Actual source code: baijfact11.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 4 by 4
  9: */
 10: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_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;
 15:   PetscInt        i, j, n = a->mbs, *bi = b->i, *bj = b->j;
 16:   PetscInt       *ajtmpold, *ajtmp, nz, row;
 17:   PetscInt       *diag_offset = b->diag, idx, *ai = a->i, *aj = a->j, *pj;
 18:   MatScalar      *pv, *v, *rtmp, *pc, *w, *x;
 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       p10, p11, p12, p13, p14, p15, p16, m10, m11, m12;
 22:   MatScalar       m13, m14, m15, m16;
 23:   MatScalar      *ba = b->a, *aa = a->a;
 24:   PetscBool       pivotinblocks = b->pivotinblocks;
 25:   PetscReal       shift         = info->shiftamount;
 26:   PetscBool       allowzeropivot, zeropivotdetected = PETSC_FALSE;

 28:   PetscFunctionBegin;
 29:   PetscCall(ISGetIndices(isrow, &r));
 30:   PetscCall(ISGetIndices(isicol, &ic));
 31:   PetscCall(PetscMalloc1(16 * (n + 1), &rtmp));
 32:   allowzeropivot = PetscNot(A->erroriffailure);

 34:   for (i = 0; i < n; i++) {
 35:     nz    = bi[i + 1] - bi[i];
 36:     ajtmp = bj + bi[i];
 37:     for (j = 0; j < nz; j++) {
 38:       x    = rtmp + 16 * ajtmp[j];
 39:       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
 40:       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
 41:     }
 42:     /* load in initial (unfactored row) */
 43:     idx      = r[i];
 44:     nz       = ai[idx + 1] - ai[idx];
 45:     ajtmpold = aj + ai[idx];
 46:     v        = aa + 16 * ai[idx];
 47:     for (j = 0; j < nz; j++) {
 48:       x     = rtmp + 16 * ic[ajtmpold[j]];
 49:       x[0]  = v[0];
 50:       x[1]  = v[1];
 51:       x[2]  = v[2];
 52:       x[3]  = v[3];
 53:       x[4]  = v[4];
 54:       x[5]  = v[5];
 55:       x[6]  = v[6];
 56:       x[7]  = v[7];
 57:       x[8]  = v[8];
 58:       x[9]  = v[9];
 59:       x[10] = v[10];
 60:       x[11] = v[11];
 61:       x[12] = v[12];
 62:       x[13] = v[13];
 63:       x[14] = v[14];
 64:       x[15] = v[15];
 65:       v += 16;
 66:     }
 67:     row = *ajtmp++;
 68:     while (row < i) {
 69:       pc  = rtmp + 16 * row;
 70:       p1  = pc[0];
 71:       p2  = pc[1];
 72:       p3  = pc[2];
 73:       p4  = pc[3];
 74:       p5  = pc[4];
 75:       p6  = pc[5];
 76:       p7  = pc[6];
 77:       p8  = pc[7];
 78:       p9  = pc[8];
 79:       p10 = pc[9];
 80:       p11 = pc[10];
 81:       p12 = pc[11];
 82:       p13 = pc[12];
 83:       p14 = pc[13];
 84:       p15 = pc[14];
 85:       p16 = pc[15];
 86:       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) {
 87:         pv    = ba + 16 * diag_offset[row];
 88:         pj    = bj + diag_offset[row] + 1;
 89:         x1    = pv[0];
 90:         x2    = pv[1];
 91:         x3    = pv[2];
 92:         x4    = pv[3];
 93:         x5    = pv[4];
 94:         x6    = pv[5];
 95:         x7    = pv[6];
 96:         x8    = pv[7];
 97:         x9    = pv[8];
 98:         x10   = pv[9];
 99:         x11   = pv[10];
100:         x12   = pv[11];
101:         x13   = pv[12];
102:         x14   = pv[13];
103:         x15   = pv[14];
104:         x16   = pv[15];
105:         pc[0] = m1 = p1 * x1 + p5 * x2 + p9 * x3 + p13 * x4;
106:         pc[1] = m2 = p2 * x1 + p6 * x2 + p10 * x3 + p14 * x4;
107:         pc[2] = m3 = p3 * x1 + p7 * x2 + p11 * x3 + p15 * x4;
108:         pc[3] = m4 = p4 * x1 + p8 * x2 + p12 * x3 + p16 * x4;

110:         pc[4] = m5 = p1 * x5 + p5 * x6 + p9 * x7 + p13 * x8;
111:         pc[5] = m6 = p2 * x5 + p6 * x6 + p10 * x7 + p14 * x8;
112:         pc[6] = m7 = p3 * x5 + p7 * x6 + p11 * x7 + p15 * x8;
113:         pc[7] = m8 = p4 * x5 + p8 * x6 + p12 * x7 + p16 * x8;

115:         pc[8] = m9 = p1 * x9 + p5 * x10 + p9 * x11 + p13 * x12;
116:         pc[9] = m10 = p2 * x9 + p6 * x10 + p10 * x11 + p14 * x12;
117:         pc[10] = m11 = p3 * x9 + p7 * x10 + p11 * x11 + p15 * x12;
118:         pc[11] = m12 = p4 * x9 + p8 * x10 + p12 * x11 + p16 * x12;

120:         pc[12] = m13 = p1 * x13 + p5 * x14 + p9 * x15 + p13 * x16;
121:         pc[13] = m14 = p2 * x13 + p6 * x14 + p10 * x15 + p14 * x16;
122:         pc[14] = m15 = p3 * x13 + p7 * x14 + p11 * x15 + p15 * x16;
123:         pc[15] = m16 = p4 * x13 + p8 * x14 + p12 * x15 + p16 * x16;

125:         nz = bi[row + 1] - diag_offset[row] - 1;
126:         pv += 16;
127:         for (j = 0; j < nz; j++) {
128:           x1  = pv[0];
129:           x2  = pv[1];
130:           x3  = pv[2];
131:           x4  = pv[3];
132:           x5  = pv[4];
133:           x6  = pv[5];
134:           x7  = pv[6];
135:           x8  = pv[7];
136:           x9  = pv[8];
137:           x10 = pv[9];
138:           x11 = pv[10];
139:           x12 = pv[11];
140:           x13 = pv[12];
141:           x14 = pv[13];
142:           x15 = pv[14];
143:           x16 = pv[15];
144:           x   = rtmp + 16 * pj[j];
145:           x[0] -= m1 * x1 + m5 * x2 + m9 * x3 + m13 * x4;
146:           x[1] -= m2 * x1 + m6 * x2 + m10 * x3 + m14 * x4;
147:           x[2] -= m3 * x1 + m7 * x2 + m11 * x3 + m15 * x4;
148:           x[3] -= m4 * x1 + m8 * x2 + m12 * x3 + m16 * x4;

150:           x[4] -= m1 * x5 + m5 * x6 + m9 * x7 + m13 * x8;
151:           x[5] -= m2 * x5 + m6 * x6 + m10 * x7 + m14 * x8;
152:           x[6] -= m3 * x5 + m7 * x6 + m11 * x7 + m15 * x8;
153:           x[7] -= m4 * x5 + m8 * x6 + m12 * x7 + m16 * x8;

155:           x[8] -= m1 * x9 + m5 * x10 + m9 * x11 + m13 * x12;
156:           x[9] -= m2 * x9 + m6 * x10 + m10 * x11 + m14 * x12;
157:           x[10] -= m3 * x9 + m7 * x10 + m11 * x11 + m15 * x12;
158:           x[11] -= m4 * x9 + m8 * x10 + m12 * x11 + m16 * x12;

160:           x[12] -= m1 * x13 + m5 * x14 + m9 * x15 + m13 * x16;
161:           x[13] -= m2 * x13 + m6 * x14 + m10 * x15 + m14 * x16;
162:           x[14] -= m3 * x13 + m7 * x14 + m11 * x15 + m15 * x16;
163:           x[15] -= m4 * x13 + m8 * x14 + m12 * x15 + m16 * x16;

165:           pv += 16;
166:         }
167:         PetscCall(PetscLogFlops(128.0 * nz + 112.0));
168:       }
169:       row = *ajtmp++;
170:     }
171:     /* finished row so stick it into b->a */
172:     pv = ba + 16 * bi[i];
173:     pj = bj + bi[i];
174:     nz = bi[i + 1] - bi[i];
175:     for (j = 0; j < nz; j++) {
176:       x      = rtmp + 16 * pj[j];
177:       pv[0]  = x[0];
178:       pv[1]  = x[1];
179:       pv[2]  = x[2];
180:       pv[3]  = x[3];
181:       pv[4]  = x[4];
182:       pv[5]  = x[5];
183:       pv[6]  = x[6];
184:       pv[7]  = x[7];
185:       pv[8]  = x[8];
186:       pv[9]  = x[9];
187:       pv[10] = x[10];
188:       pv[11] = x[11];
189:       pv[12] = x[12];
190:       pv[13] = x[13];
191:       pv[14] = x[14];
192:       pv[15] = x[15];
193:       pv += 16;
194:     }
195:     /* invert diagonal block */
196:     w = ba + 16 * diag_offset[i];
197:     if (pivotinblocks) {
198:       PetscCall(PetscKernel_A_gets_inverse_A_4(w, shift, allowzeropivot, &zeropivotdetected));
199:       if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
200:     } else {
201:       PetscCall(PetscKernel_A_gets_inverse_A_4_nopivot(w));
202:     }
203:   }

205:   PetscCall(PetscFree(rtmp));
206:   PetscCall(ISRestoreIndices(isicol, &ic));
207:   PetscCall(ISRestoreIndices(isrow, &r));

209:   C->ops->solve          = MatSolve_SeqBAIJ_4_inplace;
210:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_inplace;
211:   C->assembled           = PETSC_TRUE;

213:   PetscCall(PetscLogFlops(1.333333333333 * 4 * 4 * 4 * b->mbs)); /* from inverting diagonal blocks */
214:   PetscFunctionReturn(PETSC_SUCCESS);
215: }

217: /* MatLUFactorNumeric_SeqBAIJ_4 -
218:      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
219:        PetscKernel_A_gets_A_times_B()
220:        PetscKernel_A_gets_A_minus_B_times_C()
221:        PetscKernel_A_gets_inverse_A()
222: */

224: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4(Mat B, Mat A, const MatFactorInfo *info)
225: {
226:   Mat             C = B;
227:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
228:   IS              isrow = b->row, isicol = b->icol;
229:   const PetscInt *r, *ic;
230:   PetscInt        i, j, k, nz, nzL, row;
231:   const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
232:   const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
233:   MatScalar      *rtmp, *pc, *mwork, *v, *pv, *aa = a->a;
234:   PetscInt        flg;
235:   PetscReal       shift;
236:   PetscBool       allowzeropivot, zeropivotdetected;

238:   PetscFunctionBegin;
239:   allowzeropivot = PetscNot(A->erroriffailure);
240:   PetscCall(ISGetIndices(isrow, &r));
241:   PetscCall(ISGetIndices(isicol, &ic));

243:   if (info->shifttype == (PetscReal)MAT_SHIFT_NONE) {
244:     shift = 0;
245:   } else { /* info->shifttype == MAT_SHIFT_INBLOCKS */
246:     shift = info->shiftamount;
247:   }

249:   /* generate work space needed by the factorization */
250:   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
251:   PetscCall(PetscArrayzero(rtmp, bs2 * n));

253:   for (i = 0; i < n; i++) {
254:     /* zero rtmp */
255:     /* L part */
256:     nz    = bi[i + 1] - bi[i];
257:     bjtmp = bj + bi[i];
258:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

260:     /* U part */
261:     nz    = bdiag[i] - bdiag[i + 1];
262:     bjtmp = bj + bdiag[i + 1] + 1;
263:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

265:     /* load in initial (unfactored row) */
266:     nz    = ai[r[i] + 1] - ai[r[i]];
267:     ajtmp = aj + ai[r[i]];
268:     v     = aa + bs2 * ai[r[i]];
269:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ic[ajtmp[j]], v + bs2 * j, bs2));

271:     /* elimination */
272:     bjtmp = bj + bi[i];
273:     nzL   = bi[i + 1] - bi[i];
274:     for (k = 0; k < nzL; k++) {
275:       row = bjtmp[k];
276:       pc  = rtmp + bs2 * row;
277:       for (flg = 0, j = 0; j < bs2; j++) {
278:         if (pc[j] != 0.0) {
279:           flg = 1;
280:           break;
281:         }
282:       }
283:       if (flg) {
284:         pv = b->a + bs2 * bdiag[row];
285:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
286:         PetscCall(PetscKernel_A_gets_A_times_B_4(pc, pv, mwork));

288:         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
289:         pv = b->a + bs2 * (bdiag[row + 1] + 1);
290:         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
291:         for (j = 0; j < nz; j++) {
292:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
293:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
294:           v = rtmp + bs2 * pj[j];
295:           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_4(v, pc, pv));
296:           pv += bs2;
297:         }
298:         PetscCall(PetscLogFlops(128.0 * nz + 112)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
299:       }
300:     }

302:     /* finished row so stick it into b->a */
303:     /* L part */
304:     pv = b->a + bs2 * bi[i];
305:     pj = b->j + bi[i];
306:     nz = bi[i + 1] - bi[i];
307:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));

309:     /* Mark diagonal and invert diagonal for simpler triangular solves */
310:     pv = b->a + bs2 * bdiag[i];
311:     pj = b->j + bdiag[i];
312:     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
313:     PetscCall(PetscKernel_A_gets_inverse_A_4(pv, shift, allowzeropivot, &zeropivotdetected));
314:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

316:     /* U part */
317:     pv = b->a + bs2 * (bdiag[i + 1] + 1);
318:     pj = b->j + bdiag[i + 1] + 1;
319:     nz = bdiag[i] - bdiag[i + 1] - 1;
320:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
321:   }

323:   PetscCall(PetscFree2(rtmp, mwork));
324:   PetscCall(ISRestoreIndices(isicol, &ic));
325:   PetscCall(ISRestoreIndices(isrow, &r));

327:   C->ops->solve          = MatSolve_SeqBAIJ_4;
328:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4;
329:   C->assembled           = PETSC_TRUE;

331:   PetscCall(PetscLogFlops(1.333333333333 * 4 * 4 * 4 * n)); /* from inverting diagonal blocks */
332:   PetscFunctionReturn(PETSC_SUCCESS);
333: }

335: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_inplace(Mat C, Mat A, const MatFactorInfo *info)
336: {
337:   /*
338:     Default Version for when blocks are 4 by 4 Using natural ordering
339: */
340:   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
341:   PetscInt     i, j, n = a->mbs, *bi = b->i, *bj = b->j;
342:   PetscInt    *ajtmpold, *ajtmp, nz, row;
343:   PetscInt    *diag_offset = b->diag, *ai = a->i, *aj = a->j, *pj;
344:   MatScalar   *pv, *v, *rtmp, *pc, *w, *x;
345:   MatScalar    p1, p2, p3, p4, m1, m2, m3, m4, m5, m6, m7, m8, m9, x1, x2, x3, x4;
346:   MatScalar    p5, p6, p7, p8, p9, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16;
347:   MatScalar    p10, p11, p12, p13, p14, p15, p16, m10, m11, m12;
348:   MatScalar    m13, m14, m15, m16;
349:   MatScalar   *ba = b->a, *aa = a->a;
350:   PetscBool    pivotinblocks = b->pivotinblocks;
351:   PetscReal    shift         = info->shiftamount;
352:   PetscBool    allowzeropivot, zeropivotdetected = PETSC_FALSE;

354:   PetscFunctionBegin;
355:   allowzeropivot = PetscNot(A->erroriffailure);
356:   PetscCall(PetscMalloc1(16 * (n + 1), &rtmp));

358:   for (i = 0; i < n; i++) {
359:     nz    = bi[i + 1] - bi[i];
360:     ajtmp = bj + bi[i];
361:     for (j = 0; j < nz; j++) {
362:       x    = rtmp + 16 * ajtmp[j];
363:       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
364:       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
365:     }
366:     /* load in initial (unfactored row) */
367:     nz       = ai[i + 1] - ai[i];
368:     ajtmpold = aj + ai[i];
369:     v        = aa + 16 * ai[i];
370:     for (j = 0; j < nz; j++) {
371:       x     = rtmp + 16 * ajtmpold[j];
372:       x[0]  = v[0];
373:       x[1]  = v[1];
374:       x[2]  = v[2];
375:       x[3]  = v[3];
376:       x[4]  = v[4];
377:       x[5]  = v[5];
378:       x[6]  = v[6];
379:       x[7]  = v[7];
380:       x[8]  = v[8];
381:       x[9]  = v[9];
382:       x[10] = v[10];
383:       x[11] = v[11];
384:       x[12] = v[12];
385:       x[13] = v[13];
386:       x[14] = v[14];
387:       x[15] = v[15];
388:       v += 16;
389:     }
390:     row = *ajtmp++;
391:     while (row < i) {
392:       pc  = rtmp + 16 * row;
393:       p1  = pc[0];
394:       p2  = pc[1];
395:       p3  = pc[2];
396:       p4  = pc[3];
397:       p5  = pc[4];
398:       p6  = pc[5];
399:       p7  = pc[6];
400:       p8  = pc[7];
401:       p9  = pc[8];
402:       p10 = pc[9];
403:       p11 = pc[10];
404:       p12 = pc[11];
405:       p13 = pc[12];
406:       p14 = pc[13];
407:       p15 = pc[14];
408:       p16 = pc[15];
409:       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) {
410:         pv    = ba + 16 * diag_offset[row];
411:         pj    = bj + diag_offset[row] + 1;
412:         x1    = pv[0];
413:         x2    = pv[1];
414:         x3    = pv[2];
415:         x4    = pv[3];
416:         x5    = pv[4];
417:         x6    = pv[5];
418:         x7    = pv[6];
419:         x8    = pv[7];
420:         x9    = pv[8];
421:         x10   = pv[9];
422:         x11   = pv[10];
423:         x12   = pv[11];
424:         x13   = pv[12];
425:         x14   = pv[13];
426:         x15   = pv[14];
427:         x16   = pv[15];
428:         pc[0] = m1 = p1 * x1 + p5 * x2 + p9 * x3 + p13 * x4;
429:         pc[1] = m2 = p2 * x1 + p6 * x2 + p10 * x3 + p14 * x4;
430:         pc[2] = m3 = p3 * x1 + p7 * x2 + p11 * x3 + p15 * x4;
431:         pc[3] = m4 = p4 * x1 + p8 * x2 + p12 * x3 + p16 * x4;

433:         pc[4] = m5 = p1 * x5 + p5 * x6 + p9 * x7 + p13 * x8;
434:         pc[5] = m6 = p2 * x5 + p6 * x6 + p10 * x7 + p14 * x8;
435:         pc[6] = m7 = p3 * x5 + p7 * x6 + p11 * x7 + p15 * x8;
436:         pc[7] = m8 = p4 * x5 + p8 * x6 + p12 * x7 + p16 * x8;

438:         pc[8] = m9 = p1 * x9 + p5 * x10 + p9 * x11 + p13 * x12;
439:         pc[9] = m10 = p2 * x9 + p6 * x10 + p10 * x11 + p14 * x12;
440:         pc[10] = m11 = p3 * x9 + p7 * x10 + p11 * x11 + p15 * x12;
441:         pc[11] = m12 = p4 * x9 + p8 * x10 + p12 * x11 + p16 * x12;

443:         pc[12] = m13 = p1 * x13 + p5 * x14 + p9 * x15 + p13 * x16;
444:         pc[13] = m14 = p2 * x13 + p6 * x14 + p10 * x15 + p14 * x16;
445:         pc[14] = m15 = p3 * x13 + p7 * x14 + p11 * x15 + p15 * x16;
446:         pc[15] = m16 = p4 * x13 + p8 * x14 + p12 * x15 + p16 * x16;
447:         nz           = bi[row + 1] - diag_offset[row] - 1;
448:         pv += 16;
449:         for (j = 0; j < nz; j++) {
450:           x1  = pv[0];
451:           x2  = pv[1];
452:           x3  = pv[2];
453:           x4  = pv[3];
454:           x5  = pv[4];
455:           x6  = pv[5];
456:           x7  = pv[6];
457:           x8  = pv[7];
458:           x9  = pv[8];
459:           x10 = pv[9];
460:           x11 = pv[10];
461:           x12 = pv[11];
462:           x13 = pv[12];
463:           x14 = pv[13];
464:           x15 = pv[14];
465:           x16 = pv[15];
466:           x   = rtmp + 16 * pj[j];
467:           x[0] -= m1 * x1 + m5 * x2 + m9 * x3 + m13 * x4;
468:           x[1] -= m2 * x1 + m6 * x2 + m10 * x3 + m14 * x4;
469:           x[2] -= m3 * x1 + m7 * x2 + m11 * x3 + m15 * x4;
470:           x[3] -= m4 * x1 + m8 * x2 + m12 * x3 + m16 * x4;

472:           x[4] -= m1 * x5 + m5 * x6 + m9 * x7 + m13 * x8;
473:           x[5] -= m2 * x5 + m6 * x6 + m10 * x7 + m14 * x8;
474:           x[6] -= m3 * x5 + m7 * x6 + m11 * x7 + m15 * x8;
475:           x[7] -= m4 * x5 + m8 * x6 + m12 * x7 + m16 * x8;

477:           x[8] -= m1 * x9 + m5 * x10 + m9 * x11 + m13 * x12;
478:           x[9] -= m2 * x9 + m6 * x10 + m10 * x11 + m14 * x12;
479:           x[10] -= m3 * x9 + m7 * x10 + m11 * x11 + m15 * x12;
480:           x[11] -= m4 * x9 + m8 * x10 + m12 * x11 + m16 * x12;

482:           x[12] -= m1 * x13 + m5 * x14 + m9 * x15 + m13 * x16;
483:           x[13] -= m2 * x13 + m6 * x14 + m10 * x15 + m14 * x16;
484:           x[14] -= m3 * x13 + m7 * x14 + m11 * x15 + m15 * x16;
485:           x[15] -= m4 * x13 + m8 * x14 + m12 * x15 + m16 * x16;

487:           pv += 16;
488:         }
489:         PetscCall(PetscLogFlops(128.0 * nz + 112.0));
490:       }
491:       row = *ajtmp++;
492:     }
493:     /* finished row so stick it into b->a */
494:     pv = ba + 16 * bi[i];
495:     pj = bj + bi[i];
496:     nz = bi[i + 1] - bi[i];
497:     for (j = 0; j < nz; j++) {
498:       x      = rtmp + 16 * pj[j];
499:       pv[0]  = x[0];
500:       pv[1]  = x[1];
501:       pv[2]  = x[2];
502:       pv[3]  = x[3];
503:       pv[4]  = x[4];
504:       pv[5]  = x[5];
505:       pv[6]  = x[6];
506:       pv[7]  = x[7];
507:       pv[8]  = x[8];
508:       pv[9]  = x[9];
509:       pv[10] = x[10];
510:       pv[11] = x[11];
511:       pv[12] = x[12];
512:       pv[13] = x[13];
513:       pv[14] = x[14];
514:       pv[15] = x[15];
515:       pv += 16;
516:     }
517:     /* invert diagonal block */
518:     w = ba + 16 * diag_offset[i];
519:     if (pivotinblocks) {
520:       PetscCall(PetscKernel_A_gets_inverse_A_4(w, shift, allowzeropivot, &zeropivotdetected));
521:       if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
522:     } else {
523:       PetscCall(PetscKernel_A_gets_inverse_A_4_nopivot(w));
524:     }
525:   }

527:   PetscCall(PetscFree(rtmp));

529:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering_inplace;
530:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_inplace;
531:   C->assembled           = PETSC_TRUE;

533:   PetscCall(PetscLogFlops(1.333333333333 * 4 * 4 * 4 * b->mbs)); /* from inverting diagonal blocks */
534:   PetscFunctionReturn(PETSC_SUCCESS);
535: }

537: /*
538:   MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering -
539:     copied from MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_inplace()
540: */
541: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering(Mat B, Mat A, const MatFactorInfo *info)
542: {
543:   Mat             C = B;
544:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
545:   PetscInt        i, j, k, nz, nzL, row;
546:   const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
547:   const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
548:   MatScalar      *rtmp, *pc, *mwork, *v, *pv, *aa = a->a;
549:   PetscInt        flg;
550:   PetscReal       shift;
551:   PetscBool       allowzeropivot, zeropivotdetected;

553:   PetscFunctionBegin;
554:   allowzeropivot = PetscNot(A->erroriffailure);

556:   /* generate work space needed by the factorization */
557:   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
558:   PetscCall(PetscArrayzero(rtmp, bs2 * n));

560:   if (info->shifttype == (PetscReal)MAT_SHIFT_NONE) {
561:     shift = 0;
562:   } else { /* info->shifttype == MAT_SHIFT_INBLOCKS */
563:     shift = info->shiftamount;
564:   }

566:   for (i = 0; i < n; i++) {
567:     /* zero rtmp */
568:     /* L part */
569:     nz    = bi[i + 1] - bi[i];
570:     bjtmp = bj + bi[i];
571:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

573:     /* U part */
574:     nz    = bdiag[i] - bdiag[i + 1];
575:     bjtmp = bj + bdiag[i + 1] + 1;
576:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

578:     /* load in initial (unfactored row) */
579:     nz    = ai[i + 1] - ai[i];
580:     ajtmp = aj + ai[i];
581:     v     = aa + bs2 * ai[i];
582:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ajtmp[j], v + bs2 * j, bs2));

584:     /* elimination */
585:     bjtmp = bj + bi[i];
586:     nzL   = bi[i + 1] - bi[i];
587:     for (k = 0; k < nzL; k++) {
588:       row = bjtmp[k];
589:       pc  = rtmp + bs2 * row;
590:       for (flg = 0, j = 0; j < bs2; j++) {
591:         if (pc[j] != 0.0) {
592:           flg = 1;
593:           break;
594:         }
595:       }
596:       if (flg) {
597:         pv = b->a + bs2 * bdiag[row];
598:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
599:         PetscCall(PetscKernel_A_gets_A_times_B_4(pc, pv, mwork));

601:         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
602:         pv = b->a + bs2 * (bdiag[row + 1] + 1);
603:         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
604:         for (j = 0; j < nz; j++) {
605:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
606:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
607:           v = rtmp + bs2 * pj[j];
608:           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_4(v, pc, pv));
609:           pv += bs2;
610:         }
611:         PetscCall(PetscLogFlops(128.0 * nz + 112)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
612:       }
613:     }

615:     /* finished row so stick it into b->a */
616:     /* L part */
617:     pv = b->a + bs2 * bi[i];
618:     pj = b->j + bi[i];
619:     nz = bi[i + 1] - bi[i];
620:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));

622:     /* Mark diagonal and invert diagonal for simpler triangular solves */
623:     pv = b->a + bs2 * bdiag[i];
624:     pj = b->j + bdiag[i];
625:     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
626:     PetscCall(PetscKernel_A_gets_inverse_A_4(pv, shift, allowzeropivot, &zeropivotdetected));
627:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

629:     /* U part */
630:     pv = b->a + bs2 * (bdiag[i + 1] + 1);
631:     pj = b->j + bdiag[i + 1] + 1;
632:     nz = bdiag[i] - bdiag[i + 1] - 1;
633:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
634:   }
635:   PetscCall(PetscFree2(rtmp, mwork));

637:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering;
638:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering;
639:   C->assembled           = PETSC_TRUE;

641:   PetscCall(PetscLogFlops(1.333333333333 * 4 * 4 * 4 * n)); /* from inverting diagonal blocks */
642:   PetscFunctionReturn(PETSC_SUCCESS);
643: }