Actual source code: baijfact5.c


  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:       Version for when blocks are 7 by 7
  9: */
 10: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_7_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, *ajtmp, *diag_offset = b->diag, *ai = a->i, *aj = a->j, *pj, *ajtmpold;
 15:   PetscInt        i, j, n = a->mbs, nz, row, idx;
 16:   MatScalar      *pv, *v, *rtmp, *pc, *w, *x;
 17:   MatScalar       p1, p2, p3, p4, m1, m2, m3, m4, m5, m6, m7, m8, m9, x1, x2, x3, x4;
 18:   MatScalar       p5, p6, p7, p8, p9, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16;
 19:   MatScalar       x17, x18, x19, x20, x21, x22, x23, x24, x25, p10, p11, p12, p13, p14;
 20:   MatScalar       p15, p16, p17, p18, p19, p20, p21, p22, p23, p24, p25, m10, m11, m12;
 21:   MatScalar       m13, m14, m15, m16, m17, m18, m19, m20, m21, m22, m23, m24, m25;
 22:   MatScalar       p26, p27, p28, p29, p30, p31, p32, p33, p34, p35, p36;
 23:   MatScalar       p37, p38, p39, p40, p41, p42, p43, p44, p45, p46, p47, p48, p49;
 24:   MatScalar       x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36;
 25:   MatScalar       x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49;
 26:   MatScalar       m26, m27, m28, m29, m30, m31, m32, m33, m34, m35, m36;
 27:   MatScalar       m37, m38, m39, m40, m41, m42, m43, m44, m45, m46, m47, m48, m49;
 28:   MatScalar      *ba = b->a, *aa = a->a;
 29:   PetscReal       shift = info->shiftamount;
 30:   PetscBool       allowzeropivot, zeropivotdetected;

 32:   PetscFunctionBegin;
 33:   allowzeropivot = PetscNot(A->erroriffailure);
 34:   PetscCall(ISGetIndices(isrow, &r));
 35:   PetscCall(ISGetIndices(isicol, &ic));
 36:   PetscCall(PetscMalloc1(49 * (n + 1), &rtmp));

 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:       x    = rtmp + 49 * ajtmp[j];
 43:       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
 44:       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
 45:       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0;
 46:       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0;
 47:       x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0;
 48:       x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0;
 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 + 49 * ai[idx];
 55:     for (j = 0; j < nz; j++) {
 56:       x     = rtmp + 49 * ic[ajtmpold[j]];
 57:       x[0]  = v[0];
 58:       x[1]  = v[1];
 59:       x[2]  = v[2];
 60:       x[3]  = v[3];
 61:       x[4]  = v[4];
 62:       x[5]  = v[5];
 63:       x[6]  = v[6];
 64:       x[7]  = v[7];
 65:       x[8]  = v[8];
 66:       x[9]  = v[9];
 67:       x[10] = v[10];
 68:       x[11] = v[11];
 69:       x[12] = v[12];
 70:       x[13] = v[13];
 71:       x[14] = v[14];
 72:       x[15] = v[15];
 73:       x[16] = v[16];
 74:       x[17] = v[17];
 75:       x[18] = v[18];
 76:       x[19] = v[19];
 77:       x[20] = v[20];
 78:       x[21] = v[21];
 79:       x[22] = v[22];
 80:       x[23] = v[23];
 81:       x[24] = v[24];
 82:       x[25] = v[25];
 83:       x[26] = v[26];
 84:       x[27] = v[27];
 85:       x[28] = v[28];
 86:       x[29] = v[29];
 87:       x[30] = v[30];
 88:       x[31] = v[31];
 89:       x[32] = v[32];
 90:       x[33] = v[33];
 91:       x[34] = v[34];
 92:       x[35] = v[35];
 93:       x[36] = v[36];
 94:       x[37] = v[37];
 95:       x[38] = v[38];
 96:       x[39] = v[39];
 97:       x[40] = v[40];
 98:       x[41] = v[41];
 99:       x[42] = v[42];
100:       x[43] = v[43];
101:       x[44] = v[44];
102:       x[45] = v[45];
103:       x[46] = v[46];
104:       x[47] = v[47];
105:       x[48] = v[48];
106:       v += 49;
107:     }
108:     row = *ajtmp++;
109:     while (row < i) {
110:       pc  = rtmp + 49 * row;
111:       p1  = pc[0];
112:       p2  = pc[1];
113:       p3  = pc[2];
114:       p4  = pc[3];
115:       p5  = pc[4];
116:       p6  = pc[5];
117:       p7  = pc[6];
118:       p8  = pc[7];
119:       p9  = pc[8];
120:       p10 = pc[9];
121:       p11 = pc[10];
122:       p12 = pc[11];
123:       p13 = pc[12];
124:       p14 = pc[13];
125:       p15 = pc[14];
126:       p16 = pc[15];
127:       p17 = pc[16];
128:       p18 = pc[17];
129:       p19 = pc[18];
130:       p20 = pc[19];
131:       p21 = pc[20];
132:       p22 = pc[21];
133:       p23 = pc[22];
134:       p24 = pc[23];
135:       p25 = pc[24];
136:       p26 = pc[25];
137:       p27 = pc[26];
138:       p28 = pc[27];
139:       p29 = pc[28];
140:       p30 = pc[29];
141:       p31 = pc[30];
142:       p32 = pc[31];
143:       p33 = pc[32];
144:       p34 = pc[33];
145:       p35 = pc[34];
146:       p36 = pc[35];
147:       p37 = pc[36];
148:       p38 = pc[37];
149:       p39 = pc[38];
150:       p40 = pc[39];
151:       p41 = pc[40];
152:       p42 = pc[41];
153:       p43 = pc[42];
154:       p44 = pc[43];
155:       p45 = pc[44];
156:       p46 = pc[45];
157:       p47 = pc[46];
158:       p48 = pc[47];
159:       p49 = pc[48];
160:       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 || p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 || p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 || p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 || p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 || p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 || p49 != 0.0) {
161:         pv    = ba + 49 * diag_offset[row];
162:         pj    = bj + diag_offset[row] + 1;
163:         x1    = pv[0];
164:         x2    = pv[1];
165:         x3    = pv[2];
166:         x4    = pv[3];
167:         x5    = pv[4];
168:         x6    = pv[5];
169:         x7    = pv[6];
170:         x8    = pv[7];
171:         x9    = pv[8];
172:         x10   = pv[9];
173:         x11   = pv[10];
174:         x12   = pv[11];
175:         x13   = pv[12];
176:         x14   = pv[13];
177:         x15   = pv[14];
178:         x16   = pv[15];
179:         x17   = pv[16];
180:         x18   = pv[17];
181:         x19   = pv[18];
182:         x20   = pv[19];
183:         x21   = pv[20];
184:         x22   = pv[21];
185:         x23   = pv[22];
186:         x24   = pv[23];
187:         x25   = pv[24];
188:         x26   = pv[25];
189:         x27   = pv[26];
190:         x28   = pv[27];
191:         x29   = pv[28];
192:         x30   = pv[29];
193:         x31   = pv[30];
194:         x32   = pv[31];
195:         x33   = pv[32];
196:         x34   = pv[33];
197:         x35   = pv[34];
198:         x36   = pv[35];
199:         x37   = pv[36];
200:         x38   = pv[37];
201:         x39   = pv[38];
202:         x40   = pv[39];
203:         x41   = pv[40];
204:         x42   = pv[41];
205:         x43   = pv[42];
206:         x44   = pv[43];
207:         x45   = pv[44];
208:         x46   = pv[45];
209:         x47   = pv[46];
210:         x48   = pv[47];
211:         x49   = pv[48];
212:         pc[0] = m1 = p1 * x1 + p8 * x2 + p15 * x3 + p22 * x4 + p29 * x5 + p36 * x6 + p43 * x7;
213:         pc[1] = m2 = p2 * x1 + p9 * x2 + p16 * x3 + p23 * x4 + p30 * x5 + p37 * x6 + p44 * x7;
214:         pc[2] = m3 = p3 * x1 + p10 * x2 + p17 * x3 + p24 * x4 + p31 * x5 + p38 * x6 + p45 * x7;
215:         pc[3] = m4 = p4 * x1 + p11 * x2 + p18 * x3 + p25 * x4 + p32 * x5 + p39 * x6 + p46 * x7;
216:         pc[4] = m5 = p5 * x1 + p12 * x2 + p19 * x3 + p26 * x4 + p33 * x5 + p40 * x6 + p47 * x7;
217:         pc[5] = m6 = p6 * x1 + p13 * x2 + p20 * x3 + p27 * x4 + p34 * x5 + p41 * x6 + p48 * x7;
218:         pc[6] = m7 = p7 * x1 + p14 * x2 + p21 * x3 + p28 * x4 + p35 * x5 + p42 * x6 + p49 * x7;

220:         pc[7] = m8 = p1 * x8 + p8 * x9 + p15 * x10 + p22 * x11 + p29 * x12 + p36 * x13 + p43 * x14;
221:         pc[8] = m9 = p2 * x8 + p9 * x9 + p16 * x10 + p23 * x11 + p30 * x12 + p37 * x13 + p44 * x14;
222:         pc[9] = m10 = p3 * x8 + p10 * x9 + p17 * x10 + p24 * x11 + p31 * x12 + p38 * x13 + p45 * x14;
223:         pc[10] = m11 = p4 * x8 + p11 * x9 + p18 * x10 + p25 * x11 + p32 * x12 + p39 * x13 + p46 * x14;
224:         pc[11] = m12 = p5 * x8 + p12 * x9 + p19 * x10 + p26 * x11 + p33 * x12 + p40 * x13 + p47 * x14;
225:         pc[12] = m13 = p6 * x8 + p13 * x9 + p20 * x10 + p27 * x11 + p34 * x12 + p41 * x13 + p48 * x14;
226:         pc[13] = m14 = p7 * x8 + p14 * x9 + p21 * x10 + p28 * x11 + p35 * x12 + p42 * x13 + p49 * x14;

228:         pc[14] = m15 = p1 * x15 + p8 * x16 + p15 * x17 + p22 * x18 + p29 * x19 + p36 * x20 + p43 * x21;
229:         pc[15] = m16 = p2 * x15 + p9 * x16 + p16 * x17 + p23 * x18 + p30 * x19 + p37 * x20 + p44 * x21;
230:         pc[16] = m17 = p3 * x15 + p10 * x16 + p17 * x17 + p24 * x18 + p31 * x19 + p38 * x20 + p45 * x21;
231:         pc[17] = m18 = p4 * x15 + p11 * x16 + p18 * x17 + p25 * x18 + p32 * x19 + p39 * x20 + p46 * x21;
232:         pc[18] = m19 = p5 * x15 + p12 * x16 + p19 * x17 + p26 * x18 + p33 * x19 + p40 * x20 + p47 * x21;
233:         pc[19] = m20 = p6 * x15 + p13 * x16 + p20 * x17 + p27 * x18 + p34 * x19 + p41 * x20 + p48 * x21;
234:         pc[20] = m21 = p7 * x15 + p14 * x16 + p21 * x17 + p28 * x18 + p35 * x19 + p42 * x20 + p49 * x21;

236:         pc[21] = m22 = p1 * x22 + p8 * x23 + p15 * x24 + p22 * x25 + p29 * x26 + p36 * x27 + p43 * x28;
237:         pc[22] = m23 = p2 * x22 + p9 * x23 + p16 * x24 + p23 * x25 + p30 * x26 + p37 * x27 + p44 * x28;
238:         pc[23] = m24 = p3 * x22 + p10 * x23 + p17 * x24 + p24 * x25 + p31 * x26 + p38 * x27 + p45 * x28;
239:         pc[24] = m25 = p4 * x22 + p11 * x23 + p18 * x24 + p25 * x25 + p32 * x26 + p39 * x27 + p46 * x28;
240:         pc[25] = m26 = p5 * x22 + p12 * x23 + p19 * x24 + p26 * x25 + p33 * x26 + p40 * x27 + p47 * x28;
241:         pc[26] = m27 = p6 * x22 + p13 * x23 + p20 * x24 + p27 * x25 + p34 * x26 + p41 * x27 + p48 * x28;
242:         pc[27] = m28 = p7 * x22 + p14 * x23 + p21 * x24 + p28 * x25 + p35 * x26 + p42 * x27 + p49 * x28;

244:         pc[28] = m29 = p1 * x29 + p8 * x30 + p15 * x31 + p22 * x32 + p29 * x33 + p36 * x34 + p43 * x35;
245:         pc[29] = m30 = p2 * x29 + p9 * x30 + p16 * x31 + p23 * x32 + p30 * x33 + p37 * x34 + p44 * x35;
246:         pc[30] = m31 = p3 * x29 + p10 * x30 + p17 * x31 + p24 * x32 + p31 * x33 + p38 * x34 + p45 * x35;
247:         pc[31] = m32 = p4 * x29 + p11 * x30 + p18 * x31 + p25 * x32 + p32 * x33 + p39 * x34 + p46 * x35;
248:         pc[32] = m33 = p5 * x29 + p12 * x30 + p19 * x31 + p26 * x32 + p33 * x33 + p40 * x34 + p47 * x35;
249:         pc[33] = m34 = p6 * x29 + p13 * x30 + p20 * x31 + p27 * x32 + p34 * x33 + p41 * x34 + p48 * x35;
250:         pc[34] = m35 = p7 * x29 + p14 * x30 + p21 * x31 + p28 * x32 + p35 * x33 + p42 * x34 + p49 * x35;

252:         pc[35] = m36 = p1 * x36 + p8 * x37 + p15 * x38 + p22 * x39 + p29 * x40 + p36 * x41 + p43 * x42;
253:         pc[36] = m37 = p2 * x36 + p9 * x37 + p16 * x38 + p23 * x39 + p30 * x40 + p37 * x41 + p44 * x42;
254:         pc[37] = m38 = p3 * x36 + p10 * x37 + p17 * x38 + p24 * x39 + p31 * x40 + p38 * x41 + p45 * x42;
255:         pc[38] = m39 = p4 * x36 + p11 * x37 + p18 * x38 + p25 * x39 + p32 * x40 + p39 * x41 + p46 * x42;
256:         pc[39] = m40 = p5 * x36 + p12 * x37 + p19 * x38 + p26 * x39 + p33 * x40 + p40 * x41 + p47 * x42;
257:         pc[40] = m41 = p6 * x36 + p13 * x37 + p20 * x38 + p27 * x39 + p34 * x40 + p41 * x41 + p48 * x42;
258:         pc[41] = m42 = p7 * x36 + p14 * x37 + p21 * x38 + p28 * x39 + p35 * x40 + p42 * x41 + p49 * x42;

260:         pc[42] = m43 = p1 * x43 + p8 * x44 + p15 * x45 + p22 * x46 + p29 * x47 + p36 * x48 + p43 * x49;
261:         pc[43] = m44 = p2 * x43 + p9 * x44 + p16 * x45 + p23 * x46 + p30 * x47 + p37 * x48 + p44 * x49;
262:         pc[44] = m45 = p3 * x43 + p10 * x44 + p17 * x45 + p24 * x46 + p31 * x47 + p38 * x48 + p45 * x49;
263:         pc[45] = m46 = p4 * x43 + p11 * x44 + p18 * x45 + p25 * x46 + p32 * x47 + p39 * x48 + p46 * x49;
264:         pc[46] = m47 = p5 * x43 + p12 * x44 + p19 * x45 + p26 * x46 + p33 * x47 + p40 * x48 + p47 * x49;
265:         pc[47] = m48 = p6 * x43 + p13 * x44 + p20 * x45 + p27 * x46 + p34 * x47 + p41 * x48 + p48 * x49;
266:         pc[48] = m49 = p7 * x43 + p14 * x44 + p21 * x45 + p28 * x46 + p35 * x47 + p42 * x48 + p49 * x49;

268:         nz = bi[row + 1] - diag_offset[row] - 1;
269:         pv += 49;
270:         for (j = 0; j < nz; j++) {
271:           x1  = pv[0];
272:           x2  = pv[1];
273:           x3  = pv[2];
274:           x4  = pv[3];
275:           x5  = pv[4];
276:           x6  = pv[5];
277:           x7  = pv[6];
278:           x8  = pv[7];
279:           x9  = pv[8];
280:           x10 = pv[9];
281:           x11 = pv[10];
282:           x12 = pv[11];
283:           x13 = pv[12];
284:           x14 = pv[13];
285:           x15 = pv[14];
286:           x16 = pv[15];
287:           x17 = pv[16];
288:           x18 = pv[17];
289:           x19 = pv[18];
290:           x20 = pv[19];
291:           x21 = pv[20];
292:           x22 = pv[21];
293:           x23 = pv[22];
294:           x24 = pv[23];
295:           x25 = pv[24];
296:           x26 = pv[25];
297:           x27 = pv[26];
298:           x28 = pv[27];
299:           x29 = pv[28];
300:           x30 = pv[29];
301:           x31 = pv[30];
302:           x32 = pv[31];
303:           x33 = pv[32];
304:           x34 = pv[33];
305:           x35 = pv[34];
306:           x36 = pv[35];
307:           x37 = pv[36];
308:           x38 = pv[37];
309:           x39 = pv[38];
310:           x40 = pv[39];
311:           x41 = pv[40];
312:           x42 = pv[41];
313:           x43 = pv[42];
314:           x44 = pv[43];
315:           x45 = pv[44];
316:           x46 = pv[45];
317:           x47 = pv[46];
318:           x48 = pv[47];
319:           x49 = pv[48];
320:           x   = rtmp + 49 * pj[j];
321:           x[0] -= m1 * x1 + m8 * x2 + m15 * x3 + m22 * x4 + m29 * x5 + m36 * x6 + m43 * x7;
322:           x[1] -= m2 * x1 + m9 * x2 + m16 * x3 + m23 * x4 + m30 * x5 + m37 * x6 + m44 * x7;
323:           x[2] -= m3 * x1 + m10 * x2 + m17 * x3 + m24 * x4 + m31 * x5 + m38 * x6 + m45 * x7;
324:           x[3] -= m4 * x1 + m11 * x2 + m18 * x3 + m25 * x4 + m32 * x5 + m39 * x6 + m46 * x7;
325:           x[4] -= m5 * x1 + m12 * x2 + m19 * x3 + m26 * x4 + m33 * x5 + m40 * x6 + m47 * x7;
326:           x[5] -= m6 * x1 + m13 * x2 + m20 * x3 + m27 * x4 + m34 * x5 + m41 * x6 + m48 * x7;
327:           x[6] -= m7 * x1 + m14 * x2 + m21 * x3 + m28 * x4 + m35 * x5 + m42 * x6 + m49 * x7;

329:           x[7] -= m1 * x8 + m8 * x9 + m15 * x10 + m22 * x11 + m29 * x12 + m36 * x13 + m43 * x14;
330:           x[8] -= m2 * x8 + m9 * x9 + m16 * x10 + m23 * x11 + m30 * x12 + m37 * x13 + m44 * x14;
331:           x[9] -= m3 * x8 + m10 * x9 + m17 * x10 + m24 * x11 + m31 * x12 + m38 * x13 + m45 * x14;
332:           x[10] -= m4 * x8 + m11 * x9 + m18 * x10 + m25 * x11 + m32 * x12 + m39 * x13 + m46 * x14;
333:           x[11] -= m5 * x8 + m12 * x9 + m19 * x10 + m26 * x11 + m33 * x12 + m40 * x13 + m47 * x14;
334:           x[12] -= m6 * x8 + m13 * x9 + m20 * x10 + m27 * x11 + m34 * x12 + m41 * x13 + m48 * x14;
335:           x[13] -= m7 * x8 + m14 * x9 + m21 * x10 + m28 * x11 + m35 * x12 + m42 * x13 + m49 * x14;

337:           x[14] -= m1 * x15 + m8 * x16 + m15 * x17 + m22 * x18 + m29 * x19 + m36 * x20 + m43 * x21;
338:           x[15] -= m2 * x15 + m9 * x16 + m16 * x17 + m23 * x18 + m30 * x19 + m37 * x20 + m44 * x21;
339:           x[16] -= m3 * x15 + m10 * x16 + m17 * x17 + m24 * x18 + m31 * x19 + m38 * x20 + m45 * x21;
340:           x[17] -= m4 * x15 + m11 * x16 + m18 * x17 + m25 * x18 + m32 * x19 + m39 * x20 + m46 * x21;
341:           x[18] -= m5 * x15 + m12 * x16 + m19 * x17 + m26 * x18 + m33 * x19 + m40 * x20 + m47 * x21;
342:           x[19] -= m6 * x15 + m13 * x16 + m20 * x17 + m27 * x18 + m34 * x19 + m41 * x20 + m48 * x21;
343:           x[20] -= m7 * x15 + m14 * x16 + m21 * x17 + m28 * x18 + m35 * x19 + m42 * x20 + m49 * x21;

345:           x[21] -= m1 * x22 + m8 * x23 + m15 * x24 + m22 * x25 + m29 * x26 + m36 * x27 + m43 * x28;
346:           x[22] -= m2 * x22 + m9 * x23 + m16 * x24 + m23 * x25 + m30 * x26 + m37 * x27 + m44 * x28;
347:           x[23] -= m3 * x22 + m10 * x23 + m17 * x24 + m24 * x25 + m31 * x26 + m38 * x27 + m45 * x28;
348:           x[24] -= m4 * x22 + m11 * x23 + m18 * x24 + m25 * x25 + m32 * x26 + m39 * x27 + m46 * x28;
349:           x[25] -= m5 * x22 + m12 * x23 + m19 * x24 + m26 * x25 + m33 * x26 + m40 * x27 + m47 * x28;
350:           x[26] -= m6 * x22 + m13 * x23 + m20 * x24 + m27 * x25 + m34 * x26 + m41 * x27 + m48 * x28;
351:           x[27] -= m7 * x22 + m14 * x23 + m21 * x24 + m28 * x25 + m35 * x26 + m42 * x27 + m49 * x28;

353:           x[28] -= m1 * x29 + m8 * x30 + m15 * x31 + m22 * x32 + m29 * x33 + m36 * x34 + m43 * x35;
354:           x[29] -= m2 * x29 + m9 * x30 + m16 * x31 + m23 * x32 + m30 * x33 + m37 * x34 + m44 * x35;
355:           x[30] -= m3 * x29 + m10 * x30 + m17 * x31 + m24 * x32 + m31 * x33 + m38 * x34 + m45 * x35;
356:           x[31] -= m4 * x29 + m11 * x30 + m18 * x31 + m25 * x32 + m32 * x33 + m39 * x34 + m46 * x35;
357:           x[32] -= m5 * x29 + m12 * x30 + m19 * x31 + m26 * x32 + m33 * x33 + m40 * x34 + m47 * x35;
358:           x[33] -= m6 * x29 + m13 * x30 + m20 * x31 + m27 * x32 + m34 * x33 + m41 * x34 + m48 * x35;
359:           x[34] -= m7 * x29 + m14 * x30 + m21 * x31 + m28 * x32 + m35 * x33 + m42 * x34 + m49 * x35;

361:           x[35] -= m1 * x36 + m8 * x37 + m15 * x38 + m22 * x39 + m29 * x40 + m36 * x41 + m43 * x42;
362:           x[36] -= m2 * x36 + m9 * x37 + m16 * x38 + m23 * x39 + m30 * x40 + m37 * x41 + m44 * x42;
363:           x[37] -= m3 * x36 + m10 * x37 + m17 * x38 + m24 * x39 + m31 * x40 + m38 * x41 + m45 * x42;
364:           x[38] -= m4 * x36 + m11 * x37 + m18 * x38 + m25 * x39 + m32 * x40 + m39 * x41 + m46 * x42;
365:           x[39] -= m5 * x36 + m12 * x37 + m19 * x38 + m26 * x39 + m33 * x40 + m40 * x41 + m47 * x42;
366:           x[40] -= m6 * x36 + m13 * x37 + m20 * x38 + m27 * x39 + m34 * x40 + m41 * x41 + m48 * x42;
367:           x[41] -= m7 * x36 + m14 * x37 + m21 * x38 + m28 * x39 + m35 * x40 + m42 * x41 + m49 * x42;

369:           x[42] -= m1 * x43 + m8 * x44 + m15 * x45 + m22 * x46 + m29 * x47 + m36 * x48 + m43 * x49;
370:           x[43] -= m2 * x43 + m9 * x44 + m16 * x45 + m23 * x46 + m30 * x47 + m37 * x48 + m44 * x49;
371:           x[44] -= m3 * x43 + m10 * x44 + m17 * x45 + m24 * x46 + m31 * x47 + m38 * x48 + m45 * x49;
372:           x[45] -= m4 * x43 + m11 * x44 + m18 * x45 + m25 * x46 + m32 * x47 + m39 * x48 + m46 * x49;
373:           x[46] -= m5 * x43 + m12 * x44 + m19 * x45 + m26 * x46 + m33 * x47 + m40 * x48 + m47 * x49;
374:           x[47] -= m6 * x43 + m13 * x44 + m20 * x45 + m27 * x46 + m34 * x47 + m41 * x48 + m48 * x49;
375:           x[48] -= m7 * x43 + m14 * x44 + m21 * x45 + m28 * x46 + m35 * x47 + m42 * x48 + m49 * x49;
376:           pv += 49;
377:         }
378:         PetscCall(PetscLogFlops(686.0 * nz + 637.0));
379:       }
380:       row = *ajtmp++;
381:     }
382:     /* finished row so stick it into b->a */
383:     pv = ba + 49 * bi[i];
384:     pj = bj + bi[i];
385:     nz = bi[i + 1] - bi[i];
386:     for (j = 0; j < nz; j++) {
387:       x      = rtmp + 49 * pj[j];
388:       pv[0]  = x[0];
389:       pv[1]  = x[1];
390:       pv[2]  = x[2];
391:       pv[3]  = x[3];
392:       pv[4]  = x[4];
393:       pv[5]  = x[5];
394:       pv[6]  = x[6];
395:       pv[7]  = x[7];
396:       pv[8]  = x[8];
397:       pv[9]  = x[9];
398:       pv[10] = x[10];
399:       pv[11] = x[11];
400:       pv[12] = x[12];
401:       pv[13] = x[13];
402:       pv[14] = x[14];
403:       pv[15] = x[15];
404:       pv[16] = x[16];
405:       pv[17] = x[17];
406:       pv[18] = x[18];
407:       pv[19] = x[19];
408:       pv[20] = x[20];
409:       pv[21] = x[21];
410:       pv[22] = x[22];
411:       pv[23] = x[23];
412:       pv[24] = x[24];
413:       pv[25] = x[25];
414:       pv[26] = x[26];
415:       pv[27] = x[27];
416:       pv[28] = x[28];
417:       pv[29] = x[29];
418:       pv[30] = x[30];
419:       pv[31] = x[31];
420:       pv[32] = x[32];
421:       pv[33] = x[33];
422:       pv[34] = x[34];
423:       pv[35] = x[35];
424:       pv[36] = x[36];
425:       pv[37] = x[37];
426:       pv[38] = x[38];
427:       pv[39] = x[39];
428:       pv[40] = x[40];
429:       pv[41] = x[41];
430:       pv[42] = x[42];
431:       pv[43] = x[43];
432:       pv[44] = x[44];
433:       pv[45] = x[45];
434:       pv[46] = x[46];
435:       pv[47] = x[47];
436:       pv[48] = x[48];
437:       pv += 49;
438:     }
439:     /* invert diagonal block */
440:     w = ba + 49 * diag_offset[i];
441:     PetscCall(PetscKernel_A_gets_inverse_A_7(w, shift, allowzeropivot, &zeropivotdetected));
442:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
443:   }

445:   PetscCall(PetscFree(rtmp));
446:   PetscCall(ISRestoreIndices(isicol, &ic));
447:   PetscCall(ISRestoreIndices(isrow, &r));

449:   C->ops->solve          = MatSolve_SeqBAIJ_7_inplace;
450:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_7_inplace;
451:   C->assembled           = PETSC_TRUE;

453:   PetscCall(PetscLogFlops(1.333333333333 * 7 * 7 * 7 * b->mbs)); /* from inverting diagonal blocks */
454:   PetscFunctionReturn(PETSC_SUCCESS);
455: }

457: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_7(Mat B, Mat A, const MatFactorInfo *info)
458: {
459:   Mat             C = B;
460:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
461:   IS              isrow = b->row, isicol = b->icol;
462:   const PetscInt *r, *ic;
463:   PetscInt        i, j, k, nz, nzL, row;
464:   const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
465:   const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
466:   MatScalar      *rtmp, *pc, *mwork, *v, *pv, *aa = a->a;
467:   PetscInt        flg;
468:   PetscReal       shift = info->shiftamount;
469:   PetscBool       allowzeropivot, zeropivotdetected;

471:   PetscFunctionBegin;
472:   allowzeropivot = PetscNot(A->erroriffailure);
473:   PetscCall(ISGetIndices(isrow, &r));
474:   PetscCall(ISGetIndices(isicol, &ic));

476:   /* generate work space needed by the factorization */
477:   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
478:   PetscCall(PetscArrayzero(rtmp, bs2 * n));

480:   for (i = 0; i < n; i++) {
481:     /* zero rtmp */
482:     /* L part */
483:     nz    = bi[i + 1] - bi[i];
484:     bjtmp = bj + bi[i];
485:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

487:     /* U part */
488:     nz    = bdiag[i] - bdiag[i + 1];
489:     bjtmp = bj + bdiag[i + 1] + 1;
490:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

492:     /* load in initial (unfactored row) */
493:     nz    = ai[r[i] + 1] - ai[r[i]];
494:     ajtmp = aj + ai[r[i]];
495:     v     = aa + bs2 * ai[r[i]];
496:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ic[ajtmp[j]], v + bs2 * j, bs2));

498:     /* elimination */
499:     bjtmp = bj + bi[i];
500:     nzL   = bi[i + 1] - bi[i];
501:     for (k = 0; k < nzL; k++) {
502:       row = bjtmp[k];
503:       pc  = rtmp + bs2 * row;
504:       for (flg = 0, j = 0; j < bs2; j++) {
505:         if (pc[j] != 0.0) {
506:           flg = 1;
507:           break;
508:         }
509:       }
510:       if (flg) {
511:         pv = b->a + bs2 * bdiag[row];
512:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
513:         PetscCall(PetscKernel_A_gets_A_times_B_7(pc, pv, mwork));

515:         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
516:         pv = b->a + bs2 * (bdiag[row + 1] + 1);
517:         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
518:         for (j = 0; j < nz; j++) {
519:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
520:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
521:           v = rtmp + bs2 * pj[j];
522:           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_7(v, pc, pv));
523:           pv += bs2;
524:         }
525:         PetscCall(PetscLogFlops(686.0 * nz + 637)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
526:       }
527:     }

529:     /* finished row so stick it into b->a */
530:     /* L part */
531:     pv = b->a + bs2 * bi[i];
532:     pj = b->j + bi[i];
533:     nz = bi[i + 1] - bi[i];
534:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));

536:     /* Mark diagonal and invert diagonal for simpler triangular solves */
537:     pv = b->a + bs2 * bdiag[i];
538:     pj = b->j + bdiag[i];
539:     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
540:     PetscCall(PetscKernel_A_gets_inverse_A_7(pv, shift, allowzeropivot, &zeropivotdetected));
541:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

543:     /* U part */
544:     pv = b->a + bs2 * (bdiag[i + 1] + 1);
545:     pj = b->j + bdiag[i + 1] + 1;
546:     nz = bdiag[i] - bdiag[i + 1] - 1;
547:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
548:   }

550:   PetscCall(PetscFree2(rtmp, mwork));
551:   PetscCall(ISRestoreIndices(isicol, &ic));
552:   PetscCall(ISRestoreIndices(isrow, &r));

554:   C->ops->solve          = MatSolve_SeqBAIJ_7;
555:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_7;
556:   C->assembled           = PETSC_TRUE;

558:   PetscCall(PetscLogFlops(1.333333333333 * 7 * 7 * 7 * n)); /* from inverting diagonal blocks */
559:   PetscFunctionReturn(PETSC_SUCCESS);
560: }

562: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_7_NaturalOrdering_inplace(Mat C, Mat A, const MatFactorInfo *info)
563: {
564:   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
565:   PetscInt     i, j, n = a->mbs, *bi = b->i, *bj = b->j;
566:   PetscInt    *ajtmpold, *ajtmp, nz, row;
567:   PetscInt    *diag_offset = b->diag, *ai = a->i, *aj = a->j, *pj;
568:   MatScalar   *pv, *v, *rtmp, *pc, *w, *x;
569:   MatScalar    x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15;
570:   MatScalar    x16, x17, x18, x19, x20, x21, x22, x23, x24, x25;
571:   MatScalar    p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12, p13, p14, p15;
572:   MatScalar    p16, p17, p18, p19, p20, p21, p22, p23, p24, p25;
573:   MatScalar    m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12, m13, m14, m15;
574:   MatScalar    m16, m17, m18, m19, m20, m21, m22, m23, m24, m25;
575:   MatScalar    p26, p27, p28, p29, p30, p31, p32, p33, p34, p35, p36;
576:   MatScalar    p37, p38, p39, p40, p41, p42, p43, p44, p45, p46, p47, p48, p49;
577:   MatScalar    x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36;
578:   MatScalar    x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49;
579:   MatScalar    m26, m27, m28, m29, m30, m31, m32, m33, m34, m35, m36;
580:   MatScalar    m37, m38, m39, m40, m41, m42, m43, m44, m45, m46, m47, m48, m49;
581:   MatScalar   *ba = b->a, *aa = a->a;
582:   PetscReal    shift = info->shiftamount;
583:   PetscBool    allowzeropivot, zeropivotdetected;

585:   PetscFunctionBegin;
586:   allowzeropivot = PetscNot(A->erroriffailure);
587:   PetscCall(PetscMalloc1(49 * (n + 1), &rtmp));
588:   for (i = 0; i < n; i++) {
589:     nz    = bi[i + 1] - bi[i];
590:     ajtmp = bj + bi[i];
591:     for (j = 0; j < nz; j++) {
592:       x    = rtmp + 49 * ajtmp[j];
593:       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
594:       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
595:       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0;
596:       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0;
597:       x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0;
598:       x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0;
599:     }
600:     /* load in initial (unfactored row) */
601:     nz       = ai[i + 1] - ai[i];
602:     ajtmpold = aj + ai[i];
603:     v        = aa + 49 * ai[i];
604:     for (j = 0; j < nz; j++) {
605:       x     = rtmp + 49 * ajtmpold[j];
606:       x[0]  = v[0];
607:       x[1]  = v[1];
608:       x[2]  = v[2];
609:       x[3]  = v[3];
610:       x[4]  = v[4];
611:       x[5]  = v[5];
612:       x[6]  = v[6];
613:       x[7]  = v[7];
614:       x[8]  = v[8];
615:       x[9]  = v[9];
616:       x[10] = v[10];
617:       x[11] = v[11];
618:       x[12] = v[12];
619:       x[13] = v[13];
620:       x[14] = v[14];
621:       x[15] = v[15];
622:       x[16] = v[16];
623:       x[17] = v[17];
624:       x[18] = v[18];
625:       x[19] = v[19];
626:       x[20] = v[20];
627:       x[21] = v[21];
628:       x[22] = v[22];
629:       x[23] = v[23];
630:       x[24] = v[24];
631:       x[25] = v[25];
632:       x[26] = v[26];
633:       x[27] = v[27];
634:       x[28] = v[28];
635:       x[29] = v[29];
636:       x[30] = v[30];
637:       x[31] = v[31];
638:       x[32] = v[32];
639:       x[33] = v[33];
640:       x[34] = v[34];
641:       x[35] = v[35];
642:       x[36] = v[36];
643:       x[37] = v[37];
644:       x[38] = v[38];
645:       x[39] = v[39];
646:       x[40] = v[40];
647:       x[41] = v[41];
648:       x[42] = v[42];
649:       x[43] = v[43];
650:       x[44] = v[44];
651:       x[45] = v[45];
652:       x[46] = v[46];
653:       x[47] = v[47];
654:       x[48] = v[48];
655:       v += 49;
656:     }
657:     row = *ajtmp++;
658:     while (row < i) {
659:       pc  = rtmp + 49 * row;
660:       p1  = pc[0];
661:       p2  = pc[1];
662:       p3  = pc[2];
663:       p4  = pc[3];
664:       p5  = pc[4];
665:       p6  = pc[5];
666:       p7  = pc[6];
667:       p8  = pc[7];
668:       p9  = pc[8];
669:       p10 = pc[9];
670:       p11 = pc[10];
671:       p12 = pc[11];
672:       p13 = pc[12];
673:       p14 = pc[13];
674:       p15 = pc[14];
675:       p16 = pc[15];
676:       p17 = pc[16];
677:       p18 = pc[17];
678:       p19 = pc[18];
679:       p20 = pc[19];
680:       p21 = pc[20];
681:       p22 = pc[21];
682:       p23 = pc[22];
683:       p24 = pc[23];
684:       p25 = pc[24];
685:       p26 = pc[25];
686:       p27 = pc[26];
687:       p28 = pc[27];
688:       p29 = pc[28];
689:       p30 = pc[29];
690:       p31 = pc[30];
691:       p32 = pc[31];
692:       p33 = pc[32];
693:       p34 = pc[33];
694:       p35 = pc[34];
695:       p36 = pc[35];
696:       p37 = pc[36];
697:       p38 = pc[37];
698:       p39 = pc[38];
699:       p40 = pc[39];
700:       p41 = pc[40];
701:       p42 = pc[41];
702:       p43 = pc[42];
703:       p44 = pc[43];
704:       p45 = pc[44];
705:       p46 = pc[45];
706:       p47 = pc[46];
707:       p48 = pc[47];
708:       p49 = pc[48];
709:       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 || p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 || p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 || p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 || p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 || p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 || p49 != 0.0) {
710:         pv    = ba + 49 * diag_offset[row];
711:         pj    = bj + diag_offset[row] + 1;
712:         x1    = pv[0];
713:         x2    = pv[1];
714:         x3    = pv[2];
715:         x4    = pv[3];
716:         x5    = pv[4];
717:         x6    = pv[5];
718:         x7    = pv[6];
719:         x8    = pv[7];
720:         x9    = pv[8];
721:         x10   = pv[9];
722:         x11   = pv[10];
723:         x12   = pv[11];
724:         x13   = pv[12];
725:         x14   = pv[13];
726:         x15   = pv[14];
727:         x16   = pv[15];
728:         x17   = pv[16];
729:         x18   = pv[17];
730:         x19   = pv[18];
731:         x20   = pv[19];
732:         x21   = pv[20];
733:         x22   = pv[21];
734:         x23   = pv[22];
735:         x24   = pv[23];
736:         x25   = pv[24];
737:         x26   = pv[25];
738:         x27   = pv[26];
739:         x28   = pv[27];
740:         x29   = pv[28];
741:         x30   = pv[29];
742:         x31   = pv[30];
743:         x32   = pv[31];
744:         x33   = pv[32];
745:         x34   = pv[33];
746:         x35   = pv[34];
747:         x36   = pv[35];
748:         x37   = pv[36];
749:         x38   = pv[37];
750:         x39   = pv[38];
751:         x40   = pv[39];
752:         x41   = pv[40];
753:         x42   = pv[41];
754:         x43   = pv[42];
755:         x44   = pv[43];
756:         x45   = pv[44];
757:         x46   = pv[45];
758:         x47   = pv[46];
759:         x48   = pv[47];
760:         x49   = pv[48];
761:         pc[0] = m1 = p1 * x1 + p8 * x2 + p15 * x3 + p22 * x4 + p29 * x5 + p36 * x6 + p43 * x7;
762:         pc[1] = m2 = p2 * x1 + p9 * x2 + p16 * x3 + p23 * x4 + p30 * x5 + p37 * x6 + p44 * x7;
763:         pc[2] = m3 = p3 * x1 + p10 * x2 + p17 * x3 + p24 * x4 + p31 * x5 + p38 * x6 + p45 * x7;
764:         pc[3] = m4 = p4 * x1 + p11 * x2 + p18 * x3 + p25 * x4 + p32 * x5 + p39 * x6 + p46 * x7;
765:         pc[4] = m5 = p5 * x1 + p12 * x2 + p19 * x3 + p26 * x4 + p33 * x5 + p40 * x6 + p47 * x7;
766:         pc[5] = m6 = p6 * x1 + p13 * x2 + p20 * x3 + p27 * x4 + p34 * x5 + p41 * x6 + p48 * x7;
767:         pc[6] = m7 = p7 * x1 + p14 * x2 + p21 * x3 + p28 * x4 + p35 * x5 + p42 * x6 + p49 * x7;

769:         pc[7] = m8 = p1 * x8 + p8 * x9 + p15 * x10 + p22 * x11 + p29 * x12 + p36 * x13 + p43 * x14;
770:         pc[8] = m9 = p2 * x8 + p9 * x9 + p16 * x10 + p23 * x11 + p30 * x12 + p37 * x13 + p44 * x14;
771:         pc[9] = m10 = p3 * x8 + p10 * x9 + p17 * x10 + p24 * x11 + p31 * x12 + p38 * x13 + p45 * x14;
772:         pc[10] = m11 = p4 * x8 + p11 * x9 + p18 * x10 + p25 * x11 + p32 * x12 + p39 * x13 + p46 * x14;
773:         pc[11] = m12 = p5 * x8 + p12 * x9 + p19 * x10 + p26 * x11 + p33 * x12 + p40 * x13 + p47 * x14;
774:         pc[12] = m13 = p6 * x8 + p13 * x9 + p20 * x10 + p27 * x11 + p34 * x12 + p41 * x13 + p48 * x14;
775:         pc[13] = m14 = p7 * x8 + p14 * x9 + p21 * x10 + p28 * x11 + p35 * x12 + p42 * x13 + p49 * x14;

777:         pc[14] = m15 = p1 * x15 + p8 * x16 + p15 * x17 + p22 * x18 + p29 * x19 + p36 * x20 + p43 * x21;
778:         pc[15] = m16 = p2 * x15 + p9 * x16 + p16 * x17 + p23 * x18 + p30 * x19 + p37 * x20 + p44 * x21;
779:         pc[16] = m17 = p3 * x15 + p10 * x16 + p17 * x17 + p24 * x18 + p31 * x19 + p38 * x20 + p45 * x21;
780:         pc[17] = m18 = p4 * x15 + p11 * x16 + p18 * x17 + p25 * x18 + p32 * x19 + p39 * x20 + p46 * x21;
781:         pc[18] = m19 = p5 * x15 + p12 * x16 + p19 * x17 + p26 * x18 + p33 * x19 + p40 * x20 + p47 * x21;
782:         pc[19] = m20 = p6 * x15 + p13 * x16 + p20 * x17 + p27 * x18 + p34 * x19 + p41 * x20 + p48 * x21;
783:         pc[20] = m21 = p7 * x15 + p14 * x16 + p21 * x17 + p28 * x18 + p35 * x19 + p42 * x20 + p49 * x21;

785:         pc[21] = m22 = p1 * x22 + p8 * x23 + p15 * x24 + p22 * x25 + p29 * x26 + p36 * x27 + p43 * x28;
786:         pc[22] = m23 = p2 * x22 + p9 * x23 + p16 * x24 + p23 * x25 + p30 * x26 + p37 * x27 + p44 * x28;
787:         pc[23] = m24 = p3 * x22 + p10 * x23 + p17 * x24 + p24 * x25 + p31 * x26 + p38 * x27 + p45 * x28;
788:         pc[24] = m25 = p4 * x22 + p11 * x23 + p18 * x24 + p25 * x25 + p32 * x26 + p39 * x27 + p46 * x28;
789:         pc[25] = m26 = p5 * x22 + p12 * x23 + p19 * x24 + p26 * x25 + p33 * x26 + p40 * x27 + p47 * x28;
790:         pc[26] = m27 = p6 * x22 + p13 * x23 + p20 * x24 + p27 * x25 + p34 * x26 + p41 * x27 + p48 * x28;
791:         pc[27] = m28 = p7 * x22 + p14 * x23 + p21 * x24 + p28 * x25 + p35 * x26 + p42 * x27 + p49 * x28;

793:         pc[28] = m29 = p1 * x29 + p8 * x30 + p15 * x31 + p22 * x32 + p29 * x33 + p36 * x34 + p43 * x35;
794:         pc[29] = m30 = p2 * x29 + p9 * x30 + p16 * x31 + p23 * x32 + p30 * x33 + p37 * x34 + p44 * x35;
795:         pc[30] = m31 = p3 * x29 + p10 * x30 + p17 * x31 + p24 * x32 + p31 * x33 + p38 * x34 + p45 * x35;
796:         pc[31] = m32 = p4 * x29 + p11 * x30 + p18 * x31 + p25 * x32 + p32 * x33 + p39 * x34 + p46 * x35;
797:         pc[32] = m33 = p5 * x29 + p12 * x30 + p19 * x31 + p26 * x32 + p33 * x33 + p40 * x34 + p47 * x35;
798:         pc[33] = m34 = p6 * x29 + p13 * x30 + p20 * x31 + p27 * x32 + p34 * x33 + p41 * x34 + p48 * x35;
799:         pc[34] = m35 = p7 * x29 + p14 * x30 + p21 * x31 + p28 * x32 + p35 * x33 + p42 * x34 + p49 * x35;

801:         pc[35] = m36 = p1 * x36 + p8 * x37 + p15 * x38 + p22 * x39 + p29 * x40 + p36 * x41 + p43 * x42;
802:         pc[36] = m37 = p2 * x36 + p9 * x37 + p16 * x38 + p23 * x39 + p30 * x40 + p37 * x41 + p44 * x42;
803:         pc[37] = m38 = p3 * x36 + p10 * x37 + p17 * x38 + p24 * x39 + p31 * x40 + p38 * x41 + p45 * x42;
804:         pc[38] = m39 = p4 * x36 + p11 * x37 + p18 * x38 + p25 * x39 + p32 * x40 + p39 * x41 + p46 * x42;
805:         pc[39] = m40 = p5 * x36 + p12 * x37 + p19 * x38 + p26 * x39 + p33 * x40 + p40 * x41 + p47 * x42;
806:         pc[40] = m41 = p6 * x36 + p13 * x37 + p20 * x38 + p27 * x39 + p34 * x40 + p41 * x41 + p48 * x42;
807:         pc[41] = m42 = p7 * x36 + p14 * x37 + p21 * x38 + p28 * x39 + p35 * x40 + p42 * x41 + p49 * x42;

809:         pc[42] = m43 = p1 * x43 + p8 * x44 + p15 * x45 + p22 * x46 + p29 * x47 + p36 * x48 + p43 * x49;
810:         pc[43] = m44 = p2 * x43 + p9 * x44 + p16 * x45 + p23 * x46 + p30 * x47 + p37 * x48 + p44 * x49;
811:         pc[44] = m45 = p3 * x43 + p10 * x44 + p17 * x45 + p24 * x46 + p31 * x47 + p38 * x48 + p45 * x49;
812:         pc[45] = m46 = p4 * x43 + p11 * x44 + p18 * x45 + p25 * x46 + p32 * x47 + p39 * x48 + p46 * x49;
813:         pc[46] = m47 = p5 * x43 + p12 * x44 + p19 * x45 + p26 * x46 + p33 * x47 + p40 * x48 + p47 * x49;
814:         pc[47] = m48 = p6 * x43 + p13 * x44 + p20 * x45 + p27 * x46 + p34 * x47 + p41 * x48 + p48 * x49;
815:         pc[48] = m49 = p7 * x43 + p14 * x44 + p21 * x45 + p28 * x46 + p35 * x47 + p42 * x48 + p49 * x49;

817:         nz = bi[row + 1] - diag_offset[row] - 1;
818:         pv += 49;
819:         for (j = 0; j < nz; j++) {
820:           x1  = pv[0];
821:           x2  = pv[1];
822:           x3  = pv[2];
823:           x4  = pv[3];
824:           x5  = pv[4];
825:           x6  = pv[5];
826:           x7  = pv[6];
827:           x8  = pv[7];
828:           x9  = pv[8];
829:           x10 = pv[9];
830:           x11 = pv[10];
831:           x12 = pv[11];
832:           x13 = pv[12];
833:           x14 = pv[13];
834:           x15 = pv[14];
835:           x16 = pv[15];
836:           x17 = pv[16];
837:           x18 = pv[17];
838:           x19 = pv[18];
839:           x20 = pv[19];
840:           x21 = pv[20];
841:           x22 = pv[21];
842:           x23 = pv[22];
843:           x24 = pv[23];
844:           x25 = pv[24];
845:           x26 = pv[25];
846:           x27 = pv[26];
847:           x28 = pv[27];
848:           x29 = pv[28];
849:           x30 = pv[29];
850:           x31 = pv[30];
851:           x32 = pv[31];
852:           x33 = pv[32];
853:           x34 = pv[33];
854:           x35 = pv[34];
855:           x36 = pv[35];
856:           x37 = pv[36];
857:           x38 = pv[37];
858:           x39 = pv[38];
859:           x40 = pv[39];
860:           x41 = pv[40];
861:           x42 = pv[41];
862:           x43 = pv[42];
863:           x44 = pv[43];
864:           x45 = pv[44];
865:           x46 = pv[45];
866:           x47 = pv[46];
867:           x48 = pv[47];
868:           x49 = pv[48];
869:           x   = rtmp + 49 * pj[j];
870:           x[0] -= m1 * x1 + m8 * x2 + m15 * x3 + m22 * x4 + m29 * x5 + m36 * x6 + m43 * x7;
871:           x[1] -= m2 * x1 + m9 * x2 + m16 * x3 + m23 * x4 + m30 * x5 + m37 * x6 + m44 * x7;
872:           x[2] -= m3 * x1 + m10 * x2 + m17 * x3 + m24 * x4 + m31 * x5 + m38 * x6 + m45 * x7;
873:           x[3] -= m4 * x1 + m11 * x2 + m18 * x3 + m25 * x4 + m32 * x5 + m39 * x6 + m46 * x7;
874:           x[4] -= m5 * x1 + m12 * x2 + m19 * x3 + m26 * x4 + m33 * x5 + m40 * x6 + m47 * x7;
875:           x[5] -= m6 * x1 + m13 * x2 + m20 * x3 + m27 * x4 + m34 * x5 + m41 * x6 + m48 * x7;
876:           x[6] -= m7 * x1 + m14 * x2 + m21 * x3 + m28 * x4 + m35 * x5 + m42 * x6 + m49 * x7;

878:           x[7] -= m1 * x8 + m8 * x9 + m15 * x10 + m22 * x11 + m29 * x12 + m36 * x13 + m43 * x14;
879:           x[8] -= m2 * x8 + m9 * x9 + m16 * x10 + m23 * x11 + m30 * x12 + m37 * x13 + m44 * x14;
880:           x[9] -= m3 * x8 + m10 * x9 + m17 * x10 + m24 * x11 + m31 * x12 + m38 * x13 + m45 * x14;
881:           x[10] -= m4 * x8 + m11 * x9 + m18 * x10 + m25 * x11 + m32 * x12 + m39 * x13 + m46 * x14;
882:           x[11] -= m5 * x8 + m12 * x9 + m19 * x10 + m26 * x11 + m33 * x12 + m40 * x13 + m47 * x14;
883:           x[12] -= m6 * x8 + m13 * x9 + m20 * x10 + m27 * x11 + m34 * x12 + m41 * x13 + m48 * x14;
884:           x[13] -= m7 * x8 + m14 * x9 + m21 * x10 + m28 * x11 + m35 * x12 + m42 * x13 + m49 * x14;

886:           x[14] -= m1 * x15 + m8 * x16 + m15 * x17 + m22 * x18 + m29 * x19 + m36 * x20 + m43 * x21;
887:           x[15] -= m2 * x15 + m9 * x16 + m16 * x17 + m23 * x18 + m30 * x19 + m37 * x20 + m44 * x21;
888:           x[16] -= m3 * x15 + m10 * x16 + m17 * x17 + m24 * x18 + m31 * x19 + m38 * x20 + m45 * x21;
889:           x[17] -= m4 * x15 + m11 * x16 + m18 * x17 + m25 * x18 + m32 * x19 + m39 * x20 + m46 * x21;
890:           x[18] -= m5 * x15 + m12 * x16 + m19 * x17 + m26 * x18 + m33 * x19 + m40 * x20 + m47 * x21;
891:           x[19] -= m6 * x15 + m13 * x16 + m20 * x17 + m27 * x18 + m34 * x19 + m41 * x20 + m48 * x21;
892:           x[20] -= m7 * x15 + m14 * x16 + m21 * x17 + m28 * x18 + m35 * x19 + m42 * x20 + m49 * x21;

894:           x[21] -= m1 * x22 + m8 * x23 + m15 * x24 + m22 * x25 + m29 * x26 + m36 * x27 + m43 * x28;
895:           x[22] -= m2 * x22 + m9 * x23 + m16 * x24 + m23 * x25 + m30 * x26 + m37 * x27 + m44 * x28;
896:           x[23] -= m3 * x22 + m10 * x23 + m17 * x24 + m24 * x25 + m31 * x26 + m38 * x27 + m45 * x28;
897:           x[24] -= m4 * x22 + m11 * x23 + m18 * x24 + m25 * x25 + m32 * x26 + m39 * x27 + m46 * x28;
898:           x[25] -= m5 * x22 + m12 * x23 + m19 * x24 + m26 * x25 + m33 * x26 + m40 * x27 + m47 * x28;
899:           x[26] -= m6 * x22 + m13 * x23 + m20 * x24 + m27 * x25 + m34 * x26 + m41 * x27 + m48 * x28;
900:           x[27] -= m7 * x22 + m14 * x23 + m21 * x24 + m28 * x25 + m35 * x26 + m42 * x27 + m49 * x28;

902:           x[28] -= m1 * x29 + m8 * x30 + m15 * x31 + m22 * x32 + m29 * x33 + m36 * x34 + m43 * x35;
903:           x[29] -= m2 * x29 + m9 * x30 + m16 * x31 + m23 * x32 + m30 * x33 + m37 * x34 + m44 * x35;
904:           x[30] -= m3 * x29 + m10 * x30 + m17 * x31 + m24 * x32 + m31 * x33 + m38 * x34 + m45 * x35;
905:           x[31] -= m4 * x29 + m11 * x30 + m18 * x31 + m25 * x32 + m32 * x33 + m39 * x34 + m46 * x35;
906:           x[32] -= m5 * x29 + m12 * x30 + m19 * x31 + m26 * x32 + m33 * x33 + m40 * x34 + m47 * x35;
907:           x[33] -= m6 * x29 + m13 * x30 + m20 * x31 + m27 * x32 + m34 * x33 + m41 * x34 + m48 * x35;
908:           x[34] -= m7 * x29 + m14 * x30 + m21 * x31 + m28 * x32 + m35 * x33 + m42 * x34 + m49 * x35;

910:           x[35] -= m1 * x36 + m8 * x37 + m15 * x38 + m22 * x39 + m29 * x40 + m36 * x41 + m43 * x42;
911:           x[36] -= m2 * x36 + m9 * x37 + m16 * x38 + m23 * x39 + m30 * x40 + m37 * x41 + m44 * x42;
912:           x[37] -= m3 * x36 + m10 * x37 + m17 * x38 + m24 * x39 + m31 * x40 + m38 * x41 + m45 * x42;
913:           x[38] -= m4 * x36 + m11 * x37 + m18 * x38 + m25 * x39 + m32 * x40 + m39 * x41 + m46 * x42;
914:           x[39] -= m5 * x36 + m12 * x37 + m19 * x38 + m26 * x39 + m33 * x40 + m40 * x41 + m47 * x42;
915:           x[40] -= m6 * x36 + m13 * x37 + m20 * x38 + m27 * x39 + m34 * x40 + m41 * x41 + m48 * x42;
916:           x[41] -= m7 * x36 + m14 * x37 + m21 * x38 + m28 * x39 + m35 * x40 + m42 * x41 + m49 * x42;

918:           x[42] -= m1 * x43 + m8 * x44 + m15 * x45 + m22 * x46 + m29 * x47 + m36 * x48 + m43 * x49;
919:           x[43] -= m2 * x43 + m9 * x44 + m16 * x45 + m23 * x46 + m30 * x47 + m37 * x48 + m44 * x49;
920:           x[44] -= m3 * x43 + m10 * x44 + m17 * x45 + m24 * x46 + m31 * x47 + m38 * x48 + m45 * x49;
921:           x[45] -= m4 * x43 + m11 * x44 + m18 * x45 + m25 * x46 + m32 * x47 + m39 * x48 + m46 * x49;
922:           x[46] -= m5 * x43 + m12 * x44 + m19 * x45 + m26 * x46 + m33 * x47 + m40 * x48 + m47 * x49;
923:           x[47] -= m6 * x43 + m13 * x44 + m20 * x45 + m27 * x46 + m34 * x47 + m41 * x48 + m48 * x49;
924:           x[48] -= m7 * x43 + m14 * x44 + m21 * x45 + m28 * x46 + m35 * x47 + m42 * x48 + m49 * x49;
925:           pv += 49;
926:         }
927:         PetscCall(PetscLogFlops(686.0 * nz + 637.0));
928:       }
929:       row = *ajtmp++;
930:     }
931:     /* finished row so stick it into b->a */
932:     pv = ba + 49 * bi[i];
933:     pj = bj + bi[i];
934:     nz = bi[i + 1] - bi[i];
935:     for (j = 0; j < nz; j++) {
936:       x      = rtmp + 49 * pj[j];
937:       pv[0]  = x[0];
938:       pv[1]  = x[1];
939:       pv[2]  = x[2];
940:       pv[3]  = x[3];
941:       pv[4]  = x[4];
942:       pv[5]  = x[5];
943:       pv[6]  = x[6];
944:       pv[7]  = x[7];
945:       pv[8]  = x[8];
946:       pv[9]  = x[9];
947:       pv[10] = x[10];
948:       pv[11] = x[11];
949:       pv[12] = x[12];
950:       pv[13] = x[13];
951:       pv[14] = x[14];
952:       pv[15] = x[15];
953:       pv[16] = x[16];
954:       pv[17] = x[17];
955:       pv[18] = x[18];
956:       pv[19] = x[19];
957:       pv[20] = x[20];
958:       pv[21] = x[21];
959:       pv[22] = x[22];
960:       pv[23] = x[23];
961:       pv[24] = x[24];
962:       pv[25] = x[25];
963:       pv[26] = x[26];
964:       pv[27] = x[27];
965:       pv[28] = x[28];
966:       pv[29] = x[29];
967:       pv[30] = x[30];
968:       pv[31] = x[31];
969:       pv[32] = x[32];
970:       pv[33] = x[33];
971:       pv[34] = x[34];
972:       pv[35] = x[35];
973:       pv[36] = x[36];
974:       pv[37] = x[37];
975:       pv[38] = x[38];
976:       pv[39] = x[39];
977:       pv[40] = x[40];
978:       pv[41] = x[41];
979:       pv[42] = x[42];
980:       pv[43] = x[43];
981:       pv[44] = x[44];
982:       pv[45] = x[45];
983:       pv[46] = x[46];
984:       pv[47] = x[47];
985:       pv[48] = x[48];
986:       pv += 49;
987:     }
988:     /* invert diagonal block */
989:     w = ba + 49 * diag_offset[i];
990:     PetscCall(PetscKernel_A_gets_inverse_A_7(w, shift, allowzeropivot, &zeropivotdetected));
991:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
992:   }

994:   PetscCall(PetscFree(rtmp));

996:   C->ops->solve          = MatSolve_SeqBAIJ_7_NaturalOrdering_inplace;
997:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_7_NaturalOrdering_inplace;
998:   C->assembled           = PETSC_TRUE;

1000:   PetscCall(PetscLogFlops(1.333333333333 * 7 * 7 * 7 * b->mbs)); /* from inverting diagonal blocks */
1001:   PetscFunctionReturn(PETSC_SUCCESS);
1002: }

1004: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_7_NaturalOrdering(Mat B, Mat A, const MatFactorInfo *info)
1005: {
1006:   Mat             C = B;
1007:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
1008:   PetscInt        i, j, k, nz, nzL, row;
1009:   const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
1010:   const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
1011:   MatScalar      *rtmp, *pc, *mwork, *v, *pv, *aa = a->a;
1012:   PetscInt        flg;
1013:   PetscReal       shift = info->shiftamount;
1014:   PetscBool       allowzeropivot, zeropivotdetected;

1016:   PetscFunctionBegin;
1017:   allowzeropivot = PetscNot(A->erroriffailure);

1019:   /* generate work space needed by the factorization */
1020:   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
1021:   PetscCall(PetscArrayzero(rtmp, bs2 * n));

1023:   for (i = 0; i < n; i++) {
1024:     /* zero rtmp */
1025:     /* L part */
1026:     nz    = bi[i + 1] - bi[i];
1027:     bjtmp = bj + bi[i];
1028:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

1030:     /* U part */
1031:     nz    = bdiag[i] - bdiag[i + 1];
1032:     bjtmp = bj + bdiag[i + 1] + 1;
1033:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

1035:     /* load in initial (unfactored row) */
1036:     nz    = ai[i + 1] - ai[i];
1037:     ajtmp = aj + ai[i];
1038:     v     = aa + bs2 * ai[i];
1039:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ajtmp[j], v + bs2 * j, bs2));

1041:     /* elimination */
1042:     bjtmp = bj + bi[i];
1043:     nzL   = bi[i + 1] - bi[i];
1044:     for (k = 0; k < nzL; k++) {
1045:       row = bjtmp[k];
1046:       pc  = rtmp + bs2 * row;
1047:       for (flg = 0, j = 0; j < bs2; j++) {
1048:         if (pc[j] != 0.0) {
1049:           flg = 1;
1050:           break;
1051:         }
1052:       }
1053:       if (flg) {
1054:         pv = b->a + bs2 * bdiag[row];
1055:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
1056:         PetscCall(PetscKernel_A_gets_A_times_B_7(pc, pv, mwork));

1058:         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
1059:         pv = b->a + bs2 * (bdiag[row + 1] + 1);
1060:         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
1061:         for (j = 0; j < nz; j++) {
1062:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
1063:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
1064:           v = rtmp + bs2 * pj[j];
1065:           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_7(v, pc, pv));
1066:           pv += bs2;
1067:         }
1068:         PetscCall(PetscLogFlops(686.0 * nz + 637)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
1069:       }
1070:     }

1072:     /* finished row so stick it into b->a */
1073:     /* L part */
1074:     pv = b->a + bs2 * bi[i];
1075:     pj = b->j + bi[i];
1076:     nz = bi[i + 1] - bi[i];
1077:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));

1079:     /* Mark diagonal and invert diagonal for simpler triangular solves */
1080:     pv = b->a + bs2 * bdiag[i];
1081:     pj = b->j + bdiag[i];
1082:     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
1083:     PetscCall(PetscKernel_A_gets_inverse_A_7(pv, shift, allowzeropivot, &zeropivotdetected));
1084:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

1086:     /* U part */
1087:     pv = b->a + bs2 * (bdiag[i + 1] + 1);
1088:     pj = b->j + bdiag[i + 1] + 1;
1089:     nz = bdiag[i] - bdiag[i + 1] - 1;
1090:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
1091:   }
1092:   PetscCall(PetscFree2(rtmp, mwork));

1094:   C->ops->solve          = MatSolve_SeqBAIJ_7_NaturalOrdering;
1095:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_7_NaturalOrdering;
1096:   C->assembled           = PETSC_TRUE;

1098:   PetscCall(PetscLogFlops(1.333333333333 * 7 * 7 * 7 * n)); /* from inverting diagonal blocks */
1099:   PetscFunctionReturn(PETSC_SUCCESS);
1100: }