*DECK DSD2S SUBROUTINE DSD2S (N, NELT, IA, JA, A, ISYM, DINV) C***BEGIN PROLOGUE DSD2S C***PURPOSE Diagonal Scaling Preconditioner SLAP Normal Eqns Set Up. C Routine to compute the inverse of the diagonal of the C matrix A*A', where A is stored in SLAP-Column format. C***LIBRARY SLATEC (SLAP) C***CATEGORY D2E C***TYPE DOUBLE PRECISION (SSD2S-S, DSD2S-D) C***KEYWORDS DIAGONAL, SLAP SPARSE C***AUTHOR Greenbaum, Anne, (Courant Institute) C Seager, Mark K., (LLNL) C Lawrence Livermore National Laboratory C PO BOX 808, L-60 C Livermore, CA 94550 (510) 423-3141 C seager@llnl.gov C***DESCRIPTION C C *Usage: C INTEGER N, NELT, IA(NELT), JA(NELT), ISYM C DOUBLE PRECISION A(NELT), DINV(N) C C CALL DSD2S( N, NELT, IA, JA, A, ISYM, DINV ) C C *Arguments: C N :IN Integer C Order of the Matrix. C NELT :IN Integer. C Number of elements in arrays IA, JA, and A. C IA :IN Integer IA(NELT). C JA :IN Integer JA(NELT). C A :IN Double Precision A(NELT). C These arrays should hold the matrix A in the SLAP Column C format. See "Description", below. C ISYM :IN Integer. C Flag to indicate symmetric storage format. C If ISYM=0, all non-zero entries of the matrix are stored. C If ISYM=1, the matrix is symmetric, and only the upper C or lower triangle of the matrix is stored. C DINV :OUT Double Precision DINV(N). C Upon return this array holds 1./DIAG(A*A'). C C *Description C =================== S L A P Column format ================== C This routine requires that the matrix A be stored in the C SLAP Column format. In this format the non-zeros are stored C counting down columns (except for the diagonal entry, which C must appear first in each "column") and are stored in the C double precision array A. In other words, for each column C in the matrix put the diagonal entry in A. Then put in the C other non-zero elements going down the column (except the C diagonal) in order. The IA array holds the row index for C each non-zero. The JA array holds the offsets into the IA, C A arrays for the beginning of each column. That is, C IA(JA(ICOL)), A(JA(ICOL)) points to the beginning of the C ICOL-th column in IA and A. IA(JA(ICOL+1)-1), C A(JA(ICOL+1)-1) points to the end of the ICOL-th column. C Note that we always have JA(N+1) = NELT+1, where N is the C number of columns in the matrix and NELT is the number of C non-zeros in the matrix. C C Here is an example of the SLAP Column storage format for a C 5x5 Matrix (in the A and IA arrays '|' denotes the end of a C column): C C 5x5 Matrix SLAP Column format for 5x5 matrix on left. C 1 2 3 4 5 6 7 8 9 10 11 C |11 12 0 0 15| A: 11 21 51 | 22 12 | 33 53 | 44 | 55 15 35 C |21 22 0 0 0| IA: 1 2 5 | 2 1 | 3 5 | 4 | 5 1 3 C | 0 0 33 0 35| JA: 1 4 6 8 9 12 C | 0 0 0 44 0| C |51 0 53 0 55| C C With the SLAP format all of the "inner loops" of this C routine should vectorize on machines with hardware support C for vector gather/scatter operations. Your compiler may C require a compiler directive to convince it that there are C no implicit vector dependencies. Compiler directives for C the Alliant FX/Fortran and CRI CFT/CFT77 compilers are C supplied with the standard SLAP distribution. C C C *Cautions: C This routine assumes that the diagonal of A is all non-zero C and that the operation DINV = 1.0/DIAG(A*A') will not under- C flow or overflow. This is done so that the loop vectorizes. C Matrices with zero or near zero or very large entries will C have numerical difficulties and must be fixed before this C routine is called. C C***SEE ALSO DSDCGN C***REFERENCES (NONE) C***ROUTINES CALLED (NONE) 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 920511 Added complete declaration section. (WRB) C 921113 Corrected C***CATEGORY line. (FNF) C 930701 Updated CATEGORY section. (FNF, WRB) C***END PROLOGUE DSD2S C .. Scalar Arguments .. INTEGER ISYM, N, NELT C .. Array Arguments .. DOUBLE PRECISION A(NELT), DINV(N) INTEGER IA(NELT), JA(NELT) C .. Local Scalars .. INTEGER I, K, KBGN, KEND C***FIRST EXECUTABLE STATEMENT DSD2S DO 10 I = 1, N DINV(I) = 0 10 CONTINUE C C Loop over each column. CVD$R NOCONCUR DO 40 I = 1, N KBGN = JA(I) KEND = JA(I+1) - 1 C C Add in the contributions for each row that has a non-zero C in this column. CLLL. OPTION ASSERT (NOHAZARD) CDIR$ IVDEP CVD$ NODEPCHK DO 20 K = KBGN, KEND DINV(IA(K)) = DINV(IA(K)) + A(K)**2 20 CONTINUE IF( ISYM.EQ.1 ) THEN C C Lower triangle stored by columns => upper triangle stored by C rows with Diagonal being the first entry. Loop across the C rest of the row. KBGN = KBGN + 1 IF( KBGN.LE.KEND ) THEN DO 30 K = KBGN, KEND DINV(I) = DINV(I) + A(K)**2 30 CONTINUE ENDIF ENDIF 40 CONTINUE DO 50 I=1,N DINV(I) = 1.0D0/DINV(I) 50 CONTINUE C RETURN C------------- LAST LINE OF DSD2S FOLLOWS ---------------------------- END