# How to define TF1 as a sum of functions with common parameters?

Dear experts,
I would like to define a fit function as follows:

F(x) = w0 * F0(x,par0) + w1 * F1(x,par0,par1) + w2 * F2(x, par0,par1) + w3 * F3(x, par0,par1)

where:

• w# are the weights of the F# components
• par# is a set of parameters
• F0 is an analytical function
• F1 is an analytical function that shares some parameters with F0 (par0)
• F2 is the convolution of F1 with itself
• F3 is the convolution of F1 and F2

I know how to build individually F0, F1, F2 and F3, but I don’t know how to make the different functions to share the common parameters.
Do you think it is possible? Are there any examples?

Thanks,
Stefania

Hi Stefania,

for simplicity, let’s assume the following:

• F0(x, par0) = 5*x + par0
• F1(x, par0, par1) = F0 * par1
• F2(x, par0, par1) = F1*42
• F3(x, par0, par1) = F1 + F2

then we can define F(x) as follows:

``````TString F0 = "(5*x + [0])";
TString F1 = Form("%s*[1]", F0.Data());
TString F2 = Form("%s*42", F1.Data());
TString F3 = Form("(%s + %s)", F1.Data(), F2.Data());
TF1* myFit = new TF1("myFit", Form("w0*%s + w1*%s + w2*%s + w3*%s", F0.Data(), F1.Data(), F2.Data(), F3.Data()));
``````
``````{
TF1 *f0 = new TF1("F0", "[0] * x"); // f0->Print();
TF1 *f1 = new TF1("F1", "pol1"); // f1->Print();
TF1 *f2 = new TF1("F2", "cheb1"); // f2->Print();
TF1 *f3 = new TF1("F3", "expo"); // f3->Print();
TF1 *f = new TF1("F", "[w0] * F0(x, [par0]) + [w1] * F1(x, [par0], [par1]) + [w2] * F2(x, [par0], [par1]) + [w3] * F3(x, [par0], [par1])");
f->Print();
}
``````

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