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<H1><A NAME="SECTION03300000000000000000">List of Notation</A></H1>
<P>
<A NAME="274">&#160;</A><A NAME="275">&#160;</A>
<P>
<PRE><TT> 
1D 		 One-dimensional (as in 1D data distribution)
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<IMG WIDTH=28 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline12064" SRC="img2.gif"> 		 Bandwidth (or throughput) for the network
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2D 		 Two-dimensional (as in 2D data distribution)
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<IMG WIDTH=45 HEIGHT=31 ALIGN=MIDDLE ALT="tex2html_wrap_inline12066" SRC="img3.gif"> 		 Total number of floating-point operations<A NAME="282">&#160;</A>
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<IMG WIDTH=78 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline12070" SRC="img5.gif"> 		 Total number of messages<A NAME="283">&#160;</A>
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CSRC_ Entry in DESC_ indicating the process column over which
<P>
        		 the first column of the array is distributed<A NAME="284">&#160;</A>
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CTXT_ Entry in DESC_ indicating the BLACS context associated with the
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        		 global array<A NAME="285">&#160;</A><A NAME="286">&#160;</A>
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<IMG WIDTH=83 HEIGHT=32 ALIGN=MIDDLE ALT="tex2html_wrap_inline12074" SRC="img7.gif"> 		 Total number of data items communicated<A NAME="288">&#160;</A>
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DESC_ Array descriptor for a global array<A NAME="289">&#160;</A>
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<I>DESCA</I>  		 Array descriptor for global array <I>A</I>
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<I>DESCB</I>  		 Array descriptor for global array <I>B</I>
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DLEN_ Length of the descriptor DESC_<A NAME="290">&#160;</A>
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DTYPE_ First entry of the descriptor DESC_, identifying
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        		 the descriptor type<A NAME="291">&#160;</A><A NAME="292">&#160;</A>
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<I>E</I>()   		 Estimated parallel efficiency<A NAME="293">&#160;</A>
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<IMG WIDTH=39 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline12088" SRC="img9.gif"> 		 Time per floating point operation in matrix-matrix multiply<A NAME="7928">&#160;</A>
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Gflop/s 		 Gigaflops (<IMG WIDTH=22 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap_inline12092" SRC="img11.gif"> floating point operations) per second
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<I>IA</I>     		 Global row index in the global array <I>A</I> indicating the
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       		 first row of <IMG WIDTH=61 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline12098" SRC="img12.gif"><A NAME="296">&#160;</A>
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<I>ICTXT</I> 		 BLACS context associated with a process grid<A NAME="297">&#160;</A>
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INFO 		 Output integer argument of driver and computational routines
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     		 indicating the success or failure of the routine
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<I>JA</I>     		 Global column index in the global array <I>A</I> indicating the
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       		 first column of <IMG WIDTH=61 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline12098" SRC="img12.gif"><A NAME="298">&#160;</A>
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<IMG WIDTH=84 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline12108" SRC="img13.gif"> 		 Least common multiple of (<IMG WIDTH=43 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline12110" SRC="img14.gif">)<A NAME="7929">&#160;</A>
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LLD_ Entry in DESC_ indicating the local leading dimension of the
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      		 local array<A NAME="305">&#160;</A>
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<IMG WIDTH=58 HEIGHT=12 ALIGN=BOTTOM ALT="tex2html_wrap_inline12116" SRC="img17.gif"> 		 Local leading dimension of the local array <I>A</I>
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<IMG WIDTH=58 HEIGHT=12 ALIGN=BOTTOM ALT="tex2html_wrap_inline12120" SRC="img18.gif"> 		 Local leading dimension of the local array <I>B</I>
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<IMG WIDTH=44 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline12124" SRC="img19.gif">(K_) 		 Number of columns that a process receives if <IMG WIDTH=23 HEIGHT=12 ALIGN=BOTTOM ALT="tex2html_wrap_inline12126" SRC="img20.gif"> columns
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               		 of a matrix are distributed over <I>c</I> columns of its process row.<A NAME="7930">&#160;</A>
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<IMG WIDTH=44 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline12132" SRC="img21.gif">(K_) 		 Number of rows that a process would receive if <IMG WIDTH=23 HEIGHT=12 ALIGN=BOTTOM ALT="tex2html_wrap_inline12126" SRC="img20.gif"> rows
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               		 of a matrix are distributed over <I>r</I> rows of its process column.<A NAME="7931">&#160;</A>
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<I>M</I>     		 Global number of rows of the distributed submatrix <IMG WIDTH=61 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline12098" SRC="img12.gif">
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M_ Entry of DESC_ indicating the number of rows in the global
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      		 array<A NAME="310">&#160;</A>
<P>
<I>MB</I>    		 Global row block size for partitioning the global matrix
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MB_ Entry in DESC_ indicating the block size used to distribute
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      		 the rows of the global array<A NAME="311">&#160;</A>
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MB/s 		 Megabyte per second
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Mflop/s 		 Megaflops (<IMG WIDTH=22 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap_inline12146" SRC="img22.gif"> floating point operations) per second
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<I>MYCOL</I>  		 The calling process's column coordinate in the process grid.<A NAME="312">&#160;</A>
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<I>MYROW</I>  		 The calling process's row coordinate in the process grid<A NAME="313">&#160;</A>
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<I>N</I>     		 Global number of columns of the distributed submatrix <IMG WIDTH=61 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline12098" SRC="img12.gif">
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N_ Entry of DESC_ indicating the number of columns in the
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      		 global array<A NAME="314">&#160;</A>
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<I>NB</I>    		 Global column block size for partitioning the global matrix
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NB_ Entry in DESC_ indicating the block size used to distribute
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      		 the columns of the global array<A NAME="315">&#160;</A>
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<I>NBRHS</I> 		 Global column block size for the solution matrix<A NAME="316">&#160;</A>
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<I>NPCOL</I>  		 Number of process columns in the process grid (equivalent to <IMG WIDTH=17 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline12162" SRC="img23.gif">)<A NAME="7932">&#160;</A>
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<I>NPROCS</I> 		 Total number of processes in the process grid (equivalent to <I>P</I>)<A NAME="319">&#160;</A>
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<I>NPROW</I>  		 Number of process rows in the process grid (equivalent to <IMG WIDTH=17 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline12172" SRC="img24.gif">)<A NAME="7933">&#160;</A>
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<I>NRHS</I>  		 Global number of columns in the global solution matrix <I>B</I><A NAME="322">&#160;</A>
<P>
NUMROC 		 TOOLS routine used to calculate the number of rows or columns
<P>
       		 in a local array<A NAME="323">&#160;</A>
<P>
<I>P</I>     		 Total number of processes in the process grid, i.e., <IMG WIDTH=57 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline12182" SRC="img25.gif"><A NAME="326">&#160;</A>
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<IMG WIDTH=17 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline12162" SRC="img23.gif"> 		 Number of process columns in the process grid<A NAME="7934">&#160;</A>
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<IMG WIDTH=17 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline12172" SRC="img24.gif"> 		 Number of process rows in the process grid<A NAME="7935">&#160;</A>
<P>
RSRC_ Entry in DESC_ indicating the process row over which the
<P>
        		 first row of the array is distributed<A NAME="331">&#160;</A>
<P>
<IMG WIDTH=61 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline12098" SRC="img12.gif"> 		 Distributed submatrix <I>A</I>(<I>IA</I>:<I>IA</I>+<I>M</I>-1,<I>JA</I>:<I>JA</I>+<I>N</I>-1)
<P>
<I>T</I>()   		 Estimated parallel execution time<A NAME="332">&#160;</A>
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<IMG WIDTH=28 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline12198" SRC="img26.gif">() 		 Estimated serial execution time<A NAME="7936">&#160;</A>
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<IMG WIDTH=13 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline12202" SRC="img28.gif"> 		 Time per floating-point operation (typically <IMG WIDTH=35 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline12204" SRC="img29.gif">)<A NAME="336">&#160;</A>
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<IMG WIDTH=18 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline12208" SRC="img30.gif"> 		 Time per message (latency)<A NAME="337">&#160;</A>
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<IMG WIDTH=18 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline12212" SRC="img31.gif"> 		 Time required to solve a problem of size <I>N</I> on <I>P</I> processors<A NAME="338">&#160;</A>
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<IMG WIDTH=30 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline12220" SRC="img33.gif"> 		 Time required to solve a problem of size <I>N</I>/2 on <I>P</I> processors<A NAME="7937">&#160;</A>
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<IMG WIDTH=12 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline12228" SRC="img35.gif"> 		 Time per data item communicated<A NAME="341">&#160;</A>
<P>
</TT></PRE>
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<P><ADDRESS>
<I>Susan Blackford <BR>
Tue May 13 09:21:01 EDT 1997</I>
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