Visualize sparsity pattern with TikZ

Question

I have a huge sparse matrix of about 10.000 x 10.000 entries with 60.000 non-zero entries. I'd like to visualize the pattern, that means zero entries are ignored and non-zero entries are marked with a small circle, maybe colored by its value.

Just printing a pixel for each entry is not enough, as the image would be scaled down and the result barely visible.

Something like Matlab's spy function would be great.

Answer 1

Something to try on. It uses tikz and pgfplotstable to fetch the data. It iterates through the table, tough you have to inform the table size beforehand in \nrows and \ncols. I have no idea about performance for big data sets, likely it will be bad (as expected).

The relationship between value and Format/Color is yours to make. Though as percusse said, 10 000x 10 000 Matrix is just too big...

MWE

\documentclass[margin=3mm]{standalone}
\usepackage{tikz,pgfplotstable,filecontents}
\begin{filecontents}{data-table.dat}
1   2   3   4   5
6   6   8   5   4
1   0   8   5   1
1   2   0   4   5
6   6   8   5   4
1   0   8   5   1
\end{filecontents}
\pgfplotstableread{data-table.dat}\mytable
\def\nrows{5}
\def\ncols{4}
\begin{document}
\begin{tikzpicture}
\foreach \i in {0,...,\nrows}{
    \foreach \j in {0,...,\ncols}{
    \pgfplotstablegetelem{\i}{\j}\of\mytable
    \ifnum\pgfplotsretval=0\relax\else
    \node[circle, minimum size=.5pt, inner sep=0pt, fill=red!\pgfplotsretval!purple, opacity=0.\pgfplotsretval] at (\j pt,-\i pt) {};
    \fi
    };
};
\end{tikzpicture}
\end{document}

Making a 60x60 Matrix with "random" integers from 0 to 50 and using the above MWE I got this: