1function X = cs_qright (V, Beta, p, Y)
2%CS_QRIGHT apply Householder vectors on the right.
3%   X = cs_qright(V,Beta,p,Y) computes X = Y*P'*H1*H2*...*Hn = Y*Q where Q is
4%   represented by the Householder vectors V, coefficients Beta, and
5%   permutation p.  p can be [], which denotes the identity permutation.
6%   To obtain Q itself, use Q = cs_qright(V,Beta,p,speye(size(V,1))).
7%
8%   Example:
9%       load west0479 ; q = colamd (west0479) ; A = west0479 (:,q) ;
10%       [Q,R] = qr (A) ; norm (Q*R-A, 1)
11%       [V,beta,p,R2] = cs_qr (A) ;
12%       Q2 = cs_qright (V, beta, p, speye(size(V,1))) ; norm (Q2*R2-A, 1)
13%
14%   See also CS_QR, CS_QLEFT.
15
16% Copyright 2006-2012, Timothy A. Davis, http://www.suitesparse.com
17
18[m n] = size (V) ;
19X = Y ;
20if (~isempty (p))
21    X = X (:,p) ;
22end
23for k = 1:n
24    X = X - (X * (Beta (k) * V (:,k))) * V (:,k)' ;
25end
26