Scale of braces of cases environment in tabular

Question

I want to format a cases environment inside a table such that the braces have some offset from the horizontal lines. By default this distance is zero, and if the rowheight is adjusted using \extrarowheight the braces simply scale proportionally. I was not able to achieve better results using \array.

Does anybody have an idea how to typeset this correctly?

\documentclass[12pt]{article}

\usepackage[a4paper, top = 0.1cm, left = 0.1cm, right = 0.1cm, bottom = 0.1cm, bindingoffset=0cm]{geometry}
\usepackage[utf8]{inputenc}
\usepackage{mathtools}
\usepackage{multirow}

\newcommand{\ROC}{\text{ROC}}

\begin{document}

\begin{tabular}{@{}c|c|c@{}}
    $F(z)$ & $\ROC(f)$ & $f[.]$\\\hline
    \multirow{2}{*}{$\dfrac{z}{z-p}$} & $|z| > |p|$ & $f[k] = \begin{cases}\hphantom{-}0, \quad &k<0\\\hphantom{-}p^k, \quad &k\ge 0\end{cases}$\\\cline{2-3}
    & $0 < |z| < |p|$ & $f[k] =  \begin{cases}-p^k, \quad &k<0\\\hphantom{-}0, \quad &k\ge 0\end{cases}$\\\hline 
    \multirow{2}{*}{\shortstack{$\dfrac{Az}{z-p} + \dfrac{\overline{A}z}{z-p}$\\$=2z\dfrac{z\text{Re}(A)-\text{Re}(A\overline{p})}{z^2 - 2z\text{Re}(p)+|p|^2}$}} & $|z| > |p|$ & $f[k] = \begin{cases}\hphantom{-}0, & k<0\\\hphantom{-}2|A||p|^k\cos(\Omega k+\varphi), &k\ge 0   \end{cases}$\\\cline{2-3}
    & $0<|z|<|p|$ & $f[k] = \begin{cases}-2|A||p|^k\cos(\Omega k+\varphi), & k<0\\\hphantom{-} 0, &k\ge 0   \end{cases}$
\end{tabular}

\end{document}

Answer 1

With use of makegapedcells defined in the makecell package:

\documentclass[12pt]{article}
\usepackage[a4paper, margin= .1cm, 
            bindingoffset=0cm]{geometry}
\usepackage{mathtools}
\usepackage{makecell, multirow}

\newcommand{\ROC}{\text{ROC}}

\begin{document}
    \[
\setcellgapes{3pt}
\makegapedcells
\begin{array}{@{}c|c|c@{}}
F(z)    &   \ROC(f)         &   f[.]    \\  
    \hline
\multirow{4.4}{*}{$\dfrac{z}{z-p}$} 
        &   |z| > |p|       &   f[k] = \begin{cases}
                            \hphantom{-}0, \quad    &  k<0   \\
                            \hphantom{-}p^k, \quad  &   k\ge 0
                                    \end{cases} \\
    \cline{2-3}
        &   0 < |z| < |p|   &   f[k] = \begin{cases}
                            -p^k, \quad         &   k<0 \\\
                            \hphantom{-}0, \quad &   k\ge 0
                                        \end{cases} \\
    \hline
\multirow{4.4}{*}{$\begin{aligned}
    & \dfrac{Az}{z-p} + \dfrac{\overline{A}z}{z-p}  \\
    & = 2z\dfrac{z\text{Re}(A)-\text{Re}(A\overline{p})}
                {z^2 - 2z\text{Re}(p)+|p|^2}
                \end{aligned}$} 
        &   |z| > |p|       &   f[k] = \begin{cases}
                                \hphantom{-}0, & k<0    \\
                                \hphantom{-}2|A||p|^k\cos(\Omega k+\varphi), &  k\ge 0
                                        \end{cases}     \\
    \cline{2-3}
    &   0<|z|<|p|           &   f[k] = \begin{cases}
                            -2|A||p|^k\cos(\Omega k+\varphi),   & k<0\\
                            \hphantom{-} 0,                     &k\ge 0   
                                \end{cases}
\end{array}
    \]
\end{document}

Note: with use of the array inside of math environment instead of the tabular, you can omit all $ in table except in \multirow cells.

Answer 2

One possibility is to use booktabs package and replace every \hline by \midrule and \cline{2-3} with \cmidrule{2-3} as follows:

\documentclass[12pt]{article}

\usepackage[a4paper, top = 0.1cm, left = 0.1cm, right = 0.1cm, bottom = 0.1cm, bindingoffset=0cm]{geometry}
\usepackage[utf8]{inputenc}
\usepackage{mathtools}
\usepackage{multirow}
\usepackage{booktabs}

\newcommand{\ROC}{\text{ROC}}

\begin{document}

\begin{tabular}{@{}c|c|c@{}}
    $F(z)$ & $\ROC(f)$ & $f[.]$\\\midrule
    \multirow{2}{*}{$\dfrac{z}{z-p}$} & $|z| > |p|$ & $f[k] = \begin{cases}\hphantom{-}0, \quad &k<0\\\hphantom{-}p^k, \quad &k\ge 0\end{cases}$\\\cmidrule{2-3}
    & $0 < |z| < |p|$ & $f[k] =  \begin{cases}-p^k, \quad &k<0\\\hphantom{-}0, \quad &k\ge 0\end{cases}$\\\midrule 
    \multirow{2}{*}{\shortstack{$\dfrac{Az}{z-p} + \dfrac{\overline{A}z}{z-p}$\\$=2z\dfrac{z\text{Re}(A)-\text{Re}(A\overline{p})}{z^2 - 2z\text{Re}(p)+|p|^2}$}} & $|z| > |p|$ & $f[k] = \begin{cases}\hphantom{-}0, & k<0\\\hphantom{-}2|A||p|^k\cos(\Omega k+\varphi), &k\ge 0   \end{cases}$\\\cmidrule{2-3}
    & $0<|z|<|p|$ & $f[k] = \begin{cases}-2|A||p|^k\cos(\Omega k+\varphi), & k<0\\\hphantom{-} 0, &k\ge 0   \end{cases}$
\end{tabular}

This gives the following output:

Answer 3

I would get rid of all vertical and almost all horizontal rules, left-align the cell contents, use array instead of tabular, double the value of \arraycolsep, and use the \addlinespace macro to create whitespace-type ("negative space") between the rows. I'd also clean up and streamline the LaTeX code; e.g., replace \overline with \bar, use an aligned environment rather than a \shortstack directive, and set up \ROC and \Re as math operators. (Many thanks to @egreg for suggesting the latter changes.)

\documentclass[12pt]{article}

\usepackage[a4paper, margin=5mm, bindingoffset=0cm]{geometry}
% \usepackage[utf8]{inputenc} % is the default
\usepackage[T1]{fontenc}
\usepackage{mathtools} % for '\DeclarePairedDelimiter' macro
\DeclarePairedDelimiter\abs\lvert\rvert
\usepackage{booktabs}

\DeclareMathOperator{\ROC}{ROC}
\renewcommand\Re{\operatorname{Re}}

\begin{document}

\[
\setlength\arraycolsep{10pt} % default: 5pt
\begin{array}{@{} lll @{}}
    F(z) & \ROC(f) & f[k] \\
    \midrule %\hline
    \dfrac{z}{z-p}
    & \abs{z} > \abs{p} 
    & \begin{cases}
             \hphantom{-}0   &\text{if $k<0$}\\
             \hphantom{-}p^k &\text{if $k\ge0$}
             \end{cases} \\
    \addlinespace %\cline{2-3}
    & 0 < \abs{z} < \abs{p} 
    & \begin{cases}
          -p^k          &\text{if $k<0$}\\
          \hphantom{-}0 &\text{if $k\ge0$}
      \end{cases} \\
    \addlinespace[2\defaultaddspace] % \hline 
     \smash[b]{%
         \begin{aligned}[t]
            &\frac{Az}{z-p} + \frac{\bar{A}z}{z-p} \\
            &=2z\frac{z\Re(A)-\Re(A\bar{p})}{z^2 - 2z\Re(p)+\abs{p}^2}
         \end{aligned}}
    & \abs{z} > \abs{p} 
    & \begin{cases}
             \hphantom{-}0  & \text{if $k<0$}\\
             \hphantom{-}2\abs{A}\abs{p}^k\cos(\Omega k+\varphi) &\text{if $k\ge0$}   
      \end{cases} \\
    \addlinespace % \cline{2-3}
    & 0<\abs{z}<\abs{p} 
    & \begin{cases}
             -2\abs{A}\abs{p}^k\cos(\Omega k+\varphi) & \text{if $k<0$}\\
             \hphantom{-} 0 &\text{if $k\ge0$}   
      \end{cases}
\end{array}
\]

\end{document}

Answer 4

Here is a version with {NiceArray} of nicematrix.

This package provides two keys cell-space-top-limit and cell-space-bottom-limit (similar to the commands \cellspacetoplimit and \cellspacebottomlimit of cellspace).

\documentclass[12pt]{article}

\usepackage[a4paper, top = 0.1cm, left = 0.1cm, right = 0.1cm, bottom = 0.1cm, bindingoffset=0cm]{geometry}
\usepackage{mathtools}
\usepackage{nicematrix}

\newcommand{\ROC}{\text{ROC}}

\begin{document}

\NiceMatrixOptions{cell-space-top-limit=3pt,cell-space-bottom-limit=3pt}

$\begin{NiceArray}{@{}c|c|c@{}}
    F(z) & \ROC(f) & f[.]\\
    \Hline
    \Block{2-1}{\dfrac{z}{z-p}} & |z| > |p| & 
    f[k] = \begin{cases}\hphantom{-}0, \quad &k<0\\\hphantom{-}p^k,     \quad &k\ge 0\end{cases}\\
    \Hline
    & 0 < |z| < |p| & f[k] =  \begin{cases}-p^k, \quad &k<0\\\hphantom{-}0, \quad &k\ge 0\end{cases}\\
    \Hline
    \Block{2-1}{\dfrac{Az}{z-p} +
  \dfrac{\overline{A}z}{z-p}\\[4mm]  =2z\dfrac{z\text{Re}(A)-\text{Re}(A\overline{p})}{z^2 - 2z\text{Re}(p)+|p|^2}} 
     & |z| > |p| & f[k] = \begin{cases}\hphantom{-}0, & k<0\\\hphantom{-}2|A||p|^k\cos(\Omega k+\varphi), &k\ge
     0   \end{cases}\\
    \Hline
    & 0<|z|<|p| & f[k] = \begin{cases}-2|A||p|^k\cos(\Omega k+\varphi), & k<0\\\hphantom{-} 0, &k\ge 0   \end{cases}
\end{NiceArray}$

\end{document}

In your case, there is two avantages in using nicematrix.

• The command \Block will center the content in the mathematical center of the merged cells (there is no need for manual adjustment as with \multirow).

• A command \Hline will draw the rule excepted in the blocks (created by \Block): it's more easy to use than \cline.

You need several compilations (because nicematrix uses PGF/Tikz nodes).