xref: /petsc/src/mat/impls/baij/seq/baijfact9.c (revision f13dfd9ea68e0ddeee984e65c377a1819eab8a8a)
1 /*
2     Factorization code for BAIJ format.
3 */
4 #include <../src/mat/impls/baij/seq/baij.h>
5 #include <petsc/private/kernels/blockinvert.h>
6 
7 /*
8       Version for when blocks are 5 by 5
9 */
10 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_inplace(Mat C, Mat A, const MatFactorInfo *info)
11 {
12   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
13   IS               isrow = b->row, isicol = b->icol;
14   const PetscInt  *r, *ic, *bi = b->i, *bj = b->j, *ajtmpold, *ajtmp;
15   PetscInt         i, j, n = a->mbs, nz, row, idx, ipvt[5];
16   const PetscInt  *diag_offset = b->diag, *ai = a->i, *aj = a->j, *pj;
17   MatScalar       *w, *pv, *rtmp, *x, *pc;
18   const MatScalar *v, *aa = a->a;
19   MatScalar        p1, p2, p3, p4, m1, m2, m3, m4, m5, m6, m7, m8, m9, x1, x2, x3, x4;
20   MatScalar        p5, p6, p7, p8, p9, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16;
21   MatScalar        x17, x18, x19, x20, x21, x22, x23, x24, x25, p10, p11, p12, p13, p14;
22   MatScalar        p15, p16, p17, p18, p19, p20, p21, p22, p23, p24, p25, m10, m11, m12;
23   MatScalar        m13, m14, m15, m16, m17, m18, m19, m20, m21, m22, m23, m24, m25;
24   MatScalar       *ba    = b->a, work[25];
25   PetscReal        shift = info->shiftamount;
26   PetscBool        allowzeropivot, zeropivotdetected;
27 
28   PetscFunctionBegin;
29   allowzeropivot = PetscNot(A->erroriffailure);
30   PetscCall(ISGetIndices(isrow, &r));
31   PetscCall(ISGetIndices(isicol, &ic));
32   PetscCall(PetscMalloc1(25 * (n + 1), &rtmp));
33 
34 #define PETSC_USE_MEMZERO 1
35 #define PETSC_USE_MEMCPY  1
36 
37   for (i = 0; i < n; i++) {
38     nz    = bi[i + 1] - bi[i];
39     ajtmp = bj + bi[i];
40     for (j = 0; j < nz; j++) {
41 #if defined(PETSC_USE_MEMZERO)
42       PetscCall(PetscArrayzero(rtmp + 25 * ajtmp[j], 25));
43 #else
44       x    = rtmp + 25 * ajtmp[j];
45       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
46       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
47       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
48 #endif
49     }
50     /* load in initial (unfactored row) */
51     idx      = r[i];
52     nz       = ai[idx + 1] - ai[idx];
53     ajtmpold = aj + ai[idx];
54     v        = aa + 25 * ai[idx];
55     for (j = 0; j < nz; j++) {
56 #if defined(PETSC_USE_MEMCPY)
57       PetscCall(PetscArraycpy(rtmp + 25 * ic[ajtmpold[j]], v, 25));
58 #else
59       x     = rtmp + 25 * ic[ajtmpold[j]];
60       x[0]  = v[0];
61       x[1]  = v[1];
62       x[2]  = v[2];
63       x[3]  = v[3];
64       x[4]  = v[4];
65       x[5]  = v[5];
66       x[6]  = v[6];
67       x[7]  = v[7];
68       x[8]  = v[8];
69       x[9]  = v[9];
70       x[10] = v[10];
71       x[11] = v[11];
72       x[12] = v[12];
73       x[13] = v[13];
74       x[14] = v[14];
75       x[15] = v[15];
76       x[16] = v[16];
77       x[17] = v[17];
78       x[18] = v[18];
79       x[19] = v[19];
80       x[20] = v[20];
81       x[21] = v[21];
82       x[22] = v[22];
83       x[23] = v[23];
84       x[24] = v[24];
85 #endif
86       v += 25;
87     }
88     row = *ajtmp++;
89     while (row < i) {
90       pc  = rtmp + 25 * row;
91       p1  = pc[0];
92       p2  = pc[1];
93       p3  = pc[2];
94       p4  = pc[3];
95       p5  = pc[4];
96       p6  = pc[5];
97       p7  = pc[6];
98       p8  = pc[7];
99       p9  = pc[8];
100       p10 = pc[9];
101       p11 = pc[10];
102       p12 = pc[11];
103       p13 = pc[12];
104       p14 = pc[13];
105       p15 = pc[14];
106       p16 = pc[15];
107       p17 = pc[16];
108       p18 = pc[17];
109       p19 = pc[18];
110       p20 = pc[19];
111       p21 = pc[20];
112       p22 = pc[21];
113       p23 = pc[22];
114       p24 = pc[23];
115       p25 = pc[24];
116       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) {
117         pv    = ba + 25 * diag_offset[row];
118         pj    = bj + diag_offset[row] + 1;
119         x1    = pv[0];
120         x2    = pv[1];
121         x3    = pv[2];
122         x4    = pv[3];
123         x5    = pv[4];
124         x6    = pv[5];
125         x7    = pv[6];
126         x8    = pv[7];
127         x9    = pv[8];
128         x10   = pv[9];
129         x11   = pv[10];
130         x12   = pv[11];
131         x13   = pv[12];
132         x14   = pv[13];
133         x15   = pv[14];
134         x16   = pv[15];
135         x17   = pv[16];
136         x18   = pv[17];
137         x19   = pv[18];
138         x20   = pv[19];
139         x21   = pv[20];
140         x22   = pv[21];
141         x23   = pv[22];
142         x24   = pv[23];
143         x25   = pv[24];
144         pc[0] = m1 = p1 * x1 + p6 * x2 + p11 * x3 + p16 * x4 + p21 * x5;
145         pc[1] = m2 = p2 * x1 + p7 * x2 + p12 * x3 + p17 * x4 + p22 * x5;
146         pc[2] = m3 = p3 * x1 + p8 * x2 + p13 * x3 + p18 * x4 + p23 * x5;
147         pc[3] = m4 = p4 * x1 + p9 * x2 + p14 * x3 + p19 * x4 + p24 * x5;
148         pc[4] = m5 = p5 * x1 + p10 * x2 + p15 * x3 + p20 * x4 + p25 * x5;
149 
150         pc[5] = m6 = p1 * x6 + p6 * x7 + p11 * x8 + p16 * x9 + p21 * x10;
151         pc[6] = m7 = p2 * x6 + p7 * x7 + p12 * x8 + p17 * x9 + p22 * x10;
152         pc[7] = m8 = p3 * x6 + p8 * x7 + p13 * x8 + p18 * x9 + p23 * x10;
153         pc[8] = m9 = p4 * x6 + p9 * x7 + p14 * x8 + p19 * x9 + p24 * x10;
154         pc[9] = m10 = p5 * x6 + p10 * x7 + p15 * x8 + p20 * x9 + p25 * x10;
155 
156         pc[10] = m11 = p1 * x11 + p6 * x12 + p11 * x13 + p16 * x14 + p21 * x15;
157         pc[11] = m12 = p2 * x11 + p7 * x12 + p12 * x13 + p17 * x14 + p22 * x15;
158         pc[12] = m13 = p3 * x11 + p8 * x12 + p13 * x13 + p18 * x14 + p23 * x15;
159         pc[13] = m14 = p4 * x11 + p9 * x12 + p14 * x13 + p19 * x14 + p24 * x15;
160         pc[14] = m15 = p5 * x11 + p10 * x12 + p15 * x13 + p20 * x14 + p25 * x15;
161 
162         pc[15] = m16 = p1 * x16 + p6 * x17 + p11 * x18 + p16 * x19 + p21 * x20;
163         pc[16] = m17 = p2 * x16 + p7 * x17 + p12 * x18 + p17 * x19 + p22 * x20;
164         pc[17] = m18 = p3 * x16 + p8 * x17 + p13 * x18 + p18 * x19 + p23 * x20;
165         pc[18] = m19 = p4 * x16 + p9 * x17 + p14 * x18 + p19 * x19 + p24 * x20;
166         pc[19] = m20 = p5 * x16 + p10 * x17 + p15 * x18 + p20 * x19 + p25 * x20;
167 
168         pc[20] = m21 = p1 * x21 + p6 * x22 + p11 * x23 + p16 * x24 + p21 * x25;
169         pc[21] = m22 = p2 * x21 + p7 * x22 + p12 * x23 + p17 * x24 + p22 * x25;
170         pc[22] = m23 = p3 * x21 + p8 * x22 + p13 * x23 + p18 * x24 + p23 * x25;
171         pc[23] = m24 = p4 * x21 + p9 * x22 + p14 * x23 + p19 * x24 + p24 * x25;
172         pc[24] = m25 = p5 * x21 + p10 * x22 + p15 * x23 + p20 * x24 + p25 * x25;
173 
174         nz = bi[row + 1] - diag_offset[row] - 1;
175         pv += 25;
176         for (j = 0; j < nz; j++) {
177           x1  = pv[0];
178           x2  = pv[1];
179           x3  = pv[2];
180           x4  = pv[3];
181           x5  = pv[4];
182           x6  = pv[5];
183           x7  = pv[6];
184           x8  = pv[7];
185           x9  = pv[8];
186           x10 = pv[9];
187           x11 = pv[10];
188           x12 = pv[11];
189           x13 = pv[12];
190           x14 = pv[13];
191           x15 = pv[14];
192           x16 = pv[15];
193           x17 = pv[16];
194           x18 = pv[17];
195           x19 = pv[18];
196           x20 = pv[19];
197           x21 = pv[20];
198           x22 = pv[21];
199           x23 = pv[22];
200           x24 = pv[23];
201           x25 = pv[24];
202           x   = rtmp + 25 * pj[j];
203           x[0] -= m1 * x1 + m6 * x2 + m11 * x3 + m16 * x4 + m21 * x5;
204           x[1] -= m2 * x1 + m7 * x2 + m12 * x3 + m17 * x4 + m22 * x5;
205           x[2] -= m3 * x1 + m8 * x2 + m13 * x3 + m18 * x4 + m23 * x5;
206           x[3] -= m4 * x1 + m9 * x2 + m14 * x3 + m19 * x4 + m24 * x5;
207           x[4] -= m5 * x1 + m10 * x2 + m15 * x3 + m20 * x4 + m25 * x5;
208 
209           x[5] -= m1 * x6 + m6 * x7 + m11 * x8 + m16 * x9 + m21 * x10;
210           x[6] -= m2 * x6 + m7 * x7 + m12 * x8 + m17 * x9 + m22 * x10;
211           x[7] -= m3 * x6 + m8 * x7 + m13 * x8 + m18 * x9 + m23 * x10;
212           x[8] -= m4 * x6 + m9 * x7 + m14 * x8 + m19 * x9 + m24 * x10;
213           x[9] -= m5 * x6 + m10 * x7 + m15 * x8 + m20 * x9 + m25 * x10;
214 
215           x[10] -= m1 * x11 + m6 * x12 + m11 * x13 + m16 * x14 + m21 * x15;
216           x[11] -= m2 * x11 + m7 * x12 + m12 * x13 + m17 * x14 + m22 * x15;
217           x[12] -= m3 * x11 + m8 * x12 + m13 * x13 + m18 * x14 + m23 * x15;
218           x[13] -= m4 * x11 + m9 * x12 + m14 * x13 + m19 * x14 + m24 * x15;
219           x[14] -= m5 * x11 + m10 * x12 + m15 * x13 + m20 * x14 + m25 * x15;
220 
221           x[15] -= m1 * x16 + m6 * x17 + m11 * x18 + m16 * x19 + m21 * x20;
222           x[16] -= m2 * x16 + m7 * x17 + m12 * x18 + m17 * x19 + m22 * x20;
223           x[17] -= m3 * x16 + m8 * x17 + m13 * x18 + m18 * x19 + m23 * x20;
224           x[18] -= m4 * x16 + m9 * x17 + m14 * x18 + m19 * x19 + m24 * x20;
225           x[19] -= m5 * x16 + m10 * x17 + m15 * x18 + m20 * x19 + m25 * x20;
226 
227           x[20] -= m1 * x21 + m6 * x22 + m11 * x23 + m16 * x24 + m21 * x25;
228           x[21] -= m2 * x21 + m7 * x22 + m12 * x23 + m17 * x24 + m22 * x25;
229           x[22] -= m3 * x21 + m8 * x22 + m13 * x23 + m18 * x24 + m23 * x25;
230           x[23] -= m4 * x21 + m9 * x22 + m14 * x23 + m19 * x24 + m24 * x25;
231           x[24] -= m5 * x21 + m10 * x22 + m15 * x23 + m20 * x24 + m25 * x25;
232 
233           pv += 25;
234         }
235         PetscCall(PetscLogFlops(250.0 * nz + 225.0));
236       }
237       row = *ajtmp++;
238     }
239     /* finished row so stick it into b->a */
240     pv = ba + 25 * bi[i];
241     pj = bj + bi[i];
242     nz = bi[i + 1] - bi[i];
243     for (j = 0; j < nz; j++) {
244 #if defined(PETSC_USE_MEMCPY)
245       PetscCall(PetscArraycpy(pv, rtmp + 25 * pj[j], 25));
246 #else
247       x      = rtmp + 25 * pj[j];
248       pv[0]  = x[0];
249       pv[1]  = x[1];
250       pv[2]  = x[2];
251       pv[3]  = x[3];
252       pv[4]  = x[4];
253       pv[5]  = x[5];
254       pv[6]  = x[6];
255       pv[7]  = x[7];
256       pv[8]  = x[8];
257       pv[9]  = x[9];
258       pv[10] = x[10];
259       pv[11] = x[11];
260       pv[12] = x[12];
261       pv[13] = x[13];
262       pv[14] = x[14];
263       pv[15] = x[15];
264       pv[16] = x[16];
265       pv[17] = x[17];
266       pv[18] = x[18];
267       pv[19] = x[19];
268       pv[20] = x[20];
269       pv[21] = x[21];
270       pv[22] = x[22];
271       pv[23] = x[23];
272       pv[24] = x[24];
273 #endif
274       pv += 25;
275     }
276     /* invert diagonal block */
277     w = ba + 25 * diag_offset[i];
278     PetscCall(PetscKernel_A_gets_inverse_A_5(w, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
279     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
280   }
281 
282   PetscCall(PetscFree(rtmp));
283   PetscCall(ISRestoreIndices(isicol, &ic));
284   PetscCall(ISRestoreIndices(isrow, &r));
285 
286   C->ops->solve          = MatSolve_SeqBAIJ_5_inplace;
287   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_inplace;
288   C->assembled           = PETSC_TRUE;
289 
290   PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * b->mbs)); /* from inverting diagonal blocks */
291   PetscFunctionReturn(PETSC_SUCCESS);
292 }
293 
294 /* MatLUFactorNumeric_SeqBAIJ_5 -
295      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
296        PetscKernel_A_gets_A_times_B()
297        PetscKernel_A_gets_A_minus_B_times_C()
298        PetscKernel_A_gets_inverse_A()
299 */
300 
301 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5(Mat B, Mat A, const MatFactorInfo *info)
302 {
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(PETSC_SUCCESS);
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 {
411   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
412   PetscInt     i, j, n = a->mbs, *bi = b->i, *bj = b->j, ipvt[5];
413   PetscInt    *ajtmpold, *ajtmp, nz, row;
414   PetscInt    *diag_offset = b->diag, *ai = a->i, *aj = a->j, *pj;
415   MatScalar   *pv, *v, *rtmp, *pc, *w, *x;
416   MatScalar    x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15;
417   MatScalar    x16, x17, x18, x19, x20, x21, x22, x23, x24, x25;
418   MatScalar    p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12, p13, p14, p15;
419   MatScalar    p16, p17, p18, p19, p20, p21, p22, p23, p24, p25;
420   MatScalar    m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12, m13, m14, m15;
421   MatScalar    m16, m17, m18, m19, m20, m21, m22, m23, m24, m25;
422   MatScalar   *ba = b->a, *aa = a->a, work[25];
423   PetscReal    shift = info->shiftamount;
424   PetscBool    allowzeropivot, zeropivotdetected;
425 
426   PetscFunctionBegin;
427   allowzeropivot = PetscNot(A->erroriffailure);
428   PetscCall(PetscMalloc1(25 * (n + 1), &rtmp));
429   for (i = 0; i < n; i++) {
430     nz    = bi[i + 1] - bi[i];
431     ajtmp = bj + bi[i];
432     for (j = 0; j < nz; j++) {
433       x    = rtmp + 25 * ajtmp[j];
434       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
435       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
436       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
437     }
438     /* load in initial (unfactored row) */
439     nz       = ai[i + 1] - ai[i];
440     ajtmpold = aj + ai[i];
441     v        = aa + 25 * ai[i];
442     for (j = 0; j < nz; j++) {
443       x     = rtmp + 25 * ajtmpold[j];
444       x[0]  = v[0];
445       x[1]  = v[1];
446       x[2]  = v[2];
447       x[3]  = v[3];
448       x[4]  = v[4];
449       x[5]  = v[5];
450       x[6]  = v[6];
451       x[7]  = v[7];
452       x[8]  = v[8];
453       x[9]  = v[9];
454       x[10] = v[10];
455       x[11] = v[11];
456       x[12] = v[12];
457       x[13] = v[13];
458       x[14] = v[14];
459       x[15] = v[15];
460       x[16] = v[16];
461       x[17] = v[17];
462       x[18] = v[18];
463       x[19] = v[19];
464       x[20] = v[20];
465       x[21] = v[21];
466       x[22] = v[22];
467       x[23] = v[23];
468       x[24] = v[24];
469       v += 25;
470     }
471     row = *ajtmp++;
472     while (row < i) {
473       pc  = rtmp + 25 * row;
474       p1  = pc[0];
475       p2  = pc[1];
476       p3  = pc[2];
477       p4  = pc[3];
478       p5  = pc[4];
479       p6  = pc[5];
480       p7  = pc[6];
481       p8  = pc[7];
482       p9  = pc[8];
483       p10 = pc[9];
484       p11 = pc[10];
485       p12 = pc[11];
486       p13 = pc[12];
487       p14 = pc[13];
488       p15 = pc[14];
489       p16 = pc[15];
490       p17 = pc[16];
491       p18 = pc[17];
492       p19 = pc[18];
493       p20 = pc[19];
494       p21 = pc[20];
495       p22 = pc[21];
496       p23 = pc[22];
497       p24 = pc[23];
498       p25 = pc[24];
499       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) {
500         pv    = ba + 25 * diag_offset[row];
501         pj    = bj + diag_offset[row] + 1;
502         x1    = pv[0];
503         x2    = pv[1];
504         x3    = pv[2];
505         x4    = pv[3];
506         x5    = pv[4];
507         x6    = pv[5];
508         x7    = pv[6];
509         x8    = pv[7];
510         x9    = pv[8];
511         x10   = pv[9];
512         x11   = pv[10];
513         x12   = pv[11];
514         x13   = pv[12];
515         x14   = pv[13];
516         x15   = pv[14];
517         x16   = pv[15];
518         x17   = pv[16];
519         x18   = pv[17];
520         x19   = pv[18];
521         x20   = pv[19];
522         x21   = pv[20];
523         x22   = pv[21];
524         x23   = pv[22];
525         x24   = pv[23];
526         x25   = pv[24];
527         pc[0] = m1 = p1 * x1 + p6 * x2 + p11 * x3 + p16 * x4 + p21 * x5;
528         pc[1] = m2 = p2 * x1 + p7 * x2 + p12 * x3 + p17 * x4 + p22 * x5;
529         pc[2] = m3 = p3 * x1 + p8 * x2 + p13 * x3 + p18 * x4 + p23 * x5;
530         pc[3] = m4 = p4 * x1 + p9 * x2 + p14 * x3 + p19 * x4 + p24 * x5;
531         pc[4] = m5 = p5 * x1 + p10 * x2 + p15 * x3 + p20 * x4 + p25 * x5;
532 
533         pc[5] = m6 = p1 * x6 + p6 * x7 + p11 * x8 + p16 * x9 + p21 * x10;
534         pc[6] = m7 = p2 * x6 + p7 * x7 + p12 * x8 + p17 * x9 + p22 * x10;
535         pc[7] = m8 = p3 * x6 + p8 * x7 + p13 * x8 + p18 * x9 + p23 * x10;
536         pc[8] = m9 = p4 * x6 + p9 * x7 + p14 * x8 + p19 * x9 + p24 * x10;
537         pc[9] = m10 = p5 * x6 + p10 * x7 + p15 * x8 + p20 * x9 + p25 * x10;
538 
539         pc[10] = m11 = p1 * x11 + p6 * x12 + p11 * x13 + p16 * x14 + p21 * x15;
540         pc[11] = m12 = p2 * x11 + p7 * x12 + p12 * x13 + p17 * x14 + p22 * x15;
541         pc[12] = m13 = p3 * x11 + p8 * x12 + p13 * x13 + p18 * x14 + p23 * x15;
542         pc[13] = m14 = p4 * x11 + p9 * x12 + p14 * x13 + p19 * x14 + p24 * x15;
543         pc[14] = m15 = p5 * x11 + p10 * x12 + p15 * x13 + p20 * x14 + p25 * x15;
544 
545         pc[15] = m16 = p1 * x16 + p6 * x17 + p11 * x18 + p16 * x19 + p21 * x20;
546         pc[16] = m17 = p2 * x16 + p7 * x17 + p12 * x18 + p17 * x19 + p22 * x20;
547         pc[17] = m18 = p3 * x16 + p8 * x17 + p13 * x18 + p18 * x19 + p23 * x20;
548         pc[18] = m19 = p4 * x16 + p9 * x17 + p14 * x18 + p19 * x19 + p24 * x20;
549         pc[19] = m20 = p5 * x16 + p10 * x17 + p15 * x18 + p20 * x19 + p25 * x20;
550 
551         pc[20] = m21 = p1 * x21 + p6 * x22 + p11 * x23 + p16 * x24 + p21 * x25;
552         pc[21] = m22 = p2 * x21 + p7 * x22 + p12 * x23 + p17 * x24 + p22 * x25;
553         pc[22] = m23 = p3 * x21 + p8 * x22 + p13 * x23 + p18 * x24 + p23 * x25;
554         pc[23] = m24 = p4 * x21 + p9 * x22 + p14 * x23 + p19 * x24 + p24 * x25;
555         pc[24] = m25 = p5 * x21 + p10 * x22 + p15 * x23 + p20 * x24 + p25 * x25;
556 
557         nz = bi[row + 1] - diag_offset[row] - 1;
558         pv += 25;
559         for (j = 0; j < nz; j++) {
560           x1  = pv[0];
561           x2  = pv[1];
562           x3  = pv[2];
563           x4  = pv[3];
564           x5  = pv[4];
565           x6  = pv[5];
566           x7  = pv[6];
567           x8  = pv[7];
568           x9  = pv[8];
569           x10 = pv[9];
570           x11 = pv[10];
571           x12 = pv[11];
572           x13 = pv[12];
573           x14 = pv[13];
574           x15 = pv[14];
575           x16 = pv[15];
576           x17 = pv[16];
577           x18 = pv[17];
578           x19 = pv[18];
579           x20 = pv[19];
580           x21 = pv[20];
581           x22 = pv[21];
582           x23 = pv[22];
583           x24 = pv[23];
584           x25 = pv[24];
585           x   = rtmp + 25 * pj[j];
586           x[0] -= m1 * x1 + m6 * x2 + m11 * x3 + m16 * x4 + m21 * x5;
587           x[1] -= m2 * x1 + m7 * x2 + m12 * x3 + m17 * x4 + m22 * x5;
588           x[2] -= m3 * x1 + m8 * x2 + m13 * x3 + m18 * x4 + m23 * x5;
589           x[3] -= m4 * x1 + m9 * x2 + m14 * x3 + m19 * x4 + m24 * x5;
590           x[4] -= m5 * x1 + m10 * x2 + m15 * x3 + m20 * x4 + m25 * x5;
591 
592           x[5] -= m1 * x6 + m6 * x7 + m11 * x8 + m16 * x9 + m21 * x10;
593           x[6] -= m2 * x6 + m7 * x7 + m12 * x8 + m17 * x9 + m22 * x10;
594           x[7] -= m3 * x6 + m8 * x7 + m13 * x8 + m18 * x9 + m23 * x10;
595           x[8] -= m4 * x6 + m9 * x7 + m14 * x8 + m19 * x9 + m24 * x10;
596           x[9] -= m5 * x6 + m10 * x7 + m15 * x8 + m20 * x9 + m25 * x10;
597 
598           x[10] -= m1 * x11 + m6 * x12 + m11 * x13 + m16 * x14 + m21 * x15;
599           x[11] -= m2 * x11 + m7 * x12 + m12 * x13 + m17 * x14 + m22 * x15;
600           x[12] -= m3 * x11 + m8 * x12 + m13 * x13 + m18 * x14 + m23 * x15;
601           x[13] -= m4 * x11 + m9 * x12 + m14 * x13 + m19 * x14 + m24 * x15;
602           x[14] -= m5 * x11 + m10 * x12 + m15 * x13 + m20 * x14 + m25 * x15;
603 
604           x[15] -= m1 * x16 + m6 * x17 + m11 * x18 + m16 * x19 + m21 * x20;
605           x[16] -= m2 * x16 + m7 * x17 + m12 * x18 + m17 * x19 + m22 * x20;
606           x[17] -= m3 * x16 + m8 * x17 + m13 * x18 + m18 * x19 + m23 * x20;
607           x[18] -= m4 * x16 + m9 * x17 + m14 * x18 + m19 * x19 + m24 * x20;
608           x[19] -= m5 * x16 + m10 * x17 + m15 * x18 + m20 * x19 + m25 * x20;
609 
610           x[20] -= m1 * x21 + m6 * x22 + m11 * x23 + m16 * x24 + m21 * x25;
611           x[21] -= m2 * x21 + m7 * x22 + m12 * x23 + m17 * x24 + m22 * x25;
612           x[22] -= m3 * x21 + m8 * x22 + m13 * x23 + m18 * x24 + m23 * x25;
613           x[23] -= m4 * x21 + m9 * x22 + m14 * x23 + m19 * x24 + m24 * x25;
614           x[24] -= m5 * x21 + m10 * x22 + m15 * x23 + m20 * x24 + m25 * x25;
615           pv += 25;
616         }
617         PetscCall(PetscLogFlops(250.0 * nz + 225.0));
618       }
619       row = *ajtmp++;
620     }
621     /* finished row so stick it into b->a */
622     pv = ba + 25 * bi[i];
623     pj = bj + bi[i];
624     nz = bi[i + 1] - bi[i];
625     for (j = 0; j < nz; j++) {
626       x      = rtmp + 25 * pj[j];
627       pv[0]  = x[0];
628       pv[1]  = x[1];
629       pv[2]  = x[2];
630       pv[3]  = x[3];
631       pv[4]  = x[4];
632       pv[5]  = x[5];
633       pv[6]  = x[6];
634       pv[7]  = x[7];
635       pv[8]  = x[8];
636       pv[9]  = x[9];
637       pv[10] = x[10];
638       pv[11] = x[11];
639       pv[12] = x[12];
640       pv[13] = x[13];
641       pv[14] = x[14];
642       pv[15] = x[15];
643       pv[16] = x[16];
644       pv[17] = x[17];
645       pv[18] = x[18];
646       pv[19] = x[19];
647       pv[20] = x[20];
648       pv[21] = x[21];
649       pv[22] = x[22];
650       pv[23] = x[23];
651       pv[24] = x[24];
652       pv += 25;
653     }
654     /* invert diagonal block */
655     w = ba + 25 * diag_offset[i];
656     PetscCall(PetscKernel_A_gets_inverse_A_5(w, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
657     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
658   }
659 
660   PetscCall(PetscFree(rtmp));
661 
662   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering_inplace;
663   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering_inplace;
664   C->assembled           = PETSC_TRUE;
665 
666   PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * b->mbs)); /* from inverting diagonal blocks */
667   PetscFunctionReturn(PETSC_SUCCESS);
668 }
669 
670 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering(Mat B, Mat A, const MatFactorInfo *info)
671 {
672   Mat             C = B;
673   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
674   PetscInt        i, j, k, nz, nzL, row;
675   const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
676   const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
677   MatScalar      *rtmp, *pc, *mwork, *v, *vv, *pv, *aa = a->a, work[25];
678   PetscInt        flg, ipvt[5];
679   PetscReal       shift = info->shiftamount;
680   PetscBool       allowzeropivot, zeropivotdetected;
681 
682   PetscFunctionBegin;
683   allowzeropivot = PetscNot(A->erroriffailure);
684 
685   /* generate work space needed by the factorization */
686   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
687   PetscCall(PetscArrayzero(rtmp, bs2 * n));
688 
689   for (i = 0; i < n; i++) {
690     /* zero rtmp */
691     /* L part */
692     nz    = bi[i + 1] - bi[i];
693     bjtmp = bj + bi[i];
694     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));
695 
696     /* U part */
697     nz    = bdiag[i] - bdiag[i + 1];
698     bjtmp = bj + bdiag[i + 1] + 1;
699     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));
700 
701     /* load in initial (unfactored row) */
702     nz    = ai[i + 1] - ai[i];
703     ajtmp = aj + ai[i];
704     v     = aa + bs2 * ai[i];
705     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ajtmp[j], v + bs2 * j, bs2));
706 
707     /* elimination */
708     bjtmp = bj + bi[i];
709     nzL   = bi[i + 1] - bi[i];
710     for (k = 0; k < nzL; k++) {
711       row = bjtmp[k];
712       pc  = rtmp + bs2 * row;
713       for (flg = 0, j = 0; j < bs2; j++) {
714         if (pc[j] != 0.0) {
715           flg = 1;
716           break;
717         }
718       }
719       if (flg) {
720         pv = b->a + bs2 * bdiag[row];
721         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
722         PetscCall(PetscKernel_A_gets_A_times_B_5(pc, pv, mwork));
723 
724         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
725         pv = b->a + bs2 * (bdiag[row + 1] + 1);
726         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
727         for (j = 0; j < nz; j++) {
728           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
729           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
730           vv = rtmp + bs2 * pj[j];
731           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_5(vv, pc, pv));
732           pv += bs2;
733         }
734         PetscCall(PetscLogFlops(250.0 * nz + 225)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
735       }
736     }
737 
738     /* finished row so stick it into b->a */
739     /* L part */
740     pv = b->a + bs2 * bi[i];
741     pj = b->j + bi[i];
742     nz = bi[i + 1] - bi[i];
743     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
744 
745     /* Mark diagonal and invert diagonal for simpler triangular solves */
746     pv = b->a + bs2 * bdiag[i];
747     pj = b->j + bdiag[i];
748     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
749     PetscCall(PetscKernel_A_gets_inverse_A_5(pv, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
750     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
751 
752     /* U part */
753     pv = b->a + bs2 * (bdiag[i + 1] + 1);
754     pj = b->j + bdiag[i + 1] + 1;
755     nz = bdiag[i] - bdiag[i + 1] - 1;
756     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
757   }
758   PetscCall(PetscFree2(rtmp, mwork));
759 
760   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering;
761   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering;
762   C->assembled           = PETSC_TRUE;
763 
764   PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * n)); /* from inverting diagonal blocks */
765   PetscFunctionReturn(PETSC_SUCCESS);
766 }
767