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请将方程式拟合到一页上的向量元素中

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请将方程式拟合到一页上的向量元素中

我试图将方程式放入一个名为的向量中，Fs我无法在一个 pdf 页面上查看所有方程式

\begin{eqnarray*}

\mathbf{Fs} &\mathbf{=}& \\

&=&T^{-1}\left[ 
\begin{array}{c}
\omega _{1}\sum_{i=1}^{T}\hat{u}_{i}+2\hat{u}_{1}\sum_{k=1}^{\left(
T-1\right) /2}\omega _{2k}+2\sum_{k=1}^{\left( T-1\right) /2}\left(
\sum_{i=1}^{T-1}\hat{u}_{i+1}\cos \left( \frac{2ki\pi }{T}\right) \right)
\omega _{2k} \\ 
\omega _{1}\sum_{i=1}^{T}\hat{u}_{i}+2\hat{u}_{1}\sum_{k=1}^{\left(
T-1\right) /2}\omega _{2k}\cos \left( \frac{2k\pi }{T}\right)
+2\sum_{k=1}^{\left( T-1\right) /2}\left[ \omega _{2k}\cos \left( \frac{%
2k\pi }{T}\right) \sum_{i=1}^{T-1}\hat{u}_{i+1}\cos \left( \frac{2ki\pi }{T}%
\right) +\omega _{2k+1}\sin \left( \frac{2k\pi }{T}\right) \sum_{i=1}^{T-1}%
\hat{u}_{i+1}\sin \left( \frac{2ki\pi }{T}\right) \right]  \\ 
\omega _{1}\sum_{i=1}^{T}\hat{u}_{i}+2\hat{u}_{1}\sum_{k=1}^{\left(
T-1\right) /2}\omega _{2k}\cos \left( \frac{4k\pi }{T}\right)
+2\sum_{k=1}^{\left( T-1\right) /2}\left[ \omega _{2k}\cos \left( \frac{%
4k\pi }{T}\right) \sum_{i=1}^{T-1}\hat{u}_{i+1}\cos \left( \frac{2ki\pi }{T}%
\right) +\omega _{2k+1}\sin \left( \frac{4k\pi }{T}\right) \sum_{i=1}^{T-1}%
\hat{u}_{i+1}\sin \left( \frac{2ki\pi }{T}\right) \right]  \\ 
\vdots  \\ 
\omega _{1}\sum_{i=1}^{T}\hat{u}_{i}+2\hat{u}_{1}\sum_{k=1}^{\left(
T-1\right) /2}\omega _{2k}\cos \left( \frac{2k\left( T-1\right) \pi }{T}%
\right) +2\sum_{k=1}^{\left( T-1\right) /2}\left[ \omega _{2k}\cos \left( 
\frac{2k\left( T-1\right) \pi }{T}\right) \sum_{i=1}^{T-1}\hat{u}_{i+1}\cos
\left( \frac{2ki\pi }{T}\right) +\omega _{2k+1}\sin \left( \frac{2k\left(
T-1\right) \pi }{T}\right) \sum_{i=1}^{T-1}\hat{u}_{i+1}\sin \left( \frac{%
2ki\pi }{T}\right) \right] 
\end{array}%
\right] 
\end{eqnarray*}

答案1

如果您使用\mfrac命令、from nccmath（中等大小的分数，~80% 的显示样式）、\smashoperatorfrommathtools和aligned最长行的环境，它甚至可以全部放在一行上。

注意nccmath还有一个medsize环境和一个\medop开关。

我将eqnarray*不再使用的 替换为align*from amsmath，并将\left[\begn{array} … \end{array}\right]构造替换为更简单的\begin{bmatrix} … \end{bmatrix}。

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{fourier, heuristica}
\usepackage[showframe]{geometry}
\usepackage{array, mathtools,bm, nccmath}

\begin{document}

\begin{align*}
  \MoveEqLeft
  \\
  \bm{Fs=}T^{-1}
                                                                                                  & \begin{bmatrix}%{c }
  \omega _{1}\sum\limits_{i=1}^{T}\hat{u}_{i}+2\hat{u}_{1}\!\!\smashoperator[r]{\sum\limits_{k=1}^{\left(
  T-1\right) /2}}\omega _{2k}+2\!\!\sum\limits_{k=1}^{\left( T-1\right) /2}\left(
  \sum\limits_{i=1}^{T-1}\hat{u}_{i+1}\cos \left( \mfrac{2ki\pi }{T}\right) \right)
  \omega _{2k} \\[3.5ex]
  %
  \begin{aligned}\omega _{1}\sum_{i=1}^{T}\hat{u}_{i}+2\hat{u}_{1}\!\!\!\smashoperator[r]{\sum\limits_{k=1}^{\left(
  T-1\right) /2}}\omega _{2k}\cos \left( \mfrac{2k\pi }{T}\right)
  +2\!\!\sum_{k=1}^{\left( T-1\right) /2}\Biggl[ \omega _{2k}\cos \left( \mfrac{2k\pi }{T}\right) & \sum_{i=1}^{T-1}\hat{u}_{i+1}\cos \left( \mfrac{2ki\pi }{T}\right) \\
  {} + {} \omega _{2k+1}\sin \left( \mfrac{2k\pi }{T}\right) & \sum_{i=1}^{T-1}%
  \hat{u}_{i+1}\sin \left( \mfrac{2ki\pi }{T}\right) \Biggr]
  \end{aligned}\\[5ex]
  %
  \begin{aligned}
  \omega _{1}\sum_{i=1}^{T}\hat{u}_{i}+2\hat{u}_{1}\!\!\!\smashoperator[r]{\sum_{k=1}^{\left(
  T-1\right) /2}}\omega _{2k}\cos \left( \mfrac{4k\pi }{T}\right)
  +2\!\!\sum_{k=1}^{\left( T-1\right) /2}\biggl[ \omega _{2k}\cos \left( \mfrac{%
  4k\pi }{T}\right) & \sum_{i=1}^{T-1}\hat{u}_{i+1}\cos \left( \mfrac{2ki\pi }{T}%
  \right) \\
  {}+{}\omega _{2k+1}\sin \left( \mfrac{4k\pi }{T}\right) & \sum_{i=1}^{T-1}%
  \hat{u}_{i+1}\sin \left( \mfrac{2ki\pi }{T}\right) \Biggr] \\
  \end{aligned}\\[-2ex]
  %
  \vdots \\[-1.5ex]
  \vdots \\
  %
  \begin{aligned}
  \omega _{1}\sum_{i=1}^{T}\hat{u}_{i}+2\hat{u}_{1}\!\!\!\smashoperator[r]{\sum_{k=1}^{\left(
  T-1\right) /2}}\omega _{2k}\cos \left( \mfrac{2k\left( T-1\right) \pi }{T}%
  \right) +2\!\!\sum_{k=1}^{\left( T-1\right) /2}\Biggl[ \omega _{2k}\cos \left(
  \mfrac{2k\left( T-1\right) \pi }{T}\right) & \sum_{i=1}^{T-1}\hat{u}_{i+1}\cos
  \left( \mfrac{2ki\pi }{T}\right) \\
  +\omega _{2k+1}\sin \left( \mfrac{2k\left(
  T-1\right) \pi }{T}\right) & \sum_{i=1}^{T-1}\hat{u}_{i+1}\sin \left(\mfrac{%
  2ki\pi }{T}\right) \Biggr] \\[0.5ex]
  \end{aligned}
  \end{bmatrix}%
\end{align*}

\vskip 1cm
 {\small\begin{align*}
      \bm{Fs=}T^{-1}
                                                                                                      &\begin{medsize} \begin{bmatrix}%{c }
      \displaystyle\omega _{1}\sum_{i=1}^{T}\hat{u}_{i}+2\hat{u}_{1}\smashoperator[r]{\sum_{k=1}^{
      \tfrac{T-1}{2}}}\omega _{2k}+2 \smashoperator[l]{\sum_{k=1}^{\tfrac{T-1}{2}}}\left(
      \sum\limits_{i=1}^{T-1}\hat{u}_{i+1}\cos \frac{2ki\pi }{T}\right)
      \omega _{2k} \\[3ex]
      %
      \displaystyle\omega _{1}\sum_{i=1}^{T}\hat{u}_{i}+2\hat{u}_{1}\smashoperator{\sum_{k=1}^{
      \tfrac{T-1}{2}}}\omega _{2k}\cos \frac{2k\pi }{T}
      +2 \smashoperator[l]{\sum_{k=1}^{\tfrac{T-1}{2}}}\left(\omega _{2k}\cos \frac{2k\pi }{T} \sum_{i=1}^{T-1}\hat{u}_{i+1}\cos \frac{2ki\pi }{T} + \omega _{2k+1}\sin \frac{2k\pi }{T} \sum_{i=1}^{T-1}%
      \hat{u}_{i+1}\sin \frac{2ki\pi }{T}\right)
     \\[3ex]
      \displaystyle\omega _{1}\sum_{i=1}^{T}\hat{u}_{i} + 2\hat{u}_{1}\smashoperator{\sum_{k=1}^{\tfrac{T-1}{2}}} \omega_{2k}\cos \mfrac{4k\pi }{T}
      + 2 \smashoperator[l]{\sum_{k=1}^{\tfrac{T-1}{2}}} \left(\omega _{2k}\cos\mfrac{%
      4k\pi }{T} \sum_{i=1}^{T-1}\hat{u}_{i+1}\cos \mfrac{2ki\pi }{T}%
      + \omega _{2k+1}\sin \mfrac{4k\pi }{T} \sum_{i=1}^{T-1}%
      \hat{u}_{i+1}\sin \mfrac{2ki\pi }{T}\right) \\
\\[-3ex]
      %
      \vdots \\[-1.5ex]
      \vdots \\[-1.5ex]
      %
      \displaystyle \omega_{1}\sum_{i=1}^{T}\hat{u}_{i}+2\hat{u}_{1}\smashoperator{\sum_{k=1}^{
      \tfrac{T-1}{2}}}\omega _{2k}\cos \frac{2k( T-1) \pi }{T}%
       +2\smashoperator[l]{\sum_{k=1}^{ \tfrac{T-1}{2}}} \left(\omega _{2k}\cos \frac{2k( T-1) \pi }{T}
      \sum_{i=1}^{T-1}\hat{u}_{i+1}\cos \frac{2ki\pi }{T}
      + \omega_{2k+1}\sin \frac{2k( T-1)\pi}{T} \sum_{i=1}^{T-1}\hat{u}_{i+1}\sin \frac{2ki\pi}{T}\right)\rule[-3.5ex]{0pt}{3ex}
      \end{bmatrix}%
\end{medsize}
    \end{align*}
}
\end{document}

在此处输入图片描述

答案2

如果您希望有人真正阅读并理解该公式，则必须将其拆分：

% arara: pdflatex

\documentclass{article}
\usepackage{mathtools}
\usepackage{upgreek}
\let\pi\uppi
\allowdisplaybreaks

\begin{document}
\begin{align*}
    \mathbf{Fs} &= T^{-1}
    \begin{bmatrix}
        A \\ 
        B \\ 
        C \\ 
        \vdots \\ 
        Z
    \end{bmatrix}
    \shortintertext{where}
    A &= \omega_{1}\sum_{i=1}^{T}\hat{u}_{i} +2\hat{u}_{1} \smashoperator{\sum_{k=1}^{(T-1)/2}}\omega_{2k} + 2 \smashoperator[l]{\sum_{k=1}^{(T-1)/2}} \bigg(\sum_{i=1}^{T-1}\hat{u}_{i+1}\cos\biggl(\frac{2ki\pi }{T}\biggr)\biggr)\omega_{2k} \\
    \begin{split}
        B &= \omega_{1}\sum_{i=1}^{T}\hat{u}_{i} + 2\hat{u}_{1}\smashoperator{\sum_{k=1}^{(T-1)/2}}\omega_{2k}\cos\biggl(\frac{2k\pi}{T}\biggr) \\
        &\qquad+2\smashoperator[l]{\sum_{k=1}^{(T-1)/2}}\Biggl[\omega_{2k}\cos\biggl(\frac{2k\pi}{T}\biggr) \sum_{i=1}^{T-1}\hat{u}_{i+1}\cos\biggl(\frac{2ki\pi}{T}\biggr) \\
        &\qquad\hphantom{+2\smashoperator[l]{\sum_{k=1}^{(T-1)/2}}\Biggl[}+ \omega_{2k+1}\sin\biggl(\frac{2k\pi}{T}\biggr) \sum_{i=1}^{T-1}\hat{u}_{i+1}\sin\biggl(\frac{2ki\pi}{T}\biggr)\Biggr]
    \end{split}\\
    \begin{split}
        C &= \omega_{1}\sum_{i=1}^{T}\hat{u}_{i}+2\hat{u}_{1}\smashoperator{\sum_{k=1}^{(T-1)/2}}\omega_{2k}\cos\biggl(\frac{4k\pi}{T}\biggr) \\
        &\qquad+2\smashoperator[l]{\sum_{k=1}^{(T-1)/2}}\Biggl[\omega_{2k}\cos\biggl(\frac{4k\pi}{T}\biggr) \sum_{i=1}^{T-1}\hat{u}_{i+1}\cos\biggl(\frac{2ki\pi}{T}\biggr) \\&\qquad\hphantom{+2\smashoperator[l]{\sum_{k=1}^{(T-1)/2}}\Biggl[}+\omega_{2k+1}\sin\biggl(\frac{4k\pi}{T}\biggr)\sum_{i=1}^{T-1}
        \hat{u}_{i+1}\sin\biggl(\frac{2ki\pi}{T}\biggr)\Biggr]
    \end{split}\\
    \begin{split}
        Z &= \omega_{1}\sum_{i=1}^{T}\hat{u}_{i} + 2\hat{u}_{1}\smashoperator{\sum_{k=1}^{(T-1)/2}}\omega_{2k}\cos\biggl(\frac{2k(T-1)\pi}{T}\biggr) \\
        &\qquad+2\smashoperator[l]{\sum_{k=1}^{(T-1)/2}}\Biggl[\omega_{2k}\cos\biggl(\frac{2k(T-1)\pi}{T}\biggr) \sum_{i=1}^{T-1}\hat{u}_{i+1}\cos\biggl(\frac{2ki\pi}{T}\biggr) \\
        &\qquad\hphantom{+2\smashoperator[l]{\sum_{k=1}^{(T-1)/2}}\Biggl[}+\omega_{2k+1}\sin\biggl(\frac{2k(T-1)\pi}{T})\sum_{i=1}^{T-1}\hat{u}_{i+1}\sin\biggl(\frac{2ki\pi}{T}\biggr)\Biggr]
    \end{split}
\end{align*}
\end{document}

在此处输入图片描述

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