Two y-axis pgfplot with ylabel and width=\linewidth badly aligned

Question

I am trying to draw a pgfplot with to different y-axis with their respective label in a full line width and I can't get an alignment of the whole tikzpicture within the margins. The problem seems to come from the ylabel which, on the left axis shift the plot to the right, and on the right axis is plotted out of the picture, ie in the margin. I try to add the ylabel style={overlay} so I get the plot centered but both ylabel are this time in the margins. For sure, I can put a 0.95\linewidth but I don't find this solution good enough since it isn't generalist.

Does anyone knows how can I fix this small example in an automatically way (meaning that pgfplot or tikz finds the right width alone)?

\documentclass{article}

\usepackage{pgfplots}
\pgfplotsset{compat=newest}

\begin{document}
\centering{}
\hrule{}
I\hfill I\hfill I\\
\begin{tikzpicture}
\begin{axis}[
  width=\linewidth,
  xmin=-5,xmax=5,
  axis y line*=left,
  axis x line*=top,
  ylabel={$y=x^{2}$ label},
  ]
  \addplot {x^2};
\end{axis}
\begin{axis}[
  width=\linewidth,
  xmin=0,xmax=15,
  domain=0:15,
  axis y line*=right,
  axis x line*=bottom,
  ylabel={$y=x$ label},
  ]
  \addplot[red] {x};
\end{axis}
\end{tikzpicture}

\end{document}

which produces this badly aligned plot

Answer 1

Of course, if you draw something that is wider than the line width, the object will extend past the right margin. You have two possibilities:

\makebox[\linewidth]{%
  \begin{tikzpicture}
  ...
  \end{tikzpicture}}

that will leave the axis' labels in the left and right margins; or

\resizebox{\linewidth}{!}{%
  \begin{tikzpicture}
  ...
  \end{tikzpicture}}

(with the graphicx package) that will rescale the diagram to fit the line width.

Of course, the best solution is to say

width=.8\linewidth

(or what you prefer) and forget about boxing and rescaling. There is no law stating that diagrams must fill the line width; to the contrary, diagrams shorter than the line width should be preferred, in my opinion, if possible.