!     Last change:  DOS  26 Jul 2000    8:31 pm
!                                       *** copyright 2000 ***
! *** filename chex46.f95               *** John F. Monahan **
!                                       **********************
      program chex46
! demo of sparse matrix multiplication
! see Example 4.6
      implicit none
      integer, parameter :: n = 10      ! dimension
      integer, parameter :: nnz = 28    ! number of nonzeroes
      integer, DIMENSION(n) :: lgthrw             ! # nonzeroes by row
      integer, DIMENSION(nnz) :: collist          ! column indices
      integer k,i,jmx,jj,j
      real, DIMENSION(nnz) :: q                   ! transition probs
      real, DIMENSION(n) :: x,y                   ! vectors
!
  21  FORMAT(10f8.4)
!
      data lgthrw/ 2, 6, 2, 1, 5, 2, 2, 1, 1, 6 /
      DATA collist/ 1,8, 2,3,5,6,9,10, 4,8, 1, 2,4,5,6,7, 9,10, 2,7,  &
     &              3, 6, 1,3,4,7,9,10 /
      DATA q/ .2, 3*.1, 2*.5, .1, .4, .6, .9, 2*.6, .3, .5, .2, .7,   &
     &        .8, .4, .3, .2, .8, .3, .2, 4*.1, .2 /
      DATA x/ 10*.1 /
!
      OPEN( UNIT=6, FILE='chex46.out' )
!                   multiply Q*x = y
      k = 0         ! count nonzero entries
      do i = 1, n
      jmx = lgthrw(i)         ! how many in this row?
      y(i) = 0.
      do jj = 1,jmx
      k = k + 1               ! next nonzero pointer
      j = collist(k)          ! column index
      y(i) = y(i) + q(k)*x(j) ! A(i,j)*x(j)
      end do  ! loop on jj
      end do  ! loop on i
      WRITE(6,21) y
      end program chex46
! *** end of filename chex46.f95        *********************