getting the same height for two side by side pgfplot figures

Question

I display two side by side pgfplots which dont have the same xmax and ymax. In a first case with (xmin=-1,xmax=3,ymin=-1,ymax=11) the two plots have the same height (see EXAMPLE 1). In a second case with (xmin=-1,xmax=12,ymin=-1,ymax=7) the two plots do not have exactly the same height. But I would like them to have the same height (see EXAMPLE 2). Maybe one has to do something specific when ymax-ymin is less than xmax-xmin ?

EXAMPLE 1 (with the same height)

\documentclass[a4paper]{article}
\usepackage{pgfplots}
\usepackage{pifont}

\begin{document}

\def\argument#1{\mathtt{#1}}
\def\constraint#1{\textsc{#1}}

\begin{tikzpicture}[scale=0.7]
\begin{scope}[xshift=0cm,yshift=0cm]
\begin{axis}[axis equal image=true,xlabel={nb\_bump\_on\_decreasing\_sequence},
ylabel={nb\_decreasing},
title style={yshift=1.2ex},
title={$\argument{sv}=12$},
xtick ={0,2,...,2},
ytick ={0,2,...,10},
minor tick num=1,
grid=both,grid style={line width=.1pt, draw=gray!10},
major grid style={line width=.2pt,draw=gray!20},
xmin=-1,xmax=4,
ymin=-1,ymax=12,
extra description/.code={
 \node (description1) at (c1) {\large\ding{172}};
 \node (description2) at (c2) {\large\ding{173}};
 \node (description3) at (c3) {\large\ding{174}};
 \node (description4) at (c4) {\large\ding{175}};
}
]
\addplot[blue!20,only marks] coordinates {(0,0)(0,1)(0,2)(0,3)(0,4)(0,5)(0,6)(0,7)(0,8)(0,9)(0,10)(0,11)};
\addplot[blue!50,only marks] coordinates {(1,4)(1,5)(1,6)(1,7)(1,8)(1,9)(1,10)(2,6)(2,7)(2,8)(2,9)(3,8)};
\addplot[red,only marks] coordinates {(1,3)};
\addplot[blue!50,densely dashed] coordinates {(0,0)(3,8)(0,11)(0,0)(0,0)};
\draw[fill=pink,opacity=0.1] (axis cs:-1.5,-1) -- (axis cs:5.0,12) -- (axis cs:5.0,12) -- 
                             (axis cs:5.0,-1) -- cycle;
\addplot[black!20,thick] coordinates {(-1.5,-1)(5.0,12)};
\draw[fill=pink,opacity=0.1] (axis cs:-1,4) -- (axis cs:4,4) -- (axis cs:4,-1) --
                             (axis cs:-1,-1) -- cycle;
\addplot[black!20,thick] coordinates {(-1,4)(4,4)};
\draw[fill=cyan,opacity=0.2] (axis cs:-1,12.0) -- (axis cs:4,7.0) -- (axis cs:4,12) -- (axis cs:-1,12) -- cycle;
\addplot[black!50,thick] coordinates {(-1,12.0)(4,7.0)};
\addplot[orange] coordinates {(1,3)(4,3)};
\addplot[orange,only marks,mark=otimes*]coordinates {(1,3)};
\addplot[orange,only marks,mark=diamond*]coordinates {(2,3)(3,3)};
\coordinate (c1) at (axis cs:4.6,10.0);
\coordinate (c2) at (axis cs:4.6,4);
\coordinate (c3) at (axis cs:4.6,7.0);
\coordinate (c4) at (axis cs:4.6,3);
\end{axis}
\end{scope}
\begin{scope}[xshift=10cm,yshift=0cm]
\begin{axis}[axis equal image=true,xlabel={nb\_bump\_on\_decreasing\_sequence},
ylabel={nb\_decreasing},
title style={yshift=1.2ex},
title={$\argument{sv}=11$},
xtick ={0,2,...,3},
ytick ={0,2,...,11},
minor tick num=1,
grid=both,grid style={line width=.1pt, draw=gray!10},
major grid style={line width=.2pt,draw=gray!20},
xmin=-1,xmax=3,
ymin=-1,ymax=11,
extra description/.code={
 \node (description1) at (c1) {\large\ding{172}};
 \node (description2) at (c2) {\large\ding{173}};
 \node (description3) at (c3) {\large\ding{174}};
 \node (description4) at (c4) {\large\ding{175}};
}
]
\addplot[blue!20,only marks] coordinates {(0,0)(0,1)(0,2)(0,3)(0,4)(0,5)(0,6)(0,7)(0,8)(0,9)(0,10)};
\addplot[blue!50,only marks] coordinates {(1,4)(1,5)(1,6)(1,7)(1,8)(1,9)(2,6)(2,7)(2,8)};
\addplot[red,only marks] coordinates {(1,3)};
\addplot[blue!50,densely dashed] coordinates {(0,0)(2,6)(2,8)(0,10)(0,0)(0,0)};
\draw[fill=pink,opacity=0.1] (axis cs:-1.5,-1) -- (axis cs:4.5,11) -- (axis cs:4.5,11) --
                             (axis cs:4.5,-1) -- cycle;
\addplot[black!20,thick] coordinates {(-1.5,-1)(4.5,11)};
\draw[fill=pink,opacity=0.1] (axis cs:-1,4) -- (axis cs:3,4) -- (axis cs:3,-1) --
                             (axis cs:-1,-1) -- cycle;
\addplot[black!20,thick] coordinates {(-1,4)(3,4)};
\draw[fill=cyan,opacity=0.2] (axis cs:-1,11.0) -- (axis cs:3,7.0) -- (axis cs:3,11) --
                             (axis cs:-1,11) -- cycle;
\addplot[black!50,thick] coordinates {(-1,11.0)(3,7.0)};
\addplot[orange] coordinates {(1,3)(3,3)};
\addplot[orange,only marks,mark=otimes*]coordinates {(1,3)};
\addplot[orange,only marks,mark=diamond*]coordinates {(2,3)};
\coordinate (c1) at (axis cs:3.55,8.0);
\coordinate (c2) at (axis cs:3.55,4);
\coordinate (c3) at (axis cs:3.55,7.0);
\coordinate (c4) at (axis cs:3.55,3);
\end{axis}
\end{scope}
\end{tikzpicture}

\end{document}

EXAMPLE 2 (where the heights differ)

\documentclass[a4paper]{article}
\usepackage{pgfplots}
\usepackage{pifont}

\begin{document}

\def\argument#1{\mathtt{#1}}
\def\constraint#1{\textsc{#1}}

\begin{tikzpicture}[scale=0.7]
\begin{scope}[xshift=0cm,yshift=0cm]
\begin{axis}[axis equal image=true,xlabel={nb\_decreasing},
ylabel={nb\_steady\_sequence},
title style={yshift=1.2ex},
title={$\argument{sv}=12$},
xtick ={0,2,...,10},
ytick ={0,2,...,7},
minor tick num=1,
grid=both,grid style={line width=.1pt, draw=gray!10},
major grid style={line width=.2pt,draw=gray!20},
xmin=-1,xmax=12,
ymin=-1,ymax=7,
extra description/.code={
 \node (description1) at (c1) {\large\ding{172}};
}
]
\addplot[blue!20,only marks]
    coordinates {(0,0)(0,1)(0,2)(0,3)(0,4)(0,5)(0,6)(1,0)(2,0)(3,0)(4,0)(5,0)(6,0)(7,0)(8,0)(9,0)(10,0)(11,0)};
\addplot[blue!50,only marks]
    coordinates {(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(7,1)(7,2)(7,3)(7,4)(8,1)(8,2)(8,3)(9,1)(9,2)(10,1)};
\addplot[blue!50,densely dashed]
    coordinates {(0,0)(11,0)(5,6)(0,6)(0,0)(0,0)};
\draw[fill=cyan,opacity=0.2] (axis cs:-1,12.0) -- (axis cs:12,-1.0) -- (axis cs:12,12) --
                             (axis cs:-1,12) -- cycle;
\addplot[black!50,thick] coordinates {(-1,12.0)(12,-1.0)};
\coordinate (c1) at (axis cs:12.6,-1.0);
\end{axis}
\end{scope}
\begin{scope}[xshift=10cm,yshift=0cm]
\begin{axis}[axis equal image=true,xlabel={nb\_decreasing},
ylabel={nb\_steady\_sequence},
title style={yshift=1.2ex},
title={$\argument{sv}=11$},
xtick ={0,2,...,11},
ytick ={0,2,...,4},
minor tick num=1,
grid=both,grid style={line width=.1pt, draw=gray!10},
major grid style={line width=.2pt,draw=gray!20},
xmin=-1,xmax=11,
ymin=-1,ymax=6,
extra description/.code={
 \node (description1) at (c1) {\large\ding{172}};
}
]
\addplot[blue!20,only marks] coordinates {(0,0)(0,1)(0,2)(0,3)(0,4)(0,5)(1,0)(2,0)(3,0)(4,0)(5,0)(6,0)(7,0)(8,0)(9,0)(10,0)};
\addplot[blue!50,only marks] coordinates {(1,1)(1,2)(1,3)(1,4)(1,5)(2,1)(2,2)(2,3)(2,4)(2,5)(3,1)(3,2)(3,3)(3,4)(3,5)(4,1)(4,2)(4,3)(4,4)(4,5)(5,1)(5,2)(5,3)(5,4)(5,5)(6,1)(6,2)(6,3)(6,4)(7,1)(7,2)(7,3)(8,1)(8,2)(9,1)};
\addplot[blue!50,densely dashed] coordinates {(0,0)(10,0)(5,5)(0,5)(0,0)(0,0)};
\draw[fill=cyan,opacity=0.2] (axis cs:-1,11.0) -- (axis cs:11,-1.0) -- (axis cs:11,11) --
                             (axis cs:-1,11) -- cycle;
\addplot[black!50,thick] coordinates {(-1,11.0)(11,-1.0)};
\coordinate (c1) at (axis cs:11.55,-1.0);
\end{axis}
\end{scope}
\end{tikzpicture}

\end{document}

Answer 1

I think perhaps what you're seeing is related to the documented behaviour for axis equal image. With that setting, pgfplots will happily rescale an axis so it no longer conforms to the height/width setting. The axis equal setting on the other hand, will respect the height/width setting, by adjusting the axis limits.

Depending on your requirements, either not using axis equal image, or using axis equal instead, might be a solution, and in addition set both width and height explicitly. (I used width=6cm, height=4.5cm below.)

Not related to your question, but you might be interested in the groupplots library, demonstrated below.

\documentclass[a4paper]{article}
\usepackage{pgfplots}
\usepgfplotslibrary{groupplots}
\pgfplotsset{compat=1.16}

\usepackage{pifont}
\newcommand\argument[1]{\mathtt{#1}}
\newcommand\constraint[1]{\textsc{#1}}


\begin{document}

Without \texttt{axis equal image}:

\begin{tikzpicture}
\begin{groupplot}[
  group style={
    group size=2 by 1,
    horizontal sep=1.5cm,
  },
  % set common options here
  footnotesize, % reduces font size of diagram
  xmin=-1,
  ymin=-1,
  width=6cm,
  height=4.5cm,
  ylabel={nb\_steady\_sequence},
  xlabel={nb\_decreasing},
  title style={yshift=1.2ex},
  minor tick num=1,
  xtick ={0,2,...,10},
  grid=both,grid style={line width=.1pt, draw=gray!10},
  major grid style={line width=.2pt,draw=gray!20},
  extra description/.code={
   \node (description1) at (c1) {\large\ding{172}};
  }
]

\nextgroupplot[
  title={$\argument{sv}=12$},
  ytick ={0,2,...,7},
  xmax=12,
  ymax=7,
]
\addplot[blue!20,only marks]
    coordinates {(0,0)(0,1)(0,2)(0,3)(0,4)(0,5)(0,6)(1,0)(2,0)(3,0)(4,0)(5,0)(6,0)(7,0)(8,0)(9,0)(10,0)(11,0)};
\addplot[blue!50,only marks]
    coordinates {(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(7,1)(7,2)(7,3)(7,4)(8,1)(8,2)(8,3)(9,1)(9,2)(10,1)};
\addplot[blue!50,densely dashed]
    coordinates {(0,0)(11,0)(5,6)(0,6)(0,0)(0,0)};
\draw[fill=cyan,opacity=0.2] (axis cs:-1,12.0) -- (axis cs:12,-1.0) -- (axis cs:12,12) --
                             (axis cs:-1,12) -- cycle;
\addplot[black!50,thick] coordinates {(-1,12.0)(12,-1.0)};
\coordinate (c1) at (axis cs:12.6,-1.0);

\nextgroupplot[
  title={$\argument{sv}=11$},
  ytick ={0,2,...,4},
  xmax=11,
  ymax=6,
]
\addplot[blue!20,only marks] coordinates {(0,0)(0,1)(0,2)(0,3)(0,4)(0,5)(1,0)(2,0)(3,0)(4,0)(5,0)(6,0)(7,0)(8,0)(9,0)(10,0)};
\addplot[blue!50,only marks] coordinates {(1,1)(1,2)(1,3)(1,4)(1,5)(2,1)(2,2)(2,3)(2,4)(2,5)(3,1)(3,2)(3,3)(3,4)(3,5)(4,1)(4,2)(4,3)(4,4)(4,5)(5,1)(5,2)(5,3)(5,4)(5,5)(6,1)(6,2)(6,3)(6,4)(7,1)(7,2)(7,3)(8,1)(8,2)(9,1)};
\addplot[blue!50,densely dashed] coordinates {(0,0)(10,0)(5,5)(0,5)(0,0)(0,0)};
\draw[fill=cyan,opacity=0.2] (axis cs:-1,11.0) -- (axis cs:11,-1.0) -- (axis cs:11,11) --
                             (axis cs:-1,11) -- cycle;
\addplot[black!50,thick] coordinates {(-1,11.0)(11,-1.0)};
\coordinate (c1) at (axis cs:11.55,-1.0);
\end{groupplot}

\end{tikzpicture}


With \texttt{axis equal} instead of \texttt{axis equal image}:

\begin{tikzpicture}
\begin{groupplot}[
  group style={
    group size=2 by 1,
    horizontal sep=1.5cm,
  },
  % set common options here
  axis equal,
  footnotesize, % reduces font size of diagram
  xmin=-1,
  ymin=-1,
  width=6cm,
  height=4.5cm,
  ylabel={nb\_steady\_sequence},
  xlabel={nb\_decreasing},
  title style={yshift=1.2ex},
  minor tick num=1,
  xtick ={0,2,...,10},
  grid=both,grid style={line width=.1pt, draw=gray!10},
  major grid style={line width=.2pt,draw=gray!20},
  extra description/.code={
   \node (description1) at (c1) {\large\ding{172}};
  }
]

\nextgroupplot[
  title={$\argument{sv}=12$},
  ytick ={0,2,...,7},
  xmax=12,
  ymax=7,
]
\addplot[blue!20,only marks]
    coordinates {(0,0)(0,1)(0,2)(0,3)(0,4)(0,5)(0,6)(1,0)(2,0)(3,0)(4,0)(5,0)(6,0)(7,0)(8,0)(9,0)(10,0)(11,0)};
\addplot[blue!50,only marks]
    coordinates {(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(7,1)(7,2)(7,3)(7,4)(8,1)(8,2)(8,3)(9,1)(9,2)(10,1)};
\addplot[blue!50,densely dashed]
    coordinates {(0,0)(11,0)(5,6)(0,6)(0,0)(0,0)};
\draw[fill=cyan,opacity=0.2] (axis cs:-1,12.0) -- (axis cs:12,-1.0) -- (axis cs:12,12) --
                             (axis cs:-1,12) -- cycle;
\addplot[black!50,thick] coordinates {(-1,12.0)(12,-1.0)};
\coordinate (c1) at (axis cs:12.6,-1.0);

\nextgroupplot[
  title={$\argument{sv}=11$},
  ytick ={0,2,...,4},
  xmax=11,
  ymax=6,
]
\addplot[blue!20,only marks] coordinates {(0,0)(0,1)(0,2)(0,3)(0,4)(0,5)(1,0)(2,0)(3,0)(4,0)(5,0)(6,0)(7,0)(8,0)(9,0)(10,0)};
\addplot[blue!50,only marks] coordinates {(1,1)(1,2)(1,3)(1,4)(1,5)(2,1)(2,2)(2,3)(2,4)(2,5)(3,1)(3,2)(3,3)(3,4)(3,5)(4,1)(4,2)(4,3)(4,4)(4,5)(5,1)(5,2)(5,3)(5,4)(5,5)(6,1)(6,2)(6,3)(6,4)(7,1)(7,2)(7,3)(8,1)(8,2)(9,1)};
\addplot[blue!50,densely dashed] coordinates {(0,0)(10,0)(5,5)(0,5)(0,0)(0,0)};
\draw[fill=cyan,opacity=0.2] (axis cs:-1,11.0) -- (axis cs:11,-1.0) -- (axis cs:11,11) --
                             (axis cs:-1,11) -- cycle;
\addplot[black!50,thick] coordinates {(-1,11.0)(11,-1.0)};
\coordinate (c1) at (axis cs:11.55,-1.0);
\end{groupplot}

\end{tikzpicture}

\end{document}