[n,b,x,nelt,ia,ja,a,isym,matvec,msolve,itol,tol,itmax,iter,err,ierr,iunit,r,z,dz,rwork,iwork]=sir(n,b,x,nelt,ia,ja,a,isym,matvec,msolve,itol,tol,itmax,iter,err,ierr,iunit,r,z,dz,rwork,iwork);

function [n,b,x,nelt,ia,ja,a,isym,matvec,msolve,itol,tol,itmax,iter,err,ierr,iunit,r,z,dz,rwork,iwork]=sir(n,b,x,nelt,ia,ja,a,isym,matvec,msolve,itol,tol,itmax,iter,err,ierr,iunit,r,z,dz,rwork,iwork);
%***BEGIN PROLOGUE  SIR
%***PURPOSE  Preconditioned Iterative Refinement Sparse Ax = b Solver.
%            Routine to solve a general linear system  Ax = b  using
%            iterative refinement with a matrix splitting.
%***LIBRARY   SLATEC (SLAP)
%***CATEGORY  D2A4, D2B4
%***TYPE      SINGLE PRECISION (SIR-S, DIR-D)
%***KEYWORDS  ITERATIVE PRECONDITION, LINEAR SYSTEM, 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, ITOL, ITMAX
%     INTEGER  ITER, IERR, IUNIT, IWORK(USER DEFINED)
%     REAL     B(N), X(N), A(NELT), TOL, ERR, R(N), Z(N), DZ(N),
%     REAL     RWORK(USER DEFINED)
%     EXTERNAL MATVEC, MSOLVE
%
%     CALL SIR(N, B, X, NELT, IA, JA, A, ISYM, MATVEC, MSOLVE, ITOL,
%    $     TOL, ITMAX, ITER, ERR, IERR, IUNIT, R, Z, DZ, RWORK, IWORK)
%
% *Arguments:
% N      :IN       Integer.
%         Order of the Matrix.
% B      :IN       Real B(N).
%         Right-hand side vector.
% X      :INOUT    Real X(N).
%         On input X is your initial guess for solution vector.
%         On output X is the final approximate solution.
% NELT   :IN       Integer.
%         Number of Non-Zeros stored in A.
% IA     :IN       Integer IA(NELT).
% JA     :IN       Integer JA(NELT).
% A      :IN       Real A(NELT).
%         These arrays contain the matrix data structure for A.
%         It could take any form.  See 'Description', below,
%         for more details.
% 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.
% MATVEC :EXT      External.
%         Name of a routine which performs the matrix vector multiply
%         Y = A*X given A and X.  The name of the MATVEC routine must
%         be declared external in the calling program.  The calling
%         sequence to MATVEC is:
%             CALL MATVEC( N, X, Y, NELT, IA, JA, A, ISYM )
%         Where N is the number of unknowns, Y is the product A*X
%         upon return, X is an input vector, NELT is the number of
%         non-zeros in the SLAP IA, JA, A storage for the matrix A.
%         ISYM is a flag which, if non-zero, denotes that A is
%         symmetric and only the lower or upper triangle is stored.
% MSOLVE :EXT      External.
%         Name of a routine which solves a linear system MZ = R for
%         Z given R with the preconditioning matrix M (M is supplied via
%         RWORK and IWORK arrays).  The name of the MSOLVE routine must
%         be declared external in the calling program.  The calling
%         sequence to MSOLVE is:
%             CALL MSOLVE(N, R, Z, NELT, IA, JA, A, ISYM, RWORK, IWORK)
%         Where N is the number of unknowns, R is the right-hand side
%         vector and Z is the solution upon return.  NELT, IA, JA, A and
%         ISYM are defined as above.  RWORK is a real array that can
%         be used to pass necessary preconditioning information and/or
%         workspace to MSOLVE.  IWORK is an integer work array for
%         the same purpose as RWORK.
% ITOL   :IN       Integer.
%         Flag to indicate type of convergence criterion.
%         If ITOL=1, iteration stops when the 2-norm of the residual
%         divided by the 2-norm of the right-hand side is less than TOL.
%         If ITOL=2, iteration stops when the 2-norm of M-inv times the
%         residual divided by the 2-norm of M-inv times the right hand
%         side is less than TOL, where M-inv is the inverse of the
%         diagonal of A.
%         ITOL=11 is often useful for checking and comparing different
%         routines.  For this case, the user must supply the 'exact'
%         solution or a very accurate approximation (one with an error
%         much less than TOL) through a common block,
%             COMMON /SSLBLK/ SOLN( )
%         If ITOL=11, iteration stops when the 2-norm of the difference
%         between the iterative approximation and the user-supplied
%         solution divided by the 2-norm of the user-supplied solution
%         is less than TOL.  Note that this requires the user to set up
%         the 'COMMON /SSLBLK/ SOLN(LENGTH)' in the calling routine.
%         The routine with this declaration should be loaded before the
%         stop test so that the correct length is used by the loader.
%         This procedure is not standard Fortran and may not work
%         correctly on your system (although it has worked on every
%         system the authors have tried).  If ITOL is not 11 then this
%         common block is indeed standard Fortran.
% TOL    :INOUT    Real.
%         Convergence criterion, as described above.  (Reset if IERR=4.)
% ITMAX  :IN       Integer.
%         Maximum number of iterations.
% ITER   :OUT      Integer.
%         Number of iterations required to reach convergence, or
%         ITMAX+1 if convergence criterion could not be achieved in
%         ITMAX iterations.
% ERR    :OUT      Real.
%         Error estimate of error in final approximate solution, as
%         defined by ITOL.
% IERR   :OUT      Integer.
%         Return error flag.
%           IERR = 0 => All went well.
%           IERR = 1 => Insufficient space allocated for WORK or IWORK.
%           IERR = 2 => Method failed to converge in ITMAX steps.
%           IERR = 3 => Error in user input.
%                       Check input values of N, ITOL.
%           IERR = 4 => User error tolerance set too tight.
%                       Reset to 500*R1MACH(3).  Iteration proceeded.
%           IERR = 5 => Preconditioning matrix, M, is not positive
%                       definite.  (r,z) < 0.
%           IERR = 6 => Matrix A is not positive definite.  (p,Ap) < 0.
% IUNIT  :IN       Integer.
%         Unit number on which to write the error at each iteration,
%         if this is desired for monitoring convergence.  If unit
%         number is 0, no writing will occur.
% R      :WORK     Real R(N).
% Z      :WORK     Real Z(N).
% DZ     :WORK     Real DZ(N).
%         Real arrays used for workspace.
% RWORK  :WORK     Real RWORK(USER DEFINED).
%         Real array that can be used by  MSOLVE.
% IWORK  :WORK     Integer IWORK(USER DEFINED).
%         Integer array that can be used by  MSOLVE.
%
% *Description:
%       The basic algorithm for iterative refinement (also known as
%       iterative improvement) is:
%
%            n+1    n    -1       n
%           X    = X  + M  (B - AX  ).
%
%           -1   -1
%       If M =  A then this  is the  standard  iterative  refinement
%       algorithm and the 'subtraction' in the  residual calculation
%       should be done in doubleprecision (which it is  not in this
%       routine).
%       If M = DIAG(A), the diagonal of A, then iterative refinement
%       is  known  as  Jacobi's  method.   The  SLAP  routine  SSJAC
%       implements this iterative strategy.
%       If M = L, the lower triangle of A, then iterative refinement
%       is known as Gauss-Seidel.   The SLAP routine SSGS implements
%       this iterative strategy.
%
%       This routine does  not care  what matrix data   structure is
%       used for  A and M.  It simply   calls  the MATVEC and MSOLVE
%       routines, with  the arguments as  described above.  The user
%       could write any type of structure and the appropriate MATVEC
%       and MSOLVE routines.  It is assumed  that A is stored in the
%       IA, JA, A  arrays in some fashion and  that M (or INV(M)) is
%       stored  in  IWORK  and  RWORK)  in  some fashion.   The SLAP
%       routines SSJAC and SSGS are examples of this procedure.
%
%       Two  examples  of  matrix  data structures  are the: 1) SLAP
%       Triad  format and 2) SLAP Column format.
%
%       =================== S L A P Triad format ===================
%
%       In  this   format only the  non-zeros are  stored.  They may
%       appear  in *ANY* order.   The user  supplies three arrays of
%       length NELT, where  NELT  is the number  of non-zeros in the
%       matrix:  (IA(NELT), JA(NELT),  A(NELT)).  For each  non-zero
%       the  user puts   the row  and  column index   of that matrix
%       element in the IA and JA arrays.  The  value of the non-zero
%       matrix  element is  placed in  the corresponding location of
%       the A  array.  This is  an extremely easy data  structure to
%       generate.  On  the other hand it  is  not too  efficient  on
%       vector  computers   for the  iterative  solution  of  linear
%       systems.  Hence, SLAP  changes this input  data structure to
%       the SLAP   Column  format for the  iteration (but   does not
%       change it back).
%
%       Here is an example of the  SLAP Triad   storage format for a
%       5x5 Matrix.  Recall that the entries may appear in any order.
%
%
%           5x5 Matrix      SLAP Triad format for 5x5 matrix on left.
%                              1  2  3  4  5  6  7  8  9 10 11
%       |11 12  0  0 15|   A: 51 12 11 33 15 53 55 22 35 44 21
%       |21 22  0  0  0|  IA:  5  1  1  3  1  5  5  2  3  4  2
%       | 0  0 33  0 35|  JA:  1  2  1  3  5  3  5  2  5  4  1
%       | 0  0  0 44  0|
%       |51  0 53  0 55|
%
%       =================== S L A P 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|
%
% *Examples:
%       See the SLAP routines SSJAC, SSGS
%
% *Cautions:
%     This routine will attempt to write to the Fortran logical output
%     unit IUNIT, if IUNIT ~= 0.  Thus, the user must make sure that
%     this logical unit is attached to a file or terminal before calling
%     this routine with a non-zero value for IUNIT.  This routine does
%     not check for the validity of a non-zero IUNIT unit number.
%
%***SEE ALSO  SSJAC, SSGS
%***REFERENCES  1. Gene Golub and Charles Van Loan, Matrix Computations,
%                  Johns Hopkins University Press, Baltimore, Maryland,
%                  1983.
%               2. Mark K. Seager, A SLAP for the Masses, in
%                  G. F. Carey, Ed., Parallel Supercomputing: Methods,
%                  Algorithms and Applications, Wiley, 1989, pp.135-155.
%***ROUTINES CALLED  ISSIR, R1MACH
%***REVISION HISTORY  (YYMMDD)
%   871119  DATE WRITTEN
%   881213  Previous REVISION DATE
%   890915  Made changes requested at July 1989 CML Meeting.  (MKS)
%   890921  Removed TeX from comments.  (FNF)
%   890922  Numerous changes to prologue to make closer to SLATEC
%           standard.  (FNF)
%   890929  Numerous changes to reduce SP/DP differences.  (FNF)
%   891004  Added new reference.
%   910411  Prologue converted to Version 4.0 format.  (BAB)
%   910502  Removed MATVEC and MSOLVE from ROUTINES CALLED list.  (FNF)
%   920407  COMMON BLOCK renamed SSLBLK.  (WRB)
%   920511  Added complete declaration section.  (WRB)
%   920929  Corrected format of references.  (FNF)
%   921019  Changed 500.0 to 500 to reduce SP/DP differences.  (FNF)
%***end PROLOGUE  SIR
%     .. Scalar Arguments ..
%     .. Array Arguments ..
persistent bnrm i k solnrm tolmin ; 

rwork_shape=size(rwork);rwork=reshape(rwork,1,[]);
iwork_shape=size(iwork);iwork=reshape(iwork,1,[]);
%     .. subroutine Arguments ..
%     .. Local Scalars ..
if isempty(bnrm), bnrm=0; end;
if isempty(solnrm), solnrm=0; end;
if isempty(tolmin), tolmin=0; end;
if isempty(i), i=0; end;
if isempty(k), k=0; end;
%     .. External Functions ..
%***FIRST EXECUTABLE STATEMENT  SIR
%
%         Check some of the input data.
%
iter = 0;
ierr = 0;
if( n<1 )
ierr = 3;
rwork_shape=zeros(rwork_shape);rwork_shape(:)=rwork(1:numel(rwork_shape));rwork=rwork_shape;
iwork_shape=zeros(iwork_shape);iwork_shape(:)=iwork(1:numel(iwork_shape));iwork=iwork_shape;
return;
end;
tolmin = 500.*r1mach(3);
if( tol<tolmin )
tol = tolmin;
ierr = 4;
end;
%
%         Calculate initial residual and pseudo-residual, and check
%         stopping criterion.
[n,x,r,nelt,ia,ja,a,isym]=matvec(n,x,r,nelt,ia,ja,a,isym);
for i = 1 : n;
r(i) = b(i) - r(i);
end; i = fix(n+1);
[n,r,z,nelt,ia,ja,a,isym,rwork,iwork]=msolve(n,r,z,nelt,ia,ja,a,isym,rwork,iwork);
%
if( issir(n,b,x,nelt,ia,ja,a,isym,msolve,itol,tol,itmax,iter,err,ierr,iunit,r,z,dz,rwork,iwork,bnrm,solnrm)==0 )
if( ierr~=0 )
rwork_shape=zeros(rwork_shape);rwork_shape(:)=rwork(1:numel(rwork_shape));rwork=rwork_shape;
iwork_shape=zeros(iwork_shape);iwork_shape(:)=iwork(1:numel(iwork_shape));iwork=iwork_shape;
return;
end;
%
%         ***** iteration loop *****
%
for k = 1 : itmax;
iter = fix(k);
%
%         Calculate new iterate x, new residual r, and new
%         pseudo-residual z.
for i = 1 : n;
x(i) = x(i) + z(i);
end; i = fix(n+1);
[n,x,r,nelt,ia,ja,a,isym]=matvec(n,x,r,nelt,ia,ja,a,isym);
for i = 1 : n;
r(i) = b(i) - r(i);
end; i = fix(n+1);
[n,r,z,nelt,ia,ja,a,isym,rwork,iwork]=msolve(n,r,z,nelt,ia,ja,a,isym,rwork,iwork);
%
%         check stopping criterion.
if( issir(n,b,x,nelt,ia,ja,a,isym,msolve,itol,tol,itmax,iter,err,ierr,iunit,r,z,dz,rwork,iwork,bnrm,solnrm)~=0 )
rwork_shape=zeros(rwork_shape);rwork_shape(:)=rwork(1:numel(rwork_shape));rwork=rwork_shape;
iwork_shape=zeros(iwork_shape);iwork_shape(:)=iwork(1:numel(iwork_shape));iwork=iwork_shape;
return;
end;
%
end; k = fix(itmax+1);
%
%         *****   end of loop  *****
%         Stopping criterion not satisfied.
iter = fix(itmax + 1);
ierr = 2;
end;
%
%------------- LAST LINE OF SIR FOLLOWS -------------------------------
rwork_shape=zeros(rwork_shape);rwork_shape(:)=rwork(1:numel(rwork_shape));rwork=rwork_shape;
iwork_shape=zeros(iwork_shape);iwork_shape(:)=iwork(1:numel(iwork_shape));iwork=iwork_shape;
end
%DECK SLLTI2