Actual source code: baijfact13.c

petsc-3.6.1 2015-08-06
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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: /*
  9:       Version for when blocks are 3 by 3
 10: */
 13: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_inplace(Mat C,Mat A,const MatFactorInfo *info)
 14: {
 15:   Mat_SeqBAIJ    *a    = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
 16:   IS             isrow = b->row,isicol = b->icol;
 18:   const PetscInt *r,*ic;
 19:   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
 20:   PetscInt       *ajtmpold,*ajtmp,nz,row,*ai=a->i,*aj=a->j;
 21:   PetscInt       *diag_offset = b->diag,idx,*pj;
 22:   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
 23:   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
 24:   MatScalar      p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
 25:   MatScalar      *ba   = b->a,*aa = a->a;
 26:   PetscReal      shift = info->shiftamount;

 29:   ISGetIndices(isrow,&r);
 30:   ISGetIndices(isicol,&ic);
 31:   PetscMalloc1(9*(n+1),&rtmp);

 33:   for (i=0; i<n; i++) {
 34:     nz    = bi[i+1] - bi[i];
 35:     ajtmp = bj + bi[i];
 36:     for  (j=0; j<nz; j++) {
 37:       x    = rtmp + 9*ajtmp[j];
 38:       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0;
 39:     }
 40:     /* load in initial (unfactored row) */
 41:     idx      = r[i];
 42:     nz       = ai[idx+1] - ai[idx];
 43:     ajtmpold = aj + ai[idx];
 44:     v        = aa + 9*ai[idx];
 45:     for (j=0; j<nz; j++) {
 46:       x    = rtmp + 9*ic[ajtmpold[j]];
 47:       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
 48:       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
 49:       v   += 9;
 50:     }
 51:     row = *ajtmp++;
 52:     while (row < i) {
 53:       pc = rtmp + 9*row;
 54:       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
 55:       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
 56:       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
 57:           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
 58:         pv    = ba + 9*diag_offset[row];
 59:         pj    = bj + diag_offset[row] + 1;
 60:         x1    = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
 61:         x5    = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
 62:         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
 63:         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
 64:         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;

 66:         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
 67:         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
 68:         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;

 70:         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
 71:         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
 72:         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
 73:         nz    = bi[row+1] - diag_offset[row] - 1;
 74:         pv   += 9;
 75:         for (j=0; j<nz; j++) {
 76:           x1    = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
 77:           x5    = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
 78:           x     = rtmp + 9*pj[j];
 79:           x[0] -= m1*x1 + m4*x2 + m7*x3;
 80:           x[1] -= m2*x1 + m5*x2 + m8*x3;
 81:           x[2] -= m3*x1 + m6*x2 + m9*x3;

 83:           x[3] -= m1*x4 + m4*x5 + m7*x6;
 84:           x[4] -= m2*x4 + m5*x5 + m8*x6;
 85:           x[5] -= m3*x4 + m6*x5 + m9*x6;

 87:           x[6] -= m1*x7 + m4*x8 + m7*x9;
 88:           x[7] -= m2*x7 + m5*x8 + m8*x9;
 89:           x[8] -= m3*x7 + m6*x8 + m9*x9;
 90:           pv   += 9;
 91:         }
 92:         PetscLogFlops(54.0*nz+36.0);
 93:       }
 94:       row = *ajtmp++;
 95:     }
 96:     /* finished row so stick it into b->a */
 97:     pv = ba + 9*bi[i];
 98:     pj = bj + bi[i];
 99:     nz = bi[i+1] - bi[i];
100:     for (j=0; j<nz; j++) {
101:       x     = rtmp + 9*pj[j];
102:       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
103:       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
104:       pv   += 9;
105:     }
106:     /* invert diagonal block */
107:     w    = ba + 9*diag_offset[i];
108:     PetscKernel_A_gets_inverse_A_3(w,shift);
109:   }

111:   PetscFree(rtmp);
112:   ISRestoreIndices(isicol,&ic);
113:   ISRestoreIndices(isrow,&r);

115:   C->ops->solve          = MatSolve_SeqBAIJ_3_inplace;
116:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_inplace;
117:   C->assembled           = PETSC_TRUE;

119:   PetscLogFlops(1.333333333333*3*3*3*b->mbs); /* from inverting diagonal blocks */
120:   return(0);
121: }

123: /* MatLUFactorNumeric_SeqBAIJ_3 -
124:      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
125:        PetscKernel_A_gets_A_times_B()
126:        PetscKernel_A_gets_A_minus_B_times_C()
127:        PetscKernel_A_gets_inverse_A()
128: */
131: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3(Mat B,Mat A,const MatFactorInfo *info)
132: {
133:   Mat            C     =B;
134:   Mat_SeqBAIJ    *a    =(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
135:   IS             isrow = b->row,isicol = b->icol;
137:   const PetscInt *r,*ic;
138:   PetscInt       i,j,k,nz,nzL,row;
139:   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
140:   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
141:   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
142:   PetscInt       flg;
143:   PetscReal      shift = info->shiftamount;

146:   ISGetIndices(isrow,&r);
147:   ISGetIndices(isicol,&ic);

149:   /* generate work space needed by the factorization */
150:   PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
151:   PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));

153:   for (i=0; i<n; i++) {
154:     /* zero rtmp */
155:     /* L part */
156:     nz    = bi[i+1] - bi[i];
157:     bjtmp = bj + bi[i];
158:     for  (j=0; j<nz; j++) {
159:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
160:     }

162:     /* U part */
163:     nz    = bdiag[i] - bdiag[i+1];
164:     bjtmp = bj + bdiag[i+1]+1;
165:     for  (j=0; j<nz; j++) {
166:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
167:     }

169:     /* load in initial (unfactored row) */
170:     nz    = ai[r[i]+1] - ai[r[i]];
171:     ajtmp = aj + ai[r[i]];
172:     v     = aa + bs2*ai[r[i]];
173:     for (j=0; j<nz; j++) {
174:       PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));
175:     }

177:     /* elimination */
178:     bjtmp = bj + bi[i];
179:     nzL   = bi[i+1] - bi[i];
180:     for (k = 0; k < nzL; k++) {
181:       row = bjtmp[k];
182:       pc  = rtmp + bs2*row;
183:       for (flg=0,j=0; j<bs2; j++) {
184:         if (pc[j]!=0.0) {
185:           flg = 1;
186:           break;
187:         }
188:       }
189:       if (flg) {
190:         pv = b->a + bs2*bdiag[row];
191:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
192:         PetscKernel_A_gets_A_times_B_3(pc,pv,mwork);

194:         pj = b->j + bdiag[row+1] + 1; /* beginning of U(row,:) */
195:         pv = b->a + bs2*(bdiag[row+1]+1);
196:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
197:         for (j=0; j<nz; j++) {
198:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
199:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
200:           v    = rtmp + bs2*pj[j];
201:           PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);
202:           pv  += bs2;
203:         }
204:         PetscLogFlops(54*nz+45); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
205:       }
206:     }

208:     /* finished row so stick it into b->a */
209:     /* L part */
210:     pv = b->a + bs2*bi[i];
211:     pj = b->j + bi[i];
212:     nz = bi[i+1] - bi[i];
213:     for (j=0; j<nz; j++) {
214:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
215:     }

217:     /* Mark diagonal and invert diagonal for simplier triangular solves */
218:     pv   = b->a + bs2*bdiag[i];
219:     pj   = b->j + bdiag[i];
220:     PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
221:     /* PetscKernel_A_gets_inverse_A(bs,pv,v_pivots,v_work); */
222:     PetscKernel_A_gets_inverse_A_3(pv,shift);

224:     /* U part */
225:     pj = b->j + bdiag[i+1] + 1;
226:     pv = b->a + bs2*(bdiag[i+1]+1);
227:     nz = bdiag[i] - bdiag[i+1] - 1;
228:     for (j=0; j<nz; j++) {
229:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
230:     }
231:   }

233:   PetscFree2(rtmp,mwork);
234:   ISRestoreIndices(isicol,&ic);
235:   ISRestoreIndices(isrow,&r);

237:   C->ops->solve          = MatSolve_SeqBAIJ_3;
238:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3;
239:   C->assembled           = PETSC_TRUE;

241:   PetscLogFlops(1.333333333333*3*3*3*n); /* from inverting diagonal blocks */
242:   return(0);
243: }

247: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
248: {
249:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
251:   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
252:   PetscInt       *ajtmpold,*ajtmp,nz,row;
253:   PetscInt       *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
254:   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
255:   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
256:   MatScalar      p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
257:   MatScalar      *ba   = b->a,*aa = a->a;
258:   PetscReal      shift = info->shiftamount;

261:   PetscMalloc1(9*(n+1),&rtmp);

263:   for (i=0; i<n; i++) {
264:     nz    = bi[i+1] - bi[i];
265:     ajtmp = bj + bi[i];
266:     for  (j=0; j<nz; j++) {
267:       x    = rtmp+9*ajtmp[j];
268:       x[0] = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = 0.0;
269:     }
270:     /* load in initial (unfactored row) */
271:     nz       = ai[i+1] - ai[i];
272:     ajtmpold = aj + ai[i];
273:     v        = aa + 9*ai[i];
274:     for (j=0; j<nz; j++) {
275:       x    = rtmp+9*ajtmpold[j];
276:       x[0] = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
277:       x[4] = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
278:       v   += 9;
279:     }
280:     row = *ajtmp++;
281:     while (row < i) {
282:       pc = rtmp + 9*row;
283:       p1 = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
284:       p5 = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
285:       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
286:           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
287:         pv    = ba + 9*diag_offset[row];
288:         pj    = bj + diag_offset[row] + 1;
289:         x1    = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
290:         x5    = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
291:         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
292:         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
293:         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;

295:         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
296:         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
297:         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;

299:         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
300:         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
301:         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;

303:         nz  = bi[row+1] - diag_offset[row] - 1;
304:         pv += 9;
305:         for (j=0; j<nz; j++) {
306:           x1    = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
307:           x5    = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
308:           x     = rtmp + 9*pj[j];
309:           x[0] -= m1*x1 + m4*x2 + m7*x3;
310:           x[1] -= m2*x1 + m5*x2 + m8*x3;
311:           x[2] -= m3*x1 + m6*x2 + m9*x3;

313:           x[3] -= m1*x4 + m4*x5 + m7*x6;
314:           x[4] -= m2*x4 + m5*x5 + m8*x6;
315:           x[5] -= m3*x4 + m6*x5 + m9*x6;

317:           x[6] -= m1*x7 + m4*x8 + m7*x9;
318:           x[7] -= m2*x7 + m5*x8 + m8*x9;
319:           x[8] -= m3*x7 + m6*x8 + m9*x9;
320:           pv   += 9;
321:         }
322:         PetscLogFlops(54.0*nz+36.0);
323:       }
324:       row = *ajtmp++;
325:     }
326:     /* finished row so stick it into b->a */
327:     pv = ba + 9*bi[i];
328:     pj = bj + bi[i];
329:     nz = bi[i+1] - bi[i];
330:     for (j=0; j<nz; j++) {
331:       x     = rtmp+9*pj[j];
332:       pv[0] = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
333:       pv[4] = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
334:       pv   += 9;
335:     }
336:     /* invert diagonal block */
337:     w    = ba + 9*diag_offset[i];
338:     PetscKernel_A_gets_inverse_A_3(w,shift);
339:   }

341:   PetscFree(rtmp);

343:   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering_inplace;
344:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering_inplace;
345:   C->assembled           = PETSC_TRUE;

347:   PetscLogFlops(1.333333333333*3*3*3*b->mbs); /* from inverting diagonal blocks */
348:   return(0);
349: }

351: /*
352:   MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering -
353:     copied from MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_inplace()
354: */
357: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
358: {
359:   Mat            C =B;
360:   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
362:   PetscInt       i,j,k,nz,nzL,row;
363:   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
364:   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
365:   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
366:   PetscInt       flg;
367:   PetscReal      shift = info->shiftamount;

370:   /* generate work space needed by the factorization */
371:   PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
372:   PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));

374:   for (i=0; i<n; i++) {
375:     /* zero rtmp */
376:     /* L part */
377:     nz    = bi[i+1] - bi[i];
378:     bjtmp = bj + bi[i];
379:     for  (j=0; j<nz; j++) {
380:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
381:     }

383:     /* U part */
384:     nz    = bdiag[i] - bdiag[i+1];
385:     bjtmp = bj + bdiag[i+1] + 1;
386:     for  (j=0; j<nz; j++) {
387:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
388:     }

390:     /* load in initial (unfactored row) */
391:     nz    = ai[i+1] - ai[i];
392:     ajtmp = aj + ai[i];
393:     v     = aa + bs2*ai[i];
394:     for (j=0; j<nz; j++) {
395:       PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));
396:     }

398:     /* elimination */
399:     bjtmp = bj + bi[i];
400:     nzL   = bi[i+1] - bi[i];
401:     for (k=0; k<nzL; k++) {
402:       row = bjtmp[k];
403:       pc  = rtmp + bs2*row;
404:       for (flg=0,j=0; j<bs2; j++) {
405:         if (pc[j]!=0.0) {
406:           flg = 1;
407:           break;
408:         }
409:       }
410:       if (flg) {
411:         pv = b->a + bs2*bdiag[row];
412:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
413:         PetscKernel_A_gets_A_times_B_3(pc,pv,mwork);

415:         pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
416:         pv = b->a + bs2*(bdiag[row+1]+1);
417:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
418:         for (j=0; j<nz; j++) {
419:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
420:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
421:           v    = rtmp + bs2*pj[j];
422:           PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);
423:           pv  += bs2;
424:         }
425:         PetscLogFlops(54*nz+45); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
426:       }
427:     }

429:     /* finished row so stick it into b->a */
430:     /* L part */
431:     pv = b->a + bs2*bi[i];
432:     pj = b->j + bi[i];
433:     nz = bi[i+1] - bi[i];
434:     for (j=0; j<nz; j++) {
435:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
436:     }

438:     /* Mark diagonal and invert diagonal for simplier triangular solves */
439:     pv   = b->a + bs2*bdiag[i];
440:     pj   = b->j + bdiag[i];
441:     PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
442:     /* PetscKernel_A_gets_inverse_A(bs,pv,v_pivots,v_work); */
443:     PetscKernel_A_gets_inverse_A_3(pv,shift);

445:     /* U part */
446:     pv = b->a + bs2*(bdiag[i+1]+1);
447:     pj = b->j + bdiag[i+1]+1;
448:     nz = bdiag[i] - bdiag[i+1] - 1;
449:     for (j=0; j<nz; j++) {
450:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
451:     }
452:   }
453:   PetscFree2(rtmp,mwork);

455:   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering;
456:   C->ops->forwardsolve   = MatForwardSolve_SeqBAIJ_3_NaturalOrdering;
457:   C->ops->backwardsolve  = MatBackwardSolve_SeqBAIJ_3_NaturalOrdering;
458:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering;
459:   C->assembled           = PETSC_TRUE;

461:   PetscLogFlops(1.333333333333*3*3*3*n); /* from inverting diagonal blocks */
462:   return(0);
463: }