如何将一行中的多个等式向左对齐？（下面还有另一行，当我将其向左移动时，上面的行会向右移动）

Question

如何将此表达式左对齐？以及字母y也左对齐？

\documentclass{article}

\usepackage{amsmath}
\usepackage{mathtools}
\begin{document}
\begin{flalign}
    \dfrac{\partial\hat F}{\partial w_{i,j}^m}
   & = 
    \dfrac{\partial\hat F}{\partial n_{i}^m}\cdot \dfrac{\partial n_i^m}{\partial w_{i,j}^m}\label{partialF/w}
  &  =
    \dfrac{\partial\hat F}{\partial n_{i}^m}\cdot 
    a_j^{m-1}
   & =
    \left(\dfrac{\partial n_i^{m+1} }{\partial n_{i}^m}\right)^T\dfrac{\partial\hat F}{\partial n_{i}^{m+1}}\cdot 
    a_j^{m-1}& =
  %  \letf(
    w_{i,j}^{m+1}\dfrac{\partial f^m(n_j^m)}{\partial n_j^m}%\right)
    \dfrac{\partial\hat F}{\partial n_{i}^{m+1}}\cdot 
    a_j^{m-1}\\
     \implies
     \dfrac{\partial\hat F}{\partial w_{i,j}^m}=\dfrac{\partial\hat F}{\partial n_{i}^m}\cdot 
    a_j^{m-1}=  w_{i,j}^{m+1}\dfrac{\partial f^m(n_j^m)}{\partial n_j^m}%\right)
    \dfrac{\partial\hat F}{\partial n_{i}^{m+1}}\cdot 
    a_j^{m-1} \label{F/w simp}
    \\
    y \nonumber
 \end{flalign}
 \end{document}

请注意，出于某种原因，在上图中（与上面的代码相对应），它\implies在左侧（如预期的那样），而在下图中则居中，我不知道为什么。我拥有的原始文档是下图。

我检查过另一篇文章如何将方程式左对齐？我遵循了这个答案的建议https://tex.stackexchange.com/a/467116/，但正如您所见，它对我来说不起作用。

有人可以帮忙吗？

提前致谢

Answer 1

我认为强制对齐不会让事情变得更清晰。而且，既然“暗示”符号可以用文字代替，那就应该这样做。

\documentclass{article}

\usepackage{amsmath}
\usepackage{mathtools}

\newcommand{\pder}[2]{\frac{#1}{#2}}


\begin{document}

\begin{align*}
%\label{partialF/w}
\pder{\hat{F}}{w_{i,j}^m}
& = \pder{\hat{F}}{n_{i}^m}\cdot \pder{n_i^m}{w_{i,j}^m}
\\
& = \pder{\hat{F}}{n_{i}^m}\cdot a_j^{m-1}
\\
& = \left(\pder{n_i^{m+1}}{n_{i}^m}\right)^{\!T}\pder{\hat{F}}{n_{i}^{m+1}}\cdot a_j^{m-1}
\\
& = w_{i,j}^{m+1}\pder{f^m(n_j^m)}{n_j^m}\pder{\hat{F}}{n_{i}^{m+1}}\cdot a_j^{m-1}
\end{align*}
or, in summary,
\begin{equation}\label{F/w simp}
\pder{\hat{F}}{w_{i,j}^m}
= \pder{\hat{F}}{n_{i}^m}\cdot a_j^{m-1}
= w_{i,j}^{m+1}\pder{f^m(n_j^m)}{n_j^m} \pder{\hat{F}}{n_{i}^{m+1}}\cdot a_j^{m-1} 
\end{equation}

\end{document}

我定义了偏导数的简写，使得输入不那么麻烦。

推导中的方程编号已被删除，因为这只是一个技术论点，并且最后一个方程包含相同的信息。

Answer 2

这可能与 Zarko 的类似，它适合页面，但我猜不出您想用最后的浮动 y 做什么。

\documentclass{article}
\usepackage{amsmath}
\usepackage{mathtools}
\begin{document}
\begin{flalign}
    \dfrac{\partial\hat F}{\partial w_{i,j}^m}
   & = 
    \dfrac{\partial\hat F}{\partial n_{i}^m}\cdot \dfrac{\partial n_i^m}{\partial w_{i,j}^m}\label{partialF/w}\\
  &  =
    \dfrac{\partial\hat F}{\partial n_{i}^m}\cdot 
    a_j^{m-1}\\
   & =
    \left(\dfrac{\partial n_i^{m+1} }{\partial n_{i}^m}\right)^T\dfrac{\partial\hat F}{\partial n_{i}^{m+1}}\cdot 
    a_j^{m-1}\\
  & =
  %  \letf(
    w_{i,j}^{m+1}\dfrac{\partial f^m(n_j^m)}{\partial n_j^m}%\right)
    \dfrac{\partial\hat F}{\partial n_{i}^{m+1}}\cdot 
    a_j^{m-1}\\
     &\implies\\
     \dfrac{\partial\hat F}{\partial w_{i,j}^m}
     &=\dfrac{\partial\hat F}{\partial n_{i}^m}\cdot 
    a_j^{m-1}\\
    &=  w_{i,j}^{m+1}\dfrac{\partial f^m(n_j^m)}{\partial n_j^m}%\right)
    \dfrac{\partial\hat F}{\partial n_{i}^{m+1}}\cdot 
    a_j^{m-1} \label{F/w simp}
    \\
    y \nonumber
 \end{flalign}
 \end{document}

或者可能是两个对齐

\documentclass{article}

\usepackage{mathtools}
\begin{document}
\begin{align}
    \frac{\partial\hat F}{\partial w_{i,j}^m}
   & = 
    \frac{\partial\hat F}{\partial n_{i}^m}\cdot \frac{\partial n_i^m}{\partial w_{i,j}^m} \label{partialF/w} \\
  &  =
    \frac{\partial\hat F}{\partial n_{i}^m}\cdot 
    a_j^{m-1}  \nonumber\\
   & =
    \left(\frac{\partial n_i^{m+1} }{\partial n_{i}^m}\right)^T\frac{\partial\hat F}{\partial n_{i}^{m+1}}\cdot 
    a_j^{m-1}  \nonumber\\
  & =
     w_{i,j}^{m+1}\frac{\partial f^m(n_j^m)}{\partial n_j^m}%\right)
    \frac{\partial\hat F}{\partial n_{i}^{m+1}}\cdot a_j^{m-1} \nonumber
\end{align}
This implies
\begin{align}
     \frac{\partial\hat F}{\partial w_{i,j}^m}
     &=\frac{\partial\hat F}{\partial n_{i}^m}\cdot 
    a_j^{m-1}\label{F/w simp} \\
    &=  w_{i,j}^{m+1}\frac{\partial f^m(n_j^m)}{\partial n_j^m}%\right)
    \frac{\partial\hat F}{\partial n_{i}^{m+1}}\cdot 
    a_j^{m-1} \nonumber
 \end{align}
something about $y$
 \end{document}

Answer 3

编辑： 已更正的是 MWE——添加了遗漏的代码行并考虑了 OP 在下面的评论中给出的更改：。

您正在寻找这样的东西吗？

\documentclass{article}
\usepackage{mathtools}

\begin{document}
\begin{align}
\frac{\partial\hat F}{\partial w_{i,j}^m}
  & = \frac{\partial\hat F}{\partial n_{i}^m}\cdot \frac{\partial n_i^m}{\partial w_{i,j}^m}  \label{partialF/w}      \\
  &  =
    \frac{\partial\hat F}{\partial n_{i}^m}\cdot
    a_j^{m-1}               \\
  & =
    \left(\frac{\partial n_i^{m+1} }{\partial n_{i}^m}\right)^T\frac{\partial\hat{ F}}{\partial n_{i}^{m+1}}\cdot
    a_j^{m-1}               \\
  & = w_{i,j}^{m+1}\frac{\partial f^m(n_j^m)}{\partial n_j^m}%\right)
    \frac{\partial\hat F}{\partial n_{i}^{m+1}}\cdot
    a_j^{m-1}               \\
\implies  \frac{\partial\hat F}{\partial w_{i,j}^m}    
    & = \frac{\partial\hat F}{\partial n_{i}^m}\cdot a_j^{m-1}
      =  w_{i,j}^{m+1}\frac{\partial f^m(n_j^m)}{\partial n_j^m} 
                      \frac{\partial\hat{F}}{\partial n_{i}^{m+1}}\cdot a_j^{m-1}           
        \label{partialF/w simp}
\end{align}
y
\end{document}

或这个？

\documentclass{article}
\usepackage{mathtools}

\begin{document}
\begin{align}
\frac{\partial\hat F}{\partial w_{i,j}^m}
  & = \frac{\partial\hat F}{\partial n_{i}^m}\cdot \frac{\partial n_i^m}{\partial w_{i,j}^m}
        \label{partialF/w}      \\
  &  = \frac{\partial\hat F}{\partial n_{i}^m}\cdot a_j^{m-1} 
     = \left(\frac{\partial n_i^{m+1} }{\partial n_{i}^m}\right)^T
             \frac{\partial\hat{ F}}{\partial n_{i}^{m+1}}\cdot a_j^{m-1}               
                        \notag  \\
  & = w_{i,j}^{m+1}\frac{\partial f^m(n_j^m)}{\partial n_j^m}
    \frac{\partial\hat F}{\partial n_{i}^{m+1}}\cdot
    a_j^{m-1}   
                                \\
\implies \frac{\partial\hat F}{\partial w_{i,j}^m}
  & = \frac{\partial\hat F}{\partial n_{i}^m}\cdot a_j^{m-1}
    =  w_{i,j}^{m+1}\frac{\partial f^m(n_j^m)}{\partial n_j^m}
    \frac{\partial\hat F}{\partial n_{i}^{m+1}}\cdot a_j^{m-1}
        \label{F/w simp}
\shortintertext{y}
\frac{\partial\hat F}{\partial w_{i,j}^m}
  & = \text{continuation of derivation}
        \label{partialF/extra}
\end{align}
\end{document}