| [n,b,x,nelt,ia,ja,a,isym,nsave,itol,tol,itmax,iter,err,ierr,iunit,rwork,lenw,iwork,leniw]=dsdomn(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]=dsdomn(n,b,x,nelt,ia,ja,a,isym,nsave,itol,tol,itmax,iter,err,ierr,iunit,rwork,lenw,iwork,leniw);
%***BEGIN PROLOGUE DSDOMN
%***PURPOSE Diagonally Scaled Orthomin Sparse Iterative Ax=b Solver.
% Routine to solve a general linear system Ax = b using
% the Orthomin method with diagonal scaling.
%***LIBRARY SLATEC (SLAP)
%***CATEGORY D2A4, D2B4
%***TYPE doubleprecision (SSDOMN-S, DSDOMN-D)
%***KEYWORDS ITERATIVE PRECONDITION, NON-SYMMETRIC LINEAR SYSTEM SOLVE,
% 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, NSAVE, ITOL, ITMAX
% INTEGER ITER, IERR, IUNIT, LENW, IWORK(10), LENIW
% doubleprecision B(N), X(N), A(NELT), TOL, ERR
% doubleprecision RWORK(7*N+3*N*NSAVE+NSAVE)
%
% CALL DSDOMN(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.
% 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.
% 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 => Breakdown of method detected.
% (p,Ap) < epsilon**2.
% 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 used for workspace.
% LENW :IN Integer.
% Length of the doubleprecision workspace, RWORK.
% LENW >= 7*N+NSAVE*(3*N+1).
% IWORK :WORK Integer IWORK(LENIW).
% Used to hold pointers into the RWORK array.
% LENIW :IN Integer.
% Length of the integer workspace, IWORK. LENIW >= 10.
%
% *Description:
% This routine is simply a driver for the DOMN routine. It
% calls the DSDS routine to set up the preconditioning and
% then calls DOMN with the appropriate MATVEC and MSOLVE
% routines.
%
% 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 ===================
%
% 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|
%
% *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.
%
%***SEE ALSO DOMN, DSLUOM
%***REFERENCES (NONE)
%***ROUTINES CALLED DCHKW, DOMN, DS2Y, DSDI, DSDS, DSMV
%***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)
% 910411 Prologue converted to Version 4.0 format. (BAB)
% 920407 COMMON BLOCK renamed DSLBLK. (WRB)
% 920511 Added complete declaration section. (WRB)
% 921113 Corrected C***CATEGORY line. (FNF)
%***end PROLOGUE DSDOMN
% .. Parameters ..
persistent locap loccsa locdin locdz locema locib lociw locp locr locrb locw locz ;
if isempty(locrb), locrb=1; end;
if isempty(locib), locib=11 ; end;
% .. Scalar Arguments ..
% .. Array Arguments ..
% .. Local Scalars ..
if isempty(locap), locap=0; end;
if isempty(loccsa), loccsa=0; end;
if isempty(locdin), locdin=0; end;
if isempty(locdz), locdz=0; end;
if isempty(locema), locema=0; end;
if isempty(lociw), lociw=0; end;
if isempty(locp), locp=0; end;
if isempty(locr), locr=0; end;
if isempty(locw), locw=0; end;
if isempty(locz), locz=0; end;
% .. External Subroutines ..
%***FIRST EXECUTABLE STATEMENT DSDOMN
%
ierr = 0;
if( n<1 || nelt<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.
lociw = fix(locib);
%
locdin = fix(locrb);
locr = fix(locdin + n);
locz = fix(locr + n);
locp = fix(locz + n);
locap = fix(locp + n.*(nsave+1));
locema = fix(locap + n.*(nsave+1));
locdz = fix(locema + n.*(nsave+1));
loccsa = fix(locdz + n);
locw = fix(loccsa + nsave);
%
% Check the workspace allocations.
[dumvar1,lociw,leniw,locw,lenw,ierr,iter,err]=dchkw('DSDOMN',lociw,leniw,locw,lenw,ierr,iter,err);
if( ierr~=0 )
return;
end;
%
iwork(4) = fix(locdin);
iwork(9) = fix(lociw);
iwork(10) = fix(locw);
%
% 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 Orthomin iteration algorithm.
[n,b,x,nelt,ia,ja,a,isym,dumvar9,dumvar10,nsave,itol,tol,itmax,iter,err,ierr,iunit,dumvar19,dumvar20,dumvar21,dumvar22,dumvar23,dumvar24,dumvar25,rwork,iwork]=domn(n,b,x,nelt,ia,ja,a,isym,@dsmv,@dsdi,nsave,itol,tol,itmax,iter,err,ierr,iunit,rwork(locr:locr+n-1),rwork(locz:locz+n-1),rwork(locp:end),rwork(locap:end),rwork(locema:end),rwork(locdz:locdz+n-1),rwork(loccsa:loccsa+nsave-1),rwork,iwork); dumvar19i=find((rwork(locr:locr+n-1))~=(dumvar19));dumvar20i=find((rwork(locz:locz+n-1))~=(dumvar20));dumvar21i=find((rwork(locp:end))~=(dumvar21));dumvar22i=find((rwork(locap:end))~=(dumvar22));dumvar23i=find((rwork(locema:end))~=(dumvar23));dumvar24i=find((rwork(locdz:locdz+n-1))~=(dumvar24));dumvar25i=find((rwork(loccsa:loccsa+nsave-1))~=(dumvar25)); rwork(locr-1+dumvar19i)=dumvar19(dumvar19i); rwork(locz-1+dumvar20i)=dumvar20(dumvar20i); rwork(locp-1+dumvar21i)=dumvar21(dumvar21i); rwork(locap-1+dumvar22i)=dumvar22(dumvar22i); rwork(locema-1+dumvar23i)=dumvar23(dumvar23i); rwork(locdz-1+dumvar24i)=dumvar24(dumvar24i); rwork(loccsa-1+dumvar25i)=dumvar25(dumvar25i);
%------------- LAST LINE OF DSDOMN FOLLOWS ----------------------------
end
%DECK DSDOT
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