subroutine spmtv(M,N,S,x,r,v,a,b)
implicit none
integer, intent(in)::M,N,S
integer,dimension(N+1),intent(in)::x
integer,dimension(S),intent(in)::r
real,dimension(S),intent(in)::v
real,dimension(M),intent(in)::a
real,dimension(N),intent(out)::b
!***
integer i,j,k
real t
!***
if(S<x(N+1)-1)then
 print *,'S too small'
 stop
endif
do i=1,N
 t=0.
 do k=x(i),x(i+1)-1
  j=r(k)
  if (j>0)t=t+v(k)*a(j)
 enddo
 b(i)=t
enddo
end subroutine spmtv