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

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
>

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]

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]
>

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]
>>
>
>