*DECK ISDCGS
INTEGER FUNCTION ISDCGS (N, B, X, NELT, IA, JA, A, ISYM, MATVEC,
+ MSOLVE, ITOL, TOL, ITMAX, ITER, ERR, IERR, IUNIT, R, R0, P, Q,
+ U, V1, V2, RWORK, IWORK, AK, BK, BNRM, SOLNRM)
C***BEGIN PROLOGUE ISDCGS
C***SUBSIDIARY
C***PURPOSE Preconditioned BiConjugate Gradient Squared Stop Test.
C This routine calculates the stop test for the BiConjugate
C Gradient Squared iteration scheme. It returns a non-zero
C if the error estimate (the type of which is determined by
C ITOL) is less than the user specified tolerance TOL.
C***LIBRARY SLATEC (SLAP)
C***CATEGORY D2A4, D2B4
C***TYPE DOUBLE PRECISION (ISSCGS-S, ISDCGS-D)
C***KEYWORDS ITERATIVE PRECONDITION, NON-SYMMETRIC LINEAR SYSTEM, SLAP,
C SPARSE, STOP TEST
C***AUTHOR Greenbaum, Anne, (Courant Institute)
C Seager, Mark K., (LLNL)
C Lawrence Livermore National Laboratory
C PO BOX 808, L-60
C Livermore, CA 94550 (510) 423-3141
C seager@llnl.gov
C***DESCRIPTION
C
C *Usage:
C INTEGER N, NELT, IA(NELT), JA(NELT), ISYM, ITOL, ITMAX, ITER
C INTEGER IERR, IUNIT, IWORK(USER DEFINED)
C DOUBLE PRECISION B(N), X(N), A(N), TOL, ERR, R(N), R0(N), P(N)
C DOUBLE PRECISION Q(N), U(N), V1(N), V2(N)
C DOUBLE PRECISION RWORK(USER DEFINED), AK, BK, BNRM, SOLNRM
C EXTERNAL MATVEC, MSOLVE
C
C IF( ISDCGS(N, B, X, NELT, IA, JA, A, ISYM, MATVEC, MSOLVE, ITOL,
C $ TOL, ITMAX, ITER, ERR, IERR, IUNIT, R, R0, P, Q, U, V1,
C $ V2, RWORK, IWORK, AK, BK, BNRM, SOLNRM) .NE. 0 )
C $ THEN ITERATION DONE
C
C *Arguments:
C N :IN Integer
C Order of the Matrix.
C B :IN Double Precision B(N).
C Right-hand side vector.
C X :INOUT Double Precision X(N).
C On input X is your initial guess for solution vector.
C On output X is the final approximate solution.
C NELT :IN Integer.
C Number of Non-Zeros stored in A.
C IA :IN Integer IA(NELT).
C JA :IN Integer JA(NELT).
C A :IN Double Precision A(NELT).
C These arrays contain the matrix data structure for A.
C It could take any form. See "Description" in SLAP routine
C DCGS for more details.
C ISYM :IN Integer.
C Flag to indicate symmetric storage format.
C If ISYM=0, all non-zero entries of the matrix are stored.
C If ISYM=1, the matrix is symmetric, and only the upper
C or lower triangle of the matrix is stored.
C MATVEC :EXT External.
C Name of a routine which performs the matrix vector multiply
C operation Y = A*X given A and X. The name of the MATVEC
C routine must be declared external in the calling program.
C The calling sequence of MATVEC is:
C CALL MATVEC( N, X, Y, NELT, IA, JA, A, ISYM )
C Where N is the number of unknowns, Y is the product A*X upon
C return, X is an input vector. NELT, IA, JA, A, and ISYM
C define the SLAP matrix data structure.
C MSOLVE :EXT External.
C Name of a routine which solves a linear system MZ = R for Z
C given R with the preconditioning matrix M (M is supplied via
C RWORK and IWORK arrays). The name of the MSOLVE routine
C must be declared external in the calling program. The
C calling sequence of MSOLVE is:
C CALL MSOLVE(N, R, Z, NELT, IA, JA, A, ISYM, RWORK, IWORK)
C Where N is the number of unknowns, R is the right-hand side
C vector, and Z is the solution upon return. NELT, IA, JA, A,
C and ISYM define the SLAP matrix data structure.
C RWORK is a double precision array that can be used to pass
C necessary preconditioning information and/or workspace to
C MSOLVE.
C IWORK is an integer work array for the same purpose as RWORK.
C ITOL :IN Integer.
C Flag to indicate type of convergence criterion.
C If ITOL=1, iteration stops when the 2-norm of the residual
C divided by the 2-norm of the right-hand side is less than TOL.
C This routine must calculate the residual from R = A*X - B.
C This is unnatural and hence expensive for this type of iter-
C ative method. ITOL=2 is *STRONGLY* recommended.
C If ITOL=2, iteration stops when the 2-norm of M-inv times the
C residual divided by the 2-norm of M-inv times the right hand
C side is less than TOL, where M-inv time a vector is the pre-
C conditioning step. This is the *NATURAL* stopping for this
C iterative method and is *STRONGLY* recommended.
C ITOL=11 is often useful for checking and comparing different
C routines. For this case, the user must supply the "exact"
C solution or a very accurate approximation (one with an error
C much less than TOL) through a common block,
C COMMON /DSLBLK/ SOLN( )
C If ITOL=11, iteration stops when the 2-norm of the difference
C between the iterative approximation and the user-supplied
C solution divided by the 2-norm of the user-supplied solution
C is less than TOL. Note that this requires the user to set up
C the "COMMON /DSLBLK/ SOLN(LENGTH)" in the calling routine.
C The routine with this declaration should be loaded before the
C stop test so that the correct length is used by the loader.
C This procedure is not standard Fortran and may not work
C correctly on your system (although it has worked on every
C system the authors have tried). If ITOL is not 11 then this
C common block is indeed standard Fortran.
C TOL :IN Double Precision.
C Convergence criterion, as described above.
C ITMAX :IN Integer.
C Maximum number of iterations.
C ITER :IN Integer.
C Current iteration count. (Must be zero on first call.)
C ITMAX iterations.
C ERR :OUT Double Precision.
C Error estimate of error in final approximate solution, as
C defined by ITOL.
C IERR :OUT Integer.
C Error flag. IERR is set to 3 if ITOL is not one of the
C acceptable values, see above.
C IUNIT :IN Integer.
C Unit number on which to write the error at each iteration,
C if this is desired for monitoring convergence. If unit
C number is 0, no writing will occur.
C R :IN Double Precision R(N).
C The residual r = b - Ax.
C R0 :WORK Double Precision R0(N).
C P :DUMMY Double Precision P(N).
C Q :DUMMY Double Precision Q(N).
C U :DUMMY Double Precision U(N).
C V1 :DUMMY Double Precision V1(N).
C Double Precision arrays used for workspace.
C V2 :WORK Double Precision V2(N).
C If ITOL.eq.1 then V2 is used to hold A * X - B on every call.
C If ITOL.eq.2 then V2 is used to hold M-inv * B on the first
C call.
C If ITOL.eq.11 then V2 is used to X - SOLN.
C RWORK :WORK Double Precision RWORK(USER DEFINED).
C Double Precision array that can be used for workspace in
C MSOLVE.
C IWORK :WORK Integer IWORK(USER DEFINED).
C Integer array that can be used for workspace in MSOLVE.
C AK :IN Double Precision.
C Current iterate BiConjugate Gradient iteration parameter.
C BK :IN Double Precision.
C Current iterate BiConjugate Gradient iteration parameter.
C BNRM :INOUT Double Precision.
C Norm of the right hand side. Type of norm depends on ITOL.
C Calculated only on the first call.
C SOLNRM :INOUT Double Precision.
C 2-Norm of the true solution, SOLN. Only computed and used
C if ITOL = 11.
C
C *Function Return Values:
C 0 : Error estimate (determined by ITOL) is *NOT* less than the
C specified tolerance, TOL. The iteration must continue.
C 1 : Error estimate (determined by ITOL) is less than the
C specified tolerance, TOL. The iteration can be considered
C complete.
C
C *Cautions:
C This routine will attempt to write to the Fortran logical output
C unit IUNIT, if IUNIT .ne. 0. Thus, the user must make sure that
C this logical unit is attached to a file or terminal before calling
C this routine with a non-zero value for IUNIT. This routine does
C not check for the validity of a non-zero IUNIT unit number.
C
C***SEE ALSO DCGS
C***ROUTINES CALLED D1MACH, DNRM2
C***COMMON BLOCKS DSLBLK
C***REVISION HISTORY (YYMMDD)
C 890404 DATE WRITTEN
C 890404 Previous REVISION DATE
C 890915 Made changes requested at July 1989 CML Meeting. (MKS)
C 890922 Numerous changes to prologue to make closer to SLATEC
C standard. (FNF)
C 890929 Numerous changes to reduce SP/DP differences. (FNF)
C 891003 Removed C***REFER TO line, per MKS.
C 910411 Prologue converted to Version 4.0 format. (BAB)
C 910502 Removed MATVEC and MSOLVE from ROUTINES CALLED list. (FNF)
C 910506 Made subsidiary to DCGS. (FNF)
C 920407 COMMON BLOCK renamed DSLBLK. (WRB)
C 920511 Added complete declaration section. (WRB)
C 920930 Corrected to not print AK,BK when ITER=0. (FNF)
C 921026 Changed 1.0E10 to D1MACH(2) and corrected D to E in
C output format. (FNF)
C 921113 Corrected C***CATEGORY line. (FNF)
C***END PROLOGUE ISDCGS
C .. Scalar Arguments ..
DOUBLE PRECISION AK, BK, BNRM, ERR, SOLNRM, TOL
INTEGER IERR, ISYM, ITER, ITMAX, ITOL, IUNIT, N, NELT
C .. Array Arguments ..
DOUBLE PRECISION A(NELT), B(N), P(N), Q(N), R(N), R0(N), RWORK(*),
+ U(N), V1(N), V2(N), X(N)
INTEGER IA(NELT), IWORK(*), JA(NELT)
C .. Subroutine Arguments ..
EXTERNAL MATVEC, MSOLVE
C .. Arrays in Common ..
DOUBLE PRECISION SOLN(1)
C .. Local Scalars ..
INTEGER I
C .. External Functions ..
DOUBLE PRECISION D1MACH, DNRM2
EXTERNAL D1MACH, DNRM2
C .. Common blocks ..
COMMON /DSLBLK/ SOLN
C***FIRST EXECUTABLE STATEMENT ISDCGS
ISDCGS = 0
C
IF( ITOL.EQ.1 ) THEN
C err = ||Residual||/||RightHandSide|| (2-Norms).
IF(ITER .EQ. 0) BNRM = DNRM2(N, B, 1)
CALL MATVEC(N, X, V2, NELT, IA, JA, A, ISYM )
DO 5 I = 1, N
V2(I) = V2(I) - B(I)
5 CONTINUE
ERR = DNRM2(N, V2, 1)/BNRM
ELSE IF( ITOL.EQ.2 ) THEN
C -1 -1
C err = ||M Residual||/||M RightHandSide|| (2-Norms).
IF(ITER .EQ. 0) THEN
CALL MSOLVE(N, B, V2, NELT, IA, JA, A, ISYM, RWORK, IWORK)
BNRM = DNRM2(N, V2, 1)
ENDIF
ERR = DNRM2(N, R, 1)/BNRM
ELSE IF( ITOL.EQ.11 ) THEN
C err = ||x-TrueSolution||/||TrueSolution|| (2-Norms).
IF(ITER .EQ. 0) SOLNRM = DNRM2(N, SOLN, 1)
DO 10 I = 1, N
V2(I) = X(I) - SOLN(I)
10 CONTINUE
ERR = DNRM2(N, V2, 1)/SOLNRM
ELSE
C
C If we get here ITOL is not one of the acceptable values.
ERR = D1MACH(2)
IERR = 3
ENDIF
C
C Print the error and Coefficients AK, BK on each step,
C if desired.
IF(IUNIT .NE. 0) THEN
IF( ITER.EQ.0 ) THEN
WRITE(IUNIT,1000) N, ITOL
WRITE(IUNIT,1010) ITER, ERR
ELSE
WRITE(IUNIT,1010) ITER, ERR, AK, BK
ENDIF
ENDIF
IF(ERR .LE. TOL) ISDCGS = 1
C
RETURN
1000 FORMAT(' Preconditioned BiConjugate Gradient Squared for ',
$ 'N, ITOL = ',I5, I5,
$ /' ITER',' Error Estimate',' Alpha',
$ ' Beta')
1010 FORMAT(1X,I4,1X,D16.7,1X,D16.7,1X,D16.7)
C------------- LAST LINE OF ISDCGS FOLLOWS ----------------------------
END