function R = qr_givens (A)
%QR_GIVENS Givens-rotation QR factorization.
% Example:
%   R = qr_givens (A)
% See also: cs_demo

%   Copyright 2006, Timothy A. Davis.
%   http://www.cise.ufl.edu/research/sparse

[m n] = size (A) ;
parent = cs_etree (sparse (A), 'col') ;
A = full (A) ;
for i = 2:m
    k = min (find (A (i,:))) ;						    %#ok
    if (isempty (k))
	continue ;
    end
    while (k > 0 && k <= min (i-1,n))
	A ([k i],k:n) = givens2 (A(k,k), A(i,k)) * A ([k i],k:n) ;
	A (i,k) = 0 ;
	k = parent (k) ;
    end
end
R = sparse (A) ;
