PSLAUUM(l) ) PSLAUUM(l)NAME
PSLAUUM - compute the product U * U' or L' * L, where the triangular
factor U or L is stored in the upper or lower triangular part of the
distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1)
SYNOPSIS
SUBROUTINE PSLAUUM( UPLO, N, A, IA, JA, DESCA )
CHARACTER UPLO
INTEGER IA, JA, N
INTEGER DESCA( * )
REAL A( * )
PURPOSE
PSLAUUM computes the product U * U' or L' * L, where the triangular
factor U or L is stored in the upper or lower triangular part of the
distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1). If UPLO = 'U' or
'u' then the upper triangle of the result is stored, overwriting the
factor U in sub( A ).
If UPLO = 'L' or 'l' then the lower triangle of the result is stored,
overwriting the factor L in sub( A ).
This is the blocked form of the algorithm, calling Level 3 PBLAS.
Notes
=====
Each global data object is described by an associated description vec‐
tor. This vector stores the information required to establish the map‐
ping 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 col‐
umn.
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
ARGUMENTS
UPLO (global input) CHARACTER*1
Specifies whether the triangular factor stored in the distrib‐
uted matrix sub( A ) is upper or lower triangular:
= 'U': Upper triangular
= 'L': Lower triangular
N (global input) INTEGER
The number of rows and columns to be operated on, i.e. the
order of the triangular factor U or L. N >= 0.
A (local input/local output) REAL pointer into the
local memory to an array of dimension (LLD_A, LOCc(JA+N-1)).
On entry, the local pieces of the triangular factor L or U. On
exit, if UPLO = 'U', the upper triangle of the distributed
matrix sub( A ) is overwritten with the upper triangle of the
product U * U'; if UPLO = 'L', the lower triangle of sub( A )
is overwritten with the lower triangle of the product L' * L.
IA (global input) INTEGER
The row index in the global array A indicating the first row of
sub( A ).
JA (global input) INTEGER
The column index in the global array A indicating the first
column of sub( A ).
DESCA (global and local input) INTEGER array of dimension DLEN_.
The array descriptor for the distributed matrix A.
ScaLAPACK version 1.7 13 August 2001 PSLAUUM(l)
