sorth.f
SUBROUTINE SORTH (VNEW, V, HES, N, LL, LDHES, KMP, SNORMW)
C***BEGIN PROLOGUE SORTH
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Warning: this routine is not intended to be user-callable.
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C***SUBSIDIARY
C***PURPOSE Internal routine for SGMRES.
C***LIBRARY SLATEC (SLAP)
C***CATEGORY D2A4, D2B4
C***TYPE SINGLE PRECISION (SORTH-S, DORTH-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 orthogonalizes the vector VNEW against the
C previous KMP vectors in the V array. It uses a modified
C Gram-Schmidt orthogonalization procedure with conditional
C reorthogonalization.
C
C *Usage:
C INTEGER N, LL, LDHES, KMP
C REAL VNEW(N), V(N,LL), HES(LDHES,LL), SNORMW
C
C CALL SORTH(VNEW, V, HES, N, LL, LDHES, KMP, SNORMW)
C
C *Arguments:
C VNEW :INOUT Real VNEW(N)
C On input, the vector of length N containing a scaled
C product of the Jacobian and the vector V(*,LL).
C On output, the new vector orthogonal to V(*,i0) to V(*,LL),
C where i0 = max(1, LL-KMP+1).
C V :IN Real V(N,LL)
C The N x LL array containing the previous LL
C orthogonal vectors V(*,1) to V(*,LL).
C HES :INOUT Real HES(LDHES,LL)
C On input, an LL x LL upper Hessenberg matrix containing,
C in HES(I,K), K.lt.LL, the scaled inner products of
C A*V(*,K) and V(*,i).
C On return, column LL of HES is filled in with
C the scaled inner products of A*V(*,LL) and V(*,i).
C N :IN Integer
C The order of the matrix A, and the length of VNEW.
C LL :IN Integer
C The current order of the matrix HES.
C LDHES :IN Integer
C The leading dimension of the HES array.
C KMP :IN Integer
C The number of previous vectors the new vector VNEW
C must be made orthogonal to (KMP .le. MAXL).
C SNORMW :OUT REAL
C Scalar containing the l-2 norm of VNEW.
C
C***SEE ALSO SGMRES
C***ROUTINES CALLED SAXPY, SDOT, SNRM2
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 910506 Made subsidiary to SGMRES. (FNF)
C 920511 Added complete declaration section. (WRB)
C***END PROLOGUE SORTH