*DECK ISSCGN INTEGER FUNCTION ISSCGN (N, B, X, NELT, IA, JA, A, ISYM, MATVEC, + MTTVEC, MSOLVE, ITOL, TOL, ITMAX, ITER, ERR, IERR, IUNIT, R, Z, + P, ATP, ATZ, DZ, ATDZ, RWORK, IWORK, AK, BK, BNRM, SOLNRM) C***BEGIN PROLOGUE ISSCGN C***SUBSIDIARY C***PURPOSE Preconditioned CG on Normal Equations Stop Test. C This routine calculates the stop test for the Conjugate C Gradient iteration scheme applied to the normal equations. C It returns a non-zero if the error estimate (the type of C which is determined by ITOL) is less than the user C specified tolerance TOL. C***LIBRARY SLATEC (SLAP) C***CATEGORY D2A4, D2B4 C***TYPE SINGLE PRECISION (ISSCGN-S, ISDCGN-D) C***KEYWORDS ITERATIVE PRECONDITION, NON-SYMMETRIC LINEAR SYSTEM, C NORMAL EQUATIONS, SLAP, SPARSE 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 ATP(N), ATZ(N), DZ(N), ATDZ(N) C REAL RWORK(USER DEFINED), AK, BK, BNRM, SOLNRM C EXTERNAL MATVEC, MTTVEC, MSOLVE C C IF( ISTPCGN(N, B, X, NELT, IA, JA, A, ISYM, MATVEC, MTTVEC, C $ MSOLVE, ITOL, TOL, ITMAX, ITER, ERR, IERR, IUNIT, R, Z, P, C $ ATP, ATZ, DZ, ATDZ, RWORK, IWORK, AK, BK, BNRM, SOLNRM) C $ .NE. 0 ) 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 :IN Real X(N). C The current approximate solution vector. 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 C SCGN routine. 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 Y = A*X given A and X. The name of the MATVEC routine must C be declared external in the calling program. The calling C sequence to 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 C upon return X is an input vector, NELT is the number of C non-zeros in the SLAP-Column IA, JA, A storage for the matrix C A. ISYM is a flag which, if non-zero, denotes that A is C symmetric and only the lower or upper triangle is stored. C MTTVEC :EXT External. C Name of a routine which performs the matrix transpose vector C multiply y = A'*X given A and X (where ' denotes transpose). C The name of the MTTVEC routine must be declared external in C the calling program. The calling sequence to MTTVEC is the C same as that for MATVEC, viz.: C CALL MTTVEC( N, X, Y, NELT, IA, JA, A, ISYM ) C Where N is the number of unknowns, Y is the product A'*X C upon return X is an input vector, NELT is the number of C non-zeros in the SLAP-Column IA, JA, A storage for the matrix C A. ISYM is a flag which, if non-zero, denotes that A is C symmetric and only the lower or upper triangle is stored. C MSOLVE :EXT External. C Name of a routine which solves a linear system MZ = R for C Z given R with the preconditioning matrix M (M is supplied via C RWORK and IWORK arrays). The name of the MSOLVE routine must C be declared external in the calling program. The calling C sequence to 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 and C ISYM are defined as above. RWORK is a real array that can C be used to pass necessary preconditioning information and/or C workspace to MSOLVE. IWORK is an integer work array for C 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 the X(N) 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 Real array used for workspace. C P :IN Real P(N). C The conjugate direction vector. C ATP :IN Real ATP(N). C A-transpose times the conjugate direction vector. C ATZ :IN Real ATZ(N). C A-transpose times the pseudo-residual. C DZ :IN Real DZ(N). C Workspace used to hold temporary vector(s). C ATDZ :WORK Real ATDZ(N). C Workspace. C RWORK :WORK Real RWORK(USER DEFINED). C Real array that can be used by MSOLVE. C IWORK :WORK Integer IWORK(USER DEFINED). C Integer array that can be used by MSOLVE. C AK :IN Real. C BK :IN Real. C Current conjugate gradient parameters alpha and beta. 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 SCGN 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 MATVEC, MTTVEC and MSOLVE from ROUTINES CALLED C list. (FNF) C 910506 Made subsidiary to SCGN. (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 ISSCGN