* SUBROUTINE QMR( N, B, X, WORK, LDW, ITER, RESID, MATVEC, \$ MATVECTRANS, PSOLVEQ, PSOLVETRANSQ, 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, * Eijkhout, Pozo, Romine, and van der Vorst, SIAM Publications, * 1993. (ftp netlib2.cs.utk.edu; cd linalg; get templates.ps). * * .. Scalar Arguments .. INTEGER N, LDW, ITER, INFO DOUBLE PRECISION RESID * .. * .. Array Arguments .. DOUBLE PRECISION X( * ), B( * ), WORK( * ) * .. * .. Function Arguments .. EXTERNAL MATVEC, MATVECTRANS, PSOLVEQ, PSOLVETRANSQ * * Purpose * ======= * * QMR Method solves the linear system Ax = b using the * Quasi-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. * * * WORK (workspace) DOUBLE PRECISION array, dimension (LDW,11). * Workspace for residual, direction vector, etc. * Note that W and WTLD, Y and YTLD, and Z and ZTLD share * workspace. * * LDW (input) INTEGER * The leading dimension of the array WORK. LDW >= max(1,N). * * 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 convergence measure for * norm( b - A*x ) / norm( b ). * On output, the final value of this measure. * * MATVEC (external subroutine) * The user must provide a subroutine to perform the * matrix-vector product * * y := alpha*A*x + beta*y, * * where alpha and beta are scalars, x and y are vectors, * and A is a matrix. Vector x must remain unchanged. * The solution is over-written on vector y. * * The call is: * * CALL MATVEC( ALPHA, X, BETA, Y ) * * The matrix is passed into the routine in a common block. * * MATVECTRANS (external subroutine) * The user must provide a subroutine to perform the * matrix-vector product * * y := alpha*A'*x + beta*y, * * where alpha and beta are scalars, x and y are vectors, * and A' is the tranpose of a matrix A. Vector x must remain * unchanged. * The solution is over-written on vector y. * * The call is: * * CALL MATVECTRANS( ALPHA, X, BETA, Y ) * * The matrix is passed into the routine in a common block. * * PSOLVEQ (external subroutine) * The user must provide a subroutine to perform the * preconditioner solve routine for the linear system * * M*x = b, * * where x and b are vectors, and M a matrix. As QMR uses left * and right preconditioning and the preconditioners are in * common, we must specify in the call which to use. Vector b * must remain unchanged. * The solution is over-written on vector x. * * The call is: * * CALL PSOLVEQ( X, B, 'LEFT' ) * * The preconditioner is passed into the routine in a common block. * * PSOLVETRANSQ (external subroutine) * The user must provide a subroutine to perform the * preconditioner solve routine for the linear system * * M'*x = b, * * where x and y are vectors, and M' is the tranpose of a * matrix M. As QMR uses left and right preconditioning and * the preconditioners are in common, we must specify in the * call which to use. Vector b must remain unchanged. * The solution is over-written on vector x. * * The call is: * * CALL PSOLVETRANSQ( X, B, 'LEFT' ) * * The preconditioner is passed into the routine in a common block. * * INFO (output) INTEGER * * = 0: Successful exit. Iterated approximate solution returned. * * > 0: Convergence to tolerance not achieved. This will be * set to the number of iterations performed. * * < 0: Illegal input parameter, or breakdown occurred * during iteration. * * Illegal parameter: * * -1: matrix dimension N < 0 * -2: LDW < N * -3: Maximum number of iterations ITER <= 0. * * BREAKDOWN: If parameters RHO or OMEGA become smaller * than some tolerance, the program will terminate. * Here we check against tolerance BREAKTOL. * * -10: RHO < BREAKTOL: RHO and RTLD have become * orthogonal. * -11: BETA < BREAKTOL: EPS too small in relation to DELTA. * Convergence has stalled. * -12: GAMMA < BREAKTOL: THETA too large. * Convergence has stalled. * -13: DELTA < BREAKTOL: Y and Z have become * orthogonal. * -14: EPS < BREAKTOL: Q and PTLD have become * orthogonal. * -15: XI < BREAKTOL: Z too small. Convergence has stalled. * * BREAKTOL is set in function GETBREAK. * * BLAS CALLS: DAXPY, DCOPY, DDOT, DNRM2, DSCAL * ============================================================== * *This variable used to communicate requests between QMR() and * QMRREVCOM() *QMR -> QMRREVCOM: 1 = init, * 2 = use saved state to resume flow. *QMRREVCOM -> QMR: -1 = done, return to main, * 1 = matvec using SCLR1/2, NDX1/2 * 2 = transpose-matvec using SCLR1/2, NDX1/2 * 3 = left prec solve using NDX1/2 * 4 = right prec solve using NDX1/2 * 5 = left prec transpose-solve using NDX1/2 * 6 = right transpose-solve using NDX1/2 INTEGER IJOB LOGICAL FTFLG * Arg/Result indices into WORK[]. INTEGER NDX1, NDX2 * Scalars passed from QMRREVCOM to QMR. DOUBLE PRECISION SCLR1, SCLR2 * Vars reqd for STOPTEST2 DOUBLE PRECISION TOL, BNRM2 * .. * .. External subroutines .. EXTERNAL QMRREVCOM, 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 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. * * 1 == R; 2 == D; 3 == P; 4 == PTLD; 5 == Q; 6 == S; 7 == V; * 8 == VTLD; 9 == W; 10 == WTLD; 11 == Y; 12 == YTLD; 13 == Z; * 14 == ZTLD; -1 == ignore; any other == error NDX1 = 1 NDX2 = -1 TOL = RESID FTFLG = .TRUE. * * First time call always init. * IJOB = 1 1 CONTINUE CALL QMRREVCOM(N, B, X, WORK, LDW, ITER, RESID, INFO, \$ NDX1, NDX2, SCLR1, SCLR2, IJOB) * On a return from REVCOM we use the table (BiCGREVCOM -> BiCG) * to decode IJOB. IF (IJOB .eq. -1) THEN * revcom wants to terminate, so do it. GOTO 2 ELSEIF (IJOB .eq. 1) THEN * call matvec. CALL MATVEC(SCLR1, WORK(NDX1), SCLR2, WORK(NDX2)) ELSEIF (IJOB .eq. 2) THEN * call transpose-matvec. CALL MATVECTRANS(SCLR1, WORK(NDX1), SCLR2, WORK(NDX2)) ELSEIF (IJOB .eq. 3) THEN * call left prec solve. CALL PSOLVEQ(WORK(NDX1), WORK(NDX2), 'LEFT') ELSEIF (IJOB .eq. 4) THEN * call right prec solve. CALL PSOLVEQ(WORK(NDX1), WORK(NDX2), 'RIGHT') ELSEIF (IJOB .eq. 5) THEN * call left prec transpose-solve. CALL PSOLVETRANSQ(WORK(NDX1), WORK(NDX2),'LEFT') ELSEIF (IJOB .eq. 6) THEN * call right prec transpose-solve. CALL PSOLVETRANSQ(WORK(NDX1), WORK(NDX2),'RIGHT') ELSEIF (IJOB .eq. 7) THEN * call matvec with X. CALL MATVEC(SCLR1, X, SCLR2, WORK(NDX2)) ELSEIF (IJOB .EQ. 8) 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 QMR * END