TikZ - Compute the array being the min of 2 arrays

Question

I define 2 arrays r and p and draw them.

I would like now to compute the min of r and p in order to draw it in a similar way. The resulting array would be {0.2, 0.4, 0.8, 0.8, 0.4, 0.0, 0.1, 0.0, 0.1 ,0.5}, but I would like to compute it automatically.

Do you have any idea ?

Here is a MWE regardig the definition and the drawing of r and p :

\begin{tikzpicture}
  \def\r{{0.2}, {0.4}, {1.0}, {0.8}, {1.0}, {0.0}, {0.3}, {0.5}, {0.1}, {0.5}};
  \def\p{{0.9}, {0.5}, {0.8}, {0.8}, {0.4}, {0.3}, {0.1}, {0.0}, {0.8}, {0.7}};

  \filldraw (0, 0.2) node {$r$}
    \foreach \y [count=\x from 0] in \r { -- (\x, \y) circle[radius=1pt] };
  \filldraw (0, 0.9) node {$r$}
    \foreach \y [count=\x from 0] in \p { -- (\x, \y) circle[radius=1pt] };

\end{tikzpicture}

Answer 1

Basic idea is to iterate through the first list and locate the nth member of the second list and save the minimum into another list.

Notes:

• You should avoid single letter variable names, or at least use \newcommand which would detect that you are overwriting existing macros. In this case \r is reviously defined. See Why do 2 identical function definitions with different names produce two different plots?

References:

• How keep a running list of strings and then process them one at a time
• Expansion issue when adding to CSV list from within a \foreach

Code:

\documentclass{article}
\usepackage{tikz}
%% https://tex.stackexchange.com/questions/14393/how-keep-a-running-list-of-strings-and-then-process-them-one-at-a-time
\makeatletter
\newcommand*@NewList{}%
\newcommand{\ApendToNewList}[1]{%
    %% https://tex.stackexchange.com/questions/83595/expansion-issue-when-adding-to-csv-list-from-within-a-foreach
    \begingroup\edef\TempValue{\endgroup%
        \noexpand\g@addto@macro\noexpand@NewList{\ifx@NewList\empty\else,\fi#1}}\TempValue%
}
\newcommand*{\ExtractNthValueOfList}[3]{%
    \foreach [count=\i from 1] \x in #3 {%
        \ifnum\i=#2\relax
            \xdef#1{\x}%
            \breakforeach%
         \fi
    }%
}
\newcommand{@NthValue}{xx}
\newcommand{\ExtractMinList}[3]{
    % #1 = variable to contain extract list
    % #2 = first list
    % #3 = second list
    \foreach [count=\j from 1] \y in #2 {%
        \ExtractNthValueOfList{@NthValue}{\j}{#3}%
        \pgfmathsetmacro{\MinValue}{min(\y,@NthValue)}%
        \ApendToNewList{\MinValue}%
        \typeout{\j, \y, @NthValue}% <--- Useful for debugging
    }%
    \edef#1{@NewList}%
}
\makeatother
\newcommand\RList{{0.2}, {0.4}, {1.0}, {0.8}, {1.0}, {0.0}, {0.3}, {0.5}, {0.1}, {0.5}}
\newcommand\PList{{0.9}, {0.5}, {0.8}, {0.8}, {0.4}, {0.3}, {0.1}, {0.0}, {0.8}, {0.7}}
\newcommand\ExtractedMinList{}% Ensure that we are not overwriting an existing macro
\begin{document}
    \ExtractMinList{\ExtractedMinList}{\RList}{\PList}%
    Extracted List=\ExtractedMinList
\end{document}