*DECK SSMTV
SUBROUTINE SSMTV (N, X, Y, NELT, IA, JA, A, ISYM)
C***BEGIN PROLOGUE SSMTV
C***PURPOSE SLAP Column Format Sparse Matrix Transpose Vector Product.
C Routine to calculate the sparse matrix vector product:
C Y = A'*X, where ' denotes transpose.
C***LIBRARY SLATEC (SLAP)
C***CATEGORY D1B4
C***TYPE SINGLE PRECISION (SSMTV-S, DSMTV-D)
C***KEYWORDS MATRIX TRANSPOSE 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 REAL X(N), Y(N), A(NELT)
C
C CALL SSMTV(N, X, Y, NELT, IA, JA, A, ISYM )
C
C *Arguments:
C N :IN Integer.
C Order of the Matrix.
C X :IN Real X(N).
C The vector that should be multiplied by the transpose of
C the matrix.
C Y :OUT Real Y(N).
C The product of the transpose 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 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
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 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 SSMV
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 SSMTV
C .. Scalar Arguments ..
INTEGER ISYM, N, NELT
C .. Array Arguments ..
REAL 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 SSMTV
C
C Zero out the result vector.
C
DO 10 I = 1, N
Y(I) = 0
10 CONTINUE
C
C Multiply by A-Transpose.
C A-Transpose is stored by rows...
CVD$R NOCONCUR
DO 30 IROW = 1, N
IBGN = JA(IROW)
IEND = JA(IROW+1)-1
CVD$ ASSOC
DO 20 I = IBGN, IEND
Y(IROW) = Y(IROW) + A(I)*X(IA(I))
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 ICOL = 1, N
JBGN = JA(ICOL)+1
JEND = JA(ICOL+1)-1
IF( JBGN.GT.JEND ) GOTO 50
CLLL. OPTION ASSERT (NOHAZARD)
CDIR$ IVDEP
CVD$ NODEPCHK
DO 40 J = JBGN, JEND
Y(IA(J)) = Y(IA(J)) + A(J)*X(ICOL)
40 CONTINUE
50 CONTINUE
ENDIF
RETURN
C------------- LAST LINE OF SSMTV FOLLOWS ----------------------------
END