SORTH(3)

SYNOPSIS
SUBROUTINE SORTH (VNEW, V, HES, N, LL, LDHES, KMP, SNORMW)

NAME
sorth - Internal routine for SGMRES.

LIBRARY
SLATEC (SLAP)

CATEGORY
D2A4, D2B4

TYPE
SINGLE PRECISION (SORTH-S, DORTH-D)

KEYWORDS
GENERALIZED MINIMUM RESIDUAL, ITERATIVE PRECONDITION, NON-SYMMETRIC LINEAR SYSTEM, SLAP, SPARSE

AUTHOR
Brown, Peter, (LLNL), pnbrown@llnl.gov Hindmarsh, Alan, (LLNL), alanh@llnl.gov Seager, Mark K., (LLNL), seager@llnl.gov Lawrence Livermore National Laboratory PO Box 808, L-60 Livermore, CA 94550 (510) 423-3141

DESCRIPTION
This routine orthogonalizes the vector VNEW against the previous KMP vectors in the V array. It uses a modified Gram-Schmidt orthogonalization procedure with conditional reorthogonalization. *Usage: INTEGER N, LL, LDHES, KMP REAL VNEW(N), V(N,LL), HES(LDHES,LL), SNORMW CALL SORTH(VNEW, V, HES, N, LL, LDHES, KMP, SNORMW) *Arguments: VNEW :INOUT Real VNEW(N) On input, the vector of length N containing a scaled product of the Jacobian and the vector V(*,LL). On output, the new vector orthogonal to V(*,i0) to V(*,LL), where i0 = max(1, LL-KMP+1). V :IN Real V(N,LL) The N x LL array containing the previous LL orthogonal vectors V(*,1) to V(*,LL). HES :INOUT Real HES(LDHES,LL) On input, an LL x LL upper Hessenberg matrix containing, in HES(I,K), K.lt.LL, the scaled inner products of A*V(*,K) and V(*,i). On return, column LL of HES is filled in with the scaled inner products of A*V(*,LL) and V(*,i). N :IN Integer The order of the matrix A, and the length of VNEW. LL :IN Integer The current order of the matrix HES. LDHES :IN Integer The leading dimension of the HES array. KMP :IN Integer The number of previous vectors the new vector VNEW must be made orthogonal to (KMP .le. MAXL). SNORMW :OUT REAL Scalar containing the l-2 norm of VNEW.

SEE ALSO
SGMRES

ROUTINES CALLED
SAXPY, SDOT, SNRM2

REVISION HISTORY (YYMMDD)
871001 DATE WRITTEN
881213 Previous REVISION DATE
890915 Made changes requested at July 1989 CML Meeting. (MKS)
890922 Numerous changes to prologue to make closer to SLATEC standard. (FNF)
890929 Numerous changes to reduce SP/DP differences. (FNF)
910411 Prologue converted to Version 4.0 format. (BAB)
910506 Made subsidiary to SGMRES. (FNF)
920511 Added complete declaration section. (WRB)