function A = frank_inv ( n )
%
%  function A = frank_inv ( n )
%
%  FRANK_INV returns the inverse of the Frank matrix.
%
%  Modified:
%
%    14 February 2000
%
%  Parameters:
%
%    Input, integer N, the order of the matrix.
%
%    Output, real A(N,N), the inverse Frank matrix.
%
  A = zeros ( n, n );

  for i = 1 : n
    for j = 1 : n

      if ( i == j-1 )

        A(i,j) = - 1.0;

      elseif ( i == j )

        if ( i == 1 )
          A(i,j) = 1.0;
        else
          A(i,j) = n + 2 - i;
        end

      elseif ( i > j )

        A(i,j) = - ( n + 1 - i ) * A(i-1,j);

      else

        A(i,j) = 0.0;

      end

    end
  end