Convolution of two functions yielding Inf/NaN


I’m trying to fit a waveform with the convolution of 2 functions. I’ve attempted to use TF1Convolution in the following way:

TF1* tf1_A = new TF1("tf1_A", "[2]*(x>[0])*TMath::Exp(-1*(x>[0])*(x-[0])*3/[1])*TMath::Power((x>[0])*(x-[0])/[1],3)*TMath::Sin((x>[0])*(x-[0])/[1])");
tf1_A->SetParameter(0, 9000.);
tf1_A->SetParameter(1, 600.);

TF1* tf1_L = new TF1("tf1_L", "gaus(0)");
tf1_L->SetParameter(0, 1);
tf1_L->SetParameter(1, 9000);
tf1_L->SetParameter(2, sigma_in);

TF1Convolution* tf1conv_AL = new TF1Convolution("tf1_L", "tf1_A", 0.0, tmax, true);
 TF1   *f = new TF1("f",*tf1conv_AL, 0.01, tmax, tf1conv_AL->GetNpar());
   f->SetParameters(9000, 600, 1, 1, 9000, sigma_in);

TCanvas* c_tf = new TCanvas();

with sigma_in=16 and tmax = 40000. The two separate functions are drawn correctly, but when I try to draw the convolution I get the following message:

Warning in <TCanvas::ResizePad>: Inf/NaN propagated to the pad. Check drawn objects.
Warning in <TCanvas::ResizePad>: c1 height changed from 0 to 10

Could you help me figure out what is wrong with the way I’m doing the convolution?


@moneta can most probably help you


I am not having a problem using code similar to yours. Can you tell me exactly what are the function parameters. so I can run exactly your code and reproduce your problem ?
I suspect is a numerical issue in the function calculation


Hi Lorenzo,

The functions I’m using so far are:

  • a Gaussian meant to describe the longitudianal diffusion of a cluster of electrons (described by tf1_L in my code) with a width of sigma_in = 16 (ns).
  • the product of a sine function, an exponential decay and a 3rd degree polynomial to describe the electronics shaping effects. This is a function of (x-(par[0])/par[1] where par[0] is supposed to be the offset (~9000 ns in my case) and par[1] is the time constant of the decay and is of the order of 600 (ns). I also make sure that the function is only defined for x>par[0] by putting in that condition. par[2] is just a normalization constant so far, I put it equal to 1, so that it’s comparable to the gaussian.
    (I will further have to convolute the result of this convolution with a third function containing TMath::Erf).
    These functions should be convoluted in the range 0…40000 (ns).

Otherwise I’m just using the parameters in the code above.


Can you please attach a running code showing this problem ? This would be helpful to understand the problem



Sure, here is the code. If I don’t do the convolution, the two functions get drawn as they should.
testROOTTF1Convolution.C (1.3 KB)


Thank you for posting the code. I can reproduce it now and I will investigate it



The problem you are inverting the function in the constructor. You should do:

	TF1Convolution* tf1conv_AL = new TF1Convolution("tf1_A", "tf1_L", 0.01, tmax, true);

where passing Ttf1_A as first function. Also I would use a smaller range for the convolution eventually since the functions are zero outside the peak


Thank you very much, this works! However, shouldn’t convolution be commutative? What’s the driving factor in which function I should put first?

Yes the convolution is commutative if you define it in the full -[-inf, +inf] range. Otherwise one needs to correct change the range when the order of the functions is reversed (e.g. if the gaussian is the first function)


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