DragonFly On-Line Manual Pages

PDLAUUM(l)                             )                            PDLAUUM(l)

NAME
       PDLAUUM - 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 PDLAUUM( UPLO, N, A, IA, JA, DESCA )
           CHARACTER UPLO
           INTEGER IA, JA, N
           INTEGER DESCA( * )
           DOUBLE PRECISION A( * )

PURPOSE
       PDLAUUM 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

ARGUMENTS
       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) DOUBLE PRECISION 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                      PDLAUUM(l)