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

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

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

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

 48:   if (a[l + k3] == 0.0) {
 49:     if (shift == 0.0) {
 50:       if (allowzeropivot) {
 51:         PetscCall(PetscInfo(NULL, "Zero pivot, row %" PetscInt_FMT "\n", k - 1));
 52:         if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
 53:       } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row %" PetscInt_FMT, k - 1);
 54:     } else {
 55:       a[l + k3] = shift;
 56:     }
 57:   }

 59:   /* interchange if necessary */
 60:   if (l != k) {
 61:     stmp      = a[l + k3];
 62:     a[l + k3] = a[k4];
 63:     a[k4]     = stmp;
 64:   }

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

 72:   /* row elimination with column indexing */
 73:   ax = &a[k4 + 1];
 74:   for (j = kp1; j <= 2; ++j) {
 75:     j3   = 2 * j;
 76:     stmp = a[l + j3];
 77:     if (l != k) {
 78:       a[l + j3] = a[k + j3];
 79:       a[k + j3] = stmp;
 80:     }

 82:     i__3 = 2 - k;
 83:     ay   = &a[1 + k + j3];
 84:     for (ll = 0; ll < i__3; ll++) ay[ll] += stmp * ax[ll];
 85:   }

 87:   ipvt[1] = 2;
 88:   if (a[6] == 0.0) {
 89:     if (PetscLikely(allowzeropivot)) {
 90:       PetscCall(PetscInfo(NULL, "Zero pivot, row 1\n"));
 91:       if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
 92:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row 1");
 93:   }

 95:   /* Now form the inverse */
 96:   /* compute inverse(u) */
 97:   for (k = 1; k <= 2; ++k) {
 98:     k3    = 2 * k;
 99:     k4    = k3 + k;
100:     a[k4] = 1.0 / a[k4];
101:     stmp  = -a[k4];
102:     i__2  = k - 1;
103:     aa    = &a[k3 + 1];
104:     for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;
105:     kp1 = k + 1;
106:     if (2 < kp1) continue;
107:     ax = aa;
108:     for (j = kp1; j <= 2; ++j) {
109:       j3        = 2 * j;
110:       stmp      = a[k + j3];
111:       a[k + j3] = 0.0;
112:       ay        = &a[j3 + 1];
113:       for (ll = 0; ll < k; ll++) ay[ll] += stmp * ax[ll];
114:     }
115:   }

117:   /* form inverse(u)*inverse(l) */
118:   k   = 1;
119:   k3  = 2 * k;
120:   kp1 = k + 1;
121:   aa  = a + k3;
122:   for (i = kp1; i <= 2; ++i) {
123:     work[i - 1] = aa[i];
124:     aa[i]       = 0.0;
125:   }
126:   for (j = kp1; j <= 2; ++j) {
127:     stmp = work[j - 1];
128:     ax   = &a[2 * j + 1];
129:     ay   = &a[k3 + 1];
130:     ay[0] += stmp * ax[0];
131:     ay[1] += stmp * ax[1];
132:   }
133:   l = ipvt[k - 1];
134:   if (l != k) {
135:     ax    = &a[k3 + 1];
136:     ay    = &a[2 * l + 1];
137:     stmp  = ax[0];
138:     ax[0] = ay[0];
139:     ay[0] = stmp;
140:     stmp  = ax[1];
141:     ax[1] = ay[1];
142:     ay[1] = stmp;
143:   }
144:   PetscFunctionReturn(PETSC_SUCCESS);
145: }

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

155:   PetscFunctionBegin;
156:   if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE;

158:   /* Parameter adjustments */
159:   a -= 10;

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

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

181:     if (a[l + k3] == 0.0) {
182:       if (shift == 0.0) {
183:         if (allowzeropivot) {
184:           PetscCall(PetscInfo(NULL, "Zero pivot, row %" PetscInt_FMT "\n", k - 1));
185:           if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
186:         } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row %" PetscInt_FMT, k - 1);
187:       } else {
188:         a[l + k3] = shift;
189:       }
190:     }

192:     /* interchange if necessary */
193:     if (l != k) {
194:       stmp      = a[l + k3];
195:       a[l + k3] = a[k4];
196:       a[k4]     = stmp;
197:     }

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

205:     /* row elimination with column indexing */
206:     ax = &a[k4 + 1];
207:     for (j = kp1; j <= 9; ++j) {
208:       j3   = 9 * j;
209:       stmp = a[l + j3];
210:       if (l != k) {
211:         a[l + j3] = a[k + j3];
212:         a[k + j3] = stmp;
213:       }

215:       i__3 = 9 - k;
216:       ay   = &a[1 + k + j3];
217:       for (ll = 0; ll < i__3; ll++) ay[ll] += stmp * ax[ll];
218:     }
219:   }
220:   ipvt[8] = 9;
221:   if (a[90] == 0.0) {
222:     if (PetscLikely(allowzeropivot)) {
223:       PetscCall(PetscInfo(NULL, "Zero pivot, row 8\n"));
224:       if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
225:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row 8");
226:   }

228:   /* Now form the inverse */
229:   /* compute inverse(u) */
230:   for (k = 1; k <= 9; ++k) {
231:     k3    = 9 * k;
232:     k4    = k3 + k;
233:     a[k4] = 1.0 / a[k4];
234:     stmp  = -a[k4];
235:     i__2  = k - 1;
236:     aa    = &a[k3 + 1];
237:     for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;
238:     kp1 = k + 1;
239:     if (9 < kp1) continue;
240:     ax = aa;
241:     for (j = kp1; j <= 9; ++j) {
242:       j3        = 9 * j;
243:       stmp      = a[k + j3];
244:       a[k + j3] = 0.0;
245:       ay        = &a[j3 + 1];
246:       for (ll = 0; ll < k; ll++) ay[ll] += stmp * ax[ll];
247:     }
248:   }

250:   /* form inverse(u)*inverse(l) */
251:   for (kb = 1; kb <= 8; ++kb) {
252:     k   = 9 - kb;
253:     k3  = 9 * k;
254:     kp1 = k + 1;
255:     aa  = a + k3;
256:     for (i = kp1; i <= 9; ++i) {
257:       work[i - 1] = aa[i];
258:       aa[i]       = 0.0;
259:     }
260:     for (j = kp1; j <= 9; ++j) {
261:       stmp = work[j - 1];
262:       ax   = &a[9 * j + 1];
263:       ay   = &a[k3 + 1];
264:       ay[0] += stmp * ax[0];
265:       ay[1] += stmp * ax[1];
266:       ay[2] += stmp * ax[2];
267:       ay[3] += stmp * ax[3];
268:       ay[4] += stmp * ax[4];
269:       ay[5] += stmp * ax[5];
270:       ay[6] += stmp * ax[6];
271:       ay[7] += stmp * ax[7];
272:       ay[8] += stmp * ax[8];
273:     }
274:     l = ipvt[k - 1];
275:     if (l != k) {
276:       ax    = &a[k3 + 1];
277:       ay    = &a[9 * l + 1];
278:       stmp  = ax[0];
279:       ax[0] = ay[0];
280:       ay[0] = stmp;
281:       stmp  = ax[1];
282:       ax[1] = ay[1];
283:       ay[1] = stmp;
284:       stmp  = ax[2];
285:       ax[2] = ay[2];
286:       ay[2] = stmp;
287:       stmp  = ax[3];
288:       ax[3] = ay[3];
289:       ay[3] = stmp;
290:       stmp  = ax[4];
291:       ax[4] = ay[4];
292:       ay[4] = stmp;
293:       stmp  = ax[5];
294:       ax[5] = ay[5];
295:       ay[5] = stmp;
296:       stmp  = ax[6];
297:       ax[6] = ay[6];
298:       ay[6] = stmp;
299:       stmp  = ax[7];
300:       ax[7] = ay[7];
301:       ay[7] = stmp;
302:       stmp  = ax[8];
303:       ax[8] = ay[8];
304:       ay[8] = stmp;
305:     }
306:   }
307:   PetscFunctionReturn(PETSC_SUCCESS);
308: }

310: /*
311:       Inverts 15 by 15 matrix using gaussian elimination with partial pivoting.

313:        Used by the sparse factorization routines in
314:      src/mat/impls/baij/seq

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

319: */

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

328:   PetscFunctionBegin;
329:   if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE;

331:   /* Parameter adjustments */
332:   a -= 16;

334:   for (k = 1; k <= 14; ++k) {
335:     kp1 = k + 1;
336:     k3  = 15 * k;
337:     k4  = k3 + k;

339:     /* find l = pivot index */
340:     i__2 = 16 - k;
341:     aa   = &a[k4];
342:     max  = PetscAbsScalar(aa[0]);
343:     l    = 1;
344:     for (ll = 1; ll < i__2; ll++) {
345:       tmp = PetscAbsScalar(aa[ll]);
346:       if (tmp > max) {
347:         max = tmp;
348:         l   = ll + 1;
349:       }
350:     }
351:     l += k - 1;
352:     ipvt[k - 1] = l;

354:     if (a[l + k3] == 0.0) {
355:       if (shift == 0.0) {
356:         if (allowzeropivot) {
357:           PetscCall(PetscInfo(NULL, "Zero pivot, row %" PetscInt_FMT "\n", k - 1));
358:           if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
359:         } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row %" PetscInt_FMT, k - 1);
360:       } else {
361:         a[l + k3] = shift;
362:       }
363:     }

365:     /* interchange if necessary */
366:     if (l != k) {
367:       stmp      = a[l + k3];
368:       a[l + k3] = a[k4];
369:       a[k4]     = stmp;
370:     }

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

378:     /* row elimination with column indexing */
379:     ax = &a[k4 + 1];
380:     for (j = kp1; j <= 15; ++j) {
381:       j3   = 15 * j;
382:       stmp = a[l + j3];
383:       if (l != k) {
384:         a[l + j3] = a[k + j3];
385:         a[k + j3] = stmp;
386:       }

388:       i__3 = 15 - k;
389:       ay   = &a[1 + k + j3];
390:       for (ll = 0; ll < i__3; ll++) ay[ll] += stmp * ax[ll];
391:     }
392:   }
393:   ipvt[14] = 15;
394:   if (a[240] == 0.0) {
395:     if (PetscLikely(allowzeropivot)) {
396:       PetscCall(PetscInfo(NULL, "Zero pivot, row 14\n"));
397:       if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
398:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row 14");
399:   }

401:   /* Now form the inverse */
402:   /* compute inverse(u) */
403:   for (k = 1; k <= 15; ++k) {
404:     k3    = 15 * k;
405:     k4    = k3 + k;
406:     a[k4] = 1.0 / a[k4];
407:     stmp  = -a[k4];
408:     i__2  = k - 1;
409:     aa    = &a[k3 + 1];
410:     for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;
411:     kp1 = k + 1;
412:     if (15 < kp1) continue;
413:     ax = aa;
414:     for (j = kp1; j <= 15; ++j) {
415:       j3        = 15 * j;
416:       stmp      = a[k + j3];
417:       a[k + j3] = 0.0;
418:       ay        = &a[j3 + 1];
419:       for (ll = 0; ll < k; ll++) ay[ll] += stmp * ax[ll];
420:     }
421:   }

423:   /* form inverse(u)*inverse(l) */
424:   for (kb = 1; kb <= 14; ++kb) {
425:     k   = 15 - kb;
426:     k3  = 15 * k;
427:     kp1 = k + 1;
428:     aa  = a + k3;
429:     for (i = kp1; i <= 15; ++i) {
430:       work[i - 1] = aa[i];
431:       aa[i]       = 0.0;
432:     }
433:     for (j = kp1; j <= 15; ++j) {
434:       stmp = work[j - 1];
435:       ax   = &a[15 * j + 1];
436:       ay   = &a[k3 + 1];
437:       ay[0] += stmp * ax[0];
438:       ay[1] += stmp * ax[1];
439:       ay[2] += stmp * ax[2];
440:       ay[3] += stmp * ax[3];
441:       ay[4] += stmp * ax[4];
442:       ay[5] += stmp * ax[5];
443:       ay[6] += stmp * ax[6];
444:       ay[7] += stmp * ax[7];
445:       ay[8] += stmp * ax[8];
446:       ay[9] += stmp * ax[9];
447:       ay[10] += stmp * ax[10];
448:       ay[11] += stmp * ax[11];
449:       ay[12] += stmp * ax[12];
450:       ay[13] += stmp * ax[13];
451:       ay[14] += stmp * ax[14];
452:     }
453:     l = ipvt[k - 1];
454:     if (l != k) {
455:       ax     = &a[k3 + 1];
456:       ay     = &a[15 * l + 1];
457:       stmp   = ax[0];
458:       ax[0]  = ay[0];
459:       ay[0]  = stmp;
460:       stmp   = ax[1];
461:       ax[1]  = ay[1];
462:       ay[1]  = stmp;
463:       stmp   = ax[2];
464:       ax[2]  = ay[2];
465:       ay[2]  = stmp;
466:       stmp   = ax[3];
467:       ax[3]  = ay[3];
468:       ay[3]  = stmp;
469:       stmp   = ax[4];
470:       ax[4]  = ay[4];
471:       ay[4]  = stmp;
472:       stmp   = ax[5];
473:       ax[5]  = ay[5];
474:       ay[5]  = stmp;
475:       stmp   = ax[6];
476:       ax[6]  = ay[6];
477:       ay[6]  = stmp;
478:       stmp   = ax[7];
479:       ax[7]  = ay[7];
480:       ay[7]  = stmp;
481:       stmp   = ax[8];
482:       ax[8]  = ay[8];
483:       ay[8]  = stmp;
484:       stmp   = ax[9];
485:       ax[9]  = ay[9];
486:       ay[9]  = stmp;
487:       stmp   = ax[10];
488:       ax[10] = ay[10];
489:       ay[10] = stmp;
490:       stmp   = ax[11];
491:       ax[11] = ay[11];
492:       ay[11] = stmp;
493:       stmp   = ax[12];
494:       ax[12] = ay[12];
495:       ay[12] = stmp;
496:       stmp   = ax[13];
497:       ax[13] = ay[13];
498:       ay[13] = stmp;
499:       stmp   = ax[14];
500:       ax[14] = ay[14];
501:       ay[14] = stmp;
502:     }
503:   }
504:   PetscFunctionReturn(PETSC_SUCCESS);
505: }