xref: /petsc/src/mat/impls/baij/seq/baijfact9.c (revision 3df6fe7bb68c28049dcc48161db5df4684fa05c1)
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 5 by 5
10 */
11 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_inplace(Mat C, Mat A, const MatFactorInfo *info)
12 {
13   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
14   IS               isrow = b->row, isicol = b->icol;
15   const PetscInt  *r, *ic, *bi = b->i, *bj = b->j, *ajtmpold, *ajtmp;
16   PetscInt         i, j, n = a->mbs, nz, row, idx, ipvt[5];
17   const PetscInt  *diag_offset = b->diag, *ai = a->i, *aj = a->j, *pj;
18   MatScalar       *w, *pv, *rtmp, *x, *pc;
19   const MatScalar *v, *aa = a->a;
20   MatScalar        p1, p2, p3, p4, m1, m2, m3, m4, m5, m6, m7, m8, m9, x1, x2, x3, x4;
21   MatScalar        p5, p6, p7, p8, p9, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16;
22   MatScalar        x17, x18, x19, x20, x21, x22, x23, x24, x25, p10, p11, p12, p13, p14;
23   MatScalar        p15, p16, p17, p18, p19, p20, p21, p22, p23, p24, p25, m10, m11, m12;
24   MatScalar        m13, m14, m15, m16, m17, m18, m19, m20, m21, m22, m23, m24, m25;
25   MatScalar       *ba    = b->a, work[25];
26   PetscReal        shift = info->shiftamount;
27   PetscBool        allowzeropivot, zeropivotdetected;
28 
29   PetscFunctionBegin;
30   allowzeropivot = PetscNot(A->erroriffailure);
31   PetscCall(ISGetIndices(isrow, &r));
32   PetscCall(ISGetIndices(isicol, &ic));
33   PetscCall(PetscMalloc1(25 * (n + 1), &rtmp));
34 
35 #define PETSC_USE_MEMZERO 1
36 #define PETSC_USE_MEMCPY  1
37 
38   for (i = 0; i < n; i++) {
39     nz    = bi[i + 1] - bi[i];
40     ajtmp = bj + bi[i];
41     for (j = 0; j < nz; j++) {
42 #if defined(PETSC_USE_MEMZERO)
43       PetscCall(PetscArrayzero(rtmp + 25 * ajtmp[j], 25));
44 #else
45       x    = rtmp + 25 * ajtmp[j];
46       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
47       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
48       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
49 #endif
50     }
51     /* load in initial (unfactored row) */
52     idx      = r[i];
53     nz       = ai[idx + 1] - ai[idx];
54     ajtmpold = aj + ai[idx];
55     v        = aa + 25 * ai[idx];
56     for (j = 0; j < nz; j++) {
57 #if defined(PETSC_USE_MEMCPY)
58       PetscCall(PetscArraycpy(rtmp + 25 * ic[ajtmpold[j]], v, 25));
59 #else
60       x                                                     = rtmp + 25 * ic[ajtmpold[j]];
61       x[0]                                                  = v[0];
62       x[1]                                                  = v[1];
63       x[2]                                                  = v[2];
64       x[3]                                                  = v[3];
65       x[4]                                                  = v[4];
66       x[5]                                                  = v[5];
67       x[6]                                                  = v[6];
68       x[7]                                                  = v[7];
69       x[8]                                                  = v[8];
70       x[9]                                                  = v[9];
71       x[10]                                                 = v[10];
72       x[11]                                                 = v[11];
73       x[12]                                                 = v[12];
74       x[13]                                                 = v[13];
75       x[14]                                                 = v[14];
76       x[15]                                                 = v[15];
77       x[16]                                                 = v[16];
78       x[17]                                                 = v[17];
79       x[18]                                                 = v[18];
80       x[19]                                                 = v[19];
81       x[20]                                                 = v[20];
82       x[21]                                                 = v[21];
83       x[22]                                                 = v[22];
84       x[23]                                                 = v[23];
85       x[24]                                                 = v[24];
86 #endif
87       v += 25;
88     }
89     row = *ajtmp++;
90     while (row < i) {
91       pc  = rtmp + 25 * row;
92       p1  = pc[0];
93       p2  = pc[1];
94       p3  = pc[2];
95       p4  = pc[3];
96       p5  = pc[4];
97       p6  = pc[5];
98       p7  = pc[6];
99       p8  = pc[7];
100       p9  = pc[8];
101       p10 = pc[9];
102       p11 = pc[10];
103       p12 = pc[11];
104       p13 = pc[12];
105       p14 = pc[13];
106       p15 = pc[14];
107       p16 = pc[15];
108       p17 = pc[16];
109       p18 = pc[17];
110       p19 = pc[18];
111       p20 = pc[19];
112       p21 = pc[20];
113       p22 = pc[21];
114       p23 = pc[22];
115       p24 = pc[23];
116       p25 = pc[24];
117       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) {
118         pv    = ba + 25 * diag_offset[row];
119         pj    = bj + diag_offset[row] + 1;
120         x1    = pv[0];
121         x2    = pv[1];
122         x3    = pv[2];
123         x4    = pv[3];
124         x5    = pv[4];
125         x6    = pv[5];
126         x7    = pv[6];
127         x8    = pv[7];
128         x9    = pv[8];
129         x10   = pv[9];
130         x11   = pv[10];
131         x12   = pv[11];
132         x13   = pv[12];
133         x14   = pv[13];
134         x15   = pv[14];
135         x16   = pv[15];
136         x17   = pv[16];
137         x18   = pv[17];
138         x19   = pv[18];
139         x20   = pv[19];
140         x21   = pv[20];
141         x22   = pv[21];
142         x23   = pv[22];
143         x24   = pv[23];
144         x25   = pv[24];
145         pc[0] = m1 = p1 * x1 + p6 * x2 + p11 * x3 + p16 * x4 + p21 * x5;
146         pc[1] = m2 = p2 * x1 + p7 * x2 + p12 * x3 + p17 * x4 + p22 * x5;
147         pc[2] = m3 = p3 * x1 + p8 * x2 + p13 * x3 + p18 * x4 + p23 * x5;
148         pc[3] = m4 = p4 * x1 + p9 * x2 + p14 * x3 + p19 * x4 + p24 * x5;
149         pc[4] = m5 = p5 * x1 + p10 * x2 + p15 * x3 + p20 * x4 + p25 * x5;
150 
151         pc[5] = m6 = p1 * x6 + p6 * x7 + p11 * x8 + p16 * x9 + p21 * x10;
152         pc[6] = m7 = p2 * x6 + p7 * x7 + p12 * x8 + p17 * x9 + p22 * x10;
153         pc[7] = m8 = p3 * x6 + p8 * x7 + p13 * x8 + p18 * x9 + p23 * x10;
154         pc[8] = m9 = p4 * x6 + p9 * x7 + p14 * x8 + p19 * x9 + p24 * x10;
155         pc[9] = m10 = p5 * x6 + p10 * x7 + p15 * x8 + p20 * x9 + p25 * x10;
156 
157         pc[10] = m11 = p1 * x11 + p6 * x12 + p11 * x13 + p16 * x14 + p21 * x15;
158         pc[11] = m12 = p2 * x11 + p7 * x12 + p12 * x13 + p17 * x14 + p22 * x15;
159         pc[12] = m13 = p3 * x11 + p8 * x12 + p13 * x13 + p18 * x14 + p23 * x15;
160         pc[13] = m14 = p4 * x11 + p9 * x12 + p14 * x13 + p19 * x14 + p24 * x15;
161         pc[14] = m15 = p5 * x11 + p10 * x12 + p15 * x13 + p20 * x14 + p25 * x15;
162 
163         pc[15] = m16 = p1 * x16 + p6 * x17 + p11 * x18 + p16 * x19 + p21 * x20;
164         pc[16] = m17 = p2 * x16 + p7 * x17 + p12 * x18 + p17 * x19 + p22 * x20;
165         pc[17] = m18 = p3 * x16 + p8 * x17 + p13 * x18 + p18 * x19 + p23 * x20;
166         pc[18] = m19 = p4 * x16 + p9 * x17 + p14 * x18 + p19 * x19 + p24 * x20;
167         pc[19] = m20 = p5 * x16 + p10 * x17 + p15 * x18 + p20 * x19 + p25 * x20;
168 
169         pc[20] = m21 = p1 * x21 + p6 * x22 + p11 * x23 + p16 * x24 + p21 * x25;
170         pc[21] = m22 = p2 * x21 + p7 * x22 + p12 * x23 + p17 * x24 + p22 * x25;
171         pc[22] = m23 = p3 * x21 + p8 * x22 + p13 * x23 + p18 * x24 + p23 * x25;
172         pc[23] = m24 = p4 * x21 + p9 * x22 + p14 * x23 + p19 * x24 + p24 * x25;
173         pc[24] = m25 = p5 * x21 + p10 * x22 + p15 * x23 + p20 * x24 + p25 * x25;
174 
175         nz = bi[row + 1] - diag_offset[row] - 1;
176         pv += 25;
177         for (j = 0; j < nz; j++) {
178           x1  = pv[0];
179           x2  = pv[1];
180           x3  = pv[2];
181           x4  = pv[3];
182           x5  = pv[4];
183           x6  = pv[5];
184           x7  = pv[6];
185           x8  = pv[7];
186           x9  = pv[8];
187           x10 = pv[9];
188           x11 = pv[10];
189           x12 = pv[11];
190           x13 = pv[12];
191           x14 = pv[13];
192           x15 = pv[14];
193           x16 = pv[15];
194           x17 = pv[16];
195           x18 = pv[17];
196           x19 = pv[18];
197           x20 = pv[19];
198           x21 = pv[20];
199           x22 = pv[21];
200           x23 = pv[22];
201           x24 = pv[23];
202           x25 = pv[24];
203           x   = rtmp + 25 * pj[j];
204           x[0] -= m1 * x1 + m6 * x2 + m11 * x3 + m16 * x4 + m21 * x5;
205           x[1] -= m2 * x1 + m7 * x2 + m12 * x3 + m17 * x4 + m22 * x5;
206           x[2] -= m3 * x1 + m8 * x2 + m13 * x3 + m18 * x4 + m23 * x5;
207           x[3] -= m4 * x1 + m9 * x2 + m14 * x3 + m19 * x4 + m24 * x5;
208           x[4] -= m5 * x1 + m10 * x2 + m15 * x3 + m20 * x4 + m25 * x5;
209 
210           x[5] -= m1 * x6 + m6 * x7 + m11 * x8 + m16 * x9 + m21 * x10;
211           x[6] -= m2 * x6 + m7 * x7 + m12 * x8 + m17 * x9 + m22 * x10;
212           x[7] -= m3 * x6 + m8 * x7 + m13 * x8 + m18 * x9 + m23 * x10;
213           x[8] -= m4 * x6 + m9 * x7 + m14 * x8 + m19 * x9 + m24 * x10;
214           x[9] -= m5 * x6 + m10 * x7 + m15 * x8 + m20 * x9 + m25 * x10;
215 
216           x[10] -= m1 * x11 + m6 * x12 + m11 * x13 + m16 * x14 + m21 * x15;
217           x[11] -= m2 * x11 + m7 * x12 + m12 * x13 + m17 * x14 + m22 * x15;
218           x[12] -= m3 * x11 + m8 * x12 + m13 * x13 + m18 * x14 + m23 * x15;
219           x[13] -= m4 * x11 + m9 * x12 + m14 * x13 + m19 * x14 + m24 * x15;
220           x[14] -= m5 * x11 + m10 * x12 + m15 * x13 + m20 * x14 + m25 * x15;
221 
222           x[15] -= m1 * x16 + m6 * x17 + m11 * x18 + m16 * x19 + m21 * x20;
223           x[16] -= m2 * x16 + m7 * x17 + m12 * x18 + m17 * x19 + m22 * x20;
224           x[17] -= m3 * x16 + m8 * x17 + m13 * x18 + m18 * x19 + m23 * x20;
225           x[18] -= m4 * x16 + m9 * x17 + m14 * x18 + m19 * x19 + m24 * x20;
226           x[19] -= m5 * x16 + m10 * x17 + m15 * x18 + m20 * x19 + m25 * x20;
227 
228           x[20] -= m1 * x21 + m6 * x22 + m11 * x23 + m16 * x24 + m21 * x25;
229           x[21] -= m2 * x21 + m7 * x22 + m12 * x23 + m17 * x24 + m22 * x25;
230           x[22] -= m3 * x21 + m8 * x22 + m13 * x23 + m18 * x24 + m23 * x25;
231           x[23] -= m4 * x21 + m9 * x22 + m14 * x23 + m19 * x24 + m24 * x25;
232           x[24] -= m5 * x21 + m10 * x22 + m15 * x23 + m20 * x24 + m25 * x25;
233 
234           pv += 25;
235         }
236         PetscCall(PetscLogFlops(250.0 * nz + 225.0));
237       }
238       row = *ajtmp++;
239     }
240     /* finished row so stick it into b->a */
241     pv = ba + 25 * bi[i];
242     pj = bj + bi[i];
243     nz = bi[i + 1] - bi[i];
244     for (j = 0; j < nz; j++) {
245 #if defined(PETSC_USE_MEMCPY)
246       PetscCall(PetscArraycpy(pv, rtmp + 25 * pj[j], 25));
247 #else
248       x                                                     = rtmp + 25 * pj[j];
249       pv[0]                                                 = x[0];
250       pv[1]                                                 = x[1];
251       pv[2]                                                 = x[2];
252       pv[3]                                                 = x[3];
253       pv[4]                                                 = x[4];
254       pv[5]                                                 = x[5];
255       pv[6]                                                 = x[6];
256       pv[7]                                                 = x[7];
257       pv[8]                                                 = x[8];
258       pv[9]                                                 = x[9];
259       pv[10]                                                = x[10];
260       pv[11]                                                = x[11];
261       pv[12]                                                = x[12];
262       pv[13]                                                = x[13];
263       pv[14]                                                = x[14];
264       pv[15]                                                = x[15];
265       pv[16]                                                = x[16];
266       pv[17]                                                = x[17];
267       pv[18]                                                = x[18];
268       pv[19]                                                = x[19];
269       pv[20]                                                = x[20];
270       pv[21]                                                = x[21];
271       pv[22]                                                = x[22];
272       pv[23]                                                = x[23];
273       pv[24]                                                = x[24];
274 #endif
275       pv += 25;
276     }
277     /* invert diagonal block */
278     w = ba + 25 * diag_offset[i];
279     PetscCall(PetscKernel_A_gets_inverse_A_5(w, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
280     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
281   }
282 
283   PetscCall(PetscFree(rtmp));
284   PetscCall(ISRestoreIndices(isicol, &ic));
285   PetscCall(ISRestoreIndices(isrow, &r));
286 
287   C->ops->solve          = MatSolve_SeqBAIJ_5_inplace;
288   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_inplace;
289   C->assembled           = PETSC_TRUE;
290 
291   PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * b->mbs)); /* from inverting diagonal blocks */
292   PetscFunctionReturn(PETSC_SUCCESS);
293 }
294 
295 /* MatLUFactorNumeric_SeqBAIJ_5 -
296      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
297        PetscKernel_A_gets_A_times_B()
298        PetscKernel_A_gets_A_minus_B_times_C()
299        PetscKernel_A_gets_inverse_A()
300 */
301 
302 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5(Mat B, Mat A, const MatFactorInfo *info)
303 {
304   Mat             C = B;
305   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
306   IS              isrow = b->row, isicol = b->icol;
307   const PetscInt *r, *ic;
308   PetscInt        i, j, k, nz, nzL, row;
309   const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
310   const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
311   MatScalar      *rtmp, *pc, *mwork, *v, *pv, *aa = a->a, work[25];
312   PetscInt        flg, ipvt[5];
313   PetscReal       shift = info->shiftamount;
314   PetscBool       allowzeropivot, zeropivotdetected;
315 
316   PetscFunctionBegin;
317   allowzeropivot = PetscNot(A->erroriffailure);
318   PetscCall(ISGetIndices(isrow, &r));
319   PetscCall(ISGetIndices(isicol, &ic));
320 
321   /* generate work space needed by the factorization */
322   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
323   PetscCall(PetscArrayzero(rtmp, bs2 * n));
324 
325   for (i = 0; i < n; i++) {
326     /* zero rtmp */
327     /* L part */
328     nz    = bi[i + 1] - bi[i];
329     bjtmp = bj + bi[i];
330     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));
331 
332     /* U part */
333     nz    = bdiag[i] - bdiag[i + 1];
334     bjtmp = bj + bdiag[i + 1] + 1;
335     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));
336 
337     /* load in initial (unfactored row) */
338     nz    = ai[r[i] + 1] - ai[r[i]];
339     ajtmp = aj + ai[r[i]];
340     v     = aa + bs2 * ai[r[i]];
341     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ic[ajtmp[j]], v + bs2 * j, bs2));
342 
343     /* elimination */
344     bjtmp = bj + bi[i];
345     nzL   = bi[i + 1] - bi[i];
346     for (k = 0; k < nzL; k++) {
347       row = bjtmp[k];
348       pc  = rtmp + bs2 * row;
349       for (flg = 0, j = 0; j < bs2; j++) {
350         if (pc[j] != 0.0) {
351           flg = 1;
352           break;
353         }
354       }
355       if (flg) {
356         pv = b->a + bs2 * bdiag[row];
357         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
358         PetscCall(PetscKernel_A_gets_A_times_B_5(pc, pv, mwork));
359 
360         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
361         pv = b->a + bs2 * (bdiag[row + 1] + 1);
362         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
363         for (j = 0; j < nz; j++) {
364           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
365           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
366           v = rtmp + bs2 * pj[j];
367           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_5(v, pc, pv));
368           pv += bs2;
369         }
370         PetscCall(PetscLogFlops(250.0 * nz + 225)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
371       }
372     }
373 
374     /* finished row so stick it into b->a */
375     /* L part */
376     pv = b->a + bs2 * bi[i];
377     pj = b->j + bi[i];
378     nz = bi[i + 1] - bi[i];
379     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
380 
381     /* Mark diagonal and invert diagonal for simpler triangular solves */
382     pv = b->a + bs2 * bdiag[i];
383     pj = b->j + bdiag[i];
384     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
385     PetscCall(PetscKernel_A_gets_inverse_A_5(pv, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
386     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
387 
388     /* U part */
389     pv = b->a + bs2 * (bdiag[i + 1] + 1);
390     pj = b->j + bdiag[i + 1] + 1;
391     nz = bdiag[i] - bdiag[i + 1] - 1;
392     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
393   }
394 
395   PetscCall(PetscFree2(rtmp, mwork));
396   PetscCall(ISRestoreIndices(isicol, &ic));
397   PetscCall(ISRestoreIndices(isrow, &r));
398 
399   C->ops->solve          = MatSolve_SeqBAIJ_5;
400   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5;
401   C->assembled           = PETSC_TRUE;
402 
403   PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * n)); /* from inverting diagonal blocks */
404   PetscFunctionReturn(PETSC_SUCCESS);
405 }
406 
407 /*
408       Version for when blocks are 5 by 5 Using natural ordering
409 */
410 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering_inplace(Mat C, Mat A, const MatFactorInfo *info)
411 {
412   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
413   PetscInt     i, j, n = a->mbs, *bi = b->i, *bj = b->j, ipvt[5];
414   PetscInt    *ajtmpold, *ajtmp, nz, row;
415   PetscInt    *diag_offset = b->diag, *ai = a->i, *aj = a->j, *pj;
416   MatScalar   *pv, *v, *rtmp, *pc, *w, *x;
417   MatScalar    x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15;
418   MatScalar    x16, x17, x18, x19, x20, x21, x22, x23, x24, x25;
419   MatScalar    p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12, p13, p14, p15;
420   MatScalar    p16, p17, p18, p19, p20, p21, p22, p23, p24, p25;
421   MatScalar    m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12, m13, m14, m15;
422   MatScalar    m16, m17, m18, m19, m20, m21, m22, m23, m24, m25;
423   MatScalar   *ba = b->a, *aa = a->a, work[25];
424   PetscReal    shift = info->shiftamount;
425   PetscBool    allowzeropivot, zeropivotdetected;
426 
427   PetscFunctionBegin;
428   allowzeropivot = PetscNot(A->erroriffailure);
429   PetscCall(PetscMalloc1(25 * (n + 1), &rtmp));
430   for (i = 0; i < n; i++) {
431     nz    = bi[i + 1] - bi[i];
432     ajtmp = bj + bi[i];
433     for (j = 0; j < nz; j++) {
434       x    = rtmp + 25 * ajtmp[j];
435       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
436       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
437       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
438     }
439     /* load in initial (unfactored row) */
440     nz       = ai[i + 1] - ai[i];
441     ajtmpold = aj + ai[i];
442     v        = aa + 25 * ai[i];
443     for (j = 0; j < nz; j++) {
444       x     = rtmp + 25 * ajtmpold[j];
445       x[0]  = v[0];
446       x[1]  = v[1];
447       x[2]  = v[2];
448       x[3]  = v[3];
449       x[4]  = v[4];
450       x[5]  = v[5];
451       x[6]  = v[6];
452       x[7]  = v[7];
453       x[8]  = v[8];
454       x[9]  = v[9];
455       x[10] = v[10];
456       x[11] = v[11];
457       x[12] = v[12];
458       x[13] = v[13];
459       x[14] = v[14];
460       x[15] = v[15];
461       x[16] = v[16];
462       x[17] = v[17];
463       x[18] = v[18];
464       x[19] = v[19];
465       x[20] = v[20];
466       x[21] = v[21];
467       x[22] = v[22];
468       x[23] = v[23];
469       x[24] = v[24];
470       v += 25;
471     }
472     row = *ajtmp++;
473     while (row < i) {
474       pc  = rtmp + 25 * row;
475       p1  = pc[0];
476       p2  = pc[1];
477       p3  = pc[2];
478       p4  = pc[3];
479       p5  = pc[4];
480       p6  = pc[5];
481       p7  = pc[6];
482       p8  = pc[7];
483       p9  = pc[8];
484       p10 = pc[9];
485       p11 = pc[10];
486       p12 = pc[11];
487       p13 = pc[12];
488       p14 = pc[13];
489       p15 = pc[14];
490       p16 = pc[15];
491       p17 = pc[16];
492       p18 = pc[17];
493       p19 = pc[18];
494       p20 = pc[19];
495       p21 = pc[20];
496       p22 = pc[21];
497       p23 = pc[22];
498       p24 = pc[23];
499       p25 = pc[24];
500       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) {
501         pv    = ba + 25 * diag_offset[row];
502         pj    = bj + diag_offset[row] + 1;
503         x1    = pv[0];
504         x2    = pv[1];
505         x3    = pv[2];
506         x4    = pv[3];
507         x5    = pv[4];
508         x6    = pv[5];
509         x7    = pv[6];
510         x8    = pv[7];
511         x9    = pv[8];
512         x10   = pv[9];
513         x11   = pv[10];
514         x12   = pv[11];
515         x13   = pv[12];
516         x14   = pv[13];
517         x15   = pv[14];
518         x16   = pv[15];
519         x17   = pv[16];
520         x18   = pv[17];
521         x19   = pv[18];
522         x20   = pv[19];
523         x21   = pv[20];
524         x22   = pv[21];
525         x23   = pv[22];
526         x24   = pv[23];
527         x25   = pv[24];
528         pc[0] = m1 = p1 * x1 + p6 * x2 + p11 * x3 + p16 * x4 + p21 * x5;
529         pc[1] = m2 = p2 * x1 + p7 * x2 + p12 * x3 + p17 * x4 + p22 * x5;
530         pc[2] = m3 = p3 * x1 + p8 * x2 + p13 * x3 + p18 * x4 + p23 * x5;
531         pc[3] = m4 = p4 * x1 + p9 * x2 + p14 * x3 + p19 * x4 + p24 * x5;
532         pc[4] = m5 = p5 * x1 + p10 * x2 + p15 * x3 + p20 * x4 + p25 * x5;
533 
534         pc[5] = m6 = p1 * x6 + p6 * x7 + p11 * x8 + p16 * x9 + p21 * x10;
535         pc[6] = m7 = p2 * x6 + p7 * x7 + p12 * x8 + p17 * x9 + p22 * x10;
536         pc[7] = m8 = p3 * x6 + p8 * x7 + p13 * x8 + p18 * x9 + p23 * x10;
537         pc[8] = m9 = p4 * x6 + p9 * x7 + p14 * x8 + p19 * x9 + p24 * x10;
538         pc[9] = m10 = p5 * x6 + p10 * x7 + p15 * x8 + p20 * x9 + p25 * x10;
539 
540         pc[10] = m11 = p1 * x11 + p6 * x12 + p11 * x13 + p16 * x14 + p21 * x15;
541         pc[11] = m12 = p2 * x11 + p7 * x12 + p12 * x13 + p17 * x14 + p22 * x15;
542         pc[12] = m13 = p3 * x11 + p8 * x12 + p13 * x13 + p18 * x14 + p23 * x15;
543         pc[13] = m14 = p4 * x11 + p9 * x12 + p14 * x13 + p19 * x14 + p24 * x15;
544         pc[14] = m15 = p5 * x11 + p10 * x12 + p15 * x13 + p20 * x14 + p25 * x15;
545 
546         pc[15] = m16 = p1 * x16 + p6 * x17 + p11 * x18 + p16 * x19 + p21 * x20;
547         pc[16] = m17 = p2 * x16 + p7 * x17 + p12 * x18 + p17 * x19 + p22 * x20;
548         pc[17] = m18 = p3 * x16 + p8 * x17 + p13 * x18 + p18 * x19 + p23 * x20;
549         pc[18] = m19 = p4 * x16 + p9 * x17 + p14 * x18 + p19 * x19 + p24 * x20;
550         pc[19] = m20 = p5 * x16 + p10 * x17 + p15 * x18 + p20 * x19 + p25 * x20;
551 
552         pc[20] = m21 = p1 * x21 + p6 * x22 + p11 * x23 + p16 * x24 + p21 * x25;
553         pc[21] = m22 = p2 * x21 + p7 * x22 + p12 * x23 + p17 * x24 + p22 * x25;
554         pc[22] = m23 = p3 * x21 + p8 * x22 + p13 * x23 + p18 * x24 + p23 * x25;
555         pc[23] = m24 = p4 * x21 + p9 * x22 + p14 * x23 + p19 * x24 + p24 * x25;
556         pc[24] = m25 = p5 * x21 + p10 * x22 + p15 * x23 + p20 * x24 + p25 * x25;
557 
558         nz = bi[row + 1] - diag_offset[row] - 1;
559         pv += 25;
560         for (j = 0; j < nz; j++) {
561           x1  = pv[0];
562           x2  = pv[1];
563           x3  = pv[2];
564           x4  = pv[3];
565           x5  = pv[4];
566           x6  = pv[5];
567           x7  = pv[6];
568           x8  = pv[7];
569           x9  = pv[8];
570           x10 = pv[9];
571           x11 = pv[10];
572           x12 = pv[11];
573           x13 = pv[12];
574           x14 = pv[13];
575           x15 = pv[14];
576           x16 = pv[15];
577           x17 = pv[16];
578           x18 = pv[17];
579           x19 = pv[18];
580           x20 = pv[19];
581           x21 = pv[20];
582           x22 = pv[21];
583           x23 = pv[22];
584           x24 = pv[23];
585           x25 = pv[24];
586           x   = rtmp + 25 * pj[j];
587           x[0] -= m1 * x1 + m6 * x2 + m11 * x3 + m16 * x4 + m21 * x5;
588           x[1] -= m2 * x1 + m7 * x2 + m12 * x3 + m17 * x4 + m22 * x5;
589           x[2] -= m3 * x1 + m8 * x2 + m13 * x3 + m18 * x4 + m23 * x5;
590           x[3] -= m4 * x1 + m9 * x2 + m14 * x3 + m19 * x4 + m24 * x5;
591           x[4] -= m5 * x1 + m10 * x2 + m15 * x3 + m20 * x4 + m25 * x5;
592 
593           x[5] -= m1 * x6 + m6 * x7 + m11 * x8 + m16 * x9 + m21 * x10;
594           x[6] -= m2 * x6 + m7 * x7 + m12 * x8 + m17 * x9 + m22 * x10;
595           x[7] -= m3 * x6 + m8 * x7 + m13 * x8 + m18 * x9 + m23 * x10;
596           x[8] -= m4 * x6 + m9 * x7 + m14 * x8 + m19 * x9 + m24 * x10;
597           x[9] -= m5 * x6 + m10 * x7 + m15 * x8 + m20 * x9 + m25 * x10;
598 
599           x[10] -= m1 * x11 + m6 * x12 + m11 * x13 + m16 * x14 + m21 * x15;
600           x[11] -= m2 * x11 + m7 * x12 + m12 * x13 + m17 * x14 + m22 * x15;
601           x[12] -= m3 * x11 + m8 * x12 + m13 * x13 + m18 * x14 + m23 * x15;
602           x[13] -= m4 * x11 + m9 * x12 + m14 * x13 + m19 * x14 + m24 * x15;
603           x[14] -= m5 * x11 + m10 * x12 + m15 * x13 + m20 * x14 + m25 * x15;
604 
605           x[15] -= m1 * x16 + m6 * x17 + m11 * x18 + m16 * x19 + m21 * x20;
606           x[16] -= m2 * x16 + m7 * x17 + m12 * x18 + m17 * x19 + m22 * x20;
607           x[17] -= m3 * x16 + m8 * x17 + m13 * x18 + m18 * x19 + m23 * x20;
608           x[18] -= m4 * x16 + m9 * x17 + m14 * x18 + m19 * x19 + m24 * x20;
609           x[19] -= m5 * x16 + m10 * x17 + m15 * x18 + m20 * x19 + m25 * x20;
610 
611           x[20] -= m1 * x21 + m6 * x22 + m11 * x23 + m16 * x24 + m21 * x25;
612           x[21] -= m2 * x21 + m7 * x22 + m12 * x23 + m17 * x24 + m22 * x25;
613           x[22] -= m3 * x21 + m8 * x22 + m13 * x23 + m18 * x24 + m23 * x25;
614           x[23] -= m4 * x21 + m9 * x22 + m14 * x23 + m19 * x24 + m24 * x25;
615           x[24] -= m5 * x21 + m10 * x22 + m15 * x23 + m20 * x24 + m25 * x25;
616           pv += 25;
617         }
618         PetscCall(PetscLogFlops(250.0 * nz + 225.0));
619       }
620       row = *ajtmp++;
621     }
622     /* finished row so stick it into b->a */
623     pv = ba + 25 * bi[i];
624     pj = bj + bi[i];
625     nz = bi[i + 1] - bi[i];
626     for (j = 0; j < nz; j++) {
627       x      = rtmp + 25 * pj[j];
628       pv[0]  = x[0];
629       pv[1]  = x[1];
630       pv[2]  = x[2];
631       pv[3]  = x[3];
632       pv[4]  = x[4];
633       pv[5]  = x[5];
634       pv[6]  = x[6];
635       pv[7]  = x[7];
636       pv[8]  = x[8];
637       pv[9]  = x[9];
638       pv[10] = x[10];
639       pv[11] = x[11];
640       pv[12] = x[12];
641       pv[13] = x[13];
642       pv[14] = x[14];
643       pv[15] = x[15];
644       pv[16] = x[16];
645       pv[17] = x[17];
646       pv[18] = x[18];
647       pv[19] = x[19];
648       pv[20] = x[20];
649       pv[21] = x[21];
650       pv[22] = x[22];
651       pv[23] = x[23];
652       pv[24] = x[24];
653       pv += 25;
654     }
655     /* invert diagonal block */
656     w = ba + 25 * diag_offset[i];
657     PetscCall(PetscKernel_A_gets_inverse_A_5(w, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
658     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
659   }
660 
661   PetscCall(PetscFree(rtmp));
662 
663   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering_inplace;
664   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering_inplace;
665   C->assembled           = PETSC_TRUE;
666 
667   PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * b->mbs)); /* from inverting diagonal blocks */
668   PetscFunctionReturn(PETSC_SUCCESS);
669 }
670 
671 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering(Mat B, Mat A, const MatFactorInfo *info)
672 {
673   Mat             C = B;
674   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
675   PetscInt        i, j, k, nz, nzL, row;
676   const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
677   const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
678   MatScalar      *rtmp, *pc, *mwork, *v, *vv, *pv, *aa = a->a, work[25];
679   PetscInt        flg, ipvt[5];
680   PetscReal       shift = info->shiftamount;
681   PetscBool       allowzeropivot, zeropivotdetected;
682 
683   PetscFunctionBegin;
684   allowzeropivot = PetscNot(A->erroriffailure);
685 
686   /* generate work space needed by the factorization */
687   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
688   PetscCall(PetscArrayzero(rtmp, bs2 * n));
689 
690   for (i = 0; i < n; i++) {
691     /* zero rtmp */
692     /* L part */
693     nz    = bi[i + 1] - bi[i];
694     bjtmp = bj + bi[i];
695     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));
696 
697     /* U part */
698     nz    = bdiag[i] - bdiag[i + 1];
699     bjtmp = bj + bdiag[i + 1] + 1;
700     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));
701 
702     /* load in initial (unfactored row) */
703     nz    = ai[i + 1] - ai[i];
704     ajtmp = aj + ai[i];
705     v     = aa + bs2 * ai[i];
706     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ajtmp[j], v + bs2 * j, bs2));
707 
708     /* elimination */
709     bjtmp = bj + bi[i];
710     nzL   = bi[i + 1] - bi[i];
711     for (k = 0; k < nzL; k++) {
712       row = bjtmp[k];
713       pc  = rtmp + bs2 * row;
714       for (flg = 0, j = 0; j < bs2; j++) {
715         if (pc[j] != 0.0) {
716           flg = 1;
717           break;
718         }
719       }
720       if (flg) {
721         pv = b->a + bs2 * bdiag[row];
722         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
723         PetscCall(PetscKernel_A_gets_A_times_B_5(pc, pv, mwork));
724 
725         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
726         pv = b->a + bs2 * (bdiag[row + 1] + 1);
727         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
728         for (j = 0; j < nz; j++) {
729           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
730           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
731           vv = rtmp + bs2 * pj[j];
732           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_5(vv, pc, pv));
733           pv += bs2;
734         }
735         PetscCall(PetscLogFlops(250.0 * nz + 225)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
736       }
737     }
738 
739     /* finished row so stick it into b->a */
740     /* L part */
741     pv = b->a + bs2 * bi[i];
742     pj = b->j + bi[i];
743     nz = bi[i + 1] - bi[i];
744     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
745 
746     /* Mark diagonal and invert diagonal for simpler triangular solves */
747     pv = b->a + bs2 * bdiag[i];
748     pj = b->j + bdiag[i];
749     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
750     PetscCall(PetscKernel_A_gets_inverse_A_5(pv, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
751     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
752 
753     /* U part */
754     pv = b->a + bs2 * (bdiag[i + 1] + 1);
755     pj = b->j + bdiag[i + 1] + 1;
756     nz = bdiag[i] - bdiag[i + 1] - 1;
757     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
758   }
759   PetscCall(PetscFree2(rtmp, mwork));
760 
761   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering;
762   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering;
763   C->assembled           = PETSC_TRUE;
764 
765   PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * n)); /* from inverting diagonal blocks */
766   PetscFunctionReturn(PETSC_SUCCESS);
767 }
768