xref: /petsc/src/mat/impls/baij/seq/baijfact13.c (revision a455e9261d77363e13c8b22a0e0ea831d71fb0ff)
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 
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     allowzeropivot = PetscNot(A->erroriffailure);
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 
153   /* generate work space needed by the factorization */
154   ierr = PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);CHKERRQ(ierr);
155   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
156 
157   for (i=0; i<n; i++) {
158     /* zero rtmp */
159     /* L part */
160     nz    = bi[i+1] - bi[i];
161     bjtmp = bj + bi[i];
162     for  (j=0; j<nz; j++) {
163       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
164     }
165 
166     /* U part */
167     nz    = bdiag[i] - bdiag[i+1];
168     bjtmp = bj + bdiag[i+1]+1;
169     for  (j=0; j<nz; j++) {
170       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
171     }
172 
173     /* load in initial (unfactored row) */
174     nz    = ai[r[i]+1] - ai[r[i]];
175     ajtmp = aj + ai[r[i]];
176     v     = aa + bs2*ai[r[i]];
177     for (j=0; j<nz; j++) {
178       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
179     }
180 
181     /* elimination */
182     bjtmp = bj + bi[i];
183     nzL   = bi[i+1] - bi[i];
184     for (k = 0; k < nzL; k++) {
185       row = bjtmp[k];
186       pc  = rtmp + bs2*row;
187       for (flg=0,j=0; j<bs2; j++) {
188         if (pc[j]!=0.0) {
189           flg = 1;
190           break;
191         }
192       }
193       if (flg) {
194         pv = b->a + bs2*bdiag[row];
195         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
196         ierr = PetscKernel_A_gets_A_times_B_3(pc,pv,mwork);CHKERRQ(ierr);
197 
198         pj = b->j + bdiag[row+1] + 1; /* beginning of U(row,:) */
199         pv = b->a + bs2*(bdiag[row+1]+1);
200         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
201         for (j=0; j<nz; j++) {
202           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
203           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
204           v    = rtmp + bs2*pj[j];
205           ierr = PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);CHKERRQ(ierr);
206           pv  += bs2;
207         }
208         ierr = PetscLogFlops(54*nz+45);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
209       }
210     }
211 
212     /* finished row so stick it into b->a */
213     /* L part */
214     pv = b->a + bs2*bi[i];
215     pj = b->j + bi[i];
216     nz = bi[i+1] - bi[i];
217     for (j=0; j<nz; j++) {
218       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
219     }
220 
221     /* Mark diagonal and invert diagonal for simplier triangular solves */
222     pv   = b->a + bs2*bdiag[i];
223     pj   = b->j + bdiag[i];
224     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
225     /* ierr = PetscKernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
226     allowzeropivot = PetscNot(A->erroriffailure);
227     ierr = PetscKernel_A_gets_inverse_A_3(pv,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
228     if (zeropivotdetected) B->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
229 
230     /* U part */
231     pj = b->j + bdiag[i+1] + 1;
232     pv = b->a + bs2*(bdiag[i+1]+1);
233     nz = bdiag[i] - bdiag[i+1] - 1;
234     for (j=0; j<nz; j++) {
235       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
236     }
237   }
238 
239   ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
240   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
241   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
242 
243   C->ops->solve          = MatSolve_SeqBAIJ_3;
244   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3;
245   C->assembled           = PETSC_TRUE;
246 
247   ierr = PetscLogFlops(1.333333333333*3*3*3*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
248   PetscFunctionReturn(0);
249 }
250 
251 #undef __FUNCT__
252 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_inplace"
253 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
254 {
255   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
256   PetscErrorCode ierr;
257   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
258   PetscInt       *ajtmpold,*ajtmp,nz,row;
259   PetscInt       *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
260   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
261   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
262   MatScalar      p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
263   MatScalar      *ba   = b->a,*aa = a->a;
264   PetscReal      shift = info->shiftamount;
265   PetscBool      allowzeropivot,zeropivotdetected;
266 
267   PetscFunctionBegin;
268   ierr = PetscMalloc1(9*(n+1),&rtmp);CHKERRQ(ierr);
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     allowzeropivot = PetscNot(A->erroriffailure);
346     ierr = PetscKernel_A_gets_inverse_A_3(w,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
347     if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
348   }
349 
350   ierr = PetscFree(rtmp);CHKERRQ(ierr);
351 
352   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering_inplace;
353   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering_inplace;
354   C->assembled           = PETSC_TRUE;
355 
356   ierr = PetscLogFlops(1.333333333333*3*3*3*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
357   PetscFunctionReturn(0);
358 }
359 
360 /*
361   MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering -
362     copied from MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_inplace()
363 */
364 #undef __FUNCT__
365 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering"
366 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
367 {
368   Mat            C =B;
369   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
370   PetscErrorCode ierr;
371   PetscInt       i,j,k,nz,nzL,row;
372   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
373   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
374   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
375   PetscInt       flg;
376   PetscReal      shift = info->shiftamount;
377   PetscBool      allowzeropivot,zeropivotdetected;
378 
379   PetscFunctionBegin;
380   /* generate work space needed by the factorization */
381   ierr = PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);CHKERRQ(ierr);
382   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
383 
384   for (i=0; i<n; i++) {
385     /* zero rtmp */
386     /* L part */
387     nz    = bi[i+1] - bi[i];
388     bjtmp = bj + bi[i];
389     for  (j=0; j<nz; j++) {
390       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
391     }
392 
393     /* U part */
394     nz    = bdiag[i] - bdiag[i+1];
395     bjtmp = bj + bdiag[i+1] + 1;
396     for  (j=0; j<nz; j++) {
397       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
398     }
399 
400     /* load in initial (unfactored row) */
401     nz    = ai[i+1] - ai[i];
402     ajtmp = aj + ai[i];
403     v     = aa + bs2*ai[i];
404     for (j=0; j<nz; j++) {
405       ierr = PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
406     }
407 
408     /* elimination */
409     bjtmp = bj + bi[i];
410     nzL   = bi[i+1] - bi[i];
411     for (k=0; k<nzL; k++) {
412       row = bjtmp[k];
413       pc  = rtmp + bs2*row;
414       for (flg=0,j=0; j<bs2; j++) {
415         if (pc[j]!=0.0) {
416           flg = 1;
417           break;
418         }
419       }
420       if (flg) {
421         pv = b->a + bs2*bdiag[row];
422         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
423         ierr = PetscKernel_A_gets_A_times_B_3(pc,pv,mwork);CHKERRQ(ierr);
424 
425         pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
426         pv = b->a + bs2*(bdiag[row+1]+1);
427         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
428         for (j=0; j<nz; j++) {
429           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
430           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
431           v    = rtmp + bs2*pj[j];
432           ierr = PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);CHKERRQ(ierr);
433           pv  += bs2;
434         }
435         ierr = PetscLogFlops(54*nz+45);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
436       }
437     }
438 
439     /* finished row so stick it into b->a */
440     /* L part */
441     pv = b->a + bs2*bi[i];
442     pj = b->j + bi[i];
443     nz = bi[i+1] - bi[i];
444     for (j=0; j<nz; j++) {
445       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
446     }
447 
448     /* Mark diagonal and invert diagonal for simplier triangular solves */
449     pv   = b->a + bs2*bdiag[i];
450     pj   = b->j + bdiag[i];
451     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
452     /* ierr = PetscKernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
453     allowzeropivot = PetscNot(A->erroriffailure);
454     ierr = PetscKernel_A_gets_inverse_A_3(pv,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
455     if (zeropivotdetected) B->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
456 
457     /* U part */
458     pv = b->a + bs2*(bdiag[i+1]+1);
459     pj = b->j + bdiag[i+1]+1;
460     nz = bdiag[i] - bdiag[i+1] - 1;
461     for (j=0; j<nz; j++) {
462       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
463     }
464   }
465   ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
466 
467   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering;
468   C->ops->forwardsolve   = MatForwardSolve_SeqBAIJ_3_NaturalOrdering;
469   C->ops->backwardsolve  = MatBackwardSolve_SeqBAIJ_3_NaturalOrdering;
470   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering;
471   C->assembled           = PETSC_TRUE;
472 
473   ierr = PetscLogFlops(1.333333333333*3*3*3*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
474   PetscFunctionReturn(0);
475 }
476 
477