# How to set the height of a plot using pgfplot?

I thought that the option height passed to \nextgroupplot is what i needed but it's not. As you can probably see in the picture, the second plot isn't two times the height of the first one. So how can I have the second plot two times the height of the first one?

Bonus: To be precise, what I would is that a distance of 1 along the y axis of the first plot is the same as a distance of 1 along the y axis of the second plot.

\documentclass[]{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{groupplots}
\pgfplotsset{compat=1.14}
\begin{document}
\begin{tikzpicture}
\begin{groupplot}[
group style={
group size=1 by 2,
vertical sep=12pt,
group name=G},
axis x line=center, axis y line=center,
xmin = 0, xmax = 4.2
]
\nextgroupplot[
width = \textwidth, height = 0.2*\textwidth,
ymin = 0, ymax = 1.2
]
\draw (0,0)
-| (.75,1) -| (1,0)
-| (1.75,1) -| (2,0)
-| (2.75,1) -| (3,0)
-| (3.75,1) -| (4,0)
-| (4.75,1) -| (5,0);
\nextgroupplot[
width = \textwidth, height = 0.4*\textwidth,
ymin = -1.2, ymax = 1.2
]
\draw (0,1)
-| (.75,-1) -| (1,1)
-| (1.75,-1) -| (2,1)
-| (2.75,-1) -| (3,1)
-| (3.75,-1) -| (4,1)
-| (4.75,-1) -| (5,1);
\end{groupplot}
\end{tikzpicture}
\end{document}


I think you are looking for unit vector ratio. This makes sure that the y units have the same meaning in both plots. As mentioned by Torbjørn T. in the comments in this question, the height means height including everything, also tick labels.

\documentclass[]{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{groupplots}
\pgfplotsset{compat=1.14}
\begin{document}
\begin{tikzpicture}
\begin{groupplot}[
group style={
group size=1 by 2,
vertical sep=12pt,
group name=G},
axis x line=center, axis y line=center,
xmin = 0, xmax = 4.2,unit vector ratio=2 1,width = \textwidth
]
\nextgroupplot[
ymin = 0, ymax = 1.2
]
\draw (0,0)
-| (.75,1) -| (1,0)
-| (1.75,1) -| (2,0)
-| (2.75,1) -| (3,0)
-| (3.75,1) -| (4,0)
-| (4.75,1) -| (5,0);
\nextgroupplot[
ymin = -1.2, ymax = 1.2
]
\draw (0,1)
-| (.75,-1) -| (1,1)
-| (1.75,-1) -| (2,1)
-| (2.75,-1) -| (3,1)
-| (3.75,-1) -| (4,1)
-| (4.75,-1) -| (5,1);
\end{groupplot}
\end{tikzpicture}
\end{document}