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

[vecchi]

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

[yus]

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()));

[Wile_E_Coyote]

{
  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();
}