function G = ifdiag(G)

% IFDIAG Algorithm in section 5.2
%	G = IFDIAG(G) performs one step of the algorithm in
%	section 5.2 to transform the upper m-by-n part of G to
%	a strongly diagonal matrix. G must be in hat format.
% 
%	An m-by-n matrix is strongly diagonal if it is diagonal
%	and if, in addition, (1) each diagonal entry after the 
%	first is an integer multiple of the preceding diagonal
%	entry, and (2) there are no negative entries, except that 
%	in a square matrix the last diagonal entry may be negative.
%
%	See also QUICKE

%	Adapted from Harold M. Edwards, "Linear Algebra."
%	Written by Serge Tchikanda 06/24/95.
%       Last revised by Serge Tchikanda 06/28/96.

A = unhat(G);
[m,n,OPERATIONS] = priority(A);

if ~isempty(m) | ~isempty(n)	        % if matrix is not diagonal
   disp(' ')
   disp('   Upper m-by-n matrix must be diagonal.')
   return		 
end


[mrows,ncols] = size(A);

for i=2:min(size(A))
    if A(i-1,i-1) ~= 0
       if rem(A(i,i),A(i-1,i-1))~=0	
          G(i-1,:) = G(i-1,:) + G(i,:);
          return
       end 
    elseif A(i-1,i-1) == 0 & A(i,i) ~= 0 
	  G(i-1,:) = G(i-1,:) + G(i,:);
          return
    end
end

for i=1:min(size(A)) 
    if A(i,i) < 0
       if i ~= ncols
	  G(:,i+1) = G(:,i+1) - G(:,i);
          return
       elseif i ~= mrows
	  G(i+1,:) = G(i+1,:) - G(i,:);
	  return
       end
    end
end

disp(' ')
disp('   Matrix is strongly diagonal.')