! this program demonstrates how to pass variable size matrices to subroutines

module tr
  implicit none
  contains

  function trace(a) ! compute trace of matrix a
    real    :: a(:,:), trace, sum=0.
    integer :: i
    do i=1,size(a,1)  ! size(a,1) and size(a,2) are dimensions of a
      sum=sum+a(i,i)
    end do
    trace=sum
  end function
end module

program trtest ! compute trace of Hilbert matrix
  use tr
  implicit none
  integer           ::  n, i, j
  real, allocatable :: a(:,:)
   
  print *, 'n ='
  read *, n
  allocate(a(n,n))
  do i=1,n
    do j=1,n
       a(i,j)=1./(i+j-1)
    end do
  end do
  print *, 'trace =', trace(a)
end program