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Reference Guide
TMatrixTCramerInv.cxx
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1// @(#)root/base:$Id$
2// Authors: Fons Rademakers, Eddy Offermann Jan 2004
3
4/*************************************************************************
5 * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. *
6 * All rights reserved. *
7 * *
8 * For the licensing terms see $ROOTSYS/LICENSE. *
9 * For the list of contributors see $ROOTSYS/README/CREDITS. *
10 *************************************************************************/
11
12/** \class TMatrixTCramerInv
13 \ingroup Matrix
14
15TMatrixTCramerInv
16
17Encapsulate templates of Cramer Inversion routines.
18
19The 4x4, 5x5 and 6x6 are adapted from routines written by
20Mark Fischler and Steven Haywood as part of the CLHEP package
21
22Although for sizes <= 6x6 the Cramer Inversion has a gain in speed
23compared to factorization schemes (like LU) , one pays a price in
24accuracy .
25
26For Example:
27~~~
28 H * H^-1 = U, where H is a 5x5 Hilbert matrix
29 U is a 5x5 Unity matrix
30
31 LU : |U_jk| < 10e-13 for j!=k
32 Cramer: |U_jk| < 10e-7 for j!=k
33~~~
34
35however Cramer algorithm is about 10 (!) times faster
36*/
37
38#include "TMatrixTCramerInv.h"
39#include "TError.h"
40
41#if !defined(R__SOLARIS) && !defined(R__ACC) && !defined(R__FBSD)
42NamespaceImp(TMatrixTCramerInv);
43#endif
44
45////////////////////////////////////////////////////////////////////////////////
46
47template<class Element>
48Bool_t TMatrixTCramerInv::Inv2x2(TMatrixT<Element> &m,Double_t *determ)
49{
50 if (m.GetNrows() != 2 || m.GetNcols() != 2 || m.GetRowLwb() != m.GetColLwb()) {
51 Error("Inv2x2","matrix should be square 2x2");
52 return kFALSE;
53 }
54
55 Element *pM = m.GetMatrixArray();
56
57 const Double_t det = pM[0] * pM[3] - pM[2] * pM[1];
58
59 if (determ)
60 *determ = det;
61
62 const Double_t s = 1./det;
63 if ( det == 0 ) {
64 Error("Inv2x2","matrix is singular");
65 return kFALSE;
66 }
67
68 const Double_t tmp = s*pM[3];
69 pM[1] *= -s;
70 pM[2] *= -s;
71 pM[3] = s*pM[0];
72 pM[0] = tmp;
73
74 return kTRUE;
75}
76
77////////////////////////////////////////////////////////////////////////////////
78
79template<class Element>
80Bool_t TMatrixTCramerInv::Inv3x3(TMatrixT<Element> &m,Double_t *determ)
81{
82 if (m.GetNrows() != 3 || m.GetNcols() != 3 || m.GetRowLwb() != m.GetColLwb()) {
83 Error("Inv3x3","matrix should be square 3x3");
84 return kFALSE;
85 }
86
87 Element *pM = m.GetMatrixArray();
88
89 const Double_t c00 = pM[4] * pM[8] - pM[5] * pM[7];
90 const Double_t c01 = pM[5] * pM[6] - pM[3] * pM[8];
91 const Double_t c02 = pM[3] * pM[7] - pM[4] * pM[6];
92 const Double_t c10 = pM[7] * pM[2] - pM[8] * pM[1];
93 const Double_t c11 = pM[8] * pM[0] - pM[6] * pM[2];
94 const Double_t c12 = pM[6] * pM[1] - pM[7] * pM[0];
95 const Double_t c20 = pM[1] * pM[5] - pM[2] * pM[4];
96 const Double_t c21 = pM[2] * pM[3] - pM[0] * pM[5];
97 const Double_t c22 = pM[0] * pM[4] - pM[1] * pM[3];
98
99 const Double_t t0 = TMath::Abs(pM[0]);
100 const Double_t t1 = TMath::Abs(pM[3]);
101 const Double_t t2 = TMath::Abs(pM[6]);
102 Double_t det;
103 Double_t tmp;
104 if (t0 >= t1) {
105 if (t2 >= t0) {
106 tmp = pM[6];
107 det = c12*c01-c11*c02;
108 } else {
109 tmp = pM[0];
110 det = c11*c22-c12*c21;
111 }
112 } else if (t2 >= t1) {
113 tmp = pM[6];
114 det = c12*c01-c11*c02;
115 } else {
116 tmp = pM[3];
117 det = c02*c21-c01*c22;
118 }
119
120 if ( det == 0 || tmp == 0) {
121 Error("Inv3x3","matrix is singular");
122 return kFALSE;
123 }
124
125 const Double_t s = tmp/det;
126 if (determ)
127 *determ = 1./s;
128
129 pM[0] = s*c00;
130 pM[1] = s*c10;
131 pM[2] = s*c20;
132 pM[3] = s*c01;
133 pM[4] = s*c11;
134 pM[5] = s*c21;
135 pM[6] = s*c02;
136 pM[7] = s*c12;
137 pM[8] = s*c22;
138
139 return kTRUE;
140}
141
142// GFij are indices for a 4x4 matrix.
143
144#define GF00 0
145#define GF01 1
146#define GF02 2
147#define GF03 3
148
149#define GF10 4
150#define GF11 5
151#define GF12 6
152#define GF13 7
153
154#define GF20 8
155#define GF21 9
156#define GF22 10
157#define GF23 11
158
159#define GF30 12
160#define GF31 13
161#define GF32 14
162#define GF33 15
163
164////////////////////////////////////////////////////////////////////////////////
165
166template<class Element>
167Bool_t TMatrixTCramerInv::Inv4x4(TMatrixT<Element> &m,Double_t *determ)
168{
169 if (m.GetNrows() != 4 || m.GetNcols() != 4 || m.GetRowLwb() != m.GetColLwb()) {
170 Error("Inv4x4","matrix should be square 4x4");
171 return kFALSE;
172 }
173
174 Element *pM = m.GetMatrixArray();
175
176 // Find all NECESSARY 2x2 dets: (18 of them)
177
178 const Double_t det2_12_01 = pM[GF10]*pM[GF21] - pM[GF11]*pM[GF20];
179 const Double_t det2_12_02 = pM[GF10]*pM[GF22] - pM[GF12]*pM[GF20];
180 const Double_t det2_12_03 = pM[GF10]*pM[GF23] - pM[GF13]*pM[GF20];
181 const Double_t det2_12_13 = pM[GF11]*pM[GF23] - pM[GF13]*pM[GF21];
182 const Double_t det2_12_23 = pM[GF12]*pM[GF23] - pM[GF13]*pM[GF22];
183 const Double_t det2_12_12 = pM[GF11]*pM[GF22] - pM[GF12]*pM[GF21];
184 const Double_t det2_13_01 = pM[GF10]*pM[GF31] - pM[GF11]*pM[GF30];
185 const Double_t det2_13_02 = pM[GF10]*pM[GF32] - pM[GF12]*pM[GF30];
186 const Double_t det2_13_03 = pM[GF10]*pM[GF33] - pM[GF13]*pM[GF30];
187 const Double_t det2_13_12 = pM[GF11]*pM[GF32] - pM[GF12]*pM[GF31];
188 const Double_t det2_13_13 = pM[GF11]*pM[GF33] - pM[GF13]*pM[GF31];
189 const Double_t det2_13_23 = pM[GF12]*pM[GF33] - pM[GF13]*pM[GF32];
190 const Double_t det2_23_01 = pM[GF20]*pM[GF31] - pM[GF21]*pM[GF30];
191 const Double_t det2_23_02 = pM[GF20]*pM[GF32] - pM[GF22]*pM[GF30];
192 const Double_t det2_23_03 = pM[GF20]*pM[GF33] - pM[GF23]*pM[GF30];
193 const Double_t det2_23_12 = pM[GF21]*pM[GF32] - pM[GF22]*pM[GF31];
194 const Double_t det2_23_13 = pM[GF21]*pM[GF33] - pM[GF23]*pM[GF31];
195 const Double_t det2_23_23 = pM[GF22]*pM[GF33] - pM[GF23]*pM[GF32];
196
197 // Find all NECESSARY 3x3 dets: (16 of them)
198
199 const Double_t det3_012_012 = pM[GF00]*det2_12_12 - pM[GF01]*det2_12_02
200 + pM[GF02]*det2_12_01;
201 const Double_t det3_012_013 = pM[GF00]*det2_12_13 - pM[GF01]*det2_12_03
202 + pM[GF03]*det2_12_01;
203 const Double_t det3_012_023 = pM[GF00]*det2_12_23 - pM[GF02]*det2_12_03
204 + pM[GF03]*det2_12_02;
205 const Double_t det3_012_123 = pM[GF01]*det2_12_23 - pM[GF02]*det2_12_13
206 + pM[GF03]*det2_12_12;
207 const Double_t det3_013_012 = pM[GF00]*det2_13_12 - pM[GF01]*det2_13_02
208 + pM[GF02]*det2_13_01;
209 const Double_t det3_013_013 = pM[GF00]*det2_13_13 - pM[GF01]*det2_13_03
210 + pM[GF03]*det2_13_01;
211 const Double_t det3_013_023 = pM[GF00]*det2_13_23 - pM[GF02]*det2_13_03
212 + pM[GF03]*det2_13_02;
213 const Double_t det3_013_123 = pM[GF01]*det2_13_23 - pM[GF02]*det2_13_13
214 + pM[GF03]*det2_13_12;
215 const Double_t det3_023_012 = pM[GF00]*det2_23_12 - pM[GF01]*det2_23_02
216 + pM[GF02]*det2_23_01;
217 const Double_t det3_023_013 = pM[GF00]*det2_23_13 - pM[GF01]*det2_23_03
218 + pM[GF03]*det2_23_01;
219 const Double_t det3_023_023 = pM[GF00]*det2_23_23 - pM[GF02]*det2_23_03
220 + pM[GF03]*det2_23_02;
221 const Double_t det3_023_123 = pM[GF01]*det2_23_23 - pM[GF02]*det2_23_13
222 + pM[GF03]*det2_23_12;
223 const Double_t det3_123_012 = pM[GF10]*det2_23_12 - pM[GF11]*det2_23_02
224 + pM[GF12]*det2_23_01;
225 const Double_t det3_123_013 = pM[GF10]*det2_23_13 - pM[GF11]*det2_23_03
226 + pM[GF13]*det2_23_01;
227 const Double_t det3_123_023 = pM[GF10]*det2_23_23 - pM[GF12]*det2_23_03
228 + pM[GF13]*det2_23_02;
229 const Double_t det3_123_123 = pM[GF11]*det2_23_23 - pM[GF12]*det2_23_13
230 + pM[GF13]*det2_23_12;
231
232 // Find the 4x4 det:
233
234 const Double_t det = pM[GF00]*det3_123_123 - pM[GF01]*det3_123_023
235 + pM[GF02]*det3_123_013 - pM[GF03]*det3_123_012;
236 if (determ)
237 *determ = det;
238
239 if ( det == 0 ) {
240 Error("Inv4x4","matrix is singular");
241 return kFALSE;
242 }
243
244 const Double_t oneOverDet = 1.0/det;
245 const Double_t mn1OverDet = - oneOverDet;
246
247 pM[GF00] = det3_123_123 * oneOverDet;
248 pM[GF01] = det3_023_123 * mn1OverDet;
249 pM[GF02] = det3_013_123 * oneOverDet;
250 pM[GF03] = det3_012_123 * mn1OverDet;
251
252 pM[GF10] = det3_123_023 * mn1OverDet;
253 pM[GF11] = det3_023_023 * oneOverDet;
254 pM[GF12] = det3_013_023 * mn1OverDet;
255 pM[GF13] = det3_012_023 * oneOverDet;
256
257 pM[GF20] = det3_123_013 * oneOverDet;
258 pM[GF21] = det3_023_013 * mn1OverDet;
259 pM[GF22] = det3_013_013 * oneOverDet;
260 pM[GF23] = det3_012_013 * mn1OverDet;
261
262 pM[GF30] = det3_123_012 * mn1OverDet;
263 pM[GF31] = det3_023_012 * oneOverDet;
264 pM[GF32] = det3_013_012 * mn1OverDet;
265 pM[GF33] = det3_012_012 * oneOverDet;
266
267 return kTRUE;
268}
269
270// GMij are indices for a 5x5 matrix.
271
272#define GM00 0
273#define GM01 1
274#define GM02 2
275#define GM03 3
276#define GM04 4
277
278#define GM10 5
279#define GM11 6
280#define GM12 7
281#define GM13 8
282#define GM14 9
283
284#define GM20 10
285#define GM21 11
286#define GM22 12
287#define GM23 13
288#define GM24 14
289
290#define GM30 15
291#define GM31 16
292#define GM32 17
293#define GM33 18
294#define GM34 19
295
296#define GM40 20
297#define GM41 21
298#define GM42 22
299#define GM43 23
300#define GM44 24
301
302////////////////////////////////////////////////////////////////////////////////
303
304template<class Element>
305Bool_t TMatrixTCramerInv::Inv5x5(TMatrixT<Element> &m,Double_t *determ)
306{
307 if (m.GetNrows() != 5 || m.GetNcols() != 5 || m.GetRowLwb() != m.GetColLwb()) {
308 Error("Inv5x5","matrix should be square 5x5");
309 return kFALSE;
310 }
311
312 Element *pM = m.GetMatrixArray();
313
314 // Find all NECESSARY 2x2 dets: (30 of them)
315
316 const Double_t det2_23_01 = pM[GM20]*pM[GM31] - pM[GM21]*pM[GM30];
317 const Double_t det2_23_02 = pM[GM20]*pM[GM32] - pM[GM22]*pM[GM30];
318 const Double_t det2_23_03 = pM[GM20]*pM[GM33] - pM[GM23]*pM[GM30];
319 const Double_t det2_23_04 = pM[GM20]*pM[GM34] - pM[GM24]*pM[GM30];
320 const Double_t det2_23_12 = pM[GM21]*pM[GM32] - pM[GM22]*pM[GM31];
321 const Double_t det2_23_13 = pM[GM21]*pM[GM33] - pM[GM23]*pM[GM31];
322 const Double_t det2_23_14 = pM[GM21]*pM[GM34] - pM[GM24]*pM[GM31];
323 const Double_t det2_23_23 = pM[GM22]*pM[GM33] - pM[GM23]*pM[GM32];
324 const Double_t det2_23_24 = pM[GM22]*pM[GM34] - pM[GM24]*pM[GM32];
325 const Double_t det2_23_34 = pM[GM23]*pM[GM34] - pM[GM24]*pM[GM33];
326 const Double_t det2_24_01 = pM[GM20]*pM[GM41] - pM[GM21]*pM[GM40];
327 const Double_t det2_24_02 = pM[GM20]*pM[GM42] - pM[GM22]*pM[GM40];
328 const Double_t det2_24_03 = pM[GM20]*pM[GM43] - pM[GM23]*pM[GM40];
329 const Double_t det2_24_04 = pM[GM20]*pM[GM44] - pM[GM24]*pM[GM40];
330 const Double_t det2_24_12 = pM[GM21]*pM[GM42] - pM[GM22]*pM[GM41];
331 const Double_t det2_24_13 = pM[GM21]*pM[GM43] - pM[GM23]*pM[GM41];
332 const Double_t det2_24_14 = pM[GM21]*pM[GM44] - pM[GM24]*pM[GM41];
333 const Double_t det2_24_23 = pM[GM22]*pM[GM43] - pM[GM23]*pM[GM42];
334 const Double_t det2_24_24 = pM[GM22]*pM[GM44] - pM[GM24]*pM[GM42];
335 const Double_t det2_24_34 = pM[GM23]*pM[GM44] - pM[GM24]*pM[GM43];
336 const Double_t det2_34_01 = pM[GM30]*pM[GM41] - pM[GM31]*pM[GM40];
337 const Double_t det2_34_02 = pM[GM30]*pM[GM42] - pM[GM32]*pM[GM40];
338 const Double_t det2_34_03 = pM[GM30]*pM[GM43] - pM[GM33]*pM[GM40];
339 const Double_t det2_34_04 = pM[GM30]*pM[GM44] - pM[GM34]*pM[GM40];
340 const Double_t det2_34_12 = pM[GM31]*pM[GM42] - pM[GM32]*pM[GM41];
341 const Double_t det2_34_13 = pM[GM31]*pM[GM43] - pM[GM33]*pM[GM41];
342 const Double_t det2_34_14 = pM[GM31]*pM[GM44] - pM[GM34]*pM[GM41];
343 const Double_t det2_34_23 = pM[GM32]*pM[GM43] - pM[GM33]*pM[GM42];
344 const Double_t det2_34_24 = pM[GM32]*pM[GM44] - pM[GM34]*pM[GM42];
345 const Double_t det2_34_34 = pM[GM33]*pM[GM44] - pM[GM34]*pM[GM43];
346
347 // Find all NECESSARY 3x3 dets: (40 of them)
348
349 const Double_t det3_123_012 = pM[GM10]*det2_23_12 - pM[GM11]*det2_23_02 + pM[GM12]*det2_23_01;
350 const Double_t det3_123_013 = pM[GM10]*det2_23_13 - pM[GM11]*det2_23_03 + pM[GM13]*det2_23_01;
351 const Double_t det3_123_014 = pM[GM10]*det2_23_14 - pM[GM11]*det2_23_04 + pM[GM14]*det2_23_01;
352 const Double_t det3_123_023 = pM[GM10]*det2_23_23 - pM[GM12]*det2_23_03 + pM[GM13]*det2_23_02;
353 const Double_t det3_123_024 = pM[GM10]*det2_23_24 - pM[GM12]*det2_23_04 + pM[GM14]*det2_23_02;
354 const Double_t det3_123_034 = pM[GM10]*det2_23_34 - pM[GM13]*det2_23_04 + pM[GM14]*det2_23_03;
355 const Double_t det3_123_123 = pM[GM11]*det2_23_23 - pM[GM12]*det2_23_13 + pM[GM13]*det2_23_12;
356 const Double_t det3_123_124 = pM[GM11]*det2_23_24 - pM[GM12]*det2_23_14 + pM[GM14]*det2_23_12;
357 const Double_t det3_123_134 = pM[GM11]*det2_23_34 - pM[GM13]*det2_23_14 + pM[GM14]*det2_23_13;
358 const Double_t det3_123_234 = pM[GM12]*det2_23_34 - pM[GM13]*det2_23_24 + pM[GM14]*det2_23_23;
359 const Double_t det3_124_012 = pM[GM10]*det2_24_12 - pM[GM11]*det2_24_02 + pM[GM12]*det2_24_01;
360 const Double_t det3_124_013 = pM[GM10]*det2_24_13 - pM[GM11]*det2_24_03 + pM[GM13]*det2_24_01;
361 const Double_t det3_124_014 = pM[GM10]*det2_24_14 - pM[GM11]*det2_24_04 + pM[GM14]*det2_24_01;
362 const Double_t det3_124_023 = pM[GM10]*det2_24_23 - pM[GM12]*det2_24_03 + pM[GM13]*det2_24_02;
363 const Double_t det3_124_024 = pM[GM10]*det2_24_24 - pM[GM12]*det2_24_04 + pM[GM14]*det2_24_02;
364 const Double_t det3_124_034 = pM[GM10]*det2_24_34 - pM[GM13]*det2_24_04 + pM[GM14]*det2_24_03;
365 const Double_t det3_124_123 = pM[GM11]*det2_24_23 - pM[GM12]*det2_24_13 + pM[GM13]*det2_24_12;
366 const Double_t det3_124_124 = pM[GM11]*det2_24_24 - pM[GM12]*det2_24_14 + pM[GM14]*det2_24_12;
367 const Double_t det3_124_134 = pM[GM11]*det2_24_34 - pM[GM13]*det2_24_14 + pM[GM14]*det2_24_13;
368 const Double_t det3_124_234 = pM[GM12]*det2_24_34 - pM[GM13]*det2_24_24 + pM[GM14]*det2_24_23;
369 const Double_t det3_134_012 = pM[GM10]*det2_34_12 - pM[GM11]*det2_34_02 + pM[GM12]*det2_34_01;
370 const Double_t det3_134_013 = pM[GM10]*det2_34_13 - pM[GM11]*det2_34_03 + pM[GM13]*det2_34_01;
371 const Double_t det3_134_014 = pM[GM10]*det2_34_14 - pM[GM11]*det2_34_04 + pM[GM14]*det2_34_01;
372 const Double_t det3_134_023 = pM[GM10]*det2_34_23 - pM[GM12]*det2_34_03 + pM[GM13]*det2_34_02;
373 const Double_t det3_134_024 = pM[GM10]*det2_34_24 - pM[GM12]*det2_34_04 + pM[GM14]*det2_34_02;
374 const Double_t det3_134_034 = pM[GM10]*det2_34_34 - pM[GM13]*det2_34_04 + pM[GM14]*det2_34_03;
375 const Double_t det3_134_123 = pM[GM11]*det2_34_23 - pM[GM12]*det2_34_13 + pM[GM13]*det2_34_12;
376 const Double_t det3_134_124 = pM[GM11]*det2_34_24 - pM[GM12]*det2_34_14 + pM[GM14]*det2_34_12;
377 const Double_t det3_134_134 = pM[GM11]*det2_34_34 - pM[GM13]*det2_34_14 + pM[GM14]*det2_34_13;
378 const Double_t det3_134_234 = pM[GM12]*det2_34_34 - pM[GM13]*det2_34_24 + pM[GM14]*det2_34_23;
379 const Double_t det3_234_012 = pM[GM20]*det2_34_12 - pM[GM21]*det2_34_02 + pM[GM22]*det2_34_01;
380 const Double_t det3_234_013 = pM[GM20]*det2_34_13 - pM[GM21]*det2_34_03 + pM[GM23]*det2_34_01;
381 const Double_t det3_234_014 = pM[GM20]*det2_34_14 - pM[GM21]*det2_34_04 + pM[GM24]*det2_34_01;
382 const Double_t det3_234_023 = pM[GM20]*det2_34_23 - pM[GM22]*det2_34_03 + pM[GM23]*det2_34_02;
383 const Double_t det3_234_024 = pM[GM20]*det2_34_24 - pM[GM22]*det2_34_04 + pM[GM24]*det2_34_02;
384 const Double_t det3_234_034 = pM[GM20]*det2_34_34 - pM[GM23]*det2_34_04 + pM[GM24]*det2_34_03;
385 const Double_t det3_234_123 = pM[GM21]*det2_34_23 - pM[GM22]*det2_34_13 + pM[GM23]*det2_34_12;
386 const Double_t det3_234_124 = pM[GM21]*det2_34_24 - pM[GM22]*det2_34_14 + pM[GM24]*det2_34_12;
387 const Double_t det3_234_134 = pM[GM21]*det2_34_34 - pM[GM23]*det2_34_14 + pM[GM24]*det2_34_13;
388 const Double_t det3_234_234 = pM[GM22]*det2_34_34 - pM[GM23]*det2_34_24 + pM[GM24]*det2_34_23;
389
390 // Find all NECESSARY 4x4 dets: (25 of them)
391
392 const Double_t det4_0123_0123 = pM[GM00]*det3_123_123 - pM[GM01]*det3_123_023
393 + pM[GM02]*det3_123_013 - pM[GM03]*det3_123_012;
394 const Double_t det4_0123_0124 = pM[GM00]*det3_123_124 - pM[GM01]*det3_123_024
395 + pM[GM02]*det3_123_014 - pM[GM04]*det3_123_012;
396 const Double_t det4_0123_0134 = pM[GM00]*det3_123_134 - pM[GM01]*det3_123_034
397 + pM[GM03]*det3_123_014 - pM[GM04]*det3_123_013;
398 const Double_t det4_0123_0234 = pM[GM00]*det3_123_234 - pM[GM02]*det3_123_034
399 + pM[GM03]*det3_123_024 - pM[GM04]*det3_123_023;
400 const Double_t det4_0123_1234 = pM[GM01]*det3_123_234 - pM[GM02]*det3_123_134
401 + pM[GM03]*det3_123_124 - pM[GM04]*det3_123_123;
402 const Double_t det4_0124_0123 = pM[GM00]*det3_124_123 - pM[GM01]*det3_124_023
403 + pM[GM02]*det3_124_013 - pM[GM03]*det3_124_012;
404 const Double_t det4_0124_0124 = pM[GM00]*det3_124_124 - pM[GM01]*det3_124_024
405 + pM[GM02]*det3_124_014 - pM[GM04]*det3_124_012;
406 const Double_t det4_0124_0134 = pM[GM00]*det3_124_134 - pM[GM01]*det3_124_034
407 + pM[GM03]*det3_124_014 - pM[GM04]*det3_124_013;
408 const Double_t det4_0124_0234 = pM[GM00]*det3_124_234 - pM[GM02]*det3_124_034
409 + pM[GM03]*det3_124_024 - pM[GM04]*det3_124_023;
410 const Double_t det4_0124_1234 = pM[GM01]*det3_124_234 - pM[GM02]*det3_124_134
411 + pM[GM03]*det3_124_124 - pM[GM04]*det3_124_123;
412 const Double_t det4_0134_0123 = pM[GM00]*det3_134_123 - pM[GM01]*det3_134_023
413 + pM[GM02]*det3_134_013 - pM[GM03]*det3_134_012;
414 const Double_t det4_0134_0124 = pM[GM00]*det3_134_124 - pM[GM01]*det3_134_024
415 + pM[GM02]*det3_134_014 - pM[GM04]*det3_134_012;
416 const Double_t det4_0134_0134 = pM[GM00]*det3_134_134 - pM[GM01]*det3_134_034
417 + pM[GM03]*det3_134_014 - pM[GM04]*det3_134_013;
418 const Double_t det4_0134_0234 = pM[GM00]*det3_134_234 - pM[GM02]*det3_134_034
419 + pM[GM03]*det3_134_024 - pM[GM04]*det3_134_023;
420 const Double_t det4_0134_1234 = pM[GM01]*det3_134_234 - pM[GM02]*det3_134_134
421 + pM[GM03]*det3_134_124 - pM[GM04]*det3_134_123;
422 const Double_t det4_0234_0123 = pM[GM00]*det3_234_123 - pM[GM01]*det3_234_023
423 + pM[GM02]*det3_234_013 - pM[GM03]*det3_234_012;
424 const Double_t det4_0234_0124 = pM[GM00]*det3_234_124 - pM[GM01]*det3_234_024
425 + pM[GM02]*det3_234_014 - pM[GM04]*det3_234_012;
426 const Double_t det4_0234_0134 = pM[GM00]*det3_234_134 - pM[GM01]*det3_234_034
427 + pM[GM03]*det3_234_014 - pM[GM04]*det3_234_013;
428 const Double_t det4_0234_0234 = pM[GM00]*det3_234_234 - pM[GM02]*det3_234_034
429 + pM[GM03]*det3_234_024 - pM[GM04]*det3_234_023;
430 const Double_t det4_0234_1234 = pM[GM01]*det3_234_234 - pM[GM02]*det3_234_134
431 + pM[GM03]*det3_234_124 - pM[GM04]*det3_234_123;
432 const Double_t det4_1234_0123 = pM[GM10]*det3_234_123 - pM[GM11]*det3_234_023
433 + pM[GM12]*det3_234_013 - pM[GM13]*det3_234_012;
434 const Double_t det4_1234_0124 = pM[GM10]*det3_234_124 - pM[GM11]*det3_234_024
435 + pM[GM12]*det3_234_014 - pM[GM14]*det3_234_012;
436 const Double_t det4_1234_0134 = pM[GM10]*det3_234_134 - pM[GM11]*det3_234_034
437 + pM[GM13]*det3_234_014 - pM[GM14]*det3_234_013;
438 const Double_t det4_1234_0234 = pM[GM10]*det3_234_234 - pM[GM12]*det3_234_034
439 + pM[GM13]*det3_234_024 - pM[GM14]*det3_234_023;
440 const Double_t det4_1234_1234 = pM[GM11]*det3_234_234 - pM[GM12]*det3_234_134
441 + pM[GM13]*det3_234_124 - pM[GM14]*det3_234_123;
442
443 // Find the 5x5 det:
444
445 const Double_t det = pM[GM00]*det4_1234_1234 - pM[GM01]*det4_1234_0234 + pM[GM02]*det4_1234_0134
446 - pM[GM03]*det4_1234_0124 + pM[GM04]*det4_1234_0123;
447 if (determ)
448 *determ = det;
449
450 if ( det == 0 ) {
451 Error("Inv5x5","matrix is singular");
452 return kFALSE;
453 }
454
455 const Double_t oneOverDet = 1.0/det;
456 const Double_t mn1OverDet = - oneOverDet;
457
458 pM[GM00] = det4_1234_1234 * oneOverDet;
459 pM[GM01] = det4_0234_1234 * mn1OverDet;
460 pM[GM02] = det4_0134_1234 * oneOverDet;
461 pM[GM03] = det4_0124_1234 * mn1OverDet;
462 pM[GM04] = det4_0123_1234 * oneOverDet;
463
464 pM[GM10] = det4_1234_0234 * mn1OverDet;
465 pM[GM11] = det4_0234_0234 * oneOverDet;
466 pM[GM12] = det4_0134_0234 * mn1OverDet;
467 pM[GM13] = det4_0124_0234 * oneOverDet;
468 pM[GM14] = det4_0123_0234 * mn1OverDet;
469
470 pM[GM20] = det4_1234_0134 * oneOverDet;
471 pM[GM21] = det4_0234_0134 * mn1OverDet;
472 pM[GM22] = det4_0134_0134 * oneOverDet;
473 pM[GM23] = det4_0124_0134 * mn1OverDet;
474 pM[GM24] = det4_0123_0134 * oneOverDet;
475
476 pM[GM30] = det4_1234_0124 * mn1OverDet;
477 pM[GM31] = det4_0234_0124 * oneOverDet;
478 pM[GM32] = det4_0134_0124 * mn1OverDet;
479 pM[GM33] = det4_0124_0124 * oneOverDet;
480 pM[GM34] = det4_0123_0124 * mn1OverDet;
481
482 pM[GM40] = det4_1234_0123 * oneOverDet;
483 pM[GM41] = det4_0234_0123 * mn1OverDet;
484 pM[GM42] = det4_0134_0123 * oneOverDet;
485 pM[GM43] = det4_0124_0123 * mn1OverDet;
486 pM[GM44] = det4_0123_0123 * oneOverDet;
487
488 return kTRUE;
489}
490
491// Aij are indices for a 6x6 matrix.
492
493#define GA00 0
494#define GA01 1
495#define GA02 2
496#define GA03 3
497#define GA04 4
498#define GA05 5
499
500#define GA10 6
501#define GA11 7
502#define GA12 8
503#define GA13 9
504#define GA14 10
505#define GA15 11
506
507#define GA20 12
508#define GA21 13
509#define GA22 14
510#define GA23 15
511#define GA24 16
512#define GA25 17
513
514#define GA30 18
515#define GA31 19
516#define GA32 20
517#define GA33 21
518#define GA34 22
519#define GA35 23
520
521#define GA40 24
522#define GA41 25
523#define GA42 26
524#define GA43 27
525#define GA44 28
526#define GA45 29
527
528#define GA50 30
529#define GA51 31
530#define GA52 32
531#define GA53 33
532#define GA54 34
533#define GA55 35
534
535////////////////////////////////////////////////////////////////////////////////
536
537template<class Element>
538Bool_t TMatrixTCramerInv::Inv6x6(TMatrixT<Element> &m,Double_t *determ)
539{
540 if (m.GetNrows() != 6 || m.GetNcols() != 6 || m.GetRowLwb() != m.GetColLwb()) {
541 Error("Inv6x6","matrix should be square 6x6");
542 return kFALSE;
543 }
544
545 Element *pM = m.GetMatrixArray();
546
547 // Find all NECESSGARY 2x2 dets: (45 of them)
548
549 const Double_t det2_34_01 = pM[GA30]*pM[GA41] - pM[GA31]*pM[GA40];
550 const Double_t det2_34_02 = pM[GA30]*pM[GA42] - pM[GA32]*pM[GA40];
551 const Double_t det2_34_03 = pM[GA30]*pM[GA43] - pM[GA33]*pM[GA40];
552 const Double_t det2_34_04 = pM[GA30]*pM[GA44] - pM[GA34]*pM[GA40];
553 const Double_t det2_34_05 = pM[GA30]*pM[GA45] - pM[GA35]*pM[GA40];
554 const Double_t det2_34_12 = pM[GA31]*pM[GA42] - pM[GA32]*pM[GA41];
555 const Double_t det2_34_13 = pM[GA31]*pM[GA43] - pM[GA33]*pM[GA41];
556 const Double_t det2_34_14 = pM[GA31]*pM[GA44] - pM[GA34]*pM[GA41];
557 const Double_t det2_34_15 = pM[GA31]*pM[GA45] - pM[GA35]*pM[GA41];
558 const Double_t det2_34_23 = pM[GA32]*pM[GA43] - pM[GA33]*pM[GA42];
559 const Double_t det2_34_24 = pM[GA32]*pM[GA44] - pM[GA34]*pM[GA42];
560 const Double_t det2_34_25 = pM[GA32]*pM[GA45] - pM[GA35]*pM[GA42];
561 const Double_t det2_34_34 = pM[GA33]*pM[GA44] - pM[GA34]*pM[GA43];
562 const Double_t det2_34_35 = pM[GA33]*pM[GA45] - pM[GA35]*pM[GA43];
563 const Double_t det2_34_45 = pM[GA34]*pM[GA45] - pM[GA35]*pM[GA44];
564 const Double_t det2_35_01 = pM[GA30]*pM[GA51] - pM[GA31]*pM[GA50];
565 const Double_t det2_35_02 = pM[GA30]*pM[GA52] - pM[GA32]*pM[GA50];
566 const Double_t det2_35_03 = pM[GA30]*pM[GA53] - pM[GA33]*pM[GA50];
567 const Double_t det2_35_04 = pM[GA30]*pM[GA54] - pM[GA34]*pM[GA50];
568 const Double_t det2_35_05 = pM[GA30]*pM[GA55] - pM[GA35]*pM[GA50];
569 const Double_t det2_35_12 = pM[GA31]*pM[GA52] - pM[GA32]*pM[GA51];
570 const Double_t det2_35_13 = pM[GA31]*pM[GA53] - pM[GA33]*pM[GA51];
571 const Double_t det2_35_14 = pM[GA31]*pM[GA54] - pM[GA34]*pM[GA51];
572 const Double_t det2_35_15 = pM[GA31]*pM[GA55] - pM[GA35]*pM[GA51];
573 const Double_t det2_35_23 = pM[GA32]*pM[GA53] - pM[GA33]*pM[GA52];
574 const Double_t det2_35_24 = pM[GA32]*pM[GA54] - pM[GA34]*pM[GA52];
575 const Double_t det2_35_25 = pM[GA32]*pM[GA55] - pM[GA35]*pM[GA52];
576 const Double_t det2_35_34 = pM[GA33]*pM[GA54] - pM[GA34]*pM[GA53];
577 const Double_t det2_35_35 = pM[GA33]*pM[GA55] - pM[GA35]*pM[GA53];
578 const Double_t det2_35_45 = pM[GA34]*pM[GA55] - pM[GA35]*pM[GA54];
579 const Double_t det2_45_01 = pM[GA40]*pM[GA51] - pM[GA41]*pM[GA50];
580 const Double_t det2_45_02 = pM[GA40]*pM[GA52] - pM[GA42]*pM[GA50];
581 const Double_t det2_45_03 = pM[GA40]*pM[GA53] - pM[GA43]*pM[GA50];
582 const Double_t det2_45_04 = pM[GA40]*pM[GA54] - pM[GA44]*pM[GA50];
583 const Double_t det2_45_05 = pM[GA40]*pM[GA55] - pM[GA45]*pM[GA50];
584 const Double_t det2_45_12 = pM[GA41]*pM[GA52] - pM[GA42]*pM[GA51];
585 const Double_t det2_45_13 = pM[GA41]*pM[GA53] - pM[GA43]*pM[GA51];
586 const Double_t det2_45_14 = pM[GA41]*pM[GA54] - pM[GA44]*pM[GA51];
587 const Double_t det2_45_15 = pM[GA41]*pM[GA55] - pM[GA45]*pM[GA51];
588 const Double_t det2_45_23 = pM[GA42]*pM[GA53] - pM[GA43]*pM[GA52];
589 const Double_t det2_45_24 = pM[GA42]*pM[GA54] - pM[GA44]*pM[GA52];
590 const Double_t det2_45_25 = pM[GA42]*pM[GA55] - pM[GA45]*pM[GA52];
591 const Double_t det2_45_34 = pM[GA43]*pM[GA54] - pM[GA44]*pM[GA53];
592 const Double_t det2_45_35 = pM[GA43]*pM[GA55] - pM[GA45]*pM[GA53];
593 const Double_t det2_45_45 = pM[GA44]*pM[GA55] - pM[GA45]*pM[GA54];
594
595 // Find all NECESSGARY 3x3 dets: (80 of them)
596
597 const Double_t det3_234_012 = pM[GA20]*det2_34_12 - pM[GA21]*det2_34_02 + pM[GA22]*det2_34_01;
598 const Double_t det3_234_013 = pM[GA20]*det2_34_13 - pM[GA21]*det2_34_03 + pM[GA23]*det2_34_01;
599 const Double_t det3_234_014 = pM[GA20]*det2_34_14 - pM[GA21]*det2_34_04 + pM[GA24]*det2_34_01;
600 const Double_t det3_234_015 = pM[GA20]*det2_34_15 - pM[GA21]*det2_34_05 + pM[GA25]*det2_34_01;
601 const Double_t det3_234_023 = pM[GA20]*det2_34_23 - pM[GA22]*det2_34_03 + pM[GA23]*det2_34_02;
602 const Double_t det3_234_024 = pM[GA20]*det2_34_24 - pM[GA22]*det2_34_04 + pM[GA24]*det2_34_02;
603 const Double_t det3_234_025 = pM[GA20]*det2_34_25 - pM[GA22]*det2_34_05 + pM[GA25]*det2_34_02;
604 const Double_t det3_234_034 = pM[GA20]*det2_34_34 - pM[GA23]*det2_34_04 + pM[GA24]*det2_34_03;
605 const Double_t det3_234_035 = pM[GA20]*det2_34_35 - pM[GA23]*det2_34_05 + pM[GA25]*det2_34_03;
606 const Double_t det3_234_045 = pM[GA20]*det2_34_45 - pM[GA24]*det2_34_05 + pM[GA25]*det2_34_04;
607 const Double_t det3_234_123 = pM[GA21]*det2_34_23 - pM[GA22]*det2_34_13 + pM[GA23]*det2_34_12;
608 const Double_t det3_234_124 = pM[GA21]*det2_34_24 - pM[GA22]*det2_34_14 + pM[GA24]*det2_34_12;
609 const Double_t det3_234_125 = pM[GA21]*det2_34_25 - pM[GA22]*det2_34_15 + pM[GA25]*det2_34_12;
610 const Double_t det3_234_134 = pM[GA21]*det2_34_34 - pM[GA23]*det2_34_14 + pM[GA24]*det2_34_13;
611 const Double_t det3_234_135 = pM[GA21]*det2_34_35 - pM[GA23]*det2_34_15 + pM[GA25]*det2_34_13;
612 const Double_t det3_234_145 = pM[GA21]*det2_34_45 - pM[GA24]*det2_34_15 + pM[GA25]*det2_34_14;
613 const Double_t det3_234_234 = pM[GA22]*det2_34_34 - pM[GA23]*det2_34_24 + pM[GA24]*det2_34_23;
614 const Double_t det3_234_235 = pM[GA22]*det2_34_35 - pM[GA23]*det2_34_25 + pM[GA25]*det2_34_23;
615 const Double_t det3_234_245 = pM[GA22]*det2_34_45 - pM[GA24]*det2_34_25 + pM[GA25]*det2_34_24;
616 const Double_t det3_234_345 = pM[GA23]*det2_34_45 - pM[GA24]*det2_34_35 + pM[GA25]*det2_34_34;
617 const Double_t det3_235_012 = pM[GA20]*det2_35_12 - pM[GA21]*det2_35_02 + pM[GA22]*det2_35_01;
618 const Double_t det3_235_013 = pM[GA20]*det2_35_13 - pM[GA21]*det2_35_03 + pM[GA23]*det2_35_01;
619 const Double_t det3_235_014 = pM[GA20]*det2_35_14 - pM[GA21]*det2_35_04 + pM[GA24]*det2_35_01;
620 const Double_t det3_235_015 = pM[GA20]*det2_35_15 - pM[GA21]*det2_35_05 + pM[GA25]*det2_35_01;
621 const Double_t det3_235_023 = pM[GA20]*det2_35_23 - pM[GA22]*det2_35_03 + pM[GA23]*det2_35_02;
622 const Double_t det3_235_024 = pM[GA20]*det2_35_24 - pM[GA22]*det2_35_04 + pM[GA24]*det2_35_02;
623 const Double_t det3_235_025 = pM[GA20]*det2_35_25 - pM[GA22]*det2_35_05 + pM[GA25]*det2_35_02;
624 const Double_t det3_235_034 = pM[GA20]*det2_35_34 - pM[GA23]*det2_35_04 + pM[GA24]*det2_35_03;
625 const Double_t det3_235_035 = pM[GA20]*det2_35_35 - pM[GA23]*det2_35_05 + pM[GA25]*det2_35_03;
626 const Double_t det3_235_045 = pM[GA20]*det2_35_45 - pM[GA24]*det2_35_05 + pM[GA25]*det2_35_04;
627 const Double_t det3_235_123 = pM[GA21]*det2_35_23 - pM[GA22]*det2_35_13 + pM[GA23]*det2_35_12;
628 const Double_t det3_235_124 = pM[GA21]*det2_35_24 - pM[GA22]*det2_35_14 + pM[GA24]*det2_35_12;
629 const Double_t det3_235_125 = pM[GA21]*det2_35_25 - pM[GA22]*det2_35_15 + pM[GA25]*det2_35_12;
630 const Double_t det3_235_134 = pM[GA21]*det2_35_34 - pM[GA23]*det2_35_14 + pM[GA24]*det2_35_13;
631 const Double_t det3_235_135 = pM[GA21]*det2_35_35 - pM[GA23]*det2_35_15 + pM[GA25]*det2_35_13;
632 const Double_t det3_235_145 = pM[GA21]*det2_35_45 - pM[GA24]*det2_35_15 + pM[GA25]*det2_35_14;
633 const Double_t det3_235_234 = pM[GA22]*det2_35_34 - pM[GA23]*det2_35_24 + pM[GA24]*det2_35_23;
634 const Double_t det3_235_235 = pM[GA22]*det2_35_35 - pM[GA23]*det2_35_25 + pM[GA25]*det2_35_23;
635 const Double_t det3_235_245 = pM[GA22]*det2_35_45 - pM[GA24]*det2_35_25 + pM[GA25]*det2_35_24;
636 const Double_t det3_235_345 = pM[GA23]*det2_35_45 - pM[GA24]*det2_35_35 + pM[GA25]*det2_35_34;
637 const Double_t det3_245_012 = pM[GA20]*det2_45_12 - pM[GA21]*det2_45_02 + pM[GA22]*det2_45_01;
638 const Double_t det3_245_013 = pM[GA20]*det2_45_13 - pM[GA21]*det2_45_03 + pM[GA23]*det2_45_01;
639 const Double_t det3_245_014 = pM[GA20]*det2_45_14 - pM[GA21]*det2_45_04 + pM[GA24]*det2_45_01;
640 const Double_t det3_245_015 = pM[GA20]*det2_45_15 - pM[GA21]*det2_45_05 + pM[GA25]*det2_45_01;
641 const Double_t det3_245_023 = pM[GA20]*det2_45_23 - pM[GA22]*det2_45_03 + pM[GA23]*det2_45_02;
642 const Double_t det3_245_024 = pM[GA20]*det2_45_24 - pM[GA22]*det2_45_04 + pM[GA24]*det2_45_02;
643 const Double_t det3_245_025 = pM[GA20]*det2_45_25 - pM[GA22]*det2_45_05 + pM[GA25]*det2_45_02;
644 const Double_t det3_245_034 = pM[GA20]*det2_45_34 - pM[GA23]*det2_45_04 + pM[GA24]*det2_45_03;
645 const Double_t det3_245_035 = pM[GA20]*det2_45_35 - pM[GA23]*det2_45_05 + pM[GA25]*det2_45_03;
646 const Double_t det3_245_045 = pM[GA20]*det2_45_45 - pM[GA24]*det2_45_05 + pM[GA25]*det2_45_04;
647 const Double_t det3_245_123 = pM[GA21]*det2_45_23 - pM[GA22]*det2_45_13 + pM[GA23]*det2_45_12;
648 const Double_t det3_245_124 = pM[GA21]*det2_45_24 - pM[GA22]*det2_45_14 + pM[GA24]*det2_45_12;
649 const Double_t det3_245_125 = pM[GA21]*det2_45_25 - pM[GA22]*det2_45_15 + pM[GA25]*det2_45_12;
650 const Double_t det3_245_134 = pM[GA21]*det2_45_34 - pM[GA23]*det2_45_14 + pM[GA24]*det2_45_13;
651 const Double_t det3_245_135 = pM[GA21]*det2_45_35 - pM[GA23]*det2_45_15 + pM[GA25]*det2_45_13;
652 const Double_t det3_245_145 = pM[GA21]*det2_45_45 - pM[GA24]*det2_45_15 + pM[GA25]*det2_45_14;
653 const Double_t det3_245_234 = pM[GA22]*det2_45_34 - pM[GA23]*det2_45_24 + pM[GA24]*det2_45_23;
654 const Double_t det3_245_235 = pM[GA22]*det2_45_35 - pM[GA23]*det2_45_25 + pM[GA25]*det2_45_23;
655 const Double_t det3_245_245 = pM[GA22]*det2_45_45 - pM[GA24]*det2_45_25 + pM[GA25]*det2_45_24;
656 const Double_t det3_245_345 = pM[GA23]*det2_45_45 - pM[GA24]*det2_45_35 + pM[GA25]*det2_45_34;
657 const Double_t det3_345_012 = pM[GA30]*det2_45_12 - pM[GA31]*det2_45_02 + pM[GA32]*det2_45_01;
658 const Double_t det3_345_013 = pM[GA30]*det2_45_13 - pM[GA31]*det2_45_03 + pM[GA33]*det2_45_01;
659 const Double_t det3_345_014 = pM[GA30]*det2_45_14 - pM[GA31]*det2_45_04 + pM[GA34]*det2_45_01;
660 const Double_t det3_345_015 = pM[GA30]*det2_45_15 - pM[GA31]*det2_45_05 + pM[GA35]*det2_45_01;
661 const Double_t det3_345_023 = pM[GA30]*det2_45_23 - pM[GA32]*det2_45_03 + pM[GA33]*det2_45_02;
662 const Double_t det3_345_024 = pM[GA30]*det2_45_24 - pM[GA32]*det2_45_04 + pM[GA34]*det2_45_02;
663 const Double_t det3_345_025 = pM[GA30]*det2_45_25 - pM[GA32]*det2_45_05 + pM[GA35]*det2_45_02;
664 const Double_t det3_345_034 = pM[GA30]*det2_45_34 - pM[GA33]*det2_45_04 + pM[GA34]*det2_45_03;
665 const Double_t det3_345_035 = pM[GA30]*det2_45_35 - pM[GA33]*det2_45_05 + pM[GA35]*det2_45_03;
666 const Double_t det3_345_045 = pM[GA30]*det2_45_45 - pM[GA34]*det2_45_05 + pM[GA35]*det2_45_04;
667 const Double_t det3_345_123 = pM[GA31]*det2_45_23 - pM[GA32]*det2_45_13 + pM[GA33]*det2_45_12;
668 const Double_t det3_345_124 = pM[GA31]*det2_45_24 - pM[GA32]*det2_45_14 + pM[GA34]*det2_45_12;
669 const Double_t det3_345_125 = pM[GA31]*det2_45_25 - pM[GA32]*det2_45_15 + pM[GA35]*det2_45_12;
670 const Double_t det3_345_134 = pM[GA31]*det2_45_34 - pM[GA33]*det2_45_14 + pM[GA34]*det2_45_13;
671 const Double_t det3_345_135 = pM[GA31]*det2_45_35 - pM[GA33]*det2_45_15 + pM[GA35]*det2_45_13;
672 const Double_t det3_345_145 = pM[GA31]*det2_45_45 - pM[GA34]*det2_45_15 + pM[GA35]*det2_45_14;
673 const Double_t det3_345_234 = pM[GA32]*det2_45_34 - pM[GA33]*det2_45_24 + pM[GA34]*det2_45_23;
674 const Double_t det3_345_235 = pM[GA32]*det2_45_35 - pM[GA33]*det2_45_25 + pM[GA35]*det2_45_23;
675 const Double_t det3_345_245 = pM[GA32]*det2_45_45 - pM[GA34]*det2_45_25 + pM[GA35]*det2_45_24;
676 const Double_t det3_345_345 = pM[GA33]*det2_45_45 - pM[GA34]*det2_45_35 + pM[GA35]*det2_45_34;
677
678 // Find all NECESSGARY 4x4 dets: (75 of them)
679
680 const Double_t det4_1234_0123 = pM[GA10]*det3_234_123 - pM[GA11]*det3_234_023
681 + pM[GA12]*det3_234_013 - pM[GA13]*det3_234_012;
682 const Double_t det4_1234_0124 = pM[GA10]*det3_234_124 - pM[GA11]*det3_234_024
683 + pM[GA12]*det3_234_014 - pM[GA14]*det3_234_012;
684 const Double_t det4_1234_0125 = pM[GA10]*det3_234_125 - pM[GA11]*det3_234_025
685 + pM[GA12]*det3_234_015 - pM[GA15]*det3_234_012;
686 const Double_t det4_1234_0134 = pM[GA10]*det3_234_134 - pM[GA11]*det3_234_034
687 + pM[GA13]*det3_234_014 - pM[GA14]*det3_234_013;
688 const Double_t det4_1234_0135 = pM[GA10]*det3_234_135 - pM[GA11]*det3_234_035
689 + pM[GA13]*det3_234_015 - pM[GA15]*det3_234_013;
690 const Double_t det4_1234_0145 = pM[GA10]*det3_234_145 - pM[GA11]*det3_234_045
691 + pM[GA14]*det3_234_015 - pM[GA15]*det3_234_014;
692 const Double_t det4_1234_0234 = pM[GA10]*det3_234_234 - pM[GA12]*det3_234_034
693 + pM[GA13]*det3_234_024 - pM[GA14]*det3_234_023;
694 const Double_t det4_1234_0235 = pM[GA10]*det3_234_235 - pM[GA12]*det3_234_035
695 + pM[GA13]*det3_234_025 - pM[GA15]*det3_234_023;
696 const Double_t det4_1234_0245 = pM[GA10]*det3_234_245 - pM[GA12]*det3_234_045
697 + pM[GA14]*det3_234_025 - pM[GA15]*det3_234_024;
698 const Double_t det4_1234_0345 = pM[GA10]*det3_234_345 - pM[GA13]*det3_234_045
699 + pM[GA14]*det3_234_035 - pM[GA15]*det3_234_034;
700 const Double_t det4_1234_1234 = pM[GA11]*det3_234_234 - pM[GA12]*det3_234_134
701 + pM[GA13]*det3_234_124 - pM[GA14]*det3_234_123;
702 const Double_t det4_1234_1235 = pM[GA11]*det3_234_235 - pM[GA12]*det3_234_135
703 + pM[GA13]*det3_234_125 - pM[GA15]*det3_234_123;
704 const Double_t det4_1234_1245 = pM[GA11]*det3_234_245 - pM[GA12]*det3_234_145
705 + pM[GA14]*det3_234_125 - pM[GA15]*det3_234_124;
706 const Double_t det4_1234_1345 = pM[GA11]*det3_234_345 - pM[GA13]*det3_234_145
707 + pM[GA14]*det3_234_135 - pM[GA15]*det3_234_134;
708 const Double_t det4_1234_2345 = pM[GA12]*det3_234_345 - pM[GA13]*det3_234_245
709 + pM[GA14]*det3_234_235 - pM[GA15]*det3_234_234;
710 const Double_t det4_1235_0123 = pM[GA10]*det3_235_123 - pM[GA11]*det3_235_023
711 + pM[GA12]*det3_235_013 - pM[GA13]*det3_235_012;
712 const Double_t det4_1235_0124 = pM[GA10]*det3_235_124 - pM[GA11]*det3_235_024
713 + pM[GA12]*det3_235_014 - pM[GA14]*det3_235_012;
714 const Double_t det4_1235_0125 = pM[GA10]*det3_235_125 - pM[GA11]*det3_235_025
715 + pM[GA12]*det3_235_015 - pM[GA15]*det3_235_012;
716 const Double_t det4_1235_0134 = pM[GA10]*det3_235_134 - pM[GA11]*det3_235_034
717 + pM[GA13]*det3_235_014 - pM[GA14]*det3_235_013;
718 const Double_t det4_1235_0135 = pM[GA10]*det3_235_135 - pM[GA11]*det3_235_035
719 + pM[GA13]*det3_235_015 - pM[GA15]*det3_235_013;
720 const Double_t det4_1235_0145 = pM[GA10]*det3_235_145 - pM[GA11]*det3_235_045
721 + pM[GA14]*det3_235_015 - pM[GA15]*det3_235_014;
722 const Double_t det4_1235_0234 = pM[GA10]*det3_235_234 - pM[GA12]*det3_235_034
723 + pM[GA13]*det3_235_024 - pM[GA14]*det3_235_023;
724 const Double_t det4_1235_0235 = pM[GA10]*det3_235_235 - pM[GA12]*det3_235_035
725 + pM[GA13]*det3_235_025 - pM[GA15]*det3_235_023;
726 const Double_t det4_1235_0245 = pM[GA10]*det3_235_245 - pM[GA12]*det3_235_045
727 + pM[GA14]*det3_235_025 - pM[GA15]*det3_235_024;
728 const Double_t det4_1235_0345 = pM[GA10]*det3_235_345 - pM[GA13]*det3_235_045
729 + pM[GA14]*det3_235_035 - pM[GA15]*det3_235_034;
730 const Double_t det4_1235_1234 = pM[GA11]*det3_235_234 - pM[GA12]*det3_235_134
731 + pM[GA13]*det3_235_124 - pM[GA14]*det3_235_123;
732 const Double_t det4_1235_1235 = pM[GA11]*det3_235_235 - pM[GA12]*det3_235_135
733 + pM[GA13]*det3_235_125 - pM[GA15]*det3_235_123;
734 const Double_t det4_1235_1245 = pM[GA11]*det3_235_245 - pM[GA12]*det3_235_145
735 + pM[GA14]*det3_235_125 - pM[GA15]*det3_235_124;
736 const Double_t det4_1235_1345 = pM[GA11]*det3_235_345 - pM[GA13]*det3_235_145
737 + pM[GA14]*det3_235_135 - pM[GA15]*det3_235_134;
738 const Double_t det4_1235_2345 = pM[GA12]*det3_235_345 - pM[GA13]*det3_235_245
739 + pM[GA14]*det3_235_235 - pM[GA15]*det3_235_234;
740 const Double_t det4_1245_0123 = pM[GA10]*det3_245_123 - pM[GA11]*det3_245_023
741 + pM[GA12]*det3_245_013 - pM[GA13]*det3_245_012;
742 const Double_t det4_1245_0124 = pM[GA10]*det3_245_124 - pM[GA11]*det3_245_024
743 + pM[GA12]*det3_245_014 - pM[GA14]*det3_245_012;
744 const Double_t det4_1245_0125 = pM[GA10]*det3_245_125 - pM[GA11]*det3_245_025
745 + pM[GA12]*det3_245_015 - pM[GA15]*det3_245_012;
746 const Double_t det4_1245_0134 = pM[GA10]*det3_245_134 - pM[GA11]*det3_245_034
747 + pM[GA13]*det3_245_014 - pM[GA14]*det3_245_013;
748 const Double_t det4_1245_0135 = pM[GA10]*det3_245_135 - pM[GA11]*det3_245_035
749 + pM[GA13]*det3_245_015 - pM[GA15]*det3_245_013;
750 const Double_t det4_1245_0145 = pM[GA10]*det3_245_145 - pM[GA11]*det3_245_045
751 + pM[GA14]*det3_245_015 - pM[GA15]*det3_245_014;
752 const Double_t det4_1245_0234 = pM[GA10]*det3_245_234 - pM[GA12]*det3_245_034
753 + pM[GA13]*det3_245_024 - pM[GA14]*det3_245_023;
754 const Double_t det4_1245_0235 = pM[GA10]*det3_245_235 - pM[GA12]*det3_245_035
755 + pM[GA13]*det3_245_025 - pM[GA15]*det3_245_023;
756 const Double_t det4_1245_0245 = pM[GA10]*det3_245_245 - pM[GA12]*det3_245_045
757 + pM[GA14]*det3_245_025 - pM[GA15]*det3_245_024;
758 const Double_t det4_1245_0345 = pM[GA10]*det3_245_345 - pM[GA13]*det3_245_045
759 + pM[GA14]*det3_245_035 - pM[GA15]*det3_245_034;
760 const Double_t det4_1245_1234 = pM[GA11]*det3_245_234 - pM[GA12]*det3_245_134
761 + pM[GA13]*det3_245_124 - pM[GA14]*det3_245_123;
762 const Double_t det4_1245_1235 = pM[GA11]*det3_245_235 - pM[GA12]*det3_245_135
763 + pM[GA13]*det3_245_125 - pM[GA15]*det3_245_123;
764 const Double_t det4_1245_1245 = pM[GA11]*det3_245_245 - pM[GA12]*det3_245_145
765 + pM[GA14]*det3_245_125 - pM[GA15]*det3_245_124;
766 const Double_t det4_1245_1345 = pM[GA11]*det3_245_345 - pM[GA13]*det3_245_145
767 + pM[GA14]*det3_245_135 - pM[GA15]*det3_245_134;
768 const Double_t det4_1245_2345 = pM[GA12]*det3_245_345 - pM[GA13]*det3_245_245
769 + pM[GA14]*det3_245_235 - pM[GA15]*det3_245_234;
770 const Double_t det4_1345_0123 = pM[GA10]*det3_345_123 - pM[GA11]*det3_345_023
771 + pM[GA12]*det3_345_013 - pM[GA13]*det3_345_012;
772 const Double_t det4_1345_0124 = pM[GA10]*det3_345_124 - pM[GA11]*det3_345_024
773 + pM[GA12]*det3_345_014 - pM[GA14]*det3_345_012;
774 const Double_t det4_1345_0125 = pM[GA10]*det3_345_125 - pM[GA11]*det3_345_025
775 + pM[GA12]*det3_345_015 - pM[GA15]*det3_345_012;
776 const Double_t det4_1345_0134 = pM[GA10]*det3_345_134 - pM[GA11]*det3_345_034
777 + pM[GA13]*det3_345_014 - pM[GA14]*det3_345_013;
778 const Double_t det4_1345_0135 = pM[GA10]*det3_345_135 - pM[GA11]*det3_345_035
779 + pM[GA13]*det3_345_015 - pM[GA15]*det3_345_013;
780 const Double_t det4_1345_0145 = pM[GA10]*det3_345_145 - pM[GA11]*det3_345_045
781 + pM[GA14]*det3_345_015 - pM[GA15]*det3_345_014;
782 const Double_t det4_1345_0234 = pM[GA10]*det3_345_234 - pM[GA12]*det3_345_034
783 + pM[GA13]*det3_345_024 - pM[GA14]*det3_345_023;
784 const Double_t det4_1345_0235 = pM[GA10]*det3_345_235 - pM[GA12]*det3_345_035
785 + pM[GA13]*det3_345_025 - pM[GA15]*det3_345_023;
786 const Double_t det4_1345_0245 = pM[GA10]*det3_345_245 - pM[GA12]*det3_345_045
787 + pM[GA14]*det3_345_025 - pM[GA15]*det3_345_024;
788 const Double_t det4_1345_0345 = pM[GA10]*det3_345_345 - pM[GA13]*det3_345_045
789 + pM[GA14]*det3_345_035 - pM[GA15]*det3_345_034;
790 const Double_t det4_1345_1234 = pM[GA11]*det3_345_234 - pM[GA12]*det3_345_134
791 + pM[GA13]*det3_345_124 - pM[GA14]*det3_345_123;
792 const Double_t det4_1345_1235 = pM[GA11]*det3_345_235 - pM[GA12]*det3_345_135
793 + pM[GA13]*det3_345_125 - pM[GA15]*det3_345_123;
794 const Double_t det4_1345_1245 = pM[GA11]*det3_345_245 - pM[GA12]*det3_345_145
795 + pM[GA14]*det3_345_125 - pM[GA15]*det3_345_124;
796 const Double_t det4_1345_1345 = pM[GA11]*det3_345_345 - pM[GA13]*det3_345_145
797 + pM[GA14]*det3_345_135 - pM[GA15]*det3_345_134;
798 const Double_t det4_1345_2345 = pM[GA12]*det3_345_345 - pM[GA13]*det3_345_245
799 + pM[GA14]*det3_345_235 - pM[GA15]*det3_345_234;
800 const Double_t det4_2345_0123 = pM[GA20]*det3_345_123 - pM[GA21]*det3_345_023
801 + pM[GA22]*det3_345_013 - pM[GA23]*det3_345_012;
802 const Double_t det4_2345_0124 = pM[GA20]*det3_345_124 - pM[GA21]*det3_345_024
803 + pM[GA22]*det3_345_014 - pM[GA24]*det3_345_012;
804 const Double_t det4_2345_0125 = pM[GA20]*det3_345_125 - pM[GA21]*det3_345_025
805 + pM[GA22]*det3_345_015 - pM[GA25]*det3_345_012;
806 const Double_t det4_2345_0134 = pM[GA20]*det3_345_134 - pM[GA21]*det3_345_034
807 + pM[GA23]*det3_345_014 - pM[GA24]*det3_345_013;
808 const Double_t det4_2345_0135 = pM[GA20]*det3_345_135 - pM[GA21]*det3_345_035
809 + pM[GA23]*det3_345_015 - pM[GA25]*det3_345_013;
810 const Double_t det4_2345_0145 = pM[GA20]*det3_345_145 - pM[GA21]*det3_345_045
811 + pM[GA24]*det3_345_015 - pM[GA25]*det3_345_014;
812 const Double_t det4_2345_0234 = pM[GA20]*det3_345_234 - pM[GA22]*det3_345_034
813 + pM[GA23]*det3_345_024 - pM[GA24]*det3_345_023;
814 const Double_t det4_2345_0235 = pM[GA20]*det3_345_235 - pM[GA22]*det3_345_035
815 + pM[GA23]*det3_345_025 - pM[GA25]*det3_345_023;
816 const Double_t det4_2345_0245 = pM[GA20]*det3_345_245 - pM[GA22]*det3_345_045
817 + pM[GA24]*det3_345_025 - pM[GA25]*det3_345_024;
818 const Double_t det4_2345_0345 = pM[GA20]*det3_345_345 - pM[GA23]*det3_345_045
819 + pM[GA24]*det3_345_035 - pM[GA25]*det3_345_034;
820 const Double_t det4_2345_1234 = pM[GA21]*det3_345_234 - pM[GA22]*det3_345_134
821 + pM[GA23]*det3_345_124 - pM[GA24]*det3_345_123;
822 const Double_t det4_2345_1235 = pM[GA21]*det3_345_235 - pM[GA22]*det3_345_135
823 + pM[GA23]*det3_345_125 - pM[GA25]*det3_345_123;
824 const Double_t det4_2345_1245 = pM[GA21]*det3_345_245 - pM[GA22]*det3_345_145
825 + pM[GA24]*det3_345_125 - pM[GA25]*det3_345_124;
826 const Double_t det4_2345_1345 = pM[GA21]*det3_345_345 - pM[GA23]*det3_345_145
827 + pM[GA24]*det3_345_135 - pM[GA25]*det3_345_134;
828 const Double_t det4_2345_2345 = pM[GA22]*det3_345_345 - pM[GA23]*det3_345_245
829 + pM[GA24]*det3_345_235 - pM[GA25]*det3_345_234;
830
831 // Find all NECESSGARY 5x5 dets: (36 of them)
832
833 const Double_t det5_01234_01234 = pM[GA00]*det4_1234_1234 - pM[GA01]*det4_1234_0234
834 + pM[GA02]*det4_1234_0134 - pM[GA03]*det4_1234_0124 + pM[GA04]*det4_1234_0123;
835 const Double_t det5_01234_01235 = pM[GA00]*det4_1234_1235 - pM[GA01]*det4_1234_0235
836 + pM[GA02]*det4_1234_0135 - pM[GA03]*det4_1234_0125 + pM[GA05]*det4_1234_0123;
837 const Double_t det5_01234_01245 = pM[GA00]*det4_1234_1245 - pM[GA01]*det4_1234_0245
838 + pM[GA02]*det4_1234_0145 - pM[GA04]*det4_1234_0125 + pM[GA05]*det4_1234_0124;
839 const Double_t det5_01234_01345 = pM[GA00]*det4_1234_1345 - pM[GA01]*det4_1234_0345
840 + pM[GA03]*det4_1234_0145 - pM[GA04]*det4_1234_0135 + pM[GA05]*det4_1234_0134;
841 const Double_t det5_01234_02345 = pM[GA00]*det4_1234_2345 - pM[GA02]*det4_1234_0345
842 + pM[GA03]*det4_1234_0245 - pM[GA04]*det4_1234_0235 + pM[GA05]*det4_1234_0234;
843 const Double_t det5_01234_12345 = pM[GA01]*det4_1234_2345 - pM[GA02]*det4_1234_1345
844 + pM[GA03]*det4_1234_1245 - pM[GA04]*det4_1234_1235 + pM[GA05]*det4_1234_1234;
845 const Double_t det5_01235_01234 = pM[GA00]*det4_1235_1234 - pM[GA01]*det4_1235_0234
846 + pM[GA02]*det4_1235_0134 - pM[GA03]*det4_1235_0124 + pM[GA04]*det4_1235_0123;
847 const Double_t det5_01235_01235 = pM[GA00]*det4_1235_1235 - pM[GA01]*det4_1235_0235
848 + pM[GA02]*det4_1235_0135 - pM[GA03]*det4_1235_0125 + pM[GA05]*det4_1235_0123;
849 const Double_t det5_01235_01245 = pM[GA00]*det4_1235_1245 - pM[GA01]*det4_1235_0245
850 + pM[GA02]*det4_1235_0145 - pM[GA04]*det4_1235_0125 + pM[GA05]*det4_1235_0124;
851 const Double_t det5_01235_01345 = pM[GA00]*det4_1235_1345 - pM[GA01]*det4_1235_0345
852 + pM[GA03]*det4_1235_0145 - pM[GA04]*det4_1235_0135 + pM[GA05]*det4_1235_0134;
853 const Double_t det5_01235_02345 = pM[GA00]*det4_1235_2345 - pM[GA02]*det4_1235_0345
854 + pM[GA03]*det4_1235_0245 - pM[GA04]*det4_1235_0235 + pM[GA05]*det4_1235_0234;
855 const Double_t det5_01235_12345 = pM[GA01]*det4_1235_2345 - pM[GA02]*det4_1235_1345
856 + pM[GA03]*det4_1235_1245 - pM[GA04]*det4_1235_1235 + pM[GA05]*det4_1235_1234;
857 const Double_t det5_01245_01234 = pM[GA00]*det4_1245_1234 - pM[GA01]*det4_1245_0234
858 + pM[GA02]*det4_1245_0134 - pM[GA03]*det4_1245_0124 + pM[GA04]*det4_1245_0123;
859 const Double_t det5_01245_01235 = pM[GA00]*det4_1245_1235 - pM[GA01]*det4_1245_0235
860 + pM[GA02]*det4_1245_0135 - pM[GA03]*det4_1245_0125 + pM[GA05]*det4_1245_0123;
861 const Double_t det5_01245_01245 = pM[GA00]*det4_1245_1245 - pM[GA01]*det4_1245_0245
862 + pM[GA02]*det4_1245_0145 - pM[GA04]*det4_1245_0125 + pM[GA05]*det4_1245_0124;
863 const Double_t det5_01245_01345 = pM[GA00]*det4_1245_1345 - pM[GA01]*det4_1245_0345
864 + pM[GA03]*det4_1245_0145 - pM[GA04]*det4_1245_0135 + pM[GA05]*det4_1245_0134;
865 const Double_t det5_01245_02345 = pM[GA00]*det4_1245_2345 - pM[GA02]*det4_1245_0345
866 + pM[GA03]*det4_1245_0245 - pM[GA04]*det4_1245_0235 + pM[GA05]*det4_1245_0234;
867 const Double_t det5_01245_12345 = pM[GA01]*det4_1245_2345 - pM[GA02]*det4_1245_1345
868 + pM[GA03]*det4_1245_1245 - pM[GA04]*det4_1245_1235 + pM[GA05]*det4_1245_1234;
869 const Double_t det5_01345_01234 = pM[GA00]*det4_1345_1234 - pM[GA01]*det4_1345_0234
870 + pM[GA02]*det4_1345_0134 - pM[GA03]*det4_1345_0124 + pM[GA04]*det4_1345_0123;
871 const Double_t det5_01345_01235 = pM[GA00]*det4_1345_1235 - pM[GA01]*det4_1345_0235
872 + pM[GA02]*det4_1345_0135 - pM[GA03]*det4_1345_0125 + pM[GA05]*det4_1345_0123;
873 const Double_t det5_01345_01245 = pM[GA00]*det4_1345_1245 - pM[GA01]*det4_1345_0245
874 + pM[GA02]*det4_1345_0145 - pM[GA04]*det4_1345_0125 + pM[GA05]*det4_1345_0124;
875 const Double_t det5_01345_01345 = pM[GA00]*det4_1345_1345 - pM[GA01]*det4_1345_0345
876 + pM[GA03]*det4_1345_0145 - pM[GA04]*det4_1345_0135 + pM[GA05]*det4_1345_0134;
877 const Double_t det5_01345_02345 = pM[GA00]*det4_1345_2345 - pM[GA02]*det4_1345_0345
878 + pM[GA03]*det4_1345_0245 - pM[GA04]*det4_1345_0235 + pM[GA05]*det4_1345_0234;
879 const Double_t det5_01345_12345 = pM[GA01]*det4_1345_2345 - pM[GA02]*det4_1345_1345
880 + pM[GA03]*det4_1345_1245 - pM[GA04]*det4_1345_1235 + pM[GA05]*det4_1345_1234;
881 const Double_t det5_02345_01234 = pM[GA00]*det4_2345_1234 - pM[GA01]*det4_2345_0234
882 + pM[GA02]*det4_2345_0134 - pM[GA03]*det4_2345_0124 + pM[GA04]*det4_2345_0123;
883 const Double_t det5_02345_01235 = pM[GA00]*det4_2345_1235 - pM[GA01]*det4_2345_0235
884 + pM[GA02]*det4_2345_0135 - pM[GA03]*det4_2345_0125 + pM[GA05]*det4_2345_0123;
885 const Double_t det5_02345_01245 = pM[GA00]*det4_2345_1245 - pM[GA01]*det4_2345_0245
886 + pM[GA02]*det4_2345_0145 - pM[GA04]*det4_2345_0125 + pM[GA05]*det4_2345_0124;
887 const Double_t det5_02345_01345 = pM[GA00]*det4_2345_1345 - pM[GA01]*det4_2345_0345
888 + pM[GA03]*det4_2345_0145 - pM[GA04]*det4_2345_0135 + pM[GA05]*det4_2345_0134;
889 const Double_t det5_02345_02345 = pM[GA00]*det4_2345_2345 - pM[GA02]*det4_2345_0345
890 + pM[GA03]*det4_2345_0245 - pM[GA04]*det4_2345_0235 + pM[GA05]*det4_2345_0234;
891 const Double_t det5_02345_12345 = pM[GA01]*det4_2345_2345 - pM[GA02]*det4_2345_1345
892 + pM[GA03]*det4_2345_1245 - pM[GA04]*det4_2345_1235 + pM[GA05]*det4_2345_1234;
893 const Double_t det5_12345_01234 = pM[GA10]*det4_2345_1234 - pM[GA11]*det4_2345_0234
894 + pM[GA12]*det4_2345_0134 - pM[GA13]*det4_2345_0124 + pM[GA14]*det4_2345_0123;
895 const Double_t det5_12345_01235 = pM[GA10]*det4_2345_1235 - pM[GA11]*det4_2345_0235
896 + pM[GA12]*det4_2345_0135 - pM[GA13]*det4_2345_0125 + pM[GA15]*det4_2345_0123;
897 const Double_t det5_12345_01245 = pM[GA10]*det4_2345_1245 - pM[GA11]*det4_2345_0245
898 + pM[GA12]*det4_2345_0145 - pM[GA14]*det4_2345_0125 + pM[GA15]*det4_2345_0124;
899 const Double_t det5_12345_01345 = pM[GA10]*det4_2345_1345 - pM[GA11]*det4_2345_0345
900 + pM[GA13]*det4_2345_0145 - pM[GA14]*det4_2345_0135 + pM[GA15]*det4_2345_0134;
901 const Double_t det5_12345_02345 = pM[GA10]*det4_2345_2345 - pM[GA12]*det4_2345_0345
902 + pM[GA13]*det4_2345_0245 - pM[GA14]*det4_2345_0235 + pM[GA15]*det4_2345_0234;
903 const Double_t det5_12345_12345 = pM[GA11]*det4_2345_2345 - pM[GA12]*det4_2345_1345
904 + pM[GA13]*det4_2345_1245 - pM[GA14]*det4_2345_1235 + pM[GA15]*det4_2345_1234;
905
906 // Find the determinant
907
908 const Double_t det = pM[GA00]*det5_12345_12345 - pM[GA01]*det5_12345_02345 + pM[GA02]*det5_12345_01345
909 - pM[GA03]*det5_12345_01245 + pM[GA04]*det5_12345_01235 - pM[GA05]*det5_12345_01234;
910 if (determ)
911 *determ = det;
912
913 if ( det == 0 ) {
914 Error("Inv6x6","matrix is singular");
915 return kFALSE;
916 }
917
918 const Double_t oneOverDet = 1.0/det;
919 const Double_t mn1OverDet = - oneOverDet;
920
921 pM[GA00] = det5_12345_12345*oneOverDet;
922 pM[GA01] = det5_02345_12345*mn1OverDet;
923 pM[GA02] = det5_01345_12345*oneOverDet;
924 pM[GA03] = det5_01245_12345*mn1OverDet;
925 pM[GA04] = det5_01235_12345*oneOverDet;
926 pM[GA05] = det5_01234_12345*mn1OverDet;
927
928 pM[GA10] = det5_12345_02345*mn1OverDet;
929 pM[GA11] = det5_02345_02345*oneOverDet;
930 pM[GA12] = det5_01345_02345*mn1OverDet;
931 pM[GA13] = det5_01245_02345*oneOverDet;
932 pM[GA14] = det5_01235_02345*mn1OverDet;
933 pM[GA15] = det5_01234_02345*oneOverDet;
934
935 pM[GA20] = det5_12345_01345*oneOverDet;
936 pM[GA21] = det5_02345_01345*mn1OverDet;
937 pM[GA22] = det5_01345_01345*oneOverDet;
938 pM[GA23] = det5_01245_01345*mn1OverDet;
939 pM[GA24] = det5_01235_01345*oneOverDet;
940 pM[GA25] = det5_01234_01345*mn1OverDet;
941
942 pM[GA30] = det5_12345_01245*mn1OverDet;
943 pM[GA31] = det5_02345_01245*oneOverDet;
944 pM[GA32] = det5_01345_01245*mn1OverDet;
945 pM[GA33] = det5_01245_01245*oneOverDet;
946 pM[GA34] = det5_01235_01245*mn1OverDet;
947 pM[GA35] = det5_01234_01245*oneOverDet;
948
949 pM[GA40] = det5_12345_01235*oneOverDet;
950 pM[GA41] = det5_02345_01235*mn1OverDet;
951 pM[GA42] = det5_01345_01235*oneOverDet;
952 pM[GA43] = det5_01245_01235*mn1OverDet;
953 pM[GA44] = det5_01235_01235*oneOverDet;
954 pM[GA45] = det5_01234_01235*mn1OverDet;
955
956 pM[GA50] = det5_12345_01234*mn1OverDet;
957 pM[GA51] = det5_02345_01234*oneOverDet;
958 pM[GA52] = det5_01345_01234*mn1OverDet;
959 pM[GA53] = det5_01245_01234*oneOverDet;
960 pM[GA54] = det5_01235_01234*mn1OverDet;
961 pM[GA55] = det5_01234_01234*oneOverDet;
962
963 return kTRUE;
964}
965
966#include "TMatrixFfwd.h"
967
968template Bool_t TMatrixTCramerInv::Inv2x2<Float_t>(TMatrixF&,Double_t*);
969template Bool_t TMatrixTCramerInv::Inv3x3<Float_t>(TMatrixF&,Double_t*);
970template Bool_t TMatrixTCramerInv::Inv4x4<Float_t>(TMatrixF&,Double_t*);
971template Bool_t TMatrixTCramerInv::Inv5x5<Float_t>(TMatrixF&,Double_t*);
972template Bool_t TMatrixTCramerInv::Inv6x6<Float_t>(TMatrixF&,Double_t*);
973
974#include "TMatrixDfwd.h"
975
976template Bool_t TMatrixTCramerInv::Inv2x2<Double_t>(TMatrixD&,Double_t*);
977template Bool_t TMatrixTCramerInv::Inv3x3<Double_t>(TMatrixD&,Double_t*);
978template Bool_t TMatrixTCramerInv::Inv4x4<Double_t>(TMatrixD&,Double_t*);
979template Bool_t TMatrixTCramerInv::Inv5x5<Double_t>(TMatrixD&,Double_t*);
980template Bool_t TMatrixTCramerInv::Inv6x6<Double_t>(TMatrixD&,Double_t*);
kFALSE
const Bool_t kFALSE
Definition: RtypesCore.h:88
Bool_t
bool Bool_t
Definition: RtypesCore.h:59
Double_t
double Double_t
Definition: RtypesCore.h:55
kTRUE
const Bool_t kTRUE
Definition: RtypesCore.h:87
NamespaceImp
#define NamespaceImp(name)
Definition: Rtypes.h:380
Error
void Error(const char *location, const char *msgfmt,...)
GA22
#define GA22
Definition: TMatrixTCramerInv.cxx:509
GF30
#define GF30
Definition: TMatrixTCramerInv.cxx:159
GM21
#define GM21
Definition: TMatrixTCramerInv.cxx:285
GA15
#define GA15
Definition: TMatrixTCramerInv.cxx:505
GM30
#define GM30
Definition: TMatrixTCramerInv.cxx:290
GA45
#define GA45
Definition: TMatrixTCramerInv.cxx:526
GF13
#define GF13
Definition: TMatrixTCramerInv.cxx:152
GA00
#define GA00
Definition: TMatrixTCramerInv.cxx:493
GA43
#define GA43
Definition: TMatrixTCramerInv.cxx:524
GA25
#define GA25
Definition: TMatrixTCramerInv.cxx:512
GF32
#define GF32
Definition: TMatrixTCramerInv.cxx:161
GM22
#define GM22
Definition: TMatrixTCramerInv.cxx:286
GM14
#define GM14
Definition: TMatrixTCramerInv.cxx:282
GM40
#define GM40
Definition: TMatrixTCramerInv.cxx:296
GA03
#define GA03
Definition: TMatrixTCramerInv.cxx:496
GF10
#define GF10
Definition: TMatrixTCramerInv.cxx:149
GA41
#define GA41
Definition: TMatrixTCramerInv.cxx:522
GM02
#define GM02
Definition: TMatrixTCramerInv.cxx:274
GF22
#define GF22
Definition: TMatrixTCramerInv.cxx:156
GF02
#define GF02
Definition: TMatrixTCramerInv.cxx:146
GA23
#define GA23
Definition: TMatrixTCramerInv.cxx:510
GM42
#define GM42
Definition: TMatrixTCramerInv.cxx:298
GA40
#define GA40
Definition: TMatrixTCramerInv.cxx:521
GF03
#define GF03
Definition: TMatrixTCramerInv.cxx:147
GA05
#define GA05
Definition: TMatrixTCramerInv.cxx:498
GM11
#define GM11
Definition: TMatrixTCramerInv.cxx:279
GA32
#define GA32
Definition: TMatrixTCramerInv.cxx:516
GA34
#define GA34
Definition: TMatrixTCramerInv.cxx:518
GA33
#define GA33
Definition: TMatrixTCramerInv.cxx:517
GA30
#define GA30
Definition: TMatrixTCramerInv.cxx:514
GM31
#define GM31
Definition: TMatrixTCramerInv.cxx:291
GA52
#define GA52
Definition: TMatrixTCramerInv.cxx:530
GM03
#define GM03
Definition: TMatrixTCramerInv.cxx:275
GF21
#define GF21
Definition: TMatrixTCramerInv.cxx:155
GM01
#define GM01
Definition: TMatrixTCramerInv.cxx:273
GA42
#define GA42
Definition: TMatrixTCramerInv.cxx:523
GM33
#define GM33
Definition: TMatrixTCramerInv.cxx:293
GA35
#define GA35
Definition: TMatrixTCramerInv.cxx:519
GA13
#define GA13
Definition: TMatrixTCramerInv.cxx:503
GA21
#define GA21
Definition: TMatrixTCramerInv.cxx:508
GF11
#define GF11
Definition: TMatrixTCramerInv.cxx:150
GM41
#define GM41
Definition: TMatrixTCramerInv.cxx:297
GF23
#define GF23
Definition: TMatrixTCramerInv.cxx:157
GA20
#define GA20
Definition: TMatrixTCramerInv.cxx:507
GM32
#define GM32
Definition: TMatrixTCramerInv.cxx:292
GM10
#define GM10
Definition: TMatrixTCramerInv.cxx:278
GF31
#define GF31
Definition: TMatrixTCramerInv.cxx:160
GM00
#define GM00
Definition: TMatrixTCramerInv.cxx:272
GA12
#define GA12
Definition: TMatrixTCramerInv.cxx:502
GM04
#define GM04
Definition: TMatrixTCramerInv.cxx:276
GF20
#define GF20
Definition: TMatrixTCramerInv.cxx:154
GA55
#define GA55
Definition: TMatrixTCramerInv.cxx:533
GM34
#define GM34
Definition: TMatrixTCramerInv.cxx:294
GM20
#define GM20
Definition: TMatrixTCramerInv.cxx:284
GA02
#define GA02
Definition: TMatrixTCramerInv.cxx:495
GA50
#define GA50
Definition: TMatrixTCramerInv.cxx:528
GA44
#define GA44
Definition: TMatrixTCramerInv.cxx:525
GA51
#define GA51
Definition: TMatrixTCramerInv.cxx:529
GA11
#define GA11
Definition: TMatrixTCramerInv.cxx:501
GM44
#define GM44
Definition: TMatrixTCramerInv.cxx:300
GF01
#define GF01
Definition: TMatrixTCramerInv.cxx:145
GM13
#define GM13
Definition: TMatrixTCramerInv.cxx:281
GF00
#define GF00
Definition: TMatrixTCramerInv.cxx:144
GF33
#define GF33
Definition: TMatrixTCramerInv.cxx:162
GM12
#define GM12
Definition: TMatrixTCramerInv.cxx:280
GA04
#define GA04
Definition: TMatrixTCramerInv.cxx:497
GA54
#define GA54
Definition: TMatrixTCramerInv.cxx:532
GM43
#define GM43
Definition: TMatrixTCramerInv.cxx:299
GA14
#define GA14
Definition: TMatrixTCramerInv.cxx:504
GA10
#define GA10
Definition: TMatrixTCramerInv.cxx:500
GA01
#define GA01
Definition: TMatrixTCramerInv.cxx:494
GM23
#define GM23
Definition: TMatrixTCramerInv.cxx:287
GM24
#define GM24
Definition: TMatrixTCramerInv.cxx:288
GA53
#define GA53
Definition: TMatrixTCramerInv.cxx:531
GA31
#define GA31
Definition: TMatrixTCramerInv.cxx:515
GA24
#define GA24
Definition: TMatrixTCramerInv.cxx:511
GF12
#define GF12
Definition: TMatrixTCramerInv.cxx:151
TMatrixT
TMatrixT.
Definition: TMatrixT.h:39
TGeant4Unit::s
static constexpr double s
Definition: TGeant4SystemOfUnits.h:162
TMath::Abs
Short_t Abs(Short_t d)
Definition: TMathBase.h:120
TMatrixTCramerInv::Inv6x6
Bool_t Inv6x6(TMatrixT< Element > &m, Double_t *determ)
TMatrixTCramerInv::Inv3x3
Bool_t Inv3x3(TMatrixT< Element > &m, Double_t *determ)
TMatrixTCramerInv::Inv4x4
Bool_t Inv4x4(TMatrixT< Element > &m, Double_t *determ)
TMatrixTCramerInv::Inv2x2
Bool_t Inv2x2(TMatrixT< Element > &m, Double_t *determ)
TMatrixTCramerInv::Inv5x5
Bool_t Inv5x5(TMatrixT< Element > &m, Double_t *determ)
m
auto * m
Definition: textangle.C:8
t1
auto * t1
Definition: textangle.C:20