pgfplots matrix plot "perfect" rectangles

Question

Edit: I removed the duplicate part of the question, which was answered here: How to change label and ticks of a pgfplots colorbar? and here: pgfplots: Reshape a MATRIX of data before conditional 3D surface plotting (Feature Request for PGFplots https://sourceforge.net/p/pgfplots/feature-requests/76/)

I'm trying to plot a matrix with pgfplots and have three questions one question regarding the following MWE. Should I ask every question separately? Edit: Yes I should have.

\documentclass{standalone}
\usepackage{pgfplots}
\usetikzlibrary{pgfplots.colormaps}
\pgfplotsset{compat=newest}

\usepackage{filecontents}
\begin{filecontents}{\jobname.dat}
x y C
0 0 32
0 1 0
0 2 0
0 3 0
0 4 0
1 0 0
1 1 16
1 2 0
1 3 0
1 4 0
2 0 0
2 1 0
2 2 16
2 3 0
2 4 0
3 0 0
3 1 0
3 2 0
3 3 16
3 4 0
4 0 0
4 1 0
4 2 0
4 3 0
4 4 16
\end{filecontents}

\begin{document}
\begin{tikzpicture}
\pgfplotsset{%
    colormap={WhiteRedBlack}{%
        rgb255=(255,255,255)
        rgb255=(255,0,0)
        rgb255=(0,0,0)
    },
}
\begin{axis}[%
    small,
    every tick label/.append style={font=\tiny},
    tick align=outside,
    minor tick num=5,
    %
    xlabel=$\beta$,
    xticklabel pos=right,
    xlabel near ticks,
    xmin=-1, xmax=5,
    xtick={0, 5, ..., 4},
    %
    ylabel=$\alpha$,
    ylabel style={rotate=-90},
    ymin=-1, ymax=5,
    ytick={0, 5, ..., 4},
    %
    point meta min=0,
    point meta max=32,
    point meta=explicit,
    %
    colorbar sampled line,
    colormap name=WhiteRedBlack,
    scale mode=scale uniformly,
]
\draw (axis description cs:0,0) -- (axis description cs:1,0);
\addplot[matrix plot, mesh/cols=5] table[meta=C] {\jobname.dat};
\end{axis}
\end{tikzpicture}
\end{document}

1. When one zooms into the drawn rectangles, one can see a short line dropping from the left-lower and right-upper corner of the rectangle, so not a "perfect" rectangle is drawn (see screenshot). Can this be fixed?

Regarding the question if this stems from a problem with the PDF viewer: I checked it with Evince, the Firefox PDF viewer, mupdf (here the lines appear) whereas Adobe Acrobat and Okular showed the PDF without these lines..

Answer 1

A complicated solution. I did not manage to pass a list of coordinates to the plot, so I ended up creating a new table from your matrix.

\documentclass[border=3.14mm,tikz]{standalone}
\usepackage{pgfplots}
\usetikzlibrary{pgfplots.colormaps}
\pgfplotsset{compat=1.16}
\usepackage{pgfplotstable}
\usepackage{filecontents}

\begin{filecontents*}{entries.dat}
32 0 0 0
0 16 0 0
0 0 16 0
0 0 0 16
\end{filecontents*}
\newcommand*{\ReadOutElement}[4]{%
    \pgfplotstablegetelem{#2}{[index]#3}\of{#1}%
    \let#4\pgfplotsretval
}
\begin{document}
\pgfplotstableread[header=false]{entries.dat}\datatable
\pgfplotstablegetrowsof{\datatable}
\pgfmathtruncatemacro{\numrows}{\pgfplotsretval}
\pgfplotstablegetcolsof{\datatable}
\pgfmathtruncatemacro{\numcols}{\pgfplotsretval}
\xdef\LstX{}
\xdef\LstY{}
\xdef\LstC{}
\foreach \Y [evaluate=\Y as \PrevY using {int(\Y-1)},count=\nY] in {1,...,\numrows}
{\pgfmathtruncatemacro{\newY}{\numrows-\Y}
\foreach \X  [evaluate=\X as \PrevX using {int(\X-1)},count=\nX] in {1,...,\numcols}
{
\ReadOutElement{\datatable}{\PrevY}{\PrevX}{\Current}
\pgfmathtruncatemacro{\nZ}{\nX+\nY}
\ifnum\nZ=2
\xdef\LstX{\PrevX}
\xdef\LstY{\PrevY}
\xdef\LstC{\Current}
\else
\xdef\LstX{\LstX,\PrevX}
\xdef\LstY{\LstY,\PrevY}
\xdef\LstC{\LstC,\Current}
\fi
}
}
\edef\temp{\noexpand\pgfplotstableset{
 create on use/x/.style={create col/set list={\LstX}},
 create on use/y/.style={create col/set list={\LstY}},
 create on use/color/.style={create col/set list={\LstC}},}}
\temp
\pgfmathtruncatemacro{\strangenum}{\numrows*\numcols}
\pgfplotstablenew[columns={x,y,color}]{\strangenum}\strangetable

%\pgfplotstabletypeset[empty cells with={---}]\strangetable
\begin{tikzpicture}
\pgfplotsset{%
    colormap={WhiteRedBlack}{%
        rgb255=(255,255,255)
        rgb255=(255,0,0)
        rgb255=(0,0,0)
    },
}
\begin{axis}[%
    small,
    every tick label/.append style={font=\tiny},
    tick align=outside,
    minor tick num=5,
    %
    xlabel=$\beta$,
    xticklabel pos=right,
    xlabel near ticks,
    xmin=-1, xmax=5,
    xtick={0, 5, ..., 4},
    %
    ylabel=$\alpha$,
    ylabel style={rotate=-90},
    ymin=-1, ymax=5,
    ytick={0, 5, ..., 4},
    %
    point meta min=0,
    point meta max=32,
    point meta=explicit,
    %
    %colorbar sampled,
    colorbar as palette,
    colorbar style={samples=3},
    colormap name=WhiteRedBlack,
    scale mode=scale uniformly,
]
\draw (axis description cs:0,0) -- (axis description cs:1,0);
 \addplot [
        matrix plot,
        %mesh/cols=4,
        point meta=explicit,
] table [meta=color,col sep=comma] \strangetable;
\end{axis}
\end{tikzpicture}
\end{document}

Let me mention that, in order to do something like you want you do not even need pgfplots.

\documentclass[border=3.14mm,tikz]{standalone}
\usepackage{pgfplotstable}
\pgfplotsset{compat=1.16}
\usepackage{filecontents}
\begin{filecontents*}{entries.dat}
32 0 0 0
0 16 0 0
0 0 16 0
0 0 0 16
\end{filecontents*}
\newcommand*{\ReadOutElement}[4]{%
    \pgfplotstablegetelem{#2}{[index]#3}\of{#1}%
    \let#4\pgfplotsretval
}
\begin{document}
\pgfplotstableread[header=false]{entries.dat}\datatable
\pgfplotstablegetrowsof{\datatable}
\pgfmathtruncatemacro{\numrows}{\pgfplotsretval}
\pgfplotstablegetcolsof{\datatable}
\pgfmathtruncatemacro{\numcols}{\pgfplotsretval}
\begin{tikzpicture}
\foreach \Y [evaluate=\Y as \PrevY using {int(\numrows-\Y)},
evaluate=\Y as \NewY using {int(\numrows-\Y+1)}] in {1,...,\numrows}
{
\foreach \X  [evaluate=\X as \PrevX using {int(\X-1)}] in {1,...,\numcols}
{
\ReadOutElement{\datatable}{\PrevY}{\PrevX}{\Current}
\ifnum\Current=0
\else
\pgfmathsetmacro{\myc}{148-4*\Current}
\fill[red!\myc!black] (\PrevX,\numrows-\PrevY-1) rectangle ++ (1,1);
\fi
}
}
\draw (0,0) grid (\numrows,\numcols);
\end{tikzpicture}
\end{document}