# dsmv.f

          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