ISSBCG(3)

SYNOPSIS
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)

NAME
issbcg - Preconditioned BiConjugate Gradient Stop Test. This routine calculates the stop test for the BiConjugate Gradient iteration scheme. It returns a non-zero if the error estimate (the type of which is determined by ITOL) is less than the user specified tolerance TOL.

LIBRARY
SLATEC (SLAP)

CATEGORY
D2A4, D2B4

TYPE
SINGLE PRECISION (ISSBCG-S, ISDBCG-D)

KEYWORDS
ITERATIVE PRECONDITION, NON-SYMMETRIC LINEAR SYSTEM, SLAP, SPARSE, STOP TEST

AUTHOR
Greenbaum, Anne, (Courant Institute) Seager, Mark K., (LLNL) Lawrence Livermore National Laboratory PO BOX 808, L-60 Livermore, CA 94550 (510) 423-3141 seager@llnl.gov

DESCRIPTION
*Usage: INTEGER N, NELT, IA(NELT), JA(NELT), ISYM, ITOL, ITMAX, ITER INTEGER IERR, IUNIT, IWORK(USER DEFINED) REAL B(N), X(N), A(N), TOL, ERR, R(N), Z(N), P(N) REAL RR(N), ZZ(N), PP(N), DZ(N) REAL RWORK(USER DEFINED), AK, BK, BNRM, SOLNRM EXTERNAL MSOLVE IF( 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) .NE. 0 ) $ THEN ITERATION DONE *Arguments: N :IN Integer Order of the Matrix. B :IN Real B(N). Right-hand side vector. X :INOUT Real X(N). On input X is your initial guess for solution vector. On output X is the final approximate solution. NELT :IN Integer. Number of Non-Zeros stored in A. IA :IN Integer IA(NELT). JA :IN Integer JA(NELT). A :IN Real A(NELT). These arrays contain the matrix data structure for A. It could take any form. See "Description", in the SLAP routine SBCG for more details. ISYM :IN Integer. Flag to indicate symmetric storage format. If ISYM=0, all non-zero entries of the matrix are stored. If ISYM=1, the matrix is symmetric, and only the upper or lower triangle of the matrix is stored. MSOLVE :EXT External. Name of a routine which solves a linear system MZ = R for Z given R with the preconditioning matrix M (M is supplied via RWORK and IWORK arrays). The name of the MSOLVE routine must be declared external in the calling program. The calling sequence of MSOLVE is: CALL MSOLVE(N, R, Z, NELT, IA, JA, A, ISYM, RWORK, IWORK) Where N is the number of unknowns, R is the right-hand side vector, and Z is the solution upon return. NELT, IA, JA, A, and ISYM define the SLAP matrix data structure. RWORK is a real array that can be used to pass necessary preconditioning information and/or workspace to MSOLVE. IWORK is an integer work array for the same purpose as RWORK. ITOL :IN Integer. Flag to indicate type of convergence criterion. If ITOL=1, iteration stops when the 2-norm of the residual divided by the 2-norm of the right-hand side is less than TOL. If ITOL=2, iteration stops when the 2-norm of M-inv times the residual divided by the 2-norm of M-inv times the right hand side is less than TOL, where M-inv is the inverse of the diagonal of A. ITOL=11 is often useful for checking and comparing different routines. For this case, the user must supply the "exact" solution or a very accurate approximation (one with an error much less than TOL) through a common block, COMMON /SSLBLK/ SOLN( ) If ITOL=11, iteration stops when the 2-norm of the difference between the iterative approximation and the user-supplied solution divided by the 2-norm of the user-supplied solution is less than TOL. Note that this requires the user to set up the "COMMON /SSLBLK/ SOLN(LENGTH)" in the calling routine. The routine with this declaration should be loaded before the stop test so that the correct length is used by the loader. This procedure is not standard Fortran and may not work correctly on your system (although it has worked on every system the authors have tried). If ITOL is not 11 then this common block is indeed standard Fortran. TOL :IN Real. Convergence criterion, as described above. ITMAX :IN Integer. Maximum number of iterations. ITER :IN Integer. Current iteration count. (Must be zero on first call.) ERR :OUT Real. Error estimate of error in final approximate solution, as defined by ITOL. IERR :OUT Integer. Error flag. IERR is set to 3 if ITOL is not one of the acceptable values, see above. IUNIT :IN Integer. Unit number on which to write the error at each iteration, if this is desired for monitoring convergence. If unit number is 0, no writing will occur. R :IN Real R(N). The residual r = b - Ax. Z :WORK Real Z(N). P :DUMMY Real P(N). RR :DUMMY Real RR(N). ZZ :DUMMY Real ZZ(N). PP :DUMMY Real PP(N). Real arrays used for workspace. DZ :WORK Real DZ(N). If ITOL.eq.0 then DZ is used to hold M-inv * B on the first call. If ITOL.eq.11 then DZ is used to hold X-SOLN. RWORK :WORK Real RWORK(USER DEFINED). Real array that can be used for workspace in MSOLVE and MTSOLV. IWORK :WORK Integer IWORK(USER DEFINED). Integer array that can be used for workspace in MSOLVE and MTSOLV. AK :IN Real. Current iterate BiConjugate Gradient iteration parameter. BK :IN Real. Current iterate BiConjugate Gradient iteration parameter. BNRM :INOUT Real. Norm of the right hand side. Type of norm depends on ITOL. Calculated only on the first call. SOLNRM :INOUT Real. 2-Norm of the true solution, SOLN. Only computed and used if ITOL = 11. *Function Return Values: 0 : Error estimate (determined by ITOL) is *NOT* less than the specified tolerance, TOL. The iteration must continue. 1 : Error estimate (determined by ITOL) is less than the specified tolerance, TOL. The iteration can be considered complete. *Cautions: This routine will attempt to write to the Fortran logical output unit IUNIT, if IUNIT .ne. 0. Thus, the user must make sure that this logical unit is attached to a file or terminal before calling this routine with a non-zero value for IUNIT. This routine does not check for the validity of a non-zero IUNIT unit number.

SEE ALSO
SBCG

ROUTINES CALLED
R1MACH, SNRM2

COMMON BLOCKS
SSLBLK

REVISION HISTORY (YYMMDD)
871119 DATE WRITTEN
881213 Previous REVISION DATE
890915 Made changes requested at July 1989 CML Meeting. (MKS)
890922 Numerous changes to prologue to make closer to SLATEC standard. (FNF)
890929 Numerous changes to reduce SP/DP differences. (FNF)
891003 Removed C***REFER TO line, per MKS.
910411 Prologue converted to Version 4.0 format. (BAB)
910502 Removed MSOLVE from ROUTINES CALLED list. (FNF)
910506 Made subsidiary to SBCG. (FNF)
920407 COMMON BLOCK renamed SSLBLK. (WRB)
920511 Added complete declaration section. (WRB)
920930 Corrected to not print AK,BK when ITER=0. (FNF)
921026 Changed 1.0E10 to R1MACH(2). (FNF)
921113 Corrected C***CATEGORY line. (FNF)