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530 lines
18 KiB
TeX
530 lines
18 KiB
TeX
\section{Communication routines}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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% HALO DATA COMMUNICATION
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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The routines in this chapter implement various global communication operators
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on vectors associated with a discretization mesh. For auxiliary communication
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routines not tied to a discretization space see~\ref{sec:toolsrout}.
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\subroutine{psb\_halo}{Halo Data Communication}
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These subroutines gathers the values of the halo
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elements, and (optionally) scale the result:
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\[ x \leftarrow \alpha x \]
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where:
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\begin{description}
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\item[$x$] is a global dense submatrix.
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\end{description}
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\begin{table}[h]
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\begin{center}
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\begin{tabular}{ll}
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\hline
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$\alpha$, $x$ & {\bf Subroutine}\\
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\hline
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Long Precision Real & psb\_halo \\
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Long Precision Complex & psb\_halo \\
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\hline
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\end{tabular}
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\end{center}
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\caption{Data types\label{tab:f90halo}}
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\end{table}
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\syntax{call psb\_halo}{x, desc\_a, info}
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\syntax*{call psb\_halo}{x, desc\_a, info, alpha, work, data}
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\begin{description}
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\item[Type:] Synchronous.
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\item[\bf On Entry]
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\item[x] global dense matrix $x$.\\
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Scope: {\bf local} \\
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Type: {\bf required} \\
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Intent: {\bf inout}.\\
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Specified as: a rank one or two array with the TARGET attribute
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containing numbers of type specified in
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Table~\ref{tab:f90halo}.
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\item[desc\_a] contains data structures for communications.\\
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Scope: {\bf local} \\
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Type: {\bf required}\\
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Intent: {\bf in}.\\
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Specified as: a structured data of type \descdata.
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\item[alpha] the scalar $\alpha$.\\
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Scope: {\bf global} \\
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Type: {\bf optional} \\
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Intent: {\bf in}.\\
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Default: $alpha = 1 $\\
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Specified as: a number of the data type indicated in Table~\ref{tab:f90halo}.
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\item[work] the work array. \\
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Scope: {\bf local} \\
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Type: {\bf optional}\\
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Intent: {\bf inout}.\\
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Specified as: a rank one array of the same type of $x$ with the
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POINTER attribute.
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\item[data] index list selector.\\
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Scope: {\bf global} \\
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Type: {\bf optional} \\
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Specified as: an integer. Values:\verb|psb_comm_halo_|,
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\verb|psb_comm_ext_|, default: \verb|psb_comm_halo_|. Chooses the
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index list on which to base the data exchange.
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\item[\bf On Return]
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\item[x] global dense result matrix $x$.\\
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Scope: {\bf local} \\
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Type: {\bf required} \\
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Intent: {\bf inout}.\\
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Returned as: a rank one or two array
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containing numbers of type specified in
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Table~\ref{tab:f90halo}.
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\item[info] the local portion of result submatrix $y$.\\
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Scope: {\bf local} \\
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Type: {\bf required} \\
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Intent: {\bf out}.\\
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An integer value that contains an error code.
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\end{description}
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\begin{figure}[h] \begin{center}
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\rotatebox{-90}{\includegraphics[scale=0.45]{figures/try8x8}}
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\end{center}
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\caption{Sample discretization mesh.\label{fig:try8x8}}
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\end{figure}
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\section*{Example of use}
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Consider the discretization mesh depicted in fig.~\ref{fig:try8x8},
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partitioned among two processes as shown by the dashed line; the data
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distribution is such that each process will own 32 entries in the
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index space, with a halo made of 8 entries placed at local indices 33
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through 40. If process 0 assigns an initial value of 1 to its entries
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in the $x$ vector, and process 1 assigns a value of 2, then after a
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call to \verb|psb_halo| the contents of the local vectors will be the
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following:
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\begin{table}
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\begin{center}
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\small\begin{tabular}{rrr@{\hspace{6\tabcolsep}}rrr}
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\multicolumn{3}{c}{Process 0}&
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\multicolumn{3}{c}{Process 1}\\
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I & GLOB(I) & X(I) & I & GLOB(I) & X(I) \\
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1 & 1 & 1.0 & 1 & 33 & 2.0 \\
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2 & 2 & 1.0 & 2 & 34 & 2.0 \\
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3 & 3 & 1.0 & 3 & 35 & 2.0 \\
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4 & 4 & 1.0 & 4 & 36 & 2.0 \\
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5 & 5 & 1.0 & 5 & 37 & 2.0 \\
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6 & 6 & 1.0 & 6 & 38 & 2.0 \\
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7 & 7 & 1.0 & 7 & 39 & 2.0 \\
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8 & 8 & 1.0 & 8 & 40 & 2.0 \\
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9 & 9 & 1.0 & 9 & 41 & 2.0 \\
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10 & 10 & 1.0 & 10 & 42 & 2.0 \\
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11 & 11 & 1.0 & 11 & 43 & 2.0 \\
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12 & 12 & 1.0 & 12 & 44 & 2.0 \\
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13 & 13 & 1.0 & 13 & 45 & 2.0 \\
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14 & 14 & 1.0 & 14 & 46 & 2.0 \\
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15 & 15 & 1.0 & 15 & 47 & 2.0 \\
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16 & 16 & 1.0 & 16 & 48 & 2.0 \\
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17 & 17 & 1.0 & 17 & 49 & 2.0 \\
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18 & 18 & 1.0 & 18 & 50 & 2.0 \\
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19 & 19 & 1.0 & 19 & 51 & 2.0 \\
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20 & 20 & 1.0 & 20 & 52 & 2.0 \\
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21 & 21 & 1.0 & 21 & 53 & 2.0 \\
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22 & 22 & 1.0 & 22 & 54 & 2.0 \\
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23 & 23 & 1.0 & 23 & 55 & 2.0 \\
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24 & 24 & 1.0 & 24 & 56 & 2.0 \\
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25 & 25 & 1.0 & 25 & 57 & 2.0 \\
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26 & 26 & 1.0 & 26 & 58 & 2.0 \\
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27 & 27 & 1.0 & 27 & 59 & 2.0 \\
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28 & 28 & 1.0 & 28 & 60 & 2.0 \\
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29 & 29 & 1.0 & 29 & 61 & 2.0 \\
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30 & 30 & 1.0 & 30 & 62 & 2.0 \\
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31 & 31 & 1.0 & 31 & 63 & 2.0 \\
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32 & 32 & 1.0 & 32 & 64 & 2.0 \\
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33 & 33 & 2.0 & 33 & 25 & 1.0 \\
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34 & 34 & 2.0 & 34 & 26 & 1.0 \\
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35 & 35 & 2.0 & 35 & 27 & 1.0 \\
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36 & 36 & 2.0 & 36 & 28 & 1.0 \\
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37 & 37 & 2.0 & 37 & 29 & 1.0 \\
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38 & 38 & 2.0 & 38 & 30 & 1.0 \\
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39 & 39 & 2.0 & 39 & 31 & 1.0 \\
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40 & 40 & 2.0 & 40 & 32 & 1.0 \\
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\end{tabular}
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\end{center}
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\end{table}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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% OVERLAP UPDATE
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subroutine{psb\_ovrl}{Overlap Update}
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These subroutines applies an overlap operator to the input vector:
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\[ x \leftarrow Q x \]
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where:
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\begin{description}
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\item[$x$] is the global dense submatrix $x$
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\item[$Q$] is the overlap operator; it is the composition of two
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operators $ P_a$ and $ P^{T}$.
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\end{description}
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\begin{table}[h]
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\begin{center}
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\begin{tabular}{ll}
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\hline
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$x$ & {\bf Subroutine}\\
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\hline
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Long Precision Real & psb\_ovrl \\
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Long Precision Complex & psb\_ovrl \\
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\hline
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\end{tabular}
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\end{center}
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\caption{Data types\label{tab:f90ovrl}}
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\end{table}
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\syntax{call psb\_ovrl}{x, desc\_a, info}
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\syntax*{call psb\_ovrl}{x, desc\_a, info, update=update\_type, work=work}
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\begin{description}
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\item[Type:] Synchronous.
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\item[\bf On Entry]
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\item[x] global dense matrix $x$.\\
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Scope: {\bf local} \\
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Type: {\bf required} \\
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Intent: {\bf inout}.\\
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Specified as: a rank one or two array
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containing numbers of type specified in
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Table~\ref{tab:f90ovrl}.
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\item[desc\_a] contains data structures for communications.\\
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Scope: {\bf local} \\
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Type: {\bf required}\\
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Intent: {\bf in}.\\
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Specified as: a structured data of type \descdata.
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\item[update] Update operator. \\
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\begin{description}
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\item[update = psb\_none\_] Do nothing;
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\item[update = psb\_add\_] Sum overlap entries, i.e. apply $P^T$;
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\item[update = psb\_avg\_] Average overlap entries, i.e. apply $P_aP^T$;
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%% \item[update = psb\_square\_root\_] square root update $\sqrt{P_a}$;
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\end{description}
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Scope: {\bf global} \\
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Intent: {\bf in}.\\
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Default: $update\_type = psb\_avg\_ $\\
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Scope: {\bf global} \\
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Specified as: a integer variable.
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\item[work] the work array. \\
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Scope: {\bf local} \\
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Type: {\bf optional}\\
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Intent: {\bf inout}.\\
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Specified as: a one dimensional array of the same type of $x$.
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\item[\bf On Return]
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\item[x] global dense result matrix $x$.\\
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Scope: {\bf local} \\
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Type: {\bf required} \\
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Intent: {\bf inout}.\\
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Specified as: an array of rank one or two
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containing numbers of type specified in
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Table~\ref{tab:f90ovrl}.
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\item[info] Error code.\\
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Scope: {\bf local} \\
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Type: {\bf required} \\
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Intent: {\bf out}.\\
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An integer value; 0 means no error has been detected.
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\end{description}
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\section*{Usage notes}
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\begin{enumerate}
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\item If there is no overlap in the data distribution associated with
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the descriptor, no operations are performed;
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\item The operator $P^{T}$ performs the reduction sum of overlap
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elements; it is a ``prolongation'' operator $P^T$ that
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replicates overlap elements, accounting for the physical replication
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of data;
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\item The operator $P_a$ performs a scaling on the overlap elements by
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the amount of replication; thus, when combined with the reduction
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operator, it implements the average of replicated elements over all of
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their instances.
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%% \item The square root update option makes it possible to applythe
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%% following operator:
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%% \[ x\leftarrow \sqrt{P_a} P^{T} K^{-1} P \sqrt{P_a} x\]
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%% In the case of a symmetric $K$, this preserves simmetry of the overall
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%% preconditioner, which would otherwise be destroyed.
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\end{enumerate}
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\begin{figure}[h] \begin{center}
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\rotatebox{-90}{\includegraphics[scale=0.65]{figures/try8x8_ov}}
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\end{center}
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\caption{Sample discretization mesh.\label{fig:try8x8_ov}}
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\end{figure}
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\section*{Example of use}
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Consider the discretization mesh depicted in fig.~\ref{fig:try8x8_ov},
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partitioned among two processes as shown by the dashed lines, with an
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overlap of 1 extra layer with respect to the partition of
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fig.~\ref{fig:try8x8}; the data
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distribution is such that each process will own 40 entries in the
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index space, with an overlap of 16 entries placed at local indices 25
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through 40; the halo will run from local index 41 through local index 48.. If process 0 assigns an initial value of 1 to its entries
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in the $x$ vector, and process 1 assigns a value of 2, then after a
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call to \verb|psb_ovrl| with \verb|psb_avg_| and a call to
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\verb|psb_halo_| the contents of the local vectors will be the
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following (showing a transition among the two subdomains)
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\begin{table}
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\begin{center}
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\footnotesize
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\begin{tabular}{rrr@{\hspace{6\tabcolsep}}rrr}
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\multicolumn{3}{c}{Process 0}&
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\multicolumn{3}{c}{Process 1}\\
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I & GLOB(I) & X(I) & I & GLOB(I) & X(I) \\
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1 & 1 & 1.0 & 1 & 33 & 1.5 \\
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2 & 2 & 1.0 & 2 & 34 & 1.5 \\
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3 & 3 & 1.0 & 3 & 35 & 1.5 \\
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4 & 4 & 1.0 & 4 & 36 & 1.5 \\
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5 & 5 & 1.0 & 5 & 37 & 1.5 \\
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6 & 6 & 1.0 & 6 & 38 & 1.5 \\
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7 & 7 & 1.0 & 7 & 39 & 1.5 \\
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8 & 8 & 1.0 & 8 & 40 & 1.5 \\
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9 & 9 & 1.0 & 9 & 41 & 2.0 \\
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10 & 10 & 1.0 & 10 & 42 & 2.0 \\
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11 & 11 & 1.0 & 11 & 43 & 2.0 \\
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12 & 12 & 1.0 & 12 & 44 & 2.0 \\
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13 & 13 & 1.0 & 13 & 45 & 2.0 \\
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14 & 14 & 1.0 & 14 & 46 & 2.0 \\
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15 & 15 & 1.0 & 15 & 47 & 2.0 \\
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16 & 16 & 1.0 & 16 & 48 & 2.0 \\
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17 & 17 & 1.0 & 17 & 49 & 2.0 \\
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18 & 18 & 1.0 & 18 & 50 & 2.0 \\
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19 & 19 & 1.0 & 19 & 51 & 2.0 \\
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20 & 20 & 1.0 & 20 & 52 & 2.0 \\
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21 & 21 & 1.0 & 21 & 53 & 2.0 \\
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22 & 22 & 1.0 & 22 & 54 & 2.0 \\
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23 & 23 & 1.0 & 23 & 55 & 2.0 \\
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24 & 24 & 1.0 & 24 & 56 & 2.0 \\
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25 & 25 & 1.5 & 25 & 57 & 2.0 \\
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26 & 26 & 1.5 & 26 & 58 & 2.0 \\
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27 & 27 & 1.5 & 27 & 59 & 2.0 \\
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28 & 28 & 1.5 & 28 & 60 & 2.0 \\
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29 & 29 & 1.5 & 29 & 61 & 2.0 \\
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30 & 30 & 1.5 & 30 & 62 & 2.0 \\
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31 & 31 & 1.5 & 31 & 63 & 2.0 \\
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32 & 32 & 1.5 & 32 & 64 & 2.0 \\
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33 & 33 & 1.5 & 33 & 25 & 1.5 \\
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34 & 34 & 1.5 & 34 & 26 & 1.5 \\
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35 & 35 & 1.5 & 35 & 27 & 1.5 \\
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36 & 36 & 1.5 & 36 & 28 & 1.5 \\
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37 & 37 & 1.5 & 37 & 29 & 1.5 \\
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38 & 38 & 1.5 & 38 & 30 & 1.5 \\
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39 & 39 & 1.5 & 39 & 31 & 1.5 \\
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40 & 40 & 1.5 & 40 & 32 & 1.5 \\
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41 & 41 & 2.0 & 41 & 17 & 1.0 \\
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42 & 42 & 2.0 & 42 & 18 & 1.0 \\
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43 & 43 & 2.0 & 43 & 19 & 1.0 \\
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44 & 44 & 2.0 & 44 & 20 & 1.0 \\
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45 & 45 & 2.0 & 45 & 21 & 1.0 \\
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46 & 46 & 2.0 & 46 & 22 & 1.0 \\
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47 & 47 & 2.0 & 47 & 23 & 1.0 \\
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48 & 48 & 2.0 & 48 & 24 & 1.0 \\
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\end{tabular}
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\end{center}
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\end{table}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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% GATHER GLOBAL DENSE MATRIX
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subroutine{psb\_gather}{Gather Global Dense Matrix}
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These subroutines collect the portions of global dense matrix
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distributed over all process into one single array stored on one
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process.
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\[ glob\_x \leftarrow collect(loc\_x_i) \]
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where:
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\begin{description}
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\item[$glob\_x$] is the global submatrix $glob\_x_{1:m,1:n}$
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\item[$loc\_x_i$] is the local portion of global dense matrix on
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process $i$.
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\item[$collect$] is the collect function.
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\end{description}
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\begin{table}[h]
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\begin{center}
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\begin{tabular}{ll}
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\hline
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$x_i, y$ & {\bf Subroutine}\\
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\hline
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Long Precision Real & psb\_gather \\
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Long Precision Complex & psb\_gather \\
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\hline
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\end{tabular}
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\end{center}
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\caption{Data types\label{tab:gather}}
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\end{table}
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\syntax{call psb\_gather}{glob\_x, loc\_x, desc\_a, info, root}
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\syntax{call psb\_gather}{glob\_x, loc\_x, desc\_a, info, root}
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\begin{description}
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\item[Type:] Synchronous.
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\item[\bf On Entry]
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\item[loc\_x] the local portion of global dense matrix
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$glob\_x$. \\
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Scope: {\bf local} \\
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Type: {\bf required}\\
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Intent: {\bf in}.\\
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Specified as: a rank one or two array containing numbers of the type
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indicated in Table~\ref{tab:gather}.
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\item[desc\_a] contains data structures for communications.\\
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Scope: {\bf local} \\
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Type: {\bf required}\\
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Intent: {\bf in}.\\
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Specified as: a structured data of type \descdata.
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\item[root] The process that holds the global copy. If $root=-1$ all
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the processes will have a copy of the global vector.\\
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Scope: {\bf global} \\
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Type: {\bf optional}\\
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Intent: {\bf in}.\\
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Specified as: an integer variable $-1\le root\le np-1$, default $-1$.
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%% \item[iglobx] Row index to define a submatrix in glob\_x into which
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%% gather the local pieces.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% Specified as: an integer variable $1\le ix\le matrix\_data(psb\_m\_)$.
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%% \item[jglobx] Column index to define a submatrix in glob\_x into which
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%% gather the local pieces.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% Specified as: an integer variable.
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%% \item[ilocx] Row index to define a submatrix in loc\_x that has to
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%% be gathered into glob\_x.\\
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%% Scope: {\bf local} \\
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%% Type: {\bf optional}\\
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%% Specified as: an integer variable.
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%% \item[jlocx] Columns index to define a submatrix in loc\_x that has
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%% to be gathered into glob\_x.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% Specified as: an integer variable.
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%% \item[k] The number of columns to gather.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% Specified as: an integer variable.
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\item[\bf On Return]
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\item[glob\_x] The array where the local parts must be gathered.\\
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Scope: {\bf global} \\
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Type: {\bf required}\\
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Intent: {\bf out}.\\
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Specified as: a rank one or two array.
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\item[info] Error code.\\
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Scope: {\bf local} \\
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Type: {\bf required} \\
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Intent: {\bf out}.\\
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An integer value; 0 means no error has been detected.
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\end{description}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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% SCATTER GLOBAL DENSE MATRIX
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subroutine{psb\_scatter}{Scatter Global Dense Matrix}
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These subroutines scatters the portions of global dense matrix owned
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by a process to all the processes in the processes grid.
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\[ loc\_x_i \leftarrow scatter(glob\_x) \]
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where:
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\begin{description}
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\item[$glob\_x$] is the global matrix $glob\_x_{1:m,1:n}$
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\item[$loc\_x_i$] is the local portion of global dense matrix on
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process $i$.
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\item[$scatter$] is the scatter function.
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\end{description}
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\begin{table}[h]
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\begin{center}
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\begin{tabular}{ll}
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\hline
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$x_i, y$ & {\bf Subroutine}\\
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\hline
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Long Precision Real & psb\_scatter \\
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Long Precision Complex & psb\_scatter \\
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\hline
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\end{tabular}
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\end{center}
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\caption{Data types\label{tab:scatter}}
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\end{table}
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\syntax{call psb\_scatter}{glob\_x, loc\_x, desc\_a, info, root}
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\syntax{call psb\_scatter}{glob\_x, loc\_x, desc\_a, info, root}
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\begin{description}
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\item[Type:] Synchronous.
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\item[\bf On Entry]
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\item[glob\_x] The array that must be scattered into local pieces.\\
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Scope: {\bf global} \\
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Type: {\bf required}\\
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Intent: {\bf in}.\\
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Specified as: a rank one or two array.
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\item[desc\_a] contains data structures for communications.\\
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Scope: {\bf local} \\
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Type: {\bf required}\\
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Intent: {\bf in}.\\
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Specified as: a structured data of type \descdata.
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\item[root] The process that holds the global copy. If $root=-1$ all
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the processes have a copy of the global vector.\\
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Scope: {\bf global} \\
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Type: {\bf optional}\\
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Intent: {\bf in}.\\
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Specified as: an integer variable $-1\le root\le np-1$, default $-1$.
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%% \item[iglobx] Row index to define a submatrix in glob\_x that has to
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%% be scattered into local pieces.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% Specified as: an integer variable $1\le ix\le matrix\_data(psb\_m\_)$.
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%% \item[jglobx] Column index to define a submatrix in glob\_x that has to
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%% be scattered into local pieces.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% Specified as: an integer variable.
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%% \item[ilocx] Row index to define a submatrix in loc\_x into which
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%% scatter the local piece of glob\_x.\\
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%% Scope: {\bf local} \\
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%% Type: {\bf optional}\\
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%% Specified as: an integer variable.
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%% \item[jlocx] Columns index to define a submatrix in loc\_x into which
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%% scatter the local piece of glob\_x.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% Specified as: an integer variable.
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%% \item[k] The number of columns to scatter.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}\\
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%% Specified as: an integer variable.
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\item[\bf On Return]
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\item[loc\_x] the local portion of global dense matrix
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$glob\_x$. \\
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Scope: {\bf local} \\
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Type: {\bf required}\\
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Intent: {\bf out}.\\
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Specified as: a rank one or two array containing numbers of the type
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indicated in Table~\ref{tab:scatter}.
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\item[info] Error code.\\
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Scope: {\bf local} \\
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Type: {\bf required} \\
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Intent: {\bf out}.\\
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An integer value; 0 means no error has been detected.
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\end{description}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "userguide"
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%%% End:
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