Actual source code: baijfact9.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 5 by 5
  9: */
 10: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_inplace(Mat C, Mat A, const MatFactorInfo *info)
 11: {
 12:   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
 13:   IS               isrow = b->row, isicol = b->icol;
 14:   const PetscInt  *r, *ic, *bi = b->i, *bj = b->j, *ajtmpold, *ajtmp;
 15:   PetscInt         i, j, n = a->mbs, nz, row, idx, ipvt[5];
 16:   const PetscInt  *diag_offset = b->diag, *ai = a->i, *aj = a->j, *pj;
 17:   MatScalar       *w, *pv, *rtmp, *x, *pc;
 18:   const MatScalar *v, *aa = a->a;
 19:   MatScalar        p1, p2, p3, p4, m1, m2, m3, m4, m5, m6, m7, m8, m9, x1, x2, x3, x4;
 20:   MatScalar        p5, p6, p7, p8, p9, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16;
 21:   MatScalar        x17, x18, x19, x20, x21, x22, x23, x24, x25, p10, p11, p12, p13, p14;
 22:   MatScalar        p15, p16, p17, p18, p19, p20, p21, p22, p23, p24, p25, m10, m11, m12;
 23:   MatScalar        m13, m14, m15, m16, m17, m18, m19, m20, m21, m22, m23, m24, m25;
 24:   MatScalar       *ba    = b->a, work[25];
 25:   PetscReal        shift = info->shiftamount;
 26:   PetscBool        allowzeropivot, zeropivotdetected;

 28:   PetscFunctionBegin;
 29:   allowzeropivot = PetscNot(A->erroriffailure);
 30:   PetscCall(ISGetIndices(isrow, &r));
 31:   PetscCall(ISGetIndices(isicol, &ic));
 32:   PetscCall(PetscMalloc1(25 * (n + 1), &rtmp));

 34: #define PETSC_USE_MEMZERO 1
 35: #define PETSC_USE_MEMCPY  1

 37:   for (i = 0; i < n; i++) {
 38:     nz    = bi[i + 1] - bi[i];
 39:     ajtmp = bj + bi[i];
 40:     for (j = 0; j < nz; j++) {
 41: #if defined(PETSC_USE_MEMZERO)
 42:       PetscCall(PetscArrayzero(rtmp + 25 * ajtmp[j], 25));
 43: #else
 44:       x    = rtmp + 25 * ajtmp[j];
 45:       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
 46:       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
 47:       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
 48: #endif
 49:     }
 50:     /* load in initial (unfactored row) */
 51:     idx      = r[i];
 52:     nz       = ai[idx + 1] - ai[idx];
 53:     ajtmpold = aj + ai[idx];
 54:     v        = aa + 25 * ai[idx];
 55:     for (j = 0; j < nz; j++) {
 56: #if defined(PETSC_USE_MEMCPY)
 57:       PetscCall(PetscArraycpy(rtmp + 25 * ic[ajtmpold[j]], v, 25));
 58: #else
 59:       x     = rtmp + 25 * ic[ajtmpold[j]];
 60:       x[0]  = v[0];
 61:       x[1]  = v[1];
 62:       x[2]  = v[2];
 63:       x[3]  = v[3];
 64:       x[4]  = v[4];
 65:       x[5]  = v[5];
 66:       x[6]  = v[6];
 67:       x[7]  = v[7];
 68:       x[8]  = v[8];
 69:       x[9]  = v[9];
 70:       x[10] = v[10];
 71:       x[11] = v[11];
 72:       x[12] = v[12];
 73:       x[13] = v[13];
 74:       x[14] = v[14];
 75:       x[15] = v[15];
 76:       x[16] = v[16];
 77:       x[17] = v[17];
 78:       x[18] = v[18];
 79:       x[19] = v[19];
 80:       x[20] = v[20];
 81:       x[21] = v[21];
 82:       x[22] = v[22];
 83:       x[23] = v[23];
 84:       x[24] = v[24];
 85: #endif
 86:       v += 25;
 87:     }
 88:     row = *ajtmp++;
 89:     while (row < i) {
 90:       pc  = rtmp + 25 * row;
 91:       p1  = pc[0];
 92:       p2  = pc[1];
 93:       p3  = pc[2];
 94:       p4  = pc[3];
 95:       p5  = pc[4];
 96:       p6  = pc[5];
 97:       p7  = pc[6];
 98:       p8  = pc[7];
 99:       p9  = pc[8];
100:       p10 = pc[9];
101:       p11 = pc[10];
102:       p12 = pc[11];
103:       p13 = pc[12];
104:       p14 = pc[13];
105:       p15 = pc[14];
106:       p16 = pc[15];
107:       p17 = pc[16];
108:       p18 = pc[17];
109:       p19 = pc[18];
110:       p20 = pc[19];
111:       p21 = pc[20];
112:       p22 = pc[21];
113:       p23 = pc[22];
114:       p24 = pc[23];
115:       p25 = pc[24];
116:       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
117:         pv    = ba + 25 * diag_offset[row];
118:         pj    = bj + diag_offset[row] + 1;
119:         x1    = pv[0];
120:         x2    = pv[1];
121:         x3    = pv[2];
122:         x4    = pv[3];
123:         x5    = pv[4];
124:         x6    = pv[5];
125:         x7    = pv[6];
126:         x8    = pv[7];
127:         x9    = pv[8];
128:         x10   = pv[9];
129:         x11   = pv[10];
130:         x12   = pv[11];
131:         x13   = pv[12];
132:         x14   = pv[13];
133:         x15   = pv[14];
134:         x16   = pv[15];
135:         x17   = pv[16];
136:         x18   = pv[17];
137:         x19   = pv[18];
138:         x20   = pv[19];
139:         x21   = pv[20];
140:         x22   = pv[21];
141:         x23   = pv[22];
142:         x24   = pv[23];
143:         x25   = pv[24];
144:         pc[0] = m1 = p1 * x1 + p6 * x2 + p11 * x3 + p16 * x4 + p21 * x5;
145:         pc[1] = m2 = p2 * x1 + p7 * x2 + p12 * x3 + p17 * x4 + p22 * x5;
146:         pc[2] = m3 = p3 * x1 + p8 * x2 + p13 * x3 + p18 * x4 + p23 * x5;
147:         pc[3] = m4 = p4 * x1 + p9 * x2 + p14 * x3 + p19 * x4 + p24 * x5;
148:         pc[4] = m5 = p5 * x1 + p10 * x2 + p15 * x3 + p20 * x4 + p25 * x5;

150:         pc[5] = m6 = p1 * x6 + p6 * x7 + p11 * x8 + p16 * x9 + p21 * x10;
151:         pc[6] = m7 = p2 * x6 + p7 * x7 + p12 * x8 + p17 * x9 + p22 * x10;
152:         pc[7] = m8 = p3 * x6 + p8 * x7 + p13 * x8 + p18 * x9 + p23 * x10;
153:         pc[8] = m9 = p4 * x6 + p9 * x7 + p14 * x8 + p19 * x9 + p24 * x10;
154:         pc[9] = m10 = p5 * x6 + p10 * x7 + p15 * x8 + p20 * x9 + p25 * x10;

156:         pc[10] = m11 = p1 * x11 + p6 * x12 + p11 * x13 + p16 * x14 + p21 * x15;
157:         pc[11] = m12 = p2 * x11 + p7 * x12 + p12 * x13 + p17 * x14 + p22 * x15;
158:         pc[12] = m13 = p3 * x11 + p8 * x12 + p13 * x13 + p18 * x14 + p23 * x15;
159:         pc[13] = m14 = p4 * x11 + p9 * x12 + p14 * x13 + p19 * x14 + p24 * x15;
160:         pc[14] = m15 = p5 * x11 + p10 * x12 + p15 * x13 + p20 * x14 + p25 * x15;

162:         pc[15] = m16 = p1 * x16 + p6 * x17 + p11 * x18 + p16 * x19 + p21 * x20;
163:         pc[16] = m17 = p2 * x16 + p7 * x17 + p12 * x18 + p17 * x19 + p22 * x20;
164:         pc[17] = m18 = p3 * x16 + p8 * x17 + p13 * x18 + p18 * x19 + p23 * x20;
165:         pc[18] = m19 = p4 * x16 + p9 * x17 + p14 * x18 + p19 * x19 + p24 * x20;
166:         pc[19] = m20 = p5 * x16 + p10 * x17 + p15 * x18 + p20 * x19 + p25 * x20;

168:         pc[20] = m21 = p1 * x21 + p6 * x22 + p11 * x23 + p16 * x24 + p21 * x25;
169:         pc[21] = m22 = p2 * x21 + p7 * x22 + p12 * x23 + p17 * x24 + p22 * x25;
170:         pc[22] = m23 = p3 * x21 + p8 * x22 + p13 * x23 + p18 * x24 + p23 * x25;
171:         pc[23] = m24 = p4 * x21 + p9 * x22 + p14 * x23 + p19 * x24 + p24 * x25;
172:         pc[24] = m25 = p5 * x21 + p10 * x22 + p15 * x23 + p20 * x24 + p25 * x25;

174:         nz = bi[row + 1] - diag_offset[row] - 1;
175:         pv += 25;
176:         for (j = 0; j < nz; j++) {
177:           x1  = pv[0];
178:           x2  = pv[1];
179:           x3  = pv[2];
180:           x4  = pv[3];
181:           x5  = pv[4];
182:           x6  = pv[5];
183:           x7  = pv[6];
184:           x8  = pv[7];
185:           x9  = pv[8];
186:           x10 = pv[9];
187:           x11 = pv[10];
188:           x12 = pv[11];
189:           x13 = pv[12];
190:           x14 = pv[13];
191:           x15 = pv[14];
192:           x16 = pv[15];
193:           x17 = pv[16];
194:           x18 = pv[17];
195:           x19 = pv[18];
196:           x20 = pv[19];
197:           x21 = pv[20];
198:           x22 = pv[21];
199:           x23 = pv[22];
200:           x24 = pv[23];
201:           x25 = pv[24];
202:           x   = rtmp + 25 * pj[j];
203:           x[0] -= m1 * x1 + m6 * x2 + m11 * x3 + m16 * x4 + m21 * x5;
204:           x[1] -= m2 * x1 + m7 * x2 + m12 * x3 + m17 * x4 + m22 * x5;
205:           x[2] -= m3 * x1 + m8 * x2 + m13 * x3 + m18 * x4 + m23 * x5;
206:           x[3] -= m4 * x1 + m9 * x2 + m14 * x3 + m19 * x4 + m24 * x5;
207:           x[4] -= m5 * x1 + m10 * x2 + m15 * x3 + m20 * x4 + m25 * x5;

209:           x[5] -= m1 * x6 + m6 * x7 + m11 * x8 + m16 * x9 + m21 * x10;
210:           x[6] -= m2 * x6 + m7 * x7 + m12 * x8 + m17 * x9 + m22 * x10;
211:           x[7] -= m3 * x6 + m8 * x7 + m13 * x8 + m18 * x9 + m23 * x10;
212:           x[8] -= m4 * x6 + m9 * x7 + m14 * x8 + m19 * x9 + m24 * x10;
213:           x[9] -= m5 * x6 + m10 * x7 + m15 * x8 + m20 * x9 + m25 * x10;

215:           x[10] -= m1 * x11 + m6 * x12 + m11 * x13 + m16 * x14 + m21 * x15;
216:           x[11] -= m2 * x11 + m7 * x12 + m12 * x13 + m17 * x14 + m22 * x15;
217:           x[12] -= m3 * x11 + m8 * x12 + m13 * x13 + m18 * x14 + m23 * x15;
218:           x[13] -= m4 * x11 + m9 * x12 + m14 * x13 + m19 * x14 + m24 * x15;
219:           x[14] -= m5 * x11 + m10 * x12 + m15 * x13 + m20 * x14 + m25 * x15;

221:           x[15] -= m1 * x16 + m6 * x17 + m11 * x18 + m16 * x19 + m21 * x20;
222:           x[16] -= m2 * x16 + m7 * x17 + m12 * x18 + m17 * x19 + m22 * x20;
223:           x[17] -= m3 * x16 + m8 * x17 + m13 * x18 + m18 * x19 + m23 * x20;
224:           x[18] -= m4 * x16 + m9 * x17 + m14 * x18 + m19 * x19 + m24 * x20;
225:           x[19] -= m5 * x16 + m10 * x17 + m15 * x18 + m20 * x19 + m25 * x20;

227:           x[20] -= m1 * x21 + m6 * x22 + m11 * x23 + m16 * x24 + m21 * x25;
228:           x[21] -= m2 * x21 + m7 * x22 + m12 * x23 + m17 * x24 + m22 * x25;
229:           x[22] -= m3 * x21 + m8 * x22 + m13 * x23 + m18 * x24 + m23 * x25;
230:           x[23] -= m4 * x21 + m9 * x22 + m14 * x23 + m19 * x24 + m24 * x25;
231:           x[24] -= m5 * x21 + m10 * x22 + m15 * x23 + m20 * x24 + m25 * x25;

233:           pv += 25;
234:         }
235:         PetscCall(PetscLogFlops(250.0 * nz + 225.0));
236:       }
237:       row = *ajtmp++;
238:     }
239:     /* finished row so stick it into b->a */
240:     pv = ba + 25 * bi[i];
241:     pj = bj + bi[i];
242:     nz = bi[i + 1] - bi[i];
243:     for (j = 0; j < nz; j++) {
244: #if defined(PETSC_USE_MEMCPY)
245:       PetscCall(PetscArraycpy(pv, rtmp + 25 * pj[j], 25));
246: #else
247:       x      = rtmp + 25 * pj[j];
248:       pv[0]  = x[0];
249:       pv[1]  = x[1];
250:       pv[2]  = x[2];
251:       pv[3]  = x[3];
252:       pv[4]  = x[4];
253:       pv[5]  = x[5];
254:       pv[6]  = x[6];
255:       pv[7]  = x[7];
256:       pv[8]  = x[8];
257:       pv[9]  = x[9];
258:       pv[10] = x[10];
259:       pv[11] = x[11];
260:       pv[12] = x[12];
261:       pv[13] = x[13];
262:       pv[14] = x[14];
263:       pv[15] = x[15];
264:       pv[16] = x[16];
265:       pv[17] = x[17];
266:       pv[18] = x[18];
267:       pv[19] = x[19];
268:       pv[20] = x[20];
269:       pv[21] = x[21];
270:       pv[22] = x[22];
271:       pv[23] = x[23];
272:       pv[24] = x[24];
273: #endif
274:       pv += 25;
275:     }
276:     /* invert diagonal block */
277:     w = ba + 25 * diag_offset[i];
278:     PetscCall(PetscKernel_A_gets_inverse_A_5(w, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
279:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
280:   }

282:   PetscCall(PetscFree(rtmp));
283:   PetscCall(ISRestoreIndices(isicol, &ic));
284:   PetscCall(ISRestoreIndices(isrow, &r));

286:   C->ops->solve          = MatSolve_SeqBAIJ_5_inplace;
287:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_inplace;
288:   C->assembled           = PETSC_TRUE;

290:   PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * b->mbs)); /* from inverting diagonal blocks */
291:   PetscFunctionReturn(PETSC_SUCCESS);
292: }

294: /* MatLUFactorNumeric_SeqBAIJ_5 -
295:      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
296:        PetscKernel_A_gets_A_times_B()
297:        PetscKernel_A_gets_A_minus_B_times_C()
298:        PetscKernel_A_gets_inverse_A()
299: */

301: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5(Mat B, Mat A, const MatFactorInfo *info)
302: {
303:   Mat             C = B;
304:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
305:   IS              isrow = b->row, isicol = b->icol;
306:   const PetscInt *r, *ic;
307:   PetscInt        i, j, k, nz, nzL, row;
308:   const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
309:   const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
310:   MatScalar      *rtmp, *pc, *mwork, *v, *pv, *aa = a->a, work[25];
311:   PetscInt        flg, ipvt[5];
312:   PetscReal       shift = info->shiftamount;
313:   PetscBool       allowzeropivot, zeropivotdetected;

315:   PetscFunctionBegin;
316:   allowzeropivot = PetscNot(A->erroriffailure);
317:   PetscCall(ISGetIndices(isrow, &r));
318:   PetscCall(ISGetIndices(isicol, &ic));

320:   /* generate work space needed by the factorization */
321:   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
322:   PetscCall(PetscArrayzero(rtmp, bs2 * n));

324:   for (i = 0; i < n; i++) {
325:     /* zero rtmp */
326:     /* L part */
327:     nz    = bi[i + 1] - bi[i];
328:     bjtmp = bj + bi[i];
329:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

331:     /* U part */
332:     nz    = bdiag[i] - bdiag[i + 1];
333:     bjtmp = bj + bdiag[i + 1] + 1;
334:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

336:     /* load in initial (unfactored row) */
337:     nz    = ai[r[i] + 1] - ai[r[i]];
338:     ajtmp = aj + ai[r[i]];
339:     v     = aa + bs2 * ai[r[i]];
340:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ic[ajtmp[j]], v + bs2 * j, bs2));

342:     /* elimination */
343:     bjtmp = bj + bi[i];
344:     nzL   = bi[i + 1] - bi[i];
345:     for (k = 0; k < nzL; k++) {
346:       row = bjtmp[k];
347:       pc  = rtmp + bs2 * row;
348:       for (flg = 0, j = 0; j < bs2; j++) {
349:         if (pc[j] != 0.0) {
350:           flg = 1;
351:           break;
352:         }
353:       }
354:       if (flg) {
355:         pv = b->a + bs2 * bdiag[row];
356:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
357:         PetscCall(PetscKernel_A_gets_A_times_B_5(pc, pv, mwork));

359:         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
360:         pv = b->a + bs2 * (bdiag[row + 1] + 1);
361:         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
362:         for (j = 0; j < nz; j++) {
363:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
364:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
365:           v = rtmp + bs2 * pj[j];
366:           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_5(v, pc, pv));
367:           pv += bs2;
368:         }
369:         PetscCall(PetscLogFlops(250.0 * nz + 225)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
370:       }
371:     }

373:     /* finished row so stick it into b->a */
374:     /* L part */
375:     pv = b->a + bs2 * bi[i];
376:     pj = b->j + bi[i];
377:     nz = bi[i + 1] - bi[i];
378:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));

380:     /* Mark diagonal and invert diagonal for simpler triangular solves */
381:     pv = b->a + bs2 * bdiag[i];
382:     pj = b->j + bdiag[i];
383:     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
384:     PetscCall(PetscKernel_A_gets_inverse_A_5(pv, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
385:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

387:     /* U part */
388:     pv = b->a + bs2 * (bdiag[i + 1] + 1);
389:     pj = b->j + bdiag[i + 1] + 1;
390:     nz = bdiag[i] - bdiag[i + 1] - 1;
391:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
392:   }

394:   PetscCall(PetscFree2(rtmp, mwork));
395:   PetscCall(ISRestoreIndices(isicol, &ic));
396:   PetscCall(ISRestoreIndices(isrow, &r));

398:   C->ops->solve          = MatSolve_SeqBAIJ_5;
399:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5;
400:   C->assembled           = PETSC_TRUE;

402:   PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * n)); /* from inverting diagonal blocks */
403:   PetscFunctionReturn(PETSC_SUCCESS);
404: }

406: /*
407:       Version for when blocks are 5 by 5 Using natural ordering
408: */
409: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering_inplace(Mat C, Mat A, const MatFactorInfo *info)
410: {
411:   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
412:   PetscInt     i, j, n = a->mbs, *bi = b->i, *bj = b->j, ipvt[5];
413:   PetscInt    *ajtmpold, *ajtmp, nz, row;
414:   PetscInt    *diag_offset = b->diag, *ai = a->i, *aj = a->j, *pj;
415:   MatScalar   *pv, *v, *rtmp, *pc, *w, *x;
416:   MatScalar    x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15;
417:   MatScalar    x16, x17, x18, x19, x20, x21, x22, x23, x24, x25;
418:   MatScalar    p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12, p13, p14, p15;
419:   MatScalar    p16, p17, p18, p19, p20, p21, p22, p23, p24, p25;
420:   MatScalar    m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12, m13, m14, m15;
421:   MatScalar    m16, m17, m18, m19, m20, m21, m22, m23, m24, m25;
422:   MatScalar   *ba = b->a, *aa = a->a, work[25];
423:   PetscReal    shift = info->shiftamount;
424:   PetscBool    allowzeropivot, zeropivotdetected;

426:   PetscFunctionBegin;
427:   allowzeropivot = PetscNot(A->erroriffailure);
428:   PetscCall(PetscMalloc1(25 * (n + 1), &rtmp));
429:   for (i = 0; i < n; i++) {
430:     nz    = bi[i + 1] - bi[i];
431:     ajtmp = bj + bi[i];
432:     for (j = 0; j < nz; j++) {
433:       x    = rtmp + 25 * ajtmp[j];
434:       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
435:       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
436:       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
437:     }
438:     /* load in initial (unfactored row) */
439:     nz       = ai[i + 1] - ai[i];
440:     ajtmpold = aj + ai[i];
441:     v        = aa + 25 * ai[i];
442:     for (j = 0; j < nz; j++) {
443:       x     = rtmp + 25 * ajtmpold[j];
444:       x[0]  = v[0];
445:       x[1]  = v[1];
446:       x[2]  = v[2];
447:       x[3]  = v[3];
448:       x[4]  = v[4];
449:       x[5]  = v[5];
450:       x[6]  = v[6];
451:       x[7]  = v[7];
452:       x[8]  = v[8];
453:       x[9]  = v[9];
454:       x[10] = v[10];
455:       x[11] = v[11];
456:       x[12] = v[12];
457:       x[13] = v[13];
458:       x[14] = v[14];
459:       x[15] = v[15];
460:       x[16] = v[16];
461:       x[17] = v[17];
462:       x[18] = v[18];
463:       x[19] = v[19];
464:       x[20] = v[20];
465:       x[21] = v[21];
466:       x[22] = v[22];
467:       x[23] = v[23];
468:       x[24] = v[24];
469:       v += 25;
470:     }
471:     row = *ajtmp++;
472:     while (row < i) {
473:       pc  = rtmp + 25 * row;
474:       p1  = pc[0];
475:       p2  = pc[1];
476:       p3  = pc[2];
477:       p4  = pc[3];
478:       p5  = pc[4];
479:       p6  = pc[5];
480:       p7  = pc[6];
481:       p8  = pc[7];
482:       p9  = pc[8];
483:       p10 = pc[9];
484:       p11 = pc[10];
485:       p12 = pc[11];
486:       p13 = pc[12];
487:       p14 = pc[13];
488:       p15 = pc[14];
489:       p16 = pc[15];
490:       p17 = pc[16];
491:       p18 = pc[17];
492:       p19 = pc[18];
493:       p20 = pc[19];
494:       p21 = pc[20];
495:       p22 = pc[21];
496:       p23 = pc[22];
497:       p24 = pc[23];
498:       p25 = pc[24];
499:       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
500:         pv    = ba + 25 * diag_offset[row];
501:         pj    = bj + diag_offset[row] + 1;
502:         x1    = pv[0];
503:         x2    = pv[1];
504:         x3    = pv[2];
505:         x4    = pv[3];
506:         x5    = pv[4];
507:         x6    = pv[5];
508:         x7    = pv[6];
509:         x8    = pv[7];
510:         x9    = pv[8];
511:         x10   = pv[9];
512:         x11   = pv[10];
513:         x12   = pv[11];
514:         x13   = pv[12];
515:         x14   = pv[13];
516:         x15   = pv[14];
517:         x16   = pv[15];
518:         x17   = pv[16];
519:         x18   = pv[17];
520:         x19   = pv[18];
521:         x20   = pv[19];
522:         x21   = pv[20];
523:         x22   = pv[21];
524:         x23   = pv[22];
525:         x24   = pv[23];
526:         x25   = pv[24];
527:         pc[0] = m1 = p1 * x1 + p6 * x2 + p11 * x3 + p16 * x4 + p21 * x5;
528:         pc[1] = m2 = p2 * x1 + p7 * x2 + p12 * x3 + p17 * x4 + p22 * x5;
529:         pc[2] = m3 = p3 * x1 + p8 * x2 + p13 * x3 + p18 * x4 + p23 * x5;
530:         pc[3] = m4 = p4 * x1 + p9 * x2 + p14 * x3 + p19 * x4 + p24 * x5;
531:         pc[4] = m5 = p5 * x1 + p10 * x2 + p15 * x3 + p20 * x4 + p25 * x5;

533:         pc[5] = m6 = p1 * x6 + p6 * x7 + p11 * x8 + p16 * x9 + p21 * x10;
534:         pc[6] = m7 = p2 * x6 + p7 * x7 + p12 * x8 + p17 * x9 + p22 * x10;
535:         pc[7] = m8 = p3 * x6 + p8 * x7 + p13 * x8 + p18 * x9 + p23 * x10;
536:         pc[8] = m9 = p4 * x6 + p9 * x7 + p14 * x8 + p19 * x9 + p24 * x10;
537:         pc[9] = m10 = p5 * x6 + p10 * x7 + p15 * x8 + p20 * x9 + p25 * x10;

539:         pc[10] = m11 = p1 * x11 + p6 * x12 + p11 * x13 + p16 * x14 + p21 * x15;
540:         pc[11] = m12 = p2 * x11 + p7 * x12 + p12 * x13 + p17 * x14 + p22 * x15;
541:         pc[12] = m13 = p3 * x11 + p8 * x12 + p13 * x13 + p18 * x14 + p23 * x15;
542:         pc[13] = m14 = p4 * x11 + p9 * x12 + p14 * x13 + p19 * x14 + p24 * x15;
543:         pc[14] = m15 = p5 * x11 + p10 * x12 + p15 * x13 + p20 * x14 + p25 * x15;

545:         pc[15] = m16 = p1 * x16 + p6 * x17 + p11 * x18 + p16 * x19 + p21 * x20;
546:         pc[16] = m17 = p2 * x16 + p7 * x17 + p12 * x18 + p17 * x19 + p22 * x20;
547:         pc[17] = m18 = p3 * x16 + p8 * x17 + p13 * x18 + p18 * x19 + p23 * x20;
548:         pc[18] = m19 = p4 * x16 + p9 * x17 + p14 * x18 + p19 * x19 + p24 * x20;
549:         pc[19] = m20 = p5 * x16 + p10 * x17 + p15 * x18 + p20 * x19 + p25 * x20;

551:         pc[20] = m21 = p1 * x21 + p6 * x22 + p11 * x23 + p16 * x24 + p21 * x25;
552:         pc[21] = m22 = p2 * x21 + p7 * x22 + p12 * x23 + p17 * x24 + p22 * x25;
553:         pc[22] = m23 = p3 * x21 + p8 * x22 + p13 * x23 + p18 * x24 + p23 * x25;
554:         pc[23] = m24 = p4 * x21 + p9 * x22 + p14 * x23 + p19 * x24 + p24 * x25;
555:         pc[24] = m25 = p5 * x21 + p10 * x22 + p15 * x23 + p20 * x24 + p25 * x25;

557:         nz = bi[row + 1] - diag_offset[row] - 1;
558:         pv += 25;
559:         for (j = 0; j < nz; j++) {
560:           x1  = pv[0];
561:           x2  = pv[1];
562:           x3  = pv[2];
563:           x4  = pv[3];
564:           x5  = pv[4];
565:           x6  = pv[5];
566:           x7  = pv[6];
567:           x8  = pv[7];
568:           x9  = pv[8];
569:           x10 = pv[9];
570:           x11 = pv[10];
571:           x12 = pv[11];
572:           x13 = pv[12];
573:           x14 = pv[13];
574:           x15 = pv[14];
575:           x16 = pv[15];
576:           x17 = pv[16];
577:           x18 = pv[17];
578:           x19 = pv[18];
579:           x20 = pv[19];
580:           x21 = pv[20];
581:           x22 = pv[21];
582:           x23 = pv[22];
583:           x24 = pv[23];
584:           x25 = pv[24];
585:           x   = rtmp + 25 * pj[j];
586:           x[0] -= m1 * x1 + m6 * x2 + m11 * x3 + m16 * x4 + m21 * x5;
587:           x[1] -= m2 * x1 + m7 * x2 + m12 * x3 + m17 * x4 + m22 * x5;
588:           x[2] -= m3 * x1 + m8 * x2 + m13 * x3 + m18 * x4 + m23 * x5;
589:           x[3] -= m4 * x1 + m9 * x2 + m14 * x3 + m19 * x4 + m24 * x5;
590:           x[4] -= m5 * x1 + m10 * x2 + m15 * x3 + m20 * x4 + m25 * x5;

592:           x[5] -= m1 * x6 + m6 * x7 + m11 * x8 + m16 * x9 + m21 * x10;
593:           x[6] -= m2 * x6 + m7 * x7 + m12 * x8 + m17 * x9 + m22 * x10;
594:           x[7] -= m3 * x6 + m8 * x7 + m13 * x8 + m18 * x9 + m23 * x10;
595:           x[8] -= m4 * x6 + m9 * x7 + m14 * x8 + m19 * x9 + m24 * x10;
596:           x[9] -= m5 * x6 + m10 * x7 + m15 * x8 + m20 * x9 + m25 * x10;

598:           x[10] -= m1 * x11 + m6 * x12 + m11 * x13 + m16 * x14 + m21 * x15;
599:           x[11] -= m2 * x11 + m7 * x12 + m12 * x13 + m17 * x14 + m22 * x15;
600:           x[12] -= m3 * x11 + m8 * x12 + m13 * x13 + m18 * x14 + m23 * x15;
601:           x[13] -= m4 * x11 + m9 * x12 + m14 * x13 + m19 * x14 + m24 * x15;
602:           x[14] -= m5 * x11 + m10 * x12 + m15 * x13 + m20 * x14 + m25 * x15;

604:           x[15] -= m1 * x16 + m6 * x17 + m11 * x18 + m16 * x19 + m21 * x20;
605:           x[16] -= m2 * x16 + m7 * x17 + m12 * x18 + m17 * x19 + m22 * x20;
606:           x[17] -= m3 * x16 + m8 * x17 + m13 * x18 + m18 * x19 + m23 * x20;
607:           x[18] -= m4 * x16 + m9 * x17 + m14 * x18 + m19 * x19 + m24 * x20;
608:           x[19] -= m5 * x16 + m10 * x17 + m15 * x18 + m20 * x19 + m25 * x20;

610:           x[20] -= m1 * x21 + m6 * x22 + m11 * x23 + m16 * x24 + m21 * x25;
611:           x[21] -= m2 * x21 + m7 * x22 + m12 * x23 + m17 * x24 + m22 * x25;
612:           x[22] -= m3 * x21 + m8 * x22 + m13 * x23 + m18 * x24 + m23 * x25;
613:           x[23] -= m4 * x21 + m9 * x22 + m14 * x23 + m19 * x24 + m24 * x25;
614:           x[24] -= m5 * x21 + m10 * x22 + m15 * x23 + m20 * x24 + m25 * x25;
615:           pv += 25;
616:         }
617:         PetscCall(PetscLogFlops(250.0 * nz + 225.0));
618:       }
619:       row = *ajtmp++;
620:     }
621:     /* finished row so stick it into b->a */
622:     pv = ba + 25 * bi[i];
623:     pj = bj + bi[i];
624:     nz = bi[i + 1] - bi[i];
625:     for (j = 0; j < nz; j++) {
626:       x      = rtmp + 25 * pj[j];
627:       pv[0]  = x[0];
628:       pv[1]  = x[1];
629:       pv[2]  = x[2];
630:       pv[3]  = x[3];
631:       pv[4]  = x[4];
632:       pv[5]  = x[5];
633:       pv[6]  = x[6];
634:       pv[7]  = x[7];
635:       pv[8]  = x[8];
636:       pv[9]  = x[9];
637:       pv[10] = x[10];
638:       pv[11] = x[11];
639:       pv[12] = x[12];
640:       pv[13] = x[13];
641:       pv[14] = x[14];
642:       pv[15] = x[15];
643:       pv[16] = x[16];
644:       pv[17] = x[17];
645:       pv[18] = x[18];
646:       pv[19] = x[19];
647:       pv[20] = x[20];
648:       pv[21] = x[21];
649:       pv[22] = x[22];
650:       pv[23] = x[23];
651:       pv[24] = x[24];
652:       pv += 25;
653:     }
654:     /* invert diagonal block */
655:     w = ba + 25 * diag_offset[i];
656:     PetscCall(PetscKernel_A_gets_inverse_A_5(w, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
657:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
658:   }

660:   PetscCall(PetscFree(rtmp));

662:   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering_inplace;
663:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering_inplace;
664:   C->assembled           = PETSC_TRUE;

666:   PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * b->mbs)); /* from inverting diagonal blocks */
667:   PetscFunctionReturn(PETSC_SUCCESS);
668: }

670: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering(Mat B, Mat A, const MatFactorInfo *info)
671: {
672:   Mat             C = B;
673:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
674:   PetscInt        i, j, k, nz, nzL, row;
675:   const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
676:   const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
677:   MatScalar      *rtmp, *pc, *mwork, *v, *vv, *pv, *aa = a->a, work[25];
678:   PetscInt        flg, ipvt[5];
679:   PetscReal       shift = info->shiftamount;
680:   PetscBool       allowzeropivot, zeropivotdetected;

682:   PetscFunctionBegin;
683:   allowzeropivot = PetscNot(A->erroriffailure);

685:   /* generate work space needed by the factorization */
686:   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
687:   PetscCall(PetscArrayzero(rtmp, bs2 * n));

689:   for (i = 0; i < n; i++) {
690:     /* zero rtmp */
691:     /* L part */
692:     nz    = bi[i + 1] - bi[i];
693:     bjtmp = bj + bi[i];
694:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

696:     /* U part */
697:     nz    = bdiag[i] - bdiag[i + 1];
698:     bjtmp = bj + bdiag[i + 1] + 1;
699:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

701:     /* load in initial (unfactored row) */
702:     nz    = ai[i + 1] - ai[i];
703:     ajtmp = aj + ai[i];
704:     v     = aa + bs2 * ai[i];
705:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ajtmp[j], v + bs2 * j, bs2));

707:     /* elimination */
708:     bjtmp = bj + bi[i];
709:     nzL   = bi[i + 1] - bi[i];
710:     for (k = 0; k < nzL; k++) {
711:       row = bjtmp[k];
712:       pc  = rtmp + bs2 * row;
713:       for (flg = 0, j = 0; j < bs2; j++) {
714:         if (pc[j] != 0.0) {
715:           flg = 1;
716:           break;
717:         }
718:       }
719:       if (flg) {
720:         pv = b->a + bs2 * bdiag[row];
721:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
722:         PetscCall(PetscKernel_A_gets_A_times_B_5(pc, pv, mwork));

724:         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
725:         pv = b->a + bs2 * (bdiag[row + 1] + 1);
726:         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
727:         for (j = 0; j < nz; j++) {
728:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
729:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
730:           vv = rtmp + bs2 * pj[j];
731:           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_5(vv, pc, pv));
732:           pv += bs2;
733:         }
734:         PetscCall(PetscLogFlops(250.0 * nz + 225)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
735:       }
736:     }

738:     /* finished row so stick it into b->a */
739:     /* L part */
740:     pv = b->a + bs2 * bi[i];
741:     pj = b->j + bi[i];
742:     nz = bi[i + 1] - bi[i];
743:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));

745:     /* Mark diagonal and invert diagonal for simpler triangular solves */
746:     pv = b->a + bs2 * bdiag[i];
747:     pj = b->j + bdiag[i];
748:     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
749:     PetscCall(PetscKernel_A_gets_inverse_A_5(pv, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
750:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

752:     /* U part */
753:     pv = b->a + bs2 * (bdiag[i + 1] + 1);
754:     pj = b->j + bdiag[i + 1] + 1;
755:     nz = bdiag[i] - bdiag[i + 1] - 1;
756:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
757:   }
758:   PetscCall(PetscFree2(rtmp, mwork));

760:   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering;
761:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering;
762:   C->assembled           = PETSC_TRUE;

764:   PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * n)); /* from inverting diagonal blocks */
765:   PetscFunctionReturn(PETSC_SUCCESS);
766: }

768: /*
769:    Version for when blocks are 9 by 9
770:  */
771: #if defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX2__) && defined(__FMA__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
772:   #include <immintrin.h>
773: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_9_NaturalOrdering(Mat B, Mat A, const MatFactorInfo *info)
774: {
775:   Mat             C = B;
776:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
777:   PetscInt        i, j, k, nz, nzL, row;
778:   const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
779:   const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
780:   MatScalar      *rtmp, *pc, *mwork, *v, *pv, *aa = a->a;
781:   PetscInt        flg;
782:   PetscReal       shift = info->shiftamount;
783:   PetscBool       allowzeropivot, zeropivotdetected;

785:   PetscFunctionBegin;
786:   allowzeropivot = PetscNot(A->erroriffailure);

788:   /* generate work space needed by the factorization */
789:   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
790:   PetscCall(PetscArrayzero(rtmp, bs2 * n));

792:   for (i = 0; i < n; i++) {
793:     /* zero rtmp */
794:     /* L part */
795:     nz    = bi[i + 1] - bi[i];
796:     bjtmp = bj + bi[i];
797:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

799:     /* U part */
800:     nz    = bdiag[i] - bdiag[i + 1];
801:     bjtmp = bj + bdiag[i + 1] + 1;
802:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

804:     /* load in initial (unfactored row) */
805:     nz    = ai[i + 1] - ai[i];
806:     ajtmp = aj + ai[i];
807:     v     = aa + bs2 * ai[i];
808:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ajtmp[j], v + bs2 * j, bs2));

810:     /* elimination */
811:     bjtmp = bj + bi[i];
812:     nzL   = bi[i + 1] - bi[i];
813:     for (k = 0; k < nzL; k++) {
814:       row = bjtmp[k];
815:       pc  = rtmp + bs2 * row;
816:       for (flg = 0, j = 0; j < bs2; j++) {
817:         if (pc[j] != 0.0) {
818:           flg = 1;
819:           break;
820:         }
821:       }
822:       if (flg) {
823:         pv = b->a + bs2 * bdiag[row];
824:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
825:         PetscCall(PetscKernel_A_gets_A_times_B_9(pc, pv, mwork));

827:         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
828:         pv = b->a + bs2 * (bdiag[row + 1] + 1);
829:         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
830:         for (j = 0; j < nz; j++) {
831:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
832:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
833:           v = rtmp + bs2 * pj[j];
834:           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_9(v, pc, pv + 81 * j));
835:           /* pv incremented in PetscKernel_A_gets_A_minus_B_times_C_9 */
836:         }
837:         PetscCall(PetscLogFlops(1458 * nz + 1377)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
838:       }
839:     }

841:     /* finished row so stick it into b->a */
842:     /* L part */
843:     pv = b->a + bs2 * bi[i];
844:     pj = b->j + bi[i];
845:     nz = bi[i + 1] - bi[i];
846:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));

848:     /* Mark diagonal and invert diagonal for simpler triangular solves */
849:     pv = b->a + bs2 * bdiag[i];
850:     pj = b->j + bdiag[i];
851:     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
852:     PetscCall(PetscKernel_A_gets_inverse_A_9(pv, shift, allowzeropivot, &zeropivotdetected));
853:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

855:     /* U part */
856:     pv = b->a + bs2 * (bdiag[i + 1] + 1);
857:     pj = b->j + bdiag[i + 1] + 1;
858:     nz = bdiag[i] - bdiag[i + 1] - 1;
859:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
860:   }
861:   PetscCall(PetscFree2(rtmp, mwork));

863:   C->ops->solve          = MatSolve_SeqBAIJ_9_NaturalOrdering;
864:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_N;
865:   C->assembled           = PETSC_TRUE;

867:   PetscCall(PetscLogFlops(1.333333333333 * 9 * 9 * 9 * n)); /* from inverting diagonal blocks */
868:   PetscFunctionReturn(PETSC_SUCCESS);
869: }

871: PetscErrorCode MatSolve_SeqBAIJ_9_NaturalOrdering(Mat A, Vec bb, Vec xx)
872: {
873:   Mat_SeqBAIJ       *a  = (Mat_SeqBAIJ *)A->data;
874:   const PetscInt    *ai = a->i, *aj = a->j, *adiag = a->diag, *vi;
875:   PetscInt           i, k, n                       = a->mbs;
876:   PetscInt           nz, bs = A->rmap->bs, bs2 = a->bs2;
877:   const MatScalar   *aa = a->a, *v;
878:   PetscScalar       *x, *s, *t, *ls;
879:   const PetscScalar *b;
880:   __m256d            a0, a1, a2, a3, a4, a5, w0, w1, w2, w3, s0, s1, s2, v0, v1, v2, v3;

882:   PetscFunctionBegin;
883:   PetscCall(VecGetArrayRead(bb, &b));
884:   PetscCall(VecGetArray(xx, &x));
885:   t = a->solve_work;

887:   /* forward solve the lower triangular */
888:   PetscCall(PetscArraycpy(t, b, bs)); /* copy 1st block of b to t */

890:   for (i = 1; i < n; i++) {
891:     v  = aa + bs2 * ai[i];
892:     vi = aj + ai[i];
893:     nz = ai[i + 1] - ai[i];
894:     s  = t + bs * i;
895:     PetscCall(PetscArraycpy(s, b + bs * i, bs)); /* copy i_th block of b to t */

897:     __m256d s0, s1, s2;
898:     s0 = _mm256_loadu_pd(s + 0);
899:     s1 = _mm256_loadu_pd(s + 4);
900:     s2 = _mm256_maskload_pd(s + 8, _mm256_set_epi64x(0LL, 0LL, 0LL, 1LL << 63));

902:     for (k = 0; k < nz; k++) {
903:       w0 = _mm256_set1_pd((t + bs * vi[k])[0]);
904:       a0 = _mm256_loadu_pd(&v[0]);
905:       s0 = _mm256_fnmadd_pd(a0, w0, s0);
906:       a1 = _mm256_loadu_pd(&v[4]);
907:       s1 = _mm256_fnmadd_pd(a1, w0, s1);
908:       a2 = _mm256_loadu_pd(&v[8]);
909:       s2 = _mm256_fnmadd_pd(a2, w0, s2);

911:       w1 = _mm256_set1_pd((t + bs * vi[k])[1]);
912:       a3 = _mm256_loadu_pd(&v[9]);
913:       s0 = _mm256_fnmadd_pd(a3, w1, s0);
914:       a4 = _mm256_loadu_pd(&v[13]);
915:       s1 = _mm256_fnmadd_pd(a4, w1, s1);
916:       a5 = _mm256_loadu_pd(&v[17]);
917:       s2 = _mm256_fnmadd_pd(a5, w1, s2);

919:       w2 = _mm256_set1_pd((t + bs * vi[k])[2]);
920:       a0 = _mm256_loadu_pd(&v[18]);
921:       s0 = _mm256_fnmadd_pd(a0, w2, s0);
922:       a1 = _mm256_loadu_pd(&v[22]);
923:       s1 = _mm256_fnmadd_pd(a1, w2, s1);
924:       a2 = _mm256_loadu_pd(&v[26]);
925:       s2 = _mm256_fnmadd_pd(a2, w2, s2);

927:       w3 = _mm256_set1_pd((t + bs * vi[k])[3]);
928:       a3 = _mm256_loadu_pd(&v[27]);
929:       s0 = _mm256_fnmadd_pd(a3, w3, s0);
930:       a4 = _mm256_loadu_pd(&v[31]);
931:       s1 = _mm256_fnmadd_pd(a4, w3, s1);
932:       a5 = _mm256_loadu_pd(&v[35]);
933:       s2 = _mm256_fnmadd_pd(a5, w3, s2);

935:       w0 = _mm256_set1_pd((t + bs * vi[k])[4]);
936:       a0 = _mm256_loadu_pd(&v[36]);
937:       s0 = _mm256_fnmadd_pd(a0, w0, s0);
938:       a1 = _mm256_loadu_pd(&v[40]);
939:       s1 = _mm256_fnmadd_pd(a1, w0, s1);
940:       a2 = _mm256_loadu_pd(&v[44]);
941:       s2 = _mm256_fnmadd_pd(a2, w0, s2);

943:       w1 = _mm256_set1_pd((t + bs * vi[k])[5]);
944:       a3 = _mm256_loadu_pd(&v[45]);
945:       s0 = _mm256_fnmadd_pd(a3, w1, s0);
946:       a4 = _mm256_loadu_pd(&v[49]);
947:       s1 = _mm256_fnmadd_pd(a4, w1, s1);
948:       a5 = _mm256_loadu_pd(&v[53]);
949:       s2 = _mm256_fnmadd_pd(a5, w1, s2);

951:       w2 = _mm256_set1_pd((t + bs * vi[k])[6]);
952:       a0 = _mm256_loadu_pd(&v[54]);
953:       s0 = _mm256_fnmadd_pd(a0, w2, s0);
954:       a1 = _mm256_loadu_pd(&v[58]);
955:       s1 = _mm256_fnmadd_pd(a1, w2, s1);
956:       a2 = _mm256_loadu_pd(&v[62]);
957:       s2 = _mm256_fnmadd_pd(a2, w2, s2);

959:       w3 = _mm256_set1_pd((t + bs * vi[k])[7]);
960:       a3 = _mm256_loadu_pd(&v[63]);
961:       s0 = _mm256_fnmadd_pd(a3, w3, s0);
962:       a4 = _mm256_loadu_pd(&v[67]);
963:       s1 = _mm256_fnmadd_pd(a4, w3, s1);
964:       a5 = _mm256_loadu_pd(&v[71]);
965:       s2 = _mm256_fnmadd_pd(a5, w3, s2);

967:       w0 = _mm256_set1_pd((t + bs * vi[k])[8]);
968:       a0 = _mm256_loadu_pd(&v[72]);
969:       s0 = _mm256_fnmadd_pd(a0, w0, s0);
970:       a1 = _mm256_loadu_pd(&v[76]);
971:       s1 = _mm256_fnmadd_pd(a1, w0, s1);
972:       a2 = _mm256_maskload_pd(v + 80, _mm256_set_epi64x(0LL, 0LL, 0LL, 1LL << 63));
973:       s2 = _mm256_fnmadd_pd(a2, w0, s2);
974:       v += bs2;
975:     }
976:     _mm256_storeu_pd(&s[0], s0);
977:     _mm256_storeu_pd(&s[4], s1);
978:     _mm256_maskstore_pd(&s[8], _mm256_set_epi64x(0LL, 0LL, 0LL, 1LL << 63), s2);
979:   }

981:   /* backward solve the upper triangular */
982:   ls = a->solve_work + A->cmap->n;
983:   for (i = n - 1; i >= 0; i--) {
984:     v  = aa + bs2 * (adiag[i + 1] + 1);
985:     vi = aj + adiag[i + 1] + 1;
986:     nz = adiag[i] - adiag[i + 1] - 1;
987:     PetscCall(PetscArraycpy(ls, t + i * bs, bs));

989:     s0 = _mm256_loadu_pd(ls + 0);
990:     s1 = _mm256_loadu_pd(ls + 4);
991:     s2 = _mm256_maskload_pd(ls + 8, _mm256_set_epi64x(0LL, 0LL, 0LL, 1LL << 63));

993:     for (k = 0; k < nz; k++) {
994:       w0 = _mm256_set1_pd((t + bs * vi[k])[0]);
995:       a0 = _mm256_loadu_pd(&v[0]);
996:       s0 = _mm256_fnmadd_pd(a0, w0, s0);
997:       a1 = _mm256_loadu_pd(&v[4]);
998:       s1 = _mm256_fnmadd_pd(a1, w0, s1);
999:       a2 = _mm256_loadu_pd(&v[8]);
1000:       s2 = _mm256_fnmadd_pd(a2, w0, s2);

1002:       /* v += 9; */
1003:       w1 = _mm256_set1_pd((t + bs * vi[k])[1]);
1004:       a3 = _mm256_loadu_pd(&v[9]);
1005:       s0 = _mm256_fnmadd_pd(a3, w1, s0);
1006:       a4 = _mm256_loadu_pd(&v[13]);
1007:       s1 = _mm256_fnmadd_pd(a4, w1, s1);
1008:       a5 = _mm256_loadu_pd(&v[17]);
1009:       s2 = _mm256_fnmadd_pd(a5, w1, s2);

1011:       /* v += 9; */
1012:       w2 = _mm256_set1_pd((t + bs * vi[k])[2]);
1013:       a0 = _mm256_loadu_pd(&v[18]);
1014:       s0 = _mm256_fnmadd_pd(a0, w2, s0);
1015:       a1 = _mm256_loadu_pd(&v[22]);
1016:       s1 = _mm256_fnmadd_pd(a1, w2, s1);
1017:       a2 = _mm256_loadu_pd(&v[26]);
1018:       s2 = _mm256_fnmadd_pd(a2, w2, s2);

1020:       /* v += 9; */
1021:       w3 = _mm256_set1_pd((t + bs * vi[k])[3]);
1022:       a3 = _mm256_loadu_pd(&v[27]);
1023:       s0 = _mm256_fnmadd_pd(a3, w3, s0);
1024:       a4 = _mm256_loadu_pd(&v[31]);
1025:       s1 = _mm256_fnmadd_pd(a4, w3, s1);
1026:       a5 = _mm256_loadu_pd(&v[35]);
1027:       s2 = _mm256_fnmadd_pd(a5, w3, s2);

1029:       /* v += 9; */
1030:       w0 = _mm256_set1_pd((t + bs * vi[k])[4]);
1031:       a0 = _mm256_loadu_pd(&v[36]);
1032:       s0 = _mm256_fnmadd_pd(a0, w0, s0);
1033:       a1 = _mm256_loadu_pd(&v[40]);
1034:       s1 = _mm256_fnmadd_pd(a1, w0, s1);
1035:       a2 = _mm256_loadu_pd(&v[44]);
1036:       s2 = _mm256_fnmadd_pd(a2, w0, s2);

1038:       /* v += 9; */
1039:       w1 = _mm256_set1_pd((t + bs * vi[k])[5]);
1040:       a3 = _mm256_loadu_pd(&v[45]);
1041:       s0 = _mm256_fnmadd_pd(a3, w1, s0);
1042:       a4 = _mm256_loadu_pd(&v[49]);
1043:       s1 = _mm256_fnmadd_pd(a4, w1, s1);
1044:       a5 = _mm256_loadu_pd(&v[53]);
1045:       s2 = _mm256_fnmadd_pd(a5, w1, s2);

1047:       /* v += 9; */
1048:       w2 = _mm256_set1_pd((t + bs * vi[k])[6]);
1049:       a0 = _mm256_loadu_pd(&v[54]);
1050:       s0 = _mm256_fnmadd_pd(a0, w2, s0);
1051:       a1 = _mm256_loadu_pd(&v[58]);
1052:       s1 = _mm256_fnmadd_pd(a1, w2, s1);
1053:       a2 = _mm256_loadu_pd(&v[62]);
1054:       s2 = _mm256_fnmadd_pd(a2, w2, s2);

1056:       /* v += 9; */
1057:       w3 = _mm256_set1_pd((t + bs * vi[k])[7]);
1058:       a3 = _mm256_loadu_pd(&v[63]);
1059:       s0 = _mm256_fnmadd_pd(a3, w3, s0);
1060:       a4 = _mm256_loadu_pd(&v[67]);
1061:       s1 = _mm256_fnmadd_pd(a4, w3, s1);
1062:       a5 = _mm256_loadu_pd(&v[71]);
1063:       s2 = _mm256_fnmadd_pd(a5, w3, s2);

1065:       /* v += 9; */
1066:       w0 = _mm256_set1_pd((t + bs * vi[k])[8]);
1067:       a0 = _mm256_loadu_pd(&v[72]);
1068:       s0 = _mm256_fnmadd_pd(a0, w0, s0);
1069:       a1 = _mm256_loadu_pd(&v[76]);
1070:       s1 = _mm256_fnmadd_pd(a1, w0, s1);
1071:       a2 = _mm256_maskload_pd(v + 80, _mm256_set_epi64x(0LL, 0LL, 0LL, 1LL << 63));
1072:       s2 = _mm256_fnmadd_pd(a2, w0, s2);
1073:       v += bs2;
1074:     }

1076:     _mm256_storeu_pd(&ls[0], s0);
1077:     _mm256_storeu_pd(&ls[4], s1);
1078:     _mm256_maskstore_pd(&ls[8], _mm256_set_epi64x(0LL, 0LL, 0LL, 1LL << 63), s2);

1080:     w0 = _mm256_setzero_pd();
1081:     w1 = _mm256_setzero_pd();
1082:     w2 = _mm256_setzero_pd();

1084:     /* first row */
1085:     v0 = _mm256_set1_pd(ls[0]);
1086:     a0 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[0]);
1087:     w0 = _mm256_fmadd_pd(a0, v0, w0);
1088:     a1 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[4]);
1089:     w1 = _mm256_fmadd_pd(a1, v0, w1);
1090:     a2 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[8]);
1091:     w2 = _mm256_fmadd_pd(a2, v0, w2);

1093:     /* second row */
1094:     v1 = _mm256_set1_pd(ls[1]);
1095:     a3 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[9]);
1096:     w0 = _mm256_fmadd_pd(a3, v1, w0);
1097:     a4 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[13]);
1098:     w1 = _mm256_fmadd_pd(a4, v1, w1);
1099:     a5 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[17]);
1100:     w2 = _mm256_fmadd_pd(a5, v1, w2);

1102:     /* third row */
1103:     v2 = _mm256_set1_pd(ls[2]);
1104:     a0 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[18]);
1105:     w0 = _mm256_fmadd_pd(a0, v2, w0);
1106:     a1 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[22]);
1107:     w1 = _mm256_fmadd_pd(a1, v2, w1);
1108:     a2 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[26]);
1109:     w2 = _mm256_fmadd_pd(a2, v2, w2);

1111:     /* fourth row */
1112:     v3 = _mm256_set1_pd(ls[3]);
1113:     a3 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[27]);
1114:     w0 = _mm256_fmadd_pd(a3, v3, w0);
1115:     a4 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[31]);
1116:     w1 = _mm256_fmadd_pd(a4, v3, w1);
1117:     a5 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[35]);
1118:     w2 = _mm256_fmadd_pd(a5, v3, w2);

1120:     /* fifth row */
1121:     v0 = _mm256_set1_pd(ls[4]);
1122:     a0 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[36]);
1123:     w0 = _mm256_fmadd_pd(a0, v0, w0);
1124:     a1 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[40]);
1125:     w1 = _mm256_fmadd_pd(a1, v0, w1);
1126:     a2 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[44]);
1127:     w2 = _mm256_fmadd_pd(a2, v0, w2);

1129:     /* sixth row */
1130:     v1 = _mm256_set1_pd(ls[5]);
1131:     a3 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[45]);
1132:     w0 = _mm256_fmadd_pd(a3, v1, w0);
1133:     a4 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[49]);
1134:     w1 = _mm256_fmadd_pd(a4, v1, w1);
1135:     a5 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[53]);
1136:     w2 = _mm256_fmadd_pd(a5, v1, w2);

1138:     /* seventh row */
1139:     v2 = _mm256_set1_pd(ls[6]);
1140:     a0 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[54]);
1141:     w0 = _mm256_fmadd_pd(a0, v2, w0);
1142:     a1 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[58]);
1143:     w1 = _mm256_fmadd_pd(a1, v2, w1);
1144:     a2 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[62]);
1145:     w2 = _mm256_fmadd_pd(a2, v2, w2);

1147:     /* eighth row */
1148:     v3 = _mm256_set1_pd(ls[7]);
1149:     a3 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[63]);
1150:     w0 = _mm256_fmadd_pd(a3, v3, w0);
1151:     a4 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[67]);
1152:     w1 = _mm256_fmadd_pd(a4, v3, w1);
1153:     a5 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[71]);
1154:     w2 = _mm256_fmadd_pd(a5, v3, w2);

1156:     /* ninth row */
1157:     v0 = _mm256_set1_pd(ls[8]);
1158:     a3 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[72]);
1159:     w0 = _mm256_fmadd_pd(a3, v0, w0);
1160:     a4 = _mm256_loadu_pd(&(aa + bs2 * adiag[i])[76]);
1161:     w1 = _mm256_fmadd_pd(a4, v0, w1);
1162:     a2 = _mm256_maskload_pd(&(aa + bs2 * adiag[i])[80], _mm256_set_epi64x(0LL, 0LL, 0LL, 1LL << 63));
1163:     w2 = _mm256_fmadd_pd(a2, v0, w2);

1165:     _mm256_storeu_pd(&(t + i * bs)[0], w0);
1166:     _mm256_storeu_pd(&(t + i * bs)[4], w1);
1167:     _mm256_maskstore_pd(&(t + i * bs)[8], _mm256_set_epi64x(0LL, 0LL, 0LL, 1LL << 63), w2);

1169:     PetscCall(PetscArraycpy(x + i * bs, t + i * bs, bs));
1170:   }

1172:   PetscCall(VecRestoreArrayRead(bb, &b));
1173:   PetscCall(VecRestoreArray(xx, &x));
1174:   PetscCall(PetscLogFlops(2.0 * (a->bs2) * (a->nz) - A->rmap->bs * A->cmap->n));
1175:   PetscFunctionReturn(PETSC_SUCCESS);
1176: }
1177: #endif