LegendreAssoc

Example describing the usage of different kinds of Associate Legendre Polynomials To execute the macro type in:

root[0] .x LegendreAssoc.C

It draws common graphs for first 5 Associate Legendre Polynomials and Spherical Associate Legendre Polynomials Their integrals on the range [-1, 1] are calculated

Author: Magdalena Slawinska
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Wednesday, August 17, 2022 at 09:34 AM.

In [1]:
R__LOAD_LIBRARY(libMathMore);

std::cout <<"Drawing associate Legendre Polynomials.." << std::endl;
TCanvas *Canvas = new TCanvas("DistCanvas", "Associate Legendre polynomials", 10, 10, 800, 500);
Canvas->Divide(2,1);
TLegend *leg1 = new TLegend(0.5, 0.7, 0.8, 0.89);
TLegend *leg2 = new TLegend(0.5, 0.7, 0.8, 0.89);
Drawing associate Legendre Polynomials..

drawing the set of Legendre functions

In [2]:
TF1* L[5];

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);

TF1* SL[5];

SL[0]= new TF1("SL_0", "ROOT::Math::sph_legendre(1, 0,x)", -TMath::Pi(), TMath::Pi());
SL[1]= new TF1("SL_1", "ROOT::Math::sph_legendre(1, 1,x)", -TMath::Pi(), TMath::Pi());
SL[2]= new TF1("SL_2", "ROOT::Math::sph_legendre(2, 0,x)", -TMath::Pi(), TMath::Pi());
SL[3]= new TF1("SL_3", "ROOT::Math::sph_legendre(2, 1,x)", -TMath::Pi(), TMath::Pi());
SL[4]= new TF1("SL_4", "ROOT::Math::sph_legendre(2, 2,x)", -TMath::Pi(), TMath::Pi() );

Canvas->cd(1);
gPad->SetGrid();
gPad->SetFillColor(kWhite);
L[0]->SetMaximum(3);
L[0]->SetMinimum(-2);
L[0]->SetTitle("Associate Legendre Polynomials");
for (int nu = 0; nu < 5; nu++) {
   L[nu]->SetLineStyle(1);
   L[nu]->SetLineWidth(2);
   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");
leg1->Draw();

Canvas->cd(2);
gPad->SetGrid();
gPad->SetFillColor(kWhite);
SL[0]->SetMaximum(1);
SL[0]->SetMinimum(-1);
SL[0]->SetTitle("Spherical Legendre Polynomials");
for (int nu = 0; nu < 5; nu++) {
   SL[nu]->SetLineStyle(1);
   SL[nu]->SetLineWidth(2);
   SL[nu]->SetLineColor(nu+1);
}

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");
leg2->Draw();

integration

In [3]:
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;
}
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

Draw all canvases

In [4]:
gROOT->GetListOfCanvases()->Draw()