[n,nelt,ia,ja,a,isym,dinv]=ssd2s(n,nelt,ia,ja,a,isym,dinv);

function [n,nelt,ia,ja,a,isym,dinv]=ssd2s(n,nelt,ia,ja,a,isym,dinv);
%***BEGIN PROLOGUE  SSD2S
%***PURPOSE  Diagonal Scaling Preconditioner SLAP Normal Eqns Set Up.
%            Routine to compute the inverse of the diagonal of the
%            matrix A*A', where A is stored in SLAP-Column format.
%***LIBRARY   SLATEC (SLAP)
%***CATEGORY  D2E
%***TYPE      SINGLE PRECISION (SSD2S-S, DSD2S-D)
%***KEYWORDS  DIAGONAL, SLAP SPARSE
%***AUTHOR  Greenbaum, Anne, (Courant Institute)
%           Seager, Mark K., (LLNL)
%             Lawrence Livermore National Laboratory
%             PO BOX 808, L-60
%             Livermore, CA 94550 [phone]
%             [e-mail]
%***DESCRIPTION
%
% *Usage:
%     INTEGER N, NELT, IA(NELT), JA(NELT), ISYM
%     REAL    A(NELT), DINV(N)
%
%     CALL SSD2S( N, NELT, IA, JA, A, ISYM, DINV )
%
% *Arguments:
% N      :IN       Integer
%         Order of the Matrix.
% NELT   :IN       Integer.
%         Number of elements in arrays IA, JA, and A.
% IA     :IN       Integer IA(NELT).
% JA     :IN       Integer JA(NELT).
% A      :IN       Real A(NELT).
%         These arrays should hold the matrix A in the SLAP Column
%         format.  See 'Description', below.
% ISYM   :IN       Integer.
%         Flag to indicate symmetric storage format.
%         If ISYM=0, all non-zero entries of the matrix are stored.
%         If ISYM=1, the matrix is symmetric, and only the upper
%         or lower triangle of the matrix is stored.
% DINV   :OUT      Real DINV(N).
%         Upon return this array holds 1./DIAG(A*A').
%
% *Description
%       =================== S L A P Column format ==================
%       This routine  requires that  the matrix A  be stored in  the
%       SLAP Column format.  In this format the non-zeros are stored
%       counting down columns (except for  the diagonal entry, which
%       must appear first in each  'column')  and are stored  in the
%       real array A.  In other words, for each column in the matrix
%       put the diagonal entry in A.  Then put in the other non-zero
%       elements going down   the  column (except  the diagonal)  in
%       order.  The IA array holds the row  index for each non-zero.
%       The JA array holds the offsets into the IA, A arrays for the
%       beginning of   each    column.    That  is,    IA(JA(ICOL)),
%       A(JA(ICOL)) points to the beginning of the ICOL-th column in
%       IA and  A.  IA(JA(ICOL+1)-1),  A(JA(ICOL+1)-1) points to the
%       end  of   the ICOL-th  column.  Note   that  we  always have
%       JA(N+1) = NELT+1, where  N  is the number of columns in  the
%       matrix and  NELT   is the number of non-zeros in the matrix.
%
%       Here is an example of the  SLAP Column  storage format for a
%       5x5 Matrix (in the A and IA arrays '|'  denotes the end of a
%       column):
%
%           5x5 Matrix      SLAP Column format for 5x5 matrix on left.
%                              1  2  3    4  5    6  7    8    9 10 11
%       |11 12  0  0 15|   A: 11 21 51 | 22 12 | 33 53 | 44 | 55 15 35
%       |21 22  0  0  0|  IA:  1  2  5 |  2  1 |  3  5 |  4 |  5  1  3
%       | 0  0 33  0 35|  JA:  1  4  6    8  9   12
%       | 0  0  0 44  0|
%       |51  0 53  0 55|
%
%       With the SLAP  format  all  of  the   'inner  loops' of this
%       routine should vectorize  on  machines with hardware support
%       for vector   gather/scatter  operations.  Your compiler  may
%       require a compiler directive to  convince it that  there are
%       no  implicit  vector  dependencies.  Compiler directives for
%       the Alliant    FX/Fortran and CRI   CFT/CFT77 compilers  are
%       supplied with the standard SLAP distribution.
%
%
% *Cautions:
%       This routine assumes that the diagonal of A is all  non-zero
%       and that the operation DINV = 1.0/DIAG(A*A') will not under-
%       flow or overflow. This is done so that the loop  vectorizes.
%       Matrices  with zero or near zero or very  large entries will
%       have numerical difficulties  and  must  be fixed before this
%       routine is called.
%
%***SEE ALSO  SSDCGN
%***REFERENCES  (NONE)
%***ROUTINES CALLED  (NONE)
%***REVISION HISTORY  (YYMMDD)
%   871119  DATE WRITTEN
%   881213  Previous REVISION DATE
%   890915  Made changes requested at July 1989 CML Meeting.  (MKS)
%   890922  Numerous changes to prologue to make closer to SLATEC
%           standard.  (FNF)
%   890929  Numerous changes to reduce SP/DP differences.  (FNF)
%   910411  Prologue converted to Version 4.0 format.  (BAB)
%   920511  Added complete declaration section.  (WRB)
%   921113  Corrected C***CATEGORY line.  (FNF)
%   930701  Updated CATEGORY section.  (FNF, WRB)
%***end PROLOGUE  SSD2S
%     .. Scalar Arguments ..
%     .. Array Arguments ..
%     .. Local Scalars ..
persistent i k kbgn kend ; 

if isempty(i), i=0; end;
if isempty(k), k=0; end;
if isempty(kbgn), kbgn=0; end;
if isempty(kend), kend=0; end;
%***FIRST EXECUTABLE STATEMENT  SSD2S
for i = 1 : n;
dinv(i) = 0;
end; i = fix(n+1);
%
%         Loop over each column.
%VD$R NOCONCUR
for i = 1 : n;
kbgn = fix(ja(i));
kend = fix(ja(i+1) - 1);
%
%         Add in the contributions for each row that has a non-zero
%         in this column.
%LLL. OPTION ASSERT (NOHAZARD)
%DIR$ IVDEP
%VD$ NODEPCHK
for k = kbgn : kend;
dinv(ia(k)) = dinv(ia(k)) + a(k).^2;
end; k = fix(kend+1);
if( isym==1 )
%
%         Lower triangle stored by columns => upper triangle stored by
%         rows with Diagonal being the first entry.  Loop across the
%         rest of the row.
kbgn = fix(kbgn + 1);
if( kbgn<=kend )
for k = kbgn : kend;
dinv(i) = dinv(i) + a(k).^2;
end; k = fix(kend+1);
end;
end;
end; i = fix(n+1);
for i = 1 : n;
dinv(i) = 1.0e0./dinv(i);
end; i = fix(n+1);
%
%------------- LAST LINE OF SSD2S FOLLOWS ----------------------------
end
%DECK SSDBCG