function B = getbasis(M)
%GETBASIS Orders the columns of M to serve as a good basis for
%	the column space of M itself.  This is accomplished using
%	a computationally intense, iterative algorithim based on the
%	Singular Value Decomposition (SVD).  The first column of B
%	is most significant the second next so, etc. in descending
%	order.
%
% Written by Finny Kuruvilla	 v1.1.0	Last updated 5-14-2001

[rows,cols]=size(M);

if rank(M)< min(rows,cols)
   error('Matrix is rank deficient.');
end

A=M;

for k=1:cols
   [U,D,V]=svd(A);		% compute the SVD of our running matrix A.
   c=U(:,1);				% use the first column of U to find our next column vector.
   coeffs=M\c;				% find the least-squares solution for which column of
   							% 	 M contributes most to the first column of U
   [maxval,pos]=max(abs(coeffs));
   B(:,k)=M(:,pos);		% grab the column of M that has highest abs least-squares coefficient.
   M(:,pos)=[];			% and delete it from M.
   P=B*inv(B'*B)*B';		% construct the projection matrix of existing basis vectors.
   A=M-P*M;					% and use it to remove the span of the existing basis from M.

   disp(sprintf('Basis %d of %d computed',k,cols));
   pause(.01);
end