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对齐等号，使该行已经对齐

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对齐等号，使该行已经对齐

我有一个align问题。基本上是以下代码：

\begin{align} 
    \nonumber & \exp\left(-\sum_{t=1}^T\lambda_t f_t(x_1)\right)\exp(-\mu-1) + \exp\left(-\sum_{t=1}^T\lambda_t f_t(x_2)\right)\exp(-\mu-1) \\ 
    \nonumber & \cdots + \exp\left(-\sum_{t=1}^T\lambda_t f_t(x_k)\right)\exp(-\mu-1)  = 1 \\ 
    \nonumber &  \sum_{i=1}^k \exp\left(-\sum_{t=1}^T \lambda_t f_t(x_i) \right)  = \exp(\mu+1) \\  
              &  \exp(-\mu-1)  = \frac{1}{\displaystyle{\sum_{i=1}^k} \exp\left(-\displaystyle{\sum_{t=1}^T} \lambda_t f_t(x_i) \right)}  
\end{align}

产生以下内容：

对齐1

但是我想让第 2、3 和 4 行的等号全部对齐，我该怎么做？（第 2 行是第 1 行的延续）。

答案1

一些想法：

代码

\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{equation}
\begin{split}
\exp\left(-\sum_{t=1}^T\lambda_t f_t(x_1)\right)\exp(-\mu-1) & + \exp\left(-\sum_{t=1}^T\lambda_t f_t(x_2)\right)\exp(-\mu-1) \\
  \cdots + \exp\left(-\sum_{t=1}^T\lambda_t f_t(x_k)\right)\exp(-\mu-1)  & = 1 \\
   \sum_{i=1}^k \exp\left(-\sum_{t=1}^T \lambda_t f_t(x_i) \right) & = \exp(\mu+1) \\
            \exp(-\mu-1) & = \frac{1}{\displaystyle{\sum_{i=1}^k} \exp\left(-\displaystyle{\sum_{t=1}^T} \lambda_t f_t(x_i) \right)}
\end{split}
\end{equation}

\begin{alignat}{6}
\mathrlap{\exp\left(-\sum_{t=1}^T\lambda_t f_t(x_1)\right)\exp(-\mu-1)  + \exp\left(-\sum_{t=1}^T\lambda_t f_t(x_2)\right)\exp(-\mu-1)} \nonumber\\
&&\dots + \exp\left(-\sum_{t=1}^T\lambda_t f_t(x_k)\right)\exp(-\mu-1)  & = 1 \nonumber\\
&&\sum_{i=1}^k \exp\left(-\sum_{t=1}^T \lambda_t f_t(x_i) \right) & = \exp(\mu+1) \nonumber\\
&&\exp(-\mu-1) & = \frac{1}{\displaystyle{\sum_{i=1}^k} \exp\left(-\displaystyle{\sum_{t=1}^T} \lambda_t f_t(x_i) \right)}
\end{alignat}

\begin{multline}
\exp\left(-\sum_{t=1}^T\lambda_t f_t(x_1)\right)\exp(-\mu-1) + \exp\left(-\sum_{t=1}^T\lambda_t f_t(x_2)\right)\exp(-\mu-1) \\
\begin{aligned}
  \cdots + \exp\left(-\sum_{t=1}^T\lambda_t f_t(x_k)\right)\exp(-\mu-1)  & = 1 \\
   \sum_{i=1}^k \exp\left(-\sum_{t=1}^T \lambda_t f_t(x_i) \right) & = \exp(\mu+1) \\
            \exp(-\mu-1) & = \frac{1}{\displaystyle{\sum_{i=1}^k} \exp\left(-\displaystyle{\sum_{t=1}^T} \lambda_t f_t(x_i) \right)}
\end{aligned}
\end{multline}
\end{document}

输出

在此处输入图片描述

答案2

这也许能满足你的要求：

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{multline}
\exp\left(-\sum_{t=1}^T\lambda_t f_t(x_1)\right)\exp(-\mu-1) + \exp\left(-\sum_{t=1}^T\lambda_t f_t(x_2)\right)\exp(-\mu-1) \\
\begin{aligned}
 \cdots + \exp\left(-\sum_{t=1}^T\lambda_t f_t(x_k)\right)\exp(-\mu-1)  &= 1 \\
 \sum_{i=1}^k \exp\left(-\sum_{t=1}^T \lambda_t f_t(x_i) \right)  &= \exp(\mu+1) \\
 \exp(-\mu-1)  &= \frac{1}{\displaystyle{\sum_{i=1}^k} \exp\left(-\displaystyle{\sum_{t=1}^T} \lambda_t f_t(x_i) \right)}
\end{aligned}
\end{multline}
\end{document}

示例代码的输出

答案3

在此处输入图片描述

\documentclass[preview,border=12pt]{standalone}
\usepackage{amsmath}
\begin{document}
\begin{gather}
\exp\left(-\sum_{t=1}^T\lambda_t f_t(x_1)\right)\exp(-\mu-1) + \exp\left(-\sum_{t=1}^T\lambda_t f_t(x_2)\right)\exp(-\mu-1) \notag\\
\begin{aligned}
 \cdots + \exp\left(-\sum_{t=1}^T\lambda_t f_t(x_k)\right)\exp(-\mu-1)  &= 1 \\
 \sum_{i=1}^k \exp\left(-\sum_{t=1}^T \lambda_t f_t(x_i) \right)  &= \exp(\mu+1) \\
 \exp(-\mu-1)  &= \frac{1}{\displaystyle{\sum_{i=1}^k} \exp\left(-\displaystyle{\sum_{t=1}^T} \lambda_t f_t(x_i) \right)}
\end{aligned}
\end{gather}
\end{document}

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