# [math] trouble with SingularValueDecomposition

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## [math] trouble with SingularValueDecomposition

 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
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## Re: [math] trouble with SingularValueDecomposition

 And what exactly are the results you are getting? On Fri, Feb 14, 2014 at 6:07 PM, Patrick Meyer <[hidden email]> 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 >             for(int j=0;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 >             for(int j=0;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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## Re: [math] trouble with SingularValueDecomposition

 In reply to this post by Patrick Meyer 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 <[hidden email]> 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 >             for(int j=0;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 >             for(int j=0;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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## RE: [math] trouble with SingularValueDecomposition

 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:[hidden email]] 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 <[hidden email]> 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 >             for(int j=0;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 >             for(int j=0;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 > > > > > > > > --------------------------------------------------------------------- To unsubscribe, e-mail: [hidden email] For additional commands, e-mail: [hidden email]