function plot (anim)

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% Full code on github: https://github.com/bvieuble/TeXFantasy
% Appears in my lecture ``Mixed precision iterative refinement'' (2023).
\newcommand{\plote}{
    \addplot[myblue,no marks,domain=-0.5:9,thick] {0.5*x - 0.75};
    \addplot[myred,no marks,domain=-0.5:9,thick,restrict y to domain={-1:5}]
    {0.65*x - 2.3};
    \addplot [only marks,mark=*] coordinates { (8,2.9) };
    \node[rotate=30] at (axis cs:7.1,1.9) {$\alertrm{\widehat{\nabla} 
    f(x_0)}$};
    \node[rotate=20] at (axis cs:6,2.6) {$f(x) = Ax-b$};
}
\newcommand{\plotf}{
    \addplot[myblue,no marks,domain=-0.5:9,thick] {0.5*x - 0.75};
    \addplot[no marks,domain=-0.5:9,thick,restrict y to domain={-1:5}]
    {0.65*x - 2.3};
    \addplot [only marks,mygreen,mark=*] coordinates { (3.55,0) };
    \node[rotate=20] at (axis cs:6,2.6) {$f(x) = Ax-b$};
    \node at (axis cs:3.55,-0.4) {\large \alertgm{$x_{1}$}};
}
\newcommand{\plotg}{
    \addplot[myblue,no marks,domain=-0.5:9,thick] {0.5*x - 0.75};
    \addplot[no marks,domain=-0.5:9,thick,restrict y to domain={-1:5}]
    {0.65*x - 2.3};
    \addplot [only marks,myred,mark=*] coordinates { (3.9,0) };
    \node[rotate=20] at (axis cs:6,2.6) {$f(x) = Ax-b$};
    \node at (axis cs:3.9,-0.4) {\large \alertrm{$\widehat{x}_{1}$}};
}
\newcommand{\ploth}{
    \addplot[myblue,no marks,domain=-0.5:9,thick] {0.5*x - 0.75};
    \draw [dashed,thick] (axis cs:{3.9,0}) -- (axis cs:{3.9,1.6});
    \addplot [only marks,mark=*] coordinates { (3.9,1.6) };
    \node at (axis cs:3.9,2.1) {$\widehat{f}(x_1)$};
    \addplot [only marks,mark=|] coordinates { (3.9,0) };
    \node at (axis cs:3.9,-0.4) {\large $\widehat{x}_{1}$};
}
\newcommand{\ploti}{
    \addplot[myblue,no marks,domain=-0.5:9,thick] {0.5*x - 0.75};
    \addplot[no marks,domain=-0.5:9,thick] {0.45*x - 0.155};
  	\addplot [only marks,mark=*] coordinates { (3.9,1.6) };
    \node[rotate=20] at (axis cs:2.7,1.5) {$\widehat{\nabla}f(x_1)$};
    \addplot [only marks,mark=|] coordinates { (3.9,0) };
    \node at (axis cs:3.9,-0.4) {\large $\widehat{x}_{1}$};
}
\newcommand{\plotj}{
    \addplot[myblue,no marks,domain=-0.5:9,thick] {0.5*x - 0.75};
    \addplot[no marks,domain=-0.5:9,thick] {0.45*x - 0.155};
    \addplot [only marks,mark=*] coordinates { (0.7,0) };
    \node at (axis cs:0.7,-0.4) {\large $\widehat{x}_{2}$};
    \addplot [only marks,mark=|] coordinates { (3.9,0) };
    \node at (axis cs:3.9,-0.4) {\large $\widehat{x}_{1}$};
}

\foreach \whichplot in
    {\plota,\plotb,\plotc,\plotd,\plote,\plotf,\plotg,\ploth,\ploti,\plotj}
{\begin{tikzpicture}
\begin{axis}
    [
        ymajorticks=false,
        xtick={8,1.5},
        xticklabels = {\large $x_0$, \large $x$},
        width=1.1\textwidth,
        height=0.6\textwidth,
        ymin=-1,
        ymax=5,
        xmax=9,
        xmin=-0.5,
        axis lines=middle,
        tick style={black, very thick},
    ]

    \whichplot

\end{axis}
\end{tikzpicture}}