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9318a5b4 1/**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
3 * *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
6 * *
7 * Permission to use, copy, modify and distribute this software and its *
8 * documentation strictly for non-commercial purposes is hereby granted *
9 * without fee, provided that the above copyright notice appears in all *
10 * copies and that both the copyright notice and this permission notice *
11 * appear in the supporting documentation. The authors make no claims *
12 * about the suitability of this software for any purpose. It is *
13 * provided "as is" without express or implied warranty. *
14 **************************************************************************/
15
16
17///////////////////////////////////////////////////////////////////////////////
18// //
19// Class to make a internal alignemnt of TPC chambers //
20//
21// Different linear tranformation investigated
22// 12 parameters - arbitrary transformation
23// 9 parameters - scaling fixed to 1
24// 6 parameters -
25////
26//// Only the 12 parameter version works so far...
27////
28////
29////
30
31#include "TLinearFitter.h"
32#include "AliTPCcalibAlign.h"
33#include "AliExternalTrackParam.h"
e4042305 34#include "AliTPCTracklet.h"
35#include "TH1D.h"
9318a5b4 36
37#include <iostream>
e4042305 38#include <sstream>
9318a5b4 39using namespace std;
40
41ClassImp(AliTPCcalibAlign)
42
43AliTPCcalibAlign::AliTPCcalibAlign()
e4042305 44 : fDphiHistArray(72*72),
45 fDthetaHistArray(72*72),
46 fDyHistArray(72*72),
47 fDzHistArray(72*72),
48 fFitterArray12(72*72),
49 fFitterArray9(72*72),
50 fFitterArray6(72*72)
9318a5b4 51{
52 //
53 // Constructor
54 //
55 for (Int_t i=0;i<72*72;++i) {
56 fPoints[i]=0;
57 }
58}
59
60AliTPCcalibAlign::~AliTPCcalibAlign() {
61 //
62 // destructor
63 //
64}
65
e4042305 66void AliTPCcalibAlign::Process(AliTPCseed *seed) {
67 TObjArray tracklets=
68 AliTPCTracklet::CreateTracklets(seed,AliTPCTracklet::kKalman,
69 kFALSE,20,2);
cbc19295 70 // TObjArray trackletsL=
71// AliTPCTracklet::CreateTracklets(seed,AliTPCTracklet::kLinear,
72// kFALSE,20,2);
73// TObjArray trackletsQ=
74// AliTPCTracklet::CreateTracklets(seed,AliTPCTracklet::kQuadratic,
75// kFALSE,20,2);
76// TObjArray trackletsR=
77// AliTPCTracklet::CreateTracklets(seed,AliTPCTracklet::kRiemann,
78// kFALSE,20,2);
e4042305 79 tracklets.SetOwner();
cbc19295 80 // trackletsL.SetOwner();
81// trackletsQ.SetOwner();
82// trackletsR.SetOwner();
e4042305 83 if (tracklets.GetEntries()==2) {
84 AliTPCTracklet *t1=static_cast<AliTPCTracklet*>(tracklets[0]);
85 AliTPCTracklet *t2=static_cast<AliTPCTracklet*>(tracklets[1]);
86 if (t1->GetSector()>t2->GetSector()) {
87 AliTPCTracklet* tmp=t1;
88 t1=t2;
89 t2=tmp;
90 }
91 AliExternalTrackParam *common1=0,*common2=0;
92 if (AliTPCTracklet::PropagateToMeanX(*t1,*t2,common1,common2))
93 ProcessTracklets(*common1,*common2,t1->GetSector(),t2->GetSector());
94 delete common1;
95 delete common2;
96 }
cbc19295 97
e4042305 98}
99
100void AliTPCcalibAlign::ProcessTracklets(const AliExternalTrackParam &tp1,
101 const AliExternalTrackParam &tp2,
102 Int_t s1,Int_t s2) {
103
104 if (s2-s1==36) {//only inner-outer
105 if (!fDphiHistArray[s1*72+s2]) {
106 stringstream name;
107 stringstream title;
108 name<<"hist_phi_"<<s1<<"_"<<s2;
109 title<<"Phi Missalignment for sectors "<<s1<<" and "<<s2;
110 fDphiHistArray[s1*72+s2]=new TH1D(name.str().c_str(),title.str().c_str(),1024,-0.01,0.01); // +/- 10 mrad
111 ((TH1D*)fDphiHistArray[s1*72+s2])->SetDirectory(0);
112 }
113 if (!fDthetaHistArray[s1*72+s2]) {
114 stringstream name;
115 stringstream title;
116 name<<"hist_theta_"<<s1<<"_"<<s2;
117 title<<"Theta Missalignment for sectors "<<s1<<" and "<<s2;
118 fDthetaHistArray[s1*72+s2]=new TH1D(name.str().c_str(),title.str().c_str(),1024,-0.01,0.01); // +/- 10 mrad
119 ((TH1D*)fDthetaHistArray[s1*72+s2])->SetDirectory(0);
120 }
121 if (!fDyHistArray[s1*72+s2]) {
122 stringstream name;
123 stringstream title;
124 name<<"hist_y_"<<s1<<"_"<<s2;
125 title<<"Y Missalignment for sectors "<<s1<<" and "<<s2;
126 fDyHistArray[s1*72+s2]=new TH1D(name.str().c_str(),title.str().c_str(),1024,-0.3,0.3); // +/- 3 mm
127 ((TH1D*)fDyHistArray[s1*72+s2])->SetDirectory(0);
128 }
129 if (!fDzHistArray[s1*72+s2]) {
130 stringstream name;
131 stringstream title;
132 name<<"hist_z_"<<s1<<"_"<<s2;
133 title<<"Z Missalignment for sectors "<<s1<<" and "<<s2;
134 fDzHistArray[s1*72+s2]=new TH1D(name.str().c_str(),title.str().c_str(),1024,-0.3,0.3); // +/- 3 mm
135 ((TH1D*)fDzHistArray[s1*72+s2])->SetDirectory(0);
136 }
137 static_cast<TH1D*>(fDphiHistArray[s1*72+s2])
138 ->Fill(TMath::ASin(tp1.GetSnp())
139 -TMath::ASin(tp2.GetSnp()));
140 static_cast<TH1D*>(fDthetaHistArray[s1*72+s2])
141 ->Fill(TMath::ATan(tp1.GetTgl())
142 -TMath::ATan(tp2.GetTgl()));
143 static_cast<TH1D*>(fDyHistArray[s1*72+s2])
144 ->Fill(tp1.GetY()
145 -tp2.GetY());
146 static_cast<TH1D*>(fDzHistArray[s1*72+s2])
147 ->Fill(tp1.GetZ()
148 -tp2.GetZ());
149 }
150 return;
151
152
153
9318a5b4 154 //
155 // Process function to fill fitters
156 //
157 Double_t t1[5],t2[5];
158 Double_t &x1=t1[0], &y1=t1[1], &z1=t1[2], &dydx1=t1[3], &dzdx1=t1[4];
cec17745 159 Double_t /*&x2=t2[0],*/ &y2=t2[1], &z2=t2[2], &dydx2=t2[3]/*, &dzdx2=t2[4]*/;
9318a5b4 160 x1 =tp1.GetX();
161 y1 =tp1.GetY();
162 z1 =tp1.GetZ();
163 Double_t snp1=tp1.GetSnp();
164 dydx1=snp1/TMath::Sqrt(1.-snp1*snp1);
165 Double_t tgl1=tp1.GetTgl();
166 // dz/dx = 1/(cos(theta)*cos(phi))
167 dzdx1=1./TMath::Sqrt((1.+tgl1*tgl1)*(1.-snp1*snp1));
168 // x2 =tp1->GetX();
169 y2 =tp2.GetY();
170 z2 =tp2.GetZ();
171 Double_t snp2=tp2.GetSnp();
172 dydx2=snp2/TMath::Sqrt(1.-snp2*snp2);
173 Double_t tgl2=tp2.GetTgl();
174 dzdx1=1./TMath::Sqrt((1.+tgl2*tgl2)*(1.-snp2*snp2));
175
176 Process12(t1,t2,GetOrMakeFitter12(s1,s2));
177 Process9(t1,t2,GetOrMakeFitter12(s1,s2));
178 Process6(t1,t2,GetOrMakeFitter12(s1,s2));
179 ++fPoints[72*s1+s2];
180}
181
182void AliTPCcalibAlign::Process12(Double_t *t1,
183 Double_t *t2,
184 TLinearFitter *fitter) {
185 // x2 = a00*x1 + a01*y1 + a02*z1 + a03
186 // y2 = a10*x1 + a11*y1 + a12*z1 + a13
187 // z2 = a20*x1 + a21*y1 + a22*z1 + a23
188 // dydx2 = (a10 + a11*dydx1 + a12*dzdx1)/(a00 + a01*dydx1 + a02*dzdx1)
189 // dzdx2 = (a20 + a21*dydx1 + a22*dzdx1)/(a00 + a01*dydx1 + a02*dzdx1)
190 //
191 // a00 a01 a02 a03 p[0] p[1] p[2] p[9]
192 // a10 a11 a12 a13 ==> p[3] p[4] p[5] p[10]
193 // a20 a21 a22 a23 p[6] p[7] p[8] p[11]
194 Double_t &x1=t1[0], &y1=t1[1], &z1=t1[2], &dydx1=t1[3], &dzdx1=t1[4];
cec17745 195 Double_t /*&x2=t2[0],*/ &y2=t2[1], &z2=t2[2], &dydx2=t2[3], &dzdx2=t2[4];
9318a5b4 196
197 // TODO:
198 Double_t sy = 1.;
199 Double_t sz = 1.;
200 Double_t sdydx = 1.;
201 Double_t sdzdx = 1.;
202
203 Double_t p[12];
204 Double_t value;
205
206 // x2 = a00*x1 + a01*y1 + a02*z1 + a03
207 // y2 = a10*x1 + a11*y1 + a12*z1 + a13
208 // y2' = a10*x1 + a11*y1 + a12*z1 + a13 + (a01*y1 + a02*z1 + a03)*dydx2
209 for (Int_t i=0; i<12;i++) p[i]=0.;
210 p[3+0] = x1; // a10
211 p[3+1] = y1; // a11
212 p[3+2] = z1; // a12
213 p[9+1] = 1.; // a13
214 p[0+1] = y1*dydx2; // a01
215 p[0+2] = z1*dydx2; // a02
216 p[9+0] = dydx2; // a03
217 value = y2;
218 fitter->AddPoint(p,value,sy);
219
220 // x2 = a00*x1 + a01*y1 + a02*z1 + a03
221 // z2 = a20*x1 + a21*y1 + a22*z1 + a23
222 // z2' = a20*x1 + a21*y1 + a22*z1 + a23 + (a01*y1 + a02*z1 + a03)*dzdx2;
223 for (Int_t i=0; i<12;i++) p[i]=0.;
224 p[6+0] = x1; // a20
225 p[6+1] = y1; // a21
226 p[6+2] = z1; // a22
227 p[9+2] = 1.; // a23
228 p[0+1] = y1*dzdx2; // a01
229 p[0+2] = z1*dzdx2; // a02
230 p[9+0] = dzdx2; // a03
231 value = z2;
232 fitter->AddPoint(p,value,sz);
233
234 // dydx2 = (a10 + a11*dydx1 + a12*dzdx1)/( a00 + a01*dydx1 + a02*dzdx1)
235 // (a10 + a11*dydx1 + a12*dzdx1) - (a00 + a01*dydx1 + a02*dzdx1)*dydx2 = 0
236 for (Int_t i=0; i<12;i++) p[i]=0.;
237 p[3+0] = 1.; // a10
238 p[3+1] = dydx1; // a11
239 p[3+2] = dzdx1; // a12
240 p[0+0] = -dydx2; // a00
241 p[0+1] = -dydx1*dydx2; // a01
242 p[0+2] = -dzdx1*dydx2; // a02
243 value = 0.;
244 fitter->AddPoint(p,value,sdydx);
245
246 // dzdx2 = (a20 + a21*dydx1 + a22*dzdx1)/( a00 + a01*dydx1 + a02*dzdx1)
247 // (a20 + a21*dydx1 + a22*dzdx1) - (a00 + a01*dydx1 + a02*dzdx1)*dzdx2 = 0
248 for (Int_t i=0; i<12;i++) p[i]=0.;
249 p[6+0] = 1; // a20
250 p[6+1] = dydx1; // a21
251 p[6+2] = dzdx1; // a22
252 p[0+0] = -dzdx2; // a00
253 p[0+1] = -dydx1*dzdx2; // a01
254 p[0+2] = -dzdx1*dzdx2; // a02
255 value = 0.;
256 fitter->AddPoint(p,value,sdzdx);
257}
258
259void AliTPCcalibAlign::Process9(Double_t *t1,
260 Double_t *t2,
261 TLinearFitter *fitter) {
262 // x2 = a00*x1 + a01*y1 + a02*z1 + a03
263 // y2 = a10*x1 + a11*y1 + a12*z1 + a13
264 // z2 = a20*x1 + a21*y1 + a22*z1 + a23
265 // dydx2 = (a10 + a11*dydx1 + a12*dzdx1)/(a00 + a01*dydx1 + a02*dzdx1)
266 // dzdx2 = (a20 + a21*dydx1 + a22*dzdx1)/(a00 + a01*dydx1 + a02*dzdx1)
267 //
268 // a00 a01 a02 a03 p[0] p[1] p[2] p[9]
269 // a10 a11 a12 a13 ==> p[3] p[4] p[5] p[10]
270 // a20 a21 a22 a23 p[6] p[7] p[8] p[11]
271 Double_t &x1=t1[0], &y1=t1[1], &z1=t1[2], &dydx1=t1[3], &dzdx1=t1[4];
cec17745 272 Double_t /*&x2=t2[0],*/ &y2=t2[1], &z2=t2[2], &dydx2=t2[3], &dzdx2=t2[4];
9318a5b4 273
274 // TODO:
275 Double_t sy = 1.;
276 Double_t sz = 1.;
277 Double_t sdydx = 1.;
278 Double_t sdzdx = 1.;
279
280 Double_t p[12];
281 Double_t value;
282
283 // x2 = a00*x1 + a01*y1 + a02*z1 + a03
284 // y2 = a10*x1 + a11*y1 + a12*z1 + a13
285 // y2' = a10*x1 + a11*y1 + a12*z1 + a13 + (a01*y1 + a03)*dydx2
286 for (Int_t i=0; i<12;i++) p[i]=0.;
287 p[3+0] = x1;
288 p[3+1] = y1;
289 p[3+2] = z1;
290 p[9+1] = 1.;
291 p[0+1] = y1*dydx2;
292 p[0+2] = z1*dydx2;
293 p[9+0] = dydx2;
294 value = y2;
295 fitter->AddPoint(p,value,sy);
296
297 // x2 = a00*x1 + a01*y1 + a02*z1 + a03
298 // z2 = a20*x1 + a21*y1 + a22*z1 + a23
299 // z2' = a20*x1 + a21*y1 + a22*z1 + a23 + (a01*y1 + a03)*dzdx2;
300 for (Int_t i=0; i<12;i++) p[i]=0.;
301 p[6+0] = x1;
302 p[6+1] = y1;
303 p[6+2] = z1;
304 p[9+2] = 1.;
305 p[0+1] = y1*dzdx2;
306 p[0+2] = z1*dzdx2;
307 p[9+0] = dzdx2;
308 value = z2;
309 fitter->AddPoint(p,value,sz);
310
311 // dydx2 = (a10 + a11*dydx1 + a12*dzdx1)/( a00 + a01*dydx1 + a02*dzdx1)
312 // (a10 + a11*dydx1 + a12*dzdx1) - (a00 + a01*dydx1 + a02*dzdx1)*dydx2 = 0
313 for (Int_t i=0; i<12;i++) p[i]=0.;
314 p[3+0] = 1.;
315 p[3+1] = dydx1;
316 p[3+2] = dzdx1;
317 p[0+0] = -dydx2;
318 p[0+1] = -dydx1*dydx2;
319 p[0+2] = -dzdx1*dydx2;
320 value = 0.;
321 fitter->AddPoint(p,value,sdydx);
322
323 // dzdx2 = (a20 + a21*dydx1 + a22*dzdx1)/( a00 + a01*dydx1 + a02*dzdx1)
324 // (a20 + a21*dydx1 + a22*dzdx1) - (a00 + a01*dydx1 + a02*dzdx1)*dzdx2 = 0
325 for (Int_t i=0; i<12;i++) p[i]=0.;
326 p[6+0] = 1;
327 p[6+1] = dydx1;
328 p[6+2] = dzdx1;
329 p[0+0] = -dzdx2;
330 p[0+1] = -dydx1*dzdx2;
331 p[0+2] = -dzdx1*dzdx2;
332 value = 0.;
333 fitter->AddPoint(p,value,sdzdx);
334}
335
336void AliTPCcalibAlign::Process6(Double_t *t1,
337 Double_t *t2,
338 TLinearFitter *fitter) {
339 // x2 = 1 *x1 +-a01*y1 + 0 +a03
340 // y2 = a01*x1 + 1 *y1 + 0 +a13
341 // z2 = a20*x1 + a21*y1 + 1 *z1 +a23
342 // dydx2 = (a10 + a11*dydx1 + a12*dzdx1)/(a00 + a01*dydx1 + a02*dzdx1)
343 // dzdx2 = (a20 + a21*dydx1 + a22*dzdx1)/(a00 + a01*dydx1 + a02*dzdx1)
344 //
345 // 1 -a01 0 a03 x -p[0] x p[3]
346 // a10 1 0 a13 ==> p[0] x x p[4]
347 // a20 a21 1 a23 p[1] p[2] x p[5]
348 Double_t &x1=t1[0], &y1=t1[1], &z1=t1[2], &dydx1=t1[3], &dzdx1=t1[4];
cec17745 349 Double_t /*&x2=t2[0],*/ &y2=t2[1], &z2=t2[2], &dydx2=t2[3], &dzdx2=t2[4];
9318a5b4 350
351 // TODO:
352 Double_t sy = 1.;
353 Double_t sz = 1.;
354 Double_t sdydx = 1.;
355 Double_t sdzdx = 1.;
356
357 Double_t p[12];
358 Double_t value;
359
360 // x2 = 1 *x1 +-a01*y1 + 0 +a03
361 // y2 = a01*x1 + 1 *y1 + 0 +a13
362 // y2' = a10*x1 + a11*y1 + a12*z1 + a13 + (a01*y1 + a02*z1 + a03)*dydx2
363 for (Int_t i=0; i<12;i++) p[i]=0.;
364 p[3+0] = x1;
365 p[3+1] = y1;
366 p[3+2] = z1;
367 p[9+1] = 1.;
368 p[0+1] = y1*dydx2;
369 p[0+2] = z1*dydx2;
370 p[9+0] = dydx2;
371 value = y2;
372 fitter->AddPoint(p,value,sy);
373
374 // x2 = 1 *x1 +-a01*y1 + 0 + a03
375 // z2 = a20*x1 + a21*y1 + 1 *z1 + a23
376 // z2' = a20*x1 + a21*y1 + a22*z1 + a23 + (a01*y1 + a02*z1 +a03)*dzdx2;
377 for (Int_t i=0; i<12;i++) p[i]=0.;
378 p[6+0] = x1;
379 p[6+1] = y1;
380 p[6+2] = z1;
381 p[9+2] = 1.;
382 p[0+1] = y1*dzdx2;
383 p[0+2] = z1*dzdx2;
384 p[9+0] = dzdx2;
385 value = z2;
386 fitter->AddPoint(p,value,sz);
387
388 // dydx2 = (a10 + a11*dydx1 + a12*dzdx1)/( a00 + a01*dydx1 + a02*dzdx1)
389 // (a10 + a11*dydx1 + a12*dzdx1) - (a00 + a01*dydx1 + a02*dzdx1)*dydx2 = 0
390 for (Int_t i=0; i<12;i++) p[i]=0.;
391 p[3+0] = 1.;
392 p[3+1] = dydx1;
393 p[3+2] = dzdx1;
394 p[0+0] = -dydx2;
395 p[0+1] = -dydx1*dydx2;
396 p[0+2] = -dzdx1*dydx2;
397 value = 0.;
398 fitter->AddPoint(p,value,sdydx);
399
400 // dzdx2 = (a20 + a21*dydx1 + a22*dzdx1)/( a00 + a01*dydx1 + a02*dzdx1)
401 // (a20 + a21*dydx1 + a22*dzdx1) - (a00 + a01*dydx1 + a02*dzdx1)*dzdx2 = 0
402 for (Int_t i=0; i<12;i++) p[i]=0.;
403 p[6+0] = 1;
404 p[6+1] = dydx1;
405 p[6+2] = dzdx1;
406 p[0+0] = -dzdx2;
407 p[0+1] = -dydx1*dzdx2;
408 p[0+2] = -dzdx1*dzdx2;
409 value = 0.;
410 fitter->AddPoint(p,value,sdzdx);
411}
412
413void AliTPCcalibAlign::Eval() {
414 TLinearFitter *f;
415 for (Int_t s1=0;s1<72;++s1)
416 for (Int_t s2=0;s2<72;++s2)
417 if ((f=GetFitter12(s1,s2))&&fPoints[72*s1+s2]>12) {
418 // cerr<<s1<<","<<s2<<": "<<fPoints[72*s1+s2]<<endl;
419 if (!f->Eval()) {
420 cerr<<"Evaluation failed for "<<s1<<","<<s2<<endl;
421 }
422 }
423 /*
424
425 fitter->Eval();
426 fitter->Eval();
427 chi212 = align->GetChisquare()/(4.*entries);
428
429 TMatrixD mat(13,13);
430 TVectorD par(13);
431 align->GetParameters(par);
432 align->GetCovarianceMatrix(mat);
433
434 //
435 //
436 for (Int_t i=0; i<12;i++){
437 palign12(i)= par(i+1);
438 for (Int_t j=0; j<12;j++){
439 pcovar12(i,j) = mat(i+1,j+1);
440 pcovar12(i,j) *= chi212;
441 }
442 }
443 //
444 for (Int_t i=0; i<12;i++){
445 psigma12(i) = TMath::Sqrt(pcovar12(i,i));
446 palignR12(i) = palign12(i)/TMath::Sqrt(pcovar12(i,i));
447 for (Int_t j=0; j<12;j++){
448 pcovarN12(i,j) = pcovar12(i,j)/TMath::Sqrt(pcovar12(i,i)*pcovar12(j,j));
449 }
450 }
451 */
452}
453
454Bool_t AliTPCcalibAlign::GetTransformation12(Int_t s1,Int_t s2,TMatrixD &a) {
455 if (!GetFitter12(s1,s2))
456 return false;
457 else {
458 TVectorD p(12);
459 cerr<<"foo"<<endl;
460 GetFitter12(s1,s2)->GetParameters(p);
461 cerr<<"bar"<<endl;
462 a.ResizeTo(4,4);
463 a[0][0]=p[0];
464 a[0][1]=p[1];
465 a[0][2]=p[2];
466 a[0][3]=p[9];
467 a[1][0]=p[3];
468 a[1][1]=p[4];
469 a[1][2]=p[5];
470 a[1][3]=p[10];
471 a[2][0]=p[6];
472 a[2][1]=p[7];
473 a[2][2]=p[8];
474 a[2][3]=p[11];
475 a[3][0]=0.;
476 a[3][1]=0.;
477 a[3][2]=0.;
478 a[3][3]=1.;
479 return true;
480 }
481}
482
483Bool_t AliTPCcalibAlign::GetTransformation9(Int_t s1,Int_t s2,TMatrixD &a) {
484 if (!GetFitter9(s1,s2))
485 return false;
486 else {
487 TVectorD p(9);
488 GetFitter9(s1,s2)->GetParameters(p);
489 a.ResizeTo(4,4);
490 a[0][0]=p[0];
491 a[0][1]=p[1];
492 a[0][2]=p[2];
493 a[0][3]=p[9];
494 a[1][0]=p[3];
495 a[1][1]=p[4];
496 a[1][2]=p[5];
497 a[1][3]=p[10];
498 a[2][0]=p[6];
499 a[2][1]=p[7];
500 a[2][2]=p[8];
501 a[2][3]=p[11];
502 a[3][0]=0.;
503 a[3][1]=0.;
504 a[3][2]=0.;
505 a[3][3]=1.;
506 return true;
507 }
508}
509
510Bool_t AliTPCcalibAlign::GetTransformation6(Int_t s1,Int_t s2,TMatrixD &a) {
511 if (!GetFitter6(s1,s2))
512 return false;
513 else {
514 TVectorD p(6);
515 cerr<<"foo"<<endl;
516 GetFitter6(s1,s2)->GetParameters(p);
517 cerr<<"bar"<<endl;
518 a.ResizeTo(4,4);
519 a[0][0]=p[0];
520 a[0][1]=p[1];
521 a[0][2]=p[2];
522 a[0][3]=p[9];
523 a[1][0]=p[3];
524 a[1][1]=p[4];
525 a[1][2]=p[5];
526 a[1][3]=p[10];
527 a[2][0]=p[6];
528 a[2][1]=p[7];
529 a[2][2]=p[8];
530 a[2][3]=p[11];
531 a[3][0]=0.;
532 a[3][1]=0.;
533 a[3][2]=0.;
534 a[3][3]=1.;
535 return true;
536 }
537}