% !TEX TS-program = LuaLaTeX
% !TEX encoding = UTF-8 Unicode
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%%
%%  This file is an example of using asmeconf with lualatex to solve and plot an ode in a landscape figure.
%%
%%  Author: John H. Lienhard V
%%          Department of Mechanical Engineering
%%          Massachusetts Institute of Technology
%%          Cambridge, MA 02139-4307 USA
%%
 %=========================================================
%% 
%% LICENSE: 
%%
%% Copyright (c) 2021 John H. Lienhard
%% Offered under the MIT license: https://ctan.org/license/mit 
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\documentclass[grid,colorlinks,nofoot]{asmeconf}

\hypersetup{%
	pdftitle={Example of asmconf with LuaLaTeX to solve an ODE},
	pdfkeywords={asmeconf, LuaLaTeX, ODE, pgfplots, landscape figure},
	pdfauthor={John H. Lienhard},
}

\usepackage[figuresright]{rotating}% to use a landscape figure


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Now use lua code

%% Runge-Kutta for simple first-order ODE
\begin{luacode*}
-- Differential equation y’(t) = f(t,y)
-- with f(t,y) = A * y * cos(t+sqrt(1+y)).
-- Initial condition: y(0) = 1
function f(t,y,A)
    return A * y * math.cos(t+math.sqrt(1+y))
end
-- Code to write PGFplots data as coordinates
function print_RKfour(tMax,npoints,A,option)
     local t0 = 0.0
     local y0 = 1.0
     local A = A
     local h = (tMax-t0)/(npoints-1)
     local t = t0
     local y = y0
     if option~=[[]] then
          tex.sprint("\\addplot["..option.."] coordinates{")
     else
          tex.sprint("\\addplot coordinates{")
     end
     tex.sprint("("..t0..","..y0..")")
     for i=1, npoints do
          k1 = h * f(t,y,A)
          k2 = h * f(t+h/2,y+k1/2,A)
          k3 = h * f(t+h/2,y+k2/2,A)
          k4 = h * f(t+h,y+k3,A)
          y = y + (k1+2*k2+2*k3+k4)/6
          t = t + h
          tex.sprint("("..t..","..y..")")
     end
     tex.sprint("}")
end
\end{luacode*}

%% Define a latex macro to call the case to be plotted
\newcommand\addLUADEDplot[4][]{%
     \directlua{print_RKfour(#2,#3,#4,[[#1]])}%
}
% SYNTAX: Solution of the initial value problem
% Code assumed t = 0 at start and y(0) = 1 
% #2 is the final time
% #3 is the number of points
% #4 is an amplitude parameter
% #1 are options passed to the pgfplots \addplot function.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% For plotting the results, call pgfplots package

\usepackage{pgfplots}% load AFTER xcolor, which was already called by asmeconf.cls
\pgfplotsset{compat=newest}% to activate latest features

\pgfplotsset{%
     width=\textwidth,%
     height=0.6\textwidth,%
     /tikz/font={\sffamily},% 
     % every axis plot/.style={line width=2pt},
    every axis/.append style={very thick},% see manual page 189
    every minor tick/.append style={very thin,black},% modifies the style `every tick'
    every minor grid/.append style={very thin, color=Snow4},
    every major tick/.append style={thin, black},% modifies the style `every minor tick'
    every major grid/.append style={thin, color=Snow4},
    major tick length={1.2em},
    minor tick length={0.5em},
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% This environment will generate the .bib file the first time you run the code
% if the .bib file already exists, it will not be overwritten
\begin{filecontents}{asmeconf-lualatex-ode-example.bib}
@online{fairbairns,
  author 	= {Robin Fairbairns and Sebastian Rahtz and Leonor Barroca},
  title 	= {A Package for Rotated Objects in \LaTeX},
  version	= {2.16d},
  organization = {Comprehensive \TeX\ Archive Network},
  year 		= {2016},
  url 		= {https://www.ctan.org/pkg/rotating},
  urldate 	= {October 2, 2019},
}      
@article{montijano2014,
   title	= {Numerical methods with {\LuaLaTeX}},
   author	= {Juan I. Montijano and Mario P{\'{e}}rez and Luis R{\'{a}}ndez and Juan Luis Varona},
   year		= 2014,
   volume	= 35,
   month	= {January},
   number	= 1,
   pages	= {51--56},
   journal	= {TUGboat},
   url		= {https://tug.org/TUGboat/tb35-1/tb109montijano.pdf},
   note		= {Open access.}
}
@manual{pgfplots,
   title 	= {Manual for Package \textsc{PGFPLOTS}},
   url		= {https://ctan.org/pkg/pgfplots},
   author 	= {Christian Feuers{\"{a}}nger},
   version 	= {1.17},
   year 	= {2020},
   organization = {Comprehensive \TeX\ Archive Network},
   month 	= feb,
   urldate	= {January 4, 2021},
}
@manual{lua,
   author 	= {Roberto {l}erusalimschy and Luiz Henrique {de Figueiredo} and Waldemar Celes},
   title    = {{L}ua 5.3 Reference Manual},
   url	 	= {https://www.lua.org/manual/5.3/},
   organization = {Pontifical Catholic University},
   address 	= {Rio de Janeiro, Brazil},
   year 	= {2017},
}
\end{filecontents}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}

\ConfName{Proceedings of the \texttt{asmeconf} \linebreak International Examples Congress and Exposition}
\ConfAcronym{AIECE21}
\ConfDate{January 20, 2021}
\ConfCity{Cambridge, MA}
\PaperNo{AIECE2021-0001}

\title{Example of \NoCaseChange{{\upshape\hologo{LuaLaTeX}}} with asmeconf.cls for ODE Integration}
 
\SetAuthors{John H.\ Lienhard V\affil{1}\CorrespondingAuthor{lienhard@mit.edu}}
\SetAffiliation{1}{Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA}

\maketitle

\versionfootnote{Version~1.01, \today}

\keywords{asmeconf, \hologo{LuaLaTeX}, ODE, pgfplots, landscape}

%%%%%%%%%  ABSTRACT  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{abstract}
This paper is an example of using {\upshape\texttt{asmeconf}} with {\upshape\hologo{LuaLaTeX}} to solve an ODE initial value problem using a fourth-order Runge-Kutta method and to plot the result using {\upshape\texttt{PGFPLOTS}}. The use of a landscape figure is also illustrated. References are given for further reading.
\end{abstract}

%%%%%%%%%  NOMENCLATURE (OPTIONAL) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{nomenclature}
\entry{$A$}{Constant parameter [--]}
\entry{$t$}{Time [s]}
\entry{$y(t)$}{Position [m]}
\end{nomenclature}

%%%%%%%%%  BODY OF PAPER %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Introduction}
\hologo{LuaLaTeX} is built upon the Lua programming language~\cite{lua}. By directly using Lua code in a \LaTeX\ file, we can accomplish a wide range of tasks, as illustrated in the open-access paper by Montijano et al.~\cite{montijano2014}.  In the present example, we follow Montijano et al.\ in solving a nonlinear first-order ordinary differential equation and plotting the result---all within a single \LaTeX\ file!

\section{Solution to an initial value problem}
We consider an initial value problem like that of Montijano et al.:
\begin{equation}\label{eqn:1}
y'(t) = A\cdot y(t) \cos\Big(t + \sqrt{1 + y(t)}\,\Big) \text{ with }y(0)=1
\end{equation}
Here, $A$ is a constant. We may adopt a fourth-order Runge-Kutta algorithm for the integration, which we shall perform to $t = 30$~s using a 400 point discretization.  The details of the Runge-Kutta algorithm and a listing of the code are given in Montijano et al. (You can also read the code in the present \texttt{.tex} file.)

The algorithm is implemented directly in the preamble of this file, and the results are plotted in Fig.~\ref{fig:1} for $A = \{0.25, 0.5, 0.75, 1.0\}$. Plotting is done using the \texttt{PGFPLOTS} package~\cite{pgfplots}.

Landscape figures may be produced at full-page size by putting \verb|\usepackage[figuresright]{rotating}| (Fig.~\ref{fig:1}) into your \texttt{.tex} file's preamble and using the \texttt{sidewaysfigure*} environment~\cite{fairbairns}.

\begin{sidewaysfigure*}
\begin{tikzpicture}
\begin{axis}[%
	 xmin=0., 
	 xmax=30., 
	 ymin=0.0, 
	 ymax=1.1,
     xtick={0,5,...,30}, 
     ytick={0,0.2,...,1.0},
     minor x tick num=4, 
     minor y tick num=3,
     xlabel={Time, $\mathsf{t}$ [s]}, 
     ylabel={Position, $\mathsf{y}$ [m]},
     xticklabel={$\mathsf{\pgfmathprintnumber{\tick}}$},
     yticklabel={$\mathsf{\pgfmathprintnumber{\tick}}$},
     legend style={ 
    	at={(0.7,0.85)},
		anchor=west,
		fill=none,
        cells={anchor=west},
     },
     ]
% tMax = 30, npoints = 400, A is the last argument
\addLUADEDplot[color=Purple4,densely dashed,,very thick]{30}{400}{0.25};% color names are from xcolor package
	\addlegendentry[fill=white]{$\mathsf{A = 0.25}$} 
\addLUADEDplot[color=Chartreuse4,dashdotted,very thick]{30}{400}{0.5};
	\addlegendentry[fill=white]{$\mathsf{A = 0.5}$} 
\addLUADEDplot[color=Red3,densely dotted,very thick]{30}{400}{0.75};
	\addlegendentry[fill=white]{$\mathsf{A = 0.75}$}
\addLUADEDplot[color=Blue3,smooth,very thick]{30}{400}{1};
	\addlegendentry[fill=white]{$\mathsf{A = 1}$} 
\end{axis}
\end{tikzpicture}
\caption{\MakeUppercase{A trial of pgfplot with Luacode Runge-Kutta integration}\label{fig:1}}
\end{sidewaysfigure*}


%%%  CONCLUSIONS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Conclusion}
\hologo{LuaLaTeX} enables numerical computations within a \LaTeX\ environment. By combining this capability with
\texttt{PGFPlots}, the need for separate numerical and/or graphics packages can be reduced.

%%%  ACKNOWLEDGMENTS %%%%%%%%%%%%%%%%%%%%%%%%%%%

\section*{Acknowledgments}
The example shown in this paper is directly based on an example given by Montijano et al.~\cite{montijano2014}. Additional examples, such as the
Lorenz attractor, are contained in that paper.


%%%  REFERENCES  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\bibliographystyle{asmeconf}%% .bst file following ASME conference format. Do not change.
\bibliography{asmeconf-lualatex-ode-example}%% this bib file will be generated from the filecontents environment upon first run of this .tex file.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\end{document}

