// Author: ruben.shahoyan@cern.ch 09/09/2006 //////////////////////////////////////////////////////////////////////////////// // // // AliCheb3D produces the interpolation of the user 3D->NDimOut arbitrary // // function supplied in "void (*fcn)(float* inp,float* out)" format // // either in a separate macro file or as a function pointer. // // Only coefficients needed to guarantee the requested precision are kept. // // // // The user-callable methods are: // // To create the interpolation use: // // AliCheb3D(const char* funName, // name of the file with user function // // or // // AliCheb3D(void (*ptr)(float*,float*),// pointer on the user function // // Int_t DimOut, // dimensionality of the function's output // // Float_t *bmin, // lower 3D bounds of interpolation domain // // Float_t *bmax, // upper 3D bounds of interpolation domain // // Int_t *npoints, // number of points in each of 3 input // // // dimension, defining the interpolation grid // // Float_t prec=1E-6); // requested max.absolute difference between // // // the interpolation and any point on grid // // // // To test obtained parameterization use the method // // TH1* TestRMS(int idim,int npoints = 1000,TH1* histo=0); // // it will compare the user output of the user function and interpolation // // for idim-th output dimension and fill the difference in the supplied // // histogram. If no histogram is supplied, it will be created. // // // // To save the interpolation data: // // SaveData(const char* filename, Bool_t append ) // // write text file with data. If append is kTRUE and the output file already // // exists, data will be added in the end of the file. // // Alternatively, SaveData(FILE* stream) will write the data to // // already existing stream. // // // // To read back already stored interpolation use either the constructor // // AliCheb3D(const char* inpFile); // // or the default constructor AliCheb3D() followed by // // AliCheb3D::LoadData(const char* inpFile); // // // // To compute the interpolation use Eval(float* par,float *res) method, with // // par being 3D vector of arguments (inside the validity region) and res is // // the array of DimOut elements for the output. // // // // If only one component (say, idim-th) of the output is needed, use faster // // Float_t Eval(Float_t *par,int idim) method. // // // // void Print(option="") will print the name, the ranges of validity and // // the absolute precision of the parameterization. Option "l" will also print // // the information about the number of coefficients for each output // // dimension. // // // // NOTE: during the evaluation no check is done for parameter vector being // // outside the interpolation region. If there is such a risk, use // // Bool_t IsInside(float *par) method. Chebyshev parameterization is not // // good for extrapolation! // // // // For the properties of Chebyshev parameterization see: // // H.Wind, CERN EP Internal Report, 81-12/Rev. // // // //////////////////////////////////////////////////////////////////////////////// #ifndef ALICHEB3D_H #define ALICHEB3D_H #include #include #include "AliCheb3DCalc.h" class TString; class TSystem; class TRandom; class TH1; class TMethodCall; class TRandom; class TROOT; class stdio; class AliCheb3D: public TNamed { public: AliCheb3D(); AliCheb3D(const AliCheb3D& src); AliCheb3D(const char* inpFile); AliCheb3D(FILE* stream); // #ifdef _INC_CREATION_ALICHEB3D_ AliCheb3D(const char* funName, Int_t DimOut, Float_t *bmin,Float_t *bmax, Int_t *npoints, Float_t prec=1E-6); AliCheb3D(void (*ptr)(float*,float*), Int_t DimOut, Float_t *bmin,Float_t *bmax, Int_t *npoints, Float_t prec=1E-6); AliCheb3D(void (*ptr)(float*,float*), int DimOut, Float_t *bmin,Float_t *bmax, Int_t *npX,Int_t *npY,Int_t *npZ, Float_t prec=1E-6); AliCheb3D(void (*ptr)(float*,float*), int DimOut, Float_t *bmin,Float_t *bmax, Float_t prec=1E-6, Bool_t run=kTRUE); #endif // ~AliCheb3D() {Clear();} // AliCheb3D& operator=(const AliCheb3D& rhs); void Eval(const Float_t *par, Float_t *res); Float_t Eval(const Float_t *par,int idim); void Eval(const Double_t *par, Double_t *res); Double_t Eval(const Double_t *par,int idim); // void EvalDeriv(int dimd, const Float_t *par, Float_t *res); void EvalDeriv2(int dimd1, int dimd2, const Float_t *par,Float_t *res); Float_t EvalDeriv(int dimd, const Float_t *par, int idim); Float_t EvalDeriv2(int dimd1,int dimd2, const Float_t *par, int idim); void EvalDeriv3D(const Float_t *par, Float_t dbdr[3][3]); void EvalDeriv3D2(const Float_t *par, Float_t dbdrdr[3][3][3]); void Print(const Option_t* opt="") const; Bool_t IsInside(const Float_t *par) const; Bool_t IsInside(const Double_t *par) const; // AliCheb3DCalc* GetChebCalc(int i) const {return (AliCheb3DCalc*)fChebCalc.UncheckedAt(i);} Float_t GetBoundMin(int i) const {return fBMin[i];} Float_t GetBoundMax(int i) const {return fBMax[i];} Float_t* GetBoundMin() const {return (float*)fBMin;} Float_t* GetBoundMax() const {return (float*)fBMax;} Float_t GetPrecision() const {return fPrec;} void ShiftBound(int id,float dif); // void LoadData(const char* inpFile); void LoadData(FILE* stream); // #ifdef _INC_CREATION_ALICHEB3D_ int* GetNCNeeded(float xyz[3],int DimVar, float mn,float mx, float prec, Int_t npCheck=30); void EstimateNPoints(float Prec, int gridBC[3][3],Int_t npd1=30,Int_t npd2=30,Int_t npd3=30); void SaveData(const char* outfile,Bool_t append=kFALSE) const; void SaveData(FILE* stream=stdout) const; // void SetUsrFunction(const char* name); void SetUsrFunction(void (*ptr)(float*,float*)); void EvalUsrFunction(const Float_t *x, Float_t *res); TH1* TestRMS(int idim,int npoints = 1000,TH1* histo=0); static Int_t CalcChebCoefs(const Float_t *funval,int np, Float_t *outCoefs, Float_t prec=-1); #endif // protected: void Clear(const Option_t* option = ""); void SetDimOut(const int d); void PrepareBoundaries(const Float_t *bmin,const Float_t *bmax); // #ifdef _INC_CREATION_ALICHEB3D_ void EvalUsrFunction(); void DefineGrid(Int_t* npoints); Int_t ChebFit(); // fit all output dimensions Int_t ChebFit(int dmOut); void SetPrecision(float prec) {fPrec = prec;} #endif // Float_t MapToInternal(Float_t x,Int_t d) const; // map x to [-1:1] Float_t MapToExternal(Float_t x,Int_t d) const {return x/fBScale[d]+fBOffset[d];} // map from [-1:1] to x Double_t MapToInternal(Double_t x,Int_t d) const; // map x to [-1:1] Double_t MapToExternal(Double_t x,Int_t d) const {return x/fBScale[d]+fBOffset[d];} // map from [-1:1] to x // protected: Int_t fDimOut; // dimension of the ouput array Float_t fPrec; // requested precision Float_t fBMin[3]; // min boundaries in each dimension Float_t fBMax[3]; // max boundaries in each dimension Float_t fBScale[3]; // scale for boundary mapping to [-1:1] interval Float_t fBOffset[3]; // offset for boundary mapping to [-1:1] interval TObjArray fChebCalc; // Chebyshev parameterization for each output dimension // Int_t fMaxCoefs; //! max possible number of coefs per parameterization Int_t fNPoints[3]; //! number of used points in each dimension Float_t fArgsTmp[3]; //! temporary vector for coefs caluclation Float_t * fResTmp; //! temporary vector for results of user function caluclation Float_t * fGrid; //! temporary buffer for Chebyshef roots grid Int_t fGridOffs[3]; //! start of grid for each dimension TString fUsrFunName; //! name of user macro containing the function of "void (*fcn)(float*,float*)" format TMethodCall* fUsrMacro; //! Pointer to MethodCall for function from user macro // ClassDef(AliCheb3D,2) // Chebyshev parametrization for 3D->N function }; //__________________________________________________________________________________________ inline Bool_t AliCheb3D::IsInside(const Float_t *par) const { // check if the point is inside of the fitted box for (int i=3;i--;) if (fBMin[i]>par[i] || par[i]>fBMax[i]) return kFALSE; return kTRUE; } //__________________________________________________________________________________________ inline Bool_t AliCheb3D::IsInside(const Double_t *par) const { // check if the point is inside of the fitted box for (int i=3;i--;) if (fBMin[i]>par[i] || par[i]>fBMax[i]) return kFALSE; return kTRUE; } //__________________________________________________________________________________________ inline void AliCheb3D::Eval(const Float_t *par, Float_t *res) { // evaluate Chebyshev parameterization for 3d->DimOut function for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i); for (int i=fDimOut;i--;) res[i] = GetChebCalc(i)->Eval(fArgsTmp); // } //__________________________________________________________________________________________ inline void AliCheb3D::Eval(const Double_t *par, Double_t *res) { // evaluate Chebyshev parameterization for 3d->DimOut function for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i); for (int i=fDimOut;i--;) res[i] = GetChebCalc(i)->Eval(fArgsTmp); // } //__________________________________________________________________________________________ inline Double_t AliCheb3D::Eval(const Double_t *par, int idim) { // evaluate Chebyshev parameterization for idim-th output dimension of 3d->DimOut function for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i); return GetChebCalc(idim)->Eval(fArgsTmp); // } //__________________________________________________________________________________________ inline Float_t AliCheb3D::Eval(const Float_t *par, int idim) { // evaluate Chebyshev parameterization for idim-th output dimension of 3d->DimOut function for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i); return GetChebCalc(idim)->Eval(fArgsTmp); // } //__________________________________________________________________________________________ inline void AliCheb3D::EvalDeriv3D(const Float_t *par, Float_t dbdr[3][3]) { // return gradient matrix for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i); for (int ib=3;ib--;) for (int id=3;id--;) dbdr[ib][id] = GetChebCalc(ib)->EvalDeriv(id,fArgsTmp)*fBScale[id]; } //__________________________________________________________________________________________ inline void AliCheb3D::EvalDeriv3D2(const Float_t *par, Float_t dbdrdr[3][3][3]) { // return gradient matrix for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i); for (int ib=3;ib--;) for (int id=3;id--;)for (int id1=3;id1--;) dbdrdr[ib][id][id1] = GetChebCalc(ib)->EvalDeriv2(id,id1,fArgsTmp)*fBScale[id]*fBScale[id1]; } //__________________________________________________________________________________________ inline void AliCheb3D::EvalDeriv(int dimd, const Float_t *par, Float_t *res) { // evaluate Chebyshev parameterization derivative for 3d->DimOut function for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i); for (int i=fDimOut;i--;) res[i] = GetChebCalc(i)->EvalDeriv(dimd,fArgsTmp)*fBScale[dimd];; // } //__________________________________________________________________________________________ inline void AliCheb3D::EvalDeriv2(int dimd1,int dimd2, const Float_t *par, Float_t *res) { // evaluate Chebyshev parameterization 2nd derivative over dimd1 and dimd2 dimensions for 3d->DimOut function for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i); for (int i=fDimOut;i--;) res[i] = GetChebCalc(i)->EvalDeriv2(dimd1,dimd2,fArgsTmp)*fBScale[dimd1]*fBScale[dimd2]; // } //__________________________________________________________________________________________ inline Float_t AliCheb3D::EvalDeriv(int dimd, const Float_t *par, int idim) { // evaluate Chebyshev parameterization derivative over dimd dimention for idim-th output dimension of 3d->DimOut function for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i); return GetChebCalc(idim)->EvalDeriv(dimd,fArgsTmp)*fBScale[dimd]; // } //__________________________________________________________________________________________ inline Float_t AliCheb3D::EvalDeriv2(int dimd1,int dimd2, const Float_t *par, int idim) { // evaluate Chebyshev parameterization 2ns derivative over dimd1 and dimd2 dimensions for idim-th output dimension of 3d->DimOut function for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i); return GetChebCalc(idim)->EvalDeriv2(dimd1,dimd2,fArgsTmp)*fBScale[dimd1]*fBScale[dimd2]; // } //__________________________________________________________________________________________ inline Float_t AliCheb3D::MapToInternal(Float_t x,Int_t d) const { // map x to [-1:1] #ifdef _BRING_TO_BOUNDARY_ T res = (x-fBOffset[d])*fBScale[d]; if (res<-1) return -1; if (res> 1) return 1; return res; #else return (x-fBOffset[d])*fBScale[d]; #endif } //__________________________________________________________________________________________ inline Double_t AliCheb3D::MapToInternal(Double_t x,Int_t d) const { // map x to [-1:1] #ifdef _BRING_TO_BOUNDARY_ T res = (x-fBOffset[d])*fBScale[d]; if (res<-1) return -1; if (res> 1) return 1; return res; #else return (x-fBOffset[d])*fBScale[d]; #endif } #endif