xref: /petsc/src/mat/impls/baij/seq/baijfact13.c (revision ccb4e88a40f0b86eaeca07ff64c64e4de2fae686)
1 
2 /*
3     Factorization code for BAIJ format.
4 */
5 #include <../src/mat/impls/baij/seq/baij.h>
6 #include <petsc/private/kernels/blockinvert.h>
7 
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;
15   PetscErrorCode ierr;
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;
26 
27   PetscFunctionBegin;
28   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
29   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
30   ierr = PetscMalloc1(9*(n+1),&rtmp);CHKERRQ(ierr);
31   allowzeropivot = PetscNot(A->erroriffailure);
32 
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;
65 
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;
69 
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;
82 
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;
86 
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         ierr = PetscLogFlops(54.0*nz+36.0);CHKERRQ(ierr);
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     ierr = PetscKernel_A_gets_inverse_A_3(w,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
109     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
110   }
111 
112   ierr = PetscFree(rtmp);CHKERRQ(ierr);
113   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
114   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
115 
116   C->ops->solve          = MatSolve_SeqBAIJ_3_inplace;
117   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_inplace;
118   C->assembled           = PETSC_TRUE;
119 
120   ierr = PetscLogFlops(1.333333333333*3*3*3*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
121   PetscFunctionReturn(0);
122 }
123 
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;
135   PetscErrorCode ierr;
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;
144 
145   PetscFunctionBegin;
146   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
147   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
148   allowzeropivot = PetscNot(A->erroriffailure);
149 
150   /* generate work space needed by the factorization */
151   ierr = PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);CHKERRQ(ierr);
152   ierr = PetscArrayzero(rtmp,bs2*n);CHKERRQ(ierr);
153 
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       ierr = PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);CHKERRQ(ierr);
161     }
162 
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       ierr = PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);CHKERRQ(ierr);
168     }
169 
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       ierr = PetscArraycpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2);CHKERRQ(ierr);
176     }
177 
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         ierr = PetscKernel_A_gets_A_times_B_3(pc,pv,mwork);CHKERRQ(ierr);
194 
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           ierr = PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);CHKERRQ(ierr);
203           pv  += bs2;
204         }
205         ierr = PetscLogFlops(54.0*nz+45);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
206       }
207     }
208 
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       ierr = PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);CHKERRQ(ierr);
216     }
217 
218     /* Mark diagonal and invert diagonal for simpler triangular solves */
219     pv   = b->a + bs2*bdiag[i];
220     pj   = b->j + bdiag[i];
221     ierr = PetscArraycpy(pv,rtmp+bs2*pj[0],bs2);CHKERRQ(ierr);
222     ierr = PetscKernel_A_gets_inverse_A_3(pv,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
223     if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
224 
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       ierr = PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);CHKERRQ(ierr);
231     }
232   }
233 
234   ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
235   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
236   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
237 
238   C->ops->solve          = MatSolve_SeqBAIJ_3;
239   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3;
240   C->assembled           = PETSC_TRUE;
241 
242   ierr = PetscLogFlops(1.333333333333*3*3*3*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
243   PetscFunctionReturn(0);
244 }
245 
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;
249   PetscErrorCode ierr;
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;
259 
260   PetscFunctionBegin;
261   ierr = PetscMalloc1(9*(n+1),&rtmp);CHKERRQ(ierr);
262   allowzeropivot = PetscNot(A->erroriffailure);
263 
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;
295 
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;
299 
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;
303 
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;
313 
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;
317 
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         ierr = PetscLogFlops(54.0*nz+36.0);CHKERRQ(ierr);
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     ierr = PetscKernel_A_gets_inverse_A_3(w,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
340     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
341   }
342 
343   ierr = PetscFree(rtmp);CHKERRQ(ierr);
344 
345   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering_inplace;
346   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering_inplace;
347   C->assembled           = PETSC_TRUE;
348 
349   ierr = PetscLogFlops(1.333333333333*3*3*3*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
350   PetscFunctionReturn(0);
351 }
352 
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;
361   PetscErrorCode ierr;
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;
369 
370   PetscFunctionBegin;
371   allowzeropivot = PetscNot(A->erroriffailure);
372 
373   /* generate work space needed by the factorization */
374   ierr = PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);CHKERRQ(ierr);
375   ierr = PetscArrayzero(rtmp,bs2*n);CHKERRQ(ierr);
376 
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       ierr = PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);CHKERRQ(ierr);
384     }
385 
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       ierr = PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);CHKERRQ(ierr);
391     }
392 
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       ierr = PetscArraycpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2);CHKERRQ(ierr);
399     }
400 
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         ierr = PetscKernel_A_gets_A_times_B_3(pc,pv,mwork);CHKERRQ(ierr);
417 
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           ierr = PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);CHKERRQ(ierr);
426           pv  += bs2;
427         }
428         ierr = PetscLogFlops(54.0*nz+45);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
429       }
430     }
431 
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       ierr = PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);CHKERRQ(ierr);
439     }
440 
441     /* Mark diagonal and invert diagonal for simpler triangular solves */
442     pv   = b->a + bs2*bdiag[i];
443     pj   = b->j + bdiag[i];
444     ierr = PetscArraycpy(pv,rtmp+bs2*pj[0],bs2);CHKERRQ(ierr);
445     ierr = PetscKernel_A_gets_inverse_A_3(pv,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
446     if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
447 
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       ierr = PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);CHKERRQ(ierr);
454     }
455   }
456   ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
457 
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;
463 
464   ierr = PetscLogFlops(1.333333333333*3*3*3*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
465   PetscFunctionReturn(0);
466 }
467 
468