[n,nelt,ia,ja,a,isym,x,b,dinv,job,itol]=dsdscl(n,nelt,ia,ja,a,isym,x,b,dinv,job,itol);

function [n,nelt,ia,ja,a,isym,x,b,dinv,job,itol]=dsdscl(n,nelt,ia,ja,a,isym,x,b,dinv,job,itol);
%***BEGIN PROLOGUE  DSDSCL
%***PURPOSE  Diagonal Scaling of system Ax = b.
%            This routine scales (and unscales) the system  Ax = b
%            by symmetric diagonal scaling.
%***LIBRARY   SLATEC (SLAP)
%***CATEGORY  D2E
%***TYPE      doubleprecision (SSDSCL-S, DSDSCL-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
%
%    This routine scales (and unscales) the system Ax = b by symmetric
%    diagonal scaling.  The new system is:
%         -1/2  -1/2  1/2      -1/2
%        D    AD    (D   x) = D    b
%    when scaling is selected with the JOB parameter.  When unscaling
%    is selected this process is reversed.  The truemlv solution is also
%    scaled or unscaled if ITOL is set appropriately, see below.
%
% *Usage:
%     INTEGER N, NELT, IA(NELT), JA(NELT), ISYM, JOB, ITOL
%     doubleprecision A(NELT), X(N), B(N), DINV(N)
%
%     CALL DSDSCL( N, NELT, IA, JA, A, ISYM, X, B, DINV, JOB, ITOL )
%
% *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       doubleprecision 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.
% X      :INOUT    doubleprecision X(N).
%         Initial guess that will be later used in the iterative
%         solution.
%         of the scaled system.
% B      :INOUT    doubleprecision B(N).
%         Right hand side vector.
% DINV   :INOUT    doubleprecision DINV(N).
%         Upon return this array holds 1./DIAG(A).
%         This is an input if JOB = 0.
% JOB    :IN       Integer.
%         Flag indicating whether to scale or not.
%         JOB non-zero means do scaling.
%         JOB = 0 means do unscaling.
% ITOL   :IN       Integer.
%         Flag indicating what type of error estimation to do in the
%         iterative method.  When ITOL = 11 the exact solution from
%         common block DSLBLK will be used.  When the system is scaled
%         then the truemlv solution must also be scaled.  If ITOL is not
%         11 then this vector is not referenced.
%
% *Common Blocks:
% SOLN    :INOUT   doubleprecision SOLN(N).  COMMON BLOCK /DSLBLK/
%         The truemlv solution, SOLN, is scaled (or unscaled) if ITOL is
%         set to 11, see above.
%
% *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
%       doubleprecision 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)  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  DSDCG
%***REFERENCES  (NONE)
%***ROUTINES CALLED  (NONE)
%***COMMON BLOCKS    DSLBLK
%***REVISION HISTORY  (YYMMDD)
%   890404  DATE WRITTEN
%   890404  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)
%   910502  Added C***FIRST EXECUTABLE STATEMENT line.  (FNF)
%   920407  COMMON BLOCK renamed DSLBLK.  (WRB)
%   920511  Added complete declaration section.  (WRB)
%   921113  Corrected C***CATEGORY line.  (FNF)
%   930701  Updated CATEGORY section.  (FNF, WRB)
%***end PROLOGUE  DSDSCL
%     .. Scalar Arguments ..
%     .. Array Arguments ..
%     .. Arrays in Common ..
persistent di icol j jbgn jend ; 

global dslblk_1; if isempty(dslblk_1), dslblk_1=zeros(1,1); end;
%     .. Local Scalars ..
if isempty(di), di=0; end;
if isempty(icol), icol=0; end;
if isempty(j), j=0; end;
if isempty(jbgn), jbgn=0; end;
if isempty(jend), jend=0; end;
%     .. Intrinsic Functions ..
%     .. Common blocks ..
% common :: ;
%% common /dslblk/ soln;
%% common /dslblk/ dslblk_1;
%***FIRST EXECUTABLE STATEMENT  DSDSCL
%
%         SCALING...
%
if( job~=0 )
for icol = 1 : n;
dinv(icol) = 1.0d0./sqrt(a(ja(icol)));
end; icol = fix(n+1);
else;
%
%         UNSCALING...
%
for icol = 1 : n;
dinv(icol) = 1.0d0./dinv(icol);
end; icol = fix(n+1);
end;
%
for icol = 1 : n;
jbgn = fix(ja(icol));
jend = fix(ja(icol+1) - 1);
di = dinv(icol);
for j = jbgn : jend;
a(j) = dinv(ia(j)).*a(j).*di;
end; j = fix(jend+1);
end; icol = fix(n+1);
%
for icol = 1 : n;
b(icol) = b(icol).*dinv(icol);
x(icol) = x(icol)./dinv(icol);
end; icol = fix(n+1);
%
%         Check to see if we need to scale the 'truemlv solution' as well.
%
if( itol==11 )
for icol = 1 : n;
dslblk_1(icol) = dslblk_1(icol)./dinv(icol);
end; icol = fix(n+1);
end;
%
%------------- LAST LINE OF DSDSCL FOLLOWS ----------------------------
end
%DECK DSDS