ISDCGN(3)

SYNOPSIS
INTEGER FUNCTION ISDCGN (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)

NAME
isdcgn - Preconditioned CG on Normal Equations Stop Test. This routine calculates the stop test for the Conjugate Gradient iteration scheme applied to the normal equations. 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
DOUBLE PRECISION (ISSCGN-S, ISDCGN-D)

KEYWORDS
ITERATIVE PRECONDITION, NON-SYMMETRIC LINEAR SYSTEM, NORMAL EQUATIONS, SLAP, SPARSE

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) DOUBLE PRECISION B(N), X(N), A(N), TOL, ERR, R(N), Z(N), P(N) DOUBLE PRECISION ATP(N), ATZ(N), DZ(N), ATDZ(N) DOUBLE PRECISION RWORK(USER DEFINED), AK, BK, BNRM, SOLNRM EXTERNAL MATVEC, MTTVEC, MSOLVE IF( ISTPCGN(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) $ .NE. 0 ) THEN ITERATION DONE *Arguments: N :IN Integer Order of the Matrix. B :IN Double Precision B(N). Right-hand side vector. X :IN Double Precision X(N). The current approximate solution vector. NELT :IN Integer. Number of Non-Zeros stored in A. IA :IN Integer IA(NELT). JA :IN Integer JA(NELT). A :IN Double Precision A(NELT). These arrays contain the matrix data structure for A. It could take any form. See "Description" in the DCGN routine. 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. MATVEC :EXT External. Name of a routine which performs the matrix vector multiply Y = A*X given A and X. The name of the MATVEC routine must be declared external in the calling program. The calling sequence to MATVEC is: CALL MATVEC( N, X, Y, NELT, IA, JA, A, ISYM ) Where N is the number of unknowns, Y is the product A*X upon return X is an input vector, NELT is the number of non-zeros in the SLAP-Column IA, JA, A storage for the matrix A. ISYM is a flag which, if non-zero, denotes that A is symmetric and only the lower or upper triangle is stored. MTTVEC :EXT External. Name of a routine which performs the matrix transpose vector multiply y = A'*X given A and X (where ' denotes transpose). The name of the MTTVEC routine must be declared external in the calling program. The calling sequence to MTTVEC is the same as that for MATVEC, viz.: CALL MTTVEC( N, X, Y, NELT, IA, JA, A, ISYM ) Where N is the number of unknowns, Y is the product A'*X upon return X is an input vector, NELT is the number of non-zeros in the SLAP-Column IA, JA, A storage for the matrix A. ISYM is a flag which, if non-zero, denotes that A is symmetric and only the lower or upper triangle 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 to 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 are defined as above. RWORK is a double precision 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 /DSLBLK/ 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 /DSLBLK/ 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 Double Precision. 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 Double Precision. Error estimate of error in the X(N) 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 Double Precision R(N). The residual R = B-AX. Z :WORK Double Precision Z(N). Double Precision array used for workspace. P :IN Double Precision P(N). The conjugate direction vector. ATP :IN Double Precision ATP(N). A-transpose times the conjugate direction vector. ATZ :IN Double Precision ATZ(N). A-transpose times the pseudo-residual. DZ :IN Double Precision DZ(N). Workspace used to hold temporary vector(s). ATDZ :WORK Double Precision ATDZ(N). Workspace. RWORK :WORK Double Precision RWORK(USER DEFINED). Double Precision array that can be used by MSOLVE. IWORK :WORK Integer IWORK(USER DEFINED). Integer array that can be used by MSOLVE. AK :IN Double Precision. BK :IN Double Precision. Current conjugate gradient parameters alpha and beta. BNRM :INOUT Double Precision. Norm of the right hand side. Type of norm depends on ITOL. Calculated only on the first call. SOLNRM :INOUT Double Precision. 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
DCGN

ROUTINES CALLED
D1MACH, DNRM2

COMMON BLOCKS
DSLBLK

REVISION HISTORY (YYMMDD)
890404 DATE WRITTEN
890404 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 MATVEC, MTTVEC and MSOLVE from ROUTINES CALLED list. (FNF)
910506 Made subsidiary to DCGN. (FNF)
920407 COMMON BLOCK renamed DSLBLK. (WRB)
920511 Added complete declaration section. (WRB)
920930 Corrected to not print AK,BK when ITER=0. (FNF)
921026 Changed 1.0E10 to D1MACH(2) and corrected D to E in output format. (FNF)
921113 Corrected C***CATEGORY line. (FNF)