# issgmr.f

          INTEGER FUNCTION ISSGMR (N, B, X, XL, NELT, IA, JA, A, ISYM,
         +   MSOLVE, NMSL, ITOL, TOL, ITMAX, ITER, ERR, IUNIT, R, Z, DZ,
         +   RWORK, IWORK, RNRM, BNRM, SB, SX, JSCAL, KMP, LGMR, MAXL,
         +   MAXLP1, V, Q, SNORMW, PROD, R0NRM, HES, JPRE)
    C***BEGIN PROLOGUE  ISSGMR
    ....
    ....
    Warning:   this routine is not intended to be user-callable.
    ....
    ....
    C***SUBSIDIARY
    C***PURPOSE  Generalized Minimum Residual Stop Test.
    C            This routine calculates the stop test for the Generalized
    C            Minimum RESidual (GMRES) iteration scheme.  It returns a
    C            non-zero if the error estimate (the type of which is
    C            determined by ITOL) is less than the user specified
    C            tolerance TOL.
    C***LIBRARY   SLATEC (SLAP)
    C***CATEGORY  D2A4, D2B4
    C***TYPE      SINGLE PRECISION (ISSGMR-S, ISDGMR-D)
    C***KEYWORDS  GMRES, LINEAR SYSTEM, SLAP, SPARSE, STOP TEST
    C***AUTHOR  Brown, Peter, (LLNL), pnbrown@llnl.gov
    C           Hindmarsh, Alan, (LLNL), alanh@llnl.gov
    C           Seager, Mark K., (LLNL), seager@llnl.gov
    C             Lawrence Livermore National Laboratory
    C             PO Box 808, L-60
    C             Livermore, CA 94550 (510) 423-3141
    C***DESCRIPTION
    C
    C *Usage:
    C      INTEGER N, NELT, IA(NELT), JA(NELT), ISYM, NMSL, ITOL
    C      INTEGER ITMAX, ITER, IUNIT, IWORK(USER DEFINED), JSCAL
    C      INTEGER KMP, LGMR, MAXL, MAXLP1, JPRE
    C      REAL B(N), X(N), XL(MAXL), A(NELT), TOL, ERR, R(N), Z(N),
    C     $     DZ(N), RWORK(USER DEFINED), RNRM, BNRM, SB(N), SX(N),
    C     $     V(N,MAXLP1), Q(2*MAXL), SNORMW, PROD, R0NRM,
    C     $     HES(MAXLP1,MAXL)
    C      EXTERNAL MSOLVE
    C
    C      IF (ISSGMR(N, B, X, XL, NELT, IA, JA, A, ISYM, MSOLVE,
    C     $     NMSL, ITOL, TOL, ITMAX, ITER, ERR, IUNIT, R, Z, DZ,
    C     $     RWORK, IWORK, RNRM, BNRM, SB, SX, JSCAL,
    C     $     KMP, LGMR, MAXL, MAXLP1, V, Q, SNORMW, PROD, R0NRM,
    C     $     HES, JPRE) .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         Approximate solution vector as of the last restart.
    C XL     :OUT      Real XL(N)
    C         An array of length N used to hold the approximate
    C         solution as of the current iteration.  Only computed by
    C         this routine when ITOL=11.
    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 SGMRES,
    C         SSLUGM and SSDGMR routines 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 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 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 NMSL   :INOUT    Integer.
    C         A counter for the number of calls to MSOLVE.
    C ITOL   :IN       Integer.
    C         Flag to indicate the type of convergence criterion used.
    C         ITOL=0  Means the  iteration stops when the test described
    C                 below on  the  residual RL  is satisfied.  This is
    C                 the  "Natural Stopping Criteria" for this routine.
    C                 Other values  of   ITOL  cause  extra,   otherwise
    C                 unnecessary, computation per iteration and     are
    C                 therefore much less efficient.
    C         ITOL=1  Means   the  iteration stops   when the first test
    C                 described below on  the residual RL  is satisfied,
    C                 and there  is either right  or  no preconditioning
    C                 being used.
    C         ITOL=2  Implies     that   the  user    is   using    left
    C                 preconditioning, and the second stopping criterion
    C                 below is used.
    C         ITOL=3  Means the  iteration stops   when  the  third test
    C                 described below on Minv*Residual is satisfied, and
    C                 there is either left  or no  preconditioning begin
    C                 used.
    C         ITOL=11 is    often  useful  for   checking  and comparing
    C                 different routines.  For this case, the  user must
    C                 supply  the  "exact" solution or  a  very accurate
    C                 approximation (one with  an  error much less  than
    C                 TOL) through a common block,
    C                     COMMON /SSLBLK/ SOLN( )
    C                 If ITOL=11, iteration stops when the 2-norm of the
    C                 difference between the iterative approximation and
    C                 the user-supplied solution  divided by the  2-norm
    C                 of the  user-supplied solution  is  less than TOL.
    C                 Note that this requires  the  user to  set up  the
    C                 "COMMON     /SSLBLK/ SOLN(LENGTH)"  in the calling
    C                 routine.  The routine with this declaration should
    C                 be loaded before the stop test so that the correct
    C                 length is used by  the loader.  This procedure  is
    C                 not standard Fortran and may not work correctly on
    C                 your   system (although  it  has  worked  on every
    C                 system the authors have tried).  If ITOL is not 11
    C                 then this 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         The iteration for which to check for convergence.
    C ERR    :OUT      Real.
    C         Error estimate of error in final approximate solution, as
    C         defined by ITOL.  Letting norm() denote the Euclidean
    C         norm, ERR is defined as follows..
    C
    C         If ITOL=0, then ERR = norm(SB*(B-A*X(L)))/norm(SB*B),
    C                               for right or no preconditioning, and
    C                         ERR = norm(SB*(M-inverse)*(B-A*X(L)))/
    C                                norm(SB*(M-inverse)*B),
    C                               for left preconditioning.
    C         If ITOL=1, then ERR = norm(SB*(B-A*X(L)))/norm(SB*B),
    C                               since right or no preconditioning
    C                               being used.
    C         If ITOL=2, then ERR = norm(SB*(M-inverse)*(B-A*X(L)))/
    C                                norm(SB*(M-inverse)*B),
    C                               since left preconditioning is being
    C                               used.
    C         If ITOL=3, then ERR =  Max  |(Minv*(B-A*X(L)))(i)/x(i)|
    C                               i=1,n
    C         If ITOL=11, then ERR = norm(SB*(X(L)-SOLN))/norm(SB*SOLN).
    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      :INOUT    Real R(N).
    C         Work array used in calling routine.  It contains
    C         information necessary to compute the residual RL = B-A*XL.
    C Z      :WORK     Real Z(N).
    C         Workspace used to hold the pseudo-residual M z = r.
    C DZ     :WORK     Real DZ(N).
    C         Workspace used to hold temporary vector(s).
    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 RNRM   :IN       Real.
    C         Norm of the current residual.  Type of norm depends on ITOL.
    C BNRM   :IN       Real.
    C         Norm of the right hand side.  Type of norm depends on ITOL.
    C SB     :IN       Real SB(N).
    C         Scaling vector for B.
    C SX     :IN       Real SX(N).
    C         Scaling vector for X.
    C JSCAL  :IN       Integer.
    C         Flag indicating if scaling arrays SB and SX are being
    C         used in the calling routine SPIGMR.
    C         JSCAL=0 means SB and SX are not used and the
    C                 algorithm will perform as if all
    C                 SB(i) = 1 and SX(i) = 1.
    C         JSCAL=1 means only SX is used, and the algorithm
    C                 performs as if all SB(i) = 1.
    C         JSCAL=2 means only SB is used, and the algorithm
    C                 performs as if all SX(i) = 1.
    C         JSCAL=3 means both SB and SX are used.
    C KMP    :IN       Integer
    C         The number of previous vectors the new vector VNEW
    C         must be made orthogonal to.  (KMP .le. MAXL)
    C LGMR   :IN       Integer
    C         The number of GMRES iterations performed on the current call
    C         to SPIGMR (i.e., # iterations since the last restart) and
    C         the current order of the upper Hessenberg
    C         matrix HES.
    C MAXL   :IN       Integer
    C         The maximum allowable order of the matrix H.
    C MAXLP1 :IN       Integer
    C         MAXPL1 = MAXL + 1, used for dynamic dimensioning of HES.
    C V      :IN       Real V(N,MAXLP1)
    C         The N by (LGMR+1) array containing the LGMR
    C         orthogonal vectors V(*,1) to V(*,LGMR).
    C Q      :IN       Real Q(2*MAXL)
    C         A real array of length 2*MAXL containing the components
    C         of the Givens rotations used in the QR decomposition
    C         of HES.
    C SNORMW :IN       Real
    C         A scalar containing the scaled norm of VNEW before it
    C         is renormalized in SPIGMR.
    C PROD   :IN       Real
    C         The product s1*s2*...*sl = the product of the sines of the
    C         Givens rotations used in the QR factorization of the
    C         Hessenberg matrix HES.
    C R0NRM  :IN       Real
    C         The scaled norm of initial residual R0.
    C HES    :IN       Real HES(MAXLP1,MAXL)
    C         The upper triangular factor of the QR decomposition
    C         of the (LGMR+1) by LGMR upper Hessenberg matrix whose
    C         entries are the scaled inner-products of A*V(*,I)
    C         and V(*,K).
    C JPRE   :IN       Integer
    C         Preconditioner type flag.
    C         (See description of IGWK(4) in SGMRES.)
    C
    C *Description
    C       When using the GMRES solver,  the preferred value  for ITOL
    C       is 0.  This is due to the fact that when ITOL=0 the norm of
    C       the residual required in the stopping test is  obtained for
    C       free, since this value is already  calculated  in the GMRES
    C       algorithm.   The  variable  RNRM contains the   appropriate
    C       norm, which is equal to norm(SB*(RL - A*XL))  when right or
    C       no   preconditioning is  being  performed,   and equal   to
    C       norm(SB*Minv*(RL - A*XL))  when using left preconditioning.
    C       Here, norm() is the Euclidean norm.  Nonzero values of ITOL
    C       require  additional work  to  calculate the  actual  scaled
    C       residual  or its scaled/preconditioned  form,  and/or   the
    C       approximate solution XL.  Hence, these values of  ITOL will
    C       not be as efficient as ITOL=0.
    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     This routine does not verify that ITOL has a valid value.
    C     The calling routine should make such a test before calling
    C     ISSGMR, as is done in SGMRES.
    C
    C***SEE ALSO  SGMRES
    C***ROUTINES CALLED  R1MACH, SCOPY, SNRM2, SRLCAL, SSCAL, SXLCAL
    C***COMMON BLOCKS    SSLBLK
    C***REVISION HISTORY  (YYMMDD)
    C   871211  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   910411  Prologue converted to Version 4.0 format.  (BAB)
    C   910502  Corrected conversion errors, etc.  (FNF)
    C   910502  Removed MSOLVE from ROUTINES CALLED list.  (FNF)
    C   910506  Made subsidiary to SGMRES.  (FNF)
    C   920407  COMMON BLOCK renamed SSLBLK.  (WRB)
    C   920511  Added complete declaration section.  (WRB)
    C   921113  Corrected C***CATEGORY line.  (FNF)
    C***END PROLOGUE  ISSGMR