# isdomn.f

          INTEGER FUNCTION ISDOMN (N, B, X, NELT, IA, JA, A, ISYM, MSOLVE,
         +   NSAVE, ITOL, TOL, ITMAX, ITER, ERR, IERR, IUNIT, R, Z, P, AP,
         +   EMAP, DZ, CSAV, RWORK, IWORK, AK, BNRM, SOLNRM)
    C***BEGIN PROLOGUE  ISDOMN
    ....
    ....
    Warning:   this routine is not intended to be user-callable.
    ....
    ....
    C***SUBSIDIARY
    C***PURPOSE  Preconditioned Orthomin Stop Test.
    C            This routine calculates the stop test for the Orthomin
    C            iteration scheme.  It returns a non-zero if the error
    C            estimate (the type of which is determined by ITOL) is
    C            less than the user specified tolerance TOL.
    C***LIBRARY   SLATEC (SLAP)
    C***CATEGORY  D2A4, D2B4
    C***TYPE      DOUBLE PRECISION (ISSOMN-S, ISDOMN-D)
    C***KEYWORDS  ITERATIVE PRECONDITION, NON-SYMMETRIC LINEAR SYSTEM,
    C             ORTHOMIN, SLAP, 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, NSAVE, ITOL, ITMAX
    C     INTEGER  ITER, IERR, IUNIT, IWORK(USER DEFINED)
    C     DOUBLE PRECISION B(N), X(N), A(NELT), TOL, ERR, R(N), Z(N)
    C     DOUBLE PRECISION P(N,0:NSAVE), AP(N,0:NSAVE), EMAP(N,0:NSAVE)
    C     DOUBLE PRECISION DZ(N), CSAV(NSAVE), RWORK(USER DEFINED), AK
    C     DOUBLE PRECISION BNRM, SOLNRM
    C     EXTERNAL MSOLVE
    C
    C     IF( ISDOMN(N, B, X, NELT, IA, JA, A, ISYM, MSOLVE, NSAVE,
    C    $     ITOL, TOL, ITMAX, ITER, ERR, IERR, IUNIT, R, Z, P, AP,
    C    $     EMAP, DZ, CSAV, RWORK, IWORK, AK, BNRM, SOLNRM)
    C    $     .NE.0 ) THEN ITERATION CONVERGED
    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      :IN       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 should hold the matrix A in either the SLAP
    C         Triad format or the SLAP Column format.  See "Description"
    C         in the DSDOMN or DSLUOM prologue.
    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
    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 double precision array
    C         that can be used to pass necessary preconditioning information
    C         and/or workspace to MSOLVE.  IWORK is an integer work array
    C         for the same purpose as RWORK.
    C NSAVE  :IN       Integer.
    C         Number of direction vectors to save and orthogonalize against.
    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 /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 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 Z      :WORK     Double Precision Z(N).
    C P      :IN       Double Precision P(N,0:NSAVE).
    C         Workspace used to hold the conjugate direction vector(s).
    C AP     :IN       Double Precision AP(N,0:NSAVE).
    C         Workspace used to hold the matrix A times the P vector(s).
    C EMAP   :IN       Double Precision EMAP(N,0:NSAVE).
    C         Workspace used to hold M-inv times the AP vector(s).
    C DZ     :WORK     Double Precision DZ(N).
    C         Workspace.
    C CSAV   :DUMMY    Double Precision CSAV(NSAVE)
    C         Reserved for future use.
    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 Orthomin iteration parameter.
    C BNRM   :OUT      Double Precision.
    C         Current solution B-norm, if ITOL = 1 or 2.
    C SOLNRM :OUT      Double Precision.
    C         True solution norm, 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  DOMN, DSDOMN, DSLUOM
    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 MSOLVE from ROUTINES CALLED list.  (FNF)
    C   910506  Made subsidiary to DOMN.  (FNF)
    C   920407  COMMON BLOCK renamed DSLBLK.  (WRB)
    C   920511  Added complete declaration section.  (WRB)
    C   920930  Corrected to not print AK 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  ISDOMN