Mdthbs

I am trying to display sparse matrices like chessboards, where white places indicates 0 entries and black ones non-zero entries (in this case matrices are boolean so every non-zero entry is a one entry), but I can't find a proper way.

Because I am looking to show more than one matrix (more in detail, I have to show matrix A and its power), I will have to print more than one on the same page and specify their layout, like figures.

For example, given this matrix as input:

| 0 | 1 | 0 |

| 1 | 0 | 1 |

| 0 | 1 | 0 |

I would expect such output:

With TikZ this is rather straightforward.

documentclass{article}

usepackage{tikz}

usetikzlibrary{matrix}

begin{document}

begin{tikzpicture}[0/.style={draw,ultra thin},1/.style={0,fill=black}]

 matrix[matrix of nodes,cells={minimum size=1.5em,anchor=center}]

 {|[0]| & |[1]| & |[0]| \

 |[1]| & |[0]| & |[1]|\

 |[0]| & |[1]| & |[0]|\

 };

end{tikzpicture}

end{document}

If you have a simple pattern as this one, you could also do

documentclass{article}

usepackage{tikz}

usetikzlibrary{matrix}

begin{document}

begin{tikzpicture}[my cell/.style={/utils/exec={%

 pgfmathtruncatemacro{itest}{mod(thepgfmatrixcurrentrow+thepgfmatrixcurrentcolumn,2)}

 ifnumitest=1

 pgfkeysalso{/tikz/fill=black}

 fi}}]

 matrix[matrix of nodes,nodes in empty cells,

 nodes={minimum size=1.5em,anchor=center,draw,ultra thin,my cell}]

 { &  &  \

  &  & \

  &  & \

 };

end{tikzpicture}

end{document}

With a fairly natural syntax:

documentclass{article}

usepackage{amsmath}



newlength{sparsesize}

setlength{sparsesize}{12pt}



newcommand{sparsezero}{%

  begingroup

  setlength{fboxsep}{-0.2pt}%

  setlength{fboxrule}{0.2pt}%

  fbox{hspace{sparsesize}rule{0pt}{sparsesize}}%

  endgroup

}

newcommand{sparseone}{rule{sparsesize}{sparsesize}}

newcommand{activate}[2]{%

  begingrouplccode`~=`#1lowercase{endgrouplet~}#2%

  mathcode`#1="8000

}



newenvironment{sparsematrix}

 {%

  renewcommand{arraystretch}{0}%

  setlength{arraycolsep}{0pt}%

  activate{0}{sparsezero}activate{1}{sparseone}%

  begin{matrix}%

 }

 {end{matrix}}



begin{document}



[

begin{pmatrix}

0 & 1 & 0 \

1 & 0 & 1 \

0 & 1 & 0

end{pmatrix}

=

begin{sparsematrix}

0 & 1 & 0 \

1 & 0 & 1 \

0 & 1 & 0

end{sparsematrix}

]



end{document}

For general matrices with integer coefficients it's a bit more difficult.

documentclass{article}

usepackage{amsmath,xparse}



newlength{sparsesize}

setlength{sparsesize}{12pt}

newcommand{sparsezero}{%

  begingroup

  setlength{fboxsep}{-0.2pt}%

  setlength{fboxrule}{0.2pt}%

  fbox{hspace{sparsesize}rule{0pt}{sparsesize}}%

  endgroup

}

newcommand{sparseone}{rule{sparsesize}{sparsesize}}



ExplSyntaxOn

NewDocumentEnvironment{sparsematrix}{b}

 {

  renewcommand{arraystretch}{0}%

  setlength{arraycolsep}{0pt}%

  {% make a subformula

   begin{matrix}

   eagleone_sparsematrix:n { #1 }

   end{matrix}

  }

 }{}



seq_new:N l__eagleone_sparsematrix_rows_seq

seq_new:N l__eagleone_sparsematrix_row_in_seq

seq_new:N l__eagleone_sparsematrix_row_out_seq



cs_new_protected:Nn eagleone_sparsematrix:n

 {

  seq_set_split:Nnn l__eagleone_sparsematrix_rows_seq { \ } { #1 }

  seq_map_function:NN l__eagleone_sparsematrix_rows_seq __eagleone_sparsematrix_row:n

 }

cs_new_protected:Nn __eagleone_sparsematrix_row:n

 {

  seq_set_split:Nnn l__eagleone_sparsematrix_row_in_seq { & } { #1 }

  seq_map_inline:Nn l__eagleone_sparsematrix_row_in_seq

   {

    int_compare:nTF { ##1 = 0 }

     {

      seq_put_right:Nn l__eagleone_sparsematrix_row_out_seq { sparsezero }

     }

     {

      seq_put_right:Nn l__eagleone_sparsematrix_row_out_seq { sparseone }

     }

   }

  seq_use:Nn l__eagleone_sparsematrix_row_out_seq { & } \

 }



ExplSyntaxOff



begin{document}



[

begin{pmatrix}

0 & 1 & 0 \

1 & 0 & 1 \

0 & 1 & 0

end{pmatrix}

=

begin{sparsematrix}

0 & 1 & 0 \

1 & 0 & 1 \

0 & 1 & 0

end{sparsematrix}

]



[

begin{sparsematrix}

0 & 1 & 0 \

1 & 0 & 1 \

0 & 1 & 0

end{sparsematrix}^2

=

begin{sparsematrix}

1 & 0 & 1 \

0 & 2 & 0 \

1 & 0 & 1

end{sparsematrix}

]



end{document}