Actual source code: baijfact9.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>

  8: /*
  9:       Version for when blocks are 5 by 5
 10: */
 11: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_inplace(Mat C, Mat A, const MatFactorInfo *info)
 12: {
 13:   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
 14:   IS               isrow = b->row, isicol = b->icol;
 15:   const PetscInt  *r, *ic, *bi = b->i, *bj = b->j, *ajtmpold, *ajtmp;
 16:   PetscInt         i, j, n = a->mbs, nz, row, idx, ipvt[5];
 17:   const PetscInt  *diag_offset = b->diag, *ai = a->i, *aj = a->j, *pj;
 18:   MatScalar       *w, *pv, *rtmp, *x, *pc;
 19:   const MatScalar *v, *aa = a->a;
 20:   MatScalar        p1, p2, p3, p4, m1, m2, m3, m4, m5, m6, m7, m8, m9, x1, x2, x3, x4;
 21:   MatScalar        p5, p6, p7, p8, p9, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16;
 22:   MatScalar        x17, x18, x19, x20, x21, x22, x23, x24, x25, p10, p11, p12, p13, p14;
 23:   MatScalar        p15, p16, p17, p18, p19, p20, p21, p22, p23, p24, p25, m10, m11, m12;
 24:   MatScalar        m13, m14, m15, m16, m17, m18, m19, m20, m21, m22, m23, m24, m25;
 25:   MatScalar       *ba    = b->a, work[25];
 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(25 * (n + 1), &rtmp));

 35: #define PETSC_USE_MEMZERO 1
 36: #define PETSC_USE_MEMCPY  1

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

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

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

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

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

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

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

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

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

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

234:           pv += 25;
235:         }
236:         PetscCall(PetscLogFlops(250.0 * nz + 225.0));
237:       }
238:       row = *ajtmp++;
239:     }
240:     /* finished row so stick it into b->a */
241:     pv = ba + 25 * bi[i];
242:     pj = bj + bi[i];
243:     nz = bi[i + 1] - bi[i];
244:     for (j = 0; j < nz; j++) {
245: #if defined(PETSC_USE_MEMCPY)
246:       PetscCall(PetscArraycpy(pv, rtmp + 25 * pj[j], 25));
247: #else
248:       x                                                     = rtmp + 25 * pj[j];
249:       pv[0]                                                 = x[0];
250:       pv[1]                                                 = x[1];
251:       pv[2]                                                 = x[2];
252:       pv[3]                                                 = x[3];
253:       pv[4]                                                 = x[4];
254:       pv[5]                                                 = x[5];
255:       pv[6]                                                 = x[6];
256:       pv[7]                                                 = x[7];
257:       pv[8]                                                 = x[8];
258:       pv[9]                                                 = x[9];
259:       pv[10]                                                = x[10];
260:       pv[11]                                                = x[11];
261:       pv[12]                                                = x[12];
262:       pv[13]                                                = x[13];
263:       pv[14]                                                = x[14];
264:       pv[15]                                                = x[15];
265:       pv[16]                                                = x[16];
266:       pv[17]                                                = x[17];
267:       pv[18]                                                = x[18];
268:       pv[19]                                                = x[19];
269:       pv[20]                                                = x[20];
270:       pv[21]                                                = x[21];
271:       pv[22]                                                = x[22];
272:       pv[23]                                                = x[23];
273:       pv[24]                                                = x[24];
274: #endif
275:       pv += 25;
276:     }
277:     /* invert diagonal block */
278:     w = ba + 25 * diag_offset[i];
279:     PetscCall(PetscKernel_A_gets_inverse_A_5(w, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
280:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
281:   }

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

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

291:   PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * b->mbs)); /* from inverting diagonal blocks */
292:   PetscFunctionReturn(PETSC_SUCCESS);
293: }

295: /* MatLUFactorNumeric_SeqBAIJ_5 -
296:      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
297:        PetscKernel_A_gets_A_times_B()
298:        PetscKernel_A_gets_A_minus_B_times_C()
299:        PetscKernel_A_gets_inverse_A()
300: */

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

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

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

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

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

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

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

360:         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
361:         pv = b->a + bs2 * (bdiag[row + 1] + 1);
362:         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
363:         for (j = 0; j < nz; j++) {
364:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
365:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
366:           v = rtmp + bs2 * pj[j];
367:           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_5(v, pc, pv));
368:           pv += bs2;
369:         }
370:         PetscCall(PetscLogFlops(250.0 * nz + 225)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
371:       }
372:     }

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

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

388:     /* U part */
389:     pv = b->a + bs2 * (bdiag[i + 1] + 1);
390:     pj = b->j + bdiag[i + 1] + 1;
391:     nz = bdiag[i] - bdiag[i + 1] - 1;
392:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
393:   }

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

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

403:   PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * n)); /* from inverting diagonal blocks */
404:   PetscFunctionReturn(PETSC_SUCCESS);
405: }

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

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

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

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

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

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

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

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

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

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

611:           x[20] -= m1 * x21 + m6 * x22 + m11 * x23 + m16 * x24 + m21 * x25;
612:           x[21] -= m2 * x21 + m7 * x22 + m12 * x23 + m17 * x24 + m22 * x25;
613:           x[22] -= m3 * x21 + m8 * x22 + m13 * x23 + m18 * x24 + m23 * x25;
614:           x[23] -= m4 * x21 + m9 * x22 + m14 * x23 + m19 * x24 + m24 * x25;
615:           x[24] -= m5 * x21 + m10 * x22 + m15 * x23 + m20 * x24 + m25 * x25;
616:           pv += 25;
617:         }
618:         PetscCall(PetscLogFlops(250.0 * nz + 225.0));
619:       }
620:       row = *ajtmp++;
621:     }
622:     /* finished row so stick it into b->a */
623:     pv = ba + 25 * bi[i];
624:     pj = bj + bi[i];
625:     nz = bi[i + 1] - bi[i];
626:     for (j = 0; j < nz; j++) {
627:       x      = rtmp + 25 * pj[j];
628:       pv[0]  = x[0];
629:       pv[1]  = x[1];
630:       pv[2]  = x[2];
631:       pv[3]  = x[3];
632:       pv[4]  = x[4];
633:       pv[5]  = x[5];
634:       pv[6]  = x[6];
635:       pv[7]  = x[7];
636:       pv[8]  = x[8];
637:       pv[9]  = x[9];
638:       pv[10] = x[10];
639:       pv[11] = x[11];
640:       pv[12] = x[12];
641:       pv[13] = x[13];
642:       pv[14] = x[14];
643:       pv[15] = x[15];
644:       pv[16] = x[16];
645:       pv[17] = x[17];
646:       pv[18] = x[18];
647:       pv[19] = x[19];
648:       pv[20] = x[20];
649:       pv[21] = x[21];
650:       pv[22] = x[22];
651:       pv[23] = x[23];
652:       pv[24] = x[24];
653:       pv += 25;
654:     }
655:     /* invert diagonal block */
656:     w = ba + 25 * diag_offset[i];
657:     PetscCall(PetscKernel_A_gets_inverse_A_5(w, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
658:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
659:   }

661:   PetscCall(PetscFree(rtmp));

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

667:   PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * b->mbs)); /* from inverting diagonal blocks */
668:   PetscFunctionReturn(PETSC_SUCCESS);
669: }

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

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

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

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

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

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

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

725:         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
726:         pv = b->a + bs2 * (bdiag[row + 1] + 1);
727:         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
728:         for (j = 0; j < nz; j++) {
729:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
730:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
731:           vv = rtmp + bs2 * pj[j];
732:           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_5(vv, pc, pv));
733:           pv += bs2;
734:         }
735:         PetscCall(PetscLogFlops(250.0 * nz + 225)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
736:       }
737:     }

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

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

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

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

765:   PetscCall(PetscLogFlops(1.333333333333 * 5 * 5 * 5 * n)); /* from inverting diagonal blocks */
766:   PetscFunctionReturn(PETSC_SUCCESS);
767: }