TikZ: Robust and automated creation of signal-flow graph (phase-variable form)

Question

Adopting this answer, the following signal-flow diagram has been created by representing the following set of state equations:

I would like to:

1- know how my code can be optimized and generalized to be more robust when the number of nodes and their connecting signals differ without having to manually edit it.

2- make the current output cleaner if possible.

\documentclass[border=5mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{decorations.markings,positioning,arrows.meta}
\newif\iflabrev
\begin{document}
    \begin{tikzpicture}
        [
        relative = false,
        node distance = 15 mm,
        label revd/.is if=labrev,
        %label revd/.default=true,
        amark/.style = {
            decoration={             
                markings,   
                mark=at position {0.5} with { 
                    \arrow{stealth},
                    \iflabrev \node[below] {#1};\else \node[above] {#1};\fi
                }
            },
            postaction={decorate}
        },
        terminal/.style 2 args={draw,circle,inner sep=2pt,label={#1:#2}},
        ]
        %
        %Place the nodes
        \node[terminal={left}{$R(S)$}] (a) at (0,0) {};
        \node[terminal={below right}{$sX_3(s)$}] (b) [right=of a] {};
        \node[terminal={below right}{$X_3(S)$}] (c) [right=of b] {};
        \node[terminal={[xshift=-4mm]below right}{$sX_2(s)$}] (d) [right=of c] {};
        \node[terminal={[xshift=-4mm]below right}{$X_2(s)$}] (e) [right=of d] {};
        \node[terminal={[xshift=-4mm]below right}{$sX_1(s)$}] (f) [right=of e] {};
        \node[terminal={[xshift=-4mm]below right}{$X_1(s)$}] (g) [right=of f] {};
        \node[terminal={right}{$Y(s)$}] (h) [right=of g] {};
        %
        %Draw the connections
        \foreach \target/\bend/\text/\loose in {b/0/7/0, d/90/5/1.5, f/90/2/1.5}
        \draw[amark=\text] (a) to[bend left=\bend,looseness=\loose] (\target);
    \draw[amark=1/s] (b) to (c);
    \foreach \source/\text/\loose in {c/-4/2, e/-3/1.5, g/1/1.5}
    \draw[amark=\text] (\source) to[bend left=90, looseness=\loose] (b);

    \foreach \target/\text/\loose in { d/-6/1.5, f/2/2}
    \draw[amark=\text] (g) to[bend left=90, looseness=\loose] (\target);

    \foreach \source/\text in {c/9, e/6}
    \draw[amark=\text] (\source) to[bend left=90, looseness=1.5] (h);

    \draw[amark=2] (c) to (d);
    \draw[amark=3] (c) to[bend right=90, looseness=1.5] (f);
    \draw[amark=1/s] (d) to (e);
    \draw[amark=-5] (e) to (f);
    \draw[amark=-2,label revd] (e) to[bend left=90, looseness=2] (d);
    \draw[amark=1/s] (f) to (g);
    \draw[amark=-4] (g) to (h);
\end{tikzpicture}

\end{document}

Answer 1

This post does not address the question of achieving a better layout. The purpose is to generate the graph from a matrix automatically. You can define a matrix via

\edef\mmat{{2,-5,3,2},{-6,-2,2,5},{1,-3,-4,7},{-4,6,9,0}}

and then the graph gets created via foreach loops. There are some annotations in the code. The perhaps most important new ingredients are the pmark style which gets the labels from the matrix entries, i.e. its arguments are the row and column index, and the semicircle style which inserts a semicircle that can be used in edges.

\documentclass[tikz,border=5mm]{standalone}
\usetikzlibrary{calc,decorations.markings,positioning,arrows.meta}
\newif\iflabrev
\begin{document}
    \begin{tikzpicture}[node distance = 15 mm,
        label revd/.is if=labrev,
        label revd/.default=true,
        amark/.style = {
            decoration={             
                markings,   
                mark=at position {0.5} with { 
                    \arrow{stealth},
                    \iflabrev \node[below] {#1};\else \node[above] {#1};\fi
                }
            },
            postaction={decorate}
        }, % make the mark an entry of the \mmat matrix
        pmark/.style n args={2}{amark={$%
            \pgfmathparse{int({\mmat}[\numexpr#1][\numexpr#2])}%
                \pgfmathresult$}},
        terminal/.style 2 args={draw,alias=ln,circle,inner sep=2pt,label={#1:#2}},
        % semicircle path
        semicircle/.style={to path={let \p1=($(\tikztotarget)-(\tikztostart)$)
            in \ifdim\x1>0pt
              (\tikztostart.north) arc[start angle=180,end angle=0,radius=0.5*\x1]
            \else
              (\tikztostart.south) arc[start angle=0,end angle=-180,radius=-0.5*\x1]
            \fi}}
        ]
        % define the  matrix 
        \edef\mmat{{2,-5,3,2},{-6,-2,2,5},{1,-3,-4,7},{-4,6,9,0}}
        \pgfmathtruncatemacro{\dimy}{dim({\mmat})} % number of rows
        \pgfmathtruncatemacro{\dimx}{dim({\mmat}[0])} % number of columns
        % create the graph
        \path % R node
        node[terminal={left}{$R(S)$},alias={X-\dimy}] (R) {}
        % loop over matrix entries
        foreach \Y [evaluate=\Y as \X using {int(\dimy-\Y)}]
        in {1,...,\numexpr\dimy-1}
        {node[right=of ln,terminal={below right}{% sX_i node
            $sX_{\X}(s)$}](sX-\X){}
        node[right=of ln,terminal={below right}{% X_i node
            $X_{\X}(s)$}](X-\X){}
        % ege from sX_i to X_i  
        (sX-\X) edge[amark={$\frac{1}{s}$}] (X-\X)
        % edge from X_{i+1} to X_i  (R had an alias)
        (X-\the\numexpr\X+1) edge[pmark={\X-1}{\X}] (sX-\X)
        % semicircle edge from X_i to sX_i
        (X-\X) edge[semicircle,label revd,pmark={\X-1}{\X-1}] (sX-\X)
        % various semicircles
        \ifnum\Y>1
         (R) edge[semicircle,pmark={\X-1}{\dimx-1}] (sX-\X) 
         foreach \Z in {1,...,\numexpr\Y-1} {
          (X-\X) edge[semicircle,pmark={\X+\Z-1}{\X-1}] (sX-\the\numexpr\X+\Z)
         }
        \fi
        }% the Y node
        node[right=of ln,terminal={right}{$Y(s)$}](Y){}
        (X-1) edge[pmark={\dimy-1}{0}] (Y)
        % semicircles goint to Y
        foreach \Y [evaluate=\Y as \X using {int(\dimy-\Y)}]
         in {1,...,\numexpr\dimy-2}
        {(X-\X) edge[semicircle,pmark={\dimy-1}{\X-1}] (Y)};
    \end{tikzpicture}
\end{document}