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98 lines
3.2 KiB
Fortran
98 lines
3.2 KiB
Fortran
*DECK DHELS
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SUBROUTINE DHELS (A, LDA, N, Q, B)
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C***BEGIN PROLOGUE DHELS
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C***SUBSIDIARY
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C***PURPOSE Internal routine for DGMRES.
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C***LIBRARY SLATEC (SLAP)
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C***CATEGORY D2A4, D2B4
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C***TYPE DOUBLE PRECISION (SHELS-S, DHELS-D)
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C***KEYWORDS GENERALIZED MINIMUM RESIDUAL, ITERATIVE PRECONDITION,
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C NON-SYMMETRIC LINEAR SYSTEM, SLAP, SPARSE
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C***AUTHOR Brown, Peter, (LLNL), pnbrown@llnl.gov
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C Hindmarsh, Alan, (LLNL), alanh@llnl.gov
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C Seager, Mark K., (LLNL), seager@llnl.gov
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C Lawrence Livermore National Laboratory
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C PO Box 808, L-60
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C Livermore, CA 94550 (510) 423-3141
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C***DESCRIPTION
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C This routine is extracted from the LINPACK routine SGESL with
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C changes due to the fact that A is an upper Hessenberg matrix.
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C
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C DHELS solves the least squares problem:
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C
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C MIN(B-A*X,B-A*X)
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C
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C using the factors computed by DHEQR.
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C
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C *Usage:
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C INTEGER LDA, N
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C DOUBLE PRECISION A(LDA,N), Q(2*N), B(N+1)
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C
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C CALL DHELS(A, LDA, N, Q, B)
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C
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C *Arguments:
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C A :IN Double Precision A(LDA,N)
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C The output from DHEQR which contains the upper
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C triangular factor R in the QR decomposition of A.
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C LDA :IN Integer
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C The leading dimension of the array A.
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C N :IN Integer
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C A is originally an (N+1) by N matrix.
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C Q :IN Double Precision Q(2*N)
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C The coefficients of the N Givens rotations
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C used in the QR factorization of A.
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C B :INOUT Double Precision B(N+1)
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C On input, B is the right hand side vector.
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C On output, B is the solution vector X.
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C
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C***SEE ALSO DGMRES
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C***ROUTINES CALLED DAXPY
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C***REVISION HISTORY (YYMMDD)
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C 890404 DATE WRITTEN
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C 890404 Previous REVISION DATE
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C 890915 Made changes requested at July 1989 CML Meeting. (MKS)
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C 890922 Numerous changes to prologue to make closer to SLATEC
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C standard. (FNF)
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C 890929 Numerous changes to reduce SP/DP differences. (FNF)
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C 910411 Prologue converted to Version 4.0 format. (BAB)
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C 910502 Added C***FIRST EXECUTABLE STATEMENT line. (FNF)
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C 910506 Made subsidiary to DGMRES. (FNF)
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C 920511 Added complete declaration section. (WRB)
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C***END PROLOGUE DHELS
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C The following is for optimized compilation on LLNL/LTSS Crays.
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CLLL. OPTIMIZE
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C .. Scalar Arguments ..
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INTEGER LDA, N
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C .. Array Arguments ..
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DOUBLE PRECISION A(LDA,*), B(*), Q(*)
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C .. Local Scalars ..
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DOUBLE PRECISION C, S, T, T1, T2
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INTEGER IQ, K, KB, KP1
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C .. External Subroutines ..
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EXTERNAL DAXPY
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C***FIRST EXECUTABLE STATEMENT DHELS
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C
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C Minimize(B-A*X,B-A*X). First form Q*B.
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C
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DO 20 K = 1, N
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KP1 = K + 1
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IQ = 2*(K-1) + 1
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C = Q(IQ)
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S = Q(IQ+1)
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T1 = B(K)
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T2 = B(KP1)
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B(K) = C*T1 - S*T2
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B(KP1) = S*T1 + C*T2
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20 CONTINUE
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C
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C Now solve R*X = Q*B.
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C
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DO 40 KB = 1, N
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K = N + 1 - KB
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B(K) = B(K)/A(K,K)
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T = -B(K)
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CALL DAXPY(K-1, T, A(1,K), 1, B(1), 1)
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40 CONTINUE
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RETURN
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C------------- LAST LINE OF DHELS FOLLOWS ----------------------------
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END
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