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[math] collinearity test: QR Decomposition rank incorrect (SVD ok)

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[math] collinearity test: QR Decomposition rank incorrect (SVD ok)

Hugo Ferreira
Hello,

I am aware that such a question have been asked before but I cannot seem
to solve this issue for a very simple example. The closest example I
have is:

https://issues.apache.org/jira/browse/MATH-1100

from which I could not get an answer.

I am trying to copy an algorithm from R's Caret package that identifies
collinear columns of a matrix [1]. I am assuming a "long" matrix and and
am using the trivial example from the reference above. However I cannot
get this to work because the QR's rank result is incorrect.

I have the following example:

import org.apache.commons.math3.linear.RealMatrix;
import org.apache.commons.math3.linear.RRQRDecomposition;
import org.apache.commons.math3.linear.Array2DRowRealMatrix;
import org.apache.commons.math3.linear.SingularValueDecomposition ;

public class QRIssue {

   public static void main(String[] args) {

     double[][] am = new double[5][];
     double[] c1 = new double[] {1.0, 1.0, 1.0, 1.0, 1.0, 1.0} ;
     double[] c2 = new double[] {1.0, 1.0, 1.0, 0.0, 0.0, 0.0} ;
     double[] c3 = new double[] {0.0, 0.0, 0.0, 1.0, 1.0, 1.0} ;
     double[] c4 = new double[] {1.0, 0.0, 0.0, 1.0, 0.0, 0.0 } ;
     double[] c6 = new double[] {0.0, 0.0, 1.0, 0.0, 0.0, 1.0 } ;

     am[0] = c1 ;
     am[1] = c2 ;
     am[2] = c3 ;
     am[3] = c4 ;
     am[4] = c6 ;

     Double threshold = 1e-1;

     Array2DRowRealMatrix m = new Array2DRowRealMatrix( am, false )  ;
// use array, don't copy
     RRQRDecomposition qr = new RRQRDecomposition( m,  threshold) ;
     RealMatrix r = qr.getR() ;
     int numColumns = r.getColumnDimension() ;
     int rank = qr.getRank( threshold ) ;
     System.out.println("QR rank: " + rank) ;
     System.out.println("QR is singular: " +
!qr.getSolver().isNonSingular()) ;
     System.out.println("QR is singular: " + (numColumns == rank) ) ;

     SingularValueDecomposition sv2 = new
org.apache.commons.math3.linear.SingularValueDecomposition(m);
     System.out.println("SVD rank: " + sv2.getRank()) ;
     }
}


For SVD I get a rank of 4 which is correct (columns 0,1,2 are collinear
: c0 = c1 + c2). But for QR I get 5. I have tried several thresholds
with no success. For several subsets of the columns above (example only
0,1,2 I get the correct answer). What am I doing wrong?

TIA,
Hugo F.


1. https://topepo.github.io/caret/pre-processing.html#lindep



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Re: [math] collinearity test: QR Decomposition rank incorrect (SVD ok)

Gilles Sadowski
FTR:
   https://issues.apache.org/jira/browse/MATH-1403

Gilles

On Thu, 23 Feb 2017 10:52:55 +0000, Hugo Ferreira wrote:

> Hello,
>
> I am aware that such a question have been asked before but I cannot
> seem to solve this issue for a very simple example. The closest
> example I have is:
>
> https://issues.apache.org/jira/browse/MATH-1100
>
> from which I could not get an answer.
>
> I am trying to copy an algorithm from R's Caret package that
> identifies collinear columns of a matrix [1]. I am assuming a "long"
> matrix and and am using the trivial example from the reference above.
> However I cannot get this to work because the QR's rank result is
> incorrect.
>
> I have the following example:
>
> import org.apache.commons.math3.linear.RealMatrix;
> import org.apache.commons.math3.linear.RRQRDecomposition;
> import org.apache.commons.math3.linear.Array2DRowRealMatrix;
> import org.apache.commons.math3.linear.SingularValueDecomposition ;
>
> public class QRIssue {
>
>   public static void main(String[] args) {
>
>     double[][] am = new double[5][];
>     double[] c1 = new double[] {1.0, 1.0, 1.0, 1.0, 1.0, 1.0} ;
>     double[] c2 = new double[] {1.0, 1.0, 1.0, 0.0, 0.0, 0.0} ;
>     double[] c3 = new double[] {0.0, 0.0, 0.0, 1.0, 1.0, 1.0} ;
>     double[] c4 = new double[] {1.0, 0.0, 0.0, 1.0, 0.0, 0.0 } ;
>     double[] c6 = new double[] {0.0, 0.0, 1.0, 0.0, 0.0, 1.0 } ;
>
>     am[0] = c1 ;
>     am[1] = c2 ;
>     am[2] = c3 ;
>     am[3] = c4 ;
>     am[4] = c6 ;
>
>     Double threshold = 1e-1;
>
>     Array2DRowRealMatrix m = new Array2DRowRealMatrix( am, false )  ;
> // use array, don't copy
>     RRQRDecomposition qr = new RRQRDecomposition( m,  threshold) ;
>     RealMatrix r = qr.getR() ;
>     int numColumns = r.getColumnDimension() ;
>     int rank = qr.getRank( threshold ) ;
>     System.out.println("QR rank: " + rank) ;
>     System.out.println("QR is singular: " +
> !qr.getSolver().isNonSingular()) ;
>     System.out.println("QR is singular: " + (numColumns == rank) ) ;
>
>     SingularValueDecomposition sv2 = new
> org.apache.commons.math3.linear.SingularValueDecomposition(m);
>     System.out.println("SVD rank: " + sv2.getRank()) ;
>     }
> }
>
>
> For SVD I get a rank of 4 which is correct (columns 0,1,2 are
> collinear : c0 = c1 + c2). But for QR I get 5. I have tried several
> thresholds with no success. For several subsets of the columns above
> (example only 0,1,2 I get the correct answer). What am I doing wrong?
>
> TIA,
> Hugo F.
>
>
> 1. https://topepo.github.io/caret/pre-processing.html#lindep
>
>



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