# dsds.f

          SUBROUTINE DSDS (N, NELT, IA, JA, A, ISYM, DINV)
    C***BEGIN PROLOGUE  DSDS
    C***PURPOSE  Diagonal Scaling Preconditioner SLAP Set Up.
    C            Routine to compute the inverse of the diagonal of a matrix
    C            stored in the SLAP Column format.
    C***LIBRARY   SLATEC (SLAP)
    C***CATEGORY  D2E
    C***TYPE      DOUBLE PRECISION (SSDS-S, DSDS-D)
    C***KEYWORDS  DIAGONAL, SLAP SPARSE
    C***AUTHOR  Greenbaum, Anne, (Courant Institute)
    C           Seager, Mark K., (LLNL)
    C             Lawrence Livermore National Laboratory
    C             PO BOX 808, L-60
    C             Livermore, CA 94550 (510) 423-3141
    C             seager@llnl.gov
    C***DESCRIPTION
    C
    C *Usage:
    C     INTEGER N, NELT, IA(NELT), JA(NELT), ISYM
    C     DOUBLE PRECISION A(NELT), DINV(N)
    C
    C     CALL DSDS( N, NELT, IA, JA, A, ISYM, DINV )
    C
    C *Arguments:
    C N      :IN       Integer.
    C         Order of the Matrix.
    C NELT   :IN       Integer.
    C         Number of elements in arrays IA, JA, and A.
    C IA     :INOUT    Integer IA(NELT).
    C JA     :INOUT    Integer JA(NELT).
    C A      :INOUT    Double Precision A(NELT).
    C         These arrays should hold the matrix A in the SLAP Column
    C         format.  See "Description", below.
    C ISYM   :IN       Integer.
    C         Flag to indicate symmetric storage format.
    C         If ISYM=0, all non-zero entries of the matrix are stored.
    C         If ISYM=1, the matrix is symmetric, and only the upper
    C         or lower triangle of the matrix is stored.
    C DINV   :OUT      Double Precision DINV(N).
    C         Upon return this array holds 1./DIAG(A).
    C
    C *Description
    C       =================== S L A P Column format ==================
    C       This routine  requires that  the matrix A  be stored in  the
    C       SLAP Column format.  In this format the non-zeros are stored
    C       counting down columns (except for  the diagonal entry, which
    C       must appear first in each  "column")  and are stored  in the
    C       double precision array A.   In other words,  for each column
    C       in the matrix put the diagonal entry in  A.  Then put in the
    C       other non-zero  elements going down  the column (except  the
    C       diagonal) in order.   The  IA array holds the  row index for
    C       each non-zero.  The JA array holds the offsets  into the IA,
    C       A arrays  for  the  beginning  of each   column.   That  is,
    C       IA(JA(ICOL)),  A(JA(ICOL)) points   to the beginning  of the
    C       ICOL-th   column    in    IA and   A.      IA(JA(ICOL+1)-1),
    C       A(JA(ICOL+1)-1) points to  the  end of the   ICOL-th column.
    C       Note that we always have  JA(N+1) = NELT+1,  where N is  the
    C       number of columns in  the matrix and NELT  is the number  of
    C       non-zeros in the matrix.
    C
    C       Here is an example of the  SLAP Column  storage format for a
    C       5x5 Matrix (in the A and IA arrays '|'  denotes the end of a
    C       column):
    C
    C           5x5 Matrix      SLAP Column format for 5x5 matrix on left.
    C                              1  2  3    4  5    6  7    8    9 10 11
    C       |11 12  0  0 15|   A: 11 21 51 | 22 12 | 33 53 | 44 | 55 15 35
    C       |21 22  0  0  0|  IA:  1  2  5 |  2  1 |  3  5 |  4 |  5  1  3
    C       | 0  0 33  0 35|  JA:  1  4  6    8  9   12
    C       | 0  0  0 44  0|
    C       |51  0 53  0 55|
    C
    C       With the SLAP  format  all  of  the   "inner  loops" of this
    C       routine should vectorize  on  machines with hardware support
    C       for vector   gather/scatter  operations.  Your compiler  may
    C       require a compiler directive to  convince it that  there are
    C       no  implicit  vector  dependencies.  Compiler directives for
    C       the Alliant    FX/Fortran and CRI   CFT/CFT77 compilers  are
    C       supplied with the standard SLAP distribution.
    C
    C
    C *Cautions:
    C       This routine assumes that the diagonal of A is all  non-zero
    C       and that the operation DINV = 1.0/DIAG(A) will not underflow
    C       or overflow.    This  is done so that the  loop  vectorizes.
    C       Matrices  with zero or near zero or very  large entries will
    C       have numerical difficulties  and  must  be fixed before this
    C       routine is called.
    C***REFERENCES  (NONE)
    C***ROUTINES CALLED  (NONE)
    C***REVISION HISTORY  (YYMMDD)
    C   890404  DATE WRITTEN
    C   890404  Previous REVISION DATE
    C   890915  Made changes requested at July 1989 CML Meeting.  (MKS)
    C   890922  Numerous changes to prologue to make closer to SLATEC
    C           standard.  (FNF)
    C   890929  Numerous changes to reduce SP/DP differences.  (FNF)
    C   910411  Prologue converted to Version 4.0 format.  (BAB)
    C   920511  Added complete declaration section.  (WRB)
    C   930701  Updated CATEGORY section.  (FNF, WRB)
    C***END PROLOGUE  DSDS