I have a set of of functions I keep re-using (as in [this question](https://topanswers.xyz/tex?q=1557)).

**My question**

How can I efficiently plot a linear combination of these functions and easily load different scenarios based on different sets of parameters?

**My target**


Easily plot scenarios based on initial values

I feel limited in my analysis to defined sets of variables The heavy/not elegant code makes me think I am dragging a bad habit (I'd like to correct) 

I clumsily use  (LinearCombination, LC)
`LC(\a,\b,\c,\d,\e,\f)=\a*\d+\b*\e+\c*\f ;`

I need your thoughts to update all this in a civilized way :)

![ImproveFunctionSetOfVariables.png](/image?hash=a6cf00d28cf3e712ab1803953f8efac6ce6333e10c35a0656fe6464b7adba747)

Explanations in the MWE below

**What I do so far**

```
\documentclass{standalone}
\usepackage{pgfplots}

\tikzset{
 declare function={  % very basic linear combination
  LC(\a,\b,\c,\d,\e,\f)=\a*\d+\b*\e+\c*\f ;  
 }
}
 
\begin{document}

% What I do so far
% This long list, not easy to read, no easy to reuse
% It works though. Feels like a 3yo answer (me last year)

\def\WOne{1}  \def\KOne{100}  \def\RROne{0}  \def\VolOne{0.20}
\def\WTwo{\WOne} \def\KTwo{\KOne} \def\RRTwo{\RROne} \def\VolTwo{\VolOne}
\def\WThree{\WOne} \def\KThree{\KOne}  \def\RRThree{\RROne}\def\VolThree{\VolOne}

 \begin{tikzpicture} 
  \begin{axis}   
   \addplot3[surf] {LC(\WOne,\WTwo,\WThree,
      \KOne * x + \VolOne * y + \RROne,
      \KTwo * x - \VolTwo * y + \RRTwo,
      \KThree * x * y * \VolThree + \RRThree
      )} ;
  \end{axis}   
 \end{tikzpicture} 

%To simplifiy inclusion of the code in my flow I use a  macro

\newcommand{\myLC}{
 \begin{tikzpicture} 
  \begin{axis}   
   \addplot3[surf] {LC(\WOne,\WTwo,\WThree,
      \KOne * x + \VolOne * y + \RROne,
      \KTwo * x - \VolTwo * y + \RRTwo,
      \KThree * x * y * \VolThree + \RRThree
      )} ;
  \end{axis}   
 \end{tikzpicture} 
}

\myLC{}

% I then have multiple (>15) sets of variables
% Set 1
\def\WOne{1} \def\KOne{100} \def\RROne{0} \def\VolOne{0.20}
\def\WTwo{0} \def\KTwo{0} \def\RRTwo{0} \def\VolTwo{0}
\def\WThree{0} \def\KThree{0}  \def\RRThree{0} \def\VolThree{0}

\myLC{}

% Set 2
\def\WOne{1} \def\KOne{100} \def\RROne{0} \def\VolOne{0.20}
\def\WTwo{-1} \def\KTwo{110} \def\RRTwo{0} \def\VolTwo{0.25}
\def\WThree{0} \def\KThree{0}  \def\RRThree{0} \def\VolThree{0}

\myLC{}

% Set 3
\def\WOne{1} \def\KOne{100} \def\RROne{0} \def\VolOne{0.20}
\def\WTwo{-2} \def\KTwo{110} \def\RRTwo{0} \def\VolTwo{0.25}
\def\WThree{1} \def\KThree{120}\def\RRThree{0} \def\VolThree{0.30}

\myLC{}

% It does the job... but I know I am wrong.

% What I could do is define my list of variables like this for each set
%Still not super convenient

\tikzset{
 declare function={  
 WOne = 1 ;
 WTwo = 1 ;
 WThree = WTwo ;
 KOne = 100 ;
 KTwo = 100 ;
 KThree = 100 ;
 RROne = 1 ;
 RRTwo = 0.50 ;
 RRThree = 0.25 ;
 TTOne = 1 ;
 TTTwo = 0.50 ;
 TTThree = 0.25 ;
 VolOne = 0.25 ;
 VolTwo = 0.25 ;
 VolThree = 0.25 ;
 }
}


 \begin{tikzpicture} 
  \begin{axis}   
   \addplot3[surf] {LC(WOne,WTwo,WThree,
      KOne * x + VolOne * y + RROne,
      KTwo * x - VolTwo * y + RRTwo,
      KThree * x * y * VolThree + RRThree
      )} ;
  \end{axis}   
 \end{tikzpicture} 

% But 
% 1 - It's certainly possible (how ?) to name this set of parameters to reuse it in another analysis
% 2 - On the cons side, I would have to change a big chuck of my code with many dependancies cope with this approach.


% I could use a macro to input (some) variables but again, readibility is poor

\newcommand{\mysecondLC}[3]{
 \begin{tikzpicture} 
  \begin{axis}   
   \addplot3[surf] {LC(#1,#2,#3,
      KOne * x + VolOne * y + RROne,
      KTwo * x - VolTwo * y + RRTwo,
      KThree * x * y * VolThree + RRThree
      )} ;
  \end{axis}   
 \end{tikzpicture} 

}

\mysecondLC{1}{1}{1} 

% I'll be limited to 9 inputs anyway (i'll have more inputs). Still, it's not easy to read....
% I would, again, have to change a big chuck of my code with many dependancies cope with this approach.


\end{document}

```

In a future question, I'll ask how to load a different format (surf, colormap) along the scenario I load. To get easily the kind of output (the real functions I use in my flow)

![ExempleDeMultiImages2.png](/image?hash=a7ec761909ce4772ba6a34d118fa01114baa1cbdd8bbf95b56baff2d5573f795)