Work with complex number in function

[Svyatoslav]

Hello everyone,

I haven’t solved my problem with complex number in function yet. Problem: I need a " | BW1 + rho * Exp(i phi) * BW2 |^2 " TF1 function. In code I expect to see something this:
TF1* core = new TF1("core"," TMath::Power( TMath::Abs( [0]*TMath::BreitWigner(x, [1], [2]) + [3] * TMath::Exp(i * [4]) * TMath::BreitWigner(x, [5], [6]) ), 2)", inf, sup);

But I don’t understand how make i in TMath::Exp(i * [4])! I looked TComplex class but didn’t understand how use them.

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ROOT Version: 6.22/08
Platform: Ubuntu
Compiler: Not Provided

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[Wile_E_Coyote]

Try:

TF1 *core = new TF1("core", "TMath::Sq(TComplex::Abs([0] * TMath::BreitWigner(x, [1], [2]) + [3] * TComplex::Exp(TComplex(0., [4])) * TMath::BreitWigner(x, [5], [6])))", 0., 1.);

and / or:

#include "TMath.h"
#include "TF1.h"

#if 1 /* 0 or 1 */

#include <complex>
double core_cpp(const double *x, const double *p)
{return std::norm(p[0] * TMath::BreitWigner(x[0], p[1], p[2]) + p[3] * std::exp(std::complex<double>(0., p[4])) * TMath::BreitWigner(x[0], p[5], p[6]));}

#else /* 0 or 1 */

#include "TComplex.h"
double core_cpp(const double *x, const double *p)
{return TMath::Sq(TComplex::Abs(p[0] * TMath::BreitWigner(x[0], p[1], p[2]) + p[3] * TComplex::Exp(TComplex(0., p[4])) * TMath::BreitWigner(x[0], p[5], p[6])));}

#endif /* 0 or 1 */

TF1 *core = new TF1("core", core_cpp, 0., 1., 7); // 7 parameters

[Svyatoslav]

@Wile_E_Coyote , thank you, it run. But later I need to do convolution with normal distributio. I try do this with CONV:
CONV(TMath::Sq(TComplex::Abs([0] * TMath::BreitWigner(x, [1], [2]) + [3] * TComplex::Exp(TComplex(0., [4])) * TMath::BreitWigner(x, [5], [6]))), TMath::Exp(-0.5*((x-[0])/[1]*(x-[0])/[1]))/(sqrt(2*TMath::Pi())*[1]))

This don’t work correct and I get:
Warning in <TCanvas::ResizePad>: Inf/NaN propagated to the pad. Check drawn objects. Warning in <TCanvas::ResizePad>: Pi0-Rho height changed from 0 to 10

There are too many variables, so the CONV can’t cope and you need to think about other ways of convolution?

[joa]

Hi,

Are you not making life complicated complicated invoking complex numbers? Your function is f=f1+e^iaf2 and you want to fit sqrt(ff) which is sqrt(f1^2×f2^2+2f1f2cos^2a)… Maybe this is easier to feed to a convoluted?

Cheers

Joa

[Svyatoslav]

Hi,

you have made a little mistake: f1^2 + f2^2 + 2 f1 f2 cos^2 (a), not f1^2 * f2^2 + 2 f1 f2 cos^2 (a). But I got the idea. I think I want to have the most general form of the formula to easily change or add participating functions. If I use the consequence formula, then with each replacement it will have to be deduced anew. And if I write the initial one and then the algorithm for its transformation, then I don’t have to calculate anything, the machine will do it.

[Wile_E_Coyote]

f1^2 + f2^2 + 2 f1 f2 cos(a)

[Wile_E_Coyote]

{
  TF1 *core = new TF1("core",
    "TMath::Sq(TComplex::Abs([0] * TMath::BreitWigner(x, [1], [2]) + [3] * TComplex::Exp(TComplex(0., [4])) * TMath::BreitWigner(x, [5], [6])))",
    0., 1.);
  // core->Print();
  TF1 *ngaus = new TF1("ngaus", "TMath::Gaus(x, [0], [1], 1)", 0., 1.);
  // ngaus->Print();
  TF1 *conv = new TF1("conv", "CONV(core, ngaus)", 0., 1.);
  // conv->Print();
  // gROOT->GetListOfFunctions()->ls();
  conv->SetLineColor(kGreen);
  conv->SetNpx(1000);
  conv->SetRange(-50., 50.);
  conv->SetParameters(
    1.,
    -2.5, 5., // BreitWigner
    1.,
    0., // e.g., TMath::Pi() TMath::PiOver2() TMath::PiOver4() 0. // Exp
    2.5, 5., // BreitWigner
    0., 10. // Gaus
  );
#if 1 /* 0 or 1 */
  core->SetLineColor(kBlue);
  core->SetNpx(conv->GetNpx());
  core->SetRange(conv->GetXmin(), conv->GetXmax());
  core->SetParameters(conv->GetParameters()); // copy the first 7 parameters
  ngaus->SetLineColor(kBlack);
  ngaus->SetNpx(conv->GetNpx());
  ngaus->SetRange(conv->GetXmin(), conv->GetXmax());
  ngaus->SetParameters(conv->GetParameters() + 7); // copy the last 2 parameters
  core->Draw();
  ngaus->Draw("SAME"); // note: often only partially visible
  conv->Draw("SAME");
#else /* 0 or 1 */
  conv->Draw();
#endif /* 0 or 1 */
}

[Svyatoslav]

Thank you, this is my solution