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

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

 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-1100from 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--------------------------------------------------------------------- To unsubscribe, e-mail: [hidden email] For additional commands, e-mail: [hidden email]