xref: /petsc/src/mat/impls/baij/seq/baijfact13.c (revision 6abefa4f446b2ea91915da4e25ea0defa83db48e)
1 #define PETSCMAT_DLL
2 
3 /*
4     Factorization code for BAIJ format.
5 */
6 #include "../src/mat/impls/baij/seq/baij.h"
7 #include "../src/mat/blockinvert.h"
8 
9 /*
10       Version for when blocks are 3 by 3
11 */
12 #undef __FUNCT__
13 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_3_inplace"
14 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_inplace(Mat C,Mat A,const MatFactorInfo *info)
15 {
16   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
17   IS             isrow = b->row,isicol = b->icol;
18   PetscErrorCode ierr;
19   const PetscInt *r,*ic;
20   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
21   PetscInt       *ajtmpold,*ajtmp,nz,row,*ai=a->i,*aj=a->j;
22   PetscInt       *diag_offset = b->diag,idx,*pj;
23   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
24   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
25   MatScalar      p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
26   MatScalar      *ba = b->a,*aa = a->a;
27   PetscReal      shift = info->shiftamount;
28 
29   PetscFunctionBegin;
30   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
31   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
32   ierr = PetscMalloc(9*(n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
33 
34   for (i=0; i<n; i++) {
35     nz    = bi[i+1] - bi[i];
36     ajtmp = bj + bi[i];
37     for  (j=0; j<nz; j++) {
38       x = rtmp + 9*ajtmp[j];
39       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0;
40     }
41     /* load in initial (unfactored row) */
42     idx      = r[i];
43     nz       = ai[idx+1] - ai[idx];
44     ajtmpold = aj + ai[idx];
45     v        = aa + 9*ai[idx];
46     for (j=0; j<nz; j++) {
47       x    = rtmp + 9*ic[ajtmpold[j]];
48       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
49       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
50       v    += 9;
51     }
52     row = *ajtmp++;
53     while (row < i) {
54       pc = rtmp + 9*row;
55       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
56       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
57       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
58           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
59         pv = ba + 9*diag_offset[row];
60         pj = bj + diag_offset[row] + 1;
61         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
62         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
63         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
64         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
65         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
66 
67         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
68         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
69         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
70 
71         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
72         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
73         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
74         nz = bi[row+1] - diag_offset[row] - 1;
75         pv += 9;
76         for (j=0; j<nz; j++) {
77           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
78           x5   = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
79           x    = rtmp + 9*pj[j];
80           x[0] -= m1*x1 + m4*x2 + m7*x3;
81           x[1] -= m2*x1 + m5*x2 + m8*x3;
82           x[2] -= m3*x1 + m6*x2 + m9*x3;
83 
84           x[3] -= m1*x4 + m4*x5 + m7*x6;
85           x[4] -= m2*x4 + m5*x5 + m8*x6;
86           x[5] -= m3*x4 + m6*x5 + m9*x6;
87 
88           x[6] -= m1*x7 + m4*x8 + m7*x9;
89           x[7] -= m2*x7 + m5*x8 + m8*x9;
90           x[8] -= m3*x7 + m6*x8 + m9*x9;
91           pv   += 9;
92         }
93         ierr = PetscLogFlops(54.0*nz+36.0);CHKERRQ(ierr);
94       }
95       row = *ajtmp++;
96     }
97     /* finished row so stick it into b->a */
98     pv = ba + 9*bi[i];
99     pj = bj + bi[i];
100     nz = bi[i+1] - bi[i];
101     for (j=0; j<nz; j++) {
102       x     = rtmp + 9*pj[j];
103       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
104       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
105       pv   += 9;
106     }
107     /* invert diagonal block */
108     w = ba + 9*diag_offset[i];
109     ierr = Kernel_A_gets_inverse_A_3(w,shift);CHKERRQ(ierr);
110   }
111 
112   ierr = PetscFree(rtmp);CHKERRQ(ierr);
113   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
114   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
115   C->ops->solve          = MatSolve_SeqBAIJ_3_inplace;
116   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_inplace;
117   C->assembled = PETSC_TRUE;
118   ierr = PetscLogFlops(1.333333333333*3*3*3*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
119   PetscFunctionReturn(0);
120 }
121 
122 /* MatLUFactorNumeric_SeqBAIJ_3 -
123      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
124        Kernel_A_gets_A_times_B()
125        Kernel_A_gets_A_minus_B_times_C()
126        Kernel_A_gets_inverse_A()
127 */
128 #undef __FUNCT__
129 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_3"
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,*ics;
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 
144   PetscFunctionBegin;
145   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
146   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
147 
148   /* generate work space needed by the factorization */
149   ierr = PetscMalloc2(bs2*n,MatScalar,&rtmp,bs2,MatScalar,&mwork);CHKERRQ(ierr);
150   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
151   ics  = ic;
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++) { if (pc[j]!=0.0) { flg = 1; break; }}
184       if (flg) {
185         pv = b->a + bs2*bdiag[row];
186         /* Kernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
187         ierr = Kernel_A_gets_A_times_B_3(pc,pv,mwork);CHKERRQ(ierr);
188 
189    	pj = b->j + bdiag[row+1] + 1; /* beginning of U(row,:) */
190 	pv = b->a + bs2*(bdiag[row+1]+1);
191 	nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
192         for (j=0; j<nz; j++) {
193           /* Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
194           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
195           v    = rtmp + bs2*pj[j];
196           ierr = Kernel_A_gets_A_minus_B_times_C_3(v,pc,pv);CHKERRQ(ierr);
197           pv  += bs2;
198         }
199         ierr = PetscLogFlops(54*nz+45);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
200       }
201     }
202 
203     /* finished row so stick it into b->a */
204     /* L part */
205     pv   = b->a + bs2*bi[i] ;
206     pj   = b->j + bi[i] ;
207     nz   = bi[i+1] - bi[i];
208     for (j=0; j<nz; j++) {
209       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
210     }
211 
212     /* Mark diagonal and invert diagonal for simplier triangular solves */
213     pv   = b->a + bs2*bdiag[i];
214     pj   = b->j + bdiag[i];
215     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
216     /* ierr = Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
217     ierr = Kernel_A_gets_inverse_A_3(pv,shift);CHKERRQ(ierr);
218 
219     /* U part */
220     pj = b->j + bdiag[i+1] + 1;
221     pv = b->a + bs2*(bdiag[i+1]+1);
222     nz = bdiag[i] - bdiag[i+1] - 1;
223     for (j=0; j<nz; j++){
224       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
225     }
226   }
227 
228   ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
229   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
230   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
231   C->ops->solve = MatSolve_SeqBAIJ_3;
232   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3;
233 
234   C->assembled = PETSC_TRUE;
235   ierr = PetscLogFlops(1.333333333333*3*3*3*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
236   PetscFunctionReturn(0);
237 }
238 
239 #undef __FUNCT__
240 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_inplace"
241 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
242 {
243   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
244   PetscErrorCode ierr;
245   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
246   PetscInt       *ajtmpold,*ajtmp,nz,row;
247   PetscInt       *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
248   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
249   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
250   MatScalar      p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
251   MatScalar      *ba = b->a,*aa = a->a;
252   PetscReal      shift = info->shiftamount;
253 
254   PetscFunctionBegin;
255   ierr = PetscMalloc(9*(n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
256 
257   for (i=0; i<n; i++) {
258     nz    = bi[i+1] - bi[i];
259     ajtmp = bj + bi[i];
260     for  (j=0; j<nz; j++) {
261       x = rtmp+9*ajtmp[j];
262       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = 0.0;
263     }
264     /* load in initial (unfactored row) */
265     nz       = ai[i+1] - ai[i];
266     ajtmpold = aj + ai[i];
267     v        = aa + 9*ai[i];
268     for (j=0; j<nz; j++) {
269       x    = rtmp+9*ajtmpold[j];
270       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
271       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
272       v    += 9;
273     }
274     row = *ajtmp++;
275     while (row < i) {
276       pc  = rtmp + 9*row;
277       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
278       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
279       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
280           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
281         pv = ba + 9*diag_offset[row];
282         pj = bj + diag_offset[row] + 1;
283         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
284         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
285         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
286         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
287         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
288 
289         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
290         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
291         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
292 
293         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
294         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
295         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
296 
297         nz = bi[row+1] - diag_offset[row] - 1;
298         pv += 9;
299         for (j=0; j<nz; j++) {
300           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
301           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
302           x    = rtmp + 9*pj[j];
303           x[0] -= m1*x1 + m4*x2 + m7*x3;
304           x[1] -= m2*x1 + m5*x2 + m8*x3;
305           x[2] -= m3*x1 + m6*x2 + m9*x3;
306 
307           x[3] -= m1*x4 + m4*x5 + m7*x6;
308           x[4] -= m2*x4 + m5*x5 + m8*x6;
309           x[5] -= m3*x4 + m6*x5 + m9*x6;
310 
311           x[6] -= m1*x7 + m4*x8 + m7*x9;
312           x[7] -= m2*x7 + m5*x8 + m8*x9;
313           x[8] -= m3*x7 + m6*x8 + m9*x9;
314           pv   += 9;
315         }
316         ierr = PetscLogFlops(54.0*nz+36.0);CHKERRQ(ierr);
317       }
318       row = *ajtmp++;
319     }
320     /* finished row so stick it into b->a */
321     pv = ba + 9*bi[i];
322     pj = bj + bi[i];
323     nz = bi[i+1] - bi[i];
324     for (j=0; j<nz; j++) {
325       x      = rtmp+9*pj[j];
326       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
327       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
328       pv   += 9;
329     }
330     /* invert diagonal block */
331     w = ba + 9*diag_offset[i];
332     ierr = Kernel_A_gets_inverse_A_3(w,shift);CHKERRQ(ierr);
333   }
334 
335   ierr = PetscFree(rtmp);CHKERRQ(ierr);
336   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering_inplace;
337   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering_inplace;
338   C->assembled = PETSC_TRUE;
339   ierr = PetscLogFlops(1.333333333333*3*3*3*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
340   PetscFunctionReturn(0);
341 }
342 
343 /*
344   MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering -
345     copied from MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_inplace()
346 */
347 #undef __FUNCT__
348 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering"
349 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
350 {
351   Mat            C=B;
352   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
353   PetscErrorCode ierr;
354   PetscInt       i,j,k,nz,nzL,row;
355   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
356   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
357   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
358   PetscInt       flg;
359   PetscReal      shift = info->shiftamount;
360 
361   PetscFunctionBegin;
362   /* generate work space needed by the factorization */
363   ierr = PetscMalloc2(bs2*n,MatScalar,&rtmp,bs2,MatScalar,&mwork);CHKERRQ(ierr);
364   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
365 
366   for (i=0; i<n; i++){
367     /* zero rtmp */
368     /* L part */
369     nz    = bi[i+1] - bi[i];
370     bjtmp = bj + bi[i];
371     for  (j=0; j<nz; j++){
372       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
373     }
374 
375     /* U part */
376     nz = bdiag[i] - bdiag[i+1];
377     bjtmp = bj + bdiag[i+1] + 1;
378     for  (j=0; j<nz; j++){
379       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
380     }
381 
382     /* load in initial (unfactored row) */
383     nz    = ai[i+1] - ai[i];
384     ajtmp = aj + ai[i];
385     v     = aa + bs2*ai[i];
386     for (j=0; j<nz; j++) {
387       ierr = PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
388     }
389 
390     /* elimination */
391     bjtmp = bj + bi[i];
392     nzL   = bi[i+1] - bi[i];
393     for(k=0;k<nzL;k++){
394       row = bjtmp[k];
395       pc = rtmp + bs2*row;
396       for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
397       if (flg) {
398         pv = b->a + bs2*bdiag[row];
399         /* Kernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
400         ierr = Kernel_A_gets_A_times_B_3(pc,pv,mwork);CHKERRQ(ierr);
401 
402         pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
403 	pv = b->a + bs2*(bdiag[row+1]+1);
404 	nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
405         for (j=0; j<nz; j++) {
406           /* Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
407           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
408           v    = rtmp + bs2*pj[j];
409           ierr = Kernel_A_gets_A_minus_B_times_C_3(v,pc,pv);CHKERRQ(ierr);
410           pv  += bs2;
411         }
412         ierr = PetscLogFlops(54*nz+45);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
413       }
414     }
415 
416     /* finished row so stick it into b->a */
417     /* L part */
418     pv   = b->a + bs2*bi[i] ;
419     pj   = b->j + bi[i] ;
420     nz   = bi[i+1] - bi[i];
421     for (j=0; j<nz; j++) {
422       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
423     }
424 
425     /* Mark diagonal and invert diagonal for simplier triangular solves */
426     pv   = b->a + bs2*bdiag[i];
427     pj   = b->j + bdiag[i];
428     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
429     /* ierr = Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
430     ierr = Kernel_A_gets_inverse_A_3(pv,shift);CHKERRQ(ierr);
431 
432     /* U part */
433     pv = b->a + bs2*(bdiag[i+1]+1);
434     pj = b->j + bdiag[i+1]+1;
435     nz = bdiag[i] - bdiag[i+1] - 1;
436     for (j=0; j<nz; j++){
437       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
438     }
439   }
440   ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
441   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering;
442   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering;
443   C->assembled = PETSC_TRUE;
444   ierr = PetscLogFlops(1.333333333333*3*3*3*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
445   PetscFunctionReturn(0);
446 }
447 
448