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|
* -*- fortran -*-
SUBROUTINE <_c>QMRREVCOM(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
<rt=real,double precision,real,double precision> RESID
INTEGER NDX1, NDX2
<_t> SCLR1, SCLR2
INTEGER IJOB
* ..
* .. Array Arguments ..
<_t> X( * ), B( * ), WORK( LDW,* )
* ..
* Purpose
* =======
*
* QMR Method solves the linear system Ax = b using the
* Quasi-Minimal Residual 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; 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 .gt. = 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.
* -5: Erroneous NDX1/NDX2 in INIT call.
* -6: Erroneous RLBL.
*
* .gt. 0: Convergence to tolerance not achieved. This will be
* set to the number of iterations performed.
*
* .ls. 0: Illegal input parameter, or breakdown occurred
* during iteration.
*
* Illegal parameter:
*
* -1: matrix dimension N .ls. 0
* -2: LDW .ls. N
* -3: Maximum number of iterations ITER .ls. = 0.
*
* BREAKDOWN: If parameters RHO or OMEGA become smaller
* than some tolerance, the program will terminate.
* Here we check against tolerance BREAKTOL.
*
* -10: RHO .ls. BREAKTOL: RHO and RTLD have become
* orthogonal.
* -11: BETA .ls. BREAKTOL: EPS too small in relation to DELT
* Convergence has stalled.
* -12: GAMMA .ls. BREAKTOL: THETA too large.
* Convergence has stalled.
* -13: DELTA .ls. BREAKTOL: Y and Z have become
* orthogonal.
* -14: EPS .ls. BREAKTOL: Q and PTLD have become
* orthogonal.
* -15: XI .ls. BREAKTOL: Z too small.
* Convergence has stalled.
*
* BREAKTOL is set in func 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 ..
<rt> ONE, ZERO
PARAMETER ( ONE = 1.0D+0 , ZERO = 0.0D+0)
*
* .. Local Scalars ..
INTEGER R, D, P, PTLD, Q, S, V, VTLD, W, WTLD, Y, YTLD,
$ Z, ZTLD, MAXIT, NEED1, NEED2
<rt> TOL, BNRM2, RHOTOL, BETATOL,
$ GAMMATOL, DELTATOL,
$ EPSTOL, XITOL,
$ <sdsd=s,d,s,d>GETBREAK,
$ <rc=ws,d,wsc,dz>NRM2
<_t> BETA, GAMMA, GAMMA1, DELTA, EPS, ETA, XI,
$ RHO, RHO1, THETA, THETA1, C1, TMPVAL,
$ <xdot=wsdot,ddot,wcdotc,wzdotc>,
$ toz
*
* indicates where to resume from. Only valid when IJOB = 2!
INTEGER RLBL
*
* saving all.
SAVE
*
* ..
* .. External Routines ..
EXTERNAL <_c>AXPY, <_c>COPY, <xdot>, <rc>NRM2, <_c>SCAL
* ..
* .. Intrinsic Funcs ..
INTRINSIC ABS, SQRT
* ..
* .. 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 (RLBL .eq. 8) GOTO 8
IF (RLBL .eq. 9) GOTO 9
IF (RLBL .eq. 10) GOTO 10
IF (RLBL .eq. 11) GOTO 11
* if neither of these, then error
INFO = -6
GOTO 20
ENDIF
*
*
*****************
1 CONTINUE
*****************
*
INFO = 0
MAXIT = ITER
TOL = RESID
*
* Alias workspace columns.
*
R = 1
D = 2
P = 3
PTLD = 4
Q = 5
S = 6
V = 7
VTLD = 8
W = 9
WTLD = 9
Y = 10
YTLD = 10
Z = 11
ZTLD = 11
*
* 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 = ((D - 1) * LDW) + 1
ELSEIF( NDX1.EQ.3 ) THEN
NEED1 = ((P - 1) * LDW) + 1
ELSEIF( NDX1.EQ.4 ) THEN
NEED1 = ((PTLD - 1) * LDW) + 1
ELSEIF( NDX1.EQ.5 ) THEN
NEED1 = ((Q - 1) * LDW) + 1
ELSEIF( NDX1.EQ.6 ) THEN
NEED1 = ((S - 1) * LDW) + 1
ELSEIF( NDX1.EQ.7 ) THEN
NEED1 = ((V - 1) * LDW) + 1
ELSEIF( NDX1.EQ.8 ) THEN
NEED1 = ((VTLD - 1) * LDW) + 1
ELSEIF( NDX1.EQ.9 ) THEN
NEED1 = ((W - 1) * LDW) + 1
ELSEIF( NDX1.EQ.10 ) THEN
NEED1 = ((WTLD - 1) * LDW) + 1
ELSEIF( NDX1.EQ.11 ) THEN
NEED1 = ((Y - 1) * LDW) + 1
ELSEIF( NDX1.EQ.12 ) THEN
NEED1 = ((YTLD - 1) * LDW) + 1
ELSEIF( NDX1.EQ.13 ) THEN
NEED1 = ((Z - 1) * LDW) + 1
ELSEIF( NDX1.EQ.14 ) THEN
NEED1 = ((ZTLD - 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 = ((D - 1) * LDW) + 1
ELSEIF( NDX2.EQ.3 ) THEN
NEED2 = ((P - 1) * LDW) + 1
ELSEIF( NDX2.EQ.4 ) THEN
NEED2 = ((PTLD - 1) * LDW) + 1
ELSEIF( NDX2.EQ.5 ) THEN
NEED2 = ((Q - 1) * LDW) + 1
ELSEIF( NDX2.EQ.6 ) THEN
NEED2 = ((S - 1) * LDW) + 1
ELSEIF( NDX2.EQ.7 ) THEN
NEED2 = ((V - 1) * LDW) + 1
ELSEIF( NDX2.EQ.8 ) THEN
NEED2 = ((VTLD - 1) * LDW) + 1
ELSEIF( NDX2.EQ.9 ) THEN
NEED2 = ((W - 1) * LDW) + 1
ELSEIF( NDX2.EQ.10 ) THEN
NEED2 = ((WTLD - 1) * LDW) + 1
ELSEIF( NDX2.EQ.11 ) THEN
NEED2 = ((Y - 1) * LDW) + 1
ELSEIF( NDX2.EQ.12 ) THEN
NEED2 = ((YTLD - 1) * LDW) + 1
ELSEIF( NDX2.EQ.13 ) THEN
NEED2 = ((Z - 1) * LDW) + 1
ELSEIF( NDX2.EQ.14 ) THEN
NEED2 = ((ZTLD - 1) * LDW) + 1
ELSE
* report error
INFO = -5
GO TO 20
ENDIF
ELSE
NEED2 = NDX2
ENDIF
*
* Set breakdown tolerances.
*
RHOTOL = <sdsd>GETBREAK()
BETATOL = <sdsd>GETBREAK()
GAMMATOL = <sdsd>GETBREAK()
DELTATOL = <sdsd>GETBREAK()
EPSTOL = <sdsd>GETBREAK()
XITOL = <sdsd>GETBREAK()
*
* Set initial residual.
*
CALL <_c>COPY( N, B, 1, WORK(1,R), 1 )
IF ( <rc>NRM2( N, X, 1 ).NE.ZERO ) THEN
*********CALL MATVEC( -ONE, X, ZERO, WORK(1,R) )
* Note: using D as temp
*********CALL <_c>COPY( N, X, 1, WORK(1,D), 1 )
SCLR1 = -ONE
SCLR2 = ZERO
NDX1 = ((D - 1) * LDW) + 1
NDX2 = ((R - 1) * LDW) + 1
RLBL = 2
IJOB = 7
RETURN
ENDIF
*****************
2 CONTINUE
*****************
*
IF ( <rc>NRM2( N, WORK(1,R), 1 ) .LT. TOL ) GO TO 30
*
BNRM2 = <rc>NRM2( N, B, 1 )
IF ( BNRM2.EQ.ZERO ) BNRM2 = ONE
*
CALL <_c>COPY( N, WORK(1,R), 1, WORK(1,VTLD), 1 )
******CALL PSOLVEQ( WORK(1,Y), WORK(1,VTLD), 'LEFT' )
*
NDX1 = ((Y - 1) * LDW) + 1
NDX2 = ((VTLD - 1) * LDW) + 1
RLBL = 3
IJOB = 3
RETURN
*****************
3 CONTINUE
*****************
*
RHO = <rc>NRM2( N, WORK(1,Y), 1 )
*
CALL <_c>COPY( N, WORK(1,R), 1, WORK(1,WTLD), 1 )
******CALL PSOLVETRANSQ( WORK(1,Z), WORK(1,WTLD), 'RIGHT' )
*
NDX1 = ((Z - 1) * LDW) + 1
NDX2 = ((WTLD - 1) * LDW) + 1
RLBL = 4
IJOB = 6
RETURN
*****************
4 CONTINUE
*****************
*
XI = <rc>NRM2( N, WORK(1,Z), 1 )
*
GAMMA = ONE
ETA = -ONE
THETA = ZERO
*
ITER = 0
*
40 CONTINUE
*
* Perform Preconditioned QMR iteration.
*
ITER = ITER + 1
*
IF ( ( ABS( RHO ).LT.RHOTOL ).OR.( ABS( XI ).LT.XITOL ) )
$ GO TO 25
*
CALL <_c>COPY( N, WORK(1,VTLD), 1, WORK(1,V), 1 )
TMPVAL = ONE / RHO
CALL <_c>SCAL( N, TMPVAL, WORK(1,V), 1 )
CALL <_c>SCAL( N, TMPVAL, WORK(1,Y), 1 )
*
TMPVAL = ONE / XI
CALL <_c>COPY( N, WORK(1,WTLD), 1, WORK(1,W), 1 )
CALL <_c>SCAL( N, TMPVAL, WORK(1,W), 1 )
CALL <_c>SCAL( N, TMPVAL, WORK(1,Z), 1 )
*
DELTA = <xdot>( N, WORK(1,Z), 1, WORK(1,Y), 1 )
IF ( ABS( DELTA ).LT.DELTATOL ) GO TO 25
*
*********CALL PSOLVEQ( WORK(1,YTLD), WORK(1,Y), 'RIGHT' )
*
NDX1 = ((YTLD - 1) * LDW) + 1
NDX2 = ((Y - 1) * LDW) + 1
RLBL = 5
IJOB = 4
RETURN
*****************
5 CONTINUE
*****************
*
*********CALL PSOLVETRANSQ( WORK(1,ZTLD), WORK(1,Z), 'LEFT' )
*
NDX1 = ((ZTLD - 1) * LDW) + 1
NDX2 = ((Z - 1) * LDW) + 1
RLBL = 6
IJOB = 5
RETURN
*****************
6 CONTINUE
*****************
*
*
IF ( ITER.GT.1 ) THEN
C1 = -( XI * DELTA / EPS )
CALL <_c>AXPY( N, C1, WORK(1,P), 1, WORK(1,YTLD), 1 )
CALL <_c>COPY( N, WORK(1,YTLD), 1, WORK(1,P), 1 )
CALL <_c>AXPY( N, -( RHO *
$ <co= , ,conjg,conjg>(DELTA / EPS) ),
$ WORK(1,Q), 1, WORK(1,ZTLD), 1 )
CALL <_c>COPY( N, WORK(1,ZTLD), 1, WORK(1,Q), 1 )
ELSE
CALL <_c>COPY( N, WORK(1,YTLD), 1, WORK(1,P), 1 )
CALL <_c>COPY( N, WORK(1,ZTLD), 1, WORK(1,Q), 1 )
ENDIF
*
*********CALL MATVEC( ONE, WORK(1,P), ZERO, WORK(1,PTLD) )
*
SCLR1 = ONE
SCLR2 = ZERO
NDX1 = ((P - 1) * LDW) + 1
NDX2 = ((PTLD - 1) * LDW) + 1
RLBL = 7
IJOB = 1
RETURN
*****************
7 CONTINUE
*****************
*
*
EPS = <xdot>( N, WORK(1,Q), 1, WORK(1,PTLD), 1 )
IF ( ABS( EPS ).LT.EPSTOL ) GO TO 25
*
BETA = EPS / DELTA
IF ( ABS( BETA ).LT.BETATOL ) GO TO 25
*
CALL <_c>COPY( N, WORK(1,PTLD), 1, WORK(1,VTLD), 1 )
CALL <_c>AXPY( N, -BETA, WORK(1,V), 1, WORK(1,VTLD), 1 )
******CALL PSOLVEQ( WORK(1,Y), WORK(1,VTLD), 'LEFT' )
*
NDX1 = ((Y - 1) * LDW) + 1
NDX2 = ((VTLD - 1) * LDW) + 1
RLBL = 8
IJOB = 3
RETURN
*
*****************
8 CONTINUE
*****************
RHO1 = RHO
RHO = <rc>NRM2( N, WORK(1,Y), 1 )
*
CALL <_c>COPY( N, WORK(1,W), 1, WORK(1,WTLD), 1 )
*********CALL MATVECTRANS( ONE, WORK(1,Q), -BETA, WORK(1,WTLD) )
*
SCLR1 = ONE
SCLR2 = -<co>(BETA)
NDX1 = ((Q - 1) * LDW) + 1
NDX2 = ((WTLD - 1) * LDW) + 1
RLBL = 9
IJOB = 2
RETURN
*****************
9 CONTINUE
*****************
*
*********CALL PSOLVETRANSQ( WORK(1,Z), WORK(1,WTLD), 'RIGHT' )
*
NDX1 = ((Z - 1) * LDW) + 1
NDX2 = ((WTLD - 1) * LDW) + 1
RLBL = 10
IJOB = 6
RETURN
*****************
10 CONTINUE
*****************
*
*
XI = <rc>NRM2( N, WORK(1,Z), 1 )
*
GAMMA1 = GAMMA
THETA1 = THETA
*
THETA = RHO / ( GAMMA1 * ABS( BETA ) )
GAMMA = ONE / SQRT( ONE + THETA**2 )
IF ( ABS( GAMMA ).LT.GAMMATOL ) GO TO 25
*
ETA = -ETA * RHO1 * GAMMA**2 / ( BETA * GAMMA1**2 )
*
IF ( ITER.GT.1 ) THEN
CALL <_c>SCAL( N, ( THETA1*GAMMA )**2, WORK(1,D), 1 )
CALL <_c>AXPY( N, ETA, WORK(1,P), 1, WORK(1,D), 1 )
CALL <_c>SCAL( N, ( THETA1 * GAMMA )**2, WORK(1,S), 1 )
CALL <_c>AXPY( N, ETA, WORK(1,PTLD), 1, WORK(1,S), 1 )
ELSE
CALL <_c>COPY( N, WORK(1,P), 1, WORK(1,D), 1 )
CALL <_c>SCAL( N, ETA, WORK(1,D), 1 )
CALL <_c>COPY( N, WORK(1,PTLD), 1, WORK(1,S), 1 )
CALL <_c>SCAL( N, ETA, WORK(1,S), 1 )
ENDIF
*
* Compute current solution vector x.
*
TMPVAL = ONE
CALL <_c>AXPY( N, TMPVAL, WORK(1,D), 1, X, 1 )
*
* Compute residual vector rk, find norm,
* then check for tolerance.
*
toz = one
CALL <_c>AXPY( N, -toz, WORK(1,S), 1, WORK(1,R), 1 )
*
*********RESID = <rc>NRM2( N, WORK(1,R), 1 ) / BNRM2
*********IF ( RESID .LE. TOL ) GO TO 30
*
NDX1 = NEED1
NDX2 = NEED2
* Prepare for resumption & return
RLBL = 11
IJOB = 8
RETURN
*
*****************
11 CONTINUE
*****************
IF( INFO.EQ.1 ) GO TO 30
*
IF ( ITER.EQ.MAXIT ) THEN
INFO = 1
GO TO 20
ENDIF
*
GO TO 40
*
20 CONTINUE
*
* Iteration fails.
*
RLBL = -1
IJOB = -1
*
RETURN
*
25 CONTINUE
*
* Method breakdown.
*
IF ( ABS( RHO ).LT.RHOTOL ) THEN
INFO = -10
ELSE IF ( ABS( BETA ).LT.BETATOL ) THEN
INFO = -11
ELSE IF ( ABS( GAMMA ).LT.GAMMATOL ) THEN
INFO = -12
ELSE IF ( ABS( DELTA ).LT.DELTATOL ) THEN
INFO = -13
ELSE IF ( ABS( EPS ).LT.EPSTOL ) THEN
INFO = -14
ELSE IF ( ABS( XI ).LT.XITOL ) THEN
INFO = -15
ENDIF
*
*
RLBL = -1
IJOB = -1
*
RETURN
*
30 CONTINUE
*
* Iteration successful; return.
*
INFO = 0
RLBL = -1
IJOB = -1
*
RETURN
*
* End of QMRREVCOM
*
END
* END SUBROUTINE <_c>QMRREVCOM
|
