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239 lines
10 KiB
Fortran
239 lines
10 KiB
Fortran
*DECK ISDOMN
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INTEGER FUNCTION ISDOMN (N, B, X, NELT, IA, JA, A, ISYM, MSOLVE,
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+ NSAVE, ITOL, TOL, ITMAX, ITER, ERR, IERR, IUNIT, R, Z, P, AP,
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+ EMAP, DZ, CSAV, RWORK, IWORK, AK, BNRM, SOLNRM)
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C***BEGIN PROLOGUE ISDOMN
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C***SUBSIDIARY
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C***PURPOSE Preconditioned Orthomin Stop Test.
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C This routine calculates the stop test for the Orthomin
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C iteration scheme. It returns a non-zero if the error
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C estimate (the type of which is determined by ITOL) is
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C less than the user specified tolerance TOL.
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C***LIBRARY SLATEC (SLAP)
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C***CATEGORY D2A4, D2B4
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C***TYPE DOUBLE PRECISION (ISSOMN-S, ISDOMN-D)
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C***KEYWORDS ITERATIVE PRECONDITION, NON-SYMMETRIC LINEAR SYSTEM,
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C ORTHOMIN, SLAP, SPARSE, STOP TEST
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C***AUTHOR Greenbaum, Anne, (Courant Institute)
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C Seager, Mark K., (LLNL)
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C Lawrence Livermore National Laboratory
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C PO BOX 808, L-60
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C Livermore, CA 94550 (510) 423-3141
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C seager@llnl.gov
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C***DESCRIPTION
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C
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C *Usage:
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C INTEGER N, NELT, IA(NELT), JA(NELT), ISYM, NSAVE, ITOL, ITMAX
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C INTEGER ITER, IERR, IUNIT, IWORK(USER DEFINED)
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C DOUBLE PRECISION B(N), X(N), A(NELT), TOL, ERR, R(N), Z(N)
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C DOUBLE PRECISION P(N,0:NSAVE), AP(N,0:NSAVE), EMAP(N,0:NSAVE)
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C DOUBLE PRECISION DZ(N), CSAV(NSAVE), RWORK(USER DEFINED), AK
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C DOUBLE PRECISION BNRM, SOLNRM
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C EXTERNAL MSOLVE
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C
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C IF( ISDOMN(N, B, X, NELT, IA, JA, A, ISYM, MSOLVE, NSAVE,
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C $ ITOL, TOL, ITMAX, ITER, ERR, IERR, IUNIT, R, Z, P, AP,
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C $ EMAP, DZ, CSAV, RWORK, IWORK, AK, BNRM, SOLNRM)
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C $ .NE.0 ) THEN ITERATION CONVERGED
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C
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C *Arguments:
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C N :IN Integer.
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C Order of the matrix.
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C B :IN Double Precision B(N).
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C Right-hand side vector.
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C X :IN Double Precision X(N).
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C On input X is your initial guess for solution vector.
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C On output X is the final approximate solution.
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C NELT :IN Integer.
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C Number of Non-Zeros stored in A.
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C IA :IN Integer IA(NELT).
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C JA :IN Integer JA(NELT).
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C A :IN Double Precision A(NELT).
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C These arrays should hold the matrix A in either the SLAP
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C Triad format or the SLAP Column format. See "Description"
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C in the DSDOMN or DSLUOM prologue.
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C ISYM :IN Integer.
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C Flag to indicate symmetric storage format.
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C If ISYM=0, all non-zero entries of the matrix are stored.
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C If ISYM=1, the matrix is symmetric, and only the upper
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C or lower triangle of the matrix is stored.
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C MSOLVE :EXT External.
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C Name of a routine which solves a linear system MZ = R for
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C Z given R with the preconditioning matrix M (M is supplied via
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C RWORK and IWORK arrays). The name of the MSOLVE routine must
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C be declared external in the calling program. The calling
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C sequence to MSOLVE is:
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C CALL MSOLVE(N, R, Z, NELT, IA, JA, A, ISYM, RWORK, IWORK)
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C Where N is the number of unknowns, R is the right-hand side
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C vector and Z is the solution upon return. NELT, IA, JA, A and
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C ISYM are defined as above. RWORK is a double precision array
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C that can be used to pass necessary preconditioning information
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C and/or workspace to MSOLVE. IWORK is an integer work array
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C for the same purpose as RWORK.
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C NSAVE :IN Integer.
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C Number of direction vectors to save and orthogonalize against.
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C ITOL :IN Integer.
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C Flag to indicate type of convergence criterion.
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C If ITOL=1, iteration stops when the 2-norm of the residual
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C divided by the 2-norm of the right-hand side is less than TOL.
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C If ITOL=2, iteration stops when the 2-norm of M-inv times the
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C residual divided by the 2-norm of M-inv times the right hand
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C side is less than TOL, where M-inv is the inverse of the
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C diagonal of A.
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C ITOL=11 is often useful for checking and comparing different
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C routines. For this case, the user must supply the "exact"
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C solution or a very accurate approximation (one with an error
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C much less than TOL) through a common block,
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C COMMON /DSLBLK/ SOLN( )
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C If ITOL=11, iteration stops when the 2-norm of the difference
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C between the iterative approximation and the user-supplied
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C solution divided by the 2-norm of the user-supplied solution
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C is less than TOL. Note that this requires the user to set up
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C the "COMMON /DSLBLK/ SOLN(LENGTH)" in the calling routine.
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C The routine with this declaration should be loaded before the
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C stop test so that the correct length is used by the loader.
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C This procedure is not standard Fortran and may not work
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C correctly on your system (although it has worked on every
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C system the authors have tried). If ITOL is not 11 then this
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C common block is indeed standard Fortran.
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C TOL :IN Double Precision.
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C Convergence criterion, as described above.
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C ITMAX :IN Integer.
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C Maximum number of iterations.
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C ITER :IN Integer.
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C Current iteration count. (Must be zero on first call.)
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C ERR :OUT Double Precision.
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C Error estimate of error in final approximate solution, as
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C defined by ITOL.
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C IERR :OUT Integer.
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C Error flag. IERR is set to 3 if ITOL is not one of the
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C acceptable values, see above.
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C IUNIT :IN Integer.
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C Unit number on which to write the error at each iteration,
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C if this is desired for monitoring convergence. If unit
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C number is 0, no writing will occur.
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C R :IN Double Precision R(N).
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C The residual R = B-AX.
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C Z :WORK Double Precision Z(N).
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C P :IN Double Precision P(N,0:NSAVE).
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C Workspace used to hold the conjugate direction vector(s).
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C AP :IN Double Precision AP(N,0:NSAVE).
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C Workspace used to hold the matrix A times the P vector(s).
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C EMAP :IN Double Precision EMAP(N,0:NSAVE).
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C Workspace used to hold M-inv times the AP vector(s).
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C DZ :WORK Double Precision DZ(N).
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C Workspace.
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C CSAV :DUMMY Double Precision CSAV(NSAVE)
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C Reserved for future use.
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C RWORK :WORK Double Precision RWORK(USER DEFINED).
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C Double Precision array that can be used for workspace in
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C MSOLVE.
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C IWORK :WORK Integer IWORK(USER DEFINED).
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C Integer array that can be used for workspace in MSOLVE.
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C AK :IN Double Precision.
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C Current iterate Orthomin iteration parameter.
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C BNRM :OUT Double Precision.
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C Current solution B-norm, if ITOL = 1 or 2.
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C SOLNRM :OUT Double Precision.
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C True solution norm, if ITOL = 11.
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C
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C *Function Return Values:
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C 0 : Error estimate (determined by ITOL) is *NOT* less than the
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C specified tolerance, TOL. The iteration must continue.
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C 1 : Error estimate (determined by ITOL) is less than the
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C specified tolerance, TOL. The iteration can be considered
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C complete.
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C
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C *Cautions:
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C This routine will attempt to write to the Fortran logical output
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C unit IUNIT, if IUNIT .ne. 0. Thus, the user must make sure that
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C this logical unit is attached to a file or terminal before calling
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C this routine with a non-zero value for IUNIT. This routine does
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C not check for the validity of a non-zero IUNIT unit number.
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C
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C***SEE ALSO DOMN, DSDOMN, DSLUOM
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C***ROUTINES CALLED D1MACH, DNRM2
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C***COMMON BLOCKS DSLBLK
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C***REVISION HISTORY (YYMMDD)
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C 890404 DATE WRITTEN
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C 890404 Previous REVISION DATE
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C 890915 Made changes requested at July 1989 CML Meeting. (MKS)
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C 890922 Numerous changes to prologue to make closer to SLATEC
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C standard. (FNF)
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C 890929 Numerous changes to reduce SP/DP differences. (FNF)
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C 891003 Removed C***REFER TO line, per MKS.
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C 910411 Prologue converted to Version 4.0 format. (BAB)
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C 910502 Removed MSOLVE from ROUTINES CALLED list. (FNF)
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C 910506 Made subsidiary to DOMN. (FNF)
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C 920407 COMMON BLOCK renamed DSLBLK. (WRB)
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C 920511 Added complete declaration section. (WRB)
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C 920930 Corrected to not print AK when ITER=0. (FNF)
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C 921026 Changed 1.0E10 to D1MACH(2) and corrected D to E in
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C output format. (FNF)
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C 921113 Corrected C***CATEGORY line. (FNF)
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C***END PROLOGUE ISDOMN
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C .. Scalar Arguments ..
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DOUBLE PRECISION AK, BNRM, ERR, SOLNRM, TOL
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INTEGER IERR, ISYM, ITER, ITMAX, ITOL, IUNIT, N, NELT, NSAVE
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C .. Array Arguments ..
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DOUBLE PRECISION A(NELT), AP(N,0:NSAVE), B(N), CSAV(NSAVE),
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+ DZ(N), EMAP(N,0:NSAVE), P(N,0:NSAVE), R(N),
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+ RWORK(*), X(N), Z(N)
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INTEGER IA(NELT), IWORK(*), JA(NELT)
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C .. Subroutine Arguments ..
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EXTERNAL MSOLVE
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C .. Arrays in Common ..
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DOUBLE PRECISION SOLN(1)
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C .. Local Scalars ..
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INTEGER I
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C .. External Functions ..
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DOUBLE PRECISION D1MACH, DNRM2
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EXTERNAL D1MACH, DNRM2
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C .. Common blocks ..
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COMMON /DSLBLK/ SOLN
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C***FIRST EXECUTABLE STATEMENT ISDOMN
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ISDOMN = 0
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C
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IF( ITOL.EQ.1 ) THEN
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C err = ||Residual||/||RightHandSide|| (2-Norms).
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IF(ITER .EQ. 0) BNRM = DNRM2(N, B, 1)
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ERR = DNRM2(N, R, 1)/BNRM
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ELSE IF( ITOL.EQ.2 ) THEN
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C -1 -1
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C err = ||M Residual||/||M RightHandSide|| (2-Norms).
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IF(ITER .EQ. 0) THEN
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CALL MSOLVE(N, B, DZ, NELT, IA, JA, A, ISYM, RWORK, IWORK)
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BNRM = DNRM2(N, DZ, 1)
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ENDIF
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ERR = DNRM2(N, Z, 1)/BNRM
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ELSE IF( ITOL.EQ.11 ) THEN
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C err = ||x-TrueSolution||/||TrueSolution|| (2-Norms).
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IF(ITER .EQ. 0) SOLNRM = DNRM2(N, SOLN, 1)
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DO 10 I = 1, N
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DZ(I) = X(I) - SOLN(I)
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10 CONTINUE
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ERR = DNRM2(N, DZ, 1)/SOLNRM
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ELSE
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C
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C If we get here ITOL is not one of the acceptable values.
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ERR = D1MACH(2)
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IERR = 3
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ENDIF
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C
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IF(IUNIT .NE. 0) THEN
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IF( ITER.EQ.0 ) THEN
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WRITE(IUNIT,1000) NSAVE, N, ITOL
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WRITE(IUNIT,1010) ITER, ERR
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ELSE
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WRITE(IUNIT,1010) ITER, ERR, AK
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ENDIF
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ENDIF
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IF(ERR .LE. TOL) ISDOMN = 1
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C
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RETURN
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1000 FORMAT(' Preconditioned Orthomin(',I3,') for ',
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$ 'N, ITOL = ',I5, I5,
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$ /' ITER',' Error Estimate',' Alpha')
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1010 FORMAT(1X,I4,1X,D16.7,1X,D16.7)
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C------------- LAST LINE OF ISDOMN FOLLOWS ----------------------------
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END
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