* SUBROUTINE BICGSTABREVCOM(N, B, X, WORK, LDW, ITER, RESID, INFO, \$ NDX1, NDX2, SCLR1, SCLR2, IJOB) * * -- 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 INTEGER NDX1, NDX2 DOUBLE PRECISION SCLR1, SCLR2 INTEGER IJOB * .. * .. Array Arguments .. DOUBLE PRECISION X( * ), B( * ), WORK( LDW,* ) * .. * * Purpose * ======= * * BICGSTAB solves the linear system A*x = b using the * BiConjugate Gradient Stabilized iterative method with * preconditioning. * * 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. This is commonly set to * the zero vector. * On exit, if INFO = 0, the iterated approximate solution. * * WORK (workspace) DOUBLE PRECISION array, dimension (LDW,7) * Workspace for residual, direction vector, etc. * Note that vectors R and S shared the same 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. * * 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. * -5: Erroneous NDX1/NDX2 in INIT call. * -6: Erroneous RLBL. * * 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: OMEGA < BREAKTOL: S and T have become * orthogonal relative to T'*T. * * BREAKTOL is set in function GETBREAK. * * NDX1 (input/output) INTEGER. * NDX2 On entry in INIT call contain indices required by interface * level for stopping test. * All other times, used as output, to indicate indices into * WORK[] for the MATVEC, PSOLVE done by the interface level. * * SCLR1 (output) DOUBLE PRECISION. * SCLR2 Used to pass the scalars used in MATVEC. Scalars are reqd because * original routines use dgemv. * * IJOB (input/output) INTEGER. * Used to communicate job code between the two levels. * * BLAS CALLS: DAXPY, DCOPY, DDOT, DNRM2, DSCAL * ============================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. INTEGER R, RTLD, P, PHAT, V, S, SHAT, T, MAXIT, \$ NEED1, NEED2 DOUBLE PRECISION TOL, ALPHA, BETA, RHO, RHO1, BNRM2, OMEGA, \$ RHOTOL, OMEGATOL, GETBREAK, DDOT, DNRM2 * indicates where to resume from. Only valid when IJOB = 2! INTEGER RLBL * * saving all. SAVE * .. * .. External Functions .. EXTERNAL GETBREAK, DAXPY, DCOPY, DDOT, DNRM2, DSCAL * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. * .. Executable Statements .. * * Entry point, so test IJOB IF (IJOB .eq. 1) THEN GOTO 1 ELSEIF (IJOB .eq. 2) THEN * here we do resumption handling IF (RLBL .eq. 2) GOTO 2 IF (RLBL .eq. 3) GOTO 3 IF (RLBL .eq. 4) GOTO 4 IF (RLBL .eq. 5) GOTO 5 IF (RLBL .eq. 6) GOTO 6 IF (RLBL .eq. 7) GOTO 7 * if neither of these, then error INFO = -6 GOTO 20 ENDIF * * ***************** 1 CONTINUE ***************** * INFO = 0 MAXIT = ITER TOL = RESID * * Alias workspace columns. * R = 1 RTLD = 2 P = 3 V = 4 T = 5 PHAT = 6 SHAT = 7 S = 1 * * Check if caller will need indexing info. * IF( NDX1.NE.-1 ) THEN IF( NDX1.EQ.1 ) THEN NEED1 = ((R - 1) * LDW) + 1 ELSEIF( NDX1.EQ.2 ) THEN NEED1 = ((RTLD - 1) * LDW) + 1 ELSEIF( NDX1.EQ.3 ) THEN NEED1 = ((P - 1) * LDW) + 1 ELSEIF( NDX1.EQ.4 ) THEN NEED1 = ((V - 1) * LDW) + 1 ELSEIF( NDX1.EQ.5 ) THEN NEED1 = ((T - 1) * LDW) + 1 ELSEIF( NDX1.EQ.6 ) THEN NEED1 = ((PHAT - 1) * LDW) + 1 ELSEIF( NDX1.EQ.7 ) THEN NEED1 = ((SHAT - 1) * LDW) + 1 ELSEIF( NDX1.EQ.8 ) THEN NEED1 = ((S - 1) * LDW) + 1 ELSE * report error INFO = -5 GO TO 20 ENDIF ELSE NEED1 = NDX1 ENDIF * IF( NDX2.NE.-1 ) THEN IF( NDX2.EQ.1 ) THEN NEED2 = ((R - 1) * LDW) + 1 ELSEIF( NDX2.EQ.2 ) THEN NEED2 = ((RTLD - 1) * LDW) + 1 ELSEIF( NDX2.EQ.3 ) THEN NEED2 = ((P - 1) * LDW) + 1 ELSEIF( NDX2.EQ.4 ) THEN NEED2 = ((V - 1) * LDW) + 1 ELSEIF( NDX2.EQ.5 ) THEN NEED2 = ((T - 1) * LDW) + 1 ELSEIF( NDX2.EQ.6 ) THEN NEED2 = ((PHAT - 1) * LDW) + 1 ELSEIF( NDX2.EQ.7 ) THEN NEED2 = ((SHAT - 1) * LDW) + 1 ELSEIF( NDX2.EQ.8 ) THEN NEED2 = ((S - 1) * LDW) + 1 ELSE * report error INFO = -5 GO TO 20 ENDIF ELSE NEED2 = NDX2 ENDIF * * Set parameter tolerances. * RHOTOL = GETBREAK() OMEGATOL = GETBREAK() * * Set initial residual. * CALL DCOPY( N, B, 1, WORK(1,R), 1 ) IF ( DNRM2( N, X, 1 ).NE.ZERO ) THEN *********CALL MATVEC( -ONE, X, ONE, WORK(1,R) ) * Note: using RTLD[] as temp. storage. *********CALL DCOPY(N, X, 1, WORK(1,RTLD), 1) SCLR1 = -ONE SCLR2 = ONE NDX1 = -1 NDX2 = ((R - 1) * LDW) + 1 * * Prepare for resumption & return RLBL = 2 IJOB = 3 RETURN * ***************** 2 CONTINUE ***************** * IF ( DNRM2( N, WORK(1,R), 1 ).LE.TOL ) GO TO 30 ENDIF CALL DCOPY( N, WORK(1,R), 1, WORK(1,RTLD), 1 ) * BNRM2 = DNRM2( N, B, 1 ) IF ( BNRM2 .EQ. ZERO ) BNRM2 = ONE * ITER = 0 * 10 CONTINUE * * Perform BiConjugate Gradient Stabilized iteration. * ITER = ITER + 1 * RHO = DDOT( N, WORK(1,RTLD), 1, WORK(1,R), 1 ) IF ( ABS( RHO ).LT.RHOTOL ) GO TO 25 * * Compute vector P. * IF ( ITER.GT.1 ) THEN BETA = ( RHO / RHO1 ) * ( ALPHA / OMEGA ) CALL DAXPY( N, -OMEGA, WORK(1,V), 1, WORK(1,P), 1 ) CALL DSCAL( N, BETA, WORK(1,P), 1 ) CALL DAXPY( N, ONE, WORK(1,R), 1, WORK(1,P), 1 ) ELSE CALL DCOPY( N, WORK(1,R), 1, WORK(1,P), 1 ) ENDIF * * Compute direction adjusting vector PHAT and scalar ALPHA. * *********CALL PSOLVE( WORK(1,PHAT), WORK(1,P) ) * NDX1 = ((PHAT - 1) * LDW) + 1 NDX2 = ((P - 1) * LDW) + 1 * Prepare for return & return RLBL = 3 IJOB = 2 RETURN * ***************** 3 CONTINUE ***************** * *********CALL MATVEC( ONE, WORK(1,PHAT), ZERO, WORK(1,V) ) * NDX1 = ((PHAT - 1) * LDW) + 1 NDX2 = ((V - 1) * LDW) + 1 * Prepare for return & return SCLR1 = ONE SCLR2 = ZERO RLBL = 4 IJOB = 1 RETURN * ***************** 4 CONTINUE ***************** * ALPHA = RHO / DDOT( N, WORK(1,RTLD), 1, WORK(1,V), 1 ) * * Early check for tolerance. * CALL DAXPY( N, -ALPHA, WORK(1,V), 1, WORK(1,R), 1 ) CALL DCOPY( N, WORK(1,R), 1, WORK(1,S), 1 ) IF ( DNRM2( N, WORK(1,S), 1 ).LE.TOL ) THEN CALL DAXPY( N, ALPHA, WORK(1,PHAT), 1, X, 1 ) RESID = DNRM2( N, WORK(1,S), 1 ) / BNRM2 GO TO 30 ELSE * * Compute stabilizer vector SHAT and scalar OMEGA. * ************CALL PSOLVE( WORK(1,SHAT), WORK(1,S) ) * NDX1 = ((SHAT - 1) * LDW) + 1 NDX2 = ((S - 1) * LDW) + 1 * Prepare for return & return RLBL = 5 IJOB = 2 RETURN * ***************** 5 CONTINUE ***************** * ************CALL MATVEC( ONE, WORK(1,SHAT), ZERO, WORK(1,T) ) * NDX1 = ((SHAT - 1) * LDW) + 1 NDX2 = ((T - 1) * LDW) + 1 * Prepare for return & return SCLR1 = ONE SCLR2 = ZERO RLBL = 6 IJOB = 1 RETURN * ***************** 6 CONTINUE ***************** * OMEGA = DDOT( N, WORK(1,T), 1, WORK(1,S), 1 ) / \$ DDOT( N, WORK(1,T), 1, WORK(1,T), 1 ) * * Compute new solution approximation vector X. * CALL DAXPY( N, ALPHA, WORK(1,PHAT), 1, X, 1 ) CALL DAXPY( N, OMEGA, WORK(1,SHAT), 1, X, 1 ) * * Compute residual R, check for tolerance. * CALL DAXPY( N, -OMEGA, WORK(1,T), 1, WORK(1,R), 1 ) * ************RESID = DNRM2( N, WORK(1,R), 1 ) / BNRM2 ************IF ( RESID.LE.TOL ) GO TO 30 * NDX1 = NEED1 NDX2 = NEED2 * Prepare for resumption & return RLBL = 7 IJOB = 4 RETURN * ***************** 7 CONTINUE ***************** IF( INFO.EQ.1 ) GO TO 30 * IF ( ITER.EQ.MAXIT ) THEN INFO = 1 GO TO 20 ENDIF * ENDIF * IF ( ABS( OMEGA ).LT.OMEGATOL ) THEN GO TO 25 ELSE RHO1 = RHO GO TO 10 ENDIF * 20 CONTINUE * * Iteration fails. * RLBL = -1 IJOB = -1 RETURN * 25 CONTINUE * * Set breakdown flag. * IF ( ABS( RHO ).LT.RHOTOL ) THEN INFO = -10 ELSE IF ( ABS( OMEGA ).LT.OMEGATOL ) THEN INFO = -11 ENDIF RLBL = -1 IJOB = -1 RETURN * 30 CONTINUE * * Iteration successful; return. * INFO = 0 RLBL = -1 IJOB = -1 RETURN * * End of BICGSTABREVCOM * END