How to use lua code from external file in lualatex?

Question

I am learning lualatex because of its abilities to use lua and make it easier for more sophisticated documents.

I am using this document for running some introductory examples. https://www.unirioja.es/cu/jvarona/downloads/numerical-methods-luatex.pdf

I have two questions.

1. Is it possible to call external Lua libraries downloaded from the web from Lua code being used in Luatex?

2. Can we write long chunks of lua code in a different file than inside the TeX file itself? Consider the Lorentez attractor examples at the end, which compiles and works well on my machine. But the lua code to produce the attractor is rather long. Is there anyway for me to write this lua code in an external file instead? The following gives me a latex compilation error where I attempted to use \input{scrap.lua}

\documentclass{article}
\usepackage{luacode}
\usepackage{pgfplots}
\usepackage{tikz}

\begin{luacode*}
  \input{scrap.lua}
\end{luacode*}

\newcommand\addLUADEDplot[3][]{%
\directlua{print_LorAttrWithEulerMethod(#2,#3,[[#1]])}%
}

\begin{document}

\begin{tikzpicture}
\begin{axis}
% SYNTAX: Solution of the Lorenz system
% with step h=0.02 sampled at 1000 points.
\addLUADEDplot[color=red,smooth]{0.02}{1000};
\addLUADEDplot[color=green,smooth]{0.02}{1000};
\addLUADEDplot[color=blue,smooth]{0.02}{1000};
\addLUADEDplot[color=cyan,smooth]{0.02}{1000};
\addLUADEDplot[color=magenta,smooth]{0.02}{1000};
\addLUADEDplot[color=yellow,smooth]{0.02}{1000};
\end{axis}
\end{tikzpicture}

\end{document}

The external file scrap.lua looks like

-- Differential equation of the Lorenz attractor
function f(x,y,z)
local sigma = 3
local rho = 26.5
local beta = 1
return {sigma*(y-x), -x*z + rho*x - y, x*y - beta*z}
end
-- Code to write PGFplots data as coordinates
function print_LorAttrWithEulerMethod(h,npoints,option)
-- The initial point (x0,y0,z0)
local x0 = 0.0
local y0 = 1.0
local z0 = 0.0
-- we add a random number between -0.25 and 0.25
local x = x0 + (math.random()-0.5)/2
local y = y0 + (math.random()-0.5)/2
local z = z0 + (math.random()-0.5)/2
if option~=[[]] then
tex.sprint("\\addplot3["..option.."] coordinates{")
else
tex.sprint("\\addplot3 coordinates{")
end
-- we dismiss the first 100 points to go into the attractor
for i=1, 100 do
m = f(x,y,z)
x = x + h * m[1]
y = y + h * m[2]
z = z + h * m[3]
end
for i=1, npoints do
m = f(x,y,z)
x = x + h * m[1]
y = y + h * m[2]
z = z + h * m[3]
tex.sprint("("..x..","..y..","..z..")")
end
tex.sprint("}")
end

The error I get is

ex))) ! LuaTeX error [\directlua]:1: unexpected symbol near '\'. \luacode@dbg@exec ...code@maybe@printdbg {#1} #1 } l.8 \end{luacode*}

              ?

Answer 1

The best way to do this is to make your external file into a module. That means, you make sure that all variables are local and in the end you return a table which exports all user-accessible functions. For example f(x,y,z) is not going to be used outside, so I won't export it. As you can see I can also export functions under a different name.

-- Differential equation of the Lorenz attractor
local function f(x,y,z)
    local sigma = 3
    local rho = 26.5
    local beta = 1
    return {sigma*(y-x), -x*z + rho*x - y, x*y - beta*z}
end

-- Code to write PGFplots data as coordinates
local function print_LorAttrWithEulerMethod(h,npoints,option)
    -- The initial point (x0,y0,z0)
    local x0 = 0.0
    local y0 = 1.0
    local z0 = 0.0
    -- we add a random number between -0.25 and 0.25
    local x = x0 + (math.random()-0.5)/2
    local y = y0 + (math.random()-0.5)/2
    local z = z0 + (math.random()-0.5)/2
    if option~=[[]] then
        tex.sprint("\\addplot3["..option.."] coordinates{")
    else
        tex.sprint("\\addplot3 coordinates{")
    end
    -- we dismiss the first 100 points to go into the attractor
    for i=1, 100 do
        local m = f(x,y,z)
        x = x + h * m[1]
        y = y + h * m[2]
        z = z + h * m[3]
    end
    for i=1, npoints do
        local m = f(x,y,z)
        x = x + h * m[1]
        y = y + h * m[2]
        z = z + h * m[3]
        tex.sprint("("..x..","..y..","..z..")")
    end
    tex.sprint("}")
end

return { LorenzAttractor = print_LorAttrWithEulerMethod }

An advantage of having the Lua code in a separate file is that you do not have to worry about catcodes. Therefore you don't need the luacode package at all. The module you created in scrap.lua can be loaded like any regular Lua module. Usually you would load it like

local scrap = require("scrap")

but that won't work in LuaTeX because the scrap variable would only be local to the \directlua chunk it is mentioned in and can hence not be used in other chunks. Therefore you have to make a global variable scrap to encapsulate the module

\directlua{scrap = require("scrap")}

The full document would read

\documentclass{article}
\usepackage{pgfplots}
\usepackage{tikz}

\directlua{scrap = require("scrap")}

\newcommand\addLUADEDplot[3][]{%
\directlua{scrap.LorenzAttractor(#2,#3,[[#1]])}%
}

\begin{document}

\begin{tikzpicture}
\begin{axis}
% SYNTAX: Solution of the Lorenz system
% with step h=0.02 sampled at 1000 points.
\addLUADEDplot[color=red,smooth]{0.02}{1000};
\addLUADEDplot[color=green,smooth]{0.02}{1000};
\addLUADEDplot[color=blue,smooth]{0.02}{1000};
\addLUADEDplot[color=cyan,smooth]{0.02}{1000};
\addLUADEDplot[color=magenta,smooth]{0.02}{1000};
\addLUADEDplot[color=yellow,smooth]{0.02}{1000};
\end{axis}
\end{tikzpicture}

\end{document}