1 #include <iostream>
2 #include "precomp.hpp"
3 #include "epnp.h"
4
5 namespace cv
6 {
7
epnp(const Mat & cameraMatrix,const Mat & opoints,const Mat & ipoints)8 epnp::epnp(const Mat& cameraMatrix, const Mat& opoints, const Mat& ipoints)
9 {
10 if (cameraMatrix.depth() == CV_32F)
11 init_camera_parameters<float>(cameraMatrix);
12 else
13 init_camera_parameters<double>(cameraMatrix);
14
15 number_of_correspondences = std::max(opoints.checkVector(3, CV_32F), opoints.checkVector(3, CV_64F));
16
17 pws.resize(3 * number_of_correspondences);
18 us.resize(2 * number_of_correspondences);
19
20 if (opoints.depth() == ipoints.depth())
21 {
22 if (opoints.depth() == CV_32F)
23 init_points<Point3f,Point2f>(opoints, ipoints);
24 else
25 init_points<Point3d,Point2d>(opoints, ipoints);
26 }
27 else if (opoints.depth() == CV_32F)
28 init_points<Point3f,Point2d>(opoints, ipoints);
29 else
30 init_points<Point3d,Point2f>(opoints, ipoints);
31
32 alphas.resize(4 * number_of_correspondences);
33 pcs.resize(3 * number_of_correspondences);
34
35 max_nr = 0;
36 A1 = NULL;
37 A2 = NULL;
38 }
39
~epnp()40 epnp::~epnp()
41 {
42 if (A1)
43 delete[] A1;
44 if (A2)
45 delete[] A2;
46 }
47
choose_control_points(void)48 void epnp::choose_control_points(void)
49 {
50 // Take C0 as the reference points centroid:
51 cws[0][0] = cws[0][1] = cws[0][2] = 0;
52 for(int i = 0; i < number_of_correspondences; i++)
53 for(int j = 0; j < 3; j++)
54 cws[0][j] += pws[3 * i + j];
55
56 for(int j = 0; j < 3; j++)
57 cws[0][j] /= number_of_correspondences;
58
59
60 // Take C1, C2, and C3 from PCA on the reference points:
61 CvMat * PW0 = cvCreateMat(number_of_correspondences, 3, CV_64F);
62
63 double pw0tpw0[3 * 3] = {}, dc[3] = {}, uct[3 * 3] = {};
64 CvMat PW0tPW0 = cvMat(3, 3, CV_64F, pw0tpw0);
65 CvMat DC = cvMat(3, 1, CV_64F, dc);
66 CvMat UCt = cvMat(3, 3, CV_64F, uct);
67
68 for(int i = 0; i < number_of_correspondences; i++)
69 for(int j = 0; j < 3; j++)
70 PW0->data.db[3 * i + j] = pws[3 * i + j] - cws[0][j];
71
72 cvMulTransposed(PW0, &PW0tPW0, 1);
73 cvSVD(&PW0tPW0, &DC, &UCt, 0, CV_SVD_MODIFY_A | CV_SVD_U_T);
74
75 cvReleaseMat(&PW0);
76
77 for(int i = 1; i < 4; i++) {
78 double k = sqrt(dc[i - 1] / number_of_correspondences);
79 for(int j = 0; j < 3; j++)
80 cws[i][j] = cws[0][j] + k * uct[3 * (i - 1) + j];
81 }
82 }
83
compute_barycentric_coordinates(void)84 void epnp::compute_barycentric_coordinates(void)
85 {
86 double cc[3 * 3] = {}, cc_inv[3 * 3] = {};
87 CvMat CC = cvMat(3, 3, CV_64F, cc);
88 CvMat CC_inv = cvMat(3, 3, CV_64F, cc_inv);
89
90 for(int i = 0; i < 3; i++)
91 for(int j = 1; j < 4; j++)
92 cc[3 * i + j - 1] = cws[j][i] - cws[0][i];
93
94 cvInvert(&CC, &CC_inv, CV_SVD);
95 double * ci = cc_inv;
96 for(int i = 0; i < number_of_correspondences; i++) {
97 double * pi = &pws[0] + 3 * i;
98 double * a = &alphas[0] + 4 * i;
99
100 for(int j = 0; j < 3; j++)
101 {
102 a[1 + j] =
103 ci[3 * j ] * (pi[0] - cws[0][0]) +
104 ci[3 * j + 1] * (pi[1] - cws[0][1]) +
105 ci[3 * j + 2] * (pi[2] - cws[0][2]);
106 }
107 a[0] = 1.0f - a[1] - a[2] - a[3];
108 }
109 }
110
fill_M(CvMat * M,const int row,const double * as,const double u,const double v)111 void epnp::fill_M(CvMat * M,
112 const int row, const double * as, const double u, const double v)
113 {
114 double * M1 = M->data.db + row * 12;
115 double * M2 = M1 + 12;
116
117 for(int i = 0; i < 4; i++) {
118 M1[3 * i ] = as[i] * fu;
119 M1[3 * i + 1] = 0.0;
120 M1[3 * i + 2] = as[i] * (uc - u);
121
122 M2[3 * i ] = 0.0;
123 M2[3 * i + 1] = as[i] * fv;
124 M2[3 * i + 2] = as[i] * (vc - v);
125 }
126 }
127
compute_ccs(const double * betas,const double * ut)128 void epnp::compute_ccs(const double * betas, const double * ut)
129 {
130 for(int i = 0; i < 4; i++)
131 ccs[i][0] = ccs[i][1] = ccs[i][2] = 0.0f;
132
133 for(int i = 0; i < 4; i++) {
134 const double * v = ut + 12 * (11 - i);
135 for(int j = 0; j < 4; j++)
136 for(int k = 0; k < 3; k++)
137 ccs[j][k] += betas[i] * v[3 * j + k];
138 }
139 }
140
compute_pcs(void)141 void epnp::compute_pcs(void)
142 {
143 for(int i = 0; i < number_of_correspondences; i++) {
144 double * a = &alphas[0] + 4 * i;
145 double * pc = &pcs[0] + 3 * i;
146
147 for(int j = 0; j < 3; j++)
148 pc[j] = a[0] * ccs[0][j] + a[1] * ccs[1][j] + a[2] * ccs[2][j] + a[3] * ccs[3][j];
149 }
150 }
151
compute_pose(Mat & R,Mat & t)152 void epnp::compute_pose(Mat& R, Mat& t)
153 {
154 choose_control_points();
155 compute_barycentric_coordinates();
156
157 CvMat * M = cvCreateMat(2 * number_of_correspondences, 12, CV_64F);
158
159 for(int i = 0; i < number_of_correspondences; i++)
160 fill_M(M, 2 * i, &alphas[0] + 4 * i, us[2 * i], us[2 * i + 1]);
161
162 double mtm[12 * 12] = {}, d[12] = {}, ut[12 * 12] = {};
163 CvMat MtM = cvMat(12, 12, CV_64F, mtm);
164 CvMat D = cvMat(12, 1, CV_64F, d);
165 CvMat Ut = cvMat(12, 12, CV_64F, ut);
166
167 cvMulTransposed(M, &MtM, 1);
168 cvSVD(&MtM, &D, &Ut, 0, CV_SVD_MODIFY_A | CV_SVD_U_T);
169 cvReleaseMat(&M);
170
171 double l_6x10[6 * 10] = {}, rho[6] = {};
172 CvMat L_6x10 = cvMat(6, 10, CV_64F, l_6x10);
173 CvMat Rho = cvMat(6, 1, CV_64F, rho);
174
175 compute_L_6x10(ut, l_6x10);
176 compute_rho(rho);
177
178 double Betas[4][4] = {}, rep_errors[4] = {};
179 double Rs[4][3][3] = {}, ts[4][3] = {};
180
181 find_betas_approx_1(&L_6x10, &Rho, Betas[1]);
182 gauss_newton(&L_6x10, &Rho, Betas[1]);
183 rep_errors[1] = compute_R_and_t(ut, Betas[1], Rs[1], ts[1]);
184
185 find_betas_approx_2(&L_6x10, &Rho, Betas[2]);
186 gauss_newton(&L_6x10, &Rho, Betas[2]);
187 rep_errors[2] = compute_R_and_t(ut, Betas[2], Rs[2], ts[2]);
188
189 find_betas_approx_3(&L_6x10, &Rho, Betas[3]);
190 gauss_newton(&L_6x10, &Rho, Betas[3]);
191 rep_errors[3] = compute_R_and_t(ut, Betas[3], Rs[3], ts[3]);
192
193 int N = 1;
194 if (rep_errors[2] < rep_errors[1]) N = 2;
195 if (rep_errors[3] < rep_errors[N]) N = 3;
196
197 Mat(3, 1, CV_64F, ts[N]).copyTo(t);
198 Mat(3, 3, CV_64F, Rs[N]).copyTo(R);
199 }
200
copy_R_and_t(const double R_src[3][3],const double t_src[3],double R_dst[3][3],double t_dst[3])201 void epnp::copy_R_and_t(const double R_src[3][3], const double t_src[3],
202 double R_dst[3][3], double t_dst[3])
203 {
204 for(int i = 0; i < 3; i++) {
205 for(int j = 0; j < 3; j++)
206 R_dst[i][j] = R_src[i][j];
207 t_dst[i] = t_src[i];
208 }
209 }
210
dist2(const double * p1,const double * p2)211 double epnp::dist2(const double * p1, const double * p2)
212 {
213 return
214 (p1[0] - p2[0]) * (p1[0] - p2[0]) +
215 (p1[1] - p2[1]) * (p1[1] - p2[1]) +
216 (p1[2] - p2[2]) * (p1[2] - p2[2]);
217 }
218
dot(const double * v1,const double * v2)219 double epnp::dot(const double * v1, const double * v2)
220 {
221 return v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
222 }
223
estimate_R_and_t(double R[3][3],double t[3])224 void epnp::estimate_R_and_t(double R[3][3], double t[3])
225 {
226 double pc0[3] = {}, pw0[3] = {};
227
228 pc0[0] = pc0[1] = pc0[2] = 0.0;
229 pw0[0] = pw0[1] = pw0[2] = 0.0;
230
231 for(int i = 0; i < number_of_correspondences; i++) {
232 const double * pc = &pcs[3 * i];
233 const double * pw = &pws[3 * i];
234
235 for(int j = 0; j < 3; j++) {
236 pc0[j] += pc[j];
237 pw0[j] += pw[j];
238 }
239 }
240 for(int j = 0; j < 3; j++) {
241 pc0[j] /= number_of_correspondences;
242 pw0[j] /= number_of_correspondences;
243 }
244
245 double abt[3 * 3] = {}, abt_d[3] = {}, abt_u[3 * 3] = {}, abt_v[3 * 3] = {};
246 CvMat ABt = cvMat(3, 3, CV_64F, abt);
247 CvMat ABt_D = cvMat(3, 1, CV_64F, abt_d);
248 CvMat ABt_U = cvMat(3, 3, CV_64F, abt_u);
249 CvMat ABt_V = cvMat(3, 3, CV_64F, abt_v);
250
251 cvSetZero(&ABt);
252 for(int i = 0; i < number_of_correspondences; i++) {
253 double * pc = &pcs[3 * i];
254 double * pw = &pws[3 * i];
255
256 for(int j = 0; j < 3; j++) {
257 abt[3 * j ] += (pc[j] - pc0[j]) * (pw[0] - pw0[0]);
258 abt[3 * j + 1] += (pc[j] - pc0[j]) * (pw[1] - pw0[1]);
259 abt[3 * j + 2] += (pc[j] - pc0[j]) * (pw[2] - pw0[2]);
260 }
261 }
262
263 cvSVD(&ABt, &ABt_D, &ABt_U, &ABt_V, CV_SVD_MODIFY_A);
264
265 for(int i = 0; i < 3; i++)
266 for(int j = 0; j < 3; j++)
267 R[i][j] = dot(abt_u + 3 * i, abt_v + 3 * j);
268
269 const double det =
270 R[0][0] * R[1][1] * R[2][2] + R[0][1] * R[1][2] * R[2][0] + R[0][2] * R[1][0] * R[2][1] -
271 R[0][2] * R[1][1] * R[2][0] - R[0][1] * R[1][0] * R[2][2] - R[0][0] * R[1][2] * R[2][1];
272
273 if (det < 0) {
274 R[2][0] = -R[2][0];
275 R[2][1] = -R[2][1];
276 R[2][2] = -R[2][2];
277 }
278
279 t[0] = pc0[0] - dot(R[0], pw0);
280 t[1] = pc0[1] - dot(R[1], pw0);
281 t[2] = pc0[2] - dot(R[2], pw0);
282 }
283
solve_for_sign(void)284 void epnp::solve_for_sign(void)
285 {
286 if (pcs[2] < 0.0) {
287 for(int i = 0; i < 4; i++)
288 for(int j = 0; j < 3; j++)
289 ccs[i][j] = -ccs[i][j];
290
291 for(int i = 0; i < number_of_correspondences; i++) {
292 pcs[3 * i ] = -pcs[3 * i];
293 pcs[3 * i + 1] = -pcs[3 * i + 1];
294 pcs[3 * i + 2] = -pcs[3 * i + 2];
295 }
296 }
297 }
298
compute_R_and_t(const double * ut,const double * betas,double R[3][3],double t[3])299 double epnp::compute_R_and_t(const double * ut, const double * betas,
300 double R[3][3], double t[3])
301 {
302 compute_ccs(betas, ut);
303 compute_pcs();
304
305 solve_for_sign();
306
307 estimate_R_and_t(R, t);
308
309 return reprojection_error(R, t);
310 }
311
reprojection_error(const double R[3][3],const double t[3])312 double epnp::reprojection_error(const double R[3][3], const double t[3])
313 {
314 double sum2 = 0.0;
315
316 for(int i = 0; i < number_of_correspondences; i++) {
317 double * pw = &pws[3 * i];
318 double Xc = dot(R[0], pw) + t[0];
319 double Yc = dot(R[1], pw) + t[1];
320 double inv_Zc = 1.0 / (dot(R[2], pw) + t[2]);
321 double ue = uc + fu * Xc * inv_Zc;
322 double ve = vc + fv * Yc * inv_Zc;
323 double u = us[2 * i], v = us[2 * i + 1];
324
325 sum2 += sqrt( (u - ue) * (u - ue) + (v - ve) * (v - ve) );
326 }
327
328 return sum2 / number_of_correspondences;
329 }
330
331 // betas10 = [B11 B12 B22 B13 B23 B33 B14 B24 B34 B44]
332 // betas_approx_1 = [B11 B12 B13 B14]
333
find_betas_approx_1(const CvMat * L_6x10,const CvMat * Rho,double * betas)334 void epnp::find_betas_approx_1(const CvMat * L_6x10, const CvMat * Rho,
335 double * betas)
336 {
337 double l_6x4[6 * 4] = {}, b4[4] = {};
338 CvMat L_6x4 = cvMat(6, 4, CV_64F, l_6x4);
339 CvMat B4 = cvMat(4, 1, CV_64F, b4);
340
341 for(int i = 0; i < 6; i++) {
342 cvmSet(&L_6x4, i, 0, cvmGet(L_6x10, i, 0));
343 cvmSet(&L_6x4, i, 1, cvmGet(L_6x10, i, 1));
344 cvmSet(&L_6x4, i, 2, cvmGet(L_6x10, i, 3));
345 cvmSet(&L_6x4, i, 3, cvmGet(L_6x10, i, 6));
346 }
347
348 cvSolve(&L_6x4, Rho, &B4, CV_SVD);
349
350 if (b4[0] < 0) {
351 betas[0] = sqrt(-b4[0]);
352 betas[1] = -b4[1] / betas[0];
353 betas[2] = -b4[2] / betas[0];
354 betas[3] = -b4[3] / betas[0];
355 } else {
356 betas[0] = sqrt(b4[0]);
357 betas[1] = b4[1] / betas[0];
358 betas[2] = b4[2] / betas[0];
359 betas[3] = b4[3] / betas[0];
360 }
361 }
362
363 // betas10 = [B11 B12 B22 B13 B23 B33 B14 B24 B34 B44]
364 // betas_approx_2 = [B11 B12 B22 ]
365
find_betas_approx_2(const CvMat * L_6x10,const CvMat * Rho,double * betas)366 void epnp::find_betas_approx_2(const CvMat * L_6x10, const CvMat * Rho,
367 double * betas)
368 {
369 double l_6x3[6 * 3] = {}, b3[3] = {};
370 CvMat L_6x3 = cvMat(6, 3, CV_64F, l_6x3);
371 CvMat B3 = cvMat(3, 1, CV_64F, b3);
372
373 for(int i = 0; i < 6; i++) {
374 cvmSet(&L_6x3, i, 0, cvmGet(L_6x10, i, 0));
375 cvmSet(&L_6x3, i, 1, cvmGet(L_6x10, i, 1));
376 cvmSet(&L_6x3, i, 2, cvmGet(L_6x10, i, 2));
377 }
378
379 cvSolve(&L_6x3, Rho, &B3, CV_SVD);
380
381 if (b3[0] < 0) {
382 betas[0] = sqrt(-b3[0]);
383 betas[1] = (b3[2] < 0) ? sqrt(-b3[2]) : 0.0;
384 } else {
385 betas[0] = sqrt(b3[0]);
386 betas[1] = (b3[2] > 0) ? sqrt(b3[2]) : 0.0;
387 }
388
389 if (b3[1] < 0) betas[0] = -betas[0];
390
391 betas[2] = 0.0;
392 betas[3] = 0.0;
393 }
394
395 // betas10 = [B11 B12 B22 B13 B23 B33 B14 B24 B34 B44]
396 // betas_approx_3 = [B11 B12 B22 B13 B23 ]
397
find_betas_approx_3(const CvMat * L_6x10,const CvMat * Rho,double * betas)398 void epnp::find_betas_approx_3(const CvMat * L_6x10, const CvMat * Rho,
399 double * betas)
400 {
401 double l_6x5[6 * 5] = {}, b5[5] = {};
402 CvMat L_6x5 = cvMat(6, 5, CV_64F, l_6x5);
403 CvMat B5 = cvMat(5, 1, CV_64F, b5);
404
405 for(int i = 0; i < 6; i++) {
406 cvmSet(&L_6x5, i, 0, cvmGet(L_6x10, i, 0));
407 cvmSet(&L_6x5, i, 1, cvmGet(L_6x10, i, 1));
408 cvmSet(&L_6x5, i, 2, cvmGet(L_6x10, i, 2));
409 cvmSet(&L_6x5, i, 3, cvmGet(L_6x10, i, 3));
410 cvmSet(&L_6x5, i, 4, cvmGet(L_6x10, i, 4));
411 }
412
413 cvSolve(&L_6x5, Rho, &B5, CV_SVD);
414
415 if (b5[0] < 0) {
416 betas[0] = sqrt(-b5[0]);
417 betas[1] = (b5[2] < 0) ? sqrt(-b5[2]) : 0.0;
418 } else {
419 betas[0] = sqrt(b5[0]);
420 betas[1] = (b5[2] > 0) ? sqrt(b5[2]) : 0.0;
421 }
422 if (b5[1] < 0) betas[0] = -betas[0];
423 betas[2] = b5[3] / betas[0];
424 betas[3] = 0.0;
425 }
426
compute_L_6x10(const double * ut,double * l_6x10)427 void epnp::compute_L_6x10(const double * ut, double * l_6x10)
428 {
429 const double * v[4];
430
431 v[0] = ut + 12 * 11;
432 v[1] = ut + 12 * 10;
433 v[2] = ut + 12 * 9;
434 v[3] = ut + 12 * 8;
435
436 double dv[4][6][3] = {};
437
438 for(int i = 0; i < 4; i++) {
439 int a = 0, b = 1;
440 for(int j = 0; j < 6; j++) {
441 dv[i][j][0] = v[i][3 * a ] - v[i][3 * b];
442 dv[i][j][1] = v[i][3 * a + 1] - v[i][3 * b + 1];
443 dv[i][j][2] = v[i][3 * a + 2] - v[i][3 * b + 2];
444
445 b++;
446 if (b > 3) {
447 a++;
448 b = a + 1;
449 }
450 }
451 }
452
453 for(int i = 0; i < 6; i++) {
454 double * row = l_6x10 + 10 * i;
455
456 row[0] = dot(dv[0][i], dv[0][i]);
457 row[1] = 2.0f * dot(dv[0][i], dv[1][i]);
458 row[2] = dot(dv[1][i], dv[1][i]);
459 row[3] = 2.0f * dot(dv[0][i], dv[2][i]);
460 row[4] = 2.0f * dot(dv[1][i], dv[2][i]);
461 row[5] = dot(dv[2][i], dv[2][i]);
462 row[6] = 2.0f * dot(dv[0][i], dv[3][i]);
463 row[7] = 2.0f * dot(dv[1][i], dv[3][i]);
464 row[8] = 2.0f * dot(dv[2][i], dv[3][i]);
465 row[9] = dot(dv[3][i], dv[3][i]);
466 }
467 }
468
compute_rho(double * rho)469 void epnp::compute_rho(double * rho)
470 {
471 rho[0] = dist2(cws[0], cws[1]);
472 rho[1] = dist2(cws[0], cws[2]);
473 rho[2] = dist2(cws[0], cws[3]);
474 rho[3] = dist2(cws[1], cws[2]);
475 rho[4] = dist2(cws[1], cws[3]);
476 rho[5] = dist2(cws[2], cws[3]);
477 }
478
compute_A_and_b_gauss_newton(const double * l_6x10,const double * rho,const double betas[4],CvMat * A,CvMat * b)479 void epnp::compute_A_and_b_gauss_newton(const double * l_6x10, const double * rho,
480 const double betas[4], CvMat * A, CvMat * b)
481 {
482 for(int i = 0; i < 6; i++) {
483 const double * rowL = l_6x10 + i * 10;
484 double * rowA = A->data.db + i * 4;
485
486 rowA[0] = 2 * rowL[0] * betas[0] + rowL[1] * betas[1] + rowL[3] * betas[2] + rowL[6] * betas[3];
487 rowA[1] = rowL[1] * betas[0] + 2 * rowL[2] * betas[1] + rowL[4] * betas[2] + rowL[7] * betas[3];
488 rowA[2] = rowL[3] * betas[0] + rowL[4] * betas[1] + 2 * rowL[5] * betas[2] + rowL[8] * betas[3];
489 rowA[3] = rowL[6] * betas[0] + rowL[7] * betas[1] + rowL[8] * betas[2] + 2 * rowL[9] * betas[3];
490
491 cvmSet(b, i, 0, rho[i] -
492 (
493 rowL[0] * betas[0] * betas[0] +
494 rowL[1] * betas[0] * betas[1] +
495 rowL[2] * betas[1] * betas[1] +
496 rowL[3] * betas[0] * betas[2] +
497 rowL[4] * betas[1] * betas[2] +
498 rowL[5] * betas[2] * betas[2] +
499 rowL[6] * betas[0] * betas[3] +
500 rowL[7] * betas[1] * betas[3] +
501 rowL[8] * betas[2] * betas[3] +
502 rowL[9] * betas[3] * betas[3]
503 ));
504 }
505 }
506
gauss_newton(const CvMat * L_6x10,const CvMat * Rho,double betas[4])507 void epnp::gauss_newton(const CvMat * L_6x10, const CvMat * Rho, double betas[4])
508 {
509 const int iterations_number = 5;
510
511 double a[6*4] = {}, b[6] = {}, x[4] = {};
512 CvMat A = cvMat(6, 4, CV_64F, a);
513 CvMat B = cvMat(6, 1, CV_64F, b);
514 CvMat X = cvMat(4, 1, CV_64F, x);
515
516 for(int k = 0; k < iterations_number; k++)
517 {
518 compute_A_and_b_gauss_newton(L_6x10->data.db, Rho->data.db,
519 betas, &A, &B);
520 qr_solve(&A, &B, &X);
521 for(int i = 0; i < 4; i++)
522 betas[i] += x[i];
523 }
524 }
525
qr_solve(CvMat * A,CvMat * b,CvMat * X)526 void epnp::qr_solve(CvMat * A, CvMat * b, CvMat * X)
527 {
528 const int nr = A->rows;
529 const int nc = A->cols;
530 if (nc <= 0 || nr <= 0)
531 return;
532
533 if (max_nr != 0 && max_nr < nr)
534 {
535 delete [] A1;
536 delete [] A2;
537 }
538 if (max_nr < nr)
539 {
540 max_nr = nr;
541 A1 = new double[nr];
542 A2 = new double[nr];
543 }
544
545 double * pA = A->data.db, * ppAkk = pA;
546 for(int k = 0; k < nc; k++)
547 {
548 double * ppAik1 = ppAkk, eta = fabs(*ppAik1);
549 for(int i = k + 1; i < nr; i++)
550 {
551 double elt = fabs(*ppAik1);
552 if (eta < elt) eta = elt;
553 ppAik1 += nc;
554 }
555 if (eta == 0)
556 {
557 A1[k] = A2[k] = 0.0;
558 //cerr << "God damnit, A is singular, this shouldn't happen." << endl;
559 return;
560 }
561 else
562 {
563 double * ppAik2 = ppAkk, sum2 = 0.0, inv_eta = 1. / eta;
564 for(int i = k; i < nr; i++)
565 {
566 *ppAik2 *= inv_eta;
567 sum2 += *ppAik2 * *ppAik2;
568 ppAik2 += nc;
569 }
570 double sigma = sqrt(sum2);
571 if (*ppAkk < 0)
572 sigma = -sigma;
573 *ppAkk += sigma;
574 A1[k] = sigma * *ppAkk;
575 A2[k] = -eta * sigma;
576 for(int j = k + 1; j < nc; j++)
577 {
578 double * ppAik = ppAkk, sum = 0;
579 for(int i = k; i < nr; i++)
580 {
581 sum += *ppAik * ppAik[j - k];
582 ppAik += nc;
583 }
584 double tau = sum / A1[k];
585 ppAik = ppAkk;
586 for(int i = k; i < nr; i++)
587 {
588 ppAik[j - k] -= tau * *ppAik;
589 ppAik += nc;
590 }
591 }
592 }
593 ppAkk += nc + 1;
594 }
595
596 // b <- Qt b
597 double * ppAjj = pA, * pb = b->data.db;
598 for(int j = 0; j < nc; j++)
599 {
600 double * ppAij = ppAjj, tau = 0;
601 for(int i = j; i < nr; i++)
602 {
603 tau += *ppAij * pb[i];
604 ppAij += nc;
605 }
606 tau /= A1[j];
607 ppAij = ppAjj;
608 for(int i = j; i < nr; i++)
609 {
610 pb[i] -= tau * *ppAij;
611 ppAij += nc;
612 }
613 ppAjj += nc + 1;
614 }
615
616 // X = R-1 b
617 double * pX = X->data.db;
618 pX[nc - 1] = pb[nc - 1] / A2[nc - 1];
619 for(int i = nc - 2; i >= 0; i--)
620 {
621 double * ppAij = pA + i * nc + (i + 1), sum = 0;
622
623 for(int j = i + 1; j < nc; j++)
624 {
625 sum += *ppAij * pX[j];
626 ppAij++;
627 }
628 pX[i] = (pb[i] - sum) / A2[i];
629 }
630 }
631
632 }
633