xref: /petsc/src/mat/impls/baij/seq/baijfact9.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 5 by 5
11 */
12 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_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  *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(0);
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   Mat             C = B;
304   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
305   IS              isrow = b->row, isicol = b->icol;
306   const PetscInt *r, *ic;
307   PetscInt        i, j, k, nz, nzL, row;
308   const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
309   const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
310   MatScalar      *rtmp, *pc, *mwork, *v, *pv, *aa = a->a, work[25];
311   PetscInt        flg, ipvt[5];
312   PetscReal       shift = info->shiftamount;
313   PetscBool       allowzeropivot, zeropivotdetected;
314 
315   PetscFunctionBegin;
316   allowzeropivot = PetscNot(A->erroriffailure);
317   PetscCall(ISGetIndices(isrow, &r));
318   PetscCall(ISGetIndices(isicol, &ic));
319 
320   /* generate work space needed by the factorization */
321   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
322   PetscCall(PetscArrayzero(rtmp, bs2 * n));
323 
324   for (i = 0; i < n; i++) {
325     /* zero rtmp */
326     /* L part */
327     nz    = bi[i + 1] - bi[i];
328     bjtmp = bj + bi[i];
329     for (j = 0; j < nz; j++) { PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2)); }
330 
331     /* U part */
332     nz    = bdiag[i] - bdiag[i + 1];
333     bjtmp = bj + bdiag[i + 1] + 1;
334     for (j = 0; j < nz; j++) { PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2)); }
335 
336     /* load in initial (unfactored row) */
337     nz    = ai[r[i] + 1] - ai[r[i]];
338     ajtmp = aj + ai[r[i]];
339     v     = aa + bs2 * ai[r[i]];
340     for (j = 0; j < nz; j++) { PetscCall(PetscArraycpy(rtmp + bs2 * ic[ajtmp[j]], v + bs2 * j, bs2)); }
341 
342     /* elimination */
343     bjtmp = bj + bi[i];
344     nzL   = bi[i + 1] - bi[i];
345     for (k = 0; k < nzL; k++) {
346       row = bjtmp[k];
347       pc  = rtmp + bs2 * row;
348       for (flg = 0, j = 0; j < bs2; j++) {
349         if (pc[j] != 0.0) {
350           flg = 1;
351           break;
352         }
353       }
354       if (flg) {
355         pv = b->a + bs2 * bdiag[row];
356         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
357         PetscCall(PetscKernel_A_gets_A_times_B_5(pc, pv, mwork));
358 
359         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
360         pv = b->a + bs2 * (bdiag[row + 1] + 1);
361         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
362         for (j = 0; j < nz; j++) {
363           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
364           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
365           v = rtmp + bs2 * pj[j];
366           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_5(v, pc, pv));
367           pv += bs2;
368         }
369         PetscCall(PetscLogFlops(250.0 * nz + 225)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
370       }
371     }
372 
373     /* finished row so stick it into b->a */
374     /* L part */
375     pv = b->a + bs2 * bi[i];
376     pj = b->j + bi[i];
377     nz = bi[i + 1] - bi[i];
378     for (j = 0; j < nz; j++) { PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2)); }
379 
380     /* Mark diagonal and invert diagonal for simpler triangular solves */
381     pv = b->a + bs2 * bdiag[i];
382     pj = b->j + bdiag[i];
383     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
384     PetscCall(PetscKernel_A_gets_inverse_A_5(pv, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
385     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
386 
387     /* U part */
388     pv = b->a + bs2 * (bdiag[i + 1] + 1);
389     pj = b->j + bdiag[i + 1] + 1;
390     nz = bdiag[i] - bdiag[i + 1] - 1;
391     for (j = 0; j < nz; j++) { PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2)); }
392   }
393 
394   PetscCall(PetscFree2(rtmp, mwork));
395   PetscCall(ISRestoreIndices(isicol, &ic));
396   PetscCall(ISRestoreIndices(isrow, &r));
397 
398   C->ops->solve          = MatSolve_SeqBAIJ_5;
399   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5;
400   C->assembled           = PETSC_TRUE;
401 
402   PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * n)); /* from inverting diagonal blocks */
403   PetscFunctionReturn(0);
404 }
405 
406 /*
407       Version for when blocks are 5 by 5 Using natural ordering
408 */
409 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering_inplace(Mat C, Mat A, const MatFactorInfo *info) {
410   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
411   PetscInt     i, j, n = a->mbs, *bi = b->i, *bj = b->j, ipvt[5];
412   PetscInt    *ajtmpold, *ajtmp, nz, row;
413   PetscInt    *diag_offset = b->diag, *ai = a->i, *aj = a->j, *pj;
414   MatScalar   *pv, *v, *rtmp, *pc, *w, *x;
415   MatScalar    x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15;
416   MatScalar    x16, x17, x18, x19, x20, x21, x22, x23, x24, x25;
417   MatScalar    p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12, p13, p14, p15;
418   MatScalar    p16, p17, p18, p19, p20, p21, p22, p23, p24, p25;
419   MatScalar    m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12, m13, m14, m15;
420   MatScalar    m16, m17, m18, m19, m20, m21, m22, m23, m24, m25;
421   MatScalar   *ba = b->a, *aa = a->a, work[25];
422   PetscReal    shift = info->shiftamount;
423   PetscBool    allowzeropivot, zeropivotdetected;
424 
425   PetscFunctionBegin;
426   allowzeropivot = PetscNot(A->erroriffailure);
427   PetscCall(PetscMalloc1(25 * (n + 1), &rtmp));
428   for (i = 0; i < n; i++) {
429     nz    = bi[i + 1] - bi[i];
430     ajtmp = bj + bi[i];
431     for (j = 0; j < nz; j++) {
432       x    = rtmp + 25 * ajtmp[j];
433       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
434       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
435       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
436     }
437     /* load in initial (unfactored row) */
438     nz       = ai[i + 1] - ai[i];
439     ajtmpold = aj + ai[i];
440     v        = aa + 25 * ai[i];
441     for (j = 0; j < nz; j++) {
442       x     = rtmp + 25 * ajtmpold[j];
443       x[0]  = v[0];
444       x[1]  = v[1];
445       x[2]  = v[2];
446       x[3]  = v[3];
447       x[4]  = v[4];
448       x[5]  = v[5];
449       x[6]  = v[6];
450       x[7]  = v[7];
451       x[8]  = v[8];
452       x[9]  = v[9];
453       x[10] = v[10];
454       x[11] = v[11];
455       x[12] = v[12];
456       x[13] = v[13];
457       x[14] = v[14];
458       x[15] = v[15];
459       x[16] = v[16];
460       x[17] = v[17];
461       x[18] = v[18];
462       x[19] = v[19];
463       x[20] = v[20];
464       x[21] = v[21];
465       x[22] = v[22];
466       x[23] = v[23];
467       x[24] = v[24];
468       v += 25;
469     }
470     row = *ajtmp++;
471     while (row < i) {
472       pc  = rtmp + 25 * row;
473       p1  = pc[0];
474       p2  = pc[1];
475       p3  = pc[2];
476       p4  = pc[3];
477       p5  = pc[4];
478       p6  = pc[5];
479       p7  = pc[6];
480       p8  = pc[7];
481       p9  = pc[8];
482       p10 = pc[9];
483       p11 = pc[10];
484       p12 = pc[11];
485       p13 = pc[12];
486       p14 = pc[13];
487       p15 = pc[14];
488       p16 = pc[15];
489       p17 = pc[16];
490       p18 = pc[17];
491       p19 = pc[18];
492       p20 = pc[19];
493       p21 = pc[20];
494       p22 = pc[21];
495       p23 = pc[22];
496       p24 = pc[23];
497       p25 = pc[24];
498       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) {
499         pv    = ba + 25 * diag_offset[row];
500         pj    = bj + diag_offset[row] + 1;
501         x1    = pv[0];
502         x2    = pv[1];
503         x3    = pv[2];
504         x4    = pv[3];
505         x5    = pv[4];
506         x6    = pv[5];
507         x7    = pv[6];
508         x8    = pv[7];
509         x9    = pv[8];
510         x10   = pv[9];
511         x11   = pv[10];
512         x12   = pv[11];
513         x13   = pv[12];
514         x14   = pv[13];
515         x15   = pv[14];
516         x16   = pv[15];
517         x17   = pv[16];
518         x18   = pv[17];
519         x19   = pv[18];
520         x20   = pv[19];
521         x21   = pv[20];
522         x22   = pv[21];
523         x23   = pv[22];
524         x24   = pv[23];
525         x25   = pv[24];
526         pc[0] = m1 = p1 * x1 + p6 * x2 + p11 * x3 + p16 * x4 + p21 * x5;
527         pc[1] = m2 = p2 * x1 + p7 * x2 + p12 * x3 + p17 * x4 + p22 * x5;
528         pc[2] = m3 = p3 * x1 + p8 * x2 + p13 * x3 + p18 * x4 + p23 * x5;
529         pc[3] = m4 = p4 * x1 + p9 * x2 + p14 * x3 + p19 * x4 + p24 * x5;
530         pc[4] = m5 = p5 * x1 + p10 * x2 + p15 * x3 + p20 * x4 + p25 * x5;
531 
532         pc[5] = m6 = p1 * x6 + p6 * x7 + p11 * x8 + p16 * x9 + p21 * x10;
533         pc[6] = m7 = p2 * x6 + p7 * x7 + p12 * x8 + p17 * x9 + p22 * x10;
534         pc[7] = m8 = p3 * x6 + p8 * x7 + p13 * x8 + p18 * x9 + p23 * x10;
535         pc[8] = m9 = p4 * x6 + p9 * x7 + p14 * x8 + p19 * x9 + p24 * x10;
536         pc[9] = m10 = p5 * x6 + p10 * x7 + p15 * x8 + p20 * x9 + p25 * x10;
537 
538         pc[10] = m11 = p1 * x11 + p6 * x12 + p11 * x13 + p16 * x14 + p21 * x15;
539         pc[11] = m12 = p2 * x11 + p7 * x12 + p12 * x13 + p17 * x14 + p22 * x15;
540         pc[12] = m13 = p3 * x11 + p8 * x12 + p13 * x13 + p18 * x14 + p23 * x15;
541         pc[13] = m14 = p4 * x11 + p9 * x12 + p14 * x13 + p19 * x14 + p24 * x15;
542         pc[14] = m15 = p5 * x11 + p10 * x12 + p15 * x13 + p20 * x14 + p25 * x15;
543 
544         pc[15] = m16 = p1 * x16 + p6 * x17 + p11 * x18 + p16 * x19 + p21 * x20;
545         pc[16] = m17 = p2 * x16 + p7 * x17 + p12 * x18 + p17 * x19 + p22 * x20;
546         pc[17] = m18 = p3 * x16 + p8 * x17 + p13 * x18 + p18 * x19 + p23 * x20;
547         pc[18] = m19 = p4 * x16 + p9 * x17 + p14 * x18 + p19 * x19 + p24 * x20;
548         pc[19] = m20 = p5 * x16 + p10 * x17 + p15 * x18 + p20 * x19 + p25 * x20;
549 
550         pc[20] = m21 = p1 * x21 + p6 * x22 + p11 * x23 + p16 * x24 + p21 * x25;
551         pc[21] = m22 = p2 * x21 + p7 * x22 + p12 * x23 + p17 * x24 + p22 * x25;
552         pc[22] = m23 = p3 * x21 + p8 * x22 + p13 * x23 + p18 * x24 + p23 * x25;
553         pc[23] = m24 = p4 * x21 + p9 * x22 + p14 * x23 + p19 * x24 + p24 * x25;
554         pc[24] = m25 = p5 * x21 + p10 * x22 + p15 * x23 + p20 * x24 + p25 * x25;
555 
556         nz = bi[row + 1] - diag_offset[row] - 1;
557         pv += 25;
558         for (j = 0; j < nz; j++) {
559           x1  = pv[0];
560           x2  = pv[1];
561           x3  = pv[2];
562           x4  = pv[3];
563           x5  = pv[4];
564           x6  = pv[5];
565           x7  = pv[6];
566           x8  = pv[7];
567           x9  = pv[8];
568           x10 = pv[9];
569           x11 = pv[10];
570           x12 = pv[11];
571           x13 = pv[12];
572           x14 = pv[13];
573           x15 = pv[14];
574           x16 = pv[15];
575           x17 = pv[16];
576           x18 = pv[17];
577           x19 = pv[18];
578           x20 = pv[19];
579           x21 = pv[20];
580           x22 = pv[21];
581           x23 = pv[22];
582           x24 = pv[23];
583           x25 = pv[24];
584           x   = rtmp + 25 * pj[j];
585           x[0] -= m1 * x1 + m6 * x2 + m11 * x3 + m16 * x4 + m21 * x5;
586           x[1] -= m2 * x1 + m7 * x2 + m12 * x3 + m17 * x4 + m22 * x5;
587           x[2] -= m3 * x1 + m8 * x2 + m13 * x3 + m18 * x4 + m23 * x5;
588           x[3] -= m4 * x1 + m9 * x2 + m14 * x3 + m19 * x4 + m24 * x5;
589           x[4] -= m5 * x1 + m10 * x2 + m15 * x3 + m20 * x4 + m25 * x5;
590 
591           x[5] -= m1 * x6 + m6 * x7 + m11 * x8 + m16 * x9 + m21 * x10;
592           x[6] -= m2 * x6 + m7 * x7 + m12 * x8 + m17 * x9 + m22 * x10;
593           x[7] -= m3 * x6 + m8 * x7 + m13 * x8 + m18 * x9 + m23 * x10;
594           x[8] -= m4 * x6 + m9 * x7 + m14 * x8 + m19 * x9 + m24 * x10;
595           x[9] -= m5 * x6 + m10 * x7 + m15 * x8 + m20 * x9 + m25 * x10;
596 
597           x[10] -= m1 * x11 + m6 * x12 + m11 * x13 + m16 * x14 + m21 * x15;
598           x[11] -= m2 * x11 + m7 * x12 + m12 * x13 + m17 * x14 + m22 * x15;
599           x[12] -= m3 * x11 + m8 * x12 + m13 * x13 + m18 * x14 + m23 * x15;
600           x[13] -= m4 * x11 + m9 * x12 + m14 * x13 + m19 * x14 + m24 * x15;
601           x[14] -= m5 * x11 + m10 * x12 + m15 * x13 + m20 * x14 + m25 * x15;
602 
603           x[15] -= m1 * x16 + m6 * x17 + m11 * x18 + m16 * x19 + m21 * x20;
604           x[16] -= m2 * x16 + m7 * x17 + m12 * x18 + m17 * x19 + m22 * x20;
605           x[17] -= m3 * x16 + m8 * x17 + m13 * x18 + m18 * x19 + m23 * x20;
606           x[18] -= m4 * x16 + m9 * x17 + m14 * x18 + m19 * x19 + m24 * x20;
607           x[19] -= m5 * x16 + m10 * x17 + m15 * x18 + m20 * x19 + m25 * x20;
608 
609           x[20] -= m1 * x21 + m6 * x22 + m11 * x23 + m16 * x24 + m21 * x25;
610           x[21] -= m2 * x21 + m7 * x22 + m12 * x23 + m17 * x24 + m22 * x25;
611           x[22] -= m3 * x21 + m8 * x22 + m13 * x23 + m18 * x24 + m23 * x25;
612           x[23] -= m4 * x21 + m9 * x22 + m14 * x23 + m19 * x24 + m24 * x25;
613           x[24] -= m5 * x21 + m10 * x22 + m15 * x23 + m20 * x24 + m25 * x25;
614           pv += 25;
615         }
616         PetscCall(PetscLogFlops(250.0 * nz + 225.0));
617       }
618       row = *ajtmp++;
619     }
620     /* finished row so stick it into b->a */
621     pv = ba + 25 * bi[i];
622     pj = bj + bi[i];
623     nz = bi[i + 1] - bi[i];
624     for (j = 0; j < nz; j++) {
625       x      = rtmp + 25 * pj[j];
626       pv[0]  = x[0];
627       pv[1]  = x[1];
628       pv[2]  = x[2];
629       pv[3]  = x[3];
630       pv[4]  = x[4];
631       pv[5]  = x[5];
632       pv[6]  = x[6];
633       pv[7]  = x[7];
634       pv[8]  = x[8];
635       pv[9]  = x[9];
636       pv[10] = x[10];
637       pv[11] = x[11];
638       pv[12] = x[12];
639       pv[13] = x[13];
640       pv[14] = x[14];
641       pv[15] = x[15];
642       pv[16] = x[16];
643       pv[17] = x[17];
644       pv[18] = x[18];
645       pv[19] = x[19];
646       pv[20] = x[20];
647       pv[21] = x[21];
648       pv[22] = x[22];
649       pv[23] = x[23];
650       pv[24] = x[24];
651       pv += 25;
652     }
653     /* invert diagonal block */
654     w = ba + 25 * diag_offset[i];
655     PetscCall(PetscKernel_A_gets_inverse_A_5(w, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
656     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
657   }
658 
659   PetscCall(PetscFree(rtmp));
660 
661   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering_inplace;
662   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering_inplace;
663   C->assembled           = PETSC_TRUE;
664 
665   PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * b->mbs)); /* from inverting diagonal blocks */
666   PetscFunctionReturn(0);
667 }
668 
669 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering(Mat B, Mat A, const MatFactorInfo *info) {
670   Mat             C = B;
671   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
672   PetscInt        i, j, k, nz, nzL, row;
673   const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
674   const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
675   MatScalar      *rtmp, *pc, *mwork, *v, *vv, *pv, *aa = a->a, work[25];
676   PetscInt        flg, ipvt[5];
677   PetscReal       shift = info->shiftamount;
678   PetscBool       allowzeropivot, zeropivotdetected;
679 
680   PetscFunctionBegin;
681   allowzeropivot = PetscNot(A->erroriffailure);
682 
683   /* generate work space needed by the factorization */
684   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
685   PetscCall(PetscArrayzero(rtmp, bs2 * n));
686 
687   for (i = 0; i < n; i++) {
688     /* zero rtmp */
689     /* L part */
690     nz    = bi[i + 1] - bi[i];
691     bjtmp = bj + bi[i];
692     for (j = 0; j < nz; j++) { PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2)); }
693 
694     /* U part */
695     nz    = bdiag[i] - bdiag[i + 1];
696     bjtmp = bj + bdiag[i + 1] + 1;
697     for (j = 0; j < nz; j++) { PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2)); }
698 
699     /* load in initial (unfactored row) */
700     nz    = ai[i + 1] - ai[i];
701     ajtmp = aj + ai[i];
702     v     = aa + bs2 * ai[i];
703     for (j = 0; j < nz; j++) { PetscCall(PetscArraycpy(rtmp + bs2 * ajtmp[j], v + bs2 * j, bs2)); }
704 
705     /* elimination */
706     bjtmp = bj + bi[i];
707     nzL   = bi[i + 1] - bi[i];
708     for (k = 0; k < nzL; k++) {
709       row = bjtmp[k];
710       pc  = rtmp + bs2 * row;
711       for (flg = 0, j = 0; j < bs2; j++) {
712         if (pc[j] != 0.0) {
713           flg = 1;
714           break;
715         }
716       }
717       if (flg) {
718         pv = b->a + bs2 * bdiag[row];
719         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
720         PetscCall(PetscKernel_A_gets_A_times_B_5(pc, pv, mwork));
721 
722         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
723         pv = b->a + bs2 * (bdiag[row + 1] + 1);
724         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
725         for (j = 0; j < nz; j++) {
726           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
727           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
728           vv = rtmp + bs2 * pj[j];
729           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_5(vv, pc, pv));
730           pv += bs2;
731         }
732         PetscCall(PetscLogFlops(250.0 * nz + 225)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
733       }
734     }
735 
736     /* finished row so stick it into b->a */
737     /* L part */
738     pv = b->a + bs2 * bi[i];
739     pj = b->j + bi[i];
740     nz = bi[i + 1] - bi[i];
741     for (j = 0; j < nz; j++) { PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2)); }
742 
743     /* Mark diagonal and invert diagonal for simpler triangular solves */
744     pv = b->a + bs2 * bdiag[i];
745     pj = b->j + bdiag[i];
746     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
747     PetscCall(PetscKernel_A_gets_inverse_A_5(pv, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
748     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
749 
750     /* U part */
751     pv = b->a + bs2 * (bdiag[i + 1] + 1);
752     pj = b->j + bdiag[i + 1] + 1;
753     nz = bdiag[i] - bdiag[i + 1] - 1;
754     for (j = 0; j < nz; j++) { PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2)); }
755   }
756   PetscCall(PetscFree2(rtmp, mwork));
757 
758   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering;
759   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering;
760   C->assembled           = PETSC_TRUE;
761 
762   PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * n)); /* from inverting diagonal blocks */
763   PetscFunctionReturn(0);
764 }
765