计算数据集的四分位数

Question

更新此更新包含可即时发现可能值的代码。这些值必须是数字，但不必是整数。前面提到的与 Beamer 的不兼容性只是因为 Beamer 似乎不可能（如果不是使用技巧的话，也许我没有尝试发现）在框架中使用诸如#1或之类的标记#2；特别是不可能在框架中定义命令。

无论如何，更新都会对 Beamer 进行处理。请参阅答案的下半部分。

第一个答案

在这个答案中，我实现了一个\Percentile宏。然而，数据的可能值（从0到7）在宏中是硬编码的。

\numexpr方便时我会使用，否则我会使用xintfrac（主要是因为我不想重写四舍五入到定点例程，但在这里一切都可以用来完成\numexpr）。为了方便编码，我使用\xintFor包xinttools。

我简要地提到，这让我发现：

我无法在 Beamer 框架中使用裸机\xintFor，因为 Beamer 解析器不喜欢看到这个#角色，

1a. 这与完全无关\xintFor：使用 Beamer 无法在框架内定义命令（将使用#1、或等...）!!!根据其性质，它与等标记一起使用，因此无法在 Beamer 框架中使用。当然，宏可以在内部使用它。#2\xintFor#1

我无法在带有的列\xintFor的表格中使用。Ssiunitx

我放弃了 Beamer，并使用可扩展宏来替代表格（但即便如此，我发现在使用siunitx时我无法按照我预期的普遍性使用它们）。siunitx

至于代码，它使用内部宏来存储单独的数据，以提高数据检索的效率。

%\documentclass{beamer} 
% Beamer is **incompatible** with non hidden \xintFor in  a frame !!!
% NO (unhidden) \xintFor in a Beamer frame !!

% Also for some reason latex+dvipng raises an error here

% This is dvipng (dvipng (TeX Live)) 1.14 Copyright 2002-2010 Jan-Ake Larsson
% [1 <raw PostScriptdvipng warning: No image output from inclusion of raw PostScript >] 

% must go via pdflatex
\documentclass[varwidth, border=6pt, ignorerest=false]{standalone}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{booktabs}
\usepackage{siunitx}
% siunitx is incompatible with use of \xintFor in a tabular !!
%

% \usepackage{xparse}

\usepackage{xintfrac, xinttools}
% xintfrac mainly for \xintRound because everything else can be emulated with
% \numexpr or \dimexpr in this context
% xinttools for the convenience of \xintFor

\newcommand*\SvendData
                {{{A}{6}}%
                 {{B}{0}}%
                 {{C}{0}}%
                 {{D}{3}}%
                 {{E}{0}}%
                 {{F}{2}}%
                 {{G}{1}}%
                 {{H}{1}}%
                 {{I}{1}}%
                 {{J}{5}}%
                 {{K}{0}}%
                 {{L}{3}}%
                 {{M}{7}}%
                 {{N}{3}}%
                 {{O}{1}}%
                 {{P}{1}}%
                 {{Q}{0}}%
                 {{R}{0}}%
                 {{S}{0}}%
                 {{T}{2}}%
                 {{U}{1}}%
                 {{V}{2}}%
                 {{W}{0}}%
                 {{X}{2}}%
                 {{Y}{1}}%
                 {{Z}{1}}%
                 {{Aa}{4}}%
                 {{Ab}{6}}%
                 {{Ac}{1}}%
                 {{Ad}{1}}%
                 {{Ae}{6}}%
                 {{Af}{2}}%
                 {{Ag}{0}}%
                 {{Ah}{3}}%
                 {{Ai}{2}}%
                 {{Aj}{1}}%
                 {{Ak}{0}}%
                 {{Al}{0}}%
                 {{Am}{0}}%
                 {{An}{0}}%
                 {{Ao}{0}}%
                 {{Ap}{4}}}

% Utility to add Data
% e.g \AddToData \SvendData{WW}{5}
% \newcommand*\AddToData [3]{\odef #1{#1{{#2}{#3}}}}
% But would be better utility to update the private \Svend@Values@..,
% \Svend@Counts@.., \Svend@Cuml@.. macros

\makeatletter

% Possible values 0, 1, 2, 3, 4, 5, 6, 7 hard coded here, we associate to each
% a macro to hold the number of its occurrences

\newcommand*\ResetCounts {%
    \xintFor ##1 in {0, 1, 2, 3, 4, 5, 6, 7}\do {\@namedef{Svend@Counts@##1}{0}}%
}

% \odef does \def with one expansion of replacement text

\newcommand*\ParseData [1]{%
% Defines the private macros underlying \elev and \HowMany
  \xintFor* ##1 in {#1}\do {%
    \expandafter\odef\csname Svend@Values@\@firstoftwo ##1\endcsname {\@secondoftwo ##1}%
    \edef\Svend@tmp {Svend@Counts@\@secondoftwo ##1}%
    \expandafter\odef\csname\Svend@tmp\endcsname 
                   {\the\numexpr\csname\Svend@tmp\endcsname + \@ne}%
  }%
}%

\newcommand*\ComputeCumu {%
% Computes and stores iteratively cumulative counts
% Again the possible values 0, 1, 2, 3, 4, 5, 6, 7 hard coded in this approach
  \xintFor ##1 in {0, 1, 2, 3, 4, 5, 6, 7}\do {%
    \xintifForFirst {\odef\Svend@tmp{\romannumeral-`0\HowMany{0}}}
                    {\odef\Svend@tmp{\the\numexpr\Svend@tmp+\HowMany{##1}}}%
    \expandafter\let\csname Svend@Cumul@##1\endcsname \Svend@tmp
    \xintifForLast {\let\HowManyTotale\Svend@tmp }{}%
  }%
}

% Percentiles: 
% I understand there are various definitions, I used this one : 
%
% P(x) (x=0,1,..,100) is the smallest value V such as the frequency of 
% event {v<= V} is at least x\%. Thus P(100) is the largest V and P(0) is the
% smallest V.

% cf http://en.wikipedia.org/wiki/Percentile 

% first (expandable) method:
% \xintiLt {a}{b}{DO THIS IF a<b}{DO THIS IF a>=b}
% \newcommand*\Percentile [1]{%
%     \xintifLt {\HowManyCumu {0}/\HowManyTotale}{#1/100}{% percentile at least 1
%     \xintifLt {\HowManyCumu {1}/\HowManyTotale}{#1/100}{% percentile at least 2
%     \xintifLt {\HowManyCumu {2}/\HowManyTotale}{#1/100}{% percentile at least 3
%     \xintifLt {\HowManyCumu {3}/\HowManyTotale}{#1/100}{% percentile at least 4
%     \xintifLt {\HowManyCumu {4}/\HowManyTotale}{#1/100}{% percentile at least 5
%     \xintifLt {\HowManyCumu {5}/\HowManyTotale}{#1/100}{% percentile at least 6
%     \xintifLt {\HowManyCumu {6}/\HowManyTotale}{#1/100}{7%
%     }{6}%
%     }{5}%
%     }{4}%
%     }{3}%
%     }{2}%
%     }{1}%
%     }{0}%
% }    

% Possibly faster expandable method, does three comparisons: 
% (based on a binary tree of the possible values)
% The other method above does between 1 and 7 comparisons depending on the input
% Speed gain would show only for larger range of values, for example from 0 to
% 127 rather than from 0 to 7
\newcommand*\Percentile [1]{%
    \xintifLt {\HowManyCumu {3}/\HowManyTotale}{#1/100}
      {% percentile at least 4
      \xintifLt {\HowManyCumu {5}/\HowManyTotale}{#1/100}
        {\xintifLt {\HowManyCumu {6}/\HowManyTotale}{#1/100}{7}{6}}
        {\xintifLt {\HowManyCumu {4}/\HowManyTotale}{#1/100}{5}{4}}%
      }
      {% percentile at most 3
      \xintifLt {\HowManyCumu {1}/\HowManyTotale}{#1/100}
        {\xintifLt {\HowManyCumu {2}/\HowManyTotale}{#1/100}{3}{2}}
        {\xintifLt {\HowManyCumu {0}/\HowManyTotale}{#1/100}{1}{0}}%
        }%
}%



\newcommand*\elev        [1]{\csname Svend@Values@#1\endcsname }
\newcommand*\HowMany     [1]{\csname Svend@Counts@#1\endcsname }
\newcommand*\HowManyCumu [1]{\csname Svend@Cumul@#1\endcsname }

\makeatother

\ResetCounts
\ParseData\SvendData
\ComputeCumu

\begin{document}

\centering
\begin{tabular}{*{14}{c}}
\toprule
\elev{A}  & \elev{B}  & \elev{C}  & \elev{D}  & \elev{E}  & \elev{F}  & \elev{G}  &
\elev{H}  & \elev{I}  & \elev{J}  & \elev{K}  & \elev{L}  & \elev{M}  & \elev{N}    \\[0.5ex]
\elev{O}  & \elev{P}  & \elev{Q}  & \elev{R}  & \elev{S}  & \elev{T}  & \elev{U}  &
\elev{V}  & \elev{W}  & \elev{X}  & \elev{Y}  & \elev{Z}  & \elev{Aa} & \elev{Ab}   \\[0.5ex]
\elev{Ac} & \elev{Ad} & \elev{Ae} & \elev{Af} & \elev{Ag} & \elev{Ah} & \elev{Ai} &
\elev{Aj} & \elev{Ak} & \elev{Al} & \elev{Am} & \elev{An} & \elev{Ao} & \elev{Ap}   \\
\bottomrule
\end{tabular}

\bigskip
% THIS WOULD BE OK:

% \begin{tabular}{*{8}{c}}
% \toprule
% \xintFor #1 in {0, 1, 2, 3, 4, 5, 6}\do {{$F(#1)$}&}{$F(7)$}\\
% \xintFor #1 in {0, 1, 2, 3, 4, 5, 6}\do
%                {\xintRound{1}{\HowManyCumu{#1}/\HowManyTotale [2]}&}100\\
% \bottomrule
% \end{tabular}

% BUT THE SAME WITH 
% \begin{tabular}{*{7}{S[table-format = 2.1]}S[table-format = 3]}
% DOESN'T WORK: ON NE PEUT PAS UTILISER \xintFor DANS UN TABULAR AVEC siunitx !!

%  We can use expandable macros with siunitx

\def\RowA #1{{$F(#1)$}}% EXTRA BRACES NEEDED FOR SIUNITX !!
\def\RowB #1{\xintRound{1}{\HowManyCumu{#1}/\HowManyTotale [2]}}

\begin{tabular}{*{7}{S[table-format = 2.1]}S[table-format = 3]}
\toprule
% PURELY EXPANDABLE MACROS: those work with siunitx ...
% ... BUT don't try to define a macro with parameter here :((
\xintListWithSep {&}{\xintApply\RowA {{0}{1}{2}{3}{4}{5}{6}{7}}}\\
\xintListWithSep {&}{\xintApply\RowB {{0}{1}{2}{3}{4}{5}{6}}}&100\\
\bottomrule
\end{tabular}

\bigskip

\begin{tabular}{*{9}{c}}
\toprule
% strange standalone problem with too long line from
% \xintFor #1 in {0, 10, 25, 33, 50, 66, 75, 90} \do {\textit{Pe}$(#1)$&}\textit{Pe}$(100)$\\
\xintFor #1 in {0, 10, 25, 33, 50, 66, 75, 90} \do {$q(#1)$&}$q(100)$\\
\xintFor #1 in {0, 10, 25, 33, 50, 66, 75, 90} \do {$\Percentile{#1}$&}$7$\\
\bottomrule
\end{tabular}

\end{document}

在此处输入图片描述

我也陷入了麻烦standalone（如代码底部所示），甚至dvipng因为一些我不知道的原因而加入了抱怨的喜剧。

第二个答案

\documentclass[10pt]{beamer}
%\usepackage[paperwidth=25cm]{geometry}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{booktabs}
\usepackage{siunitx}
\usepackage{xintfrac, xinttools}
% EXTENDED DATA
\newcommand*\SvendData
                {{{A}{6}}%
                 {{B}{0}}%
                 {{C}{0}}%
                 {{D}{3}}%
                 {{E}{0}}%
                 {{F}{2}}%
                 {{G}{1}}%
                 {{H}{1}}%
                 {{I}{1}}%
                 {{J}{5}}%
                 {{K}{0}}%
                 {{L}{3}}%
                 {{M}{7}}%
                 {{N}{3}}%
                 {{O}{1}}%
                 {{P}{1}}%
                 {{Q}{0}}%
                 {{R}{0}}%
                 {{S}{0}}%
                 {{T}{2}}%
                 {{U}{1}}%
                 {{V}{2}}%
                 {{W}{0}}%
                 {{X}{2}}%
                 {{Y}{1}}%
                 {{Z}{1}}%
                 {{Aa}{4}}%
                 {{Ab}{6}}%
                 {{Ac}{1}}%
                 {{Ad}{1}}%
                 {{Ae}{6}}%
                 {{Af}{2}}%
                 {{Ag}{0}}%
                 {{Ah}{3}}%
                 {{Ai}{2}}%
                 {{Aj}{1}}%
                 {{Ak}{0}}%
                 {{Al}{0}}%
                 {{Am}{0}}%
                 {{An}{0}}%
                 {{Ao}{0}}%
                 {{Ap}{4}}%
                 {{NA}{6.5}}%
                 {{NB}{0.5}}%
                 {{NC}{0.5}}%
                 {{ND}{3.5}}%
                 {{NE}{0.5}}%
                 {{NF}{2.5}}%
                 {{NG}{1.5}}%
                 {{NH}{1.5}}%
                 {{NI}{1.5}}%
                 {{NJ}{5.5}}%
                 {{NK}{0.5}}%
                 {{NL}{3.5}}%
                 {{NM}{7.5}}%
                 {{NN}{3.5}}%
                 {{NO}{1.5}}%
                 {{NP}{1.5}}%
                 {{NQ}{0.5}}%
                 {{NR}{0.5}}%
                 {{NS}{0.5}}%
                 {{NT}{2.5}}%
                 {{NU}{1.5}}%
                 {{NV}{2.5}}%
                 {{NW}{0.5}}%
                 {{NX}{2.5}}%
                 {{NY}{1.5}}%
                 {{NZ}{1.5}}%
                 {{NAa}{4.5}}%
                 {{NAb}{6.5}}%
                 {{NAc}{1.5}}%
                 {{NAd}{1.5}}%
                 {{NAe}{6.5}}%
                 {{NAf}{2.5}}%
                 {{NAg}{0.5}}%
                 {{NAh}{3.5}}%
                 {{NAi}{2.5}}%
                 {{NAj}{1.5}}%
                 {{NAk}{0.5}}%
                 {{NAl}{0.5}}%
                 {{NAm}{0.5}}%
                 {{NAn}{0.5}}%
                 {{NAo}{0.5}}%
                 {{NAp}{4.5}}}

\makeatletter

% \odef does \def with one expansion of replacement text

\newcommand*\SvendValues {}
\newcommand*\SvendNumValues {}


\newcommand*\ParseData [1]{%
% Defines the private macros underlying \elev and \HowMany
% This version creates \SvendValues ordered list of values.
%
% For inner efficiency this \SvendValues is with braces, not commas
% (to be used with \xintFor* not \xintFor)
%
% The values do not have to be integers. But they must be numeric quantities
% as understood by xintfrac.
%
  \def\SvendValues {}%
  \def\SvendNumValues {0}%
  \xintFor* ##1 in {#1}\do 
  {%
% get the possibly new value
    \odef\Svend@tmpD {\@firstoftwo ##1}%
    \odef\Svend@tmpV {\@secondoftwo ##1}%
% and insert it at the correct location in \SvendValues
% (the better would be to manage some kind of heap tree but I have not
% invested the needed time)
%
    \def\SvendValues@Tmp {}%
    \def\Svend@tmpflag  {0}%
% 0 = initial state, 
% 1 = inserted, finish, 
% 2 = was already there
    \xintifForFirst 
    {\odef\SvendValues {\expandafter{\Svend@tmpV}}%
     \def\SvendNumValues{1}%
     \expandafter\odef\csname Svend@Counts@\Svend@tmpV\endcsname {0}}% will be increased below
    {\xintFor* ##2 in {\SvendValues}\do 
      {%
      \if0\Svend@tmpflag\expandafter\@firstoftwo\else\expandafter\@secondoftwo\fi
         {\xintifCmp {\Svend@tmpV}{##2}
          {\def\Svend@tmpflag{1}%
           \oodef\SvendValues@Tmp
                 {\expandafter\SvendValues@Tmp \expandafter{\Svend@tmpV}{##2}}}% new < old
          {\def\Svend@tmpflag{2}\odef\SvendValues@Tmp {\SvendValues@Tmp {##2}}}% old = new
          {\odef\SvendValues@Tmp {\SvendValues@Tmp {##2}}}% new > old
         }
         {\odef\SvendValues@Tmp{\SvendValues@Tmp {##2}}}%
      }%
     \if0\Svend@tmpflag
         \oodef\SvendValues@Tmp{\expandafter\SvendValues@Tmp\expandafter {\Svend@tmpV}}%
     \fi
     \let\SvendValues\SvendValues@Tmp
%\typeout{\SvendValues}% debugging
     \if2\Svend@tmpflag
      \else
      % new value
      \expandafter\odef\csname Svend@Counts@\Svend@tmpV\endcsname {0}% will be increased below
      \odef\SvendNumValues {\the\numexpr\SvendNumValues+\@ne}\fi
    }%
% continued as in earlier code
    \expandafter\odef\csname Svend@Values@\Svend@tmpD\endcsname {\Svend@tmpV}%
    \expandafter\odef\csname Svend@Counts@\Svend@tmpV\endcsname 
                   {\the\numexpr\csname Svend@Counts@\Svend@tmpV\endcsname + \@ne}%
  }% end of external \xintFor loop
}%

\newcommand*\ComputeCumu {%
% Computes and stores iteratively cumulative counts
% THIS VERSION USES \SvendValues
  \xintFor* ##1 in {\SvendValues}\do {%
    \xintifForFirst {\odef\Svend@tmp{\romannumeral-`0\HowMany{##1}}}
                    {\odef\Svend@tmp{\the\numexpr\Svend@tmp+\HowMany{##1}}}%
    \expandafter\let\csname Svend@Cumul@##1\endcsname \Svend@tmp
    \xintifForLast {\let\HowManyTotale\Svend@tmp }{}%
  }%
}

% Percentiles: 
%
% P(x) (x=0,1,..,100) is the smallest value V such as the frequency of 
% event {v<= V} is at least x\%. Thus P(100) is the largest V and P(0) is the
% smallest V.

% 
% THIS VERSION USES \SvendValues
% It has nothing hardcoded.

\catcode`_ 11
\def\Percentile@helper #1#2% space below is to stop premature expansion
    { \if1\xintifLt {\HowManyCumu {#2}/\HowManyTotale}{#1/100}{0}{1}\xint_dothis{#2}\fi}

\newcommand*\Percentile [1]{% expandable !
    \xintApplyUnbraced{\Percentile@helper {#1}}\SvendValues\xint_orthat {}%
}

\catcode`_ 8

\newcommand*\elev        [1]{\csname Svend@Values@#1\endcsname }
\newcommand*\HowMany     [1]{\csname Svend@Counts@#1\endcsname }
\newcommand*\HowManyCumu [1]{\csname Svend@Cumul@#1\endcsname }

\let\firstoftwo\@firstoftwo
\let\secondoftwo\@secondoftwo
\makeatother


\ParseData\SvendData
\ComputeCumu
%\typeout{\meaning\SvendValues}

% for first tabular
% WITH BEAMER I CAN NOT DEFINE THIS IN THE FRAME !!!!!!

% ANY \newcommand MUST BE IN THE PREAMBLE WITH BEAMER !!!!!!

\newcommand*\Row [1]{\stepcounter{rowcount}%
                     \elev{\firstoftwo #1}%
                     \ifnum\value{rowcount}<14
                     \expandafter\firstoftwo\else\expandafter\secondoftwo\fi
                     {&}{\setcounter{rowcount}{0}\\[0.5ex]}}

% for middle data (not a tabular, would be too wide)
\newcommand*\ShowCumu [1]{$F(#1)=\xintRound{1}{\HowManyCumu{#1}/\HowManyTotale [2]}$}

% for third tabular

\newcommand*\RowA [1]{$q(#1)$}%
\newcommand*\RowB [1]{$\Percentile{#1}$}



\newcounter{rowcount}


\begin{document}\small

% DEBUGGING (not possible with  Beamer! because of #1...)
% \HowMany{0}

% \xintFor*#1 in \SvendValues\do {[#1,\HowMany{#1}], }
% \SvendNumValues

% \xintNthElt{0}{\SvendData}

% \HowManyTotale

\begin{frame}
\centering
\setcounter{rowcount}{0}%

\begin{tabular}{*{14}{c}}
\toprule
\xintApplyUnbraced \Row\SvendData
\bottomrule
\end{tabular}

\bigskip

% (This is too wide hence would make letters in my png appear too small)

% DEFINITIONS LIKE THIS MUST BE MOVED TO PREAMBLE IF BEAMER CLASS !!
% \def\RowA #1{{$F(#1)$}}% EXTRA BRACES NEEDED FOR SIUNITX !!
% \def\RowB #1{\xintRound{1}{\HowManyCumu{#1}/\HowManyTotale [2]}}

% \centerline{\begin{tabular}{*{\SvendNumValues}{S[table-format = 2.1]}}
% \toprule
% \xintListWithSep {&}{\xintApply\RowA \SvendValues}\\
% \xintListWithSep {&}{\xintApply\RowB \SvendValues}\\
% \bottomrule
% \end{tabular}}

\xintListWithSep{,\quad }{\xintApply\ShowCumu \SvendValues}

\bigskip

\begin{tabular}{*{10}{c}}
\toprule
\xintListWithSep {&}{\xintApply\RowA {{0}{10}{25}{33}{50}{66}{75}{90}{100}}}\\
\xintListWithSep {&}{\xintApply\RowB {{0}{10}{25}{33}{50}{66}{75}{90}{100}}}\\
\bottomrule
\end{tabular}

\end{frame}

\end{document}

在此处输入图片描述

Answer 1

更新此更新包含可即时发现可能值的代码。这些值必须是数字，但不必是整数。前面提到的与 Beamer 的不兼容性只是因为 Beamer 似乎不可能（如果不是使用技巧的话，也许我没有尝试发现）在框架中使用诸如#1或之类的标记#2；特别是不可能在框架中定义命令。

无论如何，更新都会对 Beamer 进行处理。请参阅答案的下半部分。

第一个答案

在这个答案中，我实现了一个\Percentile宏。然而，数据的可能值（从0到7）在宏中是硬编码的。

\numexpr方便时我会使用，否则我会使用xintfrac（主要是因为我不想重写四舍五入到定点例程，但在这里一切都可以用来完成\numexpr）。为了方便编码，我使用\xintFor包xinttools。

我简要地提到，这让我发现：

我无法在 Beamer 框架中使用裸机\xintFor，因为 Beamer 解析器不喜欢看到这个#角色，

1a. 这与完全无关\xintFor：使用 Beamer 无法在框架内定义命令（将使用#1、或等...）!!!根据其性质，它与等标记一起使用，因此无法在 Beamer 框架中使用。当然，宏可以在内部使用它。#2\xintFor#1

我无法在带有的列\xintFor的表格中使用。Ssiunitx

我放弃了 Beamer，并使用可扩展宏来替代表格（但即便如此，我发现在使用siunitx时我无法按照我预期的普遍性使用它们）。siunitx

至于代码，它使用内部宏来存储单独的数据，以提高数据检索的效率。

%\documentclass{beamer} 
% Beamer is **incompatible** with non hidden \xintFor in  a frame !!!
% NO (unhidden) \xintFor in a Beamer frame !!

% Also for some reason latex+dvipng raises an error here

% This is dvipng (dvipng (TeX Live)) 1.14 Copyright 2002-2010 Jan-Ake Larsson
% [1 <raw PostScriptdvipng warning: No image output from inclusion of raw PostScript >] 

% must go via pdflatex
\documentclass[varwidth, border=6pt, ignorerest=false]{standalone}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{booktabs}
\usepackage{siunitx}
% siunitx is incompatible with use of \xintFor in a tabular !!
%

% \usepackage{xparse}

\usepackage{xintfrac, xinttools}
% xintfrac mainly for \xintRound because everything else can be emulated with
% \numexpr or \dimexpr in this context
% xinttools for the convenience of \xintFor

\newcommand*\SvendData
                {{{A}{6}}%
                 {{B}{0}}%
                 {{C}{0}}%
                 {{D}{3}}%
                 {{E}{0}}%
                 {{F}{2}}%
                 {{G}{1}}%
                 {{H}{1}}%
                 {{I}{1}}%
                 {{J}{5}}%
                 {{K}{0}}%
                 {{L}{3}}%
                 {{M}{7}}%
                 {{N}{3}}%
                 {{O}{1}}%
                 {{P}{1}}%
                 {{Q}{0}}%
                 {{R}{0}}%
                 {{S}{0}}%
                 {{T}{2}}%
                 {{U}{1}}%
                 {{V}{2}}%
                 {{W}{0}}%
                 {{X}{2}}%
                 {{Y}{1}}%
                 {{Z}{1}}%
                 {{Aa}{4}}%
                 {{Ab}{6}}%
                 {{Ac}{1}}%
                 {{Ad}{1}}%
                 {{Ae}{6}}%
                 {{Af}{2}}%
                 {{Ag}{0}}%
                 {{Ah}{3}}%
                 {{Ai}{2}}%
                 {{Aj}{1}}%
                 {{Ak}{0}}%
                 {{Al}{0}}%
                 {{Am}{0}}%
                 {{An}{0}}%
                 {{Ao}{0}}%
                 {{Ap}{4}}}

% Utility to add Data
% e.g \AddToData \SvendData{WW}{5}
% \newcommand*\AddToData [3]{\odef #1{#1{{#2}{#3}}}}
% But would be better utility to update the private \Svend@Values@..,
% \Svend@Counts@.., \Svend@Cuml@.. macros

\makeatletter

% Possible values 0, 1, 2, 3, 4, 5, 6, 7 hard coded here, we associate to each
% a macro to hold the number of its occurrences

\newcommand*\ResetCounts {%
    \xintFor ##1 in {0, 1, 2, 3, 4, 5, 6, 7}\do {\@namedef{Svend@Counts@##1}{0}}%
}

% \odef does \def with one expansion of replacement text

\newcommand*\ParseData [1]{%
% Defines the private macros underlying \elev and \HowMany
  \xintFor* ##1 in {#1}\do {%
    \expandafter\odef\csname Svend@Values@\@firstoftwo ##1\endcsname {\@secondoftwo ##1}%
    \edef\Svend@tmp {Svend@Counts@\@secondoftwo ##1}%
    \expandafter\odef\csname\Svend@tmp\endcsname 
                   {\the\numexpr\csname\Svend@tmp\endcsname + \@ne}%
  }%
}%

\newcommand*\ComputeCumu {%
% Computes and stores iteratively cumulative counts
% Again the possible values 0, 1, 2, 3, 4, 5, 6, 7 hard coded in this approach
  \xintFor ##1 in {0, 1, 2, 3, 4, 5, 6, 7}\do {%
    \xintifForFirst {\odef\Svend@tmp{\romannumeral-`0\HowMany{0}}}
                    {\odef\Svend@tmp{\the\numexpr\Svend@tmp+\HowMany{##1}}}%
    \expandafter\let\csname Svend@Cumul@##1\endcsname \Svend@tmp
    \xintifForLast {\let\HowManyTotale\Svend@tmp }{}%
  }%
}

% Percentiles: 
% I understand there are various definitions, I used this one : 
%
% P(x) (x=0,1,..,100) is the smallest value V such as the frequency of 
% event {v<= V} is at least x\%. Thus P(100) is the largest V and P(0) is the
% smallest V.

% cf http://en.wikipedia.org/wiki/Percentile 

% first (expandable) method:
% \xintiLt {a}{b}{DO THIS IF a<b}{DO THIS IF a>=b}
% \newcommand*\Percentile [1]{%
%     \xintifLt {\HowManyCumu {0}/\HowManyTotale}{#1/100}{% percentile at least 1
%     \xintifLt {\HowManyCumu {1}/\HowManyTotale}{#1/100}{% percentile at least 2
%     \xintifLt {\HowManyCumu {2}/\HowManyTotale}{#1/100}{% percentile at least 3
%     \xintifLt {\HowManyCumu {3}/\HowManyTotale}{#1/100}{% percentile at least 4
%     \xintifLt {\HowManyCumu {4}/\HowManyTotale}{#1/100}{% percentile at least 5
%     \xintifLt {\HowManyCumu {5}/\HowManyTotale}{#1/100}{% percentile at least 6
%     \xintifLt {\HowManyCumu {6}/\HowManyTotale}{#1/100}{7%
%     }{6}%
%     }{5}%
%     }{4}%
%     }{3}%
%     }{2}%
%     }{1}%
%     }{0}%
% }    

% Possibly faster expandable method, does three comparisons: 
% (based on a binary tree of the possible values)
% The other method above does between 1 and 7 comparisons depending on the input
% Speed gain would show only for larger range of values, for example from 0 to
% 127 rather than from 0 to 7
\newcommand*\Percentile [1]{%
    \xintifLt {\HowManyCumu {3}/\HowManyTotale}{#1/100}
      {% percentile at least 4
      \xintifLt {\HowManyCumu {5}/\HowManyTotale}{#1/100}
        {\xintifLt {\HowManyCumu {6}/\HowManyTotale}{#1/100}{7}{6}}
        {\xintifLt {\HowManyCumu {4}/\HowManyTotale}{#1/100}{5}{4}}%
      }
      {% percentile at most 3
      \xintifLt {\HowManyCumu {1}/\HowManyTotale}{#1/100}
        {\xintifLt {\HowManyCumu {2}/\HowManyTotale}{#1/100}{3}{2}}
        {\xintifLt {\HowManyCumu {0}/\HowManyTotale}{#1/100}{1}{0}}%
        }%
}%



\newcommand*\elev        [1]{\csname Svend@Values@#1\endcsname }
\newcommand*\HowMany     [1]{\csname Svend@Counts@#1\endcsname }
\newcommand*\HowManyCumu [1]{\csname Svend@Cumul@#1\endcsname }

\makeatother

\ResetCounts
\ParseData\SvendData
\ComputeCumu

\begin{document}

\centering
\begin{tabular}{*{14}{c}}
\toprule
\elev{A}  & \elev{B}  & \elev{C}  & \elev{D}  & \elev{E}  & \elev{F}  & \elev{G}  &
\elev{H}  & \elev{I}  & \elev{J}  & \elev{K}  & \elev{L}  & \elev{M}  & \elev{N}    \\[0.5ex]
\elev{O}  & \elev{P}  & \elev{Q}  & \elev{R}  & \elev{S}  & \elev{T}  & \elev{U}  &
\elev{V}  & \elev{W}  & \elev{X}  & \elev{Y}  & \elev{Z}  & \elev{Aa} & \elev{Ab}   \\[0.5ex]
\elev{Ac} & \elev{Ad} & \elev{Ae} & \elev{Af} & \elev{Ag} & \elev{Ah} & \elev{Ai} &
\elev{Aj} & \elev{Ak} & \elev{Al} & \elev{Am} & \elev{An} & \elev{Ao} & \elev{Ap}   \\
\bottomrule
\end{tabular}

\bigskip
% THIS WOULD BE OK:

% \begin{tabular}{*{8}{c}}
% \toprule
% \xintFor #1 in {0, 1, 2, 3, 4, 5, 6}\do {{$F(#1)$}&}{$F(7)$}\\
% \xintFor #1 in {0, 1, 2, 3, 4, 5, 6}\do
%                {\xintRound{1}{\HowManyCumu{#1}/\HowManyTotale [2]}&}100\\
% \bottomrule
% \end{tabular}

% BUT THE SAME WITH 
% \begin{tabular}{*{7}{S[table-format = 2.1]}S[table-format = 3]}
% DOESN'T WORK: ON NE PEUT PAS UTILISER \xintFor DANS UN TABULAR AVEC siunitx !!

%  We can use expandable macros with siunitx

\def\RowA #1{{$F(#1)$}}% EXTRA BRACES NEEDED FOR SIUNITX !!
\def\RowB #1{\xintRound{1}{\HowManyCumu{#1}/\HowManyTotale [2]}}

\begin{tabular}{*{7}{S[table-format = 2.1]}S[table-format = 3]}
\toprule
% PURELY EXPANDABLE MACROS: those work with siunitx ...
% ... BUT don't try to define a macro with parameter here :((
\xintListWithSep {&}{\xintApply\RowA {{0}{1}{2}{3}{4}{5}{6}{7}}}\\
\xintListWithSep {&}{\xintApply\RowB {{0}{1}{2}{3}{4}{5}{6}}}&100\\
\bottomrule
\end{tabular}

\bigskip

\begin{tabular}{*{9}{c}}
\toprule
% strange standalone problem with too long line from
% \xintFor #1 in {0, 10, 25, 33, 50, 66, 75, 90} \do {\textit{Pe}$(#1)$&}\textit{Pe}$(100)$\\
\xintFor #1 in {0, 10, 25, 33, 50, 66, 75, 90} \do {$q(#1)$&}$q(100)$\\
\xintFor #1 in {0, 10, 25, 33, 50, 66, 75, 90} \do {$\Percentile{#1}$&}$7$\\
\bottomrule
\end{tabular}

\end{document}

在此处输入图片描述

我也陷入了麻烦standalone（如代码底部所示），甚至dvipng因为一些我不知道的原因而加入了抱怨的喜剧。

第二个答案

\documentclass[10pt]{beamer}
%\usepackage[paperwidth=25cm]{geometry}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{booktabs}
\usepackage{siunitx}
\usepackage{xintfrac, xinttools}
% EXTENDED DATA
\newcommand*\SvendData
                {{{A}{6}}%
                 {{B}{0}}%
                 {{C}{0}}%
                 {{D}{3}}%
                 {{E}{0}}%
                 {{F}{2}}%
                 {{G}{1}}%
                 {{H}{1}}%
                 {{I}{1}}%
                 {{J}{5}}%
                 {{K}{0}}%
                 {{L}{3}}%
                 {{M}{7}}%
                 {{N}{3}}%
                 {{O}{1}}%
                 {{P}{1}}%
                 {{Q}{0}}%
                 {{R}{0}}%
                 {{S}{0}}%
                 {{T}{2}}%
                 {{U}{1}}%
                 {{V}{2}}%
                 {{W}{0}}%
                 {{X}{2}}%
                 {{Y}{1}}%
                 {{Z}{1}}%
                 {{Aa}{4}}%
                 {{Ab}{6}}%
                 {{Ac}{1}}%
                 {{Ad}{1}}%
                 {{Ae}{6}}%
                 {{Af}{2}}%
                 {{Ag}{0}}%
                 {{Ah}{3}}%
                 {{Ai}{2}}%
                 {{Aj}{1}}%
                 {{Ak}{0}}%
                 {{Al}{0}}%
                 {{Am}{0}}%
                 {{An}{0}}%
                 {{Ao}{0}}%
                 {{Ap}{4}}%
                 {{NA}{6.5}}%
                 {{NB}{0.5}}%
                 {{NC}{0.5}}%
                 {{ND}{3.5}}%
                 {{NE}{0.5}}%
                 {{NF}{2.5}}%
                 {{NG}{1.5}}%
                 {{NH}{1.5}}%
                 {{NI}{1.5}}%
                 {{NJ}{5.5}}%
                 {{NK}{0.5}}%
                 {{NL}{3.5}}%
                 {{NM}{7.5}}%
                 {{NN}{3.5}}%
                 {{NO}{1.5}}%
                 {{NP}{1.5}}%
                 {{NQ}{0.5}}%
                 {{NR}{0.5}}%
                 {{NS}{0.5}}%
                 {{NT}{2.5}}%
                 {{NU}{1.5}}%
                 {{NV}{2.5}}%
                 {{NW}{0.5}}%
                 {{NX}{2.5}}%
                 {{NY}{1.5}}%
                 {{NZ}{1.5}}%
                 {{NAa}{4.5}}%
                 {{NAb}{6.5}}%
                 {{NAc}{1.5}}%
                 {{NAd}{1.5}}%
                 {{NAe}{6.5}}%
                 {{NAf}{2.5}}%
                 {{NAg}{0.5}}%
                 {{NAh}{3.5}}%
                 {{NAi}{2.5}}%
                 {{NAj}{1.5}}%
                 {{NAk}{0.5}}%
                 {{NAl}{0.5}}%
                 {{NAm}{0.5}}%
                 {{NAn}{0.5}}%
                 {{NAo}{0.5}}%
                 {{NAp}{4.5}}}

\makeatletter

% \odef does \def with one expansion of replacement text

\newcommand*\SvendValues {}
\newcommand*\SvendNumValues {}


\newcommand*\ParseData [1]{%
% Defines the private macros underlying \elev and \HowMany
% This version creates \SvendValues ordered list of values.
%
% For inner efficiency this \SvendValues is with braces, not commas
% (to be used with \xintFor* not \xintFor)
%
% The values do not have to be integers. But they must be numeric quantities
% as understood by xintfrac.
%
  \def\SvendValues {}%
  \def\SvendNumValues {0}%
  \xintFor* ##1 in {#1}\do 
  {%
% get the possibly new value
    \odef\Svend@tmpD {\@firstoftwo ##1}%
    \odef\Svend@tmpV {\@secondoftwo ##1}%
% and insert it at the correct location in \SvendValues
% (the better would be to manage some kind of heap tree but I have not
% invested the needed time)
%
    \def\SvendValues@Tmp {}%
    \def\Svend@tmpflag  {0}%
% 0 = initial state, 
% 1 = inserted, finish, 
% 2 = was already there
    \xintifForFirst 
    {\odef\SvendValues {\expandafter{\Svend@tmpV}}%
     \def\SvendNumValues{1}%
     \expandafter\odef\csname Svend@Counts@\Svend@tmpV\endcsname {0}}% will be increased below
    {\xintFor* ##2 in {\SvendValues}\do 
      {%
      \if0\Svend@tmpflag\expandafter\@firstoftwo\else\expandafter\@secondoftwo\fi
         {\xintifCmp {\Svend@tmpV}{##2}
          {\def\Svend@tmpflag{1}%
           \oodef\SvendValues@Tmp
                 {\expandafter\SvendValues@Tmp \expandafter{\Svend@tmpV}{##2}}}% new < old
          {\def\Svend@tmpflag{2}\odef\SvendValues@Tmp {\SvendValues@Tmp {##2}}}% old = new
          {\odef\SvendValues@Tmp {\SvendValues@Tmp {##2}}}% new > old
         }
         {\odef\SvendValues@Tmp{\SvendValues@Tmp {##2}}}%
      }%
     \if0\Svend@tmpflag
         \oodef\SvendValues@Tmp{\expandafter\SvendValues@Tmp\expandafter {\Svend@tmpV}}%
     \fi
     \let\SvendValues\SvendValues@Tmp
%\typeout{\SvendValues}% debugging
     \if2\Svend@tmpflag
      \else
      % new value
      \expandafter\odef\csname Svend@Counts@\Svend@tmpV\endcsname {0}% will be increased below
      \odef\SvendNumValues {\the\numexpr\SvendNumValues+\@ne}\fi
    }%
% continued as in earlier code
    \expandafter\odef\csname Svend@Values@\Svend@tmpD\endcsname {\Svend@tmpV}%
    \expandafter\odef\csname Svend@Counts@\Svend@tmpV\endcsname 
                   {\the\numexpr\csname Svend@Counts@\Svend@tmpV\endcsname + \@ne}%
  }% end of external \xintFor loop
}%

\newcommand*\ComputeCumu {%
% Computes and stores iteratively cumulative counts
% THIS VERSION USES \SvendValues
  \xintFor* ##1 in {\SvendValues}\do {%
    \xintifForFirst {\odef\Svend@tmp{\romannumeral-`0\HowMany{##1}}}
                    {\odef\Svend@tmp{\the\numexpr\Svend@tmp+\HowMany{##1}}}%
    \expandafter\let\csname Svend@Cumul@##1\endcsname \Svend@tmp
    \xintifForLast {\let\HowManyTotale\Svend@tmp }{}%
  }%
}

% Percentiles: 
%
% P(x) (x=0,1,..,100) is the smallest value V such as the frequency of 
% event {v<= V} is at least x\%. Thus P(100) is the largest V and P(0) is the
% smallest V.

% 
% THIS VERSION USES \SvendValues
% It has nothing hardcoded.

\catcode`_ 11
\def\Percentile@helper #1#2% space below is to stop premature expansion
    { \if1\xintifLt {\HowManyCumu {#2}/\HowManyTotale}{#1/100}{0}{1}\xint_dothis{#2}\fi}

\newcommand*\Percentile [1]{% expandable !
    \xintApplyUnbraced{\Percentile@helper {#1}}\SvendValues\xint_orthat {}%
}

\catcode`_ 8

\newcommand*\elev        [1]{\csname Svend@Values@#1\endcsname }
\newcommand*\HowMany     [1]{\csname Svend@Counts@#1\endcsname }
\newcommand*\HowManyCumu [1]{\csname Svend@Cumul@#1\endcsname }

\let\firstoftwo\@firstoftwo
\let\secondoftwo\@secondoftwo
\makeatother


\ParseData\SvendData
\ComputeCumu
%\typeout{\meaning\SvendValues}

% for first tabular
% WITH BEAMER I CAN NOT DEFINE THIS IN THE FRAME !!!!!!

% ANY \newcommand MUST BE IN THE PREAMBLE WITH BEAMER !!!!!!

\newcommand*\Row [1]{\stepcounter{rowcount}%
                     \elev{\firstoftwo #1}%
                     \ifnum\value{rowcount}<14
                     \expandafter\firstoftwo\else\expandafter\secondoftwo\fi
                     {&}{\setcounter{rowcount}{0}\\[0.5ex]}}

% for middle data (not a tabular, would be too wide)
\newcommand*\ShowCumu [1]{$F(#1)=\xintRound{1}{\HowManyCumu{#1}/\HowManyTotale [2]}$}

% for third tabular

\newcommand*\RowA [1]{$q(#1)$}%
\newcommand*\RowB [1]{$\Percentile{#1}$}



\newcounter{rowcount}


\begin{document}\small

% DEBUGGING (not possible with  Beamer! because of #1...)
% \HowMany{0}

% \xintFor*#1 in \SvendValues\do {[#1,\HowMany{#1}], }
% \SvendNumValues

% \xintNthElt{0}{\SvendData}

% \HowManyTotale

\begin{frame}
\centering
\setcounter{rowcount}{0}%

\begin{tabular}{*{14}{c}}
\toprule
\xintApplyUnbraced \Row\SvendData
\bottomrule
\end{tabular}

\bigskip

% (This is too wide hence would make letters in my png appear too small)

% DEFINITIONS LIKE THIS MUST BE MOVED TO PREAMBLE IF BEAMER CLASS !!
% \def\RowA #1{{$F(#1)$}}% EXTRA BRACES NEEDED FOR SIUNITX !!
% \def\RowB #1{\xintRound{1}{\HowManyCumu{#1}/\HowManyTotale [2]}}

% \centerline{\begin{tabular}{*{\SvendNumValues}{S[table-format = 2.1]}}
% \toprule
% \xintListWithSep {&}{\xintApply\RowA \SvendValues}\\
% \xintListWithSep {&}{\xintApply\RowB \SvendValues}\\
% \bottomrule
% \end{tabular}}

\xintListWithSep{,\quad }{\xintApply\ShowCumu \SvendValues}

\bigskip

\begin{tabular}{*{10}{c}}
\toprule
\xintListWithSep {&}{\xintApply\RowA {{0}{10}{25}{33}{50}{66}{75}{90}{100}}}\\
\xintListWithSep {&}{\xintApply\RowB {{0}{10}{25}{33}{50}{66}{75}{90}{100}}}\\
\bottomrule
\end{tabular}

\end{frame}

\end{document}

在此处输入图片描述

计算数据集的四分位数

答案1

相关内容