Parameterisation of the measured mag. field map. (R. Shahoyan)
[u/mrichter/AliRoot.git] / STEER / AliCheb3D.h
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0eea9d4d 1#ifndef ALICHEB3D_H
2#define ALICHEB3D_H
3/* Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
4 * See cxx source for full Copyright notice */
5
6/* $Id$ */
7
8// Author: ruben.shahoyan@cern.ch 09/09/2006
9//
10////////////////////////////////////////////////////////////////////////////////
11// //
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. //
16// //
17// The user-callable methods are: //
18// To create the interpolation use: //
19// AliCheb3D(const char* funName, // name of the file with user function //
20// or //
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 //
29// //
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. //
35// //
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. //
42// //
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); //
47// //
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. //
51// //
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. //
54// //
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 //
58// dimension. //
59// //
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! //
64// //
65// For the properties of Chebyshev parameterization see: //
66// H.Wind, CERN EP Internal Report, 81-12/Rev. //
67// //
68////////////////////////////////////////////////////////////////////////////////
69
70
71#include <stdio.h>
72#include <TNamed.h>
73#include <TMethodCall.h>
74#include <TMath.h>
75#include <TH1.h>
76#include <TObjArray.h>
77
78class TString;
79class TSystem;
80class TRandom;
81
82
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_
86
87class AliCheb3DCalc: public TNamed
88{
89 public:
90 AliCheb3DCalc();
91 AliCheb3DCalc(FILE* stream); // read coefs from text file
92 ~AliCheb3DCalc() {Clear();}
93 //
94 void Print(Option_t* opt="") const;
95 void LoadData(FILE* stream);
96 Float_t Eval(Float_t *par) const;
97 //
98#ifdef _INC_CREATION_ALICHEB3D_
99 void SaveData(const char* outfile,Bool_t append=kFALSE) const;
100 void SaveData(FILE* stream=stdout) const;
101#endif
102 //
103 static void ReadLine(TString& str,FILE* stream);
104 //
105 protected:
106 //
107 void Clear(Option_t* option = "");
108 void Init0();
109 Float_t ChebEval1D(Float_t x, const Float_t * array, int ncf) const;
110 void InitRows(int nr);
111 void InitCols(int nc);
112 void InitElemBound2D(int ne);
113 void InitCoefs(int nc);
114 Int_t* GetNColsAtRow() const {return fNColsAtRow;}
115 Int_t* GetColAtRowBg() const {return fColAtRowBg;}
116 Int_t* GetCoefBound2D0() const {return fCoefBound2D0;}
117 Int_t* GetCoefBound2D1() const {return fCoefBound2D1;}
118 Float_t * GetCoefs() const {return fCoefs;}
119 //
120 protected:
121 Int_t fNCoefs; // total number of coeeficients
122 Int_t fNRows; // number of significant rows in the 3D coeffs matrix
123 Int_t fNCols; // max number of significant cols in the 3D coeffs matrix
124 Int_t fNElemBound2D; // number of elements (fNRows*fNCols) to store for the 2D boundary of significant coeffs
125 Int_t* fNColsAtRow; //[fNRows] number of sighificant columns (2nd dim) at each row of 3D coefs matrix
126 Int_t* fColAtRowBg; //[fNRows] beginnig of significant columns (2nd dim) for row in the 2D boundary matrix
127 Int_t* fCoefBound2D0; //[fNElemBound2D] 2D matrix defining the boundary of significance for 3D coeffs.matrix (Ncoefs for col/row)
128 Int_t* fCoefBound2D1; //[fNElemBound2D] 2D matrix defining the start beginnig of significant coeffs for col/row
129 Float_t * fCoefs; //[fNCoefs] array of Chebyshev coefficients
130 //
131 Float_t * fTmpCf1; //[fNCols] temp. coeffs for 2d summation
132 Float_t * fTmpCf0; //[fNRows] temp. coeffs for 1d summation
133 //
134 ClassDef(AliCheb3DCalc,1) // Class for interpolation of 3D->1 function by Chebyshev parametrization
135};
136
137
138class AliCheb3D: public TNamed
139{
140 public:
141 AliCheb3D();
142 AliCheb3D(const char* inpFile); // read coefs from text file
143 AliCheb3D(FILE*); // read coefs from stream
144 //
145#ifdef _INC_CREATION_ALICHEB3D_
146 AliCheb3D(const char* funName, Int_t DimOut, Float_t *bmin,Float_t *bmax, Int_t *npoints, Float_t prec=1E-6);
147 AliCheb3D(void (*ptr)(float*,float*), Int_t DimOut, Float_t *bmin,Float_t *bmax, Int_t *npoints, Float_t prec=1E-6);
148#endif
149 //
150 ~AliCheb3D() {Clear();}
151 //
152 void Eval(Float_t *par,Float_t *res);
153 Float_t Eval(Float_t *par,int idim);
154 void Print(Option_t* opt="") const;
155 Bool_t IsInside(Float_t *par) const;
156 AliCheb3DCalc* GetChebCalc(int i) const {return (AliCheb3DCalc*)fChebCalc.UncheckedAt(i);}
157 Float_t GetBoundMin(int i) const {return fBMin[i];}
158 Float_t GetBoundMax(int i) const {return fBMax[i];}
159 Float_t GetPrecision() const {return fPrec;}
160 void ShiftBound(int id,float dif);
161 //
162 void LoadData(const char* inpFile);
163 void LoadData(FILE* stream);
164 //
165#ifdef _INC_CREATION_ALICHEB3D_
166 void SaveData(const char* outfile,Bool_t append=kFALSE) const;
167 void SaveData(FILE* stream=stdout) const;
168 //
169 void SetUsrFunction(const char* name);
170 void SetUsrFunction(void (*ptr)(float*,float*));
171 void EvalUsrFunction(Float_t *x, Float_t *res);
172 TH1* TestRMS(int idim,int npoints = 1000,TH1* histo=0);
173#endif
174 //
175 protected:
176 void Init0();
177 void Clear(Option_t* option = "");
178 void SetDimOut(int d);
179 void PrepareBoundaries(Float_t *bmin,Float_t *bmax);
180 //
181#ifdef _INC_CREATION_ALICHEB3D_
182 void EvalUsrFunction();
183 void DefineGrid(Int_t* npoints);
184 Int_t ChebFit(); // fit all output dimensions
185 Int_t ChebFit(int dmOut);
186 Int_t CalcChebCoefs(Float_t *funval,int np, Float_t *outCoefs, Float_t prec=-1);
187#endif
188 //
189 void Cyl2CartCyl(float *rphiz, float *b) const;
190 void Cart2Cyl(float *xyz,float *rphiz) const;
191 //
192 Float_t MapToInternal(Float_t x,Int_t d) const {return (x-fBOffset[d])*fBScale[d];} // map x to [-1:1]
193 Float_t MapToExternal(Float_t x,Int_t d) const {return x/fBScale[d]+fBOffset[d];} // map from [-1:1] to x
194 //
195 protected:
196 Int_t fDimOut; // dimension of the ouput array
197 Float_t fPrec; // requested precision
198 Float_t fBMin[3]; // min boundaries in each dimension
199 Float_t fBMax[3]; // max boundaries in each dimension
200 Float_t fBScale[3]; // scale for boundary mapping to [-1:1] interval
201 Float_t fBOffset[3]; // offset for boundary mapping to [-1:1] interval
202 TObjArray fChebCalc; // Chebyshev parameterization for each output dimension
203 //
204 Int_t fMaxCoefs; //! max possible number of coefs per parameterization
205 Int_t fNPoints[3]; //! number of used points in each dimension
206 Float_t fArgsTmp[3]; //! temporary vector for coefs caluclation
207 Float_t fBuff[6]; //! buffer for coordinate transformations
208 Float_t * fResTmp; //! temporary vector for results of user function caluclation
209 Float_t * fGrid; //! temporary buffer for Chebyshef roots grid
210 Int_t fGridOffs[3]; //! start of grid for each dimension
211 TString fUsrFunName; //! name of user macro containing the function of "void (*fcn)(float*,float*)" format
212 TMethodCall* fUsrMacro; //! Pointer to MethodCall for function from user macro
213 //
214 ClassDef(AliCheb3D,1) // Chebyshev parametrization for 3D->N function
215};
216
217// Pointer on user function (faster altrnative to TMethodCall)
218#ifdef _INC_CREATION_ALICHEB3D_
219void (*gUsrFunAliCheb3D) (float* ,float* );
220#endif
221
222//__________________________________________________________________________________________
223#ifdef _INC_CREATION_ALICHEB3D_
224inline void AliCheb3D::EvalUsrFunction()
225{
226 // call user supplied function
227 if (gUsrFunAliCheb3D) gUsrFunAliCheb3D(fArgsTmp,fResTmp);
228 else fUsrMacro->Execute();
229}
230#endif
231
232//__________________________________________________________________________________________
233inline Bool_t AliCheb3D::IsInside(Float_t *par) const
234{
235 // check if the point is inside of the fitted box
236 for (int i=3;i--;) if(par[i]<fBMin[i]||par[i]>fBMax[i]) return kFALSE;
237 return kTRUE;
238}
239
240//__________________________________________________________________________________________
241inline Float_t AliCheb3DCalc::ChebEval1D(Float_t x, const Float_t * array, int ncf ) const
242{
243 // evaluate 1D Chebyshev parameterization. x is the argument mapped to [-1:1] interval
244 Float_t b0, b1, b2;
245 Float_t x2 = x+x;
246 b0 = array[--ncf];
247 b1 = b2 = 0;
248 for (int i=ncf;i--;) {
249 b2 = b1;
250 b1 = b0;
251 b0 = array[i] + x2*b1 -b2;
252 }
253 return b0 - x*b1;
254}
255
256//__________________________________________________________________________________________
257inline void AliCheb3D::Eval(Float_t *par, Float_t *res)
258{
259 // evaluate Chebyshev parameterization for 3d->DimOut function
260 for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i);
261 for (int i=fDimOut;i--;) res[i] = GetChebCalc(i)->Eval(fArgsTmp);
262 //
263}
264
265//__________________________________________________________________________________________
266inline Float_t AliCheb3D::Eval(Float_t *par, int idim)
267{
268 // evaluate Chebyshev parameterization for idim-th output dimension of 3d->DimOut function
269 for (int i=3;i--;) fArgsTmp[i] = MapToInternal(par[i],i);
270 return GetChebCalc(idim)->Eval(fArgsTmp);
271 //
272}
273
274//__________________________________________________________________________________________________
275inline void AliCheb3D::Cyl2CartCyl(float *rphiz, float *b) const
276{
277 // convert field in cylindrical coordinates to cartesian system, point is in cyl.system
278 float btr = TMath::Sqrt(b[0]*b[0]+b[1]*b[1]);
279 float ang = TMath::ATan2(b[1],b[0]) + rphiz[1];
280 b[0] = btr*TMath::Cos(ang);
281 b[1] = btr*TMath::Sin(ang);
282 //
283}
284
285//__________________________________________________________________________________________________
286inline void AliCheb3D::Cart2Cyl(float *xyz,float *rphiz) const
287{
288 // convert cartesian coordinate to cylindrical one
289 rphiz[0] = TMath::Sqrt(xyz[0]*xyz[0]+xyz[1]*xyz[1]);
290 rphiz[1] = TMath::ATan2(xyz[1],xyz[0]);
291 rphiz[2] = xyz[2];
292}
293
294#endif