xref: /petsc/src/mat/impls/baij/seq/baijfact13.c (revision 2b8d69ca7ea5fe9190df62c1dce3bbd66fce84dd)
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   PetscBool      allowzeropivot,zeropivotdetected;
28 
29   PetscFunctionBegin;
30   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
31   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
32   ierr = PetscMalloc1(9*(n+1),&rtmp);CHKERRQ(ierr);
33   allowzeropivot = PetscNot(A->erroriffailure);
34 
35   for (i=0; i<n; i++) {
36     nz    = bi[i+1] - bi[i];
37     ajtmp = bj + bi[i];
38     for  (j=0; j<nz; j++) {
39       x    = rtmp + 9*ajtmp[j];
40       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0;
41     }
42     /* load in initial (unfactored row) */
43     idx      = r[i];
44     nz       = ai[idx+1] - ai[idx];
45     ajtmpold = aj + ai[idx];
46     v        = aa + 9*ai[idx];
47     for (j=0; j<nz; j++) {
48       x    = rtmp + 9*ic[ajtmpold[j]];
49       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
50       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
51       v   += 9;
52     }
53     row = *ajtmp++;
54     while (row < i) {
55       pc = rtmp + 9*row;
56       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
57       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
58       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
59           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
60         pv    = ba + 9*diag_offset[row];
61         pj    = bj + diag_offset[row] + 1;
62         x1    = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
63         x5    = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
64         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
65         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
66         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
67 
68         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
69         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
70         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
71 
72         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
73         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
74         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
75         nz    = bi[row+1] - diag_offset[row] - 1;
76         pv   += 9;
77         for (j=0; j<nz; j++) {
78           x1    = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
79           x5    = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
80           x     = rtmp + 9*pj[j];
81           x[0] -= m1*x1 + m4*x2 + m7*x3;
82           x[1] -= m2*x1 + m5*x2 + m8*x3;
83           x[2] -= m3*x1 + m6*x2 + m9*x3;
84 
85           x[3] -= m1*x4 + m4*x5 + m7*x6;
86           x[4] -= m2*x4 + m5*x5 + m8*x6;
87           x[5] -= m3*x4 + m6*x5 + m9*x6;
88 
89           x[6] -= m1*x7 + m4*x8 + m7*x9;
90           x[7] -= m2*x7 + m5*x8 + m8*x9;
91           x[8] -= m3*x7 + m6*x8 + m9*x9;
92           pv   += 9;
93         }
94         ierr = PetscLogFlops(54.0*nz+36.0);CHKERRQ(ierr);
95       }
96       row = *ajtmp++;
97     }
98     /* finished row so stick it into b->a */
99     pv = ba + 9*bi[i];
100     pj = bj + bi[i];
101     nz = bi[i+1] - bi[i];
102     for (j=0; j<nz; j++) {
103       x     = rtmp + 9*pj[j];
104       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
105       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
106       pv   += 9;
107     }
108     /* invert diagonal block */
109     w    = ba + 9*diag_offset[i];
110     ierr = PetscKernel_A_gets_inverse_A_3(w,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
111     if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
112   }
113 
114   ierr = PetscFree(rtmp);CHKERRQ(ierr);
115   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
116   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
117 
118   C->ops->solve          = MatSolve_SeqBAIJ_3_inplace;
119   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_inplace;
120   C->assembled           = PETSC_TRUE;
121 
122   ierr = PetscLogFlops(1.333333333333*3*3*3*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
123   PetscFunctionReturn(0);
124 }
125 
126 /* MatLUFactorNumeric_SeqBAIJ_3 -
127      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
128        PetscKernel_A_gets_A_times_B()
129        PetscKernel_A_gets_A_minus_B_times_C()
130        PetscKernel_A_gets_inverse_A()
131 */
132 #undef __FUNCT__
133 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_3"
134 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3(Mat B,Mat A,const MatFactorInfo *info)
135 {
136   Mat            C     =B;
137   Mat_SeqBAIJ    *a    =(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
138   IS             isrow = b->row,isicol = b->icol;
139   PetscErrorCode ierr;
140   const PetscInt *r,*ic;
141   PetscInt       i,j,k,nz,nzL,row;
142   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
143   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
144   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
145   PetscInt       flg;
146   PetscReal      shift = info->shiftamount;
147   PetscBool      allowzeropivot,zeropivotdetected;
148 
149   PetscFunctionBegin;
150   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
151   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
152   allowzeropivot = PetscNot(A->erroriffailure);
153 
154   /* generate work space needed by the factorization */
155   ierr = PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);CHKERRQ(ierr);
156   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
157 
158   for (i=0; i<n; i++) {
159     /* zero rtmp */
160     /* L part */
161     nz    = bi[i+1] - bi[i];
162     bjtmp = bj + bi[i];
163     for  (j=0; j<nz; j++) {
164       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
165     }
166 
167     /* U part */
168     nz    = bdiag[i] - bdiag[i+1];
169     bjtmp = bj + bdiag[i+1]+1;
170     for  (j=0; j<nz; j++) {
171       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
172     }
173 
174     /* load in initial (unfactored row) */
175     nz    = ai[r[i]+1] - ai[r[i]];
176     ajtmp = aj + ai[r[i]];
177     v     = aa + bs2*ai[r[i]];
178     for (j=0; j<nz; j++) {
179       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
180     }
181 
182     /* elimination */
183     bjtmp = bj + bi[i];
184     nzL   = bi[i+1] - bi[i];
185     for (k = 0; k < nzL; k++) {
186       row = bjtmp[k];
187       pc  = rtmp + bs2*row;
188       for (flg=0,j=0; j<bs2; j++) {
189         if (pc[j]!=0.0) {
190           flg = 1;
191           break;
192         }
193       }
194       if (flg) {
195         pv = b->a + bs2*bdiag[row];
196         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
197         ierr = PetscKernel_A_gets_A_times_B_3(pc,pv,mwork);CHKERRQ(ierr);
198 
199         pj = b->j + bdiag[row+1] + 1; /* beginning of U(row,:) */
200         pv = b->a + bs2*(bdiag[row+1]+1);
201         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
202         for (j=0; j<nz; j++) {
203           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
204           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
205           v    = rtmp + bs2*pj[j];
206           ierr = PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);CHKERRQ(ierr);
207           pv  += bs2;
208         }
209         ierr = PetscLogFlops(54*nz+45);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
210       }
211     }
212 
213     /* finished row so stick it into b->a */
214     /* L part */
215     pv = b->a + bs2*bi[i];
216     pj = b->j + bi[i];
217     nz = bi[i+1] - bi[i];
218     for (j=0; j<nz; j++) {
219       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
220     }
221 
222     /* Mark diagonal and invert diagonal for simplier triangular solves */
223     pv   = b->a + bs2*bdiag[i];
224     pj   = b->j + bdiag[i];
225     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
226     ierr = PetscKernel_A_gets_inverse_A_3(pv,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
227     if (zeropivotdetected) B->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
228 
229     /* U part */
230     pj = b->j + bdiag[i+1] + 1;
231     pv = b->a + bs2*(bdiag[i+1]+1);
232     nz = bdiag[i] - bdiag[i+1] - 1;
233     for (j=0; j<nz; j++) {
234       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
235     }
236   }
237 
238   ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
239   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
240   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
241 
242   C->ops->solve          = MatSolve_SeqBAIJ_3;
243   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3;
244   C->assembled           = PETSC_TRUE;
245 
246   ierr = PetscLogFlops(1.333333333333*3*3*3*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
247   PetscFunctionReturn(0);
248 }
249 
250 #undef __FUNCT__
251 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_inplace"
252 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
253 {
254   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
255   PetscErrorCode ierr;
256   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
257   PetscInt       *ajtmpold,*ajtmp,nz,row;
258   PetscInt       *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
259   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
260   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
261   MatScalar      p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
262   MatScalar      *ba   = b->a,*aa = a->a;
263   PetscReal      shift = info->shiftamount;
264   PetscBool      allowzeropivot,zeropivotdetected;
265 
266   PetscFunctionBegin;
267   ierr = PetscMalloc1(9*(n+1),&rtmp);CHKERRQ(ierr);
268   allowzeropivot = PetscNot(A->erroriffailure);
269 
270   for (i=0; i<n; i++) {
271     nz    = bi[i+1] - bi[i];
272     ajtmp = bj + bi[i];
273     for  (j=0; j<nz; j++) {
274       x    = rtmp+9*ajtmp[j];
275       x[0] = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = 0.0;
276     }
277     /* load in initial (unfactored row) */
278     nz       = ai[i+1] - ai[i];
279     ajtmpold = aj + ai[i];
280     v        = aa + 9*ai[i];
281     for (j=0; j<nz; j++) {
282       x    = rtmp+9*ajtmpold[j];
283       x[0] = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
284       x[4] = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
285       v   += 9;
286     }
287     row = *ajtmp++;
288     while (row < i) {
289       pc = rtmp + 9*row;
290       p1 = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
291       p5 = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
292       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
293           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
294         pv    = ba + 9*diag_offset[row];
295         pj    = bj + diag_offset[row] + 1;
296         x1    = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
297         x5    = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
298         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
299         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
300         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
301 
302         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
303         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
304         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
305 
306         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
307         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
308         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
309 
310         nz  = bi[row+1] - diag_offset[row] - 1;
311         pv += 9;
312         for (j=0; j<nz; j++) {
313           x1    = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
314           x5    = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
315           x     = rtmp + 9*pj[j];
316           x[0] -= m1*x1 + m4*x2 + m7*x3;
317           x[1] -= m2*x1 + m5*x2 + m8*x3;
318           x[2] -= m3*x1 + m6*x2 + m9*x3;
319 
320           x[3] -= m1*x4 + m4*x5 + m7*x6;
321           x[4] -= m2*x4 + m5*x5 + m8*x6;
322           x[5] -= m3*x4 + m6*x5 + m9*x6;
323 
324           x[6] -= m1*x7 + m4*x8 + m7*x9;
325           x[7] -= m2*x7 + m5*x8 + m8*x9;
326           x[8] -= m3*x7 + m6*x8 + m9*x9;
327           pv   += 9;
328         }
329         ierr = PetscLogFlops(54.0*nz+36.0);CHKERRQ(ierr);
330       }
331       row = *ajtmp++;
332     }
333     /* finished row so stick it into b->a */
334     pv = ba + 9*bi[i];
335     pj = bj + bi[i];
336     nz = bi[i+1] - bi[i];
337     for (j=0; j<nz; j++) {
338       x     = rtmp+9*pj[j];
339       pv[0] = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
340       pv[4] = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
341       pv   += 9;
342     }
343     /* invert diagonal block */
344     w    = ba + 9*diag_offset[i];
345     ierr = PetscKernel_A_gets_inverse_A_3(w,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
346     if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
347   }
348 
349   ierr = PetscFree(rtmp);CHKERRQ(ierr);
350 
351   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering_inplace;
352   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering_inplace;
353   C->assembled           = PETSC_TRUE;
354 
355   ierr = PetscLogFlops(1.333333333333*3*3*3*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
356   PetscFunctionReturn(0);
357 }
358 
359 /*
360   MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering -
361     copied from MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_inplace()
362 */
363 #undef __FUNCT__
364 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering"
365 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
366 {
367   Mat            C =B;
368   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
369   PetscErrorCode ierr;
370   PetscInt       i,j,k,nz,nzL,row;
371   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
372   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
373   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
374   PetscInt       flg;
375   PetscReal      shift = info->shiftamount;
376   PetscBool      allowzeropivot,zeropivotdetected;
377 
378   PetscFunctionBegin;
379   allowzeropivot = PetscNot(A->erroriffailure);
380 
381   /* generate work space needed by the factorization */
382   ierr = PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);CHKERRQ(ierr);
383   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
384 
385   for (i=0; i<n; i++) {
386     /* zero rtmp */
387     /* L part */
388     nz    = bi[i+1] - bi[i];
389     bjtmp = bj + bi[i];
390     for  (j=0; j<nz; j++) {
391       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
392     }
393 
394     /* U part */
395     nz    = bdiag[i] - bdiag[i+1];
396     bjtmp = bj + bdiag[i+1] + 1;
397     for  (j=0; j<nz; j++) {
398       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
399     }
400 
401     /* load in initial (unfactored row) */
402     nz    = ai[i+1] - ai[i];
403     ajtmp = aj + ai[i];
404     v     = aa + bs2*ai[i];
405     for (j=0; j<nz; j++) {
406       ierr = PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
407     }
408 
409     /* elimination */
410     bjtmp = bj + bi[i];
411     nzL   = bi[i+1] - bi[i];
412     for (k=0; k<nzL; k++) {
413       row = bjtmp[k];
414       pc  = rtmp + bs2*row;
415       for (flg=0,j=0; j<bs2; j++) {
416         if (pc[j]!=0.0) {
417           flg = 1;
418           break;
419         }
420       }
421       if (flg) {
422         pv = b->a + bs2*bdiag[row];
423         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
424         ierr = PetscKernel_A_gets_A_times_B_3(pc,pv,mwork);CHKERRQ(ierr);
425 
426         pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
427         pv = b->a + bs2*(bdiag[row+1]+1);
428         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
429         for (j=0; j<nz; j++) {
430           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
431           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
432           v    = rtmp + bs2*pj[j];
433           ierr = PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);CHKERRQ(ierr);
434           pv  += bs2;
435         }
436         ierr = PetscLogFlops(54*nz+45);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
437       }
438     }
439 
440     /* finished row so stick it into b->a */
441     /* L part */
442     pv = b->a + bs2*bi[i];
443     pj = b->j + bi[i];
444     nz = bi[i+1] - bi[i];
445     for (j=0; j<nz; j++) {
446       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
447     }
448 
449     /* Mark diagonal and invert diagonal for simplier triangular solves */
450     pv   = b->a + bs2*bdiag[i];
451     pj   = b->j + bdiag[i];
452     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
453     ierr = PetscKernel_A_gets_inverse_A_3(pv,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
454     if (zeropivotdetected) B->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
455 
456     /* U part */
457     pv = b->a + bs2*(bdiag[i+1]+1);
458     pj = b->j + bdiag[i+1]+1;
459     nz = bdiag[i] - bdiag[i+1] - 1;
460     for (j=0; j<nz; j++) {
461       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
462     }
463   }
464   ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
465 
466   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering;
467   C->ops->forwardsolve   = MatForwardSolve_SeqBAIJ_3_NaturalOrdering;
468   C->ops->backwardsolve  = MatBackwardSolve_SeqBAIJ_3_NaturalOrdering;
469   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering;
470   C->assembled           = PETSC_TRUE;
471 
472   ierr = PetscLogFlops(1.333333333333*3*3*3*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
473   PetscFunctionReturn(0);
474 }
475 
476