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From "Patrick Meyer" <meyer...@gmail.com>
Subject RE: [math] trouble with SingularValueDecomposition
Date Mon, 17 Feb 2014 03:48:23 GMT
Thanks again Ted. 

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] 
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 
> 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 am trying to track down a bug in some code and that’s 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 
> with the Commons Math implementation.
>
> The results I got were:
>
>
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> > *sum(abs(m - u * s * v')) = 4.31946146e-16S =    1.002319690998
> >  1.002319690998    1.000000000000
>
> U =    0.994059401897 0.067747631244
> > -0.085183120170    0.106158721369 -0.776140124790 0.621559999170
> >  0.024004819899 0.626910492138 0.778721390145 V =    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 = {
> >
> >                 {1.0,  -0.053071807862720116,  0.04236086650321309},
> >
> >                 {0.05307180786272012,  1.0,  0.0058054424137053435},
> >
> >                 {-0.04236086650321309,  -0.005805442413705342,  1.0}
> >
> >         };
> >
> >
> >
> >         RealMatrix X = new Array2DRowRealMatrix(x);
> >
> >
> >
> >         SingularValueDecomposition svd = new 
> > SingularValueDecomposition(X);
> >
> >
> >
> >         RealMatrix U = svd.getU();
> >
> >         for(int i=0;i<U.getRowDimension();i++){
> >
> >             for(int j=0;j<U.getColumnDimension();j++){
> >
> >                 System.out.print(U.getEntry(i,j) + "  ");
> >
> >             }
> >
> >             System.out.println();
> >
> >         }
> >
> >
> >
> >         System.out.println();
> >
> >         System.out.println();
> >
> >         RealMatrix V = svd.getV();
> >
> >         for(int i=0;i<V.getRowDimension();i++){
> >
> >             for(int j=0;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=3, byrow=TRUE)
> >
> > 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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