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NAME

       PSLAQSY  -  equilibrate  a  symmetric  distributed  matrix  sub(  A ) =
       A(IA:IA+N-1,JA:JA+N-1) using the scaling factors in the vectors SR  and
       SC

SYNOPSIS

       SUBROUTINE PSLAQSY( UPLO,  N,  A,  IA,  JA, DESCA, SR, SC, SCOND, AMAX,
                           EQUED )

           CHARACTER       EQUED, UPLO

           INTEGER         IA, JA, N

           REAL            AMAX, SCOND

           INTEGER         DESCA( * )

           REAL            A( * ), SC( * ), SR( * )

PURPOSE

       PSLAQSY  equilibrates  a  symmetric  distributed  matrix  sub(  A  )  =
       A(IA:IA+N-1,JA:JA+N-1)  using the scaling factors in the vectors SR and
       SC.

       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  whether  the  upper  or lower triangular part of the
               symmetric distributed matrix sub( A ) is to be referenced:
               = ’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 distributed submatrix sub( A ). N >= 0.

       A       (input/output) REAL pointer into the local
               memory to an array of local dimension (LLD_A,LOCc(JA+N-1)).  On
               entry, the local pieces of  the  distributed  symmetric  matrix
               sub(  A  ).  If UPLO = ’U’, the leading N-by-N upper triangular
               part of sub( A ) contains the  upper  triangular  part  of  the
               matrix,  and  the strictly lower triangular part of sub( A ) is
               not referenced.  If  UPLO  =  ’L’,  the  leading  N-by-N  lower
               triangular  part of sub( A ) contains the lower triangular part
               of the matrix, and the strictly upper trian- gular part of sub(
               A  )  is  not  referenced.   On  exit,  if  EQUED  =  ’Y’,  the
               equilibrated matrix:
               diag(SR(IA:IA+N-1)) * sub( A ) * diag(SC(JA:JA+N-1)).

       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.

       SR      (local input) REAL array, dimension LOCr(M_A)
               The scale factors for  A(IA:IA+M-1,JA:JA+N-1).  SR  is  aligned
               with  the  distributed  matrix  A,  and replicated across every
               process column. SR is tied to the distributed matrix A.

       SC      (local input) REAL array, dimension LOCc(N_A)
               The scale factors for sub( A ). SC is  aligned  with  the  dis-
               tributed  matrix  A, and replicated down every process row.  SC
               is tied to the distributed matrix A.

       SCOND   (global input) REAL
               Ratio of the smallest SR(i) (respectively SC(j)) to the largest
               SR(i)  (respectively SC(j)), with IA <= i <= IA+N-1 and JA <= j
               <= JA+N-1.

       AMAX    (global input) REAL
               Absolute value of the largest distributed submatrix entry.

       EQUED   (output) CHARACTER*1
               Specifies whether or not equilibration was done.   =  ’N’:   No
               equilibration.
               = ’Y’:  Equilibration was done, i.e., sub( A ) has been re-
               placed by:
               diag(SR(IA:IA+N-1)) * sub( A ) * diag(SC(JA:JA+N-1)).

PARAMETERS

       THRESH  is  a  threshold value used to decide if scaling should be done
       based on the ratio of the scaling factors.  If SCOND < THRESH,  scaling
       is done.

       LARGE  and  SMALL are threshold values used to decide if scaling should
       be done based on the absolute size of the largest matrix  element.   If
       AMAX > LARGE or AMAX < SMALL, scaling is done.