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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