NAME

       PSLAUU2 - 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 matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1)

SYNOPSIS

       SUBROUTINE PSLAUU2( UPLO, N, A, IA, JA, DESCA )

           CHARACTER       UPLO

           INTEGER         IA, JA, N

           INTEGER         DESCA( * )

           REAL            A( * )

PURPOSE

       PSLAUU2 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 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 unblocked form of the algorithm, calling Level 2 BLAS.  No communication is performed by this
       routine, the matrix to operate on should be strictly local to one process.

       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  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 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.