*DECK DSMV SUBROUTINE DSMV (N, X, Y, NELT, IA, JA, A, ISYM) C***BEGIN PROLOGUE DSMV C***PURPOSE SLAP Column Format Sparse Matrix Vector Product. C Routine to calculate the sparse matrix vector product: C Y = A*X. C***LIBRARY SLATEC (SLAP) C***CATEGORY D1B4 C***TYPE DOUBLE PRECISION (SSMV-S, DSMV-D) C***KEYWORDS MATRIX VECTOR MULTIPLY, 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 X(N), Y(N), A(NELT) C C CALL DSMV(N, X, Y, NELT, IA, JA, A, ISYM ) C C *Arguments: C N :IN Integer. C Order of the Matrix. C X :IN Double Precision X(N). C The vector that should be multiplied by the matrix. C Y :OUT Double Precision Y(N). C The product of the matrix and the vector. C NELT :IN Integer. C Number of Non-Zeros stored in 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 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 the "inner loops" of this routine C should vectorize on machines with hardware support for C vector gather/scatter operations. Your compiler may require C a compiler directive to convince it that there are no C implicit vector dependencies. Compiler directives for the C Alliant FX/Fortran and CRI CFT/CFT77 compilers are supplied C with the standard SLAP distribution. C C *Cautions: C This routine assumes that the matrix A is stored in SLAP C Column format. It does not check for this (for speed) and C evil, ugly, ornery and nasty things will happen if the matrix C data structure is, in fact, not SLAP Column. Beware of the C wrong data structure!!! C C***SEE ALSO DSMTV 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 930701 Updated CATEGORY section. (FNF, WRB) C***END PROLOGUE DSMV C .. Scalar Arguments .. INTEGER ISYM, N, NELT C .. Array Arguments .. DOUBLE PRECISION A(NELT), X(N), Y(N) INTEGER IA(NELT), JA(NELT) C .. Local Scalars .. INTEGER I, IBGN, ICOL, IEND, IROW, J, JBGN, JEND C***FIRST EXECUTABLE STATEMENT DSMV C C Zero out the result vector. C DO 10 I = 1, N Y(I) = 0 10 CONTINUE C C Multiply by A. C CVD\$R NOCONCUR DO 30 ICOL = 1, N IBGN = JA(ICOL) IEND = JA(ICOL+1)-1 CLLL. OPTION ASSERT (NOHAZARD) CDIR\$ IVDEP CVD\$ NODEPCHK DO 20 I = IBGN, IEND Y(IA(I)) = Y(IA(I)) + A(I)*X(ICOL) 20 CONTINUE 30 CONTINUE C IF( ISYM.EQ.1 ) THEN C C The matrix is non-symmetric. Need to get the other half in... C This loops assumes that the diagonal is the first entry in C each column. C DO 50 IROW = 1, N JBGN = JA(IROW)+1 JEND = JA(IROW+1)-1 IF( JBGN.GT.JEND ) GOTO 50 DO 40 J = JBGN, JEND Y(IROW) = Y(IROW) + A(J)*X(IA(J)) 40 CONTINUE 50 CONTINUE ENDIF RETURN C------------- LAST LINE OF DSMV FOLLOWS ---------------------------- END