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__ "MatGetOrdering_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 MatGetOrdering_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 = 0.0; 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 = 0.0; 69 past = 0.0; 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_COMM_SELF,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 } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) { 122 ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr); 123 ierr = MatSeqSBAIJSetPreallocation(*B,1,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 124 (*B)->ops->iccfactorsymbolic = MatICCFactorSymbolic_SeqAIJ; 125 (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ; 126 } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor type not supported"); 127 (*B)->factortype = ftype; 128 PetscFunctionReturn(0); 129 } 130 EXTERN_C_END 131 132 #undef __FUNCT__ 133 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ_inplace" 134 PetscErrorCode MatLUFactorSymbolic_SeqAIJ_inplace(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 135 { 136 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 137 IS isicol; 138 PetscErrorCode ierr; 139 const PetscInt *r,*ic; 140 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 141 PetscInt *bi,*bj,*ajtmp; 142 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 143 PetscReal f; 144 PetscInt nlnk,*lnk,k,**bi_ptr; 145 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 146 PetscBT lnkbt; 147 148 PetscFunctionBegin; 149 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"matrix must be square"); 150 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 151 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 152 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 153 154 /* get new row pointers */ 155 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 156 bi[0] = 0; 157 158 /* bdiag is location of diagonal in factor */ 159 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 160 bdiag[0] = 0; 161 162 /* linked list for storing column indices of the active row */ 163 nlnk = n + 1; 164 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 165 166 ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr); 167 168 /* initial FreeSpace size is f*(ai[n]+1) */ 169 f = info->fill; 170 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 171 current_space = free_space; 172 173 for (i=0; i<n; i++) { 174 /* copy previous fill into linked list */ 175 nzi = 0; 176 nnz = ai[r[i]+1] - ai[r[i]]; 177 if (!nnz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 178 ajtmp = aj + ai[r[i]]; 179 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 180 nzi += nlnk; 181 182 /* add pivot rows into linked list */ 183 row = lnk[n]; 184 while (row < i) { 185 nzbd = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */ 186 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 187 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 188 nzi += nlnk; 189 row = lnk[row]; 190 } 191 bi[i+1] = bi[i] + nzi; 192 im[i] = nzi; 193 194 /* mark bdiag */ 195 nzbd = 0; 196 nnz = nzi; 197 k = lnk[n]; 198 while (nnz-- && k < i){ 199 nzbd++; 200 k = lnk[k]; 201 } 202 bdiag[i] = bi[i] + nzbd; 203 204 /* if free space is not available, make more free space */ 205 if (current_space->local_remaining<nzi) { 206 nnz = (n - i)*nzi; /* estimated and max additional space needed */ 207 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 208 reallocs++; 209 } 210 211 /* copy data into free space, then initialize lnk */ 212 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 213 bi_ptr[i] = current_space->array; 214 current_space->array += nzi; 215 current_space->local_used += nzi; 216 current_space->local_remaining -= nzi; 217 } 218 #if defined(PETSC_USE_INFO) 219 if (ai[n] != 0) { 220 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 221 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 222 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 223 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr); 224 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 225 } else { 226 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 227 } 228 #endif 229 230 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 231 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 232 233 /* destroy list of free space and other temporary array(s) */ 234 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 235 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); 236 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 237 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 238 239 /* put together the new matrix */ 240 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 241 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 242 b = (Mat_SeqAIJ*)(B)->data; 243 b->free_a = PETSC_TRUE; 244 b->free_ij = PETSC_TRUE; 245 b->singlemalloc = PETSC_FALSE; 246 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 247 b->j = bj; 248 b->i = bi; 249 b->diag = bdiag; 250 b->ilen = 0; 251 b->imax = 0; 252 b->row = isrow; 253 b->col = iscol; 254 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 255 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 256 b->icol = isicol; 257 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 258 259 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 260 ierr = PetscLogObjectMemory(B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 261 b->maxnz = b->nz = bi[n] ; 262 263 (B)->factortype = MAT_FACTOR_LU; 264 (B)->info.factor_mallocs = reallocs; 265 (B)->info.fill_ratio_given = f; 266 267 if (ai[n]) { 268 (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 269 } else { 270 (B)->info.fill_ratio_needed = 0.0; 271 } 272 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 273 if (a->inode.size) { 274 (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace; 275 } 276 PetscFunctionReturn(0); 277 } 278 279 #undef __FUNCT__ 280 #define __FUNCT__ "MatLUFactorSymbolic_SeqAIJ" 281 PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 282 { 283 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 284 IS isicol; 285 PetscErrorCode ierr; 286 const PetscInt *r,*ic; 287 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j; 288 PetscInt *bi,*bj,*ajtmp; 289 PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im; 290 PetscReal f; 291 PetscInt nlnk,*lnk,k,**bi_ptr; 292 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 293 PetscBT lnkbt; 294 PetscTruth olddatastruct=PETSC_FALSE; 295 296 PetscFunctionBegin; 297 /* Uncomment the oldatastruct part only while testing new data structure for MatSolve() */ 298 ierr = PetscOptionsGetTruth(PETSC_NULL,"-lu_old",&olddatastruct,PETSC_NULL);CHKERRQ(ierr); 299 if(olddatastruct){ 300 ierr = MatLUFactorSymbolic_SeqAIJ_inplace(B,A,isrow,iscol,info);CHKERRQ(ierr); 301 PetscFunctionReturn(0); 302 } 303 304 if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"matrix must be square"); 305 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 306 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 307 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 308 309 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 310 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 311 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 312 bi[0] = bdiag[0] = 0; 313 314 /* linked list for storing column indices of the active row */ 315 nlnk = n + 1; 316 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 317 318 ierr = PetscMalloc2(n+1,PetscInt**,&bi_ptr,n+1,PetscInt,&im);CHKERRQ(ierr); 319 320 /* initial FreeSpace size is f*(ai[n]+1) */ 321 f = info->fill; 322 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 323 current_space = free_space; 324 325 for (i=0; i<n; i++) { 326 /* copy previous fill into linked list */ 327 nzi = 0; 328 nnz = ai[r[i]+1] - ai[r[i]]; 329 if (!nnz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 330 ajtmp = aj + ai[r[i]]; 331 ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 332 nzi += nlnk; 333 334 /* add pivot rows into linked list */ 335 row = lnk[n]; 336 while (row < i){ 337 nzbd = bdiag[row] + 1; /* num of entries in the row with column index <= row */ 338 ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */ 339 ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr); 340 nzi += nlnk; 341 row = lnk[row]; 342 } 343 bi[i+1] = bi[i] + nzi; 344 im[i] = nzi; 345 346 /* mark bdiag */ 347 nzbd = 0; 348 nnz = nzi; 349 k = lnk[n]; 350 while (nnz-- && k < i){ 351 nzbd++; 352 k = lnk[k]; 353 } 354 bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */ 355 356 /* if free space is not available, make more free space */ 357 if (current_space->local_remaining<nzi) { 358 nnz = 2*(n - i)*nzi; /* estimated and max additional space needed */ 359 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 360 reallocs++; 361 } 362 363 /* copy data into free space, then initialize lnk */ 364 ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 365 bi_ptr[i] = current_space->array; 366 current_space->array += nzi; 367 current_space->local_used += nzi; 368 current_space->local_remaining -= nzi; 369 } 370 #if defined(PETSC_USE_INFO) 371 if (ai[n] != 0) { 372 PetscReal af = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 373 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 374 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 375 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr); 376 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 377 } else { 378 ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr); 379 } 380 #endif 381 382 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 383 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 384 385 /* destroy list of free space and other temporary array(s) */ 386 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 387 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 388 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 389 ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr); 390 391 /* put together the new matrix */ 392 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 393 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 394 b = (Mat_SeqAIJ*)(B)->data; 395 b->free_a = PETSC_TRUE; 396 b->free_ij = PETSC_TRUE; 397 b->singlemalloc = PETSC_FALSE; 398 ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 399 b->j = bj; 400 b->i = bi; 401 b->diag = bdiag; 402 b->ilen = 0; 403 b->imax = 0; 404 b->row = isrow; 405 b->col = iscol; 406 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 407 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 408 b->icol = isicol; 409 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 410 411 /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */ 412 ierr = PetscLogObjectMemory(B,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 413 b->maxnz = b->nz = bdiag[0]+1; 414 B->factortype = MAT_FACTOR_LU; 415 B->info.factor_mallocs = reallocs; 416 B->info.fill_ratio_given = f; 417 418 if (ai[n]) { 419 B->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 420 } else { 421 B->info.fill_ratio_needed = 0.0; 422 } 423 B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 424 if (a->inode.size) { 425 B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode; 426 } 427 PetscFunctionReturn(0); 428 } 429 430 /* 431 Trouble in factorization, should we dump the original matrix? 432 */ 433 #undef __FUNCT__ 434 #define __FUNCT__ "MatFactorDumpMatrix" 435 PetscErrorCode MatFactorDumpMatrix(Mat A) 436 { 437 PetscErrorCode ierr; 438 PetscTruth flg = PETSC_FALSE; 439 440 PetscFunctionBegin; 441 ierr = PetscOptionsGetTruth(PETSC_NULL,"-mat_factor_dump_on_error",&flg,PETSC_NULL);CHKERRQ(ierr); 442 if (flg) { 443 PetscViewer viewer; 444 char filename[PETSC_MAX_PATH_LEN]; 445 446 ierr = PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);CHKERRQ(ierr); 447 ierr = PetscViewerBinaryOpen(((PetscObject)A)->comm,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr); 448 ierr = MatView(A,viewer);CHKERRQ(ierr); 449 ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr); 450 } 451 PetscFunctionReturn(0); 452 } 453 454 #undef __FUNCT__ 455 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ" 456 PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 457 { 458 Mat C=B; 459 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 460 IS isrow = b->row,isicol = b->icol; 461 PetscErrorCode ierr; 462 const PetscInt *r,*ic,*ics; 463 const PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bdiag=b->diag; 464 PetscInt i,j,k,nz,nzL,row,*pj; 465 const PetscInt *ajtmp,*bjtmp; 466 MatScalar *rtmp,*pc,multiplier,*pv; 467 const MatScalar *aa=a->a,*v; 468 PetscTruth row_identity,col_identity; 469 FactorShiftCtx sctx; 470 const PetscInt *ddiag; 471 PetscReal rs; 472 MatScalar d; 473 474 PetscFunctionBegin; 475 /* MatPivotSetUp(): initialize shift context sctx */ 476 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 477 478 if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 479 ddiag = a->diag; 480 sctx.shift_top = info->zeropivot; 481 for (i=0; i<n; i++) { 482 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 483 d = (aa)[ddiag[i]]; 484 rs = -PetscAbsScalar(d) - PetscRealPart(d); 485 v = aa+ai[i]; 486 nz = ai[i+1] - ai[i]; 487 for (j=0; j<nz; j++) 488 rs += PetscAbsScalar(v[j]); 489 if (rs>sctx.shift_top) sctx.shift_top = rs; 490 } 491 sctx.shift_top *= 1.1; 492 sctx.nshift_max = 5; 493 sctx.shift_lo = 0.; 494 sctx.shift_hi = 1.; 495 } 496 497 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 498 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 499 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 500 ics = ic; 501 502 do { 503 sctx.newshift = PETSC_FALSE; 504 for (i=0; i<n; i++){ 505 /* zero rtmp */ 506 /* L part */ 507 nz = bi[i+1] - bi[i]; 508 bjtmp = bj + bi[i]; 509 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 510 511 /* U part */ 512 nz = bdiag[i]-bdiag[i+1]; 513 bjtmp = bj + bdiag[i+1]+1; 514 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 515 516 /* load in initial (unfactored row) */ 517 nz = ai[r[i]+1] - ai[r[i]]; 518 ajtmp = aj + ai[r[i]]; 519 v = aa + ai[r[i]]; 520 for (j=0; j<nz; j++) { 521 rtmp[ics[ajtmp[j]]] = v[j]; 522 } 523 /* ZeropivotApply() */ 524 rtmp[i] += sctx.shift_amount; /* shift the diagonal of the matrix */ 525 526 /* elimination */ 527 bjtmp = bj + bi[i]; 528 row = *bjtmp++; 529 nzL = bi[i+1] - bi[i]; 530 for(k=0; k < nzL;k++) { 531 pc = rtmp + row; 532 if (*pc != 0.0) { 533 pv = b->a + bdiag[row]; 534 multiplier = *pc * (*pv); 535 *pc = multiplier; 536 pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */ 537 pv = b->a + bdiag[row+1]+1; 538 nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */ 539 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 540 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 541 } 542 row = *bjtmp++; 543 } 544 545 /* finished row so stick it into b->a */ 546 rs = 0.0; 547 /* L part */ 548 pv = b->a + bi[i] ; 549 pj = b->j + bi[i] ; 550 nz = bi[i+1] - bi[i]; 551 for (j=0; j<nz; j++) { 552 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 553 } 554 555 /* U part */ 556 pv = b->a + bdiag[i+1]+1; 557 pj = b->j + bdiag[i+1]+1; 558 nz = bdiag[i] - bdiag[i+1]-1; 559 for (j=0; j<nz; j++) { 560 pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]); 561 } 562 563 sctx.rs = rs; 564 sctx.pv = rtmp[i]; 565 ierr = MatPivotCheck(info,&sctx,i);CHKERRQ(ierr); 566 if(sctx.newshift) break; /* break for-loop */ 567 rtmp[i] = sctx.pv; /* sctx.pv might be updated in the case of MAT_SHIFT_INBLOCKS */ 568 569 /* Mark diagonal and invert diagonal for simplier triangular solves */ 570 pv = b->a + bdiag[i]; 571 *pv = 1.0/rtmp[i]; 572 573 } /* endof for (i=0; i<n; i++){ */ 574 575 /* MatPivotRefine() */ 576 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max){ 577 /* 578 * if no shift in this attempt & shifting & started shifting & can refine, 579 * then try lower shift 580 */ 581 sctx.shift_hi = sctx.shift_fraction; 582 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 583 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 584 sctx.newshift = PETSC_TRUE; 585 sctx.nshift++; 586 } 587 } while (sctx.newshift); 588 589 ierr = PetscFree(rtmp);CHKERRQ(ierr); 590 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 591 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 592 593 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 594 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 595 if (row_identity && col_identity) { 596 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 597 } else { 598 C->ops->solve = MatSolve_SeqAIJ; 599 } 600 C->ops->solveadd = MatSolveAdd_SeqAIJ; 601 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ; 602 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ; 603 C->ops->matsolve = MatMatSolve_SeqAIJ; 604 C->assembled = PETSC_TRUE; 605 C->preallocated = PETSC_TRUE; 606 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 607 608 /* MatShiftView(A,info,&sctx) */ 609 if (sctx.nshift){ 610 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 611 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); 612 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 613 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 614 } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS){ 615 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftamount);CHKERRQ(ierr); 616 } 617 } 618 ierr = Mat_CheckInode_FactorLU(C,PETSC_FALSE);CHKERRQ(ierr); 619 PetscFunctionReturn(0); 620 } 621 622 #undef __FUNCT__ 623 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_inplace" 624 PetscErrorCode MatLUFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info) 625 { 626 Mat C=B; 627 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 628 IS isrow = b->row,isicol = b->icol; 629 PetscErrorCode ierr; 630 const PetscInt *r,*ic,*ics; 631 PetscInt nz,row,i,j,n=A->rmap->n,diag; 632 const PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 633 const PetscInt *ajtmp,*bjtmp,*diag_offset = b->diag,*pj; 634 MatScalar *pv,*rtmp,*pc,multiplier,d; 635 const MatScalar *v,*aa=a->a; 636 PetscReal rs=0.0; 637 FactorShiftCtx sctx; 638 const PetscInt *ddiag; 639 PetscTruth row_identity, col_identity; 640 641 PetscFunctionBegin; 642 /* MatPivotSetUp(): initialize shift context sctx */ 643 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 644 645 if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 646 ddiag = a->diag; 647 sctx.shift_top = info->zeropivot; 648 for (i=0; i<n; i++) { 649 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 650 d = (aa)[ddiag[i]]; 651 rs = -PetscAbsScalar(d) - PetscRealPart(d); 652 v = aa+ai[i]; 653 nz = ai[i+1] - ai[i]; 654 for (j=0; j<nz; j++) 655 rs += PetscAbsScalar(v[j]); 656 if (rs>sctx.shift_top) sctx.shift_top = rs; 657 } 658 sctx.shift_top *= 1.1; 659 sctx.nshift_max = 5; 660 sctx.shift_lo = 0.; 661 sctx.shift_hi = 1.; 662 } 663 664 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 665 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 666 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 667 ics = ic; 668 669 do { 670 sctx.newshift = PETSC_FALSE; 671 for (i=0; i<n; i++){ 672 nz = bi[i+1] - bi[i]; 673 bjtmp = bj + bi[i]; 674 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 675 676 /* load in initial (unfactored row) */ 677 nz = ai[r[i]+1] - ai[r[i]]; 678 ajtmp = aj + ai[r[i]]; 679 v = aa + ai[r[i]]; 680 for (j=0; j<nz; j++) { 681 rtmp[ics[ajtmp[j]]] = v[j]; 682 } 683 rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 684 685 row = *bjtmp++; 686 while (row < i) { 687 pc = rtmp + row; 688 if (*pc != 0.0) { 689 pv = b->a + diag_offset[row]; 690 pj = b->j + diag_offset[row] + 1; 691 multiplier = *pc / *pv++; 692 *pc = multiplier; 693 nz = bi[row+1] - diag_offset[row] - 1; 694 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 695 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 696 } 697 row = *bjtmp++; 698 } 699 /* finished row so stick it into b->a */ 700 pv = b->a + bi[i] ; 701 pj = b->j + bi[i] ; 702 nz = bi[i+1] - bi[i]; 703 diag = diag_offset[i] - bi[i]; 704 rs = 0.0; 705 for (j=0; j<nz; j++) { 706 pv[j] = rtmp[pj[j]]; 707 rs += PetscAbsScalar(pv[j]); 708 } 709 rs -= PetscAbsScalar(pv[diag]); 710 711 sctx.rs = rs; 712 sctx.pv = pv[diag]; 713 ierr = MatPivotCheck(info,&sctx,i);CHKERRQ(ierr); 714 if (sctx.newshift) break; 715 pv[diag] = sctx.pv; 716 } 717 718 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 719 /* 720 * if no shift in this attempt & shifting & started shifting & can refine, 721 * then try lower shift 722 */ 723 sctx.shift_hi = sctx.shift_fraction; 724 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 725 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 726 sctx.newshift = PETSC_TRUE; 727 sctx.nshift++; 728 } 729 } while (sctx.newshift); 730 731 /* invert diagonal entries for simplier triangular solves */ 732 for (i=0; i<n; i++) { 733 b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]]; 734 } 735 ierr = PetscFree(rtmp);CHKERRQ(ierr); 736 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 737 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 738 739 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 740 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 741 if (row_identity && col_identity) { 742 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_inplace; 743 } else { 744 C->ops->solve = MatSolve_SeqAIJ_inplace; 745 } 746 C->ops->solveadd = MatSolveAdd_SeqAIJ_inplace; 747 C->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 748 C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace; 749 C->ops->matsolve = MatMatSolve_SeqAIJ_inplace; 750 C->assembled = PETSC_TRUE; 751 C->preallocated = PETSC_TRUE; 752 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 753 if (sctx.nshift){ 754 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 755 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); 756 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 757 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 758 } 759 } 760 (C)->ops->solve = MatSolve_SeqAIJ_inplace; 761 (C)->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 762 ierr = Mat_CheckInode(C,PETSC_FALSE);CHKERRQ(ierr); 763 PetscFunctionReturn(0); 764 } 765 766 /* 767 This routine implements inplace ILU(0) with row or/and column permutations. 768 Input: 769 A - original matrix 770 Output; 771 A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i] 772 a->j (col index) is permuted by the inverse of colperm, then sorted 773 a->a reordered accordingly with a->j 774 a->diag (ptr to diagonal elements) is updated. 775 */ 776 #undef __FUNCT__ 777 #define __FUNCT__ "MatLUFactorNumeric_SeqAIJ_InplaceWithPerm" 778 PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info) 779 { 780 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 781 IS isrow = a->row,isicol = a->icol; 782 PetscErrorCode ierr; 783 const PetscInt *r,*ic,*ics; 784 PetscInt i,j,n=A->rmap->n,*ai=a->i,*aj=a->j; 785 PetscInt *ajtmp,nz,row; 786 PetscInt *diag = a->diag,nbdiag,*pj; 787 PetscScalar *rtmp,*pc,multiplier,d; 788 MatScalar *pv,*v; 789 PetscReal rs; 790 FactorShiftCtx sctx; 791 const MatScalar *aa=a->a,*vtmp; 792 793 PetscFunctionBegin; 794 if (A != B) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address"); 795 796 /* MatPivotSetUp(): initialize shift context sctx */ 797 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 798 799 if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 800 const PetscInt *ddiag = a->diag; 801 sctx.shift_top = info->zeropivot; 802 for (i=0; i<n; i++) { 803 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 804 d = (aa)[ddiag[i]]; 805 rs = -PetscAbsScalar(d) - PetscRealPart(d); 806 vtmp = aa+ai[i]; 807 nz = ai[i+1] - ai[i]; 808 for (j=0; j<nz; j++) 809 rs += PetscAbsScalar(vtmp[j]); 810 if (rs>sctx.shift_top) sctx.shift_top = rs; 811 } 812 sctx.shift_top *= 1.1; 813 sctx.nshift_max = 5; 814 sctx.shift_lo = 0.; 815 sctx.shift_hi = 1.; 816 } 817 818 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 819 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 820 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&rtmp);CHKERRQ(ierr); 821 ierr = PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));CHKERRQ(ierr); 822 ics = ic; 823 824 #if defined(MV) 825 sctx.shift_top = 0.; 826 sctx.nshift_max = 0; 827 sctx.shift_lo = 0.; 828 sctx.shift_hi = 0.; 829 sctx.shift_fraction = 0.; 830 831 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 832 sctx.shift_top = 0.; 833 for (i=0; i<n; i++) { 834 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 835 d = (a->a)[diag[i]]; 836 rs = -PetscAbsScalar(d) - PetscRealPart(d); 837 v = a->a+ai[i]; 838 nz = ai[i+1] - ai[i]; 839 for (j=0; j<nz; j++) 840 rs += PetscAbsScalar(v[j]); 841 if (rs>sctx.shift_top) sctx.shift_top = rs; 842 } 843 if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot; 844 sctx.shift_top *= 1.1; 845 sctx.nshift_max = 5; 846 sctx.shift_lo = 0.; 847 sctx.shift_hi = 1.; 848 } 849 850 sctx.shift_amount = 0.; 851 sctx.nshift = 0; 852 #endif 853 854 do { 855 sctx.newshift = PETSC_FALSE; 856 for (i=0; i<n; i++){ 857 /* load in initial unfactored row */ 858 nz = ai[r[i]+1] - ai[r[i]]; 859 ajtmp = aj + ai[r[i]]; 860 v = a->a + ai[r[i]]; 861 /* sort permuted ajtmp and values v accordingly */ 862 for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]]; 863 ierr = PetscSortIntWithScalarArray(nz,ajtmp,v);CHKERRQ(ierr); 864 865 diag[r[i]] = ai[r[i]]; 866 for (j=0; j<nz; j++) { 867 rtmp[ajtmp[j]] = v[j]; 868 if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */ 869 } 870 rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */ 871 872 row = *ajtmp++; 873 while (row < i) { 874 pc = rtmp + row; 875 if (*pc != 0.0) { 876 pv = a->a + diag[r[row]]; 877 pj = aj + diag[r[row]] + 1; 878 879 multiplier = *pc / *pv++; 880 *pc = multiplier; 881 nz = ai[r[row]+1] - diag[r[row]] - 1; 882 for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j]; 883 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 884 } 885 row = *ajtmp++; 886 } 887 /* finished row so overwrite it onto a->a */ 888 pv = a->a + ai[r[i]] ; 889 pj = aj + ai[r[i]] ; 890 nz = ai[r[i]+1] - ai[r[i]]; 891 nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */ 892 893 rs = 0.0; 894 for (j=0; j<nz; j++) { 895 pv[j] = rtmp[pj[j]]; 896 if (j != nbdiag) rs += PetscAbsScalar(pv[j]); 897 } 898 899 sctx.rs = rs; 900 sctx.pv = pv[nbdiag]; 901 ierr = MatPivotCheck(info,&sctx,i);CHKERRQ(ierr); 902 if (sctx.newshift) break; 903 pv[nbdiag] = sctx.pv; 904 } 905 906 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) { 907 /* 908 * if no shift in this attempt & shifting & started shifting & can refine, 909 * then try lower shift 910 */ 911 sctx.shift_hi = sctx.shift_fraction; 912 sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.; 913 sctx.shift_amount = sctx.shift_fraction * sctx.shift_top; 914 sctx.newshift = PETSC_TRUE; 915 sctx.nshift++; 916 } 917 } while (sctx.newshift); 918 919 /* invert diagonal entries for simplier triangular solves */ 920 for (i=0; i<n; i++) { 921 a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]]; 922 } 923 924 ierr = PetscFree(rtmp);CHKERRQ(ierr); 925 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 926 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 927 A->ops->solve = MatSolve_SeqAIJ_InplaceWithPerm; 928 A->ops->solveadd = MatSolveAdd_SeqAIJ_inplace; 929 A->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace; 930 A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace; 931 A->assembled = PETSC_TRUE; 932 A->preallocated = PETSC_TRUE; 933 ierr = PetscLogFlops(A->cmap->n);CHKERRQ(ierr); 934 if (sctx.nshift){ 935 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 936 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); 937 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 938 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 939 } 940 } 941 PetscFunctionReturn(0); 942 } 943 944 /* ----------------------------------------------------------- */ 945 #undef __FUNCT__ 946 #define __FUNCT__ "MatLUFactor_SeqAIJ" 947 PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info) 948 { 949 PetscErrorCode ierr; 950 Mat C; 951 952 PetscFunctionBegin; 953 ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr); 954 ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr); 955 ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr); 956 A->ops->solve = C->ops->solve; 957 A->ops->solvetranspose = C->ops->solvetranspose; 958 ierr = MatHeaderCopy(A,C);CHKERRQ(ierr); 959 ierr = PetscLogObjectParent(A,((Mat_SeqAIJ*)(A->data))->icol);CHKERRQ(ierr); 960 PetscFunctionReturn(0); 961 } 962 /* ----------------------------------------------------------- */ 963 964 965 #undef __FUNCT__ 966 #define __FUNCT__ "MatSolve_SeqAIJ_inplace" 967 PetscErrorCode MatSolve_SeqAIJ_inplace(Mat A,Vec bb,Vec xx) 968 { 969 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 970 IS iscol = a->col,isrow = a->row; 971 PetscErrorCode ierr; 972 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 973 PetscInt nz; 974 const PetscInt *rout,*cout,*r,*c; 975 PetscScalar *x,*tmp,*tmps,sum; 976 const PetscScalar *b; 977 const MatScalar *aa = a->a,*v; 978 979 PetscFunctionBegin; 980 if (!n) PetscFunctionReturn(0); 981 982 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 983 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 984 tmp = a->solve_work; 985 986 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 987 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 988 989 /* forward solve the lower triangular */ 990 tmp[0] = b[*r++]; 991 tmps = tmp; 992 for (i=1; i<n; i++) { 993 v = aa + ai[i] ; 994 vi = aj + ai[i] ; 995 nz = a->diag[i] - ai[i]; 996 sum = b[*r++]; 997 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 998 tmp[i] = sum; 999 } 1000 1001 /* backward solve the upper triangular */ 1002 for (i=n-1; i>=0; i--){ 1003 v = aa + a->diag[i] + 1; 1004 vi = aj + a->diag[i] + 1; 1005 nz = ai[i+1] - a->diag[i] - 1; 1006 sum = tmp[i]; 1007 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1008 x[*c--] = tmp[i] = sum*aa[a->diag[i]]; 1009 } 1010 1011 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1012 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1013 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1014 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1015 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1016 PetscFunctionReturn(0); 1017 } 1018 1019 #undef __FUNCT__ 1020 #define __FUNCT__ "MatMatSolve_SeqAIJ_inplace" 1021 PetscErrorCode MatMatSolve_SeqAIJ_inplace(Mat A,Mat B,Mat X) 1022 { 1023 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1024 IS iscol = a->col,isrow = a->row; 1025 PetscErrorCode ierr; 1026 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1027 PetscInt nz,neq; 1028 const PetscInt *rout,*cout,*r,*c; 1029 PetscScalar *x,*b,*tmp,*tmps,sum; 1030 const MatScalar *aa = a->a,*v; 1031 PetscTruth bisdense,xisdense; 1032 1033 PetscFunctionBegin; 1034 if (!n) PetscFunctionReturn(0); 1035 1036 ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 1037 if (!bisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1038 ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 1039 if (!xisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1040 1041 ierr = MatGetArray(B,&b);CHKERRQ(ierr); 1042 ierr = MatGetArray(X,&x);CHKERRQ(ierr); 1043 1044 tmp = a->solve_work; 1045 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1046 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1047 1048 for (neq=0; neq<B->cmap->n; neq++){ 1049 /* forward solve the lower triangular */ 1050 tmp[0] = b[r[0]]; 1051 tmps = tmp; 1052 for (i=1; i<n; i++) { 1053 v = aa + ai[i] ; 1054 vi = aj + ai[i] ; 1055 nz = a->diag[i] - ai[i]; 1056 sum = b[r[i]]; 1057 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1058 tmp[i] = sum; 1059 } 1060 /* backward solve the upper triangular */ 1061 for (i=n-1; i>=0; i--){ 1062 v = aa + a->diag[i] + 1; 1063 vi = aj + a->diag[i] + 1; 1064 nz = ai[i+1] - a->diag[i] - 1; 1065 sum = tmp[i]; 1066 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1067 x[c[i]] = tmp[i] = sum*aa[a->diag[i]]; 1068 } 1069 1070 b += n; 1071 x += n; 1072 } 1073 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1074 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1075 ierr = MatRestoreArray(B,&b);CHKERRQ(ierr); 1076 ierr = MatRestoreArray(X,&x);CHKERRQ(ierr); 1077 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1078 PetscFunctionReturn(0); 1079 } 1080 1081 #undef __FUNCT__ 1082 #define __FUNCT__ "MatMatSolve_SeqAIJ" 1083 PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X) 1084 { 1085 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1086 IS iscol = a->col,isrow = a->row; 1087 PetscErrorCode ierr; 1088 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag; 1089 PetscInt nz,neq; 1090 const PetscInt *rout,*cout,*r,*c; 1091 PetscScalar *x,*b,*tmp,sum; 1092 const MatScalar *aa = a->a,*v; 1093 PetscTruth bisdense,xisdense; 1094 1095 PetscFunctionBegin; 1096 if (!n) PetscFunctionReturn(0); 1097 1098 ierr = PetscTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);CHKERRQ(ierr); 1099 if (!bisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix"); 1100 ierr = PetscTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);CHKERRQ(ierr); 1101 if (!xisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix"); 1102 1103 ierr = MatGetArray(B,&b);CHKERRQ(ierr); 1104 ierr = MatGetArray(X,&x);CHKERRQ(ierr); 1105 1106 tmp = a->solve_work; 1107 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1108 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1109 1110 for (neq=0; neq<B->cmap->n; neq++){ 1111 /* forward solve the lower triangular */ 1112 tmp[0] = b[r[0]]; 1113 v = aa; 1114 vi = aj; 1115 for (i=1; i<n; i++) { 1116 nz = ai[i+1] - ai[i]; 1117 sum = b[r[i]]; 1118 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 1119 tmp[i] = sum; 1120 v += nz; vi += nz; 1121 } 1122 1123 /* backward solve the upper triangular */ 1124 for (i=n-1; i>=0; i--){ 1125 v = aa + adiag[i+1]+1; 1126 vi = aj + adiag[i+1]+1; 1127 nz = adiag[i]-adiag[i+1]-1; 1128 sum = tmp[i]; 1129 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 1130 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 1131 } 1132 1133 b += n; 1134 x += n; 1135 } 1136 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1137 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1138 ierr = MatRestoreArray(B,&b);CHKERRQ(ierr); 1139 ierr = MatRestoreArray(X,&x);CHKERRQ(ierr); 1140 ierr = PetscLogFlops(B->cmap->n*(2.0*a->nz - n));CHKERRQ(ierr); 1141 PetscFunctionReturn(0); 1142 } 1143 1144 #undef __FUNCT__ 1145 #define __FUNCT__ "MatSolve_SeqAIJ_InplaceWithPerm" 1146 PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx) 1147 { 1148 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1149 IS iscol = a->col,isrow = a->row; 1150 PetscErrorCode ierr; 1151 const PetscInt *r,*c,*rout,*cout; 1152 PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j; 1153 PetscInt nz,row; 1154 PetscScalar *x,*b,*tmp,*tmps,sum; 1155 const MatScalar *aa = a->a,*v; 1156 1157 PetscFunctionBegin; 1158 if (!n) PetscFunctionReturn(0); 1159 1160 ierr = VecGetArray(bb,&b);CHKERRQ(ierr); 1161 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1162 tmp = a->solve_work; 1163 1164 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1165 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1166 1167 /* forward solve the lower triangular */ 1168 tmp[0] = b[*r++]; 1169 tmps = tmp; 1170 for (row=1; row<n; row++) { 1171 i = rout[row]; /* permuted row */ 1172 v = aa + ai[i] ; 1173 vi = aj + ai[i] ; 1174 nz = a->diag[i] - ai[i]; 1175 sum = b[*r++]; 1176 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1177 tmp[row] = sum; 1178 } 1179 1180 /* backward solve the upper triangular */ 1181 for (row=n-1; row>=0; row--){ 1182 i = rout[row]; /* permuted row */ 1183 v = aa + a->diag[i] + 1; 1184 vi = aj + a->diag[i] + 1; 1185 nz = ai[i+1] - a->diag[i] - 1; 1186 sum = tmp[row]; 1187 PetscSparseDenseMinusDot(sum,tmps,v,vi,nz); 1188 x[*c--] = tmp[row] = sum*aa[a->diag[i]]; 1189 } 1190 1191 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1192 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1193 ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr); 1194 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1195 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1196 PetscFunctionReturn(0); 1197 } 1198 1199 /* ----------------------------------------------------------- */ 1200 #include "../src/mat/impls/aij/seq/ftn-kernels/fsolve.h" 1201 #undef __FUNCT__ 1202 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering_inplace" 1203 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx) 1204 { 1205 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1206 PetscErrorCode ierr; 1207 PetscInt n = A->rmap->n; 1208 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag; 1209 PetscScalar *x; 1210 const PetscScalar *b; 1211 const MatScalar *aa = a->a; 1212 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1213 PetscInt adiag_i,i,nz,ai_i; 1214 const PetscInt *vi; 1215 const MatScalar *v; 1216 PetscScalar sum; 1217 #endif 1218 1219 PetscFunctionBegin; 1220 if (!n) PetscFunctionReturn(0); 1221 1222 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1223 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1224 1225 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ) 1226 fortransolveaij_(&n,x,ai,aj,adiag,aa,b); 1227 #else 1228 /* forward solve the lower triangular */ 1229 x[0] = b[0]; 1230 for (i=1; i<n; i++) { 1231 ai_i = ai[i]; 1232 v = aa + ai_i; 1233 vi = aj + ai_i; 1234 nz = adiag[i] - ai_i; 1235 sum = b[i]; 1236 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1237 x[i] = sum; 1238 } 1239 1240 /* backward solve the upper triangular */ 1241 for (i=n-1; i>=0; i--){ 1242 adiag_i = adiag[i]; 1243 v = aa + adiag_i + 1; 1244 vi = aj + adiag_i + 1; 1245 nz = ai[i+1] - adiag_i - 1; 1246 sum = x[i]; 1247 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 1248 x[i] = sum*aa[adiag_i]; 1249 } 1250 #endif 1251 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 1252 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1253 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1254 PetscFunctionReturn(0); 1255 } 1256 1257 #undef __FUNCT__ 1258 #define __FUNCT__ "MatSolveAdd_SeqAIJ_inplace" 1259 PetscErrorCode MatSolveAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec yy,Vec xx) 1260 { 1261 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1262 IS iscol = a->col,isrow = a->row; 1263 PetscErrorCode ierr; 1264 PetscInt i, n = A->rmap->n,j; 1265 PetscInt nz; 1266 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j; 1267 PetscScalar *x,*tmp,sum; 1268 const PetscScalar *b; 1269 const MatScalar *aa = a->a,*v; 1270 1271 PetscFunctionBegin; 1272 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1273 1274 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1275 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1276 tmp = a->solve_work; 1277 1278 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1279 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1); 1280 1281 /* forward solve the lower triangular */ 1282 tmp[0] = b[*r++]; 1283 for (i=1; i<n; i++) { 1284 v = aa + ai[i] ; 1285 vi = aj + ai[i] ; 1286 nz = a->diag[i] - ai[i]; 1287 sum = b[*r++]; 1288 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1289 tmp[i] = sum; 1290 } 1291 1292 /* backward solve the upper triangular */ 1293 for (i=n-1; i>=0; i--){ 1294 v = aa + a->diag[i] + 1; 1295 vi = aj + a->diag[i] + 1; 1296 nz = ai[i+1] - a->diag[i] - 1; 1297 sum = tmp[i]; 1298 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1299 tmp[i] = sum*aa[a->diag[i]]; 1300 x[*c--] += tmp[i]; 1301 } 1302 1303 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1304 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1305 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1306 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1307 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1308 1309 PetscFunctionReturn(0); 1310 } 1311 1312 #undef __FUNCT__ 1313 #define __FUNCT__ "MatSolveAdd_SeqAIJ" 1314 PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx) 1315 { 1316 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1317 IS iscol = a->col,isrow = a->row; 1318 PetscErrorCode ierr; 1319 PetscInt i, n = A->rmap->n,j; 1320 PetscInt nz; 1321 const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag; 1322 PetscScalar *x,*tmp,sum; 1323 const PetscScalar *b; 1324 const MatScalar *aa = a->a,*v; 1325 1326 PetscFunctionBegin; 1327 if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);} 1328 1329 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1330 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1331 tmp = a->solve_work; 1332 1333 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1334 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1335 1336 /* forward solve the lower triangular */ 1337 tmp[0] = b[r[0]]; 1338 v = aa; 1339 vi = aj; 1340 for (i=1; i<n; i++) { 1341 nz = ai[i+1] - ai[i]; 1342 sum = b[r[i]]; 1343 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1344 tmp[i] = sum; 1345 v += nz; vi += nz; 1346 } 1347 1348 /* backward solve the upper triangular */ 1349 v = aa + adiag[n-1]; 1350 vi = aj + adiag[n-1]; 1351 for (i=n-1; i>=0; i--){ 1352 nz = adiag[i] - adiag[i+1] - 1; 1353 sum = tmp[i]; 1354 for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]]; 1355 tmp[i] = sum*v[nz]; 1356 x[c[i]] += tmp[i]; 1357 v += nz+1; vi += nz+1; 1358 } 1359 1360 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1361 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1362 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1363 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1364 ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr); 1365 1366 PetscFunctionReturn(0); 1367 } 1368 1369 #undef __FUNCT__ 1370 #define __FUNCT__ "MatSolveTranspose_SeqAIJ_inplace" 1371 PetscErrorCode MatSolveTranspose_SeqAIJ_inplace(Mat A,Vec bb,Vec xx) 1372 { 1373 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1374 IS iscol = a->col,isrow = a->row; 1375 PetscErrorCode ierr; 1376 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1377 PetscInt i,n = A->rmap->n,j; 1378 PetscInt nz; 1379 PetscScalar *x,*tmp,s1; 1380 const MatScalar *aa = a->a,*v; 1381 const PetscScalar *b; 1382 1383 PetscFunctionBegin; 1384 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1385 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1386 tmp = a->solve_work; 1387 1388 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1389 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1390 1391 /* copy the b into temp work space according to permutation */ 1392 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1393 1394 /* forward solve the U^T */ 1395 for (i=0; i<n; i++) { 1396 v = aa + diag[i] ; 1397 vi = aj + diag[i] + 1; 1398 nz = ai[i+1] - diag[i] - 1; 1399 s1 = tmp[i]; 1400 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1401 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1402 tmp[i] = s1; 1403 } 1404 1405 /* backward solve the L^T */ 1406 for (i=n-1; i>=0; i--){ 1407 v = aa + diag[i] - 1 ; 1408 vi = aj + diag[i] - 1 ; 1409 nz = diag[i] - ai[i]; 1410 s1 = tmp[i]; 1411 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1412 } 1413 1414 /* copy tmp into x according to permutation */ 1415 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1416 1417 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1418 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1419 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1420 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1421 1422 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1423 PetscFunctionReturn(0); 1424 } 1425 1426 #undef __FUNCT__ 1427 #define __FUNCT__ "MatSolveTranspose_SeqAIJ" 1428 PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx) 1429 { 1430 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1431 IS iscol = a->col,isrow = a->row; 1432 PetscErrorCode ierr; 1433 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1434 PetscInt i,n = A->rmap->n,j; 1435 PetscInt nz; 1436 PetscScalar *x,*tmp,s1; 1437 const MatScalar *aa = a->a,*v; 1438 const PetscScalar *b; 1439 1440 PetscFunctionBegin; 1441 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1442 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1443 tmp = a->solve_work; 1444 1445 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1446 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1447 1448 /* copy the b into temp work space according to permutation */ 1449 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1450 1451 /* forward solve the U^T */ 1452 for (i=0; i<n; i++) { 1453 v = aa + adiag[i+1] + 1; 1454 vi = aj + adiag[i+1] + 1; 1455 nz = adiag[i] - adiag[i+1] - 1; 1456 s1 = tmp[i]; 1457 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1458 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1459 tmp[i] = s1; 1460 } 1461 1462 /* backward solve the L^T */ 1463 for (i=n-1; i>=0; i--){ 1464 v = aa + ai[i]; 1465 vi = aj + ai[i]; 1466 nz = ai[i+1] - ai[i]; 1467 s1 = tmp[i]; 1468 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1469 } 1470 1471 /* copy tmp into x according to permutation */ 1472 for (i=0; i<n; i++) x[r[i]] = tmp[i]; 1473 1474 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1475 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1476 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1477 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1478 1479 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1480 PetscFunctionReturn(0); 1481 } 1482 1483 #undef __FUNCT__ 1484 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ_inplace" 1485 PetscErrorCode MatSolveTransposeAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec zz,Vec xx) 1486 { 1487 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1488 IS iscol = a->col,isrow = a->row; 1489 PetscErrorCode ierr; 1490 const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi; 1491 PetscInt i,n = A->rmap->n,j; 1492 PetscInt nz; 1493 PetscScalar *x,*tmp,s1; 1494 const MatScalar *aa = a->a,*v; 1495 const PetscScalar *b; 1496 1497 PetscFunctionBegin; 1498 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1499 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1500 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1501 tmp = a->solve_work; 1502 1503 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1504 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1505 1506 /* copy the b into temp work space according to permutation */ 1507 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1508 1509 /* forward solve the U^T */ 1510 for (i=0; i<n; i++) { 1511 v = aa + diag[i] ; 1512 vi = aj + diag[i] + 1; 1513 nz = ai[i+1] - diag[i] - 1; 1514 s1 = tmp[i]; 1515 s1 *= (*v++); /* multiply by inverse of diagonal entry */ 1516 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1517 tmp[i] = s1; 1518 } 1519 1520 /* backward solve the L^T */ 1521 for (i=n-1; i>=0; i--){ 1522 v = aa + diag[i] - 1 ; 1523 vi = aj + diag[i] - 1 ; 1524 nz = diag[i] - ai[i]; 1525 s1 = tmp[i]; 1526 for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j]; 1527 } 1528 1529 /* copy tmp into x according to permutation */ 1530 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1531 1532 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1533 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1534 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1535 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1536 1537 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1538 PetscFunctionReturn(0); 1539 } 1540 1541 #undef __FUNCT__ 1542 #define __FUNCT__ "MatSolveTransposeAdd_SeqAIJ" 1543 PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx) 1544 { 1545 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 1546 IS iscol = a->col,isrow = a->row; 1547 PetscErrorCode ierr; 1548 const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi; 1549 PetscInt i,n = A->rmap->n,j; 1550 PetscInt nz; 1551 PetscScalar *x,*tmp,s1; 1552 const MatScalar *aa = a->a,*v; 1553 const PetscScalar *b; 1554 1555 PetscFunctionBegin; 1556 if (zz != xx) {ierr = VecCopy(zz,xx);CHKERRQ(ierr);} 1557 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 1558 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 1559 tmp = a->solve_work; 1560 1561 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 1562 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 1563 1564 /* copy the b into temp work space according to permutation */ 1565 for (i=0; i<n; i++) tmp[i] = b[c[i]]; 1566 1567 /* forward solve the U^T */ 1568 for (i=0; i<n; i++) { 1569 v = aa + adiag[i+1] + 1; 1570 vi = aj + adiag[i+1] + 1; 1571 nz = adiag[i] - adiag[i+1] - 1; 1572 s1 = tmp[i]; 1573 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 1574 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1575 tmp[i] = s1; 1576 } 1577 1578 1579 /* backward solve the L^T */ 1580 for (i=n-1; i>=0; i--){ 1581 v = aa + ai[i] ; 1582 vi = aj + ai[i]; 1583 nz = ai[i+1] - ai[i]; 1584 s1 = tmp[i]; 1585 for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j]; 1586 } 1587 1588 /* copy tmp into x according to permutation */ 1589 for (i=0; i<n; i++) x[r[i]] += tmp[i]; 1590 1591 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 1592 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 1593 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 1594 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 1595 1596 ierr = PetscLogFlops(2.0*a->nz-A->cmap->n);CHKERRQ(ierr); 1597 PetscFunctionReturn(0); 1598 } 1599 1600 /* ----------------------------------------------------------------*/ 1601 1602 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat,Mat,MatDuplicateOption,PetscTruth); 1603 1604 /* 1605 ilu() under revised new data structure. 1606 Factored arrays bj and ba are stored as 1607 L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:) 1608 1609 bi=fact->i is an array of size n+1, in which 1610 bi+ 1611 bi[i]: points to 1st entry of L(i,:),i=0,...,n-1 1612 bi[n]: points to L(n-1,n-1)+1 1613 1614 bdiag=fact->diag is an array of size n+1,in which 1615 bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1 1616 bdiag[n]: points to entry of U(n-1,0)-1 1617 1618 U(i,:) contains bdiag[i] as its last entry, i.e., 1619 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 1620 */ 1621 #undef __FUNCT__ 1622 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_ilu0" 1623 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1624 { 1625 1626 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1627 PetscErrorCode ierr; 1628 const PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag; 1629 PetscInt i,j,k=0,nz,*bi,*bj,*bdiag; 1630 PetscTruth missing; 1631 IS isicol; 1632 1633 PetscFunctionBegin; 1634 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 1635 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 1636 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 1637 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1638 1639 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr); 1640 b = (Mat_SeqAIJ*)(fact)->data; 1641 1642 /* allocate matrix arrays for new data structure */ 1643 ierr = PetscMalloc3(ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,n+1,PetscInt,&b->i);CHKERRQ(ierr); 1644 ierr = PetscLogObjectMemory(fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1645 b->singlemalloc = PETSC_TRUE; 1646 if (!b->diag){ 1647 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr); 1648 ierr = PetscLogObjectMemory(fact,(n+1)*sizeof(PetscInt));CHKERRQ(ierr); 1649 } 1650 bdiag = b->diag; 1651 1652 if (n > 0) { 1653 ierr = PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));CHKERRQ(ierr); 1654 } 1655 1656 /* set bi and bj with new data structure */ 1657 bi = b->i; 1658 bj = b->j; 1659 1660 /* L part */ 1661 bi[0] = 0; 1662 for (i=0; i<n; i++){ 1663 nz = adiag[i] - ai[i]; 1664 bi[i+1] = bi[i] + nz; 1665 aj = a->j + ai[i]; 1666 for (j=0; j<nz; j++){ 1667 /* *bj = aj[j]; bj++; */ 1668 bj[k++] = aj[j]; 1669 } 1670 } 1671 1672 /* U part */ 1673 bdiag[n] = bi[n]-1; 1674 for (i=n-1; i>=0; i--){ 1675 nz = ai[i+1] - adiag[i] - 1; 1676 aj = a->j + adiag[i] + 1; 1677 for (j=0; j<nz; j++){ 1678 /* *bj = aj[j]; bj++; */ 1679 bj[k++] = aj[j]; 1680 } 1681 /* diag[i] */ 1682 /* *bj = i; bj++; */ 1683 bj[k++] = i; 1684 bdiag[i] = bdiag[i+1] + nz + 1; 1685 } 1686 1687 fact->factortype = MAT_FACTOR_ILU; 1688 fact->info.factor_mallocs = 0; 1689 fact->info.fill_ratio_given = info->fill; 1690 fact->info.fill_ratio_needed = 1.0; 1691 fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1692 1693 b = (Mat_SeqAIJ*)(fact)->data; 1694 b->row = isrow; 1695 b->col = iscol; 1696 b->icol = isicol; 1697 ierr = PetscMalloc((fact->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1698 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1699 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1700 PetscFunctionReturn(0); 1701 } 1702 1703 #undef __FUNCT__ 1704 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ" 1705 PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1706 { 1707 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1708 IS isicol; 1709 PetscErrorCode ierr; 1710 const PetscInt *r,*ic; 1711 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j; 1712 PetscInt *bi,*cols,nnz,*cols_lvl; 1713 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1714 PetscInt i,levels,diagonal_fill; 1715 PetscTruth col_identity,row_identity; 1716 PetscReal f; 1717 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1718 PetscBT lnkbt; 1719 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1720 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1721 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1722 1723 PetscFunctionBegin; 1724 /* Uncomment the old data struct part only while testing new data structure for MatSolve() */ 1725 /* 1726 PetscTruth olddatastruct=PETSC_FALSE; 1727 ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_old",&olddatastruct,PETSC_NULL);CHKERRQ(ierr); 1728 if(olddatastruct){ 1729 ierr = MatILUFactorSymbolic_SeqAIJ_inplace(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1730 PetscFunctionReturn(0); 1731 } 1732 */ 1733 1734 levels = (PetscInt)info->levels; 1735 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1736 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1737 1738 if (!levels && row_identity && col_identity) { 1739 /* special case: ilu(0) with natural ordering */ 1740 ierr = MatILUFactorSymbolic_SeqAIJ_ilu0(fact,A,isrow,iscol,info);CHKERRQ(ierr); 1741 if (a->inode.size) { 1742 fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode; 1743 } 1744 PetscFunctionReturn(0); 1745 } 1746 1747 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 1748 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1749 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1750 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1751 1752 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1753 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1754 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1755 bi[0] = bdiag[0] = 0; 1756 1757 ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr); 1758 1759 /* create a linked list for storing column indices of the active row */ 1760 nlnk = n + 1; 1761 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1762 1763 /* initial FreeSpace size is f*(ai[n]+1) */ 1764 f = info->fill; 1765 diagonal_fill = (PetscInt)info->diagonal_fill; 1766 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1767 current_space = free_space; 1768 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1769 current_space_lvl = free_space_lvl; 1770 1771 for (i=0; i<n; i++) { 1772 nzi = 0; 1773 /* copy current row into linked list */ 1774 nnz = ai[r[i]+1] - ai[r[i]]; 1775 if (!nnz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1776 cols = aj + ai[r[i]]; 1777 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1778 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1779 nzi += nlnk; 1780 1781 /* make sure diagonal entry is included */ 1782 if (diagonal_fill && lnk[i] == -1) { 1783 fm = n; 1784 while (lnk[fm] < i) fm = lnk[fm]; 1785 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1786 lnk[fm] = i; 1787 lnk_lvl[i] = 0; 1788 nzi++; dcount++; 1789 } 1790 1791 /* add pivot rows into the active row */ 1792 nzbd = 0; 1793 prow = lnk[n]; 1794 while (prow < i) { 1795 nnz = bdiag[prow]; 1796 cols = bj_ptr[prow] + nnz + 1; 1797 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1798 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1799 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1800 nzi += nlnk; 1801 prow = lnk[prow]; 1802 nzbd++; 1803 } 1804 bdiag[i] = nzbd; 1805 bi[i+1] = bi[i] + nzi; 1806 1807 /* if free space is not available, make more free space */ 1808 if (current_space->local_remaining<nzi) { 1809 nnz = 2*nzi*(n - i); /* estimated and max additional space needed */ 1810 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 1811 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 1812 reallocs++; 1813 } 1814 1815 /* copy data into free_space and free_space_lvl, then initialize lnk */ 1816 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 1817 bj_ptr[i] = current_space->array; 1818 bjlvl_ptr[i] = current_space_lvl->array; 1819 1820 /* make sure the active row i has diagonal entry */ 1821 if (*(bj_ptr[i]+bdiag[i]) != i) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\ntry running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 1822 1823 current_space->array += nzi; 1824 current_space->local_used += nzi; 1825 current_space->local_remaining -= nzi; 1826 current_space_lvl->array += nzi; 1827 current_space_lvl->local_used += nzi; 1828 current_space_lvl->local_remaining -= nzi; 1829 } 1830 1831 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 1832 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 1833 1834 /* destroy list of free space and other temporary arrays */ 1835 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 1836 1837 /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */ 1838 ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr); 1839 1840 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 1841 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 1842 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 1843 1844 #if defined(PETSC_USE_INFO) 1845 { 1846 PetscReal af = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 1847 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 1848 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 1849 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 1850 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 1851 if (diagonal_fill) { 1852 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 1853 } 1854 } 1855 #endif 1856 1857 /* put together the new matrix */ 1858 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 1859 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 1860 b = (Mat_SeqAIJ*)(fact)->data; 1861 b->free_a = PETSC_TRUE; 1862 b->free_ij = PETSC_TRUE; 1863 b->singlemalloc = PETSC_FALSE; 1864 ierr = PetscMalloc((bdiag[0]+1)*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 1865 b->j = bj; 1866 b->i = bi; 1867 b->diag = bdiag; 1868 b->ilen = 0; 1869 b->imax = 0; 1870 b->row = isrow; 1871 b->col = iscol; 1872 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1873 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1874 b->icol = isicol; 1875 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1876 /* In b structure: Free imax, ilen, old a, old j. 1877 Allocate bdiag, solve_work, new a, new j */ 1878 ierr = PetscLogObjectMemory(fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 1879 b->maxnz = b->nz = bdiag[0]+1; 1880 (fact)->info.factor_mallocs = reallocs; 1881 (fact)->info.fill_ratio_given = f; 1882 (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]); 1883 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ; 1884 if (a->inode.size) { 1885 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode; 1886 } 1887 PetscFunctionReturn(0); 1888 } 1889 1890 #undef __FUNCT__ 1891 #define __FUNCT__ "MatILUFactorSymbolic_SeqAIJ_inplace" 1892 PetscErrorCode MatILUFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info) 1893 { 1894 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b; 1895 IS isicol; 1896 PetscErrorCode ierr; 1897 const PetscInt *r,*ic; 1898 PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,d; 1899 PetscInt *bi,*cols,nnz,*cols_lvl; 1900 PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0; 1901 PetscInt i,levels,diagonal_fill; 1902 PetscTruth col_identity,row_identity; 1903 PetscReal f; 1904 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL; 1905 PetscBT lnkbt; 1906 PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr; 1907 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 1908 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 1909 PetscTruth missing; 1910 1911 PetscFunctionBegin; 1912 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 1913 f = info->fill; 1914 levels = (PetscInt)info->levels; 1915 diagonal_fill = (PetscInt)info->diagonal_fill; 1916 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 1917 1918 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 1919 ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr); 1920 if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */ 1921 ierr = MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr); 1922 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 1923 if (a->inode.size) { 1924 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace; 1925 } 1926 fact->factortype = MAT_FACTOR_ILU; 1927 (fact)->info.factor_mallocs = 0; 1928 (fact)->info.fill_ratio_given = info->fill; 1929 (fact)->info.fill_ratio_needed = 1.0; 1930 b = (Mat_SeqAIJ*)(fact)->data; 1931 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 1932 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 1933 b->row = isrow; 1934 b->col = iscol; 1935 b->icol = isicol; 1936 ierr = PetscMalloc(((fact)->rmap->n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 1937 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 1938 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 1939 PetscFunctionReturn(0); 1940 } 1941 1942 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 1943 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 1944 1945 /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */ 1946 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 1947 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); 1948 bi[0] = bdiag[0] = 0; 1949 1950 ierr = PetscMalloc2(n,PetscInt*,&bj_ptr,n,PetscInt*,&bjlvl_ptr);CHKERRQ(ierr); 1951 1952 /* create a linked list for storing column indices of the active row */ 1953 nlnk = n + 1; 1954 ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1955 1956 /* initial FreeSpace size is f*(ai[n]+1) */ 1957 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr); 1958 current_space = free_space; 1959 ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr); 1960 current_space_lvl = free_space_lvl; 1961 1962 for (i=0; i<n; i++) { 1963 nzi = 0; 1964 /* copy current row into linked list */ 1965 nnz = ai[r[i]+1] - ai[r[i]]; 1966 if (!nnz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 1967 cols = aj + ai[r[i]]; 1968 lnk[i] = -1; /* marker to indicate if diagonal exists */ 1969 ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 1970 nzi += nlnk; 1971 1972 /* make sure diagonal entry is included */ 1973 if (diagonal_fill && lnk[i] == -1) { 1974 fm = n; 1975 while (lnk[fm] < i) fm = lnk[fm]; 1976 lnk[i] = lnk[fm]; /* insert diagonal into linked list */ 1977 lnk[fm] = i; 1978 lnk_lvl[i] = 0; 1979 nzi++; dcount++; 1980 } 1981 1982 /* add pivot rows into the active row */ 1983 nzbd = 0; 1984 prow = lnk[n]; 1985 while (prow < i) { 1986 nnz = bdiag[prow]; 1987 cols = bj_ptr[prow] + nnz + 1; 1988 cols_lvl = bjlvl_ptr[prow] + nnz + 1; 1989 nnz = bi[prow+1] - bi[prow] - nnz - 1; 1990 ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr); 1991 nzi += nlnk; 1992 prow = lnk[prow]; 1993 nzbd++; 1994 } 1995 bdiag[i] = nzbd; 1996 bi[i+1] = bi[i] + nzi; 1997 1998 /* if free space is not available, make more free space */ 1999 if (current_space->local_remaining<nzi) { 2000 nnz = nzi*(n - i); /* estimated and max additional space needed */ 2001 ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr); 2002 ierr = PetscFreeSpaceGet(nnz,¤t_space_lvl);CHKERRQ(ierr); 2003 reallocs++; 2004 } 2005 2006 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2007 ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2008 bj_ptr[i] = current_space->array; 2009 bjlvl_ptr[i] = current_space_lvl->array; 2010 2011 /* make sure the active row i has diagonal entry */ 2012 if (*(bj_ptr[i]+bdiag[i]) != i) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\ntry running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i); 2013 2014 current_space->array += nzi; 2015 current_space->local_used += nzi; 2016 current_space->local_remaining -= nzi; 2017 current_space_lvl->array += nzi; 2018 current_space_lvl->local_used += nzi; 2019 current_space_lvl->local_remaining -= nzi; 2020 } 2021 2022 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 2023 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 2024 2025 /* destroy list of free space and other temporary arrays */ 2026 ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 2027 ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr); /* copy free_space -> bj */ 2028 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2029 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2030 ierr = PetscFree2(bj_ptr,bjlvl_ptr);CHKERRQ(ierr); 2031 2032 #if defined(PETSC_USE_INFO) 2033 { 2034 PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2035 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr); 2036 ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2037 ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr); 2038 ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr); 2039 if (diagonal_fill) { 2040 ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr); 2041 } 2042 } 2043 #endif 2044 2045 /* put together the new matrix */ 2046 ierr = MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 2047 ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr); 2048 b = (Mat_SeqAIJ*)(fact)->data; 2049 b->free_a = PETSC_TRUE; 2050 b->free_ij = PETSC_TRUE; 2051 b->singlemalloc = PETSC_FALSE; 2052 ierr = PetscMalloc(bi[n]*sizeof(PetscScalar),&b->a);CHKERRQ(ierr); 2053 b->j = bj; 2054 b->i = bi; 2055 for (i=0; i<n; i++) bdiag[i] += bi[i]; 2056 b->diag = bdiag; 2057 b->ilen = 0; 2058 b->imax = 0; 2059 b->row = isrow; 2060 b->col = iscol; 2061 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 2062 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 2063 b->icol = isicol; 2064 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2065 /* In b structure: Free imax, ilen, old a, old j. 2066 Allocate bdiag, solve_work, new a, new j */ 2067 ierr = PetscLogObjectMemory(fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));CHKERRQ(ierr); 2068 b->maxnz = b->nz = bi[n] ; 2069 (fact)->info.factor_mallocs = reallocs; 2070 (fact)->info.fill_ratio_given = f; 2071 (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]); 2072 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace; 2073 if (a->inode.size) { 2074 (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace; 2075 } 2076 PetscFunctionReturn(0); 2077 } 2078 2079 #undef __FUNCT__ 2080 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ" 2081 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info) 2082 { 2083 Mat C = B; 2084 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2085 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2086 IS ip=b->row,iip = b->icol; 2087 PetscErrorCode ierr; 2088 const PetscInt *rip,*riip; 2089 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp; 2090 PetscInt *ai=a->i,*aj=a->j; 2091 PetscInt k,jmin,jmax,*c2r,*il,col,nexti,ili,nz; 2092 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2093 PetscTruth perm_identity; 2094 FactorShiftCtx sctx; 2095 PetscReal rs; 2096 MatScalar d,*v; 2097 2098 PetscFunctionBegin; 2099 /* MatPivotSetUp(): initialize shift context sctx */ 2100 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 2101 2102 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 2103 sctx.shift_top = info->zeropivot; 2104 for (i=0; i<mbs; i++) { 2105 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 2106 d = (aa)[a->diag[i]]; 2107 rs = -PetscAbsScalar(d) - PetscRealPart(d); 2108 v = aa+ai[i]; 2109 nz = ai[i+1] - ai[i]; 2110 for (j=0; j<nz; j++) 2111 rs += PetscAbsScalar(v[j]); 2112 if (rs>sctx.shift_top) sctx.shift_top = rs; 2113 } 2114 sctx.shift_top *= 1.1; 2115 sctx.nshift_max = 5; 2116 sctx.shift_lo = 0.; 2117 sctx.shift_hi = 1.; 2118 } 2119 2120 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2121 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2122 2123 /* allocate working arrays 2124 c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col 2125 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 2126 */ 2127 ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&c2r);CHKERRQ(ierr); 2128 2129 do { 2130 sctx.newshift = PETSC_FALSE; 2131 2132 for (i=0; i<mbs; i++) c2r[i] = mbs; 2133 il[0] = 0; 2134 2135 for (k = 0; k<mbs; k++){ 2136 /* zero rtmp */ 2137 nz = bi[k+1] - bi[k]; 2138 bjtmp = bj + bi[k]; 2139 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2140 2141 /* load in initial unfactored row */ 2142 bval = ba + bi[k]; 2143 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2144 for (j = jmin; j < jmax; j++){ 2145 col = riip[aj[j]]; 2146 if (col >= k){ /* only take upper triangular entry */ 2147 rtmp[col] = aa[j]; 2148 *bval++ = 0.0; /* for in-place factorization */ 2149 } 2150 } 2151 /* shift the diagonal of the matrix: ZeropivotApply() */ 2152 rtmp[k] += sctx.shift_amount; /* shift the diagonal of the matrix */ 2153 2154 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2155 dk = rtmp[k]; 2156 i = c2r[k]; /* first row to be added to k_th row */ 2157 2158 while (i < k){ 2159 nexti = c2r[i]; /* next row to be added to k_th row */ 2160 2161 /* compute multiplier, update diag(k) and U(i,k) */ 2162 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2163 uikdi = - ba[ili]*ba[bdiag[i]]; /* diagonal(k) */ 2164 dk += uikdi*ba[ili]; /* update diag[k] */ 2165 ba[ili] = uikdi; /* -U(i,k) */ 2166 2167 /* add multiple of row i to k-th row */ 2168 jmin = ili + 1; jmax = bi[i+1]; 2169 if (jmin < jmax){ 2170 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2171 /* update il and c2r for row i */ 2172 il[i] = jmin; 2173 j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i; 2174 } 2175 i = nexti; 2176 } 2177 2178 /* copy data into U(k,:) */ 2179 rs = 0.0; 2180 jmin = bi[k]; jmax = bi[k+1]-1; 2181 if (jmin < jmax) { 2182 for (j=jmin; j<jmax; j++){ 2183 col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]); 2184 } 2185 /* add the k-th row into il and c2r */ 2186 il[k] = jmin; 2187 i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k; 2188 } 2189 2190 /* MatPivotCheck() */ 2191 sctx.rs = rs; 2192 sctx.pv = dk; 2193 ierr = MatPivotCheck(info,&sctx,i);CHKERRQ(ierr); 2194 if(sctx.newshift) break; 2195 dk = sctx.pv; 2196 2197 ba[bdiag[k]] = 1.0/dk; /* U(k,k) */ 2198 } 2199 } while (sctx.newshift); 2200 2201 ierr = PetscFree3(rtmp,il,c2r);CHKERRQ(ierr); 2202 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2203 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2204 2205 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2206 if (perm_identity){ 2207 B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2208 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering; 2209 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering; 2210 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering; 2211 } else { 2212 B->ops->solve = MatSolve_SeqSBAIJ_1; 2213 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1; 2214 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1; 2215 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1; 2216 } 2217 2218 C->assembled = PETSC_TRUE; 2219 C->preallocated = PETSC_TRUE; 2220 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2221 2222 /* MatPivotView() */ 2223 if (sctx.nshift){ 2224 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 2225 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); 2226 } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 2227 ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2228 } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS){ 2229 ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftamount);CHKERRQ(ierr); 2230 } 2231 } 2232 PetscFunctionReturn(0); 2233 } 2234 2235 #undef __FUNCT__ 2236 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqAIJ_inplace" 2237 PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info) 2238 { 2239 Mat C = B; 2240 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data; 2241 Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data; 2242 IS ip=b->row,iip = b->icol; 2243 PetscErrorCode ierr; 2244 const PetscInt *rip,*riip; 2245 PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp; 2246 PetscInt *ai=a->i,*aj=a->j; 2247 PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz; 2248 MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi; 2249 PetscTruth perm_identity; 2250 FactorShiftCtx sctx; 2251 PetscReal rs; 2252 MatScalar d,*v; 2253 2254 PetscFunctionBegin; 2255 /* MatPivotSetUp(): initialize shift context sctx */ 2256 ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr); 2257 2258 if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */ 2259 sctx.shift_top = info->zeropivot; 2260 for (i=0; i<mbs; i++) { 2261 /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */ 2262 d = (aa)[a->diag[i]]; 2263 rs = -PetscAbsScalar(d) - PetscRealPart(d); 2264 v = aa+ai[i]; 2265 nz = ai[i+1] - ai[i]; 2266 for (j=0; j<nz; j++) 2267 rs += PetscAbsScalar(v[j]); 2268 if (rs>sctx.shift_top) sctx.shift_top = rs; 2269 } 2270 sctx.shift_top *= 1.1; 2271 sctx.nshift_max = 5; 2272 sctx.shift_lo = 0.; 2273 sctx.shift_hi = 1.; 2274 } 2275 2276 ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr); 2277 ierr = ISGetIndices(iip,&riip);CHKERRQ(ierr); 2278 2279 /* initialization */ 2280 ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr); 2281 2282 do { 2283 sctx.newshift = PETSC_FALSE; 2284 2285 for (i=0; i<mbs; i++) jl[i] = mbs; 2286 il[0] = 0; 2287 2288 for (k = 0; k<mbs; k++){ 2289 /* zero rtmp */ 2290 nz = bi[k+1] - bi[k]; 2291 bjtmp = bj + bi[k]; 2292 for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0; 2293 2294 bval = ba + bi[k]; 2295 /* initialize k-th row by the perm[k]-th row of A */ 2296 jmin = ai[rip[k]]; jmax = ai[rip[k]+1]; 2297 for (j = jmin; j < jmax; j++){ 2298 col = riip[aj[j]]; 2299 if (col >= k){ /* only take upper triangular entry */ 2300 rtmp[col] = aa[j]; 2301 *bval++ = 0.0; /* for in-place factorization */ 2302 } 2303 } 2304 /* shift the diagonal of the matrix */ 2305 if (sctx.nshift) rtmp[k] += sctx.shift_amount; 2306 2307 /* modify k-th row by adding in those rows i with U(i,k)!=0 */ 2308 dk = rtmp[k]; 2309 i = jl[k]; /* first row to be added to k_th row */ 2310 2311 while (i < k){ 2312 nexti = jl[i]; /* next row to be added to k_th row */ 2313 2314 /* compute multiplier, update diag(k) and U(i,k) */ 2315 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 2316 uikdi = - ba[ili]*ba[bi[i]]; /* diagonal(k) */ 2317 dk += uikdi*ba[ili]; 2318 ba[ili] = uikdi; /* -U(i,k) */ 2319 2320 /* add multiple of row i to k-th row */ 2321 jmin = ili + 1; jmax = bi[i+1]; 2322 if (jmin < jmax){ 2323 for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j]; 2324 /* update il and jl for row i */ 2325 il[i] = jmin; 2326 j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; 2327 } 2328 i = nexti; 2329 } 2330 2331 /* shift the diagonals when zero pivot is detected */ 2332 /* compute rs=sum of abs(off-diagonal) */ 2333 rs = 0.0; 2334 jmin = bi[k]+1; 2335 nz = bi[k+1] - jmin; 2336 bcol = bj + jmin; 2337 for (j=0; j<nz; j++) { 2338 rs += PetscAbsScalar(rtmp[bcol[j]]); 2339 } 2340 2341 sctx.rs = rs; 2342 sctx.pv = dk; 2343 ierr = MatPivotCheck(info,&sctx,k);CHKERRQ(ierr); 2344 if (sctx.newshift) break; 2345 dk = sctx.pv; 2346 2347 /* copy data into U(k,:) */ 2348 ba[bi[k]] = 1.0/dk; /* U(k,k) */ 2349 jmin = bi[k]+1; jmax = bi[k+1]; 2350 if (jmin < jmax) { 2351 for (j=jmin; j<jmax; j++){ 2352 col = bj[j]; ba[j] = rtmp[col]; 2353 } 2354 /* add the k-th row into il and jl */ 2355 il[k] = jmin; 2356 i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; 2357 } 2358 } 2359 } while (sctx.newshift); 2360 2361 ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr); 2362 ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr); 2363 ierr = ISRestoreIndices(iip,&riip);CHKERRQ(ierr); 2364 2365 ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr); 2366 if (perm_identity){ 2367 B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2368 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2369 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2370 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace; 2371 } else { 2372 B->ops->solve = MatSolve_SeqSBAIJ_1_inplace; 2373 B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_inplace; 2374 B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_inplace; 2375 B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_inplace; 2376 } 2377 2378 C->assembled = PETSC_TRUE; 2379 C->preallocated = PETSC_TRUE; 2380 ierr = PetscLogFlops(C->rmap->n);CHKERRQ(ierr); 2381 if (sctx.nshift){ 2382 if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) { 2383 ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2384 } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { 2385 ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr); 2386 } 2387 } 2388 PetscFunctionReturn(0); 2389 } 2390 2391 /* 2392 icc() under revised new data structure. 2393 Factored arrays bj and ba are stored as 2394 U(0,:),...,U(i,:),U(n-1,:) 2395 2396 ui=fact->i is an array of size n+1, in which 2397 ui+ 2398 ui[i]: points to 1st entry of U(i,:),i=0,...,n-1 2399 ui[n]: points to U(n-1,n-1)+1 2400 2401 udiag=fact->diag is an array of size n,in which 2402 udiag[i]: points to diagonal of U(i,:), i=0,...,n-1 2403 2404 U(i,:) contains udiag[i] as its last entry, i.e., 2405 U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i]) 2406 */ 2407 2408 #undef __FUNCT__ 2409 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ" 2410 PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2411 { 2412 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2413 Mat_SeqSBAIJ *b; 2414 PetscErrorCode ierr; 2415 PetscTruth perm_identity,missing; 2416 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2417 const PetscInt *rip,*riip; 2418 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2419 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2420 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2421 PetscReal fill=info->fill,levels=info->levels; 2422 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2423 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2424 PetscBT lnkbt; 2425 IS iperm; 2426 2427 PetscFunctionBegin; 2428 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2429 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2430 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2431 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2432 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2433 2434 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2435 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2436 ui[0] = 0; 2437 2438 /* ICC(0) without matrix ordering: simply rearrange column indices */ 2439 if (!levels && perm_identity) { 2440 for (i=0; i<am; i++) { 2441 ncols = ai[i+1] - a->diag[i]; 2442 ui[i+1] = ui[i] + ncols; 2443 udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */ 2444 } 2445 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2446 cols = uj; 2447 for (i=0; i<am; i++) { 2448 aj = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */ 2449 ncols = ai[i+1] - a->diag[i] -1; 2450 for (j=0; j<ncols; j++) *cols++ = aj[j]; 2451 *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */ 2452 } 2453 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2454 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2455 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2456 2457 /* initialization */ 2458 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2459 2460 /* jl: linked list for storing indices of the pivot rows 2461 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2462 ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr); 2463 for (i=0; i<am; i++){ 2464 jl[i] = am; il[i] = 0; 2465 } 2466 2467 /* create and initialize a linked list for storing column indices of the active row k */ 2468 nlnk = am + 1; 2469 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2470 2471 /* initial FreeSpace size is fill*(ai[am]+1) */ 2472 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2473 current_space = free_space; 2474 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2475 current_space_lvl = free_space_lvl; 2476 2477 for (k=0; k<am; k++){ /* for each active row k */ 2478 /* initialize lnk by the column indices of row rip[k] of A */ 2479 nzk = 0; 2480 ncols = ai[rip[k]+1] - ai[rip[k]]; 2481 if (!ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2482 ncols_upper = 0; 2483 for (j=0; j<ncols; j++){ 2484 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2485 if (riip[i] >= k){ /* only take upper triangular entry */ 2486 ajtmp[ncols_upper] = i; 2487 ncols_upper++; 2488 } 2489 } 2490 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2491 nzk += nlnk; 2492 2493 /* update lnk by computing fill-in for each pivot row to be merged in */ 2494 prow = jl[k]; /* 1st pivot row */ 2495 2496 while (prow < k){ 2497 nextprow = jl[prow]; 2498 2499 /* merge prow into k-th row */ 2500 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2501 jmax = ui[prow+1]; 2502 ncols = jmax-jmin; 2503 i = jmin - ui[prow]; 2504 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2505 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2506 j = *(uj - 1); 2507 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2508 nzk += nlnk; 2509 2510 /* update il and jl for prow */ 2511 if (jmin < jmax){ 2512 il[prow] = jmin; 2513 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2514 } 2515 prow = nextprow; 2516 } 2517 2518 /* if free space is not available, make more free space */ 2519 if (current_space->local_remaining<nzk) { 2520 i = am - k + 1; /* num of unfactored rows */ 2521 i *= PetscMin(nzk, i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2522 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2523 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2524 reallocs++; 2525 } 2526 2527 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2528 if (nzk == 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2529 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2530 2531 /* add the k-th row into il and jl */ 2532 if (nzk > 1){ 2533 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2534 jl[k] = jl[i]; jl[i] = k; 2535 il[k] = ui[k] + 1; 2536 } 2537 uj_ptr[k] = current_space->array; 2538 uj_lvl_ptr[k] = current_space_lvl->array; 2539 2540 current_space->array += nzk; 2541 current_space->local_used += nzk; 2542 current_space->local_remaining -= nzk; 2543 2544 current_space_lvl->array += nzk; 2545 current_space_lvl->local_used += nzk; 2546 current_space_lvl->local_remaining -= nzk; 2547 2548 ui[k+1] = ui[k] + nzk; 2549 } 2550 2551 #if defined(PETSC_USE_INFO) 2552 if (ai[am] != 0) { 2553 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2554 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2555 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2556 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2557 } else { 2558 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2559 } 2560 #endif 2561 2562 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2563 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2564 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2565 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2566 2567 /* destroy list of free space and other temporary array(s) */ 2568 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2569 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */ 2570 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2571 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2572 2573 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2574 2575 /* put together the new matrix in MATSEQSBAIJ format */ 2576 b = (Mat_SeqSBAIJ*)(fact)->data; 2577 b->singlemalloc = PETSC_FALSE; 2578 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2579 b->j = uj; 2580 b->i = ui; 2581 b->diag = udiag; 2582 b->free_diag = PETSC_TRUE; 2583 b->ilen = 0; 2584 b->imax = 0; 2585 b->row = perm; 2586 b->col = perm; 2587 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2588 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2589 b->icol = iperm; 2590 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2591 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2592 ierr = PetscLogObjectMemory(fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2593 b->maxnz = b->nz = ui[am]; 2594 b->free_a = PETSC_TRUE; 2595 b->free_ij = PETSC_TRUE; 2596 2597 fact->info.factor_mallocs = reallocs; 2598 fact->info.fill_ratio_given = fill; 2599 if (ai[am] != 0) { 2600 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2601 } else { 2602 fact->info.fill_ratio_needed = 0.0; 2603 } 2604 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2605 PetscFunctionReturn(0); 2606 } 2607 2608 #undef __FUNCT__ 2609 #define __FUNCT__ "MatICCFactorSymbolic_SeqAIJ_inplace" 2610 PetscErrorCode MatICCFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2611 { 2612 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2613 Mat_SeqSBAIJ *b; 2614 PetscErrorCode ierr; 2615 PetscTruth perm_identity,missing; 2616 PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag; 2617 const PetscInt *rip,*riip; 2618 PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow; 2619 PetscInt nlnk,*lnk,*lnk_lvl=PETSC_NULL,d; 2620 PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr; 2621 PetscReal fill=info->fill,levels=info->levels; 2622 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2623 PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL; 2624 PetscBT lnkbt; 2625 IS iperm; 2626 2627 PetscFunctionBegin; 2628 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2629 ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr); 2630 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d); 2631 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2632 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2633 2634 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2635 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2636 ui[0] = 0; 2637 2638 /* ICC(0) without matrix ordering: simply copies fill pattern */ 2639 if (!levels && perm_identity) { 2640 2641 for (i=0; i<am; i++) { 2642 ui[i+1] = ui[i] + ai[i+1] - a->diag[i]; 2643 udiag[i] = ui[i]; 2644 } 2645 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2646 cols = uj; 2647 for (i=0; i<am; i++) { 2648 aj = a->j + a->diag[i]; 2649 ncols = ui[i+1] - ui[i]; 2650 for (j=0; j<ncols; j++) *cols++ = *aj++; 2651 } 2652 } else { /* case: levels>0 || (levels=0 && !perm_identity) */ 2653 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2654 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2655 2656 /* initialization */ 2657 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ajtmp);CHKERRQ(ierr); 2658 2659 /* jl: linked list for storing indices of the pivot rows 2660 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2661 ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&jl,am,PetscInt,&il);CHKERRQ(ierr); 2662 for (i=0; i<am; i++){ 2663 jl[i] = am; il[i] = 0; 2664 } 2665 2666 /* create and initialize a linked list for storing column indices of the active row k */ 2667 nlnk = am + 1; 2668 ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2669 2670 /* initial FreeSpace size is fill*(ai[am]+1) */ 2671 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2672 current_space = free_space; 2673 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space_lvl);CHKERRQ(ierr); 2674 current_space_lvl = free_space_lvl; 2675 2676 for (k=0; k<am; k++){ /* for each active row k */ 2677 /* initialize lnk by the column indices of row rip[k] of A */ 2678 nzk = 0; 2679 ncols = ai[rip[k]+1] - ai[rip[k]]; 2680 if (!ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2681 ncols_upper = 0; 2682 for (j=0; j<ncols; j++){ 2683 i = *(aj + ai[rip[k]] + j); /* unpermuted column index */ 2684 if (riip[i] >= k){ /* only take upper triangular entry */ 2685 ajtmp[ncols_upper] = i; 2686 ncols_upper++; 2687 } 2688 } 2689 ierr = PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr); 2690 nzk += nlnk; 2691 2692 /* update lnk by computing fill-in for each pivot row to be merged in */ 2693 prow = jl[k]; /* 1st pivot row */ 2694 2695 while (prow < k){ 2696 nextprow = jl[prow]; 2697 2698 /* merge prow into k-th row */ 2699 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2700 jmax = ui[prow+1]; 2701 ncols = jmax-jmin; 2702 i = jmin - ui[prow]; 2703 cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2704 uj = uj_lvl_ptr[prow] + i; /* levels of cols */ 2705 j = *(uj - 1); 2706 ierr = PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);CHKERRQ(ierr); 2707 nzk += nlnk; 2708 2709 /* update il and jl for prow */ 2710 if (jmin < jmax){ 2711 il[prow] = jmin; 2712 j = *cols; jl[prow] = jl[j]; jl[j] = prow; 2713 } 2714 prow = nextprow; 2715 } 2716 2717 /* if free space is not available, make more free space */ 2718 if (current_space->local_remaining<nzk) { 2719 i = am - k + 1; /* num of unfactored rows */ 2720 i *= PetscMin(nzk, (i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2721 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2722 ierr = PetscFreeSpaceGet(i,¤t_space_lvl);CHKERRQ(ierr); 2723 reallocs++; 2724 } 2725 2726 /* copy data into free_space and free_space_lvl, then initialize lnk */ 2727 if (!nzk) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k); 2728 ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr); 2729 2730 /* add the k-th row into il and jl */ 2731 if (nzk > 1){ 2732 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2733 jl[k] = jl[i]; jl[i] = k; 2734 il[k] = ui[k] + 1; 2735 } 2736 uj_ptr[k] = current_space->array; 2737 uj_lvl_ptr[k] = current_space_lvl->array; 2738 2739 current_space->array += nzk; 2740 current_space->local_used += nzk; 2741 current_space->local_remaining -= nzk; 2742 2743 current_space_lvl->array += nzk; 2744 current_space_lvl->local_used += nzk; 2745 current_space_lvl->local_remaining -= nzk; 2746 2747 ui[k+1] = ui[k] + nzk; 2748 } 2749 2750 #if defined(PETSC_USE_INFO) 2751 if (ai[am] != 0) { 2752 PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]); 2753 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2754 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2755 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2756 } else { 2757 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2758 } 2759 #endif 2760 2761 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2762 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2763 ierr = PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);CHKERRQ(ierr); 2764 ierr = PetscFree(ajtmp);CHKERRQ(ierr); 2765 2766 /* destroy list of free space and other temporary array(s) */ 2767 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2768 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 2769 ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2770 ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr); 2771 2772 } /* end of case: levels>0 || (levels=0 && !perm_identity) */ 2773 2774 /* put together the new matrix in MATSEQSBAIJ format */ 2775 2776 b = (Mat_SeqSBAIJ*)fact->data; 2777 b->singlemalloc = PETSC_FALSE; 2778 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2779 b->j = uj; 2780 b->i = ui; 2781 b->diag = udiag; 2782 b->free_diag = PETSC_TRUE; 2783 b->ilen = 0; 2784 b->imax = 0; 2785 b->row = perm; 2786 b->col = perm; 2787 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2788 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2789 b->icol = iperm; 2790 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2791 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2792 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2793 b->maxnz = b->nz = ui[am]; 2794 b->free_a = PETSC_TRUE; 2795 b->free_ij = PETSC_TRUE; 2796 2797 fact->info.factor_mallocs = reallocs; 2798 fact->info.fill_ratio_given = fill; 2799 if (ai[am] != 0) { 2800 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2801 } else { 2802 fact->info.fill_ratio_needed = 0.0; 2803 } 2804 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace; 2805 PetscFunctionReturn(0); 2806 } 2807 2808 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2809 { 2810 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2811 Mat_SeqSBAIJ *b; 2812 PetscErrorCode ierr; 2813 PetscTruth perm_identity; 2814 PetscReal fill = info->fill; 2815 const PetscInt *rip,*riip; 2816 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2817 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2818 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag; 2819 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2820 PetscBT lnkbt; 2821 IS iperm; 2822 2823 PetscFunctionBegin; 2824 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2825 /* check whether perm is the identity mapping */ 2826 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2827 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2828 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2829 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2830 2831 /* initialization */ 2832 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2833 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&udiag);CHKERRQ(ierr); 2834 ui[0] = 0; 2835 2836 /* jl: linked list for storing indices of the pivot rows 2837 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2838 ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr); 2839 for (i=0; i<am; i++){ 2840 jl[i] = am; il[i] = 0; 2841 } 2842 2843 /* create and initialize a linked list for storing column indices of the active row k */ 2844 nlnk = am + 1; 2845 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2846 2847 /* initial FreeSpace size is fill*(ai[am]+1) */ 2848 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 2849 current_space = free_space; 2850 2851 for (k=0; k<am; k++){ /* for each active row k */ 2852 /* initialize lnk by the column indices of row rip[k] of A */ 2853 nzk = 0; 2854 ncols = ai[rip[k]+1] - ai[rip[k]]; 2855 if (!ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 2856 ncols_upper = 0; 2857 for (j=0; j<ncols; j++){ 2858 i = riip[*(aj + ai[rip[k]] + j)]; 2859 if (i >= k){ /* only take upper triangular entry */ 2860 cols[ncols_upper] = i; 2861 ncols_upper++; 2862 } 2863 } 2864 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2865 nzk += nlnk; 2866 2867 /* update lnk by computing fill-in for each pivot row to be merged in */ 2868 prow = jl[k]; /* 1st pivot row */ 2869 2870 while (prow < k){ 2871 nextprow = jl[prow]; 2872 /* merge prow into k-th row */ 2873 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 2874 jmax = ui[prow+1]; 2875 ncols = jmax-jmin; 2876 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 2877 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 2878 nzk += nlnk; 2879 2880 /* update il and jl for prow */ 2881 if (jmin < jmax){ 2882 il[prow] = jmin; 2883 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 2884 } 2885 prow = nextprow; 2886 } 2887 2888 /* if free space is not available, make more free space */ 2889 if (current_space->local_remaining<nzk) { 2890 i = am - k + 1; /* num of unfactored rows */ 2891 i *= PetscMin(nzk,i-1); /* i*nzk, i*(i-1): estimated and max additional space needed */ 2892 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 2893 reallocs++; 2894 } 2895 2896 /* copy data into free space, then initialize lnk */ 2897 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 2898 2899 /* add the k-th row into il and jl */ 2900 if (nzk > 1){ 2901 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 2902 jl[k] = jl[i]; jl[i] = k; 2903 il[k] = ui[k] + 1; 2904 } 2905 ui_ptr[k] = current_space->array; 2906 current_space->array += nzk; 2907 current_space->local_used += nzk; 2908 current_space->local_remaining -= nzk; 2909 2910 ui[k+1] = ui[k] + nzk; 2911 } 2912 2913 #if defined(PETSC_USE_INFO) 2914 if (ai[am] != 0) { 2915 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 2916 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 2917 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 2918 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 2919 } else { 2920 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 2921 } 2922 #endif 2923 2924 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 2925 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 2926 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 2927 2928 /* destroy list of free space and other temporary array(s) */ 2929 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 2930 ierr = PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag);CHKERRQ(ierr); /* store matrix factor */ 2931 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 2932 2933 /* put together the new matrix in MATSEQSBAIJ format */ 2934 2935 b = (Mat_SeqSBAIJ*)fact->data; 2936 b->singlemalloc = PETSC_FALSE; 2937 b->free_a = PETSC_TRUE; 2938 b->free_ij = PETSC_TRUE; 2939 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 2940 b->j = uj; 2941 b->i = ui; 2942 b->diag = udiag; 2943 b->free_diag = PETSC_TRUE; 2944 b->ilen = 0; 2945 b->imax = 0; 2946 b->row = perm; 2947 b->col = perm; 2948 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2949 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 2950 b->icol = iperm; 2951 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 2952 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 2953 ierr = PetscLogObjectMemory(fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 2954 b->maxnz = b->nz = ui[am]; 2955 2956 fact->info.factor_mallocs = reallocs; 2957 fact->info.fill_ratio_given = fill; 2958 if (ai[am] != 0) { 2959 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 2960 } else { 2961 fact->info.fill_ratio_needed = 0.0; 2962 } 2963 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ; 2964 PetscFunctionReturn(0); 2965 } 2966 2967 #undef __FUNCT__ 2968 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqAIJ_inplace" 2969 PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info) 2970 { 2971 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 2972 Mat_SeqSBAIJ *b; 2973 PetscErrorCode ierr; 2974 PetscTruth perm_identity; 2975 PetscReal fill = info->fill; 2976 const PetscInt *rip,*riip; 2977 PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow; 2978 PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow; 2979 PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr; 2980 PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL; 2981 PetscBT lnkbt; 2982 IS iperm; 2983 2984 PetscFunctionBegin; 2985 if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n); 2986 /* check whether perm is the identity mapping */ 2987 ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr); 2988 ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr); 2989 ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr); 2990 ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr); 2991 2992 /* initialization */ 2993 ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr); 2994 ui[0] = 0; 2995 2996 /* jl: linked list for storing indices of the pivot rows 2997 il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */ 2998 ierr = PetscMalloc4(am,PetscInt*,&ui_ptr,am,PetscInt,&jl,am,PetscInt,&il,am,PetscInt,&cols);CHKERRQ(ierr); 2999 for (i=0; i<am; i++){ 3000 jl[i] = am; il[i] = 0; 3001 } 3002 3003 /* create and initialize a linked list for storing column indices of the active row k */ 3004 nlnk = am + 1; 3005 ierr = PetscLLCreate(am,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3006 3007 /* initial FreeSpace size is fill*(ai[am]+1) */ 3008 ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+1)),&free_space);CHKERRQ(ierr); 3009 current_space = free_space; 3010 3011 for (k=0; k<am; k++){ /* for each active row k */ 3012 /* initialize lnk by the column indices of row rip[k] of A */ 3013 nzk = 0; 3014 ncols = ai[rip[k]+1] - ai[rip[k]]; 3015 if (!ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k); 3016 ncols_upper = 0; 3017 for (j=0; j<ncols; j++){ 3018 i = riip[*(aj + ai[rip[k]] + j)]; 3019 if (i >= k){ /* only take upper triangular entry */ 3020 cols[ncols_upper] = i; 3021 ncols_upper++; 3022 } 3023 } 3024 ierr = PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3025 nzk += nlnk; 3026 3027 /* update lnk by computing fill-in for each pivot row to be merged in */ 3028 prow = jl[k]; /* 1st pivot row */ 3029 3030 while (prow < k){ 3031 nextprow = jl[prow]; 3032 /* merge prow into k-th row */ 3033 jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */ 3034 jmax = ui[prow+1]; 3035 ncols = jmax-jmin; 3036 uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */ 3037 ierr = PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3038 nzk += nlnk; 3039 3040 /* update il and jl for prow */ 3041 if (jmin < jmax){ 3042 il[prow] = jmin; 3043 j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow; 3044 } 3045 prow = nextprow; 3046 } 3047 3048 /* if free space is not available, make more free space */ 3049 if (current_space->local_remaining<nzk) { 3050 i = am - k + 1; /* num of unfactored rows */ 3051 i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */ 3052 ierr = PetscFreeSpaceGet(i,¤t_space);CHKERRQ(ierr); 3053 reallocs++; 3054 } 3055 3056 /* copy data into free space, then initialize lnk */ 3057 ierr = PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr); 3058 3059 /* add the k-th row into il and jl */ 3060 if (nzk-1 > 0){ 3061 i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */ 3062 jl[k] = jl[i]; jl[i] = k; 3063 il[k] = ui[k] + 1; 3064 } 3065 ui_ptr[k] = current_space->array; 3066 current_space->array += nzk; 3067 current_space->local_used += nzk; 3068 current_space->local_remaining -= nzk; 3069 3070 ui[k+1] = ui[k] + nzk; 3071 } 3072 3073 #if defined(PETSC_USE_INFO) 3074 if (ai[am] != 0) { 3075 PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]); 3076 ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr); 3077 ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr); 3078 ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr); 3079 } else { 3080 ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr); 3081 } 3082 #endif 3083 3084 ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr); 3085 ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr); 3086 ierr = PetscFree4(ui_ptr,jl,il,cols);CHKERRQ(ierr); 3087 3088 /* destroy list of free space and other temporary array(s) */ 3089 ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr); 3090 ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr); 3091 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3092 3093 /* put together the new matrix in MATSEQSBAIJ format */ 3094 3095 b = (Mat_SeqSBAIJ*)fact->data; 3096 b->singlemalloc = PETSC_FALSE; 3097 b->free_a = PETSC_TRUE; 3098 b->free_ij = PETSC_TRUE; 3099 ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr); 3100 b->j = uj; 3101 b->i = ui; 3102 b->diag = 0; 3103 b->ilen = 0; 3104 b->imax = 0; 3105 b->row = perm; 3106 b->col = perm; 3107 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3108 ierr = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr); 3109 b->icol = iperm; 3110 b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */ 3111 ierr = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3112 ierr = PetscLogObjectMemory(fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3113 b->maxnz = b->nz = ui[am]; 3114 3115 fact->info.factor_mallocs = reallocs; 3116 fact->info.fill_ratio_given = fill; 3117 if (ai[am] != 0) { 3118 fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]); 3119 } else { 3120 fact->info.fill_ratio_needed = 0.0; 3121 } 3122 fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace; 3123 PetscFunctionReturn(0); 3124 } 3125 3126 #undef __FUNCT__ 3127 #define __FUNCT__ "MatSolve_SeqAIJ_NaturalOrdering" 3128 PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx) 3129 { 3130 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3131 PetscErrorCode ierr; 3132 PetscInt n = A->rmap->n; 3133 const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag,*vi; 3134 PetscScalar *x,sum; 3135 const PetscScalar *b; 3136 const MatScalar *aa = a->a,*v; 3137 PetscInt i,nz; 3138 3139 PetscFunctionBegin; 3140 if (!n) PetscFunctionReturn(0); 3141 3142 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 3143 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3144 3145 /* forward solve the lower triangular */ 3146 x[0] = b[0]; 3147 v = aa; 3148 vi = aj; 3149 for (i=1; i<n; i++) { 3150 nz = ai[i+1] - ai[i]; 3151 sum = b[i]; 3152 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3153 v += nz; 3154 vi += nz; 3155 x[i] = sum; 3156 } 3157 3158 /* backward solve the upper triangular */ 3159 for (i=n-1; i>=0; i--){ 3160 v = aa + adiag[i+1] + 1; 3161 vi = aj + adiag[i+1] + 1; 3162 nz = adiag[i] - adiag[i+1]-1; 3163 sum = x[i]; 3164 PetscSparseDenseMinusDot(sum,x,v,vi,nz); 3165 x[i] = sum*v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */ 3166 } 3167 3168 ierr = PetscLogFlops(2.0*a->nz - A->cmap->n);CHKERRQ(ierr); 3169 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 3170 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3171 PetscFunctionReturn(0); 3172 } 3173 3174 #undef __FUNCT__ 3175 #define __FUNCT__ "MatSolve_SeqAIJ" 3176 PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx) 3177 { 3178 Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data; 3179 IS iscol = a->col,isrow = a->row; 3180 PetscErrorCode ierr; 3181 PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz; 3182 const PetscInt *rout,*cout,*r,*c; 3183 PetscScalar *x,*tmp,sum; 3184 const PetscScalar *b; 3185 const MatScalar *aa = a->a,*v; 3186 3187 PetscFunctionBegin; 3188 if (!n) PetscFunctionReturn(0); 3189 3190 ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr); 3191 ierr = VecGetArray(xx,&x);CHKERRQ(ierr); 3192 tmp = a->solve_work; 3193 3194 ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout; 3195 ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout; 3196 3197 /* forward solve the lower triangular */ 3198 tmp[0] = b[r[0]]; 3199 v = aa; 3200 vi = aj; 3201 for (i=1; i<n; i++) { 3202 nz = ai[i+1] - ai[i]; 3203 sum = b[r[i]]; 3204 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3205 tmp[i] = sum; 3206 v += nz; vi += nz; 3207 } 3208 3209 /* backward solve the upper triangular */ 3210 for (i=n-1; i>=0; i--){ 3211 v = aa + adiag[i+1]+1; 3212 vi = aj + adiag[i+1]+1; 3213 nz = adiag[i]-adiag[i+1]-1; 3214 sum = tmp[i]; 3215 PetscSparseDenseMinusDot(sum,tmp,v,vi,nz); 3216 x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */ 3217 } 3218 3219 ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr); 3220 ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr); 3221 ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr); 3222 ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr); 3223 ierr = PetscLogFlops(2*a->nz - A->cmap->n);CHKERRQ(ierr); 3224 PetscFunctionReturn(0); 3225 } 3226 3227 #undef __FUNCT__ 3228 #define __FUNCT__ "MatILUDTFactor_SeqAIJ" 3229 /* 3230 This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer seperate functions in the matrix function table for dt factors 3231 */ 3232 PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact) 3233 { 3234 Mat B = *fact; 3235 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b; 3236 IS isicol; 3237 PetscErrorCode ierr; 3238 const PetscInt *r,*ic; 3239 PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag; 3240 PetscInt *bi,*bj,*bdiag,*bdiag_rev; 3241 PetscInt row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au; 3242 PetscInt nlnk,*lnk; 3243 PetscBT lnkbt; 3244 PetscTruth row_identity,icol_identity; 3245 MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp; 3246 const PetscInt *ics; 3247 PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp; 3248 PetscReal dt=info->dt,dtcol=info->dtcol,shift=info->shiftamount; 3249 PetscInt dtcount=(PetscInt)info->dtcount,nnz_max; 3250 PetscTruth missing; 3251 3252 PetscFunctionBegin; 3253 3254 if (dt == PETSC_DEFAULT) dt = 0.005; 3255 if (dtcol == PETSC_DEFAULT) dtcol = 0.01; /* XXX unused! */ 3256 if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax); 3257 3258 /* ------- symbolic factorization, can be reused ---------*/ 3259 ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr); 3260 if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i); 3261 adiag=a->diag; 3262 3263 ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr); 3264 3265 /* bdiag is location of diagonal in factor */ 3266 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr); /* becomes b->diag */ 3267 ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag_rev);CHKERRQ(ierr); /* temporary */ 3268 3269 /* allocate row pointers bi */ 3270 ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr); 3271 3272 /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */ 3273 if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */ 3274 nnz_max = ai[n]+2*n*dtcount+2; 3275 3276 ierr = PetscMalloc((nnz_max+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr); 3277 ierr = PetscMalloc((nnz_max+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr); 3278 3279 /* put together the new matrix */ 3280 ierr = MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr); 3281 ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr); 3282 b = (Mat_SeqAIJ*)B->data; 3283 b->free_a = PETSC_TRUE; 3284 b->free_ij = PETSC_TRUE; 3285 b->singlemalloc = PETSC_FALSE; 3286 b->a = ba; 3287 b->j = bj; 3288 b->i = bi; 3289 b->diag = bdiag; 3290 b->ilen = 0; 3291 b->imax = 0; 3292 b->row = isrow; 3293 b->col = iscol; 3294 ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr); 3295 ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr); 3296 b->icol = isicol; 3297 ierr = PetscMalloc((n+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr); 3298 3299 ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr); 3300 b->maxnz = nnz_max; 3301 3302 B->factortype = MAT_FACTOR_ILUDT; 3303 B->info.factor_mallocs = 0; 3304 B->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]); 3305 CHKMEMQ; 3306 /* ------- end of symbolic factorization ---------*/ 3307 3308 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3309 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3310 ics = ic; 3311 3312 /* linked list for storing column indices of the active row */ 3313 nlnk = n + 1; 3314 ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3315 3316 /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */ 3317 ierr = PetscMalloc2(n,PetscInt,&im,n,PetscInt,&jtmp);CHKERRQ(ierr); 3318 /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */ 3319 ierr = PetscMalloc2(n,MatScalar,&rtmp,n,MatScalar,&vtmp);CHKERRQ(ierr); 3320 ierr = PetscMemzero(rtmp,n*sizeof(MatScalar));CHKERRQ(ierr); 3321 3322 bi[0] = 0; 3323 bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */ 3324 bdiag_rev[n] = bdiag[0]; 3325 bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */ 3326 for (i=0; i<n; i++) { 3327 /* copy initial fill into linked list */ 3328 nzi = 0; /* nonzeros for active row i */ 3329 nzi = ai[r[i]+1] - ai[r[i]]; 3330 if (!nzi) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i); 3331 nzi_al = adiag[r[i]] - ai[r[i]]; 3332 nzi_au = ai[r[i]+1] - adiag[r[i]] -1; 3333 ajtmp = aj + ai[r[i]]; 3334 ierr = PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr); 3335 3336 /* load in initial (unfactored row) */ 3337 aatmp = a->a + ai[r[i]]; 3338 for (j=0; j<nzi; j++) { 3339 rtmp[ics[*ajtmp++]] = *aatmp++; 3340 } 3341 3342 /* add pivot rows into linked list */ 3343 row = lnk[n]; 3344 while (row < i ) { 3345 nzi_bl = bi[row+1] - bi[row] + 1; 3346 bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */ 3347 ierr = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr); 3348 nzi += nlnk; 3349 row = lnk[row]; 3350 } 3351 3352 /* copy data from lnk into jtmp, then initialize lnk */ 3353 ierr = PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr); 3354 3355 /* numerical factorization */ 3356 bjtmp = jtmp; 3357 row = *bjtmp++; /* 1st pivot row */ 3358 while ( row < i ) { 3359 pc = rtmp + row; 3360 pv = ba + bdiag[row]; /* 1./(diag of the pivot row) */ 3361 multiplier = (*pc) * (*pv); 3362 *pc = multiplier; 3363 if (PetscAbsScalar(*pc) > dt){ /* apply tolerance dropping rule */ 3364 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3365 pv = ba + bdiag[row+1] + 1; 3366 /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */ 3367 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3368 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3369 ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); 3370 } 3371 row = *bjtmp++; 3372 } 3373 3374 /* copy sparse rtmp into contiguous vtmp; separate L and U part */ 3375 diag_tmp = rtmp[i]; /* save diagonal value - may not needed?? */ 3376 nzi_bl = 0; j = 0; 3377 while (jtmp[j] < i){ /* Note: jtmp is sorted */ 3378 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3379 nzi_bl++; j++; 3380 } 3381 nzi_bu = nzi - nzi_bl -1; 3382 while (j < nzi){ 3383 vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0; 3384 j++; 3385 } 3386 3387 bjtmp = bj + bi[i]; 3388 batmp = ba + bi[i]; 3389 /* apply level dropping rule to L part */ 3390 ncut = nzi_al + dtcount; 3391 if (ncut < nzi_bl){ 3392 ierr = PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);CHKERRQ(ierr); 3393 ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr); 3394 } else { 3395 ncut = nzi_bl; 3396 } 3397 for (j=0; j<ncut; j++){ 3398 bjtmp[j] = jtmp[j]; 3399 batmp[j] = vtmp[j]; 3400 /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */ 3401 } 3402 bi[i+1] = bi[i] + ncut; 3403 nzi = ncut + 1; 3404 3405 /* apply level dropping rule to U part */ 3406 ncut = nzi_au + dtcount; 3407 if (ncut < nzi_bu){ 3408 ierr = PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr); 3409 ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr); 3410 } else { 3411 ncut = nzi_bu; 3412 } 3413 nzi += ncut; 3414 3415 /* mark bdiagonal */ 3416 bdiag[i+1] = bdiag[i] - (ncut + 1); 3417 bdiag_rev[n-i-1] = bdiag[i+1]; 3418 bi[2*n - i] = bi[2*n - i +1] - (ncut + 1); 3419 bjtmp = bj + bdiag[i]; 3420 batmp = ba + bdiag[i]; 3421 *bjtmp = i; 3422 *batmp = diag_tmp; /* rtmp[i]; */ 3423 if (*batmp == 0.0) { 3424 *batmp = dt+shift; 3425 /* printf(" row %d add shift %g\n",i,shift); */ 3426 } 3427 *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */ 3428 /* printf(" (%d,%g),",*bjtmp,*batmp); */ 3429 3430 bjtmp = bj + bdiag[i+1]+1; 3431 batmp = ba + bdiag[i+1]+1; 3432 for (k=0; k<ncut; k++){ 3433 bjtmp[k] = jtmp[nzi_bl+1+k]; 3434 batmp[k] = vtmp[nzi_bl+1+k]; 3435 /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */ 3436 } 3437 /* printf("\n"); */ 3438 3439 im[i] = nzi; /* used by PetscLLAddSortedLU() */ 3440 /* 3441 printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]); 3442 printf(" ----------------------------\n"); 3443 */ 3444 } /* for (i=0; i<n; i++) */ 3445 /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */ 3446 if (bi[n] >= bdiag[n]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"end of L array %d cannot >= the beginning of U array %d",bi[n],bdiag[n]); 3447 3448 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3449 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3450 3451 ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr); 3452 ierr = PetscFree2(im,jtmp);CHKERRQ(ierr); 3453 ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr); 3454 ierr = PetscFree(bdiag_rev);CHKERRQ(ierr); 3455 3456 ierr = PetscLogFlops(B->cmap->n);CHKERRQ(ierr); 3457 b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n]; 3458 3459 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3460 ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr); 3461 if (row_identity && icol_identity) { 3462 B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 3463 } else { 3464 B->ops->solve = MatSolve_SeqAIJ; 3465 } 3466 3467 B->ops->solveadd = 0; 3468 B->ops->solvetranspose = 0; 3469 B->ops->solvetransposeadd = 0; 3470 B->ops->matsolve = 0; 3471 B->assembled = PETSC_TRUE; 3472 B->preallocated = PETSC_TRUE; 3473 PetscFunctionReturn(0); 3474 } 3475 3476 /* a wraper of MatILUDTFactor_SeqAIJ() */ 3477 #undef __FUNCT__ 3478 #define __FUNCT__ "MatILUDTFactorSymbolic_SeqAIJ" 3479 /* 3480 This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer seperate functions in the matrix function table for dt factors 3481 */ 3482 3483 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info) 3484 { 3485 PetscErrorCode ierr; 3486 3487 PetscFunctionBegin; 3488 ierr = MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);CHKERRQ(ierr); 3489 PetscFunctionReturn(0); 3490 } 3491 3492 /* 3493 same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors 3494 - intend to replace existing MatLUFactorNumeric_SeqAIJ() 3495 */ 3496 #undef __FUNCT__ 3497 #define __FUNCT__ "MatILUDTFactorNumeric_SeqAIJ" 3498 /* 3499 This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer seperate functions in the matrix function table for dt factors 3500 */ 3501 3502 PetscErrorCode PETSCMAT_DLLEXPORT MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info) 3503 { 3504 Mat C=fact; 3505 Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ *)C->data; 3506 IS isrow = b->row,isicol = b->icol; 3507 PetscErrorCode ierr; 3508 const PetscInt *r,*ic,*ics; 3509 PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j; 3510 PetscInt *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj; 3511 MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a; 3512 PetscReal dt=info->dt,shift=info->shiftamount; 3513 PetscTruth row_identity, col_identity; 3514 3515 PetscFunctionBegin; 3516 ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr); 3517 ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr); 3518 ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 3519 ics = ic; 3520 3521 for (i=0; i<n; i++){ 3522 /* initialize rtmp array */ 3523 nzl = bi[i+1] - bi[i]; /* num of nozeros in L(i,:) */ 3524 bjtmp = bj + bi[i]; 3525 for (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0; 3526 rtmp[i] = 0.0; 3527 nzu = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */ 3528 bjtmp = bj + bdiag[i+1] + 1; 3529 for (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0; 3530 3531 /* load in initial unfactored row of A */ 3532 /* printf("row %d\n",i); */ 3533 nz = ai[r[i]+1] - ai[r[i]]; 3534 ajtmp = aj + ai[r[i]]; 3535 v = aa + ai[r[i]]; 3536 for (j=0; j<nz; j++) { 3537 rtmp[ics[*ajtmp++]] = v[j]; 3538 /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */ 3539 } 3540 /* printf("\n"); */ 3541 3542 /* numerical factorization */ 3543 bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */ 3544 nzl = bi[i+1] - bi[i]; /* num of entries in L(i,:) */ 3545 k = 0; 3546 while (k < nzl){ 3547 row = *bjtmp++; 3548 /* printf(" prow %d\n",row); */ 3549 pc = rtmp + row; 3550 pv = b->a + bdiag[row]; /* 1./(diag of the pivot row) */ 3551 multiplier = (*pc) * (*pv); 3552 *pc = multiplier; 3553 if (PetscAbsScalar(multiplier) > dt){ 3554 pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */ 3555 pv = b->a + bdiag[row+1] + 1; 3556 nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */ 3557 for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++); 3558 /* ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr); */ 3559 } 3560 k++; 3561 } 3562 3563 /* finished row so stick it into b->a */ 3564 /* L-part */ 3565 pv = b->a + bi[i] ; 3566 pj = bj + bi[i] ; 3567 nzl = bi[i+1] - bi[i]; 3568 for (j=0; j<nzl; j++) { 3569 pv[j] = rtmp[pj[j]]; 3570 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3571 } 3572 3573 /* diagonal: invert diagonal entries for simplier triangular solves */ 3574 if (rtmp[i] == 0.0) rtmp[i] = dt+shift; 3575 b->a[bdiag[i]] = 1.0/rtmp[i]; 3576 /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */ 3577 3578 /* U-part */ 3579 pv = b->a + bdiag[i+1] + 1; 3580 pj = bj + bdiag[i+1] + 1; 3581 nzu = bdiag[i] - bdiag[i+1] - 1; 3582 for (j=0; j<nzu; j++) { 3583 pv[j] = rtmp[pj[j]]; 3584 /* printf(" (%d,%g),",pj[j],pv[j]); */ 3585 } 3586 /* printf("\n"); */ 3587 } 3588 3589 ierr = PetscFree(rtmp);CHKERRQ(ierr); 3590 ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr); 3591 ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr); 3592 3593 ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr); 3594 ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr); 3595 if (row_identity && col_identity) { 3596 C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering; 3597 } else { 3598 C->ops->solve = MatSolve_SeqAIJ; 3599 } 3600 C->ops->solveadd = 0; 3601 C->ops->solvetranspose = 0; 3602 C->ops->solvetransposeadd = 0; 3603 C->ops->matsolve = 0; 3604 C->assembled = PETSC_TRUE; 3605 C->preallocated = PETSC_TRUE; 3606 ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr); 3607 PetscFunctionReturn(0); 3608 } 3609