TDecompSVD fails to converge

Roofit and RooStats
1

I am having issues with TDecompSVD not converging on some occasions and getting the message “Error in TDecompSVD::Diagonalize: no convergence after 31 steps”. I narrowed it down to this minimal example:

main.cpp

// g++ `root-config --cflags --glibs` -o main main.cpp

#include <iostream>
#include "TROOT.h"
#include "TMatrixT.h"
#include "TVectorT.h"
#include "TDecompSVD.h"
#include "RVersion.h"

using namespace std;

int main(int argc, char** argv)
{	
	cout << ROOT_RELEASE << endl;
	

	double a = 1.689339828220179e-03;
	double b = 1.689339828220178e-03;
	double c = 1.5e-4;
	TMatrixD m(4, 3);
		
	m(0,0) =  a; m(0,1) =  a; m(0,2) = -c;
	m(1,0) =  a; m(1,1) =  a; m(1,2) =  c;
	m(2,0) = -b; m(2,1) = -b; m(2,2) =  c;
	m(3,0) = -b; m(3,1) = -b; m(3,2) = -c;
	
	m.Print();
	
	
	TDecompSVD s(m);
	
	s.Decompose();
	s.Print();
	
	return 0; 
}

Compiling with g++ root-config --cflags --glibs -o main main.cpp and running gives me the output

6.04/14

4x3 matrix is as follows

     |      0    |      1    |      2    |
--------------------------------------------
   0 |   0.001689    0.001689    -0.00015
   1 |   0.001689    0.001689     0.00015
   2 |  -0.001689   -0.001689     0.00015
   3 |  -0.001689   -0.001689    -0.00015

Error in <TDecompSVD::Diagonalize>: no convergence after 31 steps
fTol       = 2.2204e-16
fDet1      = 0.0000e+00
fDet2      = 0.0000e+00
fCondition = -1.0000e+00
fRowLwb    = 0
fColLwb    = 0

4x4 matrix is as follows

     |      0    |      1    |      2    |      3    |
---------------------------------------------------------
   0 |       -0.5        -0.5         0.5         0.5
   1 |       -0.5      0.8333      0.1667      0.1667
   2 |     0.2236     0.07454     -0.5217      0.8199
   3 |     0.6708      0.2236      0.6708      0.2236


4x3 matrix is as follows

     |      0    |      1    |      2    |
--------------------------------------------
   0 |    -0.7071     -0.7071           0
   1 |    -0.7071      0.7071          -0
   2 |          0          -0          -1
   3 |          0           0          -0


Vector (3) fSig is as follows

     |        1  |
------------------
   0 |0.00477817
   1 |-0
   2 |0.000223607

The SVD of this matrix does work in both Mathematica and the GNU Scientific Library. Also, note that TDecompSVD does converge if you change the variable b to be exactly the same as a.

Is this a bug maybe, or am I doing something wrong?
main.cpp (702 Bytes)

2

Normalize the matrix by for instance dividing every element through a and
the SVD will work.

Probably it has to be checked whether the input to the Diagonalization procedure
has to be scaled making it more robust.