Example describing the usage of different kinds of Associate Legendre Polynomials To execute the macro type in:
It draws common graphs for first 5 Associate Legendre Polynomials and Spherical Associate Legendre Polynomials Their integrals on the range [-1, 1] are calculated
Drawing associate Legendre Polynomials..
Calculating integrals of Associate Legendre Polynomials on [-1, 1]
Integral [-1,1] for Associated Legendre Polynomial of Degree 0 = 0
Integral [-1,1] for Associated Legendre Polynomial of Degree 1 = 1.5708
Integral [-1,1] for Associated Legendre Polynomial of Degree 2 = 5.55112e-17
Integral [-1,1] for Associated Legendre Polynomial of Degree 3 = 0
Integral [-1,1] for Associated Legendre Polynomial of Degree 4 = 4
#include <cmath>
{
std::cout <<"Drawing associate Legendre Polynomials.." << std::endl;
TCanvas *Canvas =
new TCanvas(
"DistCanvas",
"Associate Legendre polynomials", 10, 10, 800, 500);
L[0]=
new TF1(
"L_0",
"ROOT::Math::assoc_legendre(1, 0,x)", -1, 1);
L[1]=
new TF1(
"L_1",
"ROOT::Math::assoc_legendre(1, 1,x)", -1, 1);
L[2]=
new TF1(
"L_2",
"ROOT::Math::assoc_legendre(2, 0,x)", -1, 1);
L[3]=
new TF1(
"L_3",
"ROOT::Math::assoc_legendre(2, 1,x)", -1, 1);
L[4]=
new TF1(
"L_4",
"ROOT::Math::assoc_legendre(2, 2,x)", -1, 1);
L[0]->SetMaximum(3);
L[0]->SetMinimum(-2);
L[0]->SetTitle("Associate Legendre Polynomials");
for (
int nu = 0;
nu < 5;
nu++) {
L[
nu]->SetLineColor(
nu+1);
}
leg1->AddEntry(L[0]->DrawCopy(),
" P^{1}_{0}(x)",
"l");
leg1->AddEntry(L[1]->DrawCopy(
"same"),
" P^{1}_{1}(x)",
"l");
leg1->AddEntry(L[2]->DrawCopy(
"same"),
" P^{2}_{0}(x)",
"l");
leg1->AddEntry(L[3]->DrawCopy(
"same"),
" P^{2}_{1}(x)",
"l");
leg1->AddEntry(L[4]->DrawCopy(
"same"),
" P^{2}_{2}(x)",
"l");
SL[0]->SetTitle(
"Spherical Legendre Polynomials");
for (
int nu = 0;
nu < 5;
nu++) {
}
leg2->AddEntry(
SL[0]->DrawCopy(),
" P^{1}_{0}(x)",
"l");
leg2->AddEntry(
SL[1]->DrawCopy(
"same"),
" P^{1}_{1}(x)",
"l");
leg2->AddEntry(
SL[2]->DrawCopy(
"same"),
" P^{2}_{0}(x)",
"l");
leg2->AddEntry(
SL[3]->DrawCopy(
"same"),
" P^{2}_{1}(x)",
"l");
leg2->AddEntry(
SL[4]->DrawCopy(
"same"),
" P^{2}_{2}(x)",
"l");
std::cout << "Calculating integrals of Associate Legendre Polynomials on [-1, 1]" << std::endl;
double integral[5];
for (
int nu = 0;
nu < 5;
nu++) {
integral[
nu] =
L[
nu]->Integral(-1.0, 1.0);
std::cout <<
"Integral [-1,1] for Associated Legendre Polynomial of Degree " <<
nu <<
"\t = \t" << integral[
nu] << std::endl;
}
}
ROOT::Detail::TRangeCast< T, true > TRangeDynCast
TRangeDynCast is an adapter class that allows the typed iteration through a TCollection.
TVirtualPad * cd(Int_t subpadnumber=0) override
Set current canvas & pad.
This class displays a legend box (TPaveText) containing several legend entries.
void Divide(Int_t nx=1, Int_t ny=1, Float_t xmargin=0.01, Float_t ymargin=0.01, Int_t color=0) override
Automatic pad generation by division.
virtual void SetGrid(Int_t valuex=1, Int_t valuey=1)=0
RooArgList L(Args_t &&... args)
- Author
- Magdalena Slawinska
Definition in file LegendreAssoc.C.