How to transpose a table in expl3

Question

I've been very impressed with xparse and expl3, and have written a wonderful document command using \ProcessList that takes a comma separated list and turns it into a (basically) 1 column table.

\stacky{A,B,C,D}
-> \begin{tabular}{rr}
   \tiny 1st & A \\
   \tiny 2nd & B \\
   \tiny 3rd & C \\
   \tiny 4th & D
   \end{tabular}

Now I've become mad with the power and want to specify more than one column at a time. Something like:

\stacksy{ 5: A,B,C,D ; 6: A,C,D,B ; 3: C,A,B,D }
-> \begin{tabular}{rrrr}
             & 5 & 6 & 3 \\ \hline
   \tiny 1st & A & A & C \\
   \tiny 2nd & B & C & A \\
   \tiny 3rd & C & D & B \\
   \tiny 4th & D & B & D \\
   \end{tabular}

Everything is fine, except that the input is in column-major order, but TeX (or the tabular environment) expects row-major order.

How do I transpose the input list of lists?

Answer 1

Here is a method that will produce a rectangular array of numbers that are given as columns.

• The syntax is stacksys{col 1;col 2;...;col n} where col i is the ith column with entries given as a comma separated list.
• I fiddled with the input a bit to show how column and row headings can be introduced.
• array can be changed to tabular if that is desired.
• \stacksys{,r1,r2;c1,1,2;c2,3,4;c3,5,6} produces:

Code:

\documentclass{article}
\usepackage{xparse}
\ExplSyntaxOn
\int_new:N \l_ss_num_cols_int
\int_new:N \l_ss_num_rows_int
\bool_new:N \l_has_run_bool

\NewDocumentCommand{\stacksys} {m}
    {
        \ss_make_table:n {#1}
        \int_step_inline:nnnn {1}{1}{\l_ss_num_rows_int}
            {
                \tl_put_right:cn {l_row_{##1}_tl}{\\}
            }
        \begin{array}{*{\int_use:N \l_ss_num_cols_int}{c}}
        \int_step_inline:nnnn {1}{1}{\l_ss_num_rows_int}
            {
                \tl_use:c {l_row_{##1}_tl}
            }
        \end{array}
        \bool_gset_false:N \l_has_run_bool
    }

\cs_new_protected:Npn \ss_make_table:n #1
    {
        \seq_set_split:Nnn \l_tmpa_seq {;} {#1}
        \int_set:Nn \l_ss_num_cols_int {\seq_count:N \l_tmpa_seq}
        \seq_map_function:NN \l_tmpa_seq \ss_process_cols:n
    }

\cs_new_protected:Npn \ss_process_cols:n #1
    {
        \int_zero:N \l_tmpa_int
        \seq_set_split:Nnn \l_tmpb_seq {,} {#1}
        \int_set:Nn \l_ss_num_rows_int {\seq_count:N \l_tmpb_seq}
        \seq_map_inline:Nn \l_tmpb_seq
            {
                \bool_if:NTF \l_has_run_bool
                    {
                      \int_incr:N \l_tmpa_int
                      \tl_put_right:cn {l_row_{\int_use:N \l_tmpa_int}_tl} {&##1}
                    }
                    {
                      \int_incr:N \l_tmpa_int
                      \tl_clear_new:c {l_row_{\int_use:N \l_tmpa_int}_tl}
                      \tl_put_right:cn {l_row_{\int_use:N \l_tmpa_int}_tl} {##1}
                    }
            }
        \bool_gset_true:N \l_has_run_bool
    }

\ExplSyntaxOff
\begin{document}
\[
\stacksys{,r1,r2;c1,1,2;c2,3,4;c3,5,6}
\]
\end{document}