function qrdemo(A)

% Visualization of the Householder QR transformation (no pivoting)
% adapted by M.E. from Cleve Moler's beautiful "lugui.m"
% from Numerical Computing with MATLAB
% (c) 2004 Cleve Moler.


 if nargin<1,  A = randn(8,5); end

[m,n] = size(A);
shg
clf
dx = 100;
dy = 30;
warns = warning('off','MATLAB:divideByZero');
set(gcf,'double','on','name','QR Demo', ...
   'menu','none','numbertitle','off','color','white', ...
   'pos',[480-(dx/2)*min(9,n) 320 (n+1)*dx (m+3)*dy], ...
   'windowbuttonupfcn','set(gcf,''tag'',''pivot'')')
stop = uicontrol('style','toggle','string','X','fontweight','bold', ...
   'back','w','pos',[(n+1)*dx-25 (m+3)*dy-25 25 25]);
axes('pos',[0 0 1 1])
axis off
Qcolor = [.90 0 0];
Rcolor = [0  0 .90];
Acolor = [0 0 0];
PartialPivotColor = [1 0 1];
PivotColor = [1 0 0];
TempColor = [1 1 1];
paws = 0.02;

% Each element has its own handle

for j = 1:n
   for i = 1:m
      t(i,j) = text('units','pixels','string',spf(A(i,j)), ...
         'fontname','courier','fontweight','bold','fontsize',14, ...
         'horiz','right','color',Acolor, ...
         'pos',[20+j*dx 20+(m+2-i)*dy],'userdata',[i j], ...
         'buttondownfcn','set(gcf,''userdata'',get(gco,''userdata''))');
   end
end

      ttl = text('units','pixels','string','Matrix A', ...
         'fontname','courier','fontweight','bold','fontsize',14, ...
         'horiz','left','color',Acolor, ...
         'pos',[(20+1*dx) 25],'userdata',[1 1], ...
         'buttondownfcn','set(gcf,''userdata'',get(gco,''userdata''))');
         %'pos',[(20+n*dx)/2+70 25],'userdata',[1 1], ...

maxcol = n;
if m<=n, maxcol=m-1; end

for p=1:maxcol
   a = A(p:m,p);
   v = a - norm(a)*[1;zeros(m-p,1)];
   H = eye(m-p+1)-2*v*v'/(v'*v);
   Q = [eye(p-1) zeros(p-1,m-p+1); zeros(m-p+1,p-1) H];
   Aold = A;
   A = Q*A;
   pause
      set(ttl,'string',sprintf('Householder Transformation %d',p))
   for k=p:n, for j=p:m
      set(t(j,k),'color',TempColor)
      drawnow
      pause(paws)
      if j==p, set(t(j,k),'string',spf(A(j,k)),'color',Rcolor)
      elseif k==p, set(t(j,k),'string',spf(A(j,k)),'color',Qcolor)
      else, set(t(j,k),'string',spf(A(j,k)),'color',Acolor)
      end
      drawnow
      pause(paws) 
   end, end
   pause(10*paws);
end
pause      
if maxcol<n
   for k=maxcol+1:n
       set(t(m,k),'string',spf(A(m,k)),'color',Rcolor); 
   end
 end
 set(ttl,'string',' ');

for s = .1:.1:1.5
   for j = 1:n
      for i = 1:m
         if i <= j
            set(t(i,j),'pos',[20+(j+.10*s)*dx 20+(m+2-i)*dy])
         else
            set(t(i,j),'pos',[20+(j-.10*s)*dx 20+(m+2-s-i)*dy])
         end
      end
   end
   drawnow
end


return

%------------------------------------------------------------

function s = spf(aij)
% Subfunction to format text strings
if aij == 0
   f = '%10.0f';
elseif (abs(aij) < 1.e-4) | (abs(aij) >= 1.e4)
   f = '%10.1e';
else
   f = '%10.4f';
end
s = sprintf(f,aij);