NAME

       PZLASE2 - 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 PZLASE2( UPLO, M, N, ALPHA, BETA, A, IA, JA, DESCA )

           CHARACTER       UPLO

           INTEGER         IA, JA, M, N

           COMPLEX*16      ALPHA, BETA

           INTEGER         DESCA( * )

           COMPLEX*16      A( * )

PURPOSE

       PZLASE2 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.  PZLASE2 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) COMPLEX*16
               The constant to which the offdiagonal elements are to be set.

       BETA    (global input) COMPLEX*16
               The constant to which the diagonal elements are to be set.

       A       (local output) COMPLEX*16 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.