*DECK SSD2S
SUBROUTINE SSD2S (N, NELT, IA, JA, A, ISYM, DINV)
C***BEGIN PROLOGUE SSD2S
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 SINGLE 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 REAL A(NELT), DINV(N)
C
C CALL SSD2S( 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 Real 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 Real 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 real array A. In other words, for each column in the matrix
C put the diagonal entry in A. Then put in the other non-zero
C elements going down the column (except the diagonal) in
C order. The IA array holds the row index for each non-zero.
C The JA array holds the offsets into the IA, A arrays for the
C beginning of each column. That is, IA(JA(ICOL)),
C A(JA(ICOL)) points to the beginning of the ICOL-th column in
C IA and A. IA(JA(ICOL+1)-1), A(JA(ICOL+1)-1) points to the
C end of the ICOL-th column. Note that we always have
C JA(N+1) = NELT+1, where N is the number of columns in the
C matrix and NELT is the number of 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 SSDCGN
C***REFERENCES (NONE)
C***ROUTINES CALLED (NONE)
C***REVISION HISTORY (YYMMDD)
C 871119 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 920511 Added complete declaration section. (WRB)
C 921113 Corrected C***CATEGORY line. (FNF)
C 930701 Updated CATEGORY section. (FNF, WRB)
C***END PROLOGUE SSD2S
C .. Scalar Arguments ..
INTEGER ISYM, N, NELT
C .. Array Arguments ..
REAL A(NELT), DINV(N)
INTEGER IA(NELT), JA(NELT)
C .. Local Scalars ..
INTEGER I, K, KBGN, KEND
C***FIRST EXECUTABLE STATEMENT SSD2S
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) = 1.0E0/DINV(I)
50 CONTINUE
C
RETURN
C------------- LAST LINE OF SSD2S FOLLOWS ----------------------------
END