*DECK ISSBCG
INTEGER FUNCTION ISSBCG (N, B, X, NELT, IA, JA, A, ISYM, MSOLVE,
+ ITOL, TOL, ITMAX, ITER, ERR, IERR, IUNIT, R, Z, P, RR, ZZ, PP,
+ DZ, RWORK, IWORK, AK, BK, BNRM, SOLNRM)
C***BEGIN PROLOGUE ISSBCG
C***SUBSIDIARY
C***PURPOSE Preconditioned BiConjugate Gradient Stop Test.
C This routine calculates the stop test for the BiConjugate
C Gradient iteration scheme. It returns a non-zero if the
C error estimate (the type of which is determined by ITOL)
C is less than the user specified tolerance TOL.
C***LIBRARY SLATEC (SLAP)
C***CATEGORY D2A4, D2B4
C***TYPE SINGLE PRECISION (ISSBCG-S, ISDBCG-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 REAL B(N), X(N), A(N), TOL, ERR, R(N), Z(N), P(N)
C REAL RR(N), ZZ(N), PP(N), DZ(N)
C REAL RWORK(USER DEFINED), AK, BK, BNRM, SOLNRM
C EXTERNAL MSOLVE
C
C IF( ISSBCG(N, B, X, NELT, IA, JA, A, ISYM, MSOLVE, ITOL, TOL,
C $ ITMAX, ITER, ERR, IERR, IUNIT, R, Z, P, RR, ZZ, PP, DZ,
C $ 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 Real B(N).
C Right-hand side vector.
C X :INOUT Real 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 Real A(NELT).
C These arrays contain the matrix data structure for A.
C It could take any form. See "Description", in the SLAP
C routine SBCG 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 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 real array that can be used to pass necessary
C preconditioning information and/or workspace to 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 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 is the inverse of the
C diagonal of A.
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 /SSLBLK/ 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 /SSLBLK/ 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 Real.
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 ERR :OUT Real.
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 Real R(N).
C The residual r = b - Ax.
C Z :WORK Real Z(N).
C P :DUMMY Real P(N).
C RR :DUMMY Real RR(N).
C ZZ :DUMMY Real ZZ(N).
C PP :DUMMY Real PP(N).
C Real arrays used for workspace.
C DZ :WORK Real DZ(N).
C If ITOL.eq.0 then DZ is used to hold M-inv * B on the first
C call. If ITOL.eq.11 then DZ is used to hold X-SOLN.
C RWORK :WORK Real RWORK(USER DEFINED).
C Real array that can be used for workspace in MSOLVE
C and MTSOLV.
C IWORK :WORK Integer IWORK(USER DEFINED).
C Integer array that can be used for workspace in MSOLVE
C and MTSOLV.
C AK :IN Real.
C Current iterate BiConjugate Gradient iteration parameter.
C BK :IN Real.
C Current iterate BiConjugate Gradient iteration parameter.
C BNRM :INOUT Real.
C Norm of the right hand side. Type of norm depends on ITOL.
C Calculated only on the first call.
C SOLNRM :INOUT Real.
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 SBCG
C***ROUTINES CALLED R1MACH, SNRM2
C***COMMON BLOCKS SSLBLK
C***REVISION HISTORY (YYMMDD)
C 871119 DATE WRITTEN
C 881213 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 MSOLVE from ROUTINES CALLED list. (FNF)
C 910506 Made subsidiary to SBCG. (FNF)
C 920407 COMMON BLOCK renamed SSLBLK. (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 R1MACH(2). (FNF)
C 921113 Corrected C***CATEGORY line. (FNF)
C***END PROLOGUE ISSBCG
C .. Scalar Arguments ..
REAL AK, BK, BNRM, ERR, SOLNRM, TOL
INTEGER IERR, ISYM, ITER, ITMAX, ITOL, IUNIT, N, NELT
C .. Array Arguments ..
REAL A(NELT), B(N), DZ(N), P(N), PP(N), R(N), RR(N), RWORK(*),
+ X(N), Z(N), ZZ(N)
INTEGER IA(NELT), IWORK(*), JA(NELT)
C .. Subroutine Arguments ..
EXTERNAL MSOLVE
C .. Arrays in Common ..
REAL SOLN(1)
C .. Local Scalars ..
INTEGER I
C .. External Functions ..
REAL R1MACH, SNRM2
EXTERNAL R1MACH, SNRM2
C .. Common blocks ..
COMMON /SSLBLK/ SOLN
C***FIRST EXECUTABLE STATEMENT ISSBCG
ISSBCG = 0
C
IF( ITOL.EQ.1 ) THEN
C err = ||Residual||/||RightHandSide|| (2-Norms).
IF(ITER .EQ. 0) BNRM = SNRM2(N, B, 1)
ERR = SNRM2(N, R, 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, DZ, NELT, IA, JA, A, ISYM, RWORK, IWORK)
BNRM = SNRM2(N, DZ, 1)
ENDIF
ERR = SNRM2(N, Z, 1)/BNRM
ELSE IF( ITOL.EQ.11 ) THEN
C err = ||x-TrueSolution||/||TrueSolution|| (2-Norms).
IF(ITER .EQ. 0) SOLNRM = SNRM2(N, SOLN, 1)
DO 10 I = 1, N
DZ(I) = X(I) - SOLN(I)
10 CONTINUE
ERR = SNRM2(N, DZ, 1)/SOLNRM
ELSE
C
C If we get here ITOL is not one of the acceptable values.
ERR = R1MACH(2)
IERR = 3
ENDIF
C
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) ISSBCG = 1
C
RETURN
1000 FORMAT(' Preconditioned BiConjugate Gradient for N, ITOL = ',
$ I5,I5,/' ITER',' Error Estimate',' Alpha',
$ ' Beta')
1010 FORMAT(1X,I4,1X,E16.7,1X,E16.7,1X,E16.7)
C------------- LAST LINE OF ISSBCG FOLLOWS ----------------------------
END