l2norm Function

  real function l2norm(matrix)
    !> The matrix to calculate the norm of
    complex, dimension(:, :), intent(in) :: matrix
    !> The shape of the matrix
    integer, dimension(2) :: matrix_shape
    !> Indicies for indexing the matrix
    integer :: i, j
    l2norm = 0.
    matrix_shape = shape(matrix)
    do j = 1, matrix_shape(2)
       do i = 1, matrix_shape(1)
          l2norm = l2norm + real(matrix(i,j) * conjg(matrix(i,j)))
       end do
    end do
    l2norm = sqrt(l2norm)

    ! We could write all of the above as
    !    l2norm = sqrt(sum(matrix*matrix))
    ! but this could run over the matrix twice
    ! and require a matrix sized temporary. Our
    ! approach avoids this. We could have an intermediate
    ! approach of
    !  do j = 1, matrix_shape(1)
    !     l2norm = l2norm + sum(matrix(:,j) * conjg(matrix(:,j)))
    !  end do
    !  l2norm = sqrt(l2norm)
    ! which might offer a bit of a middle ground
    ! Also note that a norm2 method was introduced in fortran 2008
    ! but that only accepts real valued arguments.
  end function l2norm