Error when using tikz node, subnode

Question

In the code below, building off solutions found here, I am trying to use the node and subnode options to draw the arrow, but I cannot get the file to compile.  Can you help me to fix the code to get the arrow to point to the text and the highlighted cell like this

Here is the code:

documentclass{article}
usepackage{tikz}
usepackage{blkarray}
usetikzlibrary{fit,calc,arrows,shapes,decorations.pathreplacing,pgfplots.groupplots, matrix}
tikzset{%
  highlight/.style={rectangle,rounded corners,fill=red!15,draw,
    fill opacity=0.5,thick,inner sep=0pt}
}
newcommand{tikzmark}[2]{tikz[overlay,remember picture,
  baseline=(#1.base)] node (#1) {#2};}
%
newcommand{Highlight}[1][submatrix]{%
    tikz[overlay,remember picture]{
    node[highlight,fit=(left.north west) (right.south east)] (#1) {};}
}
begin{document}
[
  M = left(begin{array}{*5{c}}
    tikzmark{left}{1} & 2 & 3 & 4 & 5 
    6 & 7 & 8 & 9 & 10 
    11 & 12 & tikzmark{right}{13} & 14 & 15 
    16 & 17 & 18 & 19 & 20
  end{array}right)
  Highlight[first]
  qquad
  M^T = left(begin{array}{*5{c}}
    tikzmark{left}{1} & 6 & 11 & 16 
    2 & 7 & 12 & 17 
    3 & 8 & tikzmark{right}{13} & 18 
    4 & 9 & 14 & 19 
    5 & 10 & 15 & 20
  end{array}right)
]
Highlight[second]
%
tikz[overlay,remember picture] {
  draw[->,thick,red,dashed] (first) -- (second) node [pos=0.66,above] {Transpose};
  node[above of=first] {$N$};
  node[above of=second] {$N^T$};
}

[
begin{blockarray}{ccccc}
x_{1} & x_{2} & x_{3} & x_{4} &  
begin{block}{[cccc|c]}
  1 & 0 & tikzmark{left}{-1} & 0 & 0 
  0 & 1 & 2 & 0 & 0 
  0 & 0 & tikz{node{subnode{d1}tikzmark{right}{0}};} & 1 & 0 
end{block}
end{blockarray}
Highlight[new1]
]

%begin{tikzpicture}[remember picture,overlay]
%    node [shift={(3.0em,-4.0ex)}, anchor=west] at ({pic cs:starta}) (X) {Tip measurement};
%    draw [mybluei, thick, -latex] (X.west) -| ($({pic cs:starta})!0.5!({pic cs:enda})+(0,-0.5ex)$);
%end{tikzpicture}

end{document}

cfr · Accepted Answer

So the problem with the code is that subnode is never defined. You can get it defined by loading the tikzmark library. However, newcommandtikzmark... will then fail as the library defines the standard tikzmark command. This problem can be avoided by simply choosing a different macro name, such as mytikzmark.

You cannot, however, use mytikzmark or tikzmark inside a node inside a TikZ picture. Indeed, the raison d'être of subnode is for use in this context precisely because tikzmarks cannot be used there.

So you can either use mytikzmark or tikzmark without the surrounding TikZ picture environment. Or you can use subnodes within one.

Here's a comparison of the two methods:

documentclass{article}
usepackage{tikz}
usepackage{blkarray}
usetikzlibrary{fit,tikzmark}
tikzset{%
  highlight/.style={rectangle,rounded corners,fill=red!15,draw, fill opacity=0.5,thick,inner sep=0pt}
}
newcommand{mytikzmark}[2]{tikz[overlay,remember picture, baseline=(#1.base)] node (#1) {#2};}

newcommand{Highlight}[1][submatrix]{%
    tikz[overlay,remember picture]{
    node[highlight,fit=(left.north west) (right.south east)] (#1) {};}
}
begin{document}
[
  begin{blockarray}{ccccc}
    x_{1} & x_{2} & x_{3} & x_{4} &  
    begin{block}{[cccc|c]}
      1 & 0 & mytikzmark{left}{-1} & 0 & 0 
      0 & 1 & 2 & 0 & 0 
      0 & 0 & tikz{node{subnode{d1}{d1}subnode{right}{0}};} & 1 & 0 
    end{block}
  end{blockarray}
  Highlight[new1]
]
tikz[remember picture,overlay]{%
  node [fit=(d1), inner sep=-2.5pt, draw=blue, circle] {};
  node [fit=(right), inner sep=-2.5pt, draw=green!50!black, circle] {};
}
[
  begin{blockarray}{ccccc}
    x_{1} & x_{2} & x_{3} & x_{4} &  
    begin{block}{[cccc|c]}
      1 & 0 & mytikzmark{left}{-1} & 0 & 0 
      0 & 1 & 2 & 0 & 0 
      0 & 0 & mytikzmark{d1}{d1} mytikzmark{right}{0} & 1 & 0 
    end{block}
  end{blockarray}
  Highlight[new1]
]
tikz[remember picture,overlay]{%
  node [fit=(d1), inner sep=-2.5pt, draw=blue, circle] {};
  node [fit=(right), inner sep=-2.5pt, draw=green!50!black, circle] {};
}

end{document}

Given your updated question, I don't think you want subnode at all. Why not just use the marks you already have?

documentclass{article}
usepackage{tikz}
usepackage{blkarray}
usetikzlibrary{fit,arrows.meta}
tikzset{%
  highlight/.style={rectangle,rounded corners,fill=red!15,draw, fill opacity=0.5,thick,inner sep=0pt}
}
newcommand{mytikzmark}[2]{tikz[overlay,remember picture, baseline=(#1.base)] node (#1) {#2};}

newcommand{Highlight}[1][submatrix]{%
    tikz[overlay,remember picture]{
    node[highlight,fit=(left.north west) (right.south east)] (#1) {};}
}
begin{document}
[
  begin{blockarray}{ccccc}
    x_{1} & x_{2} & x_{3} & x_{4} &  
    begin{block}{[cccc|c]}
      1 & 0 & mytikzmark{left}{-1} & 0 & 0 
      0 & 1 & 2 & 0 & 0 
      0 & 0 & mytikzmark{right}{0} & 1 & 0 
    end{block}
  end{blockarray}
  Highlight[new1]
]
tikz[remember picture,overlay]{%
  draw [LaTeX-] (new1.south) ++(0,-2.5pt) [out=-90,in=160] to ++(5mm,-10mm) node [right, xshift=-2.5mm, font=itshape, text=red, align=center] {freevariable};
}

end{document}

F. Pantigny · Answer

Here is what you can do with the environment {bNiceArray} of nicematrix (with the lastest version: v. 5.12 of 2021-03-10).
That environment is similar to {array} (of array) but constructs PGF/Tikz nodes under the cells, rows and columns).
I have used these nodes to draw the arrow and its label. For the highlighted column, there is a built-in command Block easy to use (you don't need transparency).
documentclass{article}
usepackage{nicematrix,tikz}

begin{document}

$begin{bNiceArray}{cccc|c}[first-row]
x_1 & x_2 & x_3 & x_4 
1   & 0   & Block[draw,fill=red!10,rounded-corners]{3-1}{}-1  & 0  & 0 
0   & 1   & 2   & 0  & 0 
0   & 0   & 0   & 1  & 0 
CodeAfter
tikz
draw [<-] (3-3.south) ++(0,-5pt) [out=-90,in=160] to ++(5mm,-10mm) 
    node [right, xshift=-2.5mm, font=itshape, text=red, align=center] {freevariable} ;
end{bNiceArray}$

end{document}

You need several compilations (because nicematrix uses PGF/tikz nodes).

Error when using tikz node, subnode

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