Actual source code: baijfact7.c

  1: /*
  2:     Factorization code for BAIJ format.
  3: */
  4: #include <../src/mat/impls/baij/seq/baij.h>
  5: #include <petsc/private/kernels/blockinvert.h>

  7: /*
  8:       Version for when blocks are 6 by 6
  9: */
 10: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_6_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 *ajtmpold, *ajtmp, *diag_offset = b->diag, *r, *ic, *bi = b->i, *bj = b->j, *ai = a->i, *aj = a->j, *pj;
 15:   PetscInt        nz, row, i, j, n = a->mbs, 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       x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36;
 24:   MatScalar       m26, m27, m28, m29, m30, m31, m32, m33, m34, m35, m36;
 25:   MatScalar      *ba = b->a, *aa = a->a;
 26:   PetscReal       shift = info->shiftamount;
 27:   PetscBool       allowzeropivot, zeropivotdetected;

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

 35:   for (i = 0; i < n; i++) {
 36:     nz    = bi[i + 1] - bi[i];
 37:     ajtmp = bj + bi[i];
 38:     for (j = 0; j < nz; j++) {
 39:       x    = rtmp + 36 * ajtmp[j];
 40:       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
 41:       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
 42:       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0;
 43:       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0;
 44:       x[34] = x[35] = 0.0;
 45:     }
 46:     /* load in initial (unfactored row) */
 47:     idx      = r[i];
 48:     nz       = ai[idx + 1] - ai[idx];
 49:     ajtmpold = aj + ai[idx];
 50:     v        = aa + 36 * ai[idx];
 51:     for (j = 0; j < nz; j++) {
 52:       x     = rtmp + 36 * ic[ajtmpold[j]];
 53:       x[0]  = v[0];
 54:       x[1]  = v[1];
 55:       x[2]  = v[2];
 56:       x[3]  = v[3];
 57:       x[4]  = v[4];
 58:       x[5]  = v[5];
 59:       x[6]  = v[6];
 60:       x[7]  = v[7];
 61:       x[8]  = v[8];
 62:       x[9]  = v[9];
 63:       x[10] = v[10];
 64:       x[11] = v[11];
 65:       x[12] = v[12];
 66:       x[13] = v[13];
 67:       x[14] = v[14];
 68:       x[15] = v[15];
 69:       x[16] = v[16];
 70:       x[17] = v[17];
 71:       x[18] = v[18];
 72:       x[19] = v[19];
 73:       x[20] = v[20];
 74:       x[21] = v[21];
 75:       x[22] = v[22];
 76:       x[23] = v[23];
 77:       x[24] = v[24];
 78:       x[25] = v[25];
 79:       x[26] = v[26];
 80:       x[27] = v[27];
 81:       x[28] = v[28];
 82:       x[29] = v[29];
 83:       x[30] = v[30];
 84:       x[31] = v[31];
 85:       x[32] = v[32];
 86:       x[33] = v[33];
 87:       x[34] = v[34];
 88:       x[35] = v[35];
 89:       v += 36;
 90:     }
 91:     row = *ajtmp++;
 92:     while (row < i) {
 93:       pc  = rtmp + 36 * row;
 94:       p1  = pc[0];
 95:       p2  = pc[1];
 96:       p3  = pc[2];
 97:       p4  = pc[3];
 98:       p5  = pc[4];
 99:       p6  = pc[5];
100:       p7  = pc[6];
101:       p8  = pc[7];
102:       p9  = pc[8];
103:       p10 = pc[9];
104:       p11 = pc[10];
105:       p12 = pc[11];
106:       p13 = pc[12];
107:       p14 = pc[13];
108:       p15 = pc[14];
109:       p16 = pc[15];
110:       p17 = pc[16];
111:       p18 = pc[17];
112:       p19 = pc[18];
113:       p20 = pc[19];
114:       p21 = pc[20];
115:       p22 = pc[21];
116:       p23 = pc[22];
117:       p24 = pc[23];
118:       p25 = pc[24];
119:       p26 = pc[25];
120:       p27 = pc[26];
121:       p28 = pc[27];
122:       p29 = pc[28];
123:       p30 = pc[29];
124:       p31 = pc[30];
125:       p32 = pc[31];
126:       p33 = pc[32];
127:       p34 = pc[33];
128:       p35 = pc[34];
129:       p36 = pc[35];
130:       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) {
131:         pv    = ba + 36 * diag_offset[row];
132:         pj    = bj + diag_offset[row] + 1;
133:         x1    = pv[0];
134:         x2    = pv[1];
135:         x3    = pv[2];
136:         x4    = pv[3];
137:         x5    = pv[4];
138:         x6    = pv[5];
139:         x7    = pv[6];
140:         x8    = pv[7];
141:         x9    = pv[8];
142:         x10   = pv[9];
143:         x11   = pv[10];
144:         x12   = pv[11];
145:         x13   = pv[12];
146:         x14   = pv[13];
147:         x15   = pv[14];
148:         x16   = pv[15];
149:         x17   = pv[16];
150:         x18   = pv[17];
151:         x19   = pv[18];
152:         x20   = pv[19];
153:         x21   = pv[20];
154:         x22   = pv[21];
155:         x23   = pv[22];
156:         x24   = pv[23];
157:         x25   = pv[24];
158:         x26   = pv[25];
159:         x27   = pv[26];
160:         x28   = pv[27];
161:         x29   = pv[28];
162:         x30   = pv[29];
163:         x31   = pv[30];
164:         x32   = pv[31];
165:         x33   = pv[32];
166:         x34   = pv[33];
167:         x35   = pv[34];
168:         x36   = pv[35];
169:         pc[0] = m1 = p1 * x1 + p7 * x2 + p13 * x3 + p19 * x4 + p25 * x5 + p31 * x6;
170:         pc[1] = m2 = p2 * x1 + p8 * x2 + p14 * x3 + p20 * x4 + p26 * x5 + p32 * x6;
171:         pc[2] = m3 = p3 * x1 + p9 * x2 + p15 * x3 + p21 * x4 + p27 * x5 + p33 * x6;
172:         pc[3] = m4 = p4 * x1 + p10 * x2 + p16 * x3 + p22 * x4 + p28 * x5 + p34 * x6;
173:         pc[4] = m5 = p5 * x1 + p11 * x2 + p17 * x3 + p23 * x4 + p29 * x5 + p35 * x6;
174:         pc[5] = m6 = p6 * x1 + p12 * x2 + p18 * x3 + p24 * x4 + p30 * x5 + p36 * x6;

176:         pc[6] = m7 = p1 * x7 + p7 * x8 + p13 * x9 + p19 * x10 + p25 * x11 + p31 * x12;
177:         pc[7] = m8 = p2 * x7 + p8 * x8 + p14 * x9 + p20 * x10 + p26 * x11 + p32 * x12;
178:         pc[8] = m9 = p3 * x7 + p9 * x8 + p15 * x9 + p21 * x10 + p27 * x11 + p33 * x12;
179:         pc[9] = m10 = p4 * x7 + p10 * x8 + p16 * x9 + p22 * x10 + p28 * x11 + p34 * x12;
180:         pc[10] = m11 = p5 * x7 + p11 * x8 + p17 * x9 + p23 * x10 + p29 * x11 + p35 * x12;
181:         pc[11] = m12 = p6 * x7 + p12 * x8 + p18 * x9 + p24 * x10 + p30 * x11 + p36 * x12;

183:         pc[12] = m13 = p1 * x13 + p7 * x14 + p13 * x15 + p19 * x16 + p25 * x17 + p31 * x18;
184:         pc[13] = m14 = p2 * x13 + p8 * x14 + p14 * x15 + p20 * x16 + p26 * x17 + p32 * x18;
185:         pc[14] = m15 = p3 * x13 + p9 * x14 + p15 * x15 + p21 * x16 + p27 * x17 + p33 * x18;
186:         pc[15] = m16 = p4 * x13 + p10 * x14 + p16 * x15 + p22 * x16 + p28 * x17 + p34 * x18;
187:         pc[16] = m17 = p5 * x13 + p11 * x14 + p17 * x15 + p23 * x16 + p29 * x17 + p35 * x18;
188:         pc[17] = m18 = p6 * x13 + p12 * x14 + p18 * x15 + p24 * x16 + p30 * x17 + p36 * x18;

190:         pc[18] = m19 = p1 * x19 + p7 * x20 + p13 * x21 + p19 * x22 + p25 * x23 + p31 * x24;
191:         pc[19] = m20 = p2 * x19 + p8 * x20 + p14 * x21 + p20 * x22 + p26 * x23 + p32 * x24;
192:         pc[20] = m21 = p3 * x19 + p9 * x20 + p15 * x21 + p21 * x22 + p27 * x23 + p33 * x24;
193:         pc[21] = m22 = p4 * x19 + p10 * x20 + p16 * x21 + p22 * x22 + p28 * x23 + p34 * x24;
194:         pc[22] = m23 = p5 * x19 + p11 * x20 + p17 * x21 + p23 * x22 + p29 * x23 + p35 * x24;
195:         pc[23] = m24 = p6 * x19 + p12 * x20 + p18 * x21 + p24 * x22 + p30 * x23 + p36 * x24;

197:         pc[24] = m25 = p1 * x25 + p7 * x26 + p13 * x27 + p19 * x28 + p25 * x29 + p31 * x30;
198:         pc[25] = m26 = p2 * x25 + p8 * x26 + p14 * x27 + p20 * x28 + p26 * x29 + p32 * x30;
199:         pc[26] = m27 = p3 * x25 + p9 * x26 + p15 * x27 + p21 * x28 + p27 * x29 + p33 * x30;
200:         pc[27] = m28 = p4 * x25 + p10 * x26 + p16 * x27 + p22 * x28 + p28 * x29 + p34 * x30;
201:         pc[28] = m29 = p5 * x25 + p11 * x26 + p17 * x27 + p23 * x28 + p29 * x29 + p35 * x30;
202:         pc[29] = m30 = p6 * x25 + p12 * x26 + p18 * x27 + p24 * x28 + p30 * x29 + p36 * x30;

204:         pc[30] = m31 = p1 * x31 + p7 * x32 + p13 * x33 + p19 * x34 + p25 * x35 + p31 * x36;
205:         pc[31] = m32 = p2 * x31 + p8 * x32 + p14 * x33 + p20 * x34 + p26 * x35 + p32 * x36;
206:         pc[32] = m33 = p3 * x31 + p9 * x32 + p15 * x33 + p21 * x34 + p27 * x35 + p33 * x36;
207:         pc[33] = m34 = p4 * x31 + p10 * x32 + p16 * x33 + p22 * x34 + p28 * x35 + p34 * x36;
208:         pc[34] = m35 = p5 * x31 + p11 * x32 + p17 * x33 + p23 * x34 + p29 * x35 + p35 * x36;
209:         pc[35] = m36 = p6 * x31 + p12 * x32 + p18 * x33 + p24 * x34 + p30 * x35 + p36 * x36;

211:         nz = bi[row + 1] - diag_offset[row] - 1;
212:         pv += 36;
213:         for (j = 0; j < nz; j++) {
214:           x1  = pv[0];
215:           x2  = pv[1];
216:           x3  = pv[2];
217:           x4  = pv[3];
218:           x5  = pv[4];
219:           x6  = pv[5];
220:           x7  = pv[6];
221:           x8  = pv[7];
222:           x9  = pv[8];
223:           x10 = pv[9];
224:           x11 = pv[10];
225:           x12 = pv[11];
226:           x13 = pv[12];
227:           x14 = pv[13];
228:           x15 = pv[14];
229:           x16 = pv[15];
230:           x17 = pv[16];
231:           x18 = pv[17];
232:           x19 = pv[18];
233:           x20 = pv[19];
234:           x21 = pv[20];
235:           x22 = pv[21];
236:           x23 = pv[22];
237:           x24 = pv[23];
238:           x25 = pv[24];
239:           x26 = pv[25];
240:           x27 = pv[26];
241:           x28 = pv[27];
242:           x29 = pv[28];
243:           x30 = pv[29];
244:           x31 = pv[30];
245:           x32 = pv[31];
246:           x33 = pv[32];
247:           x34 = pv[33];
248:           x35 = pv[34];
249:           x36 = pv[35];
250:           x   = rtmp + 36 * pj[j];
251:           x[0] -= m1 * x1 + m7 * x2 + m13 * x3 + m19 * x4 + m25 * x5 + m31 * x6;
252:           x[1] -= m2 * x1 + m8 * x2 + m14 * x3 + m20 * x4 + m26 * x5 + m32 * x6;
253:           x[2] -= m3 * x1 + m9 * x2 + m15 * x3 + m21 * x4 + m27 * x5 + m33 * x6;
254:           x[3] -= m4 * x1 + m10 * x2 + m16 * x3 + m22 * x4 + m28 * x5 + m34 * x6;
255:           x[4] -= m5 * x1 + m11 * x2 + m17 * x3 + m23 * x4 + m29 * x5 + m35 * x6;
256:           x[5] -= m6 * x1 + m12 * x2 + m18 * x3 + m24 * x4 + m30 * x5 + m36 * x6;

258:           x[6] -= m1 * x7 + m7 * x8 + m13 * x9 + m19 * x10 + m25 * x11 + m31 * x12;
259:           x[7] -= m2 * x7 + m8 * x8 + m14 * x9 + m20 * x10 + m26 * x11 + m32 * x12;
260:           x[8] -= m3 * x7 + m9 * x8 + m15 * x9 + m21 * x10 + m27 * x11 + m33 * x12;
261:           x[9] -= m4 * x7 + m10 * x8 + m16 * x9 + m22 * x10 + m28 * x11 + m34 * x12;
262:           x[10] -= m5 * x7 + m11 * x8 + m17 * x9 + m23 * x10 + m29 * x11 + m35 * x12;
263:           x[11] -= m6 * x7 + m12 * x8 + m18 * x9 + m24 * x10 + m30 * x11 + m36 * x12;

265:           x[12] -= m1 * x13 + m7 * x14 + m13 * x15 + m19 * x16 + m25 * x17 + m31 * x18;
266:           x[13] -= m2 * x13 + m8 * x14 + m14 * x15 + m20 * x16 + m26 * x17 + m32 * x18;
267:           x[14] -= m3 * x13 + m9 * x14 + m15 * x15 + m21 * x16 + m27 * x17 + m33 * x18;
268:           x[15] -= m4 * x13 + m10 * x14 + m16 * x15 + m22 * x16 + m28 * x17 + m34 * x18;
269:           x[16] -= m5 * x13 + m11 * x14 + m17 * x15 + m23 * x16 + m29 * x17 + m35 * x18;
270:           x[17] -= m6 * x13 + m12 * x14 + m18 * x15 + m24 * x16 + m30 * x17 + m36 * x18;

272:           x[18] -= m1 * x19 + m7 * x20 + m13 * x21 + m19 * x22 + m25 * x23 + m31 * x24;
273:           x[19] -= m2 * x19 + m8 * x20 + m14 * x21 + m20 * x22 + m26 * x23 + m32 * x24;
274:           x[20] -= m3 * x19 + m9 * x20 + m15 * x21 + m21 * x22 + m27 * x23 + m33 * x24;
275:           x[21] -= m4 * x19 + m10 * x20 + m16 * x21 + m22 * x22 + m28 * x23 + m34 * x24;
276:           x[22] -= m5 * x19 + m11 * x20 + m17 * x21 + m23 * x22 + m29 * x23 + m35 * x24;
277:           x[23] -= m6 * x19 + m12 * x20 + m18 * x21 + m24 * x22 + m30 * x23 + m36 * x24;

279:           x[24] -= m1 * x25 + m7 * x26 + m13 * x27 + m19 * x28 + m25 * x29 + m31 * x30;
280:           x[25] -= m2 * x25 + m8 * x26 + m14 * x27 + m20 * x28 + m26 * x29 + m32 * x30;
281:           x[26] -= m3 * x25 + m9 * x26 + m15 * x27 + m21 * x28 + m27 * x29 + m33 * x30;
282:           x[27] -= m4 * x25 + m10 * x26 + m16 * x27 + m22 * x28 + m28 * x29 + m34 * x30;
283:           x[28] -= m5 * x25 + m11 * x26 + m17 * x27 + m23 * x28 + m29 * x29 + m35 * x30;
284:           x[29] -= m6 * x25 + m12 * x26 + m18 * x27 + m24 * x28 + m30 * x29 + m36 * x30;

286:           x[30] -= m1 * x31 + m7 * x32 + m13 * x33 + m19 * x34 + m25 * x35 + m31 * x36;
287:           x[31] -= m2 * x31 + m8 * x32 + m14 * x33 + m20 * x34 + m26 * x35 + m32 * x36;
288:           x[32] -= m3 * x31 + m9 * x32 + m15 * x33 + m21 * x34 + m27 * x35 + m33 * x36;
289:           x[33] -= m4 * x31 + m10 * x32 + m16 * x33 + m22 * x34 + m28 * x35 + m34 * x36;
290:           x[34] -= m5 * x31 + m11 * x32 + m17 * x33 + m23 * x34 + m29 * x35 + m35 * x36;
291:           x[35] -= m6 * x31 + m12 * x32 + m18 * x33 + m24 * x34 + m30 * x35 + m36 * x36;

293:           pv += 36;
294:         }
295:         PetscCall(PetscLogFlops(432.0 * nz + 396.0));
296:       }
297:       row = *ajtmp++;
298:     }
299:     /* finished row so stick it into b->a */
300:     pv = ba + 36 * bi[i];
301:     pj = bj + bi[i];
302:     nz = bi[i + 1] - bi[i];
303:     for (j = 0; j < nz; j++) {
304:       x      = rtmp + 36 * pj[j];
305:       pv[0]  = x[0];
306:       pv[1]  = x[1];
307:       pv[2]  = x[2];
308:       pv[3]  = x[3];
309:       pv[4]  = x[4];
310:       pv[5]  = x[5];
311:       pv[6]  = x[6];
312:       pv[7]  = x[7];
313:       pv[8]  = x[8];
314:       pv[9]  = x[9];
315:       pv[10] = x[10];
316:       pv[11] = x[11];
317:       pv[12] = x[12];
318:       pv[13] = x[13];
319:       pv[14] = x[14];
320:       pv[15] = x[15];
321:       pv[16] = x[16];
322:       pv[17] = x[17];
323:       pv[18] = x[18];
324:       pv[19] = x[19];
325:       pv[20] = x[20];
326:       pv[21] = x[21];
327:       pv[22] = x[22];
328:       pv[23] = x[23];
329:       pv[24] = x[24];
330:       pv[25] = x[25];
331:       pv[26] = x[26];
332:       pv[27] = x[27];
333:       pv[28] = x[28];
334:       pv[29] = x[29];
335:       pv[30] = x[30];
336:       pv[31] = x[31];
337:       pv[32] = x[32];
338:       pv[33] = x[33];
339:       pv[34] = x[34];
340:       pv[35] = x[35];
341:       pv += 36;
342:     }
343:     /* invert diagonal block */
344:     w = ba + 36 * diag_offset[i];
345:     PetscCall(PetscKernel_A_gets_inverse_A_6(w, shift, allowzeropivot, &zeropivotdetected));
346:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
347:   }

349:   PetscCall(PetscFree(rtmp));
350:   PetscCall(ISRestoreIndices(isicol, &ic));
351:   PetscCall(ISRestoreIndices(isrow, &r));

353:   C->ops->solve          = MatSolve_SeqBAIJ_6_inplace;
354:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_6_inplace;
355:   C->assembled           = PETSC_TRUE;

357:   PetscCall(PetscLogFlops(1.333333333333 * 6 * 6 * 6 * b->mbs)); /* from inverting diagonal blocks */
358:   PetscFunctionReturn(PETSC_SUCCESS);
359: }

361: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_6(Mat B, Mat A, const MatFactorInfo *info)
362: {
363:   Mat             C = B;
364:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
365:   IS              isrow = b->row, isicol = b->icol;
366:   const PetscInt *r, *ic;
367:   PetscInt        i, j, k, nz, nzL, row;
368:   const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
369:   const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
370:   MatScalar      *rtmp, *pc, *mwork, *v, *pv, *aa = a->a;
371:   PetscInt        flg;
372:   PetscReal       shift = info->shiftamount;
373:   PetscBool       allowzeropivot, zeropivotdetected;

375:   PetscFunctionBegin;
376:   allowzeropivot = PetscNot(A->erroriffailure);
377:   PetscCall(ISGetIndices(isrow, &r));
378:   PetscCall(ISGetIndices(isicol, &ic));

380:   /* generate work space needed by the factorization */
381:   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
382:   PetscCall(PetscArrayzero(rtmp, bs2 * n));

384:   for (i = 0; i < n; i++) {
385:     /* zero rtmp */
386:     /* L part */
387:     nz    = bi[i + 1] - bi[i];
388:     bjtmp = bj + bi[i];
389:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

391:     /* U part */
392:     nz    = bdiag[i] - bdiag[i + 1];
393:     bjtmp = bj + bdiag[i + 1] + 1;
394:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

396:     /* load in initial (unfactored row) */
397:     nz    = ai[r[i] + 1] - ai[r[i]];
398:     ajtmp = aj + ai[r[i]];
399:     v     = aa + bs2 * ai[r[i]];
400:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ic[ajtmp[j]], v + bs2 * j, bs2));

402:     /* elimination */
403:     bjtmp = bj + bi[i];
404:     nzL   = bi[i + 1] - bi[i];
405:     for (k = 0; k < nzL; k++) {
406:       row = bjtmp[k];
407:       pc  = rtmp + bs2 * row;
408:       for (flg = 0, j = 0; j < bs2; j++) {
409:         if (pc[j] != 0.0) {
410:           flg = 1;
411:           break;
412:         }
413:       }
414:       if (flg) {
415:         pv = b->a + bs2 * bdiag[row];
416:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
417:         PetscCall(PetscKernel_A_gets_A_times_B_6(pc, pv, mwork));

419:         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
420:         pv = b->a + bs2 * (bdiag[row + 1] + 1);
421:         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
422:         for (j = 0; j < nz; j++) {
423:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
424:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
425:           v = rtmp + bs2 * pj[j];
426:           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_6(v, pc, pv));
427:           pv += bs2;
428:         }
429:         PetscCall(PetscLogFlops(432.0 * nz + 396)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
430:       }
431:     }

433:     /* finished row so stick it into b->a */
434:     /* L part */
435:     pv = b->a + bs2 * bi[i];
436:     pj = b->j + bi[i];
437:     nz = bi[i + 1] - bi[i];
438:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));

440:     /* Mark diagonal and invert diagonal for simpler triangular solves */
441:     pv = b->a + bs2 * bdiag[i];
442:     pj = b->j + bdiag[i];
443:     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
444:     PetscCall(PetscKernel_A_gets_inverse_A_6(pv, shift, allowzeropivot, &zeropivotdetected));
445:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

447:     /* U part */
448:     pv = b->a + bs2 * (bdiag[i + 1] + 1);
449:     pj = b->j + bdiag[i + 1] + 1;
450:     nz = bdiag[i] - bdiag[i + 1] - 1;
451:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
452:   }

454:   PetscCall(PetscFree2(rtmp, mwork));
455:   PetscCall(ISRestoreIndices(isicol, &ic));
456:   PetscCall(ISRestoreIndices(isrow, &r));

458:   C->ops->solve          = MatSolve_SeqBAIJ_6;
459:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_6;
460:   C->assembled           = PETSC_TRUE;

462:   PetscCall(PetscLogFlops(1.333333333333 * 6 * 6 * 6 * n)); /* from inverting diagonal blocks */
463:   PetscFunctionReturn(PETSC_SUCCESS);
464: }

466: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_6_NaturalOrdering_inplace(Mat C, Mat A, const MatFactorInfo *info)
467: {
468:   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
469:   PetscInt     i, j, n = a->mbs, *bi = b->i, *bj = b->j;
470:   PetscInt    *ajtmpold, *ajtmp, nz, row;
471:   PetscInt    *diag_offset = b->diag, *ai = a->i, *aj = a->j, *pj;
472:   MatScalar   *pv, *v, *rtmp, *pc, *w, *x;
473:   MatScalar    x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15;
474:   MatScalar    x16, x17, x18, x19, x20, x21, x22, x23, x24, x25;
475:   MatScalar    p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12, p13, p14, p15;
476:   MatScalar    p16, p17, p18, p19, p20, p21, p22, p23, p24, p25;
477:   MatScalar    m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12, m13, m14, m15;
478:   MatScalar    m16, m17, m18, m19, m20, m21, m22, m23, m24, m25;
479:   MatScalar    p26, p27, p28, p29, p30, p31, p32, p33, p34, p35, p36;
480:   MatScalar    x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36;
481:   MatScalar    m26, m27, m28, m29, m30, m31, m32, m33, m34, m35, m36;
482:   MatScalar   *ba = b->a, *aa = a->a;
483:   PetscReal    shift = info->shiftamount;
484:   PetscBool    allowzeropivot, zeropivotdetected;

486:   PetscFunctionBegin;
487:   allowzeropivot = PetscNot(A->erroriffailure);
488:   PetscCall(PetscMalloc1(36 * (n + 1), &rtmp));
489:   for (i = 0; i < n; i++) {
490:     nz    = bi[i + 1] - bi[i];
491:     ajtmp = bj + bi[i];
492:     for (j = 0; j < nz; j++) {
493:       x    = rtmp + 36 * ajtmp[j];
494:       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
495:       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
496:       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0;
497:       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0;
498:       x[34] = x[35] = 0.0;
499:     }
500:     /* load in initial (unfactored row) */
501:     nz       = ai[i + 1] - ai[i];
502:     ajtmpold = aj + ai[i];
503:     v        = aa + 36 * ai[i];
504:     for (j = 0; j < nz; j++) {
505:       x     = rtmp + 36 * ajtmpold[j];
506:       x[0]  = v[0];
507:       x[1]  = v[1];
508:       x[2]  = v[2];
509:       x[3]  = v[3];
510:       x[4]  = v[4];
511:       x[5]  = v[5];
512:       x[6]  = v[6];
513:       x[7]  = v[7];
514:       x[8]  = v[8];
515:       x[9]  = v[9];
516:       x[10] = v[10];
517:       x[11] = v[11];
518:       x[12] = v[12];
519:       x[13] = v[13];
520:       x[14] = v[14];
521:       x[15] = v[15];
522:       x[16] = v[16];
523:       x[17] = v[17];
524:       x[18] = v[18];
525:       x[19] = v[19];
526:       x[20] = v[20];
527:       x[21] = v[21];
528:       x[22] = v[22];
529:       x[23] = v[23];
530:       x[24] = v[24];
531:       x[25] = v[25];
532:       x[26] = v[26];
533:       x[27] = v[27];
534:       x[28] = v[28];
535:       x[29] = v[29];
536:       x[30] = v[30];
537:       x[31] = v[31];
538:       x[32] = v[32];
539:       x[33] = v[33];
540:       x[34] = v[34];
541:       x[35] = v[35];
542:       v += 36;
543:     }
544:     row = *ajtmp++;
545:     while (row < i) {
546:       pc  = rtmp + 36 * row;
547:       p1  = pc[0];
548:       p2  = pc[1];
549:       p3  = pc[2];
550:       p4  = pc[3];
551:       p5  = pc[4];
552:       p6  = pc[5];
553:       p7  = pc[6];
554:       p8  = pc[7];
555:       p9  = pc[8];
556:       p10 = pc[9];
557:       p11 = pc[10];
558:       p12 = pc[11];
559:       p13 = pc[12];
560:       p14 = pc[13];
561:       p15 = pc[14];
562:       p16 = pc[15];
563:       p17 = pc[16];
564:       p18 = pc[17];
565:       p19 = pc[18];
566:       p20 = pc[19];
567:       p21 = pc[20];
568:       p22 = pc[21];
569:       p23 = pc[22];
570:       p24 = pc[23];
571:       p25 = pc[24];
572:       p26 = pc[25];
573:       p27 = pc[26];
574:       p28 = pc[27];
575:       p29 = pc[28];
576:       p30 = pc[29];
577:       p31 = pc[30];
578:       p32 = pc[31];
579:       p33 = pc[32];
580:       p34 = pc[33];
581:       p35 = pc[34];
582:       p36 = pc[35];
583:       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) {
584:         pv    = ba + 36 * diag_offset[row];
585:         pj    = bj + diag_offset[row] + 1;
586:         x1    = pv[0];
587:         x2    = pv[1];
588:         x3    = pv[2];
589:         x4    = pv[3];
590:         x5    = pv[4];
591:         x6    = pv[5];
592:         x7    = pv[6];
593:         x8    = pv[7];
594:         x9    = pv[8];
595:         x10   = pv[9];
596:         x11   = pv[10];
597:         x12   = pv[11];
598:         x13   = pv[12];
599:         x14   = pv[13];
600:         x15   = pv[14];
601:         x16   = pv[15];
602:         x17   = pv[16];
603:         x18   = pv[17];
604:         x19   = pv[18];
605:         x20   = pv[19];
606:         x21   = pv[20];
607:         x22   = pv[21];
608:         x23   = pv[22];
609:         x24   = pv[23];
610:         x25   = pv[24];
611:         x26   = pv[25];
612:         x27   = pv[26];
613:         x28   = pv[27];
614:         x29   = pv[28];
615:         x30   = pv[29];
616:         x31   = pv[30];
617:         x32   = pv[31];
618:         x33   = pv[32];
619:         x34   = pv[33];
620:         x35   = pv[34];
621:         x36   = pv[35];
622:         pc[0] = m1 = p1 * x1 + p7 * x2 + p13 * x3 + p19 * x4 + p25 * x5 + p31 * x6;
623:         pc[1] = m2 = p2 * x1 + p8 * x2 + p14 * x3 + p20 * x4 + p26 * x5 + p32 * x6;
624:         pc[2] = m3 = p3 * x1 + p9 * x2 + p15 * x3 + p21 * x4 + p27 * x5 + p33 * x6;
625:         pc[3] = m4 = p4 * x1 + p10 * x2 + p16 * x3 + p22 * x4 + p28 * x5 + p34 * x6;
626:         pc[4] = m5 = p5 * x1 + p11 * x2 + p17 * x3 + p23 * x4 + p29 * x5 + p35 * x6;
627:         pc[5] = m6 = p6 * x1 + p12 * x2 + p18 * x3 + p24 * x4 + p30 * x5 + p36 * x6;

629:         pc[6] = m7 = p1 * x7 + p7 * x8 + p13 * x9 + p19 * x10 + p25 * x11 + p31 * x12;
630:         pc[7] = m8 = p2 * x7 + p8 * x8 + p14 * x9 + p20 * x10 + p26 * x11 + p32 * x12;
631:         pc[8] = m9 = p3 * x7 + p9 * x8 + p15 * x9 + p21 * x10 + p27 * x11 + p33 * x12;
632:         pc[9] = m10 = p4 * x7 + p10 * x8 + p16 * x9 + p22 * x10 + p28 * x11 + p34 * x12;
633:         pc[10] = m11 = p5 * x7 + p11 * x8 + p17 * x9 + p23 * x10 + p29 * x11 + p35 * x12;
634:         pc[11] = m12 = p6 * x7 + p12 * x8 + p18 * x9 + p24 * x10 + p30 * x11 + p36 * x12;

636:         pc[12] = m13 = p1 * x13 + p7 * x14 + p13 * x15 + p19 * x16 + p25 * x17 + p31 * x18;
637:         pc[13] = m14 = p2 * x13 + p8 * x14 + p14 * x15 + p20 * x16 + p26 * x17 + p32 * x18;
638:         pc[14] = m15 = p3 * x13 + p9 * x14 + p15 * x15 + p21 * x16 + p27 * x17 + p33 * x18;
639:         pc[15] = m16 = p4 * x13 + p10 * x14 + p16 * x15 + p22 * x16 + p28 * x17 + p34 * x18;
640:         pc[16] = m17 = p5 * x13 + p11 * x14 + p17 * x15 + p23 * x16 + p29 * x17 + p35 * x18;
641:         pc[17] = m18 = p6 * x13 + p12 * x14 + p18 * x15 + p24 * x16 + p30 * x17 + p36 * x18;

643:         pc[18] = m19 = p1 * x19 + p7 * x20 + p13 * x21 + p19 * x22 + p25 * x23 + p31 * x24;
644:         pc[19] = m20 = p2 * x19 + p8 * x20 + p14 * x21 + p20 * x22 + p26 * x23 + p32 * x24;
645:         pc[20] = m21 = p3 * x19 + p9 * x20 + p15 * x21 + p21 * x22 + p27 * x23 + p33 * x24;
646:         pc[21] = m22 = p4 * x19 + p10 * x20 + p16 * x21 + p22 * x22 + p28 * x23 + p34 * x24;
647:         pc[22] = m23 = p5 * x19 + p11 * x20 + p17 * x21 + p23 * x22 + p29 * x23 + p35 * x24;
648:         pc[23] = m24 = p6 * x19 + p12 * x20 + p18 * x21 + p24 * x22 + p30 * x23 + p36 * x24;

650:         pc[24] = m25 = p1 * x25 + p7 * x26 + p13 * x27 + p19 * x28 + p25 * x29 + p31 * x30;
651:         pc[25] = m26 = p2 * x25 + p8 * x26 + p14 * x27 + p20 * x28 + p26 * x29 + p32 * x30;
652:         pc[26] = m27 = p3 * x25 + p9 * x26 + p15 * x27 + p21 * x28 + p27 * x29 + p33 * x30;
653:         pc[27] = m28 = p4 * x25 + p10 * x26 + p16 * x27 + p22 * x28 + p28 * x29 + p34 * x30;
654:         pc[28] = m29 = p5 * x25 + p11 * x26 + p17 * x27 + p23 * x28 + p29 * x29 + p35 * x30;
655:         pc[29] = m30 = p6 * x25 + p12 * x26 + p18 * x27 + p24 * x28 + p30 * x29 + p36 * x30;

657:         pc[30] = m31 = p1 * x31 + p7 * x32 + p13 * x33 + p19 * x34 + p25 * x35 + p31 * x36;
658:         pc[31] = m32 = p2 * x31 + p8 * x32 + p14 * x33 + p20 * x34 + p26 * x35 + p32 * x36;
659:         pc[32] = m33 = p3 * x31 + p9 * x32 + p15 * x33 + p21 * x34 + p27 * x35 + p33 * x36;
660:         pc[33] = m34 = p4 * x31 + p10 * x32 + p16 * x33 + p22 * x34 + p28 * x35 + p34 * x36;
661:         pc[34] = m35 = p5 * x31 + p11 * x32 + p17 * x33 + p23 * x34 + p29 * x35 + p35 * x36;
662:         pc[35] = m36 = p6 * x31 + p12 * x32 + p18 * x33 + p24 * x34 + p30 * x35 + p36 * x36;

664:         nz = bi[row + 1] - diag_offset[row] - 1;
665:         pv += 36;
666:         for (j = 0; j < nz; j++) {
667:           x1  = pv[0];
668:           x2  = pv[1];
669:           x3  = pv[2];
670:           x4  = pv[3];
671:           x5  = pv[4];
672:           x6  = pv[5];
673:           x7  = pv[6];
674:           x8  = pv[7];
675:           x9  = pv[8];
676:           x10 = pv[9];
677:           x11 = pv[10];
678:           x12 = pv[11];
679:           x13 = pv[12];
680:           x14 = pv[13];
681:           x15 = pv[14];
682:           x16 = pv[15];
683:           x17 = pv[16];
684:           x18 = pv[17];
685:           x19 = pv[18];
686:           x20 = pv[19];
687:           x21 = pv[20];
688:           x22 = pv[21];
689:           x23 = pv[22];
690:           x24 = pv[23];
691:           x25 = pv[24];
692:           x26 = pv[25];
693:           x27 = pv[26];
694:           x28 = pv[27];
695:           x29 = pv[28];
696:           x30 = pv[29];
697:           x31 = pv[30];
698:           x32 = pv[31];
699:           x33 = pv[32];
700:           x34 = pv[33];
701:           x35 = pv[34];
702:           x36 = pv[35];
703:           x   = rtmp + 36 * pj[j];
704:           x[0] -= m1 * x1 + m7 * x2 + m13 * x3 + m19 * x4 + m25 * x5 + m31 * x6;
705:           x[1] -= m2 * x1 + m8 * x2 + m14 * x3 + m20 * x4 + m26 * x5 + m32 * x6;
706:           x[2] -= m3 * x1 + m9 * x2 + m15 * x3 + m21 * x4 + m27 * x5 + m33 * x6;
707:           x[3] -= m4 * x1 + m10 * x2 + m16 * x3 + m22 * x4 + m28 * x5 + m34 * x6;
708:           x[4] -= m5 * x1 + m11 * x2 + m17 * x3 + m23 * x4 + m29 * x5 + m35 * x6;
709:           x[5] -= m6 * x1 + m12 * x2 + m18 * x3 + m24 * x4 + m30 * x5 + m36 * x6;

711:           x[6] -= m1 * x7 + m7 * x8 + m13 * x9 + m19 * x10 + m25 * x11 + m31 * x12;
712:           x[7] -= m2 * x7 + m8 * x8 + m14 * x9 + m20 * x10 + m26 * x11 + m32 * x12;
713:           x[8] -= m3 * x7 + m9 * x8 + m15 * x9 + m21 * x10 + m27 * x11 + m33 * x12;
714:           x[9] -= m4 * x7 + m10 * x8 + m16 * x9 + m22 * x10 + m28 * x11 + m34 * x12;
715:           x[10] -= m5 * x7 + m11 * x8 + m17 * x9 + m23 * x10 + m29 * x11 + m35 * x12;
716:           x[11] -= m6 * x7 + m12 * x8 + m18 * x9 + m24 * x10 + m30 * x11 + m36 * x12;

718:           x[12] -= m1 * x13 + m7 * x14 + m13 * x15 + m19 * x16 + m25 * x17 + m31 * x18;
719:           x[13] -= m2 * x13 + m8 * x14 + m14 * x15 + m20 * x16 + m26 * x17 + m32 * x18;
720:           x[14] -= m3 * x13 + m9 * x14 + m15 * x15 + m21 * x16 + m27 * x17 + m33 * x18;
721:           x[15] -= m4 * x13 + m10 * x14 + m16 * x15 + m22 * x16 + m28 * x17 + m34 * x18;
722:           x[16] -= m5 * x13 + m11 * x14 + m17 * x15 + m23 * x16 + m29 * x17 + m35 * x18;
723:           x[17] -= m6 * x13 + m12 * x14 + m18 * x15 + m24 * x16 + m30 * x17 + m36 * x18;

725:           x[18] -= m1 * x19 + m7 * x20 + m13 * x21 + m19 * x22 + m25 * x23 + m31 * x24;
726:           x[19] -= m2 * x19 + m8 * x20 + m14 * x21 + m20 * x22 + m26 * x23 + m32 * x24;
727:           x[20] -= m3 * x19 + m9 * x20 + m15 * x21 + m21 * x22 + m27 * x23 + m33 * x24;
728:           x[21] -= m4 * x19 + m10 * x20 + m16 * x21 + m22 * x22 + m28 * x23 + m34 * x24;
729:           x[22] -= m5 * x19 + m11 * x20 + m17 * x21 + m23 * x22 + m29 * x23 + m35 * x24;
730:           x[23] -= m6 * x19 + m12 * x20 + m18 * x21 + m24 * x22 + m30 * x23 + m36 * x24;

732:           x[24] -= m1 * x25 + m7 * x26 + m13 * x27 + m19 * x28 + m25 * x29 + m31 * x30;
733:           x[25] -= m2 * x25 + m8 * x26 + m14 * x27 + m20 * x28 + m26 * x29 + m32 * x30;
734:           x[26] -= m3 * x25 + m9 * x26 + m15 * x27 + m21 * x28 + m27 * x29 + m33 * x30;
735:           x[27] -= m4 * x25 + m10 * x26 + m16 * x27 + m22 * x28 + m28 * x29 + m34 * x30;
736:           x[28] -= m5 * x25 + m11 * x26 + m17 * x27 + m23 * x28 + m29 * x29 + m35 * x30;
737:           x[29] -= m6 * x25 + m12 * x26 + m18 * x27 + m24 * x28 + m30 * x29 + m36 * x30;

739:           x[30] -= m1 * x31 + m7 * x32 + m13 * x33 + m19 * x34 + m25 * x35 + m31 * x36;
740:           x[31] -= m2 * x31 + m8 * x32 + m14 * x33 + m20 * x34 + m26 * x35 + m32 * x36;
741:           x[32] -= m3 * x31 + m9 * x32 + m15 * x33 + m21 * x34 + m27 * x35 + m33 * x36;
742:           x[33] -= m4 * x31 + m10 * x32 + m16 * x33 + m22 * x34 + m28 * x35 + m34 * x36;
743:           x[34] -= m5 * x31 + m11 * x32 + m17 * x33 + m23 * x34 + m29 * x35 + m35 * x36;
744:           x[35] -= m6 * x31 + m12 * x32 + m18 * x33 + m24 * x34 + m30 * x35 + m36 * x36;

746:           pv += 36;
747:         }
748:         PetscCall(PetscLogFlops(432.0 * nz + 396.0));
749:       }
750:       row = *ajtmp++;
751:     }
752:     /* finished row so stick it into b->a */
753:     pv = ba + 36 * bi[i];
754:     pj = bj + bi[i];
755:     nz = bi[i + 1] - bi[i];
756:     for (j = 0; j < nz; j++) {
757:       x      = rtmp + 36 * pj[j];
758:       pv[0]  = x[0];
759:       pv[1]  = x[1];
760:       pv[2]  = x[2];
761:       pv[3]  = x[3];
762:       pv[4]  = x[4];
763:       pv[5]  = x[5];
764:       pv[6]  = x[6];
765:       pv[7]  = x[7];
766:       pv[8]  = x[8];
767:       pv[9]  = x[9];
768:       pv[10] = x[10];
769:       pv[11] = x[11];
770:       pv[12] = x[12];
771:       pv[13] = x[13];
772:       pv[14] = x[14];
773:       pv[15] = x[15];
774:       pv[16] = x[16];
775:       pv[17] = x[17];
776:       pv[18] = x[18];
777:       pv[19] = x[19];
778:       pv[20] = x[20];
779:       pv[21] = x[21];
780:       pv[22] = x[22];
781:       pv[23] = x[23];
782:       pv[24] = x[24];
783:       pv[25] = x[25];
784:       pv[26] = x[26];
785:       pv[27] = x[27];
786:       pv[28] = x[28];
787:       pv[29] = x[29];
788:       pv[30] = x[30];
789:       pv[31] = x[31];
790:       pv[32] = x[32];
791:       pv[33] = x[33];
792:       pv[34] = x[34];
793:       pv[35] = x[35];
794:       pv += 36;
795:     }
796:     /* invert diagonal block */
797:     w = ba + 36 * diag_offset[i];
798:     PetscCall(PetscKernel_A_gets_inverse_A_6(w, shift, allowzeropivot, &zeropivotdetected));
799:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
800:   }

802:   PetscCall(PetscFree(rtmp));

804:   C->ops->solve          = MatSolve_SeqBAIJ_6_NaturalOrdering_inplace;
805:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_6_NaturalOrdering_inplace;
806:   C->assembled           = PETSC_TRUE;

808:   PetscCall(PetscLogFlops(1.333333333333 * 6 * 6 * 6 * b->mbs)); /* from inverting diagonal blocks */
809:   PetscFunctionReturn(PETSC_SUCCESS);
810: }

812: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_6_NaturalOrdering(Mat B, Mat A, const MatFactorInfo *info)
813: {
814:   Mat             C = B;
815:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
816:   PetscInt        i, j, k, nz, nzL, row;
817:   const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
818:   const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
819:   MatScalar      *rtmp, *pc, *mwork, *v, *pv, *aa = a->a;
820:   PetscInt        flg;
821:   PetscReal       shift = info->shiftamount;
822:   PetscBool       allowzeropivot, zeropivotdetected;

824:   PetscFunctionBegin;
825:   allowzeropivot = PetscNot(A->erroriffailure);

827:   /* generate work space needed by the factorization */
828:   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
829:   PetscCall(PetscArrayzero(rtmp, bs2 * n));

831:   for (i = 0; i < n; i++) {
832:     /* zero rtmp */
833:     /* L part */
834:     nz    = bi[i + 1] - bi[i];
835:     bjtmp = bj + bi[i];
836:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

838:     /* U part */
839:     nz    = bdiag[i] - bdiag[i + 1];
840:     bjtmp = bj + bdiag[i + 1] + 1;
841:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

843:     /* load in initial (unfactored row) */
844:     nz    = ai[i + 1] - ai[i];
845:     ajtmp = aj + ai[i];
846:     v     = aa + bs2 * ai[i];
847:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ajtmp[j], v + bs2 * j, bs2));

849:     /* elimination */
850:     bjtmp = bj + bi[i];
851:     nzL   = bi[i + 1] - bi[i];
852:     for (k = 0; k < nzL; k++) {
853:       row = bjtmp[k];
854:       pc  = rtmp + bs2 * row;
855:       for (flg = 0, j = 0; j < bs2; j++) {
856:         if (pc[j] != 0.0) {
857:           flg = 1;
858:           break;
859:         }
860:       }
861:       if (flg) {
862:         pv = b->a + bs2 * bdiag[row];
863:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
864:         PetscCall(PetscKernel_A_gets_A_times_B_6(pc, pv, mwork));

866:         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
867:         pv = b->a + bs2 * (bdiag[row + 1] + 1);
868:         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
869:         for (j = 0; j < nz; j++) {
870:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
871:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
872:           v = rtmp + bs2 * pj[j];
873:           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_6(v, pc, pv));
874:           pv += bs2;
875:         }
876:         PetscCall(PetscLogFlops(432.0 * nz + 396)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
877:       }
878:     }

880:     /* finished row so stick it into b->a */
881:     /* L part */
882:     pv = b->a + bs2 * bi[i];
883:     pj = b->j + bi[i];
884:     nz = bi[i + 1] - bi[i];
885:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));

887:     /* Mark diagonal and invert diagonal for simpler triangular solves */
888:     pv = b->a + bs2 * bdiag[i];
889:     pj = b->j + bdiag[i];
890:     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
891:     PetscCall(PetscKernel_A_gets_inverse_A_6(pv, shift, allowzeropivot, &zeropivotdetected));
892:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

894:     /* U part */
895:     pv = b->a + bs2 * (bdiag[i + 1] + 1);
896:     pj = b->j + bdiag[i + 1] + 1;
897:     nz = bdiag[i] - bdiag[i + 1] - 1;
898:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
899:   }
900:   PetscCall(PetscFree2(rtmp, mwork));

902:   C->ops->solve          = MatSolve_SeqBAIJ_6_NaturalOrdering;
903:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_6_NaturalOrdering;
904:   C->assembled           = PETSC_TRUE;

906:   PetscCall(PetscLogFlops(1.333333333333 * 6 * 6 * 6 * n)); /* from inverting diagonal blocks */
907:   PetscFunctionReturn(PETSC_SUCCESS);
908: }