有没有简单的方法可以获取数学函数的值表？
考虑以下示例和伪代码：
\documentclass{article}
\usepackage{pgfplots}
\usepackage[nomessages]{fp}% http://ctan.org/pkg/fp
\usepackage{xstring}% http://ctan.org/pkg/xstring
\usepackage{xparse}% http://ctan.org/pkg/xparse
\usepackage[locale=DE]{siunitx}
\begin{document}
\def\f(#1){#1^2} %%It should also be possible to use gnuplots x**2 syntax for the value table
\sisetup{zero-decimal-to-integer}
\def\pf(#1){\pgfmathparse{\f(#1)}\num{\pgfmathresult}}
\begin{center}
\begin{tikzpicture}
\begin{axis}[domain=-2:10]
\addplot+[no markers] gnuplot {\f(x)};
\addplot+[mark=x,samples at={1,...,10}] gnuplot {\f(x)};
\end{axis}
\end{tikzpicture}
\end{center}
Then I want a value table, something like generated automatically.
%% \gen_value_table[samples at={1,...,10},orientation=horizontal]{\f}
\begin{tabular}{*{10}{c|}c}
$x$& 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\\hline
$f(x) $ & \pf(1) & \pf(2) & \pf(3) & \pf(4) & \pf(5) & \pf(6) &\pf(7) & \pf(8) & \pf(9) & \pf(10)
\end{tabular}
%% \gen_value_table[samples at={1,2,3.5,10},orientation=horizontal]{\f}
\begin{tabular}{*{4}{c|}c}
$x$ & 1 & 2 & 3.5 & 10 \\\hline
$f(x)$ & \pf(1) & \pf(2) & \pf(3.5) & \pf(10)
\end{tabular}
%% \gen_value_table[samples at={1,2,3.5,10},orientation=]{\f}
\begin{tabular}{c|c}
$x$ & $f(x)$ \\\hline
1 & \pf(1) \\
2 & \pf(2) \\
3,5 & \pf(3.5) \\
10 & \pf(10)
\end{tabular}
\end{document}
答案1
正如 percusse 和 cmhughes 在他们的评论中指出的那样，你可以尝试使用该pgfplotstable包来满足你的需求。这里有一些代码作为起点，我认为它对于垂直表格来说效果很好，但对于水平表格来说效果不佳。虽然解决方案并不完美，但希望它是一个很好的起点，值得尝试。
请注意，您不能将密钥samples at与 一起使用\addplot gnuplot。这始终使用domain和samples来生成值。
\documentclass[
ngerman,
english, % <-- comment me to use German language
DIV=12,
]{scrartcl}
\usepackage{babel}
\usepackage{caption}
\usepackage{booktabs}
\usepackage{siunitx}
\sisetup{
% just to show where the `\num' command is used
color=green,
}
% this adds the German and UK number format styles to the `siunitx'
% as well as to the tikz/pgf settings and uses them according to
% the actual active language
\addto\extrasngerman{\sisetup{locale = DE}\SendSettingsToPgf}
\addto\extrasenglish{\sisetup{locale = UK}\SendSettingsToPgf}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
% define maximum number of entries in the table
\def\MaxItems{13}
% define which samples should be used (in the plot and table)
\def\Samples{1,1.5,2,3,...,10}
% define stuff that should be used all over the document
\pgfplotstableset{
% to show when there are defined too much cells
empty cells with={NaN},
% -----
% define how the `new' column shall be filled:
create on use/x/.style={
% % unfortunately using `\Samples' here causes an error;
% % don't know why
% create col/set list=\Samples
% so the list entries have to be given here explicitly
create col/set list={1,1.5,2,3,...,10}
},
% create columns that uses the function you need the values for
create on use/x square/.style={
% this fills cells with `0' (zero), when `\MaxItems' is
% larger than the `set list' (or `\Samples')
create col/expr={\thisrow{x}^2}
},
create on use/minus x cube/.style={
create col/expr={-1*\thisrow{x}^3}
},
% -----
% define headers for the corresponding columns
columns/x/.style={
column name=$x$,
dec sep align,
},
columns/x square/.style={
column name=$x^2$,
},
columns/minus x cube/.style={
column name=$-x^3$,
dec sep align,
},
% ----------------------
% I cannot find the following key in the manual
% it doesn't cause an error but also does not do anything
% --> is it intended that one isn't able to set a style for all columns
% or am I missing something in the manual that this can be done?
every column/.append style={
dec sep align,
},
% ----------------------
% % if only vertical tables would be used,
% % one could fix the column name
% every first column/.style={
% column name=$x$,
% },
% -----
% use booktabs to make tables look nicer
every head row/.style={
before row=\toprule,
after row=\midrule,
},
every last row/.style={
after row=\bottomrule,
},
}
% create a new table with `\MaxItem' rows and column 'new':
\pgfplotstablenew[
columns={
x,
x square
},
]{\MaxItems}{\loadedtable}
% % ---------------------------------
% % save table to disc, if you want
% \pgfplotstablesave[
% columns={
% x,
% x square
% },
% ]{\loadedtable}{table-out.txt}
% % ---------------------------------
\sisetup{zero-decimal-to-integer}
\def\pf(#1){\pgfmathparse{\f(#1)}\num{\pgfmathresult}}
\def\f(#1){#1^2} %%It should also be possible to use gnuplots x**2 syntax for the value table
\begin{document}
\section{Create plot}
\begin{center}
\begin{tikzpicture}
\begin{axis}[
domain=-2:10,
]
% define the function to plot
% (it can also be included directly to the argument after
% `expression'. It is only defined here so you don't have to
% change it at several places when the function changes.)
\def\Function{x^2}
% plot the (continuous) function
% (in the `domain' with `samples')
\addplot+ [no markers]
expression {\Function};
% plot points at `samples at'
\addplot+ [mark=x,samples at=\Samples]
expression {\Function};
% plot points from table
% (the points were stated at `set list')
\addplot+ [mark=o]
table {\loadedtable};
% % you can also plot the points from saved table.
% \addplot+ [mark=o]
% table {table-out.txt};
\end{axis}
\end{tikzpicture}
\end{center}
\section{Create tables ``automatically''}
Then I want a value table, something like generated automatically.
\begin{center}
\captionof{table}{Original manual vertical table (\emph{left}) and new
``automatic'' table (\emph{right})}
%% \gen_value_table[samples at={1,2,3.5,10},orientation=]{\f}
\begin{tabular}{c|c}
$x$ & $f(x)$ \\\hline
1 & \pf(1) \\
2 & \pf(2) \\
3,5 & \pf(3.5) \\
10 & \pf(10) \\
\end{tabular}
%
% show (``automatic'') table
\pgfplotstabletypeset{\loadedtable}
%
\pgfplotstabletypeset[
columns={
x,
x square
},
]{
x
1
2
3.5
10
}
\end{center}
\begin{center}
\captionof{table}{Original manual horizontal table (\emph{top}) and new
``automatic'' table (\emph{down})}
%% \gen_value_table[samples at={1,...,10},orientation=horizontal]{\f}
\begin{tabular}{*{10}{c|}c}
$x$& 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\\hline
$f(x) $ & \pf(1) & \pf(2) & \pf(3) & \pf(4) & \pf(5) & \pf(6) &\pf(7) & \pf(8) & \pf(9) & \pf(10)
\end{tabular}
\vspace{2ex}
% -----
% up to here everything is fine, but when transposing the table an
% additional header row is created (--> don't know how it can be suppressed).
% Also I don't know why the ``LaTeX'' column headers get lost and only the
% column header from the table is printed
\pgfplotstabletranspose{\loadedtableTransposed}{\loadedtable}
\pgfplotstabletypeset[
every first column/.append style={
string type,
},
input colnames to=,
]{\loadedtableTransposed}
\end{center}
\end{document}
答案2
我发现这个包解决了我的问题：
\documentclass{article}
\usepackage{array}
\usepackage{amsmath}
\usepackage{tabularcalc} % tabellen van functiewaarden
\begin{document}
\tcsetcoltype{|r|}{>{\centering\arraybackslash}m{1.5cm}|}
\htablecalc [1]{$x$}{x=-3,-2,-1,0,1,2,3} {$f(x)$}{2*x+3}
\end{document}
