Dtyjlui

I was not able to use tikzmarknodes within the matrix example below. I have included an image of the arrows I want to draw and the MWE

documentclass{article}

usepackage{tikz}

usetikzlibrary{tikzmark,matrix,calc}



begin{document}

begin{tikzpicture}[declare function={f(x)=1/ln(2)*ln(x);}]

matrix[matrix of math nodes,nodes={align=center,inner sep=3pt,

   text height=1.5ex,text depth=.25ex,draw=gray!40,ultra thin},draw,inner 

   sep=0pt,ampersand replacement=&] (mat1)

    at (-5,0){

   |[fill=green!40!gray,text width=15mm]| x, text{or} 2^{y}  & | 

   [fill=green!40!gray,text width=11mm]| y \ 

                 |[text width=15mm]|   1                      & |[text 

      width=11mm]|  

     {pgfmathparse{f(1)}pgfmathprintnumber{pgfmathresult}}\

                                     |[text width=15mm]|   2                       

     & |[text width=11mm]|  

     {pgfmathparse{f(2)}pgfmathprintnumber{pgfmathresult}}\

                                     |[text width=15mm]|   4                      

      & |[text width=11mm]|  

     {pgfmathparse{f(4)}pgfmathprintnumber{pgfmathresult}}\

                                     |[text width=15mm]|   8                      

      & |[text width=11mm]|  

     {pgfmathparse{f(8)}pgfmathprintnumber{pgfmathresult}}\

                                     |[text width=15mm]|   frac{1}{2}                      

      & |[text width=11mm]|  

     {pgfmathparse{f(.5)}pgfmathprintnumber{pgfmathresult}}\

                                     |[text width=15mm]|   frac{1}{4}                      

      & |[text width=11mm]|  

     {pgfmathparse{f(.25)}pgfmathprintnumber{pgfmathresult}}\

                                    };

      node at ([yshift=-.8cm,xshift=2cm]mat1.south) 

            [circle,draw,font=small,inner sep=1pt] (1){$1$};

            node at (1) [right=5pt,text=red] {Select $y$};

      node at ([yshift=-1.5cm,xshift=.7cm]mat1.south) 

            [circle,draw,font=small,inner sep=1pt] (2){$2$};                                       

            node at (2) [right=5pt,text=red] {Compute $x$};

 end{tikzpicture}

 end{document}

This outputs:

The arrows I am trying to draw :

You do not need tikzmark here because tikzmark is needed to make a non-node a node, but everything you are playing with here are nodes. EDIT: Fixed the directions of the arrows (big thanks to manoooh) and borrowed column 1/.append style={nodes={text width=15mm}},column 2/.append style={nodes={text width=9mm}} from Zarkos answer. (However, I disagree with replacing pgfmathparse{f(1)}pgfmathprintnumber{pgfmathresult} by something using pgfmathtruncatemacro because this won't work once you have non-integer results.)

documentclass{article}

usepackage{amsmath}

usepackage{tikz}

usetikzlibrary{matrix}

begin{document}

begin{tikzpicture}[declare function={f(x)=1/ln(2)*ln(x);}]

matrix[matrix of math nodes,nodes={align=center,inner sep=3pt,

   text height=1.5ex,text depth=.25ex,draw=gray!40,ultra thin},

   draw,inner sep=0pt,ampersand replacement=&,

   column 1/.append style={nodes={text width=15mm}},  

   column 2/.append style={nodes={text width=9mm}} ] (mat1)

    at (-5,0){

   |[fill=green!40!gray]| x~text{or}~2^{y}  & | 

   [fill=green!40!gray]| y \ 

     1  &  {pgfmathparse{f(1)}pgfmathprintnumber{pgfmathresult}}\

     2  &  {pgfmathparse{f(2)}pgfmathprintnumber{pgfmathresult}}\

     4  &  {pgfmathparse{f(4)}pgfmathprintnumber{pgfmathresult}}\

     8  &  {pgfmathparse{f(8)}pgfmathprintnumber{pgfmathresult}}\

     frac{1}{2} & {pgfmathparse{f(.5)}pgfmathprintnumber{pgfmathresult}}\

    frac{1}{4} & {pgfmathparse{f(.25)}pgfmathprintnumber{pgfmathresult}}\

                                    };

      node at ([yshift=-.8cm,xshift=2cm]mat1.south) 

            [circle,draw,font=small,inner sep=1pt,label={[red]right:Select $y$}] (1){$1$};

      node at ([yshift=-1.5cm,xshift=.7cm]mat1.south) 

            [circle,draw,font=small,inner sep=1pt,label={[red]right:Compute

            $x$}] (2){$2$};        

     draw[latex-] (mat1-7-1|-mat1.south) |- (2);

     draw[latex-] (mat1-7-2|-mat1.south) |- (1);

end{tikzpicture}

end{document}

off-topic (since topic is solved by @marmot answer), but it may be handy at writing of your matrices ...

• with use of column 1/.append style={nodes={text width=15mm} (and similarly for column 2) you can remove |[text width=11mm]| from all cells


• with use of pgfmathtruncatemacro{L}{f(<value>)}L instead pgfmathparse{f(.5)}pgfmathprintnumber{pgfmathresult} gives slightly shorter code


• for nodes below matrix i would define common style


• 
  

  use of ampersand replacement=& is not necessary

  
  
  

  documentclass{article}
  
  usepackage{amsmath}
  
  usepackage{tikz}
  
  usetikzlibrary{matrix}
  
  
  
  begin{document}
  
      begin{tikzpicture}[
  
  declare function = {f(x)=1/ln(2)*ln(x);},
  
       circ/.style = {circle,draw,font=small,inner sep=1pt, % <---
  
                      label={[red]right:#1}}                 % <--- 
  
                          ]
  
  matrix[matrix of math nodes,
  
          nodes = {align=center,inner sep=3pt,
  
                   text height=2ex, text depth=1ex,         % <---
  
                   draw=gray!40,very thin},
  
          draw, inner sep=0pt,
  
          column 1/.append style={nodes={text width=15mm}},  % <---
  
          column 2/.append style={nodes={text width=9mm}}    % <---
  
          ] (mat1)
  
  {
  
  |[fill=green!40!gray]| xtext{, or }2^{y}                  % <---
  
      & |[fill=green!40!gray]| y              \             % <---
  
  1   & {pgfmathtruncatemacro{L}{f(1)}L}   \             % <---
  
  2   & {pgfmathtruncatemacro{L}{f(2)}L}   \
  
  4   & {pgfmathtruncatemacro{L}{f(4)}L}   \
  
  8   & {pgfmathtruncatemacro{L}{f(8)}L}   \
  
  frac{1}{2} & {pgfmathtruncatemacro{L}{f(0.5)}L}     \
  
  frac{1}{4} & {pgfmathtruncatemacro{L}{f(0.25)}L}    \
  
  };
  
  node at ([yshift=- 8mm] mat1.south east)   [circ=Select  $y$] (c1) {1}; % <---
  
  node at ([yshift=-18mm] mat1-7-2)          [circ=Compute $x$] (c2) {2}; % <---
  
  draw[latex-] (mat1-7-2) |- (c1);  % <---
  
  draw[latex-] (mat1-7-1) |- (c2);  % <---
  
      end{tikzpicture}
  
  end{document}
  
  

  
  

edit:

• corrected direction of arrows


• 
  

  added version with use of original way of calculation of values in the second column, i.e. with pgfmathparse{f(1)}pgfmathprintnumber{pgfmathresult} (as noted marmot in his answer, it enable calculation of real values), for which is defined new command calculation :

  
  
  

  documentclass[tikz, margin=3mm]{standalone}
  
  usetikzlibrary{matrix}
  
  usepackage{amsmath}
  
      begin{tikzpicture}[
  
  declare function = {f(x)=1/ln(2)*ln(x);},
  
       circ/.style = {circle,draw,font=small,inner sep=1pt,  % <---
  
                      label={[red]right:#1}}                  % <---
  
                          ]
  
  newcommandcalculation[1]{pgfmathparse{f(#1)}%
  
                             pgfmathprintnumber{pgfmathresult}}  % <---
  
  matrix[matrix of math nodes,
  
          nodes = {text height=1.5ex, text depth=0.5ex,       % <---
  
                   align=center, inner ysep=4pt,
  
                   draw=gray!40,very thin},
  
          draw, inner sep=0pt,
  
          column 1/.append style={nodes={text width=15mm}},   
  
          column 2/.append style={nodes={text width=11mm}},   
  
          row 1/.style = {nodes={fill=green!40!gray}}         % <---
  
          ] (mat1)
  
  {
  
  xtext{, or }2^{y}                                          % <---
  
      & y                             \                      % <---
  
  1   & {calculation{1}}             \                      % <---
  
  2   & {calculation{2}}             \
  
  4   & {calculation{4}}             \
  
  8   & {calculation{8}}             \
  
  frac{1}{2} & {calculation{0.5}}   \
  
  frac{1}{4} & {calculation{0.25}}  \
  
  };
  
  node at ([yshift=- 8mm] mat1.south east)   [circ=Select  $y$] (c1) {1}; % <---
  
  node at ([yshift=-18mm] mat1-7-2)          [circ=Compute $x$] (c2) {2}; % <---
  
  draw[latex-] (mat1-7-2) |- (c1);  % <---
  
  draw[latex-] (mat1-7-1) |- (c2);  % <---
  
      end{tikzpicture}
  
  end{document}
  
  

  
  

the result is the same as above.