?? varpro_qr.m
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function [Q, R, P, r] = varpro_qr (X, defeps);%VARPRO_QR Special QR decomposition%% [Q, R, P, r] = varpro_qr (X, defeps);% makes Q*X*P == R ( == [R1(r,r), R2(r,n-r); 0(m-r,r), 0(m-r,n-r)]).%% defeps: limit for rank-deficiency%% r: rank of R (with respect to defeps) [m, n] = size(X); [Q, R, P] = qr(X); normr = norm(R); r = 1; while (r <= min(m,n)), if (norm(R(r,r:n)) < defeps*normr), break; end; r = r + 1; end r = r - 1; Q = Q';end % varpro_qr
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