How to draw in pgfplot until intersection with plot line?

Question

I am trying to draw an arrow from the left side of my diagram and until it intersects with the plot.

However I get this error message:

! Package pgf Error: No shape named intersection-1 is known.

I know that might mean that there is no intersection. But I don't understand how those two things could not intersect...

\documentclass{memoir}
\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{intersections}

\begin{document}
\begin{figure}
\begin{tikzpicture}
\begin{axis}[ymin=0,ymax=100,xmin=5E-13,xmax=3E-4,
xlabel=Concentration,
ylabel=Effect (\%),
axis lines=left,
width=2\marginparwidth,
height=1.4\marginparwidth,
ytick={0,25,50,75,100},
xmode = log,
tick label style = {font=\footnotesize},
]
\addplot [color=black, name path=P] coordinates {
    (1E-4, 0)
    (1E-5, 0)
    (1E-6, 2)
    (1E-7, 21)
    (1E-8, 66)
    (1E-9, 88)
    (1E-10, 94)
    (1E-11, 95)
    (1E-12, 96)
    };
\addplot [only marks] coordinates {
    (1E-4, 0)
    (1E-5, 0)
    (1E-6, 2)
    (1E-7, 21)
    (1E-8, 66)
    (1E-9, 88)
    (1E-10, 94)
    (1E-11, 95)
    (1E-12, 96)
    };

\path [name path=A] (1E-12, 50) -- (1E-4, 50);
\path [name intersections={of=A and P}];
\draw[->, thick] (1E-12, 50) -- (intersection-1); 
    \end{axis}

\end{tikzpicture}
\end{figure}

\end{document}

Answer 1

The best way to debug this sort of stuff is to first change the \path to a \draw so you can see what intersections you are looking for. Using \draw for the horizontal line:

\draw [name path=A] (1E-12, 50) -- (1E-4, 50);

you don't see the line on the graph. Hence, no intersections. Within pgfplots's axis environment you need to use the axis cs coordinate system. So, changing this to:

\draw [name path=A] (axis cs: 1E-12, 50) -- (axis cs: 1E-4, 50);

you can see the horizontal line. Changing the above back to \path you obtain:

Code:

\documentclass{memoir}
\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{intersections}
\begin{document}
\begin{figure}
\begin{tikzpicture}
\begin{axis}[ymin=0,ymax=100,xmin=5E-13,xmax=3E-4,
xlabel=Concentration,
ylabel=Effect (%),
axis lines=left,
width=2\marginparwidth,
height=1.4\marginparwidth,
ytick={0,25,50,75,100},
xmode = log,
tick label style = {font=\footnotesize},
]
\addplot [color=black, name path=P] coordinates {
    (1E-4, 0)
    (1E-5, 0)
    (1E-6, 2)
    (1E-7, 21)
    (1E-8, 66)
    (1E-9, 88)
    (1E-10, 94)
    (1E-11, 95)
    (1E-12, 96)
    };
\addplot [only marks] coordinates {
    (1E-4, 0)
    (1E-5, 0)
    (1E-6, 2)
    (1E-7, 21)
    (1E-8, 66)
    (1E-9, 88)
    (1E-10, 94)
    (1E-11, 95)
    (1E-12, 96)
    };
\path [name path=A] (axis cs: 1E-12, 50) -- (axis cs: 1E-4, 50);
\path [name intersections={of=A and P}];
\draw[-latex, thick, red] (1E-12, 50) -- (intersection-1); 
\end{axis}
\end{tikzpicture}
\end{figure}
\end{document}