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<H2><A NAME="SECTION04411000000000000000">Process Grid</A></H2>
<A NAME="2242"> </A>
<A NAME="secgrid"> </A>
<P>
The <I>P</I><A NAME="2244"> </A> processes of an abstract
parallel computer are often represented
as a one-dimensional linear array of
processes labeled <IMG WIDTH=105 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline14493" SRC="img244.gif">.
For reasons described below, it is often
more convenient to map this one-dimensional
array of processes into a two-dimensional
rectangular grid, or <B>process grid</B>.
(A process grid is also referred to as a
process mesh.)<A NAME="2246"> </A>
This grid will have <IMG WIDTH=17 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline12172" SRC="img24.gif"> process rows
and <IMG WIDTH=17 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline12162" SRC="img23.gif"> process columns, where <IMG WIDTH=89 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline14499" SRC="img245.gif">. A process can now be
referenced by its row and column coordinates,
(<IMG WIDTH=39 HEIGHT=17 ALIGN=MIDDLE ALT="tex2html_wrap_inline14501" SRC="img246.gif">), within the grid, where <IMG WIDTH=88 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline14503" SRC="img247.gif">,
and <IMG WIDTH=87 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline14505" SRC="img248.gif">). An example of
such a mapping is shown in figure <A HREF="node70.html#fig8natgrid">4.1</A>,
where <IMG WIDTH=50 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline12422" SRC="img43.gif"> and <IMG WIDTH=49 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline14509" SRC="img249.gif">.
<P>
<P><A NAME="2278"> </A><A NAME="fig8natgrid"> </A><IMG WIDTH=242 HEIGHT=133 ALIGN=BOTTOM ALT="figure2256" SRC="img251.gif"><BR>
<STRONG>Figure 4.1:</STRONG> Eight processes mapped to a <IMG WIDTH=37 HEIGHT=22 ALIGN=MIDDLE ALT="tex2html_wrap_inline14511" SRC="img250.gif"> process grid<BR>
<P>
<P>
In figure <A HREF="node70.html#fig8natgrid">4.1</A>, the
processes are mapped to the process
grid by using <B>row-major order</B><A NAME="2283"> </A>;
in other words, the numbering of
the processes increases sequentially
across each row. Similarly, the
processes can be mapped in a
<B>column-major order</B><A NAME="2285"> </A>
whereby the numbering of the
processes proceeds down each
column of the process grid.
The BLACS routine BLACS_GRIDINIT<A NAME="2286"> </A>
performs this task of mapping
the processes to the process
grid. By default, BLACS_GRIDINIT
assumes a row-major ordering, although
a column-major ordering can also be
specified. The companion routine
BLACS_GRIDMAP is a more general
form of BLACS_GRIDINIT and allows
the user to define the mapping of
the processes<A NAME="2287"> </A>.
Refer to the Appendix <A HREF="node185.html#chapqrefblacs">D.3</A>
for further details.
<P>
All ScaLAPACK routines, with the
exception of the band linear system
routines, allow the processes to be
viewed as a one-dimensional or
two-dimensional process grid.
The band routines support only
one-dimensional process grids.
<P>
<BR> <HR>
<P><ADDRESS>
<I>Susan Blackford <BR>
Tue May 13 09:21:01 EDT 1997</I>
</ADDRESS>
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