Actual source code: baijfact13.c

petsc-3.11.3 2019-06-26
Report Typos and Errors

  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: */
 11: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_inplace(Mat C,Mat A,const MatFactorInfo *info)
 12: {
 13:   Mat_SeqBAIJ    *a    = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
 14:   IS             isrow = b->row,isicol = b->icol;
 16:   const PetscInt *r,*ic;
 17:   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
 18:   PetscInt       *ajtmpold,*ajtmp,nz,row,*ai=a->i,*aj=a->j;
 19:   PetscInt       *diag_offset = b->diag,idx,*pj;
 20:   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
 21:   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
 22:   MatScalar      p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
 23:   MatScalar      *ba   = b->a,*aa = a->a;
 24:   PetscReal      shift = info->shiftamount;
 25:   PetscBool      allowzeropivot,zeropivotdetected;

 28:   ISGetIndices(isrow,&r);
 29:   ISGetIndices(isicol,&ic);
 30:   PetscMalloc1(9*(n+1),&rtmp);
 31:   allowzeropivot = PetscNot(A->erroriffailure);

 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,allowzeropivot,&zeropivotdetected);
109:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
110:   }

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

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

120:   PetscLogFlops(1.333333333333*3*3*3*b->mbs); /* from inverting diagonal blocks */
121:   return(0);
122: }

124: /* MatLUFactorNumeric_SeqBAIJ_3 -
125:      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
126:        PetscKernel_A_gets_A_times_B()
127:        PetscKernel_A_gets_A_minus_B_times_C()
128:        PetscKernel_A_gets_inverse_A()
129: */
130: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3(Mat B,Mat A,const MatFactorInfo *info)
131: {
132:   Mat            C     =B;
133:   Mat_SeqBAIJ    *a    =(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
134:   IS             isrow = b->row,isicol = b->icol;
136:   const PetscInt *r,*ic;
137:   PetscInt       i,j,k,nz,nzL,row;
138:   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
139:   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
140:   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
141:   PetscInt       flg;
142:   PetscReal      shift = info->shiftamount;
143:   PetscBool      allowzeropivot,zeropivotdetected;

146:   ISGetIndices(isrow,&r);
147:   ISGetIndices(isicol,&ic);
148:   allowzeropivot = PetscNot(A->erroriffailure);

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

154:   for (i=0; i<n; i++) {
155:     /* zero rtmp */
156:     /* L part */
157:     nz    = bi[i+1] - bi[i];
158:     bjtmp = bj + bi[i];
159:     for  (j=0; j<nz; j++) {
160:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
161:     }

163:     /* U part */
164:     nz    = bdiag[i] - bdiag[i+1];
165:     bjtmp = bj + bdiag[i+1]+1;
166:     for  (j=0; j<nz; j++) {
167:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
168:     }

170:     /* load in initial (unfactored row) */
171:     nz    = ai[r[i]+1] - ai[r[i]];
172:     ajtmp = aj + ai[r[i]];
173:     v     = aa + bs2*ai[r[i]];
174:     for (j=0; j<nz; j++) {
175:       PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));
176:     }

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

195:         pj = b->j + bdiag[row+1] + 1; /* beginning of U(row,:) */
196:         pv = b->a + bs2*(bdiag[row+1]+1);
197:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
198:         for (j=0; j<nz; j++) {
199:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
200:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
201:           v    = rtmp + bs2*pj[j];
202:           PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);
203:           pv  += bs2;
204:         }
205:         PetscLogFlops(54*nz+45); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
206:       }
207:     }

209:     /* finished row so stick it into b->a */
210:     /* L part */
211:     pv = b->a + bs2*bi[i];
212:     pj = b->j + bi[i];
213:     nz = bi[i+1] - bi[i];
214:     for (j=0; j<nz; j++) {
215:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
216:     }

218:     /* Mark diagonal and invert diagonal for simplier triangular solves */
219:     pv   = b->a + bs2*bdiag[i];
220:     pj   = b->j + bdiag[i];
221:     PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
222:     PetscKernel_A_gets_inverse_A_3(pv,shift,allowzeropivot,&zeropivotdetected);
223:     if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

225:     /* U part */
226:     pj = b->j + bdiag[i+1] + 1;
227:     pv = b->a + bs2*(bdiag[i+1]+1);
228:     nz = bdiag[i] - bdiag[i+1] - 1;
229:     for (j=0; j<nz; j++) {
230:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
231:     }
232:   }

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

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

242:   PetscLogFlops(1.333333333333*3*3*3*n); /* from inverting diagonal blocks */
243:   return(0);
244: }

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

261:   PetscMalloc1(9*(n+1),&rtmp);
262:   allowzeropivot = PetscNot(A->erroriffailure);

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

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

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

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

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

318:           x[6] -= m1*x7 + m4*x8 + m7*x9;
319:           x[7] -= m2*x7 + m5*x8 + m8*x9;
320:           x[8] -= m3*x7 + m6*x8 + m9*x9;
321:           pv   += 9;
322:         }
323:         PetscLogFlops(54.0*nz+36.0);
324:       }
325:       row = *ajtmp++;
326:     }
327:     /* finished row so stick it into b->a */
328:     pv = ba + 9*bi[i];
329:     pj = bj + bi[i];
330:     nz = bi[i+1] - bi[i];
331:     for (j=0; j<nz; j++) {
332:       x     = rtmp+9*pj[j];
333:       pv[0] = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
334:       pv[4] = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
335:       pv   += 9;
336:     }
337:     /* invert diagonal block */
338:     w    = ba + 9*diag_offset[i];
339:     PetscKernel_A_gets_inverse_A_3(w,shift,allowzeropivot,&zeropivotdetected);
340:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
341:   }

343:   PetscFree(rtmp);

345:   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering_inplace;
346:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering_inplace;
347:   C->assembled           = PETSC_TRUE;

349:   PetscLogFlops(1.333333333333*3*3*3*b->mbs); /* from inverting diagonal blocks */
350:   return(0);
351: }

353: /*
354:   MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering -
355:     copied from MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_inplace()
356: */
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;
368:   PetscBool      allowzeropivot,zeropivotdetected;

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

373:   /* generate work space needed by the factorization */
374:   PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
375:   PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));

377:   for (i=0; i<n; i++) {
378:     /* zero rtmp */
379:     /* L part */
380:     nz    = bi[i+1] - bi[i];
381:     bjtmp = bj + bi[i];
382:     for  (j=0; j<nz; j++) {
383:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
384:     }

386:     /* U part */
387:     nz    = bdiag[i] - bdiag[i+1];
388:     bjtmp = bj + bdiag[i+1] + 1;
389:     for  (j=0; j<nz; j++) {
390:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
391:     }

393:     /* load in initial (unfactored row) */
394:     nz    = ai[i+1] - ai[i];
395:     ajtmp = aj + ai[i];
396:     v     = aa + bs2*ai[i];
397:     for (j=0; j<nz; j++) {
398:       PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));
399:     }

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

418:         pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
419:         pv = b->a + bs2*(bdiag[row+1]+1);
420:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
421:         for (j=0; j<nz; j++) {
422:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
423:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
424:           v    = rtmp + bs2*pj[j];
425:           PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);
426:           pv  += bs2;
427:         }
428:         PetscLogFlops(54*nz+45); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
429:       }
430:     }

432:     /* finished row so stick it into b->a */
433:     /* L part */
434:     pv = b->a + bs2*bi[i];
435:     pj = b->j + bi[i];
436:     nz = bi[i+1] - bi[i];
437:     for (j=0; j<nz; j++) {
438:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
439:     }

441:     /* Mark diagonal and invert diagonal for simplier triangular solves */
442:     pv   = b->a + bs2*bdiag[i];
443:     pj   = b->j + bdiag[i];
444:     PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
445:     PetscKernel_A_gets_inverse_A_3(pv,shift,allowzeropivot,&zeropivotdetected);
446:     if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

448:     /* U part */
449:     pv = b->a + bs2*(bdiag[i+1]+1);
450:     pj = b->j + bdiag[i+1]+1;
451:     nz = bdiag[i] - bdiag[i+1] - 1;
452:     for (j=0; j<nz; j++) {
453:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
454:     }
455:   }
456:   PetscFree2(rtmp,mwork);

458:   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering;
459:   C->ops->forwardsolve   = MatForwardSolve_SeqBAIJ_3_NaturalOrdering;
460:   C->ops->backwardsolve  = MatBackwardSolve_SeqBAIJ_3_NaturalOrdering;
461:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering;
462:   C->assembled           = PETSC_TRUE;

464:   PetscLogFlops(1.333333333333*3*3*3*n); /* from inverting diagonal blocks */
465:   return(0);
466: }