1 #define PETSCMAT_DLL 2 3 4 #include "../src/mat/impls/aij/seq/aij.h" 5 #include "../src/mat/impls/sbaij/seq/sbaij.h" 6 #include "petscbt.h" 7 #include "../src/mat/utils/freespace.h" 8 9 EXTERN_C_BEGIN 10 #undef __FUNCT__ 11 #define __FUNCT__ "MatOrdering_Flow_SeqAIJ" 12 /* 13 Computes an ordering to get most of the large numerical values in the lower triangular part of the matrix 14 */ 15 PetscErrorCode MatOrdering_Flow_SeqAIJ(Mat mat,const MatOrderingType type,IS *irow,IS *icol) 16 { 17 Mat_SeqAIJ *a = (Mat_SeqAIJ*)mat->data; 18 PetscErrorCode ierr; 19 PetscInt i,j,jj,k, kk,n = mat->rmap->n, current = 0, newcurrent = 0,*order; 20 const PetscInt *ai = a->i, *aj = a->j; 21 const PetscScalar *aa = a->a; 22 PetscTruth *done; 23 PetscReal best,past = 0,future; 24 25 PetscFunctionBegin; 26 /* pick initial row */ 27 best = -1; 28 for (i=0; i<n; i++) { 29 future = 0; 30 for (j=ai[i]; j<ai[i+1]; j++) { 31 if (aj[j] != i) future += PetscAbsScalar(aa[j]); else past = PetscAbsScalar(aa[j]); 32 } 33 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 34 if (past/future > best) { 35 best = past/future; 36 current = i; 37 } 38 } 39 40 ierr = PetscMalloc(n*sizeof(PetscTruth),&done);CHKERRQ(ierr); 41 ierr = PetscMalloc(n*sizeof(PetscInt),&order);CHKERRQ(ierr); 42 ierr = PetscMemzero(done,n*sizeof(PetscTruth));CHKERRQ(ierr); 43 order[0] = current; 44 for (i=0; i<n-1; i++) { 45 done[current] = PETSC_TRUE; 46 best = -1; 47 /* loop over all neighbors of current pivot */ 48 for (j=ai[current]; j<ai[current+1]; j++) { 49 jj = aj[j]; 50 if (done[jj]) continue; 51 /* loop over columns of potential next row computing weights for below and above diagonal */ 52 past = future = 0.0; 53 for (k=ai[jj]; k<ai[jj+1]; k++) { 54 kk = aj[k]; 55 if (done[kk]) past += PetscAbsScalar(aa[k]); 56 else if (kk != jj) future += PetscAbsScalar(aa[k]); 57 } 58 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 59 if (past/future > best) { 60 best = past/future; 61 newcurrent = jj; 62 } 63 } 64 if (best == -1) { /* no neighbors to select from so select best of all that remain */ 65 best = -1; 66 for (k=0; k<n; k++) { 67 if (done[k]) continue; 68 future = 0; 69 past = 0; 70 for (j=ai[k]; j<ai[k+1]; j++) { 71 kk = aj[j]; 72 if (done[kk]) past += PetscAbsScalar(aa[j]); 73 else if (kk != k) future += PetscAbsScalar(aa[j]); 74 } 75 if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */ 76 if (past/future > best) { 77 best = past/future; 78 newcurrent = k; 79 } 80 } 81 } 82 if (current == newcurrent) SETERRQ(PETSC_ERR_PLIB,"newcurrent cannot be current"); 83 current = newcurrent; 84 order[i+1] = current; 85 } 86 ierr = ISCreateGeneral(PETSC_COMM_SELF,n,order,irow);CHKERRQ(ierr); 87 *icol = *irow; 88 ierr = PetscObjectReference((PetscObject)*irow);CHKERRQ(ierr); 89 ierr = PetscFree(done);CHKERRQ(ierr); 90 ierr = PetscFree(order);CHKERRQ(ierr); 91 PetscFunctionReturn(0); 92 } 93 EXTERN_C_END 94 95 EXTERN_C_BEGIN 96 #undef __FUNCT__ 97 #define __FUNCT__ "MatGetFactorAvailable_seqaij_petsc" 98 PetscErrorCode MatGetFactorAvailable_seqaij_petsc(Mat A,MatFactorType ftype,PetscTruth *flg) 99 { 100 PetscFunctionBegin; 101 *flg = PETSC_TRUE; 102 PetscFunctionReturn(0); 103 } 104 EXTERN_C_END 105 106 EXTERN_C_BEGIN 107 #undef __FUNCT__ 108 #define __FUNCT__ "MatGetFactor_seqaij_petsc" 109 PetscErrorCode MatGetFactor_seqaij_petsc(Mat A,MatFactorType ftype,Mat *B) 110 { 111 PetscInt n = A->rmap->n; 112 PetscErrorCode ierr; 113 114 PetscFunctionBegin; 115 ierr = MatCreate(((PetscObject)A)->comm,B);CHKERRQ(ierr); 116 ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr); 117 if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT){ 118 ierr = MatSetType(*B,MATSEQAIJ);CHKERRQ(ierr); 119 (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJ; 120 (*B)->ops->lufactorsymbolic = MatLUFactorSymbolic_SeqAIJ; 121 (*B)->ops->iludtfactor = MatILUDTFactor_SeqAIJ; 122 } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) { 123 ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr); 124 ierr = MatSeqSBAIJSetPreallocation(*B,1,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 125 (*B)->ops->iccfactorsymbolic = MatICCFactorSymbolic_SeqAIJ; 126 (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ; 127 } else SETERRQ(PETSC_ERR_SUP,"Factor type not supported"); 128 (*B)->factor = ftype; 129 PetscFunctionReturn(0); 130 } 131 EXTERN_C_END 132 133 #undef __FUNCT__ 134 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ" 135 PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 136 { 137 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 138 IS isicol; 139 PetscErrorCode ierr; 140 const PetscInt *r,*ic; 141 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 142 PetscInt *bi,*bj,*ajtmp; 143 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 144 PetscReal f; 145 PetscInt nlnk,*lnk,k,**bi_ptr; 146 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 147 PetscBT lnkbt; 148 PetscTruth newdatastruct=PETSC_FALSE; 149 PetscTruth newdatastruct_v2 = PETSC_FALSE; 150 151 PetscFunctionBegin; 152 ierr = PetscOptionsGetTruth(PETSC_NULL,"-lu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 153 if(newdatastruct){ 154 ierr = MatLUFactorSymbolic_SeqAIJ_newdatastruct(B,A,isrow,iscol,info);CHKERRQ(ierr); 155 PetscFunctionReturn(0); 156 } 157 ierr = PetscOptionsGetTruth(PETSC_NULL,"-lu_new_v2",&newdatastruct_v2,PETSC_NULL);CHKERRQ(ierr); 158 if(newdatastruct_v2){ 159 ierr = MatLUFactorSymbolic_SeqAIJ_newdatastruct_v2(B,A,isrow,iscol,info);CHKERRQ(ierr); 160 PetscFunctionReturn(0); 161 } 162 163 164 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square"); 165 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 166 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 167 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 168 169 /* get new row pointers */ 170 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 171 bi[0] = 0; 172 173 /* bdiag is location of diagonal in factor */ 174 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 175 bdiag[0] = 0; 176 177 /* linked list for storing column indices of the active row */ 178 nlnk = n + 1; 179 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 180 181 ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr); 182 183 /* initial FreeSpace size is f*(ai[n]+1) */ 184 f = info->fill; 185 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 186 current_space = free_space; 187 188 for (i=0; i<n; i++) { 189 /* copy previous fill into linked list */ 190 nzi = 0; 191 nnz = ai[r[i]+1] - ai[r[i]]; 192 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 193 ajtmp = aj + ai[r[i]]; 194 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 195 nzi += nlnk; 196 197 /* add pivot rows into linked list */ 198 row = lnk[n]; 199 while (row < i) { 200 nzbd = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */ 201 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 202 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 203 nzi += nlnk; 204 row = lnk[row]; 205 } 206 bi[i+1] = bi[i] + nzi; 207 im[i] = nzi; 208 209 /* mark bdiag */ 210 nzbd = 0; 211 nnz = nzi; 212 k = lnk[n]; 213 while (nnz-- && k < i){ 214 nzbd++; 215 k = lnk[k]; 216 } 217 bdiag[i] = bi[i] + nzbd; 218 219 /* if free space is not available, make more free space */ 220 if (current_space->local_remaining<nzi) { 221 nnz = (n - i)*nzi; /* estimated and max additional space needed */ 222 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 223 reallocs++; 224 } 225 226 /* copy data into free space, then initialize lnk */ 227 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 228 bi_ptr[i] = current_space->array; 229 current_space->array += nzi; 230 current_space->local_used += nzi; 231 current_space->local_remaining -= nzi; 232 } 233 #if defined(PETSC_USE_INFO) 234 if (ai[n] != 0) { 235 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 236 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 237 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 238 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr); 239 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 240 } else { 241 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 242 } 243 #endif 244 245 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 246 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 247 248 /* destroy list of free space and other temporary array(s) */ 249 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 250 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); 251 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 252 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 253 254 /* put together the new matrix */ 255 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 256 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 257 b = (Mat_SeqAIJ*)(B)->data; 258 b->free_a = PETSC_TRUE; 259 b->free_ij = PETSC_TRUE; 260 b->singlemalloc = PETSC_FALSE; 261 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 262 b->j = bj; 263 b->i = bi; 264 b->diag = bdiag; 265 b->ilen = 0; 266 b->imax = 0; 267 b->row = isrow; 268 b->col = iscol; 269 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 270 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 271 b->icol = isicol; 272 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 273 274 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 275 ierr = PetscLogObjectMemory(B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 276 b->maxnz = b->nz = bi[n] ; 277 278 (B)->factor = MAT_FACTOR_LU; 279 (B)->info.factor_mallocs = reallocs; 280 (B)->info.fill_ratio_given = f; 281 282 if (ai[n]) { 283 (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 284 } else { 285 (B)->info.fill_ratio_needed = 0.0; 286 } 287 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 288 (B)->ops->solve = MatSolve_SeqAIJ; 289 (B)->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 290 /* switch to inodes if appropriate */ 291 ierr = MatLUFactorSymbolic_Inode(B,A,isrow,iscol,info);CHKERRQ(ierr); 292 PetscFunctionReturn(0); 293 } 294 295 #undef __FUNCT__ 296 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ_newdatastruct" 297 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_newdatastruct(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 298 { 299 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 300 IS isicol; 301 PetscErrorCode ierr; 302 const PetscInt *r,*ic; 303 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 304 PetscInt *bi,*bj,*ajtmp; 305 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 306 PetscReal f; 307 PetscInt nlnk,*lnk,k,**bi_ptr; 308 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 309 PetscBT lnkbt; 310 311 PetscFunctionBegin; 312 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square"); 313 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 314 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 315 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 316 317 /* get new row pointers */ 318 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 319 bi[0] = 0; 320 321 /* bdiag is location of diagonal in factor */ 322 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 323 bdiag[0] = 0; 324 325 /* linked list for storing column indices of the active row */ 326 nlnk = n + 1; 327 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 328 329 ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr); 330 331 /* initial FreeSpace size is f*(ai[n]+1) */ 332 f = info->fill; 333 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 334 current_space = free_space; 335 336 for (i=0; i<n; i++) { 337 /* copy previous fill into linked list */ 338 nzi = 0; 339 nnz = ai[r[i]+1] - ai[r[i]]; 340 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 341 ajtmp = aj + ai[r[i]]; 342 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 343 nzi += nlnk; 344 345 /* add pivot rows into linked list */ 346 row = lnk[n]; 347 while (row < i){ 348 nzbd = bdiag[row] + 1; /* num of entries in the row with column index <= row */ 349 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 350 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 351 nzi += nlnk; 352 row = lnk[row]; 353 } 354 bi[i+1] = bi[i] + nzi; 355 im[i] = nzi; 356 357 /* mark bdiag */ 358 nzbd = 0; 359 nnz = nzi; 360 k = lnk[n]; 361 while (nnz-- && k < i){ 362 nzbd++; 363 k = lnk[k]; 364 } 365 bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */ 366 367 /* if free space is not available, make more free space */ 368 if (current_space->local_remaining<nzi) { 369 nnz = 2*(n - i)*nzi; /* estimated and max additional space needed */ 370 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 371 reallocs++; 372 } 373 374 /* copy data into free space, then initialize lnk */ 375 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 376 bi_ptr[i] = current_space->array; 377 current_space->array += nzi; 378 current_space->local_used += nzi; 379 current_space->local_remaining -= nzi; 380 } 381 #if defined(PETSC_USE_INFO) 382 if (ai[n] != 0) { 383 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 384 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 385 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 386 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr); 387 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 388 } else { 389 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 390 } 391 #endif 392 393 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 394 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 395 396 /* destroy list of free space and other temporary array(s) */ 397 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 398 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 399 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 400 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 401 402 /* put together the new matrix */ 403 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 404 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 405 b = (Mat_SeqAIJ*)(B)->data; 406 b->free_a = PETSC_TRUE; 407 b->free_ij = PETSC_TRUE; 408 b->singlemalloc = PETSC_FALSE; 409 ierr = PetscMalloc((bi[2*n+1])*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 410 b->j = bj; 411 b->i = bi; 412 b->diag = bdiag; 413 b->ilen = 0; 414 b->imax = 0; 415 b->row = isrow; 416 b->col = iscol; 417 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 418 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 419 b->icol = isicol; 420 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 421 422 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 423 ierr = PetscLogObjectMemory(B,bi[2*n+1]*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 424 b->maxnz = b->nz = bi[2*n+1] ; 425 426 (B)->factor = MAT_FACTOR_LU; 427 (B)->info.factor_mallocs = reallocs; 428 (B)->info.fill_ratio_given = f; 429 430 if (ai[n]) { 431 (B)->info.fill_ratio_needed = ((PetscReal)bi[2*n+1])/((PetscReal)ai[n]); 432 } else { 433 (B)->info.fill_ratio_needed = 0.0; 434 } 435 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 436 PetscFunctionReturn(0); 437 } 438 439 #undef __FUNCT__ 440 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ_newdatastruct_v2" 441 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_newdatastruct_v2(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 442 { 443 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 444 IS isicol; 445 PetscErrorCode ierr; 446 const PetscInt *r,*ic; 447 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 448 PetscInt *bi,*bj,*ajtmp; 449 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 450 PetscReal f; 451 PetscInt nlnk,*lnk,k,**bi_ptr; 452 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 453 PetscBT lnkbt; 454 455 PetscFunctionBegin; 456 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square"); 457 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 458 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 459 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 460 461 /* get new row pointers */ 462 /* ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); */ 463 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 464 bi[0] = 0; 465 466 /* bdiag is location of diagonal in factor */ 467 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 468 bdiag[0] = 0; 469 470 /* linked list for storing column indices of the active row */ 471 nlnk = n + 1; 472 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 473 474 ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr); 475 476 /* initial FreeSpace size is f*(ai[n]+1) */ 477 f = info->fill; 478 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 479 current_space = free_space; 480 481 for (i=0; i<n; i++) { 482 /* copy previous fill into linked list */ 483 nzi = 0; 484 nnz = ai[r[i]+1] - ai[r[i]]; 485 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 486 ajtmp = aj + ai[r[i]]; 487 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 488 nzi += nlnk; 489 490 /* add pivot rows into linked list */ 491 row = lnk[n]; 492 while (row < i){ 493 nzbd = bdiag[row] + 1; /* num of entries in the row with column index <= row */ 494 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 495 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 496 nzi += nlnk; 497 row = lnk[row]; 498 } 499 bi[i+1] = bi[i] + nzi; 500 im[i] = nzi; 501 502 /* mark bdiag */ 503 nzbd = 0; 504 nnz = nzi; 505 k = lnk[n]; 506 while (nnz-- && k < i){ 507 nzbd++; 508 k = lnk[k]; 509 } 510 bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */ 511 512 /* if free space is not available, make more free space */ 513 if (current_space->local_remaining<nzi) { 514 nnz = 2*(n - i)*nzi; /* estimated and max additional space needed */ 515 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 516 reallocs++; 517 } 518 519 /* copy data into free space, then initialize lnk */ 520 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 521 bi_ptr[i] = current_space->array; 522 current_space->array += nzi; 523 current_space->local_used += nzi; 524 current_space->local_remaining -= nzi; 525 } 526 #if defined(PETSC_USE_INFO) 527 if (ai[n] != 0) { 528 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 529 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 530 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 531 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr); 532 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 533 } else { 534 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 535 } 536 #endif 537 538 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 539 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 540 541 /* destroy list of free space and other temporary array(s) */ 542 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 543 /* ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); */ 544 ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 545 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 546 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 547 548 /* put together the new matrix */ 549 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 550 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 551 b = (Mat_SeqAIJ*)(B)->data; 552 b->free_a = PETSC_TRUE; 553 b->free_ij = PETSC_TRUE; 554 b->singlemalloc = PETSC_FALSE; 555 /*ierr = PetscMalloc((bi[2*n+1])*sizeof(PetscScalar),&b->a);CHKERRQ(ierr);*/ 556 ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 557 b->j = bj; 558 b->i = bi; 559 b->diag = bdiag; 560 b->ilen = 0; 561 b->imax = 0; 562 b->row = isrow; 563 b->col = iscol; 564 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 565 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 566 b->icol = isicol; 567 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 568 569 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 570 /* ierr = PetscLogObjectMemory(B,bi[2*n+1]*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 571 b->maxnz = b->nz = bi[2*n+1] ; */ 572 ierr = PetscLogObjectMemory(B,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 573 b->maxnz = b->nz = bdiag[0]+1; 574 (B)->factor = MAT_FACTOR_LU; 575 (B)->info.factor_mallocs = reallocs; 576 (B)->info.fill_ratio_given = f; 577 578 if (ai[n]) { 579 /* (B)->info.fill_ratio_needed = ((PetscReal)bi[2*n+1])/((PetscReal)ai[n]); */ 580 (B)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 581 } else { 582 (B)->info.fill_ratio_needed = 0.0; 583 } 584 /* (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct;*/ 585 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct_v2; 586 PetscFunctionReturn(0); 587 } 588 589 /* 590 Trouble in factorization, should we dump the original matrix? 591 */ 592 #undef __FUNCT__ 593 #define __FUNCT__ "MatFactorDumpMatrix" 594 PetscErrorCode MatFactorDumpMatrix(Mat A) 595 { 596 PetscErrorCode ierr; 597 PetscTruth flg = PETSC_FALSE; 598 599 PetscFunctionBegin; 600 ierr = PetscOptionsGetTruth(PETSC_NULL,"-mat_factor_dump_on_error",&flg,PETSC_NULL);CHKERRQ(ierr); 601 if (flg) { 602 PetscViewer viewer; 603 char filename[PETSC_MAX_PATH_LEN]; 604 605 ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr); 606 ierr = PetscViewerBinaryOpen(((PetscObject)A)->comm,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr); 607 ierr = MatView(A,viewer);CHKERRQ(ierr); 608 ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr); 609 } 610 PetscFunctionReturn(0); 611 } 612 613 extern PetscErrorCode MatSolve_Inode(Mat,Vec,Vec); 614 615 /* ----------------------------------------------------------- */ 616 extern PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat,Vec,Vec); 617 extern PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat,Vec,Vec); 618 619 #undef __FUNCT__ 620 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_newdatastruct" 621 PetscErrorCode MatLUFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info) 622 { 623 Mat C=B; 624 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 625 IS isrow = b->row,isicol = b->icol; 626 PetscErrorCode ierr; 627 const PetscInt *r,*ic,*ics; 628 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 629 PetscInt *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj; 630 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 631 PetscTruth row_identity,col_identity; 632 633 LUShift_Ctx sctx; 634 PetscInt *ddiag,newshift; 635 PetscReal rs; 636 MatScalar d; 637 638 PetscFunctionBegin; 639 /* ZeropivotSetUp(): initialize shift context sctx */ 640 sctx.nshift = 0; 641 sctx.nshift_max = 0; 642 sctx.shift_top = 0.0; 643 sctx.shift_lo = 0.0; 644 sctx.shift_hi = 0.0; 645 sctx.shift_fraction = 0.0; 646 sctx.shift_amount = 0.0; 647 648 /* if both shift schemes are chosen by user, only use info->shiftpd */ 649 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 650 ddiag = a->diag; 651 sctx.shift_top = info->zeropivot; 652 for (i=0; i<n; i++) { 653 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 654 d = (aa)[ddiag[i]]; 655 rs = -PetscAbsScalar(d) - PetscRealPart(d); 656 v = aa+ai[i]; 657 nz = ai[i+1] - ai[i]; 658 for (j=0; j<nz; j++) 659 rs += PetscAbsScalar(v[j]); 660 if (rs>sctx.shift_top) sctx.shift_top = rs; 661 } 662 sctx.shift_top *= 1.1; 663 sctx.nshift_max = 5; 664 sctx.shift_lo = 0.; 665 sctx.shift_hi = 1.; 666 } 667 668 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 669 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 670 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 671 ics = ic; 672 673 do { 674 sctx.lushift = PETSC_FALSE; 675 for (i=0; i<n; i++){ 676 /* zero rtmp */ 677 /* L part */ 678 nz = bi[i+1] - bi[i]; 679 bjtmp = bj + bi[i]; 680 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 681 682 /* U part */ 683 nz = bi[2*n-i+1] - bi[2*n-i]; 684 bjtmp = bj + bi[2*n-i]; 685 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 686 687 /* load in initial (unfactored row) */ 688 nz = ai[r[i]+1] - ai[r[i]]; 689 ajtmp = aj + ai[r[i]]; 690 v = aa + ai[r[i]]; 691 for (j=0; j<nz; j++) { 692 rtmp[ics[ajtmp[j]]] = v[j]; 693 } 694 /* ZeropivotApply() */ 695 rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 696 697 /* elimination */ 698 bjtmp = bj + bi[i]; 699 row = *bjtmp++; 700 nzL = bi[i+1] - bi[i]; 701 k = 0; 702 while (k < nzL) { 703 pc = rtmp + row; 704 if (*pc != 0.0) { 705 pv = b->a + bdiag[row]; 706 multiplier = *pc * (*pv); 707 *pc = multiplier; 708 pj = b->j + bi[2*n-row]; /* begining of U(row,:) */ 709 pv = b->a + bi[2*n-row]; 710 nz = bi[2*n-row+1] - bi[2*n-row] - 1; /* num of entries in U(row,:), excluding diag */ 711 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 712 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 713 } 714 row = *bjtmp++; k++; 715 } 716 717 /* finished row so stick it into b->a */ 718 rs = 0.0; 719 /* L part */ 720 pv = b->a + bi[i] ; 721 pj = b->j + bi[i] ; 722 nz = bi[i+1] - bi[i]; 723 for (j=0; j<nz; j++) { 724 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 725 } 726 727 /* U part */ 728 pv = b->a + bi[2*n-i]; 729 pj = b->j + bi[2*n-i]; 730 nz = bi[2*n-i+1] - bi[2*n-i] - 1; 731 for (j=0; j<nz; j++) { 732 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 733 } 734 735 /* ZeropivotCheck() */ 736 sctx.rs = rs; 737 sctx.pv = rtmp[i]; 738 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 739 if (newshift == 1) break; 740 741 /* Mark diagonal and invert diagonal for simplier triangular solves */ 742 pv = b->a + bdiag[i]; 743 *pv = 1.0/rtmp[i]; 744 745 } /* endof for (i=0; i<n; i++){ */ 746 747 /* ZeropivotRefine() */ 748 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max){ 749 /* 750 * if no shift in this attempt & shifting & started shifting & can refine, 751 * then try lower shift 752 */ 753 sctx.shift_hi = sctx.shift_fraction; 754 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 755 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 756 sctx.lushift = PETSC_TRUE; 757 sctx.nshift++; 758 } 759 } while (sctx.lushift); 760 761 ierr = PetscFree(rtmp);CHKERRQ(ierr); 762 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 763 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 764 765 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 766 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 767 if (row_identity && col_identity) { 768 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct; 769 } else { 770 C->ops->solve = MatSolve_SeqAIJ_newdatastruct; 771 } 772 773 C->ops->solveadd = 0; 774 C->ops->solvetranspose = 0; 775 C->ops->solvetransposeadd = 0; 776 C->ops->matsolve = 0; 777 C->assembled = PETSC_TRUE; 778 C->preallocated = PETSC_TRUE; 779 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 780 781 /* ZeropivotView() */ 782 if (sctx.nshift){ 783 if (info->shiftpd) { 784 ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %G, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,sctx.shift_amount,sctx.shift_fraction,sctx.shift_top);CHKERRQ(ierr); 785 } else if (info->shiftnz) { 786 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 787 } 788 } 789 PetscFunctionReturn(0); 790 } 791 792 /* ----------------------------------------------------------- */ 793 extern PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct_v2(Mat,Vec,Vec); 794 extern PetscErrorCode MatSolve_SeqAIJ_newdatastruct_v2(Mat,Vec,Vec); 795 796 #undef __FUNCT__ 797 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_newdatastruct_v2" 798 PetscErrorCode MatLUFactorNumeric_SeqAIJ_newdatastruct_v2(Mat B,Mat A,const MatFactorInfo *info) 799 { 800 Mat C=B; 801 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 802 IS isrow = b->row,isicol = b->icol; 803 PetscErrorCode ierr; 804 const PetscInt *r,*ic,*ics; 805 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 806 PetscInt *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj; 807 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 808 PetscTruth row_identity,col_identity; 809 810 LUShift_Ctx sctx; 811 PetscInt *ddiag,newshift; 812 PetscReal rs; 813 MatScalar d; 814 815 PetscFunctionBegin; 816 /* ZeropivotSetUp(): initialize shift context sctx */ 817 sctx.nshift = 0; 818 sctx.nshift_max = 0; 819 sctx.shift_top = 0.0; 820 sctx.shift_lo = 0.0; 821 sctx.shift_hi = 0.0; 822 sctx.shift_fraction = 0.0; 823 sctx.shift_amount = 0.0; 824 825 /* if both shift schemes are chosen by user, only use info->shiftpd */ 826 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 827 ddiag = a->diag; 828 sctx.shift_top = info->zeropivot; 829 for (i=0; i<n; i++) { 830 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 831 d = (aa)[ddiag[i]]; 832 rs = -PetscAbsScalar(d) - PetscRealPart(d); 833 v = aa+ai[i]; 834 nz = ai[i+1] - ai[i]; 835 for (j=0; j<nz; j++) 836 rs += PetscAbsScalar(v[j]); 837 if (rs>sctx.shift_top) sctx.shift_top = rs; 838 } 839 sctx.shift_top *= 1.1; 840 sctx.nshift_max = 5; 841 sctx.shift_lo = 0.; 842 sctx.shift_hi = 1.; 843 } 844 845 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 846 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 847 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 848 ics = ic; 849 850 do { 851 sctx.lushift = PETSC_FALSE; 852 for (i=0; i<n; i++){ 853 /* zero rtmp */ 854 /* L part */ 855 nz = bi[i+1] - bi[i]; 856 bjtmp = bj + bi[i]; 857 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 858 859 /* U part */ 860 /* nz = bi[2*n-i+1] - bi[2*n-i]; 861 bjtmp = bj + bi[2*n-i]; */ 862 nz = bdiag[i]-bdiag[i+1]; 863 bjtmp = bj + bdiag[i+1]+1; 864 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 865 866 /* load in initial (unfactored row) */ 867 nz = ai[r[i]+1] - ai[r[i]]; 868 ajtmp = aj + ai[r[i]]; 869 v = aa + ai[r[i]]; 870 for (j=0; j<nz; j++) { 871 rtmp[ics[ajtmp[j]]] = v[j]; 872 } 873 /* ZeropivotApply() */ 874 rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 875 876 /* elimination */ 877 bjtmp = bj + bi[i]; 878 row = *bjtmp++; 879 nzL = bi[i+1] - bi[i]; 880 for(k=0; k < nzL;k++) { 881 pc = rtmp + row; 882 if (*pc != 0.0) { 883 pv = b->a + bdiag[row]; 884 multiplier = *pc * (*pv); 885 *pc = multiplier; 886 /* pj = b->j + bi[2*n-row]; */ /* begining of U(row,:) */ 887 /* pv = b->a + bi[2*n-row]; 888 nz = bi[2*n-row+1] - bi[2*n-row] - 1; */ /* num of entries in U(row,:), excluding diag */ 889 pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */ 890 pv = b->a + bdiag[row+1]+1; 891 nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */ 892 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 893 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 894 } 895 row = *bjtmp++; 896 } 897 898 /* finished row so stick it into b->a */ 899 rs = 0.0; 900 /* L part */ 901 pv = b->a + bi[i] ; 902 pj = b->j + bi[i] ; 903 nz = bi[i+1] - bi[i]; 904 for (j=0; j<nz; j++) { 905 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 906 } 907 908 /* U part */ 909 /* pv = b->a + bi[2*n-i]; 910 pj = b->j + bi[2*n-i]; 911 nz = bi[2*n-i+1] - bi[2*n-i] - 1; 912 */ 913 pv = b->a + bdiag[i+1]+1; 914 pj = b->j + bdiag[i+1]+1; 915 nz = bdiag[i] - bdiag[i+1]-1; 916 for (j=0; j<nz; j++) { 917 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 918 } 919 920 /* ZeropivotCheck() */ 921 sctx.rs = rs; 922 sctx.pv = rtmp[i]; 923 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 924 if (newshift == 1) break; 925 926 /* Mark diagonal and invert diagonal for simplier triangular solves */ 927 pv = b->a + bdiag[i]; 928 *pv = 1.0/rtmp[i]; 929 930 } /* endof for (i=0; i<n; i++){ */ 931 932 /* ZeropivotRefine() */ 933 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max){ 934 /* 935 * if no shift in this attempt & shifting & started shifting & can refine, 936 * then try lower shift 937 */ 938 sctx.shift_hi = sctx.shift_fraction; 939 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 940 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 941 sctx.lushift = PETSC_TRUE; 942 sctx.nshift++; 943 } 944 } while (sctx.lushift); 945 946 ierr = PetscFree(rtmp);CHKERRQ(ierr); 947 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 948 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 949 950 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 951 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 952 if (row_identity && col_identity) { 953 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct_v2; 954 } else { 955 C->ops->solve = MatSolve_SeqAIJ_newdatastruct_v2; 956 } 957 958 C->ops->solveadd = 0; 959 C->ops->solvetranspose = 0; 960 C->ops->solvetransposeadd = 0; 961 C->ops->matsolve = 0; 962 C->assembled = PETSC_TRUE; 963 C->preallocated = PETSC_TRUE; 964 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 965 966 /* ZeropivotView() */ 967 if (sctx.nshift){ 968 if (info->shiftpd) { 969 ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %G, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,sctx.shift_amount,sctx.shift_fraction,sctx.shift_top);CHKERRQ(ierr); 970 } else if (info->shiftnz) { 971 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 972 } 973 } 974 PetscFunctionReturn(0); 975 } 976 977 #undef __FUNCT__ 978 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ" 979 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 980 { 981 Mat C=B; 982 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 983 IS isrow = b->row,isicol = b->icol; 984 PetscErrorCode ierr; 985 const PetscInt *r,*ic,*ics; 986 PetscInt nz,row,i,j,n=A->rmap->n,diag; 987 const PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 988 const PetscInt *ajtmp,*bjtmp,*diag_offset = b->diag,*pj; 989 MatScalar *pv,*rtmp,*pc,multiplier,d; 990 const MatScalar *v,*aa=a->a; 991 PetscReal rs=0.0; 992 LUShift_Ctx sctx; 993 PetscInt newshift,*ddiag; 994 995 PetscFunctionBegin; 996 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 997 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 998 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 999 ics = ic; 1000 1001 /* initialize shift context sctx */ 1002 sctx.nshift = 0; 1003 sctx.nshift_max = 0; 1004 sctx.shift_top = 0.0; 1005 sctx.shift_lo = 0.0; 1006 sctx.shift_hi = 0.0; 1007 sctx.shift_fraction = 0.0; 1008 sctx.shift_amount = 0.0; 1009 1010 /* if both shift schemes are chosen by user, only use info->shiftpd */ 1011 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 1012 ddiag = a->diag; 1013 sctx.shift_top = info->zeropivot; 1014 for (i=0; i<n; i++) { 1015 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 1016 d = (aa)[ddiag[i]]; 1017 rs = -PetscAbsScalar(d) - PetscRealPart(d); 1018 v = aa+ai[i]; 1019 nz = ai[i+1] - ai[i]; 1020 for (j=0; j<nz; j++) 1021 rs += PetscAbsScalar(v[j]); 1022 if (rs>sctx.shift_top) sctx.shift_top = rs; 1023 } 1024 sctx.shift_top *= 1.1; 1025 sctx.nshift_max = 5; 1026 sctx.shift_lo = 0.; 1027 sctx.shift_hi = 1.; 1028 } 1029 1030 do { 1031 sctx.lushift = PETSC_FALSE; 1032 for (i=0; i<n; i++){ 1033 nz = bi[i+1] - bi[i]; 1034 bjtmp = bj + bi[i]; 1035 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 1036 1037 /* load in initial (unfactored row) */ 1038 nz = ai[r[i]+1] - ai[r[i]]; 1039 ajtmp = aj + ai[r[i]]; 1040 v = aa + ai[r[i]]; 1041 for (j=0; j<nz; j++) { 1042 rtmp[ics[ajtmp[j]]] = v[j]; 1043 } 1044 rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 1045 /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */ 1046 1047 row = *bjtmp++; 1048 while (row < i) { 1049 pc = rtmp + row; 1050 if (*pc != 0.0) { 1051 pv = b->a + diag_offset[row]; 1052 pj = b->j + diag_offset[row] + 1; 1053 multiplier = *pc / *pv++; 1054 *pc = multiplier; 1055 nz = bi[row+1] - diag_offset[row] - 1; 1056 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 1057 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 1058 } 1059 row = *bjtmp++; 1060 } 1061 /* finished row so stick it into b->a */ 1062 pv = b->a + bi[i] ; 1063 pj = b->j + bi[i] ; 1064 nz = bi[i+1] - bi[i]; 1065 diag = diag_offset[i] - bi[i]; 1066 rs = 0.0; 1067 for (j=0; j<nz; j++) { 1068 pv[j] = rtmp[pj[j]]; 1069 rs += PetscAbsScalar(pv[j]); 1070 } 1071 rs -= PetscAbsScalar(pv[diag]); 1072 1073 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 1074 sctx.rs = rs; 1075 sctx.pv = pv[diag]; 1076 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 1077 if (newshift == 1) break; 1078 } 1079 1080 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 1081 /* 1082 * if no shift in this attempt & shifting & started shifting & can refine, 1083 * then try lower shift 1084 */ 1085 sctx.shift_hi = sctx.shift_fraction; 1086 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 1087 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 1088 sctx.lushift = PETSC_TRUE; 1089 sctx.nshift++; 1090 } 1091 } while (sctx.lushift); 1092 1093 /* invert diagonal entries for simplier triangular solves */ 1094 for (i=0; i<n; i++) { 1095 b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]]; 1096 } 1097 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1098 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1099 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1100 if (b->inode.use) { 1101 C->ops->solve = MatSolve_Inode; 1102 } else { 1103 PetscTruth row_identity, col_identity; 1104 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1105 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 1106 if (row_identity && col_identity) { 1107 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 1108 } else { 1109 C->ops->solve = MatSolve_SeqAIJ; 1110 } 1111 } 1112 C->ops->solveadd = MatSolveAdd_SeqAIJ; 1113 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 1114 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 1115 C->ops->matsolve = MatMatSolve_SeqAIJ; 1116 C->assembled = PETSC_TRUE; 1117 C->preallocated = PETSC_TRUE; 1118 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 1119 if (sctx.nshift){ 1120 if (info->shiftpd) { 1121 ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %G, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,sctx.shift_amount,sctx.shift_fraction,sctx.shift_top);CHKERRQ(ierr); 1122 } else if (info->shiftnz) { 1123 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 1124 } 1125 } 1126 PetscFunctionReturn(0); 1127 } 1128 1129 /* 1130 This routine implements inplace ILU(0) with row or/and column permutations. 1131 Input: 1132 A - original matrix 1133 Output; 1134 A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i] 1135 a->j (col index) is permuted by the inverse of colperm, then sorted 1136 a->a reordered accordingly with a->j 1137 a->diag (ptr to diagonal elements) is updated. 1138 */ 1139 #undef __FUNCT__ 1140 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm" 1141 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info) 1142 { 1143 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 1144 IS isrow = a->row,isicol = a->icol; 1145 PetscErrorCode ierr; 1146 const PetscInt *r,*ic,*ics; 1147 PetscInt i,j,n=A->rmap->n,*ai=a->i,*aj=a->j; 1148 PetscInt *ajtmp,nz,row; 1149 PetscInt *diag = a->diag,nbdiag,*pj; 1150 PetscScalar *rtmp,*pc,multiplier,d; 1151 MatScalar *v,*pv; 1152 PetscReal rs; 1153 LUShift_Ctx sctx; 1154 PetscInt newshift; 1155 1156 PetscFunctionBegin; 1157 if (A != B) SETERRQ(PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address"); 1158 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1159 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1160 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr); 1161 ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr); 1162 ics = ic; 1163 1164 sctx.shift_top = 0; 1165 sctx.nshift_max = 0; 1166 sctx.shift_lo = 0; 1167 sctx.shift_hi = 0; 1168 sctx.shift_fraction = 0; 1169 1170 /* if both shift schemes are chosen by user, only use info->shiftpd */ 1171 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 1172 sctx.shift_top = 0; 1173 for (i=0; i<n; i++) { 1174 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 1175 d = (a->a)[diag[i]]; 1176 rs = -PetscAbsScalar(d) - PetscRealPart(d); 1177 v = a->a+ai[i]; 1178 nz = ai[i+1] - ai[i]; 1179 for (j=0; j<nz; j++) 1180 rs += PetscAbsScalar(v[j]); 1181 if (rs>sctx.shift_top) sctx.shift_top = rs; 1182 } 1183 if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot; 1184 sctx.shift_top *= 1.1; 1185 sctx.nshift_max = 5; 1186 sctx.shift_lo = 0.; 1187 sctx.shift_hi = 1.; 1188 } 1189 1190 sctx.shift_amount = 0; 1191 sctx.nshift = 0; 1192 do { 1193 sctx.lushift = PETSC_FALSE; 1194 for (i=0; i<n; i++){ 1195 /* load in initial unfactored row */ 1196 nz = ai[r[i]+1] - ai[r[i]]; 1197 ajtmp = aj + ai[r[i]]; 1198 v = a->a + ai[r[i]]; 1199 /* sort permuted ajtmp and values v accordingly */ 1200 for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]]; 1201 ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr); 1202 1203 diag[r[i]] = ai[r[i]]; 1204 for (j=0; j<nz; j++) { 1205 rtmp[ajtmp[j]] = v[j]; 1206 if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */ 1207 } 1208 rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 1209 1210 row = *ajtmp++; 1211 while (row < i) { 1212 pc = rtmp + row; 1213 if (*pc != 0.0) { 1214 pv = a->a + diag[r[row]]; 1215 pj = aj + diag[r[row]] + 1; 1216 1217 multiplier = *pc / *pv++; 1218 *pc = multiplier; 1219 nz = ai[r[row]+1] - diag[r[row]] - 1; 1220 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 1221 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 1222 } 1223 row = *ajtmp++; 1224 } 1225 /* finished row so overwrite it onto a->a */ 1226 pv = a->a + ai[r[i]] ; 1227 pj = aj + ai[r[i]] ; 1228 nz = ai[r[i]+1] - ai[r[i]]; 1229 nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */ 1230 1231 rs = 0.0; 1232 for (j=0; j<nz; j++) { 1233 pv[j] = rtmp[pj[j]]; 1234 if (j != nbdiag) rs += PetscAbsScalar(pv[j]); 1235 } 1236 1237 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 1238 sctx.rs = rs; 1239 sctx.pv = pv[nbdiag]; 1240 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 1241 if (newshift == 1) break; 1242 } 1243 1244 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 1245 /* 1246 * if no shift in this attempt & shifting & started shifting & can refine, 1247 * then try lower shift 1248 */ 1249 sctx.shift_hi = sctx.shift_fraction; 1250 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 1251 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 1252 sctx.lushift = PETSC_TRUE; 1253 sctx.nshift++; 1254 } 1255 } while (sctx.lushift); 1256 1257 /* invert diagonal entries for simplier triangular solves */ 1258 for (i=0; i<n; i++) { 1259 a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]]; 1260 } 1261 1262 ierr = PetscFree(rtmp);CHKERRQ(ierr); 1263 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1264 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1265 A->ops->solve = MatSolve_SeqAIJ_InplaceWithPerm; 1266 A->ops->solveadd = MatSolveAdd_SeqAIJ; 1267 A->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 1268 A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 1269 A->assembled = PETSC_TRUE; 1270 A->preallocated = PETSC_TRUE; 1271 ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr); 1272 if (sctx.nshift){ 1273 if (info->shiftpd) { 1274 ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %G, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,sctx.shift_amount,sctx.shift_fraction,sctx.shift_top);CHKERRQ(ierr); 1275 } else if (info->shiftnz) { 1276 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 1277 } 1278 } 1279 PetscFunctionReturn(0); 1280 } 1281 1282 /* ----------------------------------------------------------- */ 1283 #undef __FUNCT__ 1284 #define __FUNCT__ "MatLUFactor_SeqAIJ" 1285 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info) 1286 { 1287 PetscErrorCode ierr; 1288 Mat C; 1289 1290 PetscFunctionBegin; 1291 ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr); 1292 ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr); 1293 ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr); 1294 A->ops->solve = C->ops->solve; 1295 A->ops->solvetranspose = C->ops->solvetranspose; 1296 ierr = MatHeaderCopy(A,C);CHKERRQ(ierr); 1297 ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr); 1298 PetscFunctionReturn(0); 1299 } 1300 /* ----------------------------------------------------------- */ 1301 1302 1303 #undef __FUNCT__ 1304 #define __FUNCT__ "MatSolve_SeqAIJ" 1305 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx) 1306 { 1307 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1308 IS iscol = a->col,isrow = a->row; 1309 PetscErrorCode ierr; 1310 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1311 PetscInt nz; 1312 const PetscInt *rout,*cout,*r,*c; 1313 PetscScalar *x,*tmp,*tmps,sum; 1314 const PetscScalar *b; 1315 const MatScalar *aa = a->a,*v; 1316 1317 PetscFunctionBegin; 1318 if (!n) PetscFunctionReturn(0); 1319 1320 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1321 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1322 tmp = a->solve_work; 1323 1324 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1325 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1326 1327 /* forward solve the lower triangular */ 1328 tmp[0] = b[*r++]; 1329 tmps = tmp; 1330 for (i=1; i<n; i++) { 1331 v = aa + ai[i] ; 1332 vi = aj + ai[i] ; 1333 nz = a->diag[i] - ai[i]; 1334 sum = b[*r++]; 1335 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1336 tmp[i] = sum; 1337 } 1338 1339 /* backward solve the upper triangular */ 1340 for (i=n-1; i>=0; i--){ 1341 v = aa + a->diag[i] + 1; 1342 vi = aj + a->diag[i] + 1; 1343 nz = ai[i+1] - a->diag[i] - 1; 1344 sum = tmp[i]; 1345 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1346 x[*c--] = tmp[i] = sum*aa[a->diag[i]]; 1347 } 1348 1349 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1350 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1351 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1352 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1353 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1354 PetscFunctionReturn(0); 1355 } 1356 1357 #undef __FUNCT__ 1358 #define __FUNCT__ "MatMatSolve_SeqAIJ" 1359 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X) 1360 { 1361 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1362 IS iscol = a->col,isrow = a->row; 1363 PetscErrorCode ierr; 1364 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1365 PetscInt nz,neq; 1366 const PetscInt *rout,*cout,*r,*c; 1367 PetscScalar *x,*b,*tmp,*tmps,sum; 1368 const MatScalar *aa = a->a,*v; 1369 PetscTruth bisdense,xisdense; 1370 1371 PetscFunctionBegin; 1372 if (!n) PetscFunctionReturn(0); 1373 1374 ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 1375 if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1376 ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 1377 if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1378 1379 ierr = MatGetArray(B,&b);CHKERRQ(ierr); 1380 ierr = MatGetArray(X,&x);CHKERRQ(ierr); 1381 1382 tmp = a->solve_work; 1383 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1384 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1385 1386 for (neq=0; neq<B->cmap->n; neq++){ 1387 /* forward solve the lower triangular */ 1388 tmp[0] = b[r[0]]; 1389 tmps = tmp; 1390 for (i=1; i<n; i++) { 1391 v = aa + ai[i] ; 1392 vi = aj + ai[i] ; 1393 nz = a->diag[i] - ai[i]; 1394 sum = b[r[i]]; 1395 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1396 tmp[i] = sum; 1397 } 1398 /* backward solve the upper triangular */ 1399 for (i=n-1; i>=0; i--){ 1400 v = aa + a->diag[i] + 1; 1401 vi = aj + a->diag[i] + 1; 1402 nz = ai[i+1] - a->diag[i] - 1; 1403 sum = tmp[i]; 1404 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1405 x[c[i]] = tmp[i] = sum*aa[a->diag[i]]; 1406 } 1407 1408 b += n; 1409 x += n; 1410 } 1411 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1412 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1413 ierr = MatRestoreArray(B,&b);CHKERRQ(ierr); 1414 ierr = MatRestoreArray(X,&x);CHKERRQ(ierr); 1415 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1416 PetscFunctionReturn(0); 1417 } 1418 1419 #undef __FUNCT__ 1420 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm" 1421 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx) 1422 { 1423 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1424 IS iscol = a->col,isrow = a->row; 1425 PetscErrorCode ierr; 1426 const PetscInt *r,*c,*rout,*cout; 1427 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1428 PetscInt nz,row; 1429 PetscScalar *x,*b,*tmp,*tmps,sum; 1430 const MatScalar *aa = a->a,*v; 1431 1432 PetscFunctionBegin; 1433 if (!n) PetscFunctionReturn(0); 1434 1435 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1436 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1437 tmp = a->solve_work; 1438 1439 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1440 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1441 1442 /* forward solve the lower triangular */ 1443 tmp[0] = b[*r++]; 1444 tmps = tmp; 1445 for (row=1; row<n; row++) { 1446 i = rout[row]; /* permuted row */ 1447 v = aa + ai[i] ; 1448 vi = aj + ai[i] ; 1449 nz = a->diag[i] - ai[i]; 1450 sum = b[*r++]; 1451 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1452 tmp[row] = sum; 1453 } 1454 1455 /* backward solve the upper triangular */ 1456 for (row=n-1; row>=0; row--){ 1457 i = rout[row]; /* permuted row */ 1458 v = aa + a->diag[i] + 1; 1459 vi = aj + a->diag[i] + 1; 1460 nz = ai[i+1] - a->diag[i] - 1; 1461 sum = tmp[row]; 1462 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1463 x[*c--] = tmp[row] = sum*aa[a->diag[i]]; 1464 } 1465 1466 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1467 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1468 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1469 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1470 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1471 PetscFunctionReturn(0); 1472 } 1473 1474 /* ----------------------------------------------------------- */ 1475 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h" 1476 #undef __FUNCT__ 1477 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering" 1478 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx) 1479 { 1480 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1481 PetscErrorCode ierr; 1482 PetscInt n = A->rmap->n; 1483 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag; 1484 PetscScalar *x; 1485 const PetscScalar *b; 1486 const MatScalar *aa = a->a; 1487 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1488 PetscInt adiag_i,i,nz,ai_i; 1489 const PetscInt *vi; 1490 const MatScalar *v; 1491 PetscScalar sum; 1492 #endif 1493 1494 PetscFunctionBegin; 1495 if (!n) PetscFunctionReturn(0); 1496 1497 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1498 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1499 1500 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1501 fortransolveaij_(&n,x,ai,aj,adiag,aa,b); 1502 #else 1503 /* forward solve the lower triangular */ 1504 x[0] = b[0]; 1505 for (i=1; i<n; i++) { 1506 ai_i = ai[i]; 1507 v = aa + ai_i; 1508 vi = aj + ai_i; 1509 nz = adiag[i] - ai_i; 1510 sum = b[i]; 1511 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1512 x[i] = sum; 1513 } 1514 1515 /* backward solve the upper triangular */ 1516 for (i=n-1; i>=0; i--){ 1517 adiag_i = adiag[i]; 1518 v = aa + adiag_i + 1; 1519 vi = aj + adiag_i + 1; 1520 nz = ai[i+1] - adiag_i - 1; 1521 sum = x[i]; 1522 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1523 x[i] = sum*aa[adiag_i]; 1524 } 1525 #endif 1526 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1527 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1528 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1529 PetscFunctionReturn(0); 1530 } 1531 1532 #undef __FUNCT__ 1533 #define __FUNCT__ "MatSolveAdd_SeqAIJ" 1534 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx) 1535 { 1536 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1537 IS iscol = a->col,isrow = a->row; 1538 PetscErrorCode ierr; 1539 PetscInt i, n = A->rmap->n,j; 1540 PetscInt nz; 1541 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j; 1542 PetscScalar *x,*tmp,sum; 1543 const PetscScalar *b; 1544 const MatScalar *aa = a->a,*v; 1545 1546 PetscFunctionBegin; 1547 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1548 1549 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1550 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1551 tmp = a->solve_work; 1552 1553 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1554 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1555 1556 /* forward solve the lower triangular */ 1557 tmp[0] = b[*r++]; 1558 for (i=1; i<n; i++) { 1559 v = aa + ai[i] ; 1560 vi = aj + ai[i] ; 1561 nz = a->diag[i] - ai[i]; 1562 sum = b[*r++]; 1563 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1564 tmp[i] = sum; 1565 } 1566 1567 /* backward solve the upper triangular */ 1568 for (i=n-1; i>=0; i--){ 1569 v = aa + a->diag[i] + 1; 1570 vi = aj + a->diag[i] + 1; 1571 nz = ai[i+1] - a->diag[i] - 1; 1572 sum = tmp[i]; 1573 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1574 tmp[i] = sum*aa[a->diag[i]]; 1575 x[*c--] += tmp[i]; 1576 } 1577 1578 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1579 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1580 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1581 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1582 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1583 1584 PetscFunctionReturn(0); 1585 } 1586 1587 #undef __FUNCT__ 1588 #define __FUNCT__ "MatSolveTranspose_SeqAIJ" 1589 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx) 1590 { 1591 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1592 IS iscol = a->col,isrow = a->row; 1593 PetscErrorCode ierr; 1594 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1595 PetscInt i,n = A->rmap->n,j; 1596 PetscInt nz; 1597 PetscScalar *x,*tmp,s1; 1598 const MatScalar *aa = a->a,*v; 1599 const PetscScalar *b; 1600 1601 PetscFunctionBegin; 1602 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1603 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1604 tmp = a->solve_work; 1605 1606 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1607 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1608 1609 /* copy the b into temp work space according to permutation */ 1610 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1611 1612 /* forward solve the U^T */ 1613 for (i=0; i<n; i++) { 1614 v = aa + diag[i] ; 1615 vi = aj + diag[i] + 1; 1616 nz = ai[i+1] - diag[i] - 1; 1617 s1 = tmp[i]; 1618 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1619 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1620 tmp[i] = s1; 1621 } 1622 1623 /* backward solve the L^T */ 1624 for (i=n-1; i>=0; i--){ 1625 v = aa + diag[i] - 1 ; 1626 vi = aj + diag[i] - 1 ; 1627 nz = diag[i] - ai[i]; 1628 s1 = tmp[i]; 1629 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1630 } 1631 1632 /* copy tmp into x according to permutation */ 1633 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1634 1635 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1636 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1637 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1638 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1639 1640 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1641 PetscFunctionReturn(0); 1642 } 1643 1644 #undef __FUNCT__ 1645 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ" 1646 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx) 1647 { 1648 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1649 IS iscol = a->col,isrow = a->row; 1650 PetscErrorCode ierr; 1651 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1652 PetscInt i,n = A->rmap->n,j; 1653 PetscInt nz; 1654 PetscScalar *x,*tmp,s1; 1655 const MatScalar *aa = a->a,*v; 1656 const PetscScalar *b; 1657 1658 PetscFunctionBegin; 1659 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1660 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1661 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1662 tmp = a->solve_work; 1663 1664 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1665 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1666 1667 /* copy the b into temp work space according to permutation */ 1668 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1669 1670 /* forward solve the U^T */ 1671 for (i=0; i<n; i++) { 1672 v = aa + diag[i] ; 1673 vi = aj + diag[i] + 1; 1674 nz = ai[i+1] - diag[i] - 1; 1675 s1 = tmp[i]; 1676 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1677 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1678 tmp[i] = s1; 1679 } 1680 1681 /* backward solve the L^T */ 1682 for (i=n-1; i>=0; i--){ 1683 v = aa + diag[i] - 1 ; 1684 vi = aj + diag[i] - 1 ; 1685 nz = diag[i] - ai[i]; 1686 s1 = tmp[i]; 1687 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1688 } 1689 1690 /* copy tmp into x according to permutation */ 1691 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1692 1693 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1694 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1695 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1696 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1697 1698 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1699 PetscFunctionReturn(0); 1700 } 1701 1702 /* ----------------------------------------------------------------*/ 1703 EXTERN PetscErrorCode Mat_CheckInode(Mat,PetscTruth); 1704 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth); 1705 1706 /* 1707 ilu(0) with natural ordering under new data structure. 1708 Factored arrays bj and ba are stored as 1709 L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:) 1710 1711 bi=fact->i is an array of size 2n+2, in which 1712 bi+ 1713 bi[i] -> 1st entry of L(i,:),i=0,...,i-1 1714 bi[n] -> points to L(n-1,:)+1 1715 bi[n+1] -> 1st entry of U(n-1,:) 1716 bi[2n-i] -> 1st entry of U(i,:) 1717 bi[2n-i+1] -> end of U(i,:)+1, the 1st entry of U(i-1,:) 1718 bi[2n] -> 1st entry of U(0,:) 1719 bi[2n+1] -> points to U(0,:)+1 1720 1721 U(i,:) contains diag[i] as its last entry, i.e., 1722 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 1723 */ 1724 #undef __FUNCT__ 1725 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct" 1726 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1727 { 1728 1729 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1730 PetscErrorCode ierr; 1731 PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag; 1732 PetscInt i,j,nz,*bi,*bj,*bdiag; 1733 1734 PetscFunctionBegin; 1735 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr); 1736 b = (Mat_SeqAIJ*)(fact)->data; 1737 1738 /* allocate matrix arrays for new data structure */ 1739 ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,2*n+2,PetscInt,&b->i);CHKERRQ(ierr); 1740 ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(2*n+2)*sizeof(PetscInt));CHKERRQ(ierr); 1741 b->singlemalloc = PETSC_TRUE; 1742 if (!b->diag){ 1743 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr); 1744 } 1745 bdiag = b->diag; 1746 1747 if (n > 0) { 1748 ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr); 1749 } 1750 1751 /* set bi and bj with new data structure */ 1752 bi = b->i; 1753 bj = b->j; 1754 1755 /* L part */ 1756 bi[0] = 0; 1757 for (i=0; i<n; i++){ 1758 nz = adiag[i] - ai[i]; 1759 bi[i+1] = bi[i] + nz; 1760 aj = a->j + ai[i]; 1761 for (j=0; j<nz; j++){ 1762 *bj = aj[j]; bj++; 1763 } 1764 } 1765 1766 /* U part */ 1767 bi[n+1] = bi[n]; 1768 for (i=n-1; i>=0; i--){ 1769 nz = ai[i+1] - adiag[i] - 1; 1770 bi[2*n-i+1] = bi[2*n-i] + nz + 1; 1771 aj = a->j + adiag[i] + 1; 1772 for (j=0; j<nz; j++){ 1773 *bj = aj[j]; bj++; 1774 } 1775 /* diag[i] */ 1776 *bj = i; bj++; 1777 bdiag[i] = bi[2*n-i+1]-1; 1778 } 1779 PetscFunctionReturn(0); 1780 } 1781 1782 #undef __FUNCT__ 1783 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_newdatastruct" 1784 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1785 { 1786 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1787 IS isicol; 1788 PetscErrorCode ierr; 1789 const PetscInt *r,*ic; 1790 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 1791 PetscInt *bi,*cols,nnz,*cols_lvl; 1792 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1793 PetscInt i,levels,diagonal_fill; 1794 PetscTruth col_identity,row_identity; 1795 PetscReal f; 1796 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1797 PetscBT lnkbt; 1798 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1799 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1800 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1801 PetscTruth missing; 1802 1803 PetscFunctionBegin; 1804 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 1805 f = info->fill; 1806 levels = (PetscInt)info->levels; 1807 diagonal_fill = (PetscInt)info->diagonal_fill; 1808 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1809 1810 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1811 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1812 1813 if (!levels && row_identity && col_identity) { 1814 /* special case: ilu(0) with natural ordering */ 1815 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1816 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 1817 1818 fact->factor = MAT_FACTOR_ILU; 1819 (fact)->info.factor_mallocs = 0; 1820 (fact)->info.fill_ratio_given = info->fill; 1821 (fact)->info.fill_ratio_needed = 1.0; 1822 b = (Mat_SeqAIJ*)(fact)->data; 1823 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1824 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1825 b->row = isrow; 1826 b->col = iscol; 1827 b->icol = isicol; 1828 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1829 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1830 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1831 /* ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */ 1832 PetscFunctionReturn(0); 1833 } 1834 1835 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1836 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1837 1838 /* get new row pointers */ 1839 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1840 bi[0] = 0; 1841 /* bdiag is location of diagonal in factor */ 1842 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1843 bdiag[0] = 0; 1844 1845 ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr); 1846 bjlvl_ptr = (PetscInt**)(bj_ptr + n); 1847 1848 /* create a linked list for storing column indices of the active row */ 1849 nlnk = n + 1; 1850 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1851 1852 /* initial FreeSpace size is f*(ai[n]+1) */ 1853 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1854 current_space = free_space; 1855 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1856 current_space_lvl = free_space_lvl; 1857 1858 for (i=0; i<n; i++) { 1859 nzi = 0; 1860 /* copy current row into linked list */ 1861 nnz = ai[r[i]+1] - ai[r[i]]; 1862 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1863 cols = aj + ai[r[i]]; 1864 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1865 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1866 nzi += nlnk; 1867 1868 /* make sure diagonal entry is included */ 1869 if (diagonal_fill && lnk[i] == -1) { 1870 fm = n; 1871 while (lnk[fm] < i) fm = lnk[fm]; 1872 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1873 lnk[fm] = i; 1874 lnk_lvl[i] = 0; 1875 nzi++; dcount++; 1876 } 1877 1878 /* add pivot rows into the active row */ 1879 nzbd = 0; 1880 prow = lnk[n]; 1881 while (prow < i) { 1882 nnz = bdiag[prow]; 1883 cols = bj_ptr[prow] + nnz + 1; 1884 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1885 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1886 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1887 nzi += nlnk; 1888 prow = lnk[prow]; 1889 nzbd++; 1890 } 1891 bdiag[i] = nzbd; 1892 bi[i+1] = bi[i] + nzi; 1893 1894 /* if free space is not available, make more free space */ 1895 if (current_space->local_remaining<nzi) { 1896 nnz = 2*nzi*(n - i); /* estimated and max additional space needed */ 1897 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1898 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1899 reallocs++; 1900 } 1901 1902 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1903 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1904 bj_ptr[i] = current_space->array; 1905 bjlvl_ptr[i] = current_space_lvl->array; 1906 1907 /* make sure the active row i has diagonal entry */ 1908 if (*(bj_ptr[i]+bdiag[i]) != i) { 1909 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1910 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1911 } 1912 1913 current_space->array += nzi; 1914 current_space->local_used += nzi; 1915 current_space->local_remaining -= nzi; 1916 current_space_lvl->array += nzi; 1917 current_space_lvl->local_used += nzi; 1918 current_space_lvl->local_remaining -= nzi; 1919 } 1920 1921 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1922 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1923 1924 /* destroy list of free space and other temporary arrays */ 1925 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1926 1927 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 1928 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 1929 1930 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1931 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1932 ierr = PetscFree(bj_ptr);CHKERRQ(ierr); 1933 1934 #if defined(PETSC_USE_INFO) 1935 { 1936 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1937 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1938 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1939 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1940 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1941 if (diagonal_fill) { 1942 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1943 } 1944 } 1945 #endif 1946 1947 /* put together the new matrix */ 1948 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1949 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1950 b = (Mat_SeqAIJ*)(fact)->data; 1951 b->free_a = PETSC_TRUE; 1952 b->free_ij = PETSC_TRUE; 1953 b->singlemalloc = PETSC_FALSE; 1954 ierr = PetscMalloc( (bi[2*n+1] )*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1955 b->j = bj; 1956 b->i = bi; 1957 b->diag = bdiag; 1958 b->ilen = 0; 1959 b->imax = 0; 1960 b->row = isrow; 1961 b->col = iscol; 1962 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1963 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1964 b->icol = isicol; 1965 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1966 /* In b structure: Free imax, ilen, old a, old j. 1967 Allocate bdiag, solve_work, new a, new j */ 1968 ierr = PetscLogObjectMemory(fact,bi[2*n+1] * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1969 b->maxnz = b->nz = bi[2*n+1] ; 1970 (fact)->info.factor_mallocs = reallocs; 1971 (fact)->info.fill_ratio_given = f; 1972 (fact)->info.fill_ratio_needed = ((PetscReal)bi[2*n+1])/((PetscReal)ai[n]); 1973 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 1974 /* ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */ 1975 PetscFunctionReturn(0); 1976 } 1977 1978 1979 /* 1980 ilu(0) with natural ordering under revised new data structure. 1981 Factored arrays bj and ba are stored as 1982 L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:) 1983 1984 bi=fact->i is an array of size n+1, in which 1985 bi+ 1986 bi[i]: points to 1st entry of L(i,:),i=0,...,n-1 1987 bi[n]: points to L(n-1,n-1)+1 1988 1989 bdiag=fact->diag is an array of size n+1,in which 1990 bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1 1991 bdiag[n]: points to diagonal of U(n-1,0)-1 1992 1993 U(i,:) contains bdiag[i] as its last entry, i.e., 1994 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 1995 */ 1996 #undef __FUNCT__ 1997 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct_v2" 1998 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct_v2(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1999 { 2000 2001 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 2002 PetscErrorCode ierr; 2003 PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag; 2004 PetscInt i,j,nz,*bi,*bj,*bdiag,bi_temp; 2005 2006 PetscFunctionBegin; 2007 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr); 2008 b = (Mat_SeqAIJ*)(fact)->data; 2009 2010 /* allocate matrix arrays for new data structure */ 2011 ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr); 2012 ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 2013 b->singlemalloc = PETSC_TRUE; 2014 if (!b->diag){ 2015 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr); 2016 ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 2017 } 2018 bdiag = b->diag; 2019 2020 if (n > 0) { 2021 ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr); 2022 } 2023 2024 /* set bi and bj with new data structure */ 2025 bi = b->i; 2026 bj = b->j; 2027 2028 /* L part */ 2029 bi[0] = 0; 2030 for (i=0; i<n; i++){ 2031 nz = adiag[i] - ai[i]; 2032 bi[i+1] = bi[i] + nz; 2033 aj = a->j + ai[i]; 2034 for (j=0; j<nz; j++){ 2035 *bj = aj[j]; bj++; 2036 } 2037 } 2038 2039 /* U part */ 2040 /* bi[n+1] = bi[n]; */ 2041 bi_temp = bi[n]; 2042 bdiag[n] = bi[n]-1; 2043 for (i=n-1; i>=0; i--){ 2044 nz = ai[i+1] - adiag[i] - 1; 2045 /* bi[2*n-i+1] = bi[2*n-i] + nz + 1; */ 2046 bi_temp = bi_temp + nz + 1; 2047 aj = a->j + adiag[i] + 1; 2048 for (j=0; j<nz; j++){ 2049 *bj = aj[j]; bj++; 2050 } 2051 /* diag[i] */ 2052 *bj = i; bj++; 2053 /* bdiag[i] = bi[2*n-i+1]-1; */ 2054 bdiag[i] = bi_temp - 1; 2055 } 2056 PetscFunctionReturn(0); 2057 } 2058 2059 #undef __FUNCT__ 2060 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_newdatastruct_v2" 2061 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_newdatastruct_v2(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 2062 { 2063 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 2064 IS isicol; 2065 PetscErrorCode ierr; 2066 const PetscInt *r,*ic; 2067 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 2068 PetscInt *bi,*cols,nnz,*cols_lvl; 2069 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 2070 PetscInt i,levels,diagonal_fill; 2071 PetscTruth col_identity,row_identity; 2072 PetscReal f; 2073 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 2074 PetscBT lnkbt; 2075 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 2076 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2077 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2078 PetscTruth missing; 2079 2080 PetscFunctionBegin; 2081 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2082 f = info->fill; 2083 levels = (PetscInt)info->levels; 2084 diagonal_fill = (PetscInt)info->diagonal_fill; 2085 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 2086 2087 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 2088 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 2089 2090 if (!levels && row_identity && col_identity) { 2091 /* special case: ilu(0) with natural ordering */ 2092 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct_v2(fact,A,isrow,iscol,info);CHKERRQ(ierr); 2093 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct_v2; 2094 2095 fact->factor = MAT_FACTOR_ILU; 2096 (fact)->info.factor_mallocs = 0; 2097 (fact)->info.fill_ratio_given = info->fill; 2098 (fact)->info.fill_ratio_needed = 1.0; 2099 b = (Mat_SeqAIJ*)(fact)->data; 2100 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2101 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2102 b->row = isrow; 2103 b->col = iscol; 2104 b->icol = isicol; 2105 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2106 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 2107 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 2108 /* ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */ 2109 PetscFunctionReturn(0); 2110 } 2111 2112 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 2113 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 2114 2115 /* get new row pointers */ 2116 /* ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); */ 2117 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 2118 bi[0] = 0; 2119 /* bdiag is location of diagonal in factor */ 2120 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 2121 bdiag[0] = 0; 2122 2123 ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr); 2124 bjlvl_ptr = (PetscInt**)(bj_ptr + n); 2125 2126 /* create a linked list for storing column indices of the active row */ 2127 nlnk = n + 1; 2128 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2129 2130 /* initial FreeSpace size is f*(ai[n]+1) */ 2131 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 2132 current_space = free_space; 2133 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 2134 current_space_lvl = free_space_lvl; 2135 2136 for (i=0; i<n; i++) { 2137 nzi = 0; 2138 /* copy current row into linked list */ 2139 nnz = ai[r[i]+1] - ai[r[i]]; 2140 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 2141 cols = aj + ai[r[i]]; 2142 lnk[i] = -1; /* marker to indicate if diagonal exists */ 2143 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2144 nzi += nlnk; 2145 2146 /* make sure diagonal entry is included */ 2147 if (diagonal_fill && lnk[i] == -1) { 2148 fm = n; 2149 while (lnk[fm] < i) fm = lnk[fm]; 2150 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 2151 lnk[fm] = i; 2152 lnk_lvl[i] = 0; 2153 nzi++; dcount++; 2154 } 2155 2156 /* add pivot rows into the active row */ 2157 nzbd = 0; 2158 prow = lnk[n]; 2159 while (prow < i) { 2160 nnz = bdiag[prow]; 2161 cols = bj_ptr[prow] + nnz + 1; 2162 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 2163 nnz = bi[prow+1] - bi[prow] - nnz - 1; 2164 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 2165 nzi += nlnk; 2166 prow = lnk[prow]; 2167 nzbd++; 2168 } 2169 bdiag[i] = nzbd; 2170 bi[i+1] = bi[i] + nzi; 2171 2172 /* if free space is not available, make more free space */ 2173 if (current_space->local_remaining<nzi) { 2174 nnz = 2*nzi*(n - i); /* estimated and max additional space needed */ 2175 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 2176 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 2177 reallocs++; 2178 } 2179 2180 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2181 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2182 bj_ptr[i] = current_space->array; 2183 bjlvl_ptr[i] = current_space_lvl->array; 2184 2185 /* make sure the active row i has diagonal entry */ 2186 if (*(bj_ptr[i]+bdiag[i]) != i) { 2187 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 2188 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 2189 } 2190 2191 current_space->array += nzi; 2192 current_space->local_used += nzi; 2193 current_space->local_remaining -= nzi; 2194 current_space_lvl->array += nzi; 2195 current_space_lvl->local_used += nzi; 2196 current_space_lvl->local_remaining -= nzi; 2197 } 2198 2199 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 2200 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 2201 2202 /* destroy list of free space and other temporary arrays */ 2203 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 2204 2205 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 2206 /* ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); */ 2207 ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 2208 2209 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2210 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2211 ierr = PetscFree(bj_ptr);CHKERRQ(ierr); 2212 2213 #if defined(PETSC_USE_INFO) 2214 { 2215 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2216 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 2217 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2218 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 2219 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 2220 if (diagonal_fill) { 2221 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 2222 } 2223 } 2224 #endif 2225 2226 /* put together the new matrix */ 2227 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 2228 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 2229 b = (Mat_SeqAIJ*)(fact)->data; 2230 b->free_a = PETSC_TRUE; 2231 b->free_ij = PETSC_TRUE; 2232 b->singlemalloc = PETSC_FALSE; 2233 /* ierr = PetscMalloc( (bi[2*n+1] )*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); */ 2234 ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 2235 b->j = bj; 2236 b->i = bi; 2237 b->diag = bdiag; 2238 b->ilen = 0; 2239 b->imax = 0; 2240 b->row = isrow; 2241 b->col = iscol; 2242 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 2243 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 2244 b->icol = isicol; 2245 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2246 /* In b structure: Free imax, ilen, old a, old j. 2247 Allocate bdiag, solve_work, new a, new j */ 2248 2249 /* ierr = PetscLogObjectMemory(fact,bi[2*n+1] * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 2250 b->maxnz = b->nz = bi[2*n+1] ; */ 2251 ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 2252 b->maxnz = b->nz = bdiag[0]+1; 2253 (fact)->info.factor_mallocs = reallocs; 2254 (fact)->info.fill_ratio_given = f; 2255 /* (fact)->info.fill_ratio_needed = ((PetscReal)bi[2*n+1])/((PetscReal)ai[n]); */ 2256 (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 2257 /* (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; */ 2258 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct_v2; 2259 /* ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */ 2260 PetscFunctionReturn(0); 2261 } 2262 2263 #undef __FUNCT__ 2264 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ" 2265 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 2266 { 2267 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 2268 IS isicol; 2269 PetscErrorCode ierr; 2270 const PetscInt *r,*ic; 2271 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 2272 PetscInt *bi,*cols,nnz,*cols_lvl; 2273 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 2274 PetscInt i,levels,diagonal_fill; 2275 PetscTruth col_identity,row_identity; 2276 PetscReal f; 2277 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 2278 PetscBT lnkbt; 2279 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 2280 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2281 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2282 PetscTruth missing; 2283 PetscTruth newdatastruct=PETSC_FALSE,newdatastruct_v2=PETSC_FALSE; 2284 2285 PetscFunctionBegin; 2286 ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 2287 if (newdatastruct){ 2288 ierr = MatILUFactorSymbolic_SeqAIJ_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr); 2289 PetscFunctionReturn(0); 2290 } 2291 ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new_v2",&newdatastruct_v2,PETSC_NULL);CHKERRQ(ierr); 2292 if(newdatastruct_v2){ 2293 ierr = MatILUFactorSymbolic_SeqAIJ_newdatastruct_v2(fact,A,isrow,iscol,info);CHKERRQ(ierr); 2294 PetscFunctionReturn(0); 2295 } 2296 2297 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2298 f = info->fill; 2299 levels = (PetscInt)info->levels; 2300 diagonal_fill = (PetscInt)info->diagonal_fill; 2301 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 2302 2303 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 2304 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 2305 if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */ 2306 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr); 2307 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 2308 2309 fact->factor = MAT_FACTOR_ILU; 2310 (fact)->info.factor_mallocs = 0; 2311 (fact)->info.fill_ratio_given = info->fill; 2312 (fact)->info.fill_ratio_needed = 1.0; 2313 b = (Mat_SeqAIJ*)(fact)->data; 2314 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2315 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2316 b->row = isrow; 2317 b->col = iscol; 2318 b->icol = isicol; 2319 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2320 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 2321 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 2322 ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 2323 PetscFunctionReturn(0); 2324 } 2325 2326 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 2327 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 2328 2329 /* get new row pointers */ 2330 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 2331 bi[0] = 0; 2332 /* bdiag is location of diagonal in factor */ 2333 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 2334 bdiag[0] = 0; 2335 2336 ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr); 2337 bjlvl_ptr = (PetscInt**)(bj_ptr + n); 2338 2339 /* create a linked list for storing column indices of the active row */ 2340 nlnk = n + 1; 2341 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2342 2343 /* initial FreeSpace size is f*(ai[n]+1) */ 2344 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 2345 current_space = free_space; 2346 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 2347 current_space_lvl = free_space_lvl; 2348 2349 for (i=0; i<n; i++) { 2350 nzi = 0; 2351 /* copy current row into linked list */ 2352 nnz = ai[r[i]+1] - ai[r[i]]; 2353 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 2354 cols = aj + ai[r[i]]; 2355 lnk[i] = -1; /* marker to indicate if diagonal exists */ 2356 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2357 nzi += nlnk; 2358 2359 /* make sure diagonal entry is included */ 2360 if (diagonal_fill && lnk[i] == -1) { 2361 fm = n; 2362 while (lnk[fm] < i) fm = lnk[fm]; 2363 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 2364 lnk[fm] = i; 2365 lnk_lvl[i] = 0; 2366 nzi++; dcount++; 2367 } 2368 2369 /* add pivot rows into the active row */ 2370 nzbd = 0; 2371 prow = lnk[n]; 2372 while (prow < i) { 2373 nnz = bdiag[prow]; 2374 cols = bj_ptr[prow] + nnz + 1; 2375 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 2376 nnz = bi[prow+1] - bi[prow] - nnz - 1; 2377 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 2378 nzi += nlnk; 2379 prow = lnk[prow]; 2380 nzbd++; 2381 } 2382 bdiag[i] = nzbd; 2383 bi[i+1] = bi[i] + nzi; 2384 2385 /* if free space is not available, make more free space */ 2386 if (current_space->local_remaining<nzi) { 2387 nnz = nzi*(n - i); /* estimated and max additional space needed */ 2388 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 2389 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 2390 reallocs++; 2391 } 2392 2393 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2394 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2395 bj_ptr[i] = current_space->array; 2396 bjlvl_ptr[i] = current_space_lvl->array; 2397 2398 /* make sure the active row i has diagonal entry */ 2399 if (*(bj_ptr[i]+bdiag[i]) != i) { 2400 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 2401 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 2402 } 2403 2404 current_space->array += nzi; 2405 current_space->local_used += nzi; 2406 current_space->local_remaining -= nzi; 2407 current_space_lvl->array += nzi; 2408 current_space_lvl->local_used += nzi; 2409 current_space_lvl->local_remaining -= nzi; 2410 } 2411 2412 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 2413 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 2414 2415 /* destroy list of free space and other temporary arrays */ 2416 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 2417 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */ 2418 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2419 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2420 ierr = PetscFree(bj_ptr);CHKERRQ(ierr); 2421 2422 #if defined(PETSC_USE_INFO) 2423 { 2424 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2425 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 2426 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2427 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 2428 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 2429 if (diagonal_fill) { 2430 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 2431 } 2432 } 2433 #endif 2434 2435 /* put together the new matrix */ 2436 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 2437 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 2438 b = (Mat_SeqAIJ*)(fact)->data; 2439 b->free_a = PETSC_TRUE; 2440 b->free_ij = PETSC_TRUE; 2441 b->singlemalloc = PETSC_FALSE; 2442 ierr = PetscMalloc( (bi[n] )*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 2443 b->j = bj; 2444 b->i = bi; 2445 for (i=0; i<n; i++) bdiag[i] += bi[i]; 2446 b->diag = bdiag; 2447 b->ilen = 0; 2448 b->imax = 0; 2449 b->row = isrow; 2450 b->col = iscol; 2451 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 2452 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 2453 b->icol = isicol; 2454 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2455 /* In b structure: Free imax, ilen, old a, old j. 2456 Allocate bdiag, solve_work, new a, new j */ 2457 ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 2458 b->maxnz = b->nz = bi[n] ; 2459 (fact)->info.factor_mallocs = reallocs; 2460 (fact)->info.fill_ratio_given = f; 2461 (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2462 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 2463 ierr = MatILUFactorSymbolic_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 2464 PetscFunctionReturn(0); 2465 } 2466 2467 #undef __FUNCT__ 2468 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_newdatastruct" 2469 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info) 2470 { 2471 Mat C = B; 2472 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2473 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2474 IS ip=b->row,iip = b->icol; 2475 PetscErrorCode ierr; 2476 const PetscInt *rip,*riip; 2477 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp; 2478 PetscInt *ai=a->i,*aj=a->j; 2479 PetscInt k,jmin,jmax,*c2r,*il,col,nexti,ili,nz; 2480 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2481 PetscReal zeropivot,shiftnz; 2482 PetscReal shiftpd; 2483 PetscTruth perm_identity; 2484 2485 PetscFunctionBegin; 2486 2487 shiftnz = info->shiftnz; 2488 shiftpd = info->shiftpd; 2489 zeropivot = info->zeropivot; 2490 2491 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2492 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2493 2494 /* allocate working arrays 2495 c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col 2496 il: for active k row, il[i] gives the index of the 1st nonzero entry in U[i,k:n-1] in bj and ba arrays 2497 */ 2498 nz = (2*mbs+1)*sizeof(PetscInt)+mbs*sizeof(MatScalar); 2499 ierr = PetscMalloc(nz,&il);CHKERRQ(ierr); 2500 c2r = il + mbs; 2501 rtmp = (MatScalar*)(c2r + mbs); 2502 2503 for (i=0; i<mbs; i++) { 2504 c2r[i] = mbs; 2505 } 2506 il[0] = 0; 2507 2508 for (k = 0; k<mbs; k++){ 2509 /* zero rtmp */ 2510 nz = bi[k+1] - bi[k]; 2511 bjtmp = bj + bi[k]; 2512 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2513 2514 /* load in initial unfactored row */ 2515 bval = ba + bi[k]; 2516 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2517 for (j = jmin; j < jmax; j++){ 2518 col = riip[aj[j]]; 2519 if (col >= k){ /* only take upper triangular entry */ 2520 rtmp[col] = aa[j]; 2521 *bval++ = 0.0; /* for in-place factorization */ 2522 } 2523 } 2524 /* shift the diagonal of the matrix */ 2525 2526 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2527 dk = rtmp[k]; 2528 i = c2r[k]; /* first row to be added to k_th row */ 2529 2530 while (i < k){ 2531 nexti = c2r[i]; /* next row to be added to k_th row */ 2532 2533 /* compute multiplier, update diag(k) and U(i,k) */ 2534 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2535 uikdi = - ba[ili]*ba[bdiag[i]]; /* diagonal(k) */ 2536 dk += uikdi*ba[ili]; /* update diag[k] */ 2537 ba[ili] = uikdi; /* -U(i,k) */ 2538 2539 /* add multiple of row i to k-th row */ 2540 jmin = ili + 1; jmax = bi[i+1]; 2541 if (jmin < jmax){ 2542 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2543 /* update il and c2r for row i */ 2544 il[i] = jmin; 2545 j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i; 2546 } 2547 i = nexti; 2548 } 2549 2550 /* copy data into U(k,:) */ 2551 ba[bdiag[k]] = 1.0/dk; /* U(k,k) */ 2552 jmin = bi[k]; jmax = bi[k+1]-1; 2553 if (jmin < jmax) { 2554 for (j=jmin; j<jmax; j++){ 2555 col = bj[j]; ba[j] = rtmp[col]; 2556 } 2557 /* add the k-th row into il and c2r */ 2558 il[k] = jmin; 2559 i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k; 2560 } 2561 } 2562 2563 ierr = PetscFree(il);CHKERRQ(ierr); 2564 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2565 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2566 2567 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2568 if (perm_identity){ 2569 (B)->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_newdatastruct; 2570 (B)->ops->solvetranspose = 0; 2571 (B)->ops->forwardsolve = 0; 2572 (B)->ops->backwardsolve = 0; 2573 } else { 2574 (B)->ops->solve = MatSolve_SeqSBAIJ_1_newdatastruct; 2575 (B)->ops->solvetranspose = 0; 2576 (B)->ops->forwardsolve = 0; 2577 (B)->ops->backwardsolve = 0; 2578 } 2579 2580 C->assembled = PETSC_TRUE; 2581 C->preallocated = PETSC_TRUE; 2582 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2583 PetscFunctionReturn(0); 2584 } 2585 2586 #undef __FUNCT__ 2587 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ" 2588 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 2589 { 2590 Mat C = B; 2591 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2592 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2593 IS ip=b->row,iip = b->icol; 2594 PetscErrorCode ierr; 2595 const PetscInt *rip,*riip; 2596 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol; 2597 PetscInt *ai=a->i,*aj=a->j; 2598 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz; 2599 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2600 PetscReal zeropivot,rs,shiftnz; 2601 PetscReal shiftpd; 2602 ChShift_Ctx sctx; 2603 PetscInt newshift; 2604 PetscTruth perm_identity; 2605 2606 PetscFunctionBegin; 2607 shiftnz = info->shiftnz; 2608 shiftpd = info->shiftpd; 2609 zeropivot = info->zeropivot; 2610 2611 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2612 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2613 2614 /* initialization */ 2615 nz = (2*mbs+1)*sizeof(PetscInt)+mbs*sizeof(MatScalar); 2616 ierr = PetscMalloc(nz,&il);CHKERRQ(ierr); 2617 jl = il + mbs; 2618 rtmp = (MatScalar*)(jl + mbs); 2619 2620 sctx.shift_amount = 0; 2621 sctx.nshift = 0; 2622 do { 2623 sctx.chshift = PETSC_FALSE; 2624 for (i=0; i<mbs; i++) { 2625 rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0; 2626 } 2627 2628 for (k = 0; k<mbs; k++){ 2629 bval = ba + bi[k]; 2630 /* initialize k-th row by the perm[k]-th row of A */ 2631 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2632 for (j = jmin; j < jmax; j++){ 2633 col = riip[aj[j]]; 2634 if (col >= k){ /* only take upper triangular entry */ 2635 rtmp[col] = aa[j]; 2636 *bval++ = 0.0; /* for in-place factorization */ 2637 } 2638 } 2639 /* shift the diagonal of the matrix */ 2640 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 2641 2642 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2643 dk = rtmp[k]; 2644 i = jl[k]; /* first row to be added to k_th row */ 2645 2646 while (i < k){ 2647 nexti = jl[i]; /* next row to be added to k_th row */ 2648 2649 /* compute multiplier, update diag(k) and U(i,k) */ 2650 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2651 uikdi = - ba[ili]*ba[bi[i]]; /* diagonal(k) */ 2652 dk += uikdi*ba[ili]; 2653 ba[ili] = uikdi; /* -U(i,k) */ 2654 2655 /* add multiple of row i to k-th row */ 2656 jmin = ili + 1; jmax = bi[i+1]; 2657 if (jmin < jmax){ 2658 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2659 /* update il and jl for row i */ 2660 il[i] = jmin; 2661 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 2662 } 2663 i = nexti; 2664 } 2665 2666 /* shift the diagonals when zero pivot is detected */ 2667 /* compute rs=sum of abs(off-diagonal) */ 2668 rs = 0.0; 2669 jmin = bi[k]+1; 2670 nz = bi[k+1] - jmin; 2671 bcol = bj + jmin; 2672 for (j=0; j<nz; j++) { 2673 rs += PetscAbsScalar(rtmp[bcol[j]]); 2674 } 2675 2676 sctx.rs = rs; 2677 sctx.pv = dk; 2678 ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr); 2679 2680 if (newshift == 1) { 2681 if (!sctx.shift_amount) { 2682 sctx.shift_amount = 1e-5; 2683 } 2684 break; 2685 } 2686 2687 /* copy data into U(k,:) */ 2688 ba[bi[k]] = 1.0/dk; /* U(k,k) */ 2689 jmin = bi[k]+1; jmax = bi[k+1]; 2690 if (jmin < jmax) { 2691 for (j=jmin; j<jmax; j++){ 2692 col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0; 2693 } 2694 /* add the k-th row into il and jl */ 2695 il[k] = jmin; 2696 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 2697 } 2698 } 2699 } while (sctx.chshift); 2700 ierr = PetscFree(il);CHKERRQ(ierr); 2701 2702 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2703 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2704 2705 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2706 if (perm_identity){ 2707 (B)->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2708 (B)->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2709 (B)->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering; 2710 (B)->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering; 2711 } else { 2712 (B)->ops->solve = MatSolve_SeqSBAIJ_1; 2713 (B)->ops->solvetranspose = MatSolve_SeqSBAIJ_1; 2714 (B)->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1; 2715 (B)->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1; 2716 } 2717 2718 C->assembled = PETSC_TRUE; 2719 C->preallocated = PETSC_TRUE; 2720 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2721 if (sctx.nshift){ 2722 if (shiftnz) { 2723 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2724 } else if (shiftpd) { 2725 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2726 } 2727 } 2728 PetscFunctionReturn(0); 2729 } 2730 2731 #undef __FUNCT__ 2732 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_newdatastruct" 2733 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2734 { 2735 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2736 Mat_SeqSBAIJ *b; 2737 PetscErrorCode ierr; 2738 PetscTruth perm_identity,missing; 2739 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2740 const PetscInt *rip,*riip; 2741 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2742 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2743 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2744 PetscReal fill=info->fill,levels=info->levels; 2745 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2746 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2747 PetscBT lnkbt; 2748 IS iperm; 2749 2750 PetscFunctionBegin; 2751 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2752 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2753 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2754 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2755 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2756 2757 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2758 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2759 ui[0] = 0; 2760 2761 /* ICC(0) without matrix ordering: simply copies fill pattern */ 2762 if (!levels && perm_identity) { 2763 2764 for (i=0; i<am; i++) { 2765 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 2766 udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */ 2767 } 2768 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2769 cols = uj; 2770 for (i=0; i<am; i++) { 2771 aj = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */ 2772 ncols = ui[i+1] - ui[i] - 1; 2773 for (j=0; j<ncols; j++) *cols++ = aj[j]; 2774 *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */ 2775 } 2776 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2777 2778 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2779 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2780 2781 /* initialization */ 2782 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2783 2784 /* jl: linked list for storing indices of the pivot rows 2785 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2786 ierr = PetscMalloc((2*am+1)*sizeof(PetscInt)+2*am*sizeof(PetscInt**),&jl);CHKERRQ(ierr); 2787 il = jl + am; 2788 uj_ptr = (PetscInt**)(il + am); 2789 uj_lvl_ptr = (PetscInt**)(uj_ptr + am); 2790 for (i=0; i<am; i++){ 2791 jl[i] = am; il[i] = 0; 2792 } 2793 2794 /* create and initialize a linked list for storing column indices of the active row k */ 2795 nlnk = am + 1; 2796 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2797 2798 /* initial FreeSpace size is fill*(ai[am]+1) */ 2799 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2800 current_space = free_space; 2801 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2802 current_space_lvl = free_space_lvl; 2803 2804 for (k=0; k<am; k++){ /* for each active row k */ 2805 /* initialize lnk by the column indices of row rip[k] of A */ 2806 nzk = 0; 2807 ncols = ai[rip[k]+1] - ai[rip[k]]; 2808 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2809 ncols_upper = 0; 2810 for (j=0; j<ncols; j++){ 2811 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2812 if (riip[i] >= k){ /* only take upper triangular entry */ 2813 ajtmp[ncols_upper] = i; 2814 ncols_upper++; 2815 } 2816 } 2817 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2818 nzk += nlnk; 2819 2820 /* update lnk by computing fill-in for each pivot row to be merged in */ 2821 prow = jl[k]; /* 1st pivot row */ 2822 2823 while (prow < k){ 2824 nextprow = jl[prow]; 2825 2826 /* merge prow into k-th row */ 2827 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2828 jmax = ui[prow+1]; 2829 ncols = jmax-jmin; 2830 i = jmin - ui[prow]; 2831 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2832 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2833 j = *(uj - 1); 2834 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2835 nzk += nlnk; 2836 2837 /* update il and jl for prow */ 2838 if (jmin < jmax){ 2839 il[prow] = jmin; 2840 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2841 } 2842 prow = nextprow; 2843 } 2844 2845 /* if free space is not available, make more free space */ 2846 if (current_space->local_remaining<nzk) { 2847 i = am - k + 1; /* num of unfactored rows */ 2848 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2849 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2850 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2851 reallocs++; 2852 } 2853 2854 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2855 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2856 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2857 2858 /* add the k-th row into il and jl */ 2859 if (nzk > 1){ 2860 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2861 jl[k] = jl[i]; jl[i] = k; 2862 il[k] = ui[k] + 1; 2863 } 2864 uj_ptr[k] = current_space->array; 2865 uj_lvl_ptr[k] = current_space_lvl->array; 2866 2867 current_space->array += nzk; 2868 current_space->local_used += nzk; 2869 current_space->local_remaining -= nzk; 2870 2871 current_space_lvl->array += nzk; 2872 current_space_lvl->local_used += nzk; 2873 current_space_lvl->local_remaining -= nzk; 2874 2875 ui[k+1] = ui[k] + nzk; 2876 } 2877 2878 #if defined(PETSC_USE_INFO) 2879 if (ai[am] != 0) { 2880 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2881 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2882 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2883 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2884 } else { 2885 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2886 } 2887 #endif 2888 2889 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2890 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2891 ierr = PetscFree(jl);CHKERRQ(ierr); 2892 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2893 2894 /* destroy list of free space and other temporary array(s) */ 2895 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2896 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); 2897 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2898 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2899 2900 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2901 2902 /* put together the new matrix in MATSEQSBAIJ format */ 2903 2904 b = (Mat_SeqSBAIJ*)(fact)->data; 2905 b->singlemalloc = PETSC_FALSE; 2906 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2907 b->j = uj; 2908 b->i = ui; 2909 b->diag = udiag; 2910 b->free_diag = PETSC_TRUE; 2911 b->ilen = 0; 2912 b->imax = 0; 2913 b->row = perm; 2914 b->col = perm; 2915 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2916 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2917 b->icol = iperm; 2918 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2919 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2920 ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2921 b->maxnz = b->nz = ui[am]; 2922 b->free_a = PETSC_TRUE; 2923 b->free_ij = PETSC_TRUE; 2924 2925 (fact)->info.factor_mallocs = reallocs; 2926 (fact)->info.fill_ratio_given = fill; 2927 if (ai[am] != 0) { 2928 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2929 } else { 2930 (fact)->info.fill_ratio_needed = 0.0; 2931 } 2932 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct; 2933 PetscFunctionReturn(0); 2934 } 2935 2936 #undef __FUNCT__ 2937 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ" 2938 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2939 { 2940 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2941 Mat_SeqSBAIJ *b; 2942 PetscErrorCode ierr; 2943 PetscTruth perm_identity,missing; 2944 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2945 const PetscInt *rip,*riip; 2946 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2947 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2948 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2949 PetscReal fill=info->fill,levels=info->levels; 2950 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2951 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2952 PetscBT lnkbt; 2953 IS iperm; 2954 PetscTruth newdatastruct=PETSC_FALSE; 2955 2956 PetscFunctionBegin; 2957 ierr = PetscOptionsGetTruth(PETSC_NULL,"-icc_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 2958 if(newdatastruct){ 2959 ierr = MatICCFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr); 2960 PetscFunctionReturn(0); 2961 } 2962 2963 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2964 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2965 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2966 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2967 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2968 2969 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2970 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2971 ui[0] = 0; 2972 2973 /* ICC(0) without matrix ordering: simply copies fill pattern */ 2974 if (!levels && perm_identity) { 2975 2976 for (i=0; i<am; i++) { 2977 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 2978 udiag[i] = ui[i]; 2979 } 2980 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2981 cols = uj; 2982 for (i=0; i<am; i++) { 2983 aj = a->j + a->diag[i]; 2984 ncols = ui[i+1] - ui[i]; 2985 for (j=0; j<ncols; j++) *cols++ = *aj++; 2986 } 2987 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2988 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2989 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2990 2991 /* initialization */ 2992 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2993 2994 /* jl: linked list for storing indices of the pivot rows 2995 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2996 ierr = PetscMalloc((2*am+1)*sizeof(PetscInt)+2*am*sizeof(PetscInt**),&jl);CHKERRQ(ierr); 2997 il = jl + am; 2998 uj_ptr = (PetscInt**)(il + am); 2999 uj_lvl_ptr = (PetscInt**)(uj_ptr + am); 3000 for (i=0; i<am; i++){ 3001 jl[i] = am; il[i] = 0; 3002 } 3003 3004 /* create and initialize a linked list for storing column indices of the active row k */ 3005 nlnk = am + 1; 3006 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 3007 3008 /* initial FreeSpace size is fill*(ai[am]+1) */ 3009 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 3010 current_space = free_space; 3011 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 3012 current_space_lvl = free_space_lvl; 3013 3014 for (k=0; k<am; k++){ /* for each active row k */ 3015 /* initialize lnk by the column indices of row rip[k] of A */ 3016 nzk = 0; 3017 ncols = ai[rip[k]+1] - ai[rip[k]]; 3018 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 3019 ncols_upper = 0; 3020 for (j=0; j<ncols; j++){ 3021 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 3022 if (riip[i] >= k){ /* only take upper triangular entry */ 3023 ajtmp[ncols_upper] = i; 3024 ncols_upper++; 3025 } 3026 } 3027 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 3028 nzk += nlnk; 3029 3030 /* update lnk by computing fill-in for each pivot row to be merged in */ 3031 prow = jl[k]; /* 1st pivot row */ 3032 3033 while (prow < k){ 3034 nextprow = jl[prow]; 3035 3036 /* merge prow into k-th row */ 3037 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 3038 jmax = ui[prow+1]; 3039 ncols = jmax-jmin; 3040 i = jmin - ui[prow]; 3041 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 3042 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 3043 j = *(uj - 1); 3044 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 3045 nzk += nlnk; 3046 3047 /* update il and jl for prow */ 3048 if (jmin < jmax){ 3049 il[prow] = jmin; 3050 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 3051 } 3052 prow = nextprow; 3053 } 3054 3055 /* if free space is not available, make more free space */ 3056 if (current_space->local_remaining<nzk) { 3057 i = am - k + 1; /* num of unfactored rows */ 3058 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 3059 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 3060 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 3061 reallocs++; 3062 } 3063 3064 /* copy data into free_space and free_space_lvl, then initialize lnk */ 3065 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 3066 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 3067 3068 /* add the k-th row into il and jl */ 3069 if (nzk > 1){ 3070 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 3071 jl[k] = jl[i]; jl[i] = k; 3072 il[k] = ui[k] + 1; 3073 } 3074 uj_ptr[k] = current_space->array; 3075 uj_lvl_ptr[k] = current_space_lvl->array; 3076 3077 current_space->array += nzk; 3078 current_space->local_used += nzk; 3079 current_space->local_remaining -= nzk; 3080 3081 current_space_lvl->array += nzk; 3082 current_space_lvl->local_used += nzk; 3083 current_space_lvl->local_remaining -= nzk; 3084 3085 ui[k+1] = ui[k] + nzk; 3086 } 3087 3088 #if defined(PETSC_USE_INFO) 3089 if (ai[am] != 0) { 3090 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 3091 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 3092 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 3093 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 3094 } else { 3095 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 3096 } 3097 #endif 3098 3099 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 3100 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 3101 ierr = PetscFree(jl);CHKERRQ(ierr); 3102 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 3103 3104 /* destroy list of free space and other temporary array(s) */ 3105 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 3106 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 3107 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3108 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 3109 3110 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 3111 3112 /* put together the new matrix in MATSEQSBAIJ format */ 3113 3114 b = (Mat_SeqSBAIJ*)(fact)->data; 3115 b->singlemalloc = PETSC_FALSE; 3116 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 3117 b->j = uj; 3118 b->i = ui; 3119 b->diag = udiag; 3120 b->free_diag = PETSC_TRUE; 3121 b->ilen = 0; 3122 b->imax = 0; 3123 b->row = perm; 3124 b->col = perm; 3125 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3126 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3127 b->icol = iperm; 3128 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 3129 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3130 ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3131 b->maxnz = b->nz = ui[am]; 3132 b->free_a = PETSC_TRUE; 3133 b->free_ij = PETSC_TRUE; 3134 3135 (fact)->info.factor_mallocs = reallocs; 3136 (fact)->info.fill_ratio_given = fill; 3137 if (ai[am] != 0) { 3138 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 3139 } else { 3140 (fact)->info.fill_ratio_needed = 0.0; 3141 } 3142 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 3143 PetscFunctionReturn(0); 3144 } 3145 3146 #undef __FUNCT__ 3147 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ" 3148 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 3149 { 3150 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3151 Mat_SeqSBAIJ *b; 3152 PetscErrorCode ierr; 3153 PetscTruth perm_identity; 3154 PetscReal fill = info->fill; 3155 const PetscInt *rip,*riip; 3156 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 3157 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 3158 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr; 3159 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 3160 PetscBT lnkbt; 3161 IS iperm; 3162 3163 PetscFunctionBegin; 3164 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 3165 /* check whether perm is the identity mapping */ 3166 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 3167 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 3168 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 3169 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 3170 3171 /* initialization */ 3172 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 3173 ui[0] = 0; 3174 3175 /* jl: linked list for storing indices of the pivot rows 3176 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 3177 ierr = PetscMalloc((3*am+1)*sizeof(PetscInt)+am*sizeof(PetscInt**),&jl);CHKERRQ(ierr); 3178 il = jl + am; 3179 cols = il + am; 3180 ui_ptr = (PetscInt**)(cols + am); 3181 for (i=0; i<am; i++){ 3182 jl[i] = am; il[i] = 0; 3183 } 3184 3185 /* create and initialize a linked list for storing column indices of the active row k */ 3186 nlnk = am + 1; 3187 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3188 3189 /* initial FreeSpace size is fill*(ai[am]+1) */ 3190 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 3191 current_space = free_space; 3192 3193 for (k=0; k<am; k++){ /* for each active row k */ 3194 /* initialize lnk by the column indices of row rip[k] of A */ 3195 nzk = 0; 3196 ncols = ai[rip[k]+1] - ai[rip[k]]; 3197 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 3198 ncols_upper = 0; 3199 for (j=0; j<ncols; j++){ 3200 i = riip[*(aj + ai[rip[k]] + j)]; 3201 if (i >= k){ /* only take upper triangular entry */ 3202 cols[ncols_upper] = i; 3203 ncols_upper++; 3204 } 3205 } 3206 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3207 nzk += nlnk; 3208 3209 /* update lnk by computing fill-in for each pivot row to be merged in */ 3210 prow = jl[k]; /* 1st pivot row */ 3211 3212 while (prow < k){ 3213 nextprow = jl[prow]; 3214 /* merge prow into k-th row */ 3215 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 3216 jmax = ui[prow+1]; 3217 ncols = jmax-jmin; 3218 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 3219 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3220 nzk += nlnk; 3221 3222 /* update il and jl for prow */ 3223 if (jmin < jmax){ 3224 il[prow] = jmin; 3225 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 3226 } 3227 prow = nextprow; 3228 } 3229 3230 /* if free space is not available, make more free space */ 3231 if (current_space->local_remaining<nzk) { 3232 i = am - k + 1; /* num of unfactored rows */ 3233 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 3234 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 3235 reallocs++; 3236 } 3237 3238 /* copy data into free space, then initialize lnk */ 3239 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 3240 3241 /* add the k-th row into il and jl */ 3242 if (nzk-1 > 0){ 3243 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 3244 jl[k] = jl[i]; jl[i] = k; 3245 il[k] = ui[k] + 1; 3246 } 3247 ui_ptr[k] = current_space->array; 3248 current_space->array += nzk; 3249 current_space->local_used += nzk; 3250 current_space->local_remaining -= nzk; 3251 3252 ui[k+1] = ui[k] + nzk; 3253 } 3254 3255 #if defined(PETSC_USE_INFO) 3256 if (ai[am] != 0) { 3257 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 3258 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 3259 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 3260 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 3261 } else { 3262 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 3263 } 3264 #endif 3265 3266 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 3267 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 3268 ierr = PetscFree(jl);CHKERRQ(ierr); 3269 3270 /* destroy list of free space and other temporary array(s) */ 3271 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 3272 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 3273 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3274 3275 /* put together the new matrix in MATSEQSBAIJ format */ 3276 3277 b = (Mat_SeqSBAIJ*)(fact)->data; 3278 b->singlemalloc = PETSC_FALSE; 3279 b->free_a = PETSC_TRUE; 3280 b->free_ij = PETSC_TRUE; 3281 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 3282 b->j = uj; 3283 b->i = ui; 3284 b->diag = 0; 3285 b->ilen = 0; 3286 b->imax = 0; 3287 b->row = perm; 3288 b->col = perm; 3289 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3290 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3291 b->icol = iperm; 3292 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 3293 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3294 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3295 b->maxnz = b->nz = ui[am]; 3296 3297 (fact)->info.factor_mallocs = reallocs; 3298 (fact)->info.fill_ratio_given = fill; 3299 if (ai[am] != 0) { 3300 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 3301 } else { 3302 (fact)->info.fill_ratio_needed = 0.0; 3303 } 3304 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 3305 PetscFunctionReturn(0); 3306 } 3307 3308 #undef __FUNCT__ 3309 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct" 3310 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx) 3311 { 3312 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3313 PetscErrorCode ierr; 3314 PetscInt n = A->rmap->n; 3315 const PetscInt *ai = a->i,*aj = a->j,*vi; 3316 PetscScalar *x,sum; 3317 const PetscScalar *b; 3318 const MatScalar *aa = a->a,*v; 3319 PetscInt i,nz; 3320 3321 PetscFunctionBegin; 3322 if (!n) PetscFunctionReturn(0); 3323 3324 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3325 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3326 3327 /* forward solve the lower triangular */ 3328 x[0] = b[0]; 3329 v = aa; 3330 vi = aj; 3331 for (i=1; i<n; i++) { 3332 nz = ai[i+1] - ai[i]; 3333 sum = b[i]; 3334 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3335 v += nz; 3336 vi += nz; 3337 x[i] = sum; 3338 } 3339 3340 /* backward solve the upper triangular */ 3341 v = aa + ai[n+1]; 3342 vi = aj + ai[n+1]; 3343 for (i=n-1; i>=0; i--){ 3344 nz = ai[2*n-i +1] - ai[2*n-i]-1; 3345 sum = x[i]; 3346 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3347 v += nz; 3348 vi += nz; vi++; 3349 x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */ 3350 } 3351 3352 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 3353 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3354 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3355 PetscFunctionReturn(0); 3356 } 3357 3358 #undef __FUNCT__ 3359 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct_v2" 3360 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct_v2(Mat A,Vec bb,Vec xx) 3361 { 3362 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3363 PetscErrorCode ierr; 3364 PetscInt n = A->rmap->n; 3365 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag,*vi; 3366 PetscScalar *x,sum; 3367 const PetscScalar *b; 3368 const MatScalar *aa = a->a,*v; 3369 PetscInt i,nz; 3370 3371 PetscFunctionBegin; 3372 if (!n) PetscFunctionReturn(0); 3373 3374 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3375 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3376 3377 /* forward solve the lower triangular */ 3378 x[0] = b[0]; 3379 v = aa; 3380 vi = aj; 3381 for (i=1; i<n; i++) { 3382 nz = ai[i+1] - ai[i]; 3383 sum = b[i]; 3384 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3385 v += nz; 3386 vi += nz; 3387 x[i] = sum; 3388 } 3389 3390 /* backward solve the upper triangular */ 3391 /* v = aa + ai[n+1]; 3392 vi = aj + ai[n+1]; */ 3393 v = aa + adiag[n-1]; 3394 vi = aj + adiag[n-1]; 3395 for (i=n-1; i>=0; i--){ 3396 nz = adiag[i] - adiag[i+1]-1; 3397 sum = x[i]; 3398 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3399 v += nz; 3400 vi += nz; vi++; 3401 x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */ 3402 } 3403 3404 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 3405 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3406 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3407 PetscFunctionReturn(0); 3408 } 3409 3410 #undef __FUNCT__ 3411 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct" 3412 PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx) 3413 { 3414 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3415 IS iscol = a->col,isrow = a->row; 3416 PetscErrorCode ierr; 3417 PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,nz,k; 3418 const PetscInt *rout,*cout,*r,*c; 3419 PetscScalar *x,*tmp,*tmps,sum; 3420 const PetscScalar *b; 3421 const MatScalar *aa = a->a,*v; 3422 3423 PetscFunctionBegin; 3424 if (!n) PetscFunctionReturn(0); 3425 3426 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3427 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3428 tmp = a->solve_work; 3429 3430 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 3431 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 3432 3433 /* forward solve the lower triangular */ 3434 tmp[0] = b[*r++]; 3435 tmps = tmp; 3436 v = aa; 3437 vi = aj; 3438 for (i=1; i<n; i++) { 3439 nz = ai[i+1] - ai[i]; 3440 sum = b[*r++]; 3441 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 3442 tmp[i] = sum; 3443 v += nz; vi += nz; 3444 } 3445 3446 /* backward solve the upper triangular */ 3447 k = n+1; 3448 v = aa + ai[k]; /* 1st entry of U(n-1,:) */ 3449 vi = aj + ai[k]; 3450 for (i=n-1; i>=0; i--){ 3451 k = 2*n-i; 3452 nz = ai[k +1] - ai[k] - 1; 3453 sum = tmp[i]; 3454 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 3455 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 3456 v += nz+1; vi += nz+1; 3457 } 3458 3459 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 3460 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 3461 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3462 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3463 ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr); 3464 PetscFunctionReturn(0); 3465 } 3466 3467 #undef __FUNCT__ 3468 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct_v2" 3469 PetscErrorCode MatSolve_SeqAIJ_newdatastruct_v2(Mat A,Vec bb,Vec xx) 3470 { 3471 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3472 IS iscol = a->col,isrow = a->row; 3473 PetscErrorCode ierr; 3474 PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz; 3475 const PetscInt *rout,*cout,*r,*c; 3476 PetscScalar *x,*tmp,sum; 3477 const PetscScalar *b; 3478 const MatScalar *aa = a->a,*v; 3479 3480 PetscFunctionBegin; 3481 if (!n) PetscFunctionReturn(0); 3482 3483 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3484 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3485 tmp = a->solve_work; 3486 3487 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 3488 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 3489 3490 /* forward solve the lower triangular */ 3491 /* tmp[0] = b[*r++]; */ 3492 tmp[0] = b[r[0]]; 3493 v = aa; 3494 vi = aj; 3495 for (i=1; i<n; i++) { 3496 nz = ai[i+1] - ai[i]; 3497 sum = b[r[i]]; 3498 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3499 tmp[i] = sum; 3500 v += nz; vi += nz; 3501 } 3502 3503 /* backward solve the upper triangular */ 3504 /* v = aa + ai[k]; *//* 1st entry of U(n-1,:) */ 3505 /* vi = aj + ai[k]; */ 3506 v = aa + adiag[n-1]; 3507 vi = aj + adiag[n-1]; 3508 for (i=n-1; i>=0; i--){ 3509 /* nz = ai[k +1] - ai[k] - 1;*/ 3510 nz = adiag[i]-adiag[i+1]-1; 3511 sum = tmp[i]; 3512 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3513 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 3514 v += nz+1; vi += nz+1; 3515 } 3516 3517 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 3518 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 3519 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3520 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3521 ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr); 3522 PetscFunctionReturn(0); 3523 } 3524 3525 #undef __FUNCT__ 3526 #define __FUNCT__ "MatILUDTFactor_SeqAIJ" 3527 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact) 3528 { 3529 Mat B = *fact; 3530 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b; 3531 IS isicol; 3532 PetscErrorCode ierr; 3533 const PetscInt *r,*ic; 3534 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag; 3535 PetscInt *bi,*bj,*bdiag,*bdiag_rev; 3536 PetscInt row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au; 3537 PetscInt nlnk,*lnk; 3538 PetscBT lnkbt; 3539 PetscTruth row_identity,icol_identity,both_identity; 3540 MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp; 3541 const PetscInt *ics; 3542 PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp; 3543 PetscReal dt=info->dt,dtcol=info->dtcol,shift=info->shiftinblocks; 3544 PetscInt dtcount=(PetscInt)info->dtcount,nnz_max; 3545 PetscTruth missing; 3546 3547 PetscFunctionBegin; 3548 3549 if (dt == PETSC_DEFAULT) dt = 0.005; 3550 if (dtcol == PETSC_DEFAULT) dtcol = 0.01; /* XXX unused! */ 3551 if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax); 3552 3553 /* ------- symbolic factorization, can be reused ---------*/ 3554 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 3555 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 3556 adiag=a->diag; 3557 3558 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 3559 3560 /* bdiag is location of diagonal in factor */ 3561 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 3562 bdiag_rev = bdiag + n+1; 3563 3564 /* allocate row pointers bi */ 3565 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 3566 3567 /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */ 3568 if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */ 3569 nnz_max = ai[n]+2*n*dtcount+2; 3570 3571 ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 3572 ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr); 3573 3574 /* put together the new matrix */ 3575 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 3576 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 3577 b = (Mat_SeqAIJ*)(B)->data; 3578 b->free_a = PETSC_TRUE; 3579 b->free_ij = PETSC_TRUE; 3580 b->singlemalloc = PETSC_FALSE; 3581 b->a = ba; 3582 b->j = bj; 3583 b->i = bi; 3584 b->diag = bdiag; 3585 b->ilen = 0; 3586 b->imax = 0; 3587 b->row = isrow; 3588 b->col = iscol; 3589 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 3590 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 3591 b->icol = isicol; 3592 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3593 3594 ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3595 b->maxnz = nnz_max; 3596 3597 (B)->factor = MAT_FACTOR_ILUDT; 3598 (B)->info.factor_mallocs = 0; 3599 (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]); 3600 CHKMEMQ; 3601 /* ------- end of symbolic factorization ---------*/ 3602 3603 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3604 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3605 ics = ic; 3606 3607 /* linked list for storing column indices of the active row */ 3608 nlnk = n + 1; 3609 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3610 3611 /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */ 3612 ierr = PetscMalloc((2*n+1)*sizeof(PetscInt),&im);CHKERRQ(ierr); 3613 jtmp = im + n; 3614 /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */ 3615 ierr = PetscMalloc((2*n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 3616 ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr); 3617 vtmp = rtmp + n; 3618 3619 bi[0] = 0; 3620 bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */ 3621 bdiag_rev[n] = bdiag[0]; 3622 bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */ 3623 for (i=0; i<n; i++) { 3624 /* copy initial fill into linked list */ 3625 nzi = 0; /* nonzeros for active row i */ 3626 nzi = ai[r[i]+1] - ai[r[i]]; 3627 if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 3628 nzi_al = adiag[r[i]] - ai[r[i]]; 3629 nzi_au = ai[r[i]+1] - adiag[r[i]] -1; 3630 ajtmp = aj + ai[r[i]]; 3631 ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3632 3633 /* load in initial (unfactored row) */ 3634 aatmp = a->a + ai[r[i]]; 3635 for (j=0; j<nzi; j++) { 3636 rtmp[ics[*ajtmp++]] = *aatmp++; 3637 } 3638 3639 /* add pivot rows into linked list */ 3640 row = lnk[n]; 3641 while (row < i ) { 3642 nzi_bl = bi[row+1] - bi[row] + 1; 3643 bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */ 3644 ierr = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr); 3645 nzi += nlnk; 3646 row = lnk[row]; 3647 } 3648 3649 /* copy data from lnk into jtmp, then initialize lnk */ 3650 ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr); 3651 3652 /* numerical factorization */ 3653 bjtmp = jtmp; 3654 row = *bjtmp++; /* 1st pivot row */ 3655 while ( row < i ) { 3656 pc = rtmp + row; 3657 pv = ba + bdiag[row]; /* 1./(diag of the pivot row) */ 3658 multiplier = (*pc) * (*pv); 3659 *pc = multiplier; 3660 if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */ 3661 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3662 pv = ba + bdiag[row+1] + 1; 3663 /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */ 3664 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3665 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3666 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 3667 } 3668 row = *bjtmp++; 3669 } 3670 3671 /* copy sparse rtmp into contiguous vtmp; separate L and U part */ 3672 diag_tmp = rtmp[i]; /* save diagonal value - may not needed?? */ 3673 nzi_bl = 0; j = 0; 3674 while (jtmp[j] < i){ /* Note: jtmp is sorted */ 3675 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3676 nzi_bl++; j++; 3677 } 3678 nzi_bu = nzi - nzi_bl -1; 3679 while (j < nzi){ 3680 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3681 j++; 3682 } 3683 3684 bjtmp = bj + bi[i]; 3685 batmp = ba + bi[i]; 3686 /* apply level dropping rule to L part */ 3687 ncut = nzi_al + dtcount; 3688 if (ncut < nzi_bl){ 3689 ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr); 3690 ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr); 3691 } else { 3692 ncut = nzi_bl; 3693 } 3694 for (j=0; j<ncut; j++){ 3695 bjtmp[j] = jtmp[j]; 3696 batmp[j] = vtmp[j]; 3697 /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */ 3698 } 3699 bi[i+1] = bi[i] + ncut; 3700 nzi = ncut + 1; 3701 3702 /* apply level dropping rule to U part */ 3703 ncut = nzi_au + dtcount; 3704 if (ncut < nzi_bu){ 3705 ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr); 3706 ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr); 3707 } else { 3708 ncut = nzi_bu; 3709 } 3710 nzi += ncut; 3711 3712 /* mark bdiagonal */ 3713 bdiag[i+1] = bdiag[i] - (ncut + 1); 3714 bdiag_rev[n-i-1] = bdiag[i+1]; 3715 bi[2*n - i] = bi[2*n - i +1] - (ncut + 1); 3716 bjtmp = bj + bdiag[i]; 3717 batmp = ba + bdiag[i]; 3718 *bjtmp = i; 3719 *batmp = diag_tmp; /* rtmp[i]; */ 3720 if (*batmp == 0.0) { 3721 *batmp = dt+shift; 3722 /* printf(" row %d add shift %g\n",i,shift); */ 3723 } 3724 *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */ 3725 /* printf(" (%d,%g),",*bjtmp,*batmp); */ 3726 3727 bjtmp = bj + bdiag[i+1]+1; 3728 batmp = ba + bdiag[i+1]+1; 3729 for (k=0; k<ncut; k++){ 3730 bjtmp[k] = jtmp[nzi_bl+1+k]; 3731 batmp[k] = vtmp[nzi_bl+1+k]; 3732 /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */ 3733 } 3734 /* printf("\n"); */ 3735 3736 im[i] = nzi; /* used by PetscLLAddSortedLU() */ 3737 /* 3738 printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]); 3739 printf(" ----------------------------\n"); 3740 */ 3741 } /* for (i=0; i<n; i++) */ 3742 /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */ 3743 if (bi[n] >= bdiag[n]) SETERRQ2(PETSC_ERR_ARG_SIZ,"end of L array %d cannot >= the beginning of U array %d",bi[n],bdiag[n]); 3744 3745 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3746 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3747 3748 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3749 ierr = PetscFree(im);CHKERRQ(ierr); 3750 ierr = PetscFree(rtmp);CHKERRQ(ierr); 3751 3752 ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr); 3753 b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n]; 3754 3755 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3756 ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr); 3757 both_identity = (PetscTruth) (row_identity && icol_identity); 3758 if (row_identity && icol_identity) { 3759 B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct; 3760 } else { 3761 B->ops->solve = MatSolve_SeqAIJ_newdatastruct; 3762 } 3763 3764 B->ops->lufactorsymbolic = MatILUDTFactorSymbolic_SeqAIJ; 3765 B->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ; 3766 B->ops->solveadd = 0; 3767 B->ops->solvetranspose = 0; 3768 B->ops->solvetransposeadd = 0; 3769 B->ops->matsolve = 0; 3770 B->assembled = PETSC_TRUE; 3771 B->preallocated = PETSC_TRUE; 3772 PetscFunctionReturn(0); 3773 } 3774 3775 /* a wraper of MatILUDTFactor_SeqAIJ() */ 3776 #undef __FUNCT__ 3777 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ" 3778 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info) 3779 { 3780 PetscErrorCode ierr; 3781 3782 PetscFunctionBegin; 3783 ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr); 3784 3785 fact->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ; 3786 PetscFunctionReturn(0); 3787 } 3788 3789 /* 3790 same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors 3791 - intend to replace existing MatLUFactorNumeric_SeqAIJ() 3792 */ 3793 #undef __FUNCT__ 3794 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ" 3795 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info) 3796 { 3797 Mat C=fact; 3798 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 3799 IS isrow = b->row,isicol = b->icol; 3800 PetscErrorCode ierr; 3801 const PetscInt *r,*ic,*ics; 3802 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 3803 PetscInt *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj; 3804 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 3805 PetscReal dt=info->dt,shift=info->shiftinblocks; 3806 PetscTruth row_identity, col_identity; 3807 3808 PetscFunctionBegin; 3809 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3810 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3811 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 3812 ics = ic; 3813 3814 for (i=0; i<n; i++){ 3815 /* initialize rtmp array */ 3816 nzl = bi[i+1] - bi[i]; /* num of nozeros in L(i,:) */ 3817 bjtmp = bj + bi[i]; 3818 for (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0; 3819 rtmp[i] = 0.0; 3820 nzu = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */ 3821 bjtmp = bj + bdiag[i+1] + 1; 3822 for (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0; 3823 3824 /* load in initial unfactored row of A */ 3825 /* printf("row %d\n",i); */ 3826 nz = ai[r[i]+1] - ai[r[i]]; 3827 ajtmp = aj + ai[r[i]]; 3828 v = aa + ai[r[i]]; 3829 for (j=0; j<nz; j++) { 3830 rtmp[ics[*ajtmp++]] = v[j]; 3831 /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */ 3832 } 3833 /* printf("\n"); */ 3834 3835 /* numerical factorization */ 3836 bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */ 3837 nzl = bi[i+1] - bi[i]; /* num of entries in L(i,:) */ 3838 k = 0; 3839 while (k < nzl){ 3840 row = *bjtmp++; 3841 /* printf(" prow %d\n",row); */ 3842 pc = rtmp + row; 3843 pv = b->a + bdiag[row]; /* 1./(diag of the pivot row) */ 3844 multiplier = (*pc) * (*pv); 3845 *pc = multiplier; 3846 if (PetscAbsScalar(multiplier) > dt){ 3847 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3848 pv = b->a + bdiag[row+1] + 1; 3849 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3850 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3851 /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */ 3852 } 3853 k++; 3854 } 3855 3856 /* finished row so stick it into b->a */ 3857 /* L-part */ 3858 pv = b->a + bi[i] ; 3859 pj = bj + bi[i] ; 3860 nzl = bi[i+1] - bi[i]; 3861 for (j=0; j<nzl; j++) { 3862 pv[j] = rtmp[pj[j]]; 3863 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3864 } 3865 3866 /* diagonal: invert diagonal entries for simplier triangular solves */ 3867 if (rtmp[i] == 0.0) rtmp[i] = dt+shift; 3868 b->a[bdiag[i]] = 1.0/rtmp[i]; 3869 /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */ 3870 3871 /* U-part */ 3872 pv = b->a + bdiag[i+1] + 1; 3873 pj = bj + bdiag[i+1] + 1; 3874 nzu = bdiag[i] - bdiag[i+1] - 1; 3875 for (j=0; j<nzu; j++) { 3876 pv[j] = rtmp[pj[j]]; 3877 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3878 } 3879 /* printf("\n"); */ 3880 } 3881 3882 ierr = PetscFree(rtmp);CHKERRQ(ierr); 3883 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3884 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3885 3886 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3887 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 3888 if (row_identity && col_identity) { 3889 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct; 3890 } else { 3891 C->ops->solve = MatSolve_SeqAIJ_newdatastruct; 3892 } 3893 C->ops->solveadd = 0; 3894 C->ops->solvetranspose = 0; 3895 C->ops->solvetransposeadd = 0; 3896 C->ops->matsolve = 0; 3897 C->assembled = PETSC_TRUE; 3898 C->preallocated = PETSC_TRUE; 3899 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 3900 PetscFunctionReturn(0); 3901 } 3902