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 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) 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.