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<?xml version="1.0" encoding="utf-8"?>
<search>
<entry>
<title>GraphQL入门到aws实战 - 1. 了解GraphQL</title>
<link href="/2023/11/08/graphql-ru-men-dao-aws-shi-zhan/"/>
<url>/2023/11/08/graphql-ru-men-dao-aws-shi-zhan/</url>
<content type="html"><![CDATA[<h1 id="准备工作"><a href="#准备工作" class="headerlink" title="准备工作"></a>准备工作</h1><p>我们使用 <code>express</code>将js运行为一个可被浏览器打开的网页（可以访问<code>localhost:4000</code>），使用 <code>express-graphql</code>将GraphQL的运行环境放入express容器中（访问的内容是<code>GraphQL的测试环境</code>）。</p><pre class="line-numbers language-javascript"><code class="language-javascript"><span class="token keyword">const</span> express <span class="token operator">=</span> <span class="token function">require</span><span class="token punctuation">(</span><span class="token string">"express"</span><span class="token punctuation">)</span><span class="token punctuation">;</span><span class="token keyword">const</span> <span class="token punctuation">{</span> graphqlHTTP <span class="token punctuation">}</span> <span class="token operator">=</span> <span class="token function">require</span><span class="token punctuation">(</span><span class="token string">"express-graphql"</span><span class="token punctuation">)</span><span class="token punctuation">;</span><span class="token keyword">const</span> app <span class="token operator">=</span> <span class="token function">express</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>app<span class="token punctuation">.</span><span class="token function">use</span><span class="token punctuation">(</span> <span class="token string">"/graphql"</span><span class="token punctuation">,</span> <span class="token function">graphqlHTTP</span><span class="token punctuation">(</span><span class="token punctuation">{</span> <span class="token comment" spellcheck="true">// 交互式地访问GraphQL</span> graphiql<span class="token punctuation">:</span> <span class="token boolean">true</span><span class="token punctuation">,</span> <span class="token punctuation">}</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>app<span class="token punctuation">.</span><span class="token function">listen</span><span class="token punctuation">(</span><span class="token number">4000</span><span class="token punctuation">)</span><span class="token punctuation">;</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><h1 id="了解graphql"><a href="#了解graphql" class="headerlink" title="了解graphql"></a>了解graphql</h1><p><code>graphql</code>的宗旨是需要的数据都要，不需要的数据一点也不要，即它可以查询多个表中的每一项信息。在传统的Rest中，如果我们需要2个表的信息，我们可能需要请求2个Rest API然后自己拼接信息，这会导致浪费大量的网络带宽请求不需要的资源。另一种解决方案是后端增加一个Rest API接口，后端进行数据库的连表查询。</p><p><code>graphql</code>就是为了解决这个痛点而生的，只要是graphql的服务器，前端需要什么数据就拿什么数据。</p><h1 id="定义有什么数据"><a href="#定义有什么数据" class="headerlink" title="定义有什么数据"></a>定义有什么数据</h1><p>和传统数据库类似的，需要有个建表语句。<code>graphql</code>也要定义数据类型。</p><pre class="line-numbers language-javascript"><code class="language-javascript"><span class="token keyword">const</span> <span class="token punctuation">{</span> buildSchema <span class="token punctuation">}</span> <span class="token operator">=</span> <span class="token function">require</span><span class="token punctuation">(</span><span class="token string">"graphql"</span><span class="token punctuation">)</span><span class="token punctuation">;</span><span class="token keyword">const</span> schema <span class="token operator">=</span> <span class="token function">buildSchema</span><span class="token punctuation">(</span><span class="token template-string"><span class="token string">` type Account{ age: Int name: String, todos: [String] } type Query { hello: String account: Account }`</span></span><span class="token punctuation">)</span><span class="token punctuation">;</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>最重要的是第8行的<code>Query</code>，它定义了前端可以执行查询语句。它代表前端查询hello的话会返回一个string，而查询account的话会返回一个Account对象。Account对象有3个字段：年龄(int类型)、名字（string类型）和待做的事（string数组）</p><h1 id="模拟数据库存储的数据"><a href="#模拟数据库存储的数据" class="headerlink" title="模拟数据库存储的数据"></a>模拟数据库存储的数据</h1><p>没有花里胡哨，简单易懂的js。</p><pre class="line-numbers language-javascript"><code class="language-javascript"><span class="token keyword">const</span> root <span class="token operator">=</span> <span class="token punctuation">{</span> hello<span class="token punctuation">:</span> <span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token operator">=</span><span class="token operator">></span> <span class="token punctuation">{</span> <span class="token keyword">return</span> <span class="token string">"hello world"</span><span class="token punctuation">;</span> <span class="token punctuation">}</span><span class="token punctuation">,</span> account<span class="token punctuation">:</span> <span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token operator">=</span><span class="token operator">></span> <span class="token punctuation">{</span> <span class="token keyword">return</span> <span class="token punctuation">{</span> age<span class="token punctuation">:</span> <span class="token number">18</span><span class="token punctuation">,</span> name<span class="token punctuation">:</span> <span class="token string">"jimmy"</span><span class="token punctuation">,</span> todos<span class="token punctuation">:</span> <span class="token punctuation">[</span><span class="token string">"eat"</span><span class="token punctuation">,</span> <span class="token string">"sleep"</span><span class="token punctuation">]</span><span class="token punctuation">,</span> <span class="token punctuation">}</span><span class="token punctuation">;</span> <span class="token punctuation">}</span><span class="token punctuation">,</span><span class="token punctuation">}</span><span class="token punctuation">;</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><h1 id="整合"><a href="#整合" class="headerlink" title="整合"></a>整合</h1><p>将上述的所有代码整合，形成一个完整的<code>hello.js</code>如下：</p><pre class="line-numbers language-javascript"><code class="language-javascript"><span class="token keyword">const</span> <span class="token punctuation">{</span> buildSchema <span class="token punctuation">}</span> <span class="token operator">=</span> <span class="token function">require</span><span class="token punctuation">(</span><span class="token string">"graphql"</span><span class="token punctuation">)</span><span class="token punctuation">;</span><span class="token keyword">const</span> express <span class="token operator">=</span> <span class="token function">require</span><span class="token punctuation">(</span><span class="token string">"express"</span><span class="token punctuation">)</span><span class="token punctuation">;</span><span class="token keyword">const</span> <span class="token punctuation">{</span> graphqlHTTP <span class="token punctuation">}</span> <span class="token operator">=</span> <span class="token function">require</span><span class="token punctuation">(</span><span class="token string">"express-graphql"</span><span class="token punctuation">)</span><span class="token punctuation">;</span><span class="token keyword">const</span> schema <span class="token operator">=</span> <span class="token function">buildSchema</span><span class="token punctuation">(</span><span class="token template-string"><span class="token string">` type Account{ age: Int name: String, todos: [String] } type Query { hello: String account: Account }`</span></span><span class="token punctuation">)</span><span class="token punctuation">;</span><span class="token keyword">const</span> root <span class="token operator">=</span> <span class="token punctuation">{</span> hello<span class="token punctuation">:</span> <span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token operator">=</span><span class="token operator">></span> <span class="token punctuation">{</span> <span class="token keyword">return</span> <span class="token string">"hello world"</span><span class="token punctuation">;</span> <span class="token punctuation">}</span><span class="token punctuation">,</span> account<span class="token punctuation">:</span> <span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token operator">=</span><span class="token operator">></span> <span class="token punctuation">{</span> <span class="token keyword">return</span> <span class="token punctuation">{</span> age<span class="token punctuation">:</span> <span class="token number">18</span><span class="token punctuation">,</span> name<span class="token punctuation">:</span> <span class="token string">"jimmy"</span><span class="token punctuation">,</span> todos<span class="token punctuation">:</span> <span class="token punctuation">[</span><span class="token string">"eat"</span><span class="token punctuation">,</span> <span class="token string">"sleep"</span><span class="token punctuation">]</span><span class="token punctuation">,</span> <span class="token punctuation">}</span><span class="token punctuation">;</span> <span class="token punctuation">}</span><span class="token punctuation">,</span><span class="token punctuation">}</span><span class="token punctuation">;</span><span class="token keyword">const</span> app <span class="token operator">=</span> <span class="token function">express</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>app<span class="token punctuation">.</span><span class="token function">use</span><span class="token punctuation">(</span> <span class="token string">"/graphql"</span><span class="token punctuation">,</span> <span class="token function">graphqlHTTP</span><span class="token punctuation">(</span><span class="token punctuation">{</span> schema<span class="token punctuation">:</span> schema<span class="token punctuation">,</span> graphiql<span class="token punctuation">:</span> <span class="token boolean">true</span><span class="token punctuation">,</span> rootValue<span class="token punctuation">:</span> root<span class="token punctuation">,</span> <span class="token punctuation">}</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>app<span class="token punctuation">.</span><span class="token function">listen</span><span class="token punctuation">(</span><span class="token number">4000</span><span class="token punctuation">)</span><span class="token punctuation">;</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>在<code>hello.js</code>存储的路径下，使用<code>node init -y</code>初始化并使用<code>npm install graphql express express-graphql -S </code>安装依赖。最后，使用 <code>node hello.js</code>运行，访问<code>localhost:4000/graphql</code>即可。</p>]]></content>
<categories>
<category> graphql </category>
</categories>
<tags>
<tag> GraphQL </tag>
<tag> aws </tag>
</tags>
</entry>
<entry>
<title>从0搭建Django项目 - 2. Django逆向工程</title>
<link href="/2023/10/26/python3-django-ni-xiang-gong-cheng/"/>
<url>/2023/10/26/python3-django-ni-xiang-gong-cheng/</url>
<content type="html"><![CDATA[<h1 id="简介"><a href="#简介" class="headerlink" title="简介"></a>简介</h1><p>最近重新研究了Django，发现也没想象中那么简单，也没那么好用。</p><p>我们会编写一个类，然后希望数据库也对应生成这个表。而逆向工程就是自动化这个步骤。</p><p>由于现在用的都是python3，所以接下来的所有命令，可能要将<code>python</code>改为<code>python3</code>.</p><h1 id="Django项目逻辑"><a href="#Django项目逻辑" class="headerlink" title="Django项目逻辑"></a>Django项目逻辑</h1><p>在新建项目后，是没有app的，项目里一开始只有django的管理端。此时我们还不能写任何的业务逻辑。</p><h2 id="目录介绍"><a href="#目录介绍" class="headerlink" title="目录介绍"></a>目录介绍</h2><p>这个管理端的文件夹的名字与你新建Django项目时的一致。比如你使用<code>django-admin startproject mysite</code>新建项目，此时你的项目名称就是mysite。目录如下：</p><pre class="line-numbers language-bash"><code class="language-bash">mysite/ manage.py mysite/ __init__.py settings.py urls.py asgi.py wsgi.py<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>你的文件将存在第一行的<code>mysite</code>目录下，而<code>manage.py</code>就是管理这个项目的入口。项目的具体设置（比如配置文件）就在<code>mysite/mysite</code>下，这个目录就是我们说的管理端。此时可以使用<code>python manage.py runserver</code>来运行Django.</p><h2 id="新建app"><a href="#新建app" class="headerlink" title="新建app"></a>新建app</h2><p>使用<code>python manager.py startapp myappname</code>来新建一个叫<code>myappname</code>的应用。因为Django使用的不是MVC模型，所以一个这样创建的app就是一个Service，这有点类似于微服务。比如用<code>python manager.py startapp account</code>来管理登录，而同时用<code>python manager.py startapp payment</code> 创建一个app来管理支付。</p><h1 id="流程"><a href="#流程" class="headerlink" title="流程"></a>流程</h1><p>终于到逆向工程的步骤了。总体步骤是：</p><ol><li>新建一个app。</li><li>在app的<code>models.py</code>中编写要被逆向的类。</li><li>使用下面的步骤完成逆向工程。</li></ol><h2 id="步骤"><a href="#步骤" class="headerlink" title="步骤"></a>步骤</h2><p>开始前，默认已经完成了上述的流程2：在app的<code>models.py</code>中编写要被逆向的类。</p><ol><li><p>和上面介绍的一样，我在Django中新建一个app叫<code>myappF23</code>。</p></li><li><p>在Django的<code>mysite/settings.py</code>中</p><pre class="line-numbers language-python"><code class="language-python">INSTALLED_APPS <span class="token operator">=</span> <span class="token punctuation">[</span> <span class="token string">'django.contrib.admin'</span><span class="token punctuation">,</span> <span class="token string">'django.contrib.auth'</span><span class="token punctuation">,</span> <span class="token string">'django.contrib.contenttypes'</span><span class="token punctuation">,</span> <span class="token string">'django.contrib.sessions'</span><span class="token punctuation">,</span> <span class="token string">'django.contrib.messages'</span><span class="token punctuation">,</span> <span class="token string">'django.contrib.staticfiles'</span><span class="token punctuation">,</span> <span class="token string">'myappF23.apps.Myappf23Config'</span><span class="token punctuation">,</span><span class="token punctuation">]</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>在第8行将告诉Django：myappF23是一个app项目，而不是一个普通文件夹。</p></li><li><p>运行<code>python manage.py makemigrations myappF23</code>，让逆向工程为<code>settings.py</code>里的<code>myappF23</code>这个app创建一个<code>migrations</code>文件夹。这里的<code>0001_initial.py</code>将是逆向工程会运行的代码。(这个<code>.py</code>文件中存储的显然是python代码。此时，你可以使用<code> python manage.py sqlmigrate myappF23 0001</code>来查看<code>0001_initial.py</code>将会执行什么具体的SQL语句)</p></li><li><p>运行<code>python manage.py migrate 0001 </code>，这步将让Django使用这个0001创建数据库。因此你的目录下会多出<code>db.sqlite3</code>文件。</p></li><li><p>在完成创建数据库后，创建超级管理员，<code>python manage.py createsuperuser</code>。</p></li><li><p>可以使用<code>127.0.0.1:8000/admin</code>，使用你在第四步创建的账号密码登录。登录后，可以在网页中对数据库进行CRUD。</p></li></ol><h2 id="更新步骤"><a href="#更新步骤" class="headerlink" title="更新步骤"></a>更新步骤</h2><p>上述步骤适用于新建，如果更改了<code>models.py</code>，还需要重新执行一遍下述步骤才能更新数据库。</p><ol><li>运行<code>python manage.py makemigrations myappF23</code>，重新生成一个0002为前缀的py文件。如果多次编写，请在文件夹下查看最新的编号。</li><li>使用<code>python manage.py migrate myappF23 0002 </code>使得更改生效。</li></ol><h3 id="更新示例"><a href="#更新示例" class="headerlink" title="更新示例"></a>更新示例</h3><p>我意外删除了一个表Course，现在想重新生成。</p><p>但是如果按照上述步骤更新，会出现报错：无法找到该表。这也是我讨厌Django的地方，非常难用，完全没考虑很多情况。</p><p>解决方法：</p><ol><li><p>先在<code>models.py</code>中注释掉Course类</p></li><li><p>运行<code>python manage.py makemigrations myappF23</code>，此时显示如下：</p><pre class="line-numbers language-shell"><code class="language-shell">Migrations for 'myappF23': myappF23/migrations/0004_delete_course.py - Delete model Course<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span></span></code></pre></li><li><p>按理说，我们应该执行<code>python manage.py migrate myappF23 0004 </code>来运行这个编号为0004的代码从而删除Course表，但是由于我已经手动删了，所以需要虚假执行。使用<code>python manage.py migrate myappF23 0004 --fake </code>.该方法多了最后的参数，代表我们已经手动替Django操作过这个步骤了，只是让Django记录一下。</p><pre class="line-numbers language-shell"><code class="language-shell">Operations to perform: Target specific migration: 0004_delete_course, from myappF23Running migrations: Applying myappF23.0004_delete_course... FAKED<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span></span></code></pre></li><li><p>取消注释Course类</p></li><li><p>重新<code>python manage.py makemigrations myappF23</code>与<code>python manage.py migrate myappF23 0005</code>。成功</p></li></ol><h1 id="类的编写"><a href="#类的编写" class="headerlink" title="类的编写"></a>类的编写</h1><p>在流程中的第二步提到，我们需要编写类，让其能被逆向，并且在Django中使用类似ORM的方式去对其CRUD。</p><p>那么，如何编写类呢？</p><p>首先，所有类必须写在 <code>models.py</code>中，并且继承<code>models.Model</code>这个类。</p><p>因此，<code>models.py</code>的第一句总是<code>from django.db import models</code>.</p><h2 id="简单示例"><a href="#简单示例" class="headerlink" title="简单示例"></a>简单示例</h2><pre class="line-numbers language-python"><code class="language-python"><span class="token comment" spellcheck="true"># CREATE TABLE "myappF23_student" ("id" integer NOT NULL PRIMARY KEY AUTOINCREMENT, "first_name" varchar(100) NOT NULL, "last_name" varchar(100) NOT NULL, "email" varchar(200) NOT NULL UNIQUE, "date_of_birth" date NOT NULL);</span><span class="token keyword">class</span> <span class="token class-name">Student</span><span class="token punctuation">(</span>models<span class="token punctuation">.</span>Model<span class="token punctuation">)</span><span class="token punctuation">:</span> STUDENT_STATUS_CHOICES <span class="token operator">=</span> <span class="token punctuation">[</span> <span class="token punctuation">(</span><span class="token string">'ER'</span><span class="token punctuation">,</span> <span class="token string">'Enrolled'</span><span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token punctuation">(</span><span class="token string">'SP'</span><span class="token punctuation">,</span> <span class="token string">'Suspended'</span><span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token punctuation">(</span><span class="token string">'GD'</span><span class="token punctuation">,</span> <span class="token string">'Graduated'</span><span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token punctuation">]</span> first_name <span class="token operator">=</span> models<span class="token punctuation">.</span>CharField<span class="token punctuation">(</span>max_length<span class="token operator">=</span><span class="token number">100</span><span class="token punctuation">)</span> last_name <span class="token operator">=</span> models<span class="token punctuation">.</span>CharField<span class="token punctuation">(</span>max_length<span class="token operator">=</span><span class="token number">100</span><span class="token punctuation">)</span> email <span class="token operator">=</span> models<span class="token punctuation">.</span>EmailField<span class="token punctuation">(</span>max_length<span class="token operator">=</span><span class="token number">200</span><span class="token punctuation">,</span> unique<span class="token operator">=</span><span class="token boolean">True</span><span class="token punctuation">)</span> date_of_birth <span class="token operator">=</span> models<span class="token punctuation">.</span>DateField<span class="token punctuation">(</span><span class="token punctuation">)</span> status <span class="token operator">=</span> models<span class="token punctuation">.</span>CharField<span class="token punctuation">(</span>max_length<span class="token operator">=</span><span class="token number">10</span><span class="token punctuation">,</span> choices<span class="token operator">=</span>STUDENT_STATUS_CHOICES<span class="token punctuation">,</span> default<span class="token operator">=</span><span class="token string">'ER'</span><span class="token punctuation">)</span> <span class="token keyword">def</span> <span class="token function">__str__</span><span class="token punctuation">(</span>self<span class="token punctuation">)</span><span class="token punctuation">:</span> <span class="token keyword">return</span> self<span class="token punctuation">.</span>first_name<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p><strong>这样创建的类会有一个默认的id作为主键。</strong>也可以使用<code>sid = models.IntegerField(primary_key=True) </code>或者<code>sid = models.AutoField(primary_key=True)</code>来给student类一个id。</p><h2 id="类与类的关系"><a href="#类与类的关系" class="headerlink" title="类与类的关系"></a>类与类的关系</h2><p>类与类之间有2中关系：<strong>多对一</strong>和<strong>多对多</strong>。注意，没有 <strong>一对多或者一对一</strong>，永远只有 **’多对’**开头的关系。</p><p> 额外创建一个类：教师类</p><pre class="line-numbers language-python"><code class="language-python"><span class="token keyword">class</span> <span class="token class-name">Instructor</span><span class="token punctuation">(</span>models<span class="token punctuation">.</span>Model<span class="token punctuation">)</span><span class="token punctuation">:</span> first_name <span class="token operator">=</span> models<span class="token punctuation">.</span>CharField<span class="token punctuation">(</span>max_length<span class="token operator">=</span><span class="token number">128</span><span class="token punctuation">)</span> last_name <span class="token operator">=</span> models<span class="token punctuation">.</span>CharField<span class="token punctuation">(</span>max_length<span class="token operator">=</span><span class="token number">128</span><span class="token punctuation">)</span> bio <span class="token operator">=</span> models<span class="token punctuation">.</span>TextField<span class="token punctuation">(</span>null<span class="token operator">=</span><span class="token boolean">True</span><span class="token punctuation">,</span> blank<span class="token operator">=</span><span class="token boolean">True</span><span class="token punctuation">)</span> <span class="token keyword">def</span> <span class="token function">__str__</span><span class="token punctuation">(</span>self<span class="token punctuation">)</span><span class="token punctuation">:</span> <span class="token keyword">return</span> self<span class="token punctuation">.</span>first_name<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>其中bio字段是老师的简介：</p><ul><li><code>blank=True</code>: 表示在表单验证时，该字段可以为空。这影响到表单的验证行为，允许用户在表单中不填写这个字段。</li><li><code>null=True</code>: 表示在数据库中，该字段可以存储为 NULL。如果这个字段不设置为可空 (<code>null=False</code>)，那么在数据库中该字段将不允许存储为 NULL 值。</li></ul><p> 再额外创建一个类：课程类</p><p>该课程有多对一（1个课程只有1个老师）和多对多（1个课程可以有多个学生上，1个学生也可以选多个课程）关系。</p><pre class="line-numbers language-python"><code class="language-python"><span class="token keyword">class</span> <span class="token class-name">Course</span><span class="token punctuation">(</span>models<span class="token punctuation">.</span>Model<span class="token punctuation">)</span><span class="token punctuation">:</span> COURSE_LEVEL_CHOICES <span class="token operator">=</span> <span class="token punctuation">[</span> <span class="token punctuation">(</span><span class="token string">'BE'</span><span class="token punctuation">,</span> <span class="token string">'Beginner'</span><span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token punctuation">(</span><span class="token string">'IN'</span><span class="token punctuation">,</span> <span class="token string">'Intermediate'</span><span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token punctuation">(</span><span class="token string">'AD'</span><span class="token punctuation">,</span> <span class="token string">'Advanced'</span><span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token punctuation">]</span> title <span class="token operator">=</span> models<span class="token punctuation">.</span>CharField<span class="token punctuation">(</span>max_length<span class="token operator">=</span><span class="token number">200</span><span class="token punctuation">)</span> description <span class="token operator">=</span> models<span class="token punctuation">.</span>TextField<span class="token punctuation">(</span><span class="token punctuation">)</span> Instructor <span class="token operator">=</span> models<span class="token punctuation">.</span>ForeignKey<span class="token punctuation">(</span>Instructor<span class="token punctuation">,</span> on_delete<span class="token operator">=</span>models<span class="token punctuation">.</span>CASCADE<span class="token punctuation">)</span> students <span class="token operator">=</span> models<span class="token punctuation">.</span>ManyToManyField<span class="token punctuation">(</span>Student<span class="token punctuation">,</span> blank<span class="token operator">=</span><span class="token boolean">True</span><span class="token punctuation">)</span> start_date <span class="token operator">=</span> models<span class="token punctuation">.</span>DateField<span class="token punctuation">(</span><span class="token punctuation">)</span> end_date <span class="token operator">=</span> models<span class="token punctuation">.</span>DateField<span class="token punctuation">(</span><span class="token punctuation">)</span> price <span class="token operator">=</span> models<span class="token punctuation">.</span>DecimalField<span class="token punctuation">(</span>max_digits<span class="token operator">=</span><span class="token number">10</span><span class="token punctuation">,</span> decimal_places<span class="token operator">=</span><span class="token number">2</span><span class="token punctuation">)</span> level <span class="token operator">=</span> models<span class="token punctuation">.</span>CharField<span class="token punctuation">(</span>max_length<span class="token operator">=</span><span class="token number">100</span><span class="token punctuation">,</span> choices<span class="token operator">=</span>COURSE_LEVEL_CHOICES<span class="token punctuation">,</span> default<span class="token operator">=</span><span class="token string">'BE'</span><span class="token punctuation">)</span> <span class="token keyword">def</span> <span class="token function">__str__</span><span class="token punctuation">(</span>self<span class="token punctuation">)</span><span class="token punctuation">:</span> <span class="token keyword">return</span> self<span class="token punctuation">.</span>title<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>肉眼可见地，多对一关系为一个普通的外键，其中第9行里的<code>on_delete=models.CASCADE</code>代表级联删除，表示如果删除了这个教授，那么对应的这个课程也会被删除。<strong>记住，因为是多对一，所以这个关系会写在“多”的类里，那个“一”应该写在前面</strong>。在本案例中，教师类写在课程类的前面，并且外键写在课程类中。</p><p>而多对多关系就无所谓定义在哪了。本案例中，因为我是先写的学生类，再写的课程类，所以我将多对多关系写在课程类中。这个关系的定义在第10行。遇到这种情况时，Django其实会额外创建一个表<code>course_student</code>来表示多对多关系。<code>blank=True</code>代表这个关联表是空也无所谓。</p><p>至此，我有了4个表：<code>course, course_student, student, instructor</code>.</p><h2 id="其他"><a href="#其他" class="headerlink" title="其他"></a>其他</h2><p>至于如何编写自增主键啥的，或者想了解更多信息的，请看文档：<a href="https://docs.djangoproject.com/en/4.2/topics/db/models/">https://docs.djangoproject.com/en/4.2/topics/db/models/</a></p><h1 id="References"><a href="#References" class="headerlink" title="References"></a>References</h1><ol><li>官方文档：<a href="https://docs.djangoproject.com/en/4.2/intro/tutorial02/">https://docs.djangoproject.com/en/4.2/intro/tutorial02/</a></li></ol>]]></content>
<categories>
<category> python </category>
</categories>
<tags>
<tag> python </tag>
<tag> Django </tag>
<tag> 逆向工程 </tag>
</tags>
</entry>
<entry>
<title>Cpp 数组与vector操作技巧</title>
<link href="/2023/10/15/cpp-shu-zu-yu-vector-cao-zuo-ji-qiao/"/>
<url>/2023/10/15/cpp-shu-zu-yu-vector-cao-zuo-ji-qiao/</url>
<content type="html"><![CDATA[<h1 id="memset填充问题"><a href="#memset填充问题" class="headerlink" title="memset填充问题"></a>memset填充问题</h1><p>我们知道，使用 <code>memset()</code>只能将整数数组填充0和-1，为了将其填充为我们想要的值，可以使用<code>fill</code>初始化而非 <code>memset()</code>。</p><pre class="line-numbers language-c++"><code class="language-c++">int ary[10];memset(ary,-2,sizeof ary); // failfill(ary, ary + 10, -2); // ok<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span></span></code></pre><p>这样，即使要填充我们想要的值是自定义类也无所谓。</p><pre class="line-numbers language-c++"><code class="language-c++">class T{ public: int a; int b; int c; T(){}; T(int a, int b) : a(a), b(b) { c = a + b; };};T ts[3];fill(ts, ts + 3, T(1, 3)); // it worksvector<T> vt(3, T(1, 2)); // ok<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>而使用<code>vector</code>则更为方便，直接在构造函数中填充3个T对象。</p><h1 id="非容器对象使用-max-element"><a href="#非容器对象使用-max-element" class="headerlink" title="非容器对象使用 max_element"></a>非容器对象使用 max_element</h1><p>容器类对象可以使用 <code>max_element</code>方法找到容器中的最大值，如：</p><pre class="line-numbers language-c++"><code class="language-c++">vector<int> v{1, 9, 5, 4};auto iter = max_element(v.begin(), v.end()); // iterator<vector<int>>cout << *iter << endl; // value of the max elementcout<< iter - v.begin()<<endl;// index of the max element<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span></span></code></pre><p>而非容器对象没有迭代器，所以会返回地址。这里上下两块的代码运行结果完全一致。</p><pre class="line-numbers language-c++"><code class="language-c++">int v[] = {1, 9, 5, 4};auto iter = max_element(v, v + 4); // address of the max elementcout << *iter << endl; // value of the max elementcout << iter - v[0] << endl; // index of the max element<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span></span></code></pre><h1 id="获得数组长度"><a href="#获得数组长度" class="headerlink" title="获得数组长度"></a>获得数组长度</h1><p>容器类对象提供 <code>size()和length()</code>函数都表示存储了几个对象，而普通数组没有。此时可使用</p><pre class="line-numbers language-c++"><code class="language-c++">#define arySize(arr) sizeof(arr) / sizeof(arr[0])int v[] = {1, 9, 5, 4};cout<< arySize(v) << endl;<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span></span></code></pre><p>第一行的宏定义来获取数组长度，类似于 python 的 <code>len()</code>函数。</p>]]></content>
<categories>
<category> C/C++ </category>
</categories>
<tags>
<tag> C/C++ </tag>
<tag> vector </tag>
</tags>
</entry>
<entry>
<title>Cpp使用pair或tuple返回多个值</title>
<link href="/2023/10/15/cpp-shi-yong-pair-huo-tuple-fan-hui-duo-ge-zhi/"/>
<url>/2023/10/15/cpp-shi-yong-pair-huo-tuple-fan-hui-duo-ge-zhi/</url>
<content type="html"><![CDATA[<h1 id="解决的问题"><a href="#解决的问题" class="headerlink" title="解决的问题"></a>解决的问题</h1><p>函数接受3个参数，并将它们由大到小排序。</p><pre class="line-numbers language-c++"><code class="language-c++">tuple<int, int, int> func(int a, int b, int c){ vector<int> ary{a, b, c};#define rall(v) v.rbegin(), v.rend() sort(rall(ary)); return make_tuple(ary[0], ary[1], ary[2]);}int main(int argc, char *argv[]){ int a, b, c; auto res1 = func(1, 2, 3); tie(a, b, c) = res1; cout << a << b << c << endl; return 0;}<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>结果输出321.</p><h1 id="详解"><a href="#详解" class="headerlink" title="详解"></a>详解</h1><p><code>tuple<></code>可以理解为一个包，可以对多个值进行打包。而这个“包”本身只是一个变量，这样就能达成“C++函数只能返回一个变量”的条件，同时满足“返回了多个值”。</p><p>上述例子中，函数<code>func()</code>返回了一个tuple变量（通过使用<code>make_tuple()</code>函数生成的）。这样调用方就能接收一个变量。</p><p>但是这个变量不能直接使用，需要使用<code>std::tie()</code>函数来解包才能使用。</p><p>上述13与14行可以改为</p><pre class="line-numbers language-c++"><code class="language-c++">tie(std::ignore, std::ignore, c) = res1;cout << a << endl;<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span></span></code></pre><p>从而只取最小值</p><h1 id="其他听闻"><a href="#其他听闻" class="headerlink" title="其他听闻"></a>其他听闻</h1><p><code>tuple</code> 即元组，可以理解为pair的扩展，可以用来将不同类型的元素存放在一起，常用于函数的多返回值。在c++ 11标准库中，加入了std::tie，在c++ 14中改进，方便使用。[1]</p><p>pair只能把2个数据打包，而tuple可以打包更多的数据，虽然超过了9个时，其方式就比较搞笑了。[2]</p><h1 id="References"><a href="#References" class="headerlink" title="References"></a>References</h1><ol><li><a href="https://www.cnblogs.com/RioTian/p/14076214.html">https://www.cnblogs.com/RioTian/p/14076214.html</a></li><li><a href="https://blog.csdn.net/whereismatrix/article/details/125071222">https://blog.csdn.net/whereismatrix/article/details/125071222</a></li></ol>]]></content>
<categories>
<category> C/C++ </category>
</categories>
<tags>
<tag> C/C++ </tag>
<tag> pair </tag>
<tag> tuple </tag>
</tags>
</entry>
<entry>
<title>创建mysql账户并在vscode中使用</title>
<link href="/2022/07/04/chuang-jian-mysql-zhang-hu-bing-zai-vscode-zhong-shi-yong/"/>
<url>/2022/07/04/chuang-jian-mysql-zhang-hu-bing-zai-vscode-zhong-shi-yong/</url>
<content type="html"><![CDATA[<h1 id="好处"><a href="#好处" class="headerlink" title="好处"></a>好处</h1><p>不使用root用户很关键。</p><h1 id="命令"><a href="#命令" class="headerlink" title="命令"></a>命令</h1><pre class="line-numbers language-sql"><code class="language-sql"><span class="token keyword">CREATE</span> <span class="token keyword">USER</span> <span class="token string">'username'</span>@'LOCALHOST<span class="token string">' IDENTIFIED BY '</span>password<span class="token string">';GRANT ALL PRIVILEGES ON databaseName.* TO username@localhost ;ALTER USER '</span>username<span class="token string">'@'</span>localhost<span class="token string">' IDENTIFIED WITH mysql_native_password BY '</span>password'<span class="token punctuation">;</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span></span></code></pre><p>将其中的username、password和databaseName变成你需要的值。</p><h1 id="vscode中"><a href="#vscode中" class="headerlink" title="vscode中"></a>vscode中</h1><ol><li>安装2个扩展：<ol><li>MySQL - 作者是 Jun Han</li><li>MySQL Syntax - 作者是Jake Bathman</li></ol></li><li>打开资源管理器，在最下面找到mysql，点击加号</li><li>输入localhost、用户名、密码和端口号，ssl证书可以直接回车不输入</li></ol>]]></content>
<categories>
<category> 运维 </category>
</categories>
<tags>
<tag> 数据库 </tag>
<tag> sql </tag>
<tag> vscode </tag>
</tags>
</entry>
<entry>
<title>从0搭建Django项目 - 1. 初始化项目</title>
<link href="/2022/03/24/xue-xi-da-jian-django-xiang-mu-1/"/>
<url>/2022/03/24/xue-xi-da-jian-django-xiang-mu-1/</url>
<content type="html"><![CDATA[<h1 id="从0搭建Django项目-1"><a href="#从0搭建Django项目-1" class="headerlink" title="从0搭建Django项目 - 1"></a>从0搭建Django项目 - 1</h1><p>项目采用python3.9+Django 4.0.3，项目github：<a href="https://github.com/VsKendo/django_demo%E3%80%82">https://github.com/VsKendo/django_demo。</a></p><p>本教程将指引你阅读官方文档，推荐在阅读官方文档的时候同步查看本教程。</p><p>更新时间：2022年3月25日</p><p>官方文档信息：</p><ul><li><p> <a href="https://docs.djangoproject.com/zh-hans/4.0/faq/help/"> Getting Help </a> </p></li><li><p> 语言： <strong>zh-hans</strong> </p></li><li><p> 文档版本： <strong>4.0</strong></p></li></ul><h2 id="安装Python和Django"><a href="#安装Python和Django" class="headerlink" title="安装Python和Django"></a>安装Python和Django</h2><p>若你还未安装Python或Django，请看官方文档【中文】：</p><p>快速下载和安装指南： <a href="https://docs.djangoproject.com/zh-hans/4.0/intro/install/">https://docs.djangoproject.com/zh-hans/4.0/intro/install/</a></p><p>这里不再赘述。</p><hr><h1 id="开始"><a href="#开始" class="headerlink" title="开始"></a>开始</h1><p>本教程需配合官方文档【中文】：<a href="https://docs.djangoproject.com/zh-hans/4.0/intro/tutorial01/">https://docs.djangoproject.com/zh-hans/4.0/intro/tutorial01/</a> 使用，因为有些官方文档已经说得很详细了，这里不再赘述。</p><p><strong>查看官方文档过程中请配合本教程使用</strong>。</p><p>当您<strong>看完</strong>官方文档“编写你的第一个 Django 应用，第 1 部分”后，建议按照本教程对项目进行修改。</p><h2 id="文件说明（tree）"><a href="#文件说明（tree）" class="headerlink" title="文件说明（tree）"></a>文件说明（tree）</h2><p>在你新建了Django项目后，你会得到以下文件。</p><pre class="line-numbers language-html"><code class="language-html">. //根目录只是你项目的容器， 名称对 Django 没有影响，可以将它重命名为任何你喜欢的名称。├── manage.py //一个让你用各种方式管理 Django 项目的命令行工具。├── ossbe //包名（项目名），引用它内部任何东西时需要用到。│ ├── __init__.py //一个空文件，告诉 Python 这个目录应该被认为是一个 Python 包。│ ├── asgi.py //运行在 ASGI 兼容的 Web 服务器上的入口。│ ├── settings.py //Django 项目的配置文件。│ ├── urls.py //Django 项目的 URL 声明，就像你网站的“目录”。│ └── wsgi.py //运行在 WSGI 兼容的Web服务器上的入口。└── templates<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><hr><h1 id="注册app"><a href="#注册app" class="headerlink" title="注册app"></a>注册app</h1><p>请修改<code>settings.py</code>中的 <code>INSTALLED_APPS</code>，加上你的网站中的Config类。</p><h3 id="注意"><a href="#注意" class="headerlink" title="注意"></a>注意</h3><p>在教程中，会让你使用 <code>python manage.py startapp websitename</code>命令创建一个<strong>网站</strong>（我更愿意称之为<strong>拦截器</strong>），这个命令可以运行多次，即一个项目中可以用这个命令创建多个网站（拦截器）。后面的 websitename 为你给网站（拦截器）的名字。每次运行这个命令，都要在 <code>INSTALLED_APPS</code>中加上一行 <code>'websitename.apps.websitenameConfig'</code>。</p><pre class="line-numbers language-python"><code class="language-python">INSTALLED_APPS <span class="token operator">=</span> <span class="token punctuation">[</span> <span class="token string">'django.contrib.admin'</span><span class="token punctuation">,</span> <span class="token string">'django.contrib.auth'</span><span class="token punctuation">,</span> <span class="token string">'django.contrib.contenttypes'</span><span class="token punctuation">,</span> <span class="token string">'django.contrib.sessions'</span><span class="token punctuation">,</span> <span class="token string">'django.contrib.messages'</span><span class="token punctuation">,</span> <span class="token string">'django.contrib.staticfiles'</span><span class="token punctuation">,</span> <span class="token string">'manager.apps.ManagerConfig'</span><span class="token punctuation">,</span><span class="token punctuation">]</span> <span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>最后一行便是我添加的，我的项目名为 ossback ，网站（拦截器）文件夹名为 manager。因此只增加一行： <code>'manager.apps.ManagerConfig'</code> 。</p><p>在往后所有的教程中，使用 <code>python manage.py startapp websitename</code>命令创建的文件夹，我都会叫它“<strong>拦截器</strong>”而非“<strong>网站</strong>”（为了避免混淆）。</p><h1 id="创建templates文件夹"><a href="#创建templates文件夹" class="headerlink" title="创建templates文件夹"></a>创建templates文件夹</h1><p>你要创建templates文件夹，用于存储html文件。这时候就要说到项目规范问题了。</p><ol><li>显然，我们目前开发的Django是<strong>前后端不分离</strong>的</li><li>每个网站都有其各自使用的 <code>html 和静态（js、css、img）文件</code>，以及可能会有公用的 <code>html 和静态（js、css、img）文件</code></li></ol><p>终上所述，后端文件和前端文件应该单独存放，我个人推荐使用如下目录结构。</p><h2 id="目录结构"><a href="#目录结构" class="headerlink" title="目录结构"></a>目录结构</h2><ol><li>每个网站都有自己的 static 文件夹，但都<strong>没有</strong> templates 文件夹。所以，在<strong>每个网站文件夹中</strong>创建static文件夹，static文件夹下再创建css、js和img文件夹，用于存储静态文件。</li><li>只有一个 templates 文件夹，其和 manage.py 同级</li><li>在 templates 文件夹中，只能出现 html 文件。</li><li>在 templates 文件夹中，子文件夹命名为 websitename1、websitename2…以及shared。用于存放网站1、网站2…和共享的 html 文件。</li><li>在 templates 文件夹的同级创建一个 common_static 文件夹，用于存放共用的css、js和img文件。</li></ol><p>目录结构大概如下：</p><pre class="line-numbers language-html"><code class="language-html">. （省略不重要的文件和文件夹）├── website1 （网站1文件夹）│ ├── __init__.py│ ├── admin.py│ ├── apps.py│ ├── models.py│ ├── static （网站1私有的静态文件的文件夹）│ │ ├── css│ │ ├── img│ │ └── js│ ├── tests.py│ ├── urls.py│ └── views.py├── website2 （网站2文件夹）│ ├── __init__.py│ ├── admin.py│ ├── apps.py│ ├── models.py│ ├── static （网站2私有的静态文件的文件夹）│ │ ├── css│ │ ├── img│ │ └── js│ ├── tests.py│ └── views.py├── collect_static (在部署到Nginx时，项目中所有静态文件会被统一放在这里)├── common_static （在开发时需要，用于存放共用的静态文件）│ ├── css│ ├── img│ └── js├── manage.py└── templates （所有前端文件位置） ├── website1 （网站1私有的 html 文件） │ └── test1.html └── website2 （网站2私有的 html 文件） └── test2.html └── shared （所有网站共用的 html 文件，如 footer.html 等） └── shared.html<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><h2 id="修改-settings-py"><a href="#修改-settings-py" class="headerlink" title="修改 settings.py"></a>修改 settings.py</h2><p>只需要修改这个文件中的一些配置，便可以正常使用了。</p><ol><li><p>在开头增加了 <code>import os</code></p></li><li><p>修改了 TEMPLATES 中的 DIRS（确保值为<code>[BASE_DIR / './templates'] </code> ） 和 context_processors （增加了 <code>'django.template.context_processors.static',</code>）</p><pre class="line-numbers language-python"><code class="language-python">TEMPLATES <span class="token operator">=</span> <span class="token punctuation">[</span> <span class="token punctuation">{</span> <span class="token string">'BACKEND'</span><span class="token punctuation">:</span> <span class="token string">'django.template.backends.django.DjangoTemplates'</span><span class="token punctuation">,</span> <span class="token string">'DIRS'</span><span class="token punctuation">:</span> <span class="token punctuation">[</span>BASE_DIR <span class="token operator">/</span> <span class="token string">'./templates'</span><span class="token punctuation">]</span> <span class="token punctuation">,</span> <span class="token string">'APP_DIRS'</span><span class="token punctuation">:</span> <span class="token boolean">True</span><span class="token punctuation">,</span> <span class="token string">'OPTIONS'</span><span class="token punctuation">:</span> <span class="token punctuation">{</span> <span class="token string">'context_processors'</span><span class="token punctuation">:</span> <span class="token punctuation">[</span> <span class="token string">'django.template.context_processors.debug'</span><span class="token punctuation">,</span> <span class="token string">'django.template.context_processors.request'</span><span class="token punctuation">,</span> <span class="token string">'django.template.context_processors.static'</span><span class="token punctuation">,</span> <span class="token string">'django.contrib.auth.context_processors.auth'</span><span class="token punctuation">,</span> <span class="token string">'django.contrib.messages.context_processors.messages'</span><span class="token punctuation">,</span> <span class="token punctuation">]</span><span class="token punctuation">,</span> <span class="token punctuation">}</span><span class="token punctuation">,</span> <span class="token punctuation">}</span><span class="token punctuation">,</span><span class="token punctuation">]</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre></li><li><p>修改了语言、时区</p><pre class="line-numbers language-python"><code class="language-python">LANGUAGE_CODE <span class="token operator">=</span> <span class="token string">'zh-hans'</span>TIME_ZONE <span class="token operator">=</span> <span class="token string">'Asia/Shanghai'</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span></span></code></pre></li><li><p>修改 <code>template_processors</code>配置，原本只有 <code>STATIC_URL</code> ，现在变为：</p><pre class="line-numbers language-python"><code class="language-python"><span class="token comment" spellcheck="true"># STATIC SETTINGS</span>STATIC_URL <span class="token operator">=</span> <span class="token string">'/static/'</span><span class="token comment" spellcheck="true"># BASE_DIR 是项目的绝对地址</span>STATIC_ROOT <span class="token operator">=</span> os<span class="token punctuation">.</span>path<span class="token punctuation">.</span>join<span class="token punctuation">(</span>BASE_DIR<span class="token punctuation">,</span> <span class="token string">'collect_static'</span><span class="token punctuation">)</span><span class="token comment" spellcheck="true"># 以下不是必须的 各个app共用的文件可以放在这</span>STATICFILES_DIRS <span class="token operator">=</span> <span class="token punctuation">(</span> os<span class="token punctuation">.</span>path<span class="token punctuation">.</span>join<span class="token punctuation">(</span>BASE_DIR<span class="token punctuation">,</span> <span class="token string">'common_static'</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token punctuation">)</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre></li></ol><p>现在，关于 Django 显示页面的基本配置已经完成，接下来就是写 html 文件了。</p><h1 id="在views中返回html文件"><a href="#在views中返回html文件" class="headerlink" title="在views中返回html文件"></a>在views中返回html文件</h1><p>根据官方文档，我们知道，以下<code>views.py</code>中的代码将返回一串文字</p><pre class="line-numbers language-python"><code class="language-python"><span class="token keyword">def</span> <span class="token function">index</span><span class="token punctuation">(</span>request<span class="token punctuation">)</span><span class="token punctuation">:</span> <span class="token keyword">return</span> HttpResponse<span class="token punctuation">(</span><span class="token string">"Hello, world. You're at the index."</span><span class="token punctuation">)</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span></span></code></pre><p>为了返回html页面，我们可以在它下面新增函数，如：</p><pre class="line-numbers language-python"><code class="language-python"><span class="token keyword">def</span> <span class="token function">test</span><span class="token punctuation">(</span>request<span class="token punctuation">)</span><span class="token punctuation">:</span> <span class="token keyword">return</span> render<span class="token punctuation">(</span>request<span class="token punctuation">,</span> <span class="token string">"test.html"</span><span class="token punctuation">)</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span></span></code></pre><p>其中的html文件在template文件夹下，内容为：</p><pre class="line-numbers language-html"><code class="language-html">{% load static %}<span class="token doctype"><!DOCTYPE html></span><span class="token tag"><span class="token tag"><span class="token punctuation"><</span>html</span> <span class="token attr-name">lang</span><span class="token attr-value"><span class="token punctuation">=</span><span class="token punctuation">"</span>en<span class="token punctuation">"</span></span><span class="token punctuation">></span></span><span class="token tag"><span class="token tag"><span class="token punctuation"><</span>head</span><span class="token punctuation">></span></span> <span class="token tag"><span class="token tag"><span class="token punctuation"><</span>meta</span> <span class="token attr-name">charset</span><span class="token attr-value"><span class="token punctuation">=</span><span class="token punctuation">"</span>UTF-8<span class="token punctuation">"</span></span><span class="token punctuation">></span></span> <span class="token tag"><span class="token tag"><span class="token punctuation"><</span>title</span><span class="token punctuation">></span></span>欢迎来到测试文件页面<span class="token tag"><span class="token tag"><span class="token punctuation"></</span>title</span><span class="token punctuation">></span></span><span class="token tag"><span class="token tag"><span class="token punctuation"></</span>head</span><span class="token punctuation">></span></span><span class="token tag"><span class="token tag"><span class="token punctuation"><</span>body</span><span class="token punctuation">></span></span><span class="token tag"><span class="token tag"><span class="token punctuation"><</span>h1</span><span class="token punctuation">></span></span>测试html页面能否被正确引用<span class="token tag"><span class="token tag"><span class="token punctuation"></</span>h1</span><span class="token punctuation">></span></span><span class="token tag"><span class="token tag"><span class="token punctuation"><</span>img</span> <span class="token attr-name">src</span><span class="token attr-value"><span class="token punctuation">=</span><span class="token punctuation">"</span>{% static <span class="token punctuation">'</span>img/avatar.png<span class="token punctuation">'</span> %}<span class="token punctuation">"</span></span> <span class="token attr-name">alt</span><span class="token attr-value"><span class="token punctuation">=</span><span class="token punctuation">"</span>无<span class="token punctuation">"</span></span><span class="token punctuation">></span></span><span class="token tag"><span class="token tag"><span class="token punctuation"><</span>img</span> <span class="token attr-name">src</span><span class="token attr-value"><span class="token punctuation">=</span><span class="token punctuation">"</span>{{ STATIC_URL }}img/avatar.png<span class="token punctuation">"</span></span> <span class="token attr-name">alt</span><span class="token attr-value"><span class="token punctuation">=</span><span class="token punctuation">"</span>无<span class="token punctuation">"</span></span><span class="token punctuation">></span></span><span class="token tag"><span class="token tag"><span class="token punctuation"></</span>body</span><span class="token punctuation">></span></span><span class="token tag"><span class="token tag"><span class="token punctuation"></</span>html</span><span class="token punctuation">></span></span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>最后，修改<code>urls.py</code>：</p><pre class="line-numbers language-python"><code class="language-python">urlpatterns <span class="token operator">=</span> <span class="token punctuation">[</span> path<span class="token punctuation">(</span><span class="token string">'index/'</span><span class="token punctuation">,</span> views<span class="token punctuation">.</span>index<span class="token punctuation">,</span> name<span class="token operator">=</span><span class="token string">'index'</span><span class="token punctuation">)</span><span class="token punctuation">,</span> path<span class="token punctuation">(</span><span class="token string">''</span><span class="token punctuation">,</span> views<span class="token punctuation">.</span>index<span class="token punctuation">,</span> name<span class="token operator">=</span><span class="token string">'index'</span><span class="token punctuation">)</span><span class="token punctuation">,</span> path<span class="token punctuation">(</span><span class="token string">'test/'</span><span class="token punctuation">,</span> views<span class="token punctuation">.</span>test<span class="token punctuation">,</span> name<span class="token operator">=</span><span class="token string">'test'</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token punctuation">]</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span></span></code></pre><h2 id="html文件引用静态文件"><a href="#html文件引用静态文件" class="headerlink" title="html文件引用静态文件"></a>html文件引用静态文件</h2><p>在 html 文件头添加 <code>{% load static %}</code>，在需要引用的位置使用 <code>{% static '路径' %}</code></p><p>如，引用 static 文件夹下的 img 文件夹中的 img1.png：</p><pre class="line-numbers language-html"><code class="language-html"><span class="token tag"><span class="token tag"><span class="token punctuation"><</span>img</span> <span class="token attr-name">src</span><span class="token attr-value"><span class="token punctuation">=</span><span class="token punctuation">"</span>{% static <span class="token punctuation">'</span>img/avatar.png<span class="token punctuation">'</span> %}<span class="token punctuation">"</span></span> <span class="token attr-name">alt</span><span class="token attr-value"><span class="token punctuation">=</span><span class="token punctuation">"</span>无<span class="token punctuation">"</span></span><span class="token punctuation">></span></span><span class="token tag"><span class="token tag"><span class="token punctuation"><</span>img</span> <span class="token attr-name">src</span><span class="token attr-value"><span class="token punctuation">=</span><span class="token punctuation">"</span>{{ STATIC_URL }}img/avatar.png<span class="token punctuation">"</span></span> <span class="token attr-name">alt</span><span class="token attr-value"><span class="token punctuation">=</span><span class="token punctuation">"</span>无<span class="token punctuation">"</span></span><span class="token punctuation">></span></span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span></span></code></pre><blockquote><p>其实，这种方法之所以能找到static文件夹，是因为 settings.py 中 STATIC_URL 的值为 ‘/static/‘</p></blockquote><p>以上两种方式都可以使用。</p><h2 id="访问我们刚创建的页面"><a href="#访问我们刚创建的页面" class="headerlink" title="访问我们刚创建的页面"></a>访问我们刚创建的页面</h2><p>url：<code>http://localhost:8000/websitename/test</code></p><p>其中 websitename 是你自己创建的拦截器的名字。</p><h1 id="创建一个新的网站（拦截器）"><a href="#创建一个新的网站（拦截器）" class="headerlink" title="创建一个新的网站（拦截器）"></a>创建一个新的网站（拦截器）</h1><p>根据单一职责原则，我们可能要使用指令 <code>python manage.py startapp websitename</code> 创建多个拦截器从而响应用户不同的请求。每次创建一个新的拦截器，你都应该至少进行以下步骤：</p><ol><li>使用指令 <code>python manage.py startapp websitename</code> </li><li>给 websitename 文件夹创建 static 文件夹。</li><li>新建 urls.py，并修改其中的内容</li><li>在项目的 urls.py 里引用你刚新建的 urls.py</li><li>在 templates 下新建 websitename 文件夹</li><li>修改 settings.py 中的 <code>INSTALLED_APPS</code>，注册新的拦截器</li></ol><hr><h1 id="References"><a href="#References" class="headerlink" title="References"></a>References</h1><ol><li>【官方中文文档】编写你的第一个 Django 应用：<a href="https://docs.djangoproject.com/zh-hans/4.0/intro/tutorial01/">https://docs.djangoproject.com/zh-hans/4.0/intro/tutorial01/</a></li><li>【该文章有一处错误】Django STATIC_URL 的理解：<a href="https://blog.csdn.net/qq_24551305/article/details/84865025">https://blog.csdn.net/qq_24551305/article/details/84865025</a></li><li>django中如何使用template_processors避免频繁的函数传递给html，使用template上下文的方法传递方法：<a href="https://blog.csdn.net/qq_37463791/article/details/103607884">https://blog.csdn.net/qq_37463791/article/details/103607884</a></li></ol>]]></content>
<categories>
<category> python </category>
</categories>
<tags>
<tag> python </tag>
<tag> Django </tag>
</tags>
</entry>
<entry>
<title>CentOS升级到CentOS Stream</title>
<link href="/2022/03/19/centos8-zhuan-yi-dao-centos-stream-shi-cuo-wu/"/>
<url>/2022/03/19/centos8-zhuan-yi-dao-centos-stream-shi-cuo-wu/</url>
<content type="html"><![CDATA[<h1 id="步骤"><a href="#步骤" class="headerlink" title="步骤"></a>步骤</h1><p>升级过程中，通常是先查看仓库是否有centos-release-stream仓库</p><pre class="line-numbers language-shell"><code class="language-shell">dnf search centos-release-stream<span aria-hidden="true" class="line-numbers-rows"><span></span></span></code></pre><p>再试图安装centos-release-stream仓库</p><pre class="line-numbers language-shell"><code class="language-shell">dnf install -y centos-release-stream<span aria-hidden="true" class="line-numbers-rows"><span></span></span></code></pre><p>这是通常会出现ERROR，导致无法升级成CentOS Stream。错误信息大概如下：</p><pre class="line-numbers language-shell"><code class="language-shell">conflicts with centos-repos(8) provided by centos-stream-repos-8-2.el8.noarch<span aria-hidden="true" class="line-numbers-rows"><span></span></span></code></pre><h1 id="解决错误"><a href="#解决错误" class="headerlink" title="解决错误"></a>解决错误</h1><p>如果你出现了这个错误，此时你使用 <code>yum update</code>应该也会出现这个错误。这是因为CentOS和CentOS Stream<strong>仓库冲突</strong>了。</p><p>所以<strong>将仓库切换为CentOS Stream的仓库</strong>即可。</p><pre class="line-numbers language-shell"><code class="language-shell">dnf swap centos-linux-repos centos-stream-repos<span aria-hidden="true" class="line-numbers-rows"><span></span></span></code></pre><p>再安装</p><pre class="line-numbers language-shell"><code class="language-shell">dnf install centos-release-stream<span aria-hidden="true" class="line-numbers-rows"><span></span></span></code></pre><p>检查是否成功</p><pre class="line-numbers language-shell"><code class="language-shell">cat /etc/centos-release<span aria-hidden="true" class="line-numbers-rows"><span></span></span></code></pre><h1 id="后话"><a href="#后话" class="headerlink" title="后话"></a>后话</h1><p>这个好像是官方故意引发的冲突，是为了防止运维使用了不同的仓库中下载的包，然后出现各种奇奇怪怪的问题。更新后记得 <code>yum update</code>一下，使用最新的软件保证安全性。</p><h1 id="References"><a href="#References" class="headerlink" title="References"></a>References</h1><p><a href="https://blog.csdn.net/weixin_66597089/article/details/122637503">https://blog.csdn.net/weixin_66597089/article/details/122637503</a></p>]]></content>
<categories>
<category> 运维 </category>
</categories>
<tags>
<tag> CentOS </tag>
<tag> CentOs Stream </tag>
<tag> linux </tag>
</tags>
</entry>
<entry>
<title>MAC - 在VsCode中运行和调试C/C++.md</title>
<link href="/2022/03/19/mac-zai-vs-code-zhong-yun-xing-he-diao-shi-c-c-md/"/>
<url>/2022/03/19/mac-zai-vs-code-zhong-yun-xing-he-diao-shi-c-c-md/</url>
<content type="html"><![CDATA[<h1 id="配置说明"><a href="#配置说明" class="headerlink" title="配置说明"></a>配置说明</h1><p>使用2020款m1的13.3英寸mbp，内存16GB。</p><h1 id="安装VsCode"><a href="#安装VsCode" class="headerlink" title="安装VsCode"></a>安装VsCode</h1><p>去<a href="https://code.visualstudio.com/">官网</a> 下载vscode。</p><p>现在vscode已经完美支持m1。</p><h1 id="安装VsCode的插件"><a href="#安装VsCode的插件" class="headerlink" title="安装VsCode的插件"></a>安装VsCode的插件</h1><ul><li>Reload：非必需。右下角多一个Reload标签，点击以后可以一键重启VsCode。</li><li>C/C++：用于运行C和C++的程序。这插件会安装gcc，这个gcc也是完美支持m1。</li><li>Code Runner：在右上角多出个箭头，可以一键运行。</li><li>CodeLLDB：用于调试，没有它vscode的断点会断不下来。</li><li>tabnine：非必需。强大的自动补全插件，基于AI。免费版每天可以补全5000次。</li></ul><h1 id="配置插件"><a href="#配置插件" class="headerlink" title="配置插件"></a>配置插件</h1><p>在<code>~/Library/Application Support/Code/User/settings.json</code>中配置<code>Code Runner</code>。</p><p>我们配置它的<code>code-runner.executorMap</code>中的</p><pre class="line-numbers language-json"><code class="language-json"><span class="token property">"cpp"</span><span class="token operator">:</span> <span class="token string">"cd $dir && g++ -std=c++11 $fileName -o $fileNameWithoutExt && $dir$fileNameWithoutExt"</span><span class="token punctuation">,</span><span aria-hidden="true" class="line-numbers-rows"><span></span></span></code></pre><p>这样code runner才会编译成c++11。要不然一堆feature用不了。现在大大小小比赛都完美支持C++11了，部分大型比赛支持C++14。</p><p>然后在<code>code-runner.executorMap</code>下面，额外增加两行：</p><pre class="line-numbers language-json"><code class="language-json"><span class="token property">"code-runner.saveFileBeforeRun"</span><span class="token operator">:</span> <span class="token boolean">true</span><span class="token punctuation">,</span><span class="token property">"code-runner.runInTerminal"</span><span class="token operator">:</span> <span class="token boolean">true</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span></span></code></pre><p>第一行会在运行前自动保存文件，不用每次都command+s保存然后再点运行。</p><p>第二行会让程序运行在控制台中，否则cin或者scanf等指令没办法输入。</p><h1 id="运行代码"><a href="#运行代码" class="headerlink" title="运行代码"></a>运行代码</h1><p>写一段代码后点击右上角运行，应该不会有问题。</p><p>vscode会自己拉起控制台，然后你就能看到你代码在vscode中的控制台运行了。</p><h1 id="调试代码"><a href="#调试代码" class="headerlink" title="调试代码"></a>调试代码</h1><p>这部分非常坑，我搞了好久。</p><p>总的来说，我们只需要在当前目录下的.vscode文件夹下新增2个json文件就好了。</p><p>新建tasks.json文件如下</p><pre class="line-numbers language-json"><code class="language-json"><span class="token punctuation">{</span> <span class="token property">"tasks"</span><span class="token operator">:</span> <span class="token punctuation">[</span> <span class="token punctuation">{</span> <span class="token property">"type"</span><span class="token operator">:</span> <span class="token string">"cppbuild"</span><span class="token punctuation">,</span> <span class="token property">"label"</span><span class="token operator">:</span> <span class="token string">"C/C++: g++"</span><span class="token punctuation">,</span> <span class="token property">"command"</span><span class="token operator">:</span> <span class="token string">"/usr/bin/g++"</span><span class="token punctuation">,</span> <span class="token property">"args"</span><span class="token operator">:</span> <span class="token punctuation">[</span> <span class="token string">"-g"</span><span class="token punctuation">,</span> <span class="token string">"${file}"</span><span class="token punctuation">,</span> <span class="token string">"-o"</span><span class="token punctuation">,</span> <span class="token string">"${fileDirname}/${fileBasenameNoExtension}"</span> <span class="token punctuation">]</span><span class="token punctuation">,</span> <span class="token property">"options"</span><span class="token operator">:</span> <span class="token punctuation">{</span> <span class="token property">"cwd"</span><span class="token operator">:</span> <span class="token string">"${fileDirname}"</span> <span class="token punctuation">}</span><span class="token punctuation">,</span> <span class="token property">"problemMatcher"</span><span class="token operator">:</span> <span class="token punctuation">[</span> <span class="token string">"$gcc"</span> <span class="token punctuation">]</span><span class="token punctuation">,</span> <span class="token property">"group"</span><span class="token operator">:</span> <span class="token punctuation">{</span> <span class="token property">"kind"</span><span class="token operator">:</span> <span class="token string">"build"</span><span class="token punctuation">,</span> <span class="token property">"isDefault"</span><span class="token operator">:</span> <span class="token boolean">true</span> <span class="token punctuation">}</span><span class="token punctuation">,</span> <span class="token property">"detail"</span><span class="token operator">:</span> <span class="token string">"调试器生成的任务。"</span> <span class="token punctuation">}</span> <span class="token punctuation">]</span><span class="token punctuation">,</span> <span class="token property">"version"</span><span class="token operator">:</span> <span class="token string">"2.0.0"</span><span class="token punctuation">}</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>新建launch.json文件如下</p><pre class="line-numbers language-json"><code class="language-json"><span class="token punctuation">{</span> <span class="token property">"version"</span><span class="token operator">:</span> <span class="token string">"0.2.0"</span><span class="token punctuation">,</span> <span class="token property">"configurations"</span><span class="token operator">:</span> <span class="token punctuation">[</span> <span class="token punctuation">{</span> <span class="token property">"preLaunchTask"</span><span class="token operator">:</span> <span class="token string">"C/C++: g++"</span><span class="token punctuation">,</span> <span class="token property">"type"</span><span class="token operator">:</span> <span class="token string">"lldb"</span><span class="token punctuation">,</span> <span class="token property">"request"</span><span class="token operator">:</span> <span class="token string">"launch"</span><span class="token punctuation">,</span> <span class="token property">"name"</span><span class="token operator">:</span> <span class="token string">"Debug"</span><span class="token punctuation">,</span> <span class="token property">"program"</span><span class="token operator">:</span> <span class="token string">"${fileDirname}/${fileBasenameNoExtension}"</span><span class="token punctuation">,</span> <span class="token property">"args"</span><span class="token operator">:</span> <span class="token punctuation">[</span><span class="token punctuation">]</span><span class="token punctuation">,</span> <span class="token property">"cwd"</span><span class="token operator">:</span> <span class="token string">"${workspaceFolder}"</span> <span class="token punctuation">}</span> <span class="token punctuation">]</span><span class="token punctuation">}</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><h1 id="开始调试"><a href="#开始调试" class="headerlink" title="开始调试"></a>开始调试</h1><p>在你要调试的位置打上断点。</p><p>3种方法来调试。</p><ol><li>快捷键：shift+command+f11</li><li>找到上方的Run，选择Start Debugging</li><li>在左边找到Run and Debug选项卡，点进去。可以看到里面有一个绿色的小箭头，点击，也是调试。</li></ol><h1 id="References"><a href="#References" class="headerlink" title="References"></a>References</h1><ol><li>MAC+VS Code+C/C++调试配置：<a href="https://blog.csdn.net/qq_37747262/article/details/81151037">https://blog.csdn.net/qq_37747262/article/details/81151037</a></li><li>解决Mac上VSCdoe断点失效问题：<a href="https://blog.csdn.net/fujz123/article/details/104426121">https://blog.csdn.net/fujz123/article/details/104426121</a></li><li>vscode的 code-runner插件运行前保存：<a href="https://www.cnblogs.com/yansc/p/13895314.html">https://www.cnblogs.com/yansc/p/13895314.html</a></li></ol>]]></content>
<categories>
<category> C/C++ </category>
</categories>
<tags>
<tag> C/C++ </tag>
<tag> VsCode </tag>
<tag> Mac </tag>
</tags>
</entry>
<entry>
<title>LaTex从入门到精通</title>
<link href="/2022/03/19/latex-cong-ru-men-dao-jing-tong/"/>
<url>/2022/03/19/latex-cong-ru-men-dao-jing-tong/</url>
<content type="html"><![CDATA[<h1 id="简介"><a href="#简介" class="headerlink" title="简介"></a>简介</h1><p>LaTeX是一种基于TeX的文档排版系统,把大片排版的格式细节隐藏在若干样式之后，以内容的逻辑结构统帅纷繁的格式，遂成为现在最流行的科技写作——尤其是数学写作的工具之一. 在Markdown中插入数学公式的语法是 <code>$数学公式$</code>和 <code>$$数学公式$$</code>.</p><h1 id="行内公式"><a href="#行内公式" class="headerlink" title="行内公式"></a>行内公式</h1><p>行内公式是可以让公式在文中与文字或其他东西混编，而不独占一行。在数学模式下，符号会使用单独的字体，字母通常是倾斜的意大利体，数字和符号则是直立体。而数学符号之间的距离也与一般的水平模式不同:</p><table><thead><tr><th>示例</th><th>显示</th></tr></thead><tbody><tr><td><code>$2x+3y=34$</code></td><td>$2x+3y=34$</td></tr><tr><td><code>2x+3y=34</code></td><td>2x+3y=34</td></tr></tbody></table><p>因此，在排版数学公式时，即使没有特殊符号的算式（如1+1=2），或者简单的一个字母变量，也建议进入数学模式，使用<code>$1+1=2$</code>，<code>$x$</code>，而不是使用排版普通文字的方式。</p><h2 id="注意"><a href="#注意" class="headerlink" title="注意"></a>注意</h2><p>并非所有的 Markdown解析器/编辑器 都支持数学公式。所以在不支持的情况下显示出来的东西可能不尽人意。hexo要安装mathjax数学公式支持插件才支持，JetBrains家的产品默认不支持。</p><p>在本博客中，使用的是2.7.9的mathjax.js解析器，并不能解析指令//和/newline。所以部分显示可能有bug。</p><h1 id="独立公式"><a href="#独立公式" class="headerlink" title="独立公式"></a>独立公式</h1><p>独立公式单独占一行,不和其他文字混编<br>示例: <code> $$c=2πr$$</code><br>显示: $$c=2πr$$</p><h1 id="断行和分页"><a href="#断行和分页" class="headerlink" title="断行和分页"></a>断行和分页</h1><p>使用 <code>\\</code>或 <code>\newline</code> 来换行。</p><p>也可以使用 <code>\\[5pt]</code>来指定换行后，与前一行之间间隔5个位置。</p><p>示例:</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span> 2x+3y=34<span class="token function selector">\\</span>x+4y=25<span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span></span></code></pre><p>显示<br>$$<br>2x+3y=34\<br>x+4y=25<br>$$</p><p>此处放上显示的效果的图片，因为本博客使用的mathjax无法解析。</p><p>真实的显示效果应该如下：</p><p><img src="https://vskendo-1255590242.cos.ap-guangzhou.myqcloud.com/2022/05/04/133602-b1.png" alt="image-20220504133602115"></p><h1 id="常用符号"><a href="#常用符号" class="headerlink" title="常用符号"></a>常用符号</h1><table><thead><tr><th>符号</th><th>示例</th><th>显示</th></tr></thead><tbody><tr><td>上下标</td><td><code>S=a_{1}^2+a_{2}^2+a_{3}^2$</code></td><td>$S=a_{1}^2+a_{2}^2+a_{3}^2$</td></tr><tr><td>括号</td><td><code>$f(x, y) = 100 * \lbrace[(x + y) * 3] - 5\rbrace$</code></td><td>$f(x, y) = 100 * \lbrace[(x + y) * 3] - 5\rbrace$</td></tr><tr><td>分数</td><td><code>$\frac{1}{3} 与 \cfrac{1}{3}$</code></td><td>$\frac{1}{3} 与 \cfrac{1}{3}$</td></tr><tr><td>开方</td><td><code>$\sqrt[3]{X}$</code>和<code>$\sqrt{5 - x}$</code></td><td>$\sqrt[3]{X}$<code>和</code>$\sqrt{5 - x}$</td></tr><tr><td>省略号</td><td><code>\dots</code>或<code>\cdots</code></td><td>$\dots$</td></tr><tr><td>加粗</td><td><code>$ f(x) = \textbf{x}^2 $ </code></td><td>$ f(x) = \textbf{x}^2 $</td></tr><tr><td>纯文本</td><td><code>$ f(x) = x^2 \mbox{abcd} $</code></td><td>$ f(x) = x^2 \mbox{abcd} $</td></tr><tr><td>特殊</td><td><code>$\TeX$ </code> 斜杠加上任意普通字符即可</td><td>$\TeX$</td></tr><tr><td>波浪线</td><td><code>$\sim$</code></td><td>$\sim$</td></tr><tr><td>空格</td><td><code>$\ $</code></td><td>$\ $</td></tr><tr><td>tab</td><td><code>$\qquad$</code></td><td>$\qquad$</td></tr><tr><td>爱心</td><td><code>$\heartsuit$</code></td><td>$\heartsuit$</td></tr></tbody></table><h1 id="其他字符"><a href="#其他字符" class="headerlink" title="其他字符"></a>其他字符</h1><p>数学中常用的字符，比如关系运算符、对数运算符、三角运算符等。</p><h2 id="关系运算符"><a href="#关系运算符" class="headerlink" title="关系运算符"></a>关系运算符</h2><table><thead><tr><th>代码</th><th>符号</th></tr></thead><tbody><tr><td>\pm</td><td>$\pm$</td></tr><tr><td>\times</td><td>$\times$</td></tr><tr><td>\div</td><td>$\div$</td></tr><tr><td>\mid</td><td>$\mid$</td></tr><tr><td>\nmid</td><td>$\nmid$</td></tr><tr><td>\cdot</td><td>$\cdot$</td></tr><tr><td>\circ</td><td>$\circ$</td></tr><tr><td>\ast</td><td>$\ast$</td></tr><tr><td>\bigodot</td><td>$\bigodot$</td></tr><tr><td>\bigotimes</td><td>$\bigotimes$</td></tr><tr><td>\bigoplus</td><td>$\bigoplus$</td></tr><tr><td>\leq</td><td>$\leq$</td></tr><tr><td>\geq</td><td>$\geq$</td></tr><tr><td>\neq</td><td>$\neq$</td></tr><tr><td>\approx</td><td>$\approx$</td></tr><tr><td>\equiv</td><td>$\equiv$</td></tr><tr><td>\sum</td><td>$\sum$</td></tr><tr><td>\prod</td><td>$\prod$</td></tr></tbody></table><h2 id="对数运算符"><a href="#对数运算符" class="headerlink" title="对数运算符"></a>对数运算符</h2><table><thead><tr><th>代码</th><th>符号</th></tr></thead><tbody><tr><td>\log</td><td>$\log$</td></tr><tr><td>\lg</td><td>$\lg$</td></tr><tr><td>\ln</td><td>$\ln$</td></tr></tbody></table><h2 id="三角运算符"><a href="#三角运算符" class="headerlink" title="三角运算符"></a>三角运算符</h2><table><thead><tr><th>代码</th><th>符号</th></tr></thead><tbody><tr><td>\bot</td><td>$\bot$</td></tr><tr><td>\angle</td><td>$\angle$</td></tr></tbody></table><p>还有\sin、\cos等，所有三角函数的缩写都可以。</p><h2 id="微积分运算符"><a href="#微积分运算符" class="headerlink" title="微积分运算符"></a>微积分运算符</h2><table><thead><tr><th>代码</th><th>符号</th></tr></thead><tbody><tr><td>\prime</td><td>$\prime$</td></tr><tr><td>\int</td><td>$\int$</td></tr><tr><td>\iint</td><td>$\iint$</td></tr><tr><td>\iiint</td><td>$\iiint$</td></tr><tr><td>\oint</td><td>$\oint$</td></tr><tr><td>\infty</td><td>$\infty$</td></tr><tr><td>\nabla</td><td>$\nabla$</td></tr><tr><td>\mathrm{d}</td><td>$\mathrm{d}$</td></tr></tbody></table><h2 id="集合运算符"><a href="#集合运算符" class="headerlink" title="集合运算符"></a>集合运算符</h2><table><thead><tr><th>代码</th><th>符号</th></tr></thead><tbody><tr><td>\emptyset</td><td>$\emptyset$</td></tr><tr><td>\in</td><td>$\in$</td></tr><tr><td>\notin</td><td>$\notin$</td></tr><tr><td>\subset</td><td>$\subset$</td></tr><tr><td>\subseteq</td><td>$\subseteq$</td></tr><tr><td>\supseteq</td><td>$\supseteq$</td></tr><tr><td>\bigcap</td><td>$\bigcap$</td></tr><tr><td>\bigcup</td><td>$\bigcup$</td></tr><tr><td>\bigvee</td><td>$\bigvee$</td></tr><tr><td>\bigwedge</td><td>$\bigwedge$</td></tr><tr><td>\biguplus</td><td>$\biguplus$</td></tr><tr><td>\bigsqcup</td><td>$\bigsqcup$</td></tr></tbody></table><h2 id="希腊字母"><a href="#希腊字母" class="headerlink" title="希腊字母"></a>希腊字母</h2><p>LATEX2$\epsilon$ 没有定义Alpha 的大写形式，因为它和普通的罗马字体A 很像。也许新的数学编码完成后会有所变化。</p><table><thead><tr><th>代码</th><th>大写</th><th>代码</th><th>小写</th></tr></thead><tbody><tr><td>A</td><td>$A$</td><td>\alpha</td><td>$\alpha$</td></tr><tr><td>B</td><td>$B$</td><td>\beta</td><td>$\beta$</td></tr><tr><td>\Gamma</td><td>$\Gamma$</td><td>\gamma</td><td>$\gamma$</td></tr><tr><td>\Delta</td><td>$\Delta$</td><td>\delta</td><td>$\delta$</td></tr><tr><td>E</td><td>$E$</td><td>\epsilon</td><td>$\epsilon$</td></tr><tr><td>Z</td><td>$Z$</td><td>\zeta</td><td>$\zeta$</td></tr><tr><td>H</td><td>$H$</td><td>\eta</td><td>$\eta$</td></tr><tr><td>\Theta</td><td>$\Theta$</td><td>\theta</td><td>$\theta$</td></tr><tr><td>I</td><td>$I$</td><td>\iota</td><td>$\iota$</td></tr><tr><td>K</td><td>$K$</td><td>\kappa</td><td>$\kappa$</td></tr><tr><td>Lambda</td><td>$\Lambda$</td><td>\lambda</td><td>$\lambda$</td></tr><tr><td>M</td><td>$M$</td><td>\mu</td><td>$\mu$</td></tr><tr><td>N</td><td>$N$</td><td>\nu</td><td>$\nu$</td></tr><tr><td>Xi</td><td>$Xi$</td><td>\xi</td><td>$\xi$</td></tr><tr><td>O</td><td>$O$</td><td>\omicron</td><td>$\omicron$</td></tr><tr><td>\Pi</td><td>$\Pi$</td><td>\pi</td><td>$\pi$</td></tr><tr><td>P</td><td>$P$</td><td>\rho</td><td>$\rho$</td></tr><tr><td>\Sigma</td><td>$\Sigma$</td><td>\sigma</td><td>$\sigma$</td></tr><tr><td>T</td><td>$T$</td><td>\tau</td><td>$\tau$</td></tr><tr><td>\Upsilon</td><td>$\Upsilon$</td><td>\upsilon</td><td>$\upsilon$</td></tr><tr><td>\Phi</td><td>$\Phi$</td><td>\phi</td><td>$\phi$</td></tr><tr><td>X</td><td>$X$</td><td>\chi</td><td>$\chi$</td></tr><tr><td>\Psi</td><td>$\Psi$</td><td>\psi</td><td>$\psi$</td></tr><tr><td>\Omega</td><td>$\Omega$</td><td>\omega</td><td>$\omega$</td></tr></tbody></table><h1 id="其他技巧"><a href="#其他技巧" class="headerlink" title="其他技巧"></a>其他技巧</h1><p>例子一：行距技巧</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span><span class="token function selector">\TeX</span><span class="token function selector">\ </span>is<span class="token function selector">\ </span>pronounced<span class="token function selector">\ </span>as<span class="token function selector">\ </span><span class="token function selector">\tau</span><span class="token function selector">\epsilon</span><span class="token function selector">\chi</span>.<span class="token function selector">\\</span><span class="token punctuation">[</span>6pt<span class="token punctuation">]</span>100-m^<span class="token punctuation">{</span>3<span class="token punctuation">}</span><span class="token function selector">\ </span>of<span class="token function selector">\ </span>water<span class="token function selector">\\</span><span class="token punctuation">[</span>6pt<span class="token punctuation">]</span>This<span class="token function selector">\ </span>comes<span class="token function selector">\ </span>from<span class="token function selector">\ </span>my<span class="token function selector">\ </span><span class="token function selector">\heartsuit</span><span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>$$<br>\TeX\ is\ pronounced\ as\<br>\tau\epsilon\chi.<br>100-m^{3}\ of\ water<br>This\ comes\ from\ my\ \heartsuit<br>$$</p><p>此处放上显示的效果的图片，因为本博客使用的mathjax无法解析。</p><p>真实的显示效果应该如下：</p><p><img src="https://vskendo-1255590242.cos.ap-guangzhou.myqcloud.com/2022/05/04/133719-6d.png" alt="image-20220504133719255"></p><p>例子二：极限、求和、分数使用技巧</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span><span class="token function selector">\lim</span>_<span class="token punctuation">{</span>n <span class="token function selector">\to</span> <span class="token function selector">\infty</span><span class="token punctuation">}</span><span class="token function selector">\sum</span>_<span class="token punctuation">{</span>k=1<span class="token punctuation">}</span>^n <span class="token function selector">\frac</span><span class="token punctuation">{</span>1<span class="token punctuation">}</span><span class="token punctuation">{</span>k^2<span class="token punctuation">}</span>= <span class="token function selector">\frac</span><span class="token punctuation">{</span><span class="token function selector">\pi</span>^2<span class="token punctuation">}</span><span class="token punctuation">{</span>6<span class="token punctuation">}</span><span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>$$<br>\lim_{n \to \infty}<br>\sum_{k=1}^n \frac{1}{k^2}<br>= \frac{\pi^2}{6}<br>$$</p><p>例子三：集合例子</p><p>数学家们通常对使用什么样的符号非常挑剔：习惯上使用“空心粗体”（blackboard bold）来表示实数集合。这种字体可用amsfonts 或amssymb 宏包中的命令\mathbb 来得到(如代码中的倒数第二行所示)。</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span> <span class="token function selector">\forall</span> x <span class="token function selector">\in</span> <span class="token function selector">\mathbf</span><span class="token punctuation">{</span>R<span class="token punctuation">}</span>:<span class="token function selector">\qquad</span> x^<span class="token punctuation">{</span>2<span class="token punctuation">}</span> <span class="token function selector">\geq</span> 0<span class="token function selector">\</span>x^<span class="token punctuation">{</span>2<span class="token punctuation">}</span> <span class="token function selector">\geq</span> 0<span class="token function selector">\qquad</span><span class="token function selector">\textrm</span><span class="token punctuation">{</span>for all <span class="token punctuation">}</span>x<span class="token function selector">\in</span><span class="token function selector">\mathbf</span><span class="token punctuation">{</span>R<span class="token punctuation">}</span><span class="token function selector">\</span>x^<span class="token punctuation">{</span>2<span class="token punctuation">}</span> <span class="token function selector">\geq</span> 0<span class="token function selector">\qquad</span><span class="token function selector">\textrm</span><span class="token punctuation">{</span>for all <span class="token punctuation">}</span>x<span class="token function selector">\in</span><span class="token function selector">\mathbb</span><span class="token punctuation">{</span>R<span class="token punctuation">}</span><span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>$$<br>\forall x \in \mathbf{R}:<br>\qquad x^{2} \geq 0<br>x^{2} \geq 0\qquad<br>\textrm{for all }x\in\mathbf{R}<br>x^{2} \geq 0\qquad<br>\textrm{for all }x\in\mathbb{R}<br>$$</p><p>例子四：简单等式</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span>a^x+y <span class="token function selector">\neq</span> a^<span class="token punctuation">{</span>x+y<span class="token punctuation">}</span><span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span></span></code></pre><p>$$<br>a^x+y \neq a^{x+y}<br>$$</p><p>例子五：平方根。方根符号的大小由LATEX自动加以调整。也可用\surd 仅给出符号。</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span><span class="token function selector">\sqrt</span><span class="token punctuation">{</span>x<span class="token punctuation">}</span> <span class="token function selector">\qquad</span><span class="token function selector">\sqrt</span><span class="token punctuation">{</span> x^<span class="token punctuation">{</span>2<span class="token punctuation">}</span>+<span class="token function selector">\sqrt</span><span class="token punctuation">{</span>y<span class="token punctuation">}</span> <span class="token punctuation">}</span><span class="token function selector">\qquad</span> <span class="token function selector">\sqrt</span><span class="token punctuation">[</span>3<span class="token punctuation">]</span><span class="token punctuation">{</span>2<span class="token punctuation">}</span><span class="token function selector">\</span><span class="token function selector">\surd</span><span class="token punctuation">[</span>x^2 + y^2<span class="token punctuation">]</span><span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>$$<br>\sqrt{x} \qquad<br>\sqrt{ x^{2}+\sqrt{y} }<br>\qquad \sqrt[3]{2}<br>\surd[x^2 + y^2]<br>$$</p><p>例子六：命令\overline 和\underline 在表达式的上、下方画出水平线。</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span><span class="token function selector">\overline</span><span class="token punctuation">{</span>m+n<span class="token punctuation">}</span> <span class="token function selector">\qquad</span><span class="token function selector">\underline</span><span class="token punctuation">{</span>m+n<span class="token punctuation">}</span><span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span></span></code></pre><p>$$<br>\overline{m+n} \qquad<br>\underline{m+n}<br>$$</p><p>例子七：命令\overbrace 和\underbrace 在表达式的上、下方给出一水平的大括号。</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span><span class="token function selector">\underbrace</span><span class="token punctuation">{</span> a+b+<span class="token function selector">\cdots</span>+z <span class="token punctuation">}</span>_<span class="token punctuation">{</span>26<span class="token punctuation">}</span><span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span></span></code></pre><p>$$<br>\underbrace{ a+b+\cdots+z }_{26}<br>$$</p><p>例子八：数学重音符号如小箭头和˜（tilde）。可覆盖多个字符的宽重音符号可由\widetilde 和\widehat 等得到。</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span>y=x^<span class="token punctuation">{</span>2<span class="token punctuation">}</span><span class="token function selector">\qquad</span> y'=2x<span class="token function selector">\qquad</span> y''=2<span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span></span></code></pre><p>$$<br>y=x^{2}\qquad y’=2x\qquad y’’=2<br>$$</p><p>例子九：向量（Vectors）通常用上方有小箭头（arrow symbols）的变量表示。这可由\vec 得到。</p><p>另两个命令\overrightarrow 和\overleftarrow在定义从A 到B 的向量时非常有用。</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span><span class="token function selector">\vec</span> a<span class="token function selector">\quad</span><span class="token function selector">\overrightarrow</span><span class="token punctuation">{</span>AB<span class="token punctuation">}</span><span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span></span></code></pre><p>$$<br>\vec a\quad\overrightarrow{AB}<br>$$</p><p>例子十：一般情况下，乘法算式中的圆点符可以省略。然而有时为了帮助读者解读复杂的公式，也有必要用命令\cdot 将圆点符表示出来。</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span>v = <span class="token punctuation">{</span><span class="token function selector">\sigma</span><span class="token punctuation">}</span>_1 <span class="token function selector">\cdot</span> <span class="token punctuation">{</span><span class="token function selector">\sigma</span><span class="token punctuation">}</span>_2<span class="token punctuation">{</span><span class="token function selector">\tau</span><span class="token punctuation">}</span>_1 <span class="token function selector">\cdot</span> <span class="token punctuation">{</span><span class="token function selector">\tau</span><span class="token punctuation">}</span>_2<span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span></span></code></pre><p>$$<br>v = {\sigma}_1 \cdot {\sigma}_2<br>{\tau}_1 \cdot {\tau}_2<br>$$</p><p>例子十一：分数（fraction）使用\frac{…}{…} 排版。一般来说，1/2 这种形式更受欢迎，因为对于少量的分式，它看起来更好些。</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span>1<span class="token function selector">\frac</span><span class="token punctuation">{</span>1<span class="token punctuation">}</span><span class="token punctuation">{</span>2<span class="token punctuation">}</span>~hours<span class="token function selector">\\</span><span class="token function selector">\frac</span><span class="token punctuation">{</span> x^<span class="token punctuation">{</span>2<span class="token punctuation">}</span> <span class="token punctuation">}</span><span class="token punctuation">{</span> k+1 <span class="token punctuation">}</span><span class="token function selector">\qquad</span>x^<span class="token punctuation">{</span> <span class="token function selector">\frac</span><span class="token punctuation">{</span>2<span class="token punctuation">}</span><span class="token punctuation">{</span>k+1<span class="token punctuation">}</span> <span class="token punctuation">}</span><span class="token function selector">\qquad</span>x^<span class="token punctuation">{</span> 1/2 <span class="token punctuation">}</span><span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>$$<br>1\frac{1}{2}~hours\<br>\frac{ x^{2} }{ k+1 }\qquad<br>x^{ \frac{2}{k+1} }\qquad<br>x^{ 1/2 }<br>$$</p><p>此处放上显示的效果的图片，因为本博客使用的mathjax无法解析。</p><p>真实的显示效果应该如下：</p><p><img src="https://vskendo-1255590242.cos.ap-guangzhou.myqcloud.com/2022/05/04/140314-6e.png" alt="image-20220504140314315"></p><p>例子十二：排版二项系数或类似的结构可以使用命令{… \choose …} 或{… \atop …}。</p><p>第二个命令与第一个命令的输出相同，只是没有括号。（注意这些旧命令在amsmath 宏集中禁止使用， 而是用\binom和\genfrac来代替。后者是所有相关结构的超集， 例如可以通过、newcommand{\newatop}[2]% 来得到\atop 的一个类似结构）</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span><span class="token punctuation">{</span>n <span class="token function selector">\choose</span> k<span class="token punctuation">}</span><span class="token function selector">\qquad</span> <span class="token punctuation">{</span>x <span class="token function selector">\atop</span> y+2<span class="token punctuation">}</span><span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span></span></code></pre><p>$$<br>{n \choose k}\qquad {x \atop y+2}<br>$$</p><p>例子十三：对于二元关系，将符号堆在一起可能更有用。\stackrel 将第一项中的符号以上标大小放在处于正常位置的第二项上。</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span><span class="token function selector">\int</span> f_N(x) <span class="token function selector">\stackrel</span><span class="token punctuation">{</span>!<span class="token punctuation">}</span><span class="token punctuation">{</span>=<span class="token punctuation">}</span> 1<span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span></span></code></pre><p>$$<br>\int f_N(x) \stackrel{!}{=} 1<br>$$</p><p>例子十四：积分运算符（integral operator）。</p><p>求和运算符（sum operator）。</p><p>乘积运算符（product operator）</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span><span class="token function selector">\sum</span>_<span class="token punctuation">{</span>i=1<span class="token punctuation">}</span>^<span class="token punctuation">{</span>n<span class="token punctuation">}</span> <span class="token function selector">\qquad</span><span class="token function selector">\int</span>_<span class="token punctuation">{</span>0<span class="token punctuation">}</span>^<span class="token punctuation">{</span><span class="token function selector">\frac</span><span class="token punctuation">{</span><span class="token function selector">\pi</span><span class="token punctuation">}</span><span class="token punctuation">{</span>2<span class="token punctuation">}</span><span class="token punctuation">}</span> <span class="token function selector">\qquad</span><span class="token function selector">\prod</span>_<span class="token function selector">\epsilon</span><span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>$$<br>\sum_{i=1}^{n} \qquad<br>\int_{0}^{\frac{\pi}{2}} \qquad<br>\prod_\epsilon<br>$$</p><p>例子十五：某些情况下有必要手工指出数学分隔符的正确大小。</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span><span class="token function selector">\Big</span>( (x+1) (x-1) <span class="token function selector">\Big</span>) ^<span class="token punctuation">{</span>2<span class="token punctuation">}</span><span class="token function selector">\\</span><span class="token function selector">\big</span>(<span class="token function selector">\Big</span>(<span class="token function selector">\bigg</span>(<span class="token function selector">\Bigg</span>(<span class="token function selector">\quad</span><span class="token function selector">\big</span><span class="token function selector">\}</span><span class="token function selector">\Big</span><span class="token function selector">\}</span><span class="token function selector">\bigg</span><span class="token function selector">\}</span><span class="token function selector">\Bigg</span><span class="token function selector">\}</span><span class="token function selector">\quad</span><span class="token function selector">\big</span><span class="token function selector">\|</span><span class="token function selector">\Big</span><span class="token function selector">\|</span><span class="token function selector">\bigg</span><span class="token function selector">\|</span><span class="token function selector">\Bigg</span><span class="token function selector">\|</span><span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>$$<br>\Big( (x+1) (x-1) \Big) ^{2}\<br>\big(\Big(\bigg(\Bigg(\quad<br>\big}\Big}\bigg}\Bigg}\quad<br>\big|\Big|\bigg|\Bigg|<br>$$</p><p>此处放上显示的效果的图片，因为本博客使用的mathjax无法解析。</p><p>真实的显示效果应该如下：</p><p><img src="https://vskendo-1255590242.cos.ap-guangzhou.myqcloud.com/2022/05/04/140243-08.png" alt="image-20220504140243018"></p><p>例子十六：如果公式中由TEX选择的的空格不令人满意，可以通过插入特殊的空格命令来进行调节。</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span><span class="token function selector">\int</span><span class="token function selector">\!</span><span class="token function selector">\!</span><span class="token function selector">\!</span><span class="token function selector">\int</span>_<span class="token punctuation">{</span>D<span class="token punctuation">}</span> g(x,y)<span class="token function selector">\,</span> x<span class="token function selector">\,</span> y<span class="token function selector">\\</span>instead of<span class="token function selector">\\</span><span class="token function selector">\int</span><span class="token function selector">\int</span>_<span class="token punctuation">{</span>D<span class="token punctuation">}</span> g(x,y)x y<span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>$$<br>\int!!!\int_{D} g(x,y)<br>, x, y\<br>instead of\<br>\int\int_{D} g(x,y)x y<br>$$</p><p>此处放上显示的效果的图片，因为本博客使用的mathjax无法解析。</p><p>真实的显示效果应该如下：</p><p><img src="https://vskendo-1255590242.cos.ap-guangzhou.myqcloud.com/2022/05/04/140225-36.png" alt="image-20220504140225122"></p><p>例子十七：排版arrays 使用array 环境来排版数组（arrays）。</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span><span class="token function selector">\mathbf</span><span class="token punctuation">{</span>X<span class="token punctuation">}</span> =<span class="token function selector">\left</span>( <span class="token function selector">\begin</span><span class="token punctuation">{</span><span class="token keyword">array</span><span class="token punctuation">}</span><span class="token punctuation">{</span>ccc<span class="token punctuation">}</span>x_<span class="token punctuation">{</span>11<span class="token punctuation">}</span> <span class="token punctuation">&</span> x_<span class="token punctuation">{</span>12<span class="token punctuation">}</span> <span class="token punctuation">&</span> <span class="token function selector">\ldots</span> <span class="token function selector">\\</span>x_<span class="token punctuation">{</span>21<span class="token punctuation">}</span> <span class="token punctuation">&</span> x_<span class="token punctuation">{</span>22<span class="token punctuation">}</span> <span class="token punctuation">&</span> <span class="token function selector">\ldots</span> <span class="token function selector">\\</span><span class="token function selector">\vdots</span> <span class="token punctuation">&</span> <span class="token function selector">\vdots</span> <span class="token punctuation">&</span> <span class="token function selector">\ddots</span><span class="token function selector">\end</span><span class="token punctuation">{</span><span class="token keyword">array</span><span class="token punctuation">}</span> <span class="token function selector">\right</span>)<span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>$$<br>\mathbf{X} =<br>\left( \begin{array}{ccc}<br>x_{11} & x_{12} & \ldots \<br>x_{21} & x_{22} & \ldots \<br>\vdots & \vdots & \ddots<br>\end{array} \right)<br>$$</p><p>此处放上显示的效果的图片，因为本博客使用的mathjax无法解析。</p><p>真实的显示效果应该如下：</p><p><img src="https://vskendo-1255590242.cos.ap-guangzhou.myqcloud.com/2022/05/04/135850-24.png" alt="image-20220504135850072"></p><p>例子十八：array 环境也可以使用“.” 作为隐藏右分隔符来排版只有一个大分隔符的表达式。</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span>y = <span class="token function selector">\left</span><span class="token function selector">\{</span> <span class="token function selector">\begin</span><span class="token punctuation">{</span><span class="token keyword">array</span><span class="token punctuation">}</span><span class="token punctuation">{</span>ll<span class="token punctuation">}</span>a <span class="token punctuation">&</span> <span class="token function selector">\textrm</span><span class="token punctuation">{</span>if <span class="token equation string">$d>c$</span><span class="token punctuation">}</span><span class="token function selector">\\</span>b+x <span class="token punctuation">&</span> <span class="token function selector">\textrm</span><span class="token punctuation">{</span>in the morning<span class="token punctuation">}</span><span class="token function selector">\\</span>l <span class="token punctuation">&</span> <span class="token function selector">\textrm</span><span class="token punctuation">{</span>all day long<span class="token punctuation">}</span><span class="token function selector">\end</span><span class="token punctuation">{</span><span class="token keyword">array</span><span class="token punctuation">}</span> <span class="token function selector">\right</span>.<span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>$$<br>y = \left{ \begin{array}{ll}<br>a & \textrm{if $d>c$}\<br>b+x & \textrm{in the morning}\<br>l & \textrm{all day long}<br>\end{array} \right.<br>$$</p><p>此处放上显示的效果的图片，因为本博客使用的mathjax无法解析。</p><p>真实的显示效果应该如下：</p><p><img src="https://vskendo-1255590242.cos.ap-guangzhou.myqcloud.com/2022/05/04/135832-6f.png" alt="image-20220504135831808"></p><p>例子十九：可以在array 环境中画线。例如分隔矩阵中的元素。</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span><span class="token function selector">\left</span>(<span class="token function selector">\begin</span><span class="token punctuation">{</span><span class="token keyword">array</span><span class="token punctuation">}</span><span class="token punctuation">{</span>c|c<span class="token punctuation">}</span>1 <span class="token punctuation">&</span> 2 <span class="token function selector">\\</span><span class="token function selector">\hline</span>3 <span class="token punctuation">&</span> 4<span class="token function selector">\end</span><span class="token punctuation">{</span><span class="token keyword">array</span><span class="token punctuation">}</span><span class="token function selector">\right</span>)<span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>$$<br>\left(\begin{array}{c|c}<br>1 & 2 \<br>\hline<br>3 & 4<br>\end{array}\right)<br>$$</p><p>此处放上显示的效果的图片，因为本博客使用的mathjax无法解析。</p><p>真实的显示效果应该如下：</p><p><img src="https://vskendo-1255590242.cos.ap-guangzhou.myqcloud.com/2022/05/04/135816-99.png" alt="image-20220504135815862"></p><p>例子二十：长方程不会自动地分割成小的。作者必须指定在哪里分割以及缩进多少。以下是最常使用的两种方法。</p><p>其中，\nonumber 命令将阻止LATEX为此方程生成一个编号。</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span><span class="token punctuation">{</span><span class="token function selector">\begin</span><span class="token punctuation">{</span><span class="token keyword">eqnarray</span><span class="token punctuation">}</span><span class="token equation string"><span class="token equation-command regex">\sin</span> x & = & x -<span class="token equation-command regex">\frac</span>{x^{3}}{3!}+<span class="token equation-command regex">\frac</span>{x^{5}}{5!}-{}<span class="token equation-command regex">\nonumber</span><span class="token equation-command regex">\\</span>& & {}-<span class="token equation-command regex">\frac</span>{x^{7}}{7!}+{}<span class="token equation-command regex">\cdots</span></span><span class="token function selector">\end</span><span class="token punctuation">{</span><span class="token keyword">eqnarray</span><span class="token punctuation">}</span><span class="token punctuation">}</span><span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>$$<br>{\begin{eqnarray}<br>\sin x & = & x -\frac{x^{3}}{3!}<br>+\frac{x^{5}}{5!}-{}<br>\nonumber\<br>& & {}-\frac{x^{7}}{7!}+{}\cdots<br>\end{eqnarray}}<br>$$</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span><span class="token function selector">\begin</span><span class="token punctuation">{</span><span class="token keyword">eqnarray</span><span class="token punctuation">}</span><span class="token equation string">{ <span class="token equation-command regex">\cos</span> x = 1-<span class="token equation-command regex">\frac</span>{x^{2}}{2!} +{} }<span class="token equation-command regex">\nonumber</span><span class="token equation-command regex">\\</span>& & {}+<span class="token equation-command regex">\frac</span>{x^{4}}{4!}-<span class="token equation-command regex">\frac</span>{x^{6}}{6!}+{}<span class="token equation-command regex">\cdots</span></span><span class="token function selector">\end</span><span class="token punctuation">{</span><span class="token keyword">eqnarray</span><span class="token punctuation">}</span><span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>$$<br>\begin{eqnarray}<br>{ \cos x = 1<br>-\frac{x^{2}}{2!} +{} }<br>\nonumber\<br>& & {}+\frac{x^{4}}{4!}<br>-\frac{x^{6}}{6!}+{}\cdots<br>\end{eqnarray}<br>$$</p><p>例子二十一：改变式样。改变式样也会影响上下界显示的方式。</p><p>在数学模式中，字体大小用四个命令来设定：</p><p>\displaystyle (123), \textstyle (123), \scriptstyle (123) and\scriptscriptstyle (123).</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span><span class="token function selector">\mathop</span><span class="token punctuation">{</span><span class="token function selector">\mathrm</span><span class="token punctuation">{</span>corr<span class="token punctuation">}</span><span class="token punctuation">}</span>(X,Y)=<span class="token function selector">\frac</span><span class="token punctuation">{</span><span class="token function selector">\displaystyle</span><span class="token function selector">\sum</span>_<span class="token punctuation">{</span>i=1<span class="token punctuation">}</span>^n(x_i-<span class="token function selector">\overline</span> x)(y_i-<span class="token function selector">\overline</span> y)<span class="token punctuation">}</span><span class="token punctuation">{</span><span class="token function selector">\displaystyle</span><span class="token function selector">\biggl</span><span class="token punctuation">[</span><span class="token function selector">\sum</span>_<span class="token punctuation">{</span>i=1<span class="token punctuation">}</span>^n(x_i-<span class="token function selector">\overline</span> x)^2<span class="token function selector">\sum</span>_<span class="token punctuation">{</span>i=1<span class="token punctuation">}</span>^n(y_i-<span class="token function selector">\overline</span> y)^2<span class="token function selector">\biggr</span><span class="token punctuation">]</span>^<span class="token punctuation">{</span>1/2<span class="token punctuation">}</span><span class="token punctuation">}</span><span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>$$<br>\mathop{\mathrm{corr}}(X,Y)=<br>\frac{\displaystyle<br>\sum_{i=1}^n(x_i-\overline x)<br>(y_i-\overline y)}<br>{\displaystyle\biggl[<br>\sum_{i=1}^n(x_i-\overline x)^2<br>\sum_{i=1}^n(y_i-\overline y)^2<br>\biggr]^{1/2}}<br>$$</p><p>差距还是很明显的。行高大小明显不一样。显然是上面的舒服。</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span><span class="token function selector">\mathop</span><span class="token punctuation">{</span><span class="token function selector">\mathrm</span><span class="token punctuation">{</span>corr<span class="token punctuation">}</span><span class="token punctuation">}</span>(X,Y)=<span class="token function selector">\frac</span><span class="token punctuation">{</span><span class="token function selector">\sum</span>_<span class="token punctuation">{</span>i=1<span class="token punctuation">}</span>^n(x_i-<span class="token function selector">\overline</span> x)(y_i-<span class="token function selector">\overline</span> y)<span class="token punctuation">}</span><span class="token punctuation">{</span><span class="token function selector">\biggl</span><span class="token punctuation">[</span><span class="token function selector">\sum</span>_<span class="token punctuation">{</span>i=1<span class="token punctuation">}</span>^n(x_i-<span class="token function selector">\overline</span> x)^2<span class="token function selector">\sum</span>_<span class="token punctuation">{</span>i=1<span class="token punctuation">}</span>^n(y_i-<span class="token function selector">\overline</span> y)^2<span class="token function selector">\biggr</span><span class="token punctuation">]</span>^<span class="token punctuation">{</span>1/2<span class="token punctuation">}</span><span class="token punctuation">}</span><span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>$$<br>\mathop{\mathrm{corr}}(X,Y)=<br>\frac{<br>\sum_{i=1}^n(x_i-\overline x)<br>(y_i-\overline y)}<br>{\biggl[<br>\sum_{i=1}^n(x_i-\overline x)^2<br>\sum_{i=1}^n(y_i-\overline y)^2<br>\biggr]^{1/2}}<br>$$</p><p>例子二十二：在LATEX中很难得到粗体符号。这也许是故意的，因为业余排版者总是过份使用粗体。字体改变命令\mathbf 给出粗体字母，但是这些是罗马字体（竖直的），而数学符号通常是斜体。</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span><span class="token function selector">\mu</span>, M <span class="token function selector">\qquad</span> <span class="token function selector">\mathbf</span><span class="token punctuation">{</span>M<span class="token punctuation">}</span> <span class="token function selector">\qquad</span><span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span></span></code></pre><p>$$<br>\mu, M \qquad \mathbf{M} \qquad<br>$$</p><p>例子二十三：推导过程</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span><span class="token function selector">\begin</span><span class="token punctuation">{</span><span class="token keyword">align</span><span class="token punctuation">}</span><span class="token equation string"> <span class="token equation-command regex">\frac</span>{<span class="token equation-command regex">\partial</span> J(<span class="token equation-command regex">\theta</span>)}{<span class="token equation-command regex">\partial</span><span class="token equation-command regex">\theta</span>_j} & = -<span class="token equation-command regex">\frac</span>1m<span class="token equation-command regex">\sum</span>_{i=0}^m(y^i - h_<span class="token equation-command regex">\theta</span>(x^i)) <span class="token equation-command regex">\frac</span>{<span class="token equation-command regex">\partial</span>}{<span class="token equation-command regex">\partial</span><span class="token equation-command regex">\theta</span>_j}(y^i-h_<span class="token equation-command regex">\theta</span>(x^i))<span class="token equation-command regex">\\</span> & = -<span class="token equation-command regex">\frac</span>1m<span class="token equation-command regex">\sum</span>_{i=0}^m(y^i-h_<span class="token equation-command regex">\theta</span>(x^i)) <span class="token equation-command regex">\frac</span>{<span class="token equation-command regex">\partial</span>}{<span class="token equation-command regex">\partial</span><span class="token equation-command regex">\theta</span>_j}(<span class="token equation-command regex">\sum</span>_{j=0}^n<span class="token equation-command regex">\theta</span>_j x^i_j-y^i)<span class="token equation-command regex">\\</span> &=-<span class="token equation-command regex">\frac</span>1m<span class="token equation-command regex">\sum</span>_{i=0}^m(y^i -h_<span class="token equation-command regex">\theta</span>(x^i)) x^i_j</span><span class="token function selector">\end</span><span class="token punctuation">{</span><span class="token keyword">align</span><span class="token punctuation">}</span><span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>$$<br>\begin{align}<br>\frac{\partial J(\theta)}{\partial\theta_j}<br>& = -\frac1m\sum_{i=0}^m(y^i - h_\theta(x^i)) \frac{\partial}{\partial\theta_j}(y^i-h_\theta(x^i))\<br>& = -\frac1m\sum_{i=0}^m(y^i-h_\theta(x^i)) \frac{\partial}{\partial\theta_j}(\sum_{j=0}^n\theta_j x^i_j-y^i)\<br>&=-\frac1m\sum_{i=0}^m(y^i -h_\theta(x^i)) x^i_j<br>\end{align}<br>$$</p><p>此处放上显示的效果的图片，因为本博客使用的mathjax无法解析。</p><p>真实的显示效果应该如下：<img src="https://vskendo-1255590242.cos.ap-guangzhou.myqcloud.com/2022/05/04/135645-95.png" alt="image-20220504135644915"></p><p>例子二十四：批量梯度下降。</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span><span class="token function selector">\frac</span><span class="token punctuation">{</span><span class="token function selector">\partial</span> J(<span class="token function selector">\theta</span>)<span class="token punctuation">}</span><span class="token punctuation">{</span><span class="token function selector">\partial</span><span class="token function selector">\theta</span>_j<span class="token punctuation">}</span> = -<span class="token function selector">\frac</span>1m<span class="token function selector">\sum</span>_<span class="token punctuation">{</span>i=0<span class="token punctuation">}</span>^m(y^i - h_<span class="token function selector">\theta</span>(x^i))x^i_j<span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span></span></code></pre><p>$$<br>\frac{\partial J(\theta)}{\partial\theta_j} = -\frac1m\sum_{i=0}^m(y^i - h_\theta(x^i))x^i_j<br>$$</p><p>例子二十五：字符下标。</p><pre class="line-numbers language-latex"><code class="language-latex"><span class="token equation string">$$</span><span class="token function selector">\max</span> <span class="token function selector">\limits</span>_<span class="token punctuation">{</span>a<x<b<span class="token punctuation">}</span><span class="token function selector">\{</span>f(x)<span class="token function selector">\}</span> <span class="token equation string">$$</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span></span></code></pre><p>$$<br>\max \limits_{a<x<b}{f(x)}<br>$$</p><h1 id="一些说明"><a href="#一些说明" class="headerlink" title="一些说明"></a>一些说明</h1><ol><li>函数名通常用罗马字体正体排版，而不是像变量名一样用意大利体排版。因此，LATEX提供下述命令来排版最重要的一些函数名。</li></ol><pre class="line-numbers language-latex"><code class="language-latex"><span class="token function selector">\arccos</span> <span class="token function selector">\cos</span> <span class="token function selector">\csc</span> <span class="token function selector">\exp</span> <span class="token function selector">\ker</span> <span class="token function selector">\limsup</span> <span class="token function selector">\min</span><span class="token function selector">\arcsin</span> <span class="token function selector">\cosh</span> <span class="token function selector">\deg</span> <span class="token function selector">\gcd</span> <span class="token function selector">\lg</span> <span class="token function selector">\ln</span> <span class="token function selector">\Pr</span><span class="token function selector">\arctan</span> <span class="token function selector">\cot</span> <span class="token function selector">\det</span> <span class="token function selector">\hom</span> <span class="token function selector">\lim</span> <span class="token function selector">\log</span> <span class="token function selector">\sec</span><span class="token function selector">\arg</span> <span class="token function selector">\coth</span> <span class="token function selector">\dim</span> <span class="token function selector">\inf</span> <span class="token function selector">\liminf</span> <span class="token function selector">\max</span> <span class="token function selector">\sin</span><span class="token function selector">\sinh</span> <span class="token function selector">\sup</span> <span class="token function selector">\tan</span> <span class="token function selector">\tanh</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><ol start="2"><li><p>如果将命令\left 放在开分隔符前，TEX会自动决定分隔符的正确大</p><p>小。注意必须用对应的右分隔符\right 来关闭每一个左分隔符\left，并</p><p>且只有当这两个分隔符排在同一行时大小才会被正确确定。如果不想在右</p><p>边放任何东西，使用隐藏的‘\right.’ !</p></li></ol><h1 id="参考"><a href="#参考" class="headerlink" title="参考"></a>参考</h1><ol><li>LaTeX写数学公式：<a href="https://www.jianshu.com/p/e6d2368e451a">https://www.jianshu.com/p/e6d2368e451a</a></li><li>LaTeX 中插入数学公式：<a href="https://blog.csdn.net/weixin_42373330/article/details/89785443">https://blog.csdn.net/weixin_42373330/article/details/89785443</a></li><li>Typora中利用LaTeX 插入数学公式: <a href="https://blog.csdn.net/happyday_d/article/details/83715440">https://blog.csdn.net/happyday_d/article/details/83715440</a></li><li>试试LaTeX插入数学公式：<a href="https://blog.csdn.net/baidu_38060633/article/details/79183905">https://blog.csdn.net/baidu_38060633/article/details/79183905</a></li><li>LaTeX官方文档：<a href="https://www.latex-project.org/help/">https://www.latex-project.org/help/</a></li><li>Tobias Oetiker,Hubert Partl, Irene Hyna and Elisabeth Schlegl. 中国CTEX 用户小组[译]. 一份不太简短的LATEX2 介绍。Version 3.20, 09 August, 2001</li></ol>]]></content>
<categories>
<category> 写作 </category>
</categories>
<tags>
<tag> LaTex </tag>
<tag> Math </tag>
</tags>
</entry>
<entry>
<title>【重坑】SQLErrorCodes loaded</title>
<link href="/2020/11/05/chong-keng-sqlerrorcodes-loaded/"/>
<url>/2020/11/05/chong-keng-sqlerrorcodes-loaded/</url>
<content type="html"><![CDATA[<h1 id="情况"><a href="#情况" class="headerlink" title="情况"></a>情况</h1><p>使用mysql 5.6版本<br>报错：异常 SQLErrorCodes loaded: [DB2, Derby, H2, HSQL, Informix, MS-SQL, MySQL, Oracle, PostgreSQL, Sybase]</p><p>通常来讲，这是我们的sql语句写错了（比如mybatis的mapper中的sql语句有错误）</p><p>但奇怪的是，我linux和windows都是同样版本的mysql，跑了同一份.sql文件。在windows平台的mysql下完美运行，而连接linux的mysql数据库就不行！</p><p>所以可能是权限设置问题（一般出现在Linux平台等对权限有要求的地方）</p><p> 这个情况在windows平台下并不常见，因为Windows对权限并没有严格要求。</p><h1 id="原因"><a href="#原因" class="headerlink" title="原因"></a>原因</h1><p>一般是由于root用户对全局host无访问权限。因此只要给root用户添加一个访问权限即可。 </p><h1 id="解决方案"><a href="#解决方案" class="headerlink" title="解决方案"></a>解决方案</h1><p>就我目前掌握的情况来看，出现这个问题的原因有很多，我遇到的是这两种情况，也是比较常见的。<br> 1.数据库的字段和输入的数据库的数据类型不匹配<br>比如说，一个字段int，你设置的长度是5，但是你输入了一个长度为6的值，就会出现这个错误。<br> 解决方法：</p><pre class="line-numbers language-bash"><code class="language-bash">找到有问题的字段，并加以改正<span aria-hidden="true" class="line-numbers-rows"><span></span></span></code></pre><p>2.权限设置问题（一般出现在Linux平台等对权限有要求的地方）<br> 这个情况在windows平台下并不常见，因为Windows对权限并没有严格要求。<br> 原因：一般是由于root用户对全局host无访问权限。因此只要给root用户添加一个访问权限即可。<br> 解决方案(此方案由网友提出，我使用后并未解决问题，正在尝试其他方法):</p><pre class="line-numbers language-bash"><code class="language-bash">登陆mysql ，执行mysql -u root -pPasswdmysql <span class="token operator">></span>grant all privileges on *.* to root@<span class="token string">"%"</span> identified by <span class="token string">"Passwd"</span><span class="token punctuation">;</span>mysql <span class="token operator">></span>flush privileges<span class="token punctuation">;</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><h1 id="参考"><a href="#参考" class="headerlink" title="参考"></a>参考</h1><p><a href="https://cloud.tencent.com/developer/article/1142524">https://cloud.tencent.com/developer/article/1142524</a></p>]]></content>
<categories>
<category> 运维 </category>
</categories>
<tags>
<tag> linux </tag>
<tag> 数据库 </tag>
<tag> sql </tag>
</tags>
</entry>
<entry>
<title>CentOs 安装本地yum仓库（createrepo+nginx实现）</title>
<link href="/2020/10/30/centos-an-zhuang-ben-di-yum-cang-ku-createrepo-nginx-shi-xian/"/>
<url>/2020/10/30/centos-an-zhuang-ben-di-yum-cang-ku-createrepo-nginx-shi-xian/</url>
<content type="html"><![CDATA[<h2 id="0-目的"><a href="#0-目的" class="headerlink" title="0. 目的"></a>0. 目的</h2><p>想要建立私有Yum仓库，方便运维。<br>我感觉搭建好以后，甚至可以当作自己的对象存储oss来用</p><h2 id="1-开始"><a href="#1-开始" class="headerlink" title="1. 开始"></a>1. 开始</h2><p>安装的系统为CentOs6。</p><pre><code>Linux gdei 2.6.32-754.el6.x86_64 #1 SMP Tue Jun 19 21:26:04 UTC 2018 x86_64 x86_64 x86_64 GNU/Linux</code></pre><p>服务器地址为：192.168.219.130（VM虚拟机）<br>先安装nginx，要不然没有网页端服务。不需要网页端的可以跳过。</p><h2 id="2-暂时关闭防火墙"><a href="#2-暂时关闭防火墙" class="headerlink" title="2. 暂时关闭防火墙"></a>2. 暂时关闭防火墙</h2><p>关闭iptables :</p><pre><code>service iptables stop</code></pre><p>关闭selinux:<br>查看SELinux状态：</p><pre><code>/usr/sbin/sestatus -v ##如果SELinux status参数为enabled即为开启状态getenforce ##也可以用这个命令检查</code></pre><p>关闭SELinux：<br>1、临时关闭（不用重启机器）：</p><pre><code>setenforce 0 ##设置SELinux 成为permissive模式 ##setenforce 1 设置SELinux 成为enforcing模式</code></pre><p>2、修改配置文件需要重启机器：<br>修改/etc/selinux/config 文件<br>将SELINUX=enforcing改为SELINUX=disabled<br>重启机器后关闭selinux</p><h2 id="3-安装createrepo"><a href="#3-安装createrepo" class="headerlink" title="3. 安装createrepo"></a>3. 安装createrepo</h2><p>准备软件仓库目录：</p><pre><code>mkdir /home/data -p</code></pre><p>使用yum的只下载不安装的方式进行下载软件(下载啥都行，此处以下载gcc为例，你也可以自己打包rmp然后放到仓库)</p><pre><code>yum install --downloadonly --downloaddir=/home/data gcc</code></pre><p>下载creatrepo：</p><pre><code>yum -y install createrepo</code></pre><p>开始运行服务：</p><pre><code>createrepo /yum/downloade/</code></pre><p>现在，自定义yum仓库已经搭建完成，目前只有gcc这一个包可供下载</p><h2 id="4-更新"><a href="#4-更新" class="headerlink" title="4. 更新"></a>4. 更新</h2><p>更新源数据：如果有新的软件包放入到软件仓库，这里就需要更新元数据。<br>也就是说每次将数据放入这个文件夹下想共享出去，放到这下面以后就要使用下面的命令更新一次。</p><pre><code>createrepo --update /home/data</code></pre><p>至此，搭建完成。</p><h2 id="5-使用Nginx制造网页端查看页面"><a href="#5-使用Nginx制造网页端查看页面" class="headerlink" title="5. 使用Nginx制造网页端查看页面"></a>5. 使用Nginx制造网页端查看页面</h2><p>要安装Nginx之前要安装epel，要不然装不了nginx</p><pre><code>yum install epel-release</code></pre><p>然后安装nginx</p><pre><code>yum install nginx</code></pre><p>开始配置nginx，配置完毕后网页端就能访问了</p><pre><code>cd /etc/nginx/conf.d/</code></pre><p>备份配置文件</p><pre><code>cp default.conf default.conf.bak</code></pre><p>开始修改配置文件</p><pre><code>vi default.conf </code></pre><p>修改成如下的样子</p><pre><code>server { listen 80; server_name 192.168.219.130; root /home/data; location / { autoindex on; autoindex_exact_size off; autoindex_localtime on; autoindex_format html; charset utf-8,gbk; root /home/data; } error_page 404 /404.html; location = /40x.html { } error_page 500 502 503 504 /50x.html; location = /50x.html { }}</code></pre><h2 id="6-成功"><a href="#6-成功" class="headerlink" title="6. 成功"></a>6. 成功</h2><p>访问192.168.219.130（服务器IP），成功！效果如下：</p><p><img src="https://vskendo-1255590242.cos.ap-guangzhou.myqcloud.com/2022/05/05/060035-e2.png" alt="image-20220505060035049"></p><p>点击文件，可以下载:</p><p><img src="https://vskendo-1255590242.cos.ap-guangzhou.myqcloud.com/2022/05/05/060047-03.png" alt="image-20220505060047071"></p><h2 id="7-使用"><a href="#7-使用" class="headerlink" title="7. 使用"></a>7. 使用</h2><p>需要使用yum的客户端，需编辑配置文件，命令操作如下所示：</p><pre class="line-numbers language-bash"><code class="language-bash"><span class="token function">cd</span> /etc/yum.repos.d/<span class="token function">cp</span> CentOS-Base.repo CentOS-Base.repo.bakvim CentOS-Base.repo<span class="token punctuation">[</span>base<span class="token punctuation">]</span> //中括号里内容要求唯一，但不要出现特殊字符name<span class="token operator">=</span>A <span class="token function">nice</span> description //此为描述信息，可以看情况填写baseurl<span class="token operator">=</span>http://192.168.219.130/ //此项为yum软件仓库位置enabled<span class="token operator">=</span>1 //此项为是否开启，1为开启, 0为不开启gpgcheck<span class="token operator">=</span>1 //此项为是否检查签名，1为检测, 0为不检测cost<span class="token operator">=</span>1000 <span class="token comment" spellcheck="true"># 默认yum仓库cost为1000, cost越小越优先</span>gpgkey<span class="token operator">=</span>0 //签名认证信息的路径//有些baseurl设置的稍微复杂，比如：//<span class="token variable">$releasever</span>/os/<span class="token variable">$basearch</span>///其中// <span class="token variable">$releasever</span> <span class="token comment" spellcheck="true"># 只替换主版本号</span>// <span class="token variable">$basearch</span> <span class="token comment" spellcheck="true"># 系统基本架构</span>//具体配置请自己根据yum的配置知识来陪<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre><p>运行以下命令生成缓存 ：</p><pre class="line-numbers language-bash"><code class="language-bash">yum clean allyum makecache<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span></span></code></pre><p>（因为有备份文件，随时可以换回来，所以不怕翻车）<br>附上阿里云的yum源配置文件下载（如果你是Centos7就将这个6换成7）</p><pre class="line-numbers language-bash"><code class="language-bash"><span class="token function">wget</span> http://mirrors.aliyun.com/repo/Centos-6.repo//用wget下载后，放到/etc/yum.repos.d/文件夹下，并改名为CentOS-Base.repo//再运行上面2个命令重新生成缓存即可。<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span></span></code></pre><h2 id="8-参考"><a href="#8-参考" class="headerlink" title="8.参考"></a>8.参考</h2><p>搭建yum私有仓库：<a href="https://www.jianshu.com/p/c7c2dea549b1?open_source=weibo_search">https://www.jianshu.com/p/c7c2dea549b1?open_source=weibo_search</a><br>搭建私有YUM仓库与内网镜像站：<a href="http://www.360doc.com/content/19/0819/08/36367108_855782032.shtml">http://www.360doc.com/content/19/0819/08/36367108_855782032.shtml</a><br>创建私有yum仓库：<a href="https://www.cnblogs.com/zakzhu/p/11632971.html">https://www.cnblogs.com/zakzhu/p/11632971.html</a><br>Linux yum 命令：<a href="https://www.runoob.com/linux/linux-yum.html">https://www.runoob.com/linux/linux-yum.html</a><br>搭建私有yum仓库：<a href="https://www.cnblogs.com/37yan/p/6879287.html">https://www.cnblogs.com/37yan/p/6879287.html</a></p>]]></content>
<categories>
<category> 运维 </category>
</categories>
<tags>
<tag> CentOs </tag>
<tag> createrepo </tag>
</tags>
</entry>
<entry>
<title>CentOS安装mfs3.0</title>
<link href="/2020/10/14/centos-an-zhuang-mfs3-0/"/>
<url>/2020/10/14/centos-an-zhuang-mfs3-0/</url>
<content type="html"><![CDATA[<h1 id="需求："><a href="#需求：" class="headerlink" title="需求："></a>需求：</h1><p>需要安装一个日志文件系统，于是服务器按要求装了centos6<br>有6块1TB的STAT hdd，还有一个300G的SAS作为系统盘。<br>日志要求使用nfs协议，考虑到维护、拓展等因素，决定搭建mfs，然后在这基础上使用nfs。<br>系统IP为内网IP：210.38.69.12/26<br>日志服务器和我的电脑IP段：10.2.100.0/19<br>（mfs好处真的多，不仅有web端管理界面，而且后期如果要加硬盘就只需要改改配置文件，维护太方便了）<br>PS：mfs可以当成raid0来用，即软RAID。6块1TB的硬盘通过mfs就变成了1块5TiB的大硬盘了！</p><h2 id="1-下载和查看官方文档"><a href="#1-下载和查看官方文档" class="headerlink" title="1 下载和查看官方文档"></a>1 下载和查看官方文档</h2><p>我是按照它一步步来的，本文可以配合官方文档来食用…<br>提供个官网，以备不时之需：</p><p>如果你是Ubuntu、MACOS系统，我的操作会和你有点不一样，这点可以在官方文档里找到解决方案<br>我会在本文最后列出一些参考网站，希望能对你有帮助。本文只是简单搭建，具体配置和优化还请自行百度。</p><h2 id="2-系统要求"><a href="#2-系统要求" class="headerlink" title="2 系统要求"></a>2 系统要求</h2><p>mfs要求使用FUSE，需要Linux API 7.8或以上，即内核版本号要在2.6.0以上。然后因为有些的Linux可能有bug，所以版本号最好在2.6.24以上。<br>centos7或以上就不需要管了肯定没问题，我刚好是6，所以用<code>uname -a</code>来查看内核版本号<br>我是2.6.32，幸好我支持…<br>其他要求就在文档里了，什么内存不小于多少多少，如何计算你需要多少空间啥的，没啥用我就不列出来了<br>【请在root下操作，请暂时关闭防火墙（centos6为iptables）或添加防火墙放行规则】</p><h2 id="3-一些概念"><a href="#3-一些概念" class="headerlink" title="3 一些概念"></a>3 一些概念</h2><p>我真不是复制黏贴党，简单说说Mfs安装的东西是什么以及有什么用。<br>Master Server（元数据服务器）：就是一个主服务器，用于控制存储服务器们<br>MetaLogger（元数据日志服务器）：备份Master服务器的变化日志文件，当master服务器损坏，这服务器可以恢复文件。【说白了如果不需要这个服务器可以不搭建】<br>Chunk Server（数据存储服务器）：这就是真正存数据的服务器了，里面挂载了大量的硬盘用来存数据，上面说的Master就是用来控制这个服务器的。<br>Client（客户端）： 可以像挂载NFS一样（但其本身不是NFS），挂载MFS文件系统。<br>一台服务器可以同时搭建Master Server+ Metalogger + Chunk Server + Client【究极四合一】</p><p>【根据上面的用途，可以得出结论：一般是搭建mfs的话是使用 一个Master和很多个这种Chunk Server，如果有需要的话还有个MetaLogger。客户端装个Client就完事了】</p><h2 id="4-开搞，安装主服务Master-Server"><a href="#4-开搞，安装主服务Master-Server" class="headerlink" title="4 开搞，安装主服务Master Server"></a>4 开搞，安装主服务Master Server</h2><p>开局先来5条命令<br><code>yum install rpm-build gcc gcc-c++ fuse-devel zlib-devel</code><br><code>useradd -s /sbin/nologin mfs</code><br><code>curl " http://ppa.moosefs.com/RPM -GPG -KEY - MooseFS " > /etc/pki/rpm -gpg/RPM -GPG -KEY -MooseFS</code><br>#centos7的话要将下面的el6改成el7<br> <code>curl " http://ppa.moosefs.com/MooseFS-3-el6.repo " > /etc/yum.repos.d/MooseFS.repo</code><br>更新一下yum<br><code>yum update</code><br>然后<br><code>yum install moosefs-master moosefs-cgi moosefs-cgiserv moosefs-cli</code><br>安装成功之后进入目录<br><code>cd / etc/ mfs</code><br>目录里有 cfg和 cfg.sample文件，通过diff我发现这两种文件是一样的…<br>我建议你先执行以下语句：<br><code>cp mfsmaster.cfg mfsmaster.cfg.bak</code><br><code>cp mfsexports.cfg mfsexports.cfg.bak</code><br>然后再是：<br><code>cp mfsmaster.cfg.sample mfsmaster.cfg</code><br><code>cp mfsexports.cfg.sample mfsexports.cfg</code><br>按照官方的说法，.cfg.sample文件是简单的例子，而.cfg是正在使用的配置文件，那既然这样我们就创建个.bak文件备份一下吧。<br>编辑mfsexports.cfg文件。这个文件是管理权限的，详细的文件意思可以百度或者看文档内的注释。<br>反正直接加上下面这条就好了<br><code>你客户端的网络号/你客户端的掩码 / rw,alldirs,maproot =0</code><br>（注意网络号不等于IP）<br>因为我电脑（win10）和日志服务器（CentOs）都在10.2.100.0/19网络中，所以我加的是<br><code>10.2.100.0/19 / rw,alldirs,maproot=0,password=mfs</code><br>即允许10.2.100.0/19中所有主机访问 MFS根目录 可读写、允许挂载任何指定的子目录、映射为root、密码为mfs<br>使用<code>mfsmaster -a start</code>来启动，网友建议启动时都加上<code>-a</code>，具体区别请自行百度。<br>其中，<code>mfsmaster stop</code>是关闭，<code>mfsmaster restart</code>是重启，这些基本知识就不说了。<br>如果没有报错，那么安装就成功了，记得将主服务器设为开机启动<br><code>chkconfig --add moosefs-master</code><br><code>chkconfig moosefs-master on</code> </p><h2 id="5-安装MFS元数据日志服务器"><a href="#5-安装MFS元数据日志服务器" class="headerlink" title="5 安装MFS元数据日志服务器"></a>5 安装MFS元数据日志服务器</h2><p>我没装，如果你要装可以看看本文最后面的参考资料。这个安装也简单。<br>【元数据日志守护进程是在安装master server 时一同安装的，最小的要求并不比master 本身大，可以被运行在任何机器上（例如任一台chunkserver），但是最好是放置在MooseFS master 的备份机上，备份master 服务器的变化日志文件，文件类型为changelog_ml.*.mfs。因为主要的master server 一旦失效，可能就会将这台metalogger 机器取代而作为master server。】</p><h2 id="6-安装web监视服务"><a href="#6-安装web监视服务" class="headerlink" title="6 安装web监视服务"></a>6 安装web监视服务</h2><p>按照官方文档的说法，只要是个Linux机器都能装这个监视服务，只要装了以后输入Master的ip就可以了。<br>但是官方强烈建议给装了Master Server的机器都装上这个web监视服务<br><code>yum install moosefs-cgi moosefs-cgiserv moosefs-cli</code><br>修改hosts文件 <code>vi /etc/hosts</code>，添加一条规则： <code>这台服务器的IP mfsmaster</code><br>然后就可以启动服务了<br><code>service moosefs-cgiserv start</code><br>web管理的URL是 <code>localhost:9425/mfs.cgi</code> ，其他电脑可以输入URL：<code>服务器IP:9425/mfs.cgi</code>进行访问<br>访问不了？看看防火墙设置！</p><h2 id="7-安装存储服务器Chunk-servers"><a href="#7-安装存储服务器Chunk-servers" class="headerlink" title="7 安装存储服务器Chunk servers"></a>7 安装存储服务器Chunk servers</h2><p>想要安装数据服务器(chunkservers)，这些机器的磁盘上不仅要有适当的剩余空间，还要求操作系统遵循POSIX 标准（如：Linux, FreeBSD, Mac OS X and OpenSolaris）。<br>如果你的Chunk服务器和Master服务器不是同一台，记得安装mfs的依赖<br><code>yum install rpm-build gcc gcc-c++ fuse-devel zlib-devel –y</code><br> <code>useradd -s /sbin/nologin mfs</code><br>然后安装<code>yum install moosefs-chunkserver</code><br>备份一下配置文件。<br><code>cd /etc/mfs</code><br><code>cp mfschunkserver.cfg mfschunkserver.cfg.bak</code><br><code>cp mfshdd.cfg mfshdd.cfg.bak</code><br><code>cp mfschunkserver.cfg.sample mfschunkserver.cfg</code><br><code>cp mfshdd.cfg.sample mfshdd.cfg</code><br>这个时候你在文件mfshdd.cfg中指定要使用哪些硬盘，然后启动服务就搞定了<br>比如假设我要使用sde和sdc两块硬盘，那么久<br><code>chown -R mfs:mfs /mnt/sde</code><br><code>chown -R mfs:mfs /mnt/sdc</code><br>然后在mfshdd.cfg文件中添加2行<br><code>/mnt/sde</code><br><code>/mnt/sdc</code><br>启动服务<br><code>service moosefs-chunkserver start</code><br>加入开机启动项<br><code>chkconfig --add moosefs-chunkserver</code><br><code>chkconfig moosefs-chunkserver on</code><br>安装完成<br>但是我的服务器插了6块1T的硬盘还没挂载…我6块硬盘分别是 sdb sdc sdd sde sdf sdg<br>于是我要先将它们格式化，然后设置成开机自动挂载，然后挂载。<br><code>mkfs -t ext3 /dev/sdb</code><br><code>mkfs -t ext3 /dev/sdc</code><br><code>mkfs -t ext3 /dev/sdd</code><br><code>mkfs -t ext3 /dev/sde</code><br><code>mkfs -t ext3 /dev/sdf</code><br><code>mkfs -t ext3 /dev/sdg</code><br>所以我要用上面的格式化指令先格式化6块盘<br>然后在mnt目录下创建6个目录<br><code>mkdir -p /mnt/sdb</code><br><code>mkdir -p /mnt/sdc</code><br><code>mkdir -p /mnt/sdd</code><br><code>mkdir -p /mnt/sde</code><br><code>mkdir -p /mnt/sdf</code><br><code>mkdir -p /mnt/sdg</code><br>然后挂载我亲爱的STAT盘<br><code>mount /dev/sdb /mnt/sdb/</code><br><code>mount /dev/sdc /mnt/sdc/</code><br><code>mount /dev/sdd /mnt/sdd/</code><br><code>mount /dev/sde /mnt/sde/</code><br><code>mount /dev/sdf /mnt/sdf/</code><br><code>mount /dev/sdg /mnt/sdg/</code><br>更改权限<br><code>chown -R mfs:mfs /mnt/sdb chown -R mfs:mfs /mnt/sdc chown -R mfs:mfs /mnt/sdd chown -R mfs:mfs /mnt/sde chown -R mfs:mfs /mnt/sdf chown -R mfs:mfs /mnt/sdg</code><br>然后还得开机自动挂载，要不然重启一下chunk服务器就找不到磁盘咯<br><code>ll /dev/disk/by-uuid/</code>查找所有硬盘的UUID<br>然后<code>vim /etc/fstab</code>，在最后面加上6行（我UUID就删了哈，不给你们看）<br><code>UUID= /mnt/sdb ext3 defaults 0 0 UUID= /mnt/sdc ext3 defaults 0 0 UUID= /mnt/sdd ext3 defaults 0 0 UUID= /mnt/sde ext3 defaults 0 0 UUID= /mnt/sdf ext3 defaults 0 0 UUID= /mnt/sdg ext3 defaults 0 0</code><br>最后在/etc/mfs/mfshdd.cfg下增加6行<br><code>/mnt/sdb /mnt/sdc /mnt/sdd /mnt/sde /mnt/sdf /mnt/sdg</code><br>启动chunk服务，增加chunk服务开机自动启动，完事。</p><h2 id="8-验证安装结果"><a href="#8-验证安装结果" class="headerlink" title="8 验证安装结果"></a>8 验证安装结果</h2><p>所有服务都搭载在210.38.69.12上，没有问题</p><p><img src="https://vskendo-1255590242.cos.ap-guangzhou.myqcloud.com/2022/05/05/060526-91.png" alt="image-20220505060526805"></p><p>至此，mfs搭建完成</p><h2 id="参考资料"><a href="#参考资料" class="headerlink" title="参考资料"></a>参考资料</h2><p>MFS官网：<a href="http://www.moosefs.com/">http://www.moosefs.com</a><br>MFS分布式文件系统：<a href="https://blog.51cto.com/13555423/2082796">https://blog.51cto.com/13555423/2082796</a><br>MFS分布式文件系统：<a href="https://cloud.tencent.com/developer/article/1520226">https://cloud.tencent.com/developer/article/1520226</a><br>Linux的企業-分布式文件系統mfs（moosefs）搭建與配置：<a href="https://www.itread01.com/content/1508786402.html">https://www.itread01.com/content/1508786402.html</a></p>]]></content>
<categories>
<category> 运维 </category>
</categories>
<tags>
<tag> CentOS </tag>
<tag> mfs </tag>
</tags>
</entry>
</search>