Actual source code: dgefa2.c


  2: /*
  3:      Inverts 2 by 2 matrix using gaussian elimination with partial pivoting.

  5:        Used by the sparse factorization routines in
  6:      src/mat/impls/baij/seq

  8:        This is a combination of the Linpack routines
  9:     dgefa() and dgedi() specialized for a size of 2.

 11: */
 12: #include <petscsys.h>

 14: PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_2(MatScalar *a, PetscReal shift, PetscBool allowzeropivot, PetscBool *zeropivotdetected)
 15: {
 16:   PetscInt   i__2, i__3, kp1, j, k, l, ll, i, ipvt[2], k3;
 17:   PetscInt   k4, j3;
 18:   MatScalar *aa, *ax, *ay, work[4], stmp;
 19:   MatReal    tmp, max;

 21:   if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE;
 22:   shift = .25 * shift * (1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[3]));

 24:   /* Parameter adjustments */
 25:   a -= 3;

 27:   k   = 1;
 28:   kp1 = k + 1;
 29:   k3  = 2 * k;
 30:   k4  = k3 + k;

 32:   /* find l = pivot index */
 33:   i__2 = 3 - k;
 34:   aa   = &a[k4];
 35:   max  = PetscAbsScalar(aa[0]);
 36:   l    = 1;
 37:   for (ll = 1; ll < i__2; ll++) {
 38:     tmp = PetscAbsScalar(aa[ll]);
 39:     if (tmp > max) {
 40:       max = tmp;
 41:       l   = ll + 1;
 42:     }
 43:   }
 44:   l += k - 1;
 45:   ipvt[k - 1] = l;

 47:   if (a[l + k3] == 0.0) {
 48:     if (shift == 0.0) {
 49:       if (allowzeropivot) {
 50:         PetscInfo(NULL, "Zero pivot, row %" PetscInt_FMT "\n", k - 1);
 51:         if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
 52:       } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row %" PetscInt_FMT, k - 1);
 53:     } else {
 54:       a[l + k3] = shift;
 55:     }
 56:   }

 58:   /* interchange if necessary */
 59:   if (l != k) {
 60:     stmp      = a[l + k3];
 61:     a[l + k3] = a[k4];
 62:     a[k4]     = stmp;
 63:   }

 65:   /* compute multipliers */
 66:   stmp = -1. / a[k4];
 67:   i__2 = 2 - k;
 68:   aa   = &a[1 + k4];
 69:   for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;

 71:   /* row elimination with column indexing */
 72:   ax = &a[k4 + 1];
 73:   for (j = kp1; j <= 2; ++j) {
 74:     j3   = 2 * j;
 75:     stmp = a[l + j3];
 76:     if (l != k) {
 77:       a[l + j3] = a[k + j3];
 78:       a[k + j3] = stmp;
 79:     }

 81:     i__3 = 2 - k;
 82:     ay   = &a[1 + k + j3];
 83:     for (ll = 0; ll < i__3; ll++) ay[ll] += stmp * ax[ll];
 84:   }

 86:   ipvt[1] = 2;
 87:   if (a[6] == 0.0) {
 88:     if (PetscLikely(allowzeropivot)) {
 89:       PetscInfo(NULL, "Zero pivot, row 1\n");
 90:       if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
 91:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row 1");
 92:   }

 94:   /* Now form the inverse */
 95:   /* compute inverse(u) */
 96:   for (k = 1; k <= 2; ++k) {
 97:     k3    = 2 * k;
 98:     k4    = k3 + k;
 99:     a[k4] = 1.0 / a[k4];
100:     stmp  = -a[k4];
101:     i__2  = k - 1;
102:     aa    = &a[k3 + 1];
103:     for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;
104:     kp1 = k + 1;
105:     if (2 < kp1) continue;
106:     ax = aa;
107:     for (j = kp1; j <= 2; ++j) {
108:       j3        = 2 * j;
109:       stmp      = a[k + j3];
110:       a[k + j3] = 0.0;
111:       ay        = &a[j3 + 1];
112:       for (ll = 0; ll < k; ll++) ay[ll] += stmp * ax[ll];
113:     }
114:   }

116:   /* form inverse(u)*inverse(l) */
117:   k   = 1;
118:   k3  = 2 * k;
119:   kp1 = k + 1;
120:   aa  = a + k3;
121:   for (i = kp1; i <= 2; ++i) {
122:     work[i - 1] = aa[i];
123:     aa[i]       = 0.0;
124:   }
125:   for (j = kp1; j <= 2; ++j) {
126:     stmp = work[j - 1];
127:     ax   = &a[2 * j + 1];
128:     ay   = &a[k3 + 1];
129:     ay[0] += stmp * ax[0];
130:     ay[1] += stmp * ax[1];
131:   }
132:   l = ipvt[k - 1];
133:   if (l != k) {
134:     ax    = &a[k3 + 1];
135:     ay    = &a[2 * l + 1];
136:     stmp  = ax[0];
137:     ax[0] = ay[0];
138:     ay[0] = stmp;
139:     stmp  = ax[1];
140:     ax[1] = ay[1];
141:     ay[1] = stmp;
142:   }
143:   return 0;
144: }

146: /* gaussian elimination with partial pivoting */
147: PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_9(MatScalar *a, PetscReal shift, PetscBool allowzeropivot, PetscBool *zeropivotdetected)
148: {
149:   PetscInt   i__2, i__3, kp1, j, k, l, ll, i, ipvt[9], kb, k3;
150:   PetscInt   k4, j3;
151:   MatScalar *aa, *ax, *ay, work[81], stmp;
152:   MatReal    tmp, max;

154:   if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE;

156:   /* Parameter adjustments */
157:   a -= 10;

159:   for (k = 1; k <= 8; ++k) {
160:     kp1 = k + 1;
161:     k3  = 9 * k;
162:     k4  = k3 + k;

164:     /* find l = pivot index */
165:     i__2 = 10 - k;
166:     aa   = &a[k4];
167:     max  = PetscAbsScalar(aa[0]);
168:     l    = 1;
169:     for (ll = 1; ll < i__2; ll++) {
170:       tmp = PetscAbsScalar(aa[ll]);
171:       if (tmp > max) {
172:         max = tmp;
173:         l   = ll + 1;
174:       }
175:     }
176:     l += k - 1;
177:     ipvt[k - 1] = l;

179:     if (a[l + k3] == 0.0) {
180:       if (shift == 0.0) {
181:         if (allowzeropivot) {
182:           PetscInfo(NULL, "Zero pivot, row %" PetscInt_FMT "\n", k - 1);
183:           if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
184:         } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row %" PetscInt_FMT, k - 1);
185:       } else {
186:         a[l + k3] = shift;
187:       }
188:     }

190:     /* interchange if necessary */
191:     if (l != k) {
192:       stmp      = a[l + k3];
193:       a[l + k3] = a[k4];
194:       a[k4]     = stmp;
195:     }

197:     /* compute multipliers */
198:     stmp = -1. / a[k4];
199:     i__2 = 9 - k;
200:     aa   = &a[1 + k4];
201:     for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;

203:     /* row elimination with column indexing */
204:     ax = &a[k4 + 1];
205:     for (j = kp1; j <= 9; ++j) {
206:       j3   = 9 * j;
207:       stmp = a[l + j3];
208:       if (l != k) {
209:         a[l + j3] = a[k + j3];
210:         a[k + j3] = stmp;
211:       }

213:       i__3 = 9 - k;
214:       ay   = &a[1 + k + j3];
215:       for (ll = 0; ll < i__3; ll++) ay[ll] += stmp * ax[ll];
216:     }
217:   }
218:   ipvt[8] = 9;
219:   if (a[90] == 0.0) {
220:     if (PetscLikely(allowzeropivot)) {
221:       PetscInfo(NULL, "Zero pivot, row 8\n");
222:       if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
223:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row 8");
224:   }

226:   /* Now form the inverse */
227:   /* compute inverse(u) */
228:   for (k = 1; k <= 9; ++k) {
229:     k3    = 9 * k;
230:     k4    = k3 + k;
231:     a[k4] = 1.0 / a[k4];
232:     stmp  = -a[k4];
233:     i__2  = k - 1;
234:     aa    = &a[k3 + 1];
235:     for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;
236:     kp1 = k + 1;
237:     if (9 < kp1) continue;
238:     ax = aa;
239:     for (j = kp1; j <= 9; ++j) {
240:       j3        = 9 * j;
241:       stmp      = a[k + j3];
242:       a[k + j3] = 0.0;
243:       ay        = &a[j3 + 1];
244:       for (ll = 0; ll < k; ll++) ay[ll] += stmp * ax[ll];
245:     }
246:   }

248:   /* form inverse(u)*inverse(l) */
249:   for (kb = 1; kb <= 8; ++kb) {
250:     k   = 9 - kb;
251:     k3  = 9 * k;
252:     kp1 = k + 1;
253:     aa  = a + k3;
254:     for (i = kp1; i <= 9; ++i) {
255:       work[i - 1] = aa[i];
256:       aa[i]       = 0.0;
257:     }
258:     for (j = kp1; j <= 9; ++j) {
259:       stmp = work[j - 1];
260:       ax   = &a[9 * j + 1];
261:       ay   = &a[k3 + 1];
262:       ay[0] += stmp * ax[0];
263:       ay[1] += stmp * ax[1];
264:       ay[2] += stmp * ax[2];
265:       ay[3] += stmp * ax[3];
266:       ay[4] += stmp * ax[4];
267:       ay[5] += stmp * ax[5];
268:       ay[6] += stmp * ax[6];
269:       ay[7] += stmp * ax[7];
270:       ay[8] += stmp * ax[8];
271:     }
272:     l = ipvt[k - 1];
273:     if (l != k) {
274:       ax    = &a[k3 + 1];
275:       ay    = &a[9 * l + 1];
276:       stmp  = ax[0];
277:       ax[0] = ay[0];
278:       ay[0] = stmp;
279:       stmp  = ax[1];
280:       ax[1] = ay[1];
281:       ay[1] = stmp;
282:       stmp  = ax[2];
283:       ax[2] = ay[2];
284:       ay[2] = stmp;
285:       stmp  = ax[3];
286:       ax[3] = ay[3];
287:       ay[3] = stmp;
288:       stmp  = ax[4];
289:       ax[4] = ay[4];
290:       ay[4] = stmp;
291:       stmp  = ax[5];
292:       ax[5] = ay[5];
293:       ay[5] = stmp;
294:       stmp  = ax[6];
295:       ax[6] = ay[6];
296:       ay[6] = stmp;
297:       stmp  = ax[7];
298:       ax[7] = ay[7];
299:       ay[7] = stmp;
300:       stmp  = ax[8];
301:       ax[8] = ay[8];
302:       ay[8] = stmp;
303:     }
304:   }
305:   return 0;
306: }

308: /*
309:       Inverts 15 by 15 matrix using gaussian elimination with partial pivoting.

311:        Used by the sparse factorization routines in
312:      src/mat/impls/baij/seq

314:        This is a combination of the Linpack routines
315:     dgefa() and dgedi() specialized for a size of 15.

317: */

319: PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_15(MatScalar *a, PetscInt *ipvt, MatScalar *work, PetscReal shift, PetscBool allowzeropivot, PetscBool *zeropivotdetected)
320: {
321:   PetscInt   i__2, i__3, kp1, j, k, l, ll, i, kb, k3;
322:   PetscInt   k4, j3;
323:   MatScalar *aa, *ax, *ay, stmp;
324:   MatReal    tmp, max;

326:   if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE;

328:   /* Parameter adjustments */
329:   a -= 16;

331:   for (k = 1; k <= 14; ++k) {
332:     kp1 = k + 1;
333:     k3  = 15 * k;
334:     k4  = k3 + k;

336:     /* find l = pivot index */
337:     i__2 = 16 - k;
338:     aa   = &a[k4];
339:     max  = PetscAbsScalar(aa[0]);
340:     l    = 1;
341:     for (ll = 1; ll < i__2; ll++) {
342:       tmp = PetscAbsScalar(aa[ll]);
343:       if (tmp > max) {
344:         max = tmp;
345:         l   = ll + 1;
346:       }
347:     }
348:     l += k - 1;
349:     ipvt[k - 1] = l;

351:     if (a[l + k3] == 0.0) {
352:       if (shift == 0.0) {
353:         if (allowzeropivot) {
354:           PetscInfo(NULL, "Zero pivot, row %" PetscInt_FMT "\n", k - 1);
355:           if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
356:         } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row %" PetscInt_FMT, k - 1);
357:       } else {
358:         a[l + k3] = shift;
359:       }
360:     }

362:     /* interchange if necessary */
363:     if (l != k) {
364:       stmp      = a[l + k3];
365:       a[l + k3] = a[k4];
366:       a[k4]     = stmp;
367:     }

369:     /* compute multipliers */
370:     stmp = -1. / a[k4];
371:     i__2 = 15 - k;
372:     aa   = &a[1 + k4];
373:     for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;

375:     /* row elimination with column indexing */
376:     ax = &a[k4 + 1];
377:     for (j = kp1; j <= 15; ++j) {
378:       j3   = 15 * j;
379:       stmp = a[l + j3];
380:       if (l != k) {
381:         a[l + j3] = a[k + j3];
382:         a[k + j3] = stmp;
383:       }

385:       i__3 = 15 - k;
386:       ay   = &a[1 + k + j3];
387:       for (ll = 0; ll < i__3; ll++) ay[ll] += stmp * ax[ll];
388:     }
389:   }
390:   ipvt[14] = 15;
391:   if (a[240] == 0.0) {
392:     if (PetscLikely(allowzeropivot)) {
393:       PetscInfo(NULL, "Zero pivot, row 14\n");
394:       if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
395:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row 14");
396:   }

398:   /* Now form the inverse */
399:   /* compute inverse(u) */
400:   for (k = 1; k <= 15; ++k) {
401:     k3    = 15 * k;
402:     k4    = k3 + k;
403:     a[k4] = 1.0 / a[k4];
404:     stmp  = -a[k4];
405:     i__2  = k - 1;
406:     aa    = &a[k3 + 1];
407:     for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;
408:     kp1 = k + 1;
409:     if (15 < kp1) continue;
410:     ax = aa;
411:     for (j = kp1; j <= 15; ++j) {
412:       j3        = 15 * j;
413:       stmp      = a[k + j3];
414:       a[k + j3] = 0.0;
415:       ay        = &a[j3 + 1];
416:       for (ll = 0; ll < k; ll++) ay[ll] += stmp * ax[ll];
417:     }
418:   }

420:   /* form inverse(u)*inverse(l) */
421:   for (kb = 1; kb <= 14; ++kb) {
422:     k   = 15 - kb;
423:     k3  = 15 * k;
424:     kp1 = k + 1;
425:     aa  = a + k3;
426:     for (i = kp1; i <= 15; ++i) {
427:       work[i - 1] = aa[i];
428:       aa[i]       = 0.0;
429:     }
430:     for (j = kp1; j <= 15; ++j) {
431:       stmp = work[j - 1];
432:       ax   = &a[15 * j + 1];
433:       ay   = &a[k3 + 1];
434:       ay[0] += stmp * ax[0];
435:       ay[1] += stmp * ax[1];
436:       ay[2] += stmp * ax[2];
437:       ay[3] += stmp * ax[3];
438:       ay[4] += stmp * ax[4];
439:       ay[5] += stmp * ax[5];
440:       ay[6] += stmp * ax[6];
441:       ay[7] += stmp * ax[7];
442:       ay[8] += stmp * ax[8];
443:       ay[9] += stmp * ax[9];
444:       ay[10] += stmp * ax[10];
445:       ay[11] += stmp * ax[11];
446:       ay[12] += stmp * ax[12];
447:       ay[13] += stmp * ax[13];
448:       ay[14] += stmp * ax[14];
449:     }
450:     l = ipvt[k - 1];
451:     if (l != k) {
452:       ax     = &a[k3 + 1];
453:       ay     = &a[15 * l + 1];
454:       stmp   = ax[0];
455:       ax[0]  = ay[0];
456:       ay[0]  = stmp;
457:       stmp   = ax[1];
458:       ax[1]  = ay[1];
459:       ay[1]  = stmp;
460:       stmp   = ax[2];
461:       ax[2]  = ay[2];
462:       ay[2]  = stmp;
463:       stmp   = ax[3];
464:       ax[3]  = ay[3];
465:       ay[3]  = stmp;
466:       stmp   = ax[4];
467:       ax[4]  = ay[4];
468:       ay[4]  = stmp;
469:       stmp   = ax[5];
470:       ax[5]  = ay[5];
471:       ay[5]  = stmp;
472:       stmp   = ax[6];
473:       ax[6]  = ay[6];
474:       ay[6]  = stmp;
475:       stmp   = ax[7];
476:       ax[7]  = ay[7];
477:       ay[7]  = stmp;
478:       stmp   = ax[8];
479:       ax[8]  = ay[8];
480:       ay[8]  = stmp;
481:       stmp   = ax[9];
482:       ax[9]  = ay[9];
483:       ay[9]  = stmp;
484:       stmp   = ax[10];
485:       ax[10] = ay[10];
486:       ay[10] = stmp;
487:       stmp   = ax[11];
488:       ax[11] = ay[11];
489:       ay[11] = stmp;
490:       stmp   = ax[12];
491:       ax[12] = ay[12];
492:       ay[12] = stmp;
493:       stmp   = ax[13];
494:       ax[13] = ay[13];
495:       ay[13] = stmp;
496:       stmp   = ax[14];
497:       ax[14] = ay[14];
498:       ay[14] = stmp;
499:     }
500:   }
501:   return 0;
502: }