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From: Ted Dunning <ted.dunning@gmail.com>
Date: Sat, 15 Feb 2014 17:02:00 -0800
Message-ID: 
 <CAJwFCa3TPcCu_oBA8-Xa_Py=8opP2XV8Pea2XRU7sx5a0vOd8A@mail.gmail.com>
Subject: Re: [math] trouble with SingularValueDecomposition
To: Commons Developers List <dev@commons.apache.org>
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Note that the only reason that the order is unconstrained is because the
two corresponding singular values are equal.

Strictly speaking, for equal singular values, any unitary transformation of
the corresponding singular vectors are also valid singular vectors.


On Sat, Feb 15, 2014 at 4:09 AM, Patrick Meyer <meyerjp3@gmail.com> wrote:

> Thanks Ted. As I mentioned my knowledge of SVD is limited, and I was not
> aware that it is OK to have a different order of the first two columns in
> the results (or the conditions under which the order doesn't matter). I a=
m
> trying to track down a bug in some code and that=E2=80=99s what led me to=
 the SVD.
> I guess I need to keep looking for the real bug.
>
> For completeness, my results R were the same as you reported. My results
> from CM are shown below and if you swap the first and second column, the
> results agree with R.
>
> U:
> 0.9940594018965339  0.06774763124429131  -0.08518312016997649
> 0.10615872136916754  -0.7761401247896214  0.6215599991704858
> 0.02400481989869077  0.6269104921377042  0.778721390144956
>
> V:
> 0.9963653125425972  0.0  -0.08518312016997495
> 0.0531395658155507  -0.7815621241949481  0.6215599991704865
> 0.06657590034559915  0.6238274168581248  0.7787213901449556
>
>
>
> -----Original Message-----
> From: Ted Dunning [mailto:ted.dunning@gmail.com]
> Sent: Saturday, February 15, 2014 2:17 AM
> To: Commons Developers List
> Subject: Re: [math] trouble with SingularValueDecomposition
>
> For what its worth, I tested the Mahout SVD which shares code lineage wit=
h
> the Commons Math implementation.
>
> The results I got were:
>
>
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> > *sum(abs(m - u * s * v')) =3D 4.31946146e-16S =3D    1.002319690998
> >  1.002319690998    1.000000000000
>
> U =3D    0.994059401897 0.067747631244
> > -0.085183120170    0.106158721369 -0.776140124790 0.621559999170
> >  0.024004819899 0.626910492138 0.778721390145 V =3D    0.996365312543
> > 0.000000000000 -0.085183120170    0.053139565816 -0.781562124195
> > 0.621559999170    0.066575900346 0.623827416858 0.778721390145*
>
>
> Note that the residue of the reconstruction is excellently small.  This
> indicates that the result is correct.
>
>
> If you compare these to the R results,
>
>
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> > *[1] 1.0023196909980066 1.0023196909980066 1.0000000000000000$u
> >           [,1]                  [,2]                  [,3][1,]
> >  0.067747631244291326 -0.994059401896534967  0.085183120169970525 [2,]
> > -0.776140124789635122 -0.106158721369163295 -0.621559999170469113[3,]
> >  0.626910492137687125 -0.024004819898688426 -0.778721390144969994$v
> >              [,1]                  [,2]                  [,3] [1,]
> >  0.00000000000000000 -0.996365312542597747  0.085183120169970497[2,]
> > -0.78156212419496163 -0.053139565815546450 -0.621559999170469668[3,]
> >  0.62382741685810772 -0.066575900345596822 -0.778721390144969550*
>
>
> These are identical to the previous results except that the first two
> singular values are equal which means that the order of the corresponding
> left and right singular vectors are different and there are sign changes =
in
> the singular vectors.
>
> My guess is that you will get the same results in Apache Commons Math.
>
>
>
> On Fri, Feb 14, 2014 at 6:07 PM, Patrick Meyer <meyerjp3@gmail.com> wrote=
:
>
> > Hi,
> >
> >
> >
> > I am using the SingularValueDecomposition class with a matrix but it
> > gives me a different result than R. My knowledge of SVD is limited, so
> > any advice is welcomed.
> >
> >
> >
> > Here's the method in Java
> >
> >
> >
> > public void svdTest(){
> >
> >
> >
> >         double[][] x =3D {
> >
> >                 {1.0,  -0.053071807862720116,  0.04236086650321309},
> >
> >                 {0.05307180786272012,  1.0,  0.0058054424137053435},
> >
> >                 {-0.04236086650321309,  -0.005805442413705342,  1.0}
> >
> >         };
> >
> >
> >
> >         RealMatrix X =3D new Array2DRowRealMatrix(x);
> >
> >
> >
> >         SingularValueDecomposition svd =3D new
> > SingularValueDecomposition(X);
> >
> >
> >
> >         RealMatrix U =3D svd.getU();
> >
> >         for(int i=3D0;i<U.getRowDimension();i++){
> >
> >             for(int j=3D0;j<U.getColumnDimension();j++){
> >
> >                 System.out.print(U.getEntry(i,j) + "  ");
> >
> >             }
> >
> >             System.out.println();
> >
> >         }
> >
> >
> >
> >         System.out.println();
> >
> >         System.out.println();
> >
> >         RealMatrix V =3D svd.getV();
> >
> >         for(int i=3D0;i<V.getRowDimension();i++){
> >
> >             for(int j=3D0;j<V.getColumnDimension();j++){
> >
> >                 System.out.print(V.getEntry(i,j) + "  ");
> >
> >             }
> >
> >             System.out.println();
> >
> >         }
> >
> >
> >
> >
> >
> >     }
> >
> >
> >
> >
> >
> > And here's the function in R.
> >
> >
> >
> > x<-matrix(c(
> >
> >                 1.0,  -0.053071807862720116,  0.04236086650321309,
> >
> >       0.05307180786272012,  1.0,  0.0058054424137053435,
> >
> >       -0.04236086650321309,  -0.005805442413705342,  1.0),
> >
> >                 nrow=3D3, byrow=3DTRUE)
> >
> > svd(x)
> >
> >
> >
> > Does anyone know why I am getting different results for U and V? I am
> > using commons math 3.1.
> >
> >
> >
> > Thanks,
> >
> > Patrick
> >
> >
> >
> >
> >
> >
> >
> >
>
>
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