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366 lines
11 KiB
TeX
366 lines
11 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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\subroutine{psb\_halo}{Halo Data Communication}
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These subroutines restore a consistent status for 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}
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\begin{description}
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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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Specified as: a rank one or two array with the POINTER 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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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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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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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[\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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Returned as: a rank one or two array with the POINTER attribute
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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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An integer value that contains an error code.
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\end{description}
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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 restore a consistent status for the overlap
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elements:
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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, choice=choice,
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update\_type=update\_type, work=work}
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\begin{description}
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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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Specified as: a rank one or two array with the POINTER attribute
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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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Specified as: a structured data of type \descdata.
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\item[choice] specify if exchange overlap elements.
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\begin{description}
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\item[choice = .true.] exchange overlap elements, i.e. apply operator
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$P^{T}$;
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\item[choice = .false.] don't exchange overlap elements
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\end{description}
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Scope: {\bf global} \\
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Type: {\bf optional} \\
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Default: $choice = .true. $\\
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Specified as: a logical variable.
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\begin{description}
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\item[update\_type = 1] normal update $P_a$;
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\item[update\_type = 2] square root update $\sqrt{P_a}$;
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\end{description}
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Scope: {\bf global} \\
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Default: $update\_type = .true. $\\
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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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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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Specified as: a pointer to 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] 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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An integer value that contains an error code.
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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, no operations
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are performed;
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\item The operator $P^{T}$ performs the reduction sum of overlap
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elements; it is the inverse of a ``stretch'' operator $P$ 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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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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 $glob\_x_{iy:iy+m-1,jy:jy+n-1}$
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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,
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root, iglobx, jglobx, ilocx, jlocx, k}
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\syntax{call psb\_gather}{glob\_x, loc\_x, desc\_a, info,
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root, iglobx, ilocx}
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\begin{description}
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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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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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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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Specified as: an integer variable $0\le ix\le np$.
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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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Specified as: a rank one or two array.
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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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An integer value that contains an error code.
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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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\[ loc\_x_i \leftarrow scatter(glob\_x_i) \]
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where:
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\begin{description}
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\item[$glob\_x$] is the global submatrix $glob\_x_{iy:iy+m-1,jy:jy+n-1}$
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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,
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root, iglobx, jglobx, ilocx, jlocx, k}
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\syntax{call psb\_scatter}{glob\_x, loc\_x, desc\_a, info,
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root, iglobx, ilocx}
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\begin{description}
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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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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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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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Specified as: an integer variable $0\le ix\le np$.
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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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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] 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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An integer value that contains an error code.
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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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