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LegendreAssoc.C File Reference

## Detailed Description

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

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 "TMath.h"
#include "TF1.h"
#include "TCanvas.h"
#include <Riostream.h>
#include "TLegend.h"
#include "TLegendEntry.h"
#include "Math/IFunction.h"
#include <cmath>
#include "TSystem.h"
void LegendreAssoc()
{
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 the set of Legendre functions
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);
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);
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
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;
}
}
Definition Rtypes.h:472
@ kWhite
Definition Rtypes.h:65
virtual void SetLineStyle(Style_t lstyle)
Set the line style.
Definition TAttLine.h:42
virtual void SetLineWidth(Width_t lwidth)
Set the line width.
Definition TAttLine.h:43
virtual void SetLineColor(Color_t lcolor)
Set the line color.
Definition TAttLine.h:40
The Canvas class.
Definition TCanvas.h:23
Set current canvas & pad.
Definition TCanvas.cxx:708
1-Dim function class
Definition TF1.h:213
virtual void SetMaximum(Double_t maximum=-1111)
Set the maximum value along Y for this function In case the function is already drawn,...
Definition TF1.cxx:3407
virtual void SetTitle(const char *title="")
Set function title if title has the form "fffffff;xxxx;yyyy", it is assumed that the function title i...
Definition TF1.cxx:3562
virtual void SetMinimum(Double_t minimum=-1111)
Set the minimum value along Y for this function In case the function is already drawn,...
Definition TF1.cxx:3420
This class displays a legend box (TPaveText) containing several legend entries.
Definition TLegend.h:23
TLegendEntry * AddEntry(const TObject *obj, const char *label="", Option_t *option="lpf")
Add a new entry to this legend.
Definition TLegend.cxx:330
virtual void Draw(Option_t *option="")
Draw this legend with its current attributes.
Definition TLegend.cxx:423
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.