Adding vertical lines around row vectors in block matrices

Question

I would like to produce a 3x3 block matrix with a layout shown in the left figure below. The matrix is split by a row vector d-e-f and a column vector b-e-h (so e represents a 1x1 submatrix). I would like to add two horizontal and two vertical lines to separate the 9 blocks (4 matrices, 4 vectors, 1 scalar).

I am using the NiceArray commands of the nicematrix package, which work as intended if I use two-row blocks (see the left matrix below). However, when I am trying to typeset the row vector d-e-f using one-row blocks (i.e. changing \Block{2-2}{d} to \Block{1-2}{d} and so on), the vertical lines break (see the example on the right). Adding/removing the \hline commands has no effect on the vertical lines. I am using TeX Live 2019 with nicematrix version 3.7.

Is there a way I can keep vertical lines around submatrix e without using two-row blocks?

\documentclass{article}
\usepackage{nicematrix}
\begin{document}

\[
\begin{pNiceArray}{cc|c|cc}[margin]
    \Block{2-2}{a} & & \Block{2-1}{b} & \Block{2-2}{c} & \\
                   & &                &                & \\\hline
    \Block{2-2}{d} & & \Block{2-1}{e} & \Block{2-2}{f} & \\
                   & &                &                & \\\hline
    \Block{2-2}{g} & & \Block{2-1}{h} & \Block{2-2}{i} & \\
                   & &                &                & \\
\end{pNiceArray}
\quad
\begin{pNiceArray}{cc|c|cc}[margin]
    \Block{2-2}{a} & & \Block{2-1}{b} & \Block{2-2}{c} & \\
                   & &                &                & \\
    \Block{1-2}{d} & & \Block{1-1}{e} & \Block{1-2}{f} & \\\hline
    \Block{2-2}{g} & & \Block{2-1}{h} & \Block{2-2}{i} & \\
                   & &                &                & \\
\end{pNiceArray}
\]

\end{document}

Update: ultimately, I'd like to substitute the a...i with formulas representing the submatrices, e.g. A_{00}, a_{01}^\mathsf{T}, etc. I'd also like to illustrate that a and i are square matrices but c and g are not necessarily square ones.

Here is an example output with realistic values:

\documentclass{article}
\usepackage{nicematrix}
\begin{document}

\setlength{\extrarowheight}{1mm}
\setlength{\arraycolsep}{8pt}
\[
\begin{pNiceArray}{ccc|c|ccccc}[margin]
    \Block{3-3}{A_{00}} & & & \Block{3-1}{a_{01}} & \Block{3-4}{A_{20}^\mathsf{T}} & & & \\
     & & & & & & & \\
     & & & & & & & \\ \hline
     % I'd like to use the following line but it doesn't work as expected:
     %\Block{1-3}{a_{01}^\mathsf{T}} & & & \Block{1-1}{0} & \Block{1-4}{a_{21}^\mathsf{T}} & & & \\
     % two-row blocks are fine:
     \Block{2-3}{a_{01}^\mathsf{T}} & & & \Block{2-1}{0} & \Block{2-4}{a_{21}^\mathsf{T}} & & & \\
     & & & & & & & \\ \hline
     \Block{4-3}{A_{20}} & & & \Block{4-1}{a_{21}} & \Block{4-4}{A_{22}} & & & \\
     & & & & & & & \\
     & & & & & & & \\
     & & & & & & & \\
\end{pNiceArray}
\]

\end{document}

Answer 1

Similar as suggested @leandriis in his comment. Your blocks are simulated with more space around submatrix:

Edit:

Considering matrix content as you provided in edited question

\documentclass{article}
\usepackage{array,
            makecell}    % new

\begin{document}
\[\setcellgapes{3pt}
  \makegapedcells
\left(
\begin{array}{ccc|c|ccc}
    &           &&          &&              &   \\
    & A_{00}    && a_{01}   &&   A_{20}^T   &   \\
    &           &&          &&              &   \\   \hline
    & a_{01}^T  && 0        &&  f           &   \\   \hline
    &           &&          &&              &   \\
    & A_{20}    && a_{21}   &&  A_{22}^T    &   \\
    &           &&          &&              &   \\
\end{array}\right)
\]
\end{document}

Note: empty rows and column are add for emphasizing where dimension submatrix are bigger than 1 x 1. If this is not necessary, simple dropout them out.

Answer 2

It turns out this is a bug in the current version of the nicematrix package. This has been fixed in version 3.8 (2020-01-02) and is available on CTAN.

If you're stuck with an older version for some reason, the bug can be worked around by adding \vline at the end of the affected cells. Applying this on the minimal working example gives the desired output:

\documentclass{article}
\usepackage{nicematrix}
\begin{document}

\setlength{\extrarowheight}{1mm}
\setlength{\arraycolsep}{8pt}
\[
\begin{pNiceArray}{ccc|c|ccccc}[margin]
    \Block{3-3}{A_{00}} & & & \Block{3-1}{a_{01}} & \Block{3-4}{A_{20}^\mathsf{T}} & & & \\
    & & & & & & & \\
    & & & & & & & \\ \hline
    \Block{1-3}{a_{01}^\mathsf{T}} & & \vline & \Block{1-1}{0} \vline & \Block{1-4}{a_{21}^\mathsf{T}} & & & \\\hline
    \Block{4-3}{A_{20}} & & & \Block{4-1}{a_{21}} & \Block{4-4}{A_{22}} & & & \\
    & & & & & & & \\
    & & & & & & & \\
    & & & & & & & \\
\end{pNiceArray}
\]

\end{document}

Answer 3

A variant solution:

\documentclass{article}
\usepackage{amsmath} %

\begin{document}


\[ \renewcommand{\arraystretch}{1.4}
  \left[\,\:\begin{matrix}
     a & \vrule & b & \vrule & c \\
    \hline
     d & \vrule & e & \vrule & f \\
    \hline
     g & \vrule & h &\vrule & i
    \end{matrix}
\,\: \right]
\]

\end{document}