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- *DECK DRLCAL
- SUBROUTINE DRLCAL (N, KMP, LL, MAXL, V, Q, RL, SNORMW, PROD,
- + R0NRM)
- C***BEGIN PROLOGUE DRLCAL
- C***SUBSIDIARY
- C***PURPOSE Internal routine for DGMRES.
- C***LIBRARY SLATEC (SLAP)
- C***CATEGORY D2A4, D2B4
- C***TYPE DOUBLE PRECISION (SRLCAL-S, DRLCAL-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 calculates the scaled residual RL from the
- C V(I)'s.
- C *Usage:
- C INTEGER N, KMP, LL, MAXL
- C DOUBLE PRECISION V(N,LL), Q(2*MAXL), RL(N), SNORMW, PROD, R0NORM
- C
- C CALL DRLCAL(N, KMP, LL, MAXL, V, Q, RL, SNORMW, PROD, R0NRM)
- 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 KMP :IN Integer
- C The number of previous V vectors the new vector VNEW
- C must be made orthogonal to. (KMP .le. MAXL)
- C LL :IN Integer
- C The current dimension of the Krylov subspace.
- C MAXL :IN Integer
- C The maximum dimension of the Krylov subspace.
- C V :IN Double Precision V(N,LL)
- C The N x LL array containing the orthogonal vectors
- C V(*,1) to V(*,LL).
- C Q :IN Double Precision Q(2*MAXL)
- C A double precision array of length 2*MAXL containing the
- C components of the Givens rotations used in the QR
- C decomposition of HES. It is loaded in DHEQR and used in
- C DHELS.
- C RL :OUT Double Precision RL(N)
- C The residual vector RL. This is either SB*(B-A*XL) if
- C not preconditioning or preconditioning on the right,
- C or SB*(M-inverse)*(B-A*XL) if preconditioning on the
- C left.
- C SNORMW :IN Double Precision
- C Scale factor.
- C PROD :IN Double Precision
- C The product s1*s2*...*sl = the product of the sines of the
- C Givens rotations used in the QR factorization of
- C the Hessenberg matrix HES.
- C R0NRM :IN Double Precision
- C The scaled norm of initial residual R0.
- C
- C***SEE ALSO DGMRES
- C***ROUTINES CALLED DCOPY, DSCAL
- 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 910506 Made subsidiary to DGMRES. (FNF)
- C 920511 Added complete declaration section. (WRB)
- C***END PROLOGUE DRLCAL
- C The following is for optimized compilation on LLNL/LTSS Crays.
- CLLL. OPTIMIZE
- C .. Scalar Arguments ..
- DOUBLE PRECISION PROD, R0NRM, SNORMW
- INTEGER KMP, LL, MAXL, N
- C .. Array Arguments ..
- DOUBLE PRECISION Q(*), RL(N), V(N,*)
- C .. Local Scalars ..
- DOUBLE PRECISION C, S, TEM
- INTEGER I, I2, IP1, K, LLM1, LLP1
- C .. External Subroutines ..
- EXTERNAL DCOPY, DSCAL
- C***FIRST EXECUTABLE STATEMENT DRLCAL
- IF (KMP .EQ. MAXL) THEN
- C
- C calculate RL. Start by copying V(*,1) into RL.
- C
- CALL DCOPY(N, V(1,1), 1, RL, 1)
- LLM1 = LL - 1
- DO 20 I = 1,LLM1
- IP1 = I + 1
- I2 = I*2
- S = Q(I2)
- C = Q(I2-1)
- DO 10 K = 1,N
- RL(K) = S*RL(K) + C*V(K,IP1)
- 10 CONTINUE
- 20 CONTINUE
- S = Q(2*LL)
- C = Q(2*LL-1)/SNORMW
- LLP1 = LL + 1
- DO 30 K = 1,N
- RL(K) = S*RL(K) + C*V(K,LLP1)
- 30 CONTINUE
- ENDIF
- C
- C When KMP < MAXL, RL vector already partially calculated.
- C Scale RL by R0NRM*PROD to obtain the residual RL.
- C
- TEM = R0NRM*PROD
- CALL DSCAL(N, TEM, RL, 1)
- RETURN
- C------------- LAST LINE OF DRLCAL FOLLOWS ----------------------------
- END
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