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)
- SUBROUTINE PSLAUUM(
- UPLO, N, A, IA, JA, DESCA )
CHARACTER UPLO INTEGER IA, JA, N INTEGER DESCA( * ) REAL A( * )
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 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
- UPLO (global input) CHARACTER*1
- Specifies whether the triangular factor stored in the distributed 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.