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 = PetscMemzero(done,n*sizeof(PetscTruth));CHKERRQ(ierr); 42 ierr = PetscMalloc(n*sizeof(PetscInt),&order);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; 149 150 PetscFunctionBegin; 151 ierr = PetscOptionsGetTruth(PETSC_NULL,"-lu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 152 if(newdatastruct){ 153 ierr = MatLUFactorSymbolic_SeqAIJ_newdatastruct(B,A,isrow,iscol,info);CHKERRQ(ierr); 154 PetscFunctionReturn(0); 155 } 156 157 158 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square"); 159 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 160 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 161 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 162 163 /* get new row pointers */ 164 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 165 bi[0] = 0; 166 167 /* bdiag is location of diagonal in factor */ 168 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 169 bdiag[0] = 0; 170 171 /* linked list for storing column indices of the active row */ 172 nlnk = n + 1; 173 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 174 175 ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr); 176 177 /* initial FreeSpace size is f*(ai[n]+1) */ 178 f = info->fill; 179 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 180 current_space = free_space; 181 182 for (i=0; i<n; i++) { 183 /* copy previous fill into linked list */ 184 nzi = 0; 185 nnz = ai[r[i]+1] - ai[r[i]]; 186 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 187 ajtmp = aj + ai[r[i]]; 188 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 189 nzi += nlnk; 190 191 /* add pivot rows into linked list */ 192 row = lnk[n]; 193 while (row < i) { 194 nzbd = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */ 195 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 196 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 197 nzi += nlnk; 198 row = lnk[row]; 199 } 200 bi[i+1] = bi[i] + nzi; 201 im[i] = nzi; 202 203 /* mark bdiag */ 204 nzbd = 0; 205 nnz = nzi; 206 k = lnk[n]; 207 while (nnz-- && k < i){ 208 nzbd++; 209 k = lnk[k]; 210 } 211 bdiag[i] = bi[i] + nzbd; 212 213 /* if free space is not available, make more free space */ 214 if (current_space->local_remaining<nzi) { 215 nnz = (n - i)*nzi; /* estimated and max additional space needed */ 216 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 217 reallocs++; 218 } 219 220 /* copy data into free space, then initialize lnk */ 221 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 222 bi_ptr[i] = current_space->array; 223 current_space->array += nzi; 224 current_space->local_used += nzi; 225 current_space->local_remaining -= nzi; 226 } 227 #if defined(PETSC_USE_INFO) 228 if (ai[n] != 0) { 229 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 230 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 231 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 232 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr); 233 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 234 } else { 235 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 236 } 237 #endif 238 239 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 240 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 241 242 /* destroy list of free space and other temporary array(s) */ 243 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 244 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); 245 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 246 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 247 248 /* put together the new matrix */ 249 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 250 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 251 b = (Mat_SeqAIJ*)(B)->data; 252 b->free_a = PETSC_TRUE; 253 b->free_ij = PETSC_TRUE; 254 b->singlemalloc = PETSC_FALSE; 255 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 256 b->j = bj; 257 b->i = bi; 258 b->diag = bdiag; 259 b->ilen = 0; 260 b->imax = 0; 261 b->row = isrow; 262 b->col = iscol; 263 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 264 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 265 b->icol = isicol; 266 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 267 268 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 269 ierr = PetscLogObjectMemory(B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 270 b->maxnz = b->nz = bi[n] ; 271 272 (B)->factor = MAT_FACTOR_LU; 273 (B)->info.factor_mallocs = reallocs; 274 (B)->info.fill_ratio_given = f; 275 276 if (ai[n]) { 277 (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 278 } else { 279 (B)->info.fill_ratio_needed = 0.0; 280 } 281 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 282 (B)->ops->solve = MatSolve_SeqAIJ; 283 (B)->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 284 /* switch to inodes if appropriate */ 285 ierr = MatLUFactorSymbolic_SeqAIJ_Inode(B,A,isrow,iscol,info);CHKERRQ(ierr); 286 PetscFunctionReturn(0); 287 } 288 289 #undef __FUNCT__ 290 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ_newdatastruct" 291 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_newdatastruct(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 292 { 293 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 294 IS isicol; 295 PetscErrorCode ierr; 296 const PetscInt *r,*ic; 297 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 298 PetscInt *bi,*bj,*ajtmp; 299 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 300 PetscReal f; 301 PetscInt nlnk,*lnk,k,**bi_ptr; 302 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 303 PetscBT lnkbt; 304 305 PetscFunctionBegin; 306 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square"); 307 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 308 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 309 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 310 311 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 312 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 313 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 314 bi[0] = bdiag[0] = 0; 315 316 /* linked list for storing column indices of the active row */ 317 nlnk = n + 1; 318 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 319 320 ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr); 321 322 /* initial FreeSpace size is f*(ai[n]+1) */ 323 f = info->fill; 324 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 325 current_space = free_space; 326 327 for (i=0; i<n; i++) { 328 /* copy previous fill into linked list */ 329 nzi = 0; 330 nnz = ai[r[i]+1] - ai[r[i]]; 331 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 332 ajtmp = aj + ai[r[i]]; 333 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 334 nzi += nlnk; 335 336 /* add pivot rows into linked list */ 337 row = lnk[n]; 338 while (row < i){ 339 nzbd = bdiag[row] + 1; /* num of entries in the row with column index <= row */ 340 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 341 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 342 nzi += nlnk; 343 row = lnk[row]; 344 } 345 bi[i+1] = bi[i] + nzi; 346 im[i] = nzi; 347 348 /* mark bdiag */ 349 nzbd = 0; 350 nnz = nzi; 351 k = lnk[n]; 352 while (nnz-- && k < i){ 353 nzbd++; 354 k = lnk[k]; 355 } 356 bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */ 357 358 /* if free space is not available, make more free space */ 359 if (current_space->local_remaining<nzi) { 360 nnz = 2*(n - i)*nzi; /* estimated and max additional space needed */ 361 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 362 reallocs++; 363 } 364 365 /* copy data into free space, then initialize lnk */ 366 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 367 bi_ptr[i] = current_space->array; 368 current_space->array += nzi; 369 current_space->local_used += nzi; 370 current_space->local_remaining -= nzi; 371 } 372 #if defined(PETSC_USE_INFO) 373 if (ai[n] != 0) { 374 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 375 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 376 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 377 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr); 378 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 379 } else { 380 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 381 } 382 #endif 383 384 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 385 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 386 387 /* destroy list of free space and other temporary array(s) */ 388 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 389 ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 390 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 391 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 392 393 /* put together the new matrix */ 394 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 395 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 396 b = (Mat_SeqAIJ*)(B)->data; 397 b->free_a = PETSC_TRUE; 398 b->free_ij = PETSC_TRUE; 399 b->singlemalloc = PETSC_FALSE; 400 ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 401 b->j = bj; 402 b->i = bi; 403 b->diag = bdiag; 404 b->ilen = 0; 405 b->imax = 0; 406 b->row = isrow; 407 b->col = iscol; 408 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 409 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 410 b->icol = isicol; 411 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 412 413 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 414 ierr = PetscLogObjectMemory(B,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 415 b->maxnz = b->nz = bdiag[0]+1; 416 (B)->factor = MAT_FACTOR_LU; 417 (B)->info.factor_mallocs = reallocs; 418 (B)->info.fill_ratio_given = f; 419 420 if (ai[n]) { 421 (B)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 422 } else { 423 (B)->info.fill_ratio_needed = 0.0; 424 } 425 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 426 PetscFunctionReturn(0); 427 } 428 429 /* 430 Trouble in factorization, should we dump the original matrix? 431 */ 432 #undef __FUNCT__ 433 #define __FUNCT__ "MatFactorDumpMatrix" 434 PetscErrorCode MatFactorDumpMatrix(Mat A) 435 { 436 PetscErrorCode ierr; 437 PetscTruth flg = PETSC_FALSE; 438 439 PetscFunctionBegin; 440 ierr = PetscOptionsGetTruth(PETSC_NULL,"-mat_factor_dump_on_error",&flg,PETSC_NULL);CHKERRQ(ierr); 441 if (flg) { 442 PetscViewer viewer; 443 char filename[PETSC_MAX_PATH_LEN]; 444 445 ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr); 446 ierr = PetscViewerBinaryOpen(((PetscObject)A)->comm,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr); 447 ierr = MatView(A,viewer);CHKERRQ(ierr); 448 ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr); 449 } 450 PetscFunctionReturn(0); 451 } 452 453 extern PetscErrorCode MatSolve_SeqAIJ_Inode(Mat,Vec,Vec); 454 455 #undef __FUNCT__ 456 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_newdatastruct" 457 PetscErrorCode MatLUFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info) 458 { 459 Mat C=B; 460 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 461 IS isrow = b->row,isicol = b->icol; 462 PetscErrorCode ierr; 463 const PetscInt *r,*ic,*ics; 464 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 465 PetscInt *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj; 466 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 467 PetscTruth row_identity,col_identity; 468 469 LUShift_Ctx sctx; 470 PetscInt *ddiag,newshift; 471 PetscReal rs; 472 MatScalar d; 473 474 PetscFunctionBegin; 475 /* MatPivotSetUp(): initialize shift context sctx */ 476 ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr); 477 478 /* if both shift schemes are chosen by user, only use info->shiftpd */ 479 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 480 ddiag = a->diag; 481 sctx.shift_top = info->zeropivot; 482 for (i=0; i<n; i++) { 483 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 484 d = (aa)[ddiag[i]]; 485 rs = -PetscAbsScalar(d) - PetscRealPart(d); 486 v = aa+ai[i]; 487 nz = ai[i+1] - ai[i]; 488 for (j=0; j<nz; j++) 489 rs += PetscAbsScalar(v[j]); 490 if (rs>sctx.shift_top) sctx.shift_top = rs; 491 } 492 sctx.shift_top *= 1.1; 493 sctx.nshift_max = 5; 494 sctx.shift_lo = 0.; 495 sctx.shift_hi = 1.; 496 } 497 498 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 499 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 500 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 501 ics = ic; 502 503 do { 504 sctx.lushift = PETSC_FALSE; 505 for (i=0; i<n; i++){ 506 /* zero rtmp */ 507 /* L part */ 508 nz = bi[i+1] - bi[i]; 509 bjtmp = bj + bi[i]; 510 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 511 512 /* U part */ 513 nz = bdiag[i]-bdiag[i+1]; 514 bjtmp = bj + bdiag[i+1]+1; 515 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 516 517 /* load in initial (unfactored row) */ 518 nz = ai[r[i]+1] - ai[r[i]]; 519 ajtmp = aj + ai[r[i]]; 520 v = aa + ai[r[i]]; 521 for (j=0; j<nz; j++) { 522 rtmp[ics[ajtmp[j]]] = v[j]; 523 } 524 /* ZeropivotApply() */ 525 rtmp[i] += sctx.shift_amount; /* shift the diagonal of the matrix */ 526 527 /* elimination */ 528 bjtmp = bj + bi[i]; 529 row = *bjtmp++; 530 nzL = bi[i+1] - bi[i]; 531 for(k=0; k < nzL;k++) { 532 pc = rtmp + row; 533 if (*pc != 0.0) { 534 pv = b->a + bdiag[row]; 535 multiplier = *pc * (*pv); 536 *pc = multiplier; 537 pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */ 538 pv = b->a + bdiag[row+1]+1; 539 nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */ 540 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 541 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 542 } 543 row = *bjtmp++; 544 } 545 546 /* finished row so stick it into b->a */ 547 rs = 0.0; 548 /* L part */ 549 pv = b->a + bi[i] ; 550 pj = b->j + bi[i] ; 551 nz = bi[i+1] - bi[i]; 552 for (j=0; j<nz; j++) { 553 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 554 } 555 556 /* U part */ 557 pv = b->a + bdiag[i+1]+1; 558 pj = b->j + bdiag[i+1]+1; 559 nz = bdiag[i] - bdiag[i+1]-1; 560 for (j=0; j<nz; j++) { 561 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 562 } 563 564 /* MatPivotCheck() */ 565 sctx.rs = rs; 566 sctx.pv = rtmp[i]; 567 /* ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); */ 568 if (info->shiftnz){ 569 ierr = MatPivotCheck_nz(info,sctx,i,newshift);CHKERRQ(ierr); 570 } else if (info->shiftpd){ 571 ierr = MatPivotCheck_pd(info,sctx,i,newshift);CHKERRQ(ierr); 572 } else if (info->shiftinblocks){ 573 ierr = MatPivotCheck_inblocks(info,sctx,i,newshift);CHKERRQ(ierr); 574 } else { 575 ierr = MatPivotCheck_none(info,sctx,i,newshift);CHKERRQ(ierr); 576 } 577 rtmp[i] = sctx.pv; 578 if (newshift == 1) break; 579 580 /* Mark diagonal and invert diagonal for simplier triangular solves */ 581 pv = b->a + bdiag[i]; 582 *pv = 1.0/rtmp[i]; 583 584 } /* endof for (i=0; i<n; i++){ */ 585 586 /* MatPivotRefine() */ 587 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max){ 588 /* 589 * if no shift in this attempt & shifting & started shifting & can refine, 590 * then try lower shift 591 */ 592 sctx.shift_hi = sctx.shift_fraction; 593 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 594 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 595 sctx.lushift = PETSC_TRUE; 596 sctx.nshift++; 597 } 598 } while (sctx.lushift); 599 600 ierr = PetscFree(rtmp);CHKERRQ(ierr); 601 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 602 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 603 604 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 605 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 606 if (row_identity && col_identity) { 607 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct_v2; 608 } else { 609 C->ops->solve = MatSolve_SeqAIJ_newdatastruct_v2; 610 } 611 612 C->ops->solveadd = 0; 613 C->ops->solvetranspose = 0; 614 C->ops->solvetransposeadd = 0; 615 C->ops->matsolve = 0; 616 C->assembled = PETSC_TRUE; 617 C->preallocated = PETSC_TRUE; 618 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 619 620 /* MatPivotView() */ 621 if (sctx.nshift){ 622 if (info->shiftpd) { 623 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); 624 } else if (info->shiftnz) { 625 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 626 } else if (info->shiftinblocks){ 627 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr); 628 } 629 } 630 PetscFunctionReturn(0); 631 } 632 633 #undef __FUNCT__ 634 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ" 635 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 636 { 637 Mat C=B; 638 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 639 IS isrow = b->row,isicol = b->icol; 640 PetscErrorCode ierr; 641 const PetscInt *r,*ic,*ics; 642 PetscInt nz,row,i,j,n=A->rmap->n,diag; 643 const PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 644 const PetscInt *ajtmp,*bjtmp,*diag_offset = b->diag,*pj; 645 MatScalar *pv,*rtmp,*pc,multiplier,d; 646 const MatScalar *v,*aa=a->a; 647 PetscReal rs=0.0; 648 LUShift_Ctx sctx; 649 PetscInt newshift,*ddiag; 650 651 PetscFunctionBegin; 652 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 653 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 654 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 655 ics = ic; 656 657 /* initialize shift context sctx */ 658 sctx.nshift = 0; 659 sctx.nshift_max = 0; 660 sctx.shift_top = 0.0; 661 sctx.shift_lo = 0.0; 662 sctx.shift_hi = 0.0; 663 sctx.shift_fraction = 0.0; 664 sctx.shift_amount = 0.0; 665 666 /* if both shift schemes are chosen by user, only use info->shiftpd */ 667 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 668 ddiag = a->diag; 669 sctx.shift_top = info->zeropivot; 670 for (i=0; i<n; i++) { 671 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 672 d = (aa)[ddiag[i]]; 673 rs = -PetscAbsScalar(d) - PetscRealPart(d); 674 v = aa+ai[i]; 675 nz = ai[i+1] - ai[i]; 676 for (j=0; j<nz; j++) 677 rs += PetscAbsScalar(v[j]); 678 if (rs>sctx.shift_top) sctx.shift_top = rs; 679 } 680 sctx.shift_top *= 1.1; 681 sctx.nshift_max = 5; 682 sctx.shift_lo = 0.; 683 sctx.shift_hi = 1.; 684 } 685 686 do { 687 sctx.lushift = PETSC_FALSE; 688 for (i=0; i<n; i++){ 689 nz = bi[i+1] - bi[i]; 690 bjtmp = bj + bi[i]; 691 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 692 693 /* load in initial (unfactored row) */ 694 nz = ai[r[i]+1] - ai[r[i]]; 695 ajtmp = aj + ai[r[i]]; 696 v = aa + ai[r[i]]; 697 for (j=0; j<nz; j++) { 698 rtmp[ics[ajtmp[j]]] = v[j]; 699 } 700 rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 701 /* if (sctx.shift_amount > 0.0) printf("row %d, shift %g\n",i,sctx.shift_amount); */ 702 703 row = *bjtmp++; 704 while (row < i) { 705 pc = rtmp + row; 706 if (*pc != 0.0) { 707 pv = b->a + diag_offset[row]; 708 pj = b->j + diag_offset[row] + 1; 709 multiplier = *pc / *pv++; 710 *pc = multiplier; 711 nz = bi[row+1] - diag_offset[row] - 1; 712 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 713 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 714 } 715 row = *bjtmp++; 716 } 717 /* finished row so stick it into b->a */ 718 pv = b->a + bi[i] ; 719 pj = b->j + bi[i] ; 720 nz = bi[i+1] - bi[i]; 721 diag = diag_offset[i] - bi[i]; 722 rs = 0.0; 723 for (j=0; j<nz; j++) { 724 pv[j] = rtmp[pj[j]]; 725 rs += PetscAbsScalar(pv[j]); 726 } 727 rs -= PetscAbsScalar(pv[diag]); 728 729 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 730 sctx.rs = rs; 731 sctx.pv = pv[diag]; 732 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 733 if (newshift == 1) break; 734 } 735 736 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 737 /* 738 * if no shift in this attempt & shifting & started shifting & can refine, 739 * then try lower shift 740 */ 741 sctx.shift_hi = sctx.shift_fraction; 742 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 743 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 744 sctx.lushift = PETSC_TRUE; 745 sctx.nshift++; 746 } 747 } while (sctx.lushift); 748 749 /* invert diagonal entries for simplier triangular solves */ 750 for (i=0; i<n; i++) { 751 b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]]; 752 } 753 ierr = PetscFree(rtmp);CHKERRQ(ierr); 754 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 755 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 756 if (b->inode.use) { 757 C->ops->solve = MatSolve_SeqAIJ_Inode; 758 } else { 759 PetscTruth row_identity, col_identity; 760 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 761 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 762 if (row_identity && col_identity) { 763 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 764 } else { 765 C->ops->solve = MatSolve_SeqAIJ; 766 } 767 } 768 C->ops->solveadd = MatSolveAdd_SeqAIJ; 769 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 770 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 771 C->ops->matsolve = MatMatSolve_SeqAIJ; 772 C->assembled = PETSC_TRUE; 773 C->preallocated = PETSC_TRUE; 774 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 775 if (sctx.nshift){ 776 if (info->shiftpd) { 777 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); 778 } else if (info->shiftnz) { 779 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 780 } 781 } 782 PetscFunctionReturn(0); 783 } 784 785 /* 786 This routine implements inplace ILU(0) with row or/and column permutations. 787 Input: 788 A - original matrix 789 Output; 790 A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i] 791 a->j (col index) is permuted by the inverse of colperm, then sorted 792 a->a reordered accordingly with a->j 793 a->diag (ptr to diagonal elements) is updated. 794 */ 795 #undef __FUNCT__ 796 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm" 797 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info) 798 { 799 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 800 IS isrow = a->row,isicol = a->icol; 801 PetscErrorCode ierr; 802 const PetscInt *r,*ic,*ics; 803 PetscInt i,j,n=A->rmap->n,*ai=a->i,*aj=a->j; 804 PetscInt *ajtmp,nz,row; 805 PetscInt *diag = a->diag,nbdiag,*pj; 806 PetscScalar *rtmp,*pc,multiplier,d; 807 MatScalar *v,*pv; 808 PetscReal rs; 809 LUShift_Ctx sctx; 810 PetscInt newshift; 811 812 PetscFunctionBegin; 813 if (A != B) SETERRQ(PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address"); 814 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 815 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 816 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr); 817 ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr); 818 ics = ic; 819 820 sctx.shift_top = 0; 821 sctx.nshift_max = 0; 822 sctx.shift_lo = 0; 823 sctx.shift_hi = 0; 824 sctx.shift_fraction = 0; 825 826 /* if both shift schemes are chosen by user, only use info->shiftpd */ 827 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 828 sctx.shift_top = 0; 829 for (i=0; i<n; i++) { 830 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 831 d = (a->a)[diag[i]]; 832 rs = -PetscAbsScalar(d) - PetscRealPart(d); 833 v = a->a+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 if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot; 840 sctx.shift_top *= 1.1; 841 sctx.nshift_max = 5; 842 sctx.shift_lo = 0.; 843 sctx.shift_hi = 1.; 844 } 845 846 sctx.shift_amount = 0; 847 sctx.nshift = 0; 848 do { 849 sctx.lushift = PETSC_FALSE; 850 for (i=0; i<n; i++){ 851 /* load in initial unfactored row */ 852 nz = ai[r[i]+1] - ai[r[i]]; 853 ajtmp = aj + ai[r[i]]; 854 v = a->a + ai[r[i]]; 855 /* sort permuted ajtmp and values v accordingly */ 856 for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]]; 857 ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr); 858 859 diag[r[i]] = ai[r[i]]; 860 for (j=0; j<nz; j++) { 861 rtmp[ajtmp[j]] = v[j]; 862 if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */ 863 } 864 rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 865 866 row = *ajtmp++; 867 while (row < i) { 868 pc = rtmp + row; 869 if (*pc != 0.0) { 870 pv = a->a + diag[r[row]]; 871 pj = aj + diag[r[row]] + 1; 872 873 multiplier = *pc / *pv++; 874 *pc = multiplier; 875 nz = ai[r[row]+1] - diag[r[row]] - 1; 876 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 877 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 878 } 879 row = *ajtmp++; 880 } 881 /* finished row so overwrite it onto a->a */ 882 pv = a->a + ai[r[i]] ; 883 pj = aj + ai[r[i]] ; 884 nz = ai[r[i]+1] - ai[r[i]]; 885 nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */ 886 887 rs = 0.0; 888 for (j=0; j<nz; j++) { 889 pv[j] = rtmp[pj[j]]; 890 if (j != nbdiag) rs += PetscAbsScalar(pv[j]); 891 } 892 893 /* 9/13/02 Victor Eijkhout suggested scaling zeropivot by rs for matrices with funny scalings */ 894 sctx.rs = rs; 895 sctx.pv = pv[nbdiag]; 896 ierr = MatLUCheckShift_inline(info,sctx,i,newshift);CHKERRQ(ierr); 897 if (newshift == 1) break; 898 } 899 900 if (info->shiftpd && !sctx.lushift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 901 /* 902 * if no shift in this attempt & shifting & started shifting & can refine, 903 * then try lower shift 904 */ 905 sctx.shift_hi = sctx.shift_fraction; 906 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 907 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 908 sctx.lushift = PETSC_TRUE; 909 sctx.nshift++; 910 } 911 } while (sctx.lushift); 912 913 /* invert diagonal entries for simplier triangular solves */ 914 for (i=0; i<n; i++) { 915 a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]]; 916 } 917 918 ierr = PetscFree(rtmp);CHKERRQ(ierr); 919 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 920 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 921 A->ops->solve = MatSolve_SeqAIJ_InplaceWithPerm; 922 A->ops->solveadd = MatSolveAdd_SeqAIJ; 923 A->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 924 A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 925 A->assembled = PETSC_TRUE; 926 A->preallocated = PETSC_TRUE; 927 ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr); 928 if (sctx.nshift){ 929 if (info->shiftpd) { 930 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); 931 } else if (info->shiftnz) { 932 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 933 } 934 } 935 PetscFunctionReturn(0); 936 } 937 938 /* ----------------------------------------------------------- */ 939 #undef __FUNCT__ 940 #define __FUNCT__ "MatLUFactor_SeqAIJ" 941 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info) 942 { 943 PetscErrorCode ierr; 944 Mat C; 945 946 PetscFunctionBegin; 947 ierr = MatGetFactor(A,MAT_SOLVER_PETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr); 948 ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr); 949 ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr); 950 A->ops->solve = C->ops->solve; 951 A->ops->solvetranspose = C->ops->solvetranspose; 952 ierr = MatHeaderCopy(A,C);CHKERRQ(ierr); 953 ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr); 954 PetscFunctionReturn(0); 955 } 956 /* ----------------------------------------------------------- */ 957 958 959 #undef __FUNCT__ 960 #define __FUNCT__ "MatSolve_SeqAIJ" 961 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx) 962 { 963 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 964 IS iscol = a->col,isrow = a->row; 965 PetscErrorCode ierr; 966 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 967 PetscInt nz; 968 const PetscInt *rout,*cout,*r,*c; 969 PetscScalar *x,*tmp,*tmps,sum; 970 const PetscScalar *b; 971 const MatScalar *aa = a->a,*v; 972 973 PetscFunctionBegin; 974 if (!n) PetscFunctionReturn(0); 975 976 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 977 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 978 tmp = a->solve_work; 979 980 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 981 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 982 983 /* forward solve the lower triangular */ 984 tmp[0] = b[*r++]; 985 tmps = tmp; 986 for (i=1; i<n; i++) { 987 v = aa + ai[i] ; 988 vi = aj + ai[i] ; 989 nz = a->diag[i] - ai[i]; 990 sum = b[*r++]; 991 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 992 tmp[i] = sum; 993 } 994 995 /* backward solve the upper triangular */ 996 for (i=n-1; i>=0; i--){ 997 v = aa + a->diag[i] + 1; 998 vi = aj + a->diag[i] + 1; 999 nz = ai[i+1] - a->diag[i] - 1; 1000 sum = tmp[i]; 1001 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1002 x[*c--] = tmp[i] = sum*aa[a->diag[i]]; 1003 } 1004 1005 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1006 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1007 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1008 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1009 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1010 PetscFunctionReturn(0); 1011 } 1012 1013 #undef __FUNCT__ 1014 #define __FUNCT__ "MatMatSolve_SeqAIJ" 1015 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X) 1016 { 1017 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1018 IS iscol = a->col,isrow = a->row; 1019 PetscErrorCode ierr; 1020 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1021 PetscInt nz,neq; 1022 const PetscInt *rout,*cout,*r,*c; 1023 PetscScalar *x,*b,*tmp,*tmps,sum; 1024 const MatScalar *aa = a->a,*v; 1025 PetscTruth bisdense,xisdense; 1026 1027 PetscFunctionBegin; 1028 if (!n) PetscFunctionReturn(0); 1029 1030 ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 1031 if (!bisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1032 ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 1033 if (!xisdense) SETERRQ(PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1034 1035 ierr = MatGetArray(B,&b);CHKERRQ(ierr); 1036 ierr = MatGetArray(X,&x);CHKERRQ(ierr); 1037 1038 tmp = a->solve_work; 1039 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1040 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1041 1042 for (neq=0; neq<B->cmap->n; neq++){ 1043 /* forward solve the lower triangular */ 1044 tmp[0] = b[r[0]]; 1045 tmps = tmp; 1046 for (i=1; i<n; i++) { 1047 v = aa + ai[i] ; 1048 vi = aj + ai[i] ; 1049 nz = a->diag[i] - ai[i]; 1050 sum = b[r[i]]; 1051 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1052 tmp[i] = sum; 1053 } 1054 /* backward solve the upper triangular */ 1055 for (i=n-1; i>=0; i--){ 1056 v = aa + a->diag[i] + 1; 1057 vi = aj + a->diag[i] + 1; 1058 nz = ai[i+1] - a->diag[i] - 1; 1059 sum = tmp[i]; 1060 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1061 x[c[i]] = tmp[i] = sum*aa[a->diag[i]]; 1062 } 1063 1064 b += n; 1065 x += n; 1066 } 1067 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1068 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1069 ierr = MatRestoreArray(B,&b);CHKERRQ(ierr); 1070 ierr = MatRestoreArray(X,&x);CHKERRQ(ierr); 1071 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1072 PetscFunctionReturn(0); 1073 } 1074 1075 #undef __FUNCT__ 1076 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm" 1077 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx) 1078 { 1079 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1080 IS iscol = a->col,isrow = a->row; 1081 PetscErrorCode ierr; 1082 const PetscInt *r,*c,*rout,*cout; 1083 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1084 PetscInt nz,row; 1085 PetscScalar *x,*b,*tmp,*tmps,sum; 1086 const MatScalar *aa = a->a,*v; 1087 1088 PetscFunctionBegin; 1089 if (!n) PetscFunctionReturn(0); 1090 1091 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1092 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1093 tmp = a->solve_work; 1094 1095 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1096 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1097 1098 /* forward solve the lower triangular */ 1099 tmp[0] = b[*r++]; 1100 tmps = tmp; 1101 for (row=1; row<n; row++) { 1102 i = rout[row]; /* permuted row */ 1103 v = aa + ai[i] ; 1104 vi = aj + ai[i] ; 1105 nz = a->diag[i] - ai[i]; 1106 sum = b[*r++]; 1107 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1108 tmp[row] = sum; 1109 } 1110 1111 /* backward solve the upper triangular */ 1112 for (row=n-1; row>=0; row--){ 1113 i = rout[row]; /* permuted row */ 1114 v = aa + a->diag[i] + 1; 1115 vi = aj + a->diag[i] + 1; 1116 nz = ai[i+1] - a->diag[i] - 1; 1117 sum = tmp[row]; 1118 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1119 x[*c--] = tmp[row] = sum*aa[a->diag[i]]; 1120 } 1121 1122 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1123 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1124 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1125 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1126 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1127 PetscFunctionReturn(0); 1128 } 1129 1130 /* ----------------------------------------------------------- */ 1131 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h" 1132 #undef __FUNCT__ 1133 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering" 1134 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx) 1135 { 1136 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1137 PetscErrorCode ierr; 1138 PetscInt n = A->rmap->n; 1139 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag; 1140 PetscScalar *x; 1141 const PetscScalar *b; 1142 const MatScalar *aa = a->a; 1143 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1144 PetscInt adiag_i,i,nz,ai_i; 1145 const PetscInt *vi; 1146 const MatScalar *v; 1147 PetscScalar sum; 1148 #endif 1149 1150 PetscFunctionBegin; 1151 if (!n) PetscFunctionReturn(0); 1152 1153 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1154 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1155 1156 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1157 fortransolveaij_(&n,x,ai,aj,adiag,aa,b); 1158 #else 1159 /* forward solve the lower triangular */ 1160 x[0] = b[0]; 1161 for (i=1; i<n; i++) { 1162 ai_i = ai[i]; 1163 v = aa + ai_i; 1164 vi = aj + ai_i; 1165 nz = adiag[i] - ai_i; 1166 sum = b[i]; 1167 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1168 x[i] = sum; 1169 } 1170 1171 /* backward solve the upper triangular */ 1172 for (i=n-1; i>=0; i--){ 1173 adiag_i = adiag[i]; 1174 v = aa + adiag_i + 1; 1175 vi = aj + adiag_i + 1; 1176 nz = ai[i+1] - adiag_i - 1; 1177 sum = x[i]; 1178 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1179 x[i] = sum*aa[adiag_i]; 1180 } 1181 #endif 1182 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1183 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1184 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1185 PetscFunctionReturn(0); 1186 } 1187 1188 #undef __FUNCT__ 1189 #define __FUNCT__ "MatSolveAdd_SeqAIJ" 1190 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx) 1191 { 1192 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1193 IS iscol = a->col,isrow = a->row; 1194 PetscErrorCode ierr; 1195 PetscInt i, n = A->rmap->n,j; 1196 PetscInt nz; 1197 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j; 1198 PetscScalar *x,*tmp,sum; 1199 const PetscScalar *b; 1200 const MatScalar *aa = a->a,*v; 1201 1202 PetscFunctionBegin; 1203 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1204 1205 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1206 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1207 tmp = a->solve_work; 1208 1209 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1210 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1211 1212 /* forward solve the lower triangular */ 1213 tmp[0] = b[*r++]; 1214 for (i=1; i<n; i++) { 1215 v = aa + ai[i] ; 1216 vi = aj + ai[i] ; 1217 nz = a->diag[i] - ai[i]; 1218 sum = b[*r++]; 1219 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1220 tmp[i] = sum; 1221 } 1222 1223 /* backward solve the upper triangular */ 1224 for (i=n-1; i>=0; i--){ 1225 v = aa + a->diag[i] + 1; 1226 vi = aj + a->diag[i] + 1; 1227 nz = ai[i+1] - a->diag[i] - 1; 1228 sum = tmp[i]; 1229 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1230 tmp[i] = sum*aa[a->diag[i]]; 1231 x[*c--] += tmp[i]; 1232 } 1233 1234 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1235 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1236 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1237 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1238 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1239 1240 PetscFunctionReturn(0); 1241 } 1242 1243 #undef __FUNCT__ 1244 #define __FUNCT__ "MatSolveTranspose_SeqAIJ" 1245 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx) 1246 { 1247 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1248 IS iscol = a->col,isrow = a->row; 1249 PetscErrorCode ierr; 1250 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1251 PetscInt i,n = A->rmap->n,j; 1252 PetscInt nz; 1253 PetscScalar *x,*tmp,s1; 1254 const MatScalar *aa = a->a,*v; 1255 const PetscScalar *b; 1256 1257 PetscFunctionBegin; 1258 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1259 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1260 tmp = a->solve_work; 1261 1262 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1263 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1264 1265 /* copy the b into temp work space according to permutation */ 1266 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1267 1268 /* forward solve the U^T */ 1269 for (i=0; i<n; i++) { 1270 v = aa + diag[i] ; 1271 vi = aj + diag[i] + 1; 1272 nz = ai[i+1] - diag[i] - 1; 1273 s1 = tmp[i]; 1274 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1275 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1276 tmp[i] = s1; 1277 } 1278 1279 /* backward solve the L^T */ 1280 for (i=n-1; i>=0; i--){ 1281 v = aa + diag[i] - 1 ; 1282 vi = aj + diag[i] - 1 ; 1283 nz = diag[i] - ai[i]; 1284 s1 = tmp[i]; 1285 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1286 } 1287 1288 /* copy tmp into x according to permutation */ 1289 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1290 1291 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1292 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1293 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1294 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1295 1296 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1297 PetscFunctionReturn(0); 1298 } 1299 1300 1301 #undef __FUNCT__ 1302 #define __FUNCT__ "MatSolveTranspose_SeqAIJ_newdatastruct_v2" 1303 PetscErrorCode MatSolveTranspose_SeqAIJ_newdatastruct_v2(Mat A,Vec bb,Vec xx) 1304 { 1305 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1306 IS iscol = a->col,isrow = a->row; 1307 PetscErrorCode ierr; 1308 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1309 PetscInt i,n = A->rmap->n,j; 1310 PetscInt nz; 1311 PetscScalar *x,*tmp,s1; 1312 const MatScalar *aa = a->a,*v; 1313 const PetscScalar *b; 1314 1315 PetscFunctionBegin; 1316 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1317 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1318 tmp = a->solve_work; 1319 1320 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1321 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1322 1323 /* copy the b into temp work space according to permutation */ 1324 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1325 1326 /* forward solve the U^T */ 1327 for (i=0; i<n; i++) { 1328 v = aa + adiag[i+1] + 1; 1329 vi = aj + adiag[i+1] + 1; 1330 nz = adiag[i] - adiag[i+1] - 1; 1331 s1 = tmp[i]; 1332 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1333 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1334 tmp[i] = s1; 1335 } 1336 1337 /* backward solve the L^T */ 1338 for (i=n-1; i>=0; i--){ 1339 v = aa + ai[i]; 1340 vi = aj + ai[i]; 1341 nz = ai[i+1] - ai[i]; 1342 s1 = tmp[i]; 1343 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1344 } 1345 1346 /* copy tmp into x according to permutation */ 1347 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 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 1354 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1355 PetscFunctionReturn(0); 1356 } 1357 1358 #undef __FUNCT__ 1359 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ" 1360 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx) 1361 { 1362 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1363 IS iscol = a->col,isrow = a->row; 1364 PetscErrorCode ierr; 1365 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1366 PetscInt i,n = A->rmap->n,j; 1367 PetscInt nz; 1368 PetscScalar *x,*tmp,s1; 1369 const MatScalar *aa = a->a,*v; 1370 const PetscScalar *b; 1371 1372 PetscFunctionBegin; 1373 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1374 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1375 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1376 tmp = a->solve_work; 1377 1378 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1379 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1380 1381 /* copy the b into temp work space according to permutation */ 1382 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1383 1384 /* forward solve the U^T */ 1385 for (i=0; i<n; i++) { 1386 v = aa + diag[i] ; 1387 vi = aj + diag[i] + 1; 1388 nz = ai[i+1] - diag[i] - 1; 1389 s1 = tmp[i]; 1390 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1391 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1392 tmp[i] = s1; 1393 } 1394 1395 /* backward solve the L^T */ 1396 for (i=n-1; i>=0; i--){ 1397 v = aa + diag[i] - 1 ; 1398 vi = aj + diag[i] - 1 ; 1399 nz = diag[i] - ai[i]; 1400 s1 = tmp[i]; 1401 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1402 } 1403 1404 /* copy tmp into x according to permutation */ 1405 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1406 1407 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1408 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1409 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 1410 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1411 1412 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1413 PetscFunctionReturn(0); 1414 } 1415 1416 /* ----------------------------------------------------------------*/ 1417 EXTERN PetscErrorCode Mat_CheckInode(Mat,PetscTruth); 1418 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth); 1419 1420 /* 1421 ilu() under revised new data structure. 1422 Factored arrays bj and ba are stored as 1423 L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:) 1424 1425 bi=fact->i is an array of size n+1, in which 1426 bi+ 1427 bi[i]: points to 1st entry of L(i,:),i=0,...,n-1 1428 bi[n]: points to L(n-1,n-1)+1 1429 1430 bdiag=fact->diag is an array of size n+1,in which 1431 bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1 1432 bdiag[n]: points to diagonal of U(n-1,0)-1 1433 1434 U(i,:) contains bdiag[i] as its last entry, i.e., 1435 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 1436 */ 1437 #undef __FUNCT__ 1438 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct" 1439 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1440 { 1441 1442 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1443 PetscErrorCode ierr; 1444 PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag; 1445 PetscInt i,j,nz,*bi,*bj,*bdiag,bi_temp; 1446 PetscTruth missing; 1447 IS isicol; 1448 1449 PetscFunctionBegin; 1450 /* printf("MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct ...\n"); */ 1451 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); 1452 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 1453 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 1454 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1455 1456 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr); 1457 b = (Mat_SeqAIJ*)(fact)->data; 1458 1459 /* allocate matrix arrays for new data structure */ 1460 ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr); 1461 ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1462 b->singlemalloc = PETSC_TRUE; 1463 if (!b->diag){ 1464 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr); 1465 ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1466 } 1467 bdiag = b->diag; 1468 1469 if (n > 0) { 1470 ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr); 1471 } 1472 1473 /* set bi and bj with new data structure */ 1474 bi = b->i; 1475 bj = b->j; 1476 1477 /* L part */ 1478 bi[0] = 0; 1479 for (i=0; i<n; i++){ 1480 nz = adiag[i] - ai[i]; 1481 bi[i+1] = bi[i] + nz; 1482 aj = a->j + ai[i]; 1483 for (j=0; j<nz; j++){ 1484 *bj = aj[j]; bj++; 1485 } 1486 } 1487 1488 /* U part */ 1489 bi_temp = bi[n]; 1490 bdiag[n] = bi[n]-1; 1491 for (i=n-1; i>=0; i--){ 1492 nz = ai[i+1] - adiag[i] - 1; 1493 bi_temp = bi_temp + nz + 1; 1494 aj = a->j + adiag[i] + 1; 1495 for (j=0; j<nz; j++){ 1496 *bj = aj[j]; bj++; 1497 } 1498 /* diag[i] */ 1499 *bj = i; bj++; 1500 bdiag[i] = bi_temp - 1; 1501 } 1502 1503 fact->factor = MAT_FACTOR_ILU; 1504 fact->info.factor_mallocs = 0; 1505 fact->info.fill_ratio_given = info->fill; 1506 fact->info.fill_ratio_needed = 1.0; 1507 fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 1508 1509 b = (Mat_SeqAIJ*)(fact)->data; 1510 b->row = isrow; 1511 b->col = iscol; 1512 b->icol = isicol; 1513 ierr = PetscMalloc((fact->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1514 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1515 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1516 PetscFunctionReturn(0); 1517 } 1518 1519 #undef __FUNCT__ 1520 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_newdatastruct" 1521 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1522 { 1523 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1524 IS isicol; 1525 PetscErrorCode ierr; 1526 const PetscInt *r,*ic; 1527 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j; 1528 PetscInt *bi,*cols,nnz,*cols_lvl; 1529 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1530 PetscInt i,levels,diagonal_fill; 1531 PetscTruth col_identity,row_identity; 1532 PetscReal f; 1533 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1534 PetscBT lnkbt; 1535 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1536 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1537 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1538 1539 PetscFunctionBegin; 1540 /* printf("MatILUFactorSymbolic_SeqAIJ_newdatastruct ...\n"); */ 1541 levels = (PetscInt)info->levels; 1542 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1543 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1544 1545 if (!levels && row_identity && col_identity) { 1546 /* special case: ilu(0) with natural ordering */ 1547 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1548 PetscFunctionReturn(0); 1549 } 1550 1551 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); 1552 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1553 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1554 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1555 1556 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1557 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1558 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1559 bi[0] = bdiag[0] = 0; 1560 1561 ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr); 1562 1563 /* create a linked list for storing column indices of the active row */ 1564 nlnk = n + 1; 1565 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1566 1567 /* initial FreeSpace size is f*(ai[n]+1) */ 1568 f = info->fill; 1569 diagonal_fill = (PetscInt)info->diagonal_fill; 1570 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1571 current_space = free_space; 1572 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1573 current_space_lvl = free_space_lvl; 1574 1575 for (i=0; i<n; i++) { 1576 nzi = 0; 1577 /* copy current row into linked list */ 1578 nnz = ai[r[i]+1] - ai[r[i]]; 1579 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1580 cols = aj + ai[r[i]]; 1581 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1582 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1583 nzi += nlnk; 1584 1585 /* make sure diagonal entry is included */ 1586 if (diagonal_fill && lnk[i] == -1) { 1587 fm = n; 1588 while (lnk[fm] < i) fm = lnk[fm]; 1589 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1590 lnk[fm] = i; 1591 lnk_lvl[i] = 0; 1592 nzi++; dcount++; 1593 } 1594 1595 /* add pivot rows into the active row */ 1596 nzbd = 0; 1597 prow = lnk[n]; 1598 while (prow < i) { 1599 nnz = bdiag[prow]; 1600 cols = bj_ptr[prow] + nnz + 1; 1601 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1602 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1603 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1604 nzi += nlnk; 1605 prow = lnk[prow]; 1606 nzbd++; 1607 } 1608 bdiag[i] = nzbd; 1609 bi[i+1] = bi[i] + nzi; 1610 1611 /* if free space is not available, make more free space */ 1612 if (current_space->local_remaining<nzi) { 1613 nnz = 2*nzi*(n - i); /* estimated and max additional space needed */ 1614 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1615 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1616 reallocs++; 1617 } 1618 1619 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1620 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1621 bj_ptr[i] = current_space->array; 1622 bjlvl_ptr[i] = current_space_lvl->array; 1623 1624 /* make sure the active row i has diagonal entry */ 1625 if (*(bj_ptr[i]+bdiag[i]) != i) { 1626 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1627 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1628 } 1629 1630 current_space->array += nzi; 1631 current_space->local_used += nzi; 1632 current_space->local_remaining -= nzi; 1633 current_space_lvl->array += nzi; 1634 current_space_lvl->local_used += nzi; 1635 current_space_lvl->local_remaining -= nzi; 1636 } 1637 1638 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1639 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1640 1641 /* destroy list of free space and other temporary arrays */ 1642 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1643 1644 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 1645 ierr = PetscFreeSpaceContiguous_LU_v2(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 1646 1647 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1648 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1649 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1650 1651 #if defined(PETSC_USE_INFO) 1652 { 1653 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1654 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1655 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1656 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1657 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1658 if (diagonal_fill) { 1659 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1660 } 1661 } 1662 #endif 1663 1664 /* put together the new matrix */ 1665 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1666 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1667 b = (Mat_SeqAIJ*)(fact)->data; 1668 b->free_a = PETSC_TRUE; 1669 b->free_ij = PETSC_TRUE; 1670 b->singlemalloc = PETSC_FALSE; 1671 ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1672 b->j = bj; 1673 b->i = bi; 1674 b->diag = bdiag; 1675 b->ilen = 0; 1676 b->imax = 0; 1677 b->row = isrow; 1678 b->col = iscol; 1679 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1680 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1681 b->icol = isicol; 1682 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1683 /* In b structure: Free imax, ilen, old a, old j. 1684 Allocate bdiag, solve_work, new a, new j */ 1685 ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1686 b->maxnz = b->nz = bdiag[0]+1; 1687 (fact)->info.factor_mallocs = reallocs; 1688 (fact)->info.fill_ratio_given = f; 1689 (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 1690 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_newdatastruct; 1691 /* ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); */ 1692 PetscFunctionReturn(0); 1693 } 1694 1695 #undef __FUNCT__ 1696 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ" 1697 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1698 { 1699 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1700 IS isicol; 1701 PetscErrorCode ierr; 1702 const PetscInt *r,*ic; 1703 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 1704 PetscInt *bi,*cols,nnz,*cols_lvl; 1705 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1706 PetscInt i,levels,diagonal_fill; 1707 PetscTruth col_identity,row_identity; 1708 PetscReal f; 1709 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1710 PetscBT lnkbt; 1711 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1712 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1713 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1714 PetscTruth missing; 1715 PetscTruth newdatastruct=PETSC_FALSE; 1716 1717 PetscFunctionBegin; 1718 ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 1719 if(newdatastruct){ 1720 ierr = MatILUFactorSymbolic_SeqAIJ_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1721 PetscFunctionReturn(0); 1722 } 1723 1724 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); 1725 f = info->fill; 1726 levels = (PetscInt)info->levels; 1727 diagonal_fill = (PetscInt)info->diagonal_fill; 1728 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1729 1730 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1731 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1732 if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */ 1733 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr); 1734 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1735 1736 fact->factor = MAT_FACTOR_ILU; 1737 (fact)->info.factor_mallocs = 0; 1738 (fact)->info.fill_ratio_given = info->fill; 1739 (fact)->info.fill_ratio_needed = 1.0; 1740 b = (Mat_SeqAIJ*)(fact)->data; 1741 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1742 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1743 b->row = isrow; 1744 b->col = iscol; 1745 b->icol = isicol; 1746 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1747 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1748 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1749 ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1750 PetscFunctionReturn(0); 1751 } 1752 1753 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1754 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1755 1756 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1757 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1758 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1759 bi[0] = bdiag[0] = 0; 1760 1761 ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr); 1762 1763 /* create a linked list for storing column indices of the active row */ 1764 nlnk = n + 1; 1765 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1766 1767 /* initial FreeSpace size is f*(ai[n]+1) */ 1768 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1769 current_space = free_space; 1770 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1771 current_space_lvl = free_space_lvl; 1772 1773 for (i=0; i<n; i++) { 1774 nzi = 0; 1775 /* copy current row into linked list */ 1776 nnz = ai[r[i]+1] - ai[r[i]]; 1777 if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1778 cols = aj + ai[r[i]]; 1779 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1780 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1781 nzi += nlnk; 1782 1783 /* make sure diagonal entry is included */ 1784 if (diagonal_fill && lnk[i] == -1) { 1785 fm = n; 1786 while (lnk[fm] < i) fm = lnk[fm]; 1787 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1788 lnk[fm] = i; 1789 lnk_lvl[i] = 0; 1790 nzi++; dcount++; 1791 } 1792 1793 /* add pivot rows into the active row */ 1794 nzbd = 0; 1795 prow = lnk[n]; 1796 while (prow < i) { 1797 nnz = bdiag[prow]; 1798 cols = bj_ptr[prow] + nnz + 1; 1799 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1800 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1801 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1802 nzi += nlnk; 1803 prow = lnk[prow]; 1804 nzbd++; 1805 } 1806 bdiag[i] = nzbd; 1807 bi[i+1] = bi[i] + nzi; 1808 1809 /* if free space is not available, make more free space */ 1810 if (current_space->local_remaining<nzi) { 1811 nnz = nzi*(n - i); /* estimated and max additional space needed */ 1812 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1813 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1814 reallocs++; 1815 } 1816 1817 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1818 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1819 bj_ptr[i] = current_space->array; 1820 bjlvl_ptr[i] = current_space_lvl->array; 1821 1822 /* make sure the active row i has diagonal entry */ 1823 if (*(bj_ptr[i]+bdiag[i]) != i) { 1824 SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\ 1825 try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1826 } 1827 1828 current_space->array += nzi; 1829 current_space->local_used += nzi; 1830 current_space->local_remaining -= nzi; 1831 current_space_lvl->array += nzi; 1832 current_space_lvl->local_used += nzi; 1833 current_space_lvl->local_remaining -= nzi; 1834 } 1835 1836 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1837 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1838 1839 /* destroy list of free space and other temporary arrays */ 1840 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1841 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */ 1842 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1843 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1844 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1845 1846 #if defined(PETSC_USE_INFO) 1847 { 1848 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1849 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1850 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1851 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1852 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1853 if (diagonal_fill) { 1854 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1855 } 1856 } 1857 #endif 1858 1859 /* put together the new matrix */ 1860 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1861 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1862 b = (Mat_SeqAIJ*)(fact)->data; 1863 b->free_a = PETSC_TRUE; 1864 b->free_ij = PETSC_TRUE; 1865 b->singlemalloc = PETSC_FALSE; 1866 ierr = PetscMalloc(bi[n]*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1867 b->j = bj; 1868 b->i = bi; 1869 for (i=0; i<n; i++) bdiag[i] += bi[i]; 1870 b->diag = bdiag; 1871 b->ilen = 0; 1872 b->imax = 0; 1873 b->row = isrow; 1874 b->col = iscol; 1875 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1876 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1877 b->icol = isicol; 1878 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1879 /* In b structure: Free imax, ilen, old a, old j. 1880 Allocate bdiag, solve_work, new a, new j */ 1881 ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1882 b->maxnz = b->nz = bi[n] ; 1883 (fact)->info.factor_mallocs = reallocs; 1884 (fact)->info.fill_ratio_given = f; 1885 (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 1886 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1887 ierr = MatILUFactorSymbolic_SeqAIJ_Inode(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1888 PetscFunctionReturn(0); 1889 } 1890 1891 #undef __FUNCT__ 1892 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_newdatastruct" 1893 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_newdatastruct(Mat B,Mat A,const MatFactorInfo *info) 1894 { 1895 Mat C = B; 1896 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 1897 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 1898 IS ip=b->row,iip = b->icol; 1899 PetscErrorCode ierr; 1900 const PetscInt *rip,*riip; 1901 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp; 1902 PetscInt *ai=a->i,*aj=a->j; 1903 PetscInt k,jmin,jmax,*c2r,*il,col,nexti,ili,nz; 1904 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 1905 PetscTruth perm_identity; 1906 1907 LUShift_Ctx sctx; 1908 PetscInt newshift; 1909 PetscReal rs; 1910 MatScalar d,*v; 1911 1912 PetscFunctionBegin; 1913 /* MatPivotSetUp(): initialize shift context sctx */ 1914 ierr = PetscMemzero(&sctx,sizeof(LUShift_Ctx));CHKERRQ(ierr); 1915 1916 /* if both shift schemes are chosen by user, only use info->shiftpd */ 1917 if (info->shiftpd) { /* set sctx.shift_top=max{rs} */ 1918 sctx.shift_top = info->zeropivot; 1919 for (i=0; i<mbs; i++) { 1920 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 1921 d = (aa)[a->diag[i]]; 1922 rs = -PetscAbsScalar(d) - PetscRealPart(d); 1923 v = aa+ai[i]; 1924 nz = ai[i+1] - ai[i]; 1925 for (j=0; j<nz; j++) 1926 rs += PetscAbsScalar(v[j]); 1927 if (rs>sctx.shift_top) sctx.shift_top = rs; 1928 } 1929 sctx.shift_top *= 1.1; 1930 sctx.nshift_max = 5; 1931 sctx.shift_lo = 0.; 1932 sctx.shift_hi = 1.; 1933 } 1934 1935 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 1936 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 1937 1938 /* allocate working arrays 1939 c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col 1940 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 1941 */ 1942 ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&c2r);CHKERRQ(ierr); 1943 1944 do { 1945 sctx.lushift = PETSC_FALSE; 1946 1947 for (i=0; i<mbs; i++) c2r[i] = mbs; 1948 il[0] = 0; 1949 1950 for (k = 0; k<mbs; k++){ 1951 /* zero rtmp */ 1952 nz = bi[k+1] - bi[k]; 1953 bjtmp = bj + bi[k]; 1954 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 1955 1956 /* load in initial unfactored row */ 1957 bval = ba + bi[k]; 1958 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 1959 for (j = jmin; j < jmax; j++){ 1960 col = riip[aj[j]]; 1961 if (col >= k){ /* only take upper triangular entry */ 1962 rtmp[col] = aa[j]; 1963 *bval++ = 0.0; /* for in-place factorization */ 1964 } 1965 } 1966 /* shift the diagonal of the matrix: ZeropivotApply() */ 1967 rtmp[k] += sctx.shift_amount; /* shift the diagonal of the matrix */ 1968 1969 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 1970 dk = rtmp[k]; 1971 i = c2r[k]; /* first row to be added to k_th row */ 1972 1973 while (i < k){ 1974 nexti = c2r[i]; /* next row to be added to k_th row */ 1975 1976 /* compute multiplier, update diag(k) and U(i,k) */ 1977 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 1978 uikdi = - ba[ili]*ba[bdiag[i]]; /* diagonal(k) */ 1979 dk += uikdi*ba[ili]; /* update diag[k] */ 1980 ba[ili] = uikdi; /* -U(i,k) */ 1981 1982 /* add multiple of row i to k-th row */ 1983 jmin = ili + 1; jmax = bi[i+1]; 1984 if (jmin < jmax){ 1985 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 1986 /* update il and c2r for row i */ 1987 il[i] = jmin; 1988 j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i; 1989 } 1990 i = nexti; 1991 } 1992 1993 /* copy data into U(k,:) */ 1994 rs = 0.0; 1995 jmin = bi[k]; jmax = bi[k+1]-1; 1996 if (jmin < jmax) { 1997 for (j=jmin; j<jmax; j++){ 1998 col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]); 1999 } 2000 /* add the k-th row into il and c2r */ 2001 il[k] = jmin; 2002 i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k; 2003 } 2004 2005 /* MatPivotCheck() */ 2006 sctx.rs = rs; 2007 sctx.pv = dk; 2008 if (info->shiftnz){ 2009 ierr = MatPivotCheck_nz(info,sctx,k,newshift);CHKERRQ(ierr); 2010 } else if (info->shiftpd){ 2011 ierr = MatPivotCheck_pd(info,sctx,k,newshift);CHKERRQ(ierr); 2012 } else if (info->shiftinblocks){ 2013 ierr = MatPivotCheck_inblocks(info,sctx,k,newshift);CHKERRQ(ierr); 2014 } else { 2015 ierr = MatPivotCheck_none(info,sctx,k,newshift);CHKERRQ(ierr); 2016 } 2017 dk = sctx.pv; 2018 if (newshift == 1) break; 2019 2020 ba[bdiag[k]] = 1.0/dk; /* U(k,k) */ 2021 } 2022 } while (sctx.lushift); 2023 2024 ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr); 2025 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2026 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2027 2028 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2029 if (perm_identity){ 2030 (B)->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_newdatastruct; 2031 (B)->ops->solvetranspose = 0; 2032 (B)->ops->forwardsolve = 0; 2033 (B)->ops->backwardsolve = 0; 2034 } else { 2035 (B)->ops->solve = MatSolve_SeqSBAIJ_1_newdatastruct; 2036 (B)->ops->solvetranspose = 0; 2037 (B)->ops->forwardsolve = 0; 2038 (B)->ops->backwardsolve = 0; 2039 } 2040 2041 C->assembled = PETSC_TRUE; 2042 C->preallocated = PETSC_TRUE; 2043 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2044 2045 /* MatPivotView() */ 2046 if (sctx.nshift){ 2047 if (info->shiftpd) { 2048 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); 2049 } else if (info->shiftnz) { 2050 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2051 } else if (info->shiftinblocks){ 2052 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftinblocks);CHKERRQ(ierr); 2053 } 2054 } 2055 PetscFunctionReturn(0); 2056 } 2057 2058 #undef __FUNCT__ 2059 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ" 2060 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 2061 { 2062 Mat C = B; 2063 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2064 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2065 IS ip=b->row,iip = b->icol; 2066 PetscErrorCode ierr; 2067 const PetscInt *rip,*riip; 2068 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp; 2069 PetscInt *ai=a->i,*aj=a->j; 2070 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz; 2071 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2072 PetscReal zeropivot,rs,shiftnz; 2073 PetscReal shiftpd; 2074 ChShift_Ctx sctx; 2075 PetscInt newshift; 2076 PetscTruth perm_identity; 2077 2078 PetscFunctionBegin; 2079 shiftnz = info->shiftnz; 2080 shiftpd = info->shiftpd; 2081 zeropivot = info->zeropivot; 2082 2083 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2084 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2085 2086 /* initialization */ 2087 ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr); 2088 sctx.shift_amount = 0; 2089 sctx.nshift = 0; 2090 do { 2091 sctx.chshift = PETSC_FALSE; 2092 for (i=0; i<mbs; i++) jl[i] = mbs; 2093 il[0] = 0; 2094 2095 for (k = 0; k<mbs; k++){ 2096 /* zero rtmp */ 2097 nz = bi[k+1] - bi[k]; 2098 bjtmp = bj + bi[k]; 2099 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2100 2101 bval = ba + bi[k]; 2102 /* initialize k-th row by the perm[k]-th row of A */ 2103 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2104 for (j = jmin; j < jmax; j++){ 2105 col = riip[aj[j]]; 2106 if (col >= k){ /* only take upper triangular entry */ 2107 rtmp[col] = aa[j]; 2108 *bval++ = 0.0; /* for in-place factorization */ 2109 } 2110 } 2111 /* shift the diagonal of the matrix */ 2112 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 2113 2114 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2115 dk = rtmp[k]; 2116 i = jl[k]; /* first row to be added to k_th row */ 2117 2118 while (i < k){ 2119 nexti = jl[i]; /* next row to be added to k_th row */ 2120 2121 /* compute multiplier, update diag(k) and U(i,k) */ 2122 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2123 uikdi = - ba[ili]*ba[bi[i]]; /* diagonal(k) */ 2124 dk += uikdi*ba[ili]; 2125 ba[ili] = uikdi; /* -U(i,k) */ 2126 2127 /* add multiple of row i to k-th row */ 2128 jmin = ili + 1; jmax = bi[i+1]; 2129 if (jmin < jmax){ 2130 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2131 /* update il and jl for row i */ 2132 il[i] = jmin; 2133 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 2134 } 2135 i = nexti; 2136 } 2137 2138 /* shift the diagonals when zero pivot is detected */ 2139 /* compute rs=sum of abs(off-diagonal) */ 2140 rs = 0.0; 2141 jmin = bi[k]+1; 2142 nz = bi[k+1] - jmin; 2143 bcol = bj + jmin; 2144 for (j=0; j<nz; j++) { 2145 rs += PetscAbsScalar(rtmp[bcol[j]]); 2146 } 2147 2148 sctx.rs = rs; 2149 sctx.pv = dk; 2150 ierr = MatCholeskyCheckShift_inline(info,sctx,k,newshift);CHKERRQ(ierr); 2151 2152 if (newshift == 1) { 2153 if (!sctx.shift_amount) { 2154 sctx.shift_amount = 1e-5; 2155 } 2156 break; 2157 } 2158 2159 /* copy data into U(k,:) */ 2160 ba[bi[k]] = 1.0/dk; /* U(k,k) */ 2161 jmin = bi[k]+1; jmax = bi[k+1]; 2162 if (jmin < jmax) { 2163 for (j=jmin; j<jmax; j++){ 2164 col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0; 2165 } 2166 /* add the k-th row into il and jl */ 2167 il[k] = jmin; 2168 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 2169 } 2170 } 2171 } while (sctx.chshift); 2172 ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr); 2173 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2174 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2175 2176 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2177 if (perm_identity){ 2178 (B)->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2179 (B)->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2180 (B)->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering; 2181 (B)->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering; 2182 } else { 2183 (B)->ops->solve = MatSolve_SeqSBAIJ_1; 2184 (B)->ops->solvetranspose = MatSolve_SeqSBAIJ_1; 2185 (B)->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1; 2186 (B)->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1; 2187 } 2188 2189 C->assembled = PETSC_TRUE; 2190 C->preallocated = PETSC_TRUE; 2191 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2192 if (sctx.nshift){ 2193 if (shiftnz) { 2194 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2195 } else if (shiftpd) { 2196 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2197 } 2198 } 2199 PetscFunctionReturn(0); 2200 } 2201 2202 /* 2203 icc() under revised new data structure. 2204 Factored arrays bj and ba are stored as 2205 U(0,:),...,U(i,:),U(n-1,:) 2206 2207 ui=fact->i is an array of size n+1, in which 2208 ui+ 2209 ui[i]: points to 1st entry of U(i,:),i=0,...,n-1 2210 ui[n]: points to U(n-1,n-1)+1 2211 2212 udiag=fact->diag is an array of size n,in which 2213 udiag[i]: points to diagonal of U(i,:), i=0,...,n-1 2214 2215 U(i,:) contains udiag[i] as its last entry, i.e., 2216 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 2217 */ 2218 2219 #undef __FUNCT__ 2220 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_newdatastruct" 2221 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2222 { 2223 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2224 Mat_SeqSBAIJ *b; 2225 PetscErrorCode ierr; 2226 PetscTruth perm_identity,missing; 2227 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2228 const PetscInt *rip,*riip; 2229 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2230 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2231 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2232 PetscReal fill=info->fill,levels=info->levels; 2233 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2234 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2235 PetscBT lnkbt; 2236 IS iperm; 2237 2238 PetscFunctionBegin; 2239 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); 2240 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2241 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2242 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2243 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2244 2245 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2246 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2247 ui[0] = 0; 2248 2249 /* ICC(0) without matrix ordering: simply rearrange column indices */ 2250 if (!levels && perm_identity) { 2251 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2252 cols = uj; 2253 for (i=0; i<am; i++) { 2254 ncols = ai[i+1] - a->diag[i]; 2255 ui[i+1] = ui[i] + ncols; 2256 udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */ 2257 2258 aj = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */ 2259 ncols--; /* exclude diagonal */ 2260 for (j=0; j<ncols; j++) *cols++ = aj[j]; 2261 *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */ 2262 } 2263 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2264 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2265 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2266 2267 /* initialization */ 2268 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2269 2270 /* jl: linked list for storing indices of the pivot rows 2271 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2272 ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr); 2273 for (i=0; i<am; i++){ 2274 jl[i] = am; il[i] = 0; 2275 } 2276 2277 /* create and initialize a linked list for storing column indices of the active row k */ 2278 nlnk = am + 1; 2279 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2280 2281 /* initial FreeSpace size is fill*(ai[am]+1) */ 2282 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2283 current_space = free_space; 2284 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2285 current_space_lvl = free_space_lvl; 2286 2287 for (k=0; k<am; k++){ /* for each active row k */ 2288 /* initialize lnk by the column indices of row rip[k] of A */ 2289 nzk = 0; 2290 ncols = ai[rip[k]+1] - ai[rip[k]]; 2291 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2292 ncols_upper = 0; 2293 for (j=0; j<ncols; j++){ 2294 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2295 if (riip[i] >= k){ /* only take upper triangular entry */ 2296 ajtmp[ncols_upper] = i; 2297 ncols_upper++; 2298 } 2299 } 2300 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2301 nzk += nlnk; 2302 2303 /* update lnk by computing fill-in for each pivot row to be merged in */ 2304 prow = jl[k]; /* 1st pivot row */ 2305 2306 while (prow < k){ 2307 nextprow = jl[prow]; 2308 2309 /* merge prow into k-th row */ 2310 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2311 jmax = ui[prow+1]; 2312 ncols = jmax-jmin; 2313 i = jmin - ui[prow]; 2314 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2315 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2316 j = *(uj - 1); 2317 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2318 nzk += nlnk; 2319 2320 /* update il and jl for prow */ 2321 if (jmin < jmax){ 2322 il[prow] = jmin; 2323 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2324 } 2325 prow = nextprow; 2326 } 2327 2328 /* if free space is not available, make more free space */ 2329 if (current_space->local_remaining<nzk) { 2330 i = am - k + 1; /* num of unfactored rows */ 2331 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2332 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2333 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2334 reallocs++; 2335 } 2336 2337 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2338 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2339 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2340 2341 /* add the k-th row into il and jl */ 2342 if (nzk > 1){ 2343 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2344 jl[k] = jl[i]; jl[i] = k; 2345 il[k] = ui[k] + 1; 2346 } 2347 uj_ptr[k] = current_space->array; 2348 uj_lvl_ptr[k] = current_space_lvl->array; 2349 2350 current_space->array += nzk; 2351 current_space->local_used += nzk; 2352 current_space->local_remaining -= nzk; 2353 2354 current_space_lvl->array += nzk; 2355 current_space_lvl->local_used += nzk; 2356 current_space_lvl->local_remaining -= nzk; 2357 2358 ui[k+1] = ui[k] + nzk; 2359 } 2360 2361 #if defined(PETSC_USE_INFO) 2362 if (ai[am] != 0) { 2363 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2364 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2365 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2366 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2367 } else { 2368 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2369 } 2370 #endif 2371 2372 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2373 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2374 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2375 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2376 2377 /* destroy list of free space and other temporary array(s) */ 2378 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2379 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor in newdatastruct */ 2380 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2381 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2382 2383 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2384 2385 /* put together the new matrix in MATSEQSBAIJ format */ 2386 2387 b = (Mat_SeqSBAIJ*)(fact)->data; 2388 b->singlemalloc = PETSC_FALSE; 2389 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2390 b->j = uj; 2391 b->i = ui; 2392 b->diag = udiag; 2393 b->free_diag = PETSC_TRUE; 2394 b->ilen = 0; 2395 b->imax = 0; 2396 b->row = perm; 2397 b->col = perm; 2398 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2399 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2400 b->icol = iperm; 2401 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2402 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2403 ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2404 b->maxnz = b->nz = ui[am]; 2405 b->free_a = PETSC_TRUE; 2406 b->free_ij = PETSC_TRUE; 2407 2408 (fact)->info.factor_mallocs = reallocs; 2409 (fact)->info.fill_ratio_given = fill; 2410 if (ai[am] != 0) { 2411 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2412 } else { 2413 (fact)->info.fill_ratio_needed = 0.0; 2414 } 2415 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct; 2416 PetscFunctionReturn(0); 2417 } 2418 2419 #undef __FUNCT__ 2420 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ" 2421 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2422 { 2423 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2424 Mat_SeqSBAIJ *b; 2425 PetscErrorCode ierr; 2426 PetscTruth perm_identity,missing; 2427 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2428 const PetscInt *rip,*riip; 2429 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2430 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2431 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2432 PetscReal fill=info->fill,levels=info->levels; 2433 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2434 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2435 PetscBT lnkbt; 2436 IS iperm; 2437 PetscTruth newdatastruct=PETSC_FALSE; 2438 2439 PetscFunctionBegin; 2440 ierr = PetscOptionsGetTruth(PETSC_NULL,"-icc_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 2441 if(newdatastruct){ 2442 ierr = MatICCFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr); 2443 PetscFunctionReturn(0); 2444 } 2445 2446 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); 2447 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2448 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2449 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2450 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2451 2452 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2453 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2454 ui[0] = 0; 2455 2456 /* ICC(0) without matrix ordering: simply copies fill pattern */ 2457 if (!levels && perm_identity) { 2458 2459 for (i=0; i<am; i++) { 2460 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 2461 udiag[i] = ui[i]; 2462 } 2463 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2464 cols = uj; 2465 for (i=0; i<am; i++) { 2466 aj = a->j + a->diag[i]; 2467 ncols = ui[i+1] - ui[i]; 2468 for (j=0; j<ncols; j++) *cols++ = *aj++; 2469 } 2470 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2471 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2472 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2473 2474 /* initialization */ 2475 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2476 2477 /* jl: linked list for storing indices of the pivot rows 2478 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2479 ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr); 2480 for (i=0; i<am; i++){ 2481 jl[i] = am; il[i] = 0; 2482 } 2483 2484 /* create and initialize a linked list for storing column indices of the active row k */ 2485 nlnk = am + 1; 2486 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2487 2488 /* initial FreeSpace size is fill*(ai[am]+1) */ 2489 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2490 current_space = free_space; 2491 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2492 current_space_lvl = free_space_lvl; 2493 2494 for (k=0; k<am; k++){ /* for each active row k */ 2495 /* initialize lnk by the column indices of row rip[k] of A */ 2496 nzk = 0; 2497 ncols = ai[rip[k]+1] - ai[rip[k]]; 2498 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2499 ncols_upper = 0; 2500 for (j=0; j<ncols; j++){ 2501 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2502 if (riip[i] >= k){ /* only take upper triangular entry */ 2503 ajtmp[ncols_upper] = i; 2504 ncols_upper++; 2505 } 2506 } 2507 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2508 nzk += nlnk; 2509 2510 /* update lnk by computing fill-in for each pivot row to be merged in */ 2511 prow = jl[k]; /* 1st pivot row */ 2512 2513 while (prow < k){ 2514 nextprow = jl[prow]; 2515 2516 /* merge prow into k-th row */ 2517 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2518 jmax = ui[prow+1]; 2519 ncols = jmax-jmin; 2520 i = jmin - ui[prow]; 2521 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2522 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2523 j = *(uj - 1); 2524 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2525 nzk += nlnk; 2526 2527 /* update il and jl for prow */ 2528 if (jmin < jmax){ 2529 il[prow] = jmin; 2530 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2531 } 2532 prow = nextprow; 2533 } 2534 2535 /* if free space is not available, make more free space */ 2536 if (current_space->local_remaining<nzk) { 2537 i = am - k + 1; /* num of unfactored rows */ 2538 i *= PetscMin(nzk, (i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2539 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2540 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2541 reallocs++; 2542 } 2543 2544 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2545 if (nzk == 0) SETERRQ1(PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2546 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2547 2548 /* add the k-th row into il and jl */ 2549 if (nzk > 1){ 2550 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2551 jl[k] = jl[i]; jl[i] = k; 2552 il[k] = ui[k] + 1; 2553 } 2554 uj_ptr[k] = current_space->array; 2555 uj_lvl_ptr[k] = current_space_lvl->array; 2556 2557 current_space->array += nzk; 2558 current_space->local_used += nzk; 2559 current_space->local_remaining -= nzk; 2560 2561 current_space_lvl->array += nzk; 2562 current_space_lvl->local_used += nzk; 2563 current_space_lvl->local_remaining -= nzk; 2564 2565 ui[k+1] = ui[k] + nzk; 2566 } 2567 2568 #if defined(PETSC_USE_INFO) 2569 if (ai[am] != 0) { 2570 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2571 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2572 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2573 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2574 } else { 2575 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2576 } 2577 #endif 2578 2579 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2580 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2581 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2582 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2583 2584 /* destroy list of free space and other temporary array(s) */ 2585 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2586 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 2587 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2588 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2589 2590 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2591 2592 /* put together the new matrix in MATSEQSBAIJ format */ 2593 2594 b = (Mat_SeqSBAIJ*)(fact)->data; 2595 b->singlemalloc = PETSC_FALSE; 2596 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2597 b->j = uj; 2598 b->i = ui; 2599 b->diag = udiag; 2600 b->free_diag = PETSC_TRUE; 2601 b->ilen = 0; 2602 b->imax = 0; 2603 b->row = perm; 2604 b->col = perm; 2605 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2606 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2607 b->icol = iperm; 2608 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2609 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2610 ierr = PetscLogObjectMemory((fact),(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2611 b->maxnz = b->nz = ui[am]; 2612 b->free_a = PETSC_TRUE; 2613 b->free_ij = PETSC_TRUE; 2614 2615 (fact)->info.factor_mallocs = reallocs; 2616 (fact)->info.fill_ratio_given = fill; 2617 if (ai[am] != 0) { 2618 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2619 } else { 2620 (fact)->info.fill_ratio_needed = 0.0; 2621 } 2622 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2623 PetscFunctionReturn(0); 2624 } 2625 2626 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_newdatastruct(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2627 { 2628 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2629 Mat_SeqSBAIJ *b; 2630 PetscErrorCode ierr; 2631 PetscTruth perm_identity; 2632 PetscReal fill = info->fill; 2633 const PetscInt *rip,*riip; 2634 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2635 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2636 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag; 2637 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2638 PetscBT lnkbt; 2639 IS iperm; 2640 2641 PetscFunctionBegin; 2642 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); 2643 /* check whether perm is the identity mapping */ 2644 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2645 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2646 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2647 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2648 2649 /* initialization */ 2650 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2651 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2652 ui[0] = 0; 2653 2654 /* jl: linked list for storing indices of the pivot rows 2655 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2656 ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr); 2657 for (i=0; i<am; i++){ 2658 jl[i] = am; il[i] = 0; 2659 } 2660 2661 /* create and initialize a linked list for storing column indices of the active row k */ 2662 nlnk = am + 1; 2663 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2664 2665 /* initial FreeSpace size is fill*(ai[am]+1) */ 2666 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2667 current_space = free_space; 2668 2669 for (k=0; k<am; k++){ /* for each active row k */ 2670 /* initialize lnk by the column indices of row rip[k] of A */ 2671 nzk = 0; 2672 ncols = ai[rip[k]+1] - ai[rip[k]]; 2673 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2674 ncols_upper = 0; 2675 for (j=0; j<ncols; j++){ 2676 i = riip[*(aj + ai[rip[k]] + j)]; 2677 if (i >= k){ /* only take upper triangular entry */ 2678 cols[ncols_upper] = i; 2679 ncols_upper++; 2680 } 2681 } 2682 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2683 nzk += nlnk; 2684 2685 /* update lnk by computing fill-in for each pivot row to be merged in */ 2686 prow = jl[k]; /* 1st pivot row */ 2687 2688 while (prow < k){ 2689 nextprow = jl[prow]; 2690 /* merge prow into k-th row */ 2691 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2692 jmax = ui[prow+1]; 2693 ncols = jmax-jmin; 2694 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2695 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2696 nzk += nlnk; 2697 2698 /* update il and jl for prow */ 2699 if (jmin < jmax){ 2700 il[prow] = jmin; 2701 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 2702 } 2703 prow = nextprow; 2704 } 2705 2706 /* if free space is not available, make more free space */ 2707 if (current_space->local_remaining<nzk) { 2708 i = am - k + 1; /* num of unfactored rows */ 2709 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2710 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2711 reallocs++; 2712 } 2713 2714 /* copy data into free space, then initialize lnk */ 2715 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 2716 2717 /* add the k-th row into il and jl */ 2718 if (nzk-1 > 0){ 2719 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2720 jl[k] = jl[i]; jl[i] = k; 2721 il[k] = ui[k] + 1; 2722 } 2723 ui_ptr[k] = current_space->array; 2724 current_space->array += nzk; 2725 current_space->local_used += nzk; 2726 current_space->local_remaining -= nzk; 2727 2728 ui[k+1] = ui[k] + nzk; 2729 } 2730 2731 #if defined(PETSC_USE_INFO) 2732 if (ai[am] != 0) { 2733 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 2734 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2735 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2736 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2737 } else { 2738 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2739 } 2740 #endif 2741 2742 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2743 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2744 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 2745 2746 /* destroy list of free space and other temporary array(s) */ 2747 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2748 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor in newdatastruct */ 2749 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2750 2751 /* put together the new matrix in MATSEQSBAIJ format */ 2752 2753 b = (Mat_SeqSBAIJ*)(fact)->data; 2754 b->singlemalloc = PETSC_FALSE; 2755 b->free_a = PETSC_TRUE; 2756 b->free_ij = PETSC_TRUE; 2757 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2758 b->j = uj; 2759 b->i = ui; 2760 b->diag = udiag; 2761 b->free_diag = PETSC_TRUE; 2762 b->ilen = 0; 2763 b->imax = 0; 2764 b->row = perm; 2765 b->col = perm; 2766 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2767 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2768 b->icol = iperm; 2769 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2770 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2771 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2772 b->maxnz = b->nz = ui[am]; 2773 2774 (fact)->info.factor_mallocs = reallocs; 2775 (fact)->info.fill_ratio_given = fill; 2776 if (ai[am] != 0) { 2777 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2778 } else { 2779 (fact)->info.fill_ratio_needed = 0.0; 2780 } 2781 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_newdatastruct; 2782 PetscFunctionReturn(0); 2783 } 2784 2785 #undef __FUNCT__ 2786 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ" 2787 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2788 { 2789 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2790 Mat_SeqSBAIJ *b; 2791 PetscErrorCode ierr; 2792 PetscTruth perm_identity; 2793 PetscReal fill = info->fill; 2794 const PetscInt *rip,*riip; 2795 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2796 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2797 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr; 2798 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2799 PetscBT lnkbt; 2800 IS iperm; 2801 PetscTruth newdatastruct=PETSC_FALSE; 2802 2803 PetscFunctionBegin; 2804 ierr = PetscOptionsGetTruth(PETSC_NULL,"-cholesky_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr); 2805 if(newdatastruct){ 2806 ierr = MatCholeskyFactorSymbolic_SeqAIJ_newdatastruct(fact,A,perm,info);CHKERRQ(ierr); 2807 PetscFunctionReturn(0); 2808 } 2809 2810 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); 2811 /* check whether perm is the identity mapping */ 2812 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2813 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2814 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2815 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2816 2817 /* initialization */ 2818 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2819 ui[0] = 0; 2820 2821 /* jl: linked list for storing indices of the pivot rows 2822 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2823 ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr); 2824 for (i=0; i<am; i++){ 2825 jl[i] = am; il[i] = 0; 2826 } 2827 2828 /* create and initialize a linked list for storing column indices of the active row k */ 2829 nlnk = am + 1; 2830 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2831 2832 /* initial FreeSpace size is fill*(ai[am]+1) */ 2833 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2834 current_space = free_space; 2835 2836 for (k=0; k<am; k++){ /* for each active row k */ 2837 /* initialize lnk by the column indices of row rip[k] of A */ 2838 nzk = 0; 2839 ncols = ai[rip[k]+1] - ai[rip[k]]; 2840 if (!ncols) SETERRQ2(PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2841 ncols_upper = 0; 2842 for (j=0; j<ncols; j++){ 2843 i = riip[*(aj + ai[rip[k]] + j)]; 2844 if (i >= k){ /* only take upper triangular entry */ 2845 cols[ncols_upper] = i; 2846 ncols_upper++; 2847 } 2848 } 2849 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2850 nzk += nlnk; 2851 2852 /* update lnk by computing fill-in for each pivot row to be merged in */ 2853 prow = jl[k]; /* 1st pivot row */ 2854 2855 while (prow < k){ 2856 nextprow = jl[prow]; 2857 /* merge prow into k-th row */ 2858 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2859 jmax = ui[prow+1]; 2860 ncols = jmax-jmin; 2861 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2862 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2863 nzk += nlnk; 2864 2865 /* update il and jl for prow */ 2866 if (jmin < jmax){ 2867 il[prow] = jmin; 2868 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 2869 } 2870 prow = nextprow; 2871 } 2872 2873 /* if free space is not available, make more free space */ 2874 if (current_space->local_remaining<nzk) { 2875 i = am - k + 1; /* num of unfactored rows */ 2876 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2877 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2878 reallocs++; 2879 } 2880 2881 /* copy data into free space, then initialize lnk */ 2882 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 2883 2884 /* add the k-th row into il and jl */ 2885 if (nzk-1 > 0){ 2886 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2887 jl[k] = jl[i]; jl[i] = k; 2888 il[k] = ui[k] + 1; 2889 } 2890 ui_ptr[k] = current_space->array; 2891 current_space->array += nzk; 2892 current_space->local_used += nzk; 2893 current_space->local_remaining -= nzk; 2894 2895 ui[k+1] = ui[k] + nzk; 2896 } 2897 2898 #if defined(PETSC_USE_INFO) 2899 if (ai[am] != 0) { 2900 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 2901 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2902 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2903 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2904 } else { 2905 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2906 } 2907 #endif 2908 2909 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2910 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2911 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 2912 2913 /* destroy list of free space and other temporary array(s) */ 2914 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2915 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 2916 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2917 2918 /* put together the new matrix in MATSEQSBAIJ format */ 2919 2920 b = (Mat_SeqSBAIJ*)(fact)->data; 2921 b->singlemalloc = PETSC_FALSE; 2922 b->free_a = PETSC_TRUE; 2923 b->free_ij = PETSC_TRUE; 2924 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2925 b->j = uj; 2926 b->i = ui; 2927 b->diag = 0; 2928 b->ilen = 0; 2929 b->imax = 0; 2930 b->row = perm; 2931 b->col = perm; 2932 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2933 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2934 b->icol = iperm; 2935 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2936 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2937 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2938 b->maxnz = b->nz = ui[am]; 2939 2940 (fact)->info.factor_mallocs = reallocs; 2941 (fact)->info.fill_ratio_given = fill; 2942 if (ai[am] != 0) { 2943 (fact)->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2944 } else { 2945 (fact)->info.fill_ratio_needed = 0.0; 2946 } 2947 (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2948 PetscFunctionReturn(0); 2949 } 2950 2951 #undef __FUNCT__ 2952 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct" 2953 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx) 2954 { 2955 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2956 PetscErrorCode ierr; 2957 PetscInt n = A->rmap->n; 2958 const PetscInt *ai = a->i,*aj = a->j,*vi; 2959 PetscScalar *x,sum; 2960 const PetscScalar *b; 2961 const MatScalar *aa = a->a,*v; 2962 PetscInt i,nz; 2963 2964 PetscFunctionBegin; 2965 if (!n) PetscFunctionReturn(0); 2966 2967 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 2968 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 2969 2970 /* forward solve the lower triangular */ 2971 x[0] = b[0]; 2972 v = aa; 2973 vi = aj; 2974 for (i=1; i<n; i++) { 2975 nz = ai[i+1] - ai[i]; 2976 sum = b[i]; 2977 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 2978 v += nz; 2979 vi += nz; 2980 x[i] = sum; 2981 } 2982 2983 /* backward solve the upper triangular */ 2984 v = aa + ai[n+1]; 2985 vi = aj + ai[n+1]; 2986 for (i=n-1; i>=0; i--){ 2987 nz = ai[2*n-i +1] - ai[2*n-i]-1; 2988 sum = x[i]; 2989 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 2990 v += nz; 2991 vi += nz; vi++; 2992 x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */ 2993 } 2994 2995 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 2996 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 2997 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 2998 PetscFunctionReturn(0); 2999 } 3000 3001 #undef __FUNCT__ 3002 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_newdatastruct_v2" 3003 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_newdatastruct_v2(Mat A,Vec bb,Vec xx) 3004 { 3005 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3006 PetscErrorCode ierr; 3007 PetscInt n = A->rmap->n; 3008 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag,*vi; 3009 PetscScalar *x,sum; 3010 const PetscScalar *b; 3011 const MatScalar *aa = a->a,*v; 3012 PetscInt i,nz; 3013 3014 PetscFunctionBegin; 3015 if (!n) PetscFunctionReturn(0); 3016 3017 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3018 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3019 3020 /* forward solve the lower triangular */ 3021 x[0] = b[0]; 3022 v = aa; 3023 vi = aj; 3024 for (i=1; i<n; i++) { 3025 nz = ai[i+1] - ai[i]; 3026 sum = b[i]; 3027 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3028 v += nz; 3029 vi += nz; 3030 x[i] = sum; 3031 } 3032 3033 /* backward solve the upper triangular */ 3034 /* v = aa + ai[n+1]; 3035 vi = aj + ai[n+1]; */ 3036 v = aa + adiag[n-1]; 3037 vi = aj + adiag[n-1]; 3038 for (i=n-1; i>=0; i--){ 3039 nz = adiag[i] - adiag[i+1]-1; 3040 sum = x[i]; 3041 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3042 v += nz; 3043 vi += nz; vi++; 3044 x[i] = *v++ *sum; /* x[i]=aa[adiag[i]]*sum; v++; */ 3045 } 3046 3047 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 3048 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3049 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3050 PetscFunctionReturn(0); 3051 } 3052 3053 #undef __FUNCT__ 3054 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct" 3055 PetscErrorCode MatSolve_SeqAIJ_newdatastruct(Mat A,Vec bb,Vec xx) 3056 { 3057 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3058 IS iscol = a->col,isrow = a->row; 3059 PetscErrorCode ierr; 3060 PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,nz,k; 3061 const PetscInt *rout,*cout,*r,*c; 3062 PetscScalar *x,*tmp,*tmps,sum; 3063 const PetscScalar *b; 3064 const MatScalar *aa = a->a,*v; 3065 3066 PetscFunctionBegin; 3067 if (!n) PetscFunctionReturn(0); 3068 3069 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3070 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3071 tmp = a->solve_work; 3072 3073 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 3074 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 3075 3076 /* forward solve the lower triangular */ 3077 tmp[0] = b[*r++]; 3078 tmps = tmp; 3079 v = aa; 3080 vi = aj; 3081 for (i=1; i<n; i++) { 3082 nz = ai[i+1] - ai[i]; 3083 sum = b[*r++]; 3084 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 3085 tmp[i] = sum; 3086 v += nz; vi += nz; 3087 } 3088 3089 /* backward solve the upper triangular */ 3090 k = n+1; 3091 v = aa + ai[k]; /* 1st entry of U(n-1,:) */ 3092 vi = aj + ai[k]; 3093 for (i=n-1; i>=0; i--){ 3094 k = 2*n-i; 3095 nz = ai[k +1] - ai[k] - 1; 3096 sum = tmp[i]; 3097 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 3098 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 3099 v += nz+1; vi += nz+1; 3100 } 3101 3102 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 3103 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 3104 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3105 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3106 ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr); 3107 PetscFunctionReturn(0); 3108 } 3109 3110 #undef __FUNCT__ 3111 #define __FUNCT__ "MatSolve_SeqAIJ_newdatastruct_v2" 3112 PetscErrorCode MatSolve_SeqAIJ_newdatastruct_v2(Mat A,Vec bb,Vec xx) 3113 { 3114 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3115 IS iscol = a->col,isrow = a->row; 3116 PetscErrorCode ierr; 3117 PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz; 3118 const PetscInt *rout,*cout,*r,*c; 3119 PetscScalar *x,*tmp,sum; 3120 const PetscScalar *b; 3121 const MatScalar *aa = a->a,*v; 3122 3123 PetscFunctionBegin; 3124 if (!n) PetscFunctionReturn(0); 3125 3126 ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3127 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3128 tmp = a->solve_work; 3129 3130 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 3131 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 3132 3133 /* forward solve the lower triangular */ 3134 tmp[0] = b[r[0]]; 3135 v = aa; 3136 vi = aj; 3137 for (i=1; i<n; i++) { 3138 nz = ai[i+1] - ai[i]; 3139 sum = b[r[i]]; 3140 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3141 tmp[i] = sum; 3142 v += nz; vi += nz; 3143 } 3144 3145 /* backward solve the upper triangular */ 3146 v = aa + adiag[n-1]; /* 1st entry of U(n-1,:) */ 3147 vi = aj + adiag[n-1]; 3148 for (i=n-1; i>=0; i--){ 3149 nz = adiag[i]-adiag[i+1]-1; 3150 sum = tmp[i]; 3151 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3152 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 3153 v += nz+1; vi += nz+1; 3154 } 3155 3156 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 3157 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 3158 ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr); 3159 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3160 ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr); 3161 PetscFunctionReturn(0); 3162 } 3163 3164 #undef __FUNCT__ 3165 #define __FUNCT__ "MatILUDTFactor_SeqAIJ" 3166 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact) 3167 { 3168 Mat B = *fact; 3169 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b; 3170 IS isicol; 3171 PetscErrorCode ierr; 3172 const PetscInt *r,*ic; 3173 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag; 3174 PetscInt *bi,*bj,*bdiag,*bdiag_rev; 3175 PetscInt row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au; 3176 PetscInt nlnk,*lnk; 3177 PetscBT lnkbt; 3178 PetscTruth row_identity,icol_identity,both_identity; 3179 MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp; 3180 const PetscInt *ics; 3181 PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp; 3182 PetscReal dt=info->dt,dtcol=info->dtcol,shift=info->shiftinblocks; 3183 PetscInt dtcount=(PetscInt)info->dtcount,nnz_max; 3184 PetscTruth missing; 3185 3186 PetscFunctionBegin; 3187 3188 if (dt == PETSC_DEFAULT) dt = 0.005; 3189 if (dtcol == PETSC_DEFAULT) dtcol = 0.01; /* XXX unused! */ 3190 if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax); 3191 3192 /* ------- symbolic factorization, can be reused ---------*/ 3193 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 3194 if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 3195 adiag=a->diag; 3196 3197 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 3198 3199 /* bdiag is location of diagonal in factor */ 3200 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); /* becomes b->diag */ 3201 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag_rev);CHKERRQ(ierr); /* temporary */ 3202 3203 /* allocate row pointers bi */ 3204 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 3205 3206 /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */ 3207 if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */ 3208 nnz_max = ai[n]+2*n*dtcount+2; 3209 3210 ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 3211 ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr); 3212 3213 /* put together the new matrix */ 3214 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 3215 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 3216 b = (Mat_SeqAIJ*)(B)->data; 3217 b->free_a = PETSC_TRUE; 3218 b->free_ij = PETSC_TRUE; 3219 b->singlemalloc = PETSC_FALSE; 3220 b->a = ba; 3221 b->j = bj; 3222 b->i = bi; 3223 b->diag = bdiag; 3224 b->ilen = 0; 3225 b->imax = 0; 3226 b->row = isrow; 3227 b->col = iscol; 3228 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 3229 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 3230 b->icol = isicol; 3231 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3232 3233 ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3234 b->maxnz = nnz_max; 3235 3236 (B)->factor = MAT_FACTOR_ILUDT; 3237 (B)->info.factor_mallocs = 0; 3238 (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]); 3239 CHKMEMQ; 3240 /* ------- end of symbolic factorization ---------*/ 3241 3242 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3243 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3244 ics = ic; 3245 3246 /* linked list for storing column indices of the active row */ 3247 nlnk = n + 1; 3248 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3249 3250 /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */ 3251 ierr = PetscMalloc2(n,PetscInt,&im,n,PetscInt,&jtmp);CHKERRQ(ierr); 3252 /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */ 3253 ierr = PetscMalloc2(n,MatScalar,&rtmp,n,MatScalar,&vtmp);CHKERRQ(ierr); 3254 ierr = PetscMemzero(rtmp,n*sizeof(MatScalar));CHKERRQ(ierr); 3255 3256 bi[0] = 0; 3257 bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */ 3258 bdiag_rev[n] = bdiag[0]; 3259 bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */ 3260 for (i=0; i<n; i++) { 3261 /* copy initial fill into linked list */ 3262 nzi = 0; /* nonzeros for active row i */ 3263 nzi = ai[r[i]+1] - ai[r[i]]; 3264 if (!nzi) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 3265 nzi_al = adiag[r[i]] - ai[r[i]]; 3266 nzi_au = ai[r[i]+1] - adiag[r[i]] -1; 3267 ajtmp = aj + ai[r[i]]; 3268 ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3269 3270 /* load in initial (unfactored row) */ 3271 aatmp = a->a + ai[r[i]]; 3272 for (j=0; j<nzi; j++) { 3273 rtmp[ics[*ajtmp++]] = *aatmp++; 3274 } 3275 3276 /* add pivot rows into linked list */ 3277 row = lnk[n]; 3278 while (row < i ) { 3279 nzi_bl = bi[row+1] - bi[row] + 1; 3280 bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */ 3281 ierr = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr); 3282 nzi += nlnk; 3283 row = lnk[row]; 3284 } 3285 3286 /* copy data from lnk into jtmp, then initialize lnk */ 3287 ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr); 3288 3289 /* numerical factorization */ 3290 bjtmp = jtmp; 3291 row = *bjtmp++; /* 1st pivot row */ 3292 while ( row < i ) { 3293 pc = rtmp + row; 3294 pv = ba + bdiag[row]; /* 1./(diag of the pivot row) */ 3295 multiplier = (*pc) * (*pv); 3296 *pc = multiplier; 3297 if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */ 3298 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3299 pv = ba + bdiag[row+1] + 1; 3300 /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */ 3301 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3302 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3303 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 3304 } 3305 row = *bjtmp++; 3306 } 3307 3308 /* copy sparse rtmp into contiguous vtmp; separate L and U part */ 3309 diag_tmp = rtmp[i]; /* save diagonal value - may not needed?? */ 3310 nzi_bl = 0; j = 0; 3311 while (jtmp[j] < i){ /* Note: jtmp is sorted */ 3312 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3313 nzi_bl++; j++; 3314 } 3315 nzi_bu = nzi - nzi_bl -1; 3316 while (j < nzi){ 3317 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3318 j++; 3319 } 3320 3321 bjtmp = bj + bi[i]; 3322 batmp = ba + bi[i]; 3323 /* apply level dropping rule to L part */ 3324 ncut = nzi_al + dtcount; 3325 if (ncut < nzi_bl){ 3326 ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr); 3327 ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr); 3328 } else { 3329 ncut = nzi_bl; 3330 } 3331 for (j=0; j<ncut; j++){ 3332 bjtmp[j] = jtmp[j]; 3333 batmp[j] = vtmp[j]; 3334 /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */ 3335 } 3336 bi[i+1] = bi[i] + ncut; 3337 nzi = ncut + 1; 3338 3339 /* apply level dropping rule to U part */ 3340 ncut = nzi_au + dtcount; 3341 if (ncut < nzi_bu){ 3342 ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr); 3343 ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr); 3344 } else { 3345 ncut = nzi_bu; 3346 } 3347 nzi += ncut; 3348 3349 /* mark bdiagonal */ 3350 bdiag[i+1] = bdiag[i] - (ncut + 1); 3351 bdiag_rev[n-i-1] = bdiag[i+1]; 3352 bi[2*n - i] = bi[2*n - i +1] - (ncut + 1); 3353 bjtmp = bj + bdiag[i]; 3354 batmp = ba + bdiag[i]; 3355 *bjtmp = i; 3356 *batmp = diag_tmp; /* rtmp[i]; */ 3357 if (*batmp == 0.0) { 3358 *batmp = dt+shift; 3359 /* printf(" row %d add shift %g\n",i,shift); */ 3360 } 3361 *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */ 3362 /* printf(" (%d,%g),",*bjtmp,*batmp); */ 3363 3364 bjtmp = bj + bdiag[i+1]+1; 3365 batmp = ba + bdiag[i+1]+1; 3366 for (k=0; k<ncut; k++){ 3367 bjtmp[k] = jtmp[nzi_bl+1+k]; 3368 batmp[k] = vtmp[nzi_bl+1+k]; 3369 /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */ 3370 } 3371 /* printf("\n"); */ 3372 3373 im[i] = nzi; /* used by PetscLLAddSortedLU() */ 3374 /* 3375 printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]); 3376 printf(" ----------------------------\n"); 3377 */ 3378 } /* for (i=0; i<n; i++) */ 3379 /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */ 3380 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]); 3381 3382 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3383 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3384 3385 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3386 ierr = PetscFree2(im,jtmp);CHKERRQ(ierr); 3387 ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr); 3388 ierr = PetscFree(bdiag_rev);CHKERRQ(ierr); 3389 3390 ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr); 3391 b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n]; 3392 3393 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3394 ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr); 3395 both_identity = (PetscTruth) (row_identity && icol_identity); 3396 if (row_identity && icol_identity) { 3397 B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct; 3398 } else { 3399 B->ops->solve = MatSolve_SeqAIJ_newdatastruct; 3400 } 3401 3402 B->ops->lufactorsymbolic = MatILUDTFactorSymbolic_SeqAIJ; 3403 B->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ; 3404 B->ops->solveadd = 0; 3405 B->ops->solvetranspose = 0; 3406 B->ops->solvetransposeadd = 0; 3407 B->ops->matsolve = 0; 3408 B->assembled = PETSC_TRUE; 3409 B->preallocated = PETSC_TRUE; 3410 PetscFunctionReturn(0); 3411 } 3412 3413 /* a wraper of MatILUDTFactor_SeqAIJ() */ 3414 #undef __FUNCT__ 3415 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ" 3416 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info) 3417 { 3418 PetscErrorCode ierr; 3419 3420 PetscFunctionBegin; 3421 ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr); 3422 3423 fact->ops->lufactornumeric = MatILUDTFactorNumeric_SeqAIJ; 3424 PetscFunctionReturn(0); 3425 } 3426 3427 /* 3428 same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors 3429 - intend to replace existing MatLUFactorNumeric_SeqAIJ() 3430 */ 3431 #undef __FUNCT__ 3432 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ" 3433 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info) 3434 { 3435 Mat C=fact; 3436 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 3437 IS isrow = b->row,isicol = b->icol; 3438 PetscErrorCode ierr; 3439 const PetscInt *r,*ic,*ics; 3440 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 3441 PetscInt *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj; 3442 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 3443 PetscReal dt=info->dt,shift=info->shiftinblocks; 3444 PetscTruth row_identity, col_identity; 3445 3446 PetscFunctionBegin; 3447 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3448 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3449 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 3450 ics = ic; 3451 3452 for (i=0; i<n; i++){ 3453 /* initialize rtmp array */ 3454 nzl = bi[i+1] - bi[i]; /* num of nozeros in L(i,:) */ 3455 bjtmp = bj + bi[i]; 3456 for (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0; 3457 rtmp[i] = 0.0; 3458 nzu = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */ 3459 bjtmp = bj + bdiag[i+1] + 1; 3460 for (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0; 3461 3462 /* load in initial unfactored row of A */ 3463 /* printf("row %d\n",i); */ 3464 nz = ai[r[i]+1] - ai[r[i]]; 3465 ajtmp = aj + ai[r[i]]; 3466 v = aa + ai[r[i]]; 3467 for (j=0; j<nz; j++) { 3468 rtmp[ics[*ajtmp++]] = v[j]; 3469 /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */ 3470 } 3471 /* printf("\n"); */ 3472 3473 /* numerical factorization */ 3474 bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */ 3475 nzl = bi[i+1] - bi[i]; /* num of entries in L(i,:) */ 3476 k = 0; 3477 while (k < nzl){ 3478 row = *bjtmp++; 3479 /* printf(" prow %d\n",row); */ 3480 pc = rtmp + row; 3481 pv = b->a + bdiag[row]; /* 1./(diag of the pivot row) */ 3482 multiplier = (*pc) * (*pv); 3483 *pc = multiplier; 3484 if (PetscAbsScalar(multiplier) > dt){ 3485 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3486 pv = b->a + bdiag[row+1] + 1; 3487 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3488 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3489 /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */ 3490 } 3491 k++; 3492 } 3493 3494 /* finished row so stick it into b->a */ 3495 /* L-part */ 3496 pv = b->a + bi[i] ; 3497 pj = bj + bi[i] ; 3498 nzl = bi[i+1] - bi[i]; 3499 for (j=0; j<nzl; j++) { 3500 pv[j] = rtmp[pj[j]]; 3501 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3502 } 3503 3504 /* diagonal: invert diagonal entries for simplier triangular solves */ 3505 if (rtmp[i] == 0.0) rtmp[i] = dt+shift; 3506 b->a[bdiag[i]] = 1.0/rtmp[i]; 3507 /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */ 3508 3509 /* U-part */ 3510 pv = b->a + bdiag[i+1] + 1; 3511 pj = bj + bdiag[i+1] + 1; 3512 nzu = bdiag[i] - bdiag[i+1] - 1; 3513 for (j=0; j<nzu; j++) { 3514 pv[j] = rtmp[pj[j]]; 3515 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3516 } 3517 /* printf("\n"); */ 3518 } 3519 3520 ierr = PetscFree(rtmp);CHKERRQ(ierr); 3521 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3522 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3523 3524 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3525 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 3526 if (row_identity && col_identity) { 3527 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_newdatastruct; 3528 } else { 3529 C->ops->solve = MatSolve_SeqAIJ_newdatastruct; 3530 } 3531 C->ops->solveadd = 0; 3532 C->ops->solvetranspose = 0; 3533 C->ops->solvetransposeadd = 0; 3534 C->ops->matsolve = 0; 3535 C->assembled = PETSC_TRUE; 3536 C->preallocated = PETSC_TRUE; 3537 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 3538 PetscFunctionReturn(0); 3539 } 3540