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.