Dear experts,

I am currently developing a double Gaussian fitting function within the range of [−4.0,4.0]. The design involves two Gaussian components:

- The first Gaussian contributes to the full range of [−4,4].
- The second Gaussian is restricted to the ranges [−4,−2] and [2,4]. Both Gaussians have a mean at 0.

However, I am encountering an issue with a discontinuity at +2 and −2, which was not the intended behavior. The second Gaussian, generated based on the data points from the specified regions, should have an extended contribution in the central peak region [−2,2]. This contribution should not depend on data points from the region [−2,2].

Below is the macro I am working with:

```
//macro.C
#include <TROOT.h>
#include <TFile.h>
#include <TH1F.h>
#include <TF1.h>
#include <TCanvas.h>
// Define the first function f1 (Gaussian with fixed mean at 0.0, symmetric in [-4, 4])
Double_t f1(Double_t *x, Double_t *par) {
Double_t arg = (x[0] - 0.0) / par[1]; // Mean fixed at 0.0
return par[0] * exp(-0.5 * arg * arg); // Gaussian: par[0] = amplitude, par[1] = sigma
}
// Define the second function f2 (only contributes in [-4, -2] and [2, 4], symmetric)
Double_t f2(Double_t *x, Double_t *par) {
if ((x[0] >= 2.0 && x[0] <= 4.0) || (x[0] >= -4.0 && x[0] <= -2.0)) {
Double_t arg = (x[0] - 0.0) / par[1]; // Mean fixed at 0.0
return par[0] * exp(-0.5 * arg * arg); // Gaussian: par[0] = amplitude, par[1] = sigma
}
return 0; // Outside the range [-4, -2] and [2, 4], f2 = 0
}
// Define the combined function F = f1 + f2
Double_t F(Double_t *x, Double_t *par) {
// par[0]: amplitude of f1, par[1]: sigma of f1
// par[2]: amplitude of f2, par[3]: sigma of f2
return f1(x, par) + f2(x, &par[2]);
}
void macro() {
// Create a histogram or load your data here
TH1F *h = new TH1F("h", "Example Histogram", 100, -4, 4);
//h->FillRandom("gaus", 100000); // Filling with random data for example
// Define the combined function F
TF1 *fitFunc = new TF1("fitFunc", F, -4, 4, 4); // 4 parameters: 2 for f1 and 2 for f2
fitFunc->SetParameters(1.0, 0.5, 0.5, 1.6);
for (int i = 0; i < 1000000; i++) {
double random_number = fitFunc->GetRandom(-4, 4);
h->Fill(random_number);
}
// Perform the fit
h->Fit("fitFunc", "R");
h->Fit("fitFunc", "R");
h->Fit("fitFunc", "R");
// Draw the result
TCanvas *c1 = new TCanvas("c1", "Fitting Example", 800, 600);
h->Draw();
fitFunc->Draw("same");
TF1* f11 = new TF1("f11", f1, -4, 4, 2);
f11->SetParameter(0, fitFunc->GetParameter(0));
f11->SetParameter(1, fitFunc->GetParameter(1));
f11->SetLineColor(kBlue);
f11->Draw("same");
TF1* f22 = new TF1("f22", f1, -4, 4, 2);
f22->SetParameter(0, fitFunc->GetParameter(2));
f22->SetParameter(1, fitFunc->GetParameter(3));
f22->SetLineColor(kGreen+3);
f22->Draw("same");
}
```

I would kindly request the experts to help constructing the model.

Thanks in Advance.

Sayan

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