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]
>
