*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