I put a comment on the wikipedia talk page. The wikipedia example is just wrong.
On Thu, Jan 19, 2012 at 8:18 AM, Ted Dunning <[email protected]> wrote: > And on the subject of correctness, R gives exactly the Mahout results. > > > x > V1 V2 V3 > 1 12 -51 4 > 2 6 167 -68 > 3 -4 24 -41 > > > qr.Q(qr(x)) > [,1] [,2] [,3] > [1,] -0.8571429 0.3942857 0.33142857 > [2,] -0.4285714 -0.9028571 -0.03428571 > [3,] 0.2857143 -0.1714286 0.94285714 > > qr.R(qr(x)) > V1 V2 V3 > [1,] -14 -21 14 > [2,] 0 -175 70 > [3,] 0 0 -35 > > > > And the results you quote from Wikipedia don't actually combine to get the > right result: > > > as.matrix(q) %*% as.matrix(r) > V1 V2 V3 > [1,] 11.99996 -50.98650 4.002192 > [2,] 5.99998 166.97736 24.000335 > [3,] 3.99994 -67.98786 -40.998769 > > q > V1 V2 V3 > 1 -0.85714 0.3110 -0.4106 > 2 -0.42857 -0.8728 0.2335 > 3 -0.28571 0.3761 0.8814 > > r > V1 V2 V3 > 1 -14 -8.4286 -2.0000 > 2 0 -187.1736 -35.1241 > 3 0 0.0000 -32.1761 > > > > > 2012/1/19 刘鎏 <[email protected]> > >> Hi, Ted >> >> Thanks for your comment. The original matrix is: >> >> qRef - 3 x 3 >> 12.00000 -51.00000 4.00000 >> 6.00000 167.00000 -68.00000 >> -4.00000 24.00000 -41.00000 >> >> The result of mahout: >> q - 3 x 3 >> -0.85714 0.39429 -0.33143 >> -0.42857 -0.90286 0.03429 >> 0.28571 -0.17143 -0.94286 >> >> r - 3 x 3 >> -14.00000 -21.00000 14.00000 >> 0.00000-175.00000 70.00000 >> 0.00000 0.00000 35.00000 >> >> The result of wiki(http://en.wikipedia.org/wiki/QR_decomposition): >> >> q - 3 x 3 >> -0.85714 0.3110 -0.4106 >> -0.42857 -0.8728 0.2335 >> -0.28571 0.3761 0.8814 >> >> r - 3 x 3 >> -14.00000 -8.4286 -2.0000 >> 0.00000 -187.1736 -35.1241 >> 0.00000 0.00000 -32.1761 >> >> I notice that there are differences in computing householder vector, given >> input vector x, >> >> In mahout, householder vector is computed as v= x/||x||, >> however in wiki, it is computed as u = x+||x||*e1, v=u/||u||. >> >> So, would you please give me some clues about why did mahout(actually >> JAMA) do like that? >> Thanks for your reply! >> >> Liu Liu >> On Thu, Jan 19, 2012 at 8:01 AM, Ted Dunning <[email protected]> >> wrote: >> >> > There are lots of QR decomposition algorithms and the results are not >> > necessarily unique, especially for rank deficient inputs. >> > >> > If you post your exact results, I could comment more specifically. >> Without >> > more details, I really can't answer your question in any specific way. >> > >> > On Wed, Jan 18, 2012 at 9:39 AM, 刘鎏 <[email protected]> wrote: >> > >> > > Hi, >> > > When I run QRDecomposition in mahout , I find the result of Q or R is >> > > different from the example in wiki( >> > > >> > >> http://en.wikipedia.org/wiki/QR_decomposition#Using_Householder_reflections >> > > ). >> > > After reading the source code, I find the implement of QR >> decomposition >> > is >> > > exactly different from the tradition way such as the procedure in >> wiki. >> > > Could any one show why mahout implement it in such a way? Thanks for >> your >> > > replies! >> > > >> > > Liu Liu >> > > >> > >> >> >> >> -- >> 刘鎏 >> >> 奇艺公司 >> 北京市海淀区海淀东三街2号欧美汇大厦8层 100080 >> >> Phone: (010) 6267-7240 >> E-mail: [email protected] >> MSN: [email protected] >> > >
