xref: /petsc/src/mat/impls/baij/seq/baijfact7.c (revision 58d68138c660dfb4e9f5b03334792cd4f2ffd7cc)
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 /*
10       Version for when blocks are 6 by 6
11 */
12 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_6_inplace(Mat C, Mat A, const MatFactorInfo *info) {
13   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
14   IS              isrow = b->row, isicol = b->icol;
15   const PetscInt *ajtmpold, *ajtmp, *diag_offset = b->diag, *r, *ic, *bi = b->i, *bj = b->j, *ai = a->i, *aj = a->j, *pj;
16   PetscInt        nz, row, i, j, n = a->mbs, idx;
17   MatScalar      *pv, *v, *rtmp, *pc, *w, *x;
18   MatScalar       p1, p2, p3, p4, m1, m2, m3, m4, m5, m6, m7, m8, m9, x1, x2, x3, x4;
19   MatScalar       p5, p6, p7, p8, p9, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16;
20   MatScalar       x17, x18, x19, x20, x21, x22, x23, x24, x25, p10, p11, p12, p13, p14;
21   MatScalar       p15, p16, p17, p18, p19, p20, p21, p22, p23, p24, p25, m10, m11, m12;
22   MatScalar       m13, m14, m15, m16, m17, m18, m19, m20, m21, m22, m23, m24, m25;
23   MatScalar       p26, p27, p28, p29, p30, p31, p32, p33, p34, p35, p36;
24   MatScalar       x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36;
25   MatScalar       m26, m27, m28, m29, m30, m31, m32, m33, m34, m35, m36;
26   MatScalar      *ba = b->a, *aa = a->a;
27   PetscReal       shift = info->shiftamount;
28   PetscBool       allowzeropivot, zeropivotdetected;
29 
30   PetscFunctionBegin;
31   allowzeropivot = PetscNot(A->erroriffailure);
32   PetscCall(ISGetIndices(isrow, &r));
33   PetscCall(ISGetIndices(isicol, &ic));
34   PetscCall(PetscMalloc1(36 * (n + 1), &rtmp));
35 
36   for (i = 0; i < n; i++) {
37     nz    = bi[i + 1] - bi[i];
38     ajtmp = bj + bi[i];
39     for (j = 0; j < nz; j++) {
40       x    = rtmp + 36 * ajtmp[j];
41       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
42       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
43       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0;
44       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0;
45       x[34] = x[35] = 0.0;
46     }
47     /* load in initial (unfactored row) */
48     idx      = r[i];
49     nz       = ai[idx + 1] - ai[idx];
50     ajtmpold = aj + ai[idx];
51     v        = aa + 36 * ai[idx];
52     for (j = 0; j < nz; j++) {
53       x     = rtmp + 36 * ic[ajtmpold[j]];
54       x[0]  = v[0];
55       x[1]  = v[1];
56       x[2]  = v[2];
57       x[3]  = v[3];
58       x[4]  = v[4];
59       x[5]  = v[5];
60       x[6]  = v[6];
61       x[7]  = v[7];
62       x[8]  = v[8];
63       x[9]  = v[9];
64       x[10] = v[10];
65       x[11] = v[11];
66       x[12] = v[12];
67       x[13] = v[13];
68       x[14] = v[14];
69       x[15] = v[15];
70       x[16] = v[16];
71       x[17] = v[17];
72       x[18] = v[18];
73       x[19] = v[19];
74       x[20] = v[20];
75       x[21] = v[21];
76       x[22] = v[22];
77       x[23] = v[23];
78       x[24] = v[24];
79       x[25] = v[25];
80       x[26] = v[26];
81       x[27] = v[27];
82       x[28] = v[28];
83       x[29] = v[29];
84       x[30] = v[30];
85       x[31] = v[31];
86       x[32] = v[32];
87       x[33] = v[33];
88       x[34] = v[34];
89       x[35] = v[35];
90       v += 36;
91     }
92     row = *ajtmp++;
93     while (row < i) {
94       pc  = rtmp + 36 * row;
95       p1  = pc[0];
96       p2  = pc[1];
97       p3  = pc[2];
98       p4  = pc[3];
99       p5  = pc[4];
100       p6  = pc[5];
101       p7  = pc[6];
102       p8  = pc[7];
103       p9  = pc[8];
104       p10 = pc[9];
105       p11 = pc[10];
106       p12 = pc[11];
107       p13 = pc[12];
108       p14 = pc[13];
109       p15 = pc[14];
110       p16 = pc[15];
111       p17 = pc[16];
112       p18 = pc[17];
113       p19 = pc[18];
114       p20 = pc[19];
115       p21 = pc[20];
116       p22 = pc[21];
117       p23 = pc[22];
118       p24 = pc[23];
119       p25 = pc[24];
120       p26 = pc[25];
121       p27 = pc[26];
122       p28 = pc[27];
123       p29 = pc[28];
124       p30 = pc[29];
125       p31 = pc[30];
126       p32 = pc[31];
127       p33 = pc[32];
128       p34 = pc[33];
129       p35 = pc[34];
130       p36 = pc[35];
131       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 || p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 || p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) {
132         pv    = ba + 36 * diag_offset[row];
133         pj    = bj + diag_offset[row] + 1;
134         x1    = pv[0];
135         x2    = pv[1];
136         x3    = pv[2];
137         x4    = pv[3];
138         x5    = pv[4];
139         x6    = pv[5];
140         x7    = pv[6];
141         x8    = pv[7];
142         x9    = pv[8];
143         x10   = pv[9];
144         x11   = pv[10];
145         x12   = pv[11];
146         x13   = pv[12];
147         x14   = pv[13];
148         x15   = pv[14];
149         x16   = pv[15];
150         x17   = pv[16];
151         x18   = pv[17];
152         x19   = pv[18];
153         x20   = pv[19];
154         x21   = pv[20];
155         x22   = pv[21];
156         x23   = pv[22];
157         x24   = pv[23];
158         x25   = pv[24];
159         x26   = pv[25];
160         x27   = pv[26];
161         x28   = pv[27];
162         x29   = pv[28];
163         x30   = pv[29];
164         x31   = pv[30];
165         x32   = pv[31];
166         x33   = pv[32];
167         x34   = pv[33];
168         x35   = pv[34];
169         x36   = pv[35];
170         pc[0] = m1 = p1 * x1 + p7 * x2 + p13 * x3 + p19 * x4 + p25 * x5 + p31 * x6;
171         pc[1] = m2 = p2 * x1 + p8 * x2 + p14 * x3 + p20 * x4 + p26 * x5 + p32 * x6;
172         pc[2] = m3 = p3 * x1 + p9 * x2 + p15 * x3 + p21 * x4 + p27 * x5 + p33 * x6;
173         pc[3] = m4 = p4 * x1 + p10 * x2 + p16 * x3 + p22 * x4 + p28 * x5 + p34 * x6;
174         pc[4] = m5 = p5 * x1 + p11 * x2 + p17 * x3 + p23 * x4 + p29 * x5 + p35 * x6;
175         pc[5] = m6 = p6 * x1 + p12 * x2 + p18 * x3 + p24 * x4 + p30 * x5 + p36 * x6;
176 
177         pc[6] = m7 = p1 * x7 + p7 * x8 + p13 * x9 + p19 * x10 + p25 * x11 + p31 * x12;
178         pc[7] = m8 = p2 * x7 + p8 * x8 + p14 * x9 + p20 * x10 + p26 * x11 + p32 * x12;
179         pc[8] = m9 = p3 * x7 + p9 * x8 + p15 * x9 + p21 * x10 + p27 * x11 + p33 * x12;
180         pc[9] = m10 = p4 * x7 + p10 * x8 + p16 * x9 + p22 * x10 + p28 * x11 + p34 * x12;
181         pc[10] = m11 = p5 * x7 + p11 * x8 + p17 * x9 + p23 * x10 + p29 * x11 + p35 * x12;
182         pc[11] = m12 = p6 * x7 + p12 * x8 + p18 * x9 + p24 * x10 + p30 * x11 + p36 * x12;
183 
184         pc[12] = m13 = p1 * x13 + p7 * x14 + p13 * x15 + p19 * x16 + p25 * x17 + p31 * x18;
185         pc[13] = m14 = p2 * x13 + p8 * x14 + p14 * x15 + p20 * x16 + p26 * x17 + p32 * x18;
186         pc[14] = m15 = p3 * x13 + p9 * x14 + p15 * x15 + p21 * x16 + p27 * x17 + p33 * x18;
187         pc[15] = m16 = p4 * x13 + p10 * x14 + p16 * x15 + p22 * x16 + p28 * x17 + p34 * x18;
188         pc[16] = m17 = p5 * x13 + p11 * x14 + p17 * x15 + p23 * x16 + p29 * x17 + p35 * x18;
189         pc[17] = m18 = p6 * x13 + p12 * x14 + p18 * x15 + p24 * x16 + p30 * x17 + p36 * x18;
190 
191         pc[18] = m19 = p1 * x19 + p7 * x20 + p13 * x21 + p19 * x22 + p25 * x23 + p31 * x24;
192         pc[19] = m20 = p2 * x19 + p8 * x20 + p14 * x21 + p20 * x22 + p26 * x23 + p32 * x24;
193         pc[20] = m21 = p3 * x19 + p9 * x20 + p15 * x21 + p21 * x22 + p27 * x23 + p33 * x24;
194         pc[21] = m22 = p4 * x19 + p10 * x20 + p16 * x21 + p22 * x22 + p28 * x23 + p34 * x24;
195         pc[22] = m23 = p5 * x19 + p11 * x20 + p17 * x21 + p23 * x22 + p29 * x23 + p35 * x24;
196         pc[23] = m24 = p6 * x19 + p12 * x20 + p18 * x21 + p24 * x22 + p30 * x23 + p36 * x24;
197 
198         pc[24] = m25 = p1 * x25 + p7 * x26 + p13 * x27 + p19 * x28 + p25 * x29 + p31 * x30;
199         pc[25] = m26 = p2 * x25 + p8 * x26 + p14 * x27 + p20 * x28 + p26 * x29 + p32 * x30;
200         pc[26] = m27 = p3 * x25 + p9 * x26 + p15 * x27 + p21 * x28 + p27 * x29 + p33 * x30;
201         pc[27] = m28 = p4 * x25 + p10 * x26 + p16 * x27 + p22 * x28 + p28 * x29 + p34 * x30;
202         pc[28] = m29 = p5 * x25 + p11 * x26 + p17 * x27 + p23 * x28 + p29 * x29 + p35 * x30;
203         pc[29] = m30 = p6 * x25 + p12 * x26 + p18 * x27 + p24 * x28 + p30 * x29 + p36 * x30;
204 
205         pc[30] = m31 = p1 * x31 + p7 * x32 + p13 * x33 + p19 * x34 + p25 * x35 + p31 * x36;
206         pc[31] = m32 = p2 * x31 + p8 * x32 + p14 * x33 + p20 * x34 + p26 * x35 + p32 * x36;
207         pc[32] = m33 = p3 * x31 + p9 * x32 + p15 * x33 + p21 * x34 + p27 * x35 + p33 * x36;
208         pc[33] = m34 = p4 * x31 + p10 * x32 + p16 * x33 + p22 * x34 + p28 * x35 + p34 * x36;
209         pc[34] = m35 = p5 * x31 + p11 * x32 + p17 * x33 + p23 * x34 + p29 * x35 + p35 * x36;
210         pc[35] = m36 = p6 * x31 + p12 * x32 + p18 * x33 + p24 * x34 + p30 * x35 + p36 * x36;
211 
212         nz = bi[row + 1] - diag_offset[row] - 1;
213         pv += 36;
214         for (j = 0; j < nz; j++) {
215           x1  = pv[0];
216           x2  = pv[1];
217           x3  = pv[2];
218           x4  = pv[3];
219           x5  = pv[4];
220           x6  = pv[5];
221           x7  = pv[6];
222           x8  = pv[7];
223           x9  = pv[8];
224           x10 = pv[9];
225           x11 = pv[10];
226           x12 = pv[11];
227           x13 = pv[12];
228           x14 = pv[13];
229           x15 = pv[14];
230           x16 = pv[15];
231           x17 = pv[16];
232           x18 = pv[17];
233           x19 = pv[18];
234           x20 = pv[19];
235           x21 = pv[20];
236           x22 = pv[21];
237           x23 = pv[22];
238           x24 = pv[23];
239           x25 = pv[24];
240           x26 = pv[25];
241           x27 = pv[26];
242           x28 = pv[27];
243           x29 = pv[28];
244           x30 = pv[29];
245           x31 = pv[30];
246           x32 = pv[31];
247           x33 = pv[32];
248           x34 = pv[33];
249           x35 = pv[34];
250           x36 = pv[35];
251           x   = rtmp + 36 * pj[j];
252           x[0] -= m1 * x1 + m7 * x2 + m13 * x3 + m19 * x4 + m25 * x5 + m31 * x6;
253           x[1] -= m2 * x1 + m8 * x2 + m14 * x3 + m20 * x4 + m26 * x5 + m32 * x6;
254           x[2] -= m3 * x1 + m9 * x2 + m15 * x3 + m21 * x4 + m27 * x5 + m33 * x6;
255           x[3] -= m4 * x1 + m10 * x2 + m16 * x3 + m22 * x4 + m28 * x5 + m34 * x6;
256           x[4] -= m5 * x1 + m11 * x2 + m17 * x3 + m23 * x4 + m29 * x5 + m35 * x6;
257           x[5] -= m6 * x1 + m12 * x2 + m18 * x3 + m24 * x4 + m30 * x5 + m36 * x6;
258 
259           x[6] -= m1 * x7 + m7 * x8 + m13 * x9 + m19 * x10 + m25 * x11 + m31 * x12;
260           x[7] -= m2 * x7 + m8 * x8 + m14 * x9 + m20 * x10 + m26 * x11 + m32 * x12;
261           x[8] -= m3 * x7 + m9 * x8 + m15 * x9 + m21 * x10 + m27 * x11 + m33 * x12;
262           x[9] -= m4 * x7 + m10 * x8 + m16 * x9 + m22 * x10 + m28 * x11 + m34 * x12;
263           x[10] -= m5 * x7 + m11 * x8 + m17 * x9 + m23 * x10 + m29 * x11 + m35 * x12;
264           x[11] -= m6 * x7 + m12 * x8 + m18 * x9 + m24 * x10 + m30 * x11 + m36 * x12;
265 
266           x[12] -= m1 * x13 + m7 * x14 + m13 * x15 + m19 * x16 + m25 * x17 + m31 * x18;
267           x[13] -= m2 * x13 + m8 * x14 + m14 * x15 + m20 * x16 + m26 * x17 + m32 * x18;
268           x[14] -= m3 * x13 + m9 * x14 + m15 * x15 + m21 * x16 + m27 * x17 + m33 * x18;
269           x[15] -= m4 * x13 + m10 * x14 + m16 * x15 + m22 * x16 + m28 * x17 + m34 * x18;
270           x[16] -= m5 * x13 + m11 * x14 + m17 * x15 + m23 * x16 + m29 * x17 + m35 * x18;
271           x[17] -= m6 * x13 + m12 * x14 + m18 * x15 + m24 * x16 + m30 * x17 + m36 * x18;
272 
273           x[18] -= m1 * x19 + m7 * x20 + m13 * x21 + m19 * x22 + m25 * x23 + m31 * x24;
274           x[19] -= m2 * x19 + m8 * x20 + m14 * x21 + m20 * x22 + m26 * x23 + m32 * x24;
275           x[20] -= m3 * x19 + m9 * x20 + m15 * x21 + m21 * x22 + m27 * x23 + m33 * x24;
276           x[21] -= m4 * x19 + m10 * x20 + m16 * x21 + m22 * x22 + m28 * x23 + m34 * x24;
277           x[22] -= m5 * x19 + m11 * x20 + m17 * x21 + m23 * x22 + m29 * x23 + m35 * x24;
278           x[23] -= m6 * x19 + m12 * x20 + m18 * x21 + m24 * x22 + m30 * x23 + m36 * x24;
279 
280           x[24] -= m1 * x25 + m7 * x26 + m13 * x27 + m19 * x28 + m25 * x29 + m31 * x30;
281           x[25] -= m2 * x25 + m8 * x26 + m14 * x27 + m20 * x28 + m26 * x29 + m32 * x30;
282           x[26] -= m3 * x25 + m9 * x26 + m15 * x27 + m21 * x28 + m27 * x29 + m33 * x30;
283           x[27] -= m4 * x25 + m10 * x26 + m16 * x27 + m22 * x28 + m28 * x29 + m34 * x30;
284           x[28] -= m5 * x25 + m11 * x26 + m17 * x27 + m23 * x28 + m29 * x29 + m35 * x30;
285           x[29] -= m6 * x25 + m12 * x26 + m18 * x27 + m24 * x28 + m30 * x29 + m36 * x30;
286 
287           x[30] -= m1 * x31 + m7 * x32 + m13 * x33 + m19 * x34 + m25 * x35 + m31 * x36;
288           x[31] -= m2 * x31 + m8 * x32 + m14 * x33 + m20 * x34 + m26 * x35 + m32 * x36;
289           x[32] -= m3 * x31 + m9 * x32 + m15 * x33 + m21 * x34 + m27 * x35 + m33 * x36;
290           x[33] -= m4 * x31 + m10 * x32 + m16 * x33 + m22 * x34 + m28 * x35 + m34 * x36;
291           x[34] -= m5 * x31 + m11 * x32 + m17 * x33 + m23 * x34 + m29 * x35 + m35 * x36;
292           x[35] -= m6 * x31 + m12 * x32 + m18 * x33 + m24 * x34 + m30 * x35 + m36 * x36;
293 
294           pv += 36;
295         }
296         PetscCall(PetscLogFlops(432.0 * nz + 396.0));
297       }
298       row = *ajtmp++;
299     }
300     /* finished row so stick it into b->a */
301     pv = ba + 36 * bi[i];
302     pj = bj + bi[i];
303     nz = bi[i + 1] - bi[i];
304     for (j = 0; j < nz; j++) {
305       x      = rtmp + 36 * pj[j];
306       pv[0]  = x[0];
307       pv[1]  = x[1];
308       pv[2]  = x[2];
309       pv[3]  = x[3];
310       pv[4]  = x[4];
311       pv[5]  = x[5];
312       pv[6]  = x[6];
313       pv[7]  = x[7];
314       pv[8]  = x[8];
315       pv[9]  = x[9];
316       pv[10] = x[10];
317       pv[11] = x[11];
318       pv[12] = x[12];
319       pv[13] = x[13];
320       pv[14] = x[14];
321       pv[15] = x[15];
322       pv[16] = x[16];
323       pv[17] = x[17];
324       pv[18] = x[18];
325       pv[19] = x[19];
326       pv[20] = x[20];
327       pv[21] = x[21];
328       pv[22] = x[22];
329       pv[23] = x[23];
330       pv[24] = x[24];
331       pv[25] = x[25];
332       pv[26] = x[26];
333       pv[27] = x[27];
334       pv[28] = x[28];
335       pv[29] = x[29];
336       pv[30] = x[30];
337       pv[31] = x[31];
338       pv[32] = x[32];
339       pv[33] = x[33];
340       pv[34] = x[34];
341       pv[35] = x[35];
342       pv += 36;
343     }
344     /* invert diagonal block */
345     w = ba + 36 * diag_offset[i];
346     PetscCall(PetscKernel_A_gets_inverse_A_6(w, shift, allowzeropivot, &zeropivotdetected));
347     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
348   }
349 
350   PetscCall(PetscFree(rtmp));
351   PetscCall(ISRestoreIndices(isicol, &ic));
352   PetscCall(ISRestoreIndices(isrow, &r));
353 
354   C->ops->solve          = MatSolve_SeqBAIJ_6_inplace;
355   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_6_inplace;
356   C->assembled           = PETSC_TRUE;
357 
358   PetscCall(PetscLogFlops(1.333333333333 * 6 * 6 * 6 * b->mbs)); /* from inverting diagonal blocks */
359   PetscFunctionReturn(0);
360 }
361 
362 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_6(Mat B, Mat A, const MatFactorInfo *info) {
363   Mat             C = B;
364   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
365   IS              isrow = b->row, isicol = b->icol;
366   const PetscInt *r, *ic;
367   PetscInt        i, j, k, nz, nzL, row;
368   const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
369   const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
370   MatScalar      *rtmp, *pc, *mwork, *v, *pv, *aa = a->a;
371   PetscInt        flg;
372   PetscReal       shift = info->shiftamount;
373   PetscBool       allowzeropivot, zeropivotdetected;
374 
375   PetscFunctionBegin;
376   allowzeropivot = PetscNot(A->erroriffailure);
377   PetscCall(ISGetIndices(isrow, &r));
378   PetscCall(ISGetIndices(isicol, &ic));
379 
380   /* generate work space needed by the factorization */
381   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
382   PetscCall(PetscArrayzero(rtmp, bs2 * n));
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++) { PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2)); }
390 
391     /* U part */
392     nz    = bdiag[i] - bdiag[i + 1];
393     bjtmp = bj + bdiag[i + 1] + 1;
394     for (j = 0; j < nz; j++) { PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2)); }
395 
396     /* load in initial (unfactored row) */
397     nz    = ai[r[i] + 1] - ai[r[i]];
398     ajtmp = aj + ai[r[i]];
399     v     = aa + bs2 * ai[r[i]];
400     for (j = 0; j < nz; j++) { PetscCall(PetscArraycpy(rtmp + bs2 * ic[ajtmp[j]], v + bs2 * j, bs2)); }
401 
402     /* elimination */
403     bjtmp = bj + bi[i];
404     nzL   = bi[i + 1] - bi[i];
405     for (k = 0; k < nzL; k++) {
406       row = bjtmp[k];
407       pc  = rtmp + bs2 * row;
408       for (flg = 0, j = 0; j < bs2; j++) {
409         if (pc[j] != 0.0) {
410           flg = 1;
411           break;
412         }
413       }
414       if (flg) {
415         pv = b->a + bs2 * bdiag[row];
416         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
417         PetscCall(PetscKernel_A_gets_A_times_B_6(pc, pv, mwork));
418 
419         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
420         pv = b->a + bs2 * (bdiag[row + 1] + 1);
421         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
422         for (j = 0; j < nz; j++) {
423           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
424           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
425           v = rtmp + bs2 * pj[j];
426           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_6(v, pc, pv));
427           pv += bs2;
428         }
429         PetscCall(PetscLogFlops(432.0 * nz + 396)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
430       }
431     }
432 
433     /* finished row so stick it into b->a */
434     /* L part */
435     pv = b->a + bs2 * bi[i];
436     pj = b->j + bi[i];
437     nz = bi[i + 1] - bi[i];
438     for (j = 0; j < nz; j++) { PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2)); }
439 
440     /* Mark diagonal and invert diagonal for simpler triangular solves */
441     pv = b->a + bs2 * bdiag[i];
442     pj = b->j + bdiag[i];
443     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
444     PetscCall(PetscKernel_A_gets_inverse_A_6(pv, shift, allowzeropivot, &zeropivotdetected));
445     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
446 
447     /* U part */
448     pv = b->a + bs2 * (bdiag[i + 1] + 1);
449     pj = b->j + bdiag[i + 1] + 1;
450     nz = bdiag[i] - bdiag[i + 1] - 1;
451     for (j = 0; j < nz; j++) { PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2)); }
452   }
453 
454   PetscCall(PetscFree2(rtmp, mwork));
455   PetscCall(ISRestoreIndices(isicol, &ic));
456   PetscCall(ISRestoreIndices(isrow, &r));
457 
458   C->ops->solve          = MatSolve_SeqBAIJ_6;
459   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_6;
460   C->assembled           = PETSC_TRUE;
461 
462   PetscCall(PetscLogFlops(1.333333333333 * 6 * 6 * 6 * n)); /* from inverting diagonal blocks */
463   PetscFunctionReturn(0);
464 }
465 
466 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_6_NaturalOrdering_inplace(Mat C, Mat A, const MatFactorInfo *info) {
467   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
468   PetscInt     i, j, n = a->mbs, *bi = b->i, *bj = b->j;
469   PetscInt    *ajtmpold, *ajtmp, nz, row;
470   PetscInt    *diag_offset = b->diag, *ai = a->i, *aj = a->j, *pj;
471   MatScalar   *pv, *v, *rtmp, *pc, *w, *x;
472   MatScalar    x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15;
473   MatScalar    x16, x17, x18, x19, x20, x21, x22, x23, x24, x25;
474   MatScalar    p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12, p13, p14, p15;
475   MatScalar    p16, p17, p18, p19, p20, p21, p22, p23, p24, p25;
476   MatScalar    m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12, m13, m14, m15;
477   MatScalar    m16, m17, m18, m19, m20, m21, m22, m23, m24, m25;
478   MatScalar    p26, p27, p28, p29, p30, p31, p32, p33, p34, p35, p36;
479   MatScalar    x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36;
480   MatScalar    m26, m27, m28, m29, m30, m31, m32, m33, m34, m35, m36;
481   MatScalar   *ba = b->a, *aa = a->a;
482   PetscReal    shift = info->shiftamount;
483   PetscBool    allowzeropivot, zeropivotdetected;
484 
485   PetscFunctionBegin;
486   allowzeropivot = PetscNot(A->erroriffailure);
487   PetscCall(PetscMalloc1(36 * (n + 1), &rtmp));
488   for (i = 0; i < n; i++) {
489     nz    = bi[i + 1] - bi[i];
490     ajtmp = bj + bi[i];
491     for (j = 0; j < nz; j++) {
492       x    = rtmp + 36 * ajtmp[j];
493       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
494       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
495       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0;
496       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0;
497       x[34] = x[35] = 0.0;
498     }
499     /* load in initial (unfactored row) */
500     nz       = ai[i + 1] - ai[i];
501     ajtmpold = aj + ai[i];
502     v        = aa + 36 * ai[i];
503     for (j = 0; j < nz; j++) {
504       x     = rtmp + 36 * ajtmpold[j];
505       x[0]  = v[0];
506       x[1]  = v[1];
507       x[2]  = v[2];
508       x[3]  = v[3];
509       x[4]  = v[4];
510       x[5]  = v[5];
511       x[6]  = v[6];
512       x[7]  = v[7];
513       x[8]  = v[8];
514       x[9]  = v[9];
515       x[10] = v[10];
516       x[11] = v[11];
517       x[12] = v[12];
518       x[13] = v[13];
519       x[14] = v[14];
520       x[15] = v[15];
521       x[16] = v[16];
522       x[17] = v[17];
523       x[18] = v[18];
524       x[19] = v[19];
525       x[20] = v[20];
526       x[21] = v[21];
527       x[22] = v[22];
528       x[23] = v[23];
529       x[24] = v[24];
530       x[25] = v[25];
531       x[26] = v[26];
532       x[27] = v[27];
533       x[28] = v[28];
534       x[29] = v[29];
535       x[30] = v[30];
536       x[31] = v[31];
537       x[32] = v[32];
538       x[33] = v[33];
539       x[34] = v[34];
540       x[35] = v[35];
541       v += 36;
542     }
543     row = *ajtmp++;
544     while (row < i) {
545       pc  = rtmp + 36 * row;
546       p1  = pc[0];
547       p2  = pc[1];
548       p3  = pc[2];
549       p4  = pc[3];
550       p5  = pc[4];
551       p6  = pc[5];
552       p7  = pc[6];
553       p8  = pc[7];
554       p9  = pc[8];
555       p10 = pc[9];
556       p11 = pc[10];
557       p12 = pc[11];
558       p13 = pc[12];
559       p14 = pc[13];
560       p15 = pc[14];
561       p16 = pc[15];
562       p17 = pc[16];
563       p18 = pc[17];
564       p19 = pc[18];
565       p20 = pc[19];
566       p21 = pc[20];
567       p22 = pc[21];
568       p23 = pc[22];
569       p24 = pc[23];
570       p25 = pc[24];
571       p26 = pc[25];
572       p27 = pc[26];
573       p28 = pc[27];
574       p29 = pc[28];
575       p30 = pc[29];
576       p31 = pc[30];
577       p32 = pc[31];
578       p33 = pc[32];
579       p34 = pc[33];
580       p35 = pc[34];
581       p36 = pc[35];
582       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 || p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 || p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) {
583         pv    = ba + 36 * diag_offset[row];
584         pj    = bj + diag_offset[row] + 1;
585         x1    = pv[0];
586         x2    = pv[1];
587         x3    = pv[2];
588         x4    = pv[3];
589         x5    = pv[4];
590         x6    = pv[5];
591         x7    = pv[6];
592         x8    = pv[7];
593         x9    = pv[8];
594         x10   = pv[9];
595         x11   = pv[10];
596         x12   = pv[11];
597         x13   = pv[12];
598         x14   = pv[13];
599         x15   = pv[14];
600         x16   = pv[15];
601         x17   = pv[16];
602         x18   = pv[17];
603         x19   = pv[18];
604         x20   = pv[19];
605         x21   = pv[20];
606         x22   = pv[21];
607         x23   = pv[22];
608         x24   = pv[23];
609         x25   = pv[24];
610         x26   = pv[25];
611         x27   = pv[26];
612         x28   = pv[27];
613         x29   = pv[28];
614         x30   = pv[29];
615         x31   = pv[30];
616         x32   = pv[31];
617         x33   = pv[32];
618         x34   = pv[33];
619         x35   = pv[34];
620         x36   = pv[35];
621         pc[0] = m1 = p1 * x1 + p7 * x2 + p13 * x3 + p19 * x4 + p25 * x5 + p31 * x6;
622         pc[1] = m2 = p2 * x1 + p8 * x2 + p14 * x3 + p20 * x4 + p26 * x5 + p32 * x6;
623         pc[2] = m3 = p3 * x1 + p9 * x2 + p15 * x3 + p21 * x4 + p27 * x5 + p33 * x6;
624         pc[3] = m4 = p4 * x1 + p10 * x2 + p16 * x3 + p22 * x4 + p28 * x5 + p34 * x6;
625         pc[4] = m5 = p5 * x1 + p11 * x2 + p17 * x3 + p23 * x4 + p29 * x5 + p35 * x6;
626         pc[5] = m6 = p6 * x1 + p12 * x2 + p18 * x3 + p24 * x4 + p30 * x5 + p36 * x6;
627 
628         pc[6] = m7 = p1 * x7 + p7 * x8 + p13 * x9 + p19 * x10 + p25 * x11 + p31 * x12;
629         pc[7] = m8 = p2 * x7 + p8 * x8 + p14 * x9 + p20 * x10 + p26 * x11 + p32 * x12;
630         pc[8] = m9 = p3 * x7 + p9 * x8 + p15 * x9 + p21 * x10 + p27 * x11 + p33 * x12;
631         pc[9] = m10 = p4 * x7 + p10 * x8 + p16 * x9 + p22 * x10 + p28 * x11 + p34 * x12;
632         pc[10] = m11 = p5 * x7 + p11 * x8 + p17 * x9 + p23 * x10 + p29 * x11 + p35 * x12;
633         pc[11] = m12 = p6 * x7 + p12 * x8 + p18 * x9 + p24 * x10 + p30 * x11 + p36 * x12;
634 
635         pc[12] = m13 = p1 * x13 + p7 * x14 + p13 * x15 + p19 * x16 + p25 * x17 + p31 * x18;
636         pc[13] = m14 = p2 * x13 + p8 * x14 + p14 * x15 + p20 * x16 + p26 * x17 + p32 * x18;
637         pc[14] = m15 = p3 * x13 + p9 * x14 + p15 * x15 + p21 * x16 + p27 * x17 + p33 * x18;
638         pc[15] = m16 = p4 * x13 + p10 * x14 + p16 * x15 + p22 * x16 + p28 * x17 + p34 * x18;
639         pc[16] = m17 = p5 * x13 + p11 * x14 + p17 * x15 + p23 * x16 + p29 * x17 + p35 * x18;
640         pc[17] = m18 = p6 * x13 + p12 * x14 + p18 * x15 + p24 * x16 + p30 * x17 + p36 * x18;
641 
642         pc[18] = m19 = p1 * x19 + p7 * x20 + p13 * x21 + p19 * x22 + p25 * x23 + p31 * x24;
643         pc[19] = m20 = p2 * x19 + p8 * x20 + p14 * x21 + p20 * x22 + p26 * x23 + p32 * x24;
644         pc[20] = m21 = p3 * x19 + p9 * x20 + p15 * x21 + p21 * x22 + p27 * x23 + p33 * x24;
645         pc[21] = m22 = p4 * x19 + p10 * x20 + p16 * x21 + p22 * x22 + p28 * x23 + p34 * x24;
646         pc[22] = m23 = p5 * x19 + p11 * x20 + p17 * x21 + p23 * x22 + p29 * x23 + p35 * x24;
647         pc[23] = m24 = p6 * x19 + p12 * x20 + p18 * x21 + p24 * x22 + p30 * x23 + p36 * x24;
648 
649         pc[24] = m25 = p1 * x25 + p7 * x26 + p13 * x27 + p19 * x28 + p25 * x29 + p31 * x30;
650         pc[25] = m26 = p2 * x25 + p8 * x26 + p14 * x27 + p20 * x28 + p26 * x29 + p32 * x30;
651         pc[26] = m27 = p3 * x25 + p9 * x26 + p15 * x27 + p21 * x28 + p27 * x29 + p33 * x30;
652         pc[27] = m28 = p4 * x25 + p10 * x26 + p16 * x27 + p22 * x28 + p28 * x29 + p34 * x30;
653         pc[28] = m29 = p5 * x25 + p11 * x26 + p17 * x27 + p23 * x28 + p29 * x29 + p35 * x30;
654         pc[29] = m30 = p6 * x25 + p12 * x26 + p18 * x27 + p24 * x28 + p30 * x29 + p36 * x30;
655 
656         pc[30] = m31 = p1 * x31 + p7 * x32 + p13 * x33 + p19 * x34 + p25 * x35 + p31 * x36;
657         pc[31] = m32 = p2 * x31 + p8 * x32 + p14 * x33 + p20 * x34 + p26 * x35 + p32 * x36;
658         pc[32] = m33 = p3 * x31 + p9 * x32 + p15 * x33 + p21 * x34 + p27 * x35 + p33 * x36;
659         pc[33] = m34 = p4 * x31 + p10 * x32 + p16 * x33 + p22 * x34 + p28 * x35 + p34 * x36;
660         pc[34] = m35 = p5 * x31 + p11 * x32 + p17 * x33 + p23 * x34 + p29 * x35 + p35 * x36;
661         pc[35] = m36 = p6 * x31 + p12 * x32 + p18 * x33 + p24 * x34 + p30 * x35 + p36 * x36;
662 
663         nz = bi[row + 1] - diag_offset[row] - 1;
664         pv += 36;
665         for (j = 0; j < nz; j++) {
666           x1  = pv[0];
667           x2  = pv[1];
668           x3  = pv[2];
669           x4  = pv[3];
670           x5  = pv[4];
671           x6  = pv[5];
672           x7  = pv[6];
673           x8  = pv[7];
674           x9  = pv[8];
675           x10 = pv[9];
676           x11 = pv[10];
677           x12 = pv[11];
678           x13 = pv[12];
679           x14 = pv[13];
680           x15 = pv[14];
681           x16 = pv[15];
682           x17 = pv[16];
683           x18 = pv[17];
684           x19 = pv[18];
685           x20 = pv[19];
686           x21 = pv[20];
687           x22 = pv[21];
688           x23 = pv[22];
689           x24 = pv[23];
690           x25 = pv[24];
691           x26 = pv[25];
692           x27 = pv[26];
693           x28 = pv[27];
694           x29 = pv[28];
695           x30 = pv[29];
696           x31 = pv[30];
697           x32 = pv[31];
698           x33 = pv[32];
699           x34 = pv[33];
700           x35 = pv[34];
701           x36 = pv[35];
702           x   = rtmp + 36 * pj[j];
703           x[0] -= m1 * x1 + m7 * x2 + m13 * x3 + m19 * x4 + m25 * x5 + m31 * x6;
704           x[1] -= m2 * x1 + m8 * x2 + m14 * x3 + m20 * x4 + m26 * x5 + m32 * x6;
705           x[2] -= m3 * x1 + m9 * x2 + m15 * x3 + m21 * x4 + m27 * x5 + m33 * x6;
706           x[3] -= m4 * x1 + m10 * x2 + m16 * x3 + m22 * x4 + m28 * x5 + m34 * x6;
707           x[4] -= m5 * x1 + m11 * x2 + m17 * x3 + m23 * x4 + m29 * x5 + m35 * x6;
708           x[5] -= m6 * x1 + m12 * x2 + m18 * x3 + m24 * x4 + m30 * x5 + m36 * x6;
709 
710           x[6] -= m1 * x7 + m7 * x8 + m13 * x9 + m19 * x10 + m25 * x11 + m31 * x12;
711           x[7] -= m2 * x7 + m8 * x8 + m14 * x9 + m20 * x10 + m26 * x11 + m32 * x12;
712           x[8] -= m3 * x7 + m9 * x8 + m15 * x9 + m21 * x10 + m27 * x11 + m33 * x12;
713           x[9] -= m4 * x7 + m10 * x8 + m16 * x9 + m22 * x10 + m28 * x11 + m34 * x12;
714           x[10] -= m5 * x7 + m11 * x8 + m17 * x9 + m23 * x10 + m29 * x11 + m35 * x12;
715           x[11] -= m6 * x7 + m12 * x8 + m18 * x9 + m24 * x10 + m30 * x11 + m36 * x12;
716 
717           x[12] -= m1 * x13 + m7 * x14 + m13 * x15 + m19 * x16 + m25 * x17 + m31 * x18;
718           x[13] -= m2 * x13 + m8 * x14 + m14 * x15 + m20 * x16 + m26 * x17 + m32 * x18;
719           x[14] -= m3 * x13 + m9 * x14 + m15 * x15 + m21 * x16 + m27 * x17 + m33 * x18;
720           x[15] -= m4 * x13 + m10 * x14 + m16 * x15 + m22 * x16 + m28 * x17 + m34 * x18;
721           x[16] -= m5 * x13 + m11 * x14 + m17 * x15 + m23 * x16 + m29 * x17 + m35 * x18;
722           x[17] -= m6 * x13 + m12 * x14 + m18 * x15 + m24 * x16 + m30 * x17 + m36 * x18;
723 
724           x[18] -= m1 * x19 + m7 * x20 + m13 * x21 + m19 * x22 + m25 * x23 + m31 * x24;
725           x[19] -= m2 * x19 + m8 * x20 + m14 * x21 + m20 * x22 + m26 * x23 + m32 * x24;
726           x[20] -= m3 * x19 + m9 * x20 + m15 * x21 + m21 * x22 + m27 * x23 + m33 * x24;
727           x[21] -= m4 * x19 + m10 * x20 + m16 * x21 + m22 * x22 + m28 * x23 + m34 * x24;
728           x[22] -= m5 * x19 + m11 * x20 + m17 * x21 + m23 * x22 + m29 * x23 + m35 * x24;
729           x[23] -= m6 * x19 + m12 * x20 + m18 * x21 + m24 * x22 + m30 * x23 + m36 * x24;
730 
731           x[24] -= m1 * x25 + m7 * x26 + m13 * x27 + m19 * x28 + m25 * x29 + m31 * x30;
732           x[25] -= m2 * x25 + m8 * x26 + m14 * x27 + m20 * x28 + m26 * x29 + m32 * x30;
733           x[26] -= m3 * x25 + m9 * x26 + m15 * x27 + m21 * x28 + m27 * x29 + m33 * x30;
734           x[27] -= m4 * x25 + m10 * x26 + m16 * x27 + m22 * x28 + m28 * x29 + m34 * x30;
735           x[28] -= m5 * x25 + m11 * x26 + m17 * x27 + m23 * x28 + m29 * x29 + m35 * x30;
736           x[29] -= m6 * x25 + m12 * x26 + m18 * x27 + m24 * x28 + m30 * x29 + m36 * x30;
737 
738           x[30] -= m1 * x31 + m7 * x32 + m13 * x33 + m19 * x34 + m25 * x35 + m31 * x36;
739           x[31] -= m2 * x31 + m8 * x32 + m14 * x33 + m20 * x34 + m26 * x35 + m32 * x36;
740           x[32] -= m3 * x31 + m9 * x32 + m15 * x33 + m21 * x34 + m27 * x35 + m33 * x36;
741           x[33] -= m4 * x31 + m10 * x32 + m16 * x33 + m22 * x34 + m28 * x35 + m34 * x36;
742           x[34] -= m5 * x31 + m11 * x32 + m17 * x33 + m23 * x34 + m29 * x35 + m35 * x36;
743           x[35] -= m6 * x31 + m12 * x32 + m18 * x33 + m24 * x34 + m30 * x35 + m36 * x36;
744 
745           pv += 36;
746         }
747         PetscCall(PetscLogFlops(432.0 * nz + 396.0));
748       }
749       row = *ajtmp++;
750     }
751     /* finished row so stick it into b->a */
752     pv = ba + 36 * bi[i];
753     pj = bj + bi[i];
754     nz = bi[i + 1] - bi[i];
755     for (j = 0; j < nz; j++) {
756       x      = rtmp + 36 * pj[j];
757       pv[0]  = x[0];
758       pv[1]  = x[1];
759       pv[2]  = x[2];
760       pv[3]  = x[3];
761       pv[4]  = x[4];
762       pv[5]  = x[5];
763       pv[6]  = x[6];
764       pv[7]  = x[7];
765       pv[8]  = x[8];
766       pv[9]  = x[9];
767       pv[10] = x[10];
768       pv[11] = x[11];
769       pv[12] = x[12];
770       pv[13] = x[13];
771       pv[14] = x[14];
772       pv[15] = x[15];
773       pv[16] = x[16];
774       pv[17] = x[17];
775       pv[18] = x[18];
776       pv[19] = x[19];
777       pv[20] = x[20];
778       pv[21] = x[21];
779       pv[22] = x[22];
780       pv[23] = x[23];
781       pv[24] = x[24];
782       pv[25] = x[25];
783       pv[26] = x[26];
784       pv[27] = x[27];
785       pv[28] = x[28];
786       pv[29] = x[29];
787       pv[30] = x[30];
788       pv[31] = x[31];
789       pv[32] = x[32];
790       pv[33] = x[33];
791       pv[34] = x[34];
792       pv[35] = x[35];
793       pv += 36;
794     }
795     /* invert diagonal block */
796     w = ba + 36 * diag_offset[i];
797     PetscCall(PetscKernel_A_gets_inverse_A_6(w, shift, allowzeropivot, &zeropivotdetected));
798     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
799   }
800 
801   PetscCall(PetscFree(rtmp));
802 
803   C->ops->solve          = MatSolve_SeqBAIJ_6_NaturalOrdering_inplace;
804   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_6_NaturalOrdering_inplace;
805   C->assembled           = PETSC_TRUE;
806 
807   PetscCall(PetscLogFlops(1.333333333333 * 6 * 6 * 6 * b->mbs)); /* from inverting diagonal blocks */
808   PetscFunctionReturn(0);
809 }
810 
811 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_6_NaturalOrdering(Mat B, Mat A, const MatFactorInfo *info) {
812   Mat             C = B;
813   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
814   PetscInt        i, j, k, nz, nzL, row;
815   const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
816   const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
817   MatScalar      *rtmp, *pc, *mwork, *v, *pv, *aa = a->a;
818   PetscInt        flg;
819   PetscReal       shift = info->shiftamount;
820   PetscBool       allowzeropivot, zeropivotdetected;
821 
822   PetscFunctionBegin;
823   allowzeropivot = PetscNot(A->erroriffailure);
824 
825   /* generate work space needed by the factorization */
826   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
827   PetscCall(PetscArrayzero(rtmp, bs2 * n));
828 
829   for (i = 0; i < n; i++) {
830     /* zero rtmp */
831     /* L part */
832     nz    = bi[i + 1] - bi[i];
833     bjtmp = bj + bi[i];
834     for (j = 0; j < nz; j++) { PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2)); }
835 
836     /* U part */
837     nz    = bdiag[i] - bdiag[i + 1];
838     bjtmp = bj + bdiag[i + 1] + 1;
839     for (j = 0; j < nz; j++) { PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2)); }
840 
841     /* load in initial (unfactored row) */
842     nz    = ai[i + 1] - ai[i];
843     ajtmp = aj + ai[i];
844     v     = aa + bs2 * ai[i];
845     for (j = 0; j < nz; j++) { PetscCall(PetscArraycpy(rtmp + bs2 * ajtmp[j], v + bs2 * j, bs2)); }
846 
847     /* elimination */
848     bjtmp = bj + bi[i];
849     nzL   = bi[i + 1] - bi[i];
850     for (k = 0; k < nzL; k++) {
851       row = bjtmp[k];
852       pc  = rtmp + bs2 * row;
853       for (flg = 0, j = 0; j < bs2; j++) {
854         if (pc[j] != 0.0) {
855           flg = 1;
856           break;
857         }
858       }
859       if (flg) {
860         pv = b->a + bs2 * bdiag[row];
861         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
862         PetscCall(PetscKernel_A_gets_A_times_B_6(pc, pv, mwork));
863 
864         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
865         pv = b->a + bs2 * (bdiag[row + 1] + 1);
866         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
867         for (j = 0; j < nz; j++) {
868           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
869           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
870           v = rtmp + bs2 * pj[j];
871           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_6(v, pc, pv));
872           pv += bs2;
873         }
874         PetscCall(PetscLogFlops(432.0 * nz + 396)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
875       }
876     }
877 
878     /* finished row so stick it into b->a */
879     /* L part */
880     pv = b->a + bs2 * bi[i];
881     pj = b->j + bi[i];
882     nz = bi[i + 1] - bi[i];
883     for (j = 0; j < nz; j++) { PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2)); }
884 
885     /* Mark diagonal and invert diagonal for simpler triangular solves */
886     pv = b->a + bs2 * bdiag[i];
887     pj = b->j + bdiag[i];
888     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
889     PetscCall(PetscKernel_A_gets_inverse_A_6(pv, shift, allowzeropivot, &zeropivotdetected));
890     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
891 
892     /* U part */
893     pv = b->a + bs2 * (bdiag[i + 1] + 1);
894     pj = b->j + bdiag[i + 1] + 1;
895     nz = bdiag[i] - bdiag[i + 1] - 1;
896     for (j = 0; j < nz; j++) { PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2)); }
897   }
898   PetscCall(PetscFree2(rtmp, mwork));
899 
900   C->ops->solve          = MatSolve_SeqBAIJ_6_NaturalOrdering;
901   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_6_NaturalOrdering;
902   C->assembled           = PETSC_TRUE;
903 
904   PetscCall(PetscLogFlops(1.333333333333 * 6 * 6 * 6 * n)); /* from inverting diagonal blocks */
905   PetscFunctionReturn(0);
906 }
907