Generating matrices with a single command

Question

Suppose I wanted to generate a 5x4 matrix. A good way to do it is to write the following commands:

    \[
    \begin{tikzpicture}
        \matrix(m) [matrix of nodes, ampersand replacement=\&, row sep=1ex, column sep=1ex, nodes in empty cells, nodes={shape=rectangle,minimum height=3ex, anchor=center},] {                                
            $A_{11}$  \& $A_{12}$ \& $A_{13}$ \& $A_{14}$  \\
            $A_{21}$  \& $A_{22}$ \& $A_{23}$ \& $A_{24}$  \\
            $A_{31}$  \& $A_{32}$ \& $A_{33}$ \& $A_{34}$  \\
            $A_{41}$  \& $A_{42}$ \& $A_{43}$ \& $A_{44}$  \\
            $A_{51}$  \& $A_{52}$ \& $A_{53}$ \& $A_{54}$  \\
        };
        \node[fit= (m-1-1.north west) (m-5-4.south east), left delimiter={[}, right delimiter={]},inner sep=1ex] {};
    \end{tikzpicture}            
    \]

(I use tikz because it allows me to format individual matrix elements and insert graphics). This can get rather tiring if I have to populate a 10x9 matrix. The idea is to write a NewDocumentCommand with three inputs: the letter denoting the matrix, the number of rows and the number of columns. Using expl3 I should be able to generate the matrix contents. Then I should be able to write something like,

    \begin{tikzpicture}
        \matrix(m) [matrix of nodes, ampersand replacement=\&, row sep=1ex, column sep=1ex, nodes in empty cells, nodes={shape=rectangle,minimum height=3ex, anchor=center},] {    
           \matrixcontents                      
        };
        \node[fit= (m-1-1.north west) (m-#2-#3.south east), left delimiter={[}, right delimiter={]},inner sep=1ex] {};
    \end{tikzpicture}

where \matrixcontents contains

            $A_{11}$  \& $A_{12}$ \& $A_{13}$ \& $A_{14}$  \\
            $A_{21}$  \& $A_{22}$ \& $A_{23}$ \& $A_{24}$  \\
            $A_{31}$  \& $A_{32}$ \& $A_{33}$ \& $A_{34}$  \\
            $A_{41}$  \& $A_{42}$ \& $A_{43}$ \& $A_{44}$  \\
            $A_{51}$  \& $A_{52}$ \& $A_{53}$ \& $A_{54}$  \\

and #2, #3 are respectively the number of rows, number of columns arguments of the NewDocumentCommand (in this example #1 is the letter A).

I am an absolute beginner with expl3 and so I have no idea how to generate \matrixcontents.

Answer 1

Here's how you can do it:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix,fit}
\ExplSyntaxOn
\NewDocumentCommand{\matrixcontents}{mmm}
 {% #1 = symbol, #2 = number of rows, #3 = number of columns
  \tl_clear:N \l_tmpa_tl
  \int_step_inline:nn { #2 }
   {% ##1 = row index
    \int_step_inline:nn { #3 - 1 }
     {% ####1 = column index
      \tl_put_right:Nn \l_tmpa_tl { $#1\sb{##1####1}$ & }
     }
    \tl_put_right:Nn \l_tmpa_tl { $#1\sb{##1#3}$ \ }
   }
  \tl_use:N \l_tmpa_tl
 }
\ExplSyntaxOff
\begin{document}
[
\begin{tikzpicture}
  \matrix(m) [
    matrix of nodes,
     ampersand replacement=&,
     row sep=1ex,
     column sep=1ex,
     nodes in empty cells,
     nodes={
       shape=rectangle,
       minimum height=3ex,
       anchor=center
     },
   ]{
      \matrixcontents{A}{5}{4}
   };
   \node[
     fit= (m-1-1.north west) (m-5-4.south east),
     left delimiter={[},
     right delimiter={]},
     inner sep=1ex
   ] {};
 \end{tikzpicture}
 ]
\end{document}

The code performs a loop on the rows and in each one a loop on the columns (the last cell in a row is special).

Even shorter:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix,fit}
\NewDocumentCommand{\symbolicmatrix}{O{}mmm}{%
  % #1 = further options, #2 = symbol, #3 = number of rows, #4 = number of columns
  \matrix(m) [
    matrix of nodes,
     ampersand replacement=&,
     row sep=1ex,
     column sep=1ex,
     nodes in empty cells,
     nodes={
       shape=rectangle,
       minimum height=3ex,
       anchor=center
     },#1,
   ]{\matrixcontents{#2}{#3}{#4}};
   \node[
     fit= (m-1-1.north west) (m-#3-#4.south east),
     left delimiter={[},
     right delimiter={]},
     inner sep=1ex
   ] {};
}
\ExplSyntaxOn
\NewDocumentCommand{\matrixcontents}{mmm}
 {% #1 = symbol, #2 = number of rows, #3 = number of columns
  \tl_clear:N \l_tmpa_tl
  \int_step_inline:nn { #2 }
   {% ##1 = row index
    \int_step_inline:nn { #3 - 1 }
     {% ####1 = column index
      \tl_put_right:Nn \l_tmpa_tl { $#1\sb{##1####1}$ & }
     }
    \tl_put_right:Nn \l_tmpa_tl { $#1\sb{##1#3}$ \ }
   }
  \tl_use:N \l_tmpa_tl
 }
\ExplSyntaxOff
\begin{document}
[
\begin{tikzpicture}
  \symbolicmatrix{A}{5}{4}
\end{tikzpicture}
]
\end{document}

The \symbolicmatrix command has a leading optional argument for more options to the \matrix command.

For instance

\[
\begin{tikzpicture}
  \symbolicmatrix[row sep=2ex,column sep=2ex]{A}{5}{4}
\end{tikzpicture}
\]

would produce

Answer 2

For information, the package nicematrix provides commands to generated matrices where each cell is in a TikZ node (it's not a tikz-matrix).

\documentclass{article}
\usepackage{nicematrix,tikz}
\begin{document}
$\bAutoNiceMatrix[name=A]{5-4}{A_{\arabic{iRow},\arabic{jCol}}}$
\begin{tikzpicture}[remember picture, overlay]
\draw [<-] (A-5-2) -- ++ (0,-5mm) node [below] {$x$} ; 
\end{tikzpicture}
\end{document}

Answer 3

This is similar to @egreg's answer, but builds the matrix body with expandable code, the result should be faster code (but I didn't benchmark). Also the tikzpicture environment is included in the macro (you might remove it if you don't want this).

I hope the comments are enough to explain the code.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix, fit}
\ExplSyntaxOn
\int_new:N \l__ted_matrix_cols_int
\tl_new:N \l__ted_matrix_variable_tl
\cs_new:Npn __ted_matrix_row:n #1
  {
    % after we built a row we need to remove the leading \exp_not:N & from the
    % first cell
    \exp_last_unbraced:Ne \use_none:nn
      {
        % \prg_replicate:nn needs two steps of expansion
        % we use it instead of an \int_map_... because there is no \int_map_...
        % that allows us to expandably forward additional arguments (#1)
        \exp_args:No \use_ii_i:on
          { \prg_replicate:nn \l__ted_matrix_cols_int __ted_matrix_cell:nnN }
          { __ted_matrix_cell:nnN 1 {#1} }
        % the \use_none:nn ends the __ted_matrix_cell:nnN loop
        \use_none:nn
      }
    \exp_not:N \
  }
\cs_generate_variant:Nn \use_ii_i:nn { o }
% simple loop to return each cell
\cs_new:Npn __ted_matrix_cell:nnN #1#2#3
  {
    % will be wrapped in two e-expansion contexts, inner one is from the row,
    % outer one is from building the entire body
    % $, #1, #2, and \sb don't need protection against further expansion.
    \exp_not:n { \exp_not:N & $ \exp_not:V \l__ted_matrix_variable_tl \sb { #2#1 } $ }
    \exp_args:Ne #3 { \int_eval:n { #1 + 1 } } {#2}
  }
\NewDocumentCommand \tmatrix { O{} m m m }
  {
    \begin{tikzpicture}
      \tl_set:Nn \l__ted_matrix_variable_tl {#2}
      % we store #4-1 because one is hardcoded by the way we start the loop to
      % build each cell of a row.
      \int_set:Nn \l__ted_matrix_cols_int { #4 - 1 }
      \exp_args:Nne \use:n
        {
          \matrix(m) [matrix~of~nodes, ampersand~replacement=&,
            row~sep=1ex, column~sep=1ex, nodes~in~empty~cells,
            nodes={shape=rectangle,minimum~height=3ex, anchor=center}, #1]
        }
        { \int_step_function:nN {#3} __ted_matrix_row:n }
        ;
      \node[fit= (m-1-1.north~west) (m-#3-#4.south~east), left~delimiter={[},
        right~delimiter={]},inner~sep=1ex]
        {};
    \end{tikzpicture}
  }
\ExplSyntaxOff
\begin{document}
\tmatrix{A}{5}{4}
\end{document}

Result: