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From: "Patrick Meyer" <meyerjp3@gmail.com>
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Subject: RE: [math] trouble with SingularValueDecomposition
Date: Sun, 16 Feb 2014 22:48:23 -0500
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Thanks again Ted.=20

For what it's worth I have been using the linear algebra features in CM =
recently and they are really nice. Thanks to everyone who contributed to =
it!

-----Original Message-----
From: Ted Dunning [mailto:ted.dunning@gmail.com]=20
Sent: Saturday, February 15, 2014 8:02 PM
To: Commons Developers List
Subject: Re: [math] trouble with SingularValueDecomposition

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=20
> not aware that it is OK to have a different order of the first two=20
> columns in the results (or the conditions under which the order=20
> doesn't matter). I am 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=20
> results from CM are shown below and if you swap the first and second=20
> 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=20
> with 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. =20
> This indicates that the result is correct.
>
>
> If you compare these to the R results,
>
>
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> > *[1] 1.0023196909980066 1.0023196909980066 1.0000000000000000$u
> >           [,1]                  [,2]                  [,3][1,]
> >  0.067747631244291326 -0.994059401896534967  0.085183120169970525=20
> > [2,]
> > -0.776140124789635122 -0.106158721369163295=20
> > -0.621559999170469113[3,]
> >  0.626910492137687125 -0.024004819898688426 -0.778721390144969994$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=20
> singular values are equal which means that the order of the=20
> corresponding left and right singular vectors are different and there=20
> 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,=20
> > 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=20
> > 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=20
> > am using commons math 3.1.
> >
> >
> >
> > Thanks,
> >
> > Patrick
> >
> >
> >
> >
> >
> >
> >
> >
>
>
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