[Tex/LaTex] Apply Math operations on loaded data inside PGF/Tikz plot

pgfmathpgfplotstabletikz-pgf

What I want: \abs{S21/S12-1}*100% where S21 and S12 are columns in txt-files

What I have: no idea; really.
I am profoundly unsure, if it is even possible in PGF/tikz to make this calculation.
If not, what alternatives would there be in TeX? PGFmath?

(I can still just take all the stuff to Matlab, calculate, re-import in TeX, but … meh.)

What I tried
I read the following three posts and tried to adapt: 1, 2 and 3 – where the latter gave me the idea, that basic operations should be possible but tricky to achieve because of the parser.

Below is a MWE (optimistically called; it does not compile) of what i want to get.

\documentclass{article}
\usepackage{amsmath,amsthm}
\usepackage{tikz} 
\usetikzlibrary{calc}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
\pgfplotsset{compat=1.14}

% sample values, extracted from 100/dB_IC_10mA_S21.txt and 100/dB_IC_10mA_S12.txt 

\pgfplotstableread[col sep=space]{% 
f1  s21
3.00000000000000000E5   -5.37923824569095640E-1
9.24624999999999990E5   -5.23021516857375080E-1
1.54925000000000020E6   -5.24032299826929030E-1 
2.17387499999999980E6   -5.18575016774617570E-1
2.79850000000000020E6   -5.17614614317642550E-1
3.42312500000000020E6   -5.28421012169730810E-1
4.04774999999999970E6   -5.25424891213584110E-1
4.67237500000000060E6   -5.24097415339730870E-1 
5.29700000000000060E6   -5.28626243766300340E-1
5.92162500000000060E6   -5.38603437681817350E-1
6.54625000000000060E6   -5.24872720444434120E-1
7.17087499999999970E6   -5.26809061504114420E-1
7.79549999999999970E6   -5.21513983574569910E-1
8.42012500000000050E6   -5.35052438394172110E-1
}\datas

\pgfplotstableread[col sep=space]{% 
f2  s12
3.00000000000000000E5   -4.61253023410550080E-1
9.24624999999999990E5   -4.44818670150491350E-1
1.54925000000000020E6   -4.45906534066983800E-1
2.17387499999999980E6   -4.54506559283727720E-1
2.79850000000000020E6   -4.50208906640044760E-1
3.42312500000000020E6   -4.52753227856168470E-1
4.04774999999999970E6   -4.53657966529585540E-1
4.67237500000000060E6   -4.64282209437626040E-1
5.29700000000000060E6   -4.51387968956751350E-1
5.92162500000000060E6   -4.59361196203085690E-1
6.54625000000000060E6   -4.66558553131420340E-1
7.17087499999999970E6   -4.44614963756639090E-1
7.79549999999999970E6   -4.57214959955166740E-1
8.42012500000000050E6   -4.54436434169834770E-1
}\datat
\begin{document}    
\begin{tikzpicture}
    \begin{axis}[
    no markers,%
    ]
%       \addplot+[thin] table [col sep=space]{100/dB_IC_10mA_S12.txt};  
% complete file of measurement data
%       \addplot+[thin] table [col sep=space]{100/dB_IC_10mA_S21.txt};  
% complete file of measurement data
%       \addplot+[thin] table [col sep=space]\abs{{100/dB_IC_10mA_S12.txt}-{100/dB_IC_10mA_S21.txt}}; 
% not working
%       \addplot+[thin] table [col sep=space]\abs{\datas - \datat}; 
% not working
    \addplot+[thin] table [col sep=space] (${\abs{\datas - \datat}}$);
    \addplot+[thin] table[col sep=space, x=(${\abs{\datas - \datat}}$),y=f2] 
    \end{axis}
    \end{tikzpicture} 
\end{document}

Best Answer

First I think you need to merge the two tables, to be able to use data from both in the same plot. See e.g. merge two tables into one for a way. Basically, you can insert a column from one table into another using

\pgfplotstablecreatecol[
  copy column from table={\datas}{[index] 1},
  ]{s21}{\datat}

To plot the result of a calculation based on columns in a table, you can use y expr=<calculation>, and in the calculation you can use \thisrow{<column name>} to access values in the table. So if I understand correctly, you want y expr={abs(\thisrow{s21}/\thisrow{s12}-1)*100}, which is used as

\addplot+[thin] table[x=f1,y expr={abs(\thisrow{s21}/\thisrow{s12}-1)*100}] {\datat};

Complete code:

\documentclass{article}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
\pgfplotsset{compat=1.13}

% sample values, extracted from 100/dB_IC_10mA_S21.txt and 100/dB_IC_10mA_S12.txt 

\pgfplotstableread[col sep=space]{% 
f1  s21
3.00000000000000000E5   -5.37923824569095640E-1
9.24624999999999990E5   -5.23021516857375080E-1
1.54925000000000020E6   -5.24032299826929030E-1 
2.17387499999999980E6   -5.18575016774617570E-1
2.79850000000000020E6   -5.17614614317642550E-1
3.42312500000000020E6   -5.28421012169730810E-1
4.04774999999999970E6   -5.25424891213584110E-1
4.67237500000000060E6   -5.24097415339730870E-1 
5.29700000000000060E6   -5.28626243766300340E-1
5.92162500000000060E6   -5.38603437681817350E-1
6.54625000000000060E6   -5.24872720444434120E-1
7.17087499999999970E6   -5.26809061504114420E-1
7.79549999999999970E6   -5.21513983574569910E-1
8.42012500000000050E6   -5.35052438394172110E-1
}\datas

\pgfplotstableread[col sep=space]{% 
f2  s12
3.00000000000000000E5   -4.61253023410550080E-1
9.24624999999999990E5   -4.44818670150491350E-1
1.54925000000000020E6   -4.45906534066983800E-1
2.17387499999999980E6   -4.54506559283727720E-1
2.79850000000000020E6   -4.50208906640044760E-1
3.42312500000000020E6   -4.52753227856168470E-1
4.04774999999999970E6   -4.53657966529585540E-1
4.67237500000000060E6   -4.64282209437626040E-1
5.29700000000000060E6   -4.51387968956751350E-1
5.92162500000000060E6   -4.59361196203085690E-1
6.54625000000000060E6   -4.66558553131420340E-1
7.17087499999999970E6   -4.44614963756639090E-1
7.79549999999999970E6   -4.57214959955166740E-1
8.42012500000000050E6   -4.54436434169834770E-1
}\datat

\pgfplotstablecreatecol[
  copy column from table={\datas}{[index] 0},
  ]{f1}{\datat}
\pgfplotstablecreatecol[
  copy column from table={\datas}{[index] 1},
  ]{s21}{\datat}
\begin{document}    
\begin{tikzpicture}
    \begin{axis}[
    no markers,%
    ]
       \addplot+[thin] table[x=f1,y=s21] {\datat};  
       \addplot+[thin] table[x=f2,y=s12] {\datat};  
    \end{axis}
    \end{tikzpicture} 

\begin{tikzpicture}
    \begin{axis}[
    no markers,%
    ]
       \addplot+[thin] table[x=f1,y expr={abs(\thisrow{s21}/\thisrow{s12}-1)*100}] {\datat};  
    \end{axis}
    \end{tikzpicture} 
\end{document}

Related Solutions

TikZ-PGF – How to Create a Color Map Contour Plot from Matrix Data

Your original input is the only and correct supported way how to communicate matrix data to pgfplots, i.e. by providing one matrix cell per row.

A format which provides the Z data as matrix in which each line in the input file is one row of the entire matrix is currently unsupported.

pgfplots – Using Percentage in PGFPlots Matrix Plot

It does not work in your MWE because you are overwriting it by also giving the option nodes near coors to the \addplot command. Remove the latter one (or specify format here), and it will print. I added a thinspace before the percentage sign, although it can also be recommended to load the siunitx package and let that format and typeset the values for you.

Anyway, here's the quickfixed version:

\documentclass[border=3pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{%
  width=5cm,
  height=18cm,
  compat=1.13,
  colormap={blackwhite}{gray(0cm)=(1); gray(1cm)=(0.5)},
  xticklabels={LPIBG, ALL, HPIBG},
  xtick={0,...,2},
  ytick=\empty
}

\begin{document}
\begin{tikzpicture}
\begin{axis}[%
  enlargelimits=false,
  xlabel style={font=\footnotesize},
  ylabel style={font=\footnotesize},
  legend style={font=\footnotesize},
  xticklabel style={font=\footnotesize},
  yticklabel style={font=\footnotesize},
  colorbar,
  colorbar style={%
    ytick={0,20,40,60,80,100},
    yticklabels={0,20,40,60,80,100},
    yticklabel={\pgfmathprintnumber\tick\,\%},
    yticklabel style={font=\footnotesize}
  },
  point meta min=0,
  point meta max=100,
  nodes near coords={\pgfmathprintnumber\pgfplotspointmeta\,\%},
  every node near coord/.append style={xshift=0pt,yshift=-7pt, black, font=\footnotesize},
]

\addplot[
matrix plot,
mesh/cols=3,
point meta=explicit]
table[meta=C]{
  x y C
  0 0 80
  1 0 36
  2 0 40
  0 1 64
  1 1 80
  2 1 60
  0 2 52
  1 2 84
  2 2 72
  0 3 72
  1 3 28
  2 3 32
  0 4 56
  1 4 84
  2 4 80
  0 5 72
  1 5 52
  2 5 44
  0 6 4
  1 6 84
  2 6 41
  0 7 37
  1 7 69
  2 7 84
  0 8 63
  1 8 53
  2 8 82
  0 9 78
  1 9 74
  2 9 39
  0 10 39
  1 10 63
  2 10 88
  0 11 76
  1 11 74
  2 11 49
  0 12 39
  1 12 6
  2 12 88
  0 13 46
  1 13 33
  2 13 75
  0 14 88
  1 14 67
  2 14 54
  0 15 79
  1 15 83
  2 15 75
  0 16 50
  1 16 46
  2 16 71
  0 17 92
  1 17 71
  2 17 75
  0 18 46
  1 18 33
  2 18 8
};
\end{axis}
\end{tikzpicture}
\end{document}

Best Answer

Related Solutions

TikZ-PGF – How to Create a Color Map Contour Plot from Matrix Data

pgfplots – Using Percentage in PGFPlots Matrix Plot

Related Question