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Timestamp:
10/17/06 17:32:52 (18 years ago)
Author:
meyer
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  • trunk/MagicSoft/Mars/mtools/MRolke.cc

    r8087 r8105  
    1 // @(#)root/physics:$Name: not supported by cvs2svn $:$Id: MRolke.cc,v 1.1 2006-10-17 12:51:31 meyer Exp $
     1// @(#)root/physics:$Name: not supported by cvs2svn $:$Id: MRolke.cc,v 1.2 2006-10-17 16:32:52 meyer Exp $
    22// Author: Jan Conrad    9/2/2004
    33
     
    115115MRolke::MRolke(Double_t CL, Option_t * /*option*/)
    116116{
    117     //constructor
    118     fUpperLimit  = 0.0;
    119     fLowerLimit  = 0.0;
    120     fCL          = CL;
    121     fSwitch      = 0; // 0: unbounded likelihood
    122     // 1: bounded likelihood
     117   //constructor
     118   fUpperLimit  = 0.0;
     119   fLowerLimit  = 0.0;
     120   fCL          = CL;
     121   fSwitch      = 0; // 0: unbounded likelihood
     122                    // 1: bounded likelihood
    123123}
    124124
     
    132132Double_t MRolke::CalculateInterval(Int_t x, Int_t y, Int_t z, Double_t bm, Double_t em,Double_t e, Int_t mid, Double_t sde, Double_t sdb, Double_t tau, Double_t b, Int_t m)
    133133{
    134     //calculate interval
    135     Int_t done = 0;
    136     Double_t limit[2];
    137 
    138     limit[1] = Interval(x,y,z,bm,em,e,mid, sde,sdb,tau,b,m);
    139 
    140     if (limit[1] > 0) {
    141         done = 1;
    142     }
    143 
    144     if (fSwitch == 0) {
    145 
    146         Int_t trial_x = x;
    147 
    148         while (done == 0) {
    149             trial_x++;
    150             limit[1] = Interval(trial_x,y,z,bm,em,e,mid, sde,sdb,tau,b,m);
    151             if (limit[1] > 0) done = 1;
    152         }
    153     }
    154 
    155     return limit[1];
     134   //calculate interval
     135   Int_t done = 0;
     136   Double_t limit[2];
     137
     138   limit[1] = Interval(x,y,z,bm,em,e,mid, sde,sdb,tau,b,m);
     139
     140   if (limit[1] > 0) {
     141      done = 1;
     142   }
     143
     144   if (fSwitch == 0) {
     145
     146      Int_t trial_x = x;
     147
     148      while (done == 0) {
     149         trial_x++;
     150         limit[1] = Interval(trial_x,y,z,bm,em,e,mid, sde,sdb,tau,b,m);
     151         if (limit[1] > 0) done = 1;
     152      }
     153   }
     154
     155   return limit[1];
    156156}
    157157
     
    162162Double_t MRolke::Interval(Int_t x, Int_t y, Int_t z, Double_t bm, Double_t em,Double_t e, Int_t mid, Double_t sde, Double_t sdb, Double_t tau, Double_t b, Int_t m)
    163163{
    164     // Calculates the Confidence Interval
    165 
    166     //Double_t dchi2 =  Chi2Percentile(1,1-fCL);
    167     Double_t dchi2 = TMath::ChisquareQuantile(fCL, 1);
    168 
    169     Double_t tempxy[2],limits[2] = {0,0};
    170     Double_t slope,fmid,low,flow,high,fhigh,test,ftest,mu0,maximum,target,l,f0;
    171     Double_t med = 0;
    172     Double_t maxiter=1000, acc = 0.00001;
    173     Int_t i;
    174     Int_t bp = 0;
    175 
    176     if ((mid != 3) && (mid != 5)) bm = (Double_t)y;
    177 
    178     if ((mid == 3) || (mid == 5)) {
    179         if (bm == 0) bm = 0.00001;
    180     }
    181 
    182     if ((mid <= 2) || (mid == 4)) bp = 1;
    183 
    184 
    185     if (bp == 1 && x == 0 && bm > 0 ){
    186 
    187         for(Int_t i = 0; i < 2; i++) {
    188             x++;
    189             tempxy[i] = Interval(x,y,z,bm,em,e,mid,sde,sdb,tau,b,m);
    190         }
    191         slope = tempxy[1] - tempxy[0];
    192         limits[1] = tempxy[0] - slope;
    193         limits[0] = 0.0;
    194         if (limits[1] < 0) limits[1] = 0.0;
    195         goto done;
    196     }
    197 
    198     if (bp != 1 && x == 0){
    199 
    200         for(Int_t i = 0; i < 2; i++) {
    201             x++;
    202             tempxy[i] = Interval(x,y,z,bm,em,e,mid,sde,sdb,tau,b,m);
    203       }
    204         slope = tempxy[1] - tempxy[0];
    205         limits[1] = tempxy[0] - slope;
    206         limits[0] = 0.0;
    207         if (limits[1] < 0) limits[1] = 0.0;
    208         goto done;
    209     }
    210 
    211     if (bp != 1  && bm == 0){
    212         for(Int_t i = 0; i < 2; i++) {
    213             bm++;
    214             limits[1] = Interval(x,y,z,bm,em,e,mid,sde,sdb,tau,b,m);
    215             tempxy[i] = limits[1];
    216         }
    217         slope = tempxy[1] - tempxy[0];
    218         limits[1] = tempxy[0] - slope;
    219         if (limits[1] < 0) limits[1] = 0;
    220         goto done;
    221     }
    222 
    223 
    224     if (x == 0 && bm == 0){
    225         x++;
    226         bm++;
    227 
    228         limits[1] = Interval(x,y,z,bm,em,e,mid,sde,sdb,tau,b,m);
    229         tempxy[0] = limits[1];
    230         x  = 1;
    231         bm = 2;
    232         limits[1] = Interval(x,y,z,bm,em,e,mid,sde,sdb,tau,b,m);
    233         tempxy[1] = limits[1];
    234         x  = 2;
    235         bm = 1;
    236         limits[1] = Interval(x,y,z,bm,em,e,mid,sde,sdb,tau,b,m);
    237         limits[1] = 3*tempxy[0] -tempxy[1] - limits[1];
    238         if (limits[1] < 0) limits[1] = 0;
    239         goto done;
    240     }
    241 
    242     mu0 = Likelihood(0,x,y,z,bm,em,e,mid,sde,sdb,tau,b,m,1);
    243 
    244     maximum = Likelihood(0,x,y,z,bm,em,e,mid,sde,sdb,tau,b,m,2);
    245 
    246     test = 0;
    247 
    248     f0 = Likelihood(test,x,y,z,bm,em,e,mid,sde,sdb,tau,b,m,3);
    249 
    250     if ( fSwitch == 1 ) {  // do this only for the unbounded likelihood case
    251         if ( mu0 < 0 ) maximum = f0;
    252     }
    253 
    254     target = maximum - dchi2;
    255 
    256     if (f0 > target) {
    257         limits[0] = 0;
    258     } else {
    259         if (mu0 < 0){
    260             limits[0] = 0;
    261             limits[1] = 0;
    262         }
    263 
    264         low   = 0;
    265         flow  = f0;
    266         high  = mu0;
    267         fhigh = maximum;
    268 
    269         for(Int_t i = 0; i < maxiter; i++) {
    270             l = (target-fhigh)/(flow-fhigh);
    271             if (l < 0.2) l = 0.2;
    272             if (l > 0.8) l = 0.8;
    273 
    274             med = l*low + (1-l)*high;
    275             if(med < 0.01){
    276                 limits[1]=0.0;
    277                 goto done;
    278             }
    279 
    280             fmid = Likelihood(med,x,y,z,bm,em,e,mid,sde,sdb,tau,b,m,3);
    281 
    282             if (fmid > target) {
    283                 high  = med;
    284                 fhigh = fmid;
    285             } else {
    286                 low  = med;
    287                 flow = fmid;
    288             }
    289             if ((high-low) < acc*high) break;
    290       }
    291         limits[0] = med;
    292     }
    293 
    294 
    295     if(mu0 > 0) {
    296         low  = mu0;
    297         flow = maximum;
    298     } else {
    299         low  = 0;
    300         flow = f0;
    301     }
    302 
    303     test = low +1 ;
    304 
    305     ftest = Likelihood(test,x,y,z,bm,em,e,mid,sde,sdb,tau,b,m,3);
    306 
    307     if (ftest < target) {
    308         high  = test;
    309         fhigh = ftest;
    310     } else {
    311         slope = (ftest - flow)/(test - low);
    312         high  = test + (target -ftest)/slope;
    313         fhigh = Likelihood(high,x,y,z,bm,em,e,mid,sde,sdb,tau,b,m,3);
    314    }
    315 
    316     for(i = 0; i < maxiter; i++) {
    317         l = (target-fhigh)/(flow-fhigh);
    318         if (l < 0.2) l = 0.2;
    319         if (l > 0.8) l = 0.8;
    320         med  = l * low + (1.-l)*high;
    321         fmid = Likelihood(med,x,y,z,bm,em,e,mid,sde,sdb,tau,b,m,3);
    322 
    323         if (fmid < target) {
     164   // Calculates the Confidence Interval
     165
     166   //Double_t dchi2 =  Chi2Percentile(1,1-fCL);
     167   Double_t dchi2 = TMath::ChisquareQuantile(fCL, 1);
     168
     169   Double_t tempxy[2],limits[2] = {0,0};
     170   Double_t slope,fmid,low,flow,high,fhigh,test,ftest,mu0,maximum,target,l,f0;
     171   Double_t med = 0;
     172   Double_t maxiter=1000, acc = 0.00001;
     173   Int_t i;
     174   Int_t bp = 0;
     175
     176   if ((mid != 3) && (mid != 5)) bm = (Double_t)y;
     177
     178   if ((mid == 3) || (mid == 5)) {
     179      if (bm == 0) bm = 0.00001;
     180   }
     181
     182   if ((mid <= 2) || (mid == 4)) bp = 1;
     183 
     184
     185   if (bp == 1 && x == 0 && bm > 0 ){
     186
     187      for(Int_t i = 0; i < 2; i++) {
     188         x++;
     189         tempxy[i] = Interval(x,y,z,bm,em,e,mid,sde,sdb,tau,b,m);
     190      }
     191      slope = tempxy[1] - tempxy[0];
     192      limits[1] = tempxy[0] - slope;
     193      limits[0] = 0.0;
     194      if (limits[1] < 0) limits[1] = 0.0;
     195      goto done;
     196   }
     197
     198   if (bp != 1 && x == 0){
     199
     200      for(Int_t i = 0; i < 2; i++) {
     201         x++;
     202         tempxy[i] = Interval(x,y,z,bm,em,e,mid,sde,sdb,tau,b,m);
     203      }
     204      slope = tempxy[1] - tempxy[0];
     205      limits[1] = tempxy[0] - slope;
     206      limits[0] = 0.0;
     207      if (limits[1] < 0) limits[1] = 0.0;
     208      goto done;
     209   }
     210
     211   if (bp != 1  && bm == 0){
     212      for(Int_t i = 0; i < 2; i++) {
     213         bm++;
     214         limits[1] = Interval(x,y,z,bm,em,e,mid,sde,sdb,tau,b,m);
     215         tempxy[i] = limits[1];
     216      }
     217      slope = tempxy[1] - tempxy[0];
     218      limits[1] = tempxy[0] - slope;
     219      if (limits[1] < 0) limits[1] = 0;
     220      goto done;
     221   }
     222
     223
     224   if (x == 0 && bm == 0){
     225      x++;
     226      bm++;
     227
     228      limits[1] = Interval(x,y,z,bm,em,e,mid,sde,sdb,tau,b,m);
     229      tempxy[0] = limits[1];
     230      x  = 1;
     231      bm = 2;
     232      limits[1] = Interval(x,y,z,bm,em,e,mid,sde,sdb,tau,b,m);
     233      tempxy[1] = limits[1];
     234      x  = 2;
     235      bm = 1;
     236      limits[1] = Interval(x,y,z,bm,em,e,mid,sde,sdb,tau,b,m);
     237      limits[1] = 3*tempxy[0] -tempxy[1] - limits[1];
     238      if (limits[1] < 0) limits[1] = 0;
     239      goto done;
     240   }
     241
     242   mu0 = Likelihood(0,x,y,z,bm,em,e,mid,sde,sdb,tau,b,m,1);
     243
     244   maximum = Likelihood(0,x,y,z,bm,em,e,mid,sde,sdb,tau,b,m,2);
     245
     246   test = 0;
     247
     248   f0 = Likelihood(test,x,y,z,bm,em,e,mid,sde,sdb,tau,b,m,3);
     249
     250   if ( fSwitch == 1 ) {  // do this only for the unbounded likelihood case
     251      if ( mu0 < 0 ) maximum = f0;
     252   }
     253
     254   target = maximum - dchi2;
     255
     256   if (f0 > target) {
     257      limits[0] = 0;
     258   } else {
     259      if (mu0 < 0){
     260         limits[0] = 0;
     261         limits[1] = 0;
     262      }
     263
     264      low   = 0;
     265      flow  = f0;
     266      high  = mu0;
     267      fhigh = maximum;
     268
     269      for(Int_t i = 0; i < maxiter; i++) {
     270         l = (target-fhigh)/(flow-fhigh);
     271         if (l < 0.2) l = 0.2;
     272         if (l > 0.8) l = 0.8;
     273
     274         med = l*low + (1-l)*high;
     275         if(med < 0.01){
     276            limits[1]=0.0;                           
     277            goto done;
     278         }
     279
     280         fmid = Likelihood(med,x,y,z,bm,em,e,mid,sde,sdb,tau,b,m,3);
     281
     282         if (fmid > target) {
    324283            high  = med;
    325284            fhigh = fmid;
    326         } else {
     285         } else {
    327286            low  = med;
    328287            flow = fmid;
    329         }
    330         if (high-low < acc*high) break;
    331     }
    332     limits[1] = med;
     288         }
     289         if ((high-low) < acc*high) break;
     290      }
     291      limits[0] = med;
     292   }
     293
     294
     295   if(mu0 > 0) {
     296      low  = mu0;
     297      flow = maximum;
     298   } else {
     299      low  = 0;
     300      flow = f0;
     301   }
     302
     303   test = low +1 ;
     304
     305   ftest = Likelihood(test,x,y,z,bm,em,e,mid,sde,sdb,tau,b,m,3);
     306
     307   if (ftest < target) {
     308      high  = test;
     309      fhigh = ftest;
     310   } else {
     311      slope = (ftest - flow)/(test - low);
     312      high  = test + (target -ftest)/slope;
     313      fhigh = Likelihood(high,x,y,z,bm,em,e,mid,sde,sdb,tau,b,m,3);
     314   }
     315
     316   for(i = 0; i < maxiter; i++) {
     317      l = (target-fhigh)/(flow-fhigh);
     318      if (l < 0.2) l = 0.2;
     319      if (l > 0.8) l = 0.8;
     320      med  = l * low + (1.-l)*high;
     321      fmid = Likelihood(med,x,y,z,bm,em,e,mid,sde,sdb,tau,b,m,3);
     322
     323      if (fmid < target) {
     324         high  = med;
     325         fhigh = fmid;
     326      } else {
     327         low  = med;
     328         flow = fmid;
     329      }
     330      if (high-low < acc*high) break;
     331   }
     332   limits[1] = med;
    333333
    334334done:
    335335
    336     if ( (mid == 4) || (mid==5) ) {
    337         limits[0] /= e;
    338         limits[1] /= e;
    339     }
    340 
    341 
    342     fUpperLimit = limits[1];
    343     fLowerLimit = TMath::Max(limits[0],0.0);
    344 
    345 
    346     return limits[1];
     336   if ( (mid == 4) || (mid==5) ) {
     337      limits[0] /= e;
     338      limits[1] /= e;
     339   }
     340
     341
     342   fUpperLimit = limits[1];
     343   fLowerLimit = TMath::Max(limits[0],0.0);
     344
     345 
     346   return limits[1];
    347347}
    348348
     
    351351Double_t MRolke::Likelihood(Double_t mu, Int_t x, Int_t y, Int_t z, Double_t bm,Double_t em, Double_t e, Int_t mid, Double_t sde, Double_t sdb, Double_t tau, Double_t b, Int_t m, Int_t what)
    352352{
    353     // Chooses between the different profile likelihood functions to use for the
    354     // different models.
    355     // Returns evaluation of the profile likelihood functions.
    356 
    357     switch (mid) {
    358     case 1: return EvalLikeMod1(mu,x,y,z,e,tau,b,m,what);
    359     case 2: return EvalLikeMod2(mu,x,y,em,e,sde,tau,b,what);
    360     case 3: return EvalLikeMod3(mu,x,bm,em,e,sde,sdb,b,what);
    361     case 4: return EvalLikeMod4(mu,x,y,tau,b,what);
    362     case 5: return EvalLikeMod5(mu,x,bm,sdb,b,what);
    363     case 6: return EvalLikeMod6(mu,x,z,e,b,m,what);
    364     case 7: return EvalLikeMod7(mu,x,em,e,sde,b,what);
    365     }
    366 
    367     return 0;
     353   // Chooses between the different profile likelihood functions to use for the
     354   // different models.
     355   // Returns evaluation of the profile likelihood functions.
     356
     357   switch (mid) {
     358      case 1: return EvalLikeMod1(mu,x,y,z,e,tau,b,m,what);
     359      case 2: return EvalLikeMod2(mu,x,y,em,e,sde,tau,b,what);
     360      case 3: return EvalLikeMod3(mu,x,bm,em,e,sde,sdb,b,what);
     361      case 4: return EvalLikeMod4(mu,x,y,tau,b,what);
     362      case 5: return EvalLikeMod5(mu,x,bm,sdb,b,what);
     363      case 6: return EvalLikeMod6(mu,x,z,e,b,m,what);
     364      case 7: return EvalLikeMod7(mu,x,em,e,sde,b,what);
     365   }
     366
     367   return 0;
    368368}
    369369
     
    371371Double_t MRolke::EvalLikeMod1(Double_t mu, Int_t x, Int_t y, Int_t z, Double_t e, Double_t tau, Double_t b, Int_t m, Int_t what)
    372372{
    373     // Calculates the Profile Likelihood for MODEL 1:
    374     //  Poisson background/ Binomial Efficiency
    375     // what = 1: Maximum likelihood estimate is returned
    376     // what = 2: Profile Likelihood of Maxmimum Likelihood estimate is returned.
    377     // what = 3: Profile Likelihood of Test hypothesis is returned
    378     // otherwise parameters as described in the beginning of the class)
    379 
    380     Double_t f  = 0;
    381     Double_t zm = Double_t(z)/m;
    382 
    383     if (what == 1) {
    384         f = (x-y/tau)/zm;
    385     }
    386 
    387     if (what == 2) {
    388         mu = (x-y/tau)/zm;
    389         b  = y/tau;
    390         Double_t e = zm;
    391         f = LikeMod1(mu,b,e,x,y,z,tau,m);
    392     }
    393 
    394     if (what == 3) {
    395         if (mu == 0){
    396             b = (x+y)/(1.0+tau);
    397             e = zm;
    398             f = LikeMod1(mu,b,e,x,y,z,tau,m);
    399         } else {
    400             MRolke g;
    401             g.ProfLikeMod1(mu,b,e,x,y,z,tau,m);
    402             f = LikeMod1(mu,b,e,x,y,z,tau,m);
    403         }
    404     }
    405 
    406     return f;
     373   // Calculates the Profile Likelihood for MODEL 1:
     374   //  Poisson background/ Binomial Efficiency
     375   // what = 1: Maximum likelihood estimate is returned
     376   // what = 2: Profile Likelihood of Maxmimum Likelihood estimate is returned.
     377   // what = 3: Profile Likelihood of Test hypothesis is returned
     378   // otherwise parameters as described in the beginning of the class)
     379
     380   Double_t f  = 0;
     381   Double_t zm = Double_t(z)/m;
     382
     383   if (what == 1) {
     384      f = (x-y/tau)/zm;
     385   }
     386
     387   if (what == 2) {
     388      mu = (x-y/tau)/zm;
     389      b  = y/tau;
     390      Double_t e = zm;
     391      f = LikeMod1(mu,b,e,x,y,z,tau,m);
     392   }
     393
     394   if (what == 3) {
     395      if (mu == 0){
     396         b = (x+y)/(1.0+tau);
     397         e = zm;
     398         f = LikeMod1(mu,b,e,x,y,z,tau,m);
     399      } else {
     400         MRolke g;
     401         g.ProfLikeMod1(mu,b,e,x,y,z,tau,m);
     402         f = LikeMod1(mu,b,e,x,y,z,tau,m);
     403      }
     404   }
     405
     406   return f;
    407407}
    408408
     
    410410Double_t MRolke::LikeMod1(Double_t mu,Double_t b, Double_t e, Int_t x, Int_t y, Int_t z, Double_t tau, Int_t m)
    411411{
    412     // Profile Likelihood function for MODEL 1:
    413     // Poisson background/ Binomial Efficiency
    414 
    415     return 2*(x*TMath::Log(e*mu+b)-(e*mu +b)-LogFactorial(x)+y*TMath::Log(tau*b)-tau*b-LogFactorial(y) + TMath::Log(TMath::Factorial(m)) - TMath::Log(TMath::Factorial(m-z)) - TMath::Log(TMath::Factorial(z))+ z * TMath::Log(e) + (m-z)*TMath::Log(1-e));
     412   // Profile Likelihood function for MODEL 1:
     413   // Poisson background/ Binomial Efficiency
     414
     415   return 2*(x*TMath::Log(e*mu+b)-(e*mu +b)-LogFactorial(x)+y*TMath::Log(tau*b)-tau*b-LogFactorial(y) + TMath::Log(TMath::Factorial(m)) - TMath::Log(TMath::Factorial(m-z)) - TMath::Log(TMath::Factorial(z))+ z * TMath::Log(e) + (m-z)*TMath::Log(1-e));
    416416}
    417417
     
    419419void MRolke::ProfLikeMod1(Double_t mu,Double_t &b,Double_t &e,Int_t x,Int_t y, Int_t z,Double_t tau,Int_t m)
    420420{
    421     // Void needed to calculate estimates of efficiency and background for model 1
    422 
    423     Double_t med = 0.0,fmid;
    424     Int_t maxiter =1000;
    425     Double_t acc = 0.00001;
    426     Double_t emin = ((m+mu*tau)-TMath::Sqrt((m+mu*tau)*(m+mu*tau)-4 * mu* tau * z))/2/mu/tau;
    427 
    428     Double_t low  = TMath::Max(1e-10,emin+1e-10);
    429     Double_t high = 1 - 1e-10;
    430 
    431     for(Int_t i = 0; i < maxiter; i++) {
    432         med = (low+high)/2.;
    433 
    434         fmid = LikeGradMod1(med,mu,x,y,z,tau,m);
    435 
    436         if(high < 0.5) acc = 0.00001*high;
    437         else           acc = 0.00001*(1-high);
    438 
    439         if ((high - low) < acc*high) break;
    440 
    441         if(fmid > 0) low  = med;
    442         else         high = med;
    443     }
    444 
    445     e = med;
    446     Double_t eta = Double_t(z)/e -Double_t(m-z)/(1-e);
    447 
    448     b = Double_t(y)/(tau -eta/mu);
     421   // Void needed to calculate estimates of efficiency and background for model 1
     422
     423   Double_t med = 0.0,fmid;
     424   Int_t maxiter =1000;
     425   Double_t acc = 0.00001;
     426   Double_t emin = ((m+mu*tau)-TMath::Sqrt((m+mu*tau)*(m+mu*tau)-4 * mu* tau * z))/2/mu/tau;
     427
     428   Double_t low  = TMath::Max(1e-10,emin+1e-10);
     429   Double_t high = 1 - 1e-10;
     430
     431   for(Int_t i = 0; i < maxiter; i++) {
     432      med = (low+high)/2.;
     433
     434      fmid = LikeGradMod1(med,mu,x,y,z,tau,m);
     435
     436      if(high < 0.5) acc = 0.00001*high;
     437      else           acc = 0.00001*(1-high);
     438
     439      if ((high - low) < acc*high) break;
     440
     441      if(fmid > 0) low  = med;
     442      else         high = med;
     443   }
     444
     445   e = med;
     446   Double_t eta = Double_t(z)/e -Double_t(m-z)/(1-e);
     447
     448   b = Double_t(y)/(tau -eta/mu);
    449449}
    450450
     
    453453{
    454454   //gradient model
    455     Double_t eta, etaprime, bprime,f;
    456     eta = static_cast<double>(z)/e - static_cast<double>(m-z)/(1.0 - e);
    457     etaprime = (-1) * (static_cast<double>(m-z)/((1.0 - e)*(1.0 - e)) + static_cast<double>(z)/(e*e));
    458     Double_t b = y/(tau - eta/mu);
    459     bprime = (b*b * etaprime)/mu/y;
    460     f =  (mu + bprime) * (x/(e * mu + b) - 1)+(y/b - tau) * bprime + eta;
    461     return f;
     455   Double_t eta, etaprime, bprime,f;
     456   eta = static_cast<double>(z)/e - static_cast<double>(m-z)/(1.0 - e);
     457   etaprime = (-1) * (static_cast<double>(m-z)/((1.0 - e)*(1.0 - e)) + static_cast<double>(z)/(e*e));
     458   Double_t b = y/(tau - eta/mu);
     459   bprime = (b*b * etaprime)/mu/y;
     460   f =  (mu + bprime) * (x/(e * mu + b) - 1)+(y/b - tau) * bprime + eta;
     461   return f;
    462462}
    463463
     
    465465Double_t MRolke::EvalLikeMod2(Double_t mu, Int_t x, Int_t y, Double_t em, Double_t e,Double_t sde, Double_t tau, Double_t b, Int_t what)
    466466{
    467     // Calculates the Profile Likelihood for MODEL 2:
    468     //  Poisson background/ Gauss Efficiency
    469     // what = 1: Maximum likelihood estimate is returned
    470     // what = 2: Profile Likelihood of Maxmimum Likelihood estimate is returned.
    471     // what = 3: Profile Likelihood of Test hypothesis is returned
    472     // otherwise parameters as described in the beginning of the class)
    473 
    474     Double_t v =  sde*sde;
    475     Double_t coef[4],roots[3];
    476     Double_t f = 0;
    477 
    478     if (what == 1) {
    479         f = (x-y/tau)/em;
    480     }
    481 
    482     if (what == 2) {
    483         mu = (x-y/tau)/em;
    484         b = y/tau;
    485         e = em;
    486         f = LikeMod2(mu,b,e,x,y,em,tau,v);
    487     }
    488 
    489     if (what == 3) {
    490         if (mu == 0 ) {
    491             b = (x+y)/(1+tau);
    492             f = LikeMod2(mu,b,e,x,y,em,tau,v);
     467   // Calculates the Profile Likelihood for MODEL 2:
     468   //  Poisson background/ Gauss Efficiency
     469   // what = 1: Maximum likelihood estimate is returned
     470   // what = 2: Profile Likelihood of Maxmimum Likelihood estimate is returned.
     471   // what = 3: Profile Likelihood of Test hypothesis is returned
     472   // otherwise parameters as described in the beginning of the class)
     473
     474   Double_t v =  sde*sde;
     475   Double_t coef[4],roots[3];
     476   Double_t f = 0;
     477
     478   if (what == 1) {
     479      f = (x-y/tau)/em;
     480   }
     481
     482   if (what == 2) {
     483      mu = (x-y/tau)/em;
     484      b = y/tau;
     485      e = em;
     486      f = LikeMod2(mu,b,e,x,y,em,tau,v);
     487   }
     488
     489   if (what == 3) {
     490      if (mu == 0 ) {
     491         b = (x+y)/(1+tau);
     492         f = LikeMod2(mu,b,e,x,y,em,tau,v);
    493493      } else {
    494             coef[3] = mu;
    495             coef[2] = mu*mu*v-2*em*mu-mu*mu*v*tau;
    496             coef[1] = ( - x)*mu*v - mu*mu*mu*v*v*tau - mu*mu*v*em + em*mu*mu*v*tau + em*em*mu - y*mu*v;
    497             coef[0] = x*mu*mu*v*v*tau + x*em*mu*v - y*mu*mu*v*v + y*em*mu*v;
    498 
    499             TMath::RootsCubic(coef,roots[0],roots[1],roots[2]);
    500 
    501             e = roots[1];
    502             b = y/(tau + (em - e)/mu/v);
    503             f = LikeMod2(mu,b,e,x,y,em,tau,v);
    504       }
    505     }
    506 
    507     return f;
     494         coef[3] = mu;
     495         coef[2] = mu*mu*v-2*em*mu-mu*mu*v*tau;
     496         coef[1] = ( - x)*mu*v - mu*mu*mu*v*v*tau - mu*mu*v*em + em*mu*mu*v*tau + em*em*mu - y*mu*v;
     497         coef[0] = x*mu*mu*v*v*tau + x*em*mu*v - y*mu*mu*v*v + y*em*mu*v;
     498
     499         TMath::RootsCubic(coef,roots[0],roots[1],roots[2]);
     500
     501         e = roots[1];
     502         b = y/(tau + (em - e)/mu/v);
     503         f = LikeMod2(mu,b,e,x,y,em,tau,v);
     504      }
     505   }
     506
     507   return f;
    508508}
    509509
     
    512512{
    513513   // Profile Likelihood function for MODEL 2:
    514     // Poisson background/Gauss Efficiency
    515 
    516     return 2*(x*TMath::Log(e*mu+b)-(e*mu+b)-LogFactorial(x)+y*TMath::Log(tau*b)-tau*b-LogFactorial(y)-0.9189385-TMath::Log(v)/2-(em-e)*(em-e)/v/2);
     514   // Poisson background/Gauss Efficiency
     515
     516   return 2*(x*TMath::Log(e*mu+b)-(e*mu+b)-LogFactorial(x)+y*TMath::Log(tau*b)-tau*b-LogFactorial(y)-0.9189385-TMath::Log(v)/2-(em-e)*(em-e)/v/2);
    517517}
    518518
     
    521521Double_t MRolke::EvalLikeMod3(Double_t mu, Int_t x, Double_t bm, Double_t em, Double_t e, Double_t sde, Double_t sdb, Double_t b, Int_t what)
    522522{
    523     // Calculates the Profile Likelihood for MODEL 3:
    524     // Gauss  background/ Gauss Efficiency
    525     // what = 1: Maximum likelihood estimate is returned
    526     // what = 2: Profile Likelihood of Maxmimum Likelihood estimate is returned.
    527     // what = 3: Profile Likelihood of Test hypothesis is returned
    528     // otherwise parameters as described in the beginning of the class)
    529 
    530     Double_t f = 0.;
    531     Double_t  v = sde*sde;
    532     Double_t  u = sdb*sdb;
    533 
    534     if (what == 1) {
    535         f = (x-bm)/em;
    536     }
    537 
    538 
    539     if (what == 2) {
    540         mu = (x-bm)/em;
    541         b  = bm;
    542         e  = em;
    543         f  = LikeMod3(mu,b,e,x,bm,em,u,v);
    544     }
    545 
    546 
    547     if(what == 3) {
    548         if(mu == 0.0){
    549             b = ((bm-u)+TMath::Sqrt((bm-u)*(bm-u)+4*x*u))/2.;
    550             e = em;
     523   // Calculates the Profile Likelihood for MODEL 3:
     524   // Gauss  background/ Gauss Efficiency
     525   // what = 1: Maximum likelihood estimate is returned
     526   // what = 2: Profile Likelihood of Maxmimum Likelihood estimate is returned.
     527   // what = 3: Profile Likelihood of Test hypothesis is returned
     528   // otherwise parameters as described in the beginning of the class)
     529
     530   Double_t f = 0.;
     531   Double_t  v = sde*sde;
     532   Double_t  u = sdb*sdb;
     533
     534   if (what == 1) {
     535      f = (x-bm)/em;
     536   }
     537
     538
     539   if (what == 2) {
     540      mu = (x-bm)/em;
     541      b  = bm;
     542      e  = em;
     543      f  = LikeMod3(mu,b,e,x,bm,em,u,v);
     544   }
     545
     546
     547   if(what == 3) {
     548      if(mu == 0.0){
     549         b = ((bm-u)+TMath::Sqrt((bm-u)*(bm-u)+4*x*u))/2.;
     550         e = em;
    551551         f = LikeMod3(mu,b,e,x,bm,em,u,v);
    552         } else {
    553             Double_t temp[3];
    554             temp[0] = mu*mu*v+u;
    555             temp[1] = mu*mu*mu*v*v+mu*v*u-mu*mu*v*em+mu*v*bm-2*u*em;
    556             temp[2] = mu*mu*v*v*bm-mu*v*u*em-mu*v*bm*em+u*em*em-mu*mu*v*v*x;
    557             e = (-temp[1]+TMath::Sqrt(temp[1]*temp[1]-4*temp[0]*temp[2]))/2/temp[0];
     552      } else {
     553         Double_t temp[3];
     554         temp[0] = mu*mu*v+u;
     555         temp[1] = mu*mu*mu*v*v+mu*v*u-mu*mu*v*em+mu*v*bm-2*u*em;
     556         temp[2] = mu*mu*v*v*bm-mu*v*u*em-mu*v*bm*em+u*em*em-mu*mu*v*v*x;
     557         e = (-temp[1]+TMath::Sqrt(temp[1]*temp[1]-4*temp[0]*temp[2]))/2/temp[0];
    558558         b = bm-(u*(em-e))/v/mu;
    559559         f = LikeMod3(mu,b,e,x,bm,em,u,v);
    560         }
    561     }
    562 
    563     return f;
     560      }
     561   }
     562
     563   return f;
    564564}
    565565
     
    567567Double_t MRolke::LikeMod3(Double_t mu,Double_t b,Double_t e,Int_t x,Double_t bm,Double_t em,Double_t u,Double_t v)
    568568{
    569     // Profile Likelihood function for MODEL 3:
    570     // Gauss background/Gauss Efficiency
    571 
    572     return 2*(x * TMath::Log(e*mu+b)-(e*mu+b)-LogFactorial(x)-1.837877-TMath::Log(u)/2-(bm-b)*(bm-b)/u/2-TMath::Log(v)/2-(em-e)*(em-e)/v/2);
     569   // Profile Likelihood function for MODEL 3:
     570   // Gauss background/Gauss Efficiency
     571
     572   return 2*(x * TMath::Log(e*mu+b)-(e*mu+b)-LogFactorial(x)-1.837877-TMath::Log(u)/2-(bm-b)*(bm-b)/u/2-TMath::Log(v)/2-(em-e)*(em-e)/v/2);
    573573}
    574574
     
    576576Double_t MRolke::EvalLikeMod4(Double_t mu, Int_t x, Int_t y, Double_t tau, Double_t b, Int_t what)
    577577{
    578     // Calculates the Profile Likelihood for MODEL 4:
    579     // Poiss  background/Efficiency known
    580     // what = 1: Maximum likelihood estimate is returned
    581     // what = 2: Profile Likelihood of Maxmimum Likelihood estimate is returned.
    582     // what = 3: Profile Likelihood of Test hypothesis is returned
    583     // otherwise parameters as described in the beginning of the class)
    584 
    585     Double_t f = 0.0;
    586 
    587     if (what == 1) f = x-y/tau;
    588     if (what == 2) {
    589         mu = x-y/tau;
    590         b  = Double_t(y)/tau;
    591         f  = LikeMod4(mu,b,x,y,tau);
    592     }
    593     if (what == 3) {
    594         if (mu == 0.0) {
    595             b = Double_t(x+y)/(1+tau);
    596             f = LikeMod4(mu,b,x,y,tau);
    597         } else {
    598             b = (x+y-(1+tau)*mu+sqrt((x+y-(1+tau)*mu)*(x+y-(1+tau)*mu)+4*(1+tau)*y*mu))/2/(1+tau);
    599             f = LikeMod4(mu,b,x,y,tau);
    600         }
    601     }
    602     return f;
     578   // Calculates the Profile Likelihood for MODEL 4:
     579   // Poiss  background/Efficiency known
     580   // what = 1: Maximum likelihood estimate is returned
     581   // what = 2: Profile Likelihood of Maxmimum Likelihood estimate is returned.
     582   // what = 3: Profile Likelihood of Test hypothesis is returned
     583   // otherwise parameters as described in the beginning of the class)
     584
     585   Double_t f = 0.0;
     586
     587   if (what == 1) f = x-y/tau;
     588   if (what == 2) {
     589      mu = x-y/tau;
     590      b  = Double_t(y)/tau;
     591      f  = LikeMod4(mu,b,x,y,tau);
     592   }
     593   if (what == 3) {
     594      if (mu == 0.0) {
     595         b = Double_t(x+y)/(1+tau);
     596         f = LikeMod4(mu,b,x,y,tau);
     597      } else {
     598         b = (x+y-(1+tau)*mu+sqrt((x+y-(1+tau)*mu)*(x+y-(1+tau)*mu)+4*(1+tau)*y*mu))/2/(1+tau);
     599         f = LikeMod4(mu,b,x,y,tau);
     600      }
     601   }
     602   return f;
    603603}
    604604
     
    606606Double_t MRolke::LikeMod4(Double_t mu,Double_t b,Int_t x,Int_t y,Double_t tau)
    607607{
    608     // Profile Likelihood function for MODEL 4:
    609     // Poiss background/Efficiency known
    610 
    611     return 2*(x*TMath::Log(mu+b)-(mu+b)-LogFactorial(x)+y*TMath::Log(tau*b)-tau*b-LogFactorial(y) );
     608   // Profile Likelihood function for MODEL 4:
     609   // Poiss background/Efficiency known
     610
     611   return 2*(x*TMath::Log(mu+b)-(mu+b)-LogFactorial(x)+y*TMath::Log(tau*b)-tau*b-LogFactorial(y) );
    612612}
    613613
     
    615615Double_t MRolke::EvalLikeMod5(Double_t mu, Int_t x, Double_t bm, Double_t sdb, Double_t b, Int_t what)
    616616{
    617     // Calculates the Profile Likelihood for MODEL 5:
    618     // Gauss  background/Efficiency known
    619     // what = 1: Maximum likelihood estimate is returned
    620     // what = 2: Profile Likelihood of Maxmimum Likelihood estimate is returned.
    621     // what = 3: Profile Likelihood of Test hypothesis is returned
    622     // otherwise parameters as described in the beginning of the class)
    623 
    624     Double_t u=sdb*sdb;
    625     Double_t f = 0;
    626 
    627     if(what == 1) {
     617   // Calculates the Profile Likelihood for MODEL 5:
     618   // Gauss  background/Efficiency known
     619   // what = 1: Maximum likelihood estimate is returned
     620   // what = 2: Profile Likelihood of Maxmimum Likelihood estimate is returned.
     621   // what = 3: Profile Likelihood of Test hypothesis is returned
     622   // otherwise parameters as described in the beginning of the class)
     623
     624   Double_t u=sdb*sdb;
     625   Double_t f = 0;
     626
     627   if(what == 1) {
    628628      f = x - bm;
    629     }
    630     if(what == 2) {
    631         mu = x-bm;
    632         b  = bm;
    633         f  = LikeMod5(mu,b,x,bm,u);
    634     }
    635 
    636     if (what == 3) {
    637         b = ((bm-u-mu)+TMath::Sqrt((bm-u-mu)*(bm-u-mu)-4*(mu*u-mu*bm-u*x)))/2;
    638         f = LikeMod5(mu,b,x,bm,u);
    639     }
    640     return f;
     629   }
     630   if(what == 2) {
     631      mu = x-bm;
     632      b  = bm;
     633      f  = LikeMod5(mu,b,x,bm,u);
     634   }
     635
     636   if (what == 3) {
     637      b = ((bm-u-mu)+TMath::Sqrt((bm-u-mu)*(bm-u-mu)-4*(mu*u-mu*bm-u*x)))/2;
     638      f = LikeMod5(mu,b,x,bm,u);
     639   }
     640   return f;
    641641}
    642642
     
    644644Double_t MRolke::LikeMod5(Double_t mu,Double_t b,Int_t x,Double_t bm,Double_t u)
    645645{
    646     // Profile Likelihood function for MODEL 5:
    647     // Gauss background/Efficiency known
    648 
    649     return 2*(x*TMath::Log(mu+b)-(mu + b)-LogFactorial(x)-0.9189385-TMath::Log(u)/2-((bm-b)*(bm-b))/u/2);
     646   // Profile Likelihood function for MODEL 5:
     647   // Gauss background/Efficiency known
     648
     649   return 2*(x*TMath::Log(mu+b)-(mu + b)-LogFactorial(x)-0.9189385-TMath::Log(u)/2-((bm-b)*(bm-b))/u/2);
    650650}
    651651
     
    653653Double_t MRolke::EvalLikeMod6(Double_t mu, Int_t x, Int_t z, Double_t e, Double_t b, Int_t m, Int_t what)
    654654{
    655     // Calculates the Profile Likelihood for MODEL 6:
    656     // Gauss  known/Efficiency binomial
    657     // what = 1: Maximum likelihood estimate is returned
    658     // what = 2: Profile Likelihood of Maxmimum Likelihood estimate is returned.
    659     // what = 3: Profile Likelihood of Test hypothesis is returned
    660     // otherwise parameters as described in the beginning of the class)
    661 
    662     Double_t coef[4],roots[3];
    663     Double_t f = 0.;
    664     Double_t zm = Double_t(z)/m;
    665 
    666     if(what==1){
    667         f = (x-b)/zm;
    668     }
    669 
    670     if(what==2){
    671         mu = (x-b)/zm;
    672         e  = zm;
    673         f  = LikeMod6(mu,b,e,x,z,m);
    674     }
    675     if(what == 3){
    676         if(mu==0){
    677             e = zm;
    678         } else {
    679             coef[3] = mu*mu;
    680             coef[2] = mu * b - mu * x - mu*mu - mu * m;
    681             coef[1] = mu * x - mu * b + mu * z - m * b;
    682             coef[0] = b * z;
    683             TMath::RootsCubic(coef,roots[0],roots[1],roots[2]);
    684             e = roots[1];
    685         }
    686         f =LikeMod6(mu,b,e,x,z,m);
    687     }
    688     return f;
     655   // Calculates the Profile Likelihood for MODEL 6:
     656   // Gauss  known/Efficiency binomial
     657   // what = 1: Maximum likelihood estimate is returned
     658   // what = 2: Profile Likelihood of Maxmimum Likelihood estimate is returned.
     659   // what = 3: Profile Likelihood of Test hypothesis is returned
     660   // otherwise parameters as described in the beginning of the class)
     661
     662   Double_t coef[4],roots[3];
     663   Double_t f = 0.;
     664   Double_t zm = Double_t(z)/m;
     665
     666   if(what==1){
     667      f = (x-b)/zm;
     668   }
     669
     670   if(what==2){
     671      mu = (x-b)/zm;
     672      e  = zm;
     673      f  = LikeMod6(mu,b,e,x,z,m);
     674   }
     675   if(what == 3){
     676      if(mu==0){
     677         e = zm;
     678      } else {
     679         coef[3] = mu*mu;
     680         coef[2] = mu * b - mu * x - mu*mu - mu * m;
     681         coef[1] = mu * x - mu * b + mu * z - m * b;
     682         coef[0] = b * z;
     683         TMath::RootsCubic(coef,roots[0],roots[1],roots[2]);
     684         e = roots[1];
     685      }
     686      f =LikeMod6(mu,b,e,x,z,m);
     687   }
     688   return f;
    689689}
    690690
     
    692692Double_t MRolke::LikeMod6(Double_t mu,Double_t b,Double_t e,Int_t x,Int_t z,Int_t m)
    693693{
    694     // Profile Likelihood function for MODEL 6:
    695     // background known/ Efficiency binomial
    696 
    697     Double_t f = 0.0;
    698 
    699     if (z > 100 || m > 100) {
    700         f = 2*(x*TMath::Log(e*mu+b)-(e*mu+b)-LogFactorial(x)+(m*TMath::Log(m)  - m)-(z*TMath::Log(z) - z)  - ((m-z)*TMath::Log(m-z) - m + z)+z*TMath::Log(e)+(m-z)*TMath::Log(1-e));
    701     } else {
    702         f = 2*(x*TMath::Log(e*mu+b)-(e*mu+b)-LogFactorial(x)+TMath::Log(TMath::Factorial(m))-TMath::Log(TMath::Factorial(z))-TMath::Log(TMath::Factorial(m-z))+z*TMath::Log(e)+(m-z)*TMath::Log(1-e));
    703     }
    704     return f;
     694   // Profile Likelihood function for MODEL 6:
     695   // background known/ Efficiency binomial
     696
     697   Double_t f = 0.0;
     698
     699   if (z > 100 || m > 100) {
     700      f = 2*(x*TMath::Log(e*mu+b)-(e*mu+b)-LogFactorial(x)+(m*TMath::Log(m)  - m)-(z*TMath::Log(z) - z)  - ((m-z)*TMath::Log(m-z) - m + z)+z*TMath::Log(e)+(m-z)*TMath::Log(1-e));
     701   } else {
     702      f = 2*(x*TMath::Log(e*mu+b)-(e*mu+b)-LogFactorial(x)+TMath::Log(TMath::Factorial(m))-TMath::Log(TMath::Factorial(z))-TMath::Log(TMath::Factorial(m-z))+z*TMath::Log(e)+(m-z)*TMath::Log(1-e));
     703   }
     704   return f;
    705705}
    706706
     
    709709Double_t MRolke::EvalLikeMod7(Double_t mu, Int_t x, Double_t em, Double_t e, Double_t sde, Double_t b, Int_t what)
    710710{
    711     // Calculates the Profile Likelihood for MODEL 7:
    712     // background known/Efficiency Gauss
    713     // what = 1: Maximum likelihood estimate is returned
    714     // what = 2: Profile Likelihood of Maxmimum Likelihood estimate is returned.
    715     // what = 3: Profile Likelihood of Test hypothesis is returned
    716     // otherwise parameters as described in the beginning of the class)
    717 
    718     Double_t v=sde*sde;
    719     Double_t f = 0.;
    720 
    721     if(what ==  1) {
    722         f = (x-b)/em;
    723     }
    724 
    725     if(what == 2) {
    726         mu = (x-b)/em;
    727         e  = em;
    728         f  = LikeMod7(mu, b, e, x, em, v);
    729     }
    730 
    731     if(what == 3) {
    732         if(mu==0) {
    733             e = em;
    734         } else {
    735             e = ( -(mu*em-b-mu*mu*v)-TMath::Sqrt((mu*em-b-mu*mu*v)*(mu*em-b-mu*mu*v)+4*mu*(x*mu*v-mu*b*v + b * em)))/( - mu)/2;
    736         }
    737         f = LikeMod7(mu, b, e, x, em, v);
    738     }
    739 
    740     return f;
     711   // Calculates the Profile Likelihood for MODEL 7:
     712   // background known/Efficiency Gauss
     713   // what = 1: Maximum likelihood estimate is returned
     714   // what = 2: Profile Likelihood of Maxmimum Likelihood estimate is returned.
     715   // what = 3: Profile Likelihood of Test hypothesis is returned
     716   // otherwise parameters as described in the beginning of the class)
     717
     718   Double_t v=sde*sde;
     719   Double_t f = 0.;
     720
     721   if(what ==  1) {
     722      f = (x-b)/em;
     723   }
     724
     725   if(what == 2) {
     726      mu = (x-b)/em;
     727      e  = em;
     728      f  = LikeMod7(mu, b, e, x, em, v);
     729   }
     730
     731   if(what == 3) {
     732      if(mu==0) {
     733         e = em;
     734      } else {
     735         e = ( -(mu*em-b-mu*mu*v)-TMath::Sqrt((mu*em-b-mu*mu*v)*(mu*em-b-mu*mu*v)+4*mu*(x*mu*v-mu*b*v + b * em)))/( - mu)/2;
     736      }
     737      f = LikeMod7(mu, b, e, x, em, v);
     738   }
     739
     740   return f;
    741741}
    742742
     
    744744Double_t MRolke::LikeMod7(Double_t mu,Double_t b,Double_t e,Int_t x,Double_t em,Double_t v)
    745745{
    746     // Profile Likelihood function for MODEL 6:
    747     // background known/ Efficiency binomial
    748 
    749     return 2*(x*TMath::Log(e*mu+b)-(e*mu + b)-LogFactorial(x)-0.9189385-TMath::Log(v)/2-(em-e)*(em-e)/v/2);
     746   // Profile Likelihood function for MODEL 6:
     747   // background known/ Efficiency binomial
     748
     749   return 2*(x*TMath::Log(e*mu+b)-(e*mu + b)-LogFactorial(x)-0.9189385-TMath::Log(v)/2-(em-e)*(em-e)/v/2);
    750750}
    751751
     
    753753Double_t MRolke::EvalPolynomial(Double_t x, const Int_t  coef[], Int_t N)
    754754{
    755     // evaluate polynomial
    756 
    757     const Int_t   *p;
    758     p = coef;
    759     Double_t ans = *p++;
    760     Int_t i = N;
    761 
    762     do
    763         ans = ans * x  +  *p++;
    764     while( --i );
    765 
    766     return ans;
     755  // evaluate polynomial
     756
     757   const Int_t   *p;
     758   p = coef;
     759   Double_t ans = *p++;
     760   Int_t i = N;
     761
     762   do
     763      ans = ans * x  +  *p++;
     764   while( --i );
     765
     766   return ans;
    767767}
    768768
     
    770770Double_t MRolke::EvalMonomial(Double_t x, const Int_t coef[], Int_t N)
    771771{
    772     // evaluate mononomial
    773 
    774     Double_t ans;
    775     const Int_t   *p;
    776 
    777     p   = coef;
    778     ans = x + *p++;
    779     Int_t i = N-1;
    780 
    781     do
    782         ans = ans * x  + *p++;
    783     while( --i );
    784 
    785     return ans;
     772   // evaluate mononomial
     773
     774   Double_t ans;
     775   const Int_t   *p;
     776
     777   p   = coef;
     778   ans = x + *p++;
     779   Int_t i = N-1;
     780
     781   do
     782      ans = ans * x  + *p++;
     783   while( --i );
     784
     785   return ans;
    786786}
    787787//--------------------------------------------------------------------------
     
    793793Double_t MRolke::LogFactorial(Int_t n)
    794794{
    795     if (n>69)
    796         return n*TMath::Log(n)-n + 0.5*TMath::Log(TMath::TwoPi()*n);
    797     else
    798         return TMath::Log(TMath::Factorial(n));
    799 }
     795   if (n>69)
     796       return n*TMath::Log(n)-n + 0.5*TMath::Log(TMath::TwoPi()*n);
     797   else
     798       return TMath::Log(TMath::Factorial(n));
     799}
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