SLATEC Routines --- DPIGMR ---
*DECK DPIGMR
SUBROUTINE DPIGMR (N, R0, SR, SZ, JSCAL, MAXL, MAXLP1, KMP, NRSTS,
+ JPRE, MATVEC, MSOLVE, NMSL, Z, V, HES, Q, LGMR, RPAR, IPAR, WK,
+ DL, RHOL, NRMAX, B, BNRM, X, XL, ITOL, TOL, NELT, IA, JA, A,
+ ISYM, IUNIT, IFLAG, ERR)
C***BEGIN PROLOGUE DPIGMR
C***SUBSIDIARY
C***PURPOSE Internal routine for DGMRES.
C***LIBRARY SLATEC (SLAP)
C***CATEGORY D2A4, D2B4
C***TYPE DOUBLE PRECISION (SPIGMR-S, DPIGMR-D)
C***KEYWORDS GENERALIZED MINIMUM RESIDUAL, ITERATIVE PRECONDITION,
C NON-SYMMETRIC LINEAR SYSTEM, SLAP, SPARSE
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 This routine solves the linear system A * Z = R0 using a
C scaled preconditioned version of the generalized minimum
C residual method. An initial guess of Z = 0 is assumed.
C
C *Usage:
C INTEGER N, JSCAL, MAXL, MAXLP1, KMP, NRSTS, JPRE, NMSL, LGMR
C INTEGER IPAR(USER DEFINED), NRMAX, ITOL, NELT, IA(NELT), JA(NELT)
C INTEGER ISYM, IUNIT, IFLAG
C DOUBLE PRECISION R0(N), SR(N), SZ(N), Z(N), V(N,MAXLP1),
C $ HES(MAXLP1,MAXL), Q(2*MAXL), RPAR(USER DEFINED),
C $ WK(N), DL(N), RHOL, B(N), BNRM, X(N), XL(N),
C $ TOL, A(NELT), ERR
C EXTERNAL MATVEC, MSOLVE
C
C CALL DPIGMR(N, R0, SR, SZ, JSCAL, MAXL, MAXLP1, KMP,
C $ NRSTS, JPRE, MATVEC, MSOLVE, NMSL, Z, V, HES, Q, LGMR,
C $ RPAR, IPAR, WK, DL, RHOL, NRMAX, B, BNRM, X, XL,
C $ ITOL, TOL, NELT, IA, JA, A, ISYM, IUNIT, IFLAG, ERR)
C
C *Arguments:
C N :IN Integer
C The order of the matrix A, and the lengths
C of the vectors SR, SZ, R0 and Z.
C R0 :IN Double Precision R0(N)
C R0 = the right hand side of the system A*Z = R0.
C R0 is also used as workspace when computing
C the final approximation.
C (R0 is the same as V(*,MAXL+1) in the call to DPIGMR.)
C SR :IN Double Precision SR(N)
C SR is a vector of length N containing the non-zero
C elements of the diagonal scaling matrix for R0.
C SZ :IN Double Precision SZ(N)
C SZ is a vector of length N containing the non-zero
C elements of the diagonal scaling matrix for Z.
C JSCAL :IN Integer
C A flag indicating whether arrays SR and SZ are used.
C JSCAL=0 means SR and SZ are not used and the
C algorithm will perform as if all
C SR(i) = 1 and SZ(i) = 1.
C JSCAL=1 means only SZ is used, and the algorithm
C performs as if all SR(i) = 1.
C JSCAL=2 means only SR is used, and the algorithm
C performs as if all SZ(i) = 1.
C JSCAL=3 means both SR and SZ are used.
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 KMP :IN Integer
C The number of previous vectors the new vector VNEW
C must be made orthogonal to. (KMP .le. MAXL)
C NRSTS :IN Integer
C Counter for the number of restarts on the current
C call to DGMRES. If NRSTS .gt. 0, then the residual
C R0 is already scaled, and so scaling of it is
C not necessary.
C JPRE :IN Integer
C Preconditioner type flag.
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, and NELT is the number of
C non-zeros in the SLAP IA, JA, A storage for the matrix A.
C 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 the routine which solves a linear system Mz = r for
C z given r with the preconditioning matrix M (M is supplied via
C RPAR and IPAR 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, RPAR, IPAR)
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 below. RPAR is a double precision array
C that can be used to pass necessary preconditioning information
C and/or workspace to MSOLVE. IPAR is an integer work array
C for the same purpose as RPAR.
C NMSL :OUT Integer
C The number of calls to MSOLVE.
C Z :OUT Double Precision Z(N)
C The final computed approximation to the solution
C of the system A*Z = R0.
C V :OUT Double Precision V(N,MAXLP1)
C The N by (LGMR+1) array containing the LGMR
C orthogonal vectors V(*,1) to V(*,LGMR).
C HES :OUT Double Precision 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 Q :OUT Double Precision Q(2*MAXL)
C A double precision array of length 2*MAXL containing the
C components of the Givens rotations used in the QR
C decomposition of HES. It is loaded in DHEQR and used in
C DHELS.
C LGMR :OUT Integer
C The number of iterations performed and
C the current order of the upper Hessenberg
C matrix HES.
C RPAR :IN Double Precision RPAR(USER DEFINED)
C Double Precision workspace passed directly to the MSOLVE
C routine.
C IPAR :IN Integer IPAR(USER DEFINED)
C Integer workspace passed directly to the MSOLVE routine.
C WK :IN Double Precision WK(N)
C A double precision work array of length N used by routines
C MATVEC and MSOLVE.
C DL :INOUT Double Precision DL(N)
C On input, a double precision work array of length N used for
C calculation of the residual norm RHO when the method is
C incomplete (KMP.lt.MAXL), and/or when using restarting.
C On output, the scaled residual vector RL. It is only loaded
C when performing restarts of the Krylov iteration.
C RHOL :OUT Double Precision
C A double precision scalar containing the norm of the final
C residual.
C NRMAX :IN Integer
C The maximum number of restarts of the Krylov iteration.
C NRMAX .gt. 0 means restarting is active, while
C NRMAX = 0 means restarting is not being used.
C B :IN Double Precision B(N)
C The right hand side of the linear system A*X = b.
C BNRM :IN Double Precision
C The scaled norm of b.
C X :IN Double Precision X(N)
C The current approximate solution as of the last
C restart.
C XL :IN Double Precision XL(N)
C An array of length N used to hold the approximate
C solution X(L) when ITOL=11.
C ITOL :IN Integer
C A flag to indicate the type of convergence criterion
C used. See the driver for its description.
C TOL :IN Double Precision
C The tolerance on residuals R0-A*Z in scaled norm.
C NELT :IN Integer
C The length of arrays IA, JA and A.
C IA :IN Integer IA(NELT)
C An integer array of length NELT containing matrix data.
C It is passed directly to the MATVEC and MSOLVE routines.
C JA :IN Integer JA(NELT)
C An integer array of length NELT containing matrix data.
C It is passed directly to the MATVEC and MSOLVE routines.
C A :IN Double Precision A(NELT)
C A double precision array of length NELT containing matrix
C data. It is passed directly to the MATVEC and MSOLVE routines.
C ISYM :IN Integer
C A flag to indicate symmetric matrix storage.
C If ISYM=0, all non-zero entries of the matrix are
C stored. If ISYM=1, the matrix is symmetric and
C only the upper or lower triangular part is stored.
C IUNIT :IN Integer
C The i/o unit number for writing intermediate residual
C norm values.
C IFLAG :OUT Integer
C An integer error flag..
C 0 means convergence in LGMR iterations, LGMR.le.MAXL.
C 1 means the convergence test did not pass in MAXL
C iterations, but the residual norm is .lt. norm(R0),
C and so Z is computed.
C 2 means the convergence test did not pass in MAXL
C iterations, residual .ge. norm(R0), and Z = 0.
C ERR :OUT Double Precision.
C Error estimate of error in final approximate solution, as
C defined by ITOL.
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 DGMRES
C***ROUTINES CALLED DAXPY, DCOPY, DHELS, DHEQR, DNRM2, DORTH, DRLCAL,
C DSCAL, ISDGMR
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 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 DGMRES. (FNF)
C 920511 Added complete declaration section. (WRB)
C***END PROLOGUE DPIGMR