Calculate x-coordinate for given y-value by interpolating data from pgfplotstable

Question

I have a text file data.txt with the following content:

-2 -2 +1
+0 +1 +3
+2 +4 +2

I read it with

\pgfplotstableread{data.txt}\data

and then plot the second column by the first column with

\addplot table [x index = 0, y expr = \thisrowno{1}  ] from \data;

I'd now like to calculate the exact x-value where the graph above crosses the y = 0 line. How can I do that?

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I failed using this answer as I don't understand how it is to use. How do I pass the correct dataset to pgfmath?

Jake also offered various solutions, but actually don't want a node, but number. Also his solution does not interpolate and does not give "exact" results.

---

MWE

\documentclass{article}

\usepackage{tikz}
\usepackage{pgfplots}
\usepackage{pgfplotstable}

\begin{document}  

    \begin{tikzpicture}

    \pgfplotstableread{data.txt}\data

    \begin{axis}
        \addplot table [x index = 0, y expr = \thisrowno{1}  ] from \data;

        % some calculations to get desired value
        \def\xroot{-0.66}
        % draw vertical line        
        \addplot[color=black,thin, dashed] coordinates {(\xroot,4)(\xroot,-2)}
        ;
        % draw zero line
        \addplot[color=black,thin, dashed] coordinates {(-2,0)(2,0)}
        ;

    \end{axis}

    \end{tikzpicture}  

\end{document}

---

Desired output (with manual calculated value):

---

Edit

I now managed to get the intersection point as a node, but how to get the coordinate values?

\documentclass{article}

\usepackage{tikz}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
\usetikzlibrary{intersections}

\begin{document}  

    \begin{tikzpicture}

    \pgfplotstableread{data.txt}\data

    \begin{axis}
        \addplot[name path global = data] table [x index = 0, y expr = \thisrowno{1} ] from \data;

        % draw zero line
        \addplot[color=black,thin, dashed,name path global = zeroline] coordinates {(-2,0)(2,0)}
        ;

        % some calculations to get desired value
        \def\xroot{-0.66}
        % draw vertical line        
        \addplot[color=black,thin, dashed] coordinates {(\xroot,4)(\xroot,-2)}
        ;

        \newcommand*{\getFirstIntersection}[3]{
            \coordinate [name intersections={of=#1 and #2, name=i}] [] (i-1) coordinate (#3);
        }

        \getFirstIntersection{zeroline}{data}{isect}
        \node [fill, color=red] at (isect) {};


    \end{axis}

    \end{tikzpicture}  

\end{document}

I further tried:

\pgfgetlastxy{\macrox}{\macroy}
\node [small dot, color=red, text=black] at (wdaII) {\pgfplotsconvertunittocoordinate{x}{\macrox}\pgfmathprintnumber[fixed,precision=1]{\pgfmathresult}};

but it returns 0 for x as well as for y.

---

Though this is a simple example, the solutions needs to be compatible with groupplots and log-scale axes.. For example this great answer just works for linear axes.

Answer 1

Here I present a solution using the function graph cut y feature of the PGFPlotsTable package. From that manual I used the example and modified it to fit your requirements using the groupplots library.

For more details on how it works please have a look at the comments of the code.

(The data files can be found in your TeX installation in the file "TeX installation folder\doc\latex\pgfplots\pgfplots.doc.src.tar.bz2" and in there in the subfolder "plotdata".)

% used PGFPlots v1.14
\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
    \usetikzlibrary{
        pgfplots.groupplots,
    }
    \pgfplotsset{
        % use this `compat' level to avoid a "dimension too large" error
        compat=1.11,
    }
        % for simplicity save the y value to which you want to find the x
        % value in a variable
        % (because we need it several times later in visualization phase)
        \pgfmathsetmacro{\ycut}{2.5e-4}
    \pgfplotstablenew[
        create on use/cut/.style={
            %
            create col/function graph cut y={
                % search for fixed L2 = \ycut
                \ycut
            }{
                % double log, each function is L2(Basis)
                x=Basis,
                y=L2,
                xmode=log,
                ymode=log,
            }{
                % now, provide each single function f_i(Basis):
                % (data files copied from PGFPlots source files in "plotdata" folder)
                {table=newexperiment1.dat},
                {table=newexperiment2.dat},
                {table=newexperiment3.dat},
            }
        },
        columns={cut},
    ]{3}\loadedtable
\begin{document}

%% For debugging purposes only: Show the data
%\pgfplotstabletypeset{\loadedtable}

\begin{tikzpicture}[
    /pgf/number format/.cd,
        fixed,
        precision=2,
]
        % also for simplicity store the found "cut" values in variables
        % (because we need them to set pins and also want to print the number)
        \pgfplotstablegetelem{0}{cut}\of{\loadedtable}
            \pgfmathsetmacro{\CutOne}{\pgfplotsretval}
        \pgfplotstablegetelem{1}{cut}\of{\loadedtable}
            \pgfmathsetmacro{\CutTwo}{\pgfplotsretval}
        \pgfplotstablegetelem{2}{cut}\of{\loadedtable}
            \pgfmathsetmacro{\CutThree}{\pgfplotsretval}
    \begin{groupplot}[
        group style={
            group size=2 by 1,
        },
        xmode=log,
        ymode=log,
        % so it is not needed to repeat this in both `\nextgroupplot's
        before end axis/.code={
            \draw [blue!30!white] (1,\ycut) -- (1e5,\ycut);
        },
    ]
    \nextgroupplot
        \addplot table [x=Basis,y=L2] {newexperiment1.dat};
        \addplot table [x=Basis,y=L2] {newexperiment2.dat};

        % add the pins to the cut coordinates and add corresponding labels
        % (with the help of the stores variables)
        \node [pin=-90:{$x=\pgfmathprintnumber{\CutOne}$}]   at (\CutOne,\ycut) {};
        \node [pin=+45:{$x=\pgfmathprintnumber{\CutTwo}$}]   at (\CutTwo,\ycut) {};
    \nextgroupplot
        \addplot table [x=Basis,y=L2] {newexperiment3.dat};

        \node [pin=+45:{$x=\pgfmathprintnumber{\CutThree}$}] at (\CutThree,\ycut) {};
    \end{groupplot}
\end{tikzpicture}
\end{document}