Different fit result from Minuit2 on different OS

[Crisps]

Dear experts

I ran the exactly same code on two different environments:

1. ROOT 6.32.08 on MacOSXarm64, built by Apple clang version 13.1.6
2. ROOT 6.32.10 on AlmaLinux 9.3, built by G++ 11.4.1
   What I did is using ROOT::Math::Minimizer (Minuit2) to minimize some chi2 function, with the exactly same code between 2 environments, but the former converged, the latter didn’t. How can I check what can be the reason caused this difference?

Here is the former output:

//Initial values
rho : 208.768
phi : -1.5865
alpha : 0.00565673
theta : 2.02477
Minuit2Minimizer: Minimize with max-calls 680 convergence for edm < 0.001 strategy 1
Minuit2Minimizer : Valid minimum - status = 0
FVAL  = 214.160692623696747
Edm   = 1.14154778132616991e-07
Nfcn  = 316
rho   = 210.335  +/-  0.0299698 (limited)
phi   = -1.58826     +/-  4.90308e-05   (limited)
alpha     = 0.0095228    +/-  2.98087e-05   (limited)
theta     = 2.14207  +/-  0.000546894   (limited)

and the latter outputs:

//initial values
rho : 208.768
phi : -1.5865
alpha : 0.00565673
theta : 2.02477
Minuit2Minimizer: Minimize with max-calls 680 convergence for edm < 0.001 strategy 1
Warning in <Minuit2>: VariableMetricBuilder No improvement in line search
Warning in <Minuit2>: VariableMetricBuilder Iterations finish without convergence; Edm 0.124551 Requested 2e-06
Warning in <Minuit2>: MnPosDef Matrix forced pos-def by adding to diagonal 0.658984
Warning in <Minuit2>: VariableMetricBuilder No improvement in line search
Warning in <Minuit2>: VariableMetricBuilder Iterations finish without convergence; Edm 82.5919 Requested 2e-06
Warning in <Minuit2>: VariableMetricBuilder FunctionMinimum is invalid after second try
Warning in <Minuit2>: Minuit2Minimizer::Minimize Minimization did NOT converge, Edm is above max
Minuit2Minimizer : Invalid minimum - status = 3
FVAL  = 4166.83
Edm   = 5.99185
Nfcn  = 466
rho : 211.643
phi : -1.58619
alpha : 0.0080292
theta : 2.16448

[lbreitwi]

Hi,

Can you please share a minimal and complete reproducer to investigate the issue?

Best,
Lukas

[Crisps]

I made a minimal reproducer, I needed to add the minimal functionalities to make it reproducible so some functions are added.
The minimization part is in the minimal() function, and I confirmed that the results are different on 2 environments.

Notice: if I hard code the initial value of minimizer as the same value calculated in the program it converges on Almalinux. I mean, instead of

fFit->SetVariable(0,     "rho",          rho,               1e-4);
    fFit->SetVariable(1,     "phi",          phi,               1e-4);
    fFit->SetVariable(2,     "alpha",        alpha,            1e-4);
    fFit->SetVariable(3,     "theta",        theta,               1e-4);

if you do

fFit->SetVariable(0,     "rho",          208.76798387,               1e-4);
    fFit->SetVariable(1,     "phi",          -1.58650429,               1e-4);
    fFit->SetVariable(2,     "alpha",        0.00565673,            1e-4);
    fFit->SetVariable(3,     "theta",        2.02477267,               1e-4);

it will converge.

minimal.cxx (5.1 KB)
graph.root (8.1 KB)
data.root (7.8 KB)
please try to run it with root -l minimal.cxx

[lbreitwi]

Hi,

Many thanks for creating the example. Following your instructions I could reproduce the issue.
@jonas do you have an idea of what could be causing the difference?

[Crisps]

@Jonas Could you please have a look of the reproducer? Many thanks!

[Crisps]

Reply to make this topic back to the top.

[jonas]

Hi @Crisps,

sorry, it looks like you were running into the corner case where difference in floating point precision between the compilers caused your fit to either fail or succeed.

Happens quite regularly in case you are accumulating a sum over multiple bins! What ROOT internally does in these cases is to avoid precision loss in the sum with the Kahan summation algorithm. You can do this too in your code, using ROOT’s helper class for that.

It’s a relatively small patch: just change the type of your accumolator variable chi2 and then call .Sum() in the end:

< void minimal_original(){
---
> void minimal_working(){
91c91
<     double chi2 = 0.;
---
>     ROOT::Math::KahanSum<double> chi2{0.0};
110,111c110,111
<     std::cout<<"chi2 == "<<chi2<<std::endl;
<     return chi2;
---
>     std::cout<<"chi2 == "<<chi2.Sum()<<std::endl;
>     return chi2.Sum();

Hope it works now everywhere!

Cheers,
Jonas

[Crisps]

Thank you Jonas, this works like a charm!