[n,b,x,nelt,ia,ja,a,isym,matvec,mttvec,msolve,mtsolv,itol,tol,itmax,iter,err,ierr,iunit,r,z,p,rr,zz,pp,dz,rwork,iwork]=dbcg(n,b,x,nelt,ia,ja,a,isym,matvec,mttvec,msolve,mtsolv,itol,tol,itmax,iter,err,ierr,iunit,r,z,p,rr,zz,pp,dz,rwork,iwork);

function [n,b,x,nelt,ia,ja,a,isym,matvec,mttvec,msolve,mtsolv,itol,tol,itmax,iter,err,ierr,iunit,r,z,p,rr,zz,pp,dz,rwork,iwork]=dbcg(n,b,x,nelt,ia,ja,a,isym,matvec,mttvec,msolve,mtsolv,itol,tol,itmax,iter,err,ierr,iunit,r,z,p,rr,zz,pp,dz,rwork,iwork);
%***BEGIN PROLOGUE  DBCG
%***PURPOSE  Preconditioned BiConjugate Gradient Sparse Ax = b Solver.
%            Routine to solve a Non-Symmetric linear system  Ax = b
%            using the Preconditioned BiConjugate Gradient method.
%***LIBRARY   SLATEC (SLAP)
%***CATEGORY  D2A4, D2B4
%***TYPE      doubleprecision (SBCG-S, DBCG-D)
%***KEYWORDS  BICONJUGATE GRADIENT, ITERATIVE PRECONDITION,
%             NON-SYMMETRIC 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)
%      doubleprecision B(N), X(N), A(NELT), TOL, ERR, R(N), Z(N), P(N)
%      doubleprecision RR(N), ZZ(N), PP(N), DZ(N)
%      doubleprecision RWORK(USER DEFINED)
%      EXTERNAL MATVEC, MTTVEC, MSOLVE, MTSOLV
%
%      CALL DBCG(N, B, X, NELT, IA, JA, A, ISYM, MATVEC, MTTVEC,
%     $     MSOLVE, MTSOLV, ITOL, TOL, ITMAX, ITER, ERR, IERR, IUNIT,
%     $     R, Z, P, RR, ZZ, PP, DZ, RWORK, IWORK)
%
% *Arguments:
% N      :IN       Integer
%         Order of the Matrix.
% B      :IN       doubleprecision B(N).
%         Right-hand side vector.
% X      :INOUT    doubleprecision 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       doubleprecision 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
%         operation  Y = A*X  given A and X.  The  name of  the MATVEC
%         routine must  be declared external  in the  calling program.
%         The calling sequence of 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, IA,  JA,  A and  ISYM
%         define the SLAP matrix data structure: see Description,below.
% MTTVEC :EXT      External.
%         Name of a routine which performs the matrix transpose vector
%         multiply y = A'*X given A and X (where ' denotes transpose).
%         The name of the MTTVEC routine must be declared external  in
%         the calling program.  The calling sequence to MTTVEC is  the
%         same as that for MTTVEC, viz.:
%             CALL MTTVEC( 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, IA, JA, A and ISYM
%         define the SLAP matrix data structure: see Description,below.
% 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 of 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 define the SLAP  matrix  data structure: see
%         Description, below.  RWORK is a  doubleprecision 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.
% MTSOLV :EXT      External.
%         Name of a routine which solves a linear system M'ZZ = RR for
%         ZZ given RR with the preconditioning matrix M (M is supplied
%         via RWORK and IWORK arrays).  The name of the MTSOLV routine
%         must be declared external in the calling program.  The call-
%         ing sequence to MTSOLV is:
%            CALL MTSOLV(N, RR, ZZ, NELT, IA, JA, A, ISYM, RWORK, IWORK)
%         Where N is the number of unknowns, RR is the right-hand side
%         vector, and ZZ is the solution upon return.  NELT, IA, JA, A
%         and  ISYM define the SLAP  matrix  data structure: see
%         Description, below.  RWORK is a  doubleprecision array that
%         can be used to pass necessary preconditioning information and/
%         or workspace to MTSOLV.  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 /DSLBLK/ 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 /DSLBLK/ 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    doubleprecision.
%         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      doubleprecision.
%         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*D1MACH(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     doubleprecision R(N).
% Z      :WORK     doubleprecision Z(N).
% P      :WORK     doubleprecision P(N).
% RR     :WORK     doubleprecision RR(N).
% ZZ     :WORK     doubleprecision ZZ(N).
% PP     :WORK     doubleprecision PP(N).
% DZ     :WORK     doubleprecision DZ(N).
%         doubleprecision arrays used for workspace.
% RWORK  :WORK     doubleprecision RWORK(USER DEFINED).
%         doubleprecision array that can be used for workspace in
%         MSOLVE and MTSOLV.
% IWORK  :WORK     Integer IWORK(USER DEFINED).
%         Integer array that can be used for workspace in MSOLVE
%         and MTSOLV.
%
% *Description
%      This routine does not care what matrix data structure is used
%       for A and M.  It simply calls MATVEC, MTTVEC, MSOLVE, MTSOLV
%       routines, with arguments as above.  The user could write any
%       type of structure, and  appropriate  MATVEC, MSOLVE, MTTVEC,
%       and MTSOLV 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 DSDBCG and DSLUBC 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  double pre-
%       cision array  A. In  other  words,  for each  column  in the
%       matrix  first 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)) are the first elements of the ICOL-
%       th column in IA and A, and IA(JA(ICOL+1)-1), A(JA(ICOL+1)-1)
%       are  the last elements 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|
%
% *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  DSDBCG, DSLUBC
%***REFERENCES  1. 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  D1MACH, DAXPY, DCOPY, DDOT, ISDBCG
%***REVISION HISTORY  (YYMMDD)
%   890404  DATE WRITTEN
%   890404  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, MTTVEC, MSOLVE, MTSOLV from ROUTINES
%           CALLED list.  (FNF)
%   920407  COMMON BLOCK renamed DSLBLK.  (WRB)
%   920511  Added complete declaration section.  (WRB)
%   920929  Corrected format of reference.  (FNF)
%   921019  Changed 500.0 to 500 to reduce SP/DP differences.  (FNF)
%   921113  Corrected C***CATEGORY line.  (FNF)
%***end PROLOGUE  DBCG
%     .. Scalar Arguments ..
%     .. Array Arguments ..
persistent ak akden bk bkden bknum bnrm fuzz 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(ak), ak=0; end;
if isempty(akden), akden=0; end;
if isempty(bk), bk=0; end;
if isempty(bkden), bkden=0; end;
if isempty(bknum), bknum=0; end;
if isempty(bnrm), bnrm=0; end;
if isempty(fuzz), fuzz=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 ..
%     .. External Subroutines ..
%     .. Intrinsic Functions ..
%***FIRST EXECUTABLE STATEMENT  DBCG
%
%         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;
[fuzz ]=d1mach(3);
tolmin = 500.*fuzz;
fuzz = fuzz.*fuzz;
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);
rr(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);
[n,rr,zz,nelt,ia,ja,a,isym,rwork,iwork]=mtsolv(n,rr,zz,nelt,ia,ja,a,isym,rwork,iwork);
%
if( isdbcg(n,b,x,nelt,ia,ja,a,isym,msolve,itol,tol,itmax,iter,err,ierr,iunit,r,z,p,rr,zz,pp,dz,rwork,iwork,ak,bk,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 coefficient BK and direction vectors P and PP.
[bknum ,n,z,dumvar4,rr]=ddot(n,z,1,rr,1);
if( abs(bknum)<=fuzz )
ierr = 6;
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;
if( iter==1 )
[n,z,dumvar3,p]=dcopy(n,z,1,p,1);
[n,zz,dumvar3,pp]=dcopy(n,zz,1,pp,1);
else;
bk = bknum./bkden;
for i = 1 : n;
p(i) = z(i) + bk.*p(i);
pp(i) = zz(i) + bk.*pp(i);
end; i = fix(n+1);
end;
bkden = bknum;
%
%         Calculate coefficient AK, new iterate X, new residuals R and
%         RR, and new pseudo-residuals Z and ZZ.
[n,p,z,nelt,ia,ja,a,isym]=matvec(n,p,z,nelt,ia,ja,a,isym);
[akden ,n,pp,dumvar4,z]=ddot(n,pp,1,z,1);
ak = bknum./akden;
if( abs(akden)<=fuzz )
ierr = 6;
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;
[n,ak,p,dumvar4,x]=daxpy(n,ak,p,1,x,1);
[n,dumvar2,z,dumvar4,r]=daxpy(n,-ak,z,1,r,1);
[n,pp,zz,nelt,ia,ja,a,isym]=mttvec(n,pp,zz,nelt,ia,ja,a,isym);
[n,dumvar2,zz,dumvar4,rr]=daxpy(n,-ak,zz,1,rr,1);
[n,r,z,nelt,ia,ja,a,isym,rwork,iwork]=msolve(n,r,z,nelt,ia,ja,a,isym,rwork,iwork);
[n,rr,zz,nelt,ia,ja,a,isym,rwork,iwork]=mtsolv(n,rr,zz,nelt,ia,ja,a,isym,rwork,iwork);
%
%         check stopping criterion.
if( isdbcg(n,b,x,nelt,ia,ja,a,isym,msolve,itol,tol,itmax,iter,err,ierr,iunit,r,z,p,rr,zz,pp,dz,rwork,iwork,ak,bk,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 DBCG 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 DBDIFF