*DECK SXLCAL SUBROUTINE SXLCAL (N, LGMR, X, XL, ZL, HES, MAXLP1, Q, V, R0NRM, + WK, SZ, JSCAL, JPRE, MSOLVE, NMSL, RPAR, IPAR, NELT, IA, JA, A, + ISYM) C***BEGIN PROLOGUE SXLCAL C***SUBSIDIARY C***PURPOSE Internal routine for SGMRES. C***LIBRARY SLATEC (SLAP) C***CATEGORY D2A4, D2B4 C***TYPE SINGLE PRECISION (SXLCAL-S, DXLCAL-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 computes the solution XL, the current SGMRES C iterate, given the V(I)'s and the QR factorization of the C Hessenberg matrix HES. This routine is only called when C ITOL=11. C C *Usage: C INTEGER N, LGMR, MAXLP1, JSCAL, JPRE, NMSL, IPAR(USER DEFINED) C INTEGER NELT, IA(NELT), JA(NELT), ISYM C REAL X(N), XL(N), ZL(N), HES(MAXLP1,MAXL), Q(2*MAXL), C $ V(N,MAXLP1), R0NRM, WK(N), SZ(N), RPAR(USER DEFINED), C $ A(NELT) C EXTERNAL MSOLVE C C CALL SXLCAL(N, LGMR, X, XL, ZL, HES, MAXLP1, Q, V, R0NRM, C $ WK, SZ, JSCAL, JPRE, MSOLVE, NMSL, RPAR, IPAR, C $ NELT, IA, JA, A, ISYM) 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 LGMR :IN Integer C The number of iterations performed and C the current order of the upper Hessenberg C matrix HES. C X :IN Real X(N) C The current approximate solution as of the last restart. C XL :OUT Real XL(N) C An array of length N used to hold the approximate C solution X(L). C Warning: XL and ZL are the same array in the calling routine. C ZL :IN Real ZL(N) C An array of length N used to hold the approximate C solution Z(L). 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) and V(*,k). C MAXLP1 :IN Integer C MAXLP1 = MAXL + 1, used for dynamic dimensioning of HES. C MAXL is the maximum allowable order of the matrix HES. 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. It is loaded in SHEQR. 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 R0NRM :IN Real C The scaled norm of the initial residual for the C current call to SPIGMR. C WK :IN Real WK(N) C A real work array of length N. C SZ :IN Real SZ(N) C 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 JPRE :IN Integer C The preconditioner type flag. 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 real array that can be C used to pass necessary preconditioning information and/or C workspace to MSOLVE. IPAR is an integer work array for the C same purpose as RPAR. C NMSL :IN Integer C The number of calls to MSOLVE. C RPAR :IN Real RPAR(USER DEFINED) C Real workspace passed directly to the MSOLVE routine. C IPAR :IN Integer IPAR(USER DEFINED) C Integer workspace passed directly to the MSOLVE routine. 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 Real A(NELT) C A real array of length NELT containing matrix data. C 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 C***SEE ALSO SGMRES C***ROUTINES CALLED SAXPY, SCOPY, SHELS C***REVISION HISTORY (YYMMDD) C 871001 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 Removed MSOLVE from ROUTINES CALLED list. (FNF) C 910506 Made subsidiary to SGMRES. (FNF) C 920511 Added complete declaration section. (WRB) C***END PROLOGUE SXLCAL