Eval of Chebyshev Polynomials

Roofit and RooStats
1

Hello,

I am trying to do a quick calculation/simulation of Synchrotron radiation using root. The procedure is described in: H. Burkhardt, CERN-OPEN-2007-018 (and implemented in GEANT4).
To be able to do that, one must evaluate Chebyshev polynomials at a given value x, in range [a,b] and for a given set of coefficients - i.e.: Chebyshev(a,b,coeffs,n,x), n=number of coefficients.
Is there a call in root to do that? searched but could not find any. Or, is there an example of Synchrotron radiation in root?

Thank you very much.
Riad.

2

Googling “Chebyshev ROOT” gave me:

root.cern.ch/root/html/ROOT__Ma … yshev.html

3

Sorry, I should have been more specific. I am trying to evaluate the series for a given number; see attached macro file. But not sure how to do it.
Cheby.C (693 Bytes)

4

Hi,

The class defining the Chebyshev polynomial in ROOT is ROOT::Math::ChebyshevPol, see

root.cern.ch/root/html/ROOT__Ma … evPol.html

You can use them as TF1, they are already defined as predefined functions in gROOT as “chebyshevN”.
So for example for using a chebyshev polynomial of degree 4 you can do:

TF1 * f = (TF1*) gROOT->GetFunction("chebyshev4");
f->SetParameters(1,1,1,1);
f->Draw();

Best Regards

Lorenzo

5

Lorenzo forgot to mention a very tiny detail that “chebyshevN” work only in ROOT 6.

6

Hi,

No, they exists also in ROOT 5.34. The name is abbreviated in that case : “chebN” instead of “chebyshevN”.

Lorenzo

7

Thank you very much. It seems that “cheb4” is Chebyshev series - not polynomial. To get the polynomial one has to set: SetParameters(0,0,0,0,1) which givesT4 = 8x^4 - 8x^2 + 1. This is not a problem.

However, it seems only up to n=9 are defined; i.e., “cheb10” will not work:

root [0] TF1 * f = (TF1*) gROOT->GetFunction(“cheb10”);
root [1] f->Draw();
Error: illegal pointer to class object f 0x0 1205 (tmpfile):1:
*** Interpreter error recovered ***

Notices also that SetParameters only takes up to 10 parameters. So cannot access Chebyshev series above n=9. I needed n=30.

8

There is no “up to 11 parameters” limit if you use one of:
void TFormula::SetParameters(const Double_t* params)
void TFormula::SetParameter(Int_t ipar, Double_t parvalue)
void TFormula::SetParameter(const char* name, Double_t parvalue)

BTW. Note that “chebN” and “chebyshevN” exist for “N = 0, …, 9” only.

9

HI,

For larger number of parameters you can use directly the ROOT::Math::ChebyshevPol class :

      // example for n = 20
       const int n = 20;
       ROOT::Math::ChebyshevPol * pol = new ROOT::Math::ChebyshevPol(n);
        Double_t min = -1;
        Double_t max = 1;
        TF1 * f1 = new TF1(TString::Format("chebyshev%d",n),pol,min,max,n+1,1);
        double p[n] = {0};
        p[n-1] = 1; 
        f1->SetParameters(p);

Lorenzo