Specifying an array columnwise in math mode

Question

I would like to do the same sort of thing as in the question How to create table column wise in LaTeX?, except that I want to do it in math mode.

To be precise: I want to enter an array of items of possibly different sizes, similar to the matrix environment, except that in the LaTeX source code I want to specify one column of items and the next column, and so on, instead of specifying the items by row as usual. I want the result to be vertically centered like the matrix environment.

I also want to be able to specify the amount of horizontal and vertical space between the items.

Here is an mwe to show what I mean.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
    x = 
    \begin{matrix}
        1 & 4 \
        2 & 5 \
        3 & \Big(6\Big) \
    \end{matrix} 
\end{equation}
\end{document}

In this LaTeX code, the items appear in the order 1, 4, 2, 5, 3, 6, but I want to specify them in the order 1, 2, 3, 4, 5, 6.

(Actually, even better than that would be 3, 2, 1, 6, 5, 4 - column-wise but with the columns specified in reverse order. But I can imagine this being difficult and will be happy enough with the 1, 2, 3, 4, 5, 6 order.)

Here's what the mwe output looks like.

There is a related question, Is there a way to automatically transpose a matrix written in Latex?, but because that question is asking specifically about transposing a matrix, the answers don't end up having a way to specify the space between elements. I'm hoping for a simpler solution along the lines of the top answer at How to create table column wise in LaTeX?, which is more about stacking boxes on top of each other than doing hefty expl3 stuff.

Answer 1

\valign primitive was designed for such a task:

\def\iskip{\vskip2pt plus1fil}
$$
  x = 
  \vcenter{\hbox{\valign{&\iskip\hbox to1.5em{\hss$#$\hss}\iskip\cr
     1 & 2 & 3 \cr
     4 & 5 & (6) \cr
  }}}
$$
\bye

Answer 2

You can even use the proposed syntax (bottom up):

\documentclass{article}
\usepackage{amsmath}
\ExplSyntaxOn
\NewDocumentCommand{\rmatrix}{O{2}m}
 {% #1 is the number of columns, default 2
  % #2 is a comma separated list of items
  \virgo_rmatrix:nn { #1 } { #2 }
 }
\seq_new:N \l__virgo_rmatrix_items_seq
\tl_new:N \l__virgo_rmatrix_body_tl
\int_new:N \l__virgo_rmatrix_rows_int
\cs_new_protected:Nn \virgo_rmatrix:nn
 {
  % this will contain the body
  \tl_clear:N \l__virgo_rmatrix_body_tl
  % make a sequence from the items
  \seq_set_from_clist:Nn \l__virgo_rmatrix_items_seq { #2 }
  % check if the number of items is a multiple of #1
  \int_compare:nF
   {
    \int_mod:nn { \seq_count:N \l__virgo_rmatrix_items_seq } { #1 } == 0
   }
   {% not a multiple, pad
    \prg_replicate:nn
     { #1 - \int_mod:nn { \seq_count:N \l__virgo_rmatrix_items_seq } { #1 } }
     { \seq_put_right:Nn \l__virgo_rmatrix_items_seq { } }
   }
  % determine the number of rows
  \int_set:Nn \l__virgo_rmatrix_rows_int
   {
    \int_div_truncate:nn { \seq_count:N \l__virgo_rmatrix_items_seq } { #1 }
   }
  % read the items
  \int_step_inline:nnnn { \l__virgo_rmatrix_rows_int } { -1 } { 1 }
   {% ##1 is the row index
    \int_step_inline:nnn { 0 } { #1 - 1 }
     {% ####1 is the column index minus 1
      \tl_put_right:Nx \l__virgo_rmatrix_body_tl
       {
        \seq_item:Nn \l__virgo_rmatrix_items_seq { ##1 + ####1*\l__virgo_rmatrix_rows_int }
        \int_compare:nTF { ####1 = #1 - 1 } { \exp_not:N \ } { & }
       }
     }
   }
   \begin{matrix}
   \tl_use:N \l__virgo_rmatrix_body_tl
   \end{matrix}
 }
\begin{document}
[
x=
\rmatrix{3,2,1,\bigl(6\bigr),5,4}
]
[
x=
\rmatrix[3]{3,2,1,\bigl(6\bigr),5,4}
]
[
x=
\rmatrix[4]{3,2,1,\bigl(6\bigr),5,4,9,8,7,10}
]
\end{document}

The number of items is made a multiple of the number of columns, the number of rows is computed by that data.

The sequence is then traversed from every multiple of the number of rows backwards.

Answer 3

Here's an imperfect self-answer, essentially formed by wrapping the answer to How to create table column wise in LaTeX? in \vcenter{\hbox{...}}.

It's imperfect because I'm just hacking away at the other answer without really understanding how it works, and also because it doesn't come out perfectly vertically centred - there must be some subtlety about \vecenter that I'm not understanding. Additionally the elements are not centred within their columns, though that's not a huge issue for me.

But on the plus side it behaves how I wanted in that the array is specified columnwise in the source, and in that it offers the desired control over spacing.

\documentclass{article}
\usepackage{amsmath}
\newenvironment{colarray}[2]{%
\vcenter\bgroup\hbox\bgroup\valign\bgroup&\vfil\vbox{\parindent=0pt\tabskip=#2\hsize=#1##}\vfil\cr}%
{\egroup\egroup\egroup}
\newcommand*\col[1]{#1\cr}
\begin{document}
\begin{equation}
    x = \begin{colarray}{4mm}{2mm}
        \col{1 & 2 & 3}
        \col{4 & 5 & \Big(6\Big)}
    \end{colarray}
\end{equation}
\end{document}

update: I figured out the vertical spacing issue. There needs to be a negative vskip to cancel out the tabskip on the last row. Unfortunately that means it has to be a newcommand and not a newenvironment, but here it is:

\documentclass{article}
\usepackage{amsmath}
% this can't be an environment because the code for \end can't have parameters.
\newcommand{\colarray}[3]{
\vcenter{\hbox{\valign{&\vfil\vbox{\parindent=0pt\tabskip=#2\hsize=#1##}\vfil\cr%
#3%
}}\vskip-#2}%
}
\newcommand*\col[1]{#1\cr}
\begin{document}
\begin{equation}
    x = \colarray{4mm}{2mm}{
        \col{1 & 2 & 3}
        \col{4 & 5 & \Big(6\Big)}
    }
\end{equation}
\end{document}

Now it's just the horizontal centering within cells that I need to figure out.

Answer 4

This is not really an answer, but too long for a comment. Hopefully it can be useful for somebody, perhaps somebody can cook up a solution for lualatex?

In ConTeXt there has for a while been possible to transpose matrices. We can define a matrix type that is transposed (done in lua) as

\definemathmatrix[virgomatrix][
    action=transpose,
    simplecommand=virgomatrix,
    distance=4em,
]

Once that is done we can add a transposed matrix with

\dm{ x = \virgomatrix{1,2,3; 4,5,\Bigl( 6 \Bigr); 7,8} }

Output:

If we also want to change the order of the rows we need to have a look at math-ali.lmt where this is defined. There we find

local actions = {
    transpose = function(m)
        local t = { }
        for j=1,#m[1] do
            local r = { }
            for i=1,#m do
                r[i] = m[i][j]
            end
            t[j] = r
        end
        return t
    end,
...
}

where the three dots is just indicating that some parts are being left out.

We can imitate this and define our own "Virgo" action (note the small change in r[i]).

\startluacode
    mathematics.registersimplematrix("Virgo",function(m)
        local t = { }
        for j=1,#m[1] do
            local r = { }
            for i=1,#m do
                r[i] = m[i][#m[1]-j+1]
            end
            t[j] = r
        end
        return t
    end)
\stopluacode

Then we can use it. We define a new type of matrix, the Virgo matrix.

\definemathmatrix[Virgomatrix][
    action={Virgo},
    simplecommand=Virgomatrix,
    distance=4em,
]

We then use this new type:

\dm{ x = \Virgomatrix{1,2,3;4,5,\Bigl( 6 \Bigr);7,8} }

The output is shown below.