Actual source code: baijfact.c

petsc-master 2019-08-18
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  2: /*
  3:     Factorization code for BAIJ format.
  4: */
  5:  #include <../src/mat/impls/baij/seq/baij.h>
  6:  #include <petsc/private/kernels/blockinvert.h>

  8: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_2(Mat B,Mat A,const MatFactorInfo *info)
  9: {
 10:   Mat            C     =B;
 11:   Mat_SeqBAIJ    *a    =(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
 12:   IS             isrow = b->row,isicol = b->icol;
 14:   const PetscInt *r,*ic;
 15:   PetscInt       i,j,k,nz,nzL,row,*pj;
 16:   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,bs2=a->bs2;
 17:   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag;
 18:   MatScalar      *rtmp,*pc,*mwork,*pv;
 19:   MatScalar      *aa=a->a,*v;
 20:   PetscInt       flg;
 21:   PetscReal      shift = info->shiftamount;
 22:   PetscBool      allowzeropivot,zeropivotdetected;

 25:   ISGetIndices(isrow,&r);
 26:   ISGetIndices(isicol,&ic);
 27:   allowzeropivot = PetscNot(A->erroriffailure);

 29:   /* generate work space needed by the factorization */
 30:   PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
 31:   PetscArrayzero(rtmp,bs2*n);

 33:   for (i=0; i<n; i++) {
 34:     /* zero rtmp */
 35:     /* L part */
 36:     nz    = bi[i+1] - bi[i];
 37:     bjtmp = bj + bi[i];
 38:     for  (j=0; j<nz; j++) {
 39:       PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
 40:     }

 42:     /* U part */
 43:     nz    = bdiag[i] - bdiag[i+1];
 44:     bjtmp = bj + bdiag[i+1]+1;
 45:     for  (j=0; j<nz; j++) {
 46:       PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
 47:     }

 49:     /* load in initial (unfactored row) */
 50:     nz    = ai[r[i]+1] - ai[r[i]];
 51:     ajtmp = aj + ai[r[i]];
 52:     v     = aa + bs2*ai[r[i]];
 53:     for (j=0; j<nz; j++) {
 54:       PetscArraycpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2);
 55:     }

 57:     /* elimination */
 58:     bjtmp = bj + bi[i];
 59:     nzL   = bi[i+1] - bi[i];
 60:     for (k=0; k < nzL; k++) {
 61:       row = bjtmp[k];
 62:       pc  = rtmp + bs2*row;
 63:       for (flg=0,j=0; j<bs2; j++) {
 64:         if (pc[j] != (PetscScalar)0.0) {
 65:           flg = 1;
 66:           break;
 67:         }
 68:       }
 69:       if (flg) {
 70:         pv = b->a + bs2*bdiag[row];
 71:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
 72:         PetscKernel_A_gets_A_times_B_2(pc,pv,mwork);

 74:         pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
 75:         pv = b->a + bs2*(bdiag[row+1]+1);
 76:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
 77:         for (j=0; j<nz; j++) {
 78:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
 79:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
 80:           v    = rtmp + 4*pj[j];
 81:           PetscKernel_A_gets_A_minus_B_times_C_2(v,pc,pv);
 82:           pv  += 4;
 83:         }
 84:         PetscLogFlops(16*nz+12); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
 85:       }
 86:     }

 88:     /* finished row so stick it into b->a */
 89:     /* L part */
 90:     pv = b->a + bs2*bi[i];
 91:     pj = b->j + bi[i];
 92:     nz = bi[i+1] - bi[i];
 93:     for (j=0; j<nz; j++) {
 94:       PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
 95:     }

 97:     /* Mark diagonal and invert diagonal for simplier triangular solves */
 98:     pv   = b->a + bs2*bdiag[i];
 99:     pj   = b->j + bdiag[i];
100:     PetscArraycpy(pv,rtmp+bs2*pj[0],bs2);
101:     PetscKernel_A_gets_inverse_A_2(pv,shift,allowzeropivot,&zeropivotdetected);
102:     if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

104:     /* U part */
105:     pv = b->a + bs2*(bdiag[i+1]+1);
106:     pj = b->j + bdiag[i+1]+1;
107:     nz = bdiag[i] - bdiag[i+1] - 1;
108:     for (j=0; j<nz; j++) {
109:       PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
110:     }
111:   }

113:   PetscFree2(rtmp,mwork);
114:   ISRestoreIndices(isicol,&ic);
115:   ISRestoreIndices(isrow,&r);

117:   C->ops->solve          = MatSolve_SeqBAIJ_2;
118:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2;
119:   C->assembled           = PETSC_TRUE;

121:   PetscLogFlops(1.333333333333*2*2*2*n); /* from inverting diagonal blocks */
122:   return(0);
123: }

125: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
126: {
127:   Mat            C =B;
128:   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
130:   PetscInt       i,j,k,nz,nzL,row,*pj;
131:   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,bs2=a->bs2;
132:   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag;
133:   MatScalar      *rtmp,*pc,*mwork,*pv;
134:   MatScalar      *aa=a->a,*v;
135:   PetscInt       flg;
136:   PetscReal      shift = info->shiftamount;
137:   PetscBool      allowzeropivot,zeropivotdetected;

140:   allowzeropivot = PetscNot(A->erroriffailure);

142:   /* generate work space needed by the factorization */
143:   PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
144:   PetscArrayzero(rtmp,bs2*n);

146:   for (i=0; i<n; i++) {
147:     /* zero rtmp */
148:     /* L part */
149:     nz    = bi[i+1] - bi[i];
150:     bjtmp = bj + bi[i];
151:     for  (j=0; j<nz; j++) {
152:       PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
153:     }

155:     /* U part */
156:     nz    = bdiag[i] - bdiag[i+1];
157:     bjtmp = bj + bdiag[i+1]+1;
158:     for  (j=0; j<nz; j++) {
159:       PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
160:     }

162:     /* load in initial (unfactored row) */
163:     nz    = ai[i+1] - ai[i];
164:     ajtmp = aj + ai[i];
165:     v     = aa + bs2*ai[i];
166:     for (j=0; j<nz; j++) {
167:       PetscArraycpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2);
168:     }

170:     /* elimination */
171:     bjtmp = bj + bi[i];
172:     nzL   = bi[i+1] - bi[i];
173:     for (k=0; k < nzL; k++) {
174:       row = bjtmp[k];
175:       pc  = rtmp + bs2*row;
176:       for (flg=0,j=0; j<bs2; j++) {
177:         if (pc[j]!=(PetscScalar)0.0) {
178:           flg = 1;
179:           break;
180:         }
181:       }
182:       if (flg) {
183:         pv = b->a + bs2*bdiag[row];
184:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
185:         PetscKernel_A_gets_A_times_B_2(pc,pv,mwork);

187:         pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
188:         pv = b->a + bs2*(bdiag[row+1]+1);
189:         nz = bdiag[row]-bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
190:         for (j=0; j<nz; j++) {
191:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
192:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
193:           v    = rtmp + 4*pj[j];
194:           PetscKernel_A_gets_A_minus_B_times_C_2(v,pc,pv);
195:           pv  += 4;
196:         }
197:         PetscLogFlops(16*nz+12); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
198:       }
199:     }

201:     /* finished row so stick it into b->a */
202:     /* L part */
203:     pv = b->a + bs2*bi[i];
204:     pj = b->j + bi[i];
205:     nz = bi[i+1] - bi[i];
206:     for (j=0; j<nz; j++) {
207:       PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
208:     }

210:     /* Mark diagonal and invert diagonal for simplier triangular solves */
211:     pv   = b->a + bs2*bdiag[i];
212:     pj   = b->j + bdiag[i];
213:     PetscArraycpy(pv,rtmp+bs2*pj[0],bs2);
214:     PetscKernel_A_gets_inverse_A_2(pv,shift,allowzeropivot,&zeropivotdetected);
215:     if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

217:     /* U part */
218:     /*
219:     pv = b->a + bs2*bi[2*n-i];
220:     pj = b->j + bi[2*n-i];
221:     nz = bi[2*n-i+1] - bi[2*n-i] - 1;
222:     */
223:     pv = b->a + bs2*(bdiag[i+1]+1);
224:     pj = b->j + bdiag[i+1]+1;
225:     nz = bdiag[i] - bdiag[i+1] - 1;
226:     for (j=0; j<nz; j++) {
227:       PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
228:     }
229:   }
230:   PetscFree2(rtmp,mwork);

232:   C->ops->solve          = MatSolve_SeqBAIJ_2_NaturalOrdering;
233:   C->ops->forwardsolve   = MatForwardSolve_SeqBAIJ_2_NaturalOrdering;
234:   C->ops->backwardsolve  = MatBackwardSolve_SeqBAIJ_2_NaturalOrdering;
235:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2_NaturalOrdering;
236:   C->assembled           = PETSC_TRUE;

238:   PetscLogFlops(1.333333333333*2*2*2*n); /* from inverting diagonal blocks */
239:   return(0);
240: }

242: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_2_inplace(Mat B,Mat A,const MatFactorInfo *info)
243: {
244:   Mat            C     = B;
245:   Mat_SeqBAIJ    *a    = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
246:   IS             isrow = b->row,isicol = b->icol;
248:   const PetscInt *r,*ic;
249:   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
250:   PetscInt       *ajtmpold,*ajtmp,nz,row;
251:   PetscInt       *diag_offset=b->diag,idx,*ai=a->i,*aj=a->j,*pj;
252:   MatScalar      *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
253:   MatScalar      p1,p2,p3,p4;
254:   MatScalar      *ba   = b->a,*aa = a->a;
255:   PetscReal      shift = info->shiftamount;
256:   PetscBool      allowzeropivot,zeropivotdetected;

259:   allowzeropivot = PetscNot(A->erroriffailure);
260:   ISGetIndices(isrow,&r);
261:   ISGetIndices(isicol,&ic);
262:   PetscMalloc1(4*(n+1),&rtmp);

264:   for (i=0; i<n; i++) {
265:     nz    = bi[i+1] - bi[i];
266:     ajtmp = bj + bi[i];
267:     for  (j=0; j<nz; j++) {
268:       x = rtmp+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0;
269:     }
270:     /* load in initial (unfactored row) */
271:     idx      = r[i];
272:     nz       = ai[idx+1] - ai[idx];
273:     ajtmpold = aj + ai[idx];
274:     v        = aa + 4*ai[idx];
275:     for (j=0; j<nz; j++) {
276:       x    = rtmp+4*ic[ajtmpold[j]];
277:       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
278:       v   += 4;
279:     }
280:     row = *ajtmp++;
281:     while (row < i) {
282:       pc = rtmp + 4*row;
283:       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
284:       if (p1 != (PetscScalar)0.0 || p2 != (PetscScalar)0.0 || p3 != (PetscScalar)0.0 || p4 != (PetscScalar)0.0) {
285:         pv    = ba + 4*diag_offset[row];
286:         pj    = bj + diag_offset[row] + 1;
287:         x1    = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
288:         pc[0] = m1 = p1*x1 + p3*x2;
289:         pc[1] = m2 = p2*x1 + p4*x2;
290:         pc[2] = m3 = p1*x3 + p3*x4;
291:         pc[3] = m4 = p2*x3 + p4*x4;
292:         nz    = bi[row+1] - diag_offset[row] - 1;
293:         pv   += 4;
294:         for (j=0; j<nz; j++) {
295:           x1    = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
296:           x     = rtmp + 4*pj[j];
297:           x[0] -= m1*x1 + m3*x2;
298:           x[1] -= m2*x1 + m4*x2;
299:           x[2] -= m1*x3 + m3*x4;
300:           x[3] -= m2*x3 + m4*x4;
301:           pv   += 4;
302:         }
303:         PetscLogFlops(16.0*nz+12.0);
304:       }
305:       row = *ajtmp++;
306:     }
307:     /* finished row so stick it into b->a */
308:     pv = ba + 4*bi[i];
309:     pj = bj + bi[i];
310:     nz = bi[i+1] - bi[i];
311:     for (j=0; j<nz; j++) {
312:       x     = rtmp+4*pj[j];
313:       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
314:       pv   += 4;
315:     }
316:     /* invert diagonal block */
317:     w    = ba + 4*diag_offset[i];
318:     PetscKernel_A_gets_inverse_A_2(w,shift,allowzeropivot,&zeropivotdetected);
319:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
320:   }

322:   PetscFree(rtmp);
323:   ISRestoreIndices(isicol,&ic);
324:   ISRestoreIndices(isrow,&r);

326:   C->ops->solve          = MatSolve_SeqBAIJ_2_inplace;
327:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2_inplace;
328:   C->assembled           = PETSC_TRUE;

330:   PetscLogFlops(1.333333333333*8*b->mbs); /* from inverting diagonal blocks */
331:   return(0);
332: }
333: /*
334:       Version for when blocks are 2 by 2 Using natural ordering
335: */
336: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
337: {
338:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
340:   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
341:   PetscInt       *ajtmpold,*ajtmp,nz,row;
342:   PetscInt       *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
343:   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
344:   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,x1,x2,x3,x4;
345:   MatScalar      *ba   = b->a,*aa = a->a;
346:   PetscReal      shift = info->shiftamount;
347:   PetscBool      allowzeropivot,zeropivotdetected;

350:   allowzeropivot = PetscNot(A->erroriffailure);
351:   PetscMalloc1(4*(n+1),&rtmp);
352:   for (i=0; i<n; i++) {
353:     nz    = bi[i+1] - bi[i];
354:     ajtmp = bj + bi[i];
355:     for  (j=0; j<nz; j++) {
356:       x    = rtmp+4*ajtmp[j];
357:       x[0] = x[1]  = x[2]  = x[3]  = 0.0;
358:     }
359:     /* load in initial (unfactored row) */
360:     nz       = ai[i+1] - ai[i];
361:     ajtmpold = aj + ai[i];
362:     v        = aa + 4*ai[i];
363:     for (j=0; j<nz; j++) {
364:       x    = rtmp+4*ajtmpold[j];
365:       x[0] = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
366:       v   += 4;
367:     }
368:     row = *ajtmp++;
369:     while (row < i) {
370:       pc = rtmp + 4*row;
371:       p1 = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
372:       if (p1 != (PetscScalar)0.0 || p2 != (PetscScalar)0.0 || p3 != (PetscScalar)0.0 || p4 != (PetscScalar)0.0) {
373:         pv    = ba + 4*diag_offset[row];
374:         pj    = bj + diag_offset[row] + 1;
375:         x1    = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
376:         pc[0] = m1 = p1*x1 + p3*x2;
377:         pc[1] = m2 = p2*x1 + p4*x2;
378:         pc[2] = m3 = p1*x3 + p3*x4;
379:         pc[3] = m4 = p2*x3 + p4*x4;
380:         nz    = bi[row+1] - diag_offset[row] - 1;
381:         pv   += 4;
382:         for (j=0; j<nz; j++) {
383:           x1    = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
384:           x     = rtmp + 4*pj[j];
385:           x[0] -= m1*x1 + m3*x2;
386:           x[1] -= m2*x1 + m4*x2;
387:           x[2] -= m1*x3 + m3*x4;
388:           x[3] -= m2*x3 + m4*x4;
389:           pv   += 4;
390:         }
391:         PetscLogFlops(16.0*nz+12.0);
392:       }
393:       row = *ajtmp++;
394:     }
395:     /* finished row so stick it into b->a */
396:     pv = ba + 4*bi[i];
397:     pj = bj + bi[i];
398:     nz = bi[i+1] - bi[i];
399:     for (j=0; j<nz; j++) {
400:       x     = rtmp+4*pj[j];
401:       pv[0] = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
402:       /*
403:       printf(" col %d:",pj[j]);
404:       PetscInt j1;
405:       for (j1=0; j1<4; j1++) printf(" %g,",*(pv+j1));
406:       printf("\n");
407:       */
408:       pv += 4;
409:     }
410:     /* invert diagonal block */
411:     w = ba + 4*diag_offset[i];
412:     PetscKernel_A_gets_inverse_A_2(w,shift, allowzeropivot,&zeropivotdetected);
413:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
414:   }

416:   PetscFree(rtmp);

418:   C->ops->solve          = MatSolve_SeqBAIJ_2_NaturalOrdering_inplace;
419:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2_NaturalOrdering_inplace;
420:   C->assembled           = PETSC_TRUE;

422:   PetscLogFlops(1.333333333333*8*b->mbs); /* from inverting diagonal blocks */
423:   return(0);
424: }

426: /* ----------------------------------------------------------- */
427: /*
428:      Version for when blocks are 1 by 1.
429: */
430: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_1(Mat B,Mat A,const MatFactorInfo *info)
431: {
432:   Mat             C     =B;
433:   Mat_SeqBAIJ     *a    =(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
434:   IS              isrow = b->row,isicol = b->icol;
435:   PetscErrorCode  ierr;
436:   const PetscInt  *r,*ic,*ics;
437:   const PetscInt  n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bdiag=b->diag;
438:   PetscInt        i,j,k,nz,nzL,row,*pj;
439:   const PetscInt  *ajtmp,*bjtmp;
440:   MatScalar       *rtmp,*pc,multiplier,*pv;
441:   const MatScalar *aa=a->a,*v;
442:   PetscBool       row_identity,col_identity;
443:   FactorShiftCtx  sctx;
444:   const PetscInt  *ddiag;
445:   PetscReal       rs;
446:   MatScalar       d;

449:   /* MatPivotSetUp(): initialize shift context sctx */
450:   PetscMemzero(&sctx,sizeof(FactorShiftCtx));

452:   if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
453:     ddiag          = a->diag;
454:     sctx.shift_top = info->zeropivot;
455:     for (i=0; i<n; i++) {
456:       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
457:       d  = (aa)[ddiag[i]];
458:       rs = -PetscAbsScalar(d) - PetscRealPart(d);
459:       v  = aa+ai[i];
460:       nz = ai[i+1] - ai[i];
461:       for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]);
462:       if (rs>sctx.shift_top) sctx.shift_top = rs;
463:     }
464:     sctx.shift_top *= 1.1;
465:     sctx.nshift_max = 5;
466:     sctx.shift_lo   = 0.;
467:     sctx.shift_hi   = 1.;
468:   }

470:   ISGetIndices(isrow,&r);
471:   ISGetIndices(isicol,&ic);
472:   PetscMalloc1(n+1,&rtmp);
473:   ics  = ic;

475:   do {
476:     sctx.newshift = PETSC_FALSE;
477:     for (i=0; i<n; i++) {
478:       /* zero rtmp */
479:       /* L part */
480:       nz    = bi[i+1] - bi[i];
481:       bjtmp = bj + bi[i];
482:       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;

484:       /* U part */
485:       nz    = bdiag[i]-bdiag[i+1];
486:       bjtmp = bj + bdiag[i+1]+1;
487:       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;

489:       /* load in initial (unfactored row) */
490:       nz    = ai[r[i]+1] - ai[r[i]];
491:       ajtmp = aj + ai[r[i]];
492:       v     = aa + ai[r[i]];
493:       for (j=0; j<nz; j++) rtmp[ics[ajtmp[j]]] = v[j];

495:       /* ZeropivotApply() */
496:       rtmp[i] += sctx.shift_amount;  /* shift the diagonal of the matrix */

498:       /* elimination */
499:       bjtmp = bj + bi[i];
500:       row   = *bjtmp++;
501:       nzL   = bi[i+1] - bi[i];
502:       for (k=0; k < nzL; k++) {
503:         pc = rtmp + row;
504:         if (*pc != (PetscScalar)0.0) {
505:           pv         = b->a + bdiag[row];
506:           multiplier = *pc * (*pv);
507:           *pc        = multiplier;

509:           pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
510:           pv = b->a + bdiag[row+1]+1;
511:           nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */
512:           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
513:           PetscLogFlops(2.0*nz);
514:         }
515:         row = *bjtmp++;
516:       }

518:       /* finished row so stick it into b->a */
519:       rs = 0.0;
520:       /* L part */
521:       pv = b->a + bi[i];
522:       pj = b->j + bi[i];
523:       nz = bi[i+1] - bi[i];
524:       for (j=0; j<nz; j++) {
525:         pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
526:       }

528:       /* U part */
529:       pv = b->a + bdiag[i+1]+1;
530:       pj = b->j + bdiag[i+1]+1;
531:       nz = bdiag[i] - bdiag[i+1]-1;
532:       for (j=0; j<nz; j++) {
533:         pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
534:       }

536:       sctx.rs = rs;
537:       sctx.pv = rtmp[i];
538:       MatPivotCheck(B,A,info,&sctx,i);
539:       if (sctx.newshift) break; /* break for-loop */
540:       rtmp[i] = sctx.pv; /* sctx.pv might be updated in the case of MAT_SHIFT_INBLOCKS */

542:       /* Mark diagonal and invert diagonal for simplier triangular solves */
543:       pv  = b->a + bdiag[i];
544:       *pv = (PetscScalar)1.0/rtmp[i];

546:     } /* endof for (i=0; i<n; i++) { */

548:     /* MatPivotRefine() */
549:     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
550:       /*
551:        * if no shift in this attempt & shifting & started shifting & can refine,
552:        * then try lower shift
553:        */
554:       sctx.shift_hi       = sctx.shift_fraction;
555:       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
556:       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
557:       sctx.newshift       = PETSC_TRUE;
558:       sctx.nshift++;
559:     }
560:   } while (sctx.newshift);

562:   PetscFree(rtmp);
563:   ISRestoreIndices(isicol,&ic);
564:   ISRestoreIndices(isrow,&r);

566:   ISIdentity(isrow,&row_identity);
567:   ISIdentity(isicol,&col_identity);
568:   if (row_identity && col_identity) {
569:     C->ops->solve          = MatSolve_SeqBAIJ_1_NaturalOrdering;
570:     C->ops->forwardsolve   = MatForwardSolve_SeqBAIJ_1_NaturalOrdering;
571:     C->ops->backwardsolve  = MatBackwardSolve_SeqBAIJ_1_NaturalOrdering;
572:     C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_1_NaturalOrdering;
573:   } else {
574:     C->ops->solve          = MatSolve_SeqBAIJ_1;
575:     C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_1;
576:   }
577:   C->assembled = PETSC_TRUE;
578:   PetscLogFlops(C->cmap->n);

580:   /* MatShiftView(A,info,&sctx) */
581:   if (sctx.nshift) {
582:     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
583:       PetscInfo4(A,"number of shift_pd tries %D, shift_amount %g, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,(double)sctx.shift_amount,(double)sctx.shift_fraction,(double)sctx.shift_top);
584:     } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
585:       PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
586:     } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) {
587:       PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %g\n",sctx.nshift,(double)info->shiftamount);
588:     }
589:   }
590:   return(0);
591: }

593: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_1_inplace(Mat C,Mat A,const MatFactorInfo *info)
594: {
595:   Mat_SeqBAIJ    *a    = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
596:   IS             isrow = b->row,isicol = b->icol;
598:   const PetscInt *r,*ic;
599:   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
600:   PetscInt       *ajtmpold,*ajtmp,nz,row,*ai = a->i,*aj = a->j;
601:   PetscInt       *diag_offset = b->diag,diag,*pj;
602:   MatScalar      *pv,*v,*rtmp,multiplier,*pc;
603:   MatScalar      *ba = b->a,*aa = a->a;
604:   PetscBool      row_identity, col_identity;

607:   ISGetIndices(isrow,&r);
608:   ISGetIndices(isicol,&ic);
609:   PetscMalloc1(n+1,&rtmp);

611:   for (i=0; i<n; i++) {
612:     nz    = bi[i+1] - bi[i];
613:     ajtmp = bj + bi[i];
614:     for  (j=0; j<nz; j++) rtmp[ajtmp[j]] = 0.0;

616:     /* load in initial (unfactored row) */
617:     nz       = ai[r[i]+1] - ai[r[i]];
618:     ajtmpold = aj + ai[r[i]];
619:     v        = aa + ai[r[i]];
620:     for (j=0; j<nz; j++) rtmp[ic[ajtmpold[j]]] =  v[j];

622:     row = *ajtmp++;
623:     while (row < i) {
624:       pc = rtmp + row;
625:       if (*pc != 0.0) {
626:         pv         = ba + diag_offset[row];
627:         pj         = bj + diag_offset[row] + 1;
628:         multiplier = *pc * *pv++;
629:         *pc        = multiplier;
630:         nz         = bi[row+1] - diag_offset[row] - 1;
631:         for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
632:         PetscLogFlops(1.0+2.0*nz);
633:       }
634:       row = *ajtmp++;
635:     }
636:     /* finished row so stick it into b->a */
637:     pv = ba + bi[i];
638:     pj = bj + bi[i];
639:     nz = bi[i+1] - bi[i];
640:     for (j=0; j<nz; j++) pv[j] = rtmp[pj[j]];
641:     diag = diag_offset[i] - bi[i];
642:     /* check pivot entry for current row */
643:     if (pv[diag] == 0.0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot: row in original ordering %D in permuted ordering %D",r[i],i);
644:     pv[diag] = 1.0/pv[diag];
645:   }

647:   PetscFree(rtmp);
648:   ISRestoreIndices(isicol,&ic);
649:   ISRestoreIndices(isrow,&r);
650:   ISIdentity(isrow,&row_identity);
651:   ISIdentity(isicol,&col_identity);
652:   if (row_identity && col_identity) {
653:     C->ops->solve          = MatSolve_SeqBAIJ_1_NaturalOrdering_inplace;
654:     C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_1_NaturalOrdering_inplace;
655:   } else {
656:     C->ops->solve          = MatSolve_SeqBAIJ_1_inplace;
657:     C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_1_inplace;
658:   }
659:   C->assembled = PETSC_TRUE;
660:   PetscLogFlops(C->cmap->n);
661:   return(0);
662: }

664: PETSC_INTERN PetscErrorCode MatGetFactor_seqbaij_petsc(Mat A,MatFactorType ftype,Mat *B)
665: {
666:   PetscInt       n = A->rmap->n;

670: #if defined(PETSC_USE_COMPLEX)
671:   if (A->hermitian && (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Hermitian Factor is not supported");
672: #endif
673:   MatCreate(PetscObjectComm((PetscObject)A),B);
674:   MatSetSizes(*B,n,n,n,n);
675:   if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT) {
676:     MatSetType(*B,MATSEQBAIJ);

678:     (*B)->ops->lufactorsymbolic  = MatLUFactorSymbolic_SeqBAIJ;
679:     (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqBAIJ;
680:   } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) {
681:     MatSetType(*B,MATSEQSBAIJ);
682:     MatSeqSBAIJSetPreallocation(*B,A->rmap->bs,MAT_SKIP_ALLOCATION,NULL);

684:     (*B)->ops->iccfactorsymbolic      = MatICCFactorSymbolic_SeqBAIJ;
685:     (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqBAIJ;
686:   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor type not supported");
687:   (*B)->factortype = ftype;

689:   PetscFree((*B)->solvertype);
690:   PetscStrallocpy(MATSOLVERPETSC,&(*B)->solvertype);
691:   return(0);
692: }

694: /* ----------------------------------------------------------- */
695: PetscErrorCode MatLUFactor_SeqBAIJ(Mat A,IS row,IS col,const MatFactorInfo *info)
696: {
698:   Mat            C;

701:   MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_LU,&C);
702:   MatLUFactorSymbolic(C,A,row,col,info);
703:   MatLUFactorNumeric(C,A,info);

705:   A->ops->solve          = C->ops->solve;
706:   A->ops->solvetranspose = C->ops->solvetranspose;

708:   MatHeaderMerge(A,&C);
709:   PetscLogObjectParent((PetscObject)A,(PetscObject)((Mat_SeqBAIJ*)(A->data))->icol);
710:   return(0);
711: }

713:  #include <../src/mat/impls/sbaij/seq/sbaij.h>
714: PetscErrorCode MatCholeskyFactorNumeric_SeqBAIJ_N(Mat C,Mat A,const MatFactorInfo *info)
715: {
717:   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data;
718:   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
719:   IS             ip=b->row;
720:   const PetscInt *rip;
721:   PetscInt       i,j,mbs=a->mbs,bs=A->rmap->bs,*bi=b->i,*bj=b->j,*bcol;
722:   PetscInt       *ai=a->i,*aj=a->j;
723:   PetscInt       k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
724:   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
725:   PetscReal      rs;
726:   FactorShiftCtx sctx;

729:   if (bs > 1) { /* convert A to a SBAIJ matrix and apply Cholesky factorization from it */
730:     if (!a->sbaijMat) {
731:       MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&a->sbaijMat);
732:     }
733:     (a->sbaijMat)->ops->choleskyfactornumeric(C,a->sbaijMat,info);
734:     MatDestroy(&a->sbaijMat);
735:     return(0);
736:   }

738:   /* MatPivotSetUp(): initialize shift context sctx */
739:   PetscMemzero(&sctx,sizeof(FactorShiftCtx));

741:   ISGetIndices(ip,&rip);
742:   PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&jl);

744:   sctx.shift_amount = 0.;
745:   sctx.nshift       = 0;
746:   do {
747:     sctx.newshift = PETSC_FALSE;
748:     for (i=0; i<mbs; i++) {
749:       rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
750:     }

752:     for (k = 0; k<mbs; k++) {
753:       bval = ba + bi[k];
754:       /* initialize k-th row by the perm[k]-th row of A */
755:       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
756:       for (j = jmin; j < jmax; j++) {
757:         col = rip[aj[j]];
758:         if (col >= k) { /* only take upper triangular entry */
759:           rtmp[col] = aa[j];
760:           *bval++   = 0.0; /* for in-place factorization */
761:         }
762:       }

764:       /* shift the diagonal of the matrix */
765:       if (sctx.nshift) rtmp[k] += sctx.shift_amount;

767:       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
768:       dk = rtmp[k];
769:       i  = jl[k]; /* first row to be added to k_th row  */

771:       while (i < k) {
772:         nexti = jl[i]; /* next row to be added to k_th row */

774:         /* compute multiplier, update diag(k) and U(i,k) */
775:         ili     = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
776:         uikdi   = -ba[ili]*ba[bi[i]]; /* diagonal(k) */
777:         dk     += uikdi*ba[ili];
778:         ba[ili] = uikdi; /* -U(i,k) */

780:         /* add multiple of row i to k-th row */
781:         jmin = ili + 1; jmax = bi[i+1];
782:         if (jmin < jmax) {
783:           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
784:           /* update il and jl for row i */
785:           il[i] = jmin;
786:           j     = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
787:         }
788:         i = nexti;
789:       }

791:       /* shift the diagonals when zero pivot is detected */
792:       /* compute rs=sum of abs(off-diagonal) */
793:       rs   = 0.0;
794:       jmin = bi[k]+1;
795:       nz   = bi[k+1] - jmin;
796:       if (nz) {
797:         bcol = bj + jmin;
798:         while (nz--) {
799:           rs += PetscAbsScalar(rtmp[*bcol]);
800:           bcol++;
801:         }
802:       }

804:       sctx.rs = rs;
805:       sctx.pv = dk;
806:       MatPivotCheck(C,A,info,&sctx,k);
807:       if (sctx.newshift) break;
808:       dk = sctx.pv;

810:       /* copy data into U(k,:) */
811:       ba[bi[k]] = 1.0/dk; /* U(k,k) */
812:       jmin      = bi[k]+1; jmax = bi[k+1];
813:       if (jmin < jmax) {
814:         for (j=jmin; j<jmax; j++) {
815:           col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0;
816:         }
817:         /* add the k-th row into il and jl */
818:         il[k] = jmin;
819:         i     = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
820:       }
821:     }
822:   } while (sctx.newshift);
823:   PetscFree3(rtmp,il,jl);

825:   ISRestoreIndices(ip,&rip);

827:   C->assembled    = PETSC_TRUE;
828:   C->preallocated = PETSC_TRUE;

830:   PetscLogFlops(C->rmap->N);
831:   if (sctx.nshift) {
832:     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
833:       PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
834:     } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
835:       PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
836:     }
837:   }
838:   return(0);
839: }

841: PetscErrorCode MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
842: {
843:   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data;
844:   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
846:   PetscInt       i,j,am=a->mbs;
847:   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
848:   PetscInt       k,jmin,*jl,*il,nexti,ili,*acol,*bcol,nz;
849:   MatScalar      *rtmp,*ba=b->a,*aa=a->a,dk,uikdi,*aval,*bval;
850:   PetscReal      rs;
851:   FactorShiftCtx sctx;

854:   /* MatPivotSetUp(): initialize shift context sctx */
855:   PetscMemzero(&sctx,sizeof(FactorShiftCtx));

857:   PetscMalloc3(am,&rtmp,am,&il,am,&jl);

859:   do {
860:     sctx.newshift = PETSC_FALSE;
861:     for (i=0; i<am; i++) {
862:       rtmp[i] = 0.0; jl[i] = am; il[0] = 0;
863:     }

865:     for (k = 0; k<am; k++) {
866:       /* initialize k-th row with elements nonzero in row perm(k) of A */
867:       nz   = ai[k+1] - ai[k];
868:       acol = aj + ai[k];
869:       aval = aa + ai[k];
870:       bval = ba + bi[k];
871:       while (nz--) {
872:         if (*acol < k) { /* skip lower triangular entries */
873:           acol++; aval++;
874:         } else {
875:           rtmp[*acol++] = *aval++;
876:           *bval++       = 0.0; /* for in-place factorization */
877:         }
878:       }

880:       /* shift the diagonal of the matrix */
881:       if (sctx.nshift) rtmp[k] += sctx.shift_amount;

883:       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
884:       dk = rtmp[k];
885:       i  = jl[k]; /* first row to be added to k_th row  */

887:       while (i < k) {
888:         nexti = jl[i]; /* next row to be added to k_th row */
889:         /* compute multiplier, update D(k) and U(i,k) */
890:         ili     = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
891:         uikdi   = -ba[ili]*ba[bi[i]];
892:         dk     += uikdi*ba[ili];
893:         ba[ili] = uikdi; /* -U(i,k) */

895:         /* add multiple of row i to k-th row ... */
896:         jmin = ili + 1;
897:         nz   = bi[i+1] - jmin;
898:         if (nz > 0) {
899:           bcol = bj + jmin;
900:           bval = ba + jmin;
901:           while (nz--) rtmp[*bcol++] += uikdi*(*bval++);
902:           /* update il and jl for i-th row */
903:           il[i] = jmin;
904:           j     = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
905:         }
906:         i = nexti;
907:       }

909:       /* shift the diagonals when zero pivot is detected */
910:       /* compute rs=sum of abs(off-diagonal) */
911:       rs   = 0.0;
912:       jmin = bi[k]+1;
913:       nz   = bi[k+1] - jmin;
914:       if (nz) {
915:         bcol = bj + jmin;
916:         while (nz--) {
917:           rs += PetscAbsScalar(rtmp[*bcol]);
918:           bcol++;
919:         }
920:       }

922:       sctx.rs = rs;
923:       sctx.pv = dk;
924:       MatPivotCheck(C,A,info,&sctx,k);
925:       if (sctx.newshift) break;    /* sctx.shift_amount is updated */
926:       dk = sctx.pv;

928:       /* copy data into U(k,:) */
929:       ba[bi[k]] = 1.0/dk;
930:       jmin      = bi[k]+1;
931:       nz        = bi[k+1] - jmin;
932:       if (nz) {
933:         bcol = bj + jmin;
934:         bval = ba + jmin;
935:         while (nz--) {
936:           *bval++       = rtmp[*bcol];
937:           rtmp[*bcol++] = 0.0;
938:         }
939:         /* add k-th row into il and jl */
940:         il[k] = jmin;
941:         i     = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
942:       }
943:     }
944:   } while (sctx.newshift);
945:   PetscFree3(rtmp,il,jl);

947:   C->ops->solve          = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
948:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
949:   C->assembled           = PETSC_TRUE;
950:   C->preallocated        = PETSC_TRUE;

952:   PetscLogFlops(C->rmap->N);
953:   if (sctx.nshift) {
954:     if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
955:       PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
956:     } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
957:       PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
958:     }
959:   }
960:   return(0);
961: }

963:  #include <petscbt.h>
964:  #include <../src/mat/utils/freespace.h>
965: PetscErrorCode MatICCFactorSymbolic_SeqBAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
966: {
967:   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data;
968:   Mat_SeqSBAIJ       *b;
969:   Mat                B;
970:   PetscErrorCode     ierr;
971:   PetscBool          perm_identity,missing;
972:   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=a->mbs,bs=A->rmap->bs,*ui;
973:   const PetscInt     *rip;
974:   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
975:   PetscInt           nlnk,*lnk,*lnk_lvl=NULL,ncols,ncols_upper,*cols,*cols_lvl,*uj,**uj_ptr,**uj_lvl_ptr;
976:   PetscReal          fill          =info->fill,levels=info->levels;
977:   PetscFreeSpaceList free_space    =NULL,current_space=NULL;
978:   PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL;
979:   PetscBT            lnkbt;

982:   MatMissingDiagonal(A,&missing,&i);
983:   if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);

985:   if (bs > 1) {
986:     if (!a->sbaijMat) {
987:       MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&a->sbaijMat);
988:     }
989:     (fact)->ops->iccfactorsymbolic = MatICCFactorSymbolic_SeqSBAIJ;  /* undue the change made in MatGetFactor_seqbaij_petsc */

991:     MatICCFactorSymbolic(fact,a->sbaijMat,perm,info);
992:     return(0);
993:   }

995:   ISIdentity(perm,&perm_identity);
996:   ISGetIndices(perm,&rip);

998:   /* special case that simply copies fill pattern */
999:   if (!levels && perm_identity) {
1000:     PetscMalloc1(am+1,&ui);
1001:     for (i=0; i<am; i++) ui[i] = ai[i+1] - a->diag[i]; /* ui: rowlengths - changes when !perm_identity */
1002:     B    = fact;
1003:     MatSeqSBAIJSetPreallocation(B,1,0,ui);


1006:     b  = (Mat_SeqSBAIJ*)B->data;
1007:     uj = b->j;
1008:     for (i=0; i<am; i++) {
1009:       aj = a->j + a->diag[i];
1010:       for (j=0; j<ui[i]; j++) *uj++ = *aj++;
1011:       b->ilen[i] = ui[i];
1012:     }
1013:     PetscFree(ui);

1015:     B->factortype = MAT_FACTOR_NONE;

1017:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1018:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1019:     B->factortype = MAT_FACTOR_ICC;

1021:     B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering;
1022:     return(0);
1023:   }

1025:   /* initialization */
1026:   PetscMalloc1(am+1,&ui);
1027:   ui[0] = 0;
1028:   PetscMalloc1(2*am+1,&cols_lvl);

1030:   /* jl: linked list for storing indices of the pivot rows
1031:      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
1032:   PetscMalloc4(am,&uj_ptr,am,&uj_lvl_ptr,am,&il,am,&jl);
1033:   for (i=0; i<am; i++) {
1034:     jl[i] = am; il[i] = 0;
1035:   }

1037:   /* create and initialize a linked list for storing column indices of the active row k */
1038:   nlnk = am + 1;
1039:   PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);

1041:   /* initial FreeSpace size is fill*(ai[am]+am)/2 */
1042:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am]/2,am/2)),&free_space);

1044:   current_space = free_space;

1046:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am]/2,am/2)),&free_space_lvl);
1047:   current_space_lvl = free_space_lvl;

1049:   for (k=0; k<am; k++) {  /* for each active row k */
1050:     /* initialize lnk by the column indices of row rip[k] of A */
1051:     nzk         = 0;
1052:     ncols       = ai[rip[k]+1] - ai[rip[k]];
1053:     ncols_upper = 0;
1054:     cols        = cols_lvl + am;
1055:     for (j=0; j<ncols; j++) {
1056:       i = rip[*(aj + ai[rip[k]] + j)];
1057:       if (i >= k) { /* only take upper triangular entry */
1058:         cols[ncols_upper]     = i;
1059:         cols_lvl[ncols_upper] = -1;  /* initialize level for nonzero entries */
1060:         ncols_upper++;
1061:       }
1062:     }
1063:     PetscIncompleteLLAdd(ncols_upper,cols,levels,cols_lvl,am,nlnk,lnk,lnk_lvl,lnkbt);
1064:     nzk += nlnk;

1066:     /* update lnk by computing fill-in for each pivot row to be merged in */
1067:     prow = jl[k]; /* 1st pivot row */

1069:     while (prow < k) {
1070:       nextprow = jl[prow];

1072:       /* merge prow into k-th row */
1073:       jmin  = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */
1074:       jmax  = ui[prow+1];
1075:       ncols = jmax-jmin;
1076:       i     = jmin - ui[prow];
1077:       cols  = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
1078:       for (j=0; j<ncols; j++) cols_lvl[j] = *(uj_lvl_ptr[prow] + i + j);
1079:       PetscIncompleteLLAddSorted(ncols,cols,levels,cols_lvl,am,nlnk,lnk,lnk_lvl,lnkbt);
1080:       nzk += nlnk;

1082:       /* update il and jl for prow */
1083:       if (jmin < jmax) {
1084:         il[prow] = jmin;

1086:         j = *cols; jl[prow] = jl[j]; jl[j] = prow;
1087:       }
1088:       prow = nextprow;
1089:     }

1091:     /* if free space is not available, make more free space */
1092:     if (current_space->local_remaining<nzk) {
1093:       i    = am - k + 1; /* num of unfactored rows */
1094:       i    = PetscMin(PetscIntMultTruncate(i,nzk), PetscIntMultTruncate(i,i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
1095:       PetscFreeSpaceGet(i,&current_space);
1096:       PetscFreeSpaceGet(i,&current_space_lvl);
1097:       reallocs++;
1098:     }

1100:     /* copy data into free_space and free_space_lvl, then initialize lnk */
1101:     PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);

1103:     /* add the k-th row into il and jl */
1104:     if (nzk-1 > 0) {
1105:       i     = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
1106:       jl[k] = jl[i]; jl[i] = k;
1107:       il[k] = ui[k] + 1;
1108:     }
1109:     uj_ptr[k]     = current_space->array;
1110:     uj_lvl_ptr[k] = current_space_lvl->array;

1112:     current_space->array           += nzk;
1113:     current_space->local_used      += nzk;
1114:     current_space->local_remaining -= nzk;

1116:     current_space_lvl->array           += nzk;
1117:     current_space_lvl->local_used      += nzk;
1118:     current_space_lvl->local_remaining -= nzk;

1120:     ui[k+1] = ui[k] + nzk;
1121:   }

1123:   ISRestoreIndices(perm,&rip);
1124:   PetscFree4(uj_ptr,uj_lvl_ptr,il,jl);
1125:   PetscFree(cols_lvl);

1127:   /* copy free_space into uj and free free_space; set uj in new datastructure; */
1128:   PetscMalloc1(ui[am]+1,&uj);
1129:   PetscFreeSpaceContiguous(&free_space,uj);
1130:   PetscIncompleteLLDestroy(lnk,lnkbt);
1131:   PetscFreeSpaceDestroy(free_space_lvl);

1133:   /* put together the new matrix in MATSEQSBAIJ format */
1134:   B    = fact;
1135:   MatSeqSBAIJSetPreallocation(B,1,MAT_SKIP_ALLOCATION,NULL);

1137:   b                = (Mat_SeqSBAIJ*)B->data;
1138:   b->singlemalloc  = PETSC_FALSE;
1139:   b->free_a        = PETSC_TRUE;
1140:   b->free_ij       = PETSC_TRUE;

1142:   PetscMalloc1(ui[am]+1,&b->a);

1144:   b->j             = uj;
1145:   b->i             = ui;
1146:   b->diag          = 0;
1147:   b->ilen          = 0;
1148:   b->imax          = 0;
1149:   b->row           = perm;
1150:   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */

1152:   PetscObjectReference((PetscObject)perm);

1154:   b->icol = perm;

1156:   PetscObjectReference((PetscObject)perm);
1157:   PetscMalloc1(am+1,&b->solve_work);
1158:   PetscLogObjectMemory((PetscObject)B,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));

1160:   b->maxnz = b->nz = ui[am];

1162:   B->info.factor_mallocs   = reallocs;
1163:   B->info.fill_ratio_given = fill;
1164:   if (ai[am] != 0.) {
1165:     /* nonzeros in lower triangular part of A (includign diagonals)= (ai[am]+am)/2 */
1166:     B->info.fill_ratio_needed = ((PetscReal)2*ui[am])/(ai[am]+am);
1167:   } else {
1168:     B->info.fill_ratio_needed = 0.0;
1169:   }
1170: #if defined(PETSC_USE_INFO)
1171:   if (ai[am] != 0) {
1172:     PetscReal af = B->info.fill_ratio_needed;
1173:     PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
1174:     PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
1175:     PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
1176:   } else {
1177:     PetscInfo(A,"Empty matrix.\n");
1178:   }
1179: #endif
1180:   if (perm_identity) {
1181:     B->ops->solve                 = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
1182:     B->ops->solvetranspose        = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
1183:     B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering;
1184:   } else {
1185:     (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N;
1186:   }
1187:   return(0);
1188: }

1190: PetscErrorCode MatCholeskyFactorSymbolic_SeqBAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
1191: {
1192:   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data;
1193:   Mat_SeqSBAIJ       *b;
1194:   Mat                B;
1195:   PetscErrorCode     ierr;
1196:   PetscBool          perm_identity,missing;
1197:   PetscReal          fill = info->fill;
1198:   const PetscInt     *rip;
1199:   PetscInt           i,mbs=a->mbs,bs=A->rmap->bs,*ai=a->i,*aj=a->j,reallocs=0,prow;
1200:   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
1201:   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr;
1202:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
1203:   PetscBT            lnkbt;

1206:   if (bs > 1) { /* convert to seqsbaij */
1207:     if (!a->sbaijMat) {
1208:       MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&a->sbaijMat);
1209:     }
1210:     (fact)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqSBAIJ; /* undue the change made in MatGetFactor_seqbaij_petsc */

1212:     MatCholeskyFactorSymbolic(fact,a->sbaijMat,perm,info);
1213:     return(0);
1214:   }

1216:   MatMissingDiagonal(A,&missing,&i);
1217:   if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);

1219:   /* check whether perm is the identity mapping */
1220:   ISIdentity(perm,&perm_identity);
1221:   if (!perm_identity) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix reordering is not supported");
1222:   ISGetIndices(perm,&rip);

1224:   /* initialization */
1225:   PetscMalloc1(mbs+1,&ui);
1226:   ui[0] = 0;

1228:   /* jl: linked list for storing indices of the pivot rows
1229:      il: il[i] points to the 1st nonzero entry of U(i,k:mbs-1) */
1230:   PetscMalloc4(mbs,&ui_ptr,mbs,&il,mbs,&jl,mbs,&cols);
1231:   for (i=0; i<mbs; i++) {
1232:     jl[i] = mbs; il[i] = 0;
1233:   }

1235:   /* create and initialize a linked list for storing column indices of the active row k */
1236:   nlnk = mbs + 1;
1237:   PetscLLCreate(mbs,mbs,nlnk,lnk,lnkbt);

1239:   /* initial FreeSpace size is fill* (ai[mbs]+mbs)/2 */
1240:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[mbs]/2,mbs/2)),&free_space);

1242:   current_space = free_space;

1244:   for (k=0; k<mbs; k++) {  /* for each active row k */
1245:     /* initialize lnk by the column indices of row rip[k] of A */
1246:     nzk         = 0;
1247:     ncols       = ai[rip[k]+1] - ai[rip[k]];
1248:     ncols_upper = 0;
1249:     for (j=0; j<ncols; j++) {
1250:       i = rip[*(aj + ai[rip[k]] + j)];
1251:       if (i >= k) { /* only take upper triangular entry */
1252:         cols[ncols_upper] = i;
1253:         ncols_upper++;
1254:       }
1255:     }
1256:     PetscLLAdd(ncols_upper,cols,mbs,nlnk,lnk,lnkbt);
1257:     nzk += nlnk;

1259:     /* update lnk by computing fill-in for each pivot row to be merged in */
1260:     prow = jl[k]; /* 1st pivot row */

1262:     while (prow < k) {
1263:       nextprow = jl[prow];
1264:       /* merge prow into k-th row */
1265:       jmin   = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:mbs-1) */
1266:       jmax   = ui[prow+1];
1267:       ncols  = jmax-jmin;
1268:       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:mbs-1) */
1269:       PetscLLAddSorted(ncols,uj_ptr,mbs,nlnk,lnk,lnkbt);
1270:       nzk   += nlnk;

1272:       /* update il and jl for prow */
1273:       if (jmin < jmax) {
1274:         il[prow] = jmin;
1275:         j        = *uj_ptr;
1276:         jl[prow] = jl[j];
1277:         jl[j]    = prow;
1278:       }
1279:       prow = nextprow;
1280:     }

1282:     /* if free space is not available, make more free space */
1283:     if (current_space->local_remaining<nzk) {
1284:       i    = mbs - k + 1; /* num of unfactored rows */
1285:       i    = PetscMin(PetscIntMultTruncate(i,nzk), PetscIntMultTruncate(i,i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
1286:       PetscFreeSpaceGet(i,&current_space);
1287:       reallocs++;
1288:     }

1290:     /* copy data into free space, then initialize lnk */
1291:     PetscLLClean(mbs,mbs,nzk,lnk,current_space->array,lnkbt);

1293:     /* add the k-th row into il and jl */
1294:     if (nzk-1 > 0) {
1295:       i     = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:mbs-1) */
1296:       jl[k] = jl[i]; jl[i] = k;
1297:       il[k] = ui[k] + 1;
1298:     }
1299:     ui_ptr[k]                       = current_space->array;
1300:     current_space->array           += nzk;
1301:     current_space->local_used      += nzk;
1302:     current_space->local_remaining -= nzk;

1304:     ui[k+1] = ui[k] + nzk;
1305:   }

1307:   ISRestoreIndices(perm,&rip);
1308:   PetscFree4(ui_ptr,il,jl,cols);

1310:   /* copy free_space into uj and free free_space; set uj in new datastructure; */
1311:   PetscMalloc1(ui[mbs]+1,&uj);
1312:   PetscFreeSpaceContiguous(&free_space,uj);
1313:   PetscLLDestroy(lnk,lnkbt);

1315:   /* put together the new matrix in MATSEQSBAIJ format */
1316:   B    = fact;
1317:   MatSeqSBAIJSetPreallocation(B,bs,MAT_SKIP_ALLOCATION,NULL);

1319:   b               = (Mat_SeqSBAIJ*)B->data;
1320:   b->singlemalloc = PETSC_FALSE;
1321:   b->free_a       = PETSC_TRUE;
1322:   b->free_ij      = PETSC_TRUE;

1324:   PetscMalloc1(ui[mbs]+1,&b->a);

1326:   b->j             = uj;
1327:   b->i             = ui;
1328:   b->diag          = 0;
1329:   b->ilen          = 0;
1330:   b->imax          = 0;
1331:   b->row           = perm;
1332:   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */

1334:   PetscObjectReference((PetscObject)perm);
1335:   b->icol  = perm;
1336:   PetscObjectReference((PetscObject)perm);
1337:   PetscMalloc1(mbs+1,&b->solve_work);
1338:   PetscLogObjectMemory((PetscObject)B,(ui[mbs]-mbs)*(sizeof(PetscInt)+sizeof(MatScalar)));
1339:   b->maxnz = b->nz = ui[mbs];

1341:   B->info.factor_mallocs   = reallocs;
1342:   B->info.fill_ratio_given = fill;
1343:   if (ai[mbs] != 0.) {
1344:     /* nonzeros in lower triangular part of A = (ai[mbs]+mbs)/2 */
1345:     B->info.fill_ratio_needed = ((PetscReal)2*ui[mbs])/(ai[mbs]+mbs);
1346:   } else {
1347:     B->info.fill_ratio_needed = 0.0;
1348:   }
1349: #if defined(PETSC_USE_INFO)
1350:   if (ai[mbs] != 0.) {
1351:     PetscReal af = B->info.fill_ratio_needed;
1352:     PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
1353:     PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
1354:     PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
1355:   } else {
1356:     PetscInfo(A,"Empty matrix.\n");
1357:   }
1358: #endif
1359:   if (perm_identity) {
1360:     B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering;
1361:   } else {
1362:     B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N;
1363:   }
1364:   return(0);
1365: }

1367: PetscErrorCode MatSolve_SeqBAIJ_N_NaturalOrdering(Mat A,Vec bb,Vec xx)
1368: {
1369:   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ*)A->data;
1370:   PetscErrorCode    ierr;
1371:   const PetscInt    *ai=a->i,*aj=a->j,*adiag=a->diag,*vi;
1372:   PetscInt          i,k,n=a->mbs;
1373:   PetscInt          nz,bs=A->rmap->bs,bs2=a->bs2;
1374:   const MatScalar   *aa=a->a,*v;
1375:   PetscScalar       *x,*s,*t,*ls;
1376:   const PetscScalar *b;

1379:   VecGetArrayRead(bb,&b);
1380:   VecGetArray(xx,&x);
1381:   t    = a->solve_work;

1383:   /* forward solve the lower triangular */
1384:   PetscArraycpy(t,b,bs); /* copy 1st block of b to t */

1386:   for (i=1; i<n; i++) {
1387:     v    = aa + bs2*ai[i];
1388:     vi   = aj + ai[i];
1389:     nz   = ai[i+1] - ai[i];
1390:     s    = t + bs*i;
1391:     PetscArraycpy(s,b+bs*i,bs); /* copy i_th block of b to t */
1392:     for (k=0;k<nz;k++) {
1393:       PetscKernel_v_gets_v_minus_A_times_w(bs,s,v,t+bs*vi[k]);
1394:       v += bs2;
1395:     }
1396:   }

1398:   /* backward solve the upper triangular */
1399:   ls = a->solve_work + A->cmap->n;
1400:   for (i=n-1; i>=0; i--) {
1401:     v    = aa + bs2*(adiag[i+1]+1);
1402:     vi   = aj + adiag[i+1]+1;
1403:     nz   = adiag[i] - adiag[i+1]-1;
1404:     PetscArraycpy(ls,t+i*bs,bs);
1405:     for (k=0; k<nz; k++) {
1406:       PetscKernel_v_gets_v_minus_A_times_w(bs,ls,v,t+bs*vi[k]);
1407:       v += bs2;
1408:     }
1409:     PetscKernel_w_gets_A_times_v(bs,ls,aa+bs2*adiag[i],t+i*bs); /* *inv(diagonal[i]) */
1410:     PetscArraycpy(x+i*bs,t+i*bs,bs);
1411:   }

1413:   VecRestoreArrayRead(bb,&b);
1414:   VecRestoreArray(xx,&x);
1415:   PetscLogFlops(2.0*(a->bs2)*(a->nz) - A->rmap->bs*A->cmap->n);
1416:   return(0);
1417: }

1419: PetscErrorCode MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx)
1420: {
1421:   Mat_SeqBAIJ        *a   =(Mat_SeqBAIJ*)A->data;
1422:   IS                 iscol=a->col,isrow=a->row;
1423:   PetscErrorCode     ierr;
1424:   const PetscInt     *r,*c,*rout,*cout,*ai=a->i,*aj=a->j,*adiag=a->diag,*vi;
1425:   PetscInt           i,m,n=a->mbs;
1426:   PetscInt           nz,bs=A->rmap->bs,bs2=a->bs2;
1427:   const MatScalar    *aa=a->a,*v;
1428:   PetscScalar        *x,*s,*t,*ls;
1429:   const PetscScalar  *b;

1432:   VecGetArrayRead(bb,&b);
1433:   VecGetArray(xx,&x);
1434:   t    = a->solve_work;

1436:   ISGetIndices(isrow,&rout); r = rout;
1437:   ISGetIndices(iscol,&cout); c = cout;

1439:   /* forward solve the lower triangular */
1440:   PetscArraycpy(t,b+bs*r[0],bs);
1441:   for (i=1; i<n; i++) {
1442:     v    = aa + bs2*ai[i];
1443:     vi   = aj + ai[i];
1444:     nz   = ai[i+1] - ai[i];
1445:     s    = t + bs*i;
1446:     PetscArraycpy(s,b+bs*r[i],bs);
1447:     for (m=0; m<nz; m++) {
1448:       PetscKernel_v_gets_v_minus_A_times_w(bs,s,v,t+bs*vi[m]);
1449:       v += bs2;
1450:     }
1451:   }

1453:   /* backward solve the upper triangular */
1454:   ls = a->solve_work + A->cmap->n;
1455:   for (i=n-1; i>=0; i--) {
1456:     v    = aa + bs2*(adiag[i+1]+1);
1457:     vi   = aj + adiag[i+1]+1;
1458:     nz   = adiag[i] - adiag[i+1] - 1;
1459:     PetscArraycpy(ls,t+i*bs,bs);
1460:     for (m=0; m<nz; m++) {
1461:       PetscKernel_v_gets_v_minus_A_times_w(bs,ls,v,t+bs*vi[m]);
1462:       v += bs2;
1463:     }
1464:     PetscKernel_w_gets_A_times_v(bs,ls,v,t+i*bs); /* *inv(diagonal[i]) */
1465:     PetscArraycpy(x + bs*c[i],t+i*bs,bs);
1466:   }
1467:   ISRestoreIndices(isrow,&rout);
1468:   ISRestoreIndices(iscol,&cout);
1469:   VecRestoreArrayRead(bb,&b);
1470:   VecRestoreArray(xx,&x);
1471:   PetscLogFlops(2.0*(a->bs2)*(a->nz) - A->rmap->bs*A->cmap->n);
1472:   return(0);
1473: }

1475: /*
1476:     For each block in an block array saves the largest absolute value in the block into another array
1477: */
1478: static PetscErrorCode MatBlockAbs_private(PetscInt nbs,PetscInt bs2,PetscScalar *blockarray,PetscReal *absarray)
1479: {
1481:   PetscInt       i,j;

1484:   PetscArrayzero(absarray,nbs+1);
1485:   for (i=0; i<nbs; i++) {
1486:     for (j=0; j<bs2; j++) {
1487:       if (absarray[i] < PetscAbsScalar(blockarray[i*nbs+j])) absarray[i] = PetscAbsScalar(blockarray[i*nbs+j]);
1488:     }
1489:   }
1490:   return(0);
1491: }

1493: /*
1494:      This needs to be renamed and called by the regular MatILUFactor_SeqBAIJ when drop tolerance is used
1495: */
1496: PetscErrorCode MatILUDTFactor_SeqBAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact)
1497: {
1498:   Mat            B = *fact;
1499:   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b;
1500:   IS             isicol;
1502:   const PetscInt *r,*ic;
1503:   PetscInt       i,mbs=a->mbs,bs=A->rmap->bs,bs2=a->bs2,*ai=a->i,*aj=a->j,*ajtmp,*adiag;
1504:   PetscInt       *bi,*bj,*bdiag;

1506:   PetscInt  row,nzi,nzi_bl,nzi_bu,*im,dtcount,nzi_al,nzi_au;
1507:   PetscInt  nlnk,*lnk;
1508:   PetscBT   lnkbt;
1509:   PetscBool row_identity,icol_identity;
1510:   MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,*multiplier,*vtmp;
1511:   PetscInt  j,nz,*pj,*bjtmp,k,ncut,*jtmp;

1513:   PetscReal dt=info->dt;          /* shift=info->shiftamount; */
1514:   PetscInt  nnz_max;
1515:   PetscBool missing;
1516:   PetscReal *vtmp_abs;
1517:   MatScalar *v_work;
1518:   PetscInt  *v_pivots;
1519:   PetscBool allowzeropivot,zeropivotdetected=PETSC_FALSE;

1522:   /* ------- symbolic factorization, can be reused ---------*/
1523:   MatMissingDiagonal(A,&missing,&i);
1524:   if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
1525:   adiag=a->diag;

1527:   ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);

1529:   /* bdiag is location of diagonal in factor */
1530:   PetscMalloc1(mbs+1,&bdiag);

1532:   /* allocate row pointers bi */
1533:   PetscMalloc1(2*mbs+2,&bi);

1535:   /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */
1536:   dtcount = (PetscInt)info->dtcount;
1537:   if (dtcount > mbs-1) dtcount = mbs-1;
1538:   nnz_max = ai[mbs]+2*mbs*dtcount +2;
1539:   /* printf("MatILUDTFactor_SeqBAIJ, bs %d, ai[mbs] %d, nnz_max  %d, dtcount %d\n",bs,ai[mbs],nnz_max,dtcount); */
1540:   PetscMalloc1(nnz_max,&bj);
1541:   nnz_max = nnz_max*bs2;
1542:   PetscMalloc1(nnz_max,&ba);

1544:   /* put together the new matrix */
1545:   MatSeqBAIJSetPreallocation(B,bs,MAT_SKIP_ALLOCATION,NULL);
1546:   PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);

1548:   b               = (Mat_SeqBAIJ*)(B)->data;
1549:   b->free_a       = PETSC_TRUE;
1550:   b->free_ij      = PETSC_TRUE;
1551:   b->singlemalloc = PETSC_FALSE;

1553:   b->a    = ba;
1554:   b->j    = bj;
1555:   b->i    = bi;
1556:   b->diag = bdiag;
1557:   b->ilen = 0;
1558:   b->imax = 0;
1559:   b->row  = isrow;
1560:   b->col  = iscol;

1562:   PetscObjectReference((PetscObject)isrow);
1563:   PetscObjectReference((PetscObject)iscol);

1565:   b->icol  = isicol;
1566:   PetscMalloc1(bs*(mbs+1),&b->solve_work);
1567:   PetscLogObjectMemory((PetscObject)B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));
1568:   b->maxnz = nnz_max/bs2;

1570:   (B)->factortype            = MAT_FACTOR_ILUDT;
1571:   (B)->info.factor_mallocs   = 0;
1572:   (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)(ai[mbs]*bs2));
1573:   /* ------- end of symbolic factorization ---------*/
1574:   ISGetIndices(isrow,&r);
1575:   ISGetIndices(isicol,&ic);

1577:   /* linked list for storing column indices of the active row */
1578:   nlnk = mbs + 1;
1579:   PetscLLCreate(mbs,mbs,nlnk,lnk,lnkbt);

1581:   /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */
1582:   PetscMalloc2(mbs,&im,mbs,&jtmp);
1583:   /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */
1584:   PetscMalloc2(mbs*bs2,&rtmp,mbs*bs2,&vtmp);
1585:   PetscMalloc1(mbs+1,&vtmp_abs);
1586:   PetscMalloc3(bs,&v_work,bs2,&multiplier,bs,&v_pivots);

1588:   allowzeropivot = PetscNot(A->erroriffailure);
1589:   bi[0]       = 0;
1590:   bdiag[0]    = (nnz_max/bs2)-1; /* location of diagonal in factor B */
1591:   bi[2*mbs+1] = bdiag[0]+1; /* endof bj and ba array */
1592:   for (i=0; i<mbs; i++) {
1593:     /* copy initial fill into linked list */
1594:     nzi = ai[r[i]+1] - ai[r[i]];
1595:     if (!nzi) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1596:     nzi_al = adiag[r[i]] - ai[r[i]];
1597:     nzi_au = ai[r[i]+1] - adiag[r[i]] -1;

1599:     /* load in initial unfactored row */
1600:     ajtmp = aj + ai[r[i]];
1601:     PetscLLAddPerm(nzi,ajtmp,ic,mbs,nlnk,lnk,lnkbt);
1602:     PetscArrayzero(rtmp,mbs*bs2);
1603:     aatmp = a->a + bs2*ai[r[i]];
1604:     for (j=0; j<nzi; j++) {
1605:       PetscArraycpy(rtmp+bs2*ic[ajtmp[j]],aatmp+bs2*j,bs2);
1606:     }

1608:     /* add pivot rows into linked list */
1609:     row = lnk[mbs];
1610:     while (row < i) {
1611:       nzi_bl = bi[row+1] - bi[row] + 1;
1612:       bjtmp  = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */
1613:       PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);
1614:       nzi   += nlnk;
1615:       row    = lnk[row];
1616:     }

1618:     /* copy data from lnk into jtmp, then initialize lnk */
1619:     PetscLLClean(mbs,mbs,nzi,lnk,jtmp,lnkbt);

1621:     /* numerical factorization */
1622:     bjtmp = jtmp;
1623:     row   = *bjtmp++; /* 1st pivot row */

1625:     while  (row < i) {
1626:       pc = rtmp + bs2*row;
1627:       pv = ba + bs2*bdiag[row]; /* inv(diag) of the pivot row */
1628:       PetscKernel_A_gets_A_times_B(bs,pc,pv,multiplier); /* pc= multiplier = pc*inv(diag[row]) */
1629:       MatBlockAbs_private(1,bs2,pc,vtmp_abs);
1630:       if (vtmp_abs[0] > dt) { /* apply tolerance dropping rule */
1631:         pj = bj + bdiag[row+1] + 1;         /* point to 1st entry of U(row,:) */
1632:         pv = ba + bs2*(bdiag[row+1] + 1);
1633:         nz = bdiag[row] - bdiag[row+1] - 1;         /* num of entries in U(row,:), excluding diagonal */
1634:         for (j=0; j<nz; j++) {
1635:           PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
1636:         }
1637:         /* PetscLogFlops(bslog*(nz+1.0)-bs); */
1638:       }
1639:       row = *bjtmp++;
1640:     }

1642:     /* copy sparse rtmp into contiguous vtmp; separate L and U part */
1643:     nzi_bl = 0; j = 0;
1644:     while (jtmp[j] < i) { /* L-part. Note: jtmp is sorted */
1645:       PetscArraycpy(vtmp+bs2*j,rtmp+bs2*jtmp[j],bs2);
1646:       nzi_bl++; j++;
1647:     }
1648:     nzi_bu = nzi - nzi_bl -1;

1650:     while (j < nzi) { /* U-part */
1651:       PetscArraycpy(vtmp+bs2*j,rtmp+bs2*jtmp[j],bs2);
1652:       j++;
1653:     }

1655:     MatBlockAbs_private(nzi,bs2,vtmp,vtmp_abs);

1657:     bjtmp = bj + bi[i];
1658:     batmp = ba + bs2*bi[i];
1659:     /* apply level dropping rule to L part */
1660:     ncut = nzi_al + dtcount;
1661:     if (ncut < nzi_bl) {
1662:       PetscSortSplitReal(ncut,nzi_bl,vtmp_abs,jtmp);
1663:       PetscSortIntWithScalarArray(ncut,jtmp,vtmp);
1664:     } else {
1665:       ncut = nzi_bl;
1666:     }
1667:     for (j=0; j<ncut; j++) {
1668:       bjtmp[j] = jtmp[j];
1669:       PetscArraycpy(batmp+bs2*j,rtmp+bs2*bjtmp[j],bs2);
1670:     }
1671:     bi[i+1] = bi[i] + ncut;
1672:     nzi     = ncut + 1;

1674:     /* apply level dropping rule to U part */
1675:     ncut = nzi_au + dtcount;
1676:     if (ncut < nzi_bu) {
1677:       PetscSortSplitReal(ncut,nzi_bu,vtmp_abs+nzi_bl+1,jtmp+nzi_bl+1);
1678:       PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);
1679:     } else {
1680:       ncut = nzi_bu;
1681:     }
1682:     nzi += ncut;

1684:     /* mark bdiagonal */
1685:     bdiag[i+1]    = bdiag[i] - (ncut + 1);
1686:     bi[2*mbs - i] = bi[2*mbs - i +1] - (ncut + 1);

1688:     bjtmp  = bj + bdiag[i];
1689:     batmp  = ba + bs2*bdiag[i];
1690:     PetscArraycpy(batmp,rtmp+bs2*i,bs2);
1691:     *bjtmp = i;

1693:     bjtmp = bj + bdiag[i+1]+1;
1694:     batmp = ba + (bdiag[i+1]+1)*bs2;

1696:     for (k=0; k<ncut; k++) {
1697:       bjtmp[k] = jtmp[nzi_bl+1+k];
1698:       PetscArraycpy(batmp+bs2*k,rtmp+bs2*bjtmp[k],bs2);
1699:     }

1701:     im[i] = nzi; /* used by PetscLLAddSortedLU() */

1703:     /* invert diagonal block for simplier triangular solves - add shift??? */
1704:     batmp = ba + bs2*bdiag[i];

1706:     PetscKernel_A_gets_inverse_A(bs,batmp,v_pivots,v_work,allowzeropivot,&zeropivotdetected);
1707:     if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1708:   } /* for (i=0; i<mbs; i++) */
1709:   PetscFree3(v_work,multiplier,v_pivots);

1711:   /* printf("end of L %d, beginning of U %d\n",bi[mbs],bdiag[mbs]); */
1712:   if (bi[mbs] >= bdiag[mbs]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"end of L array %d cannot >= the beginning of U array %d",bi[mbs],bdiag[mbs]);

1714:   ISRestoreIndices(isrow,&r);
1715:   ISRestoreIndices(isicol,&ic);

1717:   PetscLLDestroy(lnk,lnkbt);

1719:   PetscFree2(im,jtmp);
1720:   PetscFree2(rtmp,vtmp);

1722:   PetscLogFlops(bs2*B->cmap->n);
1723:   b->maxnz = b->nz = bi[mbs] + bdiag[0] - bdiag[mbs];

1725:   ISIdentity(isrow,&row_identity);
1726:   ISIdentity(isicol,&icol_identity);
1727:   if (row_identity && icol_identity) {
1728:     B->ops->solve = MatSolve_SeqBAIJ_N_NaturalOrdering;
1729:   } else {
1730:     B->ops->solve = MatSolve_SeqBAIJ_N;
1731:   }

1733:   B->ops->solveadd          = 0;
1734:   B->ops->solvetranspose    = 0;
1735:   B->ops->solvetransposeadd = 0;
1736:   B->ops->matsolve          = 0;
1737:   B->assembled              = PETSC_TRUE;
1738:   B->preallocated           = PETSC_TRUE;
1739:   return(0);
1740: }