expl3 - An environment to explain the calculation of an expected value (finite case)

Question

I would like to automate the production of the following output (the formatting is not so good but I will do a better one later).

This picture has been obtained using this code :

\documentclass[12pt,a4paper]{article}
\usepackage{nicematrix}
\usepackage{tikz}
\usetikzlibrary{fit}
\usepackage{tcolorbox}
\tcbuselibrary{theorems}
\begin{document}
$\begin{NiceArray}{r|c|c|c|c|c}[name=tab]
    x_k  & 0      & 1   & 2   & 3    & 4    \
    \hline
    p_k  & 0.2000 & 0.2 & 0.4 & 0.05 & 0.15  \
\end{NiceArray}$
\begin{tikzpicture}[remember picture,overlay]
    \node[draw = red,
          rounded corners,
          fit = (tab-1-2.north west) (tab-1-2.north east) 
                (tab-2-2.south west) (tab-2-2.south east)] {};
    \node[draw = blue,
          rounded corners,
          fit = (tab-1-4.north west) (tab-1-4.north east) 
                (tab-2-4.south west) (tab-2-4.south east)] {};
    \node[draw = black!60!green,
          rounded corners,
          fit = (tab-1-6.north west) (tab-1-6.north east) 
                (tab-2-6.south west) (tab-2-6.south east)] {};
\end{tikzpicture}
$E(X) = \sum_k p_k x_k$
$E(X) = \tcboxmath[colframe = red]%
       {0.2000 \cdot 0}
      + 0.2    \cdot 1
      + \tcboxmath[colframe = blue]%
       {0.4    \cdot 2}
      + 0.05   \cdot 3
      + \tcboxmath[colframe = black!60!green]%
       {0.15   \cdot 4}$
\end{document}

I would like to only type the array part of the code.

\begin{exvalexpval}
    x_k  & 0      & 1   & 2   & 3    & 4    \\
    \hline
    p_k  & 0.2000 & 0.2 & 0.4 & 0.05 & 0.15  \\
\end{exvalexpval}

The algorithm could be the following one but I do not know how to do that with expl3.

Store the xk value in a list.
Store the pk value in other list.
Use the lenght of the lists to build the argument r|c|c|c|c|c of NiceArray.
Use the two lists to build the content after the table.
Wich colors ? In practice I think that no more than five colors red, blue, black!60!green, orange and gray will be really needed. If more colors are needed, just use a cycle of colors.

Note : I do not want to calculate the value of the expected value. There will be cases of use with formal values in the table.

Some hints: see latex3 functions in (sub)package l3seq, especially the \seq_set_split:Nnn and mapping functions. They are documented in interface3.pdf. And you may also input in csv format and use existing csv-parsing packages. — muzimuzhi Z, Aug 08 '20 at 20:14

Rmano · Answer 1 · 2020-08-10T18:51:24.853

This is my first go at the code. I am trying to learn LaTeX3, so I shamelessly admit this is a bit a bait so that someone will bleah over it and will try to teach me the correct way...

In this first code (this is just my second snippet in expl3), there are no color boxes, etc --- it's just a proof of concept. I have to think a bit more about how to do it. There is also no check whatsoever --- put lists with different lengths here and anything can happen.

\documentclass[fleqn]{article}
\usepackage{amsmath}
\usepackage{expl3}
\usepackage{xparse}
\ExplSyntaxOn
\seq_new:N \l_mbc_listx_seq
\seq_new:N \l_mbc_listp_seq
\NewDocumentCommand\ShowExpectedCalculation{mmmmm} % x, p, index, list x, list p
{
    \seq_set_split:Nnn \l_mbc_listx_seq {,} {#4}
    \seq_set_split:Nnn \l_mbc_listp_seq {,} {#5}
    \int_zero_new:N \l_mbc_N_int
    \int_set:Nn \l_mbc_N_int { \seq_count:N \l_mbc_listx_seq }
    %
    % generate the first table
    %
    \[
    \begin{array}{l|*{\int_use:N \l_mbc_N_int}{c}}
        #1\sb{#3} & \seq_use:Nn \l_mbc_listx_seq { & } \\
        #2\sb{#3} & \seq_use:Nn \l_mbc_listp_seq { & } \\
    \end{array}
    \]
    %
    % generate the generic formula. Use \sb here, `_` in ExplSyntaxOn is a normal letter
    %
    \[
        E(x) = \sum\sb{#3=1}\sp{\int_use:N \l_mbc_N_int} #1\sb{#3}#2\sb{#3}
    \]
    %
    % generate the expansion of the sum in a new sequence list
    %
    \int_zero_new:N \l_cnt_int
    \int_incr:N \l_cnt_int
    \fp_zero_new:N \l_expected_fb
    \seq_clear_new:N \l_tmp_seq
    \int_do_while:nn {\l_cnt_int <= \int_use:N \l_mbc_N_int}
    {
        \seq_put_right:Nx \l_tmp_seq {
            {\seq_item:Nn  \l_mbc_listx_seq {\int_use:N \l_cnt_int}}
            \cdot
            {\seq_item:Nn  \l_mbc_listp_seq {\int_use:N \l_cnt_int}}
        }
        \fp_add:Nn \l_expected_fb {
            \seq_item:Nn  \l_mbc_listx_seq {\int_use:N \l_cnt_int}
            *
            \seq_item:Nn  \l_mbc_listp_seq {\int_use:N \l_cnt_int}
         }
        \int_incr:N \l_cnt_int
    }
\[
    E(x) = \seq_use:Nn \l_tmp_seq {+} = \fp_use:N \l_expected_fb
\]

}
\ExplSyntaxOff
\begin{document}
\ShowExpectedCalculation{x}{p}{k}{0, 1, 2, 3, 4}{0.2, 0.2, 0.4, 0.05, 0.15}
\ShowExpectedCalculation{L}{p}{i}{-1, 0, 1}{0.2, 0.4, 0.4}
\ShowExpectedCalculation{Y}{p}{j+z}{3}{1}
\end{document}

There is probably a better way to map together a couple (or three, that I need in case of color) sequences, but I have not yet read it ;-)...

Great ! For the colors it seems that Tikz offers cycle functiion but I do not yet use it. — projetmbc, Aug 10 '20 at 18:44
I have to mix your solution with others that I have to obtain the table like syntax. — projetmbc, Aug 10 '20 at 20:23
The macro \sb has to be used each time with to print an underscore in an expl3 macro. Am I right ? — projetmbc, Aug 11 '20 at 21:53
The problem is that expl3 redefine the underscore as a normal character, so you have to use \sb for the math subscript. I used also \sp for symmetry, not really needed. — Rmano, Aug 12 '20 at 07:09
@projetmbc I'd use expansion to insert a subscript char (\char_generate:nn { `\_ } { 8 }), but that's a matter of personal preference — Joseph Wright, Aug 12 '20 at 09:43

projetmbc · Accepted Answer · 2020-08-12T12:38:45.290

Here is a possible solution.

\documentclass{article}
\usepackage{nicematrix}
\usepackage{tikz}
\usetikzlibrary{fit}
\usepackage{tcolorbox}
\tcbuselibrary{theorems}
% Sources
%   * https://tex.stackexchange.com/a/475291/6880
%   * https://tex.stackexchange.com/a/558343/6880
%   * https://tex.stackexchange.com/a/558185/6880
\newcommand\decoframe[3]{
    \begin{tikzpicture}[remember picture, overlay]
    \node[draw = #1,
          rounded corners,
          thick,
          fit = (#2.north west) (#2.north east) 
                (#3.south west) (#3.south east)] {};
    \end{tikzpicture}
}
\newcommand\decobox[2]{
    \tcboxmath[colframe = #1,
               left = 0mm, right = 0mm, top = 0mm, bottom = 0mm,
               boxsep = 1mm, ,boxrule = 1pt]{#2}
}
\ExplSyntaxOn
% Global variables used.
    \seq_new:N \l__tnscalc_colors_seq
    \tl_new:N \l__tnscalc_actual_color_temp_tl
\seq_new:N \l__tnscalc_calcexpval_seq
\seq_new:N \l__tnscalc_subseq_seq
\tl_new:N \l__tnscalc_xline_temp_tl
\tl_new:N \l__tnscalc_pline_temp_tl

\int_new:N \l__tnscalc_nbline_int
\int_new:N \l__tnscalc_numcol_int
\int_new:N \l__tnscalc_numcol_deco_int
\int_new:N \l__tnscalc_numcol_decotwo_int


% #1 : line separator
% #2 : cell separator
% #3 : content
    \NewDocumentCommand{\calcexpval}{O{red,blue,orange,gray} m m +m} {
        \tnscalc_calcexpval:nnnn{#1}{#2}{#3}{#4}
    }
% The internal version of the general purpose macro
    \cs_new_protected:Nn \tnscalc_calcexpval:nnnn {
% #1 (option) : colors
% #2 : line separator
% #3 : cell separator
% #4 : content
% Colors.
        \seq_set_split:Nnn \l__tnscalc_colors_seq { , } { #1 }
% Split into lines
        \seq_set_split:Nnn \l__tnscalc_calcexpval_seq { #2 } { #4 }
    \int_set:Nn \l__tnscalc_nbline_int { \seq_count:N \l__tnscalc_calcexpval_seq }


% Split each line into cells.
        \seq_pop_left:NN \l__tnscalc_calcexpval_seq \l__tnscalc_xline_temp_tl
        \seq_set_split:NnV \l__tnscalc_x_seq { #3 } \l__tnscalc_xline_temp_tl
    \seq_pop_left:NN \l__tnscalc_calcexpval_seq \l__tnscalc_pline_temp_tl
    \seq_set_split:NnV \l__tnscalc_p_seq { #3 } \l__tnscalc_pline_temp_tl


% Number of columns (offensive programming)
        \int_set:Nn \l__tnscalc_numcol_int { \seq_count:N \l__tnscalc_x_seq }
    \int_set:Nn \l__tnscalc_numcol_deco_int { 2 }


% The table of values

        [%|{\int_use:N \l_mbc_N_int}{c}
            \begin{NiceArray}{r{\int_use:N \l__tnscalc_numcol_int}{|c}}
                x\sb{k} & \l__tnscalc_xline_temp_tl \
                \hline
                p\sb{k} & \l__tnscalc_pline_temp_tl
                \CodeAfter

                \int_add:Nn \l__tnscalc_numcol_int {2}
                \bool_while_do:nn { \int_compare_p:nNn \l__tnscalc_numcol_deco_int < \l__tnscalc_numcol_int }{
                    \seq_pop_left:NN \l__tnscalc_colors_seq \l__tnscalc_actual_color_temp_tl
                    \seq_put_right:NV \l__tnscalc_colors_seq {\l__tnscalc_actual_color_temp_tl}
                    \decoframe{\l__tnscalc_actual_color_temp_tl}{1-\int_use:N \l__tnscalc_numcol_deco_int}{2-\int_use:N \l__tnscalc_numcol_deco_int}
                \int_add:Nn \l__tnscalc_numcol_deco_int {2}
            }
        \end{NiceArray}
    \]


% Explain the calculus of the expected value.
        \int_set:Nn \l__tnscalc_numcol_deco_int { 1 }
    $E(X) = \sum\limits\sb{k=1}^{\int_use:N \l__tnscalc_numcol_int} p\sb{k} \cdot x\sb{k}$

    \par

    $E(X) = 

    \bool_while_do:nn { \int_compare_p:nNn \l__tnscalc_numcol_int &gt; 0 }{
        \seq_pop_left:NN \l__tnscalc_x_seq \l__tnscalc_xval_tl
        \seq_pop_left:NN \l__tnscalc_p_seq \l__tnscalc_pval_tl

        \bool_if:NTF { \int_compare_p:nNn { \int_eval:n{ \int_mod:nn \l__tnscalc_numcol_deco_int 2} } = 1 }  { 
        \seq_pop_left:NN \l__tnscalc_colors_seq \l__tnscalc_actual_color_temp_tl
        \seq_put_right:NV \l__tnscalc_colors_seq {\l__tnscalc_actual_color_temp_tl}

        \decobox{\l__tnscalc_actual_color_temp_tl}{\l__tnscalc_xval_tl \cdot \l__tnscalc_pval_tl}
    } {
        \l__tnscalc_xval_tl \cdot \l__tnscalc_pval_tl
    }

        \bool_if:NTF { \int_compare_p:nNn \l__tnscalc_numcol_int = 1 }  { } { + }

        \int_add:Nn \l__tnscalc_numcol_deco_int {1}
        \int_add:Nn \l__tnscalc_numcol_int {-1}
    }
    $
} 

\ExplSyntaxOff
\setlength\parindent{0pt}
\begin{document}
Let's try...
\calcexpval{\}{&}{
    0      & 1   & 2   & 3    & 4    \
    0.2000 & 0.2 & 0.4 & 0.05 & 0.15
}
With the default cycle of colors.
\calcexpval{\}{&}{
    0      & 1   \
    0.2000 & 0.2
}
With an odd number of columns and the cycle of colors \verb#blue,gray#.
\calcexpval[blue,gray]{\}{&}{
    0      & 1   & 2   \
    0.2000 & 0.2 & 0.4
}
With a single( ? ) column and the cycle of colors \verb#black#..
\calcexpval[black]{\}{&}{
    0      \
    0.2000
}
%With the short cycle of colors \verb#blue,red#..
\calcexpval[blue,red]{\}{&}{
    0      & 1   & 2   & 3    & 4    & 1   & 2   & 3    \
    0.2000 & 0.2 & 0.4 & 0.05 & 0.15 & 0.2 & 0.4 & 0.05
}
\end{document}

expl3 - An environment to explain the calculation of an expected value (finite case)

2 Answers2

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