relibc_openlibm/slatec/isdcgn.f

*DECK ISDCGN
      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)
C***BEGIN PROLOGUE  ISDCGN
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      DOUBLE 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     DOUBLE PRECISION B(N), X(N), A(N), TOL, ERR, R(N), Z(N), P(N)
C     DOUBLE PRECISION ATP(N), ATZ(N), DZ(N), ATDZ(N)
C     DOUBLE PRECISION 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       Double Precision B(N).
C         Right-hand side vector.
C X      :IN       Double Precision 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       Double Precision A(NELT).
C         These arrays contain the matrix data structure for A.
C         It could take any form.  See "Description" in the
C         DCGN 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 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 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 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       Double Precision R(N).
C         The residual R = B-AX.
C Z      :WORK     Double Precision Z(N).
C         Double Precision array used for workspace.
C P      :IN       Double Precision P(N).
C         The conjugate direction vector.
C ATP    :IN       Double Precision ATP(N).
C         A-transpose times the conjugate direction vector.
C ATZ    :IN       Double Precision ATZ(N).
C         A-transpose times the pseudo-residual.
C DZ     :IN       Double Precision DZ(N).
C         Workspace used to hold temporary vector(s).
C ATDZ   :WORK     Double Precision ATDZ(N).
C         Workspace.
C RWORK  :WORK     Double Precision RWORK(USER DEFINED).
C         Double Precision 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       Double Precision.
C BK     :IN       Double Precision.
C         Current conjugate gradient parameters alpha and beta.
C BNRM   :INOUT    Double Precision.
C         Norm of the right hand side.  Type of norm depends on ITOL.
C         Calculated only on the first call.
C SOLNRM :INOUT    Double Precision.
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  DCGN
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 MATVEC, MTTVEC and MSOLVE from ROUTINES CALLED
C           list.  (FNF)
C   910506  Made subsidiary to DCGN.  (FNF)
C   920407  COMMON BLOCK renamed DSLBLK.  (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 D1MACH(2) and corrected D to E in
C           output format.  (FNF)
C   921113  Corrected C***CATEGORY line.  (FNF)
C***END PROLOGUE  ISDCGN
C     .. Scalar Arguments ..
      DOUBLE PRECISION AK, BK, BNRM, ERR, SOLNRM, TOL
      INTEGER IERR, ISYM, ITER, ITMAX, ITOL, IUNIT, N, NELT
C     .. Array Arguments ..
      DOUBLE PRECISION A(N), ATDZ(N), ATP(N), ATZ(N), B(N), DZ(N), P(N),
     +                 R(N), RWORK(*), X(N), Z(N)
      INTEGER IA(NELT), IWORK(*), JA(NELT)
C     .. Subroutine Arguments ..
      EXTERNAL MATVEC, MSOLVE, MTTVEC
C     .. Arrays in Common ..
      DOUBLE PRECISION SOLN(1)
C     .. Local Scalars ..
      INTEGER I
C     .. External Functions ..
      DOUBLE PRECISION D1MACH, DNRM2
      EXTERNAL D1MACH, DNRM2
C     .. Common blocks ..
      COMMON /DSLBLK/ SOLN
C***FIRST EXECUTABLE STATEMENT  ISDCGN
      ISDCGN = 0
C
      IF( ITOL.EQ.1 ) THEN
C         err = ||Residual||/||RightHandSide|| (2-Norms).
         IF(ITER .EQ. 0) BNRM = DNRM2(N, B, 1)
         ERR = DNRM2(N, R, 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, DZ, NELT, IA, JA, A, ISYM, RWORK, IWORK)
            CALL MTTVEC(N, DZ, ATDZ, NELT, IA, JA, A, ISYM)
            BNRM = DNRM2(N, ATDZ, 1)
         ENDIF
         ERR = DNRM2(N, ATZ, 1)/BNRM
      ELSE IF( ITOL.EQ.11 ) THEN
C         err = ||x-TrueSolution||/||TrueSolution|| (2-Norms).
         IF(ITER .EQ. 0) SOLNRM = DNRM2(N, SOLN, 1)
         DO 10 I = 1, N
            DZ(I) = X(I) - SOLN(I)
 10      CONTINUE
         ERR = DNRM2(N, DZ, 1)/SOLNRM
      ELSE
C
C         If we get here ITOL is not one of the acceptable values.
         ERR = D1MACH(2)
         IERR = 3
      ENDIF
C
      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 ) ISDCGN = 1
C
      RETURN
 1000 FORMAT(' PCG Applied to the Normal Equations for ',
     $     'N, ITOL = ',I5, I5,
     $     /' ITER','   Error Estimate','            Alpha',
     $     '             Beta')
 1010 FORMAT(1X,I4,1X,D16.7,1X,D16.7,1X,D16.7)
C------------- LAST LINE OF ISDCGN FOLLOWS ----------------------------
      END