xref: /petsc/src/mat/impls/baij/seq/baijfact13.c (revision bebe2cf65d55febe21a5af8db2bd2e168caaa2e7)
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 #undef __FUNCT__
12 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_3_inplace"
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;
17   PetscErrorCode ierr;
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;
27 
28   PetscFunctionBegin;
29   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
30   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
31   ierr = PetscMalloc1(9*(n+1),&rtmp);CHKERRQ(ierr);
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);CHKERRQ(ierr);
109   }
110 
111   ierr = PetscFree(rtmp);CHKERRQ(ierr);
112   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
113   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
114 
115   C->ops->solve          = MatSolve_SeqBAIJ_3_inplace;
116   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_inplace;
117   C->assembled           = PETSC_TRUE;
118 
119   ierr = PetscLogFlops(1.333333333333*3*3*3*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
120   PetscFunctionReturn(0);
121 }
122 
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 */
129 #undef __FUNCT__
130 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_3"
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;
136   PetscErrorCode ierr;
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;
144 
145   PetscFunctionBegin;
146   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
147   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
148 
149   /* generate work space needed by the factorization */
150   ierr = PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);CHKERRQ(ierr);
151   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
152 
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       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
160     }
161 
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       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
167     }
168 
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       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
175     }
176 
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         ierr = PetscKernel_A_gets_A_times_B_3(pc,pv,mwork);CHKERRQ(ierr);
193 
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           ierr = PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);CHKERRQ(ierr);
202           pv  += bs2;
203         }
204         ierr = PetscLogFlops(54*nz+45);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
205       }
206     }
207 
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       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
215     }
216 
217     /* Mark diagonal and invert diagonal for simplier triangular solves */
218     pv   = b->a + bs2*bdiag[i];
219     pj   = b->j + bdiag[i];
220     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
221     /* ierr = PetscKernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
222     ierr = PetscKernel_A_gets_inverse_A_3(pv,shift);CHKERRQ(ierr);
223 
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       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
230     }
231   }
232 
233   ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
234   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
235   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
236 
237   C->ops->solve          = MatSolve_SeqBAIJ_3;
238   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3;
239   C->assembled           = PETSC_TRUE;
240 
241   ierr = PetscLogFlops(1.333333333333*3*3*3*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
242   PetscFunctionReturn(0);
243 }
244 
245 #undef __FUNCT__
246 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_inplace"
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;
250   PetscErrorCode ierr;
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;
259 
260   PetscFunctionBegin;
261   ierr = PetscMalloc1(9*(n+1),&rtmp);CHKERRQ(ierr);
262 
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;
294 
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;
298 
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;
302 
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;
312 
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;
316 
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         ierr = PetscLogFlops(54.0*nz+36.0);CHKERRQ(ierr);
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     ierr = PetscKernel_A_gets_inverse_A_3(w,shift);CHKERRQ(ierr);
339   }
340 
341   ierr = PetscFree(rtmp);CHKERRQ(ierr);
342 
343   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering_inplace;
344   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering_inplace;
345   C->assembled           = PETSC_TRUE;
346 
347   ierr = PetscLogFlops(1.333333333333*3*3*3*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
348   PetscFunctionReturn(0);
349 }
350 
351 /*
352   MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering -
353     copied from MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_inplace()
354 */
355 #undef __FUNCT__
356 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering"
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 
369   PetscFunctionBegin;
370   /* generate work space needed by the factorization */
371   ierr = PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);CHKERRQ(ierr);
372   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
373 
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       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
381     }
382 
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       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
388     }
389 
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       ierr = PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
396     }
397 
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         ierr = PetscKernel_A_gets_A_times_B_3(pc,pv,mwork);CHKERRQ(ierr);
414 
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           ierr = PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);CHKERRQ(ierr);
423           pv  += bs2;
424         }
425         ierr = PetscLogFlops(54*nz+45);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
426       }
427     }
428 
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       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
436     }
437 
438     /* Mark diagonal and invert diagonal for simplier triangular solves */
439     pv   = b->a + bs2*bdiag[i];
440     pj   = b->j + bdiag[i];
441     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
442     /* ierr = PetscKernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
443     ierr = PetscKernel_A_gets_inverse_A_3(pv,shift);CHKERRQ(ierr);
444 
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       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
451     }
452   }
453   ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
454 
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;
460 
461   ierr = PetscLogFlops(1.333333333333*3*3*3*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
462   PetscFunctionReturn(0);
463 }
464 
465