Landau definition in ROOT

faca87 · June 17, 2021, 2:13pm

Hello, In a Landau fit

TF1 *fitev = new TF1("Fit", "landau");

I get three parameters

fitev->SetParName(0,"C");
fitev->SetParName(1,"MPV");
 fitev->SetParName(2,"#sigma");

I see the definition of Landau function is ROOT: Probability Density Functions (PDF)

then are

My MPV = the lambda
my sigma = c
my C= the under the curve???

@moneta surely you know it

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moneta · June 17, 2021, 2:42pm

Hi,
p[1] and p[2] are just some location and scaling parameter , rescaling a landau(x) in a landau( ( x - p[1] )/p[2]), so p[1] is not exactly the landau MPV. See ROOT: TMath Namespace Reference

p[0] is instead a normalization parameter which corresponds to the area under the curve, since landau(x) is a normalized function (its integral is 1).

Cheers

Lorenzo

faca87 · June 17, 2021, 2:54pm

Thank you @moneta
In the link I read

mu is a location parameter and correspond approximately to the most probable value and sigma is a scale parameter (not the sigma of the full distribution which is not defined)

Then, for exampl, in this plot

can I say that MPV= p[1] =0.327703 ± 0.000045 , or would I do a big error?
Otherway, what is the relation between p[1] and MPV?

Thank you

Wile_E_Coyote · June 17, 2021, 2:55pm

gROOT->GetFunction("landau")->Print();
gROOT->GetFunction("landaun")->Print();

See also “landau” and “landaun” descriptions in the old TFormula::Analyze method description.

faca87 · June 17, 2021, 3:00pm

Thank you @Wile_E_Coyote

root [1] gROOT->GetFunction("landau")->Print();
Formula based function:     landau
               landau : landau Ndim= 1, Npar= 3, Number= 400
 Formula expression:
        [Constant]*TMath::Landau(x,[MPV],[Sigma],false)

then, I think I can approximate the MPV…

Ps. I can’t understand the difference bewenn landau and landaun

In the same way the expression "landau" is a substitute for [0]*[TMath](https://root.cern/root/html534/TMath.html)::[Landau](https://root.cern/root/html534/TMath.html#TMath:Landau)(x,[1],[2],[kFALSE](https://root.cern/root/html534/ListOfTypes.html#Bool_t)) to obtain a standard normalized landau, use "landaun" instead of "landau" the expression "landaun" is a substitute for [0]*[TMath](https://root.cern/root/html534/TMath.html)::[Landau](https://root.cern/root/html534/TMath.html#TMath:Landau)(x,[1],[2],[kTRUE](https://root.cern/root/html534/ListOfTypes.html#Bool_t)) WARNING: landau and landaun are mutually exclusive in the same expression.

ie. what is the diffence between false and true in the formua?

Wile_E_Coyote · June 17, 2021, 3:05pm

TMath::Landau

moneta · June 17, 2021, 3:09pm

For the correct MPV, just do:

TF1 f("f","landau",0.2,2.);
f.SetParameters( p0,p1,p2); 
double mpv = f.GetMaximumX();

Lorenzo

faca87 · June 17, 2021, 3:51pm

HEllo @moneta, I wrote

TF1 f1("f1","landau",0.2,2.);
			f1.SetParametrs(p0,p1,p2); 
			double mpv1 = f1.GetMaximumX();

	TF1 f2("f2","landau",0.2,2.);
			f2.SetParametrs(p0,p1,p2); 
			double mpv2 = f2.GetMaximumX();

but I get this error

/data_collamaf/DataFausto/Muon_Collider/III_anno/Tesi/Simulazioni_per_tesi/LEMMA_R=075_d=2cm_gaussian300um/Circolari/Energia_depositata/Be_1.5mm/simlemmaev.cpp:80:20: error: use of undeclared identifier 'p0'
                        f1.SetParametrs(p0,p1,p2);
                                        ^
/data_collamaf/DataFausto/Muon_Collider/III_anno/Tesi/Simulazioni_per_tesi/LEMMA_R=075_d=2cm_gaussian300um/Circolari/Energia_depositata/Be_1.5mm/simlemmaev.cpp:80:23: error: use of undeclared identifier 'p1'
                        f1.SetParametrs(p0,p1,p2);
                                           ^
/data_collamaf/DataFausto/Muon_Collider/III_anno/Tesi/Simulazioni_per_tesi/LEMMA_R=075_d=2cm_gaussian300um/Circolari/Energia_depositata/Be_1.5mm/simlemmaev.cpp:80:26: error: use of undeclared identifier 'p2'
                        f1.SetParametrs(p0,p1,p2);
                                              ^
/data_collamaf/DataFausto/Muon_Collider/III_anno/Tesi/Simulazioni_per_tesi/LEMMA_R=075_d=2cm_gaussian300um/Circolari/Energia_depositata/Be_1.5mm/simlemmaev.cpp:143:7: error: no member named 'SetParametrs' in 'TF1'
                        f2.SetParametrs(p0,p1,p2);
                        ~~ ^
/data_collamaf/DataFausto/Muon_Collider/III_anno/Tesi/Simulazioni_per_tesi/LEMMA_R=075_d=2cm_gaussian300um/Circolari/Energia_depositata/Be_1.5mm/simlemmaev.cpp:143:20: error: use of undeclared identifier 'p0'
                        f2.SetParametrs(p0,p1,p2);
                                        ^
/data_collamaf/DataFausto/Muon_Collider/III_anno/Tesi/Simulazioni_per_tesi/LEMMA_R=075_d=2cm_gaussian300um/Circolari/Energia_depositata/Be_1.5mm/simlemmaev.cpp:143:23: error: use of undeclared identifier 'p1'
                        f2.SetParametrs(p0,p1,p2);
                                           ^
/data_collamaf/DataFausto/Muon_Collider/III_anno/Tesi/Simulazioni_per_tesi/LEMMA_R=075_d=2cm_gaussian300um/Circolari/Energia_depositata/Be_1.5mm/simlemmaev.cpp:143:26: error: use of undeclared identifier 'p2'
                        f2.SetParametrs(p0,p1,p2);

moneta · June 17, 2021, 4:03pm

It is SetParameters and not SetParametrs and then you have to define or use directly the values for the 3 parameters of the Landau that you are using to make the figure above !

faca87 · June 17, 2021, 4:38pm

Thank you @moneta! it worked,
just last question please.
Is there a way to get the uncertinty on the MPV?

moneta · June 17, 2021, 6:09pm

Hi,
Which uncertainty ? The one obtained from a fit using a Landau ?

faca87 · June 17, 2021, 6:38pm

Hi @moneta the uncertainty on this value

TF1 f(“f”,“landau”,0.2,2.);
f.SetParameters( p0,p1,p2);
double mpv = f.GetMaximumX();

Wile_E_Coyote · June 17, 2021, 7:05pm

You can control the accuracy using the “epsilon” and “maxiter” parameters: TF1::GetMaximumX

faca87 · June 17, 2021, 7:22pm

Hi @Wile_E_Coyote I don’t see how to get the uncertainty…

Or is it just a function Draw (i.e not release to the fit), then it doesn’t have uncertainty?

moneta · June 18, 2021, 7:36am

Hi,
TF1::GetMaximumX it is a function based on the Brent 1d minimisation method. See ROOT: ROOT::Math::BrentMinimizer1D Class Reference.
The numerical uncertainty of the result is controlled, by the epsilon parameter, i.e. it will be smaller than epsilon when using a large value for maxiter (maximum number of iterations).

Lorenzo

faca87 · June 18, 2021, 8:24am

Hello @moneta, then the GetMaxmiumX (and consequently the MPV) doesn’t have uncertainty?? right?

moneta · June 18, 2021, 8:27am

There is always some numerical uncertainty in every calculation done. This can be controlled and kept small, but cannot be less than the double numerical precision ( ~ 1.E-16).

faca87 · June 18, 2021, 8:36am

Thank you @moneta, so is there a code to get its value?

moneta · June 18, 2021, 10:14am

Hi,
Which value ? The actual uncertainty of a calculation ? No, there is not something implemented in ROOT, since it can be difficult and very tricky. You can just use the provided epsilon as a rough upper estimation. But why do you need that precise value ? Normally other uncertainties (e.g. statistical in estimating your function parameters) are much larger

Lorenzo

faca87 · June 18, 2021, 10:41am

I see, then I will just use the parameter! thank you @moneta