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% $Header$

\documentclass{article}

% Use the Cactus ThornGuide style file
% (Automatically used from Cactus distribution, if you have a
%  thorn without the Cactus Flesh download this from the Cactus
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\newlength{\tableWidth} \newlength{\maxVarWidth} \newlength{\paraWidth} \newlength{\descWidth} \begin{document}

% The author of the documentation
\author{Bela Szilagyi \textless bela.szilagyi@jpl.nasa.gov\textgreater \\ N T Bishop \textless N T Bishop {\textless}bishont@unisa.ac.za{\textgreater}\textgreater \\ Chi Wai Lai \textless Kevin {\textless}laicw@astro.unisa.ac.za{\textgreater}\textgreater}

% The title of the document (not necessarily the name of the Thorn)
\title{NullExact}

% the date your document was last changed, if your document is in CVS,
% please use:
%    \date{$ $Date: 2005-08-25 07:12:30 -0400 (Thu, 25 Aug 2005) $ $}
\date{August 25 2005}

\maketitle

% Do not delete next line
% START CACTUS THORNGUIDE

% Add all definitions used in this documentation here
%   \def\mydef etc

% Add an abstract for this thorn's documentation
\begin{abstract}

\end{abstract}

% The following sections are suggestive only.
% Remove them or add your own.

\section{Introduction}

\section{Physical System}

\section{Numerical Implementation}

\section{Using This Thorn}

\subsection{Obtaining This Thorn}

\subsection{Basic Usage}

\subsection{Special Behaviour}

\subsection{Interaction With Other Thorns}

\subsection{Examples}

\subsection{Support and Feedback}

\section{History}

\subsection{Thorn Source Code}

\subsection{Thorn Documentation}

\subsection{Acknowledgements}


\begin{thebibliography}{9}

\end{thebibliography}

% Do not delete next line
% END CACTUS THORNGUIDE



\section{Parameters} 


\parskip = 0pt

\setlength{\tableWidth}{160mm}

\setlength{\paraWidth}{\tableWidth}
\setlength{\descWidth}{\tableWidth}
\settowidth{\maxVarWidth}{nullexact\_maxevolvedarraysize}

\addtolength{\paraWidth}{-\maxVarWidth}
\addtolength{\paraWidth}{-\columnsep}
\addtolength{\paraWidth}{-\columnsep}
\addtolength{\paraWidth}{-\columnsep}

\addtolength{\descWidth}{-\columnsep}
\addtolength{\descWidth}{-\columnsep}
\addtolength{\descWidth}{-\columnsep}
\noindent \begin{tabular*}{\tableWidth}{|c|l@{\extracolsep{\fill}}r|}
\hline
\multicolumn{1}{|p{\maxVarWidth}}{a\_r0} & {\bf Scope:} private & REAL \\\hline
\multicolumn{3}{|p{\descWidth}|}{{\bf Description:}   {\em Constant part of Bondi Radius}} \\
\hline{\bf Range} & &  {\bf Default:} (none) \\\multicolumn{1}{|p{\maxVarWidth}|}{\centering -1:1} & \multicolumn{2}{p{\paraWidth}|}{amplitude of the perturbation} \\\hline
\end{tabular*}

\vspace{0.5cm}\noindent \begin{tabular*}{\tableWidth}{|c|l@{\extracolsep{\fill}}r|}
\hline
\multicolumn{1}{|p{\maxVarWidth}}{amplitude} & {\bf Scope:} private & REAL \\\hline
\multicolumn{3}{|p{\descWidth}|}{{\bf Description:}   {\em testbed amplitude}} \\
\hline{\bf Range} & &  {\bf Default:} (none) \\\multicolumn{1}{|p{\maxVarWidth}|}{\centering *:*} & \multicolumn{2}{p{\paraWidth}|}{no restrictions} \\\hline
\end{tabular*}

\vspace{0.5cm}\noindent \begin{tabular*}{\tableWidth}{|c|l@{\extracolsep{\fill}}r|}
\hline
\multicolumn{1}{|p{\maxVarWidth}}{analytic\_fields} & {\bf Scope:} private & BOOLEAN \\\hline
\multicolumn{3}{|p{\descWidth}|}{{\bf Description:}   {\em should the analytic values of the fields be computed?}} \\
\hline & & {\bf Default:} no \\\hline
\end{tabular*}

\vspace{0.5cm}\noindent \begin{tabular*}{\tableWidth}{|c|l@{\extracolsep{\fill}}r|}
\hline
\multicolumn{1}{|p{\maxVarWidth}}{beta0i} & {\bf Scope:} private & REAL \\\hline
\multicolumn{3}{|p{\descWidth}|}{{\bf Description:}   {\em Imaginary part of constant beta0 in linearized solution}} \\
\hline{\bf Range} & &  {\bf Default:} (none) \\\multicolumn{1}{|p{\maxVarWidth}|}{\centering *:*} & \multicolumn{2}{p{\paraWidth}|}{no restrictions} \\\hline
\end{tabular*}

\vspace{0.5cm}\noindent \begin{tabular*}{\tableWidth}{|c|l@{\extracolsep{\fill}}r|}
\hline
\multicolumn{1}{|p{\maxVarWidth}}{beta0r} & {\bf Scope:} private & REAL \\\hline
\multicolumn{3}{|p{\descWidth}|}{{\bf Description:}   {\em Real part of constant beta0 in linearized solution}} \\
\hline{\bf Range} & &  {\bf Default:} (none) \\\multicolumn{1}{|p{\maxVarWidth}|}{\centering *:*} & \multicolumn{2}{p{\paraWidth}|}{no restrictions} \\\hline
\end{tabular*}

\vspace{0.5cm}\noindent \begin{tabular*}{\tableWidth}{|c|l@{\extracolsep{\fill}}r|}
\hline
\multicolumn{1}{|p{\maxVarWidth}}{constant\_c1i} & {\bf Scope:} private & REAL \\\hline
\multicolumn{3}{|p{\descWidth}|}{{\bf Description:}   {\em Imaginary part of constant C1 in linearized solution}} \\
\hline{\bf Range} & &  {\bf Default:} (none) \\\multicolumn{1}{|p{\maxVarWidth}|}{\centering *:*} & \multicolumn{2}{p{\paraWidth}|}{no restrictions} \\\hline
\end{tabular*}

\vspace{0.5cm}\noindent \begin{tabular*}{\tableWidth}{|c|l@{\extracolsep{\fill}}r|}
\hline
\multicolumn{1}{|p{\maxVarWidth}}{constant\_c1r} & {\bf Scope:} private & REAL \\\hline
\multicolumn{3}{|p{\descWidth}|}{{\bf Description:}   {\em Real part of constant C1 in linearized solution}} \\
\hline{\bf Range} & &  {\bf Default:} (none) \\\multicolumn{1}{|p{\maxVarWidth}|}{\centering *:*} & \multicolumn{2}{p{\paraWidth}|}{no restrictions} \\\hline
\end{tabular*}

\vspace{0.5cm}\noindent \begin{tabular*}{\tableWidth}{|c|l@{\extracolsep{\fill}}r|}
\hline
\multicolumn{1}{|p{\maxVarWidth}}{constant\_c2i} & {\bf Scope:} private & REAL \\\hline
\multicolumn{3}{|p{\descWidth}|}{{\bf Description:}   {\em Imaginary part of constant C2 in linearized solution}} \\
\hline{\bf Range} & &  {\bf Default:} (none) \\\multicolumn{1}{|p{\maxVarWidth}|}{\centering *:*} & \multicolumn{2}{p{\paraWidth}|}{no restrictions} \\\hline
\end{tabular*}

\vspace{0.5cm}\noindent \begin{tabular*}{\tableWidth}{|c|l@{\extracolsep{\fill}}r|}
\hline
\multicolumn{1}{|p{\maxVarWidth}}{constant\_c2r} & {\bf Scope:} private & REAL \\\hline
\multicolumn{3}{|p{\descWidth}|}{{\bf Description:}   {\em Real part of constant C2 in linearized solution}} \\
\hline{\bf Range} & &  {\bf Default:} (none) \\\multicolumn{1}{|p{\maxVarWidth}|}{\centering *:*} & \multicolumn{2}{p{\paraWidth}|}{no restrictions} \\\hline
\end{tabular*}

\vspace{0.5cm}\noindent \begin{tabular*}{\tableWidth}{|c|l@{\extracolsep{\fill}}r|}
\hline
\multicolumn{1}{|p{\maxVarWidth}}{error\_mask\_type} & {\bf Scope:} private & KEYWORD \\\hline
\multicolumn{3}{|p{\descWidth}|}{{\bf Description:}   {\em type of mask for error in J}} \\
\hline{\bf Range} & &  {\bf Default:} none \\\multicolumn{1}{|p{\maxVarWidth}|}{\centering none} & \multicolumn{2}{p{\paraWidth}|}{no mask} \\\multicolumn{1}{|p{\maxVarWidth}|}{\centering EG\_mask} & \multicolumn{2}{p{\paraWidth}|}{mask all the active points} \\\multicolumn{1}{|p{\maxVarWidth}|}{\centering EQ\_mask} & \multicolumn{2}{p{\paraWidth}|}{mask only the equator points} \\\multicolumn{1}{|p{\maxVarWidth}|}{\centering EV\_mask} & \multicolumn{2}{p{\paraWidth}|}{mask only the evolution points} \\\multicolumn{1}{|p{\maxVarWidth}|}{\centering guard\_mask} & \multicolumn{2}{p{\paraWidth}|}{mask only the guard points} \\\hline
\end{tabular*}

\vspace{0.5cm}\noindent \begin{tabular*}{\tableWidth}{|c|l@{\extracolsep{\fill}}r|}
\hline
\multicolumn{1}{|p{\maxVarWidth}}{f\_r0} & {\bf Scope:} private & REAL \\\hline
\multicolumn{3}{|p{\descWidth}|}{{\bf Description:}   {\em Constant part of Bondi Radius}} \\
\hline{\bf Range} & &  {\bf Default:} 1 \\\multicolumn{1}{|p{\maxVarWidth}|}{\centering 0:*} & \multicolumn{2}{p{\paraWidth}|}{frequency of the perturbation} \\\hline
\end{tabular*}

\vspace{0.5cm}\noindent \begin{tabular*}{\tableWidth}{|c|l@{\extracolsep{\fill}}r|}
\hline
\multicolumn{1}{|p{\maxVarWidth}}{omm} & {\bf Scope:} private & REAL \\\hline
\multicolumn{3}{|p{\descWidth}|}{{\bf Description:}   {\em frequency}} \\
\hline{\bf Range} & &  {\bf Default:} (none) \\\multicolumn{1}{|p{\maxVarWidth}|}{\centering *:*} & \multicolumn{2}{p{\paraWidth}|}{no restrictions} \\\hline
\end{tabular*}

\vspace{0.5cm}\noindent \begin{tabular*}{\tableWidth}{|c|l@{\extracolsep{\fill}}r|}
\hline
\multicolumn{1}{|p{\maxVarWidth}}{testbed\_id} & {\bf Scope:} private & INT \\\hline
\multicolumn{3}{|p{\descWidth}|}{{\bf Description:}   {\em what testbed should we use?}} \\
\hline{\bf Range} & &  {\bf Default:} (none) \\\multicolumn{1}{|p{\maxVarWidth}|}{\centering } & \multicolumn{2}{p{\paraWidth}|}{minkowski, in the natural associated Bondi frame} \\\multicolumn{1}{|p{\maxVarWidth}|}{\centering 1} & \multicolumn{2}{p{\paraWidth}|}{noise around minkoswski} \\\multicolumn{1}{|p{\maxVarWidth}|}{\centering 2} & \multicolumn{2}{p{\paraWidth}|}{this is a linear l=2,3 testbed} \\\hline
\end{tabular*}

\vspace{0.5cm}\noindent \begin{tabular*}{\tableWidth}{|c|l@{\extracolsep{\fill}}r|}
\hline
\multicolumn{1}{|p{\maxVarWidth}}{verbose} & {\bf Scope:} private & BOOLEAN \\\hline
\multicolumn{3}{|p{\descWidth}|}{{\bf Description:}   {\em should this thorn be verbose?}} \\
\hline & & {\bf Default:} no \\\hline
\end{tabular*}

\vspace{0.5cm}\noindent \begin{tabular*}{\tableWidth}{|c|l@{\extracolsep{\fill}}r|}
\hline
\multicolumn{1}{|p{\maxVarWidth}}{l\_in\_ylm} & {\bf Scope:} restricted & INT \\\hline
\multicolumn{3}{|p{\descWidth}|}{{\bf Description:}   {\em l in Ylm}} \\
\hline{\bf Range} & &  {\bf Default:} 2 \\\multicolumn{1}{|p{\maxVarWidth}|}{\centering 0:*} & \multicolumn{2}{p{\paraWidth}|}{positive} \\\hline
\end{tabular*}

\vspace{0.5cm}\noindent \begin{tabular*}{\tableWidth}{|c|l@{\extracolsep{\fill}}r|}
\hline
\multicolumn{1}{|p{\maxVarWidth}}{m\_in\_ylm} & {\bf Scope:} restricted & INT \\\hline
\multicolumn{3}{|p{\descWidth}|}{{\bf Description:}   {\em m in Ylm}} \\
\hline{\bf Range} & &  {\bf Default:} (none) \\\multicolumn{1}{|p{\maxVarWidth}|}{\centering *:*} & \multicolumn{2}{p{\paraWidth}|}{must be between -l and +l} \\\hline
\end{tabular*}

\vspace{0.5cm}\noindent \begin{tabular*}{\tableWidth}{|c|l@{\extracolsep{\fill}}r|}
\hline
\multicolumn{1}{|p{\maxVarWidth}}{nullexact\_maxevolvedarraysize} & {\bf Scope:} restricted & INT \\\hline
\multicolumn{3}{|p{\descWidth}|}{{\bf Description:}   {\em The maximum size of evolved grid arrays used by Null2DWave}} \\
\hline{\bf Range} & &  {\bf Default:} 1 \\\multicolumn{1}{|p{\maxVarWidth}|}{\centering 1:*} & \multicolumn{2}{p{\paraWidth}|}{The size of the generator grid arrays} \\\hline
\end{tabular*}

\vspace{0.5cm}\noindent \begin{tabular*}{\tableWidth}{|c|l@{\extracolsep{\fill}}r|}
\hline
\multicolumn{1}{|p{\maxVarWidth}}{nullexact\_numarrayevolvedvars} & {\bf Scope:} restricted & INT \\\hline
\multicolumn{3}{|p{\descWidth}|}{{\bf Description:}   {\em The maximum number of evolved grid arrays used by NullExact}} \\
\hline{\bf Range} & &  {\bf Default:} 2 \\\multicolumn{1}{|p{\maxVarWidth}|}{\centering 2:2} & \multicolumn{2}{p{\paraWidth}|}{Is is only the News} \\\hline
\end{tabular*}

\vspace{0.5cm}\noindent \begin{tabular*}{\tableWidth}{|c|l@{\extracolsep{\fill}}r|}
\hline
\multicolumn{1}{|p{\maxVarWidth}}{linearized\_news} & {\bf Scope:} shared from NULLNEWS & BOOLEAN \\\hline
\end{tabular*}

\vspace{0.5cm}\parskip = 10pt 

\section{Interfaces} 


\parskip = 0pt

\vspace{3mm} \subsection*{General}

\noindent {\bf Implements}: 

nullexact
\vspace{2mm}

\noindent {\bf Inherits}: 

nullvars

nullgrid

nullnews

nullconstr

nullinterp

nullevolve
\vspace{2mm}
\subsection*{Grid Variables}
\vspace{5mm}\subsubsection{PRIVATE GROUPS}

\vspace{5mm}

\begin{tabular*}{150mm}{|c|c@{\extracolsep{\fill}}|rl|} \hline 
~ {\bf Group Names} ~ & ~ {\bf Variable Names} ~  &{\bf Details} ~ & ~\\ 
\hline 
realcharfuncs\_e &  & compact & 0 \\ 
 & wcn\_e & description & Error in Evolved Real-valued Characteristic Fields \\ 
 & bcn\_e & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & NullGrid::N\_radial\_pts \\ 
 &  & variable type & REAL \\ 
\hline 
realconstr\_e &  & compact & 0 \\ 
 & R01n\_e & description & Error in constraints \\ 
 & R01s\_e & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & NullGrid::N\_radial\_pts \\ 
 &  & variable type & REAL \\ 
\hline 
cmplxcharfuncs\_basic\_e\_split &  & compact & 0 \\ 
 & jcnr & description & Error in Evolved complex-valued Characteristic Fields (basic set \\ 
& ~ & description &  real and imag part) \\ 
 & jcni & dimensions & 2 \\ 
 & jcnr\_e & distribution & DEFAULT \\ 
 & jcni\_e & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & NullGrid::N\_radial\_pts \\ 
 &  & variable type & REAL \\ 
\hline 
cmplxcharfuncs\_basic\_e\_mask &  & compact & 0 \\ 
 & Mjcn\_e & description & Error in Evolved complex-valued Characteristic Fields (basic set) \\ 
 & Mucn\_e & dimensions & 2 \\ 
 & Meth2jcn\_e & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & NullGrid::N\_radial\_pts \\ 
 &  & variable type & COMPLEX \\ 
\hline 
cmplxcharfuncs\_basic\_e &  & compact & 0 \\ 
 & jcn\_e & description & Error in Evolved complex-valued Characteristic Fields (basic set) \\ 
 & ucn\_e & dimensions & 2 \\ 
 & qcn\_e & distribution & DEFAULT \\ 
 & eth2jcn\_e & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & NullGrid::N\_radial\_pts \\ 
 &  & variable type & COMPLEX \\ 
\hline 
cmplxcharfuncs\_aux\_e &  & compact & 0 \\ 
 & nucn\_e & description & Error in Evolved complex-valued Characteristic Fields (auxiliary set) \\ 
 & cbcn\_e & dimensions & 2 \\ 
 & ckcn\_e & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & NullGrid::N\_radial\_pts \\ 
 &  & variable type & COMPLEX \\ 
\hline 
\end{tabular*} 



\vspace{5mm}
\vspace{5mm}

\begin{tabular*}{150mm}{|c|c@{\extracolsep{\fill}}|rl|} \hline 
~ {\bf Group Names} ~ & ~ {\bf Variable Names} ~  &{\bf Details} ~ & ~ \\ 
\hline 
realcharfuncs\_e\_south &  & compact & 0 \\ 
 & wcs\_e & description & Error in Evolved Real-valued Characteristic Fields (south) \\ 
 & bcs\_e & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & NullGrid::N\_radial\_pts \\ 
 &  & variable type & REAL \\ 
\hline 
cmplxcharfuncs\_basic\_e\_south &  & compact & 0 \\ 
 & jcs\_e & description & Error in Evolved complex-valued Characteristic Fields (basic set \\ 
& ~ & description &  south) \\ 
 & ucs\_e & dimensions & 2 \\ 
 & qcs\_e & distribution & DEFAULT \\ 
 & eth2jcs\_e & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & NullGrid::N\_radial\_pts \\ 
 &  & variable type & COMPLEX \\ 
\hline 
cmplxcharfuncs\_aux\_e\_south &  & compact & 0 \\ 
 & nucs\_e & description & Error in Evolved complex-valued Characteristic Fields (auxiliary set \\ 
& ~ & description &  south) \\ 
 & cbcs\_e & dimensions & 2 \\ 
 & ckcs\_e & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & NullGrid::N\_radial\_pts \\ 
 &  & variable type & COMPLEX \\ 
\hline 
newsbr & NewsBr & compact & 0 \\ 
 &  & description & Real part of Bondi News \\ 
 &  & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & REAL \\ 
\hline 
newsbi & NewsBi & compact & 0 \\ 
 &  & description & Imaginary part of Bondi News \\ 
 &  & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & REAL \\ 
\hline 
hmu &  & compact & 0 \\ 
 & muh & description & real part of omega - 1 \\ 
 & EQmuh & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & REAL \\ 
\hline 
\end{tabular*} 



\vspace{5mm}
\vspace{5mm}

\begin{tabular*}{150mm}{|c|c@{\extracolsep{\fill}}|rl|} \hline 
~ {\bf Group Names} ~ & ~ {\bf Variable Names} ~  &{\bf Details} ~ & ~ \\ 
\hline 
hj\_l &  & compact & 0 \\ 
 & Jh\_l & description & derivative of J \\ 
& ~ & description &  over x \\ 
 & Jh\_l & description &  evolved values \\ 
 & EQJh\_l & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & COMPLEX \\ 
\hline 
mu\_err &  & compact & 0 \\ 
 & mu\_e & description & error in real part of omega - 1 \\ 
 & EGmu\_e & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & REAL \\ 
\hline 
j\_l\_err &  & compact & 0 \\ 
 & aJ\_l\_e & description & error in J\_l \\ 
 & EGaJ\_l\_e & dimensions & 2 \\ 
 & nJ\_l\_e & distribution & DEFAULT \\ 
 & EGnJ\_l\_e & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & COMPLEX \\ 
\hline 
newsr\_e & Newsr\_e & compact & 0 \\ 
 &  & description & error in real part of News \\ 
 &  & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & REAL \\ 
\hline 
newsi\_e & Newsi\_e & compact & 0 \\ 
 &  & description & error in imaginary part of News \\ 
 &  & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & REAL \\ 
\hline 
newsbr\_e & NewsBr\_e & compact & 0 \\ 
 &  & description & error in real part of Bondi News \\ 
 &  & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & REAL \\ 
\hline 
\end{tabular*} 



\vspace{5mm}
\vspace{5mm}

\begin{tabular*}{150mm}{|c|c@{\extracolsep{\fill}}|rl|} \hline 
~ {\bf Group Names} ~ & ~ {\bf Variable Names} ~  &{\bf Details} ~ & ~ \\ 
\hline 
newsbi\_e & NewsBi\_e & compact & 0 \\ 
 &  & description & error in imaginary part of Bondi News \\ 
 &  & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & REAL \\ 
\hline 
newsb\_e & NewsB\_e & compact & 0 \\ 
 &  & description & error in Bondi News \\ 
 &  & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & COMPLEX \\ 
\hline 
psi4r\_e & Psi4r\_e & compact & 0 \\ 
 &  & description & error in real part of Psi4 \\ 
 &  & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & REAL \\ 
\hline 
psi4i\_e & Psi4i\_e & compact & 0 \\ 
 &  & description & error in imaginary part of Psi4 \\ 
 &  & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & REAL \\ 
\hline 
psi4\_e & Psi4\_e & compact & 0 \\ 
 &  & description & error in Psi4 \\ 
 &  & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & COMPLEX \\ 
\hline 
ubondi\_e & uBondi\_e & compact & 0 \\ 
 &  & description & error in Bondi time associated with the Bondi News \\ 
 &  & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & REAL \\ 
\hline 
\end{tabular*} 



\vspace{5mm}
\vspace{5mm}

\begin{tabular*}{150mm}{|c|c@{\extracolsep{\fill}}|rl|} \hline 
~ {\bf Group Names} ~ & ~ {\bf Variable Names} ~  &{\bf Details} ~ & ~ \\ 
\hline 
ana\_j\_l & ana\_J\_l & compact & 0 \\ 
 &  & description & analytic J\_l \\ 
 &  & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & COMPLEX \\ 
\hline 
num\_j\_l & num\_J\_l & compact & 0 \\ 
 &  & description & derivative of J \\ 
& ~ & description &  over x \\ 
 &  & description &  numeric values \\ 
 &  & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & COMPLEX \\ 
\hline 
ana\_mu & ana\_mu & compact & 0 \\ 
 &  & description & analytic Omega \\ 
 &  & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & REAL \\ 
\hline 
ana\_news & ana\_News & compact & 0 \\ 
 &  & description & analytic complex-valued News (basic set) \\ 
 &  & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & COMPLEX \\ 
\hline 
ana\_psi4 & ana\_Psi4 & compact & 0 \\ 
 &  & description & analytic complex-valued Psi4 (basic set) \\ 
 &  & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & COMPLEX \\ 
\hline 
ana\_j &  & compact & 0 \\ 
 & ana\_jcn & description & Error in Evolved complex-valued Characteristic Fields J \\ 
 & ana\_jcs & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & NullGrid::N\_radial\_pts \\ 
 &  & variable type & COMPLEX \\ 
\hline 
\end{tabular*} 



\vspace{5mm}
\vspace{5mm}

\begin{tabular*}{150mm}{|c|c@{\extracolsep{\fill}}|rl|} \hline 
~ {\bf Group Names} ~ & ~ {\bf Variable Names} ~  &{\bf Details} ~ & ~ \\ 
\hline 
ana\_u &  & compact & 0 \\ 
 & ana\_ucn & description & Error in Evolved complex-valued Characteristic Fields U \\ 
 & ana\_ucs & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & NullGrid::N\_radial\_pts \\ 
 &  & variable type & COMPLEX \\ 
\hline 
ana\_q &  & compact & 0 \\ 
 & ana\_qcn & description & Error in Evolved complex-valued Characteristic Fields Q \\ 
 & ana\_qcs & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & NullGrid::N\_radial\_pts \\ 
 &  & variable type & COMPLEX \\ 
\hline 
dotnews\_mol & dotNews\_MoL & compact & 0 \\ 
 &  & description & real dotNews for MoL - this is the real part of Psi4 \\ 
 &  & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 2 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & REAL \\ 
\hline 
news\_mol & News\_MoL & compact & 0 \\ 
 &  & description & real News for MoL - this is the real part of integral Psi4 \\ 
 &  & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 2 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & REAL \\ 
\hline 
errnews\_mol & errNews\_MoL & compact & 0 \\ 
 &  & description & difference between News from MoL integration of Psi4 and evolved News \\ 
 &  & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & REAL \\ 
\hline 
ylm\_group &  & compact & 0 \\ 
 & Ylm\_2 & description & Ylm\_s by patch \\ 
 & Ylm\_1 & dimensions & 2 \\ 
 & Ylm\_0 & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & vararray\_size & 2 \\ 
 &  & variable type & COMPLEX \\ 
\hline 
\end{tabular*} 



\vspace{5mm}
\vspace{5mm}

\begin{tabular*}{150mm}{|c|c@{\extracolsep{\fill}}|rl|} \hline 
~ {\bf Group Names} ~ & ~ {\bf Variable Names} ~  &{\bf Details} ~ & ~ \\ 
\hline 
wtexact\_mask &  & compact & 0 \\ 
 & WTexact\_maskn & description & Worldtube mask \\ 
 & WTexact\_masks & dimensions & 2 \\ 
 &  & distribution & DEFAULT \\ 
 &  & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
& ~ & ghostsize & NULLGRID::N\_ANG\_GHOST\_PTS \\ 
 &  & group type & ARRAY \\ 
 &  & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
& ~ & size & (NULLGRID::N\_ANG\_PTS\_INSIDE\_EQ+2*(NULLGRID::N\_ANG\_EV\_OUTSIDE\_EQ+NULLGRID::N\_ANG\_STENCIL\_SIZE)) \\ 
 &  & timelevels & 1 \\ 
 &  & variable type & INT \\ 
\hline 
\end{tabular*} 



\vspace{5mm}\parskip = 10pt 

\section{Schedule} 


\parskip = 0pt


\noindent This section lists all the variables which are assigned storage by thorn PITTNullCode/NullExact.  Storage can either last for the duration of the run ({\bf Always} means that if this thorn is activated storage will be assigned, {\bf Conditional} means that if this thorn is activated storage will be assigned for the duration of the run if some condition is met), or can be turned on for the duration of a schedule function.


\subsection*{Storage}

\hspace{5mm}

 \begin{tabular*}{160mm}{ll} 

{\bf Always:}& {\bf Conditional:} \\ 
 News\_MoL[2] dotNews\_MoL[2] errNews\_MoL &  Ylm\_group WTexact\_mask\\ 
~ &  NullSHRExtract::x\_wt[2] NullSHRExtract::WT\_r0\\ 
~ &  NullSHRExtract::j\_wt[2] NullSHRExtract::beta\_wt[2] NullSHRExtract::w\_wt[2]\\ 
~ &  NullSHRExtract::q\_wt[2] NullSHRExtract::u\_wt[2] NullSHRExtract::u\_x\_wt\\ 
~ &  NullSHRExtract::j\_l NullSHRExtract::beta\_l NullSHRExtract::u\_l NullSHRExtract::w\_l\\ 
~ & ~\\ 
\end{tabular*} 


\subsection*{Scheduled Functions}
\vspace{5mm}

\noindent {\bf CCTK\_INITIAL}   (conditional) 

\hspace{5mm} nullexact\_precalcylm 

\hspace{5mm}{\it precalculate spherical harmonics } 


\hspace{5mm}

 \begin{tabular*}{160mm}{cll} 
~ & Before:  & nullevol\_boundaryinit \\ 
~& ~ &nullevol\_initial\\ 
~ & Language:  & fortran \\ 
~ & Type:  & function \\ 
\end{tabular*} 


\vspace{5mm}

\noindent {\bf CCTK\_ANALYSIS}   (conditional) 

\hspace{5mm} nullexact\_error\_cmplx 

\hspace{5mm}{\it error in characteristic evolution variables } 


\hspace{5mm}

 \begin{tabular*}{160mm}{cll} 
~ & Language:  & fortran \\ 
~ & Storage:  & cmplxcharfuncs\_basic\_e\_split \\ 
~& ~ &cmplxcharfuncs\_basic\_e\_mask\\ 
~& ~ &cmplxcharfuncs\_basic\_e\\ 
~& ~ &cmplxcharfuncs\_basic\_e\_south\\ 
~ & Triggers:  & cmplxcharfuncs\_basic\_e\_split \\ 
~& ~ &cmplxcharfuncs\_basic\_e\_mask\\ 
~& ~ &cmplxcharfuncs\_basic\_e\\ 
~& ~ &cmplxcharfuncs\_basic\_e\_south\\ 
~ & Type:  & function \\ 
\end{tabular*} 


\vspace{5mm}

\noindent {\bf NullEvol\_Initial}   (conditional) 

\hspace{5mm} nullexact\_initial 

\hspace{5mm}{\it exact initial data for j } 


\hspace{5mm}

 \begin{tabular*}{160mm}{cll} 
~ & After:  & nullevol\_initialdata \\ 
~ & Before:  & nullevol\_initialslice \\ 
~ & Language:  & fortran \\ 
~ & Type:  & function \\ 
\end{tabular*} 


\vspace{5mm}

\noindent {\bf NullEvol\_Initial} 

\hspace{5mm} nullexact\_initmol 

\hspace{5mm}{\it initial data } 


\hspace{5mm}

 \begin{tabular*}{160mm}{cll} 
~ & After:  & nullevol\_initialslice \\ 
~ & Language:  & fortran \\ 
~ & Options:  & global \\ 
~ & Type:  & function \\ 
\end{tabular*} 


\vspace{5mm}

\noindent {\bf MoL\_Register} 

\hspace{5mm} nullexact\_molregister 

\hspace{5mm}{\it register variables for mol } 


\hspace{5mm}

 \begin{tabular*}{160mm}{cll} 
~ & Language:  & c \\ 
~ & Type:  & function \\ 
\end{tabular*} 


\vspace{5mm}

\noindent {\bf MoL\_CalcRHS} 

\hspace{5mm} nullexact\_dotnewsmol 

\hspace{5mm}{\it calculate the integral of psi4 } 


\hspace{5mm}

 \begin{tabular*}{160mm}{cll} 
~ & Language:  & fortran \\ 
~ & Sync:  & dotnews\_mol \\ 
~ & Type:  & function \\ 
\end{tabular*} 


\vspace{5mm}

\noindent {\bf CCTK\_ANALYSIS}   (conditional) 

\hspace{5mm} nullexact\_error\_newsb 

\hspace{5mm}{\it error in characteristic evolution variables } 


\hspace{5mm}

 \begin{tabular*}{160mm}{cll} 
~ & Language:  & fortran \\ 
~ & Storage:  & newsb\_e \\ 
~& ~ &ubondi\_e\\ 
~& ~ &newsbi\_e\\ 
~& ~ &newsbr\_e\\ 
~& ~ &newsbr\\ 
~& ~ &newsbi\\ 
~& ~ &newsr\_e\\ 
~& ~ &newsi\_e\\ 
~& ~ &psi4r\_e\\ 
~& ~ &psi4i\_e\\ 
~& ~ &psi4\_e\\ 
~& ~ &mu\_err\\ 
~& ~ &hmu\\ 
~& ~ &j\_l\_err\\ 
~& ~ &hj\_l\\ 
~ & Triggers:  & newsb\_e \\ 
~& ~ &ubondi\_e\\ 
~& ~ &newsbi\_e\\ 
~& ~ &newsbr\_e\\ 
~& ~ &newsbr\\ 
~& ~ &newsbi\\ 
~& ~ &newsr\_e\\ 
~& ~ &newsi\_e\\ 
~& ~ &psi4r\_e\\ 
~& ~ &psi4i\_e\\ 
~& ~ &psi4\_e\\ 
~& ~ &mu\_err\\ 
~& ~ &hmu\\ 
~& ~ &j\_l\_err\\ 
~& ~ &hj\_l\\ 
~ & Type:  & function \\ 
\end{tabular*} 


\vspace{5mm}

\noindent {\bf CCTK\_ANALYSIS}   (conditional) 

\hspace{5mm} nullexact\_error\_real 

\hspace{5mm}{\it error in characteristic evolution variables } 


\hspace{5mm}

 \begin{tabular*}{160mm}{cll} 
~ & Language:  & fortran \\ 
~ & Storage:  & realcharfuncs\_e \\ 
~& ~ &realcharfuncs\_e\_south\\ 
~ & Triggers:  & realcharfuncs\_e \\ 
~& ~ &realcharfuncs\_e\_south\\ 
~ & Type:  & function \\ 
\end{tabular*} 


\vspace{5mm}

\noindent {\bf CCTK\_ANALYSIS}   (conditional) 

\hspace{5mm} nullexact\_error\_constr 

\hspace{5mm}{\it error in constraints } 


\hspace{5mm}

 \begin{tabular*}{160mm}{cll} 
~ & After:  & nullconstr\_driver \\ 
~ & Language:  & fortran \\ 
~ & Storage:  & realconstr\_e \\ 
~ & Triggers:  & realconstr\_e \\ 
~ & Type:  & function \\ 
\end{tabular*} 


\vspace{5mm}

\noindent {\bf CCTK\_ANALYSIS}   (conditional) 

\hspace{5mm} nullexact\_error\_cmplxaux 

\hspace{5mm}{\it error in characteristic evolution variables } 


\hspace{5mm}

 \begin{tabular*}{160mm}{cll} 
~ & Language:  & fortran \\ 
~ & Storage:  & cmplxcharfuncs\_aux\_e \\ 
~& ~ &cmplxcharfuncs\_aux\_e\_south\\ 
~ & Triggers:  & cmplxcharfuncs\_aux\_e \\ 
~& ~ &cmplxcharfuncs\_aux\_e\_south\\ 
~ & Type:  & function \\ 
\end{tabular*} 


\vspace{5mm}

\noindent {\bf CCTK\_ANALYSIS}   (conditional) 

\hspace{5mm} nullexact\_anafields 

\hspace{5mm}{\it error in characteristic evolution variables } 


\hspace{5mm}

 \begin{tabular*}{160mm}{cll} 
~ & Language:  & fortran \\ 
~ & Storage:  & ana\_news \\ 
~& ~ &ana\_mu\\ 
~& ~ &ana\_psi4\\ 
~& ~ &ana\_j\\ 
~& ~ &ana\_q\\ 
~& ~ &ana\_u\\ 
~& ~ &ana\_j\_l\\ 
~& ~ &num\_j\_l\\ 
~ & Triggers:  & ana\_news \\ 
~& ~ &ana\_mu\\ 
~& ~ &ana\_psi4\\ 
~& ~ &ana\_j\\ 
~& ~ &ana\_q\\ 
~& ~ &ana\_u\\ 
~& ~ &ana\_j\_l\\ 
~& ~ &num\_j\_l\\ 
~ & Type:  & function \\ 
\end{tabular*} 


\vspace{5mm}

\noindent {\bf NullEvol\_BoundaryInit}   (conditional) 

\hspace{5mm} nullexact\_boundary 

\hspace{5mm}{\it exact boundary data for the characteristic evolution variables } 


\hspace{5mm}

 \begin{tabular*}{160mm}{cll} 
~ & Language:  & fortran \\ 
~ & Type:  & function \\ 
\end{tabular*} 


\vspace{5mm}

\noindent {\bf NullEvol\_BoundaryInit}   (conditional) 

\hspace{5mm} nullexact\_boundarypast 

\hspace{5mm}{\it exact boundary data for the characteristic evolution variables, past level } 


\hspace{5mm}

 \begin{tabular*}{160mm}{cll} 
~ & Language:  & fortran \\ 
~ & Type:  & function \\ 
\end{tabular*} 


\vspace{5mm}

\noindent {\bf NullEvol\_Boundary}   (conditional) 

\hspace{5mm} nullexact\_boundary 

\hspace{5mm}{\it exact boundary data for the characteristic evolution variables } 


\hspace{5mm}

 \begin{tabular*}{160mm}{cll} 
~ & Language:  & fortran \\ 
~ & Type:  & function \\ 
\end{tabular*} 



\vspace{5mm}\parskip = 10pt 
\end{document}
