\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
%  homepage at www.cactuscode.org)
\usepackage{../../../../doc/ThornGuide/cactus}

\begin{document}

\title{PUGHReduce}
\author{Gabrielle Allen, Thomas Radke}
\date{$ $Date$ $}
\maketitle

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\begin{abstract}
Reductions operations which are performed using the PUGH driver
\end{abstract}

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\section{Purpose}
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This thorn registers a number of reduction operators with the flesh. The
reductions are performed using internals of the PUGH driver, so that this
thorn can only be used when {\tt CactusPUGH/PUGH} is active.\\

The reduction operations this thorn registers are\\

\begin{tabular}{|l|l|l|}
\hline
Reduction Operator & Calculates & By \\
\hline
{\tt average$^*$, mean$^*$}   & the average/mean of a grid variable & $ \sum{ GV }/N $ \\
{\tt count}   & the number of grid points in a grid variable & $ N $ \\
{\tt maximum$^*$}   & the maximum of a grid variable & $ \max{ GV } $ \\
{\tt minimum$^*$}   & the minimum of a grid variable & $ \min{ GV } $ \\
{\tt norm1, L1Norm}         & the L1 norm of a grid variable & $ \left(\Sigma |GV| \right)/N $ \\
{\tt norm2, L2Norm}         & the L2 norm of a grid variable & $ \sqrt[2]{(\Sigma |GV|^2)/N} $ \\
{\tt norm3, L3Norm}         & the L3 norm of a grid variable & $ \sqrt[3]{(\Sigma |GV|^3)/N} $ \\
{\tt norm4, L4Norm}         & the L4 norm of a grid variable & $ \sqrt[4]{(\Sigma |GV|^4)/N} $ \\
{\tt norm\_inf, LinfNorm}     & the Infinitity norm of a grid variable & $ \max{| GV |} $ \\
{\tt sum$^*$}       & the sum of the elements of a grid variable & $ \sum{ GV } $ \\
\hline
\end{tabular}\\

Reduction operators with multiple names are just synonyms for the same kind of
reduction operation. In the formulas $GV$ is the grid variable to be reduced,
and $N$ denotes the number of its elements. Reduction operators marked with
$^*$ cannot be applied to grid variables of complex datatype.
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\section{Examples}
%
The following C example illustrates how the get the maximum value of a grid
function.
%
\begin{verbatim}
  int vindex;             /* grid variable index */
  CCTK_REAL result;       /* resulting reduction value */
  int target_proc;        /* processor to hold the result */
  int reduction_handle;   /* handle for reduction operator */
  char *reduction_name;   /* reduction operator to use */


  /* want to get the maximum for the wavetoy grid function */
  reduction_name = "maximum";
  vindex = CCTK_VarIndex ("wavetoy::phi");

  /* the reduction result will be obtained by processor 0 only */
  target_proc = 0;

  /* get the handle for the given reduction operator */
  reduction_handle = CCTK_ReductionHandle (reduction_name);
  if (reduction_handle >= 0)
  {
    /* now do the reduction using the flesh's generic reduction API
      (passing in one input, expecting one output value of REAL type) */
    if (CCTK_Reduce (cctkGH, target_proc, reduction_handle,
                     1, CCTK_VARIABLE_REAL, &result, 1, vindex) == 0)
    {
      if (CCTK_MyProc (cctkGH) == target_proc)
      {
        printf ("%s reduction value is %f\n", reduction_name, result);
      }
    }
    else
    {
      CCTK_VWarn (1, __LINE__, __FILE__, CCTK_THORNSTRING,
                  "%s reduction failed", reduction_name);
    }
  }
  else
  {
    CCTK_VWarn (1, __LINE__, __FILE__, CCTK_THORNSTRING,
                "Invalid reduction operator '%s'", reduction_name);
  }
\end{verbatim}

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\end{document}