| [n,b,x,nelt,ia,ja,a,isym,matvec,msolve,itol,tol,itmax,iter,err,ierr,iunit,r,z,dz,rwork,iwork]=dir(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]=dir(n,b,x,nelt,ia,ja,a,isym,matvec,msolve,itol,tol,itmax,iter,err,ierr,iunit,r,z,dz,rwork,iwork);
%***BEGIN PROLOGUE DIR
%***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 doubleprecision (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 (510) 423-3141
% seager@llnl.gov
%***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), DZ(N)
% doubleprecision RWORK(USER DEFINED)
% EXTERNAL MATVEC, MSOLVE
%
% CALL DIR(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 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
% 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 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.
% 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).
% DZ :WORK doubleprecision DZ(N).
% doubleprecision arrays used for workspace.
% RWORK :WORK doubleprecision RWORK(USER DEFINED).
% doubleprecision 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 DSJAC
% implements this iterative strategy.
% If M = L, the lower triangle of A, then iterative refinement
% is known as Gauss-Seidel. The SLAP routine DSGS 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 DSJAC and DSGS 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|
%
% *Examples:
% See the SLAP routines DSJAC, DSGS
%
% *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 DSJAC, DSGS
%***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 D1MACH, ISDIR
%***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 and MSOLVE from ROUTINES CALLED list. (FNF)
% 920407 COMMON BLOCK renamed DSLBLK. (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 DIR
% .. 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 DIR
%
% Check some of the input data.
%
iter = 0;
ierr = 0;
if( n<1 )
ierr = 3;
rwork_shape=zeros(rwork_shape);rwork_shape(1:numel(rwork))=rwork;rwork=rwork_shape;
iwork_shape=zeros(iwork_shape);iwork_shape(1:numel(iwork))=iwork;iwork=iwork_shape;
return;
end;
tolmin = 500.*d1mach(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 = n+1;
[n,r,z,nelt,ia,ja,a,isym,rwork,iwork]=msolve(n,r,z,nelt,ia,ja,a,isym,rwork,iwork);
%
if( isdir(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(1:numel(rwork))=rwork;rwork=rwork_shape;
iwork_shape=zeros(iwork_shape);iwork_shape(1:numel(iwork))=iwork;iwork=iwork_shape;
return;
end;
%
% ***** iteration loop *****
%
for k = 1 : itmax;
iter = 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 = 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 = 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( isdir(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(1:numel(rwork))=rwork;rwork=rwork_shape;
iwork_shape=zeros(iwork_shape);iwork_shape(1:numel(iwork))=iwork;iwork=iwork_shape;
return;
end;
%
end; k = itmax+1;
%
% ***** end of loop *****
% Stopping criterion not satisfied.
iter = itmax + 1;
ierr = 2;
rwork_shape=zeros(rwork_shape);rwork_shape(1:numel(rwork))=rwork;rwork=rwork_shape;
iwork_shape=zeros(iwork_shape);iwork_shape(1:numel(iwork))=iwork;iwork=iwork_shape;
end;
%
%------------- LAST LINE OF DIR FOLLOWS -------------------------------
eml;
%*==djairy.f2 processed by SPAG 6.50Rc at 08:31 on 20 Jul 2006
%DECK DJAIRY
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