| [n,b,x,nelt,ia,ja,a,isym,nsave,itol,tol,itmax,iter,err,ierr,iunit,rwork,lenw,iwork,leniw]=dsdgmr(n,b,x,nelt,ia,ja,a,isym,nsave,itol,tol,itmax,iter,err,ierr,iunit,rwork,lenw,iwork,leniw); |
function [n,b,x,nelt,ia,ja,a,isym,nsave,itol,tol,itmax,iter,err,ierr,iunit,rwork,lenw,iwork,leniw]=dsdgmr(n,b,x,nelt,ia,ja,a,isym,nsave,itol,tol,itmax,iter,err,ierr,iunit,rwork,lenw,iwork,leniw);
%***BEGIN PROLOGUE DSDGMR
%***PURPOSE Diagonally scaled GMRES iterative sparse Ax=b solver.
% This routine uses the generalized minimum residual
% (GMRES) method with diagonal scaling to solve possibly
% non-symmetric linear systems of the form: Ax = b.
%***LIBRARY SLATEC (SLAP)
%***CATEGORY D2A4, D2B4
%***TYPE doubleprecision (SSDGMR-S, DSDGMR-D)
%***KEYWORDS GENERALIZED MINIMUM RESIDUAL, ITERATIVE PRECONDITION,
% NON-SYMMETRIC LINEAR SYSTEM, SLAP, SPARSE
%***AUTHOR Brown, Peter, (LLNL), pnbrown@llnl.gov
% Hindmarsh, Alan, (LLNL), alanh@llnl.gov
% Seager, Mark K., (LLNL), seager@llnl.gov
% Lawrence Livermore National Laboratory
% PO Box 808, L-60
% Livermore, CA 94550 (510) 423-3141
%***DESCRIPTION
%
% *Usage:
% INTEGER N, NELT, IA(NELT), JA(NELT), ISYM, NSAVE, ITOL
% INTEGER ITMAX, ITER, IERR, IUNIT, LENW, IWORK(LENIW), LENIW
% doubleprecision B(N), X(N), A(NELT), TOL, ERR, RWORK(LENW)
%
% CALL DSDGMR(N, B, X, NELT, IA, JA, A, ISYM, NSAVE,
% $ ITOL, TOL, ITMAX, ITER, ERR, IERR, IUNIT,
% $ RWORK, LENW, IWORK, LENIW)
%
% *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 should hold the matrix A in either the SLAP
% Triad format or the SLAP Column format. See 'Description',
% below. If the SLAP Triad format is chosen it is changed
% internally to the SLAP Column format.
% 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.
% NSAVE :IN Integer.
% Number of direction vectors to savemlv and orthogonalize against.
% Must be greater than 1.
% ITOL :IN Integer.
% Flag to indicate the type of convergence criterion used.
% ITOL=0 Means the iteration stops when the test described
% below on the residual RL is satisfied. This is
% the 'Natural Stopping Criteria' for this routine.
% Other values of ITOL cause extra, otherwise
% unnecessary, computation per iteration and are
% therefore much less efficient. See ISDGMR (the
% stop test routine) for more information.
% ITOL=1 Means the iteration stops when the first test
% described below on the residual RL is satisfied,
% and there is either right or no preconditioning
% being used.
% ITOL=2 Implies that the user is using left
% preconditioning, and the second stopping criterion
% below is used.
% ITOL=3 Means the iteration stops when the third test
% described below on Minv*Residual is satisfied, and
% there is either left or no preconditioning begin
% used.
% 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 below. If TOL is set
% to zero on input, then a default value of 500*(the smallest
% positive magnitude, machine epsilon) is used.
% ITMAX :IN Integer.
% Maximum number of iterations. This routine uses the default
% of NRMAX = ITMAX/NSAVE to determine when each restart
% should occur. See the description of NRMAX and MAXL in
% DGMRES for a full and frightfully interesting discussion of
% this topic.
% 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. Letting norm() denote the Euclidean
% norm, ERR is defined as follows...
% If ITOL=0, then ERR = norm(SB*(B-A*X(L)))/norm(SB*B),
% for right or no preconditioning, and
% ERR = norm(SB*(M-inverse)*(B-A*X(L)))/
% norm(SB*(M-inverse)*B),
% for left preconditioning.
% If ITOL=1, then ERR = norm(SB*(B-A*X(L)))/norm(SB*B),
% since right or no preconditioning
% being used.
% If ITOL=2, then ERR = norm(SB*(M-inverse)*(B-A*X(L)))/
% norm(SB*(M-inverse)*B),
% since left preconditioning is being
% used.
% If ITOL=3, then ERR = Max |(Minv*(B-A*X(L)),i)/x(i)|
% i=1,n
% If ITOL=11, then ERR = norm(SB*(X(L)-SOLN))/norm(SB*SOLN).
% IERR :OUT Integer.
% Return error flag.
% IERR = 0 => All went well.
% IERR = 1 => Insufficient storage allocated for
% RGWK or IGWK.
% IERR = 2 => Routine DPIGMR failed to reduce the norm
% of the current residual on its last call,
% and so the iteration has stalled. In
% this case, X equals the last computed
% approximation. The user must either
% increase MAXL, or choose a different
% initial guess.
% IERR =-1 => Insufficient length for RGWK array.
% IGWK(6) contains the required minimum
% length of the RGWK array.
% IERR =-2 => Inconsistent ITOL and JPRE values.
% For IERR <= 2, RGWK(1) = RHOL, which is the norm on the
% left-hand-side of the relevant stopping test defined
% below associated with the residual for the current
% approximation X(L).
% 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.
% RWORK :WORK doubleprecision RWORK(LENW).
% doubleprecision array of size LENW.
% LENW :IN Integer.
% Length of the doubleprecision workspace, RWORK.
% LENW >= 1 + N*(NSAVE+7) + NSAVE*(NSAVE+3).
% For the recommended values of NSAVE (10), RWORK has size at
% least 131 + 17*N.
% IWORK :INOUT Integer IWORK(USER DEFINED >= 30).
% Used to hold pointers into the RWORK array.
% Upon return the following locations of IWORK hold information
% which may be of use to the user:
% IWORK(9) Amount of Integer workspace actually used.
% IWORK(10) Amount of doubleprecision workspace actually used.
% LENIW :IN Integer.
% Length of the integer workspace IWORK. LENIW >= 30.
%
% *Description:
% DSDGMR solves a linear system A*X = B rewritten in the form:
%
% (SB*A*(M-inverse)*(SX-inverse))*(SX*M*X) = SB*B,
%
% with right preconditioning, or
%
% (SB*(M-inverse)*A*(SX-inverse))*(SX*X) = SB*(M-inverse)*B,
%
% with left preconditioning, where A is an n-by-n doubleprecision
% matrix, X and B are N-vectors, SB and SX are diagonal scaling
% matrices, and M is the diagonal of A. It uses
% preconditioned Krylov subpace methods based on the
% generalized minimum residual method (GMRES). This routine
% is a driver routine which assumes a SLAP matrix data
% structure and sets up the necessary information to do
% diagonal preconditioning and calls the main GMRES routine
% DGMRES for the solution of the linear system. DGMRES
% optionally performs either the full orthogonalization
% version of the GMRES algorithm or an incomplete variant of
% it. Both versions use restarting of the linear iteration by
% default, although the user can disable this feature.
%
% The GMRES algorithm generates a sequence of approximations
% X(L) to the truemlv solution of the above linear system. The
% convergence criteria for stopping the iteration is based on
% the size of the scaled norm of the residual R(L) = B -
% A*X(L). The actual stopping test is either:
%
% norm(SB*(B-A*X(L))) <= TOL*norm(SB*B),
%
% for right preconditioning, or
%
% norm(SB*(M-inverse)*(B-A*X(L))) <=
% TOL*norm(SB*(M-inverse)*B),
%
% for left preconditioning, where norm() denotes the Euclidean
% norm, and TOL is a positive scalar less than one input by
% the user. If TOL equals zero when DSDGMR is called, then a
% default value of 500*(the smallest positive magnitude,
% machine epsilon) is used. If the scaling arrays SB and SX
% are used, then ideally they should be chosen so that the
% vectors SX*X(or SX*M*X) and SB*B have all their components
% approximately equal to one in magnitude. If one wants to
% use the same scaling in X and B, then SB and SX can be the
% same array in the calling program.
%
% The following is a list of the other routines and their
% functions used by GMRES:
% DGMRES Contains the matrix structure independent driver
% routine for GMRES.
% DPIGMR Contains the main iteration loop for GMRES.
% DORTH Orthogonalizes a new vector against older basis vectors.
% DHEQR Computes a QR decomposition of a Hessenberg matrix.
% DHELS Solves a Hessenberg least-squares system, using QR
% factors.
% RLCALC Computes the scaled residual RL.
% XLCALC Computes the solution XL.
% ISDGMR User-replaceable stopping routine.
%
% The Sparse Linear Algebra Package (SLAP) utilizes two matrix
% data structures: 1) the SLAP Triad format or 2) the SLAP
% Column format. The user can hand this routine either of the
% of these data structures and SLAP will figure out which on
% is being used and act accordingly.
%
% =================== S L A P Triad format ===================
% This routine requires that the matrix A be stored in the
% SLAP 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 ==================
%
% 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|
%
% *Side Effects:
% The SLAP Triad format (IA, JA, A) is modified internally to be
% the SLAP Column format. See above.
%
% *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.
%
%***REFERENCES 1. Peter N. Brown and A. C. Hindmarsh, Reduced Storage
% Matrix Methods in Stiff ODE Systems, Lawrence Liver-
% more National Laboratory Report UCRL-95088, Rev. 1,
% Livermore, California, June 1987.
%***ROUTINES CALLED DCHKW, DGMRES, DS2Y, DSDI, DSDS, DSMV
%***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)
% 920407 COMMON BLOCK renamed DSLBLK. (WRB)
% 920511 Added complete declaration section. (WRB)
% 920929 Corrected format of references. (FNF)
%***end PROLOGUE DSDGMR
% The following is for optimized compilation on LLNL/LTSS Crays.
%LLL. OPTIMIZE
% .. Parameters ..
persistent locdin locib locigw lociw locrb locrgw locw myitol ;
if isempty(locrb), locrb=1; end;
if isempty(locib), locib=11 ; end;
% .. Scalar Arguments ..
% .. Array Arguments ..
% .. Local Scalars ..
if isempty(locdin), locdin=0; end;
if isempty(locigw), locigw=0; end;
if isempty(lociw), lociw=0; end;
if isempty(locrgw), locrgw=0; end;
if isempty(locw), locw=0; end;
if isempty(myitol), myitol=0; end;
% .. External Subroutines ..
%***FIRST EXECUTABLE STATEMENT DSDGMR
%
ierr = 0;
err = 0;
if( nsave<=1 )
ierr = 3;
return;
end;
%
% Change the SLAP input matrix IA, JA, A to SLAP-Column format.
[n,nelt,ia,ja,a,isym]=ds2y(n,nelt,ia,ja,a,isym);
%
% Set up the workspace. We assume MAXL=KMP=NSAVE.
locigw = fix(locib);
lociw = fix(locigw + 20);
%
locdin = fix(locrb);
locrgw = fix(locdin + n);
locw = fix(locrgw + 1 + n.*(nsave+6) + nsave.*(nsave+3));
%
iwork(4) = fix(locdin);
iwork(9) = fix(lociw);
iwork(10) = fix(locw);
%
% Check the workspace allocations.
[dumvar1,lociw,leniw,locw,lenw,ierr,iter,err]=dchkw('DSDGMR',lociw,leniw,locw,lenw,ierr,iter,err);
if( ierr~=0 )
return;
end;
%
% Compute the inverse of the diagonal of the matrix.
[n,nelt,ia,ja,a,isym,rwork(locdin:locdin+n-1)]=dsds(n,nelt,ia,ja,a,isym,rwork(locdin:locdin+n-1));
%
% Perform the Diagonally Scaled Generalized Minimum
% Residual iteration algorithm. The following DGMRES
% defaults are used MAXL = KMP = NSAVE, JSCAL = 0,
% JPRE = -1, NRMAX = ITMAX/NSAVE
iwork(locigw) = fix(nsave);
iwork(locigw+1) = fix(nsave);
iwork(locigw+2) = 0;
iwork(locigw+3) = -1;
iwork(locigw+4) = fix(fix(itmax./nsave));
myitol = 0;
%
rwork_orig=rwork; rwork_orig=rwork; [n,b,x,nelt,ia,ja,a,isym,dumvar9,dumvar10,myitol,tol,itmax,iter,err,ierr,iunit,rwork,dumvar19,dumvar20,dumvar21,dumvar22,dumvar23,dumvar24,iwork]=dgmres(n,b,x,nelt,ia,ja,a,isym,@dsmv,@dsdi,myitol,tol,itmax,iter,err,ierr,iunit,rwork,rwork,rwork(locrgw:locrgw+lenw-locrgw-1),lenw-locrgw,iwork(locigw:locigw+20-1),20,rwork,iwork); rwork(dumvar24~=rwork_orig)=dumvar24(dumvar24~=rwork_orig); rwork(dumvar19~=rwork_orig)=dumvar19(dumvar19~=rwork_orig); dumvar20i=find((rwork(locrgw:locrgw+lenw-locrgw-1))~=(dumvar20));dumvar22i=find((iwork(locigw:locigw+20-1))~=(dumvar22)); rwork(locrgw-1+dumvar20i)=dumvar20(dumvar20i); iwork(locigw-1+dumvar22i)=dumvar22(dumvar22i);
%
if( iter>itmax )
ierr = 2;
end;
%------------- LAST LINE OF DSDGMR FOLLOWS ----------------------------
end
%DECK DSDI
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