The code would like this, but how to finish the rest ？
\documentclass{article}
\begin{document}
\ExplSyntaxOn
\NewDocumentCommand{\average}{m}{%
}
\ExplSyntaxOff
\average{1,3.7,5} % would return 3.233
\average{1,3.7,5,3.2*2,7.9} % would return 4.8. the argument number is arbitrary but limited
\end{document}
The following defines a fully expandable variant of your \average macro. I also added an optional argument to provide the rounding precision.
You don't need anything else to also access variables, be they defined as macros or fp variables.
\documentclass{article}
\ExplSyntaxOn
\cs_new:Npn \xcn_mean:n #1
{ \fp_eval:n { ( \clist_use:nn {#1} { + } ) / \clist_count:n {#1} } }
\NewExpandableDocumentCommand \average { o m }
{
\IfNoValueTF {#1}
{ \xcn_mean:n {#2} }
{ \fp_eval:n { round ( \xcn_mean:n {#2}, #1 ) } }
}
\fp_new_variable:n { aaa }
\fp_set_variable:nn { aaa } { 3.7 }
\ExplSyntaxOff
\begin{document}
\average[3]{1,aaa,5} % would return 3.233
\average{1,3.7,5,3.2*2,7.9} % would return 4.8. the argument number is arbitrary but limited
\end{document}
An extended variant that also allows to calculate the mean of the return values of a function. I use expkv-cs to split the optional argument as a key=value argument with the two keys round and f. The notation V:~ in the key definition list is the same as \exp_args:NV for keys in expkv and the other related packages (note that the ~ is only to be used in \ExplSyntaxOn, outside of that scope it should be V: ).
\documentclass{article}
\usepackage{expkv-cs}
\ExplSyntaxOn
\cs_new:Npn \xcn_mean:n #1
{ \fp_eval:n { ( \clist_use:nn {#1} { + } ) / \clist_count:n {#1} } }
\cs_new:Npn \xcn_mean_function:nn #1#2
{
\fp_eval:n
{
( \clist_map_tokens:nn {#2} { \__xcn_mean_function_aux:nn {#1} } )
/ \clist_count:n {#2}
}
}
\cs_new:Npn \__xcn_mean_function_aux:nn #1#2 { +(#1(#2)) }
\NewExpandableDocumentCommand \average { O{} m }
{ \__xcn_average:nn {#1} {#2} }
\ekvcSplitAndForward \__xcn_average:nn \__xcn_average_aux:nnn
{
V:~ round = \c_novalue_tl
,V:~ f = \c_novalue_tl
}
\cs_new:Npn \__xcn_average_aux:nnn #1#2#3
{
% #1: round
% #2: f
% #3: clist
\tl_if_novalue:nTF {#1}
{ \__xcn_average_aux:nn {#2} {#3} }
{ \fp_eval:n { round ( \__xcn_average_aux:nn {#2} {#3}, #1 ) } }
}
\cs_new:Npn \__xcn_average_aux:nn #1#2
{
\tl_if_novalue:nTF {#1}
{ \xcn_mean:n {#2} }
{ \xcn_mean_function:nn {#1} {#2} }
}
\fp_new_variable:n { aaa }
\fp_set_variable:nn { aaa } { 3.7 }
\fp_new_function:n { sq }
\fp_set_function:nnn { sq } { x } { x**2 }
\ExplSyntaxOff
\begin{document}
\average[round=3]{1,aaa,5} % would return 3.233
\average{1,3.7,5,3.2*2,7.9} % would return 4.8. the argument number is arbitrary but limited
\average[f=sq]{1, 2, 3, 4} % 30/4 = 7.5
\end{document}
\clist_use:nn {#1} { + } is very simple and concise code. Of course it's possible to loop manually, as I said, I just don't see the reason to.
The expandable \average macro can be created in OpTeX using \expr and \foreach:
\optdef\average[3]#1{\immediateassignment\tmpnum=0
\expr[\the\opt]{(0\foreach#1,\do##1,{+(##1)\incrtmpnum})/\the\tmpnum}}
\def\incrtmpnum{\immediateassignment\advance\tmpnum by1 }
\average{1,3.7,5} % would return 3.233
\average[1]{1,3.7,5,3.2*2,7.9} % would return 4.8. the argument number is arbitrary but li
\message{\average[5]{2,3}}
\bye
If the main point is learn expl3, this is the wrong answer. But if the goal is make easy descriptives statistics as the mean or median, or some more complex, consider include the R language in the LateX document:
File name: mwe.Rnw (locally, use mwe.Rtex in Overleaf)
\documentclass{article}
\parskip1em\parindent0pt
\begin{document}
<<echo=F>>=
require(knitr)
@
Mean of \Sexpr{combine_words(c(1,3.7,5))} would return roughly
\Sexpr{round(mean(c(1,3.7,5)),2)} (more precisely,
\Sexpr{mean(c(1,3.7,5))})
<<data,echo=F>>=
# complex data better in a object x
x <- c(1,3.7,5,3.2*2,7.9)
@
Mean of x values (\Sexpr{x}) is \Sexpr{mean(x)} with a SD of
\Sexpr{sd(x)} (rounded \Sexpr{round(sd(x),1)}) but the median is
\Sexpr{median(x)}.
<<echo=F,fig.cap="Average of x in a box and wisker plot",fig.pos="h!">>=
boxplot(x,xlab="My x values")
@
\end{document}
It's very hard to follow your journey along fp variables…
However, it's possible to define an expandable \average command that copes with each of your various methods.
\documentclass{article}
\ExplSyntaxOn
\NewExpandableDocumentCommand{\average}{O{20}m}
{% #1 = accuracy, #2 = list of fp expressions
\xcn_average:nn {#1} {#2}
}
\cs_new:Nn \xcn_average:nn
{
\fp_eval:n { round ( 0 \clist_map_function:nN {#2} \__xcn_average_item:n , #1 ) }
}
\cs_new:Nn \__xcn_average_item:n
{
+ \fp_eval:n {#1}
}
%% method with fp variables
\fp_new_variable:n { aaa }
\fp_set_variable:nn { aaa } { 3.5 }
% method with commands
\newcommand{\bbb}{4.5}
\ExplSyntaxOff
\begin{document}
\average{2,4,aaa,\bbb,pi}
\average[3]{2,4,aaa,\bbb,pi}
\edef\test{\average[4]{2,4,aaa,\bbb,pi}}
\texttt{\meaning\test}
\end{document}
z=2*x+3*y , and let x=5,y=6 . then define a function that can calculate z , and treat {5,6} as a list to be used by expl3 and the result is 2*5+3*6=28.
O{20} do ? keep 20 decimal places? Why there is a 0 in round(0 \clist_… ?
l3fp's output, for instance \fpeval{1e-21}. Better check for an optional argument :)