NAME

       PSLASE2 - initialize an M-by-N distributed matrix sub( A ) denoting A(IA:IA+M-1,JA:JA+N-1)
       to BETA on the diagonal and ALPHA on the offdiagonals

SYNOPSIS

       SUBROUTINE PSLASE2( UPLO, M, N, ALPHA, BETA, A, IA, JA, DESCA )

           CHARACTER       UPLO

           INTEGER         IA, JA, M, N

           REAL            ALPHA, BETA

           INTEGER         DESCA( * )

           REAL            A( * )

PURPOSE

       PSLASE2 initializes an M-by-N distributed matrix sub( A ) denoting  A(IA:IA+M-1,JA:JA+N-1)
       to  BETA  on  the  diagonal  and  ALPHA  on  the offdiagonals.  PSLASE2 requires that only
       dimension of the matrix operand is distributed.

       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
               Specifies the part of the distributed matrix sub( A ) to be set:
               =  'U':       Upper  triangular part is set; the strictly lower triangular part of
               sub( A ) is not changed; = 'L':      Lower triangular part is  set;  the  strictly
               upper  triangular  part  of sub( A ) is not changed; Otherwise:  All of the matrix
               sub( A ) is set.

       M       (global input) INTEGER
               The number of rows to be operated on i.e the number of  rows  of  the  distributed
               submatrix sub( A ). M >= 0.

       N       (global input) INTEGER
               The  number  of  columns  to  be  operated  on  i.e  the  number of columns of the
               distributed submatrix sub( A ). N >= 0.

       ALPHA   (global input) REAL
               The constant to which the offdiagonal elements are to be set.

       BETA    (global input) REAL
               The constant to which the diagonal elements are to be set.

       A       (local output) REAL pointer into the local memory
               to an array of dimension (LLD_A,LOCc(JA+N-1)).   This  array  contains  the  local
               pieces  of the distributed matrix sub( A ) to be set.  On exit, the leading M-by-N
               submatrix sub( A ) is set as follows:

               if UPLO = 'U', A(IA+i-1,JA+j-1) =  ALPHA,  1<=i<=j-1,  1<=j<=N,  if  UPLO  =  'L',
               A(IA+i-1,JA+j-1)  =  ALPHA,  j+1<=i<=M, 1<=j<=N, otherwise,     A(IA+i-1,JA+j-1) =
               ALPHA, 1<=i<=M, 1<=j<=N, IA+i.NE.JA+j, and, for all UPLO, A(IA+i-1,JA+i-1) = BETA,
               1<=i<=min(M,N).

       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.