ROOT Version: 6.18/00
Platform: linux
Compiler: gcc (GCC) 9.1.1
I have a serious problem with inconsistent results from Minuit. I previously was using ROOT v5.34/36 to run TFractionFitter on data and recently switched to v6.18/00 running on a new machine.
Running my codes on the same data I can get a good fit from TFractionFitter using v5.34, but when I try the same codes and data on v6.18 (using a different maching), the fits fail. Both machines in this case are 64-bit.
Because this is very difficult problem it is not a simple matter for me to submit a minimal working example for testing. But I have noticed some odd differences in the output from Minuit that may help explain the cause of the problem. I hope a Minuit expert can help me.
Here is the Minuit output from v5.34:
**********
** 1 **SET PRINT 1
**********
PARAMETER DEFINITIONS:
NO. NAME VALUE STEP SIZE LIMITS
1 frac0 2.50000e-01 1.00000e-02 no limits
2 frac1 2.50000e-01 1.00000e-02 no limits
3 frac2 2.50000e-01 1.00000e-02 no limits
4 frac3 2.50000e-01 1.00000e-02 no limits
**********
** 2 **SET LIMIT 0 0 1
**********
PARAMETER 1 LIMITS SET TO 0 1
PARAMETER 2 LIMITS SET TO 0 1
PARAMETER 3 LIMITS SET TO 0 1
PARAMETER 4 LIMITS SET TO 0 1
**********
** 3 **SET LIMIT 1 0 1
**********
PARAMETER 1 LIMITS SET TO 0 1
**********
** 4 **SET LIMIT 2 0 1
**********
PARAMETER 2 LIMITS SET TO 0 1
**********
** 5 **SET LIMIT 3 0 1
**********
PARAMETER 3 LIMITS SET TO 0 1
**********
** 6 **SET STR 2
**********
NOW USING STRATEGY 2: MAKE SURE MINIMUM TRUE, ERRORS CORRECT
**********
** 7 **SET ERRDEF 0.5
**********
**********
** 8 **MINIMIZE
**********
FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
START MIGRAD MINIMIZATION. STRATEGY 2. CONVERGENCE WHEN EDM .LT. 5.00e-05
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-255749 FROM HESSE STATUS=OK 35 CALLS 36 TOTAL
EDM=43.2291 STRATEGY= 2 ERROR MATRIX ACCURATE
EXT PARAMETER STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 frac0 2.50000e-01 3.71645e-02 5.00000e-01 -9.05987e+01
2 frac1 2.50000e-01 6.04088e-02 5.00000e-01 -2.95201e+01
3 frac2 2.50000e-01 5.35927e-02 5.00000e-01 2.86233e+01
4 frac3 2.50000e-01 3.17427e-02 5.00000e-01 9.18599e+01
ERR DEF= 0.5
MIGRAD FAILS TO FIND IMPROVEMENT
MACHINE ACCURACY LIMITS FURTHER IMPROVEMENT.
MIGRAD MINIMIZATION HAS CONVERGED.
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
EIGENVALUES OF SECOND-DERIVATIVE MATRIX:
-5.1185e-03 1.2490e-01 8.6336e-01 3.0169e+00
MINUIT WARNING IN HESSE
============== MATRIX FORCED POS-DEF BY ADDING 0.008135 TO DIAGONAL.
FCN=-255789 FROM HESSE STATUS=NOT POSDEF 31 CALLS 207 TOTAL
EDM=0.00122958 STRATEGY= 2 ERR MATRIX NOT POS-DEF
EXT PARAMETER APPROXIMATE STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 frac0 6.01291e-01 1.97451e-01 2.26382e-02 5.00374e-01
2 frac1 7.34540e-02 6.06160e-01 4.34221e-02 2.00789e-01
3 frac2 1.79586e-01 2.83960e-01 2.78163e-02 2.37737e-01
4 frac3 1.46658e-01 7.54516e-02 2.03263e-02 1.12382e-01
ERR DEF= 0.5
MINUIT WARNING IN MIGRAD
============== Negative diagonal element 1 in Error Matrix
MINUIT WARNING IN MIGRAD
============== Negative diagonal element 2 in Error Matrix
MINUIT WARNING IN MIGRAD
============== Negative diagonal element 3 in Error Matrix
MINUIT WARNING IN MIGRAD
============== 3.69655 added to diagonal of error matrix
MIGRAD FAILS TO FIND IMPROVEMENT
MACHINE ACCURACY LIMITS FURTHER IMPROVEMENT.
MIGRAD MINIMIZATION HAS CONVERGED.
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
EIGENVALUES OF SECOND-DERIVATIVE MATRIX:
-6.7876e-03 1.2446e-01 8.6326e-01 3.0191e+00
MINUIT WARNING IN HESSE
============== MATRIX FORCED POS-DEF BY ADDING 0.009807 TO DIAGONAL.
FCN=-255789 FROM HESSE STATUS=NOT POSDEF 39 CALLS 292 TOTAL
EDM=3.41157e-05 STRATEGY= 2 ERR MATRIX NOT POS-DEF
EXT PARAMETER APPROXIMATE STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 frac0 5.98507e-01 1.96422e-01 2.25787e-02 2.64019e-02
2 frac1 7.74552e-02 5.92064e-01 4.31920e-02 2.21204e-03
3 frac2 1.76761e-01 2.83785e-01 2.78705e-02 -2.86413e-03
4 frac3 1.47307e-01 7.54910e-02 2.03120e-02 -1.75195e-02
ERR DEF= 0.5
MIGRAD MINIMIZATION HAS CONVERGED.
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-255789 FROM MIGRAD STATUS=CONVERGED 326 CALLS 327 TOTAL
EDM=3.7573e-06 STRATEGY= 2 ERROR MATRIX ACCURATE
EXT PARAMETER STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 frac0 5.97914e-01 1.19340e-01 1.80629e-03 1.56320e-02
2 frac1 7.87048e-02 2.16312e-01 6.91071e-04 3.91671e-03
3 frac2 1.75893e-01 1.90154e-01 2.22964e-03 -5.66387e-03
4 frac3 1.47498e-01 5.85531e-02 8.12478e-03 -2.29628e-02
ERR DEF= 0.5
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 4 ERR DEF=0.5
1.453e-02 -2.756e-02 1.739e-02 -3.644e-03
-2.756e-02 6.310e-02 -4.632e-02 1.085e-02
1.739e-02 -4.632e-02 3.964e-02 -1.050e-02
-3.644e-03 1.085e-02 -1.050e-02 3.460e-03
PARAMETER CORRELATION COEFFICIENTS
NO. GLOBAL 1 2 3 4
1 0.96483 1.000 -0.910 0.725 -0.514
2 0.99130 -0.910 1.000 -0.926 0.735
3 0.98825 0.725 -0.926 1.000 -0.897
4 0.93661 -0.514 0.735 -0.897 1.000
**********
** 9 **CALL FCN 3
**********
energy bin: 0
chi2/NDOF: 22.5884/19
GetProb(): 0.255956
pfrac: (0.597914 +/- 0.118696)
hfrac: (0.0787048 +/- 0.251176)
nfrac: (0.175893 +/- 0.199006)
ifrac: (0.147498 +/- 0.0586209)
Here is the output from Minuit using ROOT v6.18/00:
Minimizer Type : Minuit
Minimizer Algorithm : minimize
Strategy : 2
Tolerance : 0.01
Max func calls : 0
Max iterations : 0
Func Precision : -1
Error definition : 0.5
Print Level : 2
**********
** 1 **SET PRINT 1
**********
**********
** 2 **SET NOGRAD
**********
PARAMETER DEFINITIONS:
NO. NAME VALUE STEP SIZE LIMITS
1 frac0 2.50000e-01 1.00000e-02 0.00000e+00 1.00000e+00
2 frac1 2.50000e-01 1.00000e-02 0.00000e+00 1.00000e+00
3 frac2 2.50000e-01 1.00000e-02 0.00000e+00 1.00000e+00
4 frac3 2.50000e-01 1.00000e-02 0.00000e+00 1.00000e+00
**********
** 3 **SET ERR 0.5
**********
**********
** 4 **SET PRINT 1
**********
**********
** 5 **SET EPS 1e-06
**********
FLOATING-POINT NUMBERS ASSUMED ACCURATE TO 1e-06
**********
** 6 **SET STR 2
**********
NOW USING STRATEGY 2: MAKE SURE MINIMUM TRUE, ERRORS CORRECT
**********
** 7 **MINIMIZE 1480 0.01
**********
FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
START MIGRAD MINIMIZATION. STRATEGY 2. CONVERGENCE WHEN EDM .LT. 1.00e-05
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-255749 FROM HESSE STATUS=OK 37 CALLS 38 TOTAL
EDM=40.6966 STRATEGY= 2 ERROR MATRIX ACCURATE
EXT PARAMETER STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 frac0 2.50000e-01 4.05011e-02 2.35601e-01 -9.05960e+01
2 frac1 2.50000e-01 6.64961e-02 5.00000e-01 -2.95098e+01
3 frac2 2.50000e-01 5.47104e-02 5.00000e-01 2.87671e+01
4 frac3 2.50000e-01 3.17741e-02 2.35601e-01 9.18157e+01
ERR DEF= 0.5
MIGRAD FAILS TO FIND IMPROVEMENT
MACHINE ACCURACY LIMITS FURTHER IMPROVEMENT.
MIGRAD MINIMIZATION HAS CONVERGED.
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
EIGENVALUES OF SECOND-DERIVATIVE MATRIX:
-1.0346e-01 3.6641e-01 8.5247e-01 2.8846e+00
MINUIT WARNING IN HESSE
============== MATRIX FORCED POS-DEF BY ADDING 0.106347 TO DIAGONAL.
FCN=-255788 FROM HESSE STATUS=NOT POSDEF 29 CALLS 315 TOTAL
EDM=5.41761 STRATEGY= 2 ERR MATRIX NOT POS-DEF
EXT PARAMETER APPROXIMATE STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 frac0 5.46871e-01 6.27784e-02 5.00000e-01 1.05649e+01
2 frac1 2.59425e-01 3.08067e-01 5.00000e-01 6.19719e+00
3 frac2 5.31693e-02 7.01852e-01 5.00000e-01 -2.10844e+00
4 frac3 1.49307e-01 1.35791e-01 5.00000e-01 -1.81188e+01
ERR DEF= 0.5
MIGRAD FAILS TO FIND IMPROVEMENT
MACHINE ACCURACY LIMITS FURTHER IMPROVEMENT.
MIGRAD MINIMIZATION HAS CONVERGED.
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
MINUIT WARNING IN HESSE
============== MATRIX FORCED POS-DEF BY ADDING 0.001190 TO DIAGONAL.
FCN=-255789 FROM HESSE STATUS=NOT POSDEF 31 CALLS 374 TOTAL
EDM=0.0746595 STRATEGY= 2 ERR MATRIX NOT POS-DEF
EXT PARAMETER APPROXIMATE STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 frac0 5.35050e-01 5.93439e-02 5.00000e-01 -5.01802e+00
2 frac1 1.85802e-01 5.88641e-01 5.00000e-01 -2.27013e+00
3 frac2 1.12919e-01 5.04089e-01 5.00000e-01 -2.25462e+00
4 frac3 1.55509e-01 1.03299e-01 5.00000e-01 -4.23635e+00
ERR DEF= 0.5
MIGRAD FAILS TO FIND IMPROVEMENT
MACHINE ACCURACY LIMITS FURTHER IMPROVEMENT.
MIGRAD MINIMIZATION HAS CONVERGED.
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
MIGRAD TERMINATED WITHOUT CONVERGENCE.
FCN=-255789 FROM MIGRAD STATUS=FAILED 413 CALLS 414 TOTAL
EDM=0.0875076 STRATEGY= 2 ERR MATRIX APPROXIMATE
EXT PARAMETER APPROXIMATE STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 frac0 5.42222e-01 5.90579e-02 2.00000e-01 -2.37432e-01
2 frac1 1.97151e-01 1.85981e-01 2.00000e-01 1.11389e+00
3 frac2 9.74603e-02 1.85787e-01 2.00000e-01 3.19277e-01
4 frac3 1.63331e-01 5.91719e-02 2.00000e-01 -7.03312e-01
ERR DEF= 0.5
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 4 ERR DEF=0.5
3.504e-03 -7.626e-03 5.676e-03 -1.282e-03
-7.626e-03 3.745e-02 -3.697e-02 9.437e-03
5.676e-03 -3.697e-02 4.031e-02 -1.095e-02
-1.282e-03 9.437e-03 -1.095e-02 3.532e-03
ERR MATRIX APPROXIMATE
PARAMETER CORRELATION COEFFICIENTS
NO. GLOBAL 1 2 3 4
1 0.84589 1.000 -0.666 0.478 -0.364
2 0.98508 -0.666 1.000 -0.952 0.821
3 0.98837 0.478 -0.952 1.000 -0.918
4 0.93727 -0.364 0.821 -0.918 1.000
ERR MATRIX APPROXIMATE
START SIMPLEX MINIMIZATION. CONVERGENCE WHEN EDM .LT. 0.01
FCN=-255789 FROM SIMPLEX STATUS=PROGRESS 12 CALLS 426 TOTAL
EDM=2.95426 STRATEGY= 2 ERR MATRIX APPROXIMATE
EXT PARAMETER APPROXIMATE INTERNAL INTERNAL
NO. NAME VALUE ERROR STEP SIZE VALUE
1 frac0 5.42222e-01 5.90579e-02 1.89663e-02 8.45442e-02
2 frac1 1.97151e-01 1.85981e-01 7.47949e-02 -6.50643e-01
3 frac2 9.74603e-02 1.85787e-01 1.00228e-01 -9.35809e-01
4 frac3 1.63331e-01 5.91719e-02 2.56108e-02 -7.38714e-01
ERR DEF= 0.5
SIMPLEX MINIMIZATION HAS CONVERGED.
FCN=-255789 FROM SIMPLEX STATUS=PROGRESS 49 CALLS 463 TOTAL
EDM=0.00877881 STRATEGY= 2 ERR MATRIX APPROXIMATE
EXT PARAMETER APPROXIMATE INTERNAL INTERNAL
NO. NAME VALUE ERROR STEP SIZE VALUE
1 frac0 5.57343e-01 5.90579e-02 1.64392e-02 1.14938e-01
2 frac1 1.77153e-01 1.85981e-01 4.02039e-02 -7.01931e-01
3 frac2 9.58102e-02 1.85787e-01 1.74254e-02 -9.41394e-01
4 frac3 1.68064e-01 5.91719e-02 1.58524e-02 -7.25984e-01
ERR DEF= 0.5
START MIGRAD MINIMIZATION. STRATEGY 2. CONVERGENCE WHEN EDM .LT. 1.00e-05
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-255789 FROM HESSE STATUS=OK 29 CALLS 492 TOTAL
EDM=0.0183508 STRATEGY= 2 ERROR MATRIX ACCURATE
EXT PARAMETER STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 frac0 5.57343e-01 7.44112e-02 4.00000e-02 -8.08407e-01
2 frac1 1.77153e-01 1.39197e-01 5.00000e-01 -2.77972e-01
3 frac2 9.58102e-02 9.54030e-02 4.00000e-02 -6.69018e-01
4 frac3 1.68064e-01 3.13407e-02 5.00000e-01 -2.20985e-01
ERR DEF= 0.5
MINUIT WARNING IN MIGRAD
============== Negative diagonal element 2 in Error Matrix
MINUIT WARNING IN MIGRAD
============== Negative diagonal element 3 in Error Matrix
MINUIT WARNING IN MIGRAD
============== 1.02683 added to diagonal of error matrix
MIGRAD FAILS TO FIND IMPROVEMENT
EIGENVALUES OF SECOND-DERIVATIVE MATRIX:
-1.3623e-02 3.5088e-01 8.5567e-01 2.8071e+00
MINUIT WARNING IN HESSE
============== MATRIX FORCED POS-DEF BY ADDING 0.016430 TO DIAGONAL.
FCN=-255789 FROM HESSE STATUS=NOT POSDEF 31 CALLS 555 TOTAL
EDM=0.0758571 STRATEGY= 2 ERR MATRIX NOT POS-DEF
EXT PARAMETER APPROXIMATE STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 frac0 5.75934e-01 9.60840e-02 5.00000e-01 -4.64489e-01
2 frac1 1.33834e-01 5.28118e-01 5.00000e-01 -1.66807e-01
3 frac2 1.29182e-01 5.32337e-01 5.00000e-01 -3.95091e-01
4 frac3 1.60249e-01 7.64695e-02 5.00000e-01 1.56880e-01
ERR DEF= 0.5
MINUIT WARNING IN MIGRAD
============== Negative diagonal element 2 in Error Matrix
MINUIT WARNING IN MIGRAD
============== Negative diagonal element 3 in Error Matrix
MINUIT WARNING IN MIGRAD
============== Negative diagonal element 4 in Error Matrix
MINUIT WARNING IN MIGRAD
============== 1.38038 added to diagonal of error matrix
MIGRAD FAILS TO FIND IMPROVEMENT
EIGENVALUES OF SECOND-DERIVATIVE MATRIX:
-1.6916e-02 3.4972e-01 8.5548e-01 2.8117e+00
MINUIT WARNING IN HESSE
============== MATRIX FORCED POS-DEF BY ADDING 0.019727 TO DIAGONAL.
FCN=-255789 FROM HESSE STATUS=NOT POSDEF 31 CALLS 652 TOTAL
EDM=0.0508473 STRATEGY= 2 ERR MATRIX NOT POS-DEF
EXT PARAMETER APPROXIMATE STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 frac0 5.81666e-01 1.10427e-01 5.00000e-01 -3.15966e-01
2 frac1 1.20282e-01 5.03246e-01 5.00000e-01 -1.25563e-01
3 frac2 1.40228e-01 5.48957e-01 5.00000e-01 -3.57134e-01
4 frac3 1.57192e-01 6.76230e-02 5.00000e-01 2.74163e-02
ERR DEF= 0.5
EIGENVALUES OF SECOND-DERIVATIVE MATRIX:
-1.1510e-02 2.8969e-01 6.2324e-01 3.0986e+00
MINUIT WARNING IN MIGRAD
============== MATRIX FORCED POS-DEF BY ADDING 0.014609 TO DIAGONAL.
EIGENVALUES OF SECOND-DERIVATIVE MATRIX:
-5.8990e-04 2.5930e-01 4.5982e-01 3.2815e+00
MINUIT WARNING IN MIGRAD
============== MATRIX FORCED POS-DEF BY ADDING 0.003871 TO DIAGONAL.
MIGRAD FAILS TO FIND IMPROVEMENT
MACHINE ACCURACY LIMITS FURTHER IMPROVEMENT.
MIGRAD MINIMIZATION HAS CONVERGED.
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
EIGENVALUES OF SECOND-DERIVATIVE MATRIX:
-2.0367e-02 3.5005e-01 8.5568e-01 2.8146e+00
MINUIT WARNING IN HESSE
============== MATRIX FORCED POS-DEF BY ADDING 0.023182 TO DIAGONAL.
MIGRAD TERMINATED WITHOUT CONVERGENCE.
FCN=-255789 FROM MIGRAD STATUS=FAILED 245 CALLS 708 TOTAL
EDM=0.0105013 STRATEGY= 2 ERR MATRIX NOT POS-DEF
EXT PARAMETER APPROXIMATE STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 frac0 5.83332e-01 1.22301e-01 5.00000e-01 -8.62767e-01
2 frac1 1.10337e-01 5.18917e-01 5.00000e-01 -2.63562e-01
3 frac2 1.49796e-01 5.61150e-01 5.00000e-01 -1.22751e-01
4 frac3 1.55522e-01 6.00837e-02 5.00000e-01 7.25211e-01
ERR DEF= 0.5
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 4 ERR DEF=0.5
1.527e-02 -5.430e-02 4.638e-02 -6.083e-03
-5.430e-02 2.114e-01 -1.838e-01 2.442e-02
4.638e-02 -1.838e-01 1.620e-01 -2.209e-02
-6.083e-03 2.442e-02 -2.209e-02 3.644e-03
ERR MATRIX NOT POS-DEF
PARAMETER CORRELATION COEFFICIENTS
NO. GLOBAL 1 2 3 4
1 0.96762 1.000 -0.956 0.932 -0.815
2 0.99728 -0.956 1.000 -0.993 0.880
3 0.99688 0.932 -0.993 1.000 -0.909
4 0.93247 -0.815 0.880 -0.909 1.000
ERR MATRIX NOT POS-DEF
Warning in <TFractionFitter::Fit>: Abnormal termination of minimization.
Notice that when Minuit starts the EDM (43.3 vs 40.7) for both runs is similar and the value of FCN is the same (-255749). But as the fits proceed the EDM for Minuit v5.34 shrinks much faster that for v6.18. At the end of the fit, the EDM for v5.34 is 4x10^-6, while for 6.18 it is only 0.01, even though the FCN is the same for both versions (-255789) and the solutions for the parameters don’t appear to be significantly different for both the failed and successful fit. v5.34 also has much smaller step sizes then v6.18 at the end of the fitting process.
Does a Minuit expert understand why, given the same input and run the same way, one of these fits fails and the other does not, and why does EDM differ so significantly between them?