[Tex/LaTex] Creating a triangular table

rotatingtablestikz-pgf

Is there a way to create something that looks like this?
enter image description here

I have looked at the \rotatebox command, but that will not get the same "jagged" edges on the bottom, and looked at How to draw a diagonally-split grid with TikZ? which seems applicable (especially in conjunction with the \rotatebox).

I was able to make this:

enter image description here

With code adapted from the link, but I have no idea how to customize it.

\documentclass[12pt]{article}
\usepackage[english]{babel}
\usepackage{amsfonts}
\usepackage{tikz}
\usepackage{rotating}
\usetikzlibrary{calc,decorations.shapes}
\tikzset{
  decorate with/.style args={#1 separated by #2}{
    fill,
    decorate,decoration={shape backgrounds,shape=#1,shape size=1.5mm,
    shape sep={#2, between borders}}
  }
}

\pgfkeys{/tikz/.cd,
   num quad/.initial=5,
   num quad/.get=\numquad,
   num quad/.store in=\numquad,
}

\begin{document}

\usetikzlibrary{calc,decorations.shapes}
\rotatebox{315}{\begin{tikzpicture}[x=0.5025cm,y=0.5025cm,line cap=round]
    \foreach \x [count=\xi] in {1,...,\numquad}{
      \foreach \y [count=\yi] in {\x,...,\numquad}{
        \node [draw, minimum size=0.5cm,outer sep=0pt,inner sep=0pt] (u-\xi\yi) at (\xi,-\yi) {};
      }
    }
    \end{tikzpicture}
}
\end{document}

Best Answer

The diamond shape is only there for drawing and filling, the text is actually only a label (which is actually a node too) to the diamond node.

This works best only with an angle of 45.
One could also solve this with a custom coordinate system (x going ↗, y going ↘) instead of rotation, the squares/diamonds could have been drawn also with a rectangular path.

The size of the shape is manually set to

minimum size=1.414cm+0.4\pgflinewidth

The co-efficient of \pgflinewidth is found empirical and is chosen so that the lines overdraw eachother, as a grid would do that.

Update:
The macro that is used by remember isn't remembered anymore after the loops. I'm using global remember for this. (The key remember=\macro is still needed since global remember doesn't apply the same parsing that remember does.)

To add j → and m → I've used my custom /utils/exec={<cond>}{<true keys>}{<false keys>} key to add a label to a label. (We could've used \ifnum here, too, or we could also replace the \ifnums by /utils/ifs.)

The mathtools package is loaded for \mathrlap to easily place the →-labels.

Code

\documentclass[tikz]{standalone}
\usepackage{mathtools}
\usetikzlibrary{shapes.geometric}
\makeatletter
\pgfqkeys{/pgf/foreach}{
  global remember/.code=%
    \pgfutil@append@tomacro{\pgffor@remember@code}{\gdef\noexpand#1{#1}}}
\pgfqkeys{/utils}{if/.code n args={3}{%
  \pgfmathifthenelse{#1}{1}{0}\ifnum\pgfmathresult=0 
  \expandafter\pgfutil@secondoftwo\else\expandafter\pgfutil@firstoftwo\fi
  {\pgfkeysalso{#2}}{\pgfkeysalso{#3}}}}
\makeatother
\begin{document}
\begin{tikzpicture}[
    rotate=-45,
    every label/.append style={text depth=+0pt},
    label position=center,
    every cell/.style={fill=gray!25},
    column 3/.style={fill=red!25},
    row 5/.style={fill=green!25},
    cell 2-2/.style={fill=gray},
    cell 3-2/.style={fill=gray!50},
    ]
\foreach \jRow[count=\jCount from 1, remember=\jCount, global remember=\jCount] in {%
        0,%
        {15750,0},%
        {7875,2625,0},%
        {9375,4375,750,0},%
        {11875,7125,2500,1000,0},%
        {15125,10500,5375,3500,5000,0}%
    } {
    \foreach \mCell[count=\mCount from 1, remember=\mCount] in \jRow {
        \node[
            diamond,
            minimum size=1.414cm+0.4\pgflinewidth,
            draw,
            every cell/.try,
            row \jCount/.try,
            column \mCount/.try,
            cell \jCount-\mCount/.try,
            label={\pgfmathprintnumber{\mCell}},
            alias=@lastnode,
            alias=@lastrow-\mCount
        ] at (\mCount-.5,\jCount-.5) {};
        \ifnum\mCount=1
            \path [late options={name=@lastnode,
              label={
                [/utils/if={\jCount==1}%
                  {label={[rotate=45,anchor=south]above left:$j\mathrlap{{}\to}$}}{}]
                above left:$\jCount$}}];
        \fi
    }
        \path [late options={name=@lastnode, label=below:$A_\jCount$}];
    }
    \foreach \jCountExtra in {1,...,\jCount}
        \path [late options={name=@lastrow-\jCountExtra, label={
          [/utils/if={\jCountExtra==1}%
            {label={[rotate=-45,anchor=south]above right:$m\mathrlap{{}\to}$}}{}]
           above right:$\jCountExtra$}}];
\end{tikzpicture}
\end{document}

Output

enter image description here

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