SMATVEC() and SMATVECP()

Fortran version: 

    SUBROUTINE SMATVEC( NCOLS, NROWS, NCOFF, NX, IX, CX, U, V )
      INTEGER, INTENT(IN   ) :: NCOLS       ! length of input vector
      INTEGER, INTENT(IN   ) :: NROWS       ! length of output vector
      INTEGER, INTENT(IN   ) :: NCOFF       ! max number of coefficients
      INTEGER, INTENT(IN   ) :: NX( NROWS ) ! number of entries per row
      INTEGER, INTENT(IN   ) :: IX( NCOFF ) ! columns list
      REAL   , INTENT(IN   ) :: CX( NCOFF ) ! coefficient array
      REAL   , INTENT(IN   ) :: U( NCOLS )  !  input vector
      REAL   , INTENT(  OUT) :: V( NROWS )  ! output vector

    SUBROUTINE SMATVECP( NCOLS, NROWS, NCOFF, NX, IX, CX, U, V )
      INTEGER, INTENT(IN   ) :: NCOLS           ! length of input vector
      INTEGER, INTENT(IN   ) :: NROWS           ! length of output vector
      INTEGER, INTENT(IN   ) :: NCOFF           ! max number of coefficients
      INTEGER, INTENT(IN   ) :: NN( 0:NROWS )   ! cumulative number of entries per row
      INTEGER, INTENT(IN   ) :: IX(   NCOFF )   ! columns list
      REAL   , INTENT(IN   ) :: CX(   NCOFF )   ! coefficient array
      REAL   , INTENT(IN   ) ::  U(   NCOLS )   !  input vector
      REAL   , INTENT(  OUT) ::  V(   NROWS )   ! output vector

C version: none

Summary:

SMATVEC() multiplies input vector U by sparse matrix <NX,IX,CX> and returns the resulting output vector V, as is done in area-source gridding.
V(R) = ΣK=NX(R-1)-1NX(R) CX(K) U(IX(K))
SMATVECP() is I/O API-3.2 or later only, is OpenMP parallel, using cumulative-count NN(0:NROWS) defined below, instead of SMATVEC NX:
NN(0) = 0
NN(R) = ΣK=1R NX(K)
NOTES:
  1. Do not have explicit INTERFACEs in MODULE M3UTILIO, since main-program declaration, single-indexing usage, and I/O for the sparse matrix <NX,IX,CX> needs F77/C style "void pointer" arguments.
  2. Both routines are OpenMP-parallel for I/O API 3.2 or later (but for repeated multiplications by the same matrix, SMATVECP() is more efficient).

See also subroutines

Bilinear interpolation package GRID2INDX(), PNTS2INDX(), and INDXMULT() from MODULE MODGCTP

BMATVEC and BILIN, DMATVEC, PMATVEC, and UNGRIDB

and programs
MTXBLEND, MTXBUILD, MTXCALC, MTXCPLE.

Fortran Usage: 

    !!  Multiply ABUF(NC1,NR1) by MATX to get ZBUF(NC2,NR2)
    ...
    INTEGER :: NR,  NC    !!  for matrix
    INTEGER :: NR1, NC1      !!  for input grid
    INTEGER :: NR2, NC2      !!  for input grid
    INTEGER, ALLOCATABLE :: MATX(:)
    INTEGER, ALLOCATABLE :: MCNT(:)
    REAL,    ALLOCATABLE :: ABUF(:,:)
    REAL,    ALLOCATABLE :: ZBUF(:,:)
    ...
    !!  [Get dimensions (NC1,NR1), (NC2,NR2) for input and output grids]
    ...
    IF ( DESC3( MTXFILE ) ) THEN
        NR = NROWS3D
        NC = NCOLS3D
    ...
    IF ( NR .NE. NC2*NR2 )...   !!  consistency-check for dimensions
    ...
    ALLOCATE( MATX( NR+2*NC ),  &
              MCNT( 0:NR ),     &
              ABUF(NC1,NR1),    &
              ZBUF(NC2,NR2), STAT=ISTAT )
    ...
    IF ( .NOT.READ3( MTXFILE, ALLVAR3, 1,0,0, MATX ) ) ...
    ...
    IF ( .NOT.READ3( DATAFILE, 'FOO', 1,0,0, ABUF ) ) ...
    ...
    CALL SMATVEC( NC1*NR1, NR, NCOEF,                   &
                  MATX(1), MATX(NR+1), MATX(NC+NR+1),   &
                  ABUF, ZBUF )
    ...
    !!  or equivalently, for a time-stepped input:
    ...
    MCNT(0) = 0
    DO K = 1, NR
        MCNT(K) = MCNT(K-1) + MATX(K)
    END DO
    ...
    DO T = 1, NSTEPS
        ...
        IF ( .NOT.READ3( ..., JDATE, JTIME, ABUF ) ) ...
        ...
        CALL SMATVECP( NC1*NR1, NR, NCOEF,              &
                       MCNT, MATX(NR+1), MATX(NC+NR+1), &
                       ABUF, ZBUF )
        ...
    END DO 
    ...

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