xref: /petsc/src/mat/impls/baij/seq/baijfact9.c (revision d5b43468fb8780a8feea140ccd6fa3e6a50411cc)
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 {
14   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
15   IS               isrow = b->row, isicol = b->icol;
16   const PetscInt  *r, *ic, *bi = b->i, *bj = b->j, *ajtmpold, *ajtmp;
17   PetscInt         i, j, n = a->mbs, nz, row, idx, ipvt[5];
18   const PetscInt  *diag_offset = b->diag, *ai = a->i, *aj = a->j, *pj;
19   MatScalar       *w, *pv, *rtmp, *x, *pc;
20   const MatScalar *v, *aa = a->a;
21   MatScalar        p1, p2, p3, p4, m1, m2, m3, m4, m5, m6, m7, m8, m9, x1, x2, x3, x4;
22   MatScalar        p5, p6, p7, p8, p9, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16;
23   MatScalar        x17, x18, x19, x20, x21, x22, x23, x24, x25, p10, p11, p12, p13, p14;
24   MatScalar        p15, p16, p17, p18, p19, p20, p21, p22, p23, p24, p25, m10, m11, m12;
25   MatScalar        m13, m14, m15, m16, m17, m18, m19, m20, m21, m22, m23, m24, m25;
26   MatScalar       *ba    = b->a, work[25];
27   PetscReal        shift = info->shiftamount;
28   PetscBool        allowzeropivot, zeropivotdetected;
29 
30   PetscFunctionBegin;
31   allowzeropivot = PetscNot(A->erroriffailure);
32   PetscCall(ISGetIndices(isrow, &r));
33   PetscCall(ISGetIndices(isicol, &ic));
34   PetscCall(PetscMalloc1(25 * (n + 1), &rtmp));
35 
36 #define PETSC_USE_MEMZERO 1
37 #define PETSC_USE_MEMCPY  1
38 
39   for (i = 0; i < n; i++) {
40     nz    = bi[i + 1] - bi[i];
41     ajtmp = bj + bi[i];
42     for (j = 0; j < nz; j++) {
43 #if defined(PETSC_USE_MEMZERO)
44       PetscCall(PetscArrayzero(rtmp + 25 * ajtmp[j], 25));
45 #else
46       x    = rtmp + 25 * ajtmp[j];
47       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
48       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
49       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
50 #endif
51     }
52     /* load in initial (unfactored row) */
53     idx      = r[i];
54     nz       = ai[idx + 1] - ai[idx];
55     ajtmpold = aj + ai[idx];
56     v        = aa + 25 * ai[idx];
57     for (j = 0; j < nz; j++) {
58 #if defined(PETSC_USE_MEMCPY)
59       PetscCall(PetscArraycpy(rtmp + 25 * ic[ajtmpold[j]], v, 25));
60 #else
61       x                                                     = rtmp + 25 * ic[ajtmpold[j]];
62       x[0]                                                  = v[0];
63       x[1]                                                  = v[1];
64       x[2]                                                  = v[2];
65       x[3]                                                  = v[3];
66       x[4]                                                  = v[4];
67       x[5]                                                  = v[5];
68       x[6]                                                  = v[6];
69       x[7]                                                  = v[7];
70       x[8]                                                  = v[8];
71       x[9]                                                  = v[9];
72       x[10]                                                 = v[10];
73       x[11]                                                 = v[11];
74       x[12]                                                 = v[12];
75       x[13]                                                 = v[13];
76       x[14]                                                 = v[14];
77       x[15]                                                 = v[15];
78       x[16]                                                 = v[16];
79       x[17]                                                 = v[17];
80       x[18]                                                 = v[18];
81       x[19]                                                 = v[19];
82       x[20]                                                 = v[20];
83       x[21]                                                 = v[21];
84       x[22]                                                 = v[22];
85       x[23]                                                 = v[23];
86       x[24]                                                 = v[24];
87 #endif
88       v += 25;
89     }
90     row = *ajtmp++;
91     while (row < i) {
92       pc  = rtmp + 25 * row;
93       p1  = pc[0];
94       p2  = pc[1];
95       p3  = pc[2];
96       p4  = pc[3];
97       p5  = pc[4];
98       p6  = pc[5];
99       p7  = pc[6];
100       p8  = pc[7];
101       p9  = pc[8];
102       p10 = pc[9];
103       p11 = pc[10];
104       p12 = pc[11];
105       p13 = pc[12];
106       p14 = pc[13];
107       p15 = pc[14];
108       p16 = pc[15];
109       p17 = pc[16];
110       p18 = pc[17];
111       p19 = pc[18];
112       p20 = pc[19];
113       p21 = pc[20];
114       p22 = pc[21];
115       p23 = pc[22];
116       p24 = pc[23];
117       p25 = pc[24];
118       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) {
119         pv    = ba + 25 * diag_offset[row];
120         pj    = bj + diag_offset[row] + 1;
121         x1    = pv[0];
122         x2    = pv[1];
123         x3    = pv[2];
124         x4    = pv[3];
125         x5    = pv[4];
126         x6    = pv[5];
127         x7    = pv[6];
128         x8    = pv[7];
129         x9    = pv[8];
130         x10   = pv[9];
131         x11   = pv[10];
132         x12   = pv[11];
133         x13   = pv[12];
134         x14   = pv[13];
135         x15   = pv[14];
136         x16   = pv[15];
137         x17   = pv[16];
138         x18   = pv[17];
139         x19   = pv[18];
140         x20   = pv[19];
141         x21   = pv[20];
142         x22   = pv[21];
143         x23   = pv[22];
144         x24   = pv[23];
145         x25   = pv[24];
146         pc[0] = m1 = p1 * x1 + p6 * x2 + p11 * x3 + p16 * x4 + p21 * x5;
147         pc[1] = m2 = p2 * x1 + p7 * x2 + p12 * x3 + p17 * x4 + p22 * x5;
148         pc[2] = m3 = p3 * x1 + p8 * x2 + p13 * x3 + p18 * x4 + p23 * x5;
149         pc[3] = m4 = p4 * x1 + p9 * x2 + p14 * x3 + p19 * x4 + p24 * x5;
150         pc[4] = m5 = p5 * x1 + p10 * x2 + p15 * x3 + p20 * x4 + p25 * x5;
151 
152         pc[5] = m6 = p1 * x6 + p6 * x7 + p11 * x8 + p16 * x9 + p21 * x10;
153         pc[6] = m7 = p2 * x6 + p7 * x7 + p12 * x8 + p17 * x9 + p22 * x10;
154         pc[7] = m8 = p3 * x6 + p8 * x7 + p13 * x8 + p18 * x9 + p23 * x10;
155         pc[8] = m9 = p4 * x6 + p9 * x7 + p14 * x8 + p19 * x9 + p24 * x10;
156         pc[9] = m10 = p5 * x6 + p10 * x7 + p15 * x8 + p20 * x9 + p25 * x10;
157 
158         pc[10] = m11 = p1 * x11 + p6 * x12 + p11 * x13 + p16 * x14 + p21 * x15;
159         pc[11] = m12 = p2 * x11 + p7 * x12 + p12 * x13 + p17 * x14 + p22 * x15;
160         pc[12] = m13 = p3 * x11 + p8 * x12 + p13 * x13 + p18 * x14 + p23 * x15;
161         pc[13] = m14 = p4 * x11 + p9 * x12 + p14 * x13 + p19 * x14 + p24 * x15;
162         pc[14] = m15 = p5 * x11 + p10 * x12 + p15 * x13 + p20 * x14 + p25 * x15;
163 
164         pc[15] = m16 = p1 * x16 + p6 * x17 + p11 * x18 + p16 * x19 + p21 * x20;
165         pc[16] = m17 = p2 * x16 + p7 * x17 + p12 * x18 + p17 * x19 + p22 * x20;
166         pc[17] = m18 = p3 * x16 + p8 * x17 + p13 * x18 + p18 * x19 + p23 * x20;
167         pc[18] = m19 = p4 * x16 + p9 * x17 + p14 * x18 + p19 * x19 + p24 * x20;
168         pc[19] = m20 = p5 * x16 + p10 * x17 + p15 * x18 + p20 * x19 + p25 * x20;
169 
170         pc[20] = m21 = p1 * x21 + p6 * x22 + p11 * x23 + p16 * x24 + p21 * x25;
171         pc[21] = m22 = p2 * x21 + p7 * x22 + p12 * x23 + p17 * x24 + p22 * x25;
172         pc[22] = m23 = p3 * x21 + p8 * x22 + p13 * x23 + p18 * x24 + p23 * x25;
173         pc[23] = m24 = p4 * x21 + p9 * x22 + p14 * x23 + p19 * x24 + p24 * x25;
174         pc[24] = m25 = p5 * x21 + p10 * x22 + p15 * x23 + p20 * x24 + p25 * x25;
175 
176         nz = bi[row + 1] - diag_offset[row] - 1;
177         pv += 25;
178         for (j = 0; j < nz; j++) {
179           x1  = pv[0];
180           x2  = pv[1];
181           x3  = pv[2];
182           x4  = pv[3];
183           x5  = pv[4];
184           x6  = pv[5];
185           x7  = pv[6];
186           x8  = pv[7];
187           x9  = pv[8];
188           x10 = pv[9];
189           x11 = pv[10];
190           x12 = pv[11];
191           x13 = pv[12];
192           x14 = pv[13];
193           x15 = pv[14];
194           x16 = pv[15];
195           x17 = pv[16];
196           x18 = pv[17];
197           x19 = pv[18];
198           x20 = pv[19];
199           x21 = pv[20];
200           x22 = pv[21];
201           x23 = pv[22];
202           x24 = pv[23];
203           x25 = pv[24];
204           x   = rtmp + 25 * pj[j];
205           x[0] -= m1 * x1 + m6 * x2 + m11 * x3 + m16 * x4 + m21 * x5;
206           x[1] -= m2 * x1 + m7 * x2 + m12 * x3 + m17 * x4 + m22 * x5;
207           x[2] -= m3 * x1 + m8 * x2 + m13 * x3 + m18 * x4 + m23 * x5;
208           x[3] -= m4 * x1 + m9 * x2 + m14 * x3 + m19 * x4 + m24 * x5;
209           x[4] -= m5 * x1 + m10 * x2 + m15 * x3 + m20 * x4 + m25 * x5;
210 
211           x[5] -= m1 * x6 + m6 * x7 + m11 * x8 + m16 * x9 + m21 * x10;
212           x[6] -= m2 * x6 + m7 * x7 + m12 * x8 + m17 * x9 + m22 * x10;
213           x[7] -= m3 * x6 + m8 * x7 + m13 * x8 + m18 * x9 + m23 * x10;
214           x[8] -= m4 * x6 + m9 * x7 + m14 * x8 + m19 * x9 + m24 * x10;
215           x[9] -= m5 * x6 + m10 * x7 + m15 * x8 + m20 * x9 + m25 * x10;
216 
217           x[10] -= m1 * x11 + m6 * x12 + m11 * x13 + m16 * x14 + m21 * x15;
218           x[11] -= m2 * x11 + m7 * x12 + m12 * x13 + m17 * x14 + m22 * x15;
219           x[12] -= m3 * x11 + m8 * x12 + m13 * x13 + m18 * x14 + m23 * x15;
220           x[13] -= m4 * x11 + m9 * x12 + m14 * x13 + m19 * x14 + m24 * x15;
221           x[14] -= m5 * x11 + m10 * x12 + m15 * x13 + m20 * x14 + m25 * x15;
222 
223           x[15] -= m1 * x16 + m6 * x17 + m11 * x18 + m16 * x19 + m21 * x20;
224           x[16] -= m2 * x16 + m7 * x17 + m12 * x18 + m17 * x19 + m22 * x20;
225           x[17] -= m3 * x16 + m8 * x17 + m13 * x18 + m18 * x19 + m23 * x20;
226           x[18] -= m4 * x16 + m9 * x17 + m14 * x18 + m19 * x19 + m24 * x20;
227           x[19] -= m5 * x16 + m10 * x17 + m15 * x18 + m20 * x19 + m25 * x20;
228 
229           x[20] -= m1 * x21 + m6 * x22 + m11 * x23 + m16 * x24 + m21 * x25;
230           x[21] -= m2 * x21 + m7 * x22 + m12 * x23 + m17 * x24 + m22 * x25;
231           x[22] -= m3 * x21 + m8 * x22 + m13 * x23 + m18 * x24 + m23 * x25;
232           x[23] -= m4 * x21 + m9 * x22 + m14 * x23 + m19 * x24 + m24 * x25;
233           x[24] -= m5 * x21 + m10 * x22 + m15 * x23 + m20 * x24 + m25 * x25;
234 
235           pv += 25;
236         }
237         PetscCall(PetscLogFlops(250.0 * nz + 225.0));
238       }
239       row = *ajtmp++;
240     }
241     /* finished row so stick it into b->a */
242     pv = ba + 25 * bi[i];
243     pj = bj + bi[i];
244     nz = bi[i + 1] - bi[i];
245     for (j = 0; j < nz; j++) {
246 #if defined(PETSC_USE_MEMCPY)
247       PetscCall(PetscArraycpy(pv, rtmp + 25 * pj[j], 25));
248 #else
249       x                                                     = rtmp + 25 * pj[j];
250       pv[0]                                                 = x[0];
251       pv[1]                                                 = x[1];
252       pv[2]                                                 = x[2];
253       pv[3]                                                 = x[3];
254       pv[4]                                                 = x[4];
255       pv[5]                                                 = x[5];
256       pv[6]                                                 = x[6];
257       pv[7]                                                 = x[7];
258       pv[8]                                                 = x[8];
259       pv[9]                                                 = x[9];
260       pv[10]                                                = x[10];
261       pv[11]                                                = x[11];
262       pv[12]                                                = x[12];
263       pv[13]                                                = x[13];
264       pv[14]                                                = x[14];
265       pv[15]                                                = x[15];
266       pv[16]                                                = x[16];
267       pv[17]                                                = x[17];
268       pv[18]                                                = x[18];
269       pv[19]                                                = x[19];
270       pv[20]                                                = x[20];
271       pv[21]                                                = x[21];
272       pv[22]                                                = x[22];
273       pv[23]                                                = x[23];
274       pv[24]                                                = x[24];
275 #endif
276       pv += 25;
277     }
278     /* invert diagonal block */
279     w = ba + 25 * diag_offset[i];
280     PetscCall(PetscKernel_A_gets_inverse_A_5(w, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
281     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
282   }
283 
284   PetscCall(PetscFree(rtmp));
285   PetscCall(ISRestoreIndices(isicol, &ic));
286   PetscCall(ISRestoreIndices(isrow, &r));
287 
288   C->ops->solve          = MatSolve_SeqBAIJ_5_inplace;
289   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_inplace;
290   C->assembled           = PETSC_TRUE;
291 
292   PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * b->mbs)); /* from inverting diagonal blocks */
293   PetscFunctionReturn(0);
294 }
295 
296 /* MatLUFactorNumeric_SeqBAIJ_5 -
297      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
298        PetscKernel_A_gets_A_times_B()
299        PetscKernel_A_gets_A_minus_B_times_C()
300        PetscKernel_A_gets_inverse_A()
301 */
302 
303 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5(Mat B, Mat A, const MatFactorInfo *info)
304 {
305   Mat             C = B;
306   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
307   IS              isrow = b->row, isicol = b->icol;
308   const PetscInt *r, *ic;
309   PetscInt        i, j, k, nz, nzL, row;
310   const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
311   const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
312   MatScalar      *rtmp, *pc, *mwork, *v, *pv, *aa = a->a, work[25];
313   PetscInt        flg, ipvt[5];
314   PetscReal       shift = info->shiftamount;
315   PetscBool       allowzeropivot, zeropivotdetected;
316 
317   PetscFunctionBegin;
318   allowzeropivot = PetscNot(A->erroriffailure);
319   PetscCall(ISGetIndices(isrow, &r));
320   PetscCall(ISGetIndices(isicol, &ic));
321 
322   /* generate work space needed by the factorization */
323   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
324   PetscCall(PetscArrayzero(rtmp, bs2 * n));
325 
326   for (i = 0; i < n; i++) {
327     /* zero rtmp */
328     /* L part */
329     nz    = bi[i + 1] - bi[i];
330     bjtmp = bj + bi[i];
331     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));
332 
333     /* U part */
334     nz    = bdiag[i] - bdiag[i + 1];
335     bjtmp = bj + bdiag[i + 1] + 1;
336     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));
337 
338     /* load in initial (unfactored row) */
339     nz    = ai[r[i] + 1] - ai[r[i]];
340     ajtmp = aj + ai[r[i]];
341     v     = aa + bs2 * ai[r[i]];
342     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ic[ajtmp[j]], v + bs2 * j, bs2));
343 
344     /* elimination */
345     bjtmp = bj + bi[i];
346     nzL   = bi[i + 1] - bi[i];
347     for (k = 0; k < nzL; k++) {
348       row = bjtmp[k];
349       pc  = rtmp + bs2 * row;
350       for (flg = 0, j = 0; j < bs2; j++) {
351         if (pc[j] != 0.0) {
352           flg = 1;
353           break;
354         }
355       }
356       if (flg) {
357         pv = b->a + bs2 * bdiag[row];
358         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
359         PetscCall(PetscKernel_A_gets_A_times_B_5(pc, pv, mwork));
360 
361         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
362         pv = b->a + bs2 * (bdiag[row + 1] + 1);
363         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
364         for (j = 0; j < nz; j++) {
365           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
366           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
367           v = rtmp + bs2 * pj[j];
368           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_5(v, pc, pv));
369           pv += bs2;
370         }
371         PetscCall(PetscLogFlops(250.0 * nz + 225)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
372       }
373     }
374 
375     /* finished row so stick it into b->a */
376     /* L part */
377     pv = b->a + bs2 * bi[i];
378     pj = b->j + bi[i];
379     nz = bi[i + 1] - bi[i];
380     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
381 
382     /* Mark diagonal and invert diagonal for simpler triangular solves */
383     pv = b->a + bs2 * bdiag[i];
384     pj = b->j + bdiag[i];
385     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
386     PetscCall(PetscKernel_A_gets_inverse_A_5(pv, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
387     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
388 
389     /* U part */
390     pv = b->a + bs2 * (bdiag[i + 1] + 1);
391     pj = b->j + bdiag[i + 1] + 1;
392     nz = bdiag[i] - bdiag[i + 1] - 1;
393     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
394   }
395 
396   PetscCall(PetscFree2(rtmp, mwork));
397   PetscCall(ISRestoreIndices(isicol, &ic));
398   PetscCall(ISRestoreIndices(isrow, &r));
399 
400   C->ops->solve          = MatSolve_SeqBAIJ_5;
401   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5;
402   C->assembled           = PETSC_TRUE;
403 
404   PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * n)); /* from inverting diagonal blocks */
405   PetscFunctionReturn(0);
406 }
407 
408 /*
409       Version for when blocks are 5 by 5 Using natural ordering
410 */
411 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering_inplace(Mat C, Mat A, const MatFactorInfo *info)
412 {
413   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
414   PetscInt     i, j, n = a->mbs, *bi = b->i, *bj = b->j, ipvt[5];
415   PetscInt    *ajtmpold, *ajtmp, nz, row;
416   PetscInt    *diag_offset = b->diag, *ai = a->i, *aj = a->j, *pj;
417   MatScalar   *pv, *v, *rtmp, *pc, *w, *x;
418   MatScalar    x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15;
419   MatScalar    x16, x17, x18, x19, x20, x21, x22, x23, x24, x25;
420   MatScalar    p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12, p13, p14, p15;
421   MatScalar    p16, p17, p18, p19, p20, p21, p22, p23, p24, p25;
422   MatScalar    m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12, m13, m14, m15;
423   MatScalar    m16, m17, m18, m19, m20, m21, m22, m23, m24, m25;
424   MatScalar   *ba = b->a, *aa = a->a, work[25];
425   PetscReal    shift = info->shiftamount;
426   PetscBool    allowzeropivot, zeropivotdetected;
427 
428   PetscFunctionBegin;
429   allowzeropivot = PetscNot(A->erroriffailure);
430   PetscCall(PetscMalloc1(25 * (n + 1), &rtmp));
431   for (i = 0; i < n; i++) {
432     nz    = bi[i + 1] - bi[i];
433     ajtmp = bj + bi[i];
434     for (j = 0; j < nz; j++) {
435       x    = rtmp + 25 * ajtmp[j];
436       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
437       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
438       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
439     }
440     /* load in initial (unfactored row) */
441     nz       = ai[i + 1] - ai[i];
442     ajtmpold = aj + ai[i];
443     v        = aa + 25 * ai[i];
444     for (j = 0; j < nz; j++) {
445       x     = rtmp + 25 * ajtmpold[j];
446       x[0]  = v[0];
447       x[1]  = v[1];
448       x[2]  = v[2];
449       x[3]  = v[3];
450       x[4]  = v[4];
451       x[5]  = v[5];
452       x[6]  = v[6];
453       x[7]  = v[7];
454       x[8]  = v[8];
455       x[9]  = v[9];
456       x[10] = v[10];
457       x[11] = v[11];
458       x[12] = v[12];
459       x[13] = v[13];
460       x[14] = v[14];
461       x[15] = v[15];
462       x[16] = v[16];
463       x[17] = v[17];
464       x[18] = v[18];
465       x[19] = v[19];
466       x[20] = v[20];
467       x[21] = v[21];
468       x[22] = v[22];
469       x[23] = v[23];
470       x[24] = v[24];
471       v += 25;
472     }
473     row = *ajtmp++;
474     while (row < i) {
475       pc  = rtmp + 25 * row;
476       p1  = pc[0];
477       p2  = pc[1];
478       p3  = pc[2];
479       p4  = pc[3];
480       p5  = pc[4];
481       p6  = pc[5];
482       p7  = pc[6];
483       p8  = pc[7];
484       p9  = pc[8];
485       p10 = pc[9];
486       p11 = pc[10];
487       p12 = pc[11];
488       p13 = pc[12];
489       p14 = pc[13];
490       p15 = pc[14];
491       p16 = pc[15];
492       p17 = pc[16];
493       p18 = pc[17];
494       p19 = pc[18];
495       p20 = pc[19];
496       p21 = pc[20];
497       p22 = pc[21];
498       p23 = pc[22];
499       p24 = pc[23];
500       p25 = pc[24];
501       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) {
502         pv    = ba + 25 * diag_offset[row];
503         pj    = bj + diag_offset[row] + 1;
504         x1    = pv[0];
505         x2    = pv[1];
506         x3    = pv[2];
507         x4    = pv[3];
508         x5    = pv[4];
509         x6    = pv[5];
510         x7    = pv[6];
511         x8    = pv[7];
512         x9    = pv[8];
513         x10   = pv[9];
514         x11   = pv[10];
515         x12   = pv[11];
516         x13   = pv[12];
517         x14   = pv[13];
518         x15   = pv[14];
519         x16   = pv[15];
520         x17   = pv[16];
521         x18   = pv[17];
522         x19   = pv[18];
523         x20   = pv[19];
524         x21   = pv[20];
525         x22   = pv[21];
526         x23   = pv[22];
527         x24   = pv[23];
528         x25   = pv[24];
529         pc[0] = m1 = p1 * x1 + p6 * x2 + p11 * x3 + p16 * x4 + p21 * x5;
530         pc[1] = m2 = p2 * x1 + p7 * x2 + p12 * x3 + p17 * x4 + p22 * x5;
531         pc[2] = m3 = p3 * x1 + p8 * x2 + p13 * x3 + p18 * x4 + p23 * x5;
532         pc[3] = m4 = p4 * x1 + p9 * x2 + p14 * x3 + p19 * x4 + p24 * x5;
533         pc[4] = m5 = p5 * x1 + p10 * x2 + p15 * x3 + p20 * x4 + p25 * x5;
534 
535         pc[5] = m6 = p1 * x6 + p6 * x7 + p11 * x8 + p16 * x9 + p21 * x10;
536         pc[6] = m7 = p2 * x6 + p7 * x7 + p12 * x8 + p17 * x9 + p22 * x10;
537         pc[7] = m8 = p3 * x6 + p8 * x7 + p13 * x8 + p18 * x9 + p23 * x10;
538         pc[8] = m9 = p4 * x6 + p9 * x7 + p14 * x8 + p19 * x9 + p24 * x10;
539         pc[9] = m10 = p5 * x6 + p10 * x7 + p15 * x8 + p20 * x9 + p25 * x10;
540 
541         pc[10] = m11 = p1 * x11 + p6 * x12 + p11 * x13 + p16 * x14 + p21 * x15;
542         pc[11] = m12 = p2 * x11 + p7 * x12 + p12 * x13 + p17 * x14 + p22 * x15;
543         pc[12] = m13 = p3 * x11 + p8 * x12 + p13 * x13 + p18 * x14 + p23 * x15;
544         pc[13] = m14 = p4 * x11 + p9 * x12 + p14 * x13 + p19 * x14 + p24 * x15;
545         pc[14] = m15 = p5 * x11 + p10 * x12 + p15 * x13 + p20 * x14 + p25 * x15;
546 
547         pc[15] = m16 = p1 * x16 + p6 * x17 + p11 * x18 + p16 * x19 + p21 * x20;
548         pc[16] = m17 = p2 * x16 + p7 * x17 + p12 * x18 + p17 * x19 + p22 * x20;
549         pc[17] = m18 = p3 * x16 + p8 * x17 + p13 * x18 + p18 * x19 + p23 * x20;
550         pc[18] = m19 = p4 * x16 + p9 * x17 + p14 * x18 + p19 * x19 + p24 * x20;
551         pc[19] = m20 = p5 * x16 + p10 * x17 + p15 * x18 + p20 * x19 + p25 * x20;
552 
553         pc[20] = m21 = p1 * x21 + p6 * x22 + p11 * x23 + p16 * x24 + p21 * x25;
554         pc[21] = m22 = p2 * x21 + p7 * x22 + p12 * x23 + p17 * x24 + p22 * x25;
555         pc[22] = m23 = p3 * x21 + p8 * x22 + p13 * x23 + p18 * x24 + p23 * x25;
556         pc[23] = m24 = p4 * x21 + p9 * x22 + p14 * x23 + p19 * x24 + p24 * x25;
557         pc[24] = m25 = p5 * x21 + p10 * x22 + p15 * x23 + p20 * x24 + p25 * x25;
558 
559         nz = bi[row + 1] - diag_offset[row] - 1;
560         pv += 25;
561         for (j = 0; j < nz; j++) {
562           x1  = pv[0];
563           x2  = pv[1];
564           x3  = pv[2];
565           x4  = pv[3];
566           x5  = pv[4];
567           x6  = pv[5];
568           x7  = pv[6];
569           x8  = pv[7];
570           x9  = pv[8];
571           x10 = pv[9];
572           x11 = pv[10];
573           x12 = pv[11];
574           x13 = pv[12];
575           x14 = pv[13];
576           x15 = pv[14];
577           x16 = pv[15];
578           x17 = pv[16];
579           x18 = pv[17];
580           x19 = pv[18];
581           x20 = pv[19];
582           x21 = pv[20];
583           x22 = pv[21];
584           x23 = pv[22];
585           x24 = pv[23];
586           x25 = pv[24];
587           x   = rtmp + 25 * pj[j];
588           x[0] -= m1 * x1 + m6 * x2 + m11 * x3 + m16 * x4 + m21 * x5;
589           x[1] -= m2 * x1 + m7 * x2 + m12 * x3 + m17 * x4 + m22 * x5;
590           x[2] -= m3 * x1 + m8 * x2 + m13 * x3 + m18 * x4 + m23 * x5;
591           x[3] -= m4 * x1 + m9 * x2 + m14 * x3 + m19 * x4 + m24 * x5;
592           x[4] -= m5 * x1 + m10 * x2 + m15 * x3 + m20 * x4 + m25 * x5;
593 
594           x[5] -= m1 * x6 + m6 * x7 + m11 * x8 + m16 * x9 + m21 * x10;
595           x[6] -= m2 * x6 + m7 * x7 + m12 * x8 + m17 * x9 + m22 * x10;
596           x[7] -= m3 * x6 + m8 * x7 + m13 * x8 + m18 * x9 + m23 * x10;
597           x[8] -= m4 * x6 + m9 * x7 + m14 * x8 + m19 * x9 + m24 * x10;
598           x[9] -= m5 * x6 + m10 * x7 + m15 * x8 + m20 * x9 + m25 * x10;
599 
600           x[10] -= m1 * x11 + m6 * x12 + m11 * x13 + m16 * x14 + m21 * x15;
601           x[11] -= m2 * x11 + m7 * x12 + m12 * x13 + m17 * x14 + m22 * x15;
602           x[12] -= m3 * x11 + m8 * x12 + m13 * x13 + m18 * x14 + m23 * x15;
603           x[13] -= m4 * x11 + m9 * x12 + m14 * x13 + m19 * x14 + m24 * x15;
604           x[14] -= m5 * x11 + m10 * x12 + m15 * x13 + m20 * x14 + m25 * x15;
605 
606           x[15] -= m1 * x16 + m6 * x17 + m11 * x18 + m16 * x19 + m21 * x20;
607           x[16] -= m2 * x16 + m7 * x17 + m12 * x18 + m17 * x19 + m22 * x20;
608           x[17] -= m3 * x16 + m8 * x17 + m13 * x18 + m18 * x19 + m23 * x20;
609           x[18] -= m4 * x16 + m9 * x17 + m14 * x18 + m19 * x19 + m24 * x20;
610           x[19] -= m5 * x16 + m10 * x17 + m15 * x18 + m20 * x19 + m25 * x20;
611 
612           x[20] -= m1 * x21 + m6 * x22 + m11 * x23 + m16 * x24 + m21 * x25;
613           x[21] -= m2 * x21 + m7 * x22 + m12 * x23 + m17 * x24 + m22 * x25;
614           x[22] -= m3 * x21 + m8 * x22 + m13 * x23 + m18 * x24 + m23 * x25;
615           x[23] -= m4 * x21 + m9 * x22 + m14 * x23 + m19 * x24 + m24 * x25;
616           x[24] -= m5 * x21 + m10 * x22 + m15 * x23 + m20 * x24 + m25 * x25;
617           pv += 25;
618         }
619         PetscCall(PetscLogFlops(250.0 * nz + 225.0));
620       }
621       row = *ajtmp++;
622     }
623     /* finished row so stick it into b->a */
624     pv = ba + 25 * bi[i];
625     pj = bj + bi[i];
626     nz = bi[i + 1] - bi[i];
627     for (j = 0; j < nz; j++) {
628       x      = rtmp + 25 * pj[j];
629       pv[0]  = x[0];
630       pv[1]  = x[1];
631       pv[2]  = x[2];
632       pv[3]  = x[3];
633       pv[4]  = x[4];
634       pv[5]  = x[5];
635       pv[6]  = x[6];
636       pv[7]  = x[7];
637       pv[8]  = x[8];
638       pv[9]  = x[9];
639       pv[10] = x[10];
640       pv[11] = x[11];
641       pv[12] = x[12];
642       pv[13] = x[13];
643       pv[14] = x[14];
644       pv[15] = x[15];
645       pv[16] = x[16];
646       pv[17] = x[17];
647       pv[18] = x[18];
648       pv[19] = x[19];
649       pv[20] = x[20];
650       pv[21] = x[21];
651       pv[22] = x[22];
652       pv[23] = x[23];
653       pv[24] = x[24];
654       pv += 25;
655     }
656     /* invert diagonal block */
657     w = ba + 25 * diag_offset[i];
658     PetscCall(PetscKernel_A_gets_inverse_A_5(w, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
659     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
660   }
661 
662   PetscCall(PetscFree(rtmp));
663 
664   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering_inplace;
665   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering_inplace;
666   C->assembled           = PETSC_TRUE;
667 
668   PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * b->mbs)); /* from inverting diagonal blocks */
669   PetscFunctionReturn(0);
670 }
671 
672 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering(Mat B, Mat A, const MatFactorInfo *info)
673 {
674   Mat             C = B;
675   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
676   PetscInt        i, j, k, nz, nzL, row;
677   const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
678   const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
679   MatScalar      *rtmp, *pc, *mwork, *v, *vv, *pv, *aa = a->a, work[25];
680   PetscInt        flg, ipvt[5];
681   PetscReal       shift = info->shiftamount;
682   PetscBool       allowzeropivot, zeropivotdetected;
683 
684   PetscFunctionBegin;
685   allowzeropivot = PetscNot(A->erroriffailure);
686 
687   /* generate work space needed by the factorization */
688   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
689   PetscCall(PetscArrayzero(rtmp, bs2 * n));
690 
691   for (i = 0; i < n; i++) {
692     /* zero rtmp */
693     /* L part */
694     nz    = bi[i + 1] - bi[i];
695     bjtmp = bj + bi[i];
696     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));
697 
698     /* U part */
699     nz    = bdiag[i] - bdiag[i + 1];
700     bjtmp = bj + bdiag[i + 1] + 1;
701     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));
702 
703     /* load in initial (unfactored row) */
704     nz    = ai[i + 1] - ai[i];
705     ajtmp = aj + ai[i];
706     v     = aa + bs2 * ai[i];
707     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ajtmp[j], v + bs2 * j, bs2));
708 
709     /* elimination */
710     bjtmp = bj + bi[i];
711     nzL   = bi[i + 1] - bi[i];
712     for (k = 0; k < nzL; k++) {
713       row = bjtmp[k];
714       pc  = rtmp + bs2 * row;
715       for (flg = 0, j = 0; j < bs2; j++) {
716         if (pc[j] != 0.0) {
717           flg = 1;
718           break;
719         }
720       }
721       if (flg) {
722         pv = b->a + bs2 * bdiag[row];
723         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
724         PetscCall(PetscKernel_A_gets_A_times_B_5(pc, pv, mwork));
725 
726         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
727         pv = b->a + bs2 * (bdiag[row + 1] + 1);
728         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
729         for (j = 0; j < nz; j++) {
730           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
731           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
732           vv = rtmp + bs2 * pj[j];
733           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_5(vv, pc, pv));
734           pv += bs2;
735         }
736         PetscCall(PetscLogFlops(250.0 * nz + 225)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
737       }
738     }
739 
740     /* finished row so stick it into b->a */
741     /* L part */
742     pv = b->a + bs2 * bi[i];
743     pj = b->j + bi[i];
744     nz = bi[i + 1] - bi[i];
745     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
746 
747     /* Mark diagonal and invert diagonal for simpler triangular solves */
748     pv = b->a + bs2 * bdiag[i];
749     pj = b->j + bdiag[i];
750     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
751     PetscCall(PetscKernel_A_gets_inverse_A_5(pv, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
752     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
753 
754     /* U part */
755     pv = b->a + bs2 * (bdiag[i + 1] + 1);
756     pj = b->j + bdiag[i + 1] + 1;
757     nz = bdiag[i] - bdiag[i + 1] - 1;
758     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
759   }
760   PetscCall(PetscFree2(rtmp, mwork));
761 
762   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering;
763   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering;
764   C->assembled           = PETSC_TRUE;
765 
766   PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * n)); /* from inverting diagonal blocks */
767   PetscFunctionReturn(0);
768 }
769