*
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