[Tex/LaTex] split and align long equation

alignequations

The following code is used to split a long in-equation.

\begin{align}
(\sum^n_{i,j=1}\frac{(S_{t})_{ij}\norm{W^T_{t+1}x_i-W^T_{t+1}x_j}_2^2}{2\norm{W^T_{t}x_i-W^T_{t}x_j}_2} - \nonumber \\
 \lambda_ttr(W^T_{t+1}XX^TW_{t+1})) \leq \nonumber \\
(\sum^n_{i,j=1}\frac{(S_{t})_{ij}\norm{W^T_tx_i-W^T_tx_j}_2^2}{2\norm{W^T_tx_i-W^T_tx_j}_2}- \nonumber \\
\lambda_ttr(W^T_tXX^TW_t))
\end{align}

The screenshot of the result is attached:
enter image description here

I'm not satisfied with the above result. Is it possible to make the
equation center aligned:

enter image description here

Best Answer

Presumably you need this number of lines because of a two column document. I would not want to center the lines because of the different operators - and \leq. Instead I would prefer a staggered output where each newline on the left of the equation starts further to the left than those after the \leq and on each side the first line is further left than the subsequent ones. One way to achieve this is:

Sample output

\documentclass[twocolumn]{article}

\usepackage{mathtools}
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
\DeclareMathOperator{\tr}{tr}

\usepackage{lipsum} % for dummy text

\begin{document}

\lipsum[1]
\begin{equation}
  \begin{split}
    \MoveEqLeft
    \sum^n_{i,j=1}\frac{(S_{t})_{ij}\norm{W^T_{t+1}x_i-W^T_{t+1}x_j}_2^2}{2\norm{W^T_{t}x_i-W^T_{t}x_j}_2} \\
    \MoveEqLeft[1] - \lambda_t\tr(W^T_{t+1}XX^TW_{t+1})\\
    &\leq
    \sum^n_{i,j=1}\frac{(S_{t})_{ij}\norm{W^T_tx_i-W^T_tx_j}_2^2}{2\norm{W^T_tx_i-W^T_tx_j}_2} \\
    &\qquad -\lambda_t\tr(W^T_tXX^TW_t)
  \end{split}
\end{equation}

\end{document}

Other changes introduced

definition of \norm via \DeclarePairedDelimiter
definition of \tr
use of just equation when it is one single equation, subsequent division with split

Another possibility would be to use multiline and perhaps mulitlined for the two sides of the equation.

Related Solutions

[Tex/LaTex] Adding text line in Equation Environment

I think flalign* and \intertext{} are very good for you.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{flalign*}
& & T_{Loop Filter}(s)&=K_{p}+\frac{K_{i}}{s} & & \\
\intertext{The overall transfer function of given PLL can be given as}
& & \frac{{\phi}_{c}(s)}{{\phi}(s)}&=\frac{T_{Loop Filter}(s)*\frac{1}{s}}{1+\frac{T_{Loop Filter}}(s)*\frac{1}{s}} & & \\
& & \frac{\phi_{c}(s)}{\phi(s)}&=\frac{K_{p}(s)+K_{i}}{s^{2}+K_{p}(s)+K_{i}} & & 
\intertext{In general transfer function for a second order closed loop control system is given as}
& & T_{second order}&=\frac{{\omega}^2+{2{\delta}}{\omega}s}{s_{2}+2{\delta}{\omega}s+{\omega}^{2}} & & \\
& \rlap{\text{On comparing}} & {\omega}&={sqrt{K_i}}  {\delta}=\frac{K_p}{2\sqrt{K_{i}}} & &
\end{flalign*}
\end{document}

[Tex/LaTex] Getting extra equation numbers using align environment

Just omit the line-break directive at the end of the final equation in a given align group. E.g.,

\begin{align}
    P(t) &= \tfrac{3}{2}[v_d(t)i_d(t)] \\
    Q(t) &= \tfrac{3}{2}[-v_d(t)i_q(t)] % <- no "\\" directive
\end{align}

As the code shows, I would also (a) remove the \left and \right qualifiers as they actually don't do anything for the cases at hand and (b) replace \frac with \tfrac.

If you have a multi-line equation that should be assigned just one equation number, don't use an align environment. Instead, use a split environment inside an equation environment.

By the way, the arrows produced by \overrightarrow look disproportionately large; consider using \vec instead. For arrows (and other diacritics) set above the characters i and j, it's traditional to omit the "dot", i.e., to use a "dotless" i and j; this may be achieved in math mode by writing \imath and \jmath. Separately, I again would not use \left and \right to autosize the round parentheses and curly braces; consider using \bigl and \bigr instead. (By the way, the outermost round parentheses may be omitted in all three rows, right?)

\documentclass{article}
\usepackage{amsmath}
\numberwithin{equation}{section}
\begin{document}

\setcounter{section}{1} % just for this example 
\setcounter{equation}{31}
\begin{align}
    P(t) &= \tfrac{3}{2}[v_d(t)i_d(t)] \\
    Q(t) &= \tfrac{3}{2}[-v_d(t)i_q(t)] 
\end{align}

\setcounter{equation}{20} % just for this example
\begin{equation}\begin{split}
P(t) 
&= \frac{
\Re\bigl\{\vec{v}(t)\vec{\imath}(t)\bigr\} + 
\Re\bigl\{\vec{v}(t)\vec{\imath}(t)^*\bigr\}}{2} \\
&\quad+ \frac{
\Re\bigl\{\vec{v}(t)\vec{\imath}(t)e^{-j\frac{4\pi}{3}}\bigr\} + 
\Re\bigl\{\vec{v}(t)\vec{\imath}(t)^*\bigr\}}{2} \\
&\quad+ \frac{
\Re\bigl\{\vec{v}(t)\vec{\imath}(t)e^{-j\frac{8\pi}{3}}\bigr\} + 
\Re\bigl\{\vec{v}(t)\vec{\imath}(t)^*\bigr\}}{2} 
\end{split}\end{equation}
\end{document}

Best Answer

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[Tex/LaTex] Adding text line in Equation Environment

[Tex/LaTex] Getting extra equation numbers using align environment

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