Actual source code: baijfact13.c

  1: #define PETSCMAT_DLL

  3: /*
  4:     Factorization code for BAIJ format. 
  5: */
 6:  #include ../src/mat/impls/baij/seq/baij.h
 7:  #include ../src/mat/blockinvert.h

  9: /*
 10:       Version for when blocks are 3 by 3
 11: */
 14: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_inplace(Mat C,Mat A,const MatFactorInfo *info)
 15: {
 16:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
 17:   IS             isrow = b->row,isicol = b->icol;
 19:   const PetscInt *r,*ic;
 20:   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
 21:   PetscInt       *ajtmpold,*ajtmp,nz,row,*ai=a->i,*aj=a->j;
 22:   PetscInt       *diag_offset = b->diag,idx,*pj;
 23:   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
 24:   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
 25:   MatScalar      p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
 26:   MatScalar      *ba = b->a,*aa = a->a;
 27:   PetscReal      shift = info->shiftamount;

 30:   ISGetIndices(isrow,&r);
 31:   ISGetIndices(isicol,&ic);
 32:   PetscMalloc(9*(n+1)*sizeof(MatScalar),&rtmp);

 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 + 9*ajtmp[j];
 39:       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0;
 40:     }
 41:     /* load in initial (unfactored row) */
 42:     idx      = r[i];
 43:     nz       = ai[idx+1] - ai[idx];
 44:     ajtmpold = aj + ai[idx];
 45:     v        = aa + 9*ai[idx];
 46:     for (j=0; j<nz; j++) {
 47:       x    = rtmp + 9*ic[ajtmpold[j]];
 48:       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
 49:       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
 50:       v    += 9;
 51:     }
 52:     row = *ajtmp++;
 53:     while (row < i) {
 54:       pc = rtmp + 9*row;
 55:       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
 56:       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
 57:       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
 58:           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
 59:         pv = ba + 9*diag_offset[row];
 60:         pj = bj + diag_offset[row] + 1;
 61:         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
 62:         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
 63:         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
 64:         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
 65:         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;

 67:         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
 68:         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
 69:         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;

 71:         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
 72:         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
 73:         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
 74:         nz = bi[row+1] - diag_offset[row] - 1;
 75:         pv += 9;
 76:         for (j=0; j<nz; j++) {
 77:           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
 78:           x5   = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
 79:           x    = rtmp + 9*pj[j];
 80:           x[0] -= m1*x1 + m4*x2 + m7*x3;
 81:           x[1] -= m2*x1 + m5*x2 + m8*x3;
 82:           x[2] -= m3*x1 + m6*x2 + m9*x3;
 83: 
 84:           x[3] -= m1*x4 + m4*x5 + m7*x6;
 85:           x[4] -= m2*x4 + m5*x5 + m8*x6;
 86:           x[5] -= m3*x4 + m6*x5 + m9*x6;

 88:           x[6] -= m1*x7 + m4*x8 + m7*x9;
 89:           x[7] -= m2*x7 + m5*x8 + m8*x9;
 90:           x[8] -= m3*x7 + m6*x8 + m9*x9;
 91:           pv   += 9;
 92:         }
 93:         PetscLogFlops(54.0*nz+36.0);
 94:       }
 95:       row = *ajtmp++;
 96:     }
 97:     /* finished row so stick it into b->a */
 98:     pv = ba + 9*bi[i];
 99:     pj = bj + bi[i];
100:     nz = bi[i+1] - bi[i];
101:     for (j=0; j<nz; j++) {
102:       x     = rtmp + 9*pj[j];
103:       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
104:       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
105:       pv   += 9;
106:     }
107:     /* invert diagonal block */
108:     w = ba + 9*diag_offset[i];
109:     Kernel_A_gets_inverse_A_3(w,shift);
110:   }

112:   PetscFree(rtmp);
113:   ISRestoreIndices(isicol,&ic);
114:   ISRestoreIndices(isrow,&r);
115:   C->ops->solve          = MatSolve_SeqBAIJ_3_inplace;
116:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_inplace;
117:   C->assembled = PETSC_TRUE;
118:   PetscLogFlops(1.333333333333*3*3*3*b->mbs); /* from inverting diagonal blocks */
119:   return(0);
120: }

122: /* MatLUFactorNumeric_SeqBAIJ_3 - 
123:      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented 
124:        Kernel_A_gets_A_times_B()
125:        Kernel_A_gets_A_minus_B_times_C()
126:        Kernel_A_gets_inverse_A()
127: */
130: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3(Mat B,Mat A,const MatFactorInfo *info)
131: {
132:   Mat            C=B;
133:   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
134:   IS             isrow = b->row,isicol = b->icol;
136:   const PetscInt *r,*ic,*ics;
137:   PetscInt       i,j,k,nz,nzL,row;
138:   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
139:   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
140:   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
141:   PetscInt       flg;
142:   PetscReal      shift = info->shiftamount;

145:   ISGetIndices(isrow,&r);
146:   ISGetIndices(isicol,&ic);

148:   /* generate work space needed by the factorization */
149:   PetscMalloc2(bs2*n,MatScalar,&rtmp,bs2,MatScalar,&mwork);
150:   PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));
151:   ics  = ic;

153:   for (i=0; i<n; i++){
154:     /* zero rtmp */
155:     /* L part */
156:     nz    = bi[i+1] - bi[i];
157:     bjtmp = bj + bi[i];
158:     for  (j=0; j<nz; j++){
159:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
160:     }

162:     /* U part */
163:     nz = bdiag[i] - bdiag[i+1];
164:     bjtmp = bj + bdiag[i+1]+1;
165:     for  (j=0; j<nz; j++){
166:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
167:     }
168: 
169:     /* load in initial (unfactored row) */
170:     nz    = ai[r[i]+1] - ai[r[i]];
171:     ajtmp = aj + ai[r[i]];
172:     v     = aa + bs2*ai[r[i]];
173:     for (j=0; j<nz; j++) {
174:       PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));
175:     }

177:     /* elimination */
178:     bjtmp = bj + bi[i];
179:     nzL   = bi[i+1] - bi[i];
180:     for(k = 0;k < nzL;k++){
181:       row = bjtmp[k];
182:       pc = rtmp + bs2*row;
183:       for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
184:       if (flg) {
185:         pv = b->a + bs2*bdiag[row];
186:         /* Kernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
187:         Kernel_A_gets_A_times_B_3(pc,pv,mwork);
188: 
189:            pj = b->j + bdiag[row+1] + 1; /* beginning of U(row,:) */
190:         pv = b->a + bs2*(bdiag[row+1]+1);
191:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
192:         for (j=0; j<nz; j++) {
193:           /* Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
194:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
195:           v    = rtmp + bs2*pj[j];
196:           Kernel_A_gets_A_minus_B_times_C_3(v,pc,pv);
197:           pv  += bs2;
198:         }
199:         PetscLogFlops(54*nz+45); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
200:       }
201:     }

203:     /* finished row so stick it into b->a */
204:     /* L part */
205:     pv   = b->a + bs2*bi[i] ;
206:     pj   = b->j + bi[i] ;
207:     nz   = bi[i+1] - bi[i];
208:     for (j=0; j<nz; j++) {
209:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
210:     }

212:     /* Mark diagonal and invert diagonal for simplier triangular solves */
213:     pv   = b->a + bs2*bdiag[i];
214:     pj   = b->j + bdiag[i];
215:     PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
216:     /* Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work); */
217:     Kernel_A_gets_inverse_A_3(pv,shift);
218: 
219:     /* U part */
220:     pj = b->j + bdiag[i+1] + 1;
221:     pv = b->a + bs2*(bdiag[i+1]+1);
222:     nz = bdiag[i] - bdiag[i+1] - 1;
223:     for (j=0; j<nz; j++){
224:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
225:     }
226:   }

228:   PetscFree2(rtmp,mwork);
229:   ISRestoreIndices(isicol,&ic);
230:   ISRestoreIndices(isrow,&r);
231:   C->ops->solve = MatSolve_SeqBAIJ_3;
232:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3;

234:   C->assembled = PETSC_TRUE;
235:   PetscLogFlops(1.333333333333*3*3*3*n); /* from inverting diagonal blocks */
236:   return(0);
237: }

241: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
242: {
243:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
245:   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
246:   PetscInt       *ajtmpold,*ajtmp,nz,row;
247:   PetscInt       *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
248:   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
249:   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
250:   MatScalar      p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
251:   MatScalar      *ba = b->a,*aa = a->a;
252:   PetscReal      shift = info->shiftamount;

255:   PetscMalloc(9*(n+1)*sizeof(MatScalar),&rtmp);

257:   for (i=0; i<n; i++) {
258:     nz    = bi[i+1] - bi[i];
259:     ajtmp = bj + bi[i];
260:     for  (j=0; j<nz; j++) {
261:       x = rtmp+9*ajtmp[j];
262:       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = 0.0;
263:     }
264:     /* load in initial (unfactored row) */
265:     nz       = ai[i+1] - ai[i];
266:     ajtmpold = aj + ai[i];
267:     v        = aa + 9*ai[i];
268:     for (j=0; j<nz; j++) {
269:       x    = rtmp+9*ajtmpold[j];
270:       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
271:       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
272:       v    += 9;
273:     }
274:     row = *ajtmp++;
275:     while (row < i) {
276:       pc  = rtmp + 9*row;
277:       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
278:       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
279:       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
280:           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
281:         pv = ba + 9*diag_offset[row];
282:         pj = bj + diag_offset[row] + 1;
283:         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
284:         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
285:         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
286:         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
287:         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;

289:         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
290:         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
291:         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;

293:         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
294:         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
295:         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;

297:         nz = bi[row+1] - diag_offset[row] - 1;
298:         pv += 9;
299:         for (j=0; j<nz; j++) {
300:           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
301:           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
302:           x    = rtmp + 9*pj[j];
303:           x[0] -= m1*x1 + m4*x2 + m7*x3;
304:           x[1] -= m2*x1 + m5*x2 + m8*x3;
305:           x[2] -= m3*x1 + m6*x2 + m9*x3;
306: 
307:           x[3] -= m1*x4 + m4*x5 + m7*x6;
308:           x[4] -= m2*x4 + m5*x5 + m8*x6;
309:           x[5] -= m3*x4 + m6*x5 + m9*x6;

311:           x[6] -= m1*x7 + m4*x8 + m7*x9;
312:           x[7] -= m2*x7 + m5*x8 + m8*x9;
313:           x[8] -= m3*x7 + m6*x8 + m9*x9;
314:           pv   += 9;
315:         }
316:         PetscLogFlops(54.0*nz+36.0);
317:       }
318:       row = *ajtmp++;
319:     }
320:     /* finished row so stick it into b->a */
321:     pv = ba + 9*bi[i];
322:     pj = bj + bi[i];
323:     nz = bi[i+1] - bi[i];
324:     for (j=0; j<nz; j++) {
325:       x      = rtmp+9*pj[j];
326:       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
327:       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
328:       pv   += 9;
329:     }
330:     /* invert diagonal block */
331:     w = ba + 9*diag_offset[i];
332:     Kernel_A_gets_inverse_A_3(w,shift);
333:   }

335:   PetscFree(rtmp);
336:   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering_inplace;
337:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering_inplace;
338:   C->assembled = PETSC_TRUE;
339:   PetscLogFlops(1.333333333333*3*3*3*b->mbs); /* from inverting diagonal blocks */
340:   return(0);
341: }

343: /*
344:   MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering -
345:     copied from MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_inplace()
346: */
349: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
350: {
351:   Mat            C=B;
352:   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
354:   PetscInt       i,j,k,nz,nzL,row;
355:   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
356:   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
357:   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
358:   PetscInt       flg;
359:   PetscReal      shift = info->shiftamount;

362:   /* generate work space needed by the factorization */
363:   PetscMalloc2(bs2*n,MatScalar,&rtmp,bs2,MatScalar,&mwork);
364:   PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));

366:   for (i=0; i<n; i++){
367:     /* zero rtmp */
368:     /* L part */
369:     nz    = bi[i+1] - bi[i];
370:     bjtmp = bj + bi[i];
371:     for  (j=0; j<nz; j++){
372:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
373:     }

375:     /* U part */
376:     nz = bdiag[i] - bdiag[i+1];
377:     bjtmp = bj + bdiag[i+1] + 1;
378:     for  (j=0; j<nz; j++){
379:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
380:     }
381: 
382:     /* load in initial (unfactored row) */
383:     nz    = ai[i+1] - ai[i];
384:     ajtmp = aj + ai[i];
385:     v     = aa + bs2*ai[i];
386:     for (j=0; j<nz; j++) {
387:       PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));
388:     }

390:     /* elimination */
391:     bjtmp = bj + bi[i];
392:     nzL   = bi[i+1] - bi[i];
393:     for(k=0;k<nzL;k++){
394:       row = bjtmp[k];
395:       pc = rtmp + bs2*row;
396:       for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
397:       if (flg) {
398:         pv = b->a + bs2*bdiag[row];
399:         /* Kernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
400:         Kernel_A_gets_A_times_B_3(pc,pv,mwork);
401: 
402:         pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
403:         pv = b->a + bs2*(bdiag[row+1]+1);
404:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
405:         for (j=0; j<nz; j++) {
406:           /* Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
407:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
408:           v    = rtmp + bs2*pj[j];
409:           Kernel_A_gets_A_minus_B_times_C_3(v,pc,pv);
410:           pv  += bs2;
411:         }
412:         PetscLogFlops(54*nz+45); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
413:       }
414:     }

416:     /* finished row so stick it into b->a */
417:     /* L part */
418:     pv   = b->a + bs2*bi[i] ;
419:     pj   = b->j + bi[i] ;
420:     nz   = bi[i+1] - bi[i];
421:     for (j=0; j<nz; j++) {
422:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
423:     }

425:     /* Mark diagonal and invert diagonal for simplier triangular solves */
426:     pv   = b->a + bs2*bdiag[i];
427:     pj   = b->j + bdiag[i];
428:     PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
429:     /* Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work); */
430:     Kernel_A_gets_inverse_A_3(pv,shift);
431: 
432:     /* U part */
433:     pv = b->a + bs2*(bdiag[i+1]+1);
434:     pj = b->j + bdiag[i+1]+1;
435:     nz = bdiag[i] - bdiag[i+1] - 1;
436:     for (j=0; j<nz; j++){
437:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
438:     }
439:   }
440:   PetscFree2(rtmp,mwork);
441:   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering;
442:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering;
443:   C->assembled = PETSC_TRUE;
444:   PetscLogFlops(1.333333333333*3*3*3*n); /* from inverting diagonal blocks */
445:   return(0);
446: }