xref: /petsc/src/mat/impls/baij/seq/baijfact13.c (revision 503c0ea9b45bcfbcebbb1ea5341243bbc69f0bea)
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   const PetscInt *r,*ic;
16   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
17   PetscInt       *ajtmpold,*ajtmp,nz,row,*ai=a->i,*aj=a->j;
18   PetscInt       *diag_offset = b->diag,idx,*pj;
19   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
20   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
21   MatScalar      p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
22   MatScalar      *ba   = b->a,*aa = a->a;
23   PetscReal      shift = info->shiftamount;
24   PetscBool      allowzeropivot,zeropivotdetected;
25 
26   PetscFunctionBegin;
27   PetscCall(ISGetIndices(isrow,&r));
28   PetscCall(ISGetIndices(isicol,&ic));
29   PetscCall(PetscMalloc1(9*(n+1),&rtmp));
30   allowzeropivot = PetscNot(A->erroriffailure);
31 
32   for (i=0; i<n; i++) {
33     nz    = bi[i+1] - bi[i];
34     ajtmp = bj + bi[i];
35     for  (j=0; j<nz; j++) {
36       x    = rtmp + 9*ajtmp[j];
37       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0;
38     }
39     /* load in initial (unfactored row) */
40     idx      = r[i];
41     nz       = ai[idx+1] - ai[idx];
42     ajtmpold = aj + ai[idx];
43     v        = aa + 9*ai[idx];
44     for (j=0; j<nz; j++) {
45       x    = rtmp + 9*ic[ajtmpold[j]];
46       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
47       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
48       v   += 9;
49     }
50     row = *ajtmp++;
51     while (row < i) {
52       pc = rtmp + 9*row;
53       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
54       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
55       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
56           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
57         pv    = ba + 9*diag_offset[row];
58         pj    = bj + diag_offset[row] + 1;
59         x1    = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
60         x5    = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
61         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
62         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
63         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
64 
65         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
66         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
67         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
68 
69         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
70         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
71         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
72         nz    = bi[row+1] - diag_offset[row] - 1;
73         pv   += 9;
74         for (j=0; j<nz; j++) {
75           x1    = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
76           x5    = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
77           x     = rtmp + 9*pj[j];
78           x[0] -= m1*x1 + m4*x2 + m7*x3;
79           x[1] -= m2*x1 + m5*x2 + m8*x3;
80           x[2] -= m3*x1 + m6*x2 + m9*x3;
81 
82           x[3] -= m1*x4 + m4*x5 + m7*x6;
83           x[4] -= m2*x4 + m5*x5 + m8*x6;
84           x[5] -= m3*x4 + m6*x5 + m9*x6;
85 
86           x[6] -= m1*x7 + m4*x8 + m7*x9;
87           x[7] -= m2*x7 + m5*x8 + m8*x9;
88           x[8] -= m3*x7 + m6*x8 + m9*x9;
89           pv   += 9;
90         }
91         PetscCall(PetscLogFlops(54.0*nz+36.0));
92       }
93       row = *ajtmp++;
94     }
95     /* finished row so stick it into b->a */
96     pv = ba + 9*bi[i];
97     pj = bj + bi[i];
98     nz = bi[i+1] - bi[i];
99     for (j=0; j<nz; j++) {
100       x     = rtmp + 9*pj[j];
101       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
102       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
103       pv   += 9;
104     }
105     /* invert diagonal block */
106     w    = ba + 9*diag_offset[i];
107     PetscCall(PetscKernel_A_gets_inverse_A_3(w,shift,allowzeropivot,&zeropivotdetected));
108     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
109   }
110 
111   PetscCall(PetscFree(rtmp));
112   PetscCall(ISRestoreIndices(isicol,&ic));
113   PetscCall(ISRestoreIndices(isrow,&r));
114 
115   C->ops->solve          = MatSolve_SeqBAIJ_3_inplace;
116   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_inplace;
117   C->assembled           = PETSC_TRUE;
118 
119   PetscCall(PetscLogFlops(1.333333333333*3*3*3*b->mbs)); /* 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 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3(Mat B,Mat A,const MatFactorInfo *info)
130 {
131   Mat            C     =B;
132   Mat_SeqBAIJ    *a    =(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
133   IS             isrow = b->row,isicol = b->icol;
134   const PetscInt *r,*ic;
135   PetscInt       i,j,k,nz,nzL,row;
136   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
137   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
138   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
139   PetscInt       flg;
140   PetscReal      shift = info->shiftamount;
141   PetscBool      allowzeropivot,zeropivotdetected;
142 
143   PetscFunctionBegin;
144   PetscCall(ISGetIndices(isrow,&r));
145   PetscCall(ISGetIndices(isicol,&ic));
146   allowzeropivot = PetscNot(A->erroriffailure);
147 
148   /* generate work space needed by the factorization */
149   PetscCall(PetscMalloc2(bs2*n,&rtmp,bs2,&mwork));
150   PetscCall(PetscArrayzero(rtmp,bs2*n));
151 
152   for (i=0; i<n; i++) {
153     /* zero rtmp */
154     /* L part */
155     nz    = bi[i+1] - bi[i];
156     bjtmp = bj + bi[i];
157     for  (j=0; j<nz; j++) {
158       PetscCall(PetscArrayzero(rtmp+bs2*bjtmp[j],bs2));
159     }
160 
161     /* U part */
162     nz    = bdiag[i] - bdiag[i+1];
163     bjtmp = bj + bdiag[i+1]+1;
164     for  (j=0; j<nz; j++) {
165       PetscCall(PetscArrayzero(rtmp+bs2*bjtmp[j],bs2));
166     }
167 
168     /* load in initial (unfactored row) */
169     nz    = ai[r[i]+1] - ai[r[i]];
170     ajtmp = aj + ai[r[i]];
171     v     = aa + bs2*ai[r[i]];
172     for (j=0; j<nz; j++) {
173       PetscCall(PetscArraycpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2));
174     }
175 
176     /* elimination */
177     bjtmp = bj + bi[i];
178     nzL   = bi[i+1] - bi[i];
179     for (k = 0; k < nzL; k++) {
180       row = bjtmp[k];
181       pc  = rtmp + bs2*row;
182       for (flg=0,j=0; j<bs2; j++) {
183         if (pc[j]!=0.0) {
184           flg = 1;
185           break;
186         }
187       }
188       if (flg) {
189         pv = b->a + bs2*bdiag[row];
190         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
191         PetscCall(PetscKernel_A_gets_A_times_B_3(pc,pv,mwork));
192 
193         pj = b->j + bdiag[row+1] + 1; /* beginning of U(row,:) */
194         pv = b->a + bs2*(bdiag[row+1]+1);
195         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
196         for (j=0; j<nz; j++) {
197           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
198           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
199           v    = rtmp + bs2*pj[j];
200           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv));
201           pv  += bs2;
202         }
203         PetscCall(PetscLogFlops(54.0*nz+45)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
204       }
205     }
206 
207     /* finished row so stick it into b->a */
208     /* L part */
209     pv = b->a + bs2*bi[i];
210     pj = b->j + bi[i];
211     nz = bi[i+1] - bi[i];
212     for (j=0; j<nz; j++) {
213       PetscCall(PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2));
214     }
215 
216     /* Mark diagonal and invert diagonal for simpler triangular solves */
217     pv   = b->a + bs2*bdiag[i];
218     pj   = b->j + bdiag[i];
219     PetscCall(PetscArraycpy(pv,rtmp+bs2*pj[0],bs2));
220     PetscCall(PetscKernel_A_gets_inverse_A_3(pv,shift,allowzeropivot,&zeropivotdetected));
221     if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
222 
223     /* U part */
224     pj = b->j + bdiag[i+1] + 1;
225     pv = b->a + bs2*(bdiag[i+1]+1);
226     nz = bdiag[i] - bdiag[i+1] - 1;
227     for (j=0; j<nz; j++) {
228       PetscCall(PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2));
229     }
230   }
231 
232   PetscCall(PetscFree2(rtmp,mwork));
233   PetscCall(ISRestoreIndices(isicol,&ic));
234   PetscCall(ISRestoreIndices(isrow,&r));
235 
236   C->ops->solve          = MatSolve_SeqBAIJ_3;
237   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3;
238   C->assembled           = PETSC_TRUE;
239 
240   PetscCall(PetscLogFlops(1.333333333333*3*3*3*n)); /* from inverting diagonal blocks */
241   PetscFunctionReturn(0);
242 }
243 
244 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
245 {
246   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
247   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
248   PetscInt       *ajtmpold,*ajtmp,nz,row;
249   PetscInt       *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
250   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
251   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
252   MatScalar      p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
253   MatScalar      *ba   = b->a,*aa = a->a;
254   PetscReal      shift = info->shiftamount;
255   PetscBool      allowzeropivot,zeropivotdetected;
256 
257   PetscFunctionBegin;
258   PetscCall(PetscMalloc1(9*(n+1),&rtmp));
259   allowzeropivot = PetscNot(A->erroriffailure);
260 
261   for (i=0; i<n; i++) {
262     nz    = bi[i+1] - bi[i];
263     ajtmp = bj + bi[i];
264     for  (j=0; j<nz; j++) {
265       x    = rtmp+9*ajtmp[j];
266       x[0] = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = 0.0;
267     }
268     /* load in initial (unfactored row) */
269     nz       = ai[i+1] - ai[i];
270     ajtmpold = aj + ai[i];
271     v        = aa + 9*ai[i];
272     for (j=0; j<nz; j++) {
273       x    = rtmp+9*ajtmpold[j];
274       x[0] = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
275       x[4] = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
276       v   += 9;
277     }
278     row = *ajtmp++;
279     while (row < i) {
280       pc = rtmp + 9*row;
281       p1 = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
282       p5 = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
283       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
284           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
285         pv    = ba + 9*diag_offset[row];
286         pj    = bj + diag_offset[row] + 1;
287         x1    = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
288         x5    = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
289         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
290         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
291         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
292 
293         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
294         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
295         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
296 
297         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
298         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
299         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
300 
301         nz  = bi[row+1] - diag_offset[row] - 1;
302         pv += 9;
303         for (j=0; j<nz; j++) {
304           x1    = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
305           x5    = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
306           x     = rtmp + 9*pj[j];
307           x[0] -= m1*x1 + m4*x2 + m7*x3;
308           x[1] -= m2*x1 + m5*x2 + m8*x3;
309           x[2] -= m3*x1 + m6*x2 + m9*x3;
310 
311           x[3] -= m1*x4 + m4*x5 + m7*x6;
312           x[4] -= m2*x4 + m5*x5 + m8*x6;
313           x[5] -= m3*x4 + m6*x5 + m9*x6;
314 
315           x[6] -= m1*x7 + m4*x8 + m7*x9;
316           x[7] -= m2*x7 + m5*x8 + m8*x9;
317           x[8] -= m3*x7 + m6*x8 + m9*x9;
318           pv   += 9;
319         }
320         PetscCall(PetscLogFlops(54.0*nz+36.0));
321       }
322       row = *ajtmp++;
323     }
324     /* finished row so stick it into b->a */
325     pv = ba + 9*bi[i];
326     pj = bj + bi[i];
327     nz = bi[i+1] - bi[i];
328     for (j=0; j<nz; j++) {
329       x     = rtmp+9*pj[j];
330       pv[0] = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
331       pv[4] = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
332       pv   += 9;
333     }
334     /* invert diagonal block */
335     w    = ba + 9*diag_offset[i];
336     PetscCall(PetscKernel_A_gets_inverse_A_3(w,shift,allowzeropivot,&zeropivotdetected));
337     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
338   }
339 
340   PetscCall(PetscFree(rtmp));
341 
342   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering_inplace;
343   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering_inplace;
344   C->assembled           = PETSC_TRUE;
345 
346   PetscCall(PetscLogFlops(1.333333333333*3*3*3*b->mbs)); /* from inverting diagonal blocks */
347   PetscFunctionReturn(0);
348 }
349 
350 /*
351   MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering -
352     copied from MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_inplace()
353 */
354 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
355 {
356   Mat            C =B;
357   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
358   PetscInt       i,j,k,nz,nzL,row;
359   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
360   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
361   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
362   PetscInt       flg;
363   PetscReal      shift = info->shiftamount;
364   PetscBool      allowzeropivot,zeropivotdetected;
365 
366   PetscFunctionBegin;
367   allowzeropivot = PetscNot(A->erroriffailure);
368 
369   /* generate work space needed by the factorization */
370   PetscCall(PetscMalloc2(bs2*n,&rtmp,bs2,&mwork));
371   PetscCall(PetscArrayzero(rtmp,bs2*n));
372 
373   for (i=0; i<n; i++) {
374     /* zero rtmp */
375     /* L part */
376     nz    = bi[i+1] - bi[i];
377     bjtmp = bj + bi[i];
378     for  (j=0; j<nz; j++) {
379       PetscCall(PetscArrayzero(rtmp+bs2*bjtmp[j],bs2));
380     }
381 
382     /* U part */
383     nz    = bdiag[i] - bdiag[i+1];
384     bjtmp = bj + bdiag[i+1] + 1;
385     for  (j=0; j<nz; j++) {
386       PetscCall(PetscArrayzero(rtmp+bs2*bjtmp[j],bs2));
387     }
388 
389     /* load in initial (unfactored row) */
390     nz    = ai[i+1] - ai[i];
391     ajtmp = aj + ai[i];
392     v     = aa + bs2*ai[i];
393     for (j=0; j<nz; j++) {
394       PetscCall(PetscArraycpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2));
395     }
396 
397     /* elimination */
398     bjtmp = bj + bi[i];
399     nzL   = bi[i+1] - bi[i];
400     for (k=0; k<nzL; k++) {
401       row = bjtmp[k];
402       pc  = rtmp + bs2*row;
403       for (flg=0,j=0; j<bs2; j++) {
404         if (pc[j]!=0.0) {
405           flg = 1;
406           break;
407         }
408       }
409       if (flg) {
410         pv = b->a + bs2*bdiag[row];
411         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
412         PetscCall(PetscKernel_A_gets_A_times_B_3(pc,pv,mwork));
413 
414         pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
415         pv = b->a + bs2*(bdiag[row+1]+1);
416         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
417         for (j=0; j<nz; j++) {
418           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
419           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
420           v    = rtmp + bs2*pj[j];
421           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv));
422           pv  += bs2;
423         }
424         PetscCall(PetscLogFlops(54.0*nz+45)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
425       }
426     }
427 
428     /* finished row so stick it into b->a */
429     /* L part */
430     pv = b->a + bs2*bi[i];
431     pj = b->j + bi[i];
432     nz = bi[i+1] - bi[i];
433     for (j=0; j<nz; j++) {
434       PetscCall(PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2));
435     }
436 
437     /* Mark diagonal and invert diagonal for simpler triangular solves */
438     pv   = b->a + bs2*bdiag[i];
439     pj   = b->j + bdiag[i];
440     PetscCall(PetscArraycpy(pv,rtmp+bs2*pj[0],bs2));
441     PetscCall(PetscKernel_A_gets_inverse_A_3(pv,shift,allowzeropivot,&zeropivotdetected));
442     if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
443 
444     /* U part */
445     pv = b->a + bs2*(bdiag[i+1]+1);
446     pj = b->j + bdiag[i+1]+1;
447     nz = bdiag[i] - bdiag[i+1] - 1;
448     for (j=0; j<nz; j++) {
449       PetscCall(PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2));
450     }
451   }
452   PetscCall(PetscFree2(rtmp,mwork));
453 
454   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering;
455   C->ops->forwardsolve   = MatForwardSolve_SeqBAIJ_3_NaturalOrdering;
456   C->ops->backwardsolve  = MatBackwardSolve_SeqBAIJ_3_NaturalOrdering;
457   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering;
458   C->assembled           = PETSC_TRUE;
459 
460   PetscCall(PetscLogFlops(1.333333333333*3*3*3*n)); /* from inverting diagonal blocks */
461   PetscFunctionReturn(0);
462 }
463