spanview.m

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function spanview(s,numvec)
% SPANVIEW is a utility for visualizing the
% span of a set of vectors in 3-space. The
% command spanview(x,n) will plot n random 
% multiples of the vector x. Each of these
% vectors is represented by a dot.
% The user is then prompted to input a second
% vector and the computer plots n random
% linear combinations of the two input vectors.
% The program keeps asking for more vectors 
% until 3 linearly independent vectors have 
% been entered.
%
% This routine was written by Steven Leon
% in August, 2002. It incorporates features
% from earlier ATLAST programs for visualizing
% the span of vectors.
if size(s)==[3,1]
    s=reshape(s,1,3);
end    
whitebg('w')
A=[];
x=[0,0]';
y=x;
z=x;
r=0;
n=0;
colors='brgmc';
close
while r<3
  n=n+1;
  if n>1
     s=input('Add another vector to S. Enter it as a triple [x y z]:  ');
     delete(t)
     hold off
  end   
  A=[A s'];
  c=randn(n,numvec);
  v=A*c;
  axiscale=3*max(max(abs(A)))+1;
  x(:,n)=[0;A(1,n)];
  y(:,n)=[0;A(2,n)];
  z(:,n)=[0;A(3,n)];
  r=fix(rank(A));
  color=[colors(mod(n,5)+1),'.'];
  plot3(x(:,n),y(:,n),z(:,n),'k')
  hold on
  plot3([-axiscale axiscale],[0 0 ],[0 0],'k',[0 0],[-axiscale axiscale],[0 0],'k',[0 0],[0 0],[-axiscale axiscale],'k')
  plot3(v(1,:),v(2,:),v(3,:),color)
  t=title(['Span of S    '    'Dimension = ' sprintf('%4.0f',r)]);
figure(1)
end
hold off