[jira] [Created] (MATH-1403) Collinearity test: QR Decomposition rank incorrect (SVD ok)

["Hugo Ferrira (JIRA)" <ji...@apache.org>]

Hugo Ferrira created MATH-1403:
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             Summary: Collinearity test: QR Decomposition rank incorrect (SVD ok)
                 Key: MATH-1403
                 URL: https://issues.apache.org/jira/browse/MATH-1403
             Project: Commons Math
          Issue Type: Bug
    Affects Versions: 3.6.1
         Environment: Linux ubuntu
JDK 8
            Reporter: Hugo Ferrira


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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