| 7984e5f7 |
1 | // |
| 2 | // Utilities used in the forward multiplcity analysis |
| 3 | // |
| 4 | // |
| 7e4038b5 |
5 | #include "AliForwardUtil.h" |
| 9d99b0dd |
6 | #include <AliAnalysisManager.h> |
| 7 | #include "AliAODForwardMult.h" |
| 8 | #include <AliLog.h> |
| 9 | #include <AliInputEventHandler.h> |
| 10 | #include <AliESDEvent.h> |
| 11 | #include <AliPhysicsSelection.h> |
| 12 | #include <AliTriggerAnalysis.h> |
| 13 | #include <AliMultiplicity.h> |
| 7e4038b5 |
14 | #include <TH2D.h> |
| 9d99b0dd |
15 | #include <TH1I.h> |
| 7f759bb7 |
16 | #include <TF1.h> |
| 17 | #include <TFitResult.h> |
| 7e4038b5 |
18 | #include <TMath.h> |
| 7f759bb7 |
19 | #include <TError.h> |
| 20 | |
| 0bd4b00f |
21 | //==================================================================== |
| 22 | UShort_t |
| 23 | AliForwardUtil::ParseCollisionSystem(const char* sys) |
| 24 | { |
| 7984e5f7 |
25 | // |
| 26 | // Parse a collision system spec given in a string. Known values are |
| 27 | // |
| 28 | // - "pp", "p-p" which returns kPP |
| 29 | // - "PbPb", "Pb-Pb", "A-A", which returns kPbPb |
| 30 | // - Everything else gives kUnknown |
| 31 | // |
| 32 | // Parameters: |
| 33 | // sys Collision system spec |
| 34 | // |
| 35 | // Return: |
| 36 | // Collision system id |
| 37 | // |
| 0bd4b00f |
38 | TString s(sys); |
| 39 | s.ToLower(); |
| 40 | if (s.Contains("p-p") || s.Contains("pp")) return AliForwardUtil::kPP; |
| 41 | if (s.Contains("pb-pb") || s.Contains("pbpb")) return AliForwardUtil::kPbPb; |
| 42 | if (s.Contains("a-a") || s.Contains("aa")) return AliForwardUtil::kPbPb; |
| 43 | return AliForwardUtil::kUnknown; |
| 44 | } |
| 45 | //____________________________________________________________________ |
| 46 | const char* |
| 47 | AliForwardUtil::CollisionSystemString(UShort_t sys) |
| 48 | { |
| 7984e5f7 |
49 | // |
| 50 | // Get a string representation of the collision system |
| 51 | // |
| 52 | // Parameters: |
| 53 | // sys Collision system |
| 54 | // - kPP -> "pp" |
| 55 | // - kPbPb -> "PbPb" |
| 56 | // - anything else gives "unknown" |
| 57 | // |
| 58 | // Return: |
| 59 | // String representation of the collision system |
| 60 | // |
| 0bd4b00f |
61 | switch (sys) { |
| 62 | case AliForwardUtil::kPP: return "pp"; |
| 63 | case AliForwardUtil::kPbPb: return "PbPb"; |
| 64 | } |
| 65 | return "unknown"; |
| 66 | } |
| 67 | //____________________________________________________________________ |
| 68 | UShort_t |
| cc83fca2 |
69 | AliForwardUtil::ParseCenterOfMassEnergy(UShort_t /* sys */, Float_t v) |
| 0bd4b00f |
70 | { |
| 7984e5f7 |
71 | // |
| 72 | // Parse the center of mass energy given as a float and return known |
| 73 | // values as a unsigned integer |
| 74 | // |
| 75 | // Parameters: |
| 76 | // sys Collision system (needed for AA) |
| 77 | // cms Center of mass energy * total charge |
| 78 | // |
| 79 | // Return: |
| 80 | // Center of mass energy per nucleon |
| 81 | // |
| 0bd4b00f |
82 | Float_t energy = v; |
| cc83fca2 |
83 | // Below no longer needed apparently |
| 84 | // if (sys == AliForwardUtil::kPbPb) energy = energy / 208 * 82; |
| 0bd4b00f |
85 | if (TMath::Abs(energy - 900.) < 10) return 900; |
| 86 | if (TMath::Abs(energy - 2400.) < 10) return 2400; |
| 87 | if (TMath::Abs(energy - 2750.) < 10) return 2750; |
| 88 | if (TMath::Abs(energy - 5500.) < 40) return 5500; |
| 89 | if (TMath::Abs(energy - 7000.) < 10) return 7000; |
| 90 | if (TMath::Abs(energy - 10000.) < 10) return 10000; |
| 91 | if (TMath::Abs(energy - 14000.) < 10) return 14000; |
| 92 | return 0; |
| 93 | } |
| 94 | //____________________________________________________________________ |
| 95 | const char* |
| 96 | AliForwardUtil::CenterOfMassEnergyString(UShort_t cms) |
| 97 | { |
| 7984e5f7 |
98 | // |
| 99 | // Get a string representation of the center of mass energy per nuclean |
| 100 | // |
| 101 | // Parameters: |
| 102 | // cms Center of mass energy per nucleon |
| 103 | // |
| 104 | // Return: |
| 105 | // String representation of the center of mass energy per nuclean |
| 106 | // |
| 0bd4b00f |
107 | return Form("%04dGeV", cms); |
| 108 | } |
| 109 | //____________________________________________________________________ |
| 110 | Short_t |
| 111 | AliForwardUtil::ParseMagneticField(Float_t v) |
| 112 | { |
| 7984e5f7 |
113 | // |
| 114 | // Parse the magnetic field (in kG) as given by a floating point number |
| 115 | // |
| 116 | // Parameters: |
| 117 | // field Magnetic field in kG |
| 118 | // |
| 119 | // Return: |
| 120 | // Short integer value of magnetic field in kG |
| 121 | // |
| 0bd4b00f |
122 | if (TMath::Abs(v - 5.) < 1 ) return +5; |
| 123 | if (TMath::Abs(v + 5.) < 1 ) return -5; |
| 124 | if (TMath::Abs(v) < 1) return 0; |
| 125 | return 999; |
| 126 | } |
| 127 | //____________________________________________________________________ |
| 128 | const char* |
| 129 | AliForwardUtil::MagneticFieldString(Short_t f) |
| 130 | { |
| 7984e5f7 |
131 | // |
| 132 | // Get a string representation of the magnetic field |
| 133 | // |
| 134 | // Parameters: |
| 135 | // field Magnetic field in kG |
| 136 | // |
| 137 | // Return: |
| 138 | // String representation of the magnetic field |
| 139 | // |
| 0bd4b00f |
140 | return Form("%01dkG", f); |
| 141 | } |
| 142 | |
| 143 | |
| 7f759bb7 |
144 | //==================================================================== |
| 145 | Int_t AliForwardUtil::fgConvolutionSteps = 100; |
| 146 | Double_t AliForwardUtil::fgConvolutionNSigma = 5; |
| 147 | namespace { |
| 7984e5f7 |
148 | // |
| 149 | // The shift of the most probable value for the ROOT function TMath::Landau |
| 150 | // |
| 7f759bb7 |
151 | const Double_t mpshift = -0.22278298; |
| 7984e5f7 |
152 | // |
| 153 | // Integration normalisation |
| 154 | // |
| 7f759bb7 |
155 | const Double_t invSq2pi = 1. / TMath::Sqrt(2*TMath::Pi()); |
| 156 | |
| 7984e5f7 |
157 | // |
| 158 | // Utility function to use in TF1 defintition |
| 159 | // |
| 7f759bb7 |
160 | Double_t landauGaus1(Double_t* xp, Double_t* pp) |
| 161 | { |
| 162 | Double_t x = xp[0]; |
| c389303e |
163 | Double_t constant = pp[AliForwardUtil::ELossFitter::kC]; |
| 164 | Double_t delta = pp[AliForwardUtil::ELossFitter::kDelta]; |
| 165 | Double_t xi = pp[AliForwardUtil::ELossFitter::kXi]; |
| 166 | Double_t sigma = pp[AliForwardUtil::ELossFitter::kSigma]; |
| 1174780f |
167 | Double_t sigmaN = pp[AliForwardUtil::ELossFitter::kSigmaN]; |
| 7f759bb7 |
168 | |
| 1174780f |
169 | return constant * AliForwardUtil::LandauGaus(x, delta, xi, sigma, sigmaN); |
| 7f759bb7 |
170 | } |
| 171 | |
| 7984e5f7 |
172 | // |
| 173 | // Utility function to use in TF1 defintition |
| 174 | // |
| 7f759bb7 |
175 | Double_t landauGausN(Double_t* xp, Double_t* pp) |
| 176 | { |
| 177 | Double_t x = xp[0]; |
| c389303e |
178 | Double_t constant = pp[AliForwardUtil::ELossFitter::kC]; |
| 179 | Double_t delta = pp[AliForwardUtil::ELossFitter::kDelta]; |
| 180 | Double_t xi = pp[AliForwardUtil::ELossFitter::kXi]; |
| 181 | Double_t sigma = pp[AliForwardUtil::ELossFitter::kSigma]; |
| 1174780f |
182 | Double_t sigmaN = pp[AliForwardUtil::ELossFitter::kSigmaN]; |
| c389303e |
183 | Int_t n = Int_t(pp[AliForwardUtil::ELossFitter::kN]); |
| 184 | Double_t* a = &(pp[AliForwardUtil::ELossFitter::kA]); |
| 7f759bb7 |
185 | |
| 1174780f |
186 | return constant * AliForwardUtil::NLandauGaus(x, delta, xi, sigma, sigmaN, |
| 7f759bb7 |
187 | n, a); |
| 188 | } |
| 7984e5f7 |
189 | // |
| 190 | // Utility function to use in TF1 defintition |
| 191 | // |
| 0bd4b00f |
192 | Double_t landauGausI(Double_t* xp, Double_t* pp) |
| 193 | { |
| 194 | Double_t x = xp[0]; |
| 195 | Double_t constant = pp[AliForwardUtil::ELossFitter::kC]; |
| 196 | Double_t delta = pp[AliForwardUtil::ELossFitter::kDelta]; |
| 197 | Double_t xi = pp[AliForwardUtil::ELossFitter::kXi]; |
| 198 | Double_t sigma = pp[AliForwardUtil::ELossFitter::kSigma]; |
| 1174780f |
199 | Double_t sigmaN = pp[AliForwardUtil::ELossFitter::kSigmaN]; |
| 0bd4b00f |
200 | Int_t i = Int_t(pp[AliForwardUtil::ELossFitter::kN]); |
| 201 | |
| 1174780f |
202 | return constant * AliForwardUtil::ILandauGaus(x,delta,xi,sigma,sigmaN,i); |
| 0bd4b00f |
203 | } |
| 7f759bb7 |
204 | |
| 205 | |
| 206 | } |
| 207 | //____________________________________________________________________ |
| 208 | Double_t |
| 209 | AliForwardUtil::Landau(Double_t x, Double_t delta, Double_t xi) |
| 210 | { |
| 7984e5f7 |
211 | // |
| 212 | // Calculate the shifted Landau |
| 213 | // @f[ |
| 214 | // f'_{L}(x;\Delta,\xi) = f_L(x;\Delta+0.22278298\xi) |
| 215 | // @f] |
| 216 | // |
| 217 | // where @f$ f_{L}@f$ is the ROOT implementation of the Landau |
| 218 | // distribution (known to have @f$ \Delta_{p}=-0.22278298@f$ for |
| 219 | // @f$\Delta=0,\xi=1@f$. |
| 220 | // |
| 221 | // Parameters: |
| 222 | // x Where to evaluate @f$ f'_{L}@f$ |
| 223 | // delta Most probable value |
| 224 | // xi The 'width' of the distribution |
| 225 | // |
| 226 | // Return: |
| 227 | // @f$ f'_{L}(x;\Delta,\xi) @f$ |
| 228 | // |
| 7f759bb7 |
229 | return TMath::Landau(x, delta - xi * mpshift, xi); |
| 230 | } |
| 231 | //____________________________________________________________________ |
| 232 | Double_t |
| 233 | AliForwardUtil::LandauGaus(Double_t x, Double_t delta, Double_t xi, |
| 1174780f |
234 | Double_t sigma, Double_t sigmaN) |
| 7f759bb7 |
235 | { |
| 7984e5f7 |
236 | // |
| 237 | // Calculate the value of a Landau convolved with a Gaussian |
| 238 | // |
| 239 | // @f[ |
| 240 | // f(x;\Delta,\xi,\sigma') = \frac{1}{\sigma' \sqrt{2 \pi}} |
| 241 | // \int_{-\infty}^{+\infty} d\Delta' f'_{L}(x;\Delta',\xi) |
| 242 | // \exp{-\frac{(\Delta-\Delta')^2}{2\sigma'^2}} |
| 243 | // @f] |
| 244 | // |
| 245 | // where @f$ f'_{L}@f$ is the Landau distribution, @f$ \Delta@f$ the |
| 246 | // energy loss, @f$ \xi@f$ the width of the Landau, and |
| 247 | // @f$ \sigma'^2=\sigma^2-\sigma_n^2 @f$. Here, @f$\sigma@f$ is the |
| 248 | // variance of the Gaussian, and @f$\sigma_n@f$ is a parameter modelling |
| 249 | // noise in the detector. |
| 250 | // |
| 251 | // Note that this function uses the constants fgConvolutionSteps and |
| 252 | // fgConvolutionNSigma |
| 253 | // |
| 254 | // References: |
| 255 | // - <a href="http://dx.doi.org/10.1016/0168-583X(84)90472-5">Nucl.Instrum.Meth.B1:16</a> |
| 256 | // - <a href="http://dx.doi.org/10.1103/PhysRevA.28.615">Phys.Rev.A28:615</a> |
| 257 | // - <a href="http://root.cern.ch/root/htmldoc/tutorials/fit/langaus.C.html">ROOT implementation</a> |
| 258 | // |
| 259 | // Parameters: |
| 260 | // x where to evaluate @f$ f@f$ |
| 261 | // delta @f$ \Delta@f$ of @f$ f(x;\Delta,\xi,\sigma')@f$ |
| 262 | // xi @f$ \xi@f$ of @f$ f(x;\Delta,\xi,\sigma')@f$ |
| 263 | // sigma @f$ \sigma@f$ of @f$\sigma'^2=\sigma^2-\sigma_n^2 @f$ |
| 264 | // sigma_n @f$ \sigma_n@f$ of @f$\sigma'^2=\sigma^2-\sigma_n^2 @f$ |
| 265 | // |
| 266 | // Return: |
| 267 | // @f$ f@f$ evaluated at @f$ x@f$. |
| 268 | // |
| 7f759bb7 |
269 | Double_t deltap = delta - xi * mpshift; |
| 1174780f |
270 | Double_t sigma2 = sigmaN*sigmaN + sigma*sigma; |
| 271 | Double_t sigma1 = sigmaN == 0 ? sigma : TMath::Sqrt(sigma2); |
| 7f759bb7 |
272 | Double_t xlow = x - fgConvolutionNSigma * sigma1; |
| c389303e |
273 | Double_t xhigh = x + fgConvolutionNSigma * sigma1; |
| 7f759bb7 |
274 | Double_t step = (xhigh - xlow) / fgConvolutionSteps; |
| 275 | Double_t sum = 0; |
| 276 | |
| 277 | for (Int_t i = 0; i <= fgConvolutionSteps/2; i++) { |
| c389303e |
278 | Double_t x1 = xlow + (i - .5) * step; |
| 279 | Double_t x2 = xhigh - (i - .5) * step; |
| 7f759bb7 |
280 | |
| 281 | sum += TMath::Landau(x1, deltap, xi, kTRUE) * TMath::Gaus(x, x1, sigma1); |
| 282 | sum += TMath::Landau(x2, deltap, xi, kTRUE) * TMath::Gaus(x, x2, sigma1); |
| 283 | } |
| 284 | return step * sum * invSq2pi / sigma1; |
| 285 | } |
| 286 | |
| 0bd4b00f |
287 | //____________________________________________________________________ |
| 288 | Double_t |
| 289 | AliForwardUtil::ILandauGaus(Double_t x, Double_t delta, Double_t xi, |
| 1174780f |
290 | Double_t sigma, Double_t sigmaN, Int_t i) |
| 0bd4b00f |
291 | { |
| 7984e5f7 |
292 | // |
| 293 | // Evaluate |
| 294 | // @f[ |
| 295 | // f_i(x;\Delta,\xi,\sigma') = f(x;\Delta_i,\xi_i,\sigma_i') |
| 296 | // @f] |
| 297 | // corresponding to @f$ i@f$ particles i.e., with the substitutions |
| 298 | // @f{eqnarray*}{ |
| 299 | // \Delta \rightarrow \Delta_i &=& i(\Delta + \xi\log(i)) |
| 300 | // \xi \rightarrow \xi_i &=& i \xi |
| 301 | // \sigma \rightarrow \sigma_i &=& \sqrt{i}\sigma |
| 302 | // \sigma'^2 \rightarrow \sigma_i'^2 &=& \sigma_n^2 + \sigma_i^2 |
| 303 | // @f} |
| 304 | // |
| 305 | // Parameters: |
| 306 | // x Where to evaluate |
| 307 | // delta @f$ \Delta@f$ |
| 308 | // xi @f$ \xi@f$ |
| 309 | // sigma @f$ \sigma@f$ |
| 310 | // sigma_n @f$ \sigma_n@f$ |
| 311 | // i @f$ i @f$ |
| 312 | // |
| 313 | // Return: |
| 314 | // @f$ f_i @f$ evaluated |
| 315 | // |
| 1174780f |
316 | Double_t deltaI = (i == 1 ? delta : i * (delta + xi * TMath::Log(i))); |
| 317 | Double_t xiI = i * xi; |
| 318 | Double_t sigmaI = (i == 1 ? sigma : TMath::Sqrt(Double_t(i))*sigma); |
| 319 | if (sigmaI < 1e-10) { |
| 0bd4b00f |
320 | // Fall back to landau |
| 1174780f |
321 | return AliForwardUtil::Landau(x, deltaI, xiI); |
| 0bd4b00f |
322 | } |
| 1174780f |
323 | return AliForwardUtil::LandauGaus(x, deltaI, xiI, sigmaI, sigmaN); |
| 0bd4b00f |
324 | } |
| 325 | |
| 326 | //____________________________________________________________________ |
| 327 | Double_t |
| 328 | AliForwardUtil::IdLandauGausdPar(Double_t x, |
| 329 | UShort_t par, Double_t dPar, |
| 330 | Double_t delta, Double_t xi, |
| 1174780f |
331 | Double_t sigma, Double_t sigmaN, |
| 0bd4b00f |
332 | Int_t i) |
| 333 | { |
| 7984e5f7 |
334 | // |
| 335 | // Numerically evaluate |
| 336 | // @f[ |
| 337 | // \left.\frac{\partial f_i}{\partial p_i}\right|_{x} |
| 338 | // @f] |
| 339 | // where @f$ p_i@f$ is the @f$ i^{\mbox{th}}@f$ parameter. The mapping |
| 340 | // of the parameters is given by |
| 341 | // |
| 342 | // - 0: @f$\Delta@f$ |
| 343 | // - 1: @f$\xi@f$ |
| 344 | // - 2: @f$\sigma@f$ |
| 345 | // - 3: @f$\sigma_n@f$ |
| 346 | // |
| 347 | // This is the partial derivative with respect to the parameter of |
| 348 | // the response function corresponding to @f$ i@f$ particles i.e., |
| 349 | // with the substitutions |
| 350 | // @f[ |
| 351 | // \Delta \rightarrow \Delta_i = i(\Delta + \xi\log(i)) |
| 352 | // \xi \rightarrow \xi_i = i \xi |
| 353 | // \sigma \rightarrow \sigma_i = \sqrt{i}\sigma |
| 354 | // \sigma'^2 \rightarrow \sigma_i'^2 = \sigma_n^2 + \sigma_i^2 |
| 355 | // @f] |
| 356 | // |
| 357 | // Parameters: |
| 358 | // x Where to evaluate |
| 359 | // ipar Parameter number |
| 360 | // dp @f$ \epsilon\delta p_i@f$ for some value of @f$\epsilon@f$ |
| 361 | // delta @f$ \Delta@f$ |
| 362 | // xi @f$ \xi@f$ |
| 363 | // sigma @f$ \sigma@f$ |
| 364 | // sigma_n @f$ \sigma_n@f$ |
| 365 | // i @f$ i@f$ |
| 366 | // |
| 367 | // Return: |
| 368 | // @f$ f_i@f$ evaluated |
| 369 | // |
| 0bd4b00f |
370 | if (dPar == 0) return 0; |
| 371 | Double_t dp = dPar; |
| 372 | Double_t d2 = dPar / 2; |
| 1174780f |
373 | Double_t deltaI = i * (delta + xi * TMath::Log(i)); |
| 374 | Double_t xiI = i * xi; |
| 0bd4b00f |
375 | Double_t si = TMath::Sqrt(Double_t(i)); |
| 1174780f |
376 | Double_t sigmaI = si*sigma; |
| 0bd4b00f |
377 | Double_t y1 = 0; |
| 378 | Double_t y2 = 0; |
| 379 | Double_t y3 = 0; |
| 380 | Double_t y4 = 0; |
| 381 | switch (par) { |
| 382 | case 0: |
| 1174780f |
383 | y1 = ILandauGaus(x, deltaI+i*dp, xiI, sigmaI, sigmaN, i); |
| 384 | y2 = ILandauGaus(x, deltaI+i*d2, xiI, sigmaI, sigmaN, i); |
| 385 | y3 = ILandauGaus(x, deltaI-i*d2, xiI, sigmaI, sigmaN, i); |
| 386 | y4 = ILandauGaus(x, deltaI-i*dp, xiI, sigmaI, sigmaN, i); |
| 0bd4b00f |
387 | break; |
| 388 | case 1: |
| 1174780f |
389 | y1 = ILandauGaus(x, deltaI, xiI+i*dp, sigmaI, sigmaN, i); |
| 390 | y2 = ILandauGaus(x, deltaI, xiI+i*d2, sigmaI, sigmaN, i); |
| 391 | y3 = ILandauGaus(x, deltaI, xiI-i*d2, sigmaI, sigmaN, i); |
| 392 | y4 = ILandauGaus(x, deltaI, xiI-i*dp, sigmaI, sigmaN, i); |
| 0bd4b00f |
393 | break; |
| 394 | case 2: |
| 1174780f |
395 | y1 = ILandauGaus(x, deltaI, xiI, sigmaI+si*dp, sigmaN, i); |
| 396 | y2 = ILandauGaus(x, deltaI, xiI, sigmaI+si*d2, sigmaN, i); |
| 397 | y3 = ILandauGaus(x, deltaI, xiI, sigmaI-si*d2, sigmaN, i); |
| 398 | y4 = ILandauGaus(x, deltaI, xiI, sigmaI-si*dp, sigmaN, i); |
| 0bd4b00f |
399 | break; |
| 400 | case 3: |
| 1174780f |
401 | y1 = ILandauGaus(x, deltaI, xiI, sigmaI, sigmaN+dp, i); |
| 402 | y2 = ILandauGaus(x, deltaI, xiI, sigmaI, sigmaN+d2, i); |
| 403 | y3 = ILandauGaus(x, deltaI, xiI, sigmaI, sigmaN-d2, i); |
| 404 | y4 = ILandauGaus(x, deltaI, xiI, sigmaI, sigmaN-dp, i); |
| 0bd4b00f |
405 | break; |
| 406 | default: |
| 407 | return 0; |
| 408 | } |
| 409 | |
| 410 | Double_t d0 = y1 - y4; |
| 411 | Double_t d1 = 2 * (y2 - y3); |
| 412 | |
| 413 | Double_t g = 1/(2*dp) * (4*d1 - d0) / 3; |
| 414 | |
| 415 | return g; |
| 416 | } |
| 417 | |
| 7f759bb7 |
418 | //____________________________________________________________________ |
| 419 | Double_t |
| 420 | AliForwardUtil::NLandauGaus(Double_t x, Double_t delta, Double_t xi, |
| 1174780f |
421 | Double_t sigma, Double_t sigmaN, Int_t n, |
| 7f759bb7 |
422 | Double_t* a) |
| 423 | { |
| 7984e5f7 |
424 | // |
| 425 | // Evaluate |
| 426 | // @f[ |
| 427 | // f_N(x;\Delta,\xi,\sigma') = \sum_{i=1}^N a_i f_i(x;\Delta,\xi,\sigma'a) |
| 428 | // @f] |
| 429 | // |
| 430 | // where @f$ f(x;\Delta,\xi,\sigma')@f$ is the convolution of a |
| 431 | // Landau with a Gaussian (see LandauGaus). Note that |
| 432 | // @f$ a_1 = 1@f$, @f$\Delta_i = i(\Delta_1 + \xi\log(i))@f$, |
| 433 | // @f$\xi_i=i\xi_1@f$, and @f$\sigma_i'^2 = \sigma_n^2 + i\sigma_1^2@f$. |
| 434 | // |
| 435 | // References: |
| 436 | // - <a href="http://dx.doi.org/10.1016/0168-583X(84)90472-5">Nucl.Instrum.Meth.B1:16</a> |
| 437 | // - <a href="http://dx.doi.org/10.1103/PhysRevA.28.615">Phys.Rev.A28:615</a> |
| 438 | // - <a href="http://root.cern.ch/root/htmldoc/tutorials/fit/langaus.C.html">ROOT implementation</a> |
| 439 | // |
| 440 | // Parameters: |
| 441 | // x Where to evaluate @f$ f_N@f$ |
| 442 | // delta @f$ \Delta_1@f$ |
| 443 | // xi @f$ \xi_1@f$ |
| 444 | // sigma @f$ \sigma_1@f$ |
| 445 | // sigma_n @f$ \sigma_n@f$ |
| 446 | // n @f$ N@f$ in the sum above. |
| 447 | // a Array of size @f$ N-1@f$ of the weights @f$ a_i@f$ for |
| 448 | // @f$ i > 1@f$ |
| 449 | // |
| 450 | // Return: |
| 451 | // @f$ f_N(x;\Delta,\xi,\sigma')@f$ |
| 452 | // |
| 1174780f |
453 | Double_t result = ILandauGaus(x, delta, xi, sigma, sigmaN, 1); |
| 0bd4b00f |
454 | for (Int_t i = 2; i <= n; i++) |
| 1174780f |
455 | result += a[i-2] * AliForwardUtil::ILandauGaus(x,delta,xi,sigma,sigmaN,i); |
| 7f759bb7 |
456 | return result; |
| 457 | } |
| 0bd4b00f |
458 | namespace { |
| 459 | const Int_t kColors[] = { kRed+1, |
| 460 | kPink+3, |
| 461 | kMagenta+2, |
| 462 | kViolet+2, |
| 463 | kBlue+1, |
| 464 | kAzure+3, |
| 465 | kCyan+1, |
| 466 | kTeal+2, |
| 467 | kGreen+2, |
| 468 | kSpring+3, |
| 469 | kYellow+2, |
| 470 | kOrange+2 }; |
| 471 | } |
| 472 | |
| 473 | //____________________________________________________________________ |
| 474 | TF1* |
| 475 | AliForwardUtil::MakeNLandauGaus(Double_t c, |
| 476 | Double_t delta, Double_t xi, |
| 1174780f |
477 | Double_t sigma, Double_t sigmaN, Int_t n, |
| 0bd4b00f |
478 | Double_t* a, |
| 479 | Double_t xmin, Double_t xmax) |
| 480 | { |
| 7984e5f7 |
481 | // |
| 482 | // Generate a TF1 object of @f$ f_N@f$ |
| 483 | // |
| 484 | // Parameters: |
| 485 | // c Constant |
| 486 | // delta @f$ \Delta@f$ |
| 487 | // xi @f$ \xi_1@f$ |
| 488 | // sigma @f$ \sigma_1@f$ |
| 489 | // sigma_n @f$ \sigma_n@f$ |
| 490 | // n @f$ N@f$ - how many particles to sum to |
| 491 | // a Array of size @f$ N-1@f$ of the weights @f$ a_i@f$ for |
| 492 | // @f$ i > 1@f$ |
| 493 | // xmin Least value of range |
| 494 | // xmax Largest value of range |
| 495 | // |
| 496 | // Return: |
| 497 | // Newly allocated TF1 object |
| 498 | // |
| 0bd4b00f |
499 | Int_t npar = AliForwardUtil::ELossFitter::kN+n; |
| 500 | TF1* landaun = new TF1(Form("nlandau%d", n), &landauGausN,xmin,xmax,npar); |
| 501 | // landaun->SetLineStyle(((n-2) % 10)+2); // start at dashed |
| 502 | landaun->SetLineColor(kColors[((n-1) % 12)]); // start at red |
| 503 | landaun->SetLineWidth(2); |
| 504 | landaun->SetNpx(500); |
| 505 | landaun->SetParNames("C","#Delta_{p}","#xi", "#sigma", "#sigma_{n}", "N"); |
| 506 | |
| 507 | // Set the initial parameters from the seed fit |
| 508 | landaun->SetParameter(AliForwardUtil::ELossFitter::kC, c); |
| 509 | landaun->SetParameter(AliForwardUtil::ELossFitter::kDelta, delta); |
| 510 | landaun->SetParameter(AliForwardUtil::ELossFitter::kXi, xi); |
| 511 | landaun->SetParameter(AliForwardUtil::ELossFitter::kSigma, sigma); |
| 1174780f |
512 | landaun->SetParameter(AliForwardUtil::ELossFitter::kSigmaN, sigmaN); |
| 0bd4b00f |
513 | landaun->FixParameter(AliForwardUtil::ELossFitter::kN, n); |
| 514 | |
| 515 | // Set the range and name of the scale parameters |
| 516 | for (UShort_t i = 2; i <= n; i++) {// Take parameters from last fit |
| 517 | landaun->SetParameter(AliForwardUtil::ELossFitter::kA+i-2, a[i-2]); |
| 518 | landaun->SetParName(AliForwardUtil::ELossFitter::kA+i-2, Form("a_{%d}", i)); |
| 519 | } |
| 520 | return landaun; |
| 521 | } |
| 522 | //____________________________________________________________________ |
| 523 | TF1* |
| 524 | AliForwardUtil::MakeILandauGaus(Double_t c, |
| 525 | Double_t delta, Double_t xi, |
| 1174780f |
526 | Double_t sigma, Double_t sigmaN, Int_t i, |
| 0bd4b00f |
527 | Double_t xmin, Double_t xmax) |
| 528 | { |
| 7984e5f7 |
529 | // |
| 530 | // Generate a TF1 object of @f$ f_I@f$ |
| 531 | // |
| 532 | // Parameters: |
| 533 | // c Constant |
| 534 | // delta @f$ \Delta@f$ |
| 535 | // xi @f$ \xi_1@f$ |
| 536 | // sigma @f$ \sigma_1@f$ |
| 537 | // sigma_n @f$ \sigma_n@f$ |
| 538 | // i @f$ i@f$ - the number of particles |
| 539 | // xmin Least value of range |
| 540 | // xmax Largest value of range |
| 541 | // |
| 542 | // Return: |
| 543 | // Newly allocated TF1 object |
| 544 | // |
| 0bd4b00f |
545 | Int_t npar = AliForwardUtil::ELossFitter::kN+1; |
| 546 | TF1* landaui = new TF1(Form("ilandau%d", i), &landauGausI,xmin,xmax,npar); |
| 547 | // landaui->SetLineStyle(((i-2) % 10)+2); // start at dashed |
| 548 | landaui->SetLineColor(kColors[((i-1) % 12)]); // start at red |
| 549 | landaui->SetLineWidth(1); |
| 550 | landaui->SetNpx(500); |
| 551 | landaui->SetParNames("C","#Delta_{p}","#xi", "#sigma", "#sigma_{n}", "i"); |
| 552 | |
| 553 | // Set the initial parameters from the seed fit |
| 554 | landaui->SetParameter(AliForwardUtil::ELossFitter::kC, c); |
| 555 | landaui->SetParameter(AliForwardUtil::ELossFitter::kDelta, delta); |
| 556 | landaui->SetParameter(AliForwardUtil::ELossFitter::kXi, xi); |
| 557 | landaui->SetParameter(AliForwardUtil::ELossFitter::kSigma, sigma); |
| 1174780f |
558 | landaui->SetParameter(AliForwardUtil::ELossFitter::kSigmaN, sigmaN); |
| 0bd4b00f |
559 | landaui->FixParameter(AliForwardUtil::ELossFitter::kN, i); |
| 560 | |
| 561 | return landaui; |
| 562 | } |
| 7f759bb7 |
563 | |
| 564 | //==================================================================== |
| 565 | AliForwardUtil::ELossFitter::ELossFitter(Double_t lowCut, |
| 566 | Double_t maxRange, |
| 567 | UShort_t minusBins) |
| 568 | : fLowCut(lowCut), fMaxRange(maxRange), fMinusBins(minusBins), |
| 569 | fFitResults(0), fFunctions(0) |
| 570 | { |
| 7984e5f7 |
571 | // |
| 572 | // Constructor |
| 573 | // |
| 574 | // Parameters: |
| 575 | // lowCut Lower cut of spectrum - data below this cuts is ignored |
| 576 | // maxRange Maximum range to fit to |
| 577 | // minusBins The number of bins below maximum to use |
| 578 | // |
| 7f759bb7 |
579 | fFitResults.SetOwner(); |
| 580 | fFunctions.SetOwner(); |
| 581 | } |
| 582 | //____________________________________________________________________ |
| 583 | AliForwardUtil::ELossFitter::~ELossFitter() |
| 584 | { |
| 7984e5f7 |
585 | // |
| 586 | // Destructor |
| 587 | // |
| 588 | // |
| 7f759bb7 |
589 | fFitResults.Delete(); |
| 590 | fFunctions.Delete(); |
| 591 | } |
| 592 | //____________________________________________________________________ |
| 593 | void |
| 594 | AliForwardUtil::ELossFitter::Clear() |
| 595 | { |
| 7984e5f7 |
596 | // |
| 597 | // Clear internal arrays |
| 598 | // |
| 599 | // |
| 7f759bb7 |
600 | fFitResults.Clear(); |
| 601 | fFunctions.Clear(); |
| 602 | } |
| 603 | //____________________________________________________________________ |
| 604 | TF1* |
| 605 | AliForwardUtil::ELossFitter::Fit1Particle(TH1* dist, Double_t sigman) |
| 606 | { |
| 7984e5f7 |
607 | // |
| 608 | // Fit a 1-particle signal to the passed energy loss distribution |
| 609 | // |
| 610 | // Note that this function clears the internal arrays first |
| 611 | // |
| 612 | // Parameters: |
| 613 | // dist Data to fit the function to |
| 614 | // sigman If larger than zero, the initial guess of the |
| 615 | // detector induced noise. If zero or less, then this |
| 616 | // parameter is ignored in the fit (fixed at 0) |
| 617 | // |
| 618 | // Return: |
| 619 | // The function fitted to the data |
| 620 | // |
| 621 | |
| 7f759bb7 |
622 | // Clear the cache |
| 623 | Clear(); |
| 624 | |
| 625 | // Find the fit range |
| 626 | dist->GetXaxis()->SetRangeUser(fLowCut, fMaxRange); |
| 627 | |
| 7f759bb7 |
628 | // Get the bin with maximum |
| 629 | Int_t maxBin = dist->GetMaximumBin(); |
| 630 | Double_t maxE = dist->GetBinLowEdge(maxBin); |
| 631 | |
| 632 | // Get the low edge |
| 633 | dist->GetXaxis()->SetRangeUser(fLowCut, maxE); |
| 634 | Int_t minBin = maxBin - fMinusBins; // dist->GetMinimumBin(); |
| 635 | Double_t minE = TMath::Max(dist->GetBinCenter(minBin),fLowCut); |
| 636 | Double_t maxEE = dist->GetBinCenter(maxBin+2*fMinusBins); |
| 637 | |
| 638 | // Restore the range |
| 639 | dist->GetXaxis()->SetRangeUser(0, fMaxRange); |
| 640 | |
| 641 | // Define the function to fit |
| 0bd4b00f |
642 | TF1* landau1 = new TF1("landau1", landauGaus1, minE,maxEE,kSigmaN+1); |
| 7f759bb7 |
643 | |
| 644 | // Set initial guesses, parameter names, and limits |
| c389303e |
645 | landau1->SetParameters(1,0.5,0.07,0.1,sigman); |
| 7f759bb7 |
646 | landau1->SetParNames("C","#Delta_{p}","#xi", "#sigma", "#sigma_{n}"); |
| c389303e |
647 | landau1->SetNpx(500); |
| 648 | landau1->SetParLimits(kDelta, minE, fMaxRange); |
| 649 | landau1->SetParLimits(kXi, 0.00, fMaxRange); |
| 650 | landau1->SetParLimits(kSigma, 0.01, 0.1); |
| 651 | if (sigman <= 0) landau1->FixParameter(kSigmaN, 0); |
| 652 | else landau1->SetParLimits(kSigmaN, 0, fMaxRange); |
| 7f759bb7 |
653 | |
| 654 | // Do the fit, getting the result object |
| 655 | TFitResultPtr r = dist->Fit(landau1, "RNQS", "", minE, maxEE); |
| c389303e |
656 | landau1->SetRange(minE, fMaxRange); |
| 7f759bb7 |
657 | fFitResults.AddAtAndExpand(new TFitResult(*r), 0); |
| 658 | fFunctions.AddAtAndExpand(landau1, 0); |
| 659 | |
| 660 | return landau1; |
| 661 | } |
| 662 | //____________________________________________________________________ |
| 663 | TF1* |
| 664 | AliForwardUtil::ELossFitter::FitNParticle(TH1* dist, UShort_t n, |
| 665 | Double_t sigman) |
| 666 | { |
| 7984e5f7 |
667 | // |
| 668 | // Fit a N-particle signal to the passed energy loss distribution |
| 669 | // |
| 670 | // If there's no 1-particle fit present, it does that first |
| 671 | // |
| 672 | // Parameters: |
| 673 | // dist Data to fit the function to |
| 674 | // n Number of particle signals to fit |
| 675 | // sigman If larger than zero, the initial guess of the |
| 676 | // detector induced noise. If zero or less, then this |
| 677 | // parameter is ignored in the fit (fixed at 0) |
| 678 | // |
| 679 | // Return: |
| 680 | // The function fitted to the data |
| 681 | // |
| 682 | |
| 7f759bb7 |
683 | // Get the seed fit result |
| 684 | TFitResult* r = static_cast<TFitResult*>(fFitResults.At(0)); |
| 685 | TF1* f = static_cast<TF1*>(fFunctions.At(0)); |
| 686 | if (!r || !f) { |
| 687 | f = Fit1Particle(dist, sigman); |
| 688 | r = static_cast<TFitResult*>(fFitResults.At(0)); |
| 689 | if (!r || !f) { |
| 690 | ::Warning("FitNLandau", "No first shot at landau fit"); |
| 691 | return 0; |
| 692 | } |
| 693 | } |
| 694 | |
| 695 | // Get some parameters from seed fit |
| c389303e |
696 | Double_t delta1 = r->Parameter(kDelta); |
| 697 | Double_t xi1 = r->Parameter(kXi); |
| 7f759bb7 |
698 | Double_t maxEi = n * (delta1 + xi1 * TMath::Log(n)) + 2 * n * xi1; |
| 699 | Double_t minE = f->GetXmin(); |
| 700 | |
| 0bd4b00f |
701 | // Array of weights |
| 702 | TArrayD a(n-1); |
| 703 | for (UShort_t i = 2; i <= n; i++) |
| 704 | a.fArray[i-2] = (n == 2 ? 0.05 : 0.000001); |
| 7f759bb7 |
705 | // Make the fit function |
| 0bd4b00f |
706 | TF1* landaun = MakeNLandauGaus(r->Parameter(kC), |
| 707 | r->Parameter(kDelta), |
| 708 | r->Parameter(kXi), |
| 709 | r->Parameter(kSigma), |
| 710 | r->Parameter(kSigmaN), |
| 711 | n,a.fArray,minE,maxEi); |
| c389303e |
712 | landaun->SetParLimits(kDelta, minE, fMaxRange); // Delta |
| 713 | landaun->SetParLimits(kXi, 0.00, fMaxRange); // xi |
| 714 | landaun->SetParLimits(kSigma, 0.01, 1); // sigma |
| 715 | // Check if we're using the noise sigma |
| 716 | if (sigman <= 0) landaun->FixParameter(kSigmaN, 0); |
| 717 | else landaun->SetParLimits(kSigmaN, 0, fMaxRange); |
| 7f759bb7 |
718 | |
| 719 | // Set the range and name of the scale parameters |
| 720 | for (UShort_t i = 2; i <= n; i++) {// Take parameters from last fit |
| c389303e |
721 | landaun->SetParLimits(kA+i-2, 0,1); |
| 7f759bb7 |
722 | } |
| 723 | |
| 724 | // Do the fit |
| 725 | TFitResultPtr tr = dist->Fit(landaun, "RSQN", "", minE, maxEi); |
| 726 | |
| c389303e |
727 | landaun->SetRange(minE, fMaxRange); |
| 7f759bb7 |
728 | fFitResults.AddAtAndExpand(new TFitResult(*tr), n-1); |
| 729 | fFunctions.AddAtAndExpand(landaun, n-1); |
| 730 | |
| 731 | return landaun; |
| 732 | } |
| 7e4038b5 |
733 | |
| 734 | //==================================================================== |
| 735 | AliForwardUtil::Histos::~Histos() |
| 736 | { |
| 7984e5f7 |
737 | // |
| 738 | // Destructor |
| 739 | // |
| 7e4038b5 |
740 | if (fFMD1i) delete fFMD1i; |
| 741 | if (fFMD2i) delete fFMD2i; |
| 742 | if (fFMD2o) delete fFMD2o; |
| 743 | if (fFMD3i) delete fFMD3i; |
| 744 | if (fFMD3o) delete fFMD3o; |
| 745 | } |
| 746 | |
| 747 | //____________________________________________________________________ |
| 748 | TH2D* |
| 749 | AliForwardUtil::Histos::Make(UShort_t d, Char_t r, |
| 750 | const TAxis& etaAxis) const |
| 751 | { |
| 7984e5f7 |
752 | // |
| 753 | // Make a histogram |
| 754 | // |
| 755 | // Parameters: |
| 756 | // d Detector |
| 757 | // r Ring |
| 758 | // etaAxis Eta axis to use |
| 759 | // |
| 760 | // Return: |
| 761 | // Newly allocated histogram |
| 762 | // |
| 7e4038b5 |
763 | Int_t ns = (r == 'I' || r == 'i') ? 20 : 40; |
| 764 | TH2D* hist = new TH2D(Form("FMD%d%c_cache", d, r), |
| 765 | Form("FMD%d%c cache", d, r), |
| 766 | etaAxis.GetNbins(), etaAxis.GetXmin(), |
| 767 | etaAxis.GetXmax(), ns, 0, 2*TMath::Pi()); |
| 768 | hist->SetXTitle("#eta"); |
| 769 | hist->SetYTitle("#phi [radians]"); |
| 770 | hist->SetZTitle("d^{2}N_{ch}/d#etad#phi"); |
| 771 | hist->Sumw2(); |
| 772 | hist->SetDirectory(0); |
| 773 | |
| 774 | return hist; |
| 775 | } |
| 776 | //____________________________________________________________________ |
| 777 | void |
| 778 | AliForwardUtil::Histos::Init(const TAxis& etaAxis) |
| 779 | { |
| 7984e5f7 |
780 | // |
| 781 | // Initialize the object |
| 782 | // |
| 783 | // Parameters: |
| 784 | // etaAxis Eta axis to use |
| 785 | // |
| 7e4038b5 |
786 | fFMD1i = Make(1, 'I', etaAxis); |
| 787 | fFMD2i = Make(2, 'I', etaAxis); |
| 788 | fFMD2o = Make(2, 'O', etaAxis); |
| 789 | fFMD3i = Make(3, 'I', etaAxis); |
| 790 | fFMD3o = Make(3, 'O', etaAxis); |
| 791 | } |
| 792 | //____________________________________________________________________ |
| 793 | void |
| 794 | AliForwardUtil::Histos::Clear(Option_t* option) |
| 795 | { |
| 7984e5f7 |
796 | // |
| 797 | // Clear data |
| 798 | // |
| 799 | // Parameters: |
| 800 | // option Not used |
| 801 | // |
| 7e4038b5 |
802 | fFMD1i->Reset(option); |
| 803 | fFMD2i->Reset(option); |
| 804 | fFMD2o->Reset(option); |
| 805 | fFMD3i->Reset(option); |
| 806 | fFMD3o->Reset(option); |
| 807 | } |
| 808 | |
| 809 | //____________________________________________________________________ |
| 810 | TH2D* |
| 811 | AliForwardUtil::Histos::Get(UShort_t d, Char_t r) const |
| 812 | { |
| 7984e5f7 |
813 | // |
| 814 | // Get the histogram for a particular detector,ring |
| 815 | // |
| 816 | // Parameters: |
| 817 | // d Detector |
| 818 | // r Ring |
| 819 | // |
| 820 | // Return: |
| 821 | // Histogram for detector,ring or nul |
| 822 | // |
| 7e4038b5 |
823 | switch (d) { |
| 824 | case 1: return fFMD1i; |
| 825 | case 2: return (r == 'I' || r == 'i' ? fFMD2i : fFMD2o); |
| 826 | case 3: return (r == 'I' || r == 'i' ? fFMD3i : fFMD3o); |
| 827 | } |
| 828 | return 0; |
| 829 | } |
| 9d99b0dd |
830 | //==================================================================== |
| 831 | TList* |
| 832 | AliForwardUtil::RingHistos::DefineOutputList(TList* d) const |
| 833 | { |
| 7984e5f7 |
834 | // |
| 835 | // Define the outout list in @a d |
| 836 | // |
| 837 | // Parameters: |
| 838 | // d Where to put the output list |
| 839 | // |
| 840 | // Return: |
| 841 | // Newly allocated TList object or null |
| 842 | // |
| 9d99b0dd |
843 | if (!d) return 0; |
| 844 | TList* list = new TList; |
| 845 | list->SetName(fName.Data()); |
| 846 | d->Add(list); |
| 847 | return list; |
| 848 | } |
| 849 | //____________________________________________________________________ |
| 850 | TList* |
| 851 | AliForwardUtil::RingHistos::GetOutputList(TList* d) const |
| 852 | { |
| 7984e5f7 |
853 | // |
| 854 | // Get our output list from the container @a d |
| 855 | // |
| 856 | // Parameters: |
| 857 | // d where to get the output list from |
| 858 | // |
| 859 | // Return: |
| 860 | // The found TList or null |
| 861 | // |
| 9d99b0dd |
862 | if (!d) return 0; |
| 863 | TList* list = static_cast<TList*>(d->FindObject(fName.Data())); |
| 864 | return list; |
| 865 | } |
| 866 | |
| 867 | //____________________________________________________________________ |
| 868 | TH1* |
| 869 | AliForwardUtil::RingHistos::GetOutputHist(TList* d, const char* name) const |
| 870 | { |
| 7984e5f7 |
871 | // |
| 872 | // Find a specific histogram in the source list @a d |
| 873 | // |
| 874 | // Parameters: |
| 875 | // d (top)-container |
| 876 | // name Name of histogram |
| 877 | // |
| 878 | // Return: |
| 879 | // Found histogram or null |
| 880 | // |
| 9d99b0dd |
881 | return static_cast<TH1*>(d->FindObject(name)); |
| 882 | } |
| 883 | |
| 7e4038b5 |
884 | // |
| 885 | // EOF |
| 886 | // |
git://git.uio.no / u / mrichter / AliRoot.git / blame