function out=lincomb(u,v,w)
%
% LINCOMB, LINCOMB(U,V), LINCOMB(U,V,W) draws a grid of parallelograms 
% determined by the row or col vectors u and v (size (2,1) or (1,2).
% Overlays the vector w, and expresses it as a linear combination
% of the vectors u and v. This program is self-demonstrating.
%
% Author: Matthias Kawski, Oct.10, 1996
% http://math.la.asu.edu/~kawski
%
% Changes: July 2000. Color of parallelogram from yellow to black.
%                     Larger grid.
%
if nargin == 0
   u=[3,1];
   v=[1,3];
   w=[7,5];
   end;
if size(u)==[2,1]; u=u'; end;
if size(v)==[2,1]; v=v'; end;
n=30;
clf
hold on
for k=[-n:n]
    plot([-n*u(1)+k*v(1),n*u(1)+k*v(1)],[-n*u(2)+k*v(2),n*u(2)+k*v(2)],'g-');
    plot([-n*v(1)+k*u(1),n*v(1)+k*u(1)],[-n*v(2)+k*u(2),n*v(2)+k*u(2)],'c-');
    end;
window=[-10,10,-10,10];
axis(window);
plot([window(1),window(2)],[0,0],'b');
plot([0,0],[window(3),window(4)],'b');
if (nargin>2) | (nargin==0)
   if size(w)==[2,1]; 
      w=w'; 
      end;
   plot([0,w(1)],[0,w(2)],'r');
   c=inv([u',v'])*w';
   text(-5,8,['w = ',num2str(c(1)),' u + ',num2str(c(2)),' v']);
   plot([0,c(1)*u(1)],[0,c(1)*u(2)],'k-');
   plot([0,c(2)*v(1)],[0,c(2)*v(2)],'k-');
   plot([c(2)*v(1),c(1)*u(1)+c(2)*v(1)],[c(2)*v(2),c(1)*u(2)+c(2)*v(2)],'k-');
   plot([c(1)*u(1),c(1)*u(1)+c(2)*v(1)],[c(1)*u(2),c(1)*u(2)+c(2)*v(2)],'k-');
   end;