6">
<h2><span class="header-section-number">12.6</span> 地理数据读写<a href="geo.html#地理数据读写" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>常见地理数据文件包括：ESRI Shapefile(.shp)、GeoJSON(.geojson)、KML(.kml)、ESRI FileGDB (.gdb)、Arc ASCII(.asc)、GeoPackage(.gpkg)等。<code>sf</code>包提供<code>read_sf</code>与<code>rast</code>函数来读入地理数据。</p>
<p>以GeoJSON为例，保定高新区-东区的四至范围储存在以下的文件当中:</p>
<p><img src="baoding.png" /></p>
<p>下面代码使用read_sf读入上述文件。</p>
<div class="sourceCode" id="cb20"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb20-1"><a href="geo.html#cb20-1" tabindex="-1"></a>dv_zone <span class="ot"><-</span> <span class="fu">read_sf</span>(<span class="at">dsn =</span> <span class="st">"保定高新区-东区.txt"</span>)</span>
<span id="cb20-2"><a href="geo.html#cb20-2" tabindex="-1"></a><span class="fu">class</span>(dv_zone)</span></code></pre></div>
<pre><code>## [1] "sf" "tbl_df" "tbl" "data.frame"</code></pre>
<div class="sourceCode" id="cb22"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb22-1"><a href="geo.html#cb22-1" tabindex="-1"></a><span class="fu">plot</span>(dv_zone)</span></code></pre></div>
<p><img src="12-geo_files/figure-html/unnamed-chunk-13-1.png" width="672" /></p>
<p>可以看到读入的对象直接是一个sf类。</p>
<p><code>sf</code>包提供<code>write_sf</code>与<code>writeRaster</code>函数写出地理数据，下面代码可以将<code>dv_zone</code>输出为gpkg文件。</p>
<div class="sourceCode" id="cb23"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb23-1"><a href="geo.html#cb23-1" tabindex="-1"></a><span class="fu">st_write</span>(<span class="at">obj =</span> dv_zone, <span class="at">dsn =</span> <span class="st">"保定高新区-东区.gpkg"</span>,</span>
<span id="cb23-2"><a href="geo.html#cb23-2" tabindex="-1"></a> <span class="at">delete_dsn =</span> T)</span></code></pre></div>
<pre><code>## Deleting source `保定高新区-东区.gpkg' using driver `GPKG'
## Writing layer `保定高新区-东区' to data source
## `保定高新区-东区.gpkg' using driver `GPKG'
## Writing 1 features with 0 fields and geometry type Polygon.</code></pre>
<p>FROM_GeoJson 用于读入geoJson数据</p>
<pre><code>file_js = FROM_GeoJson(url_file_string = name)
plg <- st_polygon(list(file_js[["features"]][[k]][["geometry"]]$coordinates))
polygon_sfc = st_sfc(plg,crs = 4326)
block = data.frame(name = name)
block_sf <- st_sf(block, geometry = polygon_sfc)
dvlp_zone <- rbind(dvlp_zone,block_sf)</code></pre>
</div>
<div id="地理数据计算" class="section level2 hasAnchor" number="12.7">
<h2><span class="header-section-number">12.7</span> 地理数据计算<a href="geo.html#地理数据计算" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p><code>st_distance</code>函数可直接的用于两个地理向量之间的距离。当地理向量采用地球坐标系时，<code>st_distance</code>函数会直接返回地球地球面距离。</p>
</div>
</div>
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