From f3a0420494c94ab0513f1e8c111cffd5bd2fe000 Mon Sep 17 00:00:00 2001 From: morsch Date: Tue, 12 Aug 2003 09:39:38 +0000 Subject: [PATCH] PathLength functions added. --- FASTSIM/AliFastGlauber.cxx | 242 +++++++++++++++++++++++++++++++++++-- FASTSIM/AliFastGlauber.h | 52 +++++--- 2 files changed, 264 insertions(+), 30 deletions(-) diff --git a/FASTSIM/AliFastGlauber.cxx b/FASTSIM/AliFastGlauber.cxx index cffcdabedf0..c533fec364a 100644 --- a/FASTSIM/AliFastGlauber.cxx +++ b/FASTSIM/AliFastGlauber.cxx @@ -27,16 +27,20 @@ ClassImp(AliFastGlauber) -TF1* AliFastGlauber::fWSb = NULL; -TF2* AliFastGlauber::fWSbz = NULL; -TF1* AliFastGlauber::fWSz = NULL; -TF1* AliFastGlauber::fWSta = NULL; -TF2* AliFastGlauber::fWStarfi = NULL; -TF1* AliFastGlauber::fWStaa = NULL; -TF1* AliFastGlauber::fWSgeo = NULL; -TF1* AliFastGlauber::fWSbinary = NULL; -TF1* AliFastGlauber::fWSN = NULL; -Float_t AliFastGlauber::fbMax = 0.; +TF1* AliFastGlauber::fWSb = NULL; +TF2* AliFastGlauber::fWSbz = NULL; +TF1* AliFastGlauber::fWSz = NULL; +TF1* AliFastGlauber::fWSta = NULL; +TF2* AliFastGlauber::fWStarfi = NULL; +TF2* AliFastGlauber::fWAlmond = NULL; +TF1* AliFastGlauber::fWStaa = NULL; +TF1* AliFastGlauber::fWSgeo = NULL; +TF1* AliFastGlauber::fWSbinary = NULL; +TF1* AliFastGlauber::fWSN = NULL; +TF1* AliFastGlauber::fWPathLength0 = NULL; +TF1* AliFastGlauber::fWPathLength = NULL; +TF1* AliFastGlauber::fWIntRadius = NULL; +Float_t AliFastGlauber::fbMax = 0.; AliFastGlauber::AliFastGlauber() { @@ -85,6 +89,26 @@ void AliFastGlauber::Init(Int_t mode) fWStarfi->SetNpx(200); fWStarfi->SetNpy(20); // +// Almond shaped interaction region +// + fWAlmond = new TF2("WAlmond", WAlmond, -fbMax, fbMax, -fbMax, fbMax, 1); + fWAlmond->SetParameter(0, 0.); + fWAlmond->SetNpx(200); + fWAlmond->SetNpy(200); +// +// Path Length as a function of Phi +// + fWPathLength0 = new TF1("WPathLength0", WPathLength0, -TMath::Pi(), TMath::Pi(), 1); + fWPathLength0->SetParameter(0, 0.); + fWPathLength = new TF1("WPathLength", WPathLength, -TMath::Pi(), TMath::Pi(), 2); +// Impact Parameter + fWPathLength->SetParameter(0, 0.); +// Number of interactions used for average + fWPathLength->SetParameter(1, 1000.); + + fWIntRadius = new TF1("WIntRadius", WIntRadius, 0., fbMax, 1); + fWIntRadius->SetParameter(0, 0.); +// // Overlap // if (! mode) { @@ -173,16 +197,69 @@ void AliFastGlauber::DrawN() fWSN->Draw(); } -void AliFastGlauber::DrawKernel() +void AliFastGlauber::DrawKernel(Double_t b) { // // Draw Kernel // TCanvas *c6 = new TCanvas("c6","Kernel",400,10,600,700); c6->cd(); + fWStarfi->SetParameter(0, b); fWStarfi->Draw(); } +void AliFastGlauber::DrawAlmond(Double_t b) +{ +// +// Draw Kernel +// + TCanvas *c7 = new TCanvas("c7","Almond",400,10,600,700); + c7->cd(); + fWAlmond->SetParameter(0, b); + fWAlmond->Draw(); +} + +void AliFastGlauber::DrawPathLength0(Double_t b) +{ +// +// Draw Kernel +// + TCanvas *c8 = new TCanvas("c8","Path Length",400,10,600,700); + c8->cd(); + fWPathLength0->SetParameter(0, b); + fWPathLength0->SetMinimum(0.); + fWPathLength0->SetMaximum(10.); + fWPathLength0->Draw(); +} + +void AliFastGlauber::DrawPathLength(Double_t b , Int_t ni) +{ +// +// Draw Kernel +// + TCanvas *c9 = new TCanvas("c9","Path Length",400,10,600,700); + c9->cd(); + fWAlmond->SetParameter(0, b); + + fWPathLength->SetParameter(0, b); + fWPathLength->SetParameter(1, Double_t (ni)); + fWPathLength->SetMinimum(0.); + fWPathLength->SetMaximum(10.); + fWPathLength->Draw(); +} + +void AliFastGlauber::DrawIntRadius(Double_t b) +{ +// +// Draw Kernel +// + TCanvas *c10 = new TCanvas("c10","Interaction Radius",400,10,600,700); + c10->cd(); + fWIntRadius->SetParameter(0, b); + fWIntRadius->SetMinimum(0.); + fWIntRadius->Draw(); +} + Double_t AliFastGlauber::WSb(Double_t* x, Double_t* par) { // @@ -261,6 +338,149 @@ Double_t AliFastGlauber::WStarfi(Double_t* x, Double_t* par) } +Double_t AliFastGlauber::WAlmond(Double_t* x, Double_t* par) +{ +// +// Almond shaped interaction region +// + Double_t b = par[0]; + Double_t xx = x[0] + b/2.; + Double_t yy = x[1]; + Double_t r1 = TMath::Sqrt(xx * xx + yy * yy); + Double_t phi = TMath::ATan2(yy,xx); + + Double_t r2 = TMath::Sqrt(r1 * r1 + b * b - 2. * r1 * b * TMath::Cos(phi)); +// +// Interaction probability calculated as product of thicknesses +// + Double_t y = fWSta->Eval(r1) * fWSta->Eval(r2); + return y; +} + +Double_t AliFastGlauber::WIntRadius(Double_t* x, Double_t* par) +{ +// +// Average radius at which interaction takes place +// +// Radius in the Almond + Double_t r = x[0]; +// Impact parameter + Double_t b = par[0]; + fWAlmond->SetParameter(0, b); +// Steps in phi + Double_t dphi = 2. * TMath::Pi() / 100.; +// Average over phi + Double_t phi = 0.; + Double_t y = 0.; + + for (Int_t i = 0; i < 100; i++) { + Double_t xx = r * TMath::Cos(phi); + Double_t yy = r * TMath::Sin(phi); + y += fWAlmond->Eval(xx,yy); + phi += dphi; + } // phi loop +// Result multiplied by Jacobian (2 pi r) + return (2. * TMath::Pi() * y * r / 100.); +} + +Double_t AliFastGlauber::WPathLength0(Double_t* x, Double_t* par) +{ +// +// Path Length as a function of phi for interaction point fixed at (0,0) +// +// +// Steps in r + const Int_t np = 100; + const Double_t dr = fbMax/Double_t(np); +// Impact parameter + Double_t b = par[0]; +// Phi direction in Almond + Double_t phi0 = x[0]; + Double_t r = 0.; + Double_t rw = 0.; + Double_t w = 0.; +// Step along radial direction phi + for (Int_t i = 0; i < np; i++) { +// +// Transform into target frame +// + Double_t xx = r * TMath::Cos(phi0) + b / 2.; + Double_t yy = r * TMath::Sin(phi0); + Double_t phi = TMath::ATan2(yy, xx); + + Double_t r1 = TMath::Sqrt(xx * xx + yy * yy); +// Radius in projectile frame + Double_t r2 = TMath::Sqrt(r1 * r1 + b * b - 2. * r1 * b * TMath::Cos(phi)); + Double_t y = fWSta->Eval(r1) * fWSta->Eval(r2); + + rw += y * r; + w += y; + r += dr; + } // radial steps +// +// My length definition (is exact for hard sphere) + return (2. * rw / w); +} + +Double_t AliFastGlauber::WPathLength(Double_t* x, Double_t* par) +{ +// +// Path Length as a function of phi +// Interaction point from random distribution +// +// +// r-steps +// + const Int_t np = 100; + const Double_t dr = fbMax/Double_t(np); +// Number of interactions + const Int_t npi = Int_t (par[1]); + +// +// Impact parameter + Double_t b = par[0]; +// Phi direction + Double_t phi0 = x[0]; + + printf("phi0 %f \n", phi0); + +// Path length + Double_t l = 0.; + + for (Int_t in = 0; in < npi; in ++) { + Double_t rw = 0.; + Double_t w = 0.; + + // Interaction point + Double_t x0, y0; + fWAlmond->GetRandom2(x0, y0); +// Initial radius + Double_t r0 = TMath::Sqrt(x0 * x0 + y0 * y0); + Int_t nps = Int_t ((fbMax - r0)/dr) - 1; + + Double_t r = 0.; +// Radial steps + for (Int_t i = 0; (i < nps ); i++) { + +// Transform into target frame + Double_t xx = x0 + r * TMath::Cos(phi0) + b / 2.; + Double_t yy = y0 + r * TMath::Sin(phi0); + Double_t phi = TMath::ATan2(yy, xx); + Double_t r1 = TMath::Sqrt(xx * xx + yy * yy); +// Radius in projectile frame + Double_t r2 = TMath::Sqrt(r1 * r1 + b * b - 2. * r1 * b * TMath::Cos(phi)); + Double_t y = fWSta->Eval(r1) * fWSta->Eval(r2); + + rw += y * r; + w += y; + r += dr; + } // steps +// Average over interactions + l += 2. * rw / w; + } // interactions + return (l / Double_t(npi)); +} + Double_t AliFastGlauber::WStaa(Double_t* x, Double_t* /*par*/) { // diff --git a/FASTSIM/AliFastGlauber.h b/FASTSIM/AliFastGlauber.h index 3670fd18bd3..df1e4d46a3c 100644 --- a/FASTSIM/AliFastGlauber.h +++ b/FASTSIM/AliFastGlauber.h @@ -18,15 +18,20 @@ class AliFastGlauber : public TObject { void SetMaxImpact(Float_t bmax = 20.) {fbMax = bmax;}; void SetHardCrossSection(Float_t xs = 6.6) {fSigmaHard = xs;} - static Double_t WSb (Double_t *xx, Double_t *par); - static Double_t WSbz (Double_t *xx, Double_t *par); - static Double_t WSz (Double_t *xx, Double_t *par); - static Double_t WSta (Double_t *xx, Double_t *par); - static Double_t WStarfi (Double_t *xx, Double_t *par); - static Double_t WStaa (Double_t *xx, Double_t *par); - static Double_t WSgeo (Double_t *xx, Double_t *par); - static Double_t WSbinary (Double_t *xx, Double_t *par); - static Double_t WSN (Double_t *xx, Double_t *par); + static Double_t WSb (Double_t *xx, Double_t *par); + static Double_t WSbz (Double_t *xx, Double_t *par); + static Double_t WSz (Double_t *xx, Double_t *par); + static Double_t WSta (Double_t *xx, Double_t *par); + static Double_t WStarfi (Double_t *xx, Double_t *par); + static Double_t WStaa (Double_t *xx, Double_t *par); + static Double_t WSgeo (Double_t *xx, Double_t *par); + static Double_t WSbinary (Double_t *xx, Double_t *par); + static Double_t WSN (Double_t *xx, Double_t *par); + static Double_t WAlmond (Double_t *xx, Double_t *par); + static Double_t WPathLength0 (Double_t *xx, Double_t *par); + static Double_t WPathLength (Double_t *xx, Double_t *par); + static Double_t WIntRadius (Double_t *xx, Double_t *par); + void Init(Int_t mode = 0); void DrawWSb(); void DrawThickness(); @@ -34,7 +39,12 @@ class AliFastGlauber : public TObject { void DrawGeo(); void DrawBinary(); void DrawN(); - void DrawKernel(); + void DrawKernel(Double_t b); + void DrawAlmond(Double_t b); + void DrawPathLength0(Double_t b); + void DrawPathLength(Double_t b, Int_t ni = 1000); + void DrawIntRadius(Double_t b); + Double_t CrossSection(Double_t b1, Double_t b2); Double_t FractionOfHardCrossSection(Double_t b1, Double_t b2); Double_t Binaries(Double_t b); @@ -45,15 +55,19 @@ class AliFastGlauber : public TObject { void GetRandom(Int_t& bin, Bool_t& hard); Float_t GetRandomImpactParameter(Float_t bmin, Float_t bmax); protected: - static TF1* fWSb; // Wood-Saxon Function (b) - static TF2* fWSbz; // Wood-Saxon Function (b, z) - static TF1* fWSz; // Wood-Saxon Function (b = b0, z) - static TF1* fWSta; // Thickness Function - static TF2* fWStarfi; // Kernel for Overlap Function - static TF1* fWStaa; // Overlap Function - static TF1* fWSgeo; // dSigma/db geometric - static TF1* fWSbinary; // dSigma/db binary - static TF1* fWSN; // dN/db binary + static TF1* fWSb; // Wood-Saxon Function (b) + static TF2* fWSbz; // Wood-Saxon Function (b, z) + static TF1* fWSz; // Wood-Saxon Function (b = b0, z) + static TF1* fWSta; // Thickness Function + static TF2* fWStarfi; // Kernel for Overlap Function + static TF1* fWStaa; // Overlap Function + static TF2* fWAlmond; // Interaction Almond + static TF1* fWPathLength0;// Path Length as a function of phi + static TF1* fWPathLength; // Path Length as a function of phi + static TF1* fWIntRadius; // Interaction Radius + static TF1* fWSgeo; // dSigma/db geometric + static TF1* fWSbinary; // dSigma/db binary + static TF1* fWSN; // dN/db binary Float_t fWSr0; // Wood-Saxon Parameter r0 Float_t fWSd; // Wood-Saxon Parameter d -- 2.27.0