* SUBROUTINE GMRES( N, B, X, RESTRT, WORK, LDW, WORK2, LDW2, \$ ITER, RESID, MATVEC, PSOLVE, INFO ) * * -- Iterative template routine -- * Univ. of Tennessee and Oak Ridge National Laboratory * October 1, 1993 * Details of this algorithm are described in "Templates for the * Solution of Linear Systems: Building Blocks for Iterative * Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra, * EiITERkhout, Pozo, Romine, and van der Vorst, SIAM Publications, * 1993. (ftp netlib2.cs.utk.edu; cd linalg; get templates.ps). * * .. Scalar Arguments .. INTEGER N, RESTRT, LDW, LDW2, ITER, INFO DOUBLE PRECISION RESID * .. * .. Array Arguments .. DOUBLE PRECISION B( * ), X( * ), WORK( * ), WORK2( * ) * .. * .. Function Arguments .. * EXTERNAL MATVEC, PSOLVE * * Purpose * ======= * * GMRES solves the linear system Ax = b using the * Generalized Minimal Residual iterative method with preconditioning. * * Convergence test: ( norm( b - A*x ) / norm( b ) ) < TOL. * For other measures, see the above reference. * * Arguments * ========= * * N (input) INTEGER. * On entry, the dimension of the matrix. * Unchanged on exit. * * B (input) DOUBLE PRECISION array, dimension N. * On entry, right hand side vector B. * Unchanged on exit. * * X (input/output) DOUBLE PRECISION array, dimension N. * On input, the initial guess; on exit, the iterated solution. * * RESTRT (input) INTEGER * Restart parameter, <= N. This parameter controls the amount * of memory required for matrix WORK2. * * WORK (workspace) DOUBLE PRECISION array, dimension (LDW,5). * Note that if the initial guess is the zero vector, then * storing the initial residual is not necessary. * * LDW (input) INTEGER * The leading dimension of the array WORK. LDW >= max(1,N). * * WORK2 (workspace) DOUBLE PRECISION array, dimension (LDW2,2*RESTRT+2). * This workspace is used for constructing and storing the * upper Hessenberg matrix. The two extra columns are used to * store the Givens rotation matrices. * * LDW2 (input) INTEGER * The leading dimension of the array WORK2. * LDW2 >= max(1,RESTRT). * * ITER (input/output) INTEGER * On input, the maximum iterations to be performed. * On output, actual number of iterations performed. * * RESID (input/output) DOUBLE PRECISION * On input, the allowable error tolerance. * On ouput, the norm of the residual vector if solution * approximated to tolerance, otherwise reset to input * tolerance. * * INFO (output) INTEGER * = 0: successful exit * = 1: maximum number of iterations performed; * convergence not achieved. * * MATVEC (external subroutine) * The user must provide a subroutine to perform the * matrix-vector product A*x = y. * Vector x must remain unchanged. The solution is * over-written on vector y. * * The call is: * * CALL MATVEC( X, Y ) * * ============================================================ * .. * .. Parameters .. INTEGER OFSET PARAMETER ( OFSET = 1000 ) * *This variable used to communicate requests between GMRES & GMRESREVCOM *GMRES -> GMRESREVCOM: 1 = init, * 2 = use saved state to resume flow. *GMRESREVCOM -> GMRES: -1 = done, return to main, * 1 = matvec using SCLR1/2, NDX1/2 * 2 = solve using NDX1/2 * 3 = matvec using WORK2 NDX1 & WORK NDX2 INTEGER IJOB LOGICAL FTFLG * * Arg/Result indices into WORK[]. INTEGER NDX1, NDX2 * Scalars passed from GMRESREVCOM to GMRES DOUBLE PRECISION SCLR1, SCLR2 * Vars reqd for STOPTEST2 DOUBLE PRECISION TOL, BNRM2 * .. * .. External subroutines .. EXTERNAL GMRESREVCOM, STOPTEST2 * .. * .. Executable Statements .. * INFO = 0 * * Test the input parameters. * IF ( N.LT.0 ) THEN INFO = -1 ELSE IF ( LDW.LT.MAX( 1, N ) ) THEN INFO = -2 ELSE IF ( ITER.LE.0 ) THEN INFO = -3 ELSE IF ( LDW2.LT.RESTRT ) THEN INFO = -4 ENDIF IF ( INFO.NE.0 ) RETURN * * Stop test may need some indexing info from REVCOM * use the init call to send the request across. REVCOM * will note these requests, and everytime it asks for * stop test to be done, it will provide the indexing info. * Note: V, and GIV contain # of history vectors each. * To access the i'th vector in V, add i to V*OFSET 1<=i<=RESTRT * To access the i'th vector in GIV, add i to GIV*OFSET 1<=i<=RESTRT * * 1 == R; 2 == S; 3 == W; 4 == Y; 5 == AV; 6 == H; 7*OFSET+i == V; * 8*OFSET+i == GIV; -1 == ignore; any other == error NDX1 = 1 NDX2 = -1 TOL = RESID FTFLG = .TRUE. * * First time call always init. * IJOB = 1 1 CONTINUE CALL GMRESREVCOM(N, B, X, RESTRT, WORK, LDW, WORK2, LDW2, \$ ITER, RESID, INFO, NDX1, NDX2, SCLR1, \$ SCLR2, IJOB) * On a return from REVCOM() we use the table * to decode IJOB. IF (IJOB .eq. -1) THEN * revcom wants to terminate, so do it. GOTO 2 ELSEIF (IJOB .eq. 1) THEN * call matvec directly with X. CALL MATVEC(SCLR1, X, SCLR2, WORK(NDX2)) ELSEIF (IJOB .eq. 2) THEN * call solve. CALL PSOLVE(WORK(NDX1), WORK(NDX2)) ELSEIF (IJOB .eq. 3) THEN * call matvec. CALL MATVEC(SCLR1, WORK(NDX1), SCLR2, WORK(NDX2)) ELSEIF (IJOB .EQ. 4) THEN * do stopping test 2 * if first time, set INFO so that BNRM2 is computed. IF( FTFLG ) INFO = -1 CALL STOPTEST2(N, WORK(NDX1), B, BNRM2, RESID, TOL, INFO) FTFLG = .FALSE. ENDIF * * done what revcom asked, set IJOB & go back to it. IJOB = 2 GOTO 1 * * come here to terminate 2 CONTINUE * RETURN * * End of GMRES.f * END *