% The program says whether a square interval matrix [m,M] pxp has Mrk=p
% it uses Theorem 13 of the paper On rank range of interval matrices
% and the program nondegpgdiag, which, given k,m,M, calculates
% the totally nongenerate pg daigonal of length k
   %If the result is 1, then Mrk(m,M)=p; if the result is 0, then Mrk(m,M)<p
   
function a=rkmax(m,M)

     p=size(m,1);
  % First we define A to be the matrix obtained from [m,M] by changing the
  % nondegenerate entries into 0


     A=zeros(p,p);
  for i=1:p
	  for j=1:p
		  if m(i,j)==M(i,j)
		  A(i,j)=m(i,j);
		  end
		  end
		  end

		  A
		  
		  a=0;

if det(A)~=0 %in this case condition (2) of theorem does not hold  
  a=1;
  return
  end
  

  U=nondegpgdiag(p,m,M)
  if size(U,1)>0  %in this case condition (1) of theorem does not hold

a=1;
return
end




	   for k=1:p-1
		   U=nondegpgdiag(k,m,M) 
		   for i=1:size(U,1) 
			   if det(A(setdiff([1:p],U(i,1:k)),setdiff([1:p],U(i,k+1:2*k))))~=0  % if this holds conditon (2) of the theorem does not hold
		   a=1;
return
		   end
		   end
		   end