dhels.f
SUBROUTINE DHELS (A, LDA, N, Q, B)
C***BEGIN PROLOGUE DHELS
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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 DGMRES.
C***LIBRARY SLATEC (SLAP)
C***CATEGORY D2A4, D2B4
C***TYPE DOUBLE PRECISION (SHELS-S, DHELS-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 is extracted from the LINPACK routine SGESL with
C changes due to the fact that A is an upper Hessenberg matrix.
C
C DHELS solves the least squares problem:
C
C MIN(B-A*X,B-A*X)
C
C using the factors computed by DHEQR.
C
C *Usage:
C INTEGER LDA, N
C DOUBLE PRECISION A(LDA,N), Q(2*N), B(N+1)
C
C CALL DHELS(A, LDA, N, Q, B)
C
C *Arguments:
C A :IN Double Precision A(LDA,N)
C The output from DHEQR which contains the upper
C triangular factor R in the QR decomposition of A.
C LDA :IN Integer
C The leading dimension of the array A.
C N :IN Integer
C A is originally an (N+1) by N matrix.
C Q :IN Double Precision Q(2*N)
C The coefficients of the N Givens rotations
C used in the QR factorization of A.
C B :INOUT Double Precision B(N+1)
C On input, B is the right hand side vector.
C On output, B is the solution vector X.
C
C***SEE ALSO DGMRES
C***ROUTINES CALLED DAXPY
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 Added C***FIRST EXECUTABLE STATEMENT line. (FNF)
C 910506 Made subsidiary to DGMRES. (FNF)
C 920511 Added complete declaration section. (WRB)
C***END PROLOGUE DHELS