// @(#)root/minuit:$Id: TLinearFitter.h 22564 2008-03-10 14:01:37Z moneta $ // Author: Anna Kreshuk 04/03/2005 /************************************************************************* * Copyright (C) 1995-2005, Rene Brun and Fons Rademakers. * * All rights reserved. * * * * For the licensing terms see $ROOTSYS/LICENSE. * * For the list of contributors see $ROOTSYS/README/CREDITS. * *************************************************************************/ #ifndef ROOT_TLinearFitter #define ROOT_TLinearFitter ////////////////////////////////////////////////////////////////////////// // // The Linear Fitter - fitting functions that are LINEAR IN PARAMETERS // // Linear fitter is used to fit a set of data points with a linear // combination of specified functions. Note, that "linear" in the name // stands only for the model dependency on parameters, the specified // functions can be nonlinear. // The general form of this kind of model is // // y(x) = a[0] + a[1]*f[1](x)+...a[n]*f[n](x) // // Functions f are fixed functions of x. For example, fitting with a // polynomial is linear fitting in this sense. // // The fitting method // // The fit is performed using the Normal Equations method with Cholesky // decomposition. // // Why should it be used? // // The linear fitter is considerably faster than general non-linear // fitters and doesn't require to set the initial values of parameters. // // Using the fitter: // // 1.Adding the data points: // 1.1 To store or not to store the input data? // - There are 2 options in the constructor - to store or not // store the input data. The advantages of storing the data // are that you'll be able to reset the fitting model without // adding all the points again, and that for very large sets // of points the chisquare is calculated more precisely. // The obvious disadvantage is the amount of memory used to // keep all the points. // - Before you start adding the points, you can change the // store/not store option by StoreData() method. // 1.2 The data can be added: // - simply point by point - AddPoint() method // - an array of points at once: // If the data is already stored in some arrays, this data // can be assigned to the linear fitter without physically // coping bytes, thanks to the Use() method of // TVector and TMatrix classes - AssignData() method // // 2.Setting the formula // 2.1 The linear formula syntax: // -Additive parts are separated by 2 plus signes "++" // --for example "1 ++ x" - for fitting a straight line // -All standard functions, undrestood by TFormula, can be used // as additive parts // --TMath functions can be used too // -Functions, used as additive parts, shouldn't have any parameters, // even if those parameters are set. // --for example, if normalizing a sum of a gaus(0, 1) and a // gaus(0, 2), don't use the built-in "gaus" of TFormula, // because it has parameters, take TMath::Gaus(x, 0, 1) instead. // -Polynomials can be used like "pol3", .."polN" // -If fitting a more than 3-dimensional formula, variables should // be numbered as follows: // -- x0, x1, x2... For example, to fit "1 ++ x0 ++ x1 ++ x2 ++ x3*x3" // 2.2 Setting the formula: // 2.2.1 If fitting a 1-2-3-dimensional formula, one can create a // TF123 based on a linear expression and pass this function // to the fitter: // --Example: // TLinearFitter *lf = new TLinearFitter(); // TF2 *f2 = new TF2("f2", "x ++ y ++ x*x*y*y", -2, 2, -2, 2); // lf->SetFormula(f2); // --The results of the fit are then stored in the function, // just like when the TH1::Fit or TGraph::Fit is used // --A linear function of this kind is by no means different // from any other function, it can be drawn, evaluated, etc. // 2.2.2 There is no need to create the function if you don't want to, // the formula can be set by expression: // --Example: // // 2 is the number of dimensions // TLinearFitter *lf = new TLinearFitter(2); // lf->SetFormula("x ++ y ++ x*x*y*y"); // --That's the only way to go, if you want to fit in more // than 3 dimensions // 2.2.3 The fastest functions to compute are polynomials and hyperplanes. // --Polynomials are set the usual way: "pol1", "pol2",... // --Hyperplanes are set by expression "hyp3", "hyp4", ... // ---The "hypN" expressions only work when the linear fitter // is used directly, not through TH1::Fit or TGraph::Fit. // To fit a graph or a histogram with a hyperplane, define // the function as "1++x++y". // ---A constant term is assumed for a hyperplane, when using // the "hypN" expression, so "hyp3" is in fact fitting with // "1++x++y++z" function. // --Fitting hyperplanes is much faster than fitting other // expressions so if performance is vital, calculate the // function values beforehand and give them to the fitter // as variables // --Example: // You want to fit "sin(x)|cos(2*x)" very fast. Calculate // sin(x) and cos(2*x) beforehand and store them in array *data. // Then: // TLinearFitter *lf=new TLinearFitter(2, "hyp2"); // lf->AssignData(npoint, 2, data, y); // // 2.3 Resetting the formula // 2.3.1 If the input data is stored (or added via AssignData() function), // the fitting formula can be reset without re-adding all the points. // --Example: // TLinearFitter *lf=new TLinearFitter("1++x++x*x"); // lf->AssignData(n, 1, x, y, e); // lf->Eval() // //looking at the parameter significance, you see, // // that maybe the fit will improve, if you take out // // the constant term // lf->SetFormula("x++x*x"); // lf->Eval(); // ... // 2.3.2 If the input data is not stored, the fitter will have to be // cleared and the data will have to be added again to try a // different formula. // // 3.Accessing the fit results // 3.1 There are methods in the fitter to access all relevant information: // --GetParameters, GetCovarianceMatrix, etc // --the t-values of parameters and their significance can be reached by // GetParTValue() and GetParSignificance() methods // 3.2 If fitting with a pre-defined TF123, the fit results are also // written into this function. // ////////////////////////////////////////////////////////////////////////// #ifndef ROOT_TVectorD #include "TVectorD.h" #endif #ifndef ROOT_TMatrixD #include "TMatrixD.h" #endif #ifndef ROOT_TFormula #include "TFormula.h" #endif #ifndef ROOT_TVirtualFitter #include "TVirtualFitter.h" #endif class TLinearFitter: public TVirtualFitter { private: TVectorD fParams; //vector of parameters TMatrixDSym fParCovar; //matrix of parameters' covariances TVectorD fTValues; //T-Values of parameters TVectorD fParSign; //significance levels of parameters TMatrixDSym fDesign; //matrix AtA TMatrixDSym fDesignTemp; //! temporary matrix, used for num.stability TMatrixDSym fDesignTemp2; //! TMatrixDSym fDesignTemp3; //! TVectorD fAtb; //vector Atb TVectorD fAtbTemp; //! temporary vector, used for num.stability TVectorD fAtbTemp2; //! TVectorD fAtbTemp3; //! TObjArray fFunctions; //array of basis functions TVectorD fY; //the values being fit Double_t fY2; //sum of square of y, used for chisquare Double_t fY2Temp; //! temporary variable used for num.stability TMatrixD fX; //values of x TVectorD fE; //the errors if they are known TFormula *fInputFunction; //the function being fit Int_t fNpoints; //number of points Int_t fNfunctions; //number of basis functions Int_t fFormulaSize; //length of the formula Int_t fNdim; //number of dimensions in the formula Int_t fNfixed; //number of fixed parameters Int_t fSpecial; //=100+n if fitting a polynomial of deg.n //=200+n if fitting an n-dimensional hyperplane char *fFormula; //the formula Bool_t fIsSet; //Has the formula been set? Bool_t fStoreData; //Is the data stored? Double_t fChisquare; //Chisquare of the fit Int_t fH; //number of good points in robust fit Bool_t fRobust; //true when performing a robust fit TBits fFitsample; //indices of points, used in the robust fit Bool_t *fFixedParams; //[fNfixed] array of fixed/released params void AddToDesign(Double_t *x, Double_t y, Double_t e); void ComputeTValues(); Int_t GraphLinearFitter(Double_t h); Int_t Graph2DLinearFitter(Double_t h); Int_t HistLinearFitter(); Int_t MultiGraphLinearFitter(Double_t h); //robust fitting functions: Int_t Partition(Int_t nmini, Int_t *indsubdat); void RDraw(Int_t *subdat, Int_t *indsubdat); void CreateSubset(Int_t ntotal, Int_t h, Int_t *index); Double_t CStep(Int_t step, Int_t h, Double_t *residuals, Int_t *index, Int_t *subdat, Int_t start, Int_t end); Bool_t Linf(); public: TLinearFitter(); TLinearFitter(Int_t ndim, const char *formula, Option_t *opt="D"); TLinearFitter(Int_t ndim); TLinearFitter(TFormula *function, Option_t *opt="D"); TLinearFitter(const TLinearFitter& tlf); virtual ~TLinearFitter(); TLinearFitter& operator=(const TLinearFitter& tlf); virtual void Add(TLinearFitter *tlf); virtual void AddPoint(Double_t *x, Double_t y, Double_t e=1); virtual void AssignData(Int_t npoints, Int_t xncols, Double_t *x, Double_t *y, Double_t *e=0); virtual void Clear(Option_t *option=""); virtual void ClearPoints(); virtual void Chisquare(); virtual Int_t Eval(); virtual Int_t EvalRobust(Double_t h=-1); virtual Int_t ExecuteCommand(const char *command, Double_t *args, Int_t nargs); virtual void FixParameter(Int_t ipar); virtual void FixParameter(Int_t ipar, Double_t parvalue); virtual void GetAtbVector(TVectorD &v); virtual Double_t GetChisquare(); virtual void GetConfidenceIntervals(Int_t n, Int_t ndim, const Double_t *x, Double_t *ci, Double_t cl=0.95); virtual void GetConfidenceIntervals(TObject *obj, Double_t cl=0.95); virtual Double_t* GetCovarianceMatrix() const; virtual void GetCovarianceMatrix(TMatrixD &matr); virtual Double_t GetCovarianceMatrixElement(Int_t i, Int_t j) const {return fParCovar(i, j);} virtual void GetDesignMatrix(TMatrixD &matr); virtual void GetErrors(TVectorD &vpar); virtual Int_t GetNumberTotalParameters() const {return fNfunctions;} virtual Int_t GetNumberFreeParameters() const {return fNfunctions-fNfixed;} virtual Int_t GetNpoints() { return fNpoints; } virtual void GetParameters(TVectorD &vpar); virtual Double_t GetParameter(Int_t ipar) const {return fParams(ipar);} virtual Int_t GetParameter(Int_t ipar,char* name,Double_t& value,Double_t& /*verr*/,Double_t& /*vlow*/, Double_t& /*vhigh*/) const; virtual const char *GetParName(Int_t ipar) const; virtual Double_t GetParError(Int_t ipar) const; virtual Double_t GetParTValue(Int_t ipar); virtual Double_t GetParSignificance(Int_t ipar); virtual void GetFitSample(TBits& bits); virtual Bool_t IsFixed(Int_t ipar) const {return fFixedParams[ipar];} virtual Int_t Merge(TCollection *list); virtual void PrintResults(Int_t level, Double_t amin=0) const; virtual void ReleaseParameter(Int_t ipar); virtual void SetBasisFunctions(TObjArray * functions); virtual void SetDim(Int_t n); virtual void SetFormula(const char* formula); virtual void SetFormula(TFormula *function); virtual void StoreData(Bool_t store) {fStoreData=store;} virtual Bool_t UpdateMatrix(); //dummy functions for TVirtualFitter: virtual Double_t Chisquare(Int_t /*npar*/, Double_t * /*params*/) const {return 0;} virtual Int_t GetErrors(Int_t /*ipar*/,Double_t & /*eplus*/, Double_t & /*eminus*/, Double_t & /*eparab*/, Double_t & /*globcc*/) const {return 0;} virtual Int_t GetStats(Double_t& /*amin*/, Double_t& /*edm*/, Double_t& /*errdef*/, Int_t& /*nvpar*/, Int_t& /*nparx*/) const {return 0;} virtual Double_t GetSumLog(Int_t /*i*/) {return 0;} virtual void SetFitMethod(const char * /*name*/) {;} virtual Int_t SetParameter(Int_t /*ipar*/,const char * /*parname*/,Double_t /*value*/,Double_t /*verr*/,Double_t /*vlow*/, Double_t /*vhigh*/) {return 0;} ClassDef(TLinearFitter, 1) //fit a set of data points with a linear combination of functions }; #endif