TikZ way to define several constants with just one macro

Question

I'm using TikZ to plot several things (geometric surfaces, line plots, etc.) in just one environment. These plots depend on several constants that I define in the same tikzpicture environment. This is a (dummy) example:

\begin{tikzpicture}
\def\a{1}
\def\g{0.5}
\def\kamax{5}
\def\M{15}
\def\T{3}

\pgfmathsetmacro{\Ra}{1 + \a*\M^(1-\g)/\kamax}
\pgfmathsetmacro{\Rb}{1 + \a*\M^(1-\g)/(4*\kamax)}
\pgfmathsetmacro{\la}{\M/(2*\T*\Ra)}
\pgfmathsetmacro{\lb}{\M/(2*\T*\Rb)}

\begin{axis}[domain=0:\M/\T, xlabel = Rate of consumption, ylabel = Time of purchase, title = Optimal time to purchase, legend pos=north west, axis equal image]
\addplot[color=blue][domain=0:\la] {0};
\addplot[color=blue][domain=\la:\lb] {2*\T - (sqrt(2*\a*\kamax*\M^(1+\g)*\T*\x*(\M-2*\T*\x)))/(\a*\M*\x)};
\addplot[color=blue][domain=\lb:\M/\T] {\T};
\addplot[color=red] coordinates {(\la,0)(\la,\T)};
\addplot[color=red] coordinates {(\lb,0)(\lb,\T)};
\end{axis}
\end{tikzpicture}

In the example, the constants defined with \def are the "essential" constants of the problem I'm studying, and those defined with \pgfmathsetmacro are needed to make the plotting easier.

After plotting the example exposed before, I would like to change some of the values of the "essential" constants and plot the same five plots again (in the same environment) to compare results. My question is: is there a way to create macro or function that takes as input my "essential" constants and returns as output the other constants?

My objective is purely to simplify the .tex reading; if I redefine the constants in the same environment after plotting the .tex compiles just fine.

Thank you very much in advance.

Answer 1

You can just pack the code into a macro like this

\newcommand*{\a}{}
\newcommand*{\g}{}
\newcommand*{\kamax}{}
\newcommand*{\M}{}
\newcommand*{\T}{}
\newcommand*{\SetupPlot}[5]{%
    \renewcommand*{\a}{#1}%
    \renewcommand*{\g}{#2}%
    \renewcommand*{\kamax}{#3}%
    \renewcommand*{\M}{#4}%
    \renewcommand*{\T}{#5}%
    \pgfmathsetmacro{\Ra}{1 + \a*\M^(1-\g)/\kamax}%
    \pgfmathsetmacro{\Rb}{1 + \a*\M^(1-\g)/(4*\kamax)}%
    \pgfmathsetmacro{\la}{\M/(2*\T*\Ra)}%
    \pgfmathsetmacro{\lb}{\M/(2*\T*\Rb)}%
}

The first lines just make sure the macors are not yet defined. You get an error message otherwise. \def will just overwrite the macros.

You can then write

\SetupPlot{1}{0.5}{5}{15}{3}

Edit: I added % at the end of the lines in the definition of \SetupPlot, because, as cfr pointed out, if you use this macro outside a tikzpicture it will produce unwanted space without the %.

Answer 2

You can use pgf/tikz keys to automatically set your variables. Since you are using tikz you might as well use \tikzset. All that you need to do is do define a key with a code handler and then have the code handler set all of your variables.

Here is one way to do this (as cfr says in the comments, the choice of variable names used here, following the OP, is unwise):

\documentclass{article}
\usepackage{tikz}
\usepackage{etoolbox}% only for \csuse in the MWE
\begin{document}

\tikzset{mysettings/.code n args={5}{% 5 arguments: \a, \g, \kamax, \M and \T
    \def\a{#1}% set the variables
    \def\g{#2}
    \def\kamax{#3}
    \def\M{#4}
    \def\T{#5}
    \pgfmathsetmacro{\Ra}{1 + \a*\M^(1-\g)/\kamax}
    \pgfmathsetmacro{\Rb}{1 + \a*\M^(1-\g)/(4*\kamax)}
    \pgfmathsetmacro{\la}{\M/(2*\T*\Ra)}
    \pgfmathsetmacro{\lb}{\M/(2*\T*\Rb)}
  }
}

\tikzset{mysettings={1}{0.5}{5}{15}{3}}
\foreach \var [count=\y]in {a,g,kamax,M,T,Ra,Rb,la,lb} {
  \var = \csuse{\var};
}

\tikzset{mysettings={2}{0.2}{1}{10}{-3}}
\foreach \var [count=\y]in {a,g,kamax,M,T,Ra,Rb,la,lb} {
  \var = \csuse{\var};
}

\end{document}

So I have defined the tikz key mysettings to take five arguments, corresponding to your parameters \a, \g, \kamax, \M and \T in this order. Passing these parameters to mysettings sets these five variables and, in addition, sets \Ra, \Rb, \la and \lb.

The for-loops at the end of the MWe are just to show that it works. The MWE produces:

Two more comments. You can also set your variables at the start of a tikzicture environment:

\begin{tikzpicture}[mysettings={1}{0.5}{5}{15}{3}]
....
\end{tikzpicture}

Rather than using \def in the definition of mysettings you might want to use \gdef in order to make the definitions "global". On the other hand, the code above makes then local which might be better in your use-case. As cfr says in the comments, this needs to be used with care.