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<H1><A NAME="SECTION05010000000000000000">Notes</A></H1>
<P>
<OL>
<LI> The specifications that follow give the calling sequence, purpose,
and descriptions of the arguments of each ScaLAPACK driver and
computational routine (but not of auxiliary routines).
<LI> Specifications of pairs of real and complex routines have been merged
(for example PSGETRF/PCGETRF).
<LI> Specifications are given only for <EM>single-precision</EM> routines.
To adapt them for the double precision version of the software, simply
interpret REAL as DOUBLE PRECISION, COMPLEX as COMPLEX*16 (or DOUBLE COMPLEX),
and the initial letters PS- and PC- of ScaLAPACK routine names as PD- and PZ-.
<LI> Specifications are arranged in alphabetical order of the real routine
name.
<LI> The text of the specifications has been derived from the leading comments
in the source-text of the routines. It makes only limited use of
mathematical typesetting facilities. To eliminate redundancy, <IMG WIDTH=25 HEIGHT=15 ALIGN=BOTTOM ALT="tex2html_wrap_inline12724" SRC="img64.gif">
has been used throughout the specifications. Thus, the reader should
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<LI> If there is a discrepancy between the specifications listed in
this section and the actual source code, the source code should be
regarded as the most up to date.
<P>
</OL>
<P>
Included in the leading comments of each subroutine (immediately preceding
the Argument section) is a brief note describing the <B>array
descriptor</B> and some commonly used expressions in calculating workspace.
For brevity, we have listed this information below and not included it
in the specifications of the routines.
<P>
<PRE>* Notes
* =====
*
* Each global data object is described by an associated description
* vector. This vector stores the information required to establish
* the mapping between an object element and its corresponding process
* and memory location.
*
* Let A be a generic term for any 2D block cyclicly distributed array.
* Such a global array has an associated description vector DESCA.
* In the following comments, the character _ should be read as
* "of the global array".
*
* NOTATION STORED IN EXPLANATION
* --------------- -------------- --------------------------------------
* DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
* DTYPE_A = 1.
* CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
* the BLACS process grid A is distribu-
* ted over. The context itself is glo-
* bal, but the handle (the integer
* value) may vary.
* M_A (global) DESCA( M_ ) The number of rows in the global
* array A.
* N_A (global) DESCA( N_ ) The number of columns in the global
* array A.
* MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
* the rows of the array.
* NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
* the columns of the array.
* RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
* row of the array A is distributed.
* CSRC_A (global) DESCA( CSRC_ ) The process column over which the
* first column of the array A is
* distributed.
* LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
* array. LLD_A >= MAX(1,LOCr(M_A)).
*
* Let K be the number of rows or columns of a distributed matrix,
* and assume that its process grid has dimension p x q.
* LOCr( K ) denotes the number of elements of K that a process
* would receive if K were distributed over the p processes of its
* process column.
* Similarly, LOCc( K ) denotes the number of elements of K that a
* process would receive if K were distributed over the q processes of
* its process row.
* The values of LOCr() and LOCc() may be determined via a call to the
* ScaLAPACK tool function, NUMROC:
* LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
* LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
* An upper bound for these quantities may be computed by:
* LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
* LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A</PRE>
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<P><ADDRESS>
<I>Susan Blackford <BR>
Tue May 13 09:21:01 EDT 1997</I>
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