| 1 | #include "TrkUtil.h"
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| 2 | #include <iostream>
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| 3 | #include <algorithm>
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| 4 | #include <TSpline.h>
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| 5 |
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| 6 | // Constructor
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| 7 | TrkUtil::TrkUtil(Double_t Bz)
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| 8 | {
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| 9 | fBz = Bz;
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| 10 | fGasSel = 0; // Default is He-Isobuthane (90-10)
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| 11 | fRmin = 0.0; // Lower DCH radius
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| 12 | fRmax = 0.0; // Higher DCH radius
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| 13 | fZmin = 0.0; // Lower DCH z
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| 14 | fZmax = 0.0; // Higher DCH z
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| 15 | }
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| 16 | TrkUtil::TrkUtil()
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| 17 | {
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| 18 | fBz = 0.0;
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| 19 | fGasSel = 0; // Default is He-Isobuthane (90-10)
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| 20 | fRmin = 0.0; // Lower DCH radius
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| 21 | fRmax = 0.0; // Higher DCH radius
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| 22 | fZmin = 0.0; // Lower DCH z
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| 23 | fZmax = 0.0; // Higher DCH z
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| 24 | }
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| 25 | //
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| 26 | // Destructor
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| 27 | TrkUtil::~TrkUtil()
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| 28 | {
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| 29 | fBz = 0.0;
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| 30 | fGasSel = 0; // Default is He-Isobuthane (90-10)
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| 31 | fRmin = 0.0; // Lower DCH radius
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| 32 | fRmax = 0.0; // Higher DCH radius
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| 33 | fZmin = 0.0; // Lower DCH z
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| 34 | fZmax = 0.0; // Higher DCH z
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| 35 | }
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| 36 | //
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| 37 | // Helix parameters from position and momentum
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| 38 | // static
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| 39 | TVectorD TrkUtil::XPtoPar(TVector3 x, TVector3 p, Double_t Q, Double_t Bz)
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| 40 | {
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| 41 | //
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| 42 | TVectorD Par(5);
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| 43 | // Transverse parameters
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| 44 | Double_t a = -Q * Bz * cSpeed(); // Units are Tesla, GeV and meters
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| 45 | Double_t pt = p.Pt();
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| 46 | Double_t C = a / (2 * pt); // Half curvature
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| 47 | //std::cout << "ObsTrk::XPtoPar: fB = " << fB << ", a = " << a << ", pt = " << pt << ", C = " << C << std::endl;
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| 48 | Double_t r2 = x(0) * x(0) + x(1) * x(1);
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| 49 | Double_t cross = x(0) * p(1) - x(1) * p(0);
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| 50 | Double_t T = sqrt(pt * pt - 2 * a * cross + a * a * r2);
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| 51 | Double_t phi0 = atan2((p(1) - a * x(0)) / T, (p(0) + a * x(1)) / T); // Phi0
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| 52 | Double_t D; // Impact parameter D
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| 53 | if (pt < 10.0) D = (T - pt) / a;
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| 54 | else D = (-2 * cross + a * r2) / (T + pt);
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| 55 | //
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| 56 | Par(0) = D; // Store D
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| 57 | Par(1) = phi0; // Store phi0
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| 58 | Par(2) = C; // Store C
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| 59 | //Longitudinal parameters
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| 60 | Double_t B = C * sqrt(TMath::Max(r2 - D * D, 0.0) / (1 + 2 * C * D));
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| 61 | Double_t st = asin(B) / C;
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| 62 | Double_t ct = p(2) / pt;
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| 63 | Double_t z0;
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| 64 | Double_t dot = x(0) * p(0) + x(1) * p(1);
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| 65 | if (dot > 0.0) z0 = x(2) - ct * st;
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| 66 | else z0 = x(2) + ct * st;
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| 67 | //
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| 68 | Par(3) = z0; // Store z0
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| 69 | Par(4) = ct; // Store cot(theta)
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| 70 | //
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| 71 | return Par;
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| 72 | }
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| 73 | // non-static
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| 74 | TVectorD TrkUtil::XPtoPar(TVector3 x, TVector3 p, Double_t Q)
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| 75 | {
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| 76 | //
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| 77 | TVectorD Par(5);
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| 78 | Double_t Bz = fBz;
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| 79 | Par = XPtoPar(x, p, Q, Bz);
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| 80 | //
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| 81 | return Par;
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| 82 | }
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| 83 | //
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| 84 | TVector3 TrkUtil::ParToX(TVectorD Par)
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| 85 | {
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| 86 | Double_t D = Par(0);
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| 87 | Double_t phi0 = Par(1);
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| 88 | Double_t z0 = Par(3);
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| 89 | //
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| 90 | TVector3 Xval;
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| 91 | Xval(0) = -D * sin(phi0);
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| 92 | Xval(1) = D * cos(phi0);
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| 93 | Xval(2) = z0;
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| 94 | //
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| 95 | return Xval;
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| 96 | }
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| 97 | //
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| 98 | TVector3 TrkUtil::ParToP(TVectorD Par)
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| 99 | {
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| 100 | if (fBz == 0.0)std::cout << "TrkUtil::ParToP: Warning Bz not set" << std::endl;
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| 101 | //
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| 102 | return ParToP(Par, fBz);
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| 103 | }
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| 104 | //
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| 105 | TVector3 TrkUtil::ParToP(TVectorD Par, Double_t Bz)
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| 106 | {
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| 107 | Double_t C = Par(2);
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| 108 | Double_t phi0 = Par(1);
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| 109 | Double_t ct = Par(4);
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| 110 | //
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| 111 | TVector3 Pval;
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| 112 | Double_t pt = Bz * cSpeed() / TMath::Abs(2 * C);
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| 113 | Pval(0) = pt * cos(phi0);
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| 114 | Pval(1) = pt * sin(phi0);
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| 115 | Pval(2) = pt * ct;
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| 116 | //
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| 117 | return Pval;
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| 118 | }
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| 119 | //
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| 120 | Double_t TrkUtil::ParToQ(TVectorD Par)
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| 121 | {
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| 122 | return TMath::Sign(1.0, -Par(2));
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| 123 | }
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| 124 |
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| 125 | //
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| 126 | // Parameter conversion to ACTS format
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| 127 | TVectorD TrkUtil::ParToACTS(TVectorD Par)
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| 128 | {
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| 129 | TVectorD pACTS(6); // Return vector
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| 130 | //
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| 131 | Double_t b = -cSpeed() * fBz / 2.;
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| 132 | pACTS(0) = 1000 * Par(0); // D from m to mm
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| 133 | pACTS(1) = 1000 * Par(3); // z0 from m to mm
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| 134 | pACTS(2) = Par(1); // Phi0 is unchanged
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| 135 | pACTS(3) = atan2(1.0, Par(4)); // Theta in [0, pi] range
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| 136 | pACTS(4) = Par(2) / (b * sqrt(1 + Par(4) * Par(4))); // q/p in GeV
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| 137 | pACTS(5) = 0.0; // Time: currently undefined
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| 138 | //
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| 139 | return pACTS;
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| 140 | }
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| 141 | // Covariance conversion to ACTS format
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| 142 | TMatrixDSym TrkUtil::CovToACTS(TVectorD Par, TMatrixDSym Cov)
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| 143 | {
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| 144 | TMatrixDSym cACTS(6); cACTS.Zero();
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| 145 | Double_t b = -cSpeed() * fBz / 2.;
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| 146 | //
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| 147 | // Fill derivative matrix
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| 148 | TMatrixD A(5, 5); A.Zero();
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| 149 | Double_t ct = Par(4); // cot(theta)
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| 150 | Double_t C = Par(2); // half curvature
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| 151 | A(0, 0) = 1000.; // D-D conversion to mm
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| 152 | A(1, 2) = 1.0; // phi0-phi0
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| 153 | A(2, 4) = 1.0 / (sqrt(1.0 + ct * ct) * b); // q/p-C
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| 154 | A(3, 1) = 1000.; // z0-z0 conversion to mm
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| 155 | A(4, 3) = -1.0 / (1.0 + ct * ct); // theta - cot(theta)
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| 156 | A(4, 4) = -C * ct / (b * pow(1.0 + ct * ct, 3.0 / 2.0)); // q/p-cot(theta)
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| 157 | //
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| 158 | TMatrixDSym Cv = Cov;
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| 159 | TMatrixD At(5, 5);
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| 160 | At.Transpose(A);
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| 161 | Cv.Similarity(At);
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| 162 | TMatrixDSub(cACTS, 0, 4, 0, 4) = Cv;
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| 163 | cACTS(5, 5) = 0.1; // Currently undefined: set to arbitrary value to avoid crashes
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| 164 | //
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| 165 | return cACTS;
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| 166 | }
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| 167 | //
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| 168 | // Parameter conversion to ILC format
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| 169 | TVectorD TrkUtil::ParToILC(TVectorD Par)
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| 170 | {
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| 171 | TVectorD pILC(5); // Return vector
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| 172 | //
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| 173 | pILC(0) = Par(0) * 1.0e3; // d0 in mm
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| 174 | pILC(1) = Par(1); // phi0 is unchanged
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| 175 | pILC(2) = -2 * Par(2) * 1.0e-3; // w in mm^-1
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| 176 | pILC(3) = Par(3) * 1.0e3; // z0 in mm
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| 177 | pILC(4) = Par(4); // tan(lambda) = cot(theta)
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| 178 | //
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| 179 | return pILC;
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| 180 | }
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| 181 | // Covariance conversion to ILC format
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| 182 | TMatrixDSym TrkUtil::CovToILC(TMatrixDSym Cov)
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| 183 | {
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| 184 | TMatrixDSym cILC(5); cILC.Zero();
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| 185 | //
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| 186 | // Fill derivative matrix
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| 187 | TMatrixD A(5, 5); A.Zero();
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| 188 | //
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| 189 | A(0, 0) = 1.0e3; // D-d0 in mm
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| 190 | A(1, 1) = 1.0; // phi0-phi0
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| 191 | A(2, 2) = -2.0e-3; // w-C
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| 192 | A(3, 3) = 1.0e3; // z0-z0 conversion to mm
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| 193 | A(4, 4) = 1.0; // tan(lambda) - cot(theta)
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| 194 | //
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| 195 | TMatrixDSym Cv = Cov;
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| 196 | TMatrixD At(5, 5);
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| 197 | At.Transpose(A);
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| 198 | Cv.Similarity(At);
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| 199 | cILC = Cv;
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| 200 | //
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| 201 | return cILC;
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| 202 | }
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| 203 | //
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| 204 | // Conversion from meters to mm
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| 205 | TVectorD TrkUtil::ParToMm(TVectorD Par) // Parameter conversion
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| 206 | {
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| 207 | TVectorD Pmm(5); // Return vector
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| 208 | //
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| 209 | Pmm(0) = Par(0) * 1.0e3; // d0 in mm
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| 210 | Pmm(1) = Par(1); // phi0 is unchanged
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| 211 | Pmm(2) = Par(2) * 1.0e-3; // C in mm^-1
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| 212 | Pmm(3) = Par(3) * 1.0e3; // z0 in mm
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| 213 | Pmm(4) = Par(4); // tan(lambda) = cot(theta) unchanged
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| 214 | //
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| 215 | return Pmm;
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| 216 | }
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| 217 | TMatrixDSym TrkUtil::CovToMm(TMatrixDSym Cov) // Covariance conversion
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| 218 | {
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| 219 | TMatrixDSym Cmm(5); Cmm.Zero();
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| 220 | //
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| 221 | // Fill derivative matrix
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| 222 | TMatrixD A(5, 5); A.Zero();
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| 223 | //
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| 224 | A(0, 0) = 1.0e3; // D-d0 in mm
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| 225 | A(1, 1) = 1.0; // phi0-phi0
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| 226 | A(2, 2) = 1.0e-3; // C-C
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| 227 | A(3, 3) = 1.0e3; // z0-z0 conversion to mm
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| 228 | A(4, 4) = 1.0; // lambda - cot(theta)
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| 229 | //
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| 230 | TMatrixDSym Cv = Cov;
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| 231 | TMatrixD At(5, 5);
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| 232 | At.Transpose(A);
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| 233 | Cv.Similarity(At);
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| 234 | Cmm = Cv;
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| 235 | //
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| 236 | return Cmm;
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| 237 | }
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| 238 | //
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| 239 | // Setup chamber volume
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| 240 | void TrkUtil::SetDchBoundaries(Double_t Rmin, Double_t Rmax, Double_t Zmin, Double_t Zmax)
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| 241 | {
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| 242 | fRmin = Rmin; // Lower DCH radius
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| 243 | fRmax = Rmax; // Higher DCH radius
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| 244 | fZmin = Zmin; // Lower DCH z
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| 245 | fZmax = Zmax; // Higher DCH z
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| 246 | }
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| 247 | //
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| 248 | // Get Trakck length inside DCH volume
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| 249 | Double_t TrkUtil::TrkLen(TVectorD Par)
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| 250 | {
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| 251 | Double_t tLength = 0.0;
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| 252 | // Check if geometry is initialized
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| 253 | if (fZmin == 0.0 && fZmax == 0.0)
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| 254 | {
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| 255 | // No geometry set so send a warning and return 0
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| 256 | std::cout << "TrkUtil::TrkLen() called without a DCH volume defined" << std::endl;
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| 257 | }
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| 258 | else
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| 259 | {
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| 260 | //******************************************************************
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| 261 | // Determine the track length inside the chamber ****
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| 262 | //******************************************************************
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| 263 | //
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| 264 | // Track pararameters
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| 265 | Double_t D = Par(0); // Transverse impact parameter
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| 266 | Double_t phi0 = Par(1); // Transverse direction at minimum approach
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| 267 | Double_t C = Par(2); // Half curvature
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| 268 | Double_t z0 = Par(3); // Z at minimum approach
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| 269 | Double_t ct = Par(4); // cot(theta)
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| 270 | //std::cout << "TrkUtil:: parameters: D= " << D << ", phi0= " << phi0
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| 271 | // << ", C= " << C << ", z0= " << z0 << ", ct= " << ct << std::endl;
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| 272 | //
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| 273 | // Track length per unit phase change
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| 274 | Double_t Scale = sqrt(1.0 + ct * ct) / (2.0 * TMath::Abs(C));
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| 275 | //
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| 276 | // Find intersections with chamber boundaries
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| 277 | //
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| 278 | Double_t phRin = 0.0; // phase of inner cylinder
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| 279 | Double_t phRin2 = 0.0; // phase of inner cylinder intersection (2nd branch)
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| 280 | Double_t phRhi = 0.0; // phase of outer cylinder intersection
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| 281 | Double_t phZmn = 0.0; // phase of left wall intersection
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| 282 | Double_t phZmx = 0.0; // phase of right wall intersection
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| 283 | // ... with inner cylinder
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| 284 | Double_t Rtop = TMath::Abs((1.0 + C * D) / C);
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| 285 |
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| 286 | if (Rtop > fRmin && TMath::Abs(D) < fRmin) // *** don't treat large D tracks for the moment ***
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| 287 | {
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| 288 | Double_t ph = 2 * asin(C * sqrt((fRmin * fRmin - D * D) / (1.0 + 2.0 * C * D)));
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| 289 | Double_t z = z0 + ct * ph / (2.0 * C);
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| 290 |
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| 291 | //std::cout << "Rin intersection: ph = " << ph<<", z= "<<z << std::endl;
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| 292 |
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| 293 | if (z < fZmax && z > fZmin) phRin = TMath::Abs(ph); // Intersection inside chamber volume
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| 294 | //
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| 295 | // Include second branch of loopers
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| 296 | Double_t Pi = 3.14159265358979323846;
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| 297 | Double_t ph2 = 2 * Pi - TMath::Abs(ph);
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| 298 | if (ph < 0)ph2 = -ph2;
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| 299 | z = z0 + ct * ph2 / (2.0 * C);
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| 300 | if (z < fZmax && z > fZmin) phRin2 = TMath::Abs(ph2); // Intersection inside chamber volume
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| 301 | }
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| 302 | // ... with outer cylinder
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| 303 | if (Rtop > fRmax && TMath::Abs(D) < fRmax) // *** don't treat large D tracks for the moment ***
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| 304 | {
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| 305 | Double_t ph = 2 * asin(C * sqrt((fRmax * fRmax - D * D) / (1.0 + 2.0 * C * D)));
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| 306 | Double_t z = z0 + ct * ph / (2.0 * C);
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| 307 | if (z < fZmax && z > fZmin) phRhi = TMath::Abs(ph); // Intersection inside chamber volume
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| 308 | }
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| 309 | // ... with left wall
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| 310 | Double_t Zdir = (fZmin - z0) / ct;
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| 311 | if (Zdir > 0.0)
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| 312 | {
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| 313 | Double_t ph = 2.0 * C * Zdir;
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| 314 | Double_t Rint = sqrt(D * D + (1.0 + 2.0 * C * D) * pow(sin(ph / 2), 2) / (C * C));
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| 315 | if (Rint < fRmax && Rint > fRmin) phZmn = TMath::Abs(ph); // Intersection inside chamber volume
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| 316 | }
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| 317 | // ... with right wall
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| 318 | Zdir = (fZmax - z0) / ct;
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| 319 | if (Zdir > 0.0)
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| 320 | {
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| 321 | Double_t ph = 2.0 * C * Zdir;
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| 322 | Double_t Rint = sqrt(D * D + (1.0 + 2.0 * C * D) * pow(sin(ph / 2), 2) / (C * C));
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| 323 | if (Rint < fRmax && Rint > fRmin) phZmx = TMath::Abs(ph); // Intersection inside chamber volume
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| 324 | }
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| 325 | //
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| 326 | // Order phases and keep the lowest two non-zero ones
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| 327 | //
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| 328 | const Int_t Nint = 5;
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| 329 | Double_t dPhase = 0.0; // Phase difference between two close intersections
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| 330 | Double_t ph_arr[Nint] = { phRin, phRin2, phRhi, phZmn, phZmx };
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| 331 | std::sort(ph_arr, ph_arr + Nint);
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| 332 | Int_t iPos = -1; // First element > 0
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| 333 | for (Int_t i = 0; i < Nint; i++)
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| 334 | {
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| 335 | if (ph_arr[i] <= 0.0) iPos = i;
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| 336 | }
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| 337 |
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| 338 | if (iPos < Nint - 2)
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| 339 | {
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| 340 | dPhase = ph_arr[iPos + 2] - ph_arr[iPos + 1];
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| 341 | tLength = dPhase * Scale;
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| 342 | }
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| 343 | }
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| 344 | return tLength;
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| 345 | }
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| 346 | //
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| 347 | // Return number of ionization clusters
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| 348 | Bool_t TrkUtil::IonClusters(Double_t& Ncl, Double_t mass, TVectorD Par)
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| 349 | {
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| 350 | //
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| 351 | // Units are meters/Tesla/GeV
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| 352 | //
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| 353 | Ncl = 0.0;
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| 354 | Bool_t Signal = kFALSE;
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| 355 | Double_t tLen = 0;
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| 356 | // Check if geometry is initialized
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| 357 | if (fZmin == 0.0 && fZmax == 0.0)
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| 358 | {
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| 359 | // No geometry set so send a warning and return 0
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| 360 | std::cout << "TrkUtil::IonClusters() called without a volume defined" << std::endl;
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| 361 | }
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| 362 | else tLen = TrkLen(Par);
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| 363 |
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| 364 | //******************************************************************
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| 365 | // Now get the number of clusters ****
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| 366 | //******************************************************************
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| 367 | //
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| 368 | Double_t muClu = 0.0; // mean number of clusters
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| 369 | Double_t bg = 0.0; // beta*gamma
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| 370 | Ncl = 0.0;
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| 371 | if (tLen > 0.0)
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| 372 | {
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| 373 | Signal = kTRUE;
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| 374 | //
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| 375 | // Find beta*gamma
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| 376 | if (fBz == 0.0)
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| 377 | {
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| 378 | Signal = kFALSE;
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| 379 | std::cout << "TrkUtil::IonClusters: Please set Bz!!!" << std::endl;
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| 380 | }
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| 381 | else
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| 382 | {
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| 383 | TVector3 p = ParToP(Par);
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| 384 | bg = p.Mag() / mass;
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| 385 | muClu = Nclusters(bg) * tLen; // Avg. number of clusters
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| 386 |
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| 387 | Ncl = gRandom->PoissonD(muClu); // Actual number of clusters
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| 388 | }
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| 389 |
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| 390 | }
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| 391 | //
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| 392 | return Signal;
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| 393 | }
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| 394 | //
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| 395 | //
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| 396 | Double_t TrkUtil::Nclusters(Double_t begam)
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| 397 | {
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| 398 | Int_t Opt = fGasSel;
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| 399 | Double_t Nclu = Nclusters(begam, Opt);
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| 400 | //
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| 401 | return Nclu;
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| 402 | }
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| 403 | //
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| 404 | Double_t TrkUtil::Nclusters(Double_t begam, Int_t Opt) {
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| 405 | //
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| 406 | // Opt = 0: He 90 - Isobutane 10
|
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| 407 | // = 1: pure He
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| 408 | // = 2: Argon 50 - Ethane 50
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| 409 | // = 3: pure Argon
|
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| 410 | //
|
|---|
| 411 | //
|
|---|
| 412 | const Int_t Npt = 18;
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| 413 | Double_t bg[Npt] = { 0.5, 0.8, 1., 2., 3., 4., 5., 8., 10.,
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| 414 | 12., 15., 20., 50., 100., 200., 500., 1000., 10000. };
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| 415 | //
|
|---|
| 416 | // He 90 - Isobutane 10
|
|---|
| 417 | Double_t ncl_He_Iso[Npt] = { 42.94, 23.6,18.97,12.98,12.2,12.13,
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|---|
| 418 | 12.24,12.73,13.03,13.29,13.63,14.08,15.56,16.43,16.8,16.95,16.98, 16.98 };
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| 419 | //
|
|---|
| 420 | // pure He
|
|---|
| 421 | Double_t ncl_He[Npt] = { 11.79,6.5,5.23,3.59,3.38,3.37,3.4,3.54,3.63,
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|---|
| 422 | 3.7,3.8,3.92,4.33,4.61,4.78,4.87,4.89, 4.89 };
|
|---|
| 423 | //
|
|---|
| 424 | // Argon 50 - Ethane 50
|
|---|
| 425 | Double_t ncl_Ar_Eth[Npt] = { 130.04,71.55,57.56,39.44,37.08,36.9,
|
|---|
| 426 | 37.25,38.76,39.68,40.49,41.53,42.91,46.8,48.09,48.59,48.85,48.93,48.93 };
|
|---|
| 427 | //
|
|---|
| 428 | // pure Argon
|
|---|
| 429 | Double_t ncl_Ar[Npt] = { 88.69,48.93,39.41,27.09,25.51,25.43,25.69,
|
|---|
| 430 | 26.78,27.44,28.02,28.77,29.78,32.67,33.75,34.24,34.57,34.68, 34.68 };
|
|---|
| 431 | //
|
|---|
| 432 | Double_t ncl[Npt];
|
|---|
| 433 | switch (Opt)
|
|---|
| 434 | {
|
|---|
| 435 | case 0: std::copy(ncl_He_Iso, ncl_He_Iso + Npt, ncl); // He-Isobutane
|
|---|
| 436 | break;
|
|---|
| 437 | case 1: std::copy(ncl_He, ncl_He + Npt, ncl); // pure He
|
|---|
| 438 | break;
|
|---|
| 439 | case 2: std::copy(ncl_Ar_Eth, ncl_Ar_Eth + Npt, ncl); // Argon - Ethane
|
|---|
| 440 | break;
|
|---|
| 441 | case 3: std::copy(ncl_Ar, ncl_Ar + Npt, ncl); // pure Argon
|
|---|
| 442 | break;
|
|---|
| 443 | }
|
|---|
| 444 | //
|
|---|
| 445 | Double_t interp = 0.0;
|
|---|
| 446 | TSpline3* sp3 = new TSpline3("sp3", bg, ncl, Npt);
|
|---|
| 447 | if (begam > bg[0] && begam < bg[Npt - 1]) interp = sp3->Eval(begam);
|
|---|
| 448 | return 100 * interp;
|
|---|
| 449 | }
|
|---|
| 450 | //
|
|---|
| 451 | Double_t TrkUtil::funcNcl(Double_t* xp, Double_t* par) {
|
|---|
| 452 | Double_t bg = xp[0];
|
|---|
| 453 | return Nclusters(bg);
|
|---|
| 454 | }
|
|---|
| 455 | //
|
|---|
| 456 | void TrkUtil::SetGasMix(Int_t Opt)
|
|---|
| 457 | {
|
|---|
| 458 | if (Opt < 0 || Opt > 3)
|
|---|
| 459 | {
|
|---|
| 460 | std::cout << "TrkUtil::SetGasMix Gas option not allowed. No action."
|
|---|
| 461 | << std::endl;
|
|---|
| 462 | }
|
|---|
| 463 | else fGasSel = Opt;
|
|---|
| 464 | }
|
|---|
