3 /* Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
4 * See cxx source for full Copyright notice */
8 // Author: ruben.shahoyan@cern.ch 09/09/2006
10 ////////////////////////////////////////////////////////////////////////////////
12 // AliCheb3D produces the interpolation of the user 3D->NDimOut arbitrary //
13 // function supplied in "void (*fcn)(float* inp,float* out)" format //
14 // either in a separate macro file or as a function pointer. //
15 // Only coefficients needed to guarantee the requested precision are kept. //
17 // The user-callable methods are: //
18 // To create the interpolation use: //
19 // AliCheb3D(const char* funName, // name of the file with user function //
21 // AliCheb3D(void (*ptr)(float*,float*),// pointer on the user function //
22 // Int_t DimOut, // dimensionality of the function's output //
23 // Float_t *bmin, // lower 3D bounds of interpolation domain //
24 // Float_t *bmax, // upper 3D bounds of interpolation domain //
25 // Int_t *npoints, // number of points in each of 3 input //
26 // // dimension, defining the interpolation grid //
27 // Float_t prec=1E-6); // requested max.absolute difference between //
28 // // the interpolation and any point on grid //
30 // To test obtained parameterization use the method //
31 // TH1* TestRMS(int idim,int npoints = 1000,TH1* histo=0); //
32 // it will compare the user output of the user function and interpolation //
33 // for idim-th output dimension and fill the difference in the supplied //
34 // histogram. If no histogram is supplied, it will be created. //
36 // To save the interpolation data: //
37 // SaveData(const char* filename, Bool_t append ) //
38 // write text file with data. If append is kTRUE and the output file already //
39 // exists, data will be added in the end of the file. //
40 // Alternatively, SaveData(FILE* stream) will write the data to //
41 // already existing stream. //
43 // To read back already stored interpolation use either the constructor //
44 // AliCheb3D(const char* inpFile); //
45 // or the default constructor AliCheb3D() followed by //
46 // AliCheb3D::LoadData(const char* inpFile); //
48 // To compute the interpolation use Eval(float* par,float *res) method, with //
49 // par being 3D vector of arguments (inside the validity region) and res is //
50 // the array of DimOut elements for the output. //
52 // If only one component (say, idim-th) of the output is needed, use faster //
53 // Float_t Eval(Float_t *par,int idim) method. //
55 // void Print(option="") will print the name, the ranges of validity and //
56 // the absolute precision of the parameterization. Option "l" will also print //
57 // the information about the number of coefficients for each output //
60 // NOTE: during the evaluation no check is done for parameter vector being //
61 // outside the interpolation region. If there is such a risk, use //
62 // Bool_t IsInside(float *par) method. Chebyshev parameterization is not //
63 // good for extrapolation! //
65 // For the properties of Chebyshev parameterization see: //
66 // H.Wind, CERN EP Internal Report, 81-12/Rev. //
68 ////////////////////////////////////////////////////////////////////////////////
73 #include <TMethodCall.h>
76 #include <TObjArray.h>
83 // to decrease the compilable code size comment this define. This will exclude the routines
84 // used for the calculation and saving of the coefficients.
85 // #define _INC_CREATION_ALICHEB3D_
87 class AliCheb3DCalc: public TNamed
91 AliCheb3DCalc(FILE* stream); // read coefs from text file
92 AliCheb3DCalc(const AliCheb3DCalc &src);
93 AliCheb3DCalc& operator= (const AliCheb3DCalc &rhs);
94 ~AliCheb3DCalc() {Clear();}
96 void Print(Option_t* opt="") const;
97 void LoadData(FILE* stream);
98 Float_t Eval(Float_t *par) const;
100 #ifdef _INC_CREATION_ALICHEB3D_
101 void SaveData(const char* outfile,Bool_t append=kFALSE) const;
102 void SaveData(FILE* stream=stdout) const;
105 static void ReadLine(TString& str,FILE* stream);
109 void Clear(Option_t* option = "");
111 Float_t ChebEval1D(Float_t x, const Float_t * array, int ncf) const;
112 void InitRows(int nr);
113 void InitCols(int nc);
114 void InitElemBound2D(int ne);
115 void InitCoefs(int nc);
116 Int_t* GetNColsAtRow() const {return fNColsAtRow;}
117 Int_t* GetColAtRowBg() const {return fColAtRowBg;}
118 Int_t* GetCoefBound2D0() const {return fCoefBound2D0;}
119 Int_t* GetCoefBound2D1() const {return fCoefBound2D1;}
120 Float_t * GetCoefs() const {return fCoefs;}
123 Int_t fNCoefs; // total number of coeeficients
124 Int_t fNRows; // number of significant rows in the 3D coeffs matrix
125 Int_t fNCols; // max number of significant cols in the 3D coeffs matrix
126 Int_t fNElemBound2D; // number of elements (fNRows*fNCols) to store for the 2D boundary of significant coeffs
127 Int_t* fNColsAtRow; //[fNRows] number of sighificant columns (2nd dim) at each row of 3D coefs matrix
128 Int_t* fColAtRowBg; //[fNRows] beginnig of significant columns (2nd dim) for row in the 2D boundary matrix
129 Int_t* fCoefBound2D0; //[fNElemBound2D] 2D matrix defining the boundary of significance for 3D coeffs.matrix (Ncoefs for col/row)
130 Int_t* fCoefBound2D1; //[fNElemBound2D] 2D matrix defining the start beginnig of significant coeffs for col/row
131 Float_t * fCoefs; //[fNCoefs] array of Chebyshev coefficients
133 Float_t * fTmpCf1; //[fNCols] temp. coeffs for 2d summation
134 Float_t * fTmpCf0; //[fNRows] temp. coeffs for 1d summation
136 ClassDef(AliCheb3DCalc,1) // Class for interpolation of 3D->1 function by Chebyshev parametrization
140 class AliCheb3D: public TNamed
144 AliCheb3D(const char* inpFile); // read coefs from text file
145 AliCheb3D(FILE*); // read coefs from stream
146 AliCheb3D(const AliCheb3D &src);
147 AliCheb3D& operator= (const AliCheb3D &rhs);
150 #ifdef _INC_CREATION_ALICHEB3D_
151 AliCheb3D(const char* funName, Int_t DimOut, Float_t *bmin,Float_t *bmax, Int_t *npoints, Float_t prec=1E-6);
152 AliCheb3D(void (*ptr)(float*,float*), Int_t DimOut, Float_t *bmin,Float_t *bmax, Int_t *npoints, Float_t prec=1E-6);
155 ~AliCheb3D() {Clear();}
157 void Eval(Float_t *par,Float_t *res);
158 Float_t Eval(Float_t *par,int idim);
159 void Print(Option_t* opt="") const;
160 Bool_t IsInside(Float_t *par) const;
161 AliCheb3DCalc* GetChebCalc(int i) const {return (AliCheb3DCalc*)fChebCalc.UncheckedAt(i);}
162 Float_t GetBoundMin(int i) const {return fBMin[i];}
163 Float_t GetBoundMax(int i) const {return fBMax[i];}
164 Float_t GetPrecision() const {return fPrec;}
165 void ShiftBound(int id,float dif);
167 void LoadData(const char* inpFile);
168 void LoadData(FILE* stream);
170 #ifdef _INC_CREATION_ALICHEB3D_
171 void SaveData(const char* outfile,Bool_t append=kFALSE) const;
172 void SaveData(FILE* stream=stdout) const;
174 void SetUsrFunction(const char* name);
175 void SetUsrFunction(void (*ptr)(float*,float*));
176 void EvalUsrFunction(Float_t *x, Float_t *res);
177 TH1* TestRMS(int idim,int npoints = 1000,TH1* histo=0);
182 void Clear(Option_t* option = "");
183 void SetDimOut(int d);
184 void PrepareBoundaries(Float_t *bmin,Float_t *bmax);
186 #ifdef _INC_CREATION_ALICHEB3D_
187 void EvalUsrFunction();
188 void DefineGrid(Int_t* npoints);
189 Int_t ChebFit(); // fit all output dimensions
190 Int_t ChebFit(int dmOut);
191 Int_t CalcChebCoefs(Float_t *funval,int np, Float_t *outCoefs, Float_t prec=-1);
194 void Cyl2CartCyl(float *rphiz, float *b) const;
195 void Cart2Cyl(float *xyz,float *rphiz) const;
197 Float_t MapToInternal(Float_t x,Int_t d) const {return (x-fBOffset[d])*fBScale[d];} // map x to [-1:1]
198 Float_t MapToExternal(Float_t x,Int_t d) const {return x/fBScale[d]+fBOffset[d];} // map from [-1:1] to x
201 Int_t fDimOut; // dimension of the ouput array
202 Float_t fPrec; // requested precision
203 Float_t fBMin[3]; // min boundaries in each dimension
204 Float_t fBMax[3]; // max boundaries in each dimension
205 Float_t fBScale[3]; // scale for boundary mapping to [-1:1] interval
206 Float_t fBOffset[3]; // offset for boundary mapping to [-1:1] interval
207 TObjArray fChebCalc; // Chebyshev parameterization for each output dimension
209 Int_t fMaxCoefs; //! max possible number of coefs per parameterization
210 Int_t fNPoints[3]; //! number of used points in each dimension
211 Float_t fArgsTmp[3]; //! temporary vector for coefs caluclation
212 Float_t fBuff[6]; //! buffer for coordinate transformations
213 Float_t * fResTmp; //! temporary vector for results of user function caluclation
214 Float_t * fGrid; //! temporary buffer for Chebyshef roots grid
215 Int_t fGridOffs[3]; //! start of grid for each dimension
216 TString fUsrFunName; //! name of user macro containing the function of "void (*fcn)(float*,float*)" format
217 TMethodCall* fUsrMacro; //! Pointer to MethodCall for function from user macro
219 ClassDef(AliCheb3D,1) // Chebyshev parametrization for 3D->N function
222 // Pointer on user function (faster altrnative to TMethodCall)
223 #ifdef _INC_CREATION_ALICHEB3D_
224 void (*gUsrFunAliCheb3D) (float* ,float* );
227 //__________________________________________________________________________________________
228 #ifdef _INC_CREATION_ALICHEB3D_
229 inline void AliCheb3D::EvalUsrFunction()
231 // call user supplied function
232 if (gUsrFunAliCheb3D) gUsrFunAliCheb3D(fArgsTmp,fResTmp);
233 else fUsrMacro->Execute();
237 //__________________________________________________________________________________________
238 inline Bool_t AliCheb3D::IsInside(Float_t *par) const
240 // check if the point is inside of the fitted box
241 for (int i=3;i--;) if(par[i]<fBMin[i]||par[i]>fBMax[i]) return kFALSE;
245 //__________________________________________________________________________________________
246 inline Float_t AliCheb3DCalc::ChebEval1D(Float_t x, const Float_t * array, int ncf ) const
248 // evaluate 1D Chebyshev parameterization. x is the argument mapped to [-1:1] interval
253 for (int i=ncf;i--;) {
256 b0 = array[i] + x2*b1 -b2;
261 //__________________________________________________________________________________________
262 inline void AliCheb3D::Eval(Float_t *par, Float_t *res)
264 // evaluate Chebyshev parameterization for 3d->DimOut function
265 for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i);
266 for (int i=fDimOut;i--;) res[i] = GetChebCalc(i)->Eval(fArgsTmp);
270 //__________________________________________________________________________________________
271 inline Float_t AliCheb3D::Eval(Float_t *par, int idim)
273 // evaluate Chebyshev parameterization for idim-th output dimension of 3d->DimOut function
274 for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i);
275 return GetChebCalc(idim)->Eval(fArgsTmp);
279 //__________________________________________________________________________________________________
280 inline void AliCheb3D::Cyl2CartCyl(float *rphiz, float *b) const
282 // convert field in cylindrical coordinates to cartesian system, point is in cyl.system
283 float btr = TMath::Sqrt(b[0]*b[0]+b[1]*b[1]);
284 float ang = TMath::ATan2(b[1],b[0]) + rphiz[1];
285 b[0] = btr*TMath::Cos(ang);
286 b[1] = btr*TMath::Sin(ang);
290 //__________________________________________________________________________________________________
291 inline void AliCheb3D::Cart2Cyl(float *xyz,float *rphiz) const
293 // convert cartesian coordinate to cylindrical one
294 rphiz[0] = TMath::Sqrt(xyz[0]*xyz[0]+xyz[1]*xyz[1]);
295 rphiz[1] = TMath::ATan2(xyz[1],xyz[0]);