% The command gauss(M) is used to perform a sequence
% of EROs on the matrix M that has already been input
% into the MATLAB workspace


% MAIN FUNCTION GAUSS
function U=gauss(M)
stop=1;
last=0; % used to control choice

M
[p,n]=size(M);

U=M;

while stop ~= 0  % begin while
   if last ~= -1
  disp(' ')
  disp('[0]  stop') 
  disp('[1]  Replacement     row(i)- m*row(j) ==> row(i)')
  disp('[2]  Interchange     row(i) <==> row(j)')
  disp('[3]  Scale           c*row(i) ==>  row(i)')
  disp('[4]  turn on rational format')
  disp('[5]  turn off rational format')
  disp('[-1] undo last operation')
else
  disp(' ')
  disp('[0]  stop')
  disp('[1]  Replacement     row(i)- m*row(j) ==> row(i)')
  disp('[2]  Interchange     row(i) <==> row(j)')
  disp('[3]  Scaling           c*row(i) ==>  row(i)')
  disp('[4]  turn on rational format')
  disp('[5]  turn off rational format')
  last=0;
end
disp(' ')     
choice = input('choice  ');
  
if last~=-1
    switch choice
      case 0
         stop=0;
      case 1  
        last=1; done=0;
         while done==0
           done=1;
           m=input('Enter nonzero multiplier m  ');
           if m==0
             disp(' ')
             disp('ERROR: m=0 ')
             disp(' ')
             done=0;
           end
        end
        done=0;
        while done==0
          done=1;
          j=input('Enter row = j to scale     ');
          i=input('Enter row = i to replace   ');
          if i<1 | i>p | j<1 | j>p
             disp(' ')
             disp('ERROR: i or j out of range ')
             disp(' ')
             done=0;
          end
          if i==j
             disp(' ')
             disp('ERROR: i=j ')
             disp(' ')
             done=0;
          end
       end
       U=replacement(U,i,j,m)
       
         case 2
         last=2; done=0;
         while done==0
            done=1;
            i=input('Enter row index i   ');
            j=input('Enter row index j   ');
            if i<1 | i>p | j<1 | j>p
               disp(' ')
               disp('ERROR: i or j out of range ')
               disp(' ')
               done=0;
            end
            if i==j
               disp(' ')
               disp('ERROR: i=j ')
               disp(' ')
               done=0;
            end
         end
         U=interchange(U,i,j)
       
      case 3
         last=3; done=0;
      while done==0
            done=1;
            c=input('Enter nonzero scalar c  ');
            i=input('Enter row index i  ');
            if i<1 | i>p
               disp(' ')
               disp('ERROR: i or j out of range ')
               disp(' ')
               done=0;
            end
            if c==0
               disp(' ')
               disp('ERROR: c=0 ')
               disp(' ')
               done=0;
            end
         end
         U=scaling(U,i,c)

              
    case 4
       format rat;
       U
    case 5
       format;
       U
    case -1
        switch last
        case 1
           disp(' ')
           disp('Inverse ERO applied. Previous matrix is ')
           U=replacement(U,i,j,-m)
        case 2
           disp(' ')
           disp('Undone. Previous matrix is ')
           U=interchange(U,i,j)
          
        case 3
            disp(' ')
           disp('Undone. Previous matrix is ')
           U=scaling(U,i,1/c)
                      
        end % switch case -1
        last=-1;
   end %switch
  end % if last
end  % end while  

% SUBFUNCTIONS

% REPLACEMENT
function B=replacement(A,i,j,m)
[p n]=size(A);
if i<1 | i>p | j<1 | j>p
  error('row index out of range')
end
if i==j
  error('i=j, rows equal')
end
B=A;
B(i,:)=A(i,:)-m*A(j,:);

% INTERCHANGE
function B=interchange(A,i,j)
B=A;
B(i,:)=A(j,:);
B(j,:)=A(i,:);

% SCALING
function B=scaling(A,i,c)
[p n]=size(A);
if i<1 | i>p
  error('row index out of range')
end
B=A;
B(i,:)=c*A(i,:);

% Linear Algebra for Engineers and Scientists
% by Kenneth Hardy 
% Prentice Hall, U.S.A.
% ISBN 0--13--906728--0