relibc_openlibm/slatec/isscgs.f

*DECK ISSCGS
      INTEGER FUNCTION ISSCGS (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  ISSCGS
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      SINGLE 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     REAL     B(N), X(N), A(N), TOL, ERR, R(N), R0(N), P(N)
C     REAL     Q(N), U(N), V1(N), V2(N)
C     REAL     RWORK(USER DEFINED), AK, BK, BNRM, SOLNRM
C     EXTERNAL MATVEC, MSOLVE
C
C     IF( ISSCGS(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       Real B(N).
C         Right-hand side vector.
C X      :INOUT    Real 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       Real A(NELT).
C         These arrays contain the matrix data structure for A.
C         It could take any form.  See "Description" in SLAP routine
C         SCGS 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 real array that can be used to pass necessary
C         preconditioning information and/or workspace to 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 /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 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       Real R(N).
C         The residual r = b - Ax.
C R0     :WORK     Real R0(N).
C P      :DUMMY    Real P(N).
C Q      :DUMMY    Real Q(N).
C U      :DUMMY    Real U(N).
C V1     :DUMMY    Real V1(N).
C         Real arrays used for workspace.
C V2     :WORK     Real 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     Real RWORK(USER DEFINED).
C         Real array that can be used for workspace in MSOLVE.
C IWORK  :WORK     Integer IWORK(USER DEFINED).
C         Integer array that can be used for workspace in MSOLVE.
C AK     :IN       Real.
C         Current iterate BiConjugate Gradient iteration parameter.
C BK     :IN       Real.
C         Current iterate BiConjugate Gradient iteration parameter.
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  SCGS
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 and MSOLVE from ROUTINES CALLED list.  (FNF)
C   910506  Made subsidiary to SCGS.  (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  ISSCGS
C     .. Scalar Arguments ..
      REAL AK, BK, BNRM, ERR, SOLNRM, TOL
      INTEGER IERR, ISYM, ITER, ITMAX, ITOL, IUNIT, N, NELT
C     .. Array Arguments ..
      REAL A(NELT), B(N), P(N), Q(N), R(N), R0(N), RWORK(*), U(N),
     +     V1(N), V2(N), X(N)
      INTEGER IA(NELT), IWORK(*), JA(NELT)
C     .. Subroutine Arguments ..
      EXTERNAL MATVEC, MSOLVE
C     .. Arrays in Common ..
      REAL SOLN(1)
C     .. Local Scalars ..
      INTEGER I
C     .. External Functions ..
      REAL R1MACH, SNRM2
      EXTERNAL R1MACH, SNRM2
C     .. Common blocks ..
      COMMON /SSLBLK/ SOLN
C***FIRST EXECUTABLE STATEMENT  ISSCGS
      ISSCGS = 0
C
      IF( ITOL.EQ.1 ) THEN
C         err = ||Residual||/||RightHandSide|| (2-Norms).
         IF(ITER .EQ. 0) BNRM = SNRM2(N, B, 1)
         CALL MATVEC(N, X, V2, NELT, IA, JA, A, ISYM )
         DO 5 I = 1, N
            V2(I) = V2(I) - B(I)
 5       CONTINUE
         ERR = SNRM2(N, V2, 1)/BNRM
      ELSE IF( ITOL.EQ.2 ) THEN
C                  -1              -1
C         err = ||M  Residual||/||M  RightHandSide|| (2-Norms).
         IF(ITER .EQ. 0) THEN
            CALL MSOLVE(N, B, V2, NELT, IA, JA, A, ISYM, RWORK, IWORK)
            BNRM = SNRM2(N, V2, 1)
         ENDIF
         ERR = SNRM2(N, R, 1)/BNRM
      ELSE IF( ITOL.EQ.11 ) THEN
C         err = ||x-TrueSolution||/||TrueSolution|| (2-Norms).
         IF(ITER .EQ. 0) SOLNRM = SNRM2(N, SOLN, 1)
         DO 10 I = 1, N
            V2(I) = X(I) - SOLN(I)
 10      CONTINUE
         ERR = SNRM2(N, V2, 1)/SOLNRM
      ELSE
C
C         If we get here ITOL is not one of the acceptable values.
         ERR = R1MACH(2)
         IERR = 3
      ENDIF
C
C         Print the error and coefficients AK, BK on each step,
C         if desired.
      IF(IUNIT .NE. 0) THEN
         IF( ITER.EQ.0 ) THEN
            WRITE(IUNIT,1000) N, ITOL
            WRITE(IUNIT,1010) ITER, ERR
         ELSE
            WRITE(IUNIT,1010) ITER, ERR, AK, BK
         ENDIF
      ENDIF
      IF(ERR .LE. TOL) ISSCGS = 1
C
      RETURN
 1000 FORMAT(' Preconditioned BiConjugate Gradient Squared for ',
     $     'N, ITOL = ',I5, I5,
     $     /' ITER','   Error Estimate','            Alpha',
     $     '             Beta')
 1010 FORMAT(1X,I4,1X,E16.7,1X,E16.7,1X,E16.7)
C------------- LAST LINE OF ISSCGS FOLLOWS ----------------------------
      END