upminterval Function

  function upminterval(start,stop,midpoint,p,q,type,base,mesh) result(array)
    integer  :: i,p,q,N,Nhalf
    real(8)  :: start,stop,midpoint,array(2*p*q+1)
    real(8),optional :: base,mesh(2*P*Q+1)
    real(8)          :: base_
    integer,optional :: type
    integer          :: type_
    type_= 0          ;if(present(type))type_=type
    base_= 2.d0       ;if(present(base))base_=base
    N=2*p*q+1
    Nhalf=p*q
    if(type_==0)then
       array(1:Nhalf+1)   = upmspace(start,midpoint,p,q,Nhalf+1,base=base_)
       array(N:Nhalf+2:-1)= upmspace(stop,midpoint,p,q,Nhalf,base=base_,iend=.false.)
    else
       array(Nhalf+1:1:-1) = upmspace(midpoint,start,p,q,Nhalf+1,base=base_)
       array(Nhalf+2:N)    = upmspace(midpoint,stop,p,q,Nhalf,base=base_,istart=.false.)
    endif
    if(present(mesh))then
       do i=1,N-1
          mesh(i)=(array(i+1)-array(i))
       enddo
       Mesh(N)=(array(N)-array(N-1))
    endif
  end function upminterval