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0eea9d4d | 1 | // Author: ruben.shahoyan@cern.ch 09/09/2006 |
40389866 | 2 | |
0eea9d4d | 3 | //////////////////////////////////////////////////////////////////////////////// |
4 | // // | |
5 | // AliCheb3D produces the interpolation of the user 3D->NDimOut arbitrary // | |
6 | // function supplied in "void (*fcn)(float* inp,float* out)" format // | |
7 | // either in a separate macro file or as a function pointer. // | |
8 | // Only coefficients needed to guarantee the requested precision are kept. // | |
9 | // // | |
10 | // The user-callable methods are: // | |
11 | // To create the interpolation use: // | |
12 | // AliCheb3D(const char* funName, // name of the file with user function // | |
13 | // or // | |
14 | // AliCheb3D(void (*ptr)(float*,float*),// pointer on the user function // | |
15 | // Int_t DimOut, // dimensionality of the function's output // | |
16 | // Float_t *bmin, // lower 3D bounds of interpolation domain // | |
17 | // Float_t *bmax, // upper 3D bounds of interpolation domain // | |
18 | // Int_t *npoints, // number of points in each of 3 input // | |
19 | // // dimension, defining the interpolation grid // | |
20 | // Float_t prec=1E-6); // requested max.absolute difference between // | |
21 | // // the interpolation and any point on grid // | |
22 | // // | |
23 | // To test obtained parameterization use the method // | |
24 | // TH1* TestRMS(int idim,int npoints = 1000,TH1* histo=0); // | |
25 | // it will compare the user output of the user function and interpolation // | |
26 | // for idim-th output dimension and fill the difference in the supplied // | |
27 | // histogram. If no histogram is supplied, it will be created. // | |
28 | // // | |
29 | // To save the interpolation data: // | |
30 | // SaveData(const char* filename, Bool_t append ) // | |
31 | // write text file with data. If append is kTRUE and the output file already // | |
32 | // exists, data will be added in the end of the file. // | |
33 | // Alternatively, SaveData(FILE* stream) will write the data to // | |
34 | // already existing stream. // | |
35 | // // | |
36 | // To read back already stored interpolation use either the constructor // | |
37 | // AliCheb3D(const char* inpFile); // | |
38 | // or the default constructor AliCheb3D() followed by // | |
39 | // AliCheb3D::LoadData(const char* inpFile); // | |
40 | // // | |
41 | // To compute the interpolation use Eval(float* par,float *res) method, with // | |
42 | // par being 3D vector of arguments (inside the validity region) and res is // | |
43 | // the array of DimOut elements for the output. // | |
44 | // // | |
45 | // If only one component (say, idim-th) of the output is needed, use faster // | |
46 | // Float_t Eval(Float_t *par,int idim) method. // | |
47 | // // | |
48 | // void Print(option="") will print the name, the ranges of validity and // | |
49 | // the absolute precision of the parameterization. Option "l" will also print // | |
50 | // the information about the number of coefficients for each output // | |
51 | // dimension. // | |
52 | // // | |
53 | // NOTE: during the evaluation no check is done for parameter vector being // | |
54 | // outside the interpolation region. If there is such a risk, use // | |
55 | // Bool_t IsInside(float *par) method. Chebyshev parameterization is not // | |
56 | // good for extrapolation! // | |
57 | // // | |
58 | // For the properties of Chebyshev parameterization see: // | |
59 | // H.Wind, CERN EP Internal Report, 81-12/Rev. // | |
60 | // // | |
61 | //////////////////////////////////////////////////////////////////////////////// | |
62 | ||
63 | ||
40389866 | 64 | #ifndef _ALICHEB3D_ |
65 | #define _ALICHEB3D_ | |
0eea9d4d | 66 | #include <stdio.h> |
67 | #include <TNamed.h> | |
68 | #include <TMethodCall.h> | |
69 | #include <TMath.h> | |
70 | #include <TH1.h> | |
71 | #include <TObjArray.h> | |
99adacae | 72 | #include "AliCheb3DCalc.h" |
73 | ||
0eea9d4d | 74 | class TString; |
75 | class TSystem; | |
76 | class TRandom; | |
40389866 | 77 | |
78 | ||
0eea9d4d | 79 | class AliCheb3D: public TNamed |
80 | { | |
81 | public: | |
40389866 | 82 | AliCheb3D(); |
83 | AliCheb3D(const AliCheb3D& src); | |
84 | AliCheb3D(const char* inpFile); | |
85 | AliCheb3D(FILE* stream); | |
0eea9d4d | 86 | // |
87 | #ifdef _INC_CREATION_ALICHEB3D_ | |
88 | AliCheb3D(const char* funName, Int_t DimOut, Float_t *bmin,Float_t *bmax, Int_t *npoints, Float_t prec=1E-6); | |
89 | AliCheb3D(void (*ptr)(float*,float*), Int_t DimOut, Float_t *bmin,Float_t *bmax, Int_t *npoints, Float_t prec=1E-6); | |
40389866 | 90 | 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); |
91 | AliCheb3D(void (*ptr)(float*,float*), int DimOut, Float_t *bmin,Float_t *bmax, Float_t prec=1E-6); | |
0eea9d4d | 92 | #endif |
93 | // | |
94 | ~AliCheb3D() {Clear();} | |
95 | // | |
40389866 | 96 | AliCheb3D& operator=(const AliCheb3D& rhs); |
0eea9d4d | 97 | void Eval(Float_t *par,Float_t *res); |
98 | Float_t Eval(Float_t *par,int idim); | |
40389866 | 99 | // |
100 | void EvalDeriv(int dimd, Float_t *par,Float_t *res); | |
1cf34ee8 | 101 | void EvalDeriv2(int dimd1, int dimd2,Float_t *par,Float_t *res); |
40389866 | 102 | Float_t EvalDeriv(int dimd,Float_t *par, int idim); |
1cf34ee8 | 103 | Float_t EvalDeriv2(int dimd1,int dimd2, Float_t *par, int idim); |
40389866 | 104 | void EvalDeriv3D(Float_t *par, Float_t dbdr[3][3]); |
1cf34ee8 | 105 | void EvalDeriv3D2(Float_t *par, Float_t dbdrdr[3][3][3]); |
0eea9d4d | 106 | void Print(Option_t* opt="") const; |
107 | Bool_t IsInside(Float_t *par) const; | |
40389866 | 108 | Bool_t IsInside(Double_t *par) const; |
0eea9d4d | 109 | AliCheb3DCalc* GetChebCalc(int i) const {return (AliCheb3DCalc*)fChebCalc.UncheckedAt(i);} |
110 | Float_t GetBoundMin(int i) const {return fBMin[i];} | |
111 | Float_t GetBoundMax(int i) const {return fBMax[i];} | |
40389866 | 112 | Float_t* GetBoundMin() const {return (float*)fBMin;} |
113 | Float_t* GetBoundMax() const {return (float*)fBMax;} | |
0eea9d4d | 114 | Float_t GetPrecision() const {return fPrec;} |
115 | void ShiftBound(int id,float dif); | |
116 | // | |
117 | void LoadData(const char* inpFile); | |
118 | void LoadData(FILE* stream); | |
119 | // | |
120 | #ifdef _INC_CREATION_ALICHEB3D_ | |
40389866 | 121 | int* GetNCNeeded(float xyz[3],int DimVar, float mn,float mx, float prec); |
122 | void EstimateNPoints(float Prec, int gridBC[3][3]); | |
0eea9d4d | 123 | void SaveData(const char* outfile,Bool_t append=kFALSE) const; |
124 | void SaveData(FILE* stream=stdout) const; | |
125 | // | |
126 | void SetUsrFunction(const char* name); | |
127 | void SetUsrFunction(void (*ptr)(float*,float*)); | |
128 | void EvalUsrFunction(Float_t *x, Float_t *res); | |
129 | TH1* TestRMS(int idim,int npoints = 1000,TH1* histo=0); | |
40389866 | 130 | static Int_t CalcChebCoefs(Float_t *funval,int np, Float_t *outCoefs, Float_t prec=-1); |
0eea9d4d | 131 | #endif |
132 | // | |
133 | protected: | |
0eea9d4d | 134 | void Clear(Option_t* option = ""); |
135 | void SetDimOut(int d); | |
136 | void PrepareBoundaries(Float_t *bmin,Float_t *bmax); | |
137 | // | |
138 | #ifdef _INC_CREATION_ALICHEB3D_ | |
139 | void EvalUsrFunction(); | |
140 | void DefineGrid(Int_t* npoints); | |
141 | Int_t ChebFit(); // fit all output dimensions | |
142 | Int_t ChebFit(int dmOut); | |
0eea9d4d | 143 | #endif |
144 | // | |
40389866 | 145 | Float_t MapToInternal(Float_t x,Int_t d) const; // map x to [-1:1] |
0eea9d4d | 146 | Float_t MapToExternal(Float_t x,Int_t d) const {return x/fBScale[d]+fBOffset[d];} // map from [-1:1] to x |
40389866 | 147 | // |
0eea9d4d | 148 | protected: |
149 | Int_t fDimOut; // dimension of the ouput array | |
150 | Float_t fPrec; // requested precision | |
151 | Float_t fBMin[3]; // min boundaries in each dimension | |
152 | Float_t fBMax[3]; // max boundaries in each dimension | |
153 | Float_t fBScale[3]; // scale for boundary mapping to [-1:1] interval | |
154 | Float_t fBOffset[3]; // offset for boundary mapping to [-1:1] interval | |
155 | TObjArray fChebCalc; // Chebyshev parameterization for each output dimension | |
156 | // | |
157 | Int_t fMaxCoefs; //! max possible number of coefs per parameterization | |
158 | Int_t fNPoints[3]; //! number of used points in each dimension | |
159 | Float_t fArgsTmp[3]; //! temporary vector for coefs caluclation | |
160 | Float_t fBuff[6]; //! buffer for coordinate transformations | |
161 | Float_t * fResTmp; //! temporary vector for results of user function caluclation | |
162 | Float_t * fGrid; //! temporary buffer for Chebyshef roots grid | |
163 | Int_t fGridOffs[3]; //! start of grid for each dimension | |
164 | TString fUsrFunName; //! name of user macro containing the function of "void (*fcn)(float*,float*)" format | |
165 | TMethodCall* fUsrMacro; //! Pointer to MethodCall for function from user macro | |
166 | // | |
167 | ClassDef(AliCheb3D,1) // Chebyshev parametrization for 3D->N function | |
168 | }; | |
169 | ||
0eea9d4d | 170 | //__________________________________________________________________________________________ |
40389866 | 171 | inline Bool_t AliCheb3D::IsInside(Float_t *par) const |
0eea9d4d | 172 | { |
40389866 | 173 | // check if the point is inside of the fitted box |
174 | const float kTol = 1.e-4; | |
175 | for (int i=3;i--;) if (fBMin[i]-par[i]>kTol || par[i]-fBMax[i]>kTol) return kFALSE; | |
176 | //if(par[i]<fBMin[i]||par[i]>fBMax[i]) return kFALSE; | |
177 | return kTRUE; | |
0eea9d4d | 178 | } |
0eea9d4d | 179 | |
180 | //__________________________________________________________________________________________ | |
40389866 | 181 | inline Bool_t AliCheb3D::IsInside(Double_t *par) const |
0eea9d4d | 182 | { |
183 | // check if the point is inside of the fitted box | |
40389866 | 184 | const float kTol = 1.e-4; |
185 | for (int i=3;i--;) if (fBMin[i]-par[i]>kTol || par[i]-fBMax[i]>kTol) return kFALSE; | |
186 | //if(par[i]<fBMin[i]||par[i]>fBMax[i]) return kFALSE; | |
0eea9d4d | 187 | return kTRUE; |
188 | } | |
189 | ||
0eea9d4d | 190 | //__________________________________________________________________________________________ |
191 | inline void AliCheb3D::Eval(Float_t *par, Float_t *res) | |
192 | { | |
193 | // evaluate Chebyshev parameterization for 3d->DimOut function | |
194 | for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i); | |
195 | for (int i=fDimOut;i--;) res[i] = GetChebCalc(i)->Eval(fArgsTmp); | |
196 | // | |
197 | } | |
198 | ||
199 | //__________________________________________________________________________________________ | |
200 | inline Float_t AliCheb3D::Eval(Float_t *par, int idim) | |
201 | { | |
202 | // evaluate Chebyshev parameterization for idim-th output dimension of 3d->DimOut function | |
203 | for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i); | |
204 | return GetChebCalc(idim)->Eval(fArgsTmp); | |
205 | // | |
206 | } | |
207 | ||
40389866 | 208 | //__________________________________________________________________________________________ |
209 | inline void AliCheb3D::EvalDeriv3D(Float_t *par, Float_t dbdr[3][3]) | |
210 | { | |
211 | // return gradient matrix | |
212 | for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i); | |
213 | for (int ib=3;ib--;) for (int id=3;id--;) dbdr[ib][id] = GetChebCalc(ib)->EvalDeriv(id,fArgsTmp)*fBScale[id]; | |
214 | } | |
215 | ||
1cf34ee8 | 216 | //__________________________________________________________________________________________ |
217 | inline void AliCheb3D::EvalDeriv3D2(Float_t *par, Float_t dbdrdr[3][3][3]) | |
218 | { | |
219 | // return gradient matrix | |
220 | for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i); | |
221 | for (int ib=3;ib--;) for (int id=3;id--;)for (int id1=3;id1--;) | |
222 | dbdrdr[ib][id][id1] = GetChebCalc(ib)->EvalDeriv2(id,id1,fArgsTmp)*fBScale[id]*fBScale[id1]; | |
223 | } | |
224 | ||
40389866 | 225 | //__________________________________________________________________________________________ |
226 | inline void AliCheb3D::EvalDeriv(int dimd,Float_t *par, Float_t *res) | |
227 | { | |
228 | // evaluate Chebyshev parameterization derivative for 3d->DimOut function | |
229 | for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i); | |
230 | for (int i=fDimOut;i--;) res[i] = GetChebCalc(i)->EvalDeriv(dimd,fArgsTmp)*fBScale[dimd];; | |
231 | // | |
232 | } | |
233 | ||
1cf34ee8 | 234 | //__________________________________________________________________________________________ |
235 | inline void AliCheb3D::EvalDeriv2(int dimd1,int dimd2,Float_t *par, Float_t *res) | |
236 | { | |
237 | // evaluate Chebyshev parameterization 2nd derivative over dimd1 and dimd2 dimensions for 3d->DimOut function | |
238 | for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i); | |
239 | for (int i=fDimOut;i--;) res[i] = GetChebCalc(i)->EvalDeriv2(dimd1,dimd2,fArgsTmp)*fBScale[dimd1]*fBScale[dimd2]; | |
240 | // | |
241 | } | |
242 | ||
40389866 | 243 | //__________________________________________________________________________________________ |
244 | inline Float_t AliCheb3D::EvalDeriv(int dimd,Float_t *par, int idim) | |
0eea9d4d | 245 | { |
40389866 | 246 | // evaluate Chebyshev parameterization derivative over dimd dimention for idim-th output dimension of 3d->DimOut function |
247 | for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i); | |
248 | return GetChebCalc(idim)->EvalDeriv(dimd,fArgsTmp)*fBScale[dimd]; | |
0eea9d4d | 249 | // |
250 | } | |
251 | ||
1cf34ee8 | 252 | //__________________________________________________________________________________________ |
253 | inline Float_t AliCheb3D::EvalDeriv2(int dimd1,int dimd2,Float_t *par, int idim) | |
254 | { | |
255 | // evaluate Chebyshev parameterization 2ns derivative over dimd1 and dimd2 dimensions for idim-th output dimension of 3d->DimOut function | |
256 | for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i); | |
257 | return GetChebCalc(idim)->EvalDeriv2(dimd1,dimd2,fArgsTmp)*fBScale[dimd1]*fBScale[dimd2]; | |
258 | // | |
259 | } | |
260 | ||
40389866 | 261 | //__________________________________________________________________________________________ |
262 | inline Float_t AliCheb3D::MapToInternal(Float_t x,Int_t d) const | |
0eea9d4d | 263 | { |
40389866 | 264 | // map x to [-1:1] |
265 | #ifdef _BRING_TO_BOUNDARY_ | |
266 | float res = (x-fBOffset[d])*fBScale[d]; | |
267 | if (res<-1) return -1; | |
268 | if (res> 1) return 1; | |
269 | return res; | |
270 | #else | |
271 | return (x-fBOffset[d])*fBScale[d]; | |
272 | #endif | |
0eea9d4d | 273 | } |
274 | ||
275 | #endif |