template<class FittingFunction, class FluctuationKernel>
class KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >
Impact parameter distribution reconstruction from experimental data.
- Template Parameters
-
| FittingFunction | Class implementing a parameterization of the relationship between mean value of observables as a function of centrality, \(\bar{X}(c_b)\) |
| FluctuationKernel | Class implementing fluctuations of the observable according to a given PDF |
Implementation of the method of estimating impact parameter distributions for experimental data presented in the articles Das et al., Phys. Rev. C 97, 014905(2018) and Rogly et al., Phys. Rev. C 98, 024902(2018).
The aim is to reproduce the inclusive distribution \(P(X)\) of an observable assumed to have a monotonic dependence on impact parameter by adjusting the parameters of a fitting function defined by
\[
P(X) = \int P(X|b) P(b) db = \int P(X|c_b) dc_b
\]
where \(c_b\) is the centrality defined by
\[
c_b = \int_0^b P(b) db
\]
\(P(X|c_b)\) is the probability distribution of the observable as a function of the centrality, which is given by some FluctuationKernel which is a PDF for any value of \(X\) given the expected mean \(\bar{X}\) and reduced variance \(\sigma^2/\bar{X}\).
The FittingFunction class has to provide the functions
double meanX(double c) const
double redVar(double c) const
which describe how \(\bar{X}\) and \(\sigma^2/\bar{X}\). depend on centrality. It must also provide the following methods:
FittingFunction::FittingFunction() default constructor
FittingFunction::FittingFunction(const FittingFunction&) copy constructor, copy parameter values
constexpr int FittingFunction::npar() const number of parameters of function
void FittingFunction::fill_params_from_array(double*) takes values of parameters from array
void FittingFunction::fill_array_from_params(double*) const puts values of parameters in array
void FittingFunction::set_par_names(
TF1&) const set names of parameters in
TF1
void FittingFunction::set_initial_parameters(
TH1*,
TF1&) set initial values and limits on parameters to fit histogram
void FittingFunction::print_fit_params() const set initial values and limits on parameters to fit histogram
void FittingFunction::backup_params() const store current values of fit parameters (internally)
void FittingFunction::restore_params() const restore previously backed up values of fit parameters
void FittingFunction::normalise_shape_function() const normalize shape parameters
We provide the following FittingFunctions and FluctuationKernels:
| FittingFunction | Function |
| algebraic_fitting_function | \(k(c_b) = (k_{\mathrm{max}}-k_{\mathrm{min}})\left[ 1 - {c_b}^{\alpha}\right]^{\gamma} + k_{\mathrm{min}}\) |
| rogly_fitting_function | \(k(c_b) = k_0 \exp{\left(-\sum_{i=1}^{N} a_i c_b^i\right)}\) |
| FluctuationKernel | Distribution | Function |
| gamma_kernel | Gamma | \(f(X) = \frac{1}{\Gamma(k)\theta^k} X^{k-1} \exp{(-X/\theta)}\) |
| BD_kernel | Binomial | \(f(X) = \frac{n!}{X!(n-X)!} p^{X}(1-p)^{n-X}\) |
| NBD_kernel | Negative binomial | \(f(X) = \frac{(X+n-1)!}{X!(n-1)!} p^{n}(1-p)^{X}\) |
Example of use
In all of the the following, the namespace prefix KVImpactParameters:: can be dropped if the following instruction is used:
Fitting a given inclusive P(X) distribution
First initialize the estimator with the required fitting function and kernel, such as for example:
--/ use 3rd order exponential polynomial
function of Rogly et al with
gamma kernel:
--/ or use algebraic
function of Frankland et al with
a binomial distribution kernel:
Impact parameter distribution reconstruction from experimental data.
Fluctuation kernel using gamma distribution for use with bayesian_estimator.
void function(const Char_t *name_, T fun, const Char_t *docstring=0)
See rogly_fitting_function, algebraic_fitting_function, gamma_kernel and NBD_kernel for more details.
Assumng a pointer TH1* h to a histogram containing the inclusive distribution for an observable filled from data, the first step is to transform the histogram into a correctly normalized probability distribution (taking bin widths into account):
void RenormaliseHisto(TH1 *h)
Then to begin the fitting process, call the method
void FitHisto(TH1 *h=nullptr)
(if the histogram to fit was already correctly normalised, you can skip the first method and call this one giving the histogram pointer as argument). This will prepare initial parameter values for the fit based on the histogram data, then perform a first fit attempt. As this first attempt is never successful, you should then open the Fit Panel by right-clicking on the histogram in the canvas, and continue fitting using "Previous Fit", adjusting the range of the fit, and if necessary the parameter limits, until a satisfactory fit is achieved.
Using the results of the fit
Once a fit has been successful, the bayesian_estimator object can be used to deduce impact parameter distributions etc. for the fitted observable. This can be just after performing the fit as in the previous section (after first calling update_fit_params() - otherwise the internal fit parameter values are not necessarily consistent with the last performed fit), or using the already known parameters from a previous fit. In the latter case, you should initialize the object using the appropriate FittingFunction constructor, e.g. for algebraic_fitting_function which requires 5 parameters \(\alpha,\gamma,\theta,X_{min},X_{max}\), you can initialise the estimator like so:
See the list of methods below which can then be used in order to exploit the fit result.
Definition at line 218 of file bayesian_estimator.h.
|
| | bayesian_estimator (Bool_t integer_variable=false) |
| |
| | bayesian_estimator (const FittingFunction &previous_fit, Bool_t integer_variable=false) |
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| virtual | ~bayesian_estimator () |
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| void | DrawBDistForSelection (TH1 *sel, TH1 *incl, double &mean, double &sigma, Option_t *opt="", Color_t color=kRed, const TString &title="") |
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| void | DrawBDistForSelectionFromIPHisto (TH1 *sel, TH1 *incl, double &mean, double &sigma, Option_t *opt="", Color_t color=kRed, const TString &title="") |
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| double | DrawBDistForXSelection (KVValueRange< double > Xrange, Option_t *opt="", Color_t color=kRed, const TString &title="") |
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| void | DrawCbDistForSelection (TH1 *sel, TH1 *incl, double &mean_cb, double &sigma_cb, Option_t *opt="", Color_t color=kRed, const TString &title="") |
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| double | DrawCbDistForXSelection (double X1, double X2, Option_t *opt="", Color_t color=kRed, const TString &title="") |
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| void | DrawFittedP_X (double norm=1.0, Option_t *opt="", Color_t color=kRed, const TString &title="") |
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| void | DrawMeanXvsCb (const TString &title="", Color_t color=-1, Option_t *opt="") |
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| void | DrawNormalisedMeanXvsb (const TString &title, Color_t color, Option_t *opt) |
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| void | FitHisto (TH1 *h=nullptr) |
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| TF1 & | GetB_dist_for_X_select () |
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| TF1 * | GetFittedP_X (double norm=1.0) |
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| impact_parameter_distribution & | GetIPDist () |
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| TF2 * | GetJointProbabilityDistribution (KVValueRange< double > b_range, KVValueRange< double > X_range) |
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| void | GetMeanAndSigmaBDistForSelection (TH1 *sel, TH1 *incl, double &mean, double &sigma) |
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| void | GetMeanAndSigmaBDistForXSelection (double X1, double X2, double &mean, double &sigma) |
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| TF1 & | GetMeanXvsCb () |
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| TGraph * | GraphBDistForXSelection (KVValueRange< double > Xrange, int npts=500) |
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| TGraph * | GraphMeanXvsb (int npts=500) |
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| TGraph * | GraphP_XForGivenB (double b, KVValueRange< double > Xrange, int npts=500) |
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| void | Print (Option_t *="") const |
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| void | RenormaliseHisto (TH1 *h) |
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| void | SetIPDistFromHisto (TH1 *ip_histo) |
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| void | SetIPDistParams (double sigmaR, double deltab) |
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| void | update_fit_params () |
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| | KVBase () |
| | Default constructor.
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| | KVBase (const Char_t *name, const Char_t *title="") |
| | Ctor for object with given name and type.
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| | KVBase (const KVBase &) |
| | copy ctor
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| virtual | ~KVBase () |
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| virtual void | Clear (Option_t *opt="") |
| | Clear object properties : name, type/title, number, label.
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| virtual void | Copy (TObject &) const |
| | Make a copy of this object.
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| const Char_t * | GetLabel () const |
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| UInt_t | GetNumber () const |
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| UInt_t | GetNumberOfObjects () const |
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| virtual TObject * | GetObject () const |
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| virtual const Char_t * | GetType () const |
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| Bool_t | HasLabel () const |
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| virtual Bool_t | IsCalled (const Char_t *name) const |
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| Bool_t | IsLabelled (const Char_t *l) const |
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| virtual Bool_t | IsType (const Char_t *typ) const |
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| virtual void | List () |
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| KVBase & | operator= (const KVBase &) |
| | copy assignment operator
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| Double_t | ProtectedGetX (const TF1 *func, Double_t val, int &status, Double_t xmin=0.0, Double_t xmax=0.0) const |
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| void | SetLabel (const Char_t *lab) |
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| virtual void | SetNumber (UInt_t num) |
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| virtual void | SetType (const Char_t *str) |
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| | TNamed () |
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| | TNamed (const char *name, const char *title) |
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| | TNamed (const TNamed &named) |
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| | TNamed (const TString &name, const TString &title) |
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| virtual | ~TNamed () |
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| void | Clear (Option_t *option="") override |
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| TObject * | Clone (const char *newname="") const override |
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| Int_t | Compare (const TObject *obj) const override |
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| void | Copy (TObject &named) const override |
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| virtual void | FillBuffer (char *&buffer) |
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| const char * | GetName () const override |
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| const char * | GetTitle () const override |
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| ULong_t | Hash () const override |
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| TClass * | IsA () const override |
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| Bool_t | IsSortable () const override |
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| void | ls (Option_t *option="") const override |
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| TNamed & | operator= (const TNamed &rhs) |
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| void | Print (Option_t *option="") const override |
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| virtual void | SetName (const char *name) |
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| virtual void | SetNameTitle (const char *name, const char *title) |
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| virtual void | SetTitle (const char *title="") |
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| virtual Int_t | Sizeof () const |
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| void | Streamer (TBuffer &) override |
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| void | StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b) |
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| | TObject () |
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| | TObject (const TObject &object) |
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| virtual | ~TObject () |
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| void | AbstractMethod (const char *method) const |
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| virtual void | AppendPad (Option_t *option="") |
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| virtual void | Browse (TBrowser *b) |
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| ULong_t | CheckedHash () |
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| virtual const char * | ClassName () const |
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| virtual void | Delete (Option_t *option="") |
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| virtual Int_t | DistancetoPrimitive (Int_t px, Int_t py) |
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| virtual void | Draw (Option_t *option="") |
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| virtual void | DrawClass () const |
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| virtual TObject * | DrawClone (Option_t *option="") const |
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| virtual void | Dump () const |
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| virtual void | Error (const char *method, const char *msgfmt,...) const |
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| virtual void | Execute (const char *method, const char *params, Int_t *error=nullptr) |
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| virtual void | Execute (TMethod *method, TObjArray *params, Int_t *error=nullptr) |
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| virtual void | ExecuteEvent (Int_t event, Int_t px, Int_t py) |
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| virtual void | Fatal (const char *method, const char *msgfmt,...) const |
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| virtual TObject * | FindObject (const char *name) const |
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| virtual TObject * | FindObject (const TObject *obj) const |
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| virtual Option_t * | GetDrawOption () const |
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| virtual const char * | GetIconName () const |
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| virtual char * | GetObjectInfo (Int_t px, Int_t py) const |
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| virtual Option_t * | GetOption () const |
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| virtual UInt_t | GetUniqueID () const |
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| virtual Bool_t | HandleTimer (TTimer *timer) |
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| Bool_t | HasInconsistentHash () const |
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| virtual void | Info (const char *method, const char *msgfmt,...) const |
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| virtual Bool_t | InheritsFrom (const char *classname) const |
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| virtual Bool_t | InheritsFrom (const TClass *cl) const |
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| virtual void | Inspect () const |
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| void | InvertBit (UInt_t f) |
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| Bool_t | IsDestructed () const |
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| virtual Bool_t | IsEqual (const TObject *obj) const |
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| virtual Bool_t | IsFolder () const |
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| R__ALWAYS_INLINE Bool_t | IsOnHeap () const |
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| R__ALWAYS_INLINE Bool_t | IsZombie () const |
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| void | MayNotUse (const char *method) const |
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| virtual Bool_t | Notify () |
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| void | Obsolete (const char *method, const char *asOfVers, const char *removedFromVers) const |
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| void | operator delete (void *ptr) |
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| void | operator delete (void *ptr, void *vp) |
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| void | operator delete[] (void *ptr) |
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| void | operator delete[] (void *ptr, void *vp) |
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| void * | operator new (size_t sz) |
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| void * | operator new (size_t sz, void *vp) |
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| void * | operator new[] (size_t sz) |
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| void * | operator new[] (size_t sz, void *vp) |
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| TObject & | operator= (const TObject &rhs) |
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| virtual void | Paint (Option_t *option="") |
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| virtual void | Pop () |
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| virtual Int_t | Read (const char *name) |
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| virtual void | RecursiveRemove (TObject *obj) |
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| void | ResetBit (UInt_t f) |
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| virtual void | SaveAs (const char *filename="", Option_t *option="") const |
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| virtual void | SavePrimitive (std::ostream &out, Option_t *option="") |
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| void | SetBit (UInt_t f) |
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| void | SetBit (UInt_t f, Bool_t set) |
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| virtual void | SetDrawOption (Option_t *option="") |
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| virtual void | SetUniqueID (UInt_t uid) |
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| void | StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b) |
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| virtual void | SysError (const char *method, const char *msgfmt,...) const |
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| R__ALWAYS_INLINE Bool_t | TestBit (UInt_t f) const |
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| Int_t | TestBits (UInt_t f) const |
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| virtual void | UseCurrentStyle () |
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| virtual void | Warning (const char *method, const char *msgfmt,...) const |
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| virtual Int_t | Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0) |
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| virtual Int_t | Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0) const |
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|
| enum | EKaliVedaBits { kIsKaliVedaObject = BIT(23)
} |
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| enum | EDeprecatedStatusBits |
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| enum | EStatusBits |
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| static Bool_t | AreEqual (Double_t x, Double_t y, Long64_t maxdif=1) |
| | Comparison between two 64-bit floating-point values.
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| static void | BackupFileWithDate (const Char_t *path) |
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| static void | CombineFiles (const Char_t *file1, const Char_t *file2, const Char_t *newfilename, Bool_t keep=kTRUE) |
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| static void | Deprecated (const char *method, const char *advice) |
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| static Bool_t | FindClassSourceFiles (const Char_t *class_name, KVString &imp_file, KVString &dec_file, const Char_t *dir_name=".") |
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| static Bool_t | FindExecutable (TString &exec, const Char_t *path="$(PATH)") |
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| static const Char_t * | FindFile (const Char_t *search, TString &wfil) |
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| static const Char_t * | GetBINDIRFilePath (const Char_t *namefile="") |
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| static const Char_t * | GetDATABASEFilePath () |
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| static const Char_t * | GetDATADIRFilePath (const Char_t *namefile="") |
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| static Bool_t | GetDataSetEnv (const Char_t *dataset, const Char_t *type, Bool_t defval) |
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| static const Char_t * | GetDataSetEnv (const Char_t *dataset, const Char_t *type, const Char_t *defval) |
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| static Double_t | GetDataSetEnv (const Char_t *dataset, const Char_t *type, Double_t defval) |
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| static const Char_t * | GetETCDIRFilePath (const Char_t *namefile="") |
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| static const Char_t * | GetExampleFilePath (const Char_t *library, const Char_t *namefile) |
| | Return full path to example file for given library (="KVMultiDet", "BackTrack", etc.)
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| static const Char_t * | GetINCDIRFilePath (const Char_t *namefile="") |
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| static const Char_t * | GetKVBuildDate () |
| | Returns KaliVeda build date.
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| static const Char_t * | GetKVBuildDir () |
| | Returns top-level directory used for build.
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| static const Char_t * | GetKVBuildTime () |
| | Returns KaliVeda build time.
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| static const Char_t * | GetKVBuildType () |
| | Returns KaliVeda build type (cmake build: Release, Debug, RelWithDebInfo, ...)
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| static const Char_t * | GetKVBuildUser () |
| | Returns username of person who performed build.
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| static const Char_t * | GetKVSourceDir () |
| | Returns top-level directory of source tree used for build.
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| static const Char_t * | GetKVVersion () |
| | Returns KaliVeda version string.
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| static const Char_t * | GetLIBDIRFilePath (const Char_t *namefile="") |
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| static const Char_t * | GetListOfPlugins (const Char_t *base) |
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| static const Char_t * | GetListOfPluginURIs (const Char_t *base) |
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| static const Char_t * | GetPluginURI (const Char_t *base, const Char_t *plugin) |
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| static void | GetTempFileName (TString &base) |
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| static const Char_t * | GetTEMPLATEDIRFilePath (const Char_t *namefile="") |
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| static const Char_t * | GetWORKDIRFilePath (const Char_t *namefile="") |
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| static const Char_t * | gitBranch () |
| | Returns git branch of sources.
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| static const Char_t * | gitCommit () |
| | Returns last git commit of sources.
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| static void | InitEnvironment () |
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| static bool | is_gnuinstall () |
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| static Bool_t | IsThisAPlugin (const TString &uri, TString &base) |
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| static TPluginHandler * | LoadPlugin (const Char_t *base, const Char_t *uri="0") |
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| static Bool_t | OpenContextMenu (const char *method, TObject *obj, const char *alt_method_name="") |
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| static void | OpenTempFile (TString &base, std::ofstream &fp) |
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| static void | PrintSplashScreen () |
| | Prints welcome message and infos on version etc.
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| static Bool_t | SearchAndOpenKVFile (const Char_t *name, KVSQLite::database &dbfile, const Char_t *kvsubdir="") |
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| static Bool_t | SearchAndOpenKVFile (const Char_t *name, std::ifstream &file, const Char_t *kvsubdir="", KVLockfile *locks=0) |
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| static Bool_t | SearchAndOpenKVFile (const Char_t *name, std::ofstream &file, const Char_t *kvsubdir="", KVLockfile *locks=0) |
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| static Bool_t | SearchKVFile (const Char_t *name, TString &fullpath, const Char_t *kvsubdir="") |
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| static const Char_t * | WorkingDirectory () |
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| static TClass * | Class () |
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| static const char * | Class_Name () |
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| static constexpr Version_t | Class_Version () |
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| static const char * | DeclFileName () |
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| static TClass * | Class () |
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| static const char * | Class_Name () |
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| static constexpr Version_t | Class_Version () |
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| static const char * | DeclFileName () |
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| static Longptr_t | GetDtorOnly () |
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| static Bool_t | GetObjectStat () |
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| static void | SetDtorOnly (void *obj) |
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| static void | SetObjectStat (Bool_t stat) |
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| | kBitMask |
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| | kCanDelete |
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| | kCannotPick |
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| | kHasUUID |
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| | kInconsistent |
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| | kInvalidObject |
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| | kIsOnHeap |
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| | kIsReferenced |
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| | kMustCleanup |
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| | kNoContextMenu |
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| | kNotDeleted |
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| | kObjInCanvas |
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| | kOverwrite |
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| | kSingleKey |
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| | kWriteDelete |
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| | kZombie |
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| virtual void | DoError (int level, const char *location, const char *fmt, va_list va) const |
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| void | MakeZombie () |
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| TString | fName |
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| TString | fTitle |
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| | kOnlyPrepStep |
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Public Member Functions inherited from KVBase
1.9.8