# How to plot the maximum and the minimum

I am interested in drawing the minimum and the maximum of two variables, i.e. min(x,y) or max(x,y). The way I was going about doing it so far was to get the contour plots using gnuplot but my attempts have not been successful.

The plots do not show well and I am not quite sure what the reason is. Here is what the code at the end of my post produces:

This is far from the actual functions, unfortunately. The maximum should be a square and the minimum two orthogonal lines as in the plot below.

\documentclass[11pt,a4paper]{article}
\usepackage{fullpage}
\usepackage{graphicx}
\usepackage{indentfirst}
\usepackage{pgfplots}
\usepackage{tikz}
\usepackage[miktex]{gnuplottex}
\pgfplotsset{compat=1.12}
\usepackage{amsmath}
\usepackage{natbib}
\usepackage{amssymb}
\usepackage{xcolor}
\usepackage{hyperref}
\hypersetup{
citecolor={black!50!black},
urlcolor={blue!80!black}

\begin{document}
\begin{tikzpicture}[scale=0.8]
\begin{axis}[
axis lines=left,
view={0}{90},
xlabel=$P_1$,
ylabel=$P_2$,
xmin=0,xmax=1,
ymin=0,ymax=1,
]
contour gnuplot={levels={0.02}}
]
{min(x,y)};
\end{axis}
\end{tikzpicture}\begin{tikzpicture}[scale=0.8]
\begin{axis}[
axis lines=left,
view={0}{90},
xlabel=$P_1$,
ylabel=$P_2$,
xmin=0,xmax=1,
ymin=0,ymax=1,
]
contour gnuplot={levels={0.2}}
]
{max(x,y)};
\end{axis}
\end{tikzpicture}

\end{document}

• Specify the domain: \addplot3[domain=-0.2:1,...... – user11232 Apr 7 '15 at 23:00
• @HarishKumar That works wonders, thank you. If you like, post that as an answer too. – JohnK Apr 7 '15 at 23:04
• John I have added an answer, and add samples too for sharp edges. – user11232 Apr 7 '15 at 23:09

Add the domain and samples to the \addplot3 options.

\documentclass[11pt,a4paper]{article}
\usepackage{pgfplots}
\usepackage[miktex]{gnuplottex}
\pgfplotsset{compat=1.12}

\begin{document}
\begin{tikzpicture}[scale=0.8]
\begin{axis}[
axis lines=left,
view={0}{90},
xlabel=$P_1$,
ylabel=$P_2$,
xmin=-0.2,xmax=1,
ymin=-0.2,ymax=1,
]
domain=-0.2:1,samples=100,contour gnuplot={levels={0.02}}
]
{min(x,y)};
\end{axis}
\end{tikzpicture}\begin{tikzpicture}[scale=0.8]
\begin{axis}[
axis lines=left,
view={0}{90},
xlabel=$P_1$,
ylabel=$P_2$,
xmin=0,xmax=1,
ymin=0,ymax=1,
clip=false
]