void setGraphOptions(TF2 &f,
const char *xname,
const char *yname)
{
TAxis::TAxis *axis1;
TAxis::TAxis *axis2;
axis1 = f.GetXaxis();
axis2 = f.GetYaxis();
axis1->SetTitle(xname);
axis2->SetTitle(yname);
setAxisOptions(axis1);
setAxisOptions(axis2);
}
void PlotPhaseVelocityFunctions( const TString &opt="")
{
#ifdef __CINT__
gSystem->Load("libplasma.so");
#endif
PlasmaGlob::Initialize();
// Palettes!
gROOT->Macro("PlasmaPalettes.C");
gStyle->SetPadTopMargin(0.06);
gStyle->SetPadGridY(0);
gStyle->SetPadGridX(0);
gStyle->SetFrameLineWidth(2);
gStyle->SetLabelSize(0.04, "xyz");
gStyle->SetTitleOffset(1.2,"y");
gStyle->SetTitleOffset(1.2,"z");
gStyle->SetNdivisions(505,"xyz");
PUnits::UnitsTable::Get();
// // SPS parameters from Pukhov, Kumar et al. PRL107,145003(2011)
// Double_t n0 = 7.76e14 / PUnits::cm3;
// Double_t nb = 1.5e12 / PUnits::cm3;
// Double_t lambda = PFunc::PlasmaWavelength(n0);
// Double_t kp = PFunc::PlasmaWavenumber(n0);
// Double_t skindepth = PFunc::PlasmaSkindepth(n0);
// Double_t r0 = 0.19 * PUnits::mm;
// Double_t z = 2.5 * PUnits::m;
// Double_t zg = -28.6 * PUnits::mm;
// Double_t E = 450 * PUnits::GeV;
// Double_t gamma = E / PConst::ProtonMassE ;
// SPS parameters from Schroeder et al. PRL107,145002(2011)
// Double_t n0 = 1.0;
// Double_t nb = 0.002;
// Double_t lambda = TMath::TwoPi();
// Double_t kp = 1.0;
// Double_t r0 = 1.0;
// Double_t z = 13105;
// Double_t E = 450 * PUnits::GeV;
// Double_t gamma = E / PConst::ProtonMassE ;
// PITZ parameters
Double_t n0 = 1.0e15 / PUnits::cm3;
Double_t nb = 1.05e13 / PUnits::cm3;
Double_t lambda = PFunc::PlasmaWavelength(n0);
Double_t kp = PFunc::PlasmaWavenumber(n0);
Double_t skindepth = PFunc::PlasmaSkindepth(n0);
Double_t r0 = 34.259 * PUnits::um;
Double_t z = 150. * PUnits::mm;
Double_t zg = -5. * PUnits::mm;
Double_t E = 25 * PUnits::MeV;
Double_t gamma = (E / PConst::ElectronMassE) + 1.0;
Double_t vb = TMath::Sqrt(1. - (1./(gamma*gamma)));
cout << " n0 = " << n0 * PUnits::cm3 << " e/cc" << endl;
cout << " Wavelength = " << PUnits::BestUnit(lambda, "Length") << endl;
cout << " Skindepth = " << PUnits::BestUnit(skindepth, "Length") << endl;
cout << " Wavenumber = " << kp * PUnits::mm << " mm^-1" << endl;
// Normalized variables
if(!opt.Contains("units")){
r0 *= kp;
nb /= n0;
n0 = 1.0;
z *= kp;
zg *= kp;
}
Double_t N = PFunc::Nefoldings(z,zg,r0,gamma,nb,n0);
Double_t r1 = (TMath::Power(3.,1./4.)/TMath::Power(8.*TMath::Pi()*N,1./2.)) * TMath::Exp(N) ;
Double_t Gamma = PFunc::PhaseGamma(z,zg,r0,gamma,nb,n0);
Double_t vph = PFunc::PhaseVelocity(z,zg,r0,gamma,nb,n0);
Double_t vph2 = PFunc::PhaseVelocity2(z,zg,gamma,nb,n0);
cout << " gamma beam = " << gamma << endl;
cout << " zeta = " << z << endl;
cout << " zeta comov. = " << zg << endl;
cout << " r0 = " << r0 << endl;
cout << " n_b0/n_0 = " << nb/n0 << endl;
cout << " nu constant = " << PFunc::Nu(r0,n0) << endl;
cout << " Number e-foldings = " << N << endl;
cout << " r1 = " << r1 << endl;
cout << " Gamma wake = " << Gamma << endl;
cout << " Wake Phase velocity = " << vph << endl;
cout << " Wake Phase velocity2 = " << vph2 << endl;
cout << " Beam phase velocity = " << vb << endl;
const Int_t NPAR = 5;
Double_t par[NPAR] = {zg,r0,gamma,nb,n0};
TF1 *fPhaseVsZ2 = new TF1("fPhaseVsZ2",PhaseVelocityVsZ2,0,z,NPAR);
fPhaseVsZ2->SetParameters(par);
TF1 *fPhaseVsZ = new TF1("fPhaseVsZ",PhaseVelocityVsZ,0,z,NPAR);
fPhaseVsZ->SetParameters(par);
Double_t par2[NPAR] = {z,r0,gamma,nb,n0};
TF1 *fPhaseVsZg2 = new TF1("fPhaseVsZg2",PhaseVelocityVsZg2,zg,0.,NPAR);
fPhaseVsZg2->SetParameters(par2);
TF1 *fPhaseVsZg = new TF1("fPhaseVsZg",PhaseVelocityVsZg,zg,0.,NPAR);
fPhaseVsZg->SetParameters(par2);
const Int_t NPAR2D = 4;
Double_t par3[NPAR2D] = {r0,gamma,nb,n0};
TF2 *fPhaseVsZVsZg2 = new TF2("fPhaseVsZVsZg2",PhaseVelocityVsZVsZg2,0.,z,zg,0.,NPAR2D);
fPhaseVsZVsZg2->SetParameters(par3);
TF2 *fPhaseVsZVsZg = new TF2("fPhaseVsZVsZg",PhaseVelocityVsZVsZg,0.,z,zg,0.,NPAR2D);
fPhaseVsZVsZg->SetParameters(par3);
char ctext[64];
TPaveText *textZetag = new TPaveText(0.13,0.85,0.38,0.92,"NDC");
PlasmaGlob::SetPaveTextStyle(textZetag,12);
textZetag->SetTextColor(kGray+3);
if(opt.Contains("units"))
sprintf(ctext,"#zeta_{0} = %6.2f mm", zg / PUnits::mm);
else
sprintf(ctext,"#zeta_{0} = %6.2f c/#omega_{p}", zg);
textZetag->AddText(ctext);
TPaveText *textZeta = new TPaveText(0.13,0.85,0.38,0.92,"NDC");
PlasmaGlob::SetPaveTextStyle(textZeta,12);
textZeta->SetTextColor(kGray+3);
if(opt.Contains("units"))
sprintf(ctext,"z_{0} = %6.2f mm", z / PUnits::mm);
else
sprintf(ctext,"z_{0} = %6.2f c/#omega_{p}", z);
textZeta->AddText(ctext);
// Graph for de-phasing:
const Int_t NP = 100;
TGraph *gPhase = new TGraph(NP);
TGraph *gPhase2 = new TGraph(NP);
Float_t phase = zg;
Float_t phase2 = zg;
Float_t Dz = z / NP;
for(Int_t i=0;i<NP;i++) {
Float_t zp = (i+1)*Dz;
Float_t v = PFunc::PhaseVelocity(zp,phase,r0,gamma,nb,n0);
phase += (v - vb) * Dz;
// cout << " z = " << zp << " phase = " << phase << endl;
if(opt.Contains("units"))
gPhase->SetPoint(i,zp,(phase-zg)*kp);
else
gPhase->SetPoint(i,zp,(phase-zg));
v = PFunc::PhaseVelocity2(zp,phase2,gamma,nb,n0);
phase2 += (v - 1) * Dz;
// cout << " z = " << zp << " phase = " << phase << endl;
if(opt.Contains("units"))
gPhase2->SetPoint(i,zp,(phase2-zg)*kp);
else
gPhase2->SetPoint(i,zp,(phase2-zg));
}
TCanvas *C = new TCanvas("C","Wake phase velocity",1000,750);
C->Divide(2,2);
TLegend *Leg = new TLegend(0.6,0.20,0.85,0.35);
PlasmaGlob::SetPaveStyle(Leg);
Leg->SetTextAlign(22);
Leg->SetTextColor(kGray+3);
Leg->SetLineColor(1);
Leg->SetBorderSize(1);
Leg->SetFillColor(0);
Leg->SetFillStyle(1001);
//Leg-> SetNColumns(2);
Leg->AddEntry(fPhaseVsZ,"PRL 107,145002","L");
Leg->AddEntry(fPhaseVsZ2,"PRL 107,145003","L");
Leg->SetTextColor(kGray+3);
C->cd(1);
fPhaseVsZ->GetYaxis()->SetTitle("(v_{p} - c)/c");
if(opt.Contains("units"))
fPhaseVsZ->GetXaxis()->SetTitle("z [m]");
else
fPhaseVsZ->GetXaxis()->SetTitle("z [c/#omega_{p}]");
fPhaseVsZ->GetYaxis()->SetRangeUser(-3e-4,0.);
fPhaseVsZ->GetXaxis()->CenterTitle();
fPhaseVsZ->GetYaxis()->CenterTitle();
fPhaseVsZ->SetLineWidth(2);
fPhaseVsZ->Draw("C");
fPhaseVsZ2->SetLineWidth(2);
fPhaseVsZ2->SetLineStyle(2);
fPhaseVsZ2->Draw("C same");
textZetag->Draw();
Leg->Draw();
C->cd(2);
fPhaseVsZg->GetYaxis()->SetTitle("(v_{p} - c)/c");
if(opt.Contains("units"))
fPhaseVsZg->GetXaxis()->SetTitle("#zeta [m]");
else
fPhaseVsZg->GetXaxis()->SetTitle("#zeta [c/#omega_{p}]");
fPhaseVsZg->GetYaxis()->SetRangeUser(-3e-4,0.);
fPhaseVsZg->GetYaxis()->SetNdivisions(505);
fPhaseVsZg->GetXaxis()->CenterTitle();
fPhaseVsZg->SetLineWidth(2);
fPhaseVsZg->GetYaxis()->CenterTitle();
fPhaseVsZg->Draw("C");
fPhaseVsZg2->SetLineWidth(2);
fPhaseVsZg2->SetLineStyle(2);
fPhaseVsZg2->Draw("C same");
textZeta->Draw();
C->cd(3);
gPhase->GetYaxis()->SetTitle("#Delta#zeta [c/#omega_{p}]");
if(opt.Contains("units")) {
gPhase->GetXaxis()->SetTitle("z [m]");
gPhase->GetXaxis()->SetNdivisions(510);
} else
gPhase->GetXaxis()->SetTitle("z [c/#omega_{p}]");
// gPhase->GetXaxis()->SetNdivisions(510);
gPhase->GetXaxis()->CenterTitle();
gPhase->GetYaxis()->CenterTitle();
gPhase->GetXaxis()->SetRangeUser(0.,z);
gPhase->GetYaxis()->SetNdivisions(505);
gPhase->SetLineWidth(2);
gPhase->Draw("AC");
gPhase2->SetLineStyle(2);
gPhase2->SetLineWidth(2);
gPhase2->Draw("C");
textZetag->Draw();
C->cd(4);
gPad->SetLeftMargin(0.18);
if(opt.Contains("units")) {
fPhaseVsZVsZg->GetYaxis()->SetTitle("#zeta [m]");
} else
fPhaseVsZVsZg->GetYaxis()->SetTitle("#zeta [c/#omega_{p}]");
if(opt.Contains("units")) {
fPhaseVsZVsZg->GetXaxis()->SetTitle("z [m]");
} else
fPhaseVsZVsZg->GetXaxis()->SetTitle("z [c/#omega_{p}]");
fPhaseVsZVsZg->GetZaxis()->SetTitle("(v_{p} - c)/c");
fPhaseVsZVsZg->GetYaxis()->SetNdivisions(505);
// fPhaseVsZVsZg->GetXaxis()->SetNdivisions(510);
fPhaseVsZVsZg->GetXaxis()->CenterTitle();
fPhaseVsZVsZg->GetXaxis()->SetTitleOffset(1.6);
fPhaseVsZVsZg->GetYaxis()->CenterTitle();
fPhaseVsZVsZg->GetYaxis()->SetTitleOffset(2.0);
fPhaseVsZVsZg->GetZaxis()->CenterTitle();
fPhaseVsZVsZg->GetZaxis()->SetTitleOffset(1.4);
fPhaseVsZVsZg->Draw("surf2");
C->cd();
// Print to a file
PlasmaGlob::imgconv(C,"./WakePhaseVelocity",opt);
// ---------------------------------------------------------
}
void annotation3d()
{
TCanvas *c = new TCanvas("c", "c", 600, 600);
c->SetTheta(30);
c->SetPhi(50);
gStyle->SetOptStat(0);
gStyle->SetHistTopMargin(0);
gStyle->SetOptTitle(kFALSE);
// Define and draw a surface
TF2 *f = new TF2("f", "[0]*cos(x)*cos(y)", -1, 1, -1, 1);
f->SetParameter(0, 1);
double s = 1./f->Integral(-1, 1, -1, 1);
f->SetParameter(0, s);
f->SetNpx(50);
f->SetNpy(50);
f->GetXaxis()->SetTitle("x");
f->GetXaxis()->SetTitleOffset(1.4);
f->GetXaxis()->SetTitleSize(0.04);
f->GetXaxis()->CenterTitle();
f->GetXaxis()->SetNdivisions(505);
f->GetXaxis()->SetTitleOffset(1.3);
f->GetXaxis()->SetLabelSize(0.03);
f->GetXaxis()->ChangeLabel(2,-1,-1,-1,kRed,-1,"X_{0}");
f->GetYaxis()->SetTitle("y");
f->GetYaxis()->CenterTitle();
f->GetYaxis()->SetTitleOffset(1.4);
f->GetYaxis()->SetTitleSize(0.04);
f->GetYaxis()->SetTitleOffset(1.3);
f->GetYaxis()->SetNdivisions(505);
f->GetYaxis()->SetLabelSize(0.03);
f->GetZaxis()->SetTitle("dP/dx");
f->GetZaxis()->CenterTitle();
f->GetZaxis()->SetTitleOffset(1.3);
f->GetZaxis()->SetNdivisions(505);
f->GetZaxis()->SetTitleSize(0.04);
f->GetZaxis()->SetLabelSize(0.03);
f->SetLineWidth(1);
f->SetLineColorAlpha(kAzure-2, 0.3);
f->Draw("surf1 fb");
// Lines for 3D annotation
double x[11] = {-0.500, -0.5, -0.5, -0.5, -0.5, -0.5, -0.5, -0.5, -0.5, -0.5, -0.500};
double y[11] = {-0.985, -0.8, -0.6, -0.4, -0.2, 0.0, 0.2, 0.4, 0.6, 0.8, 0.985};
double z[11];
for (int i = 0; i < 11; ++i) z[i] = s*cos(x[i])*cos(y[i]);
TPolyLine3D *g2 = new TPolyLine3D(11, x, y, z);
double xx[2] = {-0.5, -0.5};
double yy[2] = {-0.985, -0.985};
double zz[2] = {0.11, s*cos(-0.5)*cos(-0.985)};
TPolyLine3D *l2 = new TPolyLine3D(2, xx, yy, zz);
g2->SetLineColor(kRed);
g2->SetLineWidth(3);
g2->Draw();
l2->SetLineColor(kRed);
l2->SetLineStyle(2);
l2->SetLineWidth(1);
l2->Draw();
// Draw text Annotations
TLatex *txt = new TLatex(0.05, 0, "f(y,x_{0})");
txt->SetTextFont(42);
txt->SetTextColor(kRed);
txt->Draw();
TLatex *txt1 = new TLatex(0.12, 0.52, "f(x,y)");
txt1->SetTextColor(kBlue);
txt1->SetTextFont(42);
txt1->Draw();
}
void PrintVertexRosenbrock()
{
// open file
std::ifstream data ("Vertex.txt", std::ios::in);
double buf;
std::vector<double> x1;
std::vector<double> x2;
std::vector<double> x3;
std::vector<double> y1;
std::vector<double> y2;
std::vector<double> y3;
// loop on file
while (1)
{
data >> buf;
if (data.eof())
{break;}
x1.push_back(buf);
data >> buf;
y1.push_back(buf);
data >> buf;
x2.push_back(buf);
data >> buf;
y2.push_back(buf);
data >> buf;
x3.push_back(buf);
data >> buf;
y3.push_back(buf);
}
// functions
//TF2* f = new TF2 ("himmelblau", "(x*x + y - 11)*(x*x + y - 11) + (x + y*y - 7)*(x + y*y - 7)", 0, 10, 0, 10); // himmelblau
gStyle->SetOptTitle(0);
TF2* f = new TF2 ("rosenbrock", "100*(y-x*x)*(y-x*x) + (1-x)*(1-x)", -1.5, 2.2, -0.5, 2.2); // rosenbrock
f->SetNpx(1000);
f->SetNpy(1000);
f->GetXaxis()->SetTitle("x");
f->GetYaxis()->SetTitle("y");
TCanvas* c1 = new TCanvas;
c1->SetLogz();
rosenbrock->Draw("COLZ");
// loop on vertex
std::vector<TLine*> vl1;
std::vector<TLine*> vl2;
std::vector<TLine*> vl3;
TLine* l1;
TLine* l2;
TLine* l3;
for (int i = 0; i < x1.size(); i++)
{
l1 = new TLine(0,0,0,0);
l2 = new TLine(0,0,0,0);
l3 = new TLine(0,0,0,0);
l1->SetLineWidth(1.5);
l2->SetLineWidth(1.5);
l3->SetLineWidth(1.5);
l1->SetLineColor(kBlue -10 + i);
l2->SetLineColor(kBlue -10 + i);
l3->SetLineColor(kBlue -10 + i);
l1->SetX1(x1.at(i));
l1->SetY1(y1.at(i));
l1->SetX2(x2.at(i));
l1->SetY2(y2.at(i));
l2->SetX1(x2.at(i));
l2->SetY1(y2.at(i));
l2->SetX2(x3.at(i));
l2->SetY2(y3.at(i));
l3->SetX1(x3.at(i));
l3->SetY1(y3.at(i));
l3->SetX2(x1.at(i));
l3->SetY2(y1.at(i));
l1->Draw("same");
l2->Draw("same");
l3->Draw("same");
}
TMarker* min = new TMarker (1,1,0);
min ->SetMarkerColor (kBlue);
min->SetMarkerStyle(20);
min->SetMarkerSize (1.0);
min->Draw();
}
